LMFDB - Embedded newform 84.9.p.b.53.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [84,9,Mod(53,84)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(84, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("84.53");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 84 = 2^{2} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	84.p (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:	$34.2198032451$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			53.10
Character	$\chi$	$=$	84.53
Dual form			84.9.p.b.65.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.07318 + 80.9417i) q^{3} +(304.163 - 175.609i) q^{5} +(517.537 + 2344.56i) q^{7} +(-6542.11 + 497.497i) q^{9} +O(q^{10})$	\(q+(3.07318 + 80.9417i) q^{3} +(304.163 - 175.609i) q^{5} +(517.537 + 2344.56i) q^{7} +(-6542.11 + 497.497i) q^{9} +(-18965.6 - 10949.8i) q^{11} +5256.11 q^{13} +(15148.8 + 24079.8i) q^{15} +(-5364.57 - 3097.23i) q^{17} +(51832.6 + 89776.8i) q^{19} +(-188182. + 49095.5i) q^{21} +(-237751. + 137265. i) q^{23} +(-133636. + 231464. i) q^{25} +(-60373.3 - 528001. i) q^{27} -272128. i q^{29} +(-53915.5 + 93384.4i) q^{31} +(828012. - 1.56876e6i) q^{33} +(569140. + 622244. i) q^{35} +(-1.46687e6 - 2.54070e6i) q^{37} +(16153.0 + 425439. i) q^{39} -3.88684e6i q^{41} -3.82188e6 q^{43} +(-1.90250e6 + 1.30017e6i) q^{45} +(3.87081e6 - 2.23481e6i) q^{47} +(-5.22911e6 + 2.42679e6i) q^{49} +(234209. - 443735. i) q^{51} +(-8.81015e6 - 5.08654e6i) q^{53} -7.69153e6 q^{55} +(-7.10739e6 + 4.47132e6i) q^{57} +(3.48596e6 + 2.01262e6i) q^{59} +(-4.96449e6 - 8.59875e6i) q^{61} +(-4.55219e6 - 1.50809e7i) q^{63} +(1.59871e6 - 923018. i) q^{65} +(-1.65440e6 + 2.86550e6i) q^{67} +(-1.18411e7 - 1.88221e7i) q^{69} -1.30051e6i q^{71} +(-1.72530e7 + 2.98831e7i) q^{73} +(-1.91458e7 - 1.01054e7i) q^{75} +(1.58571e7 - 5.01330e7i) q^{77} +(-2.99380e6 - 5.18541e6i) q^{79} +(4.25517e7 - 6.50936e6i) q^{81} +6.41735e7i q^{83} -2.17560e6 q^{85} +(2.20265e7 - 836298. i) q^{87} +(5.01926e7 - 2.89787e7i) q^{89} +(2.72023e6 + 1.23233e7i) q^{91} +(-7.72438e6 - 4.07703e6i) q^{93} +(3.15311e7 + 1.82045e7i) q^{95} +6.99710e7 q^{97} +(1.29523e8 + 6.21996e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 81 q^{3} - 34 q^{7} + 4771 q^{9}+O(q^{10}) $ 40 * q + 81 * q^3 - 34 * q^7 + 4771 * q^9	$ 40 q + 81 q^{3} - 34 q^{7} + 4771 q^{9} - 55464 q^{13} + 68482 q^{15} + 311690 q^{19} - 172343 q^{21} + 1766792 q^{25} - 3451932 q^{27} + 31596 q^{31} + 1874885 q^{33} - 1853482 q^{37} + 11217526 q^{39} - 13372600 q^{43} - 527785 q^{45} - 12653462 q^{49} - 1103461 q^{51} + 71577224 q^{55} - 17195214 q^{57} - 21761970 q^{61} + 21945045 q^{63} - 26337350 q^{67} - 5588722 q^{69} + 41115682 q^{73} - 17971730 q^{75} - 120916932 q^{79} - 24550133 q^{81} + 139250060 q^{85} - 16321046 q^{87} + 345074940 q^{91} + 25774675 q^{93} - 707216948 q^{97} - 94510994 q^{99}+O(q^{100}) $ 40 * q + 81 * q^3 - 34 * q^7 + 4771 * q^9 - 55464 * q^13 + 68482 * q^15 + 311690 * q^19 - 172343 * q^21 + 1766792 * q^25 - 3451932 * q^27 + 31596 * q^31 + 1874885 * q^33 - 1853482 * q^37 + 11217526 * q^39 - 13372600 * q^43 - 527785 * q^45 - 12653462 * q^49 - 1103461 * q^51 + 71577224 * q^55 - 17195214 * q^57 - 21761970 * q^61 + 21945045 * q^63 - 26337350 * q^67 - 5588722 * q^69 + 41115682 * q^73 - 17971730 * q^75 - 120916932 * q^79 - 24550133 * q^81 + 139250060 * q^85 - 16321046 * q^87 + 345074940 * q^91 + 25774675 * q^93 - 707216948 * q^97 - 94510994 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/84\mathbb{Z}\right)^\times$.

$n$	$29$	$43$	$73$
$\chi(n)$	$-1$	$1$	$e\left(\frac{2}{3}\right)$

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
$3$	3.07318	+	80.9417i	0.0379405	+	0.999280i
$3$	3.07318	+	80.9417i	0.0379405	+	0.999280i
$4$		0			0
$5$	304.163	−	175.609i	0.486661	−	0.280974i	−0.236527	−	0.971625i	$-0.576009\pi$
$5$	304.163	−	175.609i	0.486661	−	0.280974i	0.723188	+	0.690651i	$0.242676\pi$
$6$		0			0
$7$	517.537	+	2344.56i	0.215550	+	0.976493i
$7$	517.537	+	2344.56i	0.215550	+	0.976493i
$8$		0			0
$9$	−6542.11	+	497.497i	−0.997121	+	0.0758263i
$10$		0			0
$11$	−18965.6	−	10949.8i	−1.29538	−	0.747888i	−0.315777	−	0.948833i	$-0.602265\pi$
$11$	−18965.6	−	10949.8i	−1.29538	−	0.747888i	−0.979602	+	0.200946i	$0.935598\pi$
$12$		0			0
$13$	5256.11			0.184031			0.0920156	−	0.995758i	$-0.470669\pi$
$13$	5256.11			0.184031			0.0920156	+	0.995758i	$0.470669\pi$
$14$		0			0
$15$	15148.8	+	24079.8i	0.299236	+	0.475650i
$16$		0			0
$17$	−5364.57	−	3097.23i	−0.0642302	−	0.0370833i	0.467541	−	0.883971i	$-0.345140\pi$
$17$	−5364.57	−	3097.23i	−0.0642302	−	0.0370833i	−0.531771	+	0.846888i	$0.678473\pi$
$18$		0			0
$19$	51832.6	+	89776.8i	0.397731	+	0.688889i	0.993446	−	0.114306i	$-0.0364646\pi$
$19$	51832.6	+	89776.8i	0.397731	+	0.688889i	−0.595715	+	0.803196i	$0.703131\pi$
$20$		0			0
$21$	−188182.	+	49095.5i	−0.967612	+	0.252444i
$22$		0			0
$23$	−237751.	+	137265.i	−0.849592	+	0.490512i	−0.860513	−	0.509428i	$-0.829857\pi$
$23$	−237751.	+	137265.i	−0.849592	+	0.490512i	0.0109212	+	0.999940i	$0.496524\pi$
$24$		0			0
$25$	−133636.	+	231464.i	−0.342108	+	0.592548i
$26$		0			0
$27$	−60373.3	−	528001.i	−0.113603	−	0.993526i
$28$		0			0
$29$		−	272128.i		−	0.384752i	−0.981321	−	0.192376i	$-0.938381\pi$
$29$		−	272128.i		−	0.384752i	0.981321	−	0.192376i	$-0.0616193\pi$
$30$		0			0
$31$	−53915.5	+	93384.4i	−0.0583804	+	0.101118i	−0.893739	−	0.448588i	$-0.851927\pi$
$31$	−53915.5	+	93384.4i	−0.0583804	+	0.101118i	0.835358	+	0.549706i	$0.185260\pi$
$32$		0			0
$33$	828012.	−	1.56876e6i	0.698202	−	1.32282i
$34$		0			0
$35$	569140.	+	622244.i	0.379269	+	0.414657i
$36$		0			0
$37$	−1.46687e6	−	2.54070e6i	−0.782683	−	1.35565i	−0.930374	−	0.366613i	$-0.880517\pi$
$37$	−1.46687e6	−	2.54070e6i	−0.782683	−	1.35565i	0.147691	−	0.989034i	$-0.452816\pi$
$38$		0			0
$39$	16153.0	+	425439.i	0.00698223	+	0.183899i
$40$		0			0
$41$		−	3.88684e6i		−	1.37550i	−0.725946	−	0.687752i	$-0.758598\pi$
$41$		−	3.88684e6i		−	1.37550i	0.725946	−	0.687752i	$-0.241402\pi$
$42$		0			0
$43$	−3.82188e6			−1.11790			−0.558950	−	0.829201i	$-0.688796\pi$
$43$	−3.82188e6			−1.11790			−0.558950	+	0.829201i	$0.688796\pi$
$44$		0			0
$45$	−1.90250e6	+	1.30017e6i	−0.463954	+	0.317066i
$46$		0			0
$47$	3.87081e6	−	2.23481e6i	0.793251	−	0.457984i	−0.0478546	−	0.998854i	$-0.515238\pi$
$47$	3.87081e6	−	2.23481e6i	0.793251	−	0.457984i	0.841106	+	0.540870i	$0.181905\pi$
$48$		0			0
$49$	−5.22911e6	+	2.42679e6i	−0.907076	+	0.420967i
$50$		0			0
$51$	234209.	−	443735.i	0.0346197	−	0.0655909i
$52$		0			0
$53$	−8.81015e6	−	5.08654e6i	−1.11655	−	0.644643i	−0.176035	−	0.984384i	$-0.556327\pi$
$53$	−8.81015e6	−	5.08654e6i	−1.11655	−	0.644643i	−0.940519	+	0.339741i	$0.889661\pi$
$54$		0			0
$55$	−7.69153e6			−0.840547
$56$		0			0
$57$	−7.10739e6	+	4.47132e6i	−0.673303	+	0.423581i
$58$		0			0
$59$	3.48596e6	+	2.01262e6i	0.287683	+	0.166094i	0.636896	−	0.770949i	$-0.280218\pi$
$59$	3.48596e6	+	2.01262e6i	0.287683	+	0.166094i	−0.349213	+	0.937043i	$0.613551\pi$
$60$		0			0
$61$	−4.96449e6	−	8.59875e6i	−0.358555	−	0.621035i	0.629165	−	0.777272i	$-0.283397\pi$
$61$	−4.96449e6	−	8.59875e6i	−0.358555	−	0.621035i	−0.987720	+	0.156237i	$0.950064\pi$
