LMFDB - Embedded newform 336.3.bh.f.241.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,3,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, 3, names="a")

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

chi := DirichletCharacter("336.145");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
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:	$9.15533688251$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{65})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 17x^{2} + 16x + 256 $ x^4 - x^3 + 17x^2 + 16x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 84)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			241.1
Root			$-1.76556 + 3.05805i$ of defining polynomial
Character	$\chi$	$=$	336.241
Dual form			336.3.bh.f.145.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.50000 + 0.866025i) q^{3} +(-8.29669 + 4.79010i) q^{5} +(-0.500000 - 6.98212i) q^{7} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(1.50000 + 0.866025i) q^{3} +(-8.29669 + 4.79010i) q^{5} +(-0.500000 - 6.98212i) q^{7} +(1.50000 + 2.59808i) q^{9} +(2.29669 - 3.97799i) q^{11} -7.84815i q^{13} -16.5934 q^{15} +(-16.5934 - 9.58020i) q^{17} +(14.2033 - 8.20028i) q^{19} +(5.29669 - 10.9062i) q^{21} +(-12.0000 - 20.7846i) q^{23} +(33.3901 - 57.8333i) q^{25} +5.19615i q^{27} -10.5934 q^{29} +(-48.2802 - 27.8746i) q^{31} +(6.89008 - 3.97799i) q^{33} +(37.5934 + 55.5335i) q^{35} +(12.2033 + 21.1367i) q^{37} +(6.79669 - 11.7722i) q^{39} +48.7131i q^{41} +18.7802 q^{43} +(-24.8901 - 14.3703i) q^{45} +(10.4066 - 6.00826i) q^{47} +(-48.5000 + 6.98212i) q^{49} +(-16.5934 - 28.7406i) q^{51} +(18.7033 - 32.3951i) q^{53} +44.0055i q^{55} +28.4066 q^{57} +(-54.7033 - 31.5830i) q^{59} +(-96.3735 + 55.6413i) q^{61} +(17.3901 - 11.7722i) q^{63} +(37.5934 + 65.1137i) q^{65} +(31.9835 - 55.3970i) q^{67} -41.5692i q^{69} -21.5603 q^{71} +(-53.5769 - 30.9326i) q^{73} +(100.170 - 57.8333i) q^{75} +(-28.9231 - 14.0468i) q^{77} +(-1.90661 - 3.30235i) q^{79} +(-4.50000 + 7.79423i) q^{81} +100.510i q^{83} +183.560 q^{85} +(-15.8901 - 9.17414i) q^{87} +(85.7802 - 49.5252i) q^{89} +(-54.7967 + 3.92407i) q^{91} +(-48.2802 - 83.6237i) q^{93} +(-78.5603 + 136.070i) q^{95} -63.5973i q^{97} +13.7802 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 6 q^{3} - 9 q^{5} - 2 q^{7} + 6 q^{9}+O(q^{10}) $ 4 * q + 6 * q^3 - 9 * q^5 - 2 * q^7 + 6 * q^9	$ 4 q + 6 q^{3} - 9 q^{5} - 2 q^{7} + 6 q^{9} - 15 q^{11} - 18 q^{15} - 18 q^{17} + 81 q^{19} - 3 q^{21} - 48 q^{23} + 61 q^{25} + 6 q^{29} - 48 q^{31} - 45 q^{33} + 102 q^{35} + 73 q^{37} + 3 q^{39} - 70 q^{43} - 27 q^{45} + 90 q^{47} - 194 q^{49} - 18 q^{51} + 99 q^{53} + 162 q^{57} - 243 q^{59} - 192 q^{61} - 3 q^{63} + 102 q^{65} + 7 q^{67} + 204 q^{71} - 45 q^{73} + 183 q^{75} - 285 q^{77} - 56 q^{79} - 18 q^{81} + 444 q^{85} + 9 q^{87} + 198 q^{89} - 195 q^{91} - 48 q^{93} - 24 q^{95} - 90 q^{99}+O(q^{100}) $ 4 * q + 6 * q^3 - 9 * q^5 - 2 * q^7 + 6 * q^9 - 15 * q^11 - 18 * q^15 - 18 * q^17 + 81 * q^19 - 3 * q^21 - 48 * q^23 + 61 * q^25 + 6 * q^29 - 48 * q^31 - 45 * q^33 + 102 * q^35 + 73 * q^37 + 3 * q^39 - 70 * q^43 - 27 * q^45 + 90 * q^47 - 194 * q^49 - 18 * q^51 + 99 * q^53 + 162 * q^57 - 243 * q^59 - 192 * q^61 - 3 * q^63 + 102 * q^65 + 7 * q^67 + 204 * q^71 - 45 * q^73 + 183 * q^75 - 285 * q^77 - 56 * q^79 - 18 * q^81 + 444 * q^85 + 9 * q^87 + 198 * q^89 - 195 * q^91 - 48 * q^93 - 24 * q^95 - 90 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	1.50000	+	0.866025i	0.500000	+	0.288675i
$3$	1.50000	+	0.866025i	0.500000	+	0.288675i
$4$		0			0
$5$	−8.29669	+	4.79010i	−1.65934	+	0.958020i	−0.686318	+	0.727302i	$0.740774\pi$
$5$	−8.29669	+	4.79010i	−1.65934	+	0.958020i	−0.973021	+	0.230718i	$0.925893\pi$
$6$		0			0
$7$	−0.500000	−	6.98212i	−0.0714286	−	0.997446i
$7$	−0.500000	−	6.98212i	−0.0714286	−	0.997446i
$8$		0			0
$9$	1.50000	+	2.59808i	0.166667	+	0.288675i
$10$		0			0
$11$	2.29669	−	3.97799i	0.208790	−	0.361635i	−0.742543	−	0.669798i	$-0.766381\pi$
$11$	2.29669	−	3.97799i	0.208790	−	0.361635i	0.951334	+	0.308163i	$0.0997141\pi$
$12$		0			0
$13$		−	7.84815i		−	0.603703i	−0.953355	−	0.301852i	$-0.902395\pi$
$13$		−	7.84815i		−	0.603703i	0.953355	−	0.301852i	$-0.0976048\pi$
$14$		0			0
$15$	−16.5934			−1.10623
$16$		0			0
$17$	−16.5934	−	9.58020i	−0.976082	−	0.563541i	−0.0749967	−	0.997184i	$-0.523895\pi$
$17$	−16.5934	−	9.58020i	−0.976082	−	0.563541i	−0.901085	+	0.433643i	$0.857228\pi$
$18$		0			0
$19$	14.2033	−	8.20028i	0.747542	−	0.431594i	−0.0772628	−	0.997011i	$-0.524618\pi$
$19$	14.2033	−	8.20028i	0.747542	−	0.431594i	0.824805	+	0.565417i	$0.191285\pi$
$20$		0			0
$21$	5.29669	−	10.9062i	0.252223	−	0.519343i
$22$		0			0
$23$	−12.0000	−	20.7846i	−0.521739	−	0.903679i	−0.999680	−	0.0252868i	$-0.991950\pi$
$23$	−12.0000	−	20.7846i	−0.521739	−	0.903679i	0.477941	−	0.878392i	$-0.341383\pi$
$24$		0			0
$25$	33.3901	−	57.8333i	1.33560	−	2.31333i
$26$		0			0
$27$			5.19615i			0.192450i
$28$		0			0
$29$	−10.5934			−0.365289			−0.182645	−	0.983179i	$-0.558466\pi$
$29$	−10.5934			−0.365289			−0.182645	+	0.983179i	$0.558466\pi$
$30$		0			0
$31$	−48.2802	−	27.8746i	−1.55742	−	0.899179i	−0.997502	−	0.0706343i	$-0.977498\pi$
$31$	−48.2802	−	27.8746i	−1.55742	−	0.899179i	−0.559922	−	0.828545i	$-0.689169\pi$
$32$		0			0
$33$	6.89008	−	3.97799i	0.208790	−	0.120545i
$34$		0			0
$35$	37.5934	+	55.5335i	1.07410	+	1.58667i
$36$		0			0
$37$	12.2033	+	21.1367i	0.329819	+	0.571263i	0.982476	−	0.186390i	$-0.0596789\pi$
$37$	12.2033	+	21.1367i	0.329819	+	0.571263i	−0.652657	+	0.757654i	$0.726346\pi$
$38$		0			0
$39$	6.79669	−	11.7722i	0.174274	−	0.301852i
$40$		0			0
$41$			48.7131i			1.18812i	0.804419	+	0.594062i	$0.202477\pi$
$41$			48.7131i			1.18812i	−0.804419	+	0.594062i	$0.797523\pi$
$42$		0			0
$43$	18.7802			0.436748			0.218374	−	0.975865i	$-0.429925\pi$
$43$	18.7802			0.436748			0.218374	+	0.975865i	$0.429925\pi$
$44$		0			0
$45$	−24.8901	−	14.3703i	−0.553113	−	0.319340i
$46$		0			0
$47$	10.4066	−	6.00826i	0.221417	−	0.127835i	−0.385189	−	0.922838i	$-0.625864\pi$
$47$	10.4066	−	6.00826i	0.221417	−	0.127835i	0.606606	+	0.795002i	$0.292530\pi$
$48$		0			0
$49$	−48.5000	+	6.98212i	−0.989796	+	0.142492i
$50$		0			0
$51$	−16.5934	−	28.7406i	−0.325361	−	0.563541i
$52$		0			0
$53$	18.7033	−	32.3951i	0.352893	−	0.611228i	−0.633862	−	0.773446i	$-0.718531\pi$
$53$	18.7033	−	32.3951i	0.352893	−	0.611228i	0.986755	+	0.162218i	$0.0518648\pi$
$54$		0			0
$55$			44.0055i			0.800101i
$56$		0			0
$57$	28.4066			0.498362
$58$		0			0
$59$	−54.7033	−	31.5830i	−0.927175	−	0.535305i	−0.0412578	−	0.999149i	$-0.513136\pi$
$59$	−54.7033	−	31.5830i	−0.927175	−	0.535305i	−0.885917	+	0.463844i	$0.846470\pi$
$60$		0			0
$61$	−96.3735	+	55.6413i	−1.57989	+	0.912152i	−0.585021	+	0.811018i	$0.698914\pi$
