LMFDB - Embedded newform 336.7.bh.d.145.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,7,Mod(145,336)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 5]))

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("336.145");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	336.bh (of order $6$, degree $2$, not 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:	$77.2981720963$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 212x^{6} + 473x^{5} + 39800x^{4} + 36821x^{3} + 985651x^{2} - 601290x + 21068100 $ x^8 - x^7 + 212x^6 + 473x^5 + 39800x^4 + 36821x^3 + 985651x^2 - 601290x + 21068100
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{12}\cdot 3\cdot 7 $
Twist minimal:	no (minimal twist has level 21)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			145.1
Root			$-6.30797 - 10.9257i$ of defining polynomial
Character	$\chi$	$=$	336.145
Dual form			336.7.bh.d.241.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(13.5000 - 7.79423i) q^{3} +(-165.302 - 95.4373i) q^{5} +(103.254 + 327.089i) q^{7} +(121.500 - 210.444i) q^{9} +O(q^{10})$	\(q+(13.5000 - 7.79423i) q^{3} +(-165.302 - 95.4373i) q^{5} +(103.254 + 327.089i) q^{7} +(121.500 - 210.444i) q^{9} +(-1027.55 - 1779.77i) q^{11} -3059.97i q^{13} -2975.44 q^{15} +(2468.38 - 1425.12i) q^{17} +(3420.04 + 1974.56i) q^{19} +(3943.34 + 3610.92i) q^{21} +(330.272 - 572.047i) q^{23} +(10404.0 + 18020.3i) q^{25} -3788.00i q^{27} -9282.66 q^{29} +(-2426.36 + 1400.86i) q^{31} +(-27743.9 - 16018.0i) q^{33} +(14148.4 - 63922.9i) q^{35} +(18466.2 - 31984.5i) q^{37} +(-23850.1 - 41309.5i) q^{39} +67941.3i q^{41} -12336.3 q^{43} +(-40168.4 + 23191.3i) q^{45} +(-127836. - 73806.3i) q^{47} +(-96326.1 + 67546.8i) q^{49} +(22215.4 - 38478.3i) q^{51} +(-109818. - 190210. i) q^{53} +392267. i q^{55} +61560.8 q^{57} +(-166725. + 96258.8i) q^{59} +(288244. + 166418. i) q^{61} +(81379.5 + 18012.1i) q^{63} +(-292035. + 505819. i) q^{65} +(174592. + 302402. i) q^{67} -10296.9i q^{69} -305650. q^{71} +(-204814. + 118249. i) q^{73} +(280909. + 162183. i) q^{75} +(476046. - 519871. i) q^{77} +(-293218. + 507869. i) q^{79} +(-29524.5 - 51137.9i) q^{81} +106377. i q^{83} -544039. q^{85} +(-125316. + 72351.2i) q^{87} +(11308.5 + 6528.95i) q^{89} +(1.00088e6 - 315955. i) q^{91} +(-21837.2 + 37823.2i) q^{93} +(-376894. - 652799. i) q^{95} -205209. i q^{97} -499390. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 108 q^{3} - 294 q^{5} + 656 q^{7} + 972 q^{9}+O(q^{10}) $ 8 * q + 108 * q^3 - 294 * q^5 + 656 * q^7 + 972 * q^9	$ 8 q + 108 q^{3} - 294 q^{5} + 656 q^{7} + 972 q^{9} + 314 q^{11} - 5292 q^{15} - 5532 q^{17} + 18234 q^{19} + 9342 q^{21} - 3928 q^{23} - 17038 q^{25} - 8300 q^{29} + 89508 q^{31} + 8478 q^{33} + 25860 q^{35} + 64706 q^{37} - 29106 q^{39} - 45740 q^{43} - 71442 q^{45} - 483276 q^{47} - 310684 q^{49} - 49788 q^{51} - 540974 q^{53} + 328212 q^{57} + 181770 q^{59} + 418224 q^{61} + 92826 q^{63} - 414204 q^{65} + 1158902 q^{67} - 1442344 q^{71} - 378666 q^{73} - 460026 q^{75} + 1065994 q^{77} - 611452 q^{79} - 236196 q^{81} - 275112 q^{85} - 112050 q^{87} - 989196 q^{89} - 304446 q^{91} + 805572 q^{93} + 591792 q^{95} + 152604 q^{99}+O(q^{100}) $ 8 * q + 108 * q^3 - 294 * q^5 + 656 * q^7 + 972 * q^9 + 314 * q^11 - 5292 * q^15 - 5532 * q^17 + 18234 * q^19 + 9342 * q^21 - 3928 * q^23 - 17038 * q^25 - 8300 * q^29 + 89508 * q^31 + 8478 * q^33 + 25860 * q^35 + 64706 * q^37 - 29106 * q^39 - 45740 * q^43 - 71442 * q^45 - 483276 * q^47 - 310684 * q^49 - 49788 * q^51 - 540974 * q^53 + 328212 * q^57 + 181770 * q^59 + 418224 * q^61 + 92826 * q^63 - 414204 * q^65 + 1158902 * q^67 - 1442344 * q^71 - 378666 * q^73 - 460026 * q^75 + 1065994 * q^77 - 611452 * q^79 - 236196 * q^81 - 275112 * q^85 - 112050 * q^87 - 989196 * q^89 - 304446 * q^91 + 805572 * q^93 + 591792 * q^95 + 152604 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{5}{6}\right)$

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
$3$	13.5000	−	7.79423i	0.500000	−	0.288675i
$3$	13.5000	−	7.79423i	0.500000	−	0.288675i
$4$		0			0
$5$	−165.302	−	95.4373i	−1.32242	−	0.763498i	−0.338304	−	0.941037i	$-0.609853\pi$
$5$	−165.302	−	95.4373i	−1.32242	−	0.763498i	−0.984114	+	0.177539i	$0.943186\pi$
$6$		0			0
$7$	103.254	+	327.089i	0.301033	+	0.953614i
$7$	103.254	+	327.089i	0.301033	+	0.953614i
$8$		0			0
$9$	121.500	−	210.444i	0.166667	−	0.288675i
$10$		0			0
$11$	−1027.55	−	1779.77i	−0.772015	−	1.33717i	−0.936457	−	0.350783i	$-0.885916\pi$
$11$	−1027.55	−	1779.77i	−0.772015	−	1.33717i	0.164442	−	0.986387i	$-0.447418\pi$
$12$		0			0
$13$		−	3059.97i		−	1.39279i	−0.717657	−	0.696396i	$-0.754786\pi$
$13$		−	3059.97i		−	1.39279i	0.717657	−	0.696396i	$-0.245214\pi$
$14$		0			0
$15$	−2975.44			−0.881612
$16$		0			0
$17$	2468.38	−	1425.12i	0.502419	−	0.290072i	−0.227293	−	0.973826i	$-0.572988\pi$
$17$	2468.38	−	1425.12i	0.502419	−	0.290072i	0.729712	+	0.683755i	$0.239654\pi$
$18$		0			0
$19$	3420.04	+	1974.56i	0.498622	+	0.287879i	0.728144	−	0.685424i	$-0.240383\pi$
$19$	3420.04	+	1974.56i	0.498622	+	0.287879i	−0.229523	+	0.973303i	$0.573716\pi$
$20$		0			0
$21$	3943.34	+	3610.92i	0.425801	+	0.389906i
$22$		0			0
$23$	330.272	−	572.047i	0.0271449	−	0.0470163i	−0.852134	−	0.523324i	$-0.824692\pi$
$23$	330.272	−	572.047i	0.0271449	−	0.0470163i	0.879279	+	0.476308i	$0.158025\pi$
$24$		0			0
$25$	10404.0	+	18020.3i	0.665859	+	1.15330i
$26$		0			0
$27$		−	3788.00i		−	0.192450i
$28$		0			0
$29$	−9282.66			−0.380609			−0.190304	−	0.981725i	$-0.560947\pi$
$29$	−9282.66			−0.380609			−0.190304	+	0.981725i	$0.560947\pi$
$30$		0			0
$31$	−2426.36	+	1400.86i	−0.0814460	+	0.0470229i	−0.540170	−	0.841556i	$-0.681640\pi$
$31$	−2426.36	+	1400.86i	−0.0814460	+	0.0470229i	0.458724	+	0.888579i	$0.348307\pi$
$32$		0			0
$33$	−27743.9	−	16018.0i	−0.772015	−	0.445723i
$34$		0			0
$35$	14148.4	−	63922.9i	0.329991	−	1.49091i
$36$		0			0
$37$	18466.2	−	31984.5i	0.364563	−	0.631442i	−0.624143	−	0.781310i	$-0.714552\pi$
$37$	18466.2	−	31984.5i	0.364563	−	0.631442i	0.988706	+	0.149868i	$0.0478849\pi$
$38$		0			0
$39$	−23850.1	−	41309.5i	−0.402065	−	0.696396i
$40$		0			0
$41$			67941.3i			0.985785i	0.870090	+	0.492892i	$0.164060\pi$
$41$			67941.3i			0.985785i	−0.870090	+	0.492892i	$0.835940\pi$
$42$		0			0
$43$	−12336.3			−0.155160			−0.0775799	−	0.996986i	$-0.524719\pi$
$43$	−12336.3			−0.155160			−0.0775799	+	0.996986i	$0.524719\pi$
$44$		0			0
$45$	−40168.4	+	23191.3i	−0.440806	+	0.254499i
$46$		0			0
$47$	−127836.	−	73806.3i	−1.23129	−	0.710886i	−0.263991	−	0.964525i	$-0.585039\pi$
$47$	−127836.	−	73806.3i	−1.23129	−	0.710886i	−0.967299	+	0.253639i	$0.918372\pi$
$48$		0			0
$49$	−96326.1	+	67546.8i	−0.818758	+	0.574139i
$50$		0			0
$51$	22215.4	−	38478.3i	0.167473	−	0.290072i
$52$		0			0
$53$	−109818.	−	190210.i	−0.737641	−	1.27763i	−0.953555	−	0.301219i	$-0.902607\pi$
$53$	−109818.	−	190210.i	−0.737641	−	1.27763i	0.215914	−	0.976412i	$-0.430727\pi$
$54$		0			0
$55$			392267.i			2.35773i
$56$		0			0
$57$	61560.8			0.332414
$58$		0			0