$62$		0			0
$63$	−4.55219e6	−	1.50809e7i	−0.288974	−	0.957337i
$64$		0			0
$65$	1.59871e6	−	923018.i	0.0895607	−	0.0517079i
$66$		0			0
$67$	−1.65440e6	+	2.86550e6i	−0.0820995	+	0.142200i	−0.904152	−	0.427212i	$-0.859496\pi$
$67$	−1.65440e6	+	2.86550e6i	−0.0820995	+	0.142200i	0.822052	+	0.569412i	$0.192829\pi$
$68$		0			0
$69$	−1.18411e7	−	1.88221e7i	−0.522393	−	0.830370i
$70$		0			0
$71$		−	1.30051e6i		−	0.0511776i	−0.999673	−	0.0255888i	$-0.991854\pi$
$71$		−	1.30051e6i		−	0.0511776i	0.999673	−	0.0255888i	$-0.00814606\pi$
$72$		0			0
$73$	−1.72530e7	+	2.98831e7i	−0.607538	+	1.05229i	0.384107	+	0.923289i	$0.374509\pi$
$73$	−1.72530e7	+	2.98831e7i	−0.607538	+	1.05229i	−0.991645	+	0.128998i	$0.958824\pi$
$74$		0			0
$75$	−1.91458e7	−	1.01054e7i	−0.605101	−	0.319380i
$76$		0			0
$77$	1.58571e7	−	5.01330e7i	0.451087	−	1.42614i
$78$		0			0
$79$	−2.99380e6	−	5.18541e6i	−0.0768625	−	0.133130i	0.825032	−	0.565086i	$-0.191157\pi$
$79$	−2.99380e6	−	5.18541e6i	−0.0768625	−	0.133130i	−0.901895	+	0.431956i	$0.857824\pi$
$80$		0			0
$81$	4.25517e7	−	6.50936e6i	0.988501	−	0.151216i
$82$		0			0
$83$			6.41735e7i			1.35221i	0.736806	+	0.676104i	$0.236333\pi$
$83$			6.41735e7i			1.35221i	−0.736806	+	0.676104i	$0.763667\pi$
$84$		0			0
$85$	−2.17560e6			−0.0416777
$86$		0			0
$87$	2.20265e7	−	836298.i	0.384475	−	0.0145977i
$88$		0			0
$89$	5.01926e7	−	2.89787e7i	0.799982	−	0.461870i	−0.0434830	−	0.999054i	$-0.513845\pi$
$89$	5.01926e7	−	2.89787e7i	0.799982	−	0.461870i	0.843465	+	0.537184i	$0.180512\pi$
$90$		0			0
$91$	2.72023e6	+	1.23233e7i	0.0396680	+	0.179705i
$92$		0			0
$93$	−7.72438e6	−	4.07703e6i	−0.103260	−	0.0545019i
$94$		0			0
$95$	3.15311e7	+	1.82045e7i	0.387120	+	0.223504i
$96$		0			0
$97$	6.99710e7			0.790371			0.395185	−	0.918601i	$-0.370680\pi$
$97$	6.99710e7			0.790371			0.395185	+	0.918601i	$0.370680\pi$
$98$		0			0
$99$	1.29523e8	+	6.21996e7i	1.34836	+	0.647511i
$100$		0			0
$101$	−9.90333e7	−	5.71769e7i	−0.951690	−	0.549459i	−0.0580846	−	0.998312i	$-0.518499\pi$
$101$	−9.90333e7	−	5.71769e7i	−0.951690	−	0.549459i	−0.893606	+	0.448853i	$0.851833\pi$
$102$		0			0
$103$	1.76954e7	+	3.06494e7i	0.157222	+	0.272316i	0.933866	−	0.357624i	$-0.116413\pi$
$103$	1.76954e7	+	3.06494e7i	0.157222	+	0.272316i	−0.776644	+	0.629940i	$0.783080\pi$
$104$		0			0
$105$	−4.86164e7	+	4.79794e7i	−0.399968	+	0.394728i
$106$		0			0
$107$	−2.24998e8	+	1.29903e8i	−1.71650	+	0.991023i	−0.791405	+	0.611293i	$0.790650\pi$
$107$	−2.24998e8	+	1.29903e8i	−1.71650	+	0.991023i	−0.925097	+	0.379730i	$0.876017\pi$
$108$		0			0
$109$	−1.69275e7	+	2.93193e7i	−0.119919	+	0.207705i	−0.919735	−	0.392539i	$-0.871597\pi$
$109$	−1.69275e7	+	2.93193e7i	−0.119919	+	0.207705i	0.799817	+	0.600244i	$0.204930\pi$
$110$		0			0
$111$	2.01141e8	−	1.26539e8i	1.32497	−	0.833553i
$112$		0			0
$113$			2.64579e8i			1.62271i	0.584553	+	0.811355i	$0.301270\pi$
$113$			2.64579e8i			1.62271i	−0.584553	+	0.811355i	$0.698730\pi$
$114$		0			0
$115$	−4.82100e7	+	8.35021e7i	−0.275642	+	0.477426i
$116$		0			0
$117$	−3.43861e7	+	2.61490e6i	−0.183501	+	0.0139544i
$118$		0			0
$119$	4.48529e6	−	1.41805e7i	0.0223667	−	0.0707136i
$120$		0			0
$121$	1.32618e8	+	2.29701e8i	0.618672	+	1.07157i
$122$		0			0
$123$	3.14608e8	−	1.19450e7i	1.37451	−	0.0521873i
$124$		0			0
$125$			2.31065e8i			0.946440i
$126$		0			0
$127$	2.30365e8			0.885526			0.442763	−	0.896639i	$-0.353998\pi$
$127$	2.30365e8			0.885526			0.442763	+	0.896639i	$0.353998\pi$
$128$		0			0
$129$	−1.17453e7	−	3.09349e8i	−0.0424137	−	1.11710i
$130$		0			0
$131$	4.91276e8	−	2.83638e8i	1.66817	−	0.963119i	0.699547	−	0.714586i	$-0.253385\pi$
$131$	4.91276e8	−	2.83638e8i	1.66817	−	0.963119i	0.968624	−	0.248533i	$-0.0799483\pi$
$132$		0			0
$133$	−1.83662e8	+	1.67987e8i	−0.586965	+	0.536871i
$134$		0			0
$135$	−1.11085e8	−	1.49996e8i	−0.334441	−	0.451591i
$136$		0			0
$137$	−2.33556e8	−	1.34844e8i	−0.662993	−	0.382779i	0.130423	−	0.991458i	$-0.458366\pi$
$137$	−2.33556e8	−	1.34844e8i	−0.662993	−	0.382779i	−0.793416	+	0.608679i	$0.791700\pi$
$138$		0			0
$139$	−3.84729e8			−1.03061			−0.515307	−	0.857006i	$-0.672322\pi$
$139$	−3.84729e8			−1.03061			−0.515307	+	0.857006i	$0.672322\pi$
$140$		0			0
$141$	1.92785e8	+	3.06442e8i	0.487750	+	0.775304i
$142$		0			0
$143$	−9.96856e7	−	5.75535e7i	−0.238390	−	0.137635i
$144$		0			0
$145$	−4.77880e7	−	8.27712e7i	−0.108105	−	0.187244i
$146$		0			0
$147$	−2.12498e8	−	4.15795e8i	−0.455079	−	0.890451i
$148$		0			0
$149$	7.04874e8	−	4.06959e8i	1.43010	−	0.825669i	0.432972	−	0.901407i	$-0.357465\pi$
$149$	7.04874e8	−	4.06959e8i	1.43010	−	0.825669i	0.997128	+	0.0757387i	$0.0241315\pi$
$150$		0			0
$151$	−1.11416e8	+	1.92977e8i	−0.214308	+	0.371192i	−0.953058	−	0.302787i	$-0.902083\pi$
$151$	−1.11416e8	+	1.92977e8i	−0.214308	+	0.371192i	0.738750	+	0.673979i	$0.235416\pi$
$152$		0			0
$153$	3.66365e7	+	1.75936e7i	0.0668571	+	0.0321062i
$154$		0			0
$155$			3.78721e7i			0.0656134i
$156$		0			0
$157$	−5.91423e8	+	1.02437e9i	−0.973419	+	1.68601i	−0.288360	+	0.957522i	$0.593110\pi$
$157$	−5.91423e8	+	1.02437e9i	−0.973419	+	1.68601i	−0.685058	+	0.728488i	$0.740223\pi$
$158$		0			0
$159$	3.84638e8	−	7.28740e8i	0.601816	−	1.14021i
$160$		0			0
$161$	−4.44871e8	−	4.86381e8i	−0.662111	−	0.723890i
$162$		0			0
$163$	−7.20435e7	−	1.24783e8i	−0.102057	−	0.176769i	0.810475	−	0.585774i	$-0.199209\pi$
$163$	−7.20435e7	−	1.24783e8i	−0.102057	−	0.176769i	−0.912532	+	0.409005i	$0.865876\pi$
$164$		0			0
$165$	−2.36374e7	−	6.22565e8i	−0.0318908	−	0.839942i
$166$		0			0
$167$			1.62019e8i			0.208305i	0.994561	+	0.104152i	$0.0332130\pi$
$167$			1.62019e8i			0.208305i	−0.994561	+	0.104152i	$0.966787\pi$
$168$		0			0
$169$	−7.88104e8			−0.966133
$170$		0			0
$171$	−3.83758e8	−	5.61543e8i	−0.448821	−	0.656748i
$172$		0			0
$173$	−6.69805e8	+	3.86712e8i	−0.747763	+	0.431721i	−0.824885	−	0.565301i	$-0.808760\pi$
$173$	−6.69805e8	+	3.86712e8i	−0.747763	+	0.431721i	0.0771221	+	0.997022i	$0.475427\pi$
$174$		0			0
$175$	−6.11842e8	−	1.93526e8i	−0.652360	−	0.206342i
$176$		0			0
$177$	−1.52192e8	+	2.88345e8i	−0.155059	+	0.293778i
$178$		0			0
$179$	6.62081e8	+	3.82253e8i	0.644910	+	0.372339i	0.786504	−	0.617586i	$-0.211889\pi$
$179$	6.62081e8	+	3.82253e8i	0.644910	+	0.372339i	−0.141593	+	0.989925i	$0.545223\pi$
$180$		0			0
$181$	−1.58706e9			−1.47870			−0.739350	−	0.673321i	$-0.764867\pi$
$181$	−1.58706e9			−1.47870			−0.739350	+	0.673321i	$0.764867\pi$
$182$		0			0
$183$	6.80741e8	−	4.28260e8i	0.606984	−	0.381859i
$184$		0			0
$185$	−8.92337e8	−	5.15191e8i	−0.761802	−	0.439826i
$186$		0			0
$187$	6.78283e7	+	1.17482e8i	0.0554683	+	0.0960739i
$188$		0			0
$189$	1.20668e9	−	4.14808e8i	0.945684	−	0.325087i
$190$		0			0
$191$	2.29634e8	−	1.32579e8i	0.172545	−	0.0996192i	−0.411240	−	0.911527i	$-0.634904\pi$
$191$	2.29634e8	−	1.32579e8i	0.172545	−	0.0996192i	0.583786	+	0.811908i	$0.301571\pi$
$192$		0			0
$193$	−1.33759e9	+	2.31678e9i	−0.964040	+	1.66977i	−0.251868	+	0.967762i	$0.581045\pi$
$193$	−1.33759e9	+	2.31678e9i	−0.964040	+	1.66977i	−0.712172	+	0.702005i	$0.752288\pi$
$194$		0			0
$195$	7.96238e7	+	1.26566e8i	0.0550686	+	0.0875344i
$196$		0			0
$197$		−	1.68956e8i		−	0.112178i	−0.998426	−	0.0560891i	$-0.982137\pi$