$61$	−96.3735	+	55.6413i	−1.57989	+	0.912152i	−0.994873	+	0.101135i	$0.967753\pi$
$62$		0			0
$63$	17.3901	−	11.7722i	0.276033	−	0.186861i
$64$		0			0
$65$	37.5934	+	65.1137i	0.578360	+	1.00175i
$66$		0			0
$67$	31.9835	−	55.3970i	0.477365	−	0.826821i	−0.522298	−	0.852763i	$-0.674925\pi$
$67$	31.9835	−	55.3970i	0.477365	−	0.826821i	0.999663	+	0.0259421i	$0.00825857\pi$
$68$		0			0
$69$		−	41.5692i		−	0.602452i
$70$		0			0
$71$	−21.5603			−0.303666			−0.151833	−	0.988406i	$-0.548518\pi$
$71$	−21.5603			−0.303666			−0.151833	+	0.988406i	$0.548518\pi$
$72$		0			0
$73$	−53.5769	−	30.9326i	−0.733929	−	0.423734i	0.0859285	−	0.996301i	$-0.472614\pi$
$73$	−53.5769	−	30.9326i	−0.733929	−	0.423734i	−0.819858	+	0.572567i	$0.805948\pi$
$74$		0			0
$75$	100.170	−	57.8333i	1.33560	−	0.771111i
$76$		0			0
$77$	−28.9231	−	14.0468i	−0.375625	−	0.182426i
$78$		0			0
$79$	−1.90661	−	3.30235i	−0.0241343	−	0.0418019i	0.853706	−	0.520755i	$-0.174350\pi$
$79$	−1.90661	−	3.30235i	−0.0241343	−	0.0418019i	−0.877840	+	0.478953i	$0.841016\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.0555556	+	0.0962250i
$82$		0			0
$83$			100.510i			1.21096i	0.795861	+	0.605479i	$0.207018\pi$
$83$			100.510i			1.21096i	−0.795861	+	0.605479i	$0.792982\pi$
$84$		0			0
$85$	183.560			2.15953
$86$		0			0
$87$	−15.8901	−	9.17414i	−0.182645	−	0.105450i
$88$		0			0
$89$	85.7802	−	49.5252i	0.963822	−	0.556463i	0.0664748	−	0.997788i	$-0.478825\pi$
$89$	85.7802	−	49.5252i	0.963822	−	0.556463i	0.897347	+	0.441325i	$0.145491\pi$
$90$		0			0
$91$	−54.7967	+	3.92407i	−0.602161	+	0.0431217i
$92$		0			0
$93$	−48.2802	−	83.6237i	−0.519142	−	0.899179i
$94$		0			0
$95$	−78.5603	+	136.070i	−0.826951	+	1.43232i
$96$		0			0
$97$		−	63.5973i		−	0.655642i	−0.944740	−	0.327821i	$-0.893686\pi$
$97$		−	63.5973i		−	0.655642i	0.944740	−	0.327821i	$-0.106314\pi$
$98$		0			0
$99$	13.7802			0.139194
$100$		0			0
$101$	104.340	+	60.2410i	1.03307	+	0.596446i	0.917864	−	0.396896i	$-0.129912\pi$
$101$	104.340	+	60.2410i	1.03307	+	0.596446i	0.115210	+	0.993341i	$0.463246\pi$
$102$		0			0
$103$	−16.3570	+	9.44373i	−0.158806	+	0.0916867i	−0.577297	−	0.816534i	$-0.695892\pi$
$103$	−16.3570	+	9.44373i	−0.158806	+	0.0916867i	0.418491	+	0.908221i	$0.362559\pi$
$104$		0			0
$105$	8.29669	+	115.857i	0.0790161	+	1.10340i
$106$		0			0
$107$	8.48347	+	14.6938i	0.0792847	+	0.137325i	0.902942	−	0.429763i	$-0.141403\pi$
$107$	8.48347	+	14.6938i	0.0792847	+	0.137325i	−0.823657	+	0.567089i	$0.808070\pi$
$108$		0			0
$109$	−28.3901	+	49.1731i	−0.260459	+	0.451129i	−0.966364	−	0.257178i	$-0.917207\pi$
$109$	−28.3901	+	49.1731i	−0.260459	+	0.451129i	0.705905	+	0.708307i	$0.250541\pi$
$110$		0			0
$111$			42.2735i			0.380842i
$112$		0			0
$113$	−156.374			−1.38384			−0.691918	−	0.721976i	$-0.743234\pi$
$113$	−156.374			−1.38384			−0.691918	+	0.721976i	$0.743234\pi$
$114$		0			0
$115$	199.121	+	114.962i	1.73148	+	0.999673i
$116$		0			0
$117$	20.3901	−	11.7722i	0.174274	−	0.100617i
$118$		0			0
$119$	−58.5934	+	120.647i	−0.492381	+	1.01384i
$120$		0			0
$121$	49.9504	+	86.5166i	0.412813	+	0.715013i
$122$		0			0
$123$	−42.1868	+	73.0696i	−0.342982	+	0.594062i
$124$		0			0
$125$			400.262i			3.20210i
$126$		0			0
$127$	25.0000			0.196850			0.0984252	−	0.995144i	$-0.468619\pi$
$127$	25.0000			0.196850			0.0984252	+	0.995144i	$0.468619\pi$
$128$		0			0
$129$	28.1702	+	16.2641i	0.218374	+	0.126078i
$130$		0			0
$131$	−87.3298	+	50.4199i	−0.666639	+	0.384884i	−0.794802	−	0.606869i	$-0.792425\pi$
$131$	−87.3298	+	50.4199i	−0.666639	+	0.384884i	0.128163	+	0.991753i	$0.459092\pi$
$132$		0			0
$133$	−64.3570	−	95.0691i	−0.483887	−	0.714805i
$134$		0			0
$135$	−24.8901	−	43.1109i	−0.184371	−	0.319340i
$136$		0			0
$137$	−21.5603	+	37.3436i	−0.157375	+	0.272581i	−0.933921	−	0.357479i	$-0.883636\pi$
$137$	−21.5603	+	37.3436i	−0.157375	+	0.272581i	0.776547	+	0.630060i	$0.216970\pi$
$138$		0			0
$139$		−	117.938i		−	0.848474i	−0.905551	−	0.424237i	$-0.860542\pi$
$139$		−	117.938i		−	0.848474i	0.905551	−	0.424237i	$-0.139458\pi$
$140$		0			0
$141$	20.8132			0.147612
$142$		0			0
$143$	−31.2198	−	18.0248i	−0.218321	−	0.126047i
$144$		0			0
$145$	87.8901	−	50.7434i	0.606138	−	0.349954i
$146$		0			0
$147$	−78.7967	−	31.5291i	−0.536032	−	0.214483i
$148$		0			0
$149$	−88.5934	−	153.448i	−0.594586	−	1.02985i	−0.993605	−	0.112911i	$-0.963982\pi$
$149$	−88.5934	−	153.448i	−0.594586	−	1.02985i	0.399019	−	0.916943i	$-0.369351\pi$
$150$		0			0
$151$	91.4835	−	158.454i	0.605851	−	1.04936i	−0.386066	−	0.922471i	$-0.626166\pi$
$151$	91.4835	−	158.454i	0.605851	−	1.04936i	0.991916	−	0.126893i	$-0.0405005\pi$
$152$		0			0
$153$		−	57.4812i		−	0.375694i
$154$		0			0
$155$	534.088			3.44573
$156$		0			0
$157$	73.1206	+	42.2162i	0.465737	+	0.268893i	0.714453	−	0.699683i	$-0.246675\pi$
$157$	73.1206	+	42.2162i	0.465737	+	0.268893i	−0.248717	+	0.968576i	$0.580009\pi$
$158$		0			0
$159$	56.1099	−	32.3951i	0.352893	−	0.203743i
$160$		0			0
$161$	−139.121	+	94.1777i	−0.864103	+	0.584955i
$162$		0			0
$163$	71.9669	+	124.650i	0.441515	+	0.764726i	0.997802	−	0.0662638i	$-0.0211079\pi$
$163$	71.9669	+	124.650i	0.441515	+	0.764726i	−0.556287	+	0.830990i	$0.687775\pi$
$164$		0			0
$165$	−38.1099	+	66.0083i	−0.230969	+	0.400050i
$166$		0			0
$167$		−	123.730i		−	0.740901i	−0.928852	−	0.370450i	$-0.879203\pi$
$167$		−	123.730i		−	0.740901i	0.928852	−	0.370450i	$-0.120797\pi$
$168$		0			0
$169$	107.407			0.635542
$170$		0			0
$171$	42.6099	+	24.6008i	0.249181	+	0.143865i
$172$		0			0
$173$	116.440	−	67.2265i	0.673062	−	0.388592i	−0.124174	−	0.992260i	$-0.539628\pi$
$173$	116.440	−	67.2265i	0.673062	−	0.388592i	0.797236	+	0.603668i	$0.206295\pi$
$174$		0			0
$175$	−420.494	−	204.217i	−2.40282	−	1.16695i
$176$		0			0
$177$	−54.7033	−	94.7489i	−0.309058	−	0.535305i
$178$		0			0
$179$	69.0000	−	119.512i	0.385475	−	0.667662i	−0.606360	−	0.795190i	$-0.707371\pi$
$179$	69.0000	−	119.512i	0.385475	−	0.667662i	0.991835	+	0.127528i	$0.0407043\pi$
$180$		0			0
$181$		−	98.5618i		−	0.544540i	−0.962221	−	0.272270i	$-0.912226\pi$
$181$		−	98.5618i		−	0.544540i	0.962221	−	0.272270i	$-0.0877744\pi$
$182$		0			0
$183$	−192.747			−1.05326
$184$		0			0
$185$	−202.494	−	116.910i	−1.09456	−	0.631946i
$186$		0			0
$187$	−76.2198	+	44.0055i	−0.407593	+	0.235324i
$188$		0			0
$189$	36.2802	−	2.59808i	0.191959	−	0.0137464i
$190$		0			0
$191$	−83.1537	−	144.026i	−0.435360	−	0.754065i	0.561965	−	0.827161i	$-0.310045\pi$
$191$	−83.1537	−	144.026i	−0.435360	−	0.754065i	−0.997325	+	0.0730957i	$0.976712\pi$
$192$		0			0
$193$	31.6537	−	54.8258i	0.164009	−	0.284072i	−0.772294	−	0.635265i	$-0.780891\pi$
$193$	31.6537	−	54.8258i	0.164009	−	0.284072i	0.936303	+	0.351194i	$0.114224\pi$
$194$		0			0
$195$			130.227i			0.667832i
$196$		0			0
$197$	184.307			0.935571			0.467785	−	0.883842i	$-0.345052\pi$
