LMFDB - Embedded newform 152.4.i.b.121.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [152,4,Mod(49,152)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(152, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("152.49");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 152 = 2^{3} \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	152.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$8.96829032087$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 160 x^{14} - 16 x^{13} + 17994 x^{12} - 1968 x^{11} + 980960 x^{10} - 136456 x^{9} + \cdots + 94780858225 $ x^16 + 160x^14 - 16x^13 + 17994x^12 - 1968x^11 + 980960x^10 - 136456x^9 + 38663755x^8 - 7001376x^7 + 799525088x^6 - 264016536x^5 + 11605656762x^4 - 2274117152x^3 + 36860318416x^2 + 7036562440x + 94780858225
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{12} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			121.2
Root			$-3.20276 + 5.54735i$ of defining polynomial
Character	$\chi$	$=$	152.121
Dual form			152.4.i.b.49.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.20276 - 5.54735i) q^{3} +(-9.34053 - 16.1783i) q^{5} -16.3159 q^{7} +(-7.01538 + 12.1510i) q^{9} +O(q^{10})$	\(q+(-3.20276 - 5.54735i) q^{3} +(-9.34053 - 16.1783i) q^{5} -16.3159 q^{7} +(-7.01538 + 12.1510i) q^{9} +53.5040 q^{11} +(-42.4763 + 73.5712i) q^{13} +(-59.8310 + 103.630i) q^{15} +(-24.0096 - 41.5858i) q^{17} +(80.5776 - 19.1375i) q^{19} +(52.2559 + 90.5098i) q^{21} +(55.9299 - 96.8734i) q^{23} +(-111.991 + 193.974i) q^{25} -83.0749 q^{27} +(-131.299 + 227.416i) q^{29} -122.316 q^{31} +(-171.361 - 296.805i) q^{33} +(152.399 + 263.963i) q^{35} -32.6003 q^{37} +544.166 q^{39} +(-207.808 - 359.934i) q^{41} +(-29.2597 - 50.6793i) q^{43} +262.109 q^{45} +(-85.2630 + 147.680i) q^{47} -76.7924 q^{49} +(-153.794 + 266.379i) q^{51} +(165.835 - 287.235i) q^{53} +(-499.756 - 865.603i) q^{55} +(-364.234 - 385.699i) q^{57} +(354.301 + 613.667i) q^{59} +(8.95247 - 15.5061i) q^{61} +(114.462 - 198.254i) q^{63} +1587.01 q^{65} +(164.655 - 285.190i) q^{67} -716.521 q^{69} +(-31.4612 - 54.4924i) q^{71} +(-281.438 - 487.466i) q^{73} +1434.72 q^{75} -872.965 q^{77} +(-154.133 - 266.967i) q^{79} +(455.484 + 788.922i) q^{81} -524.252 q^{83} +(-448.525 + 776.867i) q^{85} +1682.07 q^{87} +(-298.185 + 516.471i) q^{89} +(693.038 - 1200.38i) q^{91} +(391.750 + 678.531i) q^{93} +(-1062.25 - 1124.85i) q^{95} +(275.060 + 476.417i) q^{97} +(-375.351 + 650.127i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 5 q^{5} - 8 q^{7} - 104 q^{9}+O(q^{10}) $ 16 * q - 5 * q^5 - 8 * q^7 - 104 * q^9	$ 16 q - 5 q^{5} - 8 q^{7} - 104 q^{9} + 46 q^{11} + 21 q^{13} - 45 q^{15} - 75 q^{17} + 241 q^{19} + 80 q^{21} - 251 q^{23} - 275 q^{25} + 48 q^{27} - 69 q^{29} + 124 q^{31} + 245 q^{33} - 240 q^{35} - 224 q^{37} + 1566 q^{39} - 630 q^{41} + 249 q^{43} - 1876 q^{45} - 421 q^{47} + 624 q^{49} + 921 q^{51} - 467 q^{53} - 1220 q^{55} + 29 q^{57} + 1094 q^{59} - 253 q^{61} + 1032 q^{63} + 4326 q^{65} + 250 q^{67} - 426 q^{69} - 1113 q^{71} - 1952 q^{73} - 2930 q^{75} + 1072 q^{77} + 861 q^{79} - 688 q^{81} + 886 q^{83} - 547 q^{85} + 2394 q^{87} - 1935 q^{89} + 904 q^{91} - 866 q^{93} + 3 q^{95} - 2126 q^{97} - 682 q^{99}+O(q^{100}) $ 16 * q - 5 * q^5 - 8 * q^7 - 104 * q^9 + 46 * q^11 + 21 * q^13 - 45 * q^15 - 75 * q^17 + 241 * q^19 + 80 * q^21 - 251 * q^23 - 275 * q^25 + 48 * q^27 - 69 * q^29 + 124 * q^31 + 245 * q^33 - 240 * q^35 - 224 * q^37 + 1566 * q^39 - 630 * q^41 + 249 * q^43 - 1876 * q^45 - 421 * q^47 + 624 * q^49 + 921 * q^51 - 467 * q^53 - 1220 * q^55 + 29 * q^57 + 1094 * q^59 - 253 * q^61 + 1032 * q^63 + 4326 * q^65 + 250 * q^67 - 426 * q^69 - 1113 * q^71 - 1952 * q^73 - 2930 * q^75 + 1072 * q^77 + 861 * q^79 - 688 * q^81 + 886 * q^83 - 547 * q^85 + 2394 * q^87 - 1935 * q^89 + 904 * q^91 - 866 * q^93 + 3 * q^95 - 2126 * q^97 - 682 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/152\mathbb{Z}\right)^\times$.

