LMFDB - Embedded newform 336.4.bc.f.17.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,4,Mod(17,336)]

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, 3, 1]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("336.17");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	336.bc (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:	$19.8246417619$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.18
Character	$\chi$	$=$	336.17
Dual form			336.4.bc.f.257.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.06041 + 4.19928i) q^{3} +(0.746155 + 1.29238i) q^{5} +(-15.9029 - 9.49205i) q^{7} +(-8.26784 + 25.7030i) q^{9} +O(q^{10})$	\(q+(3.06041 + 4.19928i) q^{3} +(0.746155 + 1.29238i) q^{5} +(-15.9029 - 9.49205i) q^{7} +(-8.26784 + 25.7030i) q^{9} +(-38.1817 - 22.0442i) q^{11} -63.3150i q^{13} +(-3.14352 + 7.08851i) q^{15} +(55.7620 - 96.5827i) q^{17} +(109.671 - 63.3189i) q^{19} +(-8.80943 - 95.8300i) q^{21} +(-176.818 + 102.086i) q^{23} +(61.3865 - 106.325i) q^{25} +(-133.237 + 43.9426i) q^{27} +115.298i q^{29} +(74.9257 + 43.2584i) q^{31} +(-24.2817 - 227.800i) q^{33} +(0.401329 - 27.6351i) q^{35} +(-53.8719 - 93.3089i) q^{37} +(265.877 - 193.770i) q^{39} +336.851 q^{41} -191.947 q^{43} +(-39.3871 + 8.49322i) q^{45} +(-158.757 - 274.975i) q^{47} +(162.802 + 301.902i) q^{49} +(576.232 - 61.4220i) q^{51} +(-321.107 - 185.391i) q^{53} -65.7936i q^{55} +(601.532 + 266.759i) q^{57} +(-187.872 + 325.404i) q^{59} +(38.7999 - 22.4012i) q^{61} +(375.456 - 330.272i) q^{63} +(81.8269 - 47.2428i) q^{65} +(207.597 - 359.569i) q^{67} +(-969.823 - 430.084i) q^{69} -676.127i q^{71} +(-587.905 - 339.427i) q^{73} +(634.354 - 67.6173i) q^{75} +(397.953 + 712.988i) q^{77} +(-289.106 - 500.746i) q^{79} +(-592.286 - 425.016i) q^{81} -253.616 q^{83} +166.428 q^{85} +(-484.170 + 352.860i) q^{87} +(-350.805 - 607.613i) q^{89} +(-600.989 + 1006.89i) q^{91} +(47.6492 + 447.022i) q^{93} +(163.664 + 94.4914i) q^{95} +142.233i q^{97} +(882.281 - 799.125i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 12 q^{7} + 14 q^{9}+O(q^{10}) $ 48 * q - 12 * q^7 + 14 * q^9	$ 48 q - 12 q^{7} + 14 q^{9} + 88 q^{15} + 270 q^{19} + 50 q^{21} - 438 q^{25} - 216 q^{31} - 372 q^{33} + 66 q^{37} - 242 q^{39} - 900 q^{43} - 294 q^{45} + 60 q^{49} + 138 q^{51} + 1384 q^{57} + 108 q^{61} - 1096 q^{63} - 6 q^{67} - 1206 q^{73} + 594 q^{75} + 588 q^{79} - 54 q^{81} - 240 q^{85} + 3522 q^{87} - 234 q^{91} - 608 q^{93} - 1988 q^{99}+O(q^{100}) $ 48 * q - 12 * q^7 + 14 * q^9 + 88 * q^15 + 270 * q^19 + 50 * q^21 - 438 * q^25 - 216 * q^31 - 372 * q^33 + 66 * q^37 - 242 * q^39 - 900 * q^43 - 294 * q^45 + 60 * q^49 + 138 * q^51 + 1384 * q^57 + 108 * q^61 - 1096 * q^63 - 6 * q^67 - 1206 * q^73 + 594 * q^75 + 588 * q^79 - 54 * q^81 - 240 * q^85 + 3522 * q^87 - 234 * q^91 - 608 * q^93 - 1988 * 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
$3$	3.06041	+	4.19928i	0.588975	+	0.808151i
$3$	3.06041	+	4.19928i	0.588975	+	0.808151i
$4$		0			0
$5$	0.746155	+	1.29238i	0.0667381	+	0.115594i	0.897464	−	0.441088i	$-0.145407\pi$
$5$	0.746155	+	1.29238i	0.0667381	+	0.115594i	−0.830726	+	0.556682i	$0.812074\pi$
$6$		0			0
$7$	−15.9029	−	9.49205i	−0.858674	−	0.512523i
$7$	−15.9029	−	9.49205i	−0.858674	−	0.512523i
$8$		0			0
$9$	−8.26784	+	25.7030i	−0.306216	+	0.951962i
$10$		0			0
$11$	−38.1817	−	22.0442i	−1.04656	−	0.604234i	−0.124879	−	0.992172i	$-0.539854\pi$
$11$	−38.1817	−	22.0442i	−1.04656	−	0.604234i	−0.921686	+	0.387938i	$0.873188\pi$
$12$		0			0
$13$		−	63.3150i		−	1.35080i	−0.737451	−	0.675401i	$-0.763971\pi$
$13$		−	63.3150i		−	1.35080i	0.737451	−	0.675401i	$-0.236029\pi$
$14$		0			0
$15$	−3.14352	+	7.08851i	−0.0541102	+	0.122016i
$16$		0			0
$17$	55.7620	−	96.5827i	0.795546	−	1.37793i	−0.126946	−	0.991910i	$-0.540517\pi$
$17$	55.7620	−	96.5827i	0.795546	−	1.37793i	0.922492	−	0.386016i	$-0.126149\pi$
$18$		0			0
$19$	109.671	−	63.3189i	1.32423	−	0.764544i	0.339829	−	0.940487i	$-0.389631\pi$
$19$	109.671	−	63.3189i	1.32423	−	0.764544i	0.984400	+	0.175943i	$0.0562974\pi$
$20$		0			0
$21$	−8.80943	−	95.8300i	−0.0915417	−	0.995801i
$22$		0			0
$23$	−176.818	+	102.086i	−1.60301	+	0.925496i	−0.612124	+	0.790762i	$0.709685\pi$
$23$	−176.818	+	102.086i	−1.60301	+	0.925496i	−0.990882	+	0.134734i	$0.956982\pi$
$24$		0			0
$25$	61.3865	−	106.325i	0.491092	−	0.850596i
$26$		0			0
$27$	−133.237	+	43.9426i	−0.949683	+	0.313213i
$28$		0			0
$29$			115.298i			0.738289i	0.929372	+	0.369145i	$0.120349\pi$
$29$			115.298i			0.738289i	−0.929372	+	0.369145i	$0.879651\pi$
$30$		0			0
$31$	74.9257	+	43.2584i	0.434099	+	0.250627i	0.701091	−	0.713072i	$-0.252697\pi$
$31$	74.9257	+	43.2584i	0.434099	+	0.250627i	−0.266993	+	0.963699i	$0.586030\pi$
$32$		0			0
$33$	−24.2817	−	227.800i	−0.128088	−	1.20166i
$34$		0			0
$35$	0.401329	−	27.6351i	0.00193820	−	0.133462i
$36$		0			0
$37$	−53.8719	−	93.3089i	−0.239365	−	0.414592i	0.721168	−	0.692761i	$-0.243606\pi$
$37$	−53.8719	−	93.3089i	−0.239365	−	0.414592i	−0.960532	+	0.278169i	$0.910272\pi$
$38$		0			0
$39$	265.877	−	193.770i	1.09165	−	0.795589i
$40$		0			0
$41$	336.851			1.28310			0.641551	−	0.767080i	$-0.278291\pi$
$41$	336.851			1.28310			0.641551	+	0.767080i	$0.278291\pi$
$42$		0			0
$43$	−191.947			−0.680734			−0.340367	−	0.940293i	$-0.610551\pi$
$43$	−191.947			−0.680734			−0.340367	+	0.940293i	$0.610551\pi$
$44$		0			0
$45$	−39.3871	+	8.49322i	−0.130477	+	0.0281354i
$46$		0			0
$47$	−158.757	−	274.975i	−0.492703	−	0.853386i	0.507262	−	0.861792i	$-0.330658\pi$
$47$	−158.757	−	274.975i	−0.492703	−	0.853386i	−0.999965	+	0.00840560i	$0.997324\pi$
$48$		0			0
$49$	162.802	+	301.902i	0.474641	+	0.880180i
$50$		0			0
$51$	576.232	−	61.4220i	1.58213	−	0.168643i
$52$		0			0
$53$	−321.107	−	185.391i	−0.832215	−	0.480480i	0.0223953	−	0.999749i	$-0.492871\pi$
$53$	−321.107	−	185.391i	−0.832215	−	0.480480i	−0.854611	+	0.519270i	$0.826204\pi$
$54$		0			0
$55$		−	65.7936i		−	0.161302i
$56$		0			0
$57$	601.532	+	266.759i	1.39781	+	0.619880i
$58$		0			0
$59$	−187.872	+	325.404i	−0.414557	+	0.718033i	−0.995382	−	0.0959950i	$-0.969397\pi$
$59$	−187.872	+	325.404i	−0.414557	+	0.718033i	0.580825	+	0.814028i	$0.302730\pi$
$60$		0			0
$61$	38.7999	−	22.4012i	0.0814397	−	0.0470192i	−0.458727	−	0.888577i	$-0.651694\pi$
$61$	38.7999	−	22.4012i	0.0814397	−	0.0470192i	0.540167	+	0.841558i	$0.318361\pi$
$62$		0			0
$63$	375.456	−	330.272i	0.750842	−	0.660482i
$64$		0			0
$65$	81.8269	−	47.2428i	0.156144	−	0.0901500i
$66$		0			0
$67$	207.597	−	359.569i	0.378538	−	0.655647i	−0.612312	−	0.790616i	$-0.709760\pi$
$67$	207.597	−	359.569i	0.378538	−	0.655647i	0.990850	+	0.134969i	$0.0430936\pi$
$68$		0			0