$59$	−166725.	+	96258.8i	−0.811792	+	0.468689i	−0.847578	−	0.530671i	$-0.821940\pi$
$59$	−166725.	+	96258.8i	−0.811792	+	0.468689i	0.0357855	+	0.999359i	$0.488607\pi$
$60$		0			0
$61$	288244.	+	166418.i	1.26990	+	0.733180i	0.974970	−	0.222338i	$-0.0713688\pi$
$61$	288244.	+	166418.i	1.26990	+	0.733180i	0.294935	+	0.955517i	$0.404702\pi$
$62$		0			0
$63$	81379.5	+	18012.1i	0.325457	+	0.0720348i
$64$		0			0
$65$	−292035.	+	505819.i	−1.06339	+	1.84185i
$66$		0			0
$67$	174592.	+	302402.i	0.580496	+	1.00545i	0.995420	+	0.0955931i	$0.0304748\pi$
$67$	174592.	+	302402.i	0.580496	+	1.00545i	−0.414924	+	0.909856i	$0.636192\pi$
$68$		0			0
$69$		−	10296.9i		−	0.0313442i
$70$		0			0
$71$	−305650.			−0.853984			−0.426992	−	0.904255i	$-0.640427\pi$
$71$	−305650.			−0.853984			−0.426992	+	0.904255i	$0.640427\pi$
$72$		0			0
$73$	−204814.	+	118249.i	−0.526490	+	0.303969i	−0.739586	−	0.673062i	$-0.764979\pi$
$73$	−204814.	+	118249.i	−0.526490	+	0.303969i	0.213096	+	0.977031i	$0.431645\pi$
$74$		0			0
$75$	280909.	+	162183.i	0.665859	+	0.384434i
$76$		0			0
$77$	476046.	−	519871.i	1.04274	−	1.13874i
$78$		0			0
$79$	−293218.	+	507869.i	−0.594716	+	1.03008i	0.398871	+	0.917007i	$0.369402\pi$
$79$	−293218.	+	507869.i	−0.594716	+	1.03008i	−0.993587	+	0.113072i	$0.963931\pi$
$80$		0			0
$81$	−29524.5	−	51137.9i	−0.0555556	−	0.0962250i
$82$		0			0
$83$			106377.i			0.186044i	0.995664	+	0.0930218i	$0.0296526\pi$
$83$			106377.i			0.186044i	−0.995664	+	0.0930218i	$0.970347\pi$
$84$		0			0
$85$	−544039.			−0.885876
$86$		0			0
$87$	−125316.	+	72351.2i	−0.190304	+	0.109872i
$88$		0			0
$89$	11308.5	+	6528.95i	0.0160411	+	0.00926134i	0.507999	−	0.861358i	$-0.330385\pi$
$89$	11308.5	+	6528.95i	0.0160411	+	0.00926134i	−0.491958	+	0.870619i	$0.663719\pi$
$90$		0			0
$91$	1.00088e6	−	315955.i	1.32819	−	0.419277i
$92$		0			0
$93$	−21837.2	+	37823.2i	−0.0271487	+	0.0470229i
$94$		0			0
$95$	−376894.	−	652799.i	−0.439591	−	0.761393i
$96$		0			0
$97$		−	205209.i		−	0.224844i	−0.993661	−	0.112422i	$-0.964139\pi$
$97$		−	205209.i		−	0.224844i	0.993661	−	0.112422i	$-0.0358609\pi$
$98$		0			0
$99$	−499390.			−0.514677
$100$		0			0
$101$	−1.21339e6	+	700549.i	−1.17770	+	0.679946i	−0.955482	−	0.295050i	$-0.904664\pi$
$101$	−1.21339e6	+	700549.i	−1.17770	+	0.679946i	−0.222220	+	0.974997i	$0.571330\pi$
$102$		0			0
$103$	−448291.	−	258821.i	−0.410250	−	0.236858i	0.280647	−	0.959811i	$-0.409451\pi$
$103$	−448291.	−	258821.i	−0.410250	−	0.236858i	−0.690897	+	0.722953i	$0.742784\pi$
$104$		0			0
$105$	−307227.	−	973235.i	−0.265394	−	0.840717i
$106$		0			0
$107$	323372.	−	560097.i	0.263968	−	0.457206i	−0.703325	−	0.710869i	$-0.748302\pi$
$107$	323372.	−	560097.i	0.263968	−	0.457206i	0.967293	+	0.253663i	$0.0816354\pi$
$108$		0			0
$109$	343631.	+	595186.i	0.265346	+	0.459593i	0.967654	−	0.252280i	$-0.0811805\pi$
$109$	343631.	+	595186.i	0.265346	+	0.459593i	−0.702308	+	0.711873i	$0.747847\pi$
$110$		0			0
$111$		−	575720.i		−	0.420962i
$112$		0			0
$113$	2.11668e6			1.46697			0.733483	−	0.679708i	$-0.237893\pi$
$113$	2.11668e6			1.46697			0.733483	+	0.679708i	$0.237893\pi$
$114$		0			0
$115$	−109189.	+	63040.4i	−0.0717937	+	0.0414501i
$116$		0			0
$117$	−643952.	−	371786.i	−0.402065	−	0.232132i
$118$		0			0
$119$	721014.	+	660232.i	0.427861	+	0.391792i
$120$		0			0
$121$	−1.22595e6	+	2.12340e6i	−0.692015	+	1.19860i
$122$		0			0
$123$	529550.	+	917207.i	0.284571	+	0.492892i
$124$		0			0
$125$		−	989318.i		−	0.506531i
$126$		0			0
$127$	−3.29012e6			−1.60620			−0.803102	−	0.595841i	$-0.796819\pi$
$127$	−3.29012e6			−1.60620			−0.803102	+	0.595841i	$0.796819\pi$
$128$		0			0
$129$	−166540.	+	96151.9i	−0.0775799	+	0.0447908i
$130$		0			0
$131$	−193424.	−	111674.i	−0.0860394	−	0.0496748i	0.456363	−	0.889794i	$-0.349152\pi$
$131$	−193424.	−	111674.i	−0.0860394	−	0.0496748i	−0.542402	+	0.840119i	$0.682485\pi$
$132$		0			0
$133$	−292725.	+	1.32254e6i	−0.124424	+	0.562153i
$134$		0			0
$135$	−361516.	+	626164.i	−0.146935	+	0.254499i
$136$		0			0
$137$	1.58525e6	+	2.74573e6i	0.616504	+	1.06782i	0.990119	+	0.140232i	$0.0447849\pi$
$137$	1.58525e6	+	2.74573e6i	0.616504	+	1.06782i	−0.373615	+	0.927584i	$0.621882\pi$
$138$		0			0
$139$			774740.i			0.288477i	0.989543	+	0.144239i	$0.0460733\pi$
$139$			774740.i			0.288477i	−0.989543	+	0.144239i	$0.953927\pi$
$140$		0			0
$141$	−2.30105e6			−0.820860
$142$		0			0
$143$	−5.44604e6	+	3.14427e6i	−1.86240	+	1.07526i
$144$		0			0
$145$	1.53444e6	+	885912.i	0.503323	+	0.290594i
$146$		0			0
$147$	−773927.	+	1.66267e6i	−0.243640	+	0.523424i
$148$		0			0
$149$	−1.75461e6	+	3.03907e6i	−0.530421	+	0.918716i	0.468949	+	0.883225i	$0.344633\pi$
$149$	−1.75461e6	+	3.03907e6i	−0.530421	+	0.918716i	−0.999370	+	0.0354908i	$0.988701\pi$
$150$		0			0
$151$	3.22601e6	+	5.58761e6i	0.936989	+	1.62291i	0.771049	+	0.636776i	$0.219732\pi$
$151$	3.22601e6	+	5.58761e6i	0.936989	+	1.62291i	0.165940	+	0.986136i	$0.446934\pi$
$152$		0			0
$153$		−	692609.i		−	0.193381i
$154$		0			0
$155$	534776.			0.143607
$156$		0			0
$157$	−4.05557e6	+	2.34148e6i	−1.04798	+	0.605051i	−0.922083	−	0.386992i	$-0.873514\pi$
$157$	−4.05557e6	+	2.34148e6i	−1.04798	+	0.605051i	−0.125896	+	0.992043i	$0.540181\pi$
$158$		0			0
$159$	−2.96508e6	−	1.71189e6i	−0.737641	−	0.425877i
$160$		0			0
$161$	221213.	+	48962.0i	0.0530069	+	0.0117323i
$162$		0			0
$163$	2.59116e6	−	4.48803e6i	0.598318	−	1.03632i	−0.394752	−	0.918788i	$-0.629169\pi$
$163$	2.59116e6	−	4.48803e6i	0.598318	−	1.03632i	0.993069	−	0.117529i	$-0.0374973\pi$
$164$		0			0
$165$	3.05742e6	+	5.29560e6i	0.680617	+	1.17886i
$166$		0			0
$167$			1.56630e6i			0.336298i	0.985762	+	0.168149i	$0.0537790\pi$
$167$			1.56630e6i			0.336298i	−0.985762	+	0.168149i	$0.946221\pi$
$168$		0			0
$169$	−4.53658e6			−0.939871
$170$		0			0
$171$	831071.	−	479819.i	0.166207	−	0.0959598i
$172$		0			0
$173$	−1.07788e6	−	622312.i	−0.208176	−	0.120190i	0.392287	−	0.919843i	$-0.371684\pi$
$173$	−1.07788e6	−	622312.i	−0.208176	−	0.120190i	−0.600463	+	0.799652i	$0.705017\pi$
$174$		0			0
$175$	−4.82000e6	+	5.26373e6i	−0.899358	+	0.982154i
$176$		0			0
$177$	−1.50053e6	+	2.59899e6i	−0.270597	+	0.468689i
$178$		0			0
$179$	1.12800e6	+	1.95375e6i	0.196675	+	0.340651i	0.947448	−	0.319909i	$-0.103652\pi$
$179$	1.12800e6	+	1.95375e6i	0.196675	+	0.340651i	−0.750773	+	0.660560i	$0.770319\pi$
$180$		0			0
$181$		−	7.97198e6i		−	1.34441i	−0.740367	−	0.672203i	$-0.765348\pi$
$181$		−	7.97198e6i		−	1.34441i	0.740367	−	0.672203i	$-0.234652\pi$
$182$		0			0
$183$	5.18839e6			0.846603
$184$		0			0
$185$	−6.10502e6	+	3.52473e6i	−0.964210	+	0.556687i
$186$		0			0
$187$	−5.07278e6	−	2.92877e6i	−0.775750	−	0.447879i
$188$		0			0
$189$	1.23901e6	−	391127.i	0.183523	−	0.0579338i
$190$		0			0
$191$	2.13087e6	−	3.69078e6i	0.305814	−	0.529685i	−0.671628	−	0.740888i	$-0.734405\pi$
$191$	2.13087e6	−	3.69078e6i	0.305814	−	0.529685i	0.977442	+	0.211203i	$0.0677382\pi$
$192$		0			0
$193$	72886.7	+	126243.i	0.0101386	+	0.0175605i	0.871050	−	0.491194i	$-0.163439\pi$
$193$	72886.7	+	126243.i	0.0101386	+	0.0175605i	−0.860912	+	0.508755i	$0.830106\pi$
