LMFDB - Embedded newform 312.4.q.e.217.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [312,4,Mod(217,312)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(312, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 0, 4])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("312.217"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 312 = 2^{3} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	312.q (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$18.4085959218$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 161 x^{10} - 1480 x^{9} + 25918 x^{8} - 119864 x^{7} + 547597 x^{6} - 230908 x^{5} + \cdots + 59049 $ x^12 + 161x^10 - 1480x^9 + 25918x^8 - 119864x^7 + 547597x^6 - 230908x^5 + 496646x^4 + 357468x^3 + 524905x^2 + 175932x + 59049
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{20} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			217.3
Root			$-0.206972 + 0.358486i$ of defining polynomial
Character	$\chi$	$=$	312.217
Dual form			312.4.q.e.289.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.50000 + 2.59808i) q^{3} -3.80742 q^{5} +(1.42598 + 2.46987i) q^{7} +(-4.50000 - 7.79423i) q^{9} +(15.6183 - 27.0517i) q^{11} +(41.2830 - 22.1971i) q^{13} +(5.71114 - 9.89198i) q^{15} +(28.8372 + 49.9474i) q^{17} +(36.2462 + 62.7803i) q^{19} -8.55588 q^{21} +(-104.854 + 181.612i) q^{23} -110.504 q^{25} +27.0000 q^{27} +(66.1062 - 114.499i) q^{29} +275.352 q^{31} +(46.8548 + 81.1550i) q^{33} +(-5.42931 - 9.40385i) q^{35} +(-183.197 + 317.306i) q^{37} +(-4.25473 + 140.552i) q^{39} +(-84.5698 + 146.479i) q^{41} +(166.089 + 287.675i) q^{43} +(17.1334 + 29.6759i) q^{45} +183.320 q^{47} +(167.433 - 290.003i) q^{49} -173.023 q^{51} -502.390 q^{53} +(-59.4654 + 102.997i) q^{55} -217.477 q^{57} +(443.397 + 767.986i) q^{59} +(452.914 + 784.470i) q^{61} +(12.8338 - 22.2288i) q^{63} +(-157.182 + 84.5138i) q^{65} +(59.8583 - 103.678i) q^{67} +(-314.561 - 544.835i) q^{69} +(-231.484 - 400.942i) q^{71} -63.0078 q^{73} +(165.755 - 287.097i) q^{75} +89.0855 q^{77} +791.154 q^{79} +(-40.5000 + 70.1481i) q^{81} +171.481 q^{83} +(-109.795 - 190.171i) q^{85} +(198.319 + 343.498i) q^{87} +(92.6713 - 160.511i) q^{89} +(113.693 + 70.3111i) q^{91} +(-413.028 + 715.386i) q^{93} +(-138.005 - 239.031i) q^{95} +(-363.951 - 630.381i) q^{97} -281.129 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 18 q^{3} + 8 q^{5} - 10 q^{7} - 54 q^{9} - 60 q^{11} + 86 q^{13} - 12 q^{15} - 56 q^{17} - 48 q^{19} + 60 q^{21} + 80 q^{23} + 508 q^{25} + 324 q^{27} - 164 q^{29} + 668 q^{31} - 180 q^{33} + 552 q^{35}+ \cdots + 1080 q^{99}+O(q^{100}) $ 12 * q - 18 * q^3 + 8 * q^5 - 10 * q^7 - 54 * q^9 - 60 * q^11 + 86 * q^13 - 12 * q^15 - 56 * q^17 - 48 * q^19 + 60 * q^21 + 80 * q^23 + 508 * q^25 + 324 * q^27 - 164 * q^29 + 668 * q^31 - 180 * q^33 + 552 * q^35 + 264 * q^37 - 192 * q^39 - 708 * q^41 - 242 * q^43 - 36 * q^45 + 856 * q^47 - 904 * q^49 + 336 * q^51 + 392 * q^53 + 608 * q^55 + 288 * q^57 - 224 * q^59 + 478 * q^61 - 90 * q^63 - 1268 * q^65 - 250 * q^67 + 240 * q^69 - 872 * q^71 + 44 * q^73 - 762 * q^75 + 1880 * q^77 - 1228 * q^79 - 486 * q^81 + 4712 * q^83 + 276 * q^85 - 492 * q^87 - 228 * q^89 + 3066 * q^91 - 1002 * q^93 - 1808 * q^95 - 530 * q^97 + 1080 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/312\mathbb{Z}\right)^\times$.

$n$	$79$	$145$	$157$	$209$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.50000	+	2.59808i	−0.288675	+	0.500000i
$3$	−1.50000	+	2.59808i	−0.288675	+	0.500000i
$4$		0			0
$5$	−3.80742			−0.340546			−0.170273	−	0.985397i	$-0.554465\pi$
$5$	−3.80742			−0.340546			−0.170273	+	0.985397i	$0.554465\pi$
$6$		0			0
$7$	1.42598	+	2.46987i	0.0769957	+	0.133360i	0.901952	−	0.431835i	$-0.142134\pi$
$7$	1.42598	+	2.46987i	0.0769957	+	0.133360i	−0.824957	+	0.565196i	$0.808801\pi$
$8$		0			0
$9$	−4.50000	−	7.79423i	−0.166667	−	0.288675i
$10$		0			0
$11$	15.6183	−	27.0517i	0.428099	−	0.741489i	−0.568605	−	0.822611i	$-0.692517\pi$
$11$	15.6183	−	27.0517i	0.428099	−	0.741489i	0.996704	+	0.0811214i	$0.0258501\pi$
$12$		0			0
$13$	41.2830	−	22.1971i	0.880758	−	0.473567i
$13$	41.2830	−	22.1971i	0.880758	−	0.473567i
$14$		0			0
$15$	5.71114	−	9.89198i	0.0983073	−	0.170273i
$16$		0			0
$17$	28.8372	+	49.9474i	0.411414	+	0.712590i	0.995045	−	0.0994294i	$-0.0317017\pi$
$17$	28.8372	+	49.9474i	0.411414	+	0.712590i	−0.583631	+	0.812019i	$0.698368\pi$
$18$		0			0
$19$	36.2462	+	62.7803i	0.437655	+	0.758042i	0.997508	−	0.0705506i	$-0.0224756\pi$
$19$	36.2462	+	62.7803i	0.437655	+	0.758042i	−0.559853	+	0.828592i	$0.689142\pi$
$20$		0			0
$21$	−8.55588			−0.0889070
$22$		0			0
$23$	−104.854	+	181.612i	−0.950586	+	1.64646i	−0.206425	+	0.978462i	$0.566183\pi$
$23$	−104.854	+	181.612i	−0.950586	+	1.64646i	−0.744161	+	0.668001i	$0.767150\pi$
$24$		0			0
$25$	−110.504			−0.884028
$26$		0			0
$27$	27.0000			0.192450
$28$		0			0
$29$	66.1062	−	114.499i	0.423297	−	0.733172i	−0.572963	−	0.819581i	$-0.694206\pi$
$29$	66.1062	−	114.499i	0.423297	−	0.733172i	0.996260	+	0.0864097i	$0.0275394\pi$
$30$		0			0
$31$	275.352			1.59531			0.797657	−	0.603112i	$-0.206073\pi$
$31$	275.352			1.59531			0.797657	+	0.603112i	$0.206073\pi$
$32$		0			0
$33$	46.8548	+	81.1550i	0.247163	+	0.428099i
$34$		0			0
$35$	−5.42931	−	9.40385i	−0.0262206	−	0.0454154i
$36$		0			0
$37$	−183.197	+	317.306i	−0.813982	+	1.40986i	0.0960748	+	0.995374i	$0.469371\pi$
$37$	−183.197	+	317.306i	−0.813982	+	1.40986i	−0.910057	+	0.414484i	$0.863962\pi$
$38$		0			0
$39$	−4.25473	+	140.552i	−0.0174693	+	0.577086i
$40$		0			0
$41$	−84.5698	+	146.479i	−0.322136	+	0.557956i	−0.980929	−	0.194369i	$-0.937734\pi$
$41$	−84.5698	+	146.479i	−0.322136	+	0.557956i	0.658793	+	0.752325i	$0.271068\pi$
$42$		0			0
$43$	166.089	+	287.675i	0.589032	+	1.02023i	0.994359	+	0.106062i	$0.0338243\pi$
$43$	166.089	+	287.675i	0.589032	+	1.02023i	−0.405327	+	0.914172i	$0.632842\pi$
$44$		0			0
$45$	17.1334	+	29.6759i	0.0567577	+	0.0983073i
$46$		0			0
$47$	183.320			0.568937			0.284468	−	0.958685i	$-0.408183\pi$
$47$	183.320			0.568937			0.284468	+	0.958685i	$0.408183\pi$
$48$		0			0
$49$	167.433	−	290.003i	0.488143	−	0.845489i
$50$		0			0
$51$	−173.023			−0.475060
$52$		0			0
$53$	−502.390			−1.30205			−0.651024	−	0.759057i	$-0.725660\pi$
$53$	−502.390			−1.30205			−0.651024	+	0.759057i	$0.725660\pi$
$54$		0			0
$55$	−59.4654	+	102.997i	−0.145788	+	0.252511i
$56$		0			0
$57$	−217.477			−0.505361
$58$		0			0
$59$	443.397	+	767.986i	0.978396	+	1.69463i	0.668239	+	0.743947i	$0.267049\pi$