$197$		−	1.68956e8i		−	0.112178i	0.998426	−	0.0560891i	$-0.0178631\pi$
$198$		0			0
$199$	1.00634e8	−	1.74303e8i	0.0641699	−	0.111145i	−0.832156	−	0.554542i	$-0.812893\pi$
$199$	1.00634e8	−	1.74303e8i	0.0641699	−	0.111145i	0.896325	+	0.443397i	$0.146227\pi$
$200$		0			0
$201$	−2.37023e8	−	1.25103e8i	−0.145213	−	0.0766452i
$202$		0			0
$203$	6.38020e8	−	1.40836e8i	0.375708	−	0.0829335i
$204$		0			0
$205$	−6.82563e8	−	1.18223e9i	−0.386480	−	0.669404i
$206$		0			0
$207$	1.48710e9	−	1.01629e9i	0.809952	−	0.553521i
$208$		0			0
$209$		−	2.27023e9i		−	1.18983i
$210$		0			0
$211$	8.43945e8			0.425779			0.212889	−	0.977076i	$-0.431713\pi$
$211$	8.43945e8			0.425779			0.212889	+	0.977076i	$0.431713\pi$
$212$		0			0
$213$	1.05265e8	−	3.99670e6i	0.0511408	−	0.00194170i
$214$		0			0
$215$	−1.16247e9	+	6.71155e8i	−0.544038	+	0.314101i
$216$		0			0
$217$	−2.46849e8	−	7.80783e7i	−0.111325	−	0.0352120i
$218$		0			0
$219$	−2.47181e9	−	1.30465e9i	−1.07458	−	0.567176i
$220$		0			0
$221$	−2.81968e7	−	1.62794e7i	−0.0118203	−	0.00682448i
$222$		0			0
$223$	2.64503e9			1.06958			0.534788	−	0.844986i	$-0.320391\pi$
$223$	2.64503e9			1.06958			0.534788	+	0.844986i	$0.320391\pi$
$224$		0			0
$225$	7.59108e8	−	1.58075e9i	0.296192	−	0.616783i
$226$		0			0
$227$	2.24625e9	+	1.29687e9i	0.845968	+	0.488420i	0.859288	−	0.511491i	$-0.170907\pi$
$227$	2.24625e9	+	1.29687e9i	0.845968	+	0.488420i	−0.0133202	+	0.999911i	$0.504240\pi$
$228$		0			0
$229$	1.63276e9	+	2.82802e9i	0.593717	+	1.02835i	0.993727	+	0.111837i	$0.0356736\pi$
$229$	1.63276e9	+	2.82802e9i	0.593717	+	1.02835i	−0.400009	+	0.916511i	$0.630993\pi$
$230$		0			0
$231$	4.10658e9	+	1.12943e9i	1.44222	+	0.396654i
$232$		0			0
$233$	1.83584e9	−	1.05993e9i	0.622891	−	0.359626i	−0.155103	−	0.987898i	$-0.549571\pi$
$233$	1.83584e9	−	1.05993e9i	0.622891	−	0.359626i	0.777994	+	0.628272i	$0.216237\pi$
$234$		0			0
$235$	7.84905e8	−	1.35950e9i	0.257363	−	0.445765i
$236$		0			0
$237$	4.10516e8	−	2.58259e8i	0.130118	−	0.0818581i
$238$		0			0
$239$			5.14130e9i			1.57573i	0.615849	+	0.787864i	$0.288813\pi$
$239$			5.14130e9i			1.57573i	−0.615849	+	0.787864i	$0.711187\pi$
$240$		0			0
$241$	−2.34527e9	+	4.06212e9i	−0.695223	+	1.20416i	0.274882	+	0.961478i	$0.411361\pi$
$241$	−2.34527e9	+	4.06212e9i	−0.695223	+	1.20416i	−0.970105	+	0.242684i	$0.921972\pi$
$242$		0			0
$243$	6.57647e8	+	3.42420e9i	0.188611	+	0.982052i
$244$		0			0
$245$	−1.16434e9	+	1.65642e9i	−0.323158	+	0.459732i
$246$		0			0
$247$	2.72438e8	+	4.71877e8i	0.0731948	+	0.126777i
$248$		0			0
$249$	−5.19431e9	+	1.97217e8i	−1.35123	+	0.0513034i
$250$		0			0
$251$			1.01750e9i			0.256353i	0.991751	+	0.128176i	$0.0409124\pi$
$251$			1.01750e9i			0.256353i	−0.991751	+	0.128176i	$0.959088\pi$
$252$		0			0
$253$	6.01213e9			1.46739
$254$		0			0
$255$	−6.68602e6	−	1.76097e8i	−0.00158127	−	0.0416477i
$256$		0			0
$257$	−6.47872e9	+	3.74049e9i	−1.48510	+	0.857425i	−0.999856	−	0.0169511i	$-0.994604\pi$
$257$	−6.47872e9	+	3.74049e9i	−1.48510	+	0.857425i	−0.485248	+	0.874377i	$0.661271\pi$
$258$		0			0
$259$	5.19766e9	−	4.75408e9i	1.15507	−	1.05649i
$260$		0			0
$261$	1.35383e8	+	1.78029e9i	0.0291743	+	0.383644i
$262$		0			0
$263$	−5.43347e9	−	3.13702e9i	−1.13568	−	0.655683i	−0.190320	−	0.981722i	$-0.560952\pi$
$263$	−5.43347e9	−	3.13702e9i	−1.13568	−	0.655683i	−0.945356	+	0.326039i	$0.894286\pi$
$264$		0			0
$265$	−3.57296e9			−0.724511
$266$		0			0
$267$	2.49984e9	+	3.97362e9i	0.491889	+	0.781882i
$268$		0			0
$269$	3.56865e9	+	2.06036e9i	0.681546	+	0.393491i	0.800437	−	0.599416i	$-0.204601\pi$
$269$	3.56865e9	+	2.06036e9i	0.681546	+	0.393491i	−0.118891	+	0.992907i	$0.537934\pi$
$270$		0			0
$271$	1.46426e9	+	2.53617e9i	0.271482	+	0.470221i	0.969242	−	0.246111i	$-0.0791529\pi$
$271$	1.46426e9	+	2.53617e9i	0.271482	+	0.470221i	−0.697759	+	0.716332i	$0.745820\pi$
$272$		0			0
$273$	−9.89106e8	+	2.58052e8i	−0.178071	+	0.0464575i
$274$		0			0
$275$	5.06898e9	−	2.92658e9i	0.886318	−	0.511716i
$276$		0			0
$277$	1.98345e9	−	3.43544e9i	0.336901	−	0.583531i	−0.646947	−	0.762535i	$-0.723954\pi$
$277$	1.98345e9	−	3.43544e9i	0.336901	−	0.583531i	0.983848	+	0.179005i	$0.0572877\pi$
$278$		0			0
$279$	3.06263e8	−	6.37754e8i	0.0505449	−	0.105253i
$280$		0			0
$281$		−	3.58332e9i		−	0.574725i	−0.957822	−	0.287362i	$-0.907222\pi$
$281$		−	3.58332e9i		−	0.574725i	0.957822	−	0.287362i	$-0.0927784\pi$
$282$		0			0
$283$	1.54115e9	−	2.66935e9i	0.240270	−	0.416160i	−0.720521	−	0.693433i	$-0.756097\pi$
$283$	1.54115e9	−	2.66935e9i	0.240270	−	0.416160i	0.960791	+	0.277273i	$0.0894307\pi$
$284$		0			0
$285$	−1.37660e9	+	2.60813e9i	−0.208655	+	0.395321i
$286$		0			0
$287$	9.11294e9	−	2.01158e9i	1.34317	−	0.296490i
$288$		0			0
$289$	−3.46869e9	−	6.00795e9i	−0.497250	−	0.861262i
$290$		0			0
$291$	2.15033e8	+	5.66357e9i	0.0299871	+	0.789802i
$292$		0			0
$293$			9.08460e8i			0.123264i	0.998099	+	0.0616319i	$0.0196305\pi$
$293$			9.08460e8i			0.123264i	−0.998099	+	0.0616319i	$0.980370\pi$
$294$		0			0
$295$	1.41373e9			0.186672
$296$		0			0
$297$	−4.63649e9	+	1.06749e10i	−0.595887	+	1.37196i
$298$		0			0
$299$	−1.24964e9	+	7.21482e8i	−0.156351	+	0.0902695i
$300$		0			0
$301$	−1.97796e9	−	8.96062e9i	−0.240964	−	1.09162i
$302$		0			0
$303$	4.32365e9	−	8.19163e9i	0.512955	−	0.971852i
$304$		0			0
$305$	−3.02003e9	−	1.74361e9i	−0.348989	−	0.201489i
$306$		0			0
$307$	−3.97074e9			−0.447011			−0.223505	−	0.974703i	$-0.571750\pi$
$307$	−3.97074e9			−0.447011			−0.223505	+	0.974703i	$0.571750\pi$
$308$		0			0
$309$	−2.42643e9	+	1.52649e9i	−0.266155	+	0.167440i
$310$		0			0
$311$	−9.43187e9	−	5.44550e9i	−1.00822	−	0.582098i	−0.0975519	−	0.995230i	$-0.531101\pi$
$311$	−9.43187e9	−	5.44550e9i	−1.00822	−	0.582098i	−0.910671	+	0.413133i	$0.864435\pi$
$312$		0			0
$313$	1.16812e9	+	2.02324e9i	0.121706	+	0.210800i	0.920440	−	0.390883i	$-0.127830\pi$
$313$	1.16812e9	+	2.02324e9i	0.121706	+	0.210800i	−0.798735	+	0.601683i	$0.794497\pi$
$314$		0			0
$315$	−4.03294e9	−	3.78764e9i	−0.409619	−	0.384704i
$316$		0			0
$317$	4.60582e9	−	2.65917e9i	0.456110	−	0.263335i	−0.254297	−	0.967126i	$-0.581844\pi$
$317$	4.60582e9	−	2.65917e9i	0.456110	−	0.263335i	0.710407	+	0.703791i	$0.248511\pi$
$318$		0			0
$319$	−2.97975e9	+	5.16108e9i	−0.287751	+	0.498400i
$320$		0			0
$321$	−1.12060e10	−	1.78125e10i	−1.05543	−	1.67767i
$322$		0			0
$323$		−	6.42151e8i		−	0.0589966i
$324$		0			0
$325$	−7.02405e8	+	1.21660e9i	−0.0629584	+	0.109047i
$326$		0			0
$327$	−2.42517e9	−	1.28004e9i	−0.212105	−	0.111952i
$328$		0			0
$329$	7.24294e9	+	7.91875e9i	0.618204	+	0.675885i
$330$		0			0
$331$	−7.11009e9	−	1.23150e10i	−0.592329	−	1.02594i	−0.993918	−	0.110124i	$-0.964875\pi$
$331$	−7.11009e9	−	1.23150e10i	−0.592329	−	1.02594i	0.401589	−	0.915820i	$-0.368458\pi$
$332$		0			0
$333$	1.08604e10	+	1.58918e10i	0.883223	+	1.29240i
$334$		0			0
$335$			1.16210e9i			0.0922712i
$336$		0			0
$337$	2.20560e10			1.71004			0.855022	−	0.518592i	$-0.173544\pi$
$337$	2.20560e10			1.71004			0.855022	+	0.518592i	$0.173544\pi$
$338$		0			0
$339$	−2.14154e10	+	8.13098e8i	−1.62154	+	0.0615664i
$340$		0			0
$341$	2.04509e9	−	1.18073e9i	0.151249	−	0.0873239i
$342$		0			0