$194$		0			0
$195$			9.10474e6i			1.22790i
$196$		0			0
$197$	−7.21313e6			−0.943463			−0.471732	−	0.881742i	$-0.656371\pi$
$197$	−7.21313e6			−0.943463			−0.471732	+	0.881742i	$0.656371\pi$
$198$		0			0
$199$	−1.52836e6	+	882399.i	−0.193940	+	0.111971i	−0.593826	−	0.804594i	$-0.702383\pi$
$199$	−1.52836e6	+	882399.i	−0.193940	+	0.111971i	0.399886	+	0.916565i	$0.369050\pi$
$200$		0			0
$201$	4.71398e6	+	2.72162e6i	0.580496	+	0.335150i
$202$		0			0
$203$	−958475.	−	3.03626e6i	−0.114576	−	0.362954i
$204$		0			0
$205$	6.48413e6	−	1.12308e7i	0.752645	−	1.30362i
$206$		0			0
$207$	−80256.0	−	139007.i	−0.00904829	−	0.0156721i
$208$		0			0
$209$		−	8.11587e6i		−	0.888989i
$210$		0			0
$211$	−1.37033e7			−1.45874			−0.729369	−	0.684121i	$-0.760186\pi$
$211$	−1.37033e7			−1.45874			−0.729369	+	0.684121i	$0.760186\pi$
$212$		0			0
$213$	−4.12628e6	+	2.38231e6i	−0.426992	+	0.246524i
$214$		0			0
$215$	2.03922e6	+	1.17734e6i	0.205186	+	0.118464i
$216$		0			0
$217$	−708738.	−	648991.i	−0.0693596	−	0.0635126i
$218$		0			0
$219$	−1.84332e6	+	3.19273e6i	−0.175497	+	0.303969i
$220$		0			0
$221$	−4.36082e6	−	7.55317e6i	−0.404010	−	0.699765i
$222$		0			0
$223$		−	2.15029e7i		−	1.93902i	−0.245055	−	0.969509i	$-0.578806\pi$
$223$		−	2.15029e7i		−	1.93902i	0.245055	−	0.969509i	$-0.421194\pi$
$224$		0			0
$225$	5.05636e6			0.443906
$226$		0			0
$227$	−3.40461e6	+	1.96565e6i	−0.291065	+	0.168046i	−0.638422	−	0.769687i	$-0.720412\pi$
$227$	−3.40461e6	+	1.96565e6i	−0.291065	+	0.168046i	0.347357	+	0.937733i	$0.387079\pi$
$228$		0			0
$229$	486988.	+	281163.i	0.0405520	+	0.0234127i	0.520139	−	0.854082i	$-0.325880\pi$
$229$	486988.	+	281163.i	0.0405520	+	0.0234127i	−0.479587	+	0.877494i	$0.659213\pi$
$230$		0			0
$231$	2.37462e6	−	1.07287e7i	0.192646	−	0.870382i
$232$		0			0
$233$	8.16657e6	−	1.41449e7i	0.645612	−	1.11823i	−0.338548	−	0.940949i	$-0.609936\pi$
$233$	8.16657e6	−	1.41449e7i	0.645612	−	1.11823i	0.984160	−	0.177284i	$-0.0567310\pi$
$234$		0			0
$235$	1.40877e7	+	2.44007e7i	1.08552	+	1.88018i
$236$		0			0
$237$			9.14164e6i			0.686719i
$238$		0			0
$239$	1.96132e7			1.43666			0.718331	−	0.695702i	$-0.244906\pi$
$239$	1.96132e7			1.43666			0.718331	+	0.695702i	$0.244906\pi$
$240$		0			0
$241$	3.11683e6	−	1.79950e6i	0.222670	−	0.128559i	−0.384516	−	0.923118i	$-0.625632\pi$
$241$	3.11683e6	−	1.79950e6i	0.222670	−	0.128559i	0.607186	+	0.794560i	$0.292298\pi$
$242$		0			0
$243$	−797162.	−	460241.i	−0.0555556	−	0.0320750i
$244$		0			0
$245$	2.23694e7	−	1.97254e6i	1.52109	−	0.134131i
$246$		0			0
$247$	6.04210e6	−	1.04652e7i	0.400956	−	0.694476i
$248$		0			0
$249$	829129.	+	1.43609e6i	0.0537061	+	0.0930218i
$250$		0			0
$251$		−	6.49855e6i		−	0.410956i	−0.978662	−	0.205478i	$-0.934125\pi$
$251$		−	6.49855e6i		−	0.410956i	0.978662	−	0.205478i	$-0.0658749\pi$
$252$		0			0
$253$	−1.35749e6			−0.0838250
$254$		0			0
$255$	−7.34452e6	+	4.24036e6i	−0.442938	+	0.255730i
$256$		0			0
$257$	2.47506e6	+	1.42897e6i	0.145810	+	0.0841832i	0.571130	−	0.820860i	$-0.306505\pi$
$257$	2.47506e6	+	1.42897e6i	0.145810	+	0.0841832i	−0.425320	+	0.905043i	$0.639839\pi$
$258$		0			0
$259$	1.23685e7	+	2.73758e6i	0.711898	+	0.157568i
$260$		0			0
$261$	−1.12784e6	+	1.95348e6i	−0.0634348	+	0.109872i
$262$		0			0
$263$	−2.49913e6	−	4.32862e6i	−0.137380	−	0.237948i	0.789124	−	0.614233i	$-0.210535\pi$
$263$	−2.49913e6	−	4.32862e6i	−0.137380	−	0.237948i	−0.926504	+	0.376285i	$0.877201\pi$
$264$		0			0
$265$			4.19228e7i			2.25275i
$266$		0			0
$267$	203553.			0.0106941
$268$		0			0
$269$	−1.76842e7	+	1.02100e7i	−0.908507	+	0.524527i	−0.879951	−	0.475065i	$-0.842424\pi$
$269$	−1.76842e7	+	1.02100e7i	−0.908507	+	0.524527i	−0.0285567	+	0.999592i	$0.509091\pi$
$270$		0			0
$271$	−1.06885e7	−	6.17102e6i	−0.537044	−	0.310062i	0.206836	−	0.978376i	$-0.433683\pi$
$271$	−1.06885e7	−	6.17102e6i	−0.537044	−	0.310062i	−0.743880	+	0.668313i	$0.767017\pi$
$272$		0			0
$273$	1.10493e7	−	1.20665e7i	0.543058	−	0.593053i
$274$		0			0
$275$	2.13814e7	−	3.70336e7i	1.02811	−	1.78073i
$276$		0			0
$277$	1.04151e7	+	1.80395e7i	0.490031	+	0.848758i	0.999934	−	0.0114733i	$-0.00365216\pi$
$277$	1.04151e7	+	1.80395e7i	0.490031	+	0.848758i	−0.509903	+	0.860232i	$0.670319\pi$
$278$		0			0
$279$			680817.i			0.0313486i
$280$		0			0
$281$	2.10143e7			0.947100			0.473550	−	0.880767i	$-0.342972\pi$
$281$	2.10143e7			0.947100			0.473550	+	0.880767i	$0.342972\pi$
$282$		0			0
$283$	−9.02737e6	+	5.21195e6i	−0.398292	+	0.229954i	−0.685747	−	0.727840i	$-0.740524\pi$
$283$	−9.02737e6	+	5.21195e6i	−0.398292	+	0.229954i	0.287455	+	0.957794i	$0.407191\pi$
$284$		0			0
$285$	−1.01761e7	−	5.87519e6i	−0.439591	−	0.253798i
$286$		0			0
$287$	−2.22229e7	+	7.01523e6i	−0.940058	+	0.296754i
$288$		0			0
$289$	−8.00684e6	+	1.38683e7i	−0.331717	+	0.574551i
$290$		0			0
$291$	−1.59945e6	−	2.77033e6i	−0.0649070	−	0.112422i
$292$		0			0
$293$		−	2.85328e7i		−	1.13433i	−0.823603	−	0.567167i	$-0.808039\pi$
$293$		−	2.85328e7i		−	1.13433i	0.823603	−	0.567167i	$-0.191961\pi$
$294$		0			0
$295$	3.67467e7			1.43137
$296$		0			0
$297$	−6.74177e6	+	3.89236e6i	−0.257338	+	0.148574i
$298$		0			0
$299$	−1.75044e6	−	1.01062e6i	−0.0654839	−	0.0378072i
$300$		0			0
$301$	−1.27378e6	−	4.03507e6i	−0.0467082	−	0.147963i
$302$		0			0
$303$	−1.09205e7	+	1.89148e7i	−0.392567	+	0.679946i
$304$		0			0
$305$	−3.17649e7	−	5.50185e7i	−1.11956	−	1.93914i
$306$		0			0
$307$			1.02269e7i			0.353450i	0.984260	+	0.176725i	$0.0565503\pi$
$307$			1.02269e7i			0.353450i	−0.984260	+	0.176725i	$0.943450\pi$
$308$		0			0
$309$	−8.06925e6			−0.273500
$310$		0			0
$311$	1.36331e7	−	7.87108e6i	0.453225	−	0.261669i	−0.255966	−	0.966686i	$-0.582394\pi$
$311$	1.36331e7	−	7.87108e6i	0.453225	−	0.261669i	0.709191	+	0.705016i	$0.249060\pi$
$312$		0			0
$313$	4.80881e7	+	2.77637e7i	1.56821	+	0.905408i	0.996378	+	0.0850387i	$0.0271014\pi$
$313$	4.80881e7	+	2.77637e7i	1.56821	+	0.905408i	0.571834	+	0.820369i	$0.306232\pi$
$314$		0			0
$315$	−1.17332e7	−	1.07441e7i	−0.375391	−	0.343746i
$316$		0			0
$317$	3.01539e6	−	5.22282e6i	0.0946600	−	0.163956i	−0.814807	−	0.579733i	$-0.803157\pi$
$317$	3.01539e6	−	5.22282e6i	0.0946600	−	0.163956i	0.909467	+	0.415777i	$0.136490\pi$
$318$		0			0
$319$	9.53842e6	+	1.65210e7i	0.293836	+	0.508938i
$320$		0			0
$321$		−	1.00817e7i		−	0.304804i
$322$		0			0
$323$	1.12560e7			0.334022
$324$		0			0
$325$	5.51416e7	−	3.18360e7i	1.60631	−	0.927403i
$326$		0			0
$327$	9.27803e6	+	5.35667e6i	0.265346	+	0.153198i
$328$		0			0
$329$	1.09416e7	−	4.94347e7i	0.307251	−	1.38818i
$330$		0			0
$331$	4.88277e6	−	8.45720e6i	0.134643	−	0.233208i	−0.790818	−	0.612051i	$-0.790345\pi$
$331$	4.88277e6	−	8.45720e6i	0.134643	−	0.233208i	0.925461	+	0.378843i	$0.123678\pi$
$332$		0			0
$333$	−4.48729e6	−	7.77222e6i	−0.121521	−	0.210481i
$334$		0			0
$335$		−	6.66502e7i		−	1.77283i
$336$		0			0
$337$	−5.70025e7			−1.48938			−0.744688	−	0.667412i	$-0.767402\pi$
$337$	−5.70025e7			−1.48938			−0.744688	+	0.667412i	$0.767402\pi$
$338$		0			0