$59$	443.397	+	767.986i	0.978396	+	1.69463i	0.310158	+	0.950685i	$0.399618\pi$
$60$		0			0
$61$	452.914	+	784.470i	0.950651	+	1.64657i	0.744022	+	0.668156i	$0.232916\pi$
$61$	452.914	+	784.470i	0.950651	+	1.64657i	0.206629	+	0.978419i	$0.433751\pi$
$62$		0			0
$63$	12.8338	−	22.2288i	0.0256652	−	0.0444535i
$64$		0			0
$65$	−157.182	+	84.5138i	−0.299939	+	0.161272i
$66$		0			0
$67$	59.8583	−	103.678i	0.109147	−	0.189048i	−0.806278	−	0.591537i	$-0.798521\pi$
$67$	59.8583	−	103.678i	0.109147	−	0.189048i	0.915425	+	0.402489i	$0.131855\pi$
$68$		0			0
$69$	−314.561	−	544.835i	−0.548821	−	0.950586i
$70$		0			0
$71$	−231.484	−	400.942i	−0.386931	−	0.670184i	0.605104	−	0.796146i	$-0.293132\pi$
$71$	−231.484	−	400.942i	−0.386931	−	0.670184i	−0.992035	+	0.125962i	$0.959798\pi$
$72$		0			0
$73$	−63.0078			−0.101021			−0.0505103	−	0.998724i	$-0.516085\pi$
$73$	−63.0078			−0.101021			−0.0505103	+	0.998724i	$0.516085\pi$
$74$		0			0
$75$	165.755	−	287.097i	0.255197	−	0.442014i
$76$		0			0
$77$	89.0855			0.131847
$78$		0			0
$79$	791.154			1.12673			0.563366	−	0.826207i	$-0.309506\pi$
$79$	791.154			1.12673			0.563366	+	0.826207i	$0.309506\pi$
$80$		0			0
$81$	−40.5000	+	70.1481i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	171.481			0.226776			0.113388	−	0.993551i	$-0.463830\pi$
$83$	171.481			0.226776			0.113388	+	0.993551i	$0.463830\pi$
$84$		0			0
$85$	−109.795	−	190.171i	−0.140106	−	0.242670i
$86$		0			0
$87$	198.319	+	343.498i	0.244391	+	0.423297i
$88$		0			0
$89$	92.6713	−	160.511i	0.110372	−	0.191171i	−0.805548	−	0.592530i	$-0.798129\pi$
$89$	92.6713	−	160.511i	0.110372	−	0.191171i	0.915920	+	0.401360i	$0.131462\pi$
$90$		0			0
$91$	113.693	+	70.3111i	0.130970	+	0.0809956i
$92$		0			0
$93$	−413.028	+	715.386i	−0.460527	+	0.797657i
$94$		0			0
$95$	−138.005	−	239.031i	−0.149042	−	0.258148i
$96$		0			0
$97$	−363.951	−	630.381i	−0.380965	−	0.659851i	0.610235	−	0.792220i	$-0.291075\pi$
$97$	−363.951	−	630.381i	−0.380965	−	0.659851i	−0.991200	+	0.132369i	$0.957742\pi$
$98$		0			0
$99$	−281.129			−0.285399
$100$		0			0
$101$	−162.970	+	282.272i	−0.160555	+	0.278090i	−0.935068	−	0.354469i	$-0.884662\pi$
$101$	−162.970	+	282.272i	−0.160555	+	0.278090i	0.774513	+	0.632558i	$0.217995\pi$
$102$		0			0
$103$	1673.67			1.60109			0.800543	−	0.599275i	$-0.204544\pi$
$103$	1673.67			1.60109			0.800543	+	0.599275i	$0.204544\pi$
$104$		0			0
$105$	32.5759			0.0302770
$106$		0			0
$107$	−37.7049	+	65.3068i	−0.0340661	+	0.0590042i	−0.882556	−	0.470208i	$-0.844179\pi$
$107$	−37.7049	+	65.3068i	−0.0340661	+	0.0590042i	0.848490	+	0.529212i	$0.177512\pi$
$108$		0			0
$109$	236.140			0.207505			0.103753	−	0.994603i	$-0.466915\pi$
$109$	236.140			0.207505			0.103753	+	0.994603i	$0.466915\pi$
$110$		0			0
$111$	−549.590	−	951.917i	−0.469953	−	0.813982i
$112$		0			0
$113$	−1061.93	−	1839.32i	−0.884054	−	1.53123i	−0.846794	−	0.531920i	$-0.821471\pi$
$113$	−1061.93	−	1839.32i	−0.884054	−	1.53123i	−0.0372595	−	0.999306i	$-0.511863\pi$
$114$		0			0
$115$	399.222	−	691.473i	0.323719	−	0.560697i
$116$		0			0
$117$	−358.783	−	221.882i	−0.283500	−	0.175325i
$118$		0			0
$119$	−82.2424	+	142.448i	−0.0633542	+	0.109733i
$120$		0			0
$121$	177.639	+	307.679i	0.133463	+	0.231164i
$122$		0			0
$123$	−253.709	−	439.437i	−0.185985	−	0.322136i
$124$		0			0
$125$	896.662			0.641599
$126$		0			0
$127$	425.946	−	737.761i	0.297611	−	0.515478i	−0.677978	−	0.735083i	$-0.737143\pi$
$127$	425.946	−	737.761i	0.297611	−	0.515478i	0.975589	+	0.219605i	$0.0704767\pi$
$128$		0			0
$129$	−996.536			−0.680156
$130$		0			0
$131$	−2154.16			−1.43672			−0.718360	−	0.695672i	$-0.755107\pi$
$131$	−2154.16			−1.43672			−0.718360	+	0.695672i	$0.755107\pi$
$132$		0			0
$133$	−103.373	+	179.047i	−0.0673952	+	0.116732i
$134$		0			0
$135$	−102.800			−0.0655382
$136$		0			0
$137$	−882.673	−	1528.84i	−0.550452	−	0.953410i	−0.998242	−	0.0592716i	$-0.981122\pi$
$137$	−882.673	−	1528.84i	−0.550452	−	0.953410i	0.447790	−	0.894139i	$-0.352211\pi$
$138$		0			0
$139$	−248.502	−	430.419i	−0.151638	−	0.262645i	0.780192	−	0.625540i	$-0.215121\pi$
$139$	−248.502	−	430.419i	−0.151638	−	0.262645i	−0.931830	+	0.362896i	$0.881788\pi$
$140$		0			0
$141$	−274.981	+	476.281i	−0.164238	+	0.284468i
$142$		0			0
$143$	44.3010	−	1463.45i	0.0259065	−	0.855806i
$144$		0			0
$145$	−251.694	+	435.947i	−0.144152	+	0.249679i
$146$		0			0
$147$	502.299	+	870.008i	0.281830	+	0.488143i
$148$		0			0
$149$	−225.926	−	391.315i	−0.124218	−	0.215153i	0.797209	−	0.603704i	$-0.206309\pi$
$149$	−225.926	−	391.315i	−0.124218	−	0.215153i	−0.921427	+	0.388551i	$0.872976\pi$
$150$		0			0
$151$	1567.08			0.844553			0.422277	−	0.906467i	$-0.361231\pi$
$151$	1567.08			0.844553			0.422277	+	0.906467i	$0.361231\pi$
$152$		0			0
$153$	259.534	−	449.527i	0.137138	−	0.237530i
$154$		0			0
$155$	−1048.38			−0.543278
$156$		0			0
$157$	−583.320			−0.296522			−0.148261	−	0.988948i	$-0.547368\pi$
$157$	−583.320			−0.296522			−0.148261	+	0.988948i	$0.547368\pi$
$158$		0			0
$159$	753.584	−	1305.25i	0.375869	−	0.651024i
$160$		0			0
$161$	−598.077			−0.292764
$162$		0			0
$163$	1244.61	+	2155.73i	0.598070	+	1.03589i	0.993106	+	0.117222i	$0.0373988\pi$
$163$	1244.61	+	2155.73i	0.598070	+	1.03589i	−0.395036	+	0.918666i	$0.629268\pi$
$164$		0			0
$165$	−178.396	−	308.991i	−0.0841705	−	0.145788i
$166$		0			0
$167$	−763.667	+	1322.71i	−0.353858	+	0.612900i	−0.986922	−	0.161199i	$-0.948464\pi$
$167$	−763.667	+	1322.71i	−0.353858	+	0.612900i	0.633064	+	0.774100i	$0.281797\pi$
$168$		0			0
$169$	1211.58	−	1832.73i	0.551468	−	0.834196i
$170$		0			0
$171$	326.216	−	565.023i	0.145885	−	0.252681i
$172$		0			0
$173$	−1323.09	−	2291.66i	−0.581461	−	1.00712i	−0.995307	−	0.0967725i	$-0.969148\pi$
$173$	−1323.09	−	2291.66i	−0.581461	−	1.00712i	0.413846	−	0.910347i	$-0.364185\pi$
$174$		0			0
$175$	−157.576	−	272.929i	−0.0680664	−	0.117894i
$176$		0			0
$177$	−2660.38			−1.12975
$178$		0			0
$179$	−973.528	+	1686.20i	−0.406508	+	0.704092i	−0.994496	−	0.104778i	$-0.966587\pi$
$179$	−973.528	+	1686.20i	−0.406508	+	0.704092i	0.587988	+	0.808870i	$0.299920\pi$
$180$		0			0
$181$	2883.62			1.18419			0.592093	−	0.805869i	$-0.298302\pi$
$181$	2883.62			1.18419			0.592093	+	0.805869i	$0.298302\pi$
$182$		0			0
$183$	−2717.48			−1.09772
$184$		0			0
$185$	697.507	−	1208.12i	0.277199	−	0.480122i
$186$		0			0
$187$	1801.55			0.704504
$188$		0			0
$189$	38.5015	+	66.6865i	0.0148178	+	0.0256652i
$190$		0			0
$191$	1368.50	+	2370.31i	0.518434	+	0.897954i	0.999771	+	0.0214184i	$0.00681822\pi$
$191$	1368.50	+	2370.31i	0.518434	+	0.897954i	−0.481336	+	0.876536i	$0.659848\pi$