$69$	−969.823	−	430.084i	−1.69207	−	0.750377i
$70$		0			0
$71$		−	676.127i		−	1.13016i	−0.825035	−	0.565081i	$-0.808845\pi$
$71$		−	676.127i		−	1.13016i	0.825035	−	0.565081i	$-0.191155\pi$
$72$		0			0
$73$	−587.905	−	339.427i	−0.942591	−	0.544205i	−0.0518191	−	0.998656i	$-0.516502\pi$
$73$	−587.905	−	339.427i	−0.942591	−	0.544205i	−0.890771	+	0.454452i	$0.849835\pi$
$74$		0			0
$75$	634.354	−	67.6173i	0.976651	−	0.104104i
$76$		0			0
$77$	397.953	+	712.988i	0.588973	+	1.05523i
$78$		0			0
$79$	−289.106	−	500.746i	−0.411733	−	0.713143i	0.583346	−	0.812224i	$-0.301743\pi$
$79$	−289.106	−	500.746i	−0.411733	−	0.713143i	−0.995079	+	0.0990805i	$0.968410\pi$
$80$		0			0
$81$	−592.286	−	425.016i	−0.812463	−	0.583013i
$82$		0			0
$83$	−253.616			−0.335397			−0.167698	−	0.985838i	$-0.553633\pi$
$83$	−253.616			−0.335397			−0.167698	+	0.985838i	$0.553633\pi$
$84$		0			0
$85$	166.428			0.212373
$86$		0			0
$87$	−484.170	+	352.860i	−0.596649	+	0.434834i
$88$		0			0
$89$	−350.805	−	607.613i	−0.417812	−	0.723672i	0.577907	−	0.816103i	$-0.303870\pi$
$89$	−350.805	−	607.613i	−0.417812	−	0.723672i	−0.995719	+	0.0924308i	$0.970536\pi$
$90$		0			0
$91$	−600.989	+	1006.89i	−0.692317	+	1.15990i
$92$		0			0
$93$	47.6492	+	447.022i	0.0531289	+	0.498430i
$94$		0			0
$95$	163.664	+	94.4914i	0.176753	+	0.102049i
$96$		0			0
$97$			142.233i			0.148883i	0.997225	+	0.0744413i	$0.0237173\pi$
$97$			142.233i			0.148883i	−0.997225	+	0.0744413i	$0.976283\pi$
$98$		0			0
$99$	882.281	−	799.125i	0.895683	−	0.811263i
$100$		0			0
$101$	210.040	−	363.799i	0.206928	−	0.358410i	−0.743817	−	0.668383i	$-0.766987\pi$
$101$	210.040	−	363.799i	0.206928	−	0.358410i	0.950745	+	0.309973i	$0.100320\pi$
$102$		0			0
$103$	1.30193	−	0.751668i	0.00124546	−	0.000719068i	−0.499377	−	0.866385i	$-0.666438\pi$
$103$	1.30193	−	0.751668i	0.00124546	−	0.000719068i	0.500623	+	0.865666i	$0.333104\pi$
$104$		0			0
$105$	117.275	−	82.8892i	0.108999	−	0.0770396i
$106$		0			0
$107$	934.464	−	539.513i	0.844280	−	0.487446i	−0.0144365	−	0.999896i	$-0.504595\pi$
$107$	934.464	−	539.513i	0.844280	−	0.487446i	0.858717	+	0.512450i	$0.171262\pi$
$108$		0			0
$109$	−506.120	+	876.625i	−0.444747	+	0.770325i	−0.998035	−	0.0626655i	$-0.980040\pi$
$109$	−506.120	+	876.625i	−0.444747	+	0.770325i	0.553287	+	0.832991i	$0.313373\pi$
$110$		0			0
$111$	226.960	−	511.786i	0.194073	−	0.437627i
$112$		0			0
$113$			1208.55i			1.00611i	0.864253	+	0.503057i	$0.167792\pi$
$113$			1208.55i			1.00611i	−0.864253	+	0.503057i	$0.832208\pi$
$114$		0			0
$115$	−263.867	−	152.344i	−0.213963	−	0.123532i
$116$		0			0
$117$	1627.38	+	523.478i	1.28591	+	0.413637i
$118$		0			0
$119$	−1803.54	+	1006.64i	−1.38933	+	0.775453i
$120$		0			0
$121$	306.393	+	530.689i	0.230198	+	0.398715i
$122$		0			0
$123$	1030.90	+	1414.53i	0.755716	+	1.03694i
$124$		0			0
$125$	369.754			0.264575
$126$		0			0
$127$	−1688.38			−1.17968			−0.589841	−	0.807520i	$-0.700809\pi$
$127$	−1688.38			−1.17968			−0.589841	+	0.807520i	$0.700809\pi$
$128$		0			0
$129$	−587.434	−	806.037i	−0.400936	−	0.550136i
$130$		0			0
$131$	−588.169	−	1018.74i	−0.392279	−	0.679448i	0.600471	−	0.799647i	$-0.294980\pi$
$131$	−588.169	−	1018.74i	−0.392279	−	0.679448i	−0.992750	+	0.120199i	$0.961647\pi$
$132$		0			0
$133$	−2345.12	−	34.0569i	−1.52893	−	0.0222038i
$134$		0			0
$135$	−156.206	−	139.404i	−0.0995855	−	0.0888742i
$136$		0			0
$137$	−239.784	−	138.439i	−0.149534	−	0.0863333i	0.423366	−	0.905959i	$-0.360848\pi$
$137$	−239.784	−	138.439i	−0.149534	−	0.0863333i	−0.572900	+	0.819625i	$0.694182\pi$
$138$		0			0
$139$			2366.60i			1.44412i	0.691830	+	0.722060i	$0.256805\pi$
$139$			2366.60i			1.44412i	−0.691830	+	0.722060i	$0.743195\pi$
$140$		0			0
$141$	668.834	−	1508.20i	0.399475	−	0.900802i
$142$		0			0
$143$	−1395.73	+	2417.47i	−0.816201	+	1.41370i
$144$		0			0
$145$	−149.009	+	86.0305i	−0.0853417	+	0.0492721i
$146$		0			0
$147$	−769.529	+	1607.59i	−0.431766	+	0.901985i
$148$		0			0
$149$	1309.54	−	756.063i	0.720011	−	0.415699i	−0.0947455	−	0.995502i	$-0.530204\pi$
$149$	1309.54	−	756.063i	0.720011	−	0.415699i	0.814757	+	0.579803i	$0.196870\pi$
$150$		0			0
$151$	184.474	−	319.518i	0.0994190	−	0.172199i	−0.812025	−	0.583622i	$-0.801635\pi$
$151$	184.474	−	319.518i	0.0994190	−	0.172199i	0.911444	+	0.411423i	$0.134968\pi$
$152$		0			0
$153$	2021.43	+	2231.78i	1.06812	+	1.17927i
$154$		0			0
$155$			129.110i			0.0669055i
$156$		0			0
$157$	−1259.50	−	727.170i	−0.640246	−	0.369646i	0.144463	−	0.989510i	$-0.453855\pi$
$157$	−1259.50	−	727.170i	−0.640246	−	0.369646i	−0.784709	+	0.619864i	$0.787188\pi$
$158$		0			0
$159$	−204.208	−	1915.79i	−0.101854	−	0.955546i
$160$		0			0
$161$	3780.92	+	54.9083i	1.85080	+	0.0268781i
$162$		0			0
$163$	1032.61	+	1788.54i	0.496199	+	0.859442i	0.999990	−	0.00438341i	$-0.00139529\pi$
$163$	1032.61	+	1788.54i	0.496199	+	0.859442i	−0.503791	+	0.863825i	$0.668062\pi$
$164$		0			0
$165$	276.285	−	201.355i	0.130356	−	0.0950028i
$166$		0			0
$167$	2908.44			1.34768			0.673838	−	0.738879i	$-0.264644\pi$
$167$	2908.44			1.34768			0.673838	+	0.738879i	$0.264644\pi$
$168$		0			0
$169$	−1811.79			−0.824665
$170$		0			0
$171$	720.737	+	3342.39i	0.322316	+	1.49473i
$172$		0			0
$173$	−394.973	−	684.113i	−0.173579	−	0.300648i	0.766089	−	0.642734i	$-0.222200\pi$
$173$	−394.973	−	684.113i	−0.173579	−	0.300648i	−0.939669	+	0.342086i	$0.888867\pi$
$174$		0			0
$175$	−1985.46	+	1108.18i	−0.857638	+	0.478689i
$176$		0			0
$177$	−1941.43	+	206.941i	−0.824443	+	0.0878794i
$178$		0			0
$179$	2681.03	+	1547.90i	1.11950	+	0.646341i	0.941272	−	0.337649i	$-0.109632\pi$
$179$	2681.03	+	1547.90i	1.11950	+	0.646341i	0.178224	+	0.983990i	$0.442965\pi$
$180$		0			0
$181$			4803.16i			1.97247i	0.165363	+	0.986233i	$0.447120\pi$
$181$			4803.16i			1.97247i	−0.165363	+	0.986233i	$0.552880\pi$
$182$		0			0
$183$	212.812	+	94.3750i	0.0859646	+	0.0381224i
$184$		0			0
$185$	80.3936	−	139.246i	0.0319495	−	0.0553381i
$186$		0			0
$187$	−4258.18	+	2458.46i	−1.66518	+	0.961392i
$188$		0			0
$189$	2535.95	+	565.879i	0.975996	+	0.217786i
$190$		0			0
$191$	372.573	−	215.105i	0.141143	−	0.0814892i	−0.427765	−	0.903890i	$-0.640699\pi$
$191$	372.573	−	215.105i	0.141143	−	0.0814892i	0.568909	+	0.822401i	$0.307366\pi$
$192$		0			0
$193$	−130.435	+	225.919i	−0.0486471	+	0.0842592i	−0.889324	−	0.457278i	$-0.848824\pi$
$193$	−130.435	+	225.919i	−0.0486471	+	0.0842592i	0.840677	+	0.541538i	$0.182158\pi$
$194$		0			0
$195$	448.809	+	199.032i	0.164820	+	0.0730921i
$196$		0			0
$197$			2576.68i			0.931881i	0.884816	+	0.465941i	$0.154284\pi$
$197$			2576.68i			0.931881i	−0.884816	+	0.465941i	$0.845716\pi$
$198$		0			0
$199$	−2877.89	−	1661.55i	−1.02517	−	0.591880i	−0.109570	−	0.993979i	$-0.534947\pi$