$339$	2.85752e7	−	1.64979e7i	0.733483	−	0.423477i
$340$		0			0
$341$	4.98642e6	+	2.87891e6i	0.125755	+	0.0726047i
$342$		0			0
$343$	−3.20399e7	−	2.45327e7i	−0.793980	−	0.607944i
$344$		0			0
$345$	−982703.	+	1.70209e6i	−0.0239312	+	0.0414501i
$346$		0			0
$347$	−1.83677e7	−	3.18139e7i	−0.439610	−	0.761426i	0.558050	−	0.829808i	$-0.311550\pi$
$347$	−1.83677e7	−	3.18139e7i	−0.439610	−	0.761426i	−0.997659	+	0.0683813i	$0.978217\pi$
$348$		0			0
$349$		−	6.58421e7i		−	1.54891i	−0.632626	−	0.774457i	$-0.718023\pi$
$349$		−	6.58421e7i		−	1.54891i	0.632626	−	0.774457i	$-0.281977\pi$
$350$		0			0
$351$	−1.15911e7			−0.268043
$352$		0			0
$353$	2.76008e7	−	1.59353e7i	0.627476	−	0.362273i	−0.152298	−	0.988335i	$-0.548667\pi$
$353$	2.76008e7	−	1.59353e7i	0.627476	−	0.362273i	0.779774	+	0.626061i	$0.215334\pi$
$354$		0			0
$355$	5.05247e7	+	2.91704e7i	1.12932	+	0.652015i
$356$		0			0
$357$	1.48797e7	+	3.29339e6i	0.327031	+	0.0723833i
$358$		0			0
$359$	−1.91128e7	+	3.31044e7i	−0.413087	+	0.715488i	−0.995226	−	0.0976018i	$-0.968883\pi$
$359$	−1.91128e7	+	3.31044e7i	−0.413087	+	0.715488i	0.582138	+	0.813090i	$0.302216\pi$
$360$		0			0
$361$	−1.57251e7	−	2.72367e7i	−0.334251	−	0.578940i
$362$		0			0
$363$			3.82212e7i			0.799070i
$364$		0			0
$365$	4.51415e7			0.928320
$366$		0			0
$367$	−8.43371e7	+	4.86920e7i	−1.70616	+	0.985053i	−0.766956	+	0.641699i	$0.778230\pi$
$367$	−8.43371e7	+	4.86920e7i	−1.70616	+	0.985053i	−0.939206	+	0.343354i	$0.888437\pi$
$368$		0			0
$369$	1.42978e7	+	8.25486e6i	0.284571	+	0.164297i
$370$		0			0
$371$	5.08765e7	−	5.55602e7i	0.996312	−	1.08803i
$372$		0			0
$373$	−1.05213e7	+	1.82235e7i	−0.202742	+	0.351160i	−0.949411	−	0.314036i	$-0.898319\pi$
$373$	−1.05213e7	+	1.82235e7i	−0.202742	+	0.351160i	0.746669	+	0.665196i	$0.231652\pi$
$374$		0			0
$375$	−7.71097e6	−	1.33558e7i	−0.146223	−	0.253265i
$376$		0			0
$377$			2.84046e7i			0.530109i
$378$		0			0
$379$	4.11794e7			0.756418			0.378209	−	0.925720i	$-0.376540\pi$
$379$	4.11794e7			0.756418			0.378209	+	0.925720i	$0.376540\pi$
$380$		0			0
$381$	−4.44166e7	+	2.56440e7i	−0.803102	+	0.463671i
$382$		0			0
$383$	1.31798e7	+	7.60939e6i	0.234592	+	0.135442i	0.612689	−	0.790324i	$-0.290088\pi$
$383$	1.31798e7	+	7.60939e6i	0.234592	+	0.135442i	−0.378096	+	0.925766i	$0.623421\pi$
$384$		0			0
$385$	−1.28306e8	+	4.05033e7i	−2.24836	+	0.709754i
$386$		0			0
$387$	−1.49886e6	+	2.59610e6i	−0.0258600	+	0.0447908i
$388$		0			0
$389$	3.37497e7	+	5.84563e7i	0.573353	+	0.993076i	0.996218	+	0.0868835i	$0.0276908\pi$
$389$	3.37497e7	+	5.84563e7i	0.573353	+	0.993076i	−0.422866	+	0.906192i	$0.638976\pi$
$390$		0			0
$391$		−	1.88271e6i		−	0.0314958i
$392$		0			0
$393$	−3.48164e6			−0.0573596
$394$		0			0
$395$	9.69393e7	−	5.59679e7i	1.57293	−	0.908130i
$396$		0			0
$397$	8.14198e6	+	4.70078e6i	0.130124	+	0.0751273i	0.563649	−	0.826014i	$-0.309397\pi$
$397$	8.14198e6	+	4.70078e6i	0.130124	+	0.0751273i	−0.433525	+	0.901142i	$0.642730\pi$
$398$		0			0
$399$	6.35642e6	+	2.01359e7i	0.100068	+	0.316995i
$400$		0			0
$401$	2.77486e7	−	4.80620e7i	0.430336	−	0.745364i	−0.566566	−	0.824016i	$-0.691728\pi$
$401$	2.77486e7	−	4.80620e7i	0.430336	−	0.745364i	0.996902	+	0.0786521i	$0.0250616\pi$
$402$		0			0
$403$	4.28658e6	+	7.42457e6i	0.0654931	+	0.113437i
$404$		0			0
$405$			1.12709e7i			0.169666i
$406$		0			0
$407$	−7.59001e7			−1.12579
$408$		0			0
$409$	1.41570e7	−	8.17357e6i	0.206920	−	0.119465i	−0.392959	−	0.919556i	$-0.628549\pi$
$409$	1.41570e7	−	8.17357e6i	0.206920	−	0.119465i	0.599879	+	0.800091i	$0.295215\pi$
$410$		0			0
$411$	4.28017e7	+	2.47116e7i	0.616504	+	0.355939i
$412$		0			0
$413$	−4.87003e7	−	4.45949e7i	−0.691324	−	0.633046i
$414$		0			0
$415$	1.01524e7	−	1.75844e7i	0.142044	−	0.246027i
$416$		0			0
$417$	6.03850e6	+	1.04590e7i	0.0832762	+	0.144239i
$418$		0			0
$419$			3.75022e7i			0.509818i	0.966965	+	0.254909i	$0.0820455\pi$
$419$			3.75022e7i			0.509818i	−0.966965	+	0.254909i	$0.917955\pi$
$420$		0			0
$421$	9.17501e7			1.22959			0.614795	−	0.788687i	$-0.289239\pi$
$421$	9.17501e7			1.22959			0.614795	+	0.788687i	$0.289239\pi$
$422$		0			0
$423$	−3.10642e7	+	1.79349e7i	−0.410430	+	0.236962i
$424$		0			0
$425$	5.13623e7	+	2.96540e7i	0.669080	+	0.386293i
$426$		0			0
$427$	−2.46711e7	+	1.11465e8i	−0.316887	+	1.43171i
$428$		0			0
$429$	−4.90144e7	+	8.48954e7i	−0.620800	+	1.07526i
$430$		0			0
$431$	−6.89035e7	−	1.19344e8i	−0.860616	−	1.49063i	−0.871336	−	0.490687i	$-0.836746\pi$
$431$	−6.89035e7	−	1.19344e8i	−0.860616	−	1.49063i	0.0107202	−	0.999943i	$-0.496588\pi$
$432$		0			0
$433$			2.00324e7i			0.246757i	0.992360	+	0.123378i	$0.0393729\pi$
$433$			2.00324e7i			0.246757i	−0.992360	+	0.123378i	$0.960627\pi$
$434$		0			0
$435$	2.76200e7			0.335549
$436$		0			0
$437$	2.25909e6	−	1.30428e6i	0.0270700	−	0.0156289i
$438$		0			0
$439$	−7.45669e7	−	4.30512e7i	−0.881359	−	0.508853i	−0.0102525	−	0.999947i	$-0.503264\pi$
$439$	−7.45669e7	−	4.30512e7i	−0.881359	−	0.508853i	−0.871106	+	0.491095i	$0.836597\pi$
$440$		0			0
$441$	2.51122e6	+	2.84782e7i	0.0292798	+	0.332045i
$442$		0			0
$443$	−4.03937e6	+	6.99640e6i	−0.0464625	+	0.0804754i	−0.888321	−	0.459222i	$-0.848128\pi$
$443$	−4.03937e6	+	6.99640e6i	−0.0464625	+	0.0804754i	0.841859	+	0.539698i	$0.181461\pi$
$444$		0			0
$445$	−1.24621e6	−	2.15850e6i	−0.0141420	−	0.0244947i
$446$		0			0
$447$			5.47032e7i			0.612477i
$448$		0			0
$449$	−5.16486e7			−0.570584			−0.285292	−	0.958441i	$-0.592091\pi$
$449$	−5.16486e7			−0.570584			−0.285292	+	0.958441i	$0.592091\pi$
$450$		0			0
$451$	1.20920e8	−	6.98132e7i	1.31816	−	0.761041i
$452$		0			0
$453$	8.71022e7	+	5.02885e7i	0.936989	+	0.540971i
$454$		0			0
$455$	−1.95602e8	−	4.32935e7i	−2.07653	−	0.459609i
$456$		0			0
$457$	1.99697e7	−	3.45885e7i	0.209229	−	0.362396i	−0.742243	−	0.670131i	$-0.766238\pi$
$457$	1.99697e7	−	3.45885e7i	0.209229	−	0.362396i	0.951472	+	0.307735i	$0.0995711\pi$
$458$		0			0
$459$	−5.39835e6	−	9.35022e6i	−0.0558243	−	0.0966905i
$460$		0			0
$461$		−	1.40914e7i		−	0.143831i	−0.997411	−	0.0719153i	$-0.977089\pi$
$461$		−	1.40914e7i		−	0.143831i	0.997411	−	0.0719153i	$-0.0229111\pi$
$462$		0			0
$463$	−1.25200e8			−1.26142			−0.630712	−	0.776017i	$-0.717237\pi$
$463$	−1.25200e8			−1.26142			−0.630712	+	0.776017i	$0.717237\pi$
$464$		0			0
$465$	7.21948e6	−	4.16817e6i	0.0718037	−	0.0414559i
$466$		0			0
$467$	8.96567e7	+	5.17633e7i	0.880303	+	0.508243i	0.870758	−	0.491711i	$-0.163628\pi$
$467$	8.96567e7	+	5.17633e7i	0.880303	+	0.508243i	0.00954455	+	0.999954i	$0.496962\pi$
$468$		0			0
$469$	−8.08851e7	+	8.83315e7i	−0.784061	+	0.856243i
$470$		0			0
$471$	−3.65001e7	+	6.32200e7i	−0.349326	+	0.605051i
$472$		0			0
$473$	1.26762e7	+	2.19558e7i	0.119786	+	0.207475i
$474$		0			0
$475$			8.21738e7i			0.766747i
$476$		0			0
$477$	−5.33714e7			−0.491760
$478$		0			0
$479$	6.75301e7	−	3.89885e7i	0.614456	−	0.354757i	−0.160251	−	0.987076i	$-0.551230\pi$
$479$	6.75301e7	−	3.89885e7i	0.614456	−	0.354757i	0.774708	+	0.632320i	$0.217897\pi$
$480$		0			0
$481$	−9.78713e7	−	5.65060e7i	−0.879468	−	0.507761i