$192$		0			0
$193$	−669.007	+	1158.75i	−0.249514	+	0.432171i	−0.963391	−	0.268100i	$-0.913604\pi$
$193$	−669.007	+	1158.75i	−0.249514	+	0.432171i	0.713877	+	0.700271i	$0.246937\pi$
$194$		0			0
$195$	16.1995	−	535.142i	0.00594910	−	0.196525i
$196$		0			0
$197$	−852.088	+	1475.86i	−0.308166	+	0.533759i	−0.977961	−	0.208787i	$-0.933049\pi$
$197$	−852.088	+	1475.86i	−0.308166	+	0.533759i	0.669795	+	0.742546i	$0.266382\pi$
$198$		0			0
$199$	−1639.73	−	2840.10i	−0.584108	−	1.01171i	−0.994986	−	0.100015i	$-0.968111\pi$
$199$	−1639.73	−	2840.10i	−0.584108	−	1.01171i	0.410878	−	0.911690i	$-0.365222\pi$
$200$		0			0
$201$	179.575	+	311.033i	0.0630162	+	0.109147i
$202$		0			0
$203$	377.065			0.130368
$204$		0			0
$205$	321.993	−	557.708i	0.109702	−	0.190010i
$206$		0			0
$207$	1887.36			0.633724
$208$		0			0
$209$	2264.41			0.749439
$210$		0			0
$211$	1549.42	−	2683.68i	0.505530	−	0.875603i	−0.494450	−	0.869206i	$-0.664631\pi$
$211$	1549.42	−	2683.68i	0.505530	−	0.875603i	0.999980	−	0.00639673i	$-0.00203616\pi$
$212$		0			0
$213$	1388.90			0.446790
$214$		0			0
$215$	−632.373	−	1095.30i	−0.200593	−	0.347437i
$216$		0			0
$217$	392.647	+	680.085i	0.122832	+	0.212752i
$218$		0			0
$219$	94.5118	−	163.699i	0.0291622	−	0.0505103i
$220$		0			0
$221$	2299.17	+	1421.88i	0.699815	+	0.432787i
$222$		0			0
$223$	−3003.48	+	5202.18i	−0.901918	+	1.56217i	−0.0769169	+	0.997038i	$0.524508\pi$
$223$	−3003.48	+	5202.18i	−0.901918	+	1.56217i	−0.825001	+	0.565131i	$0.808826\pi$
$224$		0			0
$225$	497.266	+	861.290i	0.147338	+	0.255197i
$226$		0			0
$227$	−1966.15	−	3405.47i	−0.574881	−	0.995723i	−0.996055	−	0.0887427i	$-0.971715\pi$
$227$	−1966.15	−	3405.47i	−0.574881	−	0.995723i	0.421174	−	0.906980i	$-0.361618\pi$
$228$		0			0
$229$	−1587.69			−0.458156			−0.229078	−	0.973408i	$-0.573571\pi$
$229$	−1587.69			−0.458156			−0.229078	+	0.973408i	$0.573571\pi$
$230$		0			0
$231$	−133.628	+	231.451i	−0.0380610	+	0.0659236i
$232$		0			0
$233$	3963.88			1.11452			0.557259	−	0.830339i	$-0.311853\pi$
$233$	3963.88			1.11452			0.557259	+	0.830339i	$0.311853\pi$
$234$		0			0
$235$	−697.979			−0.193749
$236$		0			0
$237$	−1186.73	+	2055.48i	−0.325260	+	0.563366i
$238$		0			0
$239$	−2034.66			−0.550676			−0.275338	−	0.961348i	$-0.588790\pi$
$239$	−2034.66			−0.550676			−0.275338	+	0.961348i	$0.588790\pi$
$240$		0			0
$241$	−200.880	−	347.934i	−0.0536922	−	0.0929975i	0.837930	−	0.545778i	$-0.183766\pi$
$241$	−200.880	−	347.934i	−0.0536922	−	0.0929975i	−0.891622	+	0.452780i	$0.850432\pi$
$242$		0			0
$243$	−121.500	−	210.444i	−0.0320750	−	0.0555556i
$244$		0			0
$245$	−637.489	+	1104.16i	−0.166235	+	0.287928i
$246$		0			0
$247$	2889.90	+	1787.20i	0.744452	+	0.460392i
$248$		0			0
$249$	−257.221	+	445.520i	−0.0654647	+	0.113388i
$250$		0			0
$251$	−643.211	−	1114.07i	−0.161749	−	0.280158i	0.773747	−	0.633495i	$-0.218380\pi$
$251$	−643.211	−	1114.07i	−0.161749	−	0.280158i	−0.935496	+	0.353337i	$0.885047\pi$
$252$		0			0
$253$	3275.26	+	5672.92i	0.813890	+	1.40970i
$254$		0			0
$255$	658.772			0.161780
$256$		0			0
$257$	2994.40	−	5186.45i	0.726792	−	1.25884i	−0.231440	−	0.972849i	$-0.574344\pi$
$257$	2994.40	−	5186.45i	0.726792	−	1.25884i	0.958232	−	0.285992i	$-0.0923229\pi$
$258$		0			0
$259$	−1044.94			−0.250692
$260$		0			0
$261$	−1189.91			−0.282198
$262$		0			0
$263$	−3696.75	+	6402.96i	−0.866735	+	1.50123i	−0.00142176	+	0.999999i	$0.500453\pi$
$263$	−3696.75	+	6402.96i	−0.866735	+	1.50123i	−0.865314	+	0.501231i	$0.832881\pi$
$264$		0			0
$265$	1912.81			0.443408
$266$		0			0
$267$	278.014	+	481.534i	0.0637235	+	0.110372i
$268$		0			0
$269$	523.627	+	906.949i	0.118684	+	0.205567i	0.919247	−	0.393682i	$-0.128799\pi$
$269$	523.627	+	906.949i	0.118684	+	0.205567i	−0.800562	+	0.599250i	$0.795466\pi$
$270$		0			0
$271$	1257.46	−	2177.98i	0.281863	−	0.488202i	−0.689980	−	0.723828i	$-0.742381\pi$
$271$	1257.46	−	2177.98i	0.281863	−	0.488202i	0.971844	+	0.235626i	$0.0757142\pi$
$272$		0			0
$273$	−353.213	+	189.916i	−0.0783055	+	0.0421034i
$274$		0			0
$275$	−1725.87	+	2989.30i	−0.378452	+	0.655497i
$276$		0			0
$277$	3998.12	+	6924.95i	0.867234	+	1.50209i	0.864812	+	0.502097i	$0.167438\pi$
$277$	3998.12	+	6924.95i	0.867234	+	1.50209i	0.00242261	+	0.999997i	$0.499229\pi$
$278$		0			0
$279$	−1239.09	−	2146.16i	−0.265886	−	0.460527i
$280$		0			0
$281$	−49.7096			−0.0105531			−0.00527656	−	0.999986i	$-0.501680\pi$
$281$	−49.7096			−0.0105531			−0.00527656	+	0.999986i	$0.501680\pi$
$282$		0			0
$283$	−1039.15	+	1799.86i	−0.218272	+	0.378059i	−0.954280	−	0.298914i	$-0.903375\pi$
$283$	−1039.15	+	1799.86i	−0.218272	+	0.378059i	0.736007	+	0.676973i	$0.236709\pi$
$284$		0			0
$285$	828.029			0.172099
$286$		0			0
$287$	−482.379			−0.0992124
$288$		0			0
$289$	793.337	−	1374.10i	0.161477	−	0.279687i
$290$		0			0
$291$	2183.70			0.439901
$292$		0			0
$293$	4757.28	+	8239.85i	0.948544	+	1.64293i	0.748495	+	0.663141i	$0.230777\pi$
$293$	4757.28	+	8239.85i	0.948544	+	1.64293i	0.200049	+	0.979786i	$0.435890\pi$
$294$		0			0
$295$	−1688.20	−	2924.05i	−0.333189	−	0.577101i
$296$		0			0
$297$	421.694	−	730.395i	0.0823877	−	0.142700i
$298$		0			0
$299$	−297.415	+	9824.93i	−0.0575250	+	1.90030i
$300$		0			0
$301$	−473.680	+	820.439i	−0.0907059	+	0.157107i
$302$		0			0
$303$	−488.909	−	846.815i	−0.0926966	−	0.160555i
$304$		0			0
$305$	−1724.44	−	2986.81i	−0.323741	−	0.560735i
$306$		0			0
$307$	−4400.52			−0.818082			−0.409041	−	0.912516i	$-0.634137\pi$
$307$	−4400.52			−0.818082			−0.409041	+	0.912516i	$0.634137\pi$
$308$		0			0
$309$	−2510.51	+	4348.33i	−0.462194	+	0.800543i
$310$		0			0
$311$	1884.39			0.343581			0.171791	−	0.985133i	$-0.445045\pi$
$311$	1884.39			0.343581			0.171791	+	0.985133i	$0.445045\pi$
$312$		0			0
$313$	−8261.53			−1.49191			−0.745957	−	0.665994i	$-0.768008\pi$
$313$	−8261.53			−1.49191			−0.745957	+	0.665994i	$0.768008\pi$
$314$		0			0
$315$	−48.8638	+	84.6346i	−0.00874020	+	0.0151385i
$316$		0			0
$317$	10463.5			1.85391			0.926956	−	0.375170i	$-0.122416\pi$
$317$	10463.5			1.85391			0.926956	+	0.375170i	$0.122416\pi$
$318$		0			0
$319$	−2064.93	−	3576.56i	−0.362426	−	0.627740i
$320$		0			0
$321$	−113.115	−	195.920i	−0.0196681	−	0.0340661i
$322$		0			0
$323$	−2090.48	+	3620.81i	−0.360115	+	0.623738i
$324$		0			0
$325$	−4561.92	+	2452.86i	−0.778615	+	0.418647i
$326$		0			0
$327$	−354.209	+	613.508i	−0.0599016	+	0.103753i
$328$		0			0
$329$	261.411	+	452.778i	0.0438057	+	0.0758737i
$330$		0			0
$331$	−2605.86	−	4513.48i	−0.432722	−	0.749496i	0.564385	−	0.825512i	$-0.309113\pi$