$199$	−2877.89	−	1661.55i	−1.02517	−	0.591880i	−0.915596	+	0.402100i	$0.868281\pi$
$200$		0			0
$201$	2145.26	−	228.669i	0.752812	−	0.0802440i
$202$		0			0
$203$	1094.42	−	1833.58i	0.378390	−	0.633950i
$204$		0			0
$205$	251.343	+	435.338i	0.0856319	+	0.148319i
$206$		0			0
$207$	−1162.01	−	5388.78i	−0.390170	−	1.80940i
$208$		0			0
$209$	−5583.25			−1.84786
$210$		0			0
$211$	5109.27			1.66700			0.833499	−	0.552521i	$-0.186334\pi$
$211$	5109.27			1.66700			0.833499	+	0.552521i	$0.186334\pi$
$212$		0			0
$213$	2839.25	−	2069.22i	0.913342	−	0.665638i
$214$		0			0
$215$	−143.222	−	248.068i	−0.0454309	−	0.0786887i
$216$		0			0
$217$	−780.922	−	1399.13i	−0.244297	−	0.437692i
$218$		0			0
$219$	−373.880	−	3507.56i	−0.115363	−	1.08228i
$220$		0			0
$221$	−6115.13	−	3530.57i	−1.86131	−	1.07462i
$222$		0			0
$223$		−	785.148i		−	0.235773i	−0.993027	−	0.117887i	$-0.962388\pi$
$223$		−	785.148i		−	0.235773i	0.993027	−	0.117887i	$-0.0376119\pi$
$224$		0			0
$225$	2225.32	+	2456.89i	0.659355	+	0.727967i
$226$		0			0
$227$	1257.04	−	2177.25i	0.367544	−	0.636605i	−0.621637	−	0.783306i	$-0.713532\pi$
$227$	1257.04	−	2177.25i	0.367544	−	0.636605i	0.989181	+	0.146701i	$0.0468654\pi$
$228$		0			0
$229$	−1051.71	+	607.206i	−0.303489	+	0.175220i	−0.644009	−	0.765018i	$-0.722730\pi$
$229$	−1051.71	+	607.206i	−0.303489	+	0.175220i	0.340520	+	0.940237i	$0.389397\pi$
$230$		0			0
$231$	−1776.14	+	3853.15i	−0.505893	+	1.09748i
$232$		0			0
$233$	−4898.18	+	2827.97i	−1.37721	+	0.795134i	−0.991823	−	0.127620i	$-0.959266\pi$
$233$	−4898.18	+	2827.97i	−1.37721	+	0.795134i	−0.385390	+	0.922754i	$0.625933\pi$
$234$		0			0
$235$	236.914	−	410.347i	0.0657641	−	0.113907i
$236$		0			0
$237$	1217.99	−	2746.52i	0.333827	−	0.752767i
$238$		0			0
$239$		−	2393.24i		−	0.647722i	−0.946105	−	0.323861i	$-0.895019\pi$
$239$		−	2393.24i		−	0.647722i	0.946105	−	0.323861i	$-0.104981\pi$
$240$		0			0
$241$	−2367.63	−	1366.95i	−0.632832	−	0.365366i	0.149016	−	0.988835i	$-0.452389\pi$
$241$	−2367.63	−	1366.95i	−0.632832	−	0.365366i	−0.781848	+	0.623469i	$0.785723\pi$
$242$		0			0
$243$	−27.8740	−	3787.89i	−0.00735851	−	0.999973i
$244$		0			0
$245$	−268.696	+	435.667i	−0.0700667	+	0.113607i
$246$		0			0
$247$	−4009.03	−	6943.85i	−1.03275	−	1.78877i
$248$		0			0
$249$	−776.166	−	1065.00i	−0.197540	−	0.271051i
$250$		0			0
$251$	2343.60			0.589350			0.294675	−	0.955598i	$-0.404789\pi$
$251$	2343.60			0.589350			0.294675	+	0.955598i	$0.404789\pi$
$252$		0			0
$253$	9001.62			2.23687
$254$		0			0
$255$	509.339	+	698.879i	0.125082	+	0.171629i
$256$		0			0
$257$	870.265	+	1507.34i	0.211228	+	0.365858i	0.952099	−	0.305789i	$-0.0989203\pi$
$257$	870.265	+	1507.34i	0.211228	+	0.365858i	−0.740871	+	0.671647i	$0.765587\pi$
$258$		0			0
$259$	−28.9757	+	1995.23i	−0.00695160	+	0.478679i
$260$		0			0
$261$	−2963.51	−	953.270i	−0.702823	−	0.226076i
$262$		0			0
$263$	3836.33	+	2214.90i	0.899460	+	0.519304i	0.877025	−	0.480445i	$-0.159525\pi$
$263$	3836.33	+	2214.90i	0.899460	+	0.519304i	0.0224353	+	0.999748i	$0.492858\pi$
$264$		0			0
$265$		−	553.322i		−	0.128265i
$266$		0			0
$267$	1477.93	−	3332.67i	0.338755	−	0.763880i
$268$		0			0
$269$	−474.036	+	821.055i	−0.107444	+	0.186099i	−0.914734	−	0.404056i	$-0.867600\pi$
$269$	−474.036	+	821.055i	−0.107444	+	0.186099i	0.807290	+	0.590155i	$0.200933\pi$
$270$		0			0
$271$	6468.41	−	3734.54i	1.44992	−	0.837111i	0.451443	−	0.892300i	$-0.350909\pi$
$271$	6468.41	−	3734.54i	1.44992	−	0.837111i	0.998476	+	0.0551885i	$0.0175760\pi$
$272$		0			0
$273$	−6067.48	+	557.769i	−1.34513	+	0.123655i
$274$		0			0
$275$	−4687.68	+	2706.43i	−1.02792	+	0.593469i
$276$		0			0
$277$	521.239	−	902.812i	0.113062	−	0.195829i	−0.803941	−	0.594709i	$-0.797267\pi$
$277$	521.239	−	902.812i	0.113062	−	0.195829i	0.917003	+	0.398879i	$0.130601\pi$
$278$		0			0
$279$	−1731.34	+	1568.16i	−0.371515	+	0.336499i
$280$		0			0
$281$		−	6820.49i		−	1.44796i	−0.689821	−	0.723980i	$-0.742311\pi$
$281$		−	6820.49i		−	1.44796i	0.689821	−	0.723980i	$-0.257689\pi$
$282$		0			0
$283$	3001.12	+	1732.70i	0.630381	+	0.363951i	0.780900	−	0.624656i	$-0.214761\pi$
$283$	3001.12	+	1732.70i	0.630381	+	0.363951i	−0.150518	+	0.988607i	$0.548094\pi$
$284$		0			0
$285$	104.082	+	976.451i	0.0216327	+	0.202947i
$286$		0			0
$287$	−5356.89	−	3197.40i	−1.10177	−	0.657619i
$288$		0			0
$289$	−3762.31	−	6516.51i	−0.765787	−	1.32638i
$290$		0			0
$291$	−597.277	+	435.292i	−0.120320	+	0.0876881i
$292$		0			0
$293$	4320.43			0.861441			0.430720	−	0.902485i	$-0.358260\pi$
$293$	4320.43			0.861441			0.430720	+	0.902485i	$0.358260\pi$
$294$		0			0
$295$	−560.726			−0.110667
$296$		0			0
$297$	6055.88	+	1259.30i	1.18316	+	0.246033i
$298$		0			0
$299$	6463.58	+	11195.2i	1.25016	+	2.16534i
$300$		0			0
$301$	3052.50	+	1821.97i	0.584529	+	0.348892i
$302$		0			0
$303$	2170.50	−	231.359i	0.411525	−	0.0438654i
$304$		0			0
$305$	57.9015	+	33.4295i	0.0108703	+	0.00627595i
$306$		0			0
$307$			3960.06i			0.736197i	0.929787	+	0.368099i	$0.119991\pi$
$307$			3960.06i			0.736197i	−0.929787	+	0.368099i	$0.880009\pi$
$308$		0			0
$309$	7.14088	+	3.16674i	0.00131466	+	0.000583009i
$310$		0			0
$311$	575.194	−	996.265i	0.104875	−	0.181650i	−0.808812	−	0.588067i	$-0.799889\pi$
$311$	575.194	−	996.265i	0.104875	−	0.181650i	0.913687	+	0.406418i	$0.133222\pi$
$312$		0			0
$313$	3560.30	−	2055.54i	0.642940	−	0.371202i	−0.142806	−	0.989751i	$-0.545613\pi$
$313$	3560.30	−	2055.54i	0.642940	−	0.371202i	0.785746	+	0.618549i	$0.212279\pi$
$314$		0			0
$315$	706.985	+	238.798i	0.126457	+	0.0427134i
$316$		0			0
$317$	984.517	−	568.411i	0.174435	−	0.100710i	−0.410240	−	0.911977i	$-0.634555\pi$
$317$	984.517	−	568.411i	0.174435	−	0.100710i	0.584676	+	0.811267i	$0.301222\pi$
$318$		0			0
$319$	2541.66	−	4402.29i	0.446100	−	0.772667i
$320$		0			0
$321$	5125.40	+	2272.94i	0.891190	+	0.395213i
$322$		0			0
$323$		−	14123.2i		−	2.43292i
$324$		0			0
$325$	−6731.94	−	3886.69i	−1.14899	−	0.663368i
$326$		0			0
$327$	−5230.12	+	557.491i	−0.884484	+	0.0942793i
$328$		0			0
$329$	−85.3893	+	5879.81i	−0.0143090	+	0.985302i
$330$		0			0
$331$	−1194.37	−	2068.70i	−0.198333	−	0.343523i	0.749655	−	0.661829i	$-0.230219\pi$
$331$	−1194.37	−	2068.70i	−0.198333	−	0.343523i	−0.947988	+	0.318306i	$0.896886\pi$
$332$		0			0
$333$	2843.72	−	613.206i	0.467973	−	0.100911i
$334$		0			0
$335$	619.599			0.101052
$336$		0			0
$337$	8103.14			1.30981			0.654906	−	0.755711i	$-0.272708\pi$
$337$	8103.14			1.30981			0.654906	+	0.755711i	$0.272708\pi$
$338$		0			0
$339$	−5075.04	+	3698.66i	−0.813093	+	0.592577i
$340$		0			0
$341$	−1907.19	−	3303.36i	−0.302875	−	0.524595i
$342$		0			0