$197$	184.307			0.935571			0.467785	+	0.883842i	$0.345052\pi$
$198$		0			0
$199$	−30.7471	−	17.7518i	−0.154508	−	0.0892052i	0.420753	−	0.907175i	$-0.361766\pi$
$199$	−30.7471	−	17.7518i	−0.154508	−	0.0892052i	−0.575261	+	0.817970i	$0.695099\pi$
$200$		0			0
$201$	95.9504	−	55.3970i	0.477365	−	0.275607i
$202$		0			0
$203$	5.29669	+	73.9643i	0.0260921	+	0.364356i
$204$		0			0
$205$	−233.340	−	404.158i	−1.13825	−	1.97150i
$206$		0			0
$207$	36.0000	−	62.3538i	0.173913	−	0.301226i
$208$		0			0
$209$		−	75.3341i		−	0.360450i
$210$		0			0
$211$	9.69259			0.0459364			0.0229682	−	0.999736i	$-0.492688\pi$
$211$	9.69259			0.0459364			0.0229682	+	0.999736i	$0.492688\pi$
$212$		0			0
$213$	−32.3405	−	18.6718i	−0.151833	−	0.0876610i
$214$		0			0
$215$	−155.813	+	89.9588i	−0.724713	+	0.418413i
$216$		0			0
$217$	−170.483	+	351.035i	−0.785638	+	1.61767i
$218$		0			0
$219$	−53.5769	−	92.7978i	−0.244643	−	0.423734i
$220$		0			0
$221$	−75.1868	+	130.227i	−0.340212	+	0.589264i
$222$		0			0
$223$			430.462i			1.93032i	0.261657	+	0.965161i	$0.415731\pi$
$223$			430.462i			1.93032i	−0.261657	+	0.965161i	$0.584269\pi$
$224$		0			0
$225$	200.340			0.890402
$226$		0			0
$227$	−164.670	−	95.0724i	−0.725420	−	0.418821i	0.0913246	−	0.995821i	$-0.470890\pi$
$227$	−164.670	−	95.0724i	−0.725420	−	0.418821i	−0.816744	+	0.577000i	$0.804223\pi$
$228$		0			0
$229$	−100.170	+	57.8333i	−0.437425	+	0.252547i	−0.702505	−	0.711679i	$-0.747935\pi$
$229$	−100.170	+	57.8333i	−0.437425	+	0.252547i	0.265080	+	0.964226i	$0.414602\pi$
$230$		0			0
$231$	−31.2198	−	46.1184i	−0.135151	−	0.199647i
$232$		0			0
$233$	−207.747	−	359.829i	−0.891618	−	1.54433i	−0.837935	−	0.545770i	$-0.816237\pi$
$233$	−207.747	−	359.829i	−0.891618	−	1.54433i	−0.0536837	−	0.998558i	$-0.517096\pi$
$234$		0			0
$235$	−57.5603	+	99.6974i	−0.244938	+	0.424244i
$236$		0			0
$237$		−	6.60470i		−	0.0278679i
$238$		0			0
$239$	−82.3074			−0.344382			−0.172191	−	0.985064i	$-0.555085\pi$
$239$	−82.3074			−0.344382			−0.172191	+	0.985064i	$0.555085\pi$
$240$		0			0
$241$	174.703	+	100.865i	0.724910	+	0.418527i	0.816557	−	0.577265i	$-0.195880\pi$
$241$	174.703	+	100.865i	0.724910	+	0.418527i	−0.0916472	+	0.995792i	$0.529213\pi$
$242$		0			0
$243$	−13.5000	+	7.79423i	−0.0555556	+	0.0320750i
$244$		0			0
$245$	368.945	−	290.248i	1.50590	−	1.18469i
$246$		0			0
$247$	−64.3570	−	111.470i	−0.260555	−	0.451294i
$248$		0			0
$249$	−87.0438	+	150.764i	−0.349573	+	0.605479i
$250$		0			0
$251$		−	117.068i		−	0.466408i	−0.972428	−	0.233204i	$-0.925079\pi$
$251$		−	117.068i		−	0.466408i	0.972428	−	0.233204i	$-0.0749210\pi$
$252$		0			0
$253$	−110.241			−0.435736
$254$		0			0
$255$	275.340	+	158.968i	1.07977	+	0.623404i
$256$		0			0
$257$	226.121	−	130.551i	0.879847	−	0.507980i	0.00923894	−	0.999957i	$-0.497059\pi$
$257$	226.121	−	130.551i	0.879847	−	0.507980i	0.870608	+	0.491978i	$0.163726\pi$
$258$		0			0
$259$	141.478	−	95.7733i	0.546246	−	0.369781i
$260$		0			0
$261$	−15.8901	−	27.5224i	−0.0608815	−	0.105450i
$262$		0			0
$263$	227.340	−	393.765i	0.864412	−	1.49721i	−0.00321691	−	0.999995i	$-0.501024\pi$
$263$	227.340	−	393.765i	0.864412	−	1.49721i	0.867629	−	0.497211i	$-0.165643\pi$
$264$		0			0
$265$			358.363i			1.35231i
$266$		0			0
$267$	171.560			0.642548
$268$		0			0
$269$	−120.517	−	69.5803i	−0.448017	−	0.258663i	0.258975	−	0.965884i	$-0.416615\pi$
$269$	−120.517	−	69.5803i	−0.448017	−	0.258663i	−0.706992	+	0.707221i	$0.749948\pi$
$270$		0			0
$271$	50.8570	−	29.3623i	0.187664	−	0.108348i	−0.403224	−	0.915101i	$-0.632111\pi$
$271$	50.8570	−	29.3623i	0.187664	−	0.108348i	0.590889	+	0.806753i	$0.298777\pi$
$272$		0			0
$273$	−85.5934	−	41.5692i	−0.313529	−	0.152268i
$274$		0			0
$275$	−153.374	−	265.651i	−0.557722	−	0.966003i
$276$		0			0
$277$	22.3901	−	38.7808i	0.0808306	−	0.140003i	−0.822776	−	0.568365i	$-0.807576\pi$
$277$	22.3901	−	38.7808i	0.0808306	−	0.140003i	0.903607	+	0.428363i	$0.140909\pi$
$278$		0			0
$279$		−	167.247i		−	0.599453i
$280$		0			0
$281$	−325.494			−1.15834			−0.579171	−	0.815206i	$-0.696624\pi$
$281$	−325.494			−1.15834			−0.579171	+	0.815206i	$0.696624\pi$
$282$		0			0
$283$	−288.511	−	166.572i	−1.01947	−	0.588593i	−0.105521	−	0.994417i	$-0.533651\pi$
$283$	−288.511	−	166.572i	−1.01947	−	0.588593i	−0.913951	+	0.405824i	$0.866984\pi$
$284$		0			0
$285$	−235.681	+	136.070i	−0.826951	+	0.477440i
$286$		0			0
$287$	340.121	−	24.3565i	1.18509	−	0.0848660i
$288$		0			0
$289$	39.0603	+	67.6545i	0.135157	+	0.234098i
$290$		0			0
$291$	55.0769	−	95.3959i	0.189268	−	0.327821i
$292$		0			0
$293$			405.135i			1.38271i	0.722514	+	0.691356i	$0.242986\pi$
$293$			405.135i			1.38271i	−0.722514	+	0.691356i	$0.757014\pi$
$294$		0			0
$295$	605.142			2.05133
$296$		0			0
$297$	20.6702	+	11.9340i	0.0695968	+	0.0401817i
$298$		0			0
$299$	−163.121	+	94.1777i	−0.545554	+	0.314976i
$300$		0			0
$301$	−9.39008	−	131.125i	−0.0311963	−	0.435632i
$302$		0			0
$303$	104.340	+	180.723i	0.344358	+	0.596446i
$304$		0			0
$305$	533.055	−	923.277i	1.74772	−	3.02714i
$306$		0			0
$307$		−	24.9530i		−	0.0812801i	−0.999174	−	0.0406400i	$-0.987060\pi$
$307$		−	24.9530i		−	0.0812801i	0.999174	−	0.0406400i	$-0.0129397\pi$
$308$		0			0
$309$	−32.7140			−0.105871
$310$		0			0
$311$	−313.307	−	180.888i	−1.00742	−	0.581634i	−0.0969843	−	0.995286i	$-0.530920\pi$
$311$	−313.307	−	180.888i	−1.00742	−	0.581634i	−0.910435	+	0.413652i	$0.864253\pi$
$312$		0			0
$313$	−118.126	+	68.2003i	−0.377401	+	0.217892i	−0.676687	−	0.736271i	$-0.736585\pi$
$313$	−118.126	+	68.2003i	−0.377401	+	0.217892i	0.299286	+	0.954163i	$0.403252\pi$
$314$		0			0
$315$	−87.8901	+	180.971i	−0.279016	+	0.574510i
$316$		0			0
$317$	271.824	+	470.813i	0.857489	+	1.48521i	0.874317	+	0.485356i	$0.161310\pi$
$317$	271.824	+	470.813i	0.857489	+	1.48521i	−0.0168280	+	0.999858i	$0.505357\pi$
$318$		0			0
$319$	−24.3298	+	42.1404i	−0.0762688	+	0.132102i
$320$		0			0
$321$			29.3876i			0.0915501i
$322$		0			0
$323$	−314.241			−0.972883
$324$		0			0
$325$	−453.884	−	262.050i	−1.39657	−	0.806308i
$326$		0			0
$327$	−85.1702	+	49.1731i	−0.260459	+	0.150376i
$328$		0			0
$329$	−47.1537	−	69.6561i	−0.143324	−	0.211721i
$330$		0			0
$331$	−70.0496	−	121.329i	−0.211630	−	0.366554i	0.740595	−	0.671952i	$-0.234544\pi$
$331$	−70.0496	−	121.329i	−0.211630	−	0.366554i	−0.952225	+	0.305398i	$0.901211\pi$
$332$		0			0
$333$	−36.6099	+	63.4102i	−0.109940	+	0.190421i
$334$		0			0
$335$			612.816i			1.82930i
$336$		0			0
$337$	311.681			0.924869			0.462435	−	0.886653i	$-0.346976\pi$
$337$	311.681			0.924869			0.462435	+	0.886653i	$0.346976\pi$
$338$		0			0
$339$	−234.560	−	135.423i	−0.691918	−	0.399479i
$340$		0			0
$341$	−221.769	+	128.039i	−0.650350	+	0.375480i
$342$		0			0
$343$	73.0000	+	335.142i	0.212828	+	0.977090i
$344$		0			0
$345$	199.121	+	344.887i	0.577161	+	0.999673i