$343$	−8.39601e9	−	1.10040e10i	−0.606592	−	0.795014i
$344$		0			0
$345$	−6.90696e9	−	3.64558e9i	−0.487540	−	0.257330i
$346$		0			0
$347$	−1.50837e9	−	8.70860e8i	−0.104038	−	0.0600662i	0.447078	−	0.894495i	$-0.352465\pi$
$347$	−1.50837e9	−	8.70860e8i	−0.104038	−	0.0600662i	−0.551116	+	0.834429i	$0.685798\pi$
$348$		0			0
$349$	−1.17299e9			−0.0790664			−0.0395332	−	0.999218i	$-0.512587\pi$
$349$	−1.17299e9			−0.0790664			−0.0395332	+	0.999218i	$0.512587\pi$
$350$		0			0
$351$	−3.17329e8	−	2.77523e9i	−0.0209065	−	0.182840i
$352$		0			0
$353$	−2.39916e10	−	1.38515e10i	−1.54511	−	0.892070i	−0.998504	−	0.0546809i	$-0.982586\pi$
$353$	−2.39916e10	−	1.38515e10i	−1.54511	−	0.892070i	−0.546607	−	0.837389i	$-0.684081\pi$
$354$		0			0
$355$	−2.28381e8	−	3.95567e8i	−0.0143796	−	0.0249061i
$356$		0			0
$357$	1.16158e9	+	3.19468e8i	0.0715113	+	0.0196677i
$358$		0			0
$359$	−7.21825e9	+	4.16746e9i	−0.434565	+	0.250896i	−0.701289	−	0.712877i	$-0.747392\pi$
$359$	−7.21825e9	+	4.16746e9i	−0.434565	+	0.250896i	0.266725	+	0.963773i	$0.414059\pi$
$360$		0			0
$361$	3.11854e9	−	5.40146e9i	0.183621	−	0.318041i
$362$		0			0
$363$	−1.81848e10	+	1.14402e10i	−1.04733	+	0.658882i
$364$		0			0
$365$			1.21191e10i			0.682809i
$366$		0			0
$367$	−1.00980e10	+	1.74902e10i	−0.556633	+	0.964117i	0.441141	+	0.897438i	$0.354574\pi$
$367$	−1.00980e10	+	1.74902e10i	−0.556633	+	0.964117i	−0.997774	+	0.0666792i	$0.978760\pi$
$368$		0			0
$369$	1.93369e9	+	2.54282e10i	0.104299	+	1.37154i
$370$		0			0
$371$	7.36612e9	−	2.32884e10i	0.388815	−	1.22926i
$372$		0			0
$373$	−1.01297e10	−	1.75452e10i	−0.523313	−	0.906404i	−0.999632	−	0.0271316i	$-0.991363\pi$
$373$	−1.01297e10	−	1.75452e10i	−0.523313	−	0.906404i	0.476319	−	0.879272i	$-0.341971\pi$
$374$		0			0
$375$	−1.87028e10	+	7.10103e8i	−0.945759	+	0.0359084i
$376$		0			0
$377$		−	1.43033e9i		−	0.0708064i
$378$		0			0
$379$	3.63264e10			1.76062			0.880310	−	0.474399i	$-0.157335\pi$
$379$	3.63264e10			1.76062			0.880310	+	0.474399i	$0.157335\pi$
$380$		0			0
$381$	7.07952e8	+	1.86461e10i	0.0335973	+	0.884888i
$382$		0			0
$383$	2.06374e10	−	1.19150e10i	0.959092	−	0.553732i	0.0631983	−	0.998001i	$-0.479870\pi$
$383$	2.06374e10	−	1.19150e10i	0.959092	−	0.553732i	0.895893	+	0.444269i	$0.146537\pi$
$384$		0			0
$385$	−3.98065e9	−	1.80332e10i	−0.181180	−	0.820788i
$386$		0			0
$387$	2.50032e10	−	1.90137e9i	1.11468	−	0.0847663i
$388$		0			0
$389$	1.58409e10	+	9.14576e9i	0.691803	+	0.399412i	0.804287	−	0.594241i	$-0.202547\pi$
$389$	1.58409e10	+	9.14576e9i	0.691803	+	0.399412i	−0.112484	+	0.993653i	$0.535881\pi$
$390$		0			0
$391$	1.70057e9			0.0727592
$392$		0			0
$393$	2.44680e10	+	3.88930e10i	1.02572	+	1.63043i
$394$		0			0
$395$	−1.82121e9	−	1.05147e9i	−0.0748119	−	0.0431927i
$396$		0			0
$397$	−6.71463e9	−	1.16301e10i	−0.270309	−	0.468188i	0.698632	−	0.715481i	$-0.253792\pi$
$397$	−6.71463e9	−	1.16301e10i	−0.270309	−	0.468188i	−0.968941	+	0.247293i	$0.920459\pi$
$398$		0			0
$399$	−1.41616e10	−	1.43496e10i	−0.558755	−	0.566173i
$400$		0			0
$401$	2.46355e10	−	1.42233e10i	0.952761	−	0.550077i	0.0588233	−	0.998268i	$-0.481265\pi$
$401$	2.46355e10	−	1.42233e10i	0.952761	−	0.550077i	0.893937	+	0.448192i	$0.147932\pi$
$402$		0			0
$403$	−2.83386e8	+	4.90839e8i	−0.0107438	+	0.0186088i
$404$		0			0
$405$	1.17996e10	−	9.45235e9i	0.438577	−	0.351334i
$406$		0			0
$407$			6.42480e10i			2.34143i
$408$		0			0
$409$	5.37779e9	−	9.31460e9i	0.192181	−	0.332867i	−0.753792	−	0.657113i	$-0.771777\pi$
$409$	5.37779e9	−	9.31460e9i	0.192181	−	0.332867i	0.945973	+	0.324246i	$0.105111\pi$
$410$		0			0
$411$	1.01967e10	−	1.93188e10i	0.357349	−	0.677038i
$412$		0			0
$413$	−2.91459e9	+	9.21464e9i	−0.100179	+	0.316722i
$414$		0			0
$415$	1.12694e10	+	1.95192e10i	0.379935	+	0.658066i
$416$		0			0
$417$	−1.18234e9	−	3.11406e10i	−0.0391020	−	1.02987i
$418$		0			0
$419$			6.21950e9i			0.201790i	0.994897	+	0.100895i	$0.0321706\pi$
$419$			6.21950e9i			0.201790i	−0.994897	+	0.100895i	$0.967829\pi$
$420$		0			0
$421$	4.21071e10			1.34038			0.670189	−	0.742191i	$-0.266213\pi$
$421$	4.21071e10			1.34038			0.670189	+	0.742191i	$0.266213\pi$
$422$		0			0
$423$	−2.42115e10	+	1.65461e10i	−0.756240	+	0.516815i
$424$		0			0
$425$	1.43380e9	−	8.27803e8i	0.0439472	−	0.0253730i
$426$		0			0
$427$	1.75910e10	−	1.60897e10i	0.529150	−	0.483991i
$428$		0			0
$429$	4.35213e9	−	8.24559e9i	0.128491	−	0.243440i
$430$		0			0
$431$	−2.76898e10	−	1.59867e10i	−0.802437	−	0.463287i	0.0418853	−	0.999122i	$-0.486664\pi$
$431$	−2.76898e10	−	1.59867e10i	−0.802437	−	0.463287i	−0.844323	+	0.535835i	$0.819997\pi$
$432$		0			0
$433$	−8.52497e9			−0.242517			−0.121258	−	0.992621i	$-0.538693\pi$
$433$	−8.52497e9			−0.242517			−0.121258	+	0.992621i	$0.538693\pi$
$434$		0			0
$435$	6.55278e9	−	4.12241e9i	0.183007	−	0.115131i
$436$		0			0
$437$	−2.46465e10	−	1.42297e10i	−0.675817	−	0.390183i
$438$		0			0
$439$	3.60666e10	+	6.24691e10i	0.971062	+	1.68193i	0.692362	+	0.721550i	$0.256570\pi$
$439$	3.60666e10	+	6.24691e10i	0.971062	+	1.68193i	0.278699	+	0.960378i	$0.410097\pi$
$440$		0			0
$441$	3.30021e10	−	1.84778e10i	0.872544	−	0.488535i
$442$		0			0
$443$	−3.78514e10	+	2.18535e10i	−0.982803	+	0.567422i	−0.903115	−	0.429398i	$-0.858726\pi$
$443$	−3.78514e10	+	2.18535e10i	−0.982803	+	0.567422i	−0.0796879	+	0.996820i	$0.525392\pi$
$444$		0			0
$445$	1.01778e10	−	1.76285e10i	0.259546	−	0.449548i
$446$		0			0
$447$	3.51062e10	+	5.58030e10i	0.879333	+	1.39774i
$448$		0			0
$449$			5.55024e10i			1.36561i	0.730601	+	0.682805i	$0.239240\pi$
$449$			5.55024e10i			1.36561i	−0.730601	+	0.682805i	$0.760760\pi$
$450$		0			0
$451$	−4.25603e10	+	7.37165e10i	−1.02872	+	1.78180i
$452$		0			0
$453$	−1.59623e10	−	8.42511e9i	−0.379056	−	0.200070i
$454$		0			0
$455$	2.99146e9	+	3.27059e9i	0.0697972	+	0.0763097i
$456$		0			0
$457$	−1.02780e10	−	1.78020e10i	−0.235636	−	0.408134i	0.723821	−	0.689988i	$-0.242384\pi$
$457$	−1.02780e10	−	1.78020e10i	−0.235636	−	0.408134i	−0.959457	+	0.281854i	$0.909051\pi$
$458$		0			0
$459$	−1.31146e9	+	3.01948e9i	−0.0295465	+	0.0680271i
$460$		0			0
$461$		−	6.02694e10i		−	1.33442i	−0.744869	−	0.667211i	$-0.767488\pi$
$461$		−	6.02694e10i		−	1.33442i	0.744869	−	0.667211i	$-0.232512\pi$
$462$		0			0
$463$	4.14183e10			0.901299			0.450649	−	0.892701i	$-0.351193\pi$
$463$	4.14183e10			0.901299			0.450649	+	0.892701i	$0.351193\pi$
$464$		0			0
$465$	−3.06543e9	+	1.16388e8i	−0.0655662	+	0.00248940i
$466$		0			0
$467$	−4.43515e10	+	2.56064e10i	−0.932484	+	0.538370i	−0.887596	−	0.460622i	$-0.847626\pi$
$467$	−4.43515e10	+	2.56064e10i	−0.932484	+	0.538370i	−0.0448874	+	0.998992i	$0.514293\pi$
$468$		0			0
$469$	−7.57454e9	−	2.39583e9i	−0.156554	−	0.0495182i
$470$		0			0
$471$	−8.47322e10	−	4.47227e10i	−1.72173	−	0.908750i
$472$		0			0
$473$	7.24844e10	+	4.18489e10i	1.44810	+	0.836064i
$474$		0			0
$475$	−2.77068e10			−0.544266
$476$		0			0
$477$	6.01675e10	+	2.88937e10i	1.16222	+	0.558123i
$478$		0			0
$479$	−9.07271e9	−	5.23813e9i	−0.172344	−	0.0995026i	0.411347	−	0.911479i	$-0.365058\pi$
$479$	−9.07271e9	−	5.23813e9i	−0.172344	−	0.0995026i	−0.583690	+	0.811976i	$0.698392\pi$
$480$		0			0
$481$	−7.71005e9	−	1.33542e10i	−0.144038	−	0.249481i