$331$	−2605.86	−	4513.48i	−0.432722	−	0.749496i	−0.997107	+	0.0760157i	$0.975780\pi$
$332$		0			0
$333$	3297.54			0.542655
$334$		0			0
$335$	−227.906	+	394.745i	−0.0371697	+	0.0643798i
$336$		0			0
$337$	2781.65			0.449632			0.224816	−	0.974401i	$-0.427822\pi$
$337$	2781.65			0.449632			0.224816	+	0.974401i	$0.427822\pi$
$338$		0			0
$339$	6371.59			1.02082
$340$		0			0
$341$	4300.53	−	7448.73i	0.682952	−	1.18291i
$342$		0			0
$343$	1933.25			0.304331
$344$		0			0
$345$	1197.67	+	2074.42i	0.186899	+	0.323719i
$346$		0			0
$347$	−5170.88	−	8956.22i	−0.799963	−	1.38558i	−0.919639	−	0.392764i	$-0.871519\pi$
$347$	−5170.88	−	8956.22i	−0.799963	−	1.38558i	0.119676	−	0.992813i	$-0.461814\pi$
$348$		0			0
$349$	−4379.50	+	7585.52i	−0.671717	+	1.16345i	0.305700	+	0.952128i	$0.401110\pi$
$349$	−4379.50	+	7585.52i	−0.671717	+	1.16345i	−0.977417	+	0.211320i	$0.932224\pi$
$350$		0			0
$351$	1114.64	−	599.322i	0.169502	−	0.0911380i
$352$		0			0
$353$	−3671.12	+	6358.56i	−0.553523	+	0.958731i	0.444493	+	0.895782i	$0.353384\pi$
$353$	−3671.12	+	6358.56i	−0.553523	+	0.958731i	−0.998017	+	0.0629485i	$0.979950\pi$
$354$		0			0
$355$	881.358	+	1526.56i	0.131768	+	0.228229i
$356$		0			0
$357$	−246.727	−	427.344i	−0.0365776	−	0.0633542i
$358$		0			0
$359$	2103.58			0.309256			0.154628	−	0.987973i	$-0.450582\pi$
$359$	2103.58			0.309256			0.154628	+	0.987973i	$0.450582\pi$
$360$		0			0
$361$	801.923	−	1388.97i	0.116915	−	0.202503i
$362$		0			0
$363$	−1065.83			−0.154109
$364$		0			0
$365$	239.898			0.0344022
$366$		0			0
$367$	−209.519	+	362.898i	−0.0298006	+	0.0516162i	−0.880541	−	0.473970i	$-0.842821\pi$
$367$	−209.519	+	362.898i	−0.0298006	+	0.0516162i	0.850740	+	0.525586i	$0.176154\pi$
$368$		0			0
$369$	1522.26			0.214757
$370$		0			0
$371$	−716.398	−	1240.84i	−0.100252	−	0.173642i
$372$		0			0
$373$	−3458.15	−	5989.70i	−0.480044	−	0.831460i	0.519694	−	0.854352i	$-0.326046\pi$
$373$	−3458.15	−	5989.70i	−0.480044	−	0.831460i	−0.999738	+	0.0228921i	$0.992713\pi$
$374$		0			0
$375$	−1344.99	+	2329.60i	−0.185214	+	0.320799i
$376$		0			0
$377$	187.509	−	6194.24i	0.0256159	−	0.846206i
$378$		0			0
$379$	1126.13	−	1950.51i	0.152626	−	0.264356i	−0.779566	−	0.626320i	$-0.784560\pi$
$379$	1126.13	−	1950.51i	0.152626	−	0.264356i	0.932192	+	0.361964i	$0.117894\pi$
$380$		0			0
$381$	1277.84	+	2213.28i	0.171826	+	0.297611i
$382$		0			0
$383$	−2049.99	−	3550.69i	−0.273498	−	0.473712i	0.696257	−	0.717792i	$-0.254847\pi$
$383$	−2049.99	−	3550.69i	−0.273498	−	0.473712i	−0.969755	+	0.244080i	$0.921514\pi$
$384$		0			0
$385$	−339.186			−0.0449001
$386$		0			0
$387$	1494.80	−	2589.08i	0.196344	−	0.340078i
$388$		0			0
$389$	9346.70			1.21824			0.609121	−	0.793077i	$-0.291522\pi$
$389$	9346.70			1.21824			0.609121	+	0.793077i	$0.291522\pi$
$390$		0			0
$391$	−12094.7			−1.56434
$392$		0			0
$393$	3231.25	−	5596.68i	0.414745	−	0.718360i
$394$		0			0
$395$	−3012.26			−0.383705
$396$		0			0
$397$	−3464.14	−	6000.07i	−0.437935	−	0.758526i	0.559595	−	0.828766i	$-0.310957\pi$
$397$	−3464.14	−	6000.07i	−0.437935	−	0.758526i	−0.997530	+	0.0702404i	$0.977623\pi$
$398$		0			0
$399$	−310.118	−	537.141i	−0.0389106	−	0.0673952i
$400$		0			0
$401$	3622.23	−	6273.89i	0.451087	−	0.781305i	−0.547367	−	0.836893i	$-0.684370\pi$
$401$	3622.23	−	6273.89i	0.451087	−	0.781305i	0.998454	+	0.0555875i	$0.0177032\pi$
$402$		0			0
$403$	11367.4	−	6112.03i	1.40508	−	0.755488i
$404$		0			0
$405$	154.201	−	267.083i	0.0189192	−	0.0327691i
$406$		0			0
$407$	5722.43	+	9911.54i	0.696930	+	1.20712i
$408$		0			0
$409$	−6210.24	−	10756.5i	−0.750798	−	1.30042i	−0.947436	−	0.319945i	$-0.896336\pi$
$409$	−6210.24	−	10756.5i	−0.750798	−	1.30042i	0.196638	−	0.980476i	$-0.436998\pi$
$410$		0			0
$411$	5296.04			0.635607
$412$		0			0
$413$	−1264.55	+	2190.27i	−0.150665	+	0.260959i
$414$		0			0
$415$	−652.899			−0.0772279
$416$		0			0
$417$	1491.01			0.175097
$418$		0			0
$419$	5807.38	−	10058.7i	0.677110	−	1.17279i	−0.298737	−	0.954335i	$-0.596565\pi$
$419$	5807.38	−	10058.7i	0.677110	−	1.17279i	0.975847	−	0.218454i	$-0.0701012\pi$
$420$		0			0
$421$	−2091.69			−0.242144			−0.121072	−	0.992644i	$-0.538633\pi$
$421$	−2091.69			−0.242144			−0.121072	+	0.992644i	$0.538633\pi$
$422$		0			0
$423$	−824.942	−	1428.84i	−0.0948228	−	0.164238i
$424$		0			0
$425$	−3186.61	−	5519.37i	−0.363702	−	0.629950i
$426$		0			0
$427$	−1291.69	+	2237.28i	−0.146392	+	0.253558i
$428$		0			0
$429$	3735.72	+	2310.28i	0.420424	+	0.260003i
$430$		0			0
$431$	−4469.65	+	7741.65i	−0.499525	+	0.865203i	−1.00000		0.000548435i	$-0.999825\pi$
$431$	−4469.65	+	7741.65i	−0.499525	+	0.865203i	0.500475	+	0.865751i	$0.333159\pi$
$432$		0			0
$433$	−7285.29	−	12618.5i	−0.808565	−	1.40048i	−0.913858	−	0.406035i	$-0.866911\pi$
$433$	−7285.29	−	12618.5i	−0.808565	−	1.40048i	0.105293	−	0.994441i	$-0.466422\pi$
$434$		0			0
$435$	−755.083	−	1307.84i	−0.0832263	−	0.144152i
$436$		0			0
$437$	−15202.2			−1.66412
$438$		0			0
$439$	−1053.74	+	1825.14i	−0.114561	+	0.198426i	−0.917604	−	0.397495i	$-0.869880\pi$
$439$	−1053.74	+	1825.14i	−0.114561	+	0.198426i	0.803043	+	0.595921i	$0.203213\pi$
$440$		0			0
$441$	−3013.80			−0.325429
$442$		0			0
$443$	1575.08			0.168926			0.0844632	−	0.996427i	$-0.473082\pi$
$443$	1575.08			0.168926			0.0844632	+	0.996427i	$0.473082\pi$
$444$		0			0
$445$	−352.839	+	611.135i	−0.0375869	+	0.0651024i
$446$		0			0
$447$	1355.55			0.143435
$448$		0			0
$449$	−8510.83	−	14741.2i	−0.894545	−	1.54940i	−0.834366	−	0.551210i	$-0.814166\pi$
$449$	−8510.83	−	14741.2i	−0.894545	−	1.54940i	−0.0601792	−	0.998188i	$-0.519167\pi$
$450$		0			0
$451$	2641.67	+	4575.50i	0.275812	+	0.477721i
$452$		0			0
$453$	−2350.63	+	4071.41i	−0.243802	+	0.422277i
$454$		0			0
$455$	−432.877	−	267.704i	−0.0446013	−	0.0275828i
$456$		0			0
$457$	−3121.54	+	5406.67i	−0.319518	+	0.553421i	−0.980387	−	0.197080i	$-0.936854\pi$
$457$	−3121.54	+	5406.67i	−0.319518	+	0.553421i	0.660870	+	0.750501i	$0.270188\pi$
$458$		0			0
$459$	778.603	+	1348.58i	0.0791767	+	0.137138i
$460$		0			0
$461$	1202.67	+	2083.08i	0.121505	+	0.210453i	0.920361	−	0.391069i	$-0.127895\pi$
$461$	1202.67	+	2083.08i	0.121505	+	0.210453i	−0.798856	+	0.601522i	$0.794561\pi$
$462$		0			0
$463$	−1528.85			−0.153460			−0.0767299	−	0.997052i	$-0.524448\pi$
$463$	−1528.85			−0.153460			−0.0767299	+	0.997052i	$0.524448\pi$
$464$		0			0
$465$	1572.57	−	2723.78i	0.156831	−	0.271639i
$466$		0			0
$467$	9991.32			0.990028			0.495014	−	0.868885i	$-0.335163\pi$
$467$	9991.32			0.990028			0.495014	+	0.868885i	$0.335163\pi$