$482$		0			0
$483$	3.36799e6	−	1.06319e6i	0.0298903	−	0.00943564i
$484$		0			0
$485$	−1.95846e7	+	3.39216e7i	−0.171668	+	0.297338i
$486$		0			0
$487$	7.13992e7	+	1.23667e8i	0.618168	+	1.07070i	0.989820	+	0.142327i	$0.0454583\pi$
$487$	7.13992e7	+	1.23667e8i	0.618168	+	1.07070i	−0.371651	+	0.928372i	$0.621208\pi$
$488$		0			0
$489$		−	8.07845e7i		−	0.690878i
$490$		0			0
$491$	−5.07818e7			−0.429006			−0.214503	−	0.976723i	$-0.568813\pi$
$491$	−5.07818e7			−0.429006			−0.214503	+	0.976723i	$0.568813\pi$
$492$		0			0
$493$	−2.29132e7	+	1.32289e7i	−0.191225	+	0.110404i
$494$		0			0
$495$	8.25503e7	+	4.76604e7i	0.680617	+	0.392955i
$496$		0			0
$497$	−3.15597e7	−	9.99750e7i	−0.257078	−	0.814371i
$498$		0			0
$499$	6.32522e7	−	1.09556e8i	0.509065	−	0.881727i	−0.490879	−	0.871228i	$-0.663324\pi$
$499$	6.32522e7	−	1.09556e8i	0.509065	−	0.881727i	0.999945	−	0.0104998i	$-0.00334224\pi$
$500$		0			0
$501$	1.22081e7	+	2.11450e7i	0.0970808	+	0.168149i
$502$		0			0
$503$			7.36652e6i			0.0578840i	0.999581	+	0.0289420i	$0.00921381\pi$
$503$			7.36652e6i			0.0578840i	−0.999581	+	0.0289420i	$0.990786\pi$
$504$		0			0
$505$	2.67434e8			2.07655
$506$		0			0
$507$	−6.12438e7	+	3.53591e7i	−0.469936	+	0.271317i
$508$		0			0
$509$	−1.98695e8	−	1.14716e8i	−1.50672	−	0.869906i	−0.999969	−	0.00781491i	$-0.997512\pi$
$509$	−1.98695e8	−	1.14716e8i	−1.50672	−	0.869906i	−0.506753	−	0.862092i	$-0.669154\pi$
$510$		0			0
$511$	−5.98260e7	−	5.47826e7i	−0.448360	−	0.410563i
$512$		0			0
$513$	7.47964e6	−	1.29551e7i	0.0554024	−	0.0959598i
$514$		0			0
$515$	4.94024e7	+	8.55674e7i	0.361681	+	0.626450i
$516$		0			0
$517$			3.03359e8i			2.19526i
$518$		0			0
$519$	−1.94018e7			−0.138784
$520$		0			0
$521$	−9.29834e7	+	5.36840e7i	−0.657495	+	0.379605i	−0.791322	−	0.611400i	$-0.790607\pi$
$521$	−9.29834e7	+	5.36840e7i	−0.657495	+	0.379605i	0.133827	+	0.991005i	$0.457273\pi$
$522$		0			0
$523$	−1.30357e8	−	7.52614e7i	−0.911230	−	0.526099i	−0.0304034	−	0.999538i	$-0.509679\pi$
$523$	−1.30357e8	−	7.52614e7i	−0.911230	−	0.526099i	−0.880827	+	0.473439i	$0.843013\pi$
$524$		0			0
$525$	−2.40432e7	+	1.08628e8i	−0.166156	+	0.750699i
$526$		0			0
$527$	−3.99279e6	+	6.91571e6i	−0.0272800	+	0.0472503i
$528$		0			0
$529$	7.37998e7	+	1.27825e8i	0.498526	+	0.863473i
$530$		0			0
$531$			4.67818e7i			0.312459i
$532$		0			0
$533$	2.07898e8			1.37299
$534$		0			0
$535$	−1.06908e8	+	6.17235e7i	−0.698151	+	0.403078i
$536$		0			0
$537$	3.04560e7	+	1.75838e7i	0.196675	+	0.113550i
$538$		0			0
$539$	2.19198e8	+	1.02031e8i	1.39981	+	0.651575i
$540$		0			0
$541$	3.02874e7	−	5.24593e7i	0.191280	−	0.331307i	−0.754395	−	0.656421i	$-0.772069\pi$
$541$	3.02874e7	−	5.24593e7i	0.191280	−	0.331307i	0.945675	+	0.325114i	$0.105403\pi$
$542$		0			0
$543$	−6.21354e7	−	1.07622e8i	−0.388097	−	0.672203i
$544$		0			0
$545$		−	1.31181e8i		−	0.810365i
$546$		0			0
$547$	2.68955e8			1.64330			0.821651	−	0.569992i	$-0.193054\pi$
$547$	2.68955e8			1.64330			0.821651	+	0.569992i	$0.193054\pi$
$548$		0			0
$549$	7.00433e7	−	4.04395e7i	0.423301	−	0.244393i
$550$		0			0
$551$	−3.17471e7	−	1.83292e7i	−0.189780	−	0.109569i
$552$		0			0
$553$	−1.96395e8	−	4.34689e7i	−1.16133	−	0.257042i
$554$		0			0
$555$	−5.49451e7	+	9.51678e7i	−0.321403	+	0.556687i
$556$		0			0
$557$	−1.00886e8	−	1.74739e8i	−0.583800	−	1.01117i	−0.995024	−	0.0996375i	$-0.968232\pi$
$557$	−1.00886e8	−	1.74739e8i	−0.583800	−	1.01117i	0.411223	−	0.911535i	$-0.365102\pi$
$558$		0			0
$559$			3.77486e7i			0.216105i
$560$		0			0
$561$	−9.13101e7			−0.517166
$562$		0			0
$563$	−1.52694e8	+	8.81577e7i	−0.855650	+	0.494010i	−0.862553	−	0.505967i	$-0.831136\pi$
$563$	−1.52694e8	+	8.81577e7i	−0.855650	+	0.494010i	0.00690346	+	0.999976i	$0.497803\pi$
$564$		0			0
$565$	−3.49892e8	−	2.02010e8i	−1.93994	−	1.12003i
$566$		0			0
$567$	1.36781e7	−	1.49374e7i	0.0750375	−	0.0819455i
$568$		0			0
$569$	−1.00368e8	+	1.73843e8i	−0.544828	+	0.943669i	0.453790	+	0.891109i	$0.350072\pi$
$569$	−1.00368e8	+	1.73843e8i	−0.544828	+	0.943669i	−0.998618	+	0.0525605i	$0.983262\pi$
$570$		0			0
$571$	−2.23204e7	−	3.86600e7i	−0.119893	−	0.207660i	0.799832	−	0.600224i	$-0.204922\pi$
$571$	−2.23204e7	−	3.86600e7i	−0.119893	−	0.207660i	−0.919725	+	0.392563i	$0.871588\pi$
$572$		0			0
$573$		−	6.64340e7i		−	0.353123i
$574$		0			0
$575$	1.37446e7			0.0722986
$576$		0			0
$577$	−2.24118e8	+	1.29395e8i	−1.16668	+	0.673581i	−0.952895	−	0.303301i	$-0.901911\pi$
$577$	−2.24118e8	+	1.29395e8i	−1.16668	+	0.673581i	−0.213781	+	0.976882i	$0.568578\pi$
$578$		0			0
$579$	1.96794e6	+	1.13619e6i	0.0101386	+	0.00585350i
$580$		0			0
$581$	−3.47949e7	+	1.09839e7i	−0.177414	+	0.0560053i
$582$		0			0
$583$	−2.25687e8	+	3.90901e8i	−1.13894	+	1.97270i
$584$		0			0
$585$	7.09644e7	+	1.22914e8i	0.354465	+	0.613951i
$586$		0			0
$587$		−	3.41902e8i		−	1.69039i	−0.534457	−	0.845196i	$-0.679484\pi$
$587$		−	3.41902e8i		−	1.69039i	0.534457	−	0.845196i	$-0.320516\pi$
$588$		0			0
$589$	−1.10643e7			−0.0541476
$590$		0			0
$591$	−9.73773e7	+	5.62208e7i	−0.471732	+	0.272354i
$592$		0			0
$593$	1.27791e8	+	7.37803e7i	0.612826	+	0.353815i	0.774071	−	0.633099i	$-0.218218\pi$
$593$	1.27791e8	+	7.37803e7i	0.612826	+	0.353815i	−0.161245	+	0.986914i	$0.551551\pi$
$594$		0			0
$595$	−5.61744e7	−	1.77949e8i	−0.266678	−	0.844784i
$596$		0			0
$597$	−1.37552e7	+	2.38248e7i	−0.0646465	+	0.111971i
$598$		0			0
$599$	−3.32461e7	−	5.75840e7i	−0.154690	−	0.267930i	0.778256	−	0.627947i	$-0.216104\pi$
$599$	−3.32461e7	−	5.75840e7i	−0.154690	−	0.267930i	−0.932946	+	0.360017i	$0.882771\pi$
$600$		0			0
$601$			3.71302e7i			0.171042i	0.996336	+	0.0855212i	$0.0272555\pi$
$601$			3.71302e7i			0.171042i	−0.996336	+	0.0855212i	$0.972744\pi$
$602$		0			0
$603$	8.48516e7			0.386998
$604$		0			0
$605$	4.05303e8	−	2.34002e8i	1.83026	−	1.05670i
$606$		0			0
$607$	−1.10132e8	−	6.35850e7i	−0.492436	−	0.284308i	0.233149	−	0.972441i	$-0.425097\pi$
$607$	−1.10132e8	−	6.35850e7i	−0.492436	−	0.284308i	−0.725584	+	0.688133i	$0.758430\pi$
$608$		0			0
$609$	−3.66047e7	−	3.35190e7i	−0.162064	−	0.148402i
$610$		0			0
$611$	−2.25845e8	+	3.91174e8i	−0.990116	+	1.71493i
$612$		0			0
$613$	7.14975e7	+	1.23837e8i	0.310391	+	0.537614i	0.978447	−	0.206498i	$-0.0662066\pi$
$613$	7.14975e7	+	1.23837e8i	0.310391	+	0.537614i	−0.668056	+	0.744111i	$0.732873\pi$
$614$		0			0
$615$		−	2.02155e8i		−	0.869079i
$616$		0			0
$617$	−2.96115e8			−1.26068			−0.630339	−	0.776320i	$-0.717084\pi$
$617$	−2.96115e8			−1.26068			−0.630339	+	0.776320i	$0.717084\pi$
$618$		0			0
$619$	−2.81343e8	+	1.62433e8i	−1.18622	+	0.684862i	−0.957444	−	0.288619i	$-0.906804\pi$
$619$	−2.81343e8	+	1.62433e8i	−1.18622	+	0.684862i	−0.228771	+	0.973480i	$0.573471\pi$
$620$		0			0
$621$	−2.16691e6	−	1.25107e6i	−0.00904829	−	0.00522403i
$622$		0			0
$623$	−967903.	+	4.37303e6i	−0.00400283	+	0.0180850i
$624$		0			0
$625$	6.81453e7	−	1.18031e8i	0.279123	−	0.483456i
$626$		0			0
$627$	−6.32569e7	−	1.09564e8i	−0.256629	−	0.444494i
$628$		0			0
$629$		−	1.05267e8i		−	0.422998i
$630$		0			0