$346$		0			0
$347$	56.1537	−	97.2611i	0.161826	−	0.280291i	−0.773697	−	0.633555i	$-0.781595\pi$
$347$	56.1537	−	97.2611i	0.161826	−	0.280291i	0.935524	+	0.353264i	$0.114928\pi$
$348$		0			0
$349$			211.526i			0.606091i	0.952976	+	0.303046i	$0.0980035\pi$
$349$			211.526i			0.606091i	−0.952976	+	0.303046i	$0.901997\pi$
$350$		0			0
$351$	40.7802			0.116183
$352$		0			0
$353$	−79.5934	−	45.9533i	−0.225477	−	0.130179i	0.383007	−	0.923746i	$-0.374889\pi$
$353$	−79.5934	−	45.9533i	−0.225477	−	0.130179i	−0.608484	+	0.793566i	$0.708222\pi$
$354$		0			0
$355$	178.879	−	103.276i	0.503886	−	0.290918i
$356$		0			0
$357$	−192.374	+	130.227i	−0.538861	+	0.364782i
$358$		0			0
$359$	235.494	+	407.888i	0.655973	+	1.13618i	0.981649	+	0.190697i	$0.0610747\pi$
$359$	235.494	+	407.888i	0.655973	+	1.13618i	−0.325676	+	0.945481i	$0.605592\pi$
$360$		0			0
$361$	−46.0107	+	79.6929i	−0.127454	+	0.220756i
$362$		0			0
$363$			173.033i			0.476676i
$364$		0			0
$365$	592.681			1.62378
$366$		0			0
$367$	386.994	+	223.431i	1.05448	+	0.608804i	0.923900	−	0.382633i	$-0.124983\pi$
$367$	386.994	+	223.431i	1.05448	+	0.608804i	0.130580	+	0.991438i	$0.458316\pi$
$368$		0			0
$369$	−126.560	+	73.0696i	−0.342982	+	0.198021i
$370$		0			0
$371$	−235.538	−	114.391i	−0.634873	−	0.308332i
$372$		0			0
$373$	26.6099	+	46.0897i	0.0713403	+	0.123565i	0.899489	−	0.436944i	$-0.143939\pi$
$373$	26.6099	+	46.0897i	0.0713403	+	0.123565i	−0.828149	+	0.560509i	$0.810606\pi$
$374$		0			0
$375$	−346.637	+	600.393i	−0.924366	+	1.60105i
$376$		0			0
$377$			83.1384i			0.220526i
$378$		0			0
$379$	−700.076			−1.84717			−0.923583	−	0.383398i	$-0.874754\pi$
$379$	−700.076			−1.84717			−0.923583	+	0.383398i	$0.874754\pi$
$380$		0			0
$381$	37.5000	+	21.6506i	0.0984252	+	0.0568258i
$382$		0			0
$383$	539.714	−	311.604i	1.40918	−	0.813588i	0.413866	−	0.910338i	$-0.364178\pi$
$383$	539.714	−	311.604i	1.40918	−	0.813588i	0.995309	+	0.0967501i	$0.0308448\pi$
$384$		0			0
$385$	307.252	−	22.0028i	0.798057	−	0.0571501i
$386$		0			0
$387$	28.1702	+	48.7923i	0.0727913	+	0.126078i
$388$		0			0
$389$	198.934	−	344.564i	0.511398	−	0.885768i	−0.488515	−	0.872556i	$-0.662461\pi$
$389$	198.934	−	344.564i	0.511398	−	0.885768i	0.999913	−	0.0132118i	$-0.00420557\pi$
$390$		0			0
$391$			459.849i			1.17609i
$392$		0			0
$393$	−174.660			−0.444426
$394$		0			0
$395$	31.6372	+	18.2657i	0.0800941	+	0.0462424i
$396$		0			0
$397$	292.830	−	169.065i	0.737606	−	0.425857i	−0.0835920	−	0.996500i	$-0.526639\pi$
$397$	292.830	−	169.065i	0.737606	−	0.425857i	0.821198	+	0.570643i	$0.193306\pi$
$398$		0			0
$399$	−14.2033	−	198.338i	−0.0355973	−	0.497089i
$400$		0			0
$401$	−9.93387	−	17.2060i	−0.0247727	−	0.0429076i	0.853373	−	0.521300i	$-0.174553\pi$
$401$	−9.93387	−	17.2060i	−0.0247727	−	0.0429076i	−0.878146	+	0.478393i	$0.841220\pi$
$402$		0			0
$403$	−218.764	+	378.910i	−0.542838	+	0.940223i
$404$		0			0
$405$		−	86.2218i		−	0.212893i
$406$		0			0
$407$	112.109			0.275452
$408$		0			0
$409$	355.313	+	205.140i	0.868736	+	0.501565i	0.866928	−	0.498433i	$-0.166091\pi$
$409$	355.313	+	205.140i	0.868736	+	0.501565i	0.00180834	+	0.999998i	$0.499424\pi$
$410$		0			0
$411$	−64.6810	+	37.3436i	−0.157375	+	0.0908603i
$412$		0			0
$413$	−193.164	+	397.737i	−0.467710	+	0.963042i
$414$		0			0
$415$	−481.450	−	833.897i	−1.16012	−	2.00939i
$416$		0			0
$417$	102.137	−	176.907i	0.244933	−	0.424237i
$418$		0			0
$419$			564.750i			1.34785i	0.738799	+	0.673926i	$0.235393\pi$
$419$			564.750i			1.34785i	−0.738799	+	0.673926i	$0.764607\pi$
$420$		0			0
$421$	384.582			0.913496			0.456748	−	0.889596i	$-0.349014\pi$
$421$	384.582			0.913496			0.456748	+	0.889596i	$0.349014\pi$
$422$		0			0
$423$	31.2198	+	18.0248i	0.0738058	+	0.0426118i
$424$		0			0
$425$	−1108.11	+	639.767i	−2.60732	+	1.50533i
$426$		0			0
$427$	436.681	+	645.071i	1.02267	+	1.51070i
$428$		0			0
$429$	−31.2198	−	54.0743i	−0.0727735	−	0.126047i
$430$		0			0
$431$	276.934	−	479.664i	0.642538	−	1.11291i	−0.342326	−	0.939581i	$-0.611215\pi$
$431$	276.934	−	479.664i	0.642538	−	1.11291i	0.984864	−	0.173327i	$-0.0554518\pi$
$432$		0			0
$433$		−	221.760i		−	0.512147i	−0.966657	−	0.256074i	$-0.917571\pi$
$433$		−	221.760i		−	0.512147i	0.966657	−	0.256074i	$-0.0824290\pi$
$434$		0			0
$435$	175.780			0.404092
$436$		0			0
$437$	−340.879	−	196.807i	−0.780044	−	0.450359i
$438$		0			0
$439$	480.791	−	277.585i	1.09520	−	0.632311i	0.160241	−	0.987078i	$-0.448773\pi$
$439$	480.791	−	277.585i	1.09520	−	0.632311i	0.934955	+	0.354766i	$0.115440\pi$
$440$		0			0
$441$	−90.8901	−	115.534i	−0.206100	−	0.261981i
$442$		0			0
$443$	−192.791	−	333.924i	−0.435194	−	0.753778i	0.562118	−	0.827057i	$-0.309987\pi$
$443$	−192.791	−	333.924i	−0.435194	−	0.753778i	−0.997311	+	0.0732794i	$0.976654\pi$
$444$		0			0
$445$	−474.461	+	821.791i	−1.06620	+	1.84672i
$446$		0			0
$447$		−	306.896i		−	0.686569i
$448$		0			0
$449$	−107.802			−0.240093			−0.120046	−	0.992768i	$-0.538304\pi$
$449$	−107.802			−0.240093			−0.120046	+	0.992768i	$0.538304\pi$
$450$		0			0
$451$	193.780	+	111.879i	0.429668	+	0.248069i
$452$		0			0
$453$	274.450	−	158.454i	0.605851	−	0.349788i
$454$		0			0
$455$	435.835	−	295.038i	0.957878	−	0.648436i
$456$		0			0
$457$	5.50000	+	9.52628i	0.0120350	+	0.0208453i	0.871980	−	0.489541i	$-0.162836\pi$
$457$	5.50000	+	9.52628i	0.0120350	+	0.0208453i	−0.859945	+	0.510386i	$0.829502\pi$
$458$		0			0
$459$	49.7802	−	86.2218i	0.108454	−	0.187847i
$460$		0			0
$461$		−	636.532i		−	1.38076i	−0.723445	−	0.690382i	$-0.757443\pi$
$461$		−	636.532i		−	1.38076i	0.723445	−	0.690382i	$-0.242557\pi$
$462$		0			0
$463$	−179.660			−0.388034			−0.194017	−	0.980998i	$-0.562152\pi$
$463$	−179.660			−0.388034			−0.194017	+	0.980998i	$0.562152\pi$
$464$		0			0
$465$	801.131	+	462.533i	1.72286	+	0.994695i
$466$		0			0
$467$	−39.6595	+	22.8974i	−0.0849240	+	0.0490309i	−0.541861	−	0.840468i	$-0.682280\pi$
$467$	−39.6595	+	22.8974i	−0.0849240	+	0.0490309i	0.456937	+	0.889499i	$0.348947\pi$
$468$		0			0
$469$	−402.780	−	195.614i	−0.858806	−	0.417087i
$470$		0			0
$471$	73.1206	+	126.649i	0.155246	+	0.268893i
$472$		0			0
$473$	43.1323	−	74.7073i	0.0911887	−	0.157944i
$474$		0			0
$475$		−	1095.23i		−	2.30575i
$476$		0			0
$477$	112.220			0.235262
$478$		0			0
$479$	−140.352	−	81.0323i	−0.293011	−	0.169170i	0.346288	−	0.938128i	$-0.387442\pi$
$479$	−140.352	−	81.0323i	−0.293011	−	0.169170i	−0.639299	+	0.768958i	$0.720775\pi$
$480$		0			0
$481$	165.884	−	95.7733i	0.344874	−	0.199113i
$482$		0			0
$483$	−290.241	+	20.7846i	−0.600914	+	0.0430323i
$484$		0			0
$485$	304.637	+	527.647i	0.628118	+	1.08793i
$486$		0			0
$487$	−332.401	+	575.735i	−0.682548	+	1.18221i	0.291653	+	0.956524i	$0.405795\pi$
$487$	−332.401	+	575.735i	−0.682548	+	1.18221i	−0.974201	+	0.225683i	$0.927539\pi$
$488$		0			0