$468$		0			0
$469$	341.427			0.0336155
$470$		0			0
$471$	874.980	−	1515.51i	0.0855986	−	0.148261i
$472$		0			0
$473$	10376.1			1.00866
$474$		0			0
$475$	−4005.34	−	6937.44i	−0.386900	−	0.670130i
$476$		0			0
$477$	2260.75	+	3915.74i	0.217008	+	0.375869i
$478$		0			0
$479$	8790.88	−	15226.2i	0.838550	−	1.45241i	−0.0525568	−	0.998618i	$-0.516737\pi$
$479$	8790.88	−	15226.2i	0.838550	−	1.45241i	0.891107	−	0.453793i	$-0.149930\pi$
$480$		0			0
$481$	−519.634	+	17165.8i	−0.0492584	+	1.62722i
$482$		0			0
$483$	897.115	−	1553.85i	0.0845137	−	0.146382i
$484$		0			0
$485$	1385.72	+	2400.13i	0.129736	+	0.224710i
$486$		0			0
$487$	−6741.70	−	11677.0i	−0.627301	−	1.08652i	−0.988091	−	0.153870i	$-0.950826\pi$
$487$	−6741.70	−	11677.0i	−0.627301	−	1.08652i	0.360790	−	0.932647i	$-0.382507\pi$
$488$		0			0
$489$	−7467.66			−0.690592
$490$		0			0
$491$	−3370.36	+	5837.64i	−0.309781	+	0.536556i	−0.978314	−	0.207126i	$-0.933589\pi$
$491$	−3370.36	+	5837.64i	−0.309781	+	0.536556i	0.668533	+	0.743682i	$0.266922\pi$
$492$		0			0
$493$	7625.26			0.696601
$494$		0			0
$495$	1070.38			0.0971917
$496$		0			0
$497$	660.184	−	1143.47i	0.0595841	−	0.103203i
$498$		0			0
$499$	−21556.6			−1.93388			−0.966941	−	0.255002i	$-0.917924\pi$
$499$	−21556.6			−1.93388			−0.966941	+	0.255002i	$0.917924\pi$
$500$		0			0
$501$	−2291.00	−	3968.13i	−0.204300	−	0.353858i
$502$		0			0
$503$	2270.63	+	3932.84i	0.201277	+	0.348622i	0.948940	−	0.315456i	$-0.102158\pi$
$503$	2270.63	+	3932.84i	0.201277	+	0.348622i	−0.747663	+	0.664078i	$0.768824\pi$
$504$		0			0
$505$	620.494	−	1074.73i	0.0546765	−	0.0947025i
$506$		0			0
$507$	2944.20	+	5896.86i	0.257903	+	0.516546i
$508$		0			0
$509$	−970.420	+	1680.82i	−0.0845051	+	0.146367i	−0.905180	−	0.425028i	$-0.860264\pi$
$509$	−970.420	+	1680.82i	−0.0845051	+	0.146367i	0.820675	+	0.571395i	$0.193598\pi$
$510$		0			0
$511$	−89.8480	−	155.621i	−0.00777816	−	0.0134722i
$512$		0			0
$513$	978.648	+	1695.07i	0.0842268	+	0.145885i
$514$		0			0
$515$	−6372.38			−0.545244
$516$		0			0
$517$	2863.15	−	4959.12i	0.243561	−	0.421861i
$518$		0			0
$519$	7938.54			0.671413
$520$		0			0
$521$	−3134.43			−0.263574			−0.131787	−	0.991278i	$-0.542071\pi$
$521$	−3134.43			−0.263574			−0.131787	+	0.991278i	$0.542071\pi$
$522$		0			0
$523$	410.124	−	710.355i	0.0342896	−	0.0593913i	−0.848371	−	0.529402i	$-0.822416\pi$
$523$	410.124	−	710.355i	0.0342896	−	0.0593913i	0.882661	+	0.470010i	$0.155750\pi$
$524$		0			0
$525$	945.455			0.0785963
$526$		0			0
$527$	7940.38	+	13753.1i	0.656334	+	1.13680i
$528$		0			0
$529$	−15905.0	−	27548.3i	−1.30723	−	2.26418i
$530$		0			0
$531$	3990.57	−	6911.88i	0.326132	−	0.564877i
$532$		0			0
$533$	−239.881	+	7924.31i	−0.0194942	+	0.643977i
$534$		0			0
$535$	143.559	−	248.651i	0.0116011	−	0.0200937i
$536$		0			0
$537$	−2920.58	−	5058.60i	−0.234697	−	0.406508i
$538$		0			0
$539$	−5230.04	−	9058.69i	−0.417947	−	0.723906i
$540$		0			0
$541$	−19160.0			−1.52265			−0.761326	−	0.648369i	$-0.775451\pi$
$541$	−19160.0			−1.52265			−0.761326	+	0.648369i	$0.775451\pi$
$542$		0			0
$543$	−4325.43	+	7491.86i	−0.341845	+	0.592093i
$544$		0			0
$545$	−899.083			−0.0706651
$546$		0			0
$547$	5356.62			0.418707			0.209353	−	0.977840i	$-0.432864\pi$
$547$	5356.62			0.418707			0.209353	+	0.977840i	$0.432864\pi$
$548$		0			0
$549$	4076.23	−	7060.23i	0.316884	−	0.548858i
$550$		0			0
$551$	9584.40			0.741033
$552$		0			0
$553$	1128.17	+	1954.05i	0.0867535	+	0.150262i
$554$		0			0
$555$	2092.52	+	3624.35i	0.160041	+	0.277199i
$556$		0			0
$557$	−5067.83	+	8777.74i	−0.385513	+	0.667728i	−0.991840	−	0.127487i	$-0.959309\pi$
$557$	−5067.83	+	8777.74i	−0.385513	+	0.667728i	0.606327	+	0.795215i	$0.292642\pi$
$558$		0			0
$559$	13242.2	+	8189.40i	1.00194	+	0.619633i
$560$		0			0
$561$	−2702.32	+	4680.56i	−0.203373	+	0.352252i
$562$		0			0
$563$	7936.19	+	13745.9i	0.594086	+	1.02899i	0.993675	+	0.112293i	$0.0358195\pi$
$563$	7936.19	+	13745.9i	0.594086	+	1.02899i	−0.399589	+	0.916694i	$0.630847\pi$
$564$		0			0
$565$	4043.22	+	7003.07i	0.301061	+	0.521453i
$566$		0			0
$567$	−231.009			−0.0171102
$568$		0			0
$569$	−1129.68	+	1956.66i	−0.0832314	+	0.144161i	−0.904636	−	0.426185i	$-0.859857\pi$
$569$	−1129.68	+	1956.66i	−0.0832314	+	0.144161i	0.821405	+	0.570346i	$0.193191\pi$
$570$		0			0
$571$	19081.9			1.39851			0.699256	−	0.714871i	$-0.253515\pi$
$571$	19081.9			1.39851			0.699256	+	0.714871i	$0.253515\pi$
$572$		0			0
$573$	−8210.98			−0.598636
$574$		0			0
$575$	11586.7	−	20068.7i	0.840345	−	1.45552i
$576$		0			0
$577$	−14477.9			−1.04458			−0.522291	−	0.852767i	$-0.674923\pi$
$577$	−14477.9			−1.04458			−0.522291	+	0.852767i	$0.674923\pi$
$578$		0			0
$579$	−2007.02	−	3476.26i	−0.144057	−	0.249514i
$580$		0			0
$581$	244.528	+	423.535i	0.0174608	+	0.0302430i
$582$		0			0
$583$	−7846.46	+	13590.5i	−0.557405	+	0.965454i
$584$		0			0
$585$	1366.04	+	844.800i	0.0965449	+	0.0597063i
$586$		0			0
$587$	−8153.14	+	14121.6i	−0.573281	+	0.992952i	0.422945	+	0.906155i	$0.360996\pi$
$587$	−8153.14	+	14121.6i	−0.573281	+	0.992952i	−0.996226	+	0.0867965i	$0.972337\pi$
$588$		0			0
$589$	9980.48	+	17286.7i	0.698198	+	1.20931i
$590$		0			0
$591$	−2556.26	−	4427.58i	−0.177920	−	0.308166i
$592$		0			0
$593$	2307.13			0.159768			0.0798840	−	0.996804i	$-0.474545\pi$
$593$	2307.13			0.159768			0.0798840	+	0.996804i	$0.474545\pi$
$594$		0			0
$595$	313.132	−	542.360i	0.0215751	−	0.0373691i
$596$		0			0
$597$	9838.39			0.674470
$598$		0			0
$599$	−9313.70			−0.635305			−0.317652	−	0.948207i	$-0.602894\pi$
$599$	−9313.70			−0.635305			−0.317652	+	0.948207i	$0.602894\pi$
$600$		0			0
$601$	5914.14	−	10243.6i	0.401402	−	0.695249i	−0.592493	−	0.805575i	$-0.701856\pi$
$601$	5914.14	−	10243.6i	0.401402	−	0.695249i	0.993895	+	0.110326i	$0.0351896\pi$
$602$		0			0
$603$	−1077.45			−0.0727648
$604$		0			0
$605$	−676.346	−	1171.47i	−0.0454502	−	0.0787220i
$606$		0			0
$607$	−7773.53	−	13464.2i	−0.519799	−	0.900318i	−0.999735	−	0.0230147i	$-0.992674\pi$
$607$	−7773.53	−	13464.2i	−0.519799	−	0.900318i	0.479936	−	0.877303i	$-0.340660\pi$
$608$		0			0
$609$	−565.597	+	979.642i	−0.0376341	+	0.0651841i
$610$		0			0
$611$	7568.02	−	4069.19i	0.501096	−	0.269430i
$612$		0			0
$613$	−9238.88	+	16002.2i	−0.608736	+	1.05436i	0.382713	+	0.923867i	$0.374990\pi$
$613$	−9238.88	+	16002.2i	−0.608736	+	1.05436i	−0.991449	+	0.130494i	$0.958344\pi$
$614$		0			0
$615$	965.979	+	1673.12i	0.0633366	+	0.109702i
$616$		0			0
$617$	2107.40	+	3650.13i	0.137505	+	0.238167i	0.926552	−	0.376167i	$-0.122758\pi$