$343$	276.653	−	6346.42i	0.0435506	−	0.999051i
$344$		0			0
$345$	−167.807	−	1574.29i	−0.0261867	−	0.245672i
$346$		0			0
$347$	−7370.32	−	4255.26i	−1.14023	−	0.658311i	−0.193742	−	0.981053i	$-0.562062\pi$
$347$	−7370.32	−	4255.26i	−1.14023	−	0.658311i	−0.946487	+	0.322741i	$0.895396\pi$
$348$		0			0
$349$			9040.47i			1.38661i	0.720646	+	0.693303i	$0.243845\pi$
$349$			9040.47i			1.38661i	−0.720646	+	0.693303i	$0.756155\pi$
$350$		0			0
$351$	2782.22	+	8435.89i	0.423089	+	1.28283i
$352$		0			0
$353$	1962.77	−	3399.62i	0.295943	−	0.512588i	−0.679261	−	0.733897i	$-0.737699\pi$
$353$	1962.77	−	3399.62i	0.295943	−	0.512588i	0.975204	+	0.221309i	$0.0710328\pi$
$354$		0			0
$355$	873.812	−	504.496i	0.130640	−	0.0754249i
$356$		0			0
$357$	−9746.75	−	4492.84i	−1.44497	−	0.666068i
$358$		0			0
$359$	−9916.87	+	5725.51i	−1.45792	+	0.841729i	−0.998909	−	0.0467024i	$-0.985129\pi$
$359$	−9916.87	+	5725.51i	−1.45792	+	0.841729i	−0.459009	+	0.888432i	$0.651795\pi$
$360$		0			0
$361$	4589.05	−	7948.48i	0.669056	−	1.15884i
$362$		0			0
$363$	−1290.82	+	2910.75i	−0.186641	+	0.420868i
$364$		0			0
$365$		−	1013.06i		−	0.145277i
$366$		0			0
$367$	1081.89	+	624.628i	0.153880	+	0.0888428i	0.574963	−	0.818179i	$-0.305016\pi$
$367$	1081.89	+	624.628i	0.153880	+	0.0888428i	−0.421083	+	0.907022i	$0.638350\pi$
$368$		0			0
$369$	−2785.03	+	8658.06i	−0.392907	+	1.22147i
$370$		0			0
$371$	3346.77	+	5996.21i	0.468344	+	0.839104i
$372$		0			0
$373$	−2714.04	−	4700.85i	−0.376749	−	0.652549i	0.613838	−	0.789432i	$-0.289625\pi$
$373$	−2714.04	−	4700.85i	−0.376749	−	0.652549i	−0.990587	+	0.136883i	$0.956291\pi$
$374$		0			0
$375$	1131.60	+	1552.70i	0.155828	+	0.213816i
$376$		0			0
$377$	7300.12			0.997283
$378$		0			0
$379$	7864.00			1.06582			0.532911	−	0.846171i	$-0.321098\pi$
$379$	7864.00			1.06582			0.532911	+	0.846171i	$0.321098\pi$
$380$		0			0
$381$	−5167.13	−	7089.97i	−0.694803	−	0.953361i
$382$		0			0
$383$	−1383.48	−	2396.26i	−0.184576	−	0.319694i	0.758858	−	0.651256i	$-0.225758\pi$
$383$	−1383.48	−	2396.26i	−0.184576	−	0.319694i	−0.943433	+	0.331562i	$0.892424\pi$
$384$		0			0
$385$	−624.516	+	1046.31i	−0.0826709	+	0.138506i
$386$		0			0
$387$	1586.98	−	4933.60i	0.208452	−	0.648033i
$388$		0			0
$389$	7115.17	+	4107.94i	0.927386	+	0.535427i	0.885984	−	0.463716i	$-0.153484\pi$
$389$	7115.17	+	4107.94i	0.927386	+	0.535427i	0.0414023	+	0.999143i	$0.486817\pi$
$390$		0			0
$391$			22770.1i			2.94510i
$392$		0			0
$393$	2477.93	−	5587.64i	0.318054	−	0.717199i
$394$		0			0
$395$	431.435	−	747.268i	0.0549566	−	0.0951877i
$396$		0			0
$397$	−1029.89	+	594.609i	−0.130199	+	0.0751702i	−0.563685	−	0.825990i	$-0.690617\pi$
$397$	−1029.89	+	594.609i	−0.130199	+	0.0751702i	0.433486	+	0.901160i	$0.357283\pi$
$398$		0			0
$399$	−7033.99	−	9952.02i	−0.882556	−	1.24868i
$400$		0			0
$401$	8525.89	−	4922.42i	1.06175	−	0.613003i	0.135835	−	0.990731i	$-0.456628\pi$
$401$	8525.89	−	4922.42i	1.06175	−	0.613003i	0.925916	+	0.377729i	$0.123295\pi$
$402$		0			0
$403$	2738.91	−	4743.92i	0.338547	−	0.586381i
$404$		0			0
$405$	107.345	−	1082.58i	0.0131704	−	0.132825i
$406$		0			0
$407$			4750.25i			0.578529i
$408$		0			0
$409$	10652.0	+	6149.94i	1.28779	+	0.743508i	0.978260	−	0.207380i	$-0.0664938\pi$
$409$	10652.0	+	6149.94i	1.28779	+	0.743508i	0.309533	+	0.950889i	$0.399827\pi$
$410$		0			0
$411$	−152.491	−	1430.60i	−0.0183013	−	0.171694i
$412$		0			0
$413$	6076.45	−	3391.56i	0.723978	−	0.404087i
$414$		0			0
$415$	−189.237	−	327.767i	−0.0223837	−	0.0387698i
$416$		0			0
$417$	−9938.03	+	7242.77i	−1.16707	+	0.850551i
$418$		0			0
$419$	−1596.17			−0.186105			−0.0930527	−	0.995661i	$-0.529663\pi$
$419$	−1596.17			−0.186105			−0.0930527	+	0.995661i	$0.529663\pi$
$420$		0			0
$421$	−6074.92			−0.703262			−0.351631	−	0.936139i	$-0.614373\pi$
$421$	−6074.92			−0.703262			−0.351631	+	0.936139i	$0.614373\pi$
$422$		0			0
$423$	8380.24	−	1807.07i	0.963265	−	0.207714i
$424$		0			0
$425$	−6846.07	−	11857.7i	−0.781373	−	1.35338i
$426$		0			0
$427$	−829.663	−	12.0488i	−0.0940286	−	0.00136553i
$428$		0			0
$429$	−14423.1	+	1537.40i	−1.62321	+	0.173021i
$430$		0			0
$431$	−2988.18	−	1725.22i	−0.333957	−	0.192810i	0.323640	−	0.946180i	$-0.395093\pi$
$431$	−2988.18	−	1725.22i	−0.333957	−	0.192810i	−0.657596	+	0.753370i	$0.728427\pi$
$432$		0			0
$433$			917.014i			0.101776i	0.998704	+	0.0508879i	$0.0162051\pi$
$433$			917.014i			0.101776i	−0.998704	+	0.0508879i	$0.983795\pi$
$434$		0			0
$435$	−817.295	−	362.443i	−0.0900834	−	0.0399490i
$436$		0			0
$437$	−12927.9	+	22391.8i	−1.41517	+	2.45114i
$438$		0			0
$439$	−997.235	+	575.754i	−0.108418	+	0.0625951i	−0.553228	−	0.833030i	$-0.686604\pi$
$439$	−997.235	+	575.754i	−0.108418	+	0.0625951i	0.444811	+	0.895625i	$0.353271\pi$
$440$		0			0
$441$	−9105.79	+	1688.42i	−0.983240	+	0.182315i
$442$		0			0
$443$	−12380.8	+	7148.04i	−1.32783	+	0.766622i	−0.984963	−	0.172763i	$-0.944730\pi$
$443$	−12380.8	+	7148.04i	−1.32783	+	0.766622i	−0.342864	+	0.939385i	$0.611397\pi$
$444$		0			0
$445$	523.510	−	906.746i	0.0557680	−	0.0965930i
$446$		0			0
$447$	7182.64	+	3185.26i	0.760016	+	0.337042i
$448$		0			0
$449$			6044.47i			0.635314i	0.948206	+	0.317657i	$0.102896\pi$
$449$			6044.47i			0.635314i	−0.948206	+	0.317657i	$0.897104\pi$
$450$		0			0
$451$	−12861.5	−	7425.60i	−1.34285	−	0.775295i
$452$		0			0
$453$	1906.31	−	203.198i	0.197718	−	0.0210752i
$454$		0			0
$455$	−1749.71	−	25.4102i	−0.180281	−	0.00261812i
$456$		0			0
$457$	−1871.52	−	3241.57i	−0.191567	−	0.331803i	0.754203	−	0.656641i	$-0.228023\pi$
$457$	−1871.52	−	3241.57i	−0.191567	−	0.331803i	−0.945770	+	0.324838i	$0.894690\pi$
$458$		0			0
$459$	−3185.47	+	15318.7i	−0.323932	+	1.55777i
$460$		0			0
$461$	1741.83			0.175976			0.0879881	−	0.996122i	$-0.471956\pi$
$461$	1741.83			0.175976			0.0879881	+	0.996122i	$0.471956\pi$
$462$		0			0
$463$	4966.97			0.498563			0.249282	−	0.968431i	$-0.419806\pi$
$463$	4966.97			0.498563			0.249282	+	0.968431i	$0.419806\pi$
$464$		0			0
$465$	−542.168	+	395.128i	−0.0540698	+	0.0394057i
$466$		0			0
$467$	808.619	+	1400.57i	0.0801251	+	0.138781i	0.903304	−	0.429002i	$-0.141135\pi$
$467$	808.619	+	1400.57i	0.0801251	+	0.138781i	−0.823178	+	0.567783i	$0.807801\pi$
$468$		0			0
$469$	−6714.44	+	3747.65i	−0.661075	+	0.368978i
$470$		0			0
$471$	−800.979	−	7514.40i	−0.0783591	−	0.735128i
$472$		0			0
$473$	7328.84	+	4231.31i	0.712432	+	0.411323i
$474$		0			0
$475$		−	15547.7i		−	1.50185i
$476$		0			0
$477$	7419.96	−	6720.61i	0.712236	−	0.645107i
$478$		0			0
$479$	9037.78	−	15653.9i	0.862101	−	1.49320i	−0.00779570	−	0.999970i	$-0.502481\pi$
$479$	9037.78	−	15653.9i	0.862101	−	1.49320i	0.869897	−	0.493234i	$-0.164185\pi$