$631$	1.40735e8			0.560163			0.280082	−	0.959976i	$-0.409638\pi$
$631$	1.40735e8			0.560163			0.280082	+	0.959976i	$0.409638\pi$
$632$		0			0
$633$	−1.84994e8	+	1.06806e8i	−0.729369	+	0.421101i
$634$		0			0
$635$	5.43864e8	+	3.14000e8i	2.12407	+	1.22633i
$636$		0			0
$637$	2.06691e8	+	2.94754e8i	0.799656	+	1.14036i
$638$		0			0
$639$	−3.71365e7	+	6.43224e7i	−0.142331	+	0.246524i
$640$		0			0
$641$	1.08339e8	+	1.87648e8i	0.411348	+	0.712476i	0.995037	−	0.0995014i	$-0.0317248\pi$
$641$	1.08339e8	+	1.87648e8i	0.411348	+	0.712476i	−0.583689	+	0.811977i	$0.698391\pi$
$642$		0			0
$643$			2.61645e8i			0.984192i	0.870541	+	0.492096i	$0.163769\pi$
$643$			2.61645e8i			0.984192i	−0.870541	+	0.492096i	$0.836231\pi$
$644$		0			0
$645$	3.67059e7			0.136791
$646$		0			0
$647$	9.29409e7	−	5.36595e7i	0.343158	−	0.198122i	−0.318510	−	0.947920i	$-0.603182\pi$
$647$	9.29409e7	−	5.36595e7i	0.343158	−	0.198122i	0.661668	+	0.749797i	$0.269849\pi$
$648$		0			0
$649$	3.42637e8	+	1.97822e8i	1.25343	+	0.723669i
$650$		0			0
$651$	−1.46263e7	−	3.23732e6i	−0.0530143	−	0.0117339i
$652$		0			0
$653$	−2.21977e8	+	3.84475e8i	−0.797200	+	1.38079i	0.124232	+	0.992253i	$0.460353\pi$
$653$	−2.21977e8	+	3.84475e8i	−0.797200	+	1.38079i	−0.921432	+	0.388539i	$0.872980\pi$
$654$		0			0
$655$	2.13156e7	+	3.69198e7i	0.0758533	+	0.131382i
$656$		0			0
$657$			5.74691e7i			0.202646i
$658$		0			0
$659$	1.87037e7			0.0653538			0.0326769	−	0.999466i	$-0.489597\pi$
$659$	1.87037e7			0.0653538			0.0326769	+	0.999466i	$0.489597\pi$
$660$		0			0
$661$	−1.85577e7	+	1.07143e7i	−0.0642570	+	0.0370988i	−0.531784	−	0.846880i	$-0.678478\pi$
$661$	−1.85577e7	+	1.07143e7i	−0.0642570	+	0.0370988i	0.467527	+	0.883979i	$0.345145\pi$
$662$		0			0
$663$	−1.17742e8	−	6.79785e7i	−0.404010	−	0.233255i
$664$		0			0
$665$	1.74608e8	−	1.90682e8i	0.593744	−	0.648404i
$666$		0			0
$667$	−3.06580e6	+	5.31012e6i	−0.0103316	+	0.0178948i
$668$		0			0
$669$	−1.67598e8	−	2.90289e8i	−0.559746	−	0.969509i
$670$		0			0
$671$		−	6.84012e8i		−	2.26410i
$672$		0			0
$673$	2.29593e8			0.753205			0.376603	−	0.926375i	$-0.377092\pi$
$673$	2.29593e8			0.753205			0.376603	+	0.926375i	$0.377092\pi$
$674$		0			0
$675$	6.82609e7	−	3.94105e7i	0.221953	−	0.128145i
$676$		0			0
$677$	1.96110e7	+	1.13224e7i	0.0632024	+	0.0364899i	0.531268	−	0.847204i	$-0.321716\pi$
$677$	1.96110e7	+	1.13224e7i	0.0632024	+	0.0364899i	−0.468066	+	0.883694i	$0.655049\pi$
$678$		0			0
$679$	6.71218e7	−	2.11888e7i	0.214415	−	0.0676856i
$680$		0			0
$681$	−3.06415e7	+	5.30726e7i	−0.0970216	+	0.168046i
$682$		0			0
$683$	1.12310e8	+	1.94527e8i	0.352499	+	0.610546i	0.986687	−	0.162633i	$-0.0519986\pi$
$683$	1.12310e8	+	1.94527e8i	0.352499	+	0.610546i	−0.634188	+	0.773179i	$0.718665\pi$
$684$		0			0
$685$		−	6.05167e8i		−	1.88280i
$686$		0			0
$687$	8.76579e6			0.0270346
$688$		0			0
$689$	−5.82036e8	+	3.36038e8i	−1.77947	+	1.02738i
$690$		0			0
$691$	−2.19279e8	−	1.26601e8i	−0.664603	−	0.383709i	0.129426	−	0.991589i	$-0.458687\pi$
$691$	−2.19279e8	−	1.26601e8i	−0.664603	−	0.383709i	−0.794029	+	0.607880i	$0.792020\pi$
$692$		0			0
$693$	−5.15642e7	−	1.63345e8i	−0.154935	−	0.490803i
$694$		0			0
$695$	7.39390e7	−	1.28066e8i	0.220252	−	0.381487i
$696$		0			0
$697$	9.68246e7	+	1.67705e8i	0.285948	+	0.495277i
$698$		0			0
$699$		−	2.54608e8i		−	0.745489i
$700$		0			0
$701$	3.18180e8			0.923674			0.461837	−	0.886965i	$-0.347191\pi$
$701$	3.18180e8			0.923674			0.461837	+	0.886965i	$0.347191\pi$
$702$		0			0
$703$	1.26311e8	−	7.29255e7i	0.363558	−	0.209900i
$704$		0			0
$705$	3.80369e8	+	2.19606e8i	1.08552	+	0.626725i
$706$		0			0
$707$	−3.54430e8	−	3.24551e8i	−1.00293	−	0.918386i
$708$		0			0
$709$	−1.35142e8	+	2.34072e8i	−0.379185	+	0.656767i	−0.990944	−	0.134277i	$-0.957129\pi$
$709$	−1.35142e8	+	2.34072e8i	−0.379185	+	0.656767i	0.611759	+	0.791044i	$0.290462\pi$
$710$		0			0
$711$	7.12521e7	+	1.23412e8i	0.198239	+	0.343360i
$712$		0			0
$713$			1.85065e6i			0.00510572i
$714$		0			0
$715$	1.20032e9			3.28383
$716$		0			0
$717$	2.64778e8	−	1.52870e8i	0.718331	−	0.414728i
$718$		0			0
$719$	−9.13702e7	−	5.27526e7i	−0.245820	−	0.141924i	0.372029	−	0.928221i	$-0.378662\pi$
$719$	−9.13702e7	−	5.27526e7i	−0.245820	−	0.141924i	−0.617849	+	0.786297i	$0.711996\pi$
$720$		0			0
$721$	3.83697e7	−	1.73356e8i	0.102372	−	0.462522i
$722$		0			0
$723$	2.80515e7	−	4.85866e7i	0.0742234	−	0.128559i
$724$		0			0
$725$	−9.65772e7	−	1.67277e8i	−0.253431	−	0.438956i
$726$		0			0
$727$		−	3.47133e8i		−	0.903425i	−0.892164	−	0.451713i	$-0.850813\pi$
$727$		−	3.47133e8i		−	0.903425i	0.892164	−	0.451713i	$-0.149187\pi$
$728$		0			0
$729$	−1.43489e7			−0.0370370
$730$		0			0
$731$	−3.04507e7	+	1.75807e7i	−0.0779552	+	0.0450074i
$732$		0			0
$733$	−4.04599e8	−	2.33596e8i	−1.02734	−	0.593134i	−0.111117	−	0.993807i	$-0.535443\pi$
$733$	−4.04599e8	−	2.33596e8i	−1.02734	−	0.593134i	−0.916221	+	0.400673i	$0.868776\pi$
$734$		0			0
$735$	2.86612e8	−	2.00981e8i	0.721827	−	0.506167i
$736$		0			0
$737$	3.58804e8	−	6.21467e8i	0.896304	−	1.55244i
$738$		0			0
$739$	1.98814e8	+	3.44356e8i	0.492623	+	0.853247i	0.999964	−	0.00849788i	$-0.00270499\pi$
$739$	1.98814e8	+	3.44356e8i	0.492623	+	0.853247i	−0.507341	+	0.861745i	$0.669372\pi$
$740$		0			0
$741$		−	1.88374e8i		−	0.462984i
$742$		0			0
$743$	−6.88913e8			−1.67957			−0.839784	−	0.542920i	$-0.817319\pi$
$743$	−6.88913e8			−1.67957			−0.839784	+	0.542920i	$0.817319\pi$
$744$		0			0
$745$	5.80080e8	−	3.34909e8i	1.40288	−	0.809951i
$746$		0			0
$747$	2.23865e7	+	1.29248e7i	0.0537061	+	0.0310073i
$748$		0			0
$749$	2.16591e8	+	4.79392e7i	0.515461	+	0.114089i
$750$		0			0
$751$	1.83282e8	−	3.17453e8i	0.432712	−	0.749480i	−0.564393	−	0.825506i	$-0.690890\pi$
$751$	1.83282e8	−	3.17453e8i	0.432712	−	0.749480i	0.997106	+	0.0760260i	$0.0242232\pi$
$752$		0			0
$753$	−5.06512e7	−	8.77305e7i	−0.118633	−	0.205478i
$754$		0			0
$755$		−	1.23152e9i		−	2.86156i
$756$		0			0
$757$	−2.07241e8			−0.477735			−0.238868	−	0.971052i	$-0.576776\pi$
$757$	−2.07241e8			−0.477735			−0.238868	+	0.971052i	$0.576776\pi$
$758$		0			0
$759$	−1.83261e7	+	1.05806e7i	−0.0419125	+	0.0241982i
$760$		0			0
$761$	−5.86021e8	−	3.38339e8i	−1.32972	−	0.767712i	−0.344461	−	0.938801i	$-0.611938\pi$
$761$	−5.86021e8	−	3.38339e8i	−1.32972	−	0.767712i	−0.985256	+	0.171088i	$0.945272\pi$
$762$		0			0
$763$	−1.59198e8	+	1.73854e8i	−0.358396	+	0.391390i
$764$		0			0
$765$	−6.61007e7	+	1.14490e8i	−0.147646	+	0.255730i
$766$		0			0
$767$	2.94549e8	+	5.10173e8i	0.652786	+	1.13066i
$768$		0			0
$769$		−	5.58023e8i		−	1.22708i	−0.789663	−	0.613540i	$-0.789745\pi$
$769$		−	5.58023e8i		−	1.22708i	0.789663	−	0.613540i	$-0.210255\pi$
$770$		0			0
$771$	4.45510e7			0.0972063
$772$		0			0
$773$	7.17689e7	−	4.14358e7i	0.155381	−	0.0897093i	−0.420293	−	0.907388i	$-0.638073\pi$
$773$	7.17689e7	−	4.14358e7i	0.155381	−	0.0897093i	0.575675	+	0.817679i	$0.304740\pi$
$774$		0			0
$775$	−5.04878e7	−	2.91492e7i	−0.108463	−	0.0626211i
$776$		0			0
$777$	1.88312e8	−	5.94456e7i	0.401435	−	0.126723i
$778$		0			0
$779$	−1.34154e8	+	2.32362e8i	−0.283787	+	0.491533i