$489$			249.301i			0.509818i
$490$		0			0
$491$	379.955			0.773840			0.386920	−	0.922113i	$-0.373539\pi$
$491$	379.955			0.773840			0.386920	+	0.922113i	$0.373539\pi$
$492$		0			0
$493$	175.780	+	101.487i	0.356552	+	0.205855i
$494$		0			0
$495$	−114.330	+	66.0083i	−0.230969	+	0.133350i
$496$		0			0
$497$	10.7802	+	150.537i	0.0216905	+	0.302891i
$498$		0			0
$499$	263.050	+	455.615i	0.527154	+	0.913057i	0.999499	+	0.0316433i	$0.0100741\pi$
$499$	263.050	+	455.615i	0.527154	+	0.913057i	−0.472346	+	0.881413i	$0.656593\pi$
$500$		0			0
$501$	107.154	−	185.596i	0.213880	−	0.370450i
$502$		0			0
$503$		−	573.504i		−	1.14017i	−0.821587	−	0.570084i	$-0.806911\pi$
$503$		−	573.504i		−	1.14017i	0.821587	−	0.570084i	$-0.193089\pi$
$504$		0			0
$505$	−1154.24			−2.28563
$506$		0			0
$507$	161.110	+	93.0169i	0.317771	+	0.183465i
$508$		0			0
$509$	100.538	−	58.0456i	0.197521	−	0.114039i	−0.397978	−	0.917395i	$-0.630288\pi$
$509$	100.538	−	58.0456i	0.197521	−	0.114039i	0.595498	+	0.803356i	$0.296955\pi$
$510$		0			0
$511$	−189.187	+	389.546i	−0.370229	+	0.762322i
$512$		0			0
$513$	42.6099	+	73.8025i	0.0830603	+	0.143865i
$514$		0			0
$515$	90.4727	−	156.703i	0.175675	−	0.304278i
$516$		0			0
$517$		−	55.1965i		−	0.106763i
$518$		0			0
$519$	232.879			0.448708
$520$		0			0
$521$	142.593	+	82.3263i	0.273692	+	0.158016i	0.630564	−	0.776137i	$-0.282824\pi$
$521$	142.593	+	82.3263i	0.273692	+	0.158016i	−0.356872	+	0.934153i	$0.616157\pi$
$522$		0			0
$523$	−435.884	+	251.658i	−0.833431	+	0.481181i	−0.855026	−	0.518585i	$-0.826459\pi$
$523$	−435.884	+	251.658i	−0.833431	+	0.481181i	0.0215952	+	0.999767i	$0.493126\pi$
$524$		0			0
$525$	−453.884	−	670.484i	−0.864541	−	1.27711i
$526$		0			0
$527$	534.088	+	925.067i	1.01345	+	1.75534i
$528$		0			0
$529$	−23.5000	+	40.7032i	−0.0444234	+	0.0769437i
$530$		0			0
$531$		−	189.498i		−	0.356870i
$532$		0			0
$533$	382.307			0.717275
$534$		0			0
$535$	−140.769	−	81.2733i	−0.263120	−	0.151913i
$536$		0			0
$537$	207.000	−	119.512i	0.385475	−	0.222554i
$538$		0			0
$539$	−83.6148	+	208.968i	−0.155130	+	0.387696i
$540$		0			0
$541$	281.050	+	486.792i	0.519500	+	0.899801i	0.999743	+	0.0226652i	$0.00721517\pi$
$541$	281.050	+	486.792i	0.519500	+	0.899801i	−0.480243	+	0.877136i	$0.659451\pi$
$542$		0			0
$543$	85.3570	−	147.843i	0.157195	−	0.272270i
$544$		0			0
$545$		−	543.965i		−	0.998101i
$546$		0			0
$547$	−200.374			−0.366314			−0.183157	−	0.983084i	$-0.558632\pi$
$547$	−200.374			−0.366314			−0.183157	+	0.983084i	$0.558632\pi$
$548$		0			0
$549$	−289.121	−	166.924i	−0.526631	−	0.304051i
$550$		0			0
$551$	−150.461	+	86.8688i	−0.273069	+	0.157657i
$552$		0			0
$553$	−22.1041	+	14.9634i	−0.0399713	+	0.0270586i
$554$		0			0
$555$	−202.494	−	350.730i	−0.364854	−	0.631946i
$556$		0			0
$557$	−218.297	+	378.101i	−0.391915	+	0.678817i	−0.992702	−	0.120592i	$-0.961521\pi$
$557$	−218.297	+	378.101i	−0.391915	+	0.678817i	0.600787	+	0.799409i	$0.294854\pi$
$558$		0			0
$559$		−	147.389i		−	0.263666i
$560$		0			0
$561$	−152.440			−0.271728
$562$		0			0
$563$	−94.9115	−	54.7972i	−0.168582	−	0.0973307i	0.413335	−	0.910579i	$-0.364364\pi$
$563$	−94.9115	−	54.7972i	−0.168582	−	0.0973307i	−0.581917	+	0.813248i	$0.697697\pi$
$564$		0			0
$565$	1297.38	−	749.045i	2.29625	−	1.32574i
$566$		0			0
$567$	56.6702	+	27.5224i	0.0999475	+	0.0485404i
$568$		0			0
$569$	−265.307	−	459.526i	−0.466270	−	0.807603i	0.532988	−	0.846123i	$-0.321069\pi$
$569$	−265.307	−	459.526i	−0.466270	−	0.807603i	−0.999258	+	0.0385200i	$0.987736\pi$
$570$		0			0
$571$	−438.631	+	759.732i	−0.768181	+	1.33053i	0.170367	+	0.985381i	$0.445505\pi$
$571$	−438.631	+	759.732i	−0.768181	+	1.33053i	−0.938548	+	0.345148i	$0.887829\pi$
$572$		0			0
$573$		−	288.053i		−	0.502710i
$574$		0			0
$575$	−1602.72			−2.78735
$576$		0			0
$577$	529.115	+	305.485i	0.917010	+	0.529436i	0.882680	−	0.469975i	$-0.155737\pi$
$577$	529.115	+	305.485i	0.917010	+	0.529436i	0.0343301	+	0.999411i	$0.489070\pi$
$578$		0			0
$579$	94.9611	−	54.8258i	0.164009	−	0.0946905i
$580$		0			0
$581$	701.769	−	50.2548i	1.20786	−	0.0864970i
$582$		0			0
$583$	−85.9115	−	148.803i	−0.147361	−	0.255237i
$584$		0			0
$585$	−112.780	+	195.341i	−0.192787	+	0.333916i
$586$		0			0
$587$			352.196i			0.599993i	0.953940	+	0.299997i	$0.0969856\pi$
$587$			352.196i			0.599993i	−0.953940	+	0.299997i	$0.903014\pi$
$588$		0			0
$589$	−914.317			−1.55232
$590$		0			0
$591$	276.461	+	159.615i	0.467785	+	0.270076i
$592$		0			0
$593$	−287.154	+	165.788i	−0.484239	+	0.279575i	−0.722181	−	0.691704i	$-0.756860\pi$
$593$	−287.154	+	165.788i	−0.484239	+	0.279575i	0.237942	+	0.971279i	$0.423527\pi$
$594$		0			0
$595$	−91.7802	−	1281.64i	−0.154252	−	2.15402i
$596$		0			0
$597$	−30.7471	−	53.2555i	−0.0515027	−	0.0892052i
$598$		0			0
$599$	−182.615	+	316.298i	−0.304866	+	0.528044i	−0.977232	−	0.212176i	$-0.931945\pi$
$599$	−182.615	+	316.298i	−0.304866	+	0.528044i	0.672365	+	0.740219i	$0.265278\pi$
$600$		0			0
$601$		−	749.102i		−	1.24643i	−0.782052	−	0.623213i	$-0.785827\pi$
$601$		−	749.102i		−	1.24643i	0.782052	−	0.623213i	$-0.214173\pi$
$602$		0			0
$603$	191.901			0.318243
$604$		0			0
$605$	−828.846	−	478.535i	−1.36999	−	0.790966i
$606$		0			0
$607$	916.850	−	529.344i	1.51046	−	0.872066i	0.510536	−	0.859856i	$-0.329447\pi$
$607$	916.850	−	529.344i	1.51046	−	0.872066i	0.999925	−	0.0122093i	$-0.00388644\pi$
$608$		0			0
$609$	−56.1099	+	115.534i	−0.0921345	+	0.189710i
$610$		0			0
$611$	−47.1537	−	81.6726i	−0.0771746	−	0.133670i
$612$		0			0
$613$	−109.286	+	189.289i	−0.178281	+	0.308791i	−0.941292	−	0.337594i	$-0.890387\pi$
$613$	−109.286	+	189.289i	−0.178281	+	0.308791i	0.763011	+	0.646385i	$0.223720\pi$
$614$		0			0
$615$		−	808.315i		−	1.31433i
$616$		0			0
$617$	559.669			0.907082			0.453541	−	0.891236i	$-0.350161\pi$
$617$	559.669			0.907082			0.453541	+	0.891236i	$0.350161\pi$
$618$		0			0
$619$	−460.159	−	265.673i	−0.743390	−	0.429197i	0.0799104	−	0.996802i	$-0.474537\pi$
$619$	−460.159	−	265.673i	−0.743390	−	0.429197i	−0.823301	+	0.567605i	$0.807870\pi$
$620$		0			0
$621$	108.000	−	62.3538i	0.173913	−	0.100409i
$622$		0			0
$623$	−388.681	−	574.165i	−0.623886	−	0.921613i
$624$		0			0
$625$	−1082.54	−	1875.02i	−1.73207	−	3.00003i
$626$		0			0
$627$	65.2413	−	113.001i	0.104053	−	0.180225i
$628$		0			0
$629$		−	467.640i		−	0.743466i
$630$		0			0
$631$	1086.53			1.72191			0.860957	−	0.508678i	$-0.169866\pi$
$631$	1086.53			1.72191			0.860957	+	0.508678i	$0.169866\pi$
$632$		0			0
$633$	14.5389	+	8.39403i	0.0229682	+	0.0132607i
$634$		0			0
$635$	−207.417	+	119.752i	−0.326641	+	0.188587i
$636$		0			0
$637$	54.7967	+	380.635i	0.0860231	+	0.597543i
$638$		0			0
$639$	−32.3405	−	56.0154i	−0.0506111	−	0.0876610i
$640$		0			0
$641$	−231.934	+	401.721i	−0.361831	+	0.626710i	−0.988262	−	0.152767i	$-0.951182\pi$