$480$		0			0
$481$	−5907.85	+	3410.90i	−0.560031	+	0.323334i
$482$		0			0
$483$	11340.6	+	16045.2i	1.06835	+	1.51155i
$484$		0			0
$485$	−183.819	+	106.128i	−0.0172099	+	0.00993614i
$486$		0			0
$487$	1003.06	−	1737.34i	0.0933323	−	0.161656i	−0.815579	−	0.578646i	$-0.803581\pi$
$487$	1003.06	−	1737.34i	0.0933323	−	0.161656i	0.908911	+	0.416989i	$0.136915\pi$
$488$		0			0
$489$	−4350.35	+	9809.87i	−0.402310	+	0.907194i
$490$		0			0
$491$			5113.90i			0.470035i	0.971991	+	0.235017i	$0.0755147\pi$
$491$			5113.90i			0.470035i	−0.971991	+	0.235017i	$0.924485\pi$
$492$		0			0
$493$	11135.8	+	6429.28i	1.01731	+	0.587343i
$494$		0			0
$495$	1691.09	+	543.971i	0.153553	+	0.0493932i
$496$		0			0
$497$	−6417.84	+	10752.4i	−0.579234	+	0.970441i
$498$		0			0
$499$	−344.131	−	596.053i	−0.0308726	−	0.0534729i	0.850176	−	0.526498i	$-0.176495\pi$
$499$	−344.131	−	596.053i	−0.0308726	−	0.0534729i	−0.881049	+	0.473025i	$0.843162\pi$
$500$		0			0
$501$	8901.01	+	12213.4i	0.793748	+	1.08913i
$502$		0			0
$503$	15360.2			1.36158			0.680792	−	0.732476i	$-0.261636\pi$
$503$	15360.2			1.36158			0.680792	+	0.732476i	$0.261636\pi$
$504$		0			0
$505$	626.888			0.0552399
$506$		0			0
$507$	−5544.81	−	7608.21i	−0.485707	−	0.666454i
$508$		0			0
$509$	829.327	+	1436.44i	0.0722186	+	0.125086i	0.899873	−	0.436151i	$-0.143659\pi$
$509$	829.327	+	1436.44i	0.0722186	+	0.125086i	−0.827655	+	0.561238i	$0.810325\pi$
$510$		0			0
$511$	6127.51	+	10978.3i	0.530460	+	0.950394i
$512$		0			0
$513$	−11829.9	+	13255.6i	−1.01813	+	1.14084i
$514$		0			0
$515$	1.94288	+	1.12172i	0.000166240	+	9.59785e-5i
$516$		0			0
$517$			13998.7i			1.19083i
$518$		0			0
$519$	1664.00	−	3752.27i	0.140735	−	0.317353i
$520$		0			0
$521$	−789.911	+	1368.17i	−0.0664235	+	0.115049i	−0.897325	−	0.441371i	$-0.854492\pi$
$521$	−789.911	+	1368.17i	−0.0664235	+	0.115049i	0.830901	+	0.556420i	$0.187825\pi$
$522$		0			0
$523$	−11073.2	+	6393.13i	−0.925810	+	0.534517i	−0.885484	−	0.464670i	$-0.846173\pi$
$523$	−11073.2	+	6393.13i	−0.925810	+	0.534517i	−0.0403260	+	0.999187i	$0.512840\pi$
$524$		0			0
$525$	−10729.9	−	4946.01i	−0.891980	−	0.411165i
$526$		0			0
$527$	8356.02	−	4824.35i	0.690691	−	0.398771i
$528$		0			0
$529$	14759.6	−	25564.4i	1.21309	−	2.10113i
$530$		0			0
$531$	−6810.55	−	7519.26i	−0.556596	−	0.614516i
$532$		0			0
$533$		−	21327.7i		−	1.73322i
$534$		0			0
$535$	1394.51	+	805.120i	0.112691	+	0.0650624i
$536$		0			0
$537$	1705.01	+	15995.6i	0.137014	+	1.28540i
$538$		0			0
$539$	439.134	−	15115.9i	0.0350925	−	1.20796i
$540$		0			0
$541$	7756.18	+	13434.1i	0.616385	+	1.06761i	0.990140	+	0.140082i	$0.0447367\pi$
$541$	7756.18	+	13434.1i	0.616385	+	1.06761i	−0.373755	+	0.927527i	$0.621930\pi$
$542$		0			0
$543$	−20169.8	+	14699.6i	−1.59405	+	1.16173i
$544$		0			0
$545$	−1510.57			−0.118726
$546$		0			0
$547$	9646.72			0.754047			0.377024	−	0.926204i	$-0.376948\pi$
$547$	9646.72			0.754047			0.377024	+	0.926204i	$0.376948\pi$
$548$		0			0
$549$	254.985	+	1182.48i	0.0198224	+	0.0919256i
$550$		0			0
$551$	7300.57	+	12645.0i	0.564455	+	0.977665i
$552$		0			0
$553$	−155.499	+	10707.5i	−0.0119575	+	0.823380i
$554$		0			0
$555$	830.769	−	88.5537i	0.0635390	−	0.00677278i
$556$		0			0
$557$	3677.83	+	2123.40i	0.279775	+	0.161528i	0.633322	−	0.773889i	$-0.281691\pi$
$557$	3677.83	+	2123.40i	0.279775	+	0.161528i	−0.353547	+	0.935417i	$0.615024\pi$
$558$		0			0
$559$			12153.1i			0.919537i
$560$		0			0
$561$	−23355.5	−	10357.4i	−1.75770	−	0.779481i
$562$		0			0
$563$	5542.49	−	9599.87i	0.414899	−	0.718626i	−0.580519	−	0.814247i	$-0.697150\pi$
$563$	5542.49	−	9599.87i	0.414899	−	0.718626i	0.995418	+	0.0956208i	$0.0304836\pi$
$564$		0			0
$565$	−1561.91	+	901.766i	−0.116301	+	0.0671462i
$566$		0			0
$567$	5384.76	+	12381.0i	0.398833	+	0.917023i
$568$		0			0
$569$	17837.0	−	10298.2i	1.31418	−	0.758741i	0.331393	−	0.943493i	$-0.392482\pi$
$569$	17837.0	−	10298.2i	1.31418	−	0.758741i	0.982785	+	0.184752i	$0.0591482\pi$
$570$		0			0
$571$	6670.13	−	11553.0i	0.488855	−	0.846721i	−0.511063	−	0.859543i	$-0.670748\pi$
$571$	6670.13	−	11553.0i	0.488855	−	0.846721i	0.999918	+	0.0128218i	$0.00408142\pi$
$572$		0			0
$573$	2043.51	+	906.227i	0.148986	+	0.0660701i
$574$		0			0
$575$			25066.8i			1.81801i
$576$		0			0
$577$	−18387.2	−	10615.9i	−1.32664	−	0.765934i	−0.341859	−	0.939751i	$-0.611056\pi$
$577$	−18387.2	−	10615.9i	−1.32664	−	0.765934i	−0.984778	+	0.173818i	$0.944390\pi$
$578$		0			0
$579$	−1347.88	+	143.674i	−0.0967461	+	0.0103124i
$580$		0			0
$581$	4033.21	+	2407.33i	0.287996	+	0.171898i
$582$		0			0
$583$	8173.60	+	14157.1i	0.580645	+	1.00571i
$584$		0			0
$585$	537.748	+	2493.79i	0.0380054	+	0.176249i
$586$		0			0
$587$	−4124.22			−0.289991			−0.144996	−	0.989432i	$-0.546317\pi$
$587$	−4124.22			−0.289991			−0.144996	+	0.989432i	$0.546317\pi$
$588$		0			0
$589$	10956.3			0.766462
$590$		0			0
$591$	−10820.2	+	7885.68i	−0.753101	+	0.548855i
$592$		0			0
$593$	2363.19	+	4093.16i	0.163650	+	0.283450i	0.936175	−	0.351534i	$-0.114340\pi$
$593$	2363.19	+	4093.16i	0.163650	+	0.283450i	−0.772525	+	0.634984i	$0.781007\pi$
$594$		0			0
$595$	−2646.69	−	1579.75i	−0.182359	−	0.108846i
$596$		0			0
$597$	−1830.20	−	17170.0i	−0.125469	−	1.17709i
$598$		0			0
$599$	−22973.7	−	13263.9i	−1.56708	−	0.904754i	−0.996507	−	0.0835069i	$-0.973388\pi$
$599$	−22973.7	−	13263.9i	−1.56708	−	0.904754i	−0.570573	−	0.821247i	$-0.693279\pi$
$600$		0			0
$601$		−	8900.07i		−	0.604062i	−0.953298	−	0.302031i	$-0.902335\pi$
$601$		−	8900.07i		−	0.604062i	0.953298	−	0.302031i	$-0.0976646\pi$
$602$		0			0
$603$	7525.62	+	8308.73i	0.508237	+	0.561124i
$604$		0			0
$605$	−457.234	+	791.952i	−0.0307260	+	0.0532189i
$606$		0			0
$607$	7559.68	−	4364.58i	0.505499	−	0.291850i	−0.225482	−	0.974247i	$-0.572396\pi$
$607$	7559.68	−	4364.58i	0.505499	−	0.291850i	0.730982	+	0.682397i	$0.239062\pi$
$608$		0			0
$609$	11049.1	−	1015.71i	0.735190	−	0.0675843i
$610$		0			0
$611$	−17410.0	+	10051.7i	−1.15276	+	0.665544i
$612$		0			0
$613$	−7393.30	+	12805.6i	−0.487133	+	0.843739i	−0.999891	−	0.0147941i	$-0.995291\pi$
$613$	−7393.30	+	12805.6i	−0.487133	+	0.843739i	0.512757	+	0.858534i	$0.328624\pi$
$614$		0			0
$615$	−1058.90	+	2387.77i	−0.0694289	+	0.156560i
$616$		0			0
$617$			13185.9i			0.860361i	0.902743	+	0.430180i	$0.141550\pi$
$617$			13185.9i			0.860361i	−0.902743	+	0.430180i	$0.858450\pi$
$618$		0			0
$619$	−7686.26	−	4437.67i	−0.499091	−	0.288150i	0.229247	−	0.973368i	$-0.426374\pi$
$619$	−7686.26	−	4437.67i	−0.499091	−	0.288150i	−0.728338	+	0.685218i	$0.759707\pi$
$620$		0			0
$621$	19072.8	−	21371.5i	1.23247	−	1.38101i
$622$		0			0
$623$	−188.685	+	12992.6i	−0.0121341	+	0.835536i