$482$		0			0
$483$	3.80013e10	−	3.75034e10i	0.698248	−	0.689099i
$484$		0			0
$485$	2.12826e10	−	1.22875e10i	0.384642	−	0.222073i
$486$		0			0
$487$	−4.86999e10	+	8.43507e10i	−0.865789	+	1.49959i	0.000472652		1.00000i	$0.499850\pi$
$487$	−4.86999e10	+	8.43507e10i	−0.865789	+	1.49959i	−0.866262	+	0.499591i	$0.833484\pi$
$488$		0			0
$489$	9.87875e9	−	6.21480e9i	0.172769	−	0.108691i
$490$		0			0
$491$		−	7.00189e10i		−	1.20473i	−0.798221	−	0.602364i	$-0.794225\pi$
$491$		−	7.00189e10i		−	1.20473i	0.798221	−	0.602364i	$-0.205775\pi$
$492$		0			0
$493$	−8.42844e8	+	1.45985e9i	−0.0142679	+	0.0247127i
$494$		0			0
$495$	5.03188e10	−	3.82651e9i	0.838127	−	0.0637356i
$496$		0			0
$497$	3.04912e9	−	6.73061e8i	0.0499746	−	0.0110314i
$498$		0			0
$499$	−9.68021e9	−	1.67666e10i	−0.156129	−	0.270423i	0.777341	−	0.629080i	$-0.216568\pi$
$499$	−9.68021e9	−	1.67666e10i	−0.156129	−	0.270423i	−0.933469	+	0.358657i	$0.883235\pi$
$500$		0			0
$501$	−1.31141e10	+	4.97912e8i	−0.208155	+	0.00790318i
$502$		0			0
$503$		−	8.67260e10i		−	1.35481i	−0.735612	−	0.677404i	$-0.763105\pi$
$503$		−	8.67260e10i		−	1.35481i	0.735612	−	0.677404i	$-0.236895\pi$
$504$		0			0
$505$	−4.01630e10			−0.617534
$506$		0			0
$507$	−2.42198e9	−	6.37905e10i	−0.0366555	−	0.965437i
$508$		0			0
$509$	−2.99763e10	+	1.73068e10i	−0.446588	+	0.257838i	−0.706388	−	0.707825i	$-0.749677\pi$
$509$	−2.99763e10	+	1.73068e10i	−0.446588	+	0.257838i	0.259800	+	0.965662i	$0.416343\pi$
$510$		0			0
$511$	−7.89917e10	−	2.49851e10i	−1.15851	−	0.366436i
$512$		0			0
$513$	4.42729e10	−	3.27878e10i	0.639246	−	0.473416i
$514$		0			0
$515$	1.07646e10	+	6.21493e9i	0.153027	+	0.0883502i
$516$		0			0
$517$	−9.78833e10			−1.37008
$518$		0			0
$519$	−3.33596e10	−	5.30267e10i	−0.459781	−	0.730845i
$520$		0			0
$521$	2.05021e10	+	1.18369e10i	0.278258	+	0.160652i	0.632634	−	0.774451i	$-0.281974\pi$
$521$	2.05021e10	+	1.18369e10i	0.278258	+	0.160652i	−0.354377	+	0.935103i	$0.615307\pi$
$522$		0			0
$523$	−1.66720e10	−	2.88768e10i	−0.222834	−	0.385960i	0.732833	−	0.680408i	$-0.238197\pi$
$523$	−1.66720e10	−	2.88768e10i	−0.222834	−	0.385960i	−0.955667	+	0.294448i	$0.904864\pi$
$524$		0			0
$525$	1.37840e10	−	5.01183e10i	0.181442	−	0.659719i
$526$		0			0
$527$	5.78467e8	−	3.33978e8i	0.00749956	−	0.00432987i
$528$		0			0
$529$	−1.47191e9	+	2.54943e9i	−0.0187957	+	0.0325552i
$530$		0			0
$531$	−2.38068e10	−	1.14325e10i	−0.299449	−	0.143802i
$532$		0			0
$533$		−	2.04297e10i		−	0.253135i
$534$		0			0
$535$	−4.56241e10	+	7.90233e10i	−0.556903	+	0.964584i
$536$		0			0
$537$	−2.89055e10	+	5.47647e10i	−0.347603	+	0.658573i
$538$		0			0
$539$	1.25746e11	+	1.12322e10i	1.48984	+	0.133079i
$540$		0			0
$541$	−2.69141e10	−	4.66165e10i	−0.314188	−	0.544190i	0.665076	−	0.746775i	$-0.268399\pi$
$541$	−2.69141e10	−	4.66165e10i	−0.314188	−	0.544190i	−0.979265	+	0.202585i	$0.935066\pi$
$542$		0			0
$543$	−4.87733e9	−	1.28460e11i	−0.0561026	−	1.47764i
$544$		0			0
$545$			1.18905e10i			0.134776i
$546$		0			0
$547$	−9.02277e10			−1.00784			−0.503919	−	0.863751i	$-0.668109\pi$
$547$	−9.02277e10			−1.00784			−0.503919	+	0.863751i	$0.668109\pi$
$548$		0			0
$549$	3.67561e10	+	5.37842e10i	0.404613	+	0.592059i
$550$		0			0
$551$	2.44308e10	−	1.41051e10i	0.265052	−	0.153028i
$552$		0			0
$553$	1.06081e10	−	9.70278e9i	0.113432	−	0.103752i
$554$		0			0
$555$	3.89581e10	−	7.38105e10i	0.410607	−	0.777941i
$556$		0			0
$557$	−5.83460e10	−	3.36861e10i	−0.606165	−	0.349969i	0.165298	−	0.986244i	$-0.447141\pi$
$557$	−5.83460e10	−	3.36861e10i	−0.606165	−	0.349969i	−0.771463	+	0.636274i	$0.780475\pi$
$558$		0			0
$559$	−2.00882e10			−0.205728
$560$		0			0
$561$	−9.30075e9	+	5.85118e9i	−0.0939002	+	0.0590734i
$562$		0			0
$563$	−3.24191e10	−	1.87172e10i	−0.322676	−	0.186297i	0.329909	−	0.944013i	$-0.392982\pi$
$563$	−3.24191e10	−	1.87172e10i	−0.322676	−	0.186297i	−0.652585	+	0.757716i	$0.726315\pi$
$564$		0			0
$565$	4.64623e10	+	8.04750e10i	0.455939	+	0.789710i
$566$		0			0
$567$	3.72836e10	+	9.63962e10i	0.360733	+	0.932669i
$568$		0			0
$569$	8.42286e10	−	4.86294e10i	0.803546	−	0.463927i	−0.0411637	−	0.999152i	$-0.513107\pi$
$569$	8.42286e10	−	4.86294e10i	0.803546	−	0.463927i	0.844710	+	0.535225i	$0.179773\pi$
$570$		0			0
$571$	−6.88613e10	+	1.19271e11i	−0.647785	+	1.12200i	0.335865	+	0.941910i	$0.390971\pi$
$571$	−6.88613e10	+	1.19271e11i	−0.647785	+	1.12200i	−0.983651	+	0.180087i	$0.942362\pi$
$572$		0			0
$573$	1.14369e10	+	1.81796e10i	0.106094	+	0.168642i
$574$		0			0
$575$		−	7.33743e10i		−	0.671232i
$576$		0			0
$577$	4.68159e10	−	8.10876e10i	0.422367	−	0.731562i	−0.573803	−	0.818993i	$-0.694533\pi$
$577$	4.68159e10	−	8.10876e10i	0.422367	−	0.731562i	0.996171	+	0.0874315i	$0.0278659\pi$
$578$		0			0
$579$	−1.91635e11	−	1.01147e11i	−1.70514	−	0.899994i
$580$		0			0
$581$	−1.50459e11	+	3.32121e10i	−1.32042	+	0.291469i
$582$		0			0
$583$	1.11393e11	+	1.92939e11i	0.964241	+	1.67011i
$584$		0			0
$585$	−9.99977e9	+	6.83384e9i	−0.0853820	+	0.0583501i
$586$		0			0
$587$			1.43541e11i			1.20899i	0.796609	+	0.604495i	$0.206625\pi$
$587$			1.43541e11i			1.20899i	−0.796609	+	0.604495i	$0.793375\pi$
$588$		0			0
$589$	−1.11783e10			−0.0928786
$590$		0			0
$591$	1.36756e10	−	5.19231e8i	0.112097	−	0.00425609i
$592$		0			0
$593$	−6.33451e10	+	3.65723e10i	−0.512264	+	0.295756i	−0.733764	−	0.679404i	$-0.762238\pi$
$593$	−6.33451e10	+	3.65723e10i	−0.512264	+	0.295756i	0.221500	+	0.975160i	$0.428905\pi$
$594$		0			0
$595$	−1.12595e9	−	5.10083e9i	−0.00898365	−	0.0406980i
$596$		0			0
$597$	1.44176e10	+	7.60980e9i	0.113500	+	0.0599068i
$598$		0			0
$599$	−1.57500e11	−	9.09327e10i	−1.22341	−	0.706338i	−0.257769	−	0.966206i	$-0.582987\pi$
$599$	−1.57500e11	−	9.09327e10i	−1.22341	−	0.706338i	−0.965644	+	0.259868i	$0.916321\pi$
$600$		0			0
$601$	−5.85889e10			−0.449073			−0.224537	−	0.974466i	$-0.572087\pi$
$601$	−5.85889e10			−0.449073			−0.224537	+	0.974466i	$0.572087\pi$
$602$		0			0
$603$	9.39767e9	−	1.95695e10i	0.0710806	−	0.148016i
$604$		0			0
$605$	8.06748e10	+	4.65776e10i	0.602166	+	0.347661i
$606$		0			0
$607$	7.51158e10	+	1.30104e11i	0.553320	+	0.958378i	0.998032	+	0.0627046i	$0.0199726\pi$
$607$	7.51158e10	+	1.30104e11i	0.553320	+	0.958378i	−0.444712	+	0.895673i	$0.646694\pi$
$608$		0			0
$609$	1.33603e10	+	5.12096e10i	0.0971283	+	0.372291i
$610$		0			0
$611$	2.03454e10	−	1.17464e10i	0.145983	−	0.0842833i
$612$		0			0
$613$	2.93318e9	−	5.08041e9i	0.0207729	−	0.0359797i	−0.855452	−	0.517882i	$-0.826721\pi$
$613$	2.93318e9	−	5.08041e9i	0.0207729	−	0.0359797i	0.876225	+	0.481902i	$0.160054\pi$
$614$		0			0
$615$	9.35944e10	−	5.88810e10i	0.654258	−	0.411600i
$616$		0			0
$617$			2.93100e10i			0.202244i	0.994874	+	0.101122i	$0.0322432\pi$
$617$			2.93100e10i			0.202244i	−0.994874	+	0.101122i	$0.967757\pi$
$618$		0			0
$619$	1.26735e11	−	2.19512e11i	0.863247	−	1.49519i	−0.00553014	−	0.999985i	$-0.501760\pi$
$619$	1.26735e11	−	2.19512e11i	0.863247	−	1.49519i	0.868777	−	0.495203i	$-0.164906\pi$
$620$		0			0
$621$	8.68300e10	+	1.17245e11i	0.583853	+	0.788368i
$622$		0			0
$623$	9.39189e10	+	1.02682e11i	0.623449	+	0.681620i
$624$		0			0
$625$	−1.16246e10	−	2.01343e10i	−0.0761828	−	0.131952i
$626$		0			0