$617$	2107.40	+	3650.13i	0.137505	+	0.238167i	−0.789046	+	0.614334i	$0.789425\pi$
$618$		0			0
$619$	16719.1			1.08562			0.542809	−	0.839856i	$-0.317361\pi$
$619$	16719.1			1.08562			0.542809	+	0.839856i	$0.317361\pi$
$620$		0			0
$621$	−2831.05	+	4903.52i	−0.182940	+	0.316862i
$622$		0			0
$623$	528.590			0.0339928
$624$		0			0
$625$	10399.0			0.665534
$626$		0			0
$627$	−3396.62	+	5883.12i	−0.216345	+	0.374720i
$628$		0			0
$629$	−21131.5			−1.33953
$630$		0			0
$631$	11348.9	+	19656.9i	0.715996	+	1.24014i	0.962574	+	0.271019i	$0.0873606\pi$
$631$	11348.9	+	19656.9i	0.715996	+	1.24014i	−0.246578	+	0.969123i	$0.579306\pi$
$632$		0			0
$633$	4648.27	+	8051.04i	0.291868	+	0.505530i
$634$		0			0
$635$	−1621.76	+	2808.97i	−0.101350	+	0.175544i
$636$		0			0
$637$	474.921	−	15688.7i	0.0295401	−	0.975840i
$638$		0			0
$639$	−2083.36	+	3608.48i	−0.128977	+	0.223395i
$640$		0			0
$641$	5530.69	+	9579.44i	0.340794	+	0.590273i	0.984580	−	0.174932i	$-0.0559707\pi$
$641$	5530.69	+	9579.44i	0.340794	+	0.590273i	−0.643786	+	0.765205i	$0.722637\pi$
$642$		0			0
$643$	2692.21	+	4663.04i	0.165117	+	0.285991i	0.936697	−	0.350141i	$-0.113866\pi$
$643$	2692.21	+	4663.04i	0.165117	+	0.285991i	−0.771580	+	0.636133i	$0.780533\pi$
$644$		0			0
$645$	3794.24			0.231625
$646$		0			0
$647$	5658.67	−	9801.10i	0.343841	−	0.595550i	−0.641302	−	0.767289i	$-0.721605\pi$
$647$	5658.67	−	9801.10i	0.343841	−	0.595550i	0.985142	+	0.171739i	$0.0549386\pi$
$648$		0			0
$649$	27700.4			1.67540
$650$		0			0
$651$	−2355.88			−0.141835
$652$		0			0
$653$	3858.15	−	6682.51i	0.231212	−	0.400470i	−0.726953	−	0.686687i	$-0.759064\pi$
$653$	3858.15	−	6682.51i	0.231212	−	0.400470i	0.958165	+	0.286217i	$0.0923977\pi$
$654$		0			0
$655$	8201.82			0.489270
$656$		0			0
$657$	283.535	+	491.098i	0.0168368	+	0.0291622i
$658$		0			0
$659$	−7112.70	−	12319.6i	−0.420442	−	0.728228i	0.575540	−	0.817773i	$-0.304792\pi$
$659$	−7112.70	−	12319.6i	−0.420442	−	0.728228i	−0.995983	+	0.0895458i	$0.971458\pi$
$660$		0			0
$661$	−3887.18	+	6732.80i	−0.228735	+	0.396181i	−0.957433	−	0.288654i	$-0.906792\pi$
$661$	−3887.18	+	6732.80i	−0.228735	+	0.396181i	0.728698	+	0.684835i	$0.240126\pi$
$662$		0			0
$663$	−7142.91	+	3840.61i	−0.418413	+	0.224973i
$664$		0			0
$665$	393.584	−	681.708i	0.0229512	−	0.0397526i
$666$		0			0
$667$	13862.9	+	24011.3i	0.804760	+	1.39389i
$668$		0			0
$669$	−9010.43	−	15606.5i	−0.520723	−	0.901918i
$670$		0			0
$671$	28294.9			1.62789
$672$		0			0
$673$	−6311.47	+	10931.8i	−0.361500	+	0.626136i	−0.988208	−	0.153118i	$-0.951069\pi$
$673$	−6311.47	+	10931.8i	−0.361500	+	0.626136i	0.626708	+	0.779254i	$0.284402\pi$
$674$		0			0
$675$	−2983.60			−0.170131
$676$		0			0
$677$	10632.0			0.603574			0.301787	−	0.953375i	$-0.402417\pi$
$677$	10632.0			0.603574			0.301787	+	0.953375i	$0.402417\pi$
$678$		0			0
$679$	1037.97	−	1797.82i	0.0586653	−	0.101611i
$680$		0			0
$681$	11796.9			0.663815
$682$		0			0
$683$	−9960.33	−	17251.8i	−0.558011	−	0.966504i	−0.997662	−	0.0683351i	$-0.978231\pi$
$683$	−9960.33	−	17251.8i	−0.558011	−	0.966504i	0.439651	−	0.898169i	$-0.355102\pi$
$684$		0			0
$685$	3360.71	+	5820.92i	0.187454	+	0.324680i
$686$		0			0
$687$	2381.54	−	4124.95i	0.132258	−	0.229078i
$688$		0			0
$689$	−20740.2	+	11151.6i	−1.14679	+	0.616607i
$690$		0			0
$691$	−9881.94	+	17116.0i	−0.544033	+	0.942292i	0.454634	+	0.890678i	$0.349770\pi$
$691$	−9881.94	+	17116.0i	−0.544033	+	0.942292i	−0.998667	+	0.0516141i	$0.983563\pi$
$692$		0			0
$693$	−400.885	−	694.352i	−0.0219745	−	0.0380610i
$694$		0			0
$695$	946.154	+	1638.79i	0.0516398	+	0.0894427i
$696$		0			0
$697$	−9755.00			−0.530125
$698$		0			0
$699$	−5945.82	+	10298.5i	−0.321733	+	0.557259i
$700$		0			0
$701$	13316.9			0.717505			0.358752	−	0.933433i	$-0.383202\pi$
$701$	13316.9			0.717505			0.358752	+	0.933433i	$0.383202\pi$
$702$		0			0
$703$	−26560.7			−1.42497
$704$		0			0
$705$	1046.97	−	1813.40i	0.0559306	−	0.0968747i
$706$		0			0
$707$	−929.566			−0.0494483
$708$		0			0
$709$	2858.93	+	4951.81i	0.151438	+	0.262298i	0.931756	−	0.363084i	$-0.118276\pi$
$709$	2858.93	+	4951.81i	0.151438	+	0.262298i	−0.780318	+	0.625382i	$0.784943\pi$
$710$		0			0
$711$	−3560.20	−	6166.44i	−0.187789	−	0.325260i
$712$		0			0
$713$	−28871.7	+	50007.2i	−1.51648	+	2.62663i
$714$		0			0
$715$	−168.673	+	5571.99i	−0.00882238	+	0.291442i
$716$		0			0
$717$	3052.00	−	5286.21i	0.158966	−	0.275338i
$718$		0			0
$719$	1638.00	+	2837.09i	0.0849610	+	0.147157i	0.905375	−	0.424614i	$-0.139590\pi$
$719$	1638.00	+	2837.09i	0.0849610	+	0.147157i	−0.820414	+	0.571771i	$0.806257\pi$
$720$		0			0
$721$	2386.63	+	4133.76i	0.123277	+	0.213522i
$722$		0			0
$723$	1205.28			0.0619984
$724$		0			0
$725$	−7304.97	+	12652.6i	−0.374206	+	0.648144i
$726$		0			0
$727$	−1495.17			−0.0762762			−0.0381381	−	0.999272i	$-0.512143\pi$
$727$	−1495.17			−0.0762762			−0.0381381	+	0.999272i	$0.512143\pi$
$728$		0			0
$729$	729.000			0.0370370
$730$		0			0
$731$	−9579.09	+	16591.5i	−0.484672	+	0.839477i
$732$		0			0
$733$	35552.7			1.79150			0.895750	−	0.444558i	$-0.146639\pi$
$733$	35552.7			1.79150			0.895750	+	0.444558i	$0.146639\pi$
$734$		0			0
$735$	−1912.47	−	3312.49i	−0.0959761	−	0.166235i
$736$		0			0
$737$	−1869.77	−	3238.53i	−0.0934516	−	0.161863i
$738$		0			0
$739$	11145.6	−	19304.7i	0.554799	−	0.960939i	−0.443121	−	0.896462i	$-0.646129\pi$
$739$	11145.6	−	19304.7i	0.554799	−	0.960939i	0.997919	−	0.0644772i	$-0.0205380\pi$
$740$		0			0
$741$	−8978.12	+	4827.37i	−0.445101	+	0.239322i
$742$		0			0
$743$	−3814.99	+	6607.76i	−0.188369	+	0.326265i	−0.944707	−	0.327916i	$-0.893654\pi$
$743$	−3814.99	+	6607.76i	−0.188369	+	0.326265i	0.756337	+	0.654182i	$0.226987\pi$
$744$		0			0
$745$	860.194	+	1489.90i	0.0423021	+	0.0732694i
$746$		0			0
$747$	−771.663	−	1336.56i	−0.0377961	−	0.0654647i
$748$		0			0
$749$	−215.066			−0.0104918
$750$		0			0
$751$	17810.5	−	30848.7i	0.865398	−	1.49891i	−0.00125352	−	0.999999i	$-0.500399\pi$
$751$	17810.5	−	30848.7i	0.865398	−	1.49891i	0.866651	−	0.498914i	$-0.166268\pi$
$752$		0			0
$753$	3859.27			0.186772
$754$		0			0
$755$	−5966.56			−0.287610
$756$		0			0
$757$	10149.2	−	17578.9i	0.487290	−	0.844011i	−0.512603	−	0.858626i	$-0.671319\pi$
$757$	10149.2	−	17578.9i	0.487290	−	0.844011i	0.999893	+	0.0146145i	$0.00465210\pi$
$758$		0			0
$759$	−19651.6			−0.939799
$760$		0			0
$761$	−8097.40	−	14025.1i	−0.385717	−	0.668081i	0.606152	−	0.795349i	$-0.292712\pi$
$761$	−8097.40	−	14025.1i	−0.385717	−	0.668081i	−0.991868	+	0.127268i	$0.959379\pi$
$762$		0			0