$641$	−231.934	+	401.721i	−0.361831	+	0.626710i	0.626431	+	0.779477i	$0.284515\pi$
$642$		0			0
$643$		−	1055.85i		−	1.64206i	−0.570883	−	0.821032i	$-0.693399\pi$
$643$		−	1055.85i		−	1.64206i	0.570883	−	0.821032i	$-0.306601\pi$
$644$		0			0
$645$	−311.626			−0.483142
$646$		0			0
$647$	682.582	+	394.089i	1.05499	+	0.609102i	0.924044	−	0.382287i	$-0.124863\pi$
$647$	682.582	+	394.089i	1.05499	+	0.609102i	0.130951	+	0.991389i	$0.458197\pi$
$648$		0			0
$649$	−251.273	+	145.073i	−0.387170	+	0.223533i
$650$		0			0
$651$	−559.731	+	378.910i	−0.859801	+	0.582043i
$652$		0			0
$653$	507.878	+	879.671i	0.777762	+	1.34712i	0.933229	+	0.359282i	$0.116978\pi$
$653$	507.878	+	879.671i	0.777762	+	1.34712i	−0.155467	+	0.987841i	$0.549688\pi$
$654$		0			0
$655$	483.032	−	836.636i	0.737454	−	1.27731i
$656$		0			0
$657$		−	185.596i		−	0.282490i
$658$		0			0
$659$	−1254.55			−1.90372			−0.951858	−	0.306540i	$-0.900829\pi$
$659$	−1254.55			−1.90372			−0.951858	+	0.306540i	$0.900829\pi$
$660$		0			0
$661$	−540.686	−	312.165i	−0.817982	−	0.472262i	0.0317383	−	0.999496i	$-0.489896\pi$
$661$	−540.686	−	312.165i	−0.817982	−	0.472262i	−0.849720	+	0.527234i	$0.823229\pi$
$662$		0			0
$663$	−225.560	+	130.227i	−0.340212	+	0.196421i
$664$		0			0
$665$	989.340	+	480.482i	1.48773	+	0.722530i
$666$		0			0
$667$	127.121	+	220.179i	0.190586	+	0.330104i
$668$		0			0
$669$	−372.791	+	645.693i	−0.557236	+	0.965161i
$670$		0			0
$671$			511.164i			0.761794i
$672$		0			0
$673$	41.4826			0.0616383			0.0308191	−	0.999525i	$-0.490188\pi$
$673$	41.4826			0.0616383			0.0308191	+	0.999525i	$0.490188\pi$
$674$		0			0
$675$	300.511	+	173.500i	0.445201	+	0.257037i
$676$		0			0
$677$	624.791	−	360.723i	0.922882	−	0.532826i	0.0383284	−	0.999265i	$-0.487797\pi$
$677$	624.791	−	360.723i	0.922882	−	0.532826i	0.884553	+	0.466439i	$0.154463\pi$
$678$		0			0
$679$	−444.044	+	31.7986i	−0.653967	+	0.0468316i
$680$		0			0
$681$	−164.670	−	285.217i	−0.241807	−	0.418821i
$682$		0			0
$683$	419.758	−	727.042i	0.614580	−	1.06448i	−0.375879	−	0.926669i	$-0.622659\pi$
$683$	419.758	−	727.042i	0.614580	−	1.06448i	0.990458	−	0.137814i	$-0.0440076\pi$
$684$		0			0
$685$		−	413.104i		−	0.603072i
$686$		0			0
$687$	−200.340			−0.291616
$688$		0			0
$689$	−254.241	−	146.786i	−0.369000	−	0.213042i
$690$		0			0
$691$	481.433	−	277.955i	0.696719	−	0.402251i	−0.109405	−	0.993997i	$-0.534895\pi$
$691$	481.433	−	277.955i	0.696719	−	0.402251i	0.806124	+	0.591746i	$0.201561\pi$
$692$		0			0
$693$	−6.89008	−	96.2147i	−0.00994240	−	0.138838i
$694$		0			0
$695$	564.934	+	978.494i	0.812854	+	1.40791i
$696$		0			0
$697$	466.681	−	808.315i	0.669557	−	1.15971i
$698$		0			0
$699$		−	719.657i		−	1.02955i
$700$		0			0
$701$	−994.769			−1.41907			−0.709535	−	0.704670i	$-0.751095\pi$
$701$	−994.769			−1.41907			−0.709535	+	0.704670i	$0.751095\pi$
$702$		0			0
$703$	346.655	+	200.141i	0.493108	+	0.284696i
$704$		0			0
$705$	−172.681	+	99.6974i	−0.244938	+	0.141415i
$706$		0			0
$707$	368.440	−	758.638i	0.521131	−	1.07304i
$708$		0			0
$709$	417.988	+	723.977i	0.589546	+	1.02112i	0.994292	+	0.106695i	$0.0340268\pi$
$709$	417.988	+	723.977i	0.589546	+	1.02112i	−0.404745	+	0.914429i	$0.632640\pi$
$710$		0			0
$711$	5.71984	−	9.90705i	0.00804478	−	0.0139340i
$712$		0			0
$713$			1337.98i			1.87655i
$714$		0			0
$715$	345.362			0.483024
$716$		0			0
$717$	−123.461	−	71.2803i	−0.172191	−	0.0994147i
$718$		0			0
$719$	−415.109	+	239.663i	−0.577342	+	0.333329i	−0.760076	−	0.649834i	$-0.774839\pi$
$719$	−415.109	+	239.663i	−0.577342	+	0.333329i	0.182734	+	0.983162i	$0.441505\pi$
$720$		0			0
$721$	74.1157	+	109.485i	0.102796	+	0.151851i
$722$		0			0
$723$	174.703	+	302.595i	0.241637	+	0.418527i
$724$		0			0
$725$	−353.714	+	612.651i	−0.487881	+	0.845035i
$726$		0			0
$727$		−	949.487i		−	1.30603i	−0.757343	−	0.653017i	$-0.773503\pi$
$727$		−	949.487i		−	1.30603i	0.757343	−	0.653017i	$-0.226497\pi$
$728$		0			0
$729$	−27.0000			−0.0370370
$730$		0			0
$731$	−311.626	−	179.918i	−0.426302	−	0.246125i
$732$		0			0
$733$	−388.071	+	224.053i	−0.529428	+	0.305666i	−0.740784	−	0.671744i	$-0.765546\pi$
$733$	−388.071	+	224.053i	−0.529428	+	0.305666i	0.211355	+	0.977409i	$0.432212\pi$
$734$		0			0
$735$	804.779	−	115.857i	1.09494	−	0.157629i
$736$		0			0
$737$	−146.912	−	254.460i	−0.199338	−	0.345264i
$738$		0			0
$739$	−29.0496	+	50.3154i	−0.0393093	+	0.0680858i	−0.885011	−	0.465571i	$-0.845849\pi$
$739$	−29.0496	+	50.3154i	−0.0393093	+	0.0680858i	0.845701	+	0.533656i	$0.179182\pi$
$740$		0			0
$741$		−	222.939i		−	0.300863i
$742$		0			0
$743$	386.043			0.519573			0.259787	−	0.965666i	$-0.416348\pi$
$743$	386.043			0.519573			0.259787	+	0.965666i	$0.416348\pi$
$744$		0			0
$745$	1470.06	+	848.742i	1.97324	+	1.13925i
$746$		0			0
$747$	−261.131	+	150.764i	−0.349573	+	0.201826i
$748$		0			0
$749$	98.3521	−	66.5795i	0.131311	−	0.0888912i
$750$		0			0
$751$	275.181	+	476.627i	0.366419	+	0.634657i	0.989003	−	0.147896i	$-0.0472502\pi$
$751$	275.181	+	476.627i	0.366419	+	0.634657i	−0.622583	+	0.782553i	$0.713917\pi$
$752$		0			0
$753$	101.384	−	175.603i	0.134640	−	0.233204i
$754$		0			0
$755$			1752.86i			2.32167i
$756$		0			0
$757$	379.187			0.500907			0.250454	−	0.968129i	$-0.419420\pi$
$757$	379.187			0.500907			0.250454	+	0.968129i	$0.419420\pi$
$758$		0			0
$759$	−165.362	−	95.4717i	−0.217868	−	0.125786i
$760$		0			0
$761$	−446.615	+	257.853i	−0.586879	+	0.338835i	−0.763862	−	0.645379i	$-0.776699\pi$
$761$	−446.615	+	257.853i	−0.586879	+	0.338835i	0.176984	+	0.984214i	$0.443366\pi$
$762$		0			0
$763$	357.527	+	173.636i	0.468581	+	0.227571i
$764$		0			0
$765$	275.340	+	476.904i	0.359922	+	0.623404i
$766$		0			0
$767$	−247.868	+	429.320i	−0.323165	+	0.559739i
$768$		0			0
$769$			548.514i			0.713282i	0.934241	+	0.356641i	$0.116078\pi$
$769$			548.514i			0.713282i	−0.934241	+	0.356641i	$0.883922\pi$
$770$		0			0
$771$	452.241			0.586565
$772$		0			0
$773$	−103.792	−	59.9242i	−0.134271	−	0.0775216i	0.431360	−	0.902180i	$-0.358034\pi$
$773$	−103.792	−	59.9242i	−0.134271	−	0.0775216i	−0.565631	+	0.824658i	$0.691367\pi$
$774$		0			0
$775$	−3224.16	+	1861.47i	−4.16020	+	2.40189i
$776$		0			0
$777$	295.159	−	21.1367i	0.379870	−	0.0272030i
$778$		0			0
$779$	399.461	+	691.887i	0.512787	+	0.888173i
$780$		0			0
$781$	−49.5174	+	85.7667i	−0.0634026	+	0.109817i
$782$		0			0
$783$		−	55.0449i		−	0.0702999i
$784$		0			0
$785$	−808.879			−1.03042
$786$		0			0
$787$	877.097	+	506.392i	1.11448	+	0.643447i	0.939987	−	0.341211i	$-0.110837\pi$
$787$	877.097	+	506.392i	1.11448	+	0.643447i	0.174495	+	0.984658i	$0.444171\pi$
$788$		0			0
$789$	682.021	−	393.765i	0.864412	−	0.499069i
$790$		0			0
$791$	78.1868	+	1091.82i	0.0988455	+	1.38030i
$792$		0			0
$793$	436.681	+	756.354i	0.550670	+	0.953788i
$794$		0			0