$627$	1.83756e11	−	6.97683e9i	1.18897	−	0.0451428i
$628$		0			0
$629$			1.81730e10i			0.116098i
$630$		0			0
$631$	8.13656e10			0.513244			0.256622	−	0.966512i	$-0.417391\pi$
$631$	8.13656e10			0.513244			0.256622	+	0.966512i	$0.417391\pi$
$632$		0			0
$633$	2.59359e9	+	6.83103e10i	0.0161543	+	0.425472i
$634$		0			0
$635$	7.00684e10	−	4.04540e10i	0.430951	−	0.248809i
$636$		0			0
$637$	−2.74848e10	+	1.27555e10i	−0.166930	+	0.0774710i
$638$		0			0
$639$	6.46999e8	+	8.50808e9i	0.00388061	+	0.0510303i
$640$		0			0
$641$	3.24373e10	+	1.87277e10i	0.192137	+	0.110931i	0.592983	−	0.805215i	$-0.297950\pi$
$641$	3.24373e10	+	1.87277e10i	0.192137	+	0.110931i	−0.400845	+	0.916146i	$0.631284\pi$
$642$		0			0
$643$	2.00046e11			1.17027			0.585134	−	0.810937i	$-0.301042\pi$
$643$	2.00046e11			1.17027			0.585134	+	0.810937i	$0.301042\pi$
$644$		0			0
$645$	−5.78969e10	−	9.20300e10i	−0.334516	−	0.531729i
$646$		0			0
$647$	7.77819e10	+	4.49074e10i	0.443876	+	0.256272i	0.705240	−	0.708968i	$-0.250839\pi$
$647$	7.77819e10	+	4.49074e10i	0.443876	+	0.256272i	−0.261365	+	0.965240i	$0.584172\pi$
$648$		0			0
$649$	−4.40756e10	−	7.63413e10i	−0.248439	−	0.430309i
$650$		0			0
$651$	5.56118e9	−	2.02203e10i	0.0309630	−	0.112581i
$652$		0			0
$653$	−2.01888e11	+	1.16560e11i	−1.11034	+	0.641057i	−0.938918	−	0.344140i	$-0.888170\pi$
$653$	−2.01888e11	+	1.16560e11i	−1.11034	+	0.641057i	−0.171425	+	0.985197i	$0.554837\pi$
$654$		0			0
$655$	9.96187e10	−	1.72545e11i	0.541222	−	0.937424i
$656$		0			0
$657$	9.80044e10	−	2.04082e11i	0.525998	−	1.09532i
$658$		0			0
$659$		−	9.81940e9i		−	0.0520647i	−0.999661	−	0.0260323i	$-0.991713\pi$
$659$		−	9.81940e9i		−	0.0520647i	0.999661	−	0.0260323i	$-0.00828729\pi$
$660$		0			0
$661$	6.56638e10	−	1.13733e11i	0.343970	−	0.595773i	−0.641196	−	0.767377i	$-0.721562\pi$
$661$	6.56638e10	−	1.13733e11i	0.343970	−	0.595773i	0.985166	+	0.171604i	$0.0548949\pi$
$662$		0			0
$663$	1.23103e9	−	2.33232e9i	0.00637110	−	0.0120708i
$664$		0			0
$665$	−2.63630e10	+	8.33481e10i	−0.134806	+	0.426196i
$666$		0			0
$667$	3.73537e10	+	6.46986e10i	0.188726	+	0.326882i
$668$		0			0
$669$	8.12866e9	+	2.14094e11i	0.0405802	+	1.06881i
$670$		0			0
$671$			2.17441e11i			1.07263i
$672$		0			0
$673$	4.64241e10			0.226299			0.113150	−	0.993578i	$-0.463906\pi$
$673$	4.64241e10			0.226299			0.113150	+	0.993578i	$0.463906\pi$
$674$		0			0
$675$	1.30281e11	+	5.65855e10i	0.627576	+	0.272578i
$676$		0			0
$677$	9.80170e10	−	5.65901e10i	0.466602	−	0.269393i	−0.248214	−	0.968705i	$-0.579844\pi$
$677$	9.80170e10	−	5.65901e10i	0.466602	−	0.269393i	0.714816	+	0.699312i	$0.246510\pi$
$678$		0			0
$679$	3.62125e10	+	1.64051e11i	0.170365	+	0.771791i
$680$		0			0
$681$	−9.80678e10	+	1.85801e11i	−0.455972	+	0.863890i
$682$		0			0
$683$	1.14701e11	+	6.62226e10i	0.527089	+	0.304315i	0.739830	−	0.672793i	$-0.234906\pi$
$683$	1.14701e11	+	6.62226e10i	0.527089	+	0.304315i	−0.212741	+	0.977109i	$0.568239\pi$
$684$		0			0
$685$	−9.47188e10			−0.430203
$686$		0			0
$687$	−2.23887e11	+	1.40849e11i	−1.00508	+	0.632306i
$688$		0			0
$689$	−4.63071e10	−	2.67354e10i	−0.205481	−	0.118634i
$690$		0			0
$691$	−7.21691e10	−	1.25001e11i	−0.316548	−	0.548277i	0.663218	−	0.748427i	$-0.269190\pi$
$691$	−7.21691e10	−	1.25001e11i	−0.316548	−	0.548277i	−0.979765	+	0.200150i	$0.935857\pi$
$692$		0			0
$693$	−7.87978e10	+	3.35865e11i	−0.341650	+	1.45623i
$694$		0			0
$695$	−1.17020e11	+	6.75617e10i	−0.501559	+	0.289575i
$696$		0			0
$697$	−1.20385e10	+	2.08512e10i	−0.0510082	+	0.0883488i
$698$		0			0
$699$	9.14340e10	+	1.45339e11i	0.383000	+	0.608798i
$700$		0			0
$701$		−	4.52990e11i		−	1.87593i	−0.346728	−	0.937966i	$-0.612707\pi$
$701$		−	4.52990e11i		−	1.87593i	0.346728	−	0.937966i	$-0.387293\pi$
$702$		0			0
$703$	1.52064e11	−	2.63382e11i	0.622594	−	1.07836i
$704$		0			0
$705$	1.12452e11	+	5.93536e10i	0.455209	+	0.240265i
$706$		0			0
$707$	8.28012e10	−	2.61780e11i	0.331405	−	1.04775i
$708$		0			0
$709$	1.02894e11	+	1.78218e11i	0.407198	+	0.705288i	0.994575	−	0.104026i	$-0.0331724\pi$
$709$	1.02894e11	+	1.78218e11i	0.407198	+	0.705288i	−0.587376	+	0.809314i	$0.699839\pi$
$710$		0			0
$711$	2.21655e10	+	3.24341e10i	0.0867359	+	0.126918i
$712$		0			0
$713$		−	2.96029e10i		−	0.114545i
$714$		0			0
$715$	−4.04275e10			−0.154687
$716$		0			0
$717$	−4.16145e11	+	1.58001e10i	−1.57459	+	0.0597839i
$718$		0			0
$719$	−2.56726e11	+	1.48221e11i	−0.960626	+	0.554618i	−0.896366	−	0.443316i	$-0.853802\pi$
$719$	−2.56726e11	+	1.48221e11i	−0.960626	+	0.554618i	−0.0642602	+	0.997933i	$0.520469\pi$
$720$		0			0
$721$	−6.27012e10	+	5.73501e10i	−0.232025	+	0.212223i
$722$		0			0
$723$	−3.36002e11	−	1.77346e11i	−1.22967	−	0.649036i
$724$		0			0
$725$	6.29878e10	+	3.63660e10i	0.227984	+	0.131627i
$726$		0			0
$727$	2.91589e11			1.04384			0.521920	−	0.852995i	$-0.325216\pi$
$727$	2.91589e11			1.04384			0.521920	+	0.852995i	$0.325216\pi$
$728$		0			0
$729$	−2.75140e11	+	6.37543e10i	−0.974189	+	0.225735i
$730$		0			0
$731$	2.05027e10	+	1.18373e10i	0.0718029	+	0.0414554i
$732$		0			0
$733$	−2.29401e11	−	3.97334e11i	−0.794655	−	1.37638i	−0.923058	−	0.384661i	$-0.874318\pi$
$733$	−2.29401e11	−	3.97334e11i	−0.794655	−	1.37638i	0.128403	−	0.991722i	$-0.459015\pi$
$734$		0			0
$735$	−1.37651e11	−	8.91529e10i	−0.471662	−	0.305482i
$736$		0			0
$737$	6.27534e10	−	3.62307e10i	0.212700	−	0.122802i
$738$		0			0
$739$	1.35783e11	−	2.35184e11i	0.455270	−	0.788551i	−0.543434	−	0.839452i	$-0.682876\pi$
$739$	1.35783e11	−	2.35184e11i	0.455270	−	0.788551i	0.998704	+	0.0509014i	$0.0162094\pi$
$740$		0			0
$741$	−3.73572e10	+	2.35018e10i	−0.123909	+	0.0779521i
$742$		0			0
$743$			1.93861e11i			0.636115i	0.948072	+	0.318057i	$0.103030\pi$
$743$			1.93861e11i			0.636115i	−0.948072	+	0.318057i	$0.896970\pi$
$744$		0			0
$745$	1.42931e11	−	2.47564e11i	0.463982	−	0.803641i
$746$		0			0
$747$	−3.19261e10	−	4.19830e11i	−0.102533	−	1.34831i
$748$		0			0
$749$	−4.21010e11	−	4.60292e11i	−1.33772	−	1.46254i
$750$		0			0
$751$	2.69574e11	+	4.66915e11i	0.847457	+	1.46784i	0.883471	+	0.468487i	$0.155201\pi$
$751$	2.69574e11	+	4.66915e11i	0.847457	+	1.46784i	−0.0360138	+	0.999351i	$0.511466\pi$
$752$		0			0
$753$	−8.23579e10	+	3.12695e9i	−0.256168	+	0.00972615i
$754$		0			0
$755$			7.82621e10i			0.240859i
$756$		0			0
$757$	−5.76575e11			−1.75579			−0.877895	−	0.478854i	$-0.841052\pi$
$757$	−5.76575e11			−1.75579			−0.877895	+	0.478854i	$0.841052\pi$
$758$		0			0
$759$	1.84763e10	+	4.86632e11i	0.0556735	+	1.46634i
$760$		0			0
$761$	3.72013e11	−	2.14782e11i	1.10922	−	0.640411i	0.170596	−	0.985341i	$-0.445431\pi$
$761$	3.72013e11	−	2.14782e11i	1.10922	−	0.640411i	0.938628	+	0.344930i	$0.112097\pi$
$762$		0			0
$763$	−7.75014e10	−	2.45137e10i	−0.228671	−	0.0723287i
$764$		0			0
$765$	1.42330e10	−	1.08235e9i	0.0415577	−	0.00316027i
$766$		0			0
$767$	1.83226e10	+	1.05786e10i	0.0529426	+	0.0305664i
$768$		0			0
$769$	−3.02231e11			−0.864240			−0.432120	−	0.901816i	$-0.642234\pi$
$769$	−3.02231e11			−0.864240			−0.432120	+	0.901816i	$0.642234\pi$
$770$		0			0
$771$	−3.22672e11	−	5.12904e11i	−0.913154	−	1.45150i
$772$		0			0
$773$	5.31443e11	+	3.06829e11i	1.48847	+	0.859366i	0.999913	−	0.0131677i	$-0.00419153\pi$