$624$		0			0
$625$	−7397.42	−	12812.7i	−0.473435	−	0.820013i
$626$		0			0
$627$	−17087.0	−	23445.6i	−1.08834	−	1.49335i
$628$		0			0
$629$	−12016.0			−0.761702
$630$		0			0
$631$	4476.58			0.282425			0.141212	−	0.989979i	$-0.454900\pi$
$631$	4476.58			0.282425			0.141212	+	0.989979i	$0.454900\pi$
$632$		0			0
$633$	15636.4	+	21455.2i	0.981821	+	1.34719i
$634$		0			0
$635$	−1259.79	−	2182.03i	−0.0787297	−	0.136364i
$636$		0			0
$637$	19114.9	−	10307.8i	1.18895	−	0.641146i
$638$		0			0
$639$	17378.5	+	5590.11i	1.07587	+	0.346074i
$640$		0			0
$641$	−22053.0	−	12732.3i	−1.35888	−	0.784549i	−0.369406	−	0.929268i	$-0.620439\pi$
$641$	−22053.0	−	12732.3i	−1.35888	−	0.784549i	−0.989473	+	0.144719i	$0.953772\pi$
$642$		0			0
$643$		−	1289.00i		−	0.0790562i	−0.999218	−	0.0395281i	$-0.987415\pi$
$643$		−	1289.00i		−	0.0790562i	0.999218	−	0.0395281i	$-0.0125855\pi$
$644$		0			0
$645$	603.387	−	1360.62i	0.0368346	−	0.0830607i
$646$		0			0
$647$	10935.1	−	18940.1i	0.664454	−	1.15087i	−0.314979	−	0.949098i	$-0.601998\pi$
$647$	10935.1	−	18940.1i	0.664454	−	1.15087i	0.979433	−	0.201769i	$-0.0646690\pi$
$648$		0			0
$649$	14346.5	−	8282.98i	0.867721	−	0.500979i
$650$		0			0
$651$	3485.40	−	7561.22i	0.209837	−	0.455219i
$652$		0			0
$653$	24479.9	−	14133.5i	1.46704	−	0.846993i	0.467716	−	0.883879i	$-0.345077\pi$
$653$	24479.9	−	14133.5i	1.46704	−	0.846993i	0.999320	+	0.0368853i	$0.0117436\pi$
$654$		0			0
$655$	877.731	−	1520.27i	0.0523600	−	0.0906901i
$656$		0			0
$657$	13585.0	−	12304.6i	0.806699	−	0.730666i
$658$		0			0
$659$			3771.24i			0.222923i	0.993769	+	0.111462i	$0.0355533\pi$
$659$			3771.24i			0.222923i	−0.993769	+	0.111462i	$0.964447\pi$
$660$		0			0
$661$	−13753.5	−	7940.60i	−0.809304	−	0.467252i	0.0374100	−	0.999300i	$-0.488089\pi$
$661$	−13753.5	−	7940.60i	−0.809304	−	0.467252i	−0.846714	+	0.532048i	$0.821423\pi$
$662$		0			0
$663$	−3888.93	−	36484.1i	−0.227803	−	2.13714i
$664$		0			0
$665$	−1705.81	−	3056.19i	−0.0994711	−	0.178216i
$666$		0			0
$667$	−11770.4	−	20386.9i	−0.683284	−	1.18348i
$668$		0			0
$669$	3297.05	−	2402.87i	0.190540	−	0.138865i
$670$		0			0
$671$	−1975.26			−0.113643
$672$		0			0
$673$	−27778.7			−1.59107			−0.795535	−	0.605908i	$-0.792810\pi$
$673$	−27778.7			−1.59107			−0.795535	+	0.605908i	$0.792810\pi$
$674$		0			0
$675$	−3506.77	+	16863.8i	−0.199964	+	0.961613i
$676$		0			0
$677$	−13442.7	−	23283.5i	−0.763140	−	1.32180i	−0.941224	−	0.337782i	$-0.890323\pi$
$677$	−13442.7	−	23283.5i	−0.763140	−	1.32180i	0.178085	−	0.984015i	$-0.443010\pi$
$678$		0			0
$679$	1350.09	−	2261.92i	0.0763057	−	0.127842i
$680$		0			0
$681$	12989.9	−	1384.63i	0.730947	−	0.0779134i
$682$		0			0
$683$	9378.55	+	5414.71i	0.525418	+	0.303350i	0.739148	−	0.673543i	$-0.235228\pi$
$683$	9378.55	+	5414.71i	0.525418	+	0.303350i	−0.213731	+	0.976893i	$0.568562\pi$
$684$		0			0
$685$		−	413.188i		−	0.0230469i
$686$		0			0
$687$	−5768.49	−	2558.13i	−0.320352	−	0.142065i
$688$		0			0
$689$	−11738.0	+	20330.9i	−0.649033	+	1.12416i
$690$		0			0
$691$	10691.3	−	6172.60i	0.588589	−	0.339822i	−0.175951	−	0.984399i	$-0.556300\pi$
$691$	10691.3	−	6172.60i	0.588589	−	0.339822i	0.764539	+	0.644577i	$0.222967\pi$
$692$		0			0
$693$	−21616.1	+	4333.70i	−1.18489	+	0.237552i
$694$		0			0
$695$	−3058.55	+	1765.85i	−0.166931	+	0.0963779i
$696$		0			0
$697$	18783.5	−	32533.9i	1.02077	−	1.76802i
$698$		0			0
$699$	−26865.8	−	11914.1i	−1.45373	−	0.644682i
$700$		0			0
$701$			5267.34i			0.283801i	0.989881	+	0.141901i	$0.0453213\pi$
$701$			5267.34i			0.283801i	−0.989881	+	0.141901i	$0.954679\pi$
$702$		0			0
$703$	−11816.4	−	6822.22i	−0.633947	−	0.366010i
$704$		0			0
$705$	2448.21	−	260.961i	0.130787	−	0.0139409i
$706$		0			0
$707$	−6793.43	+	3791.74i	−0.361377	+	0.201702i
$708$		0			0
$709$	10754.8	+	18627.9i	0.569684	+	0.986721i	0.996597	+	0.0824288i	$0.0262677\pi$
$709$	10754.8	+	18627.9i	0.569684	+	0.986721i	−0.426913	+	0.904293i	$0.640399\pi$
$710$		0			0
$711$	15260.9	−	3290.79i	0.804965	−	0.173579i
$712$		0			0
$713$	−17664.3			−0.927817
$714$		0			0
$715$	−4165.72			−0.217887
$716$		0			0
$717$	10049.9	−	7324.27i	0.523457	−	0.381492i
$718$		0			0
$719$	−2279.94	−	3948.98i	−0.118258	−	0.204829i	0.800819	−	0.598906i	$-0.204398\pi$
$719$	−2279.94	−	3948.98i	−0.118258	−	0.204829i	−0.919077	+	0.394077i	$0.871064\pi$
$720$		0			0
$721$	−27.8392	−	0.404294i	−0.00143798	−	2.08831e-5i
$722$		0			0
$723$	−1505.70	−	14125.8i	−0.0774517	−	0.726616i
$724$		0			0
$725$	12259.1	+	7077.77i	0.627986	+	0.362568i
$726$		0			0
$727$		−	9960.71i		−	0.508146i	−0.967185	−	0.254073i	$-0.918230\pi$
$727$		−	9960.71i		−	0.508146i	0.967185	−	0.254073i	$-0.0817704\pi$
$728$		0			0
$729$	15821.1	−	11709.5i	0.803795	−	0.594906i
$730$		0			0
$731$	−10703.3	+	18538.7i	−0.541555	+	0.938002i
$732$		0			0
$733$	6931.71	−	4002.03i	0.349289	−	0.201662i	−0.315083	−	0.949064i	$-0.602032\pi$
$733$	6931.71	−	4002.03i	0.349289	−	0.201662i	0.664372	+	0.747402i	$0.268699\pi$
$734$		0			0
$735$	−2651.80	+	204.990i	−0.133079	+	0.0102873i
$736$		0			0
$737$	−15852.8	+	9152.64i	−0.792329	+	0.457451i
$738$		0			0
$739$	−7231.28	+	12525.0i	−0.359955	+	0.623461i	−0.987953	−	0.154754i	$-0.950541\pi$
$739$	−7231.28	+	12525.0i	−0.359955	+	0.623461i	0.627998	+	0.778215i	$0.283875\pi$
$740$		0			0
$741$	16889.9	−	38086.0i	0.837335	−	1.88816i
$742$		0			0
$743$		−	27770.8i		−	1.37121i	−0.727973	−	0.685606i	$-0.759537\pi$
$743$		−	27770.8i		−	1.37121i	0.727973	−	0.685606i	$-0.240463\pi$
$744$		0			0
$745$	1954.24	+	1128.28i	0.0961044	+	0.0554859i
$746$		0			0
$747$	2096.85	−	6518.67i	0.102704	−	0.319285i
$748$		0			0
$749$	−19981.7	−	290.184i	−0.974788	−	0.0141563i
$750$		0			0
$751$	19225.3	+	33299.2i	0.934144	+	1.61798i	0.776154	+	0.630543i	$0.217168\pi$
$751$	19225.3	+	33299.2i	0.934144	+	1.61798i	0.157989	+	0.987441i	$0.449499\pi$
$752$		0			0
$753$	7172.37	+	9841.43i	0.347112	+	0.476283i
$754$		0			0
$755$	550.584			0.0265402
$756$		0			0
$757$	−4148.07			−0.199160			−0.0995800	−	0.995030i	$-0.531750\pi$
$757$	−4148.07			−0.199160			−0.0995800	+	0.995030i	$0.531750\pi$
$758$		0			0
$759$	27548.6	+	37800.3i	1.31746	+	1.80772i
$760$		0			0
$761$	−17318.5	−	29996.6i	−0.824962	−	1.42888i	−0.901948	−	0.431844i	$-0.857863\pi$
$761$	−17318.5	−	29996.6i	−0.824962	−	1.42888i	0.0769859	−	0.997032i	$-0.475470\pi$
$762$		0			0
$763$	16369.7	−	9136.72i	0.776702	−	0.433515i
$764$		0			0
$765$	−1376.00	+	4277.71i	−0.0650321	+	0.202171i
$766$		0			0
$767$	20602.9	+	11895.1i	0.969921	+	0.559984i
$768$		0			0
$769$			22003.5i			1.03182i	0.856644	+	0.515908i	$0.172545\pi$
$769$			22003.5i			1.03182i	−0.856644	+	0.515908i	$0.827455\pi$
$770$		0			0