$795$	−310.351	+	537.544i	−0.390379	+	0.676156i
$796$		0			0
$797$			1067.63i			1.33956i	0.742561	+	0.669779i	$0.233611\pi$
$797$			1067.63i			1.33956i	−0.742561	+	0.669779i	$0.766389\pi$
$798$		0			0
$799$	−230.241			−0.288162
$800$		0			0
$801$	257.340	+	148.576i	0.321274	+	0.185488i
$802$		0			0
$803$	−246.099	+	142.085i	−0.306475	+	0.176943i
$804$		0			0
$805$	703.121	−	1447.77i	0.873442	−	1.79847i
$806$		0			0
$807$	−120.517	−	208.741i	−0.149339	−	0.258663i
$808$		0			0
$809$	425.527	−	737.035i	0.525992	−	0.911044i	−0.473550	−	0.880767i	$-0.657028\pi$
$809$	425.527	−	737.035i	0.525992	−	0.911044i	0.999542	−	0.0302773i	$-0.00963903\pi$
$810$		0			0
$811$			364.378i			0.449294i	0.974440	+	0.224647i	$0.0721229\pi$
$811$			364.378i			0.449294i	−0.974440	+	0.224647i	$0.927877\pi$
$812$		0			0
$813$	101.714			0.125110
$814$		0			0
$815$	−1194.18	−	689.457i	−1.46525	−	0.845960i
$816$		0			0
$817$	266.740	−	154.003i	0.326488	−	0.188498i
$818$		0			0
$819$	−92.3901	−	136.480i	−0.112808	−	0.166642i
$820$		0			0
$821$	−21.5049	−	37.2476i	−0.0261936	−	0.0453686i	0.852631	−	0.522513i	$-0.175005\pi$
$821$	−21.5049	−	37.2476i	−0.0261936	−	0.0453686i	−0.878825	+	0.477144i	$0.841672\pi$
$822$		0			0
$823$	331.747	−	574.603i	0.403095	−	0.698181i	−0.591003	−	0.806670i	$-0.701268\pi$
$823$	331.747	−	574.603i	0.403095	−	0.698181i	0.994098	+	0.108489i	$0.0346011\pi$
$824$		0			0
$825$		−	531.302i		−	0.644002i
$826$		0			0
$827$	684.811			0.828067			0.414034	−	0.910262i	$-0.364120\pi$
$827$	684.811			0.828067			0.414034	+	0.910262i	$0.364120\pi$
$828$		0			0
$829$	−1080.69	−	623.934i	−1.30360	−	0.752635i	−0.322582	−	0.946542i	$-0.604551\pi$
$829$	−1080.69	−	623.934i	−1.30360	−	0.752635i	−0.981020	+	0.193907i	$0.937884\pi$
$830$		0			0
$831$	67.1702	−	38.7808i	0.0808306	−	0.0466676i
$832$		0			0
$833$	871.669	+	348.783i	1.04642	+	0.418706i
$834$		0			0
$835$	592.681	+	1026.55i	0.709798	+	1.22941i
$836$		0			0
$837$	144.840	−	250.871i	0.173047	−	0.299726i
$838$		0			0
$839$		−	1289.61i		−	1.53708i	−0.639802	−	0.768540i	$-0.720984\pi$
$839$		−	1289.61i		−	1.53708i	0.639802	−	0.768540i	$-0.279016\pi$
$840$		0			0
$841$	−728.780			−0.866564
$842$		0			0
$843$	−488.241	−	281.886i	−0.579171	−	0.334385i
$844$		0			0
$845$	−891.120	+	514.488i	−1.05458	+	0.608862i
$846$		0			0
$847$	579.094	−	392.018i	0.683700	−	0.462831i
$848$		0			0
$849$	−288.511	−	499.715i	−0.339824	−	0.588593i
$850$		0			0
$851$	292.879	−	507.282i	0.344159	−	0.596101i
$852$		0			0
$853$		−	141.122i		−	0.165442i	−0.996573	−	0.0827208i	$-0.973639\pi$
$853$		−	141.122i		−	0.165442i	0.996573	−	0.0827208i	$-0.0263610\pi$
$854$		0			0
$855$	−471.362			−0.551300
$856$		0			0
$857$	141.187	+	81.5142i	0.164745	+	0.0951158i	0.580106	−	0.814541i	$-0.303011\pi$
$857$	141.187	+	81.5142i	0.164745	+	0.0951158i	−0.415360	+	0.909657i	$0.636345\pi$
$858$		0			0
$859$	264.484	−	152.700i	0.307898	−	0.177765i	−0.338087	−	0.941115i	$-0.609780\pi$
$859$	264.484	−	152.700i	0.307898	−	0.177765i	0.645985	+	0.763350i	$0.276447\pi$
$860$		0			0
$861$	531.274	+	258.018i	0.617043	+	0.299673i
$862$		0			0
$863$	−247.681	−	428.996i	−0.287000	−	0.497098i	0.686092	−	0.727515i	$-0.259325\pi$
$863$	−247.681	−	428.996i	−0.287000	−	0.497098i	−0.973092	+	0.230416i	$0.925991\pi$
$864$		0			0
$865$	−644.043	+	1115.51i	−0.744558	+	1.28961i
$866$		0			0
$867$			135.309i			0.156066i
$868$		0			0
$869$	−17.5156			−0.0201561
$870$		0			0
$871$	−434.764	−	251.011i	−0.499155	−	0.288187i
$872$		0			0
$873$	165.231	−	95.3959i	0.189268	−	0.109274i
$874$		0			0
$875$	2794.68	−	200.131i	3.19392	−	0.228721i
$876$		0			0
$877$	45.3950	+	78.6264i	0.0517617	+	0.0896538i	0.890745	−	0.454503i	$-0.150183\pi$
$877$	45.3950	+	78.6264i	0.0517617	+	0.0896538i	−0.838984	+	0.544157i	$0.816850\pi$
$878$		0			0
$879$	−350.857	+	607.702i	−0.399155	+	0.691356i
$880$		0			0
$881$		−	1403.61i		−	1.59320i	−0.604508	−	0.796599i	$-0.706630\pi$
$881$		−	1403.61i		−	1.59320i	0.604508	−	0.796599i	$-0.293370\pi$
$882$		0			0
$883$	−1595.94			−1.80741			−0.903705	−	0.428155i	$-0.859164\pi$
$883$	−1595.94			−1.80741			−0.903705	+	0.428155i	$0.859164\pi$
$884$		0			0
$885$	907.713	+	524.068i	1.02566	+	0.592168i
$886$		0			0
$887$	178.010	−	102.774i	0.200687	−	0.115867i	−0.396289	−	0.918126i	$-0.629702\pi$
$887$	178.010	−	102.774i	0.200687	−	0.115867i	0.596976	+	0.802259i	$0.296369\pi$
$888$		0			0
$889$	−12.5000	−	174.553i	−0.0140607	−	0.196348i
$890$		0			0
$891$	20.6702	+	35.8019i	0.0231989	+	0.0401817i
$892$		0			0
$893$	98.5389	−	170.674i	0.110346	−	0.191125i
$894$		0			0
$895$			1322.07i			1.47717i
$896$		0			0
$897$	−326.241			−0.363703
$898$		0			0
$899$	511.450	+	295.286i	0.568910	+	0.328461i
$900$		0			0
$901$	−620.702	+	358.363i	−0.688904	+	0.397739i
$902$		0			0
$903$	99.4727	−	204.820i	0.110158	−	0.226822i
$904$		0			0
$905$	472.121	+	817.737i	0.521680	+	0.903577i
$906$		0			0
$907$	205.378	−	355.726i	0.226437	−	0.392201i	−0.730313	−	0.683113i	$-0.760626\pi$
$907$	205.378	−	355.726i	0.226437	−	0.392201i	0.956750	+	0.290913i	$0.0939589\pi$
$908$		0			0
$909$			361.446i			0.397630i
$910$		0			0
$911$	−800.218			−0.878395			−0.439198	−	0.898390i	$-0.644737\pi$
$911$	−800.218			−0.878395			−0.439198	+	0.898390i	$0.644737\pi$
$912$		0			0
$913$	399.826	+	230.840i	0.437925	+	0.252836i
$914$		0			0
$915$	1599.16	−	923.277i	1.74772	−	1.00905i
$916$		0			0
$917$	395.702	+	584.537i	0.431518	+	0.637445i
$918$		0			0
$919$	−716.071	−	1240.27i	−0.779185	−	1.34959i	−0.932412	−	0.361397i	$-0.882300\pi$
$919$	−716.071	−	1240.27i	−0.779185	−	1.34959i	0.153227	−	0.988191i	$-0.451033\pi$
$920$		0			0
$921$	21.6099	−	37.4295i	0.0234635	−	0.0406400i
$922$		0			0
$923$			169.209i			0.183325i
$924$		0			0
$925$	1629.88			1.76203
$926$		0			0
$927$	−49.0710	−	28.3312i	−0.0529353	−	0.0305622i
$928$		0			0
$929$	−291.945	+	168.555i	−0.314258	+	0.181437i	−0.648830	−	0.760933i	$-0.724741\pi$
$929$	−291.945	+	168.555i	−0.314258	+	0.181437i	0.334572	+	0.942370i	$0.391408\pi$
$930$		0			0
$931$	−631.605	+	496.883i	−0.678416	+	0.533709i
$932$		0			0
$933$	−313.307	−	542.664i	−0.335806	−	0.581634i
$934$		0			0
$935$	421.582	−	730.201i	0.450890	−	0.780964i
$936$		0			0
$937$		−	53.3634i		−	0.0569513i	−0.999594	−	0.0284756i	$-0.990935\pi$
$937$		−	53.3634i		−	0.0569513i	0.999594	−	0.0284756i	$-0.00906531\pi$
$938$		0			0
$939$	−236.253			−0.251601
$940$		0			0
$941$	−1100.92	−	635.617i	−1.16995	−	0.675470i	−0.216280	−	0.976331i	$-0.569393\pi$
$941$	−1100.92	−	635.617i	−1.16995	−	0.675470i	−0.953668	+	0.300861i	$0.902726\pi$
$942$		0			0
$943$	1012.48	−	584.557i	1.07368	−	0.619891i
$944$		0			0
$945$	−288.560	+	195.341i	−0.305355	+	0.206710i
$946$		0			0
$947$	266.428	+	461.467i	0.281339	+	0.487293i	0.971715	−	0.236157i	$-0.0758881\pi$
$947$	266.428	+	461.467i	0.281339	+	0.487293i	−0.690376	+	0.723451i	$0.742555\pi$