$773$	5.31443e11	+	3.06829e11i	1.48847	+	0.859366i	0.488553	+	0.872534i	$0.337525\pi$
$774$		0			0
$775$	−1.44101e10	−	2.49590e10i	−0.0399447	−	0.0691863i
$776$		0			0
$777$	4.00776e11	+	4.06097e11i	1.09956	+	1.11416i
$778$		0			0
$779$	3.48948e11	−	2.01465e11i	0.947570	−	0.547080i
$780$		0			0
$781$	−1.42404e10	+	2.46650e10i	−0.0382751	+	0.0662944i
$782$		0			0
$783$	−1.43684e11	+	1.64293e10i	−0.382261	+	0.0437090i
$784$		0			0
$785$			4.15436e11i			1.09402i
$786$		0			0
$787$	2.22703e11	−	3.85734e11i	0.580534	−	1.00552i	−0.414882	−	0.909875i	$-0.636177\pi$
$787$	2.22703e11	−	3.85734e11i	0.580534	−	1.00552i	0.995416	−	0.0956397i	$-0.0304897\pi$
$788$		0			0
$789$	2.37217e11	−	4.49435e11i	0.612123	−	1.15973i
$790$		0			0
$791$	−6.20320e11	+	1.36929e11i	−1.58457	+	0.349776i
$792$		0			0
$793$	−2.60939e10	−	4.51960e10i	−0.0659852	−	0.114290i
$794$		0			0
$795$	−1.09803e10	−	2.89201e11i	−0.0274883	−	0.723989i
$796$		0			0
$797$		−	4.19587e11i		−	1.03989i	−0.854199	−	0.519947i	$-0.825952\pi$
$797$		−	4.19587e11i		−	1.03989i	0.854199	−	0.519947i	$-0.174048\pi$
$798$		0			0
$799$	−2.76870e10			−0.0679342
$800$		0			0
$801$	−3.13949e11	+	2.14553e11i	−0.762657	+	0.521200i
$802$		0			0
$803$	6.54429e11	−	3.77835e11i	1.57398	−	0.908740i
$804$		0			0
$805$	−2.20726e11	−	6.98157e10i	−0.525618	−	0.166253i
$806$		0			0
$807$	−1.55802e11	+	2.95185e11i	−0.367349	+	0.695985i
$808$		0			0
$809$	−3.33490e11	−	1.92541e11i	−0.778554	−	0.449498i	0.0573635	−	0.998353i	$-0.481731\pi$
$809$	−3.33490e11	−	1.92541e11i	−0.778554	−	0.449498i	−0.835918	+	0.548855i	$0.815064\pi$
$810$		0			0
$811$	−3.48989e11			−0.806729			−0.403365	−	0.915039i	$-0.632159\pi$
$811$	−3.48989e11			−0.806729			−0.403365	+	0.915039i	$0.632159\pi$
$812$		0			0
$813$	−2.00782e11	+	1.26314e11i	−0.459582	+	0.289127i
$814$		0			0
$815$	−4.38259e10	−	2.53029e10i	−0.0993347	−	0.0573509i
$816$		0			0
$817$	−1.98098e11	−	3.43116e11i	−0.444623	−	0.770110i
$818$		0			0
$819$	−2.39268e10	−	7.92669e10i	−0.0531802	−	0.176180i
$820$		0			0
$821$	−5.42071e11	+	3.12965e11i	−1.19312	+	0.688847i	−0.959012	−	0.283364i	$-0.908550\pi$
$821$	−5.42071e11	+	3.12965e11i	−1.19312	+	0.688847i	−0.234106	+	0.972211i	$0.575216\pi$
$822$		0			0
$823$	8.27256e10	−	1.43285e11i	0.180319	−	0.312321i	−0.761670	−	0.647965i	$-0.775620\pi$
$823$	8.27256e10	−	1.43285e11i	0.180319	−	0.312321i	0.941989	+	0.335644i	$0.108954\pi$
$824$		0			0
$825$	2.52460e11	+	4.01298e11i	0.544975	+	0.866265i
$826$		0			0
$827$		−	4.00173e11i		−	0.855511i	−0.903894	−	0.427756i	$-0.859304\pi$
$827$		−	4.00173e11i		−	0.855511i	0.903894	−	0.427756i	$-0.140696\pi$
$828$		0			0
$829$	3.84418e11	−	6.65832e11i	0.813927	−	1.40976i	−0.0961681	−	0.995365i	$-0.530659\pi$
$829$	3.84418e11	−	6.65832e11i	0.813927	−	1.40976i	0.910096	−	0.414399i	$-0.136008\pi$
$830$		0			0
$831$	2.84166e11	+	1.49986e11i	0.595893	+	0.314519i
$832$		0			0
$833$	3.55683e10	+	3.17711e9i	0.0738725	+	0.00659860i
$834$		0			0
$835$	2.84519e10	+	4.92801e10i	0.0585281	+	0.101374i
$836$		0			0
$837$	5.25621e10	+	2.28295e10i	0.107095	+	0.0465152i
$838$		0			0
$839$			1.62737e11i			0.328427i	0.986425	+	0.164214i	$0.0525087\pi$
$839$			1.62737e11i			0.328427i	−0.986425	+	0.164214i	$0.947491\pi$
$840$		0			0
$841$	4.26193e11			0.851966
$842$		0			0
$843$	2.90040e11	−	1.10122e10i	0.574311	−	0.0218053i
$844$		0			0
$845$	−2.39712e11	+	1.38398e11i	−0.470179	+	0.271458i
$846$		0			0
$847$	−4.69912e11	+	4.29809e11i	−0.913026	+	0.835106i
$848$		0			0
$849$	2.20798e11	+	1.16540e11i	0.424976	+	0.224308i
$850$		0			0
$851$	6.97500e11	+	4.02702e11i	1.32992	+	0.767831i
$852$		0			0
$853$	7.31968e11			1.38260			0.691299	−	0.722569i	$-0.257039\pi$
$853$	7.31968e11			1.38260			0.691299	+	0.722569i	$0.257039\pi$
$854$		0			0
$855$	−2.15337e11	−	1.03409e11i	−0.402953	−	0.193506i
$856$		0			0
$857$	−5.35957e11	−	3.09435e11i	−0.993589	−	0.573649i	−0.0872440	−	0.996187i	$-0.527806\pi$
$857$	−5.35957e11	−	3.09435e11i	−0.993589	−	0.573649i	−0.906345	+	0.422538i	$0.861139\pi$
$858$		0			0
$859$	1.98464e11	+	3.43750e11i	0.364510	+	0.631350i	0.988697	−	0.149925i	$-0.0479031\pi$
$859$	1.98464e11	+	3.43750e11i	0.364510	+	0.631350i	−0.624187	+	0.781275i	$0.714570\pi$
$860$		0			0
$861$	1.90827e11	+	7.31434e11i	0.347237	+	1.33095i
$862$		0			0
$863$	1.17285e10	−	6.77144e9i	0.0211445	−	0.0122078i	−0.489390	−	0.872065i	$-0.662781\pi$
$863$	1.17285e10	−	6.77144e9i	0.0211445	−	0.0122078i	0.510535	+	0.859857i	$0.329447\pi$
$864$		0			0
$865$	−1.35820e11	+	2.35247e11i	−0.242605	+	0.420203i
$866$		0			0
$867$	4.75634e11	−	2.99225e11i	0.841776	−	0.529568i
$868$		0			0
$869$			1.31126e11i			0.229938i
$870$		0			0
$871$	−8.69570e9	+	1.50614e10i	−0.0151089	+	0.0261693i
$872$		0			0
$873$	−4.57758e11	+	3.48103e10i	−0.788095	+	0.0599309i
$874$		0			0
$875$	−5.41744e11	+	1.19584e11i	−0.924192	+	0.204006i
$876$		0			0
$877$	3.82473e11	+	6.62463e11i	0.646551	+	1.11986i	0.983941	+	0.178494i	$0.0571224\pi$
$877$	3.82473e11	+	6.62463e11i	0.646551	+	1.11986i	−0.337390	+	0.941365i	$0.609544\pi$
$878$		0			0
$879$	−7.35323e10	+	2.79186e9i	−0.123175	+	0.00467668i
$880$		0			0
$881$			2.96363e11i			0.491949i	0.969276	+	0.245974i	$0.0791079\pi$
$881$			2.96363e11i			0.491949i	−0.969276	+	0.245974i	$0.920892\pi$
$882$		0			0
$883$	−5.25932e11			−0.865141			−0.432571	−	0.901600i	$-0.642393\pi$
$883$	−5.25932e11			−0.865141			−0.432571	+	0.901600i	$0.642393\pi$
$884$		0			0
$885$	4.34465e9	+	1.14430e11i	0.00708243	+	0.186538i
$886$		0			0
$887$	−5.27686e11	+	3.04660e11i	−0.852474	+	0.492176i	−0.861485	−	0.507783i	$-0.830465\pi$
$887$	−5.27686e11	+	3.04660e11i	−0.852474	+	0.492176i	0.00901088	+	0.999959i	$0.497132\pi$
$888$		0			0
$889$	1.19222e11	+	5.40104e11i	0.190875	+	0.864709i
$890$		0			0
$891$	−8.78297e11	−	3.42480e11i	−1.39358	−	0.543405i
$892$		0			0
$893$	4.01269e11	+	2.31673e11i	0.631000	+	0.364308i
$894$		0			0
$895$	2.68507e11			0.418470
$896$		0			0
$897$	−6.22384e10	−	9.89311e10i	−0.0961365	−	0.152814i
$898$		0			0
$899$	2.54125e10	+	1.46719e10i	0.0389053	+	0.0224620i
$900$		0			0
$901$	3.15084e10	+	5.45742e10i	0.0478110	+	0.0828110i
$902$		0			0
$903$	7.19209e11	−	1.87637e11i	1.08169	−	0.282207i
$904$		0			0
$905$	−4.82726e11	+	2.78702e11i	−0.719625	+	0.415476i
$906$		0			0
$907$	−8.06279e10	+	1.39652e11i	−0.119140	+	0.206356i	−0.919427	−	0.393261i	$-0.871347\pi$
$907$	−8.06279e10	+	1.39652e11i	−0.119140	+	0.206356i	0.800287	+	0.599617i	$0.204680\pi$
$908$		0			0
$909$	6.76332e11	+	3.24789e11i	0.990614	+	0.475714i
$910$		0			0
$911$		−	3.61832e11i		−	0.525332i	−0.964887	−	0.262666i	$-0.915398\pi$
$911$		−	3.61832e11i		−	0.525332i	0.964887	−	0.262666i	$-0.0846017\pi$
$912$		0			0
$913$	7.02688e11	−	1.21709e12i	1.01130	−	1.75162i
$914$		0			0
$915$	1.31850e11	−	2.49805e11i	0.188103	−	0.356382i
$916$		0			0
$917$	9.19260e11	+	1.00503e12i	1.30005	+	1.42136i
$918$		0			0
$919$	5.60480e11	+	9.70779e11i	0.785774	+	1.36100i	0.928535	+	0.371244i	$0.121069\pi$
$919$	5.60480e11	+	9.70779e11i	0.785774	+	1.36100i	−0.142761	+	0.989757i	$0.545598\pi$
$920$		0			0
$921$	−1.22028e10	−	3.21398e11i	−0.0169598	−	0.446689i
$922$		0			0
$923$		−	6.83563e9i		−	0.00941828i
$924$		0			0