$780$		0			0
$781$	3.14072e8	+	5.43988e8i	0.659289	+	1.14192i
$782$		0			0
$783$			3.51627e7i			0.0732482i
$784$		0			0
$785$	8.93859e8			1.84782
$786$		0			0
$787$	4.59435e8	−	2.65255e8i	0.942541	−	0.544176i	0.0517851	−	0.998658i	$-0.483509\pi$
$787$	4.59435e8	−	2.65255e8i	0.942541	−	0.544176i	0.890756	+	0.454482i	$0.150176\pi$
$788$		0			0
$789$	−6.74766e7	−	3.89576e7i	−0.137380	−	0.0793161i
$790$		0			0
$791$	2.18556e8	+	6.92344e8i	0.441605	+	1.39892i
$792$		0			0
$793$	5.09233e8	−	8.82017e8i	1.02117	−	1.76871i
$794$		0			0
$795$	3.26756e8	+	5.65958e8i	0.650313	+	1.12637i
$796$		0			0
$797$		−	4.96880e8i		−	0.981469i	−0.871309	−	0.490735i	$-0.836728\pi$
$797$		−	4.96880e8i		−	0.981469i	0.871309	−	0.490735i	$-0.163272\pi$
$798$		0			0
$799$	−4.20732e8			−0.824831
$800$		0			0
$801$	2.74796e6	−	1.58654e6i	0.00534703	−	0.00308711i
$802$		0			0
$803$	4.20913e8	+	2.43014e8i	0.812917	+	0.469338i
$804$		0			0
$805$	−3.18941e7	−	2.92055e7i	−0.0611397	−	0.0559856i
$806$		0			0
$807$	−1.59158e8	+	2.75669e8i	−0.302836	+	0.524527i
$808$		0			0
$809$	2.10152e8	+	3.63994e8i	0.396906	+	0.687461i	0.993342	−	0.115199i	$-0.0367506\pi$
$809$	2.10152e8	+	3.63994e8i	0.396906	+	0.687461i	−0.596437	+	0.802660i	$0.703417\pi$
$810$		0			0
$811$		−	4.27809e8i		−	0.802025i	−0.916073	−	0.401012i	$-0.868658\pi$
$811$		−	4.27809e8i		−	0.802025i	0.916073	−	0.401012i	$-0.131342\pi$
$812$		0			0
$813$	−1.92393e8			−0.358029
$814$		0			0
$815$	−8.56650e8	+	4.94587e8i	−1.58245	+	0.913629i
$816$		0			0
$817$	−4.21907e7	−	2.43588e7i	−0.0773660	−	0.0446673i
$818$		0			0
$819$	5.51164e7	−	2.49018e8i	0.100330	−	0.453294i
$820$		0			0
$821$	−4.76401e8	+	8.25152e8i	−0.860882	+	1.49109i	0.0101968	+	0.999948i	$0.496754\pi$
$821$	−4.76401e8	+	8.25152e8i	−0.860882	+	1.49109i	−0.871079	+	0.491143i	$0.836579\pi$
$822$		0			0
$823$	−3.70614e8	−	6.41923e8i	−0.664848	−	1.15155i	−0.979326	−	0.202287i	$-0.935163\pi$
$823$	−3.70614e8	−	6.41923e8i	−0.664848	−	1.15155i	0.314478	−	0.949265i	$-0.398171\pi$
$824$		0			0
$825$		−	6.66606e8i		−	1.18715i
$826$		0			0
$827$	7.61072e8			1.34558			0.672790	−	0.739834i	$-0.265096\pi$
$827$	7.61072e8			1.34558			0.672790	+	0.739834i	$0.265096\pi$
$828$		0			0
$829$	−7.06469e8	+	4.07880e8i	−1.24002	+	0.715928i	−0.969099	−	0.246673i	$-0.920663\pi$
$829$	−7.06469e8	+	4.07880e8i	−1.24002	+	0.715928i	−0.270924	+	0.962601i	$0.587329\pi$
$830$		0			0
$831$	2.81207e8	+	1.62355e8i	0.490031	+	0.282919i
$832$		0			0
$833$	−1.41507e8	+	3.04008e8i	−0.244818	+	0.525956i
$834$		0			0
$835$	1.49483e8	−	2.58912e8i	0.256763	−	0.444726i
$836$		0			0
$837$	5.30644e6	+	9.19103e6i	0.00904955	+	0.0156743i
$838$		0			0
$839$			1.07654e9i			1.82283i	0.411491	+	0.911414i	$0.365008\pi$
$839$			1.07654e9i			1.82283i	−0.411491	+	0.911414i	$0.634992\pi$
$840$		0			0
$841$	−5.08655e8			−0.855137
$842$		0			0
$843$	2.83693e8	−	1.63790e8i	0.473550	−	0.273404i
$844$		0			0
$845$	7.49906e8	+	4.32959e8i	1.24290	+	0.717590i
$846$		0			0
$847$	−8.21126e8	−	1.81744e8i	−1.35132	−	0.299095i
$848$		0			0
$849$	−8.12463e7	+	1.40723e8i	−0.132764	+	0.229954i
$850$		0			0
$851$	−1.21977e7	−	2.11271e7i	−0.0197921	−	0.0342808i
$852$		0			0
$853$		−	9.74565e8i		−	1.57023i	−0.619349	−	0.785116i	$-0.712603\pi$
$853$		−	9.74565e8i		−	1.57023i	0.619349	−	0.785116i	$-0.287397\pi$
$854$		0			0
$855$	−1.83170e8			−0.293060
$856$		0			0
$857$	−8.31953e8	+	4.80328e8i	−1.32177	+	0.763125i	−0.984011	−	0.178107i	$-0.943003\pi$
$857$	−8.31953e8	+	4.80328e8i	−1.32177	+	0.763125i	−0.337760	+	0.941232i	$0.609669\pi$
$858$		0			0
$859$	−4.22688e8	−	2.44039e8i	−0.666869	−	0.385017i	0.128020	−	0.991772i	$-0.459138\pi$
$859$	−4.22688e8	−	2.44039e8i	−0.666869	−	0.385017i	−0.794889	+	0.606755i	$0.792471\pi$
$860$		0			0
$861$	−2.45330e8	+	2.67916e8i	−0.384363	+	0.419748i
$862$		0			0
$863$	1.61373e8	−	2.79507e8i	0.251073	−	0.434871i	−0.712749	−	0.701420i	$-0.752550\pi$
$863$	1.61373e8	−	2.79507e8i	0.251073	−	0.434871i	0.963821	+	0.266549i	$0.0858833\pi$
$864$		0			0
$865$	1.18784e8	+	2.05739e8i	0.183530	+	0.317884i
$866$		0			0
$867$			2.49629e8i			0.383034i
$868$		0			0
$869$	1.20519e9			1.83652
$870$		0			0
$871$	9.25339e8	−	5.34245e8i	1.40038	−	0.808511i
$872$		0			0
$873$	−4.31851e7	−	2.49329e7i	−0.0649070	−	0.0374741i
$874$		0			0
$875$	3.23595e8	−	1.02151e8i	0.483035	−	0.152482i
$876$		0			0
$877$	−4.68948e8	+	8.12242e8i	−0.695226	+	1.20417i	0.274878	+	0.961479i	$0.411362\pi$
$877$	−4.68948e8	+	8.12242e8i	−0.695226	+	1.20417i	−0.970104	+	0.242688i	$0.921971\pi$
$878$		0			0
$879$	−2.22391e8	−	3.85192e8i	−0.327454	−	0.567167i
$880$		0			0
$881$			9.47337e8i			1.38540i	0.721224	+	0.692702i	$0.243580\pi$
$881$			9.47337e8i			1.38540i	−0.721224	+	0.692702i	$0.756420\pi$
$882$		0			0
$883$	−1.52054e8			−0.220860			−0.110430	−	0.993884i	$-0.535223\pi$
$883$	−1.52054e8			−0.220860			−0.110430	+	0.993884i	$0.535223\pi$
$884$		0			0
$885$	4.96080e8	−	2.86412e8i	0.715686	−	0.413201i
$886$		0			0
$887$	−1.02528e9	−	5.91948e8i	−1.46917	−	0.848228i	−0.469771	−	0.882788i	$-0.655664\pi$
$887$	−1.02528e9	−	5.91948e8i	−1.46917	−	0.848228i	−0.999403	+	0.0345605i	$0.988997\pi$
$888$		0			0
$889$	−3.39719e8	−	1.07616e9i	−0.483521	−	1.53170i
$890$		0			0
$891$	−6.06759e7	+	1.05094e8i	−0.0857795	+	0.148574i
$892$		0			0
$893$	−2.91470e8	−	5.04842e8i	−0.409298	−	0.708926i
$894$		0			0
$895$		−	4.30612e8i		−	0.600644i
$896$		0			0
$897$	−3.15080e7			−0.0436560
$898$		0			0
$899$	2.25231e7	−	1.30037e7i	0.0309990	−	0.0178973i
$900$		0			0
$901$	−5.42144e8	−	3.13007e8i	−0.741209	−	0.427937i
$902$		0			0
$903$	−4.86462e7	−	4.45454e7i	−0.0660672	−	0.0604977i
$904$		0			0
$905$	−7.60824e8	+	1.31779e9i	−1.02645	+	1.77787i
$906$		0			0
$907$	1.69886e8	+	2.94252e8i	0.227686	+	0.394364i	0.957122	−	0.289685i	$-0.0935507\pi$
$907$	1.69886e8	+	2.94252e8i	0.227686	+	0.394364i	−0.729436	+	0.684049i	$0.760217\pi$
$908$		0			0
$909$			3.40467e8i			0.453297i
$910$		0			0
$911$	9.44286e8			1.24896			0.624480	−	0.781041i	$-0.285311\pi$
$911$	9.44286e8			1.24896			0.624480	+	0.781041i	$0.285311\pi$
$912$		0			0
$913$	1.89327e8	−	1.09308e8i	0.248772	−	0.143628i
$914$		0			0
$915$	−8.57653e8	−	4.95166e8i	−1.11956	−	0.646380i
$916$		0			0
$917$	1.65554e7	−	7.47978e7i	0.0214699	−	0.0970021i
$918$		0			0
$919$	−1.87277e8	+	3.24374e8i	−0.241290	+	0.417926i	−0.961082	−	0.276264i	$-0.910904\pi$
$919$	−1.87277e8	+	3.24374e8i	−0.241290	+	0.417926i	0.719792	+	0.694189i	$0.244237\pi$
$920$		0			0
$921$	7.97106e7	+	1.38063e8i	0.102032	+	0.176725i
$922$		0			0
$923$			9.35280e8i			1.18942i
$924$		0			0
$925$	7.68494e8			0.970991
$926$		0			0
$927$	−1.08935e8	+	6.28936e7i	−0.136750	+	0.0789527i
$928$		0			0
$929$	7.89503e8	+	4.55820e8i	0.984707	+	0.568521i	0.903688	−	0.428192i	$-0.140849\pi$
$929$	7.89503e8	+	4.55820e8i	0.984707	+	0.568521i	0.0810189	+	0.996713i	$0.474183\pi$
$930$		0			0
$931$	−4.62815e8	+	4.08112e7i	−0.573533	+	0.0505743i
$932$		0			0
$933$	1.22698e8	−	2.12519e8i	0.151075	−	0.261669i
$934$		0			0
$935$	5.59028e8	+	9.68265e8i	0.683910	+	1.18457i