$948$		0			0
$949$	−242.764	+	420.479i	−0.255810	+	0.443076i
$950$		0			0
$951$			941.626i			0.990143i
$952$		0			0
$953$	−1665.54			−1.74768			−0.873839	−	0.486215i	$-0.838377\pi$
$953$	−1665.54			−1.74768			−0.873839	+	0.486215i	$0.838377\pi$
$954$		0			0
$955$	1379.80	+	796.629i	1.44482	+	0.834166i
$956$		0			0
$957$	−72.9893	+	42.1404i	−0.0762688	+	0.0440338i
$958$		0			0
$959$	271.517	+	131.865i	0.283126	+	0.137503i
$960$		0			0
$961$	1073.48	+	1859.33i	1.11705	+	1.93478i
$962$		0			0
$963$	−25.4504	+	44.0814i	−0.0264282	+	0.0457751i
$964$		0			0
$965$			606.497i			0.628495i
$966$		0			0
$967$	−1328.19			−1.37351			−0.686756	−	0.726888i	$-0.740966\pi$
$967$	−1328.19			−1.37351			−0.686756	+	0.726888i	$0.740966\pi$
$968$		0			0
$969$	−471.362	−	272.141i	−0.486442	−	0.280847i
$970$		0			0
$971$	185.186	−	106.917i	0.190717	−	0.110110i	−0.401601	−	0.915815i	$-0.631546\pi$
$971$	185.186	−	106.917i	0.190717	−	0.110110i	0.592318	+	0.805704i	$0.298213\pi$
$972$		0			0
$973$	−823.456	+	58.9689i	−0.846306	+	0.0606053i
$974$		0			0
$975$	−453.884	−	786.151i	−0.465522	−	0.806308i
$976$		0			0
$977$	508.121	−	880.091i	0.520083	−	0.900809i	−0.479645	−	0.877463i	$-0.659235\pi$
$977$	508.121	−	880.091i	0.520083	−	0.900809i	0.999727	−	0.0233467i	$-0.00743216\pi$
$978$		0			0
$979$		−	454.977i		−	0.464736i
$980$		0			0
$981$	−170.340			−0.173640
$982$		0			0
$983$	−360.835	−	208.328i	−0.367075	−	0.211931i	0.305105	−	0.952319i	$-0.401308\pi$
$983$	−360.835	−	208.328i	−0.367075	−	0.211931i	−0.672180	+	0.740388i	$0.734642\pi$
$984$		0			0
$985$	−1529.14	+	882.851i	−1.55243	+	0.896295i
$986$		0			0
$987$	−10.4066	−	145.320i	−0.0105437	−	0.147234i
$988$		0			0
$989$	−225.362	−	390.338i	−0.227868	−	0.394680i
$990$		0			0
$991$	−623.214	+	1079.44i	−0.628874	+	1.08924i	0.358904	+	0.933374i	$0.383150\pi$
$991$	−623.214	+	1079.44i	−0.628874	+	1.08924i	−0.987778	+	0.155867i	$0.950183\pi$
$992$		0			0
$993$		−	242.659i		−	0.244370i
$994$		0			0
$995$	340.132			0.341841
$996$		0			0
$997$	−614.588	−	354.833i	−0.616438	−	0.355901i	0.159043	−	0.987272i	$-0.449159\pi$
$997$	−614.588	−	354.833i	−0.616438	−	0.355901i	−0.775481	+	0.631371i	$0.782492\pi$
$998$		0			0
$999$	−109.830	+	63.4102i	−0.109940	+	0.0634737i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.3.bh.f.241.1		4
3.2	odd	2		1008.3.cg.m.577.2		4
4.3	odd	2		84.3.m.b.73.1	yes	4
7.3	odd	6		2352.3.f.f.97.4		4
7.4	even	3		2352.3.f.f.97.1		4
7.5	odd	6	inner	336.3.bh.f.145.1		4
12.11	even	2		252.3.z.e.73.2		4
20.3	even	4		2100.3.be.d.1249.4		8
20.7	even	4		2100.3.be.d.1249.1		8
20.19	odd	2		2100.3.bd.f.1501.1		4
21.5	even	6		1008.3.cg.m.145.2		4
28.3	even	6		588.3.d.b.97.2		4
28.11	odd	6		588.3.d.b.97.3		4
28.19	even	6		84.3.m.b.61.1	✓	4
28.23	odd	6		588.3.m.d.313.2		4
28.27	even	2		588.3.m.d.325.2		4
84.11	even	6		1764.3.d.f.685.4		4
84.23	even	6		1764.3.z.h.901.1		4
84.47	odd	6		252.3.z.e.145.2		4
84.59	odd	6		1764.3.d.f.685.1		4
84.83	odd	2		1764.3.z.h.325.1		4
140.19	even	6		2100.3.bd.f.901.2		4
140.47	odd	12		2100.3.be.d.649.4		8
140.103	odd	12		2100.3.be.d.649.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.3.m.b.61.1	✓	4	28.19	even	6
84.3.m.b.73.1	yes	4	4.3	odd	2
252.3.z.e.73.2		4	12.11	even	2
252.3.z.e.145.2		4	84.47	odd	6
336.3.bh.f.145.1		4	7.5	odd	6	inner
336.3.bh.f.241.1		4	1.1	even	1	trivial
588.3.d.b.97.2		4	28.3	even	6
588.3.d.b.97.3		4	28.11	odd	6
588.3.m.d.313.2		4	28.23	odd	6
588.3.m.d.325.2		4	28.27	even	2
1008.3.cg.m.145.2		4	21.5	even	6
1008.3.cg.m.577.2		4	3.2	odd	2
1764.3.d.f.685.1		4	84.59	odd	6
1764.3.d.f.685.4		4	84.11	even	6
1764.3.z.h.325.1		4	84.83	odd	2
1764.3.z.h.901.1		4	84.23	even	6
2100.3.bd.f.901.2		4	140.19	even	6
2100.3.bd.f.1501.1		4	20.19	odd	2
2100.3.be.d.649.1		8	140.103	odd	12
2100.3.be.d.649.4		8	140.47	odd	12
2100.3.be.d.1249.1		8	20.7	even	4
2100.3.be.d.1249.4		8	20.3	even	4
2352.3.f.f.97.1		4	7.4	even	3
2352.3.f.f.97.4		4	7.3	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:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	336.bh (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.50000 + 0.866025i) q^{3} +(-8.29669 + 4.79010i) q^{5} +(-0.500000 - 6.98212i) q^{7} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(1.50000 + 0.866025i) q^{3} +(-8.29669 + 4.79010i) q^{5} +(-0.500000 - 6.98212i) q^{7} +(1.50000 + 2.59808i) q^{9} +(2.29669 - 3.97799i) q^{11} -7.84815i q^{13} -16.5934 q^{15} +(-16.5934 - 9.58020i) q^{17} +(14.2033 - 8.20028i) q^{19} +(5.29669 - 10.9062i) q^{21} +(-12.0000 - 20.7846i) q^{23} +(33.3901 - 57.8333i) q^{25} +5.19615i q^{27} -10.5934 q^{29} +(-48.2802 - 27.8746i) q^{31} +(6.89008 - 3.97799i) q^{33} +(37.5934 + 55.5335i) q^{35} +(12.2033 + 21.1367i) q^{37} +(6.79669 - 11.7722i) q^{39} +48.7131i q^{41} +18.7802 q^{43} +(-24.8901 - 14.3703i) q^{45} +(10.4066 - 6.00826i) q^{47} +(-48.5000 + 6.98212i) q^{49} +(-16.5934 - 28.7406i) q^{51} +(18.7033 - 32.3951i) q^{53} +44.0055i q^{55} +28.4066 q^{57} +(-54.7033 - 31.5830i) q^{59} +(-96.3735 + 55.6413i) q^{61} +(17.3901 - 11.7722i) q^{63} +(37.5934 + 65.1137i) q^{65} +(31.9835 - 55.3970i) q^{67} -41.5692i q^{69} -21.5603 q^{71} +(-53.5769 - 30.9326i) q^{73} +(100.170 - 57.8333i) q^{75} +(-28.9231 - 14.0468i) q^{77} +(-1.90661 - 3.30235i) q^{79} +(-4.50000 + 7.79423i) q^{81} +100.510i q^{83} +183.560 q^{85} +(-15.8901 - 9.17414i) q^{87} +(85.7802 - 49.5252i) q^{89} +(-54.7967 + 3.92407i) q^{91} +(-48.2802 - 83.6237i) q^{93} +(-78.5603 + 136.070i) q^{95} -63.5973i q^{97} +13.7802 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 6 q^{3} - 9 q^{5} - 2 q^{7} + 6 q^{9}+O(q^{10}) \) 4 * q + 6 * q^3 - 9 * q^5 - 2 * q^7 + 6 * q^9	\( 4 q + 6 q^{3} - 9 q^{5} - 2 q^{7} + 6 q^{9} - 15 q^{11} - 18 q^{15} - 18 q^{17} + 81 q^{19} - 3 q^{21} - 48 q^{23} + 61 q^{25} + 6 q^{29} - 48 q^{31} - 45 q^{33} + 102 q^{35} + 73 q^{37} + 3 q^{39} - 70 q^{43} - 27 q^{45} + 90 q^{47} - 194 q^{49} - 18 q^{51} + 99 q^{53} + 162 q^{57} - 243 q^{59} - 192 q^{61} - 3 q^{63} + 102 q^{65} + 7 q^{67} + 204 q^{71} - 45 q^{73} + 183 q^{75} - 285 q^{77} - 56 q^{79} - 18 q^{81} + 444 q^{85} + 9 q^{87} + 198 q^{89} - 195 q^{91} - 48 q^{93} - 24 q^{95} - 90 q^{99}+O(q^{100}) \) 4 * q + 6 * q^3 - 9 * q^5 - 2 * q^7 + 6 * q^9 - 15 * q^11 - 18 * q^15 - 18 * q^17 + 81 * q^19 - 3 * q^21 - 48 * q^23 + 61 * q^25 + 6 * q^29 - 48 * q^31 - 45 * q^33 + 102 * q^35 + 73 * q^37 + 3 * q^39 - 70 * q^43 - 27 * q^45 + 90 * q^47 - 194 * q^49 - 18 * q^51 + 99 * q^53 + 162 * q^57 - 243 * q^59 - 192 * q^61 - 3 * q^63 + 102 * q^65 + 7 * q^67 + 204 * q^71 - 45 * q^73 + 183 * q^75 - 285 * q^77 - 56 * q^79 - 18 * q^81 + 444 * q^85 + 9 * q^87 + 198 * q^89 - 195 * q^91 - 48 * q^93 - 24 * q^95 - 90 * q^99

Introduction

L-functions

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