$771$	−3666.39	+	8267.57i	−0.171260	+	0.386186i
$772$		0			0
$773$	−6121.65	+	10603.0i	−0.284839	+	0.493355i	−0.972570	−	0.232610i	$-0.925273\pi$
$773$	−6121.65	+	10603.0i	−0.284839	+	0.493355i	0.687731	+	0.725965i	$0.258607\pi$
$774$		0			0
$775$	9198.86	−	5310.96i	0.426365	−	0.246162i
$776$		0			0
$777$	−8467.21	+	5984.55i	−0.390939	+	0.276312i
$778$		0			0
$779$	36942.9	−	21329.0i	1.69912	−	0.980989i
$780$		0			0
$781$	−14904.7	+	25815.7i	−0.682883	+	1.18279i
$782$		0			0
$783$	−5066.51	−	15362.0i	−0.231242	−	0.701141i
$784$		0			0
$785$		−	2170.33i		−	0.0986780i
$786$		0			0
$787$	−12206.1	−	7047.21i	−0.552861	−	0.319194i	0.197414	−	0.980320i	$-0.436746\pi$
$787$	−12206.1	−	7047.21i	−0.552861	−	0.319194i	−0.750275	+	0.661126i	$0.770079\pi$
$788$		0			0
$789$	2439.72	+	22888.3i	0.110084	+	1.03276i
$790$		0			0
$791$	11471.6	−	19219.4i	0.515657	−	0.863924i
$792$		0			0
$793$	−1418.33	−	2456.62i	−0.0635137	−	0.110009i
$794$		0			0
$795$	2323.55	−	1693.39i	0.103658	−	0.0755451i
$796$		0			0
$797$	−3585.24			−0.159342			−0.0796711	−	0.996821i	$-0.525387\pi$
$797$	−3585.24			−0.159342			−0.0796711	+	0.996821i	$0.525387\pi$
$798$		0			0
$799$	−35410.4			−1.56787
$800$		0			0
$801$	18517.9	−	3993.09i	0.816849	−	0.176141i
$802$		0			0
$803$	14964.8	+	25919.8i	0.657654	+	1.13909i
$804$		0			0
$805$	2750.19	+	4927.35i	0.120412	+	0.215734i
$806$		0			0
$807$	−4898.58	+	522.152i	−0.213678	+	0.0227765i
$808$		0			0
$809$	11021.3	+	6363.12i	0.478970	+	0.276533i	0.719987	−	0.693987i	$-0.244148\pi$
$809$	11021.3	+	6363.12i	0.478970	+	0.276533i	−0.241017	+	0.970521i	$0.577481\pi$
$810$		0			0
$811$			17781.2i			0.769892i	0.922939	+	0.384946i	$0.125780\pi$
$811$			17781.2i			0.769892i	−0.922939	+	0.384946i	$0.874220\pi$
$812$		0			0
$813$	35478.3	+	15733.4i	1.53048	+	0.678716i
$814$		0			0
$815$	−1540.98	+	2669.05i	−0.0662308	+	0.114715i
$816$		0			0
$817$	−21051.1	+	12153.8i	−0.901449	+	0.520452i
$818$		0			0
$819$	−20911.2	−	23772.0i	−0.892180	−	1.01424i
$820$		0			0
$821$	−12336.7	+	7122.58i	−0.524425	+	0.302777i	−0.738743	−	0.673987i	$-0.764580\pi$
$821$	−12336.7	+	7122.58i	−0.524425	+	0.302777i	0.214318	+	0.976764i	$0.431247\pi$
$822$		0			0
$823$	733.277	−	1270.07i	0.0310576	−	0.0537934i	−0.850079	−	0.526655i	$-0.823446\pi$
$823$	733.277	−	1270.07i	0.0310576	−	0.0537934i	0.881136	+	0.472862i	$0.156779\pi$
$824$		0			0
$825$	−25711.3	−	11402.1i	−1.08503	−	0.481175i
$826$		0			0
$827$		−	23108.5i		−	0.971660i	−0.874053	−	0.485830i	$-0.838517\pi$
$827$		−	23108.5i		−	0.971660i	0.874053	−	0.485830i	$-0.161483\pi$
$828$		0			0
$829$	−35106.0	−	20268.5i	−1.47079	−	0.849159i	−0.471324	−	0.881960i	$-0.656224\pi$
$829$	−35106.0	−	20268.5i	−1.47079	−	0.849159i	−0.999462	+	0.0328016i	$0.989557\pi$
$830$		0			0
$831$	5386.36	−	574.145i	0.224851	−	0.0239674i
$832$		0			0
$833$	38236.6	+	1110.82i	1.59042	+	0.0462034i
$834$		0			0
$835$	2170.15	+	3758.81i	0.0899414	+	0.155783i
$836$		0			0
$837$	−11883.8	−	2471.18i	−0.490756	−	0.102051i
$838$		0			0
$839$	24497.2			1.00803			0.504015	−	0.863695i	$-0.331855\pi$
$839$	24497.2			1.00803			0.504015	+	0.863695i	$0.331855\pi$
$840$		0			0
$841$	11095.3			0.454929
$842$		0			0
$843$	28641.1	−	20873.5i	1.17017	−	0.852812i
$844$		0			0
$845$	−1351.88	−	2341.52i	−0.0550366	−	0.0953262i
$846$		0			0
$847$	164.798	−	11347.8i	0.00668538	−	0.460347i
$848$		0			0
$849$	1908.57	+	17905.3i	0.0771517	+	0.723801i
$850$		0			0
$851$	19051.1	+	10999.1i	0.767406	+	0.443062i
$852$		0			0
$853$		−	23408.6i		−	0.939620i	−0.882768	−	0.469810i	$-0.844322\pi$
$853$		−	23408.6i		−	0.939620i	0.882768	−	0.469810i	$-0.155678\pi$
$854$		0			0
$855$	−3781.85	+	3425.41i	−0.151271	+	0.137013i
$856$		0			0
$857$	8400.44	−	14550.0i	0.334835	−	0.579951i	−0.648618	−	0.761114i	$-0.724653\pi$
$857$	8400.44	−	14550.0i	0.334835	−	0.579951i	0.983453	+	0.181163i	$0.0579861\pi$
$858$		0			0
$859$	−7611.10	+	4394.27i	−0.302314	+	0.174541i	−0.643482	−	0.765461i	$-0.722511\pi$
$859$	−7611.10	+	4394.27i	−0.302314	+	0.174541i	0.341168	+	0.940002i	$0.389177\pi$
$860$		0			0
$861$	−2967.46	−	32280.4i	−0.117457	−	1.27772i
$862$		0			0
$863$	−13328.5	+	7695.24i	−0.525734	+	0.303533i	−0.739278	−	0.673401i	$-0.764833\pi$
$863$	−13328.5	+	7695.24i	−0.525734	+	0.303533i	0.213543	+	0.976934i	$0.431500\pi$
$864$		0			0
$865$	589.422	−	1020.91i	0.0231687	−	0.0401294i
$866$		0			0
$867$	15850.4	−	35742.2i	0.620887	−	1.40008i
$868$		0			0
$869$			25492.4i			0.995134i
$870$		0			0
$871$	−22766.1	−	13144.0i	−0.885649	−	0.511330i
$872$		0			0
$873$	−3655.82	−	1175.96i	−0.141731	−	0.0455903i
$874$		0			0
$875$	−5880.15	−	3509.73i	−0.227183	−	0.135600i
$876$		0			0
$877$	22668.7	+	39263.3i	0.872825	+	1.51178i	0.859062	+	0.511872i	$0.171048\pi$
$877$	22668.7	+	39263.3i	0.872825	+	1.51178i	0.0137631	+	0.999905i	$0.495619\pi$
$878$		0			0
$879$	13222.3	+	18142.7i	0.507367	+	0.696174i
$880$		0			0
$881$	11607.6			0.443893			0.221947	−	0.975059i	$-0.428759\pi$
$881$	11607.6			0.443893			0.221947	+	0.975059i	$0.428759\pi$
$882$		0			0
$883$	−30488.1			−1.16195			−0.580977	−	0.813920i	$-0.697329\pi$
$883$	−30488.1			−1.16195			−0.580977	+	0.813920i	$0.697329\pi$
$884$		0			0
$885$	−1716.05	−	2354.65i	−0.0651801	−	0.0894356i
$886$		0			0
$887$	−1007.03	−	1744.23i	−0.0381204	−	0.0660265i	0.846336	−	0.532650i	$-0.178804\pi$
$887$	−1007.03	−	1744.23i	−0.0381204	−	0.0660265i	−0.884456	+	0.466623i	$0.845470\pi$
$888$		0			0
$889$	26850.1	+	16026.2i	1.01296	+	0.604613i
$890$		0			0
$891$	13245.3	+	29284.3i	0.498019	+	1.10108i
$892$		0			0
$893$	−34822.1	−	20104.6i	−1.30490	−	0.753386i
$894$		0			0
$895$			4619.88i			0.172542i
$896$		0			0
$897$	−27230.8	+	61404.3i	−1.01361	+	2.28565i
$898$		0			0
$899$	−4987.63	+	8638.83i	−0.185035	+	0.320490i
$900$		0			0
$901$	−35811.1	+	20675.6i	−1.32413	+	0.764487i
$902$		0			0
$903$	1690.94	+	18394.2i	0.0623156	+	0.677876i
$904$		0			0
$905$	−6207.50	+	3583.90i	−0.228005	+	0.131639i
$906$		0			0
$907$	6309.04	−	10927.6i	0.230968	−	0.400048i	−0.727125	−	0.686505i	$-0.759144\pi$
$907$	6309.04	−	10927.6i	0.230968	−	0.400048i	0.958093	+	0.286456i	$0.0924774\pi$
$908$		0			0
$909$	7614.15	+	8406.48i	0.277828	+	0.306738i
$910$		0			0
$911$			3835.14i			0.139477i	0.997565	+	0.0697387i	$0.0222166\pi$
$911$			3835.14i			0.139477i	−0.997565	+	0.0697387i	$0.977783\pi$
$912$		0			0
$913$	9683.47	+	5590.75i	0.351014	+	0.202658i
$914$		0			0
$915$	36.8226	+	345.452i	0.00133040	+	0.0124812i
$916$		0			0
$917$	−316.355	+	21783.8i	−0.0113925	+	0.784476i
$918$		0			0
$919$	−2525.46	−	4374.23i	−0.0906500	−	0.157010i	0.817135	−	0.576447i	$-0.195561\pi$
$919$	−2525.46	−	4374.23i	−0.0906500	−	0.157010i	−0.907785	+	0.419436i	$0.862228\pi$