$936$		0			0
$937$		−	3.76597e8i		−	0.457781i	−0.973452	−	0.228890i	$-0.926490\pi$
$937$		−	3.76597e8i		−	0.457781i	0.973452	−	0.228890i	$-0.0735097\pi$
$938$		0			0
$939$	8.65586e8			1.04547
$940$		0			0
$941$	2.17999e8	−	1.25862e8i	0.261629	−	0.151051i	−0.363449	−	0.931614i	$-0.618401\pi$
$941$	2.17999e8	−	1.25862e8i	0.261629	−	0.151051i	0.625077	+	0.780563i	$0.285067\pi$
$942$		0			0
$943$	3.88656e7	+	2.24391e7i	0.0463479	+	0.0267590i
$944$		0			0
$945$	−2.42140e8	−	5.35939e7i	−0.286926	−	0.0635068i
$946$		0			0
$947$	−1.32933e8	+	2.30247e8i	−0.156525	+	0.271109i	−0.933613	−	0.358282i	$-0.883363\pi$
$947$	−1.32933e8	+	2.30247e8i	−0.156525	+	0.271109i	0.777088	+	0.629392i	$0.216696\pi$
$948$		0			0
$949$	3.61838e8	+	6.26723e8i	0.423366	+	0.733292i
$950$		0			0
$951$		−	9.40107e7i		−	0.109304i
$952$		0			0
$953$	−5.38039e8			−0.621635			−0.310817	−	0.950470i	$-0.600603\pi$
$953$	−5.38039e8			−0.621635			−0.310817	+	0.950470i	$0.600603\pi$
$954$		0			0
$955$	−7.04475e8	+	4.06729e8i	−0.808827	+	0.466976i
$956$		0			0
$957$	2.57537e8	+	1.48689e8i	0.293836	+	0.169646i
$958$		0			0
$959$	−7.34416e8	+	8.02027e8i	−0.832696	+	0.909355i
$960$		0			0
$961$	−4.39827e8	+	7.61803e8i	−0.495578	+	0.858366i
$962$		0			0
$963$	−7.85794e7	−	1.36104e8i	−0.0879893	−	0.152402i
$964$		0			0
$965$		−	2.78244e7i		−	0.0309631i
$966$		0			0
$967$	1.16138e9			1.28439			0.642194	−	0.766542i	$-0.278024\pi$
$967$	1.16138e9			1.28439			0.642194	+	0.766542i	$0.278024\pi$
$968$		0			0
$969$	1.51956e8	−	8.77316e7i	0.167011	−	0.0964240i
$970$		0			0
$971$	−1.30640e9	−	7.54248e8i	−1.42698	−	0.823866i	−0.430097	−	0.902783i	$-0.641521\pi$
$971$	−1.30640e9	−	7.54248e8i	−1.42698	−	0.823866i	−0.996881	+	0.0789166i	$0.974854\pi$
$972$		0			0
$973$	−2.53409e8	+	7.99953e7i	−0.275096	+	0.0868412i
$974$		0			0
$975$	4.96274e8	−	8.59572e8i	0.535436	−	0.927403i
$976$		0			0
$977$	6.03772e7	+	1.04576e8i	0.0647425	+	0.112137i	0.896580	−	0.442882i	$-0.146044\pi$
$977$	6.03772e7	+	1.04576e8i	0.0647425	+	0.112137i	−0.831837	+	0.555020i	$0.812711\pi$
$978$		0			0
$979$		−	2.68354e7i		−	0.0285996i
$980$		0			0
$981$	1.67005e8			0.176897
$982$		0			0
$983$	1.86333e7	−	1.07580e7i	0.0196169	−	0.0113258i	−0.490159	−	0.871633i	$-0.663061\pi$
$983$	1.86333e7	−	1.07580e7i	0.0196169	−	0.0113258i	0.509776	+	0.860307i	$0.329728\pi$
$984$		0			0
$985$	1.19235e9	+	6.88401e8i	1.24765	+	0.720333i
$986$		0			0
$987$	−2.37594e8	−	7.52650e8i	−0.247106	−	0.782783i
$988$		0			0
$989$	−4.07433e6	+	7.05694e6i	−0.00421179	+	0.00729504i
$990$		0			0
$991$	−3.07940e7	−	5.33368e7i	−0.0316407	−	0.0548033i	0.849771	−	0.527151i	$-0.176740\pi$
$991$	−3.07940e7	−	5.33368e7i	−0.0316407	−	0.0548033i	−0.881412	+	0.472348i	$0.843407\pi$
$992$		0			0
$993$		−	1.52230e8i		−	0.155472i
$994$		0			0
$995$	3.36855e8			0.341959
$996$		0			0
$997$	6.72319e8	−	3.88164e8i	0.678406	−	0.391678i	−0.120848	−	0.992671i	$-0.538561\pi$
$997$	6.72319e8	−	3.88164e8i	0.678406	−	0.391678i	0.799254	+	0.600993i	$0.205228\pi$
$998$		0			0
$999$	−1.21157e8	−	6.99500e7i	−0.121521	−	0.0701603i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.7.bh.d.145.1		8
4.3	odd	2		21.7.f.a.19.4	yes	8
7.3	odd	6	inner	336.7.bh.d.241.1		8
12.11	even	2		63.7.m.d.19.1		8
28.3	even	6		21.7.f.a.10.4	✓	8
28.11	odd	6		147.7.f.d.31.4		8
28.19	even	6		147.7.d.b.97.2		8
28.23	odd	6		147.7.d.b.97.1		8
28.27	even	2		147.7.f.d.19.4		8
84.23	even	6		441.7.d.c.244.7		8
84.47	odd	6		441.7.d.c.244.8		8
84.59	odd	6		63.7.m.d.10.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.7.f.a.10.4	✓	8	28.3	even	6
21.7.f.a.19.4	yes	8	4.3	odd	2
63.7.m.d.10.1		8	84.59	odd	6
63.7.m.d.19.1		8	12.11	even	2
147.7.d.b.97.1		8	28.23	odd	6
147.7.d.b.97.2		8	28.19	even	6
147.7.f.d.19.4		8	28.27	even	2
147.7.f.d.31.4		8	28.11	odd	6
336.7.bh.d.145.1		8	1.1	even	1	trivial
336.7.bh.d.241.1		8	7.3	odd	6	inner
441.7.d.c.244.7		8	84.23	even	6
441.7.d.c.244.8		8	84.47	odd	6

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:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	336.bh (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(13.5000 - 7.79423i) q^{3} +(-165.302 - 95.4373i) q^{5} +(103.254 + 327.089i) q^{7} +(121.500 - 210.444i) q^{9} +O(q^{10})\)	\(q+(13.5000 - 7.79423i) q^{3} +(-165.302 - 95.4373i) q^{5} +(103.254 + 327.089i) q^{7} +(121.500 - 210.444i) q^{9} +(-1027.55 - 1779.77i) q^{11} -3059.97i q^{13} -2975.44 q^{15} +(2468.38 - 1425.12i) q^{17} +(3420.04 + 1974.56i) q^{19} +(3943.34 + 3610.92i) q^{21} +(330.272 - 572.047i) q^{23} +(10404.0 + 18020.3i) q^{25} -3788.00i q^{27} -9282.66 q^{29} +(-2426.36 + 1400.86i) q^{31} +(-27743.9 - 16018.0i) q^{33} +(14148.4 - 63922.9i) q^{35} +(18466.2 - 31984.5i) q^{37} +(-23850.1 - 41309.5i) q^{39} +67941.3i q^{41} -12336.3 q^{43} +(-40168.4 + 23191.3i) q^{45} +(-127836. - 73806.3i) q^{47} +(-96326.1 + 67546.8i) q^{49} +(22215.4 - 38478.3i) q^{51} +(-109818. - 190210. i) q^{53} +392267. i q^{55} +61560.8 q^{57} +(-166725. + 96258.8i) q^{59} +(288244. + 166418. i) q^{61} +(81379.5 + 18012.1i) q^{63} +(-292035. + 505819. i) q^{65} +(174592. + 302402. i) q^{67} -10296.9i q^{69} -305650. q^{71} +(-204814. + 118249. i) q^{73} +(280909. + 162183. i) q^{75} +(476046. - 519871. i) q^{77} +(-293218. + 507869. i) q^{79} +(-29524.5 - 51137.9i) q^{81} +106377. i q^{83} -544039. q^{85} +(-125316. + 72351.2i) q^{87} +(11308.5 + 6528.95i) q^{89} +(1.00088e6 - 315955. i) q^{91} +(-21837.2 + 37823.2i) q^{93} +(-376894. - 652799. i) q^{95} -205209. i q^{97} -499390. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 108 q^{3} - 294 q^{5} + 656 q^{7} + 972 q^{9}+O(q^{10}) \) 8 * q + 108 * q^3 - 294 * q^5 + 656 * q^7 + 972 * q^9	\( 8 q + 108 q^{3} - 294 q^{5} + 656 q^{7} + 972 q^{9} + 314 q^{11} - 5292 q^{15} - 5532 q^{17} + 18234 q^{19} + 9342 q^{21} - 3928 q^{23} - 17038 q^{25} - 8300 q^{29} + 89508 q^{31} + 8478 q^{33} + 25860 q^{35} + 64706 q^{37} - 29106 q^{39} - 45740 q^{43} - 71442 q^{45} - 483276 q^{47} - 310684 q^{49} - 49788 q^{51} - 540974 q^{53} + 328212 q^{57} + 181770 q^{59} + 418224 q^{61} + 92826 q^{63} - 414204 q^{65} + 1158902 q^{67} - 1442344 q^{71} - 378666 q^{73} - 460026 q^{75} + 1065994 q^{77} - 611452 q^{79} - 236196 q^{81} - 275112 q^{85} - 112050 q^{87} - 989196 q^{89} - 304446 q^{91} + 805572 q^{93} + 591792 q^{95} + 152604 q^{99}+O(q^{100}) \) 8 * q + 108 * q^3 - 294 * q^5 + 656 * q^7 + 972 * q^9 + 314 * q^11 - 5292 * q^15 - 5532 * q^17 + 18234 * q^19 + 9342 * q^21 - 3928 * q^23 - 17038 * q^25 - 8300 * q^29 + 89508 * q^31 + 8478 * q^33 + 25860 * q^35 + 64706 * q^37 - 29106 * q^39 - 45740 * q^43 - 71442 * q^45 - 483276 * q^47 - 310684 * q^49 - 49788 * q^51 - 540974 * q^53 + 328212 * q^57 + 181770 * q^59 + 418224 * q^61 + 92826 * q^63 - 414204 * q^65 + 1158902 * q^67 - 1442344 * q^71 - 378666 * q^73 - 460026 * q^75 + 1065994 * q^77 - 611452 * q^79 - 236196 * q^81 - 275112 * q^85 - 112050 * q^87 - 989196 * q^89 - 304446 * q^91 + 805572 * q^93 + 591792 * q^95 + 152604 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more