$763$	336.730	+	583.234i	0.0159770	+	0.0276730i
$764$		0			0
$765$	−988.158	+	1711.54i	−0.0467018	+	0.0808900i
$766$		0			0
$767$	35351.9	+	21862.7i	1.66425	+	1.02922i
$768$		0			0
$769$	16696.9	−	28920.0i	0.782974	−	1.35615i	−0.147228	−	0.989103i	$-0.547035\pi$
$769$	16696.9	−	28920.0i	0.782974	−	1.35615i	0.930202	−	0.367049i	$-0.119632\pi$
$770$		0			0
$771$	8983.20	+	15559.4i	0.419614	+	0.726792i
$772$		0			0
$773$	−13267.6	−	22980.1i	−0.617337	−	1.06926i	−0.989970	−	0.141280i	$-0.954878\pi$
$773$	−13267.6	−	22980.1i	−0.617337	−	1.06926i	0.372633	−	0.927979i	$-0.378455\pi$
$774$		0			0
$775$	−30427.4			−1.41030
$776$		0			0
$777$	1567.41	−	2714.83i	0.0723687	−	0.125346i
$778$		0			0
$779$	−12261.3			−0.563938
$780$		0			0
$781$	−14461.5			−0.662579
$782$		0			0
$783$	1784.87	−	3091.48i	0.0814635	−	0.141099i
$784$		0			0
$785$	2220.95			0.100980
$786$		0			0
$787$	8821.73	+	15279.7i	0.399569	+	0.692073i	0.993673	−	0.112315i	$-0.0358265\pi$
$787$	8821.73	+	15279.7i	0.399569	+	0.692073i	−0.594104	+	0.804388i	$0.702493\pi$
$788$		0			0
$789$	−11090.3	−	19208.9i	−0.500410	−	0.866735i
$790$		0			0
$791$	3028.59	−	5245.67i	0.136137	−	0.235796i
$792$		0			0
$793$	36110.6	+	22331.9i	1.61706	+	1.00004i
$794$		0			0
$795$	−2869.22	+	4969.63i	−0.128001	+	0.221704i
$796$		0			0
$797$	−12555.6	−	21747.0i	−0.558022	−	0.966523i	−0.997661	−	0.0683486i	$-0.978227\pi$
$797$	−12555.6	−	21747.0i	−0.558022	−	0.966523i	0.439639	−	0.898175i	$-0.355106\pi$
$798$		0			0
$799$	5286.44	+	9156.38i	0.234069	+	0.405419i
$800$		0			0
$801$	−1668.08			−0.0735816
$802$		0			0
$803$	−984.074	+	1704.47i	−0.0432469	+	0.0749057i
$804$		0			0
$805$	2277.13			0.0996998
$806$		0			0
$807$	−3141.76			−0.137045
$808$		0			0
$809$	12842.0	−	22242.9i	0.558095	−	0.966649i	−0.439560	−	0.898213i	$-0.644866\pi$
$809$	12842.0	−	22242.9i	0.558095	−	0.966649i	0.997656	−	0.0684361i	$-0.0218009\pi$
$810$		0			0
$811$	−13001.9			−0.562959			−0.281480	−	0.959567i	$-0.590825\pi$
$811$	−13001.9			−0.562959			−0.281480	+	0.959567i	$0.590825\pi$
$812$		0			0
$813$	3772.37	+	6533.93i	0.162734	+	0.281863i
$814$		0			0
$815$	−4738.76	−	8207.77i	−0.203671	−	0.352768i
$816$		0			0
$817$	−12040.2	+	20854.3i	−0.515586	+	0.893022i
$818$		0			0
$819$	36.4029	−	1202.55i	0.00155314	−	0.0513070i
$820$		0			0
$821$	−15274.8	+	26456.7i	−0.649322	+	1.12466i	0.333963	+	0.942586i	$0.391614\pi$
$821$	−15274.8	+	26456.7i	−0.649322	+	1.12466i	−0.983285	+	0.182073i	$0.941719\pi$
$822$		0			0
$823$	10099.8	+	17493.4i	0.427773	+	0.740924i	0.996675	−	0.0814813i	$-0.0259651\pi$
$823$	10099.8	+	17493.4i	0.427773	+	0.740924i	−0.568902	+	0.822405i	$0.692632\pi$
$824$		0			0
$825$	−5177.62	−	8967.91i	−0.218499	−	0.378452i
$826$		0			0
$827$	−43905.1			−1.84611			−0.923054	−	0.384670i	$-0.874315\pi$
$827$	−43905.1			−1.84611			−0.923054	+	0.384670i	$0.874315\pi$
$828$		0			0
$829$	16815.3	−	29125.0i	0.704488	−	1.22021i	−0.262388	−	0.964963i	$-0.584510\pi$
$829$	16815.3	−	29125.0i	0.704488	−	1.22021i	0.966876	−	0.255247i	$-0.0821568\pi$
$830$		0			0
$831$	−23988.7			−1.00140
$832$		0			0
$833$	19313.2			0.803316
$834$		0			0
$835$	2907.60	−	5036.12i	0.120505	−	0.208721i
$836$		0			0
$837$	7434.51			0.307018
$838$		0			0
$839$	−4030.10	−	6980.33i	−0.165834	−	0.287232i	0.771117	−	0.636693i	$-0.219698\pi$
$839$	−4030.10	−	6980.33i	−0.165834	−	0.287232i	−0.936951	+	0.349461i	$0.886365\pi$
$840$		0			0
$841$	3454.45	+	5983.28i	0.141640	+	0.245327i
$842$		0			0
$843$	74.5644	−	129.149i	0.00304642	−	0.00527656i
$844$		0			0
$845$	−4612.98	+	6977.97i	−0.187801	+	0.284082i
$846$		0			0
$847$	−506.619	+	877.489i	−0.0205521	+	0.0355973i
$848$		0			0
$849$	−3117.45	−	5399.59i	−0.126020	−	0.218272i
$850$		0			0
$851$	−38417.6	−	66541.3i	−1.54752	−	2.68038i
$852$		0			0
$853$	10203.0			0.409547			0.204774	−	0.978809i	$-0.434354\pi$
$853$	10203.0			0.409547			0.204774	+	0.978809i	$0.434354\pi$
$854$		0			0
$855$	−1242.04	+	2151.28i	−0.0496807	+	0.0860494i
$856$		0			0
$857$	16302.0			0.649786			0.324893	−	0.945751i	$-0.394672\pi$
$857$	16302.0			0.649786			0.324893	+	0.945751i	$0.394672\pi$
$858$		0			0
$859$	−15836.3			−0.629019			−0.314509	−	0.949254i	$-0.601840\pi$
$859$	−15836.3			−0.629019			−0.314509	+	0.949254i	$0.601840\pi$
$860$		0			0
$861$	723.569	−	1253.26i	0.0286401	−	0.0496062i
$862$		0			0
$863$	4868.59			0.192038			0.0960190	−	0.995380i	$-0.469389\pi$
$863$	4868.59			0.192038			0.0960190	+	0.995380i	$0.469389\pi$
$864$		0			0
$865$	5037.57	+	8725.32i	0.198014	+	0.342971i
$866$		0			0
$867$	2380.01	+	4122.30i	0.0932288	+	0.161477i
$868$		0			0
$869$	12356.5	−	21402.0i	0.482353	−	0.835460i
$870$		0			0
$871$	169.787	−	5608.81i	0.00660508	−	0.218194i
$872$		0			0
$873$	−3275.56	+	5673.43i	−0.126988	+	0.219950i
$874$		0			0
$875$	1278.62	+	2214.64i	0.0494004	+	0.0855640i
$876$		0			0
$877$	8526.79	+	14768.8i	0.328312	+	0.568652i	0.982177	−	0.187959i	$-0.0601871\pi$
$877$	8526.79	+	14768.8i	0.328312	+	0.568652i	−0.653865	+	0.756611i	$0.726854\pi$
$878$		0			0
$879$	−28543.7			−1.09528
$880$		0			0
$881$	−12258.6	+	21232.4i	−0.468787	+	0.811963i	−0.999363	−	0.0356741i	$-0.988642\pi$
$881$	−12258.6	+	21232.4i	−0.468787	+	0.811963i	0.530576	+	0.847637i	$0.321976\pi$
$882$		0			0
$883$	28530.6			1.08735			0.543676	−	0.839295i	$-0.317032\pi$
$883$	28530.6			1.08735			0.543676	+	0.839295i	$0.317032\pi$
$884$		0			0
$885$	10129.2			0.384734
$886$		0			0
$887$	11508.2	−	19932.8i	0.435634	−	0.754540i	−0.561713	−	0.827332i	$-0.689858\pi$
$887$	11508.2	−	19932.8i	0.435634	−	0.754540i	0.997347	+	0.0727922i	$0.0231910\pi$
$888$		0			0
$889$	2429.57			0.0916592
$890$		0			0
$891$	1265.08	+	2191.18i	0.0475666	+	0.0823877i
$892$		0			0
$893$	6644.67	+	11508.9i	0.248998	+	0.431278i
$894$		0			0
$895$	3706.63	−	6420.08i	0.138435	−	0.239776i
$896$		0			0
$897$	−25079.8	−	15510.1i	−0.933545	−	0.577332i
$898$		0			0
$899$	18202.5	−	31527.6i	0.675291	−	1.16964i
$900$		0			0
$901$	−14487.5	−	25093.1i	−0.535681	−	0.927826i
$902$		0			0
$903$	−1421.04	−	2461.32i	−0.0523691	−	0.0907059i
$904$		0			0
$905$	−10979.2			−0.403270
$906$		0			0
$907$	2268.15	−	3928.55i	0.0830350	−	0.143821i	−0.821517	−	0.570184i	$-0.806872\pi$
$907$	2268.15	−	3928.55i	0.0830350	−	0.143821i	0.904552	+	0.426363i	$0.140205\pi$
$908$		0			0
$909$	2933.45			0.107037
$910$		0			0
$911$	15771.7			0.573590			0.286795	−	0.957992i	$-0.407410\pi$
$911$	15771.7			0.573590			0.286795	+	0.957992i	$0.407410\pi$
$912$		0			0
$913$	2678.23	−	4638.83i	0.0970827	−	0.168152i
$914$		0			0