$920$		0			0
$921$	−16629.4	+	12119.4i	−0.594958	+	0.433602i
$922$		0			0
$923$	−42809.0			−1.52663
$924$		0			0
$925$	−13228.0			−0.470200
$926$		0			0
$927$	8.55597	+	39.6781i	0.000303145	+	0.00140582i
$928$		0			0
$929$	19120.6	+	33117.8i	0.675271	+	1.16960i	0.976390	+	0.216017i	$0.0693065\pi$
$929$	19120.6	+	33117.8i	0.675271	+	1.16960i	−0.301119	+	0.953587i	$0.597360\pi$
$930$		0			0
$931$	36970.8	+	22801.6i	1.30147	+	0.802676i
$932$		0			0
$933$	5943.92	−	633.577i	0.208569	−	0.0222319i
$934$		0			0
$935$	−6354.52	−	3668.78i	−0.222262	−	0.128323i
$936$		0			0
$937$		−	33083.3i		−	1.15345i	−0.816938	−	0.576726i	$-0.804330\pi$
$937$		−	33083.3i		−	1.15345i	0.816938	−	0.576726i	$-0.195670\pi$
$938$		0			0
$939$	19527.8	+	8659.91i	0.678663	+	0.300964i
$940$		0			0
$941$	5484.84	−	9500.02i	0.190011	−	0.329109i	−0.755242	−	0.655446i	$-0.772481\pi$
$941$	5484.84	−	9500.02i	0.190011	−	0.329109i	0.945254	+	0.326336i	$0.105814\pi$
$942$		0			0
$943$	−59561.3	+	34387.7i	−2.05682	+	1.18751i
$944$		0			0
$945$	1160.88	+	3699.64i	0.0399614	+	0.127354i
$946$		0			0
$947$	3166.59	−	1828.23i	0.108659	−	0.0627344i	−0.444686	−	0.895687i	$-0.646685\pi$
$947$	3166.59	−	1828.23i	0.108659	−	0.0627344i	0.553345	+	0.832952i	$0.313351\pi$
$948$		0			0
$949$	−21490.8	+	37223.2i	−0.735113	+	1.27325i
$950$		0			0
$951$	5399.94	+	2394.69i	0.184127	+	0.0816542i
$952$		0			0
$953$			623.517i			0.0211938i	0.999944	+	0.0105969i	$0.00337316\pi$
$953$			623.517i			0.0211938i	−0.999944	+	0.0105969i	$0.996627\pi$
$954$		0			0
$955$	555.994	+	321.003i	0.0188393	+	0.0108769i
$956$		0			0
$957$	26264.9	−	2799.64i	0.887174	−	0.0945660i
$958$		0			0
$959$	2499.17	+	4477.62i	0.0841528	+	0.150772i
$960$		0			0
$961$	−11152.9	−	19317.4i	−0.374372	−	0.648432i
$962$		0			0
$963$	6141.09	+	28479.1i	0.205497	+	0.952987i
$964$		0			0
$965$	−389.298			−0.0129865
$966$		0			0
$967$	−14981.3			−0.498206			−0.249103	−	0.968477i	$-0.580136\pi$
$967$	−14981.3			−0.498206			−0.249103	+	0.968477i	$0.580136\pi$
$968$		0			0
$969$	59307.0	−	43222.6i	1.96617	−	1.43293i
$970$		0			0
$971$	−9937.59	−	17212.4i	−0.328437	−	0.568870i	0.653765	−	0.756698i	$-0.273189\pi$
$971$	−9937.59	−	17212.4i	−0.328437	−	0.568870i	−0.982202	+	0.187828i	$0.939855\pi$
$972$		0			0
$973$	22463.9	−	37635.8i	0.740145	−	1.24003i
$974$		0			0
$975$	−4281.19	−	40164.1i	−0.140623	−	1.31926i
$976$		0			0
$977$	−25325.3	−	14621.6i	−0.829302	−	0.478798i	0.0243113	−	0.999704i	$-0.492261\pi$
$977$	−25325.3	−	14621.6i	−0.829302	−	0.478798i	−0.853614	+	0.520906i	$0.825594\pi$
$978$		0			0
$979$			30932.9i			1.00983i
$980$		0			0
$981$	−18347.3	−	20256.6i	−0.597131	−	0.659269i
$982$		0			0
$983$	−23062.9	+	39946.2i	−0.748315	+	1.29612i	0.200315	+	0.979732i	$0.435803\pi$
$983$	−23062.9	+	39946.2i	−0.748315	+	1.29612i	−0.948630	+	0.316388i	$0.897530\pi$
$984$		0			0
$985$	−3330.04	+	1922.60i	−0.107720	+	0.0621920i
$986$		0			0
$987$	−24952.3	+	17636.0i	−0.804700	+	0.568755i
$988$		0			0
$989$	33939.6	−	19595.1i	1.09122	−	0.630017i
$990$		0			0
$991$	16854.6	−	29193.0i	0.540266	−	0.935769i	−0.458622	−	0.888631i	$-0.651657\pi$
$991$	16854.6	−	29193.0i	0.540266	−	0.935769i	0.998888	−	0.0471373i	$-0.0150098\pi$
$992$		0			0
$993$	5031.81	−	11346.5i	0.160805	−	0.362610i
$994$		0			0
$995$		−	4959.09i		−	0.158004i
$996$		0			0
$997$	−48238.5	−	27850.5i	−1.53233	−	0.884689i	−0.999254	−	0.0386188i	$-0.987704\pi$
$997$	−48238.5	−	27850.5i	−1.53233	−	0.884689i	−0.533072	−	0.846070i	$-0.678962\pi$
$998$		0			0
$999$	11278.0	+	10064.9i	0.357176	+	0.318758i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.4.bc.f.17.18		48
3.2	odd	2	inner	336.4.bc.f.17.24		48
4.3	odd	2		168.4.u.a.17.7	yes	48
7.5	odd	6	inner	336.4.bc.f.257.24		48
12.11	even	2		168.4.u.a.17.1	✓	48
21.5	even	6	inner	336.4.bc.f.257.18		48
28.19	even	6		168.4.u.a.89.1	yes	48
84.47	odd	6		168.4.u.a.89.7	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.4.u.a.17.1	✓	48	12.11	even	2
168.4.u.a.17.7	yes	48	4.3	odd	2
168.4.u.a.89.1	yes	48	28.19	even	6
168.4.u.a.89.7	yes	48	84.47	odd	6
336.4.bc.f.17.18		48	1.1	even	1	trivial
336.4.bc.f.17.24		48	3.2	odd	2	inner
336.4.bc.f.257.18		48	21.5	even	6	inner
336.4.bc.f.257.24		48	7.5	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(3.06041 + 4.19928i) q^{3} +(0.746155 + 1.29238i) q^{5} +(-15.9029 - 9.49205i) q^{7} +(-8.26784 + 25.7030i) q^{9} +O(q^{10})\)	\(q+(3.06041 + 4.19928i) q^{3} +(0.746155 + 1.29238i) q^{5} +(-15.9029 - 9.49205i) q^{7} +(-8.26784 + 25.7030i) q^{9} +(-38.1817 - 22.0442i) q^{11} -63.3150i q^{13} +(-3.14352 + 7.08851i) q^{15} +(55.7620 - 96.5827i) q^{17} +(109.671 - 63.3189i) q^{19} +(-8.80943 - 95.8300i) q^{21} +(-176.818 + 102.086i) q^{23} +(61.3865 - 106.325i) q^{25} +(-133.237 + 43.9426i) q^{27} +115.298i q^{29} +(74.9257 + 43.2584i) q^{31} +(-24.2817 - 227.800i) q^{33} +(0.401329 - 27.6351i) q^{35} +(-53.8719 - 93.3089i) q^{37} +(265.877 - 193.770i) q^{39} +336.851 q^{41} -191.947 q^{43} +(-39.3871 + 8.49322i) q^{45} +(-158.757 - 274.975i) q^{47} +(162.802 + 301.902i) q^{49} +(576.232 - 61.4220i) q^{51} +(-321.107 - 185.391i) q^{53} -65.7936i q^{55} +(601.532 + 266.759i) q^{57} +(-187.872 + 325.404i) q^{59} +(38.7999 - 22.4012i) q^{61} +(375.456 - 330.272i) q^{63} +(81.8269 - 47.2428i) q^{65} +(207.597 - 359.569i) q^{67} +(-969.823 - 430.084i) q^{69} -676.127i q^{71} +(-587.905 - 339.427i) q^{73} +(634.354 - 67.6173i) q^{75} +(397.953 + 712.988i) q^{77} +(-289.106 - 500.746i) q^{79} +(-592.286 - 425.016i) q^{81} -253.616 q^{83} +166.428 q^{85} +(-484.170 + 352.860i) q^{87} +(-350.805 - 607.613i) q^{89} +(-600.989 + 1006.89i) q^{91} +(47.6492 + 447.022i) q^{93} +(163.664 + 94.4914i) q^{95} +142.233i q^{97} +(882.281 - 799.125i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 12 q^{7} + 14 q^{9}+O(q^{10}) \) 48 * q - 12 * q^7 + 14 * q^9	\( 48 q - 12 q^{7} + 14 q^{9} + 88 q^{15} + 270 q^{19} + 50 q^{21} - 438 q^{25} - 216 q^{31} - 372 q^{33} + 66 q^{37} - 242 q^{39} - 900 q^{43} - 294 q^{45} + 60 q^{49} + 138 q^{51} + 1384 q^{57} + 108 q^{61} - 1096 q^{63} - 6 q^{67} - 1206 q^{73} + 594 q^{75} + 588 q^{79} - 54 q^{81} - 240 q^{85} + 3522 q^{87} - 234 q^{91} - 608 q^{93} - 1988 q^{99}+O(q^{100}) \) 48 * q - 12 * q^7 + 14 * q^9 + 88 * q^15 + 270 * q^19 + 50 * q^21 - 438 * q^25 - 216 * q^31 - 372 * q^33 + 66 * q^37 - 242 * q^39 - 900 * q^43 - 294 * q^45 + 60 * q^49 + 138 * q^51 + 1384 * q^57 + 108 * q^61 - 1096 * q^63 - 6 * q^67 - 1206 * q^73 + 594 * q^75 + 588 * q^79 - 54 * q^81 - 240 * q^85 + 3522 * q^87 - 234 * q^91 - 608 * q^93 - 1988 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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