$925$	7.84107e11			1.07105
$926$		0			0
$927$	−1.31013e11	−	1.91708e11i	−0.177418	−	0.259610i
$928$		0			0
$929$	3.60741e11	−	2.08274e11i	0.484320	−	0.279622i	−0.237895	−	0.971291i	$-0.576457\pi$
$929$	3.60741e11	−	2.08274e11i	0.484320	−	0.279622i	0.722215	+	0.691669i	$0.243124\pi$
$930$		0			0
$931$	−4.88908e11	−	3.43666e11i	−0.650771	−	0.457444i
$932$		0			0
$933$	4.11782e11	−	7.80167e11i	0.543426	−	1.02958i
$934$		0			0
$935$	4.12617e10	+	2.38225e10i	0.0539885	+	0.0311702i
$936$		0			0
$937$	−1.20353e12			−1.56134			−0.780670	−	0.624944i	$-0.785122\pi$
$937$	−1.20353e12			−1.56134			−0.780670	+	0.624944i	$0.785122\pi$
$938$		0			0
$939$	−1.60175e11	+	1.00767e11i	−0.206031	+	0.129616i
$940$		0			0
$941$	1.24560e12	+	7.19150e11i	1.58863	+	0.917194i	0.993534	+	0.113536i	$0.0362178\pi$
$941$	1.24560e12	+	7.19150e11i	1.58863	+	0.917194i	0.595092	+	0.803657i	$0.297115\pi$
$942$		0			0
$943$	5.33529e11	+	9.24100e11i	0.674701	+	1.16862i
$944$		0			0
$945$	2.94184e11	−	3.38073e11i	0.368886	−	0.423920i
$946$		0			0
$947$	5.12016e11	−	2.95613e11i	0.636625	−	0.367556i	−0.146688	−	0.989183i	$-0.546861\pi$
$947$	5.12016e11	−	2.95613e11i	0.636625	−	0.367556i	0.783313	+	0.621627i	$0.213528\pi$
$948$		0			0
$949$	−9.06838e10	+	1.57069e11i	−0.111806	+	0.193653i
$950$		0			0
$951$	2.29392e11	+	3.64630e11i	0.280451	+	0.445790i
$952$		0			0
$953$		−	1.23642e12i		−	1.49897i	−0.662020	−	0.749486i	$-0.730301\pi$
$953$		−	1.23642e12i		−	1.49897i	0.662020	−	0.749486i	$-0.269699\pi$
$954$		0			0
$955$	4.65642e10	−	8.06515e10i	0.0559807	−	0.0969615i
$956$		0			0
$957$	−4.26904e11	−	2.25325e11i	−0.508958	−	0.268635i
$958$		0			0
$959$	1.95275e11	−	6.17372e11i	0.230873	−	0.729916i
$960$		0			0
$961$	4.20632e11	+	7.28556e11i	0.493183	+	0.854219i
$962$		0			0
$963$	1.40734e12	−	9.61775e11i	1.63641	−	1.11833i
$964$		0			0
$965$			9.39572e11i			1.08348i
$966$		0			0
$967$	−3.68784e11			−0.421761			−0.210880	−	0.977512i	$-0.567633\pi$
$967$	−3.68784e11			−0.421761			−0.210880	+	0.977512i	$0.567633\pi$
$968$		0			0
$969$	5.19768e10	−	1.97345e9i	0.0589542	−	0.00223836i
$970$		0			0
$971$	−1.16250e12	+	6.71168e11i	−1.30772	+	0.755012i	−0.981715	−	0.190356i	$-0.939036\pi$
$971$	−1.16250e12	+	6.71168e11i	−1.30772	+	0.755012i	−0.326005	+	0.945368i	$0.605703\pi$
$972$		0			0
$973$	−1.99111e11	−	9.02020e11i	−0.222149	−	1.00639i
$974$		0			0
$975$	−1.00632e11	−	5.31150e10i	−0.111357	−	0.0587758i
$976$		0			0
$977$	−1.23413e12	−	7.12528e11i	−1.35452	−	0.782030i	−0.365638	−	0.930757i	$-0.619149\pi$
$977$	−1.23413e12	−	7.12528e11i	−1.35452	−	0.782030i	−0.988878	+	0.148727i	$0.952482\pi$
$978$		0			0
$979$	−1.26925e12			−1.38171
$980$		0			0
$981$	9.61553e10	−	2.00231e11i	0.103824	−	0.216200i
$982$		0			0
$983$	−7.46080e11	−	4.30749e11i	−0.799045	−	0.461329i	0.0440921	−	0.999027i	$-0.485961\pi$
$983$	−7.46080e11	−	4.30749e11i	−0.799045	−	0.461329i	−0.843137	+	0.537699i	$0.819294\pi$
$984$		0			0
$985$	−2.96701e10	−	5.13901e10i	−0.0315191	−	0.0545927i
$986$		0			0
$987$	−6.18698e11	+	6.10592e11i	−0.651944	+	0.643402i
$988$		0			0
$989$	9.08654e11	−	5.24612e11i	0.949759	−	0.548344i
$990$		0			0
$991$	−8.80347e11	+	1.52481e12i	−0.912765	+	1.58096i	−0.102625	+	0.994720i	$0.532724\pi$
$991$	−8.80347e11	+	1.52481e12i	−0.912765	+	1.58096i	−0.810141	+	0.586236i	$0.800609\pi$
$992$		0			0
$993$	9.74949e11	−	6.13349e11i	1.00273	−	0.630827i
$994$		0			0
$995$		−	7.06886e10i		−	0.0721202i
$996$		0			0
$997$	2.26364e10	−	3.92074e10i	0.0229101	−	0.0396815i	−0.854343	−	0.519710i	$-0.826040\pi$
$997$	2.26364e10	−	3.92074e10i	0.0229101	−	0.0396815i	0.877253	+	0.480028i	$0.159374\pi$
$998$		0			0
$999$	−1.25293e12	+	9.27900e11i	−1.25796	+	0.931621i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	84.9.p.b.53.10	yes	40
3.2	odd	2	inner	84.9.p.b.53.4	✓	40
7.2	even	3	inner	84.9.p.b.65.4	yes	40
21.2	odd	6	inner	84.9.p.b.65.10	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.9.p.b.53.4	✓	40	3.2	odd	2	inner
84.9.p.b.53.10	yes	40	1.1	even	1	trivial
84.9.p.b.65.4	yes	40	7.2	even	3	inner
84.9.p.b.65.10	yes	40	21.2	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:	\( N \)	\(=\)	\( 84 = 2^{2} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	84.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(3.07318 + 80.9417i) q^{3} +(304.163 - 175.609i) q^{5} +(517.537 + 2344.56i) q^{7} +(-6542.11 + 497.497i) q^{9} +O(q^{10})\)	\(q+(3.07318 + 80.9417i) q^{3} +(304.163 - 175.609i) q^{5} +(517.537 + 2344.56i) q^{7} +(-6542.11 + 497.497i) q^{9} +(-18965.6 - 10949.8i) q^{11} +5256.11 q^{13} +(15148.8 + 24079.8i) q^{15} +(-5364.57 - 3097.23i) q^{17} +(51832.6 + 89776.8i) q^{19} +(-188182. + 49095.5i) q^{21} +(-237751. + 137265. i) q^{23} +(-133636. + 231464. i) q^{25} +(-60373.3 - 528001. i) q^{27} -272128. i q^{29} +(-53915.5 + 93384.4i) q^{31} +(828012. - 1.56876e6i) q^{33} +(569140. + 622244. i) q^{35} +(-1.46687e6 - 2.54070e6i) q^{37} +(16153.0 + 425439. i) q^{39} -3.88684e6i q^{41} -3.82188e6 q^{43} +(-1.90250e6 + 1.30017e6i) q^{45} +(3.87081e6 - 2.23481e6i) q^{47} +(-5.22911e6 + 2.42679e6i) q^{49} +(234209. - 443735. i) q^{51} +(-8.81015e6 - 5.08654e6i) q^{53} -7.69153e6 q^{55} +(-7.10739e6 + 4.47132e6i) q^{57} +(3.48596e6 + 2.01262e6i) q^{59} +(-4.96449e6 - 8.59875e6i) q^{61} +(-4.55219e6 - 1.50809e7i) q^{63} +(1.59871e6 - 923018. i) q^{65} +(-1.65440e6 + 2.86550e6i) q^{67} +(-1.18411e7 - 1.88221e7i) q^{69} -1.30051e6i q^{71} +(-1.72530e7 + 2.98831e7i) q^{73} +(-1.91458e7 - 1.01054e7i) q^{75} +(1.58571e7 - 5.01330e7i) q^{77} +(-2.99380e6 - 5.18541e6i) q^{79} +(4.25517e7 - 6.50936e6i) q^{81} +6.41735e7i q^{83} -2.17560e6 q^{85} +(2.20265e7 - 836298. i) q^{87} +(5.01926e7 - 2.89787e7i) q^{89} +(2.72023e6 + 1.23233e7i) q^{91} +(-7.72438e6 - 4.07703e6i) q^{93} +(3.15311e7 + 1.82045e7i) q^{95} +6.99710e7 q^{97} +(1.29523e8 + 6.21996e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 81 q^{3} - 34 q^{7} + 4771 q^{9}+O(q^{10}) \) 40 * q + 81 * q^3 - 34 * q^7 + 4771 * q^9	\( 40 q + 81 q^{3} - 34 q^{7} + 4771 q^{9} - 55464 q^{13} + 68482 q^{15} + 311690 q^{19} - 172343 q^{21} + 1766792 q^{25} - 3451932 q^{27} + 31596 q^{31} + 1874885 q^{33} - 1853482 q^{37} + 11217526 q^{39} - 13372600 q^{43} - 527785 q^{45} - 12653462 q^{49} - 1103461 q^{51} + 71577224 q^{55} - 17195214 q^{57} - 21761970 q^{61} + 21945045 q^{63} - 26337350 q^{67} - 5588722 q^{69} + 41115682 q^{73} - 17971730 q^{75} - 120916932 q^{79} - 24550133 q^{81} + 139250060 q^{85} - 16321046 q^{87} + 345074940 q^{91} + 25774675 q^{93} - 707216948 q^{97} - 94510994 q^{99}+O(q^{100}) \) 40 * q + 81 * q^3 - 34 * q^7 + 4771 * q^9 - 55464 * q^13 + 68482 * q^15 + 311690 * q^19 - 172343 * q^21 + 1766792 * q^25 - 3451932 * q^27 + 31596 * q^31 + 1874885 * q^33 - 1853482 * q^37 + 11217526 * q^39 - 13372600 * q^43 - 527785 * q^45 - 12653462 * q^49 - 1103461 * q^51 + 71577224 * q^55 - 17195214 * q^57 - 21761970 * q^61 + 21945045 * q^63 - 26337350 * q^67 - 5588722 * q^69 + 41115682 * q^73 - 17971730 * q^75 - 120916932 * q^79 - 24550133 * q^81 + 139250060 * q^85 - 16321046 * q^87 + 345074940 * q^91 + 25774675 * q^93 - 707216948 * q^97 - 94510994 * q^99

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