$915$	10346.6			0.373823
$916$		0			0
$917$	−3071.80	−	5320.51i	−0.110621	−	0.191602i
$918$		0			0
$919$	−3513.63	−	6085.78i	−0.126119	−	0.218445i	0.796051	−	0.605230i	$-0.206919\pi$
$919$	−3513.63	−	6085.78i	−0.126119	−	0.218445i	−0.922170	+	0.386785i	$0.873586\pi$
$920$		0			0
$921$	6600.78	−	11432.9i	0.236160	−	0.409041i
$922$		0			0
$923$	−18456.1	−	11413.8i	−0.658170	−	0.407032i
$924$		0			0
$925$	20243.9	−	35063.4i	0.719583	−	1.24635i
$926$		0			0
$927$	−7531.53	−	13045.0i	−0.266848	−	0.462194i
$928$		0			0
$929$	10563.5	+	18296.5i	0.373064	+	0.646167i	0.990035	−	0.140819i	$-0.0449737\pi$
$929$	10563.5	+	18296.5i	0.373064	+	0.646167i	−0.616971	+	0.786986i	$0.711640\pi$
$930$		0			0
$931$	24275.3			0.854554
$932$		0			0
$933$	−2826.58	+	4895.78i	−0.0991834	+	0.171791i
$934$		0			0
$935$	−6859.25			−0.239916
$936$		0			0
$937$	−3740.82			−0.130424			−0.0652120	−	0.997871i	$-0.520772\pi$
$937$	−3740.82			−0.130424			−0.0652120	+	0.997871i	$0.520772\pi$
$938$		0			0
$939$	12392.3	−	21464.1i	0.430679	−	0.745957i
$940$		0			0
$941$	19247.6			0.666794			0.333397	−	0.942786i	$-0.391805\pi$
$941$	19247.6			0.666794			0.333397	+	0.942786i	$0.391805\pi$
$942$		0			0
$943$	−17734.9	−	30717.7i	−0.612436	−	1.06077i
$944$		0			0
$945$	−146.591	−	253.904i	−0.00504616	−	0.00874020i
$946$		0			0
$947$	2308.36	−	3998.20i	0.0792098	−	0.137195i	−0.823699	−	0.567027i	$-0.808094\pi$
$947$	2308.36	−	3998.20i	0.0792098	−	0.137195i	0.902909	+	0.429831i	$0.141427\pi$
$948$		0			0
$949$	−2601.15	+	1398.59i	−0.0889748	+	0.0478401i
$950$		0			0
$951$	−15695.3	+	27185.0i	−0.535178	+	0.926956i
$952$		0			0
$953$	−18465.3	−	31982.8i	−0.627648	−	1.08712i	−0.988022	−	0.154311i	$-0.950684\pi$
$953$	−18465.3	−	31982.8i	−0.627648	−	1.08712i	0.360374	−	0.932808i	$-0.382649\pi$
$954$		0			0
$955$	−5210.45	−	9024.76i	−0.176551	−	0.305795i
$956$		0			0
$957$	12389.6			0.418493
$958$		0			0
$959$	2517.35	−	4360.18i	0.0847648	−	0.146817i
$960$		0			0
$961$	46027.9			1.54503
$962$		0			0
$963$	678.688			0.0227107
$964$		0			0
$965$	2547.19	−	4411.87i	0.0849711	−	0.147174i
$966$		0			0
$967$	−46234.2			−1.53753			−0.768764	−	0.639532i	$-0.779128\pi$
$967$	−46234.2			−1.53753			−0.768764	+	0.639532i	$0.779128\pi$
$968$		0			0
$969$	−6271.43	−	10862.4i	−0.207913	−	0.360115i
$970$		0			0
$971$	4182.77	+	7244.77i	0.138240	+	0.239439i	0.926831	−	0.375480i	$-0.122522\pi$
$971$	4182.77	+	7244.77i	0.138240	+	0.239439i	−0.788590	+	0.614919i	$0.789189\pi$
$972$		0			0
$973$	708.719	−	1227.54i	0.0233510	−	0.0404451i
$974$		0			0
$975$	470.162	−	15531.5i	0.0154433	−	0.510160i
$976$		0			0
$977$	−17324.2	+	30006.5i	−0.567300	+	0.982592i	0.429532	+	0.903052i	$0.358679\pi$
$977$	−17324.2	+	30006.5i	−0.567300	+	0.982592i	−0.996832	+	0.0795401i	$0.974655\pi$
$978$		0			0
$979$	−2894.73	−	5013.82i	−0.0945006	−	0.163680i
$980$		0			0
$981$	−1062.63	−	1840.53i	−0.0345842	−	0.0599016i
$982$		0			0
$983$	18374.0			0.596174			0.298087	−	0.954539i	$-0.403651\pi$
$983$	18374.0			0.596174			0.298087	+	0.954539i	$0.403651\pi$
$984$		0			0
$985$	3244.26	−	5619.22i	0.104945	−	0.181770i
$986$		0			0
$987$	−1568.47			−0.0505825
$988$		0			0
$989$	−69660.2			−2.23970
$990$		0			0
$991$	−7812.32	+	13531.3i	−0.250420	+	0.433741i	−0.963642	−	0.267198i	$-0.913902\pi$
$991$	−7812.32	+	13531.3i	−0.250420	+	0.433741i	0.713221	+	0.700939i	$0.247235\pi$
$992$		0			0
$993$	15635.1			0.499664
$994$		0			0
$995$	6243.16	+	10813.5i	0.198916	+	0.344533i
$996$		0			0
$997$	−23308.2	−	40370.9i	−0.740399	−	1.28241i	−0.952314	−	0.305120i	$-0.901303\pi$
$997$	−23308.2	−	40370.9i	−0.740399	−	1.28241i	0.211915	−	0.977288i	$-0.432030\pi$
$998$		0			0
$999$	−4946.31	+	8567.26i	−0.156651	+	0.271327i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	312.4.q.e.217.3	✓	12
4.3	odd	2		624.4.q.n.529.3		12
13.3	even	3	inner	312.4.q.e.289.3	yes	12
52.3	odd	6		624.4.q.n.289.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
312.4.q.e.217.3	✓	12	1.1	even	1	trivial
312.4.q.e.289.3	yes	12	13.3	even	3	inner
624.4.q.n.289.3		12	52.3	odd	6
624.4.q.n.529.3		12	4.3	odd	2

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 312 = 2^{3} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	312.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.50000 + 2.59808i) q^{3} -3.80742 q^{5} +(1.42598 + 2.46987i) q^{7} +(-4.50000 - 7.79423i) q^{9} +(15.6183 - 27.0517i) q^{11} +(41.2830 - 22.1971i) q^{13} +(5.71114 - 9.89198i) q^{15} +(28.8372 + 49.9474i) q^{17} +(36.2462 + 62.7803i) q^{19} -8.55588 q^{21} +(-104.854 + 181.612i) q^{23} -110.504 q^{25} +27.0000 q^{27} +(66.1062 - 114.499i) q^{29} +275.352 q^{31} +(46.8548 + 81.1550i) q^{33} +(-5.42931 - 9.40385i) q^{35} +(-183.197 + 317.306i) q^{37} +(-4.25473 + 140.552i) q^{39} +(-84.5698 + 146.479i) q^{41} +(166.089 + 287.675i) q^{43} +(17.1334 + 29.6759i) q^{45} +183.320 q^{47} +(167.433 - 290.003i) q^{49} -173.023 q^{51} -502.390 q^{53} +(-59.4654 + 102.997i) q^{55} -217.477 q^{57} +(443.397 + 767.986i) q^{59} +(452.914 + 784.470i) q^{61} +(12.8338 - 22.2288i) q^{63} +(-157.182 + 84.5138i) q^{65} +(59.8583 - 103.678i) q^{67} +(-314.561 - 544.835i) q^{69} +(-231.484 - 400.942i) q^{71} -63.0078 q^{73} +(165.755 - 287.097i) q^{75} +89.0855 q^{77} +791.154 q^{79} +(-40.5000 + 70.1481i) q^{81} +171.481 q^{83} +(-109.795 - 190.171i) q^{85} +(198.319 + 343.498i) q^{87} +(92.6713 - 160.511i) q^{89} +(113.693 + 70.3111i) q^{91} +(-413.028 + 715.386i) q^{93} +(-138.005 - 239.031i) q^{95} +(-363.951 - 630.381i) q^{97} -281.129 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 18 q^{3} + 8 q^{5} - 10 q^{7} - 54 q^{9} - 60 q^{11} + 86 q^{13} - 12 q^{15} - 56 q^{17} - 48 q^{19} + 60 q^{21} + 80 q^{23} + 508 q^{25} + 324 q^{27} - 164 q^{29} + 668 q^{31} - 180 q^{33} + 552 q^{35}+ \cdots + 1080 q^{99}+O(q^{100}) \) 12 * q - 18 * q^3 + 8 * q^5 - 10 * q^7 - 54 * q^9 - 60 * q^11 + 86 * q^13 - 12 * q^15 - 56 * q^17 - 48 * q^19 + 60 * q^21 + 80 * q^23 + 508 * q^25 + 324 * q^27 - 164 * q^29 + 668 * q^31 - 180 * q^33 + 552 * q^35 + 264 * q^37 - 192 * q^39 - 708 * q^41 - 242 * q^43 - 36 * q^45 + 856 * q^47 - 904 * q^49 + 336 * q^51 + 392 * q^53 + 608 * q^55 + 288 * q^57 - 224 * q^59 + 478 * q^61 - 90 * q^63 - 1268 * q^65 - 250 * q^67 + 240 * q^69 - 872 * q^71 + 44 * q^73 - 762 * q^75 + 1880 * q^77 - 1228 * q^79 - 486 * q^81 + 4712 * q^83 + 276 * q^85 - 492 * q^87 - 228 * q^89 + 3066 * q^91 - 1002 * q^93 - 1808 * q^95 - 530 * q^97 + 1080 * q^99

Introduction

L-functions

Modular forms

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