$n$	$39$	$77$	$97$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−3.20276	−	5.54735i	−0.616372	−	1.06759i	−0.990142	−	0.140066i	$-0.955268\pi$
$3$	−3.20276	−	5.54735i	−0.616372	−	1.06759i	0.373770	−	0.927521i	$-0.378065\pi$
$4$		0			0
$5$	−9.34053	−	16.1783i	−0.835442	−	1.44703i	−0.893670	−	0.448725i	$-0.851878\pi$
$5$	−9.34053	−	16.1783i	−0.835442	−	1.44703i	0.0582275	−	0.998303i	$-0.481455\pi$
$6$		0			0
$7$	−16.3159			−0.880974			−0.440487	−	0.897759i	$-0.645194\pi$
$7$	−16.3159			−0.880974			−0.440487	+	0.897759i	$0.645194\pi$
$8$		0			0
$9$	−7.01538	+	12.1510i	−0.259829	+	0.450037i
$10$		0			0
$11$	53.5040			1.46655			0.733276	−	0.679931i	$-0.237990\pi$
$11$	53.5040			1.46655			0.733276	+	0.679931i	$0.237990\pi$
$12$		0			0
$13$	−42.4763	+	73.5712i	−0.906217	+	1.56961i	−0.0869407	+	0.996213i	$0.527709\pi$
$13$	−42.4763	+	73.5712i	−0.906217	+	1.56961i	−0.819276	+	0.573400i	$0.805624\pi$
$14$		0			0
$15$	−59.8310	+	103.630i	−1.02989	+	1.78382i
$16$		0			0
$17$	−24.0096	−	41.5858i	−0.342540	−	0.593297i	0.642364	−	0.766400i	$-0.277954\pi$
$17$	−24.0096	−	41.5858i	−0.342540	−	0.593297i	−0.984904	+	0.173103i	$0.944621\pi$
$18$		0			0
$19$	80.5776	−	19.1375i	0.972936	−	0.231076i
$19$	80.5776	−	19.1375i	0.972936	−	0.231076i
$20$		0			0
$21$	52.2559	+	90.5098i	0.543008	+	0.940517i
$22$		0			0
$23$	55.9299	−	96.8734i	0.507052	−	0.878239i	−0.492915	−	0.870077i	$-0.664069\pi$
$23$	55.9299	−	96.8734i	0.507052	−	0.878239i	0.999967	−	0.00816171i	$-0.00259798\pi$
$24$		0			0
$25$	−111.991	+	193.974i	−0.895928	+	1.55179i
$26$		0			0
$27$	−83.0749			−0.592139
$28$		0			0
$29$	−131.299	+	227.416i	−0.840744	+	1.45621i	0.0485233	+	0.998822i	$0.484549\pi$
$29$	−131.299	+	227.416i	−0.840744	+	1.45621i	−0.889267	+	0.457389i	$0.848785\pi$
$30$		0			0
$31$	−122.316			−0.708666			−0.354333	−	0.935119i	$-0.615292\pi$
$31$	−122.316			−0.708666			−0.354333	+	0.935119i	$0.615292\pi$
$32$		0			0
$33$	−171.361	−	296.805i	−0.903941	−	1.56567i
$34$		0			0
$35$	152.399	+	263.963i	0.736003	+	1.27479i
$36$		0			0
$37$	−32.6003			−0.144850			−0.0724250	−	0.997374i	$-0.523074\pi$
$37$	−32.6003			−0.144850			−0.0724250	+	0.997374i	$0.523074\pi$
$38$		0			0
$39$	544.166			2.23427
$40$		0			0
$41$	−207.808	−	359.934i	−0.791565	−	1.37103i	−0.924997	−	0.379974i	$-0.875933\pi$
$41$	−207.808	−	359.934i	−0.791565	−	1.37103i	0.133432	−	0.991058i	$-0.457400\pi$
$42$		0			0
$43$	−29.2597	−	50.6793i	−0.103769	−	0.179733i	0.809466	−	0.587167i	$-0.199757\pi$
$43$	−29.2597	−	50.6793i	−0.103769	−	0.179733i	−0.913235	+	0.407434i	$0.866424\pi$
$44$		0			0
$45$	262.109			0.868288
$46$		0			0
$47$	−85.2630	+	147.680i	−0.264615	+	0.458326i	−0.967463	−	0.253014i	$-0.918578\pi$
$47$	−85.2630	+	147.680i	−0.264615	+	0.458326i	0.702848	+	0.711340i	$0.251911\pi$
$48$		0			0
$49$	−76.7924			−0.223884
$50$		0			0
$51$	−153.794	+	266.379i	−0.422264	+	0.731383i
$52$		0			0
$53$	165.835	−	287.235i	0.429797	−	0.744430i	−0.567058	−	0.823678i	$-0.691919\pi$
$53$	165.835	−	287.235i	0.429797	−	0.744430i	0.996855	+	0.0792481i	$0.0252519\pi$
$54$		0			0
$55$	−499.756	−	865.603i	−1.22522	−	2.12214i
$56$		0			0
$57$	−364.234	−	385.699i	−0.846384	−	0.896265i
$58$		0			0
$59$	354.301	+	613.667i	0.781798	+	1.35411i	0.930894	+	0.365290i	$0.119030\pi$
$59$	354.301	+	613.667i	0.781798	+	1.35411i	−0.149096	+	0.988823i	$0.547636\pi$
$60$		0			0
$61$	8.95247	−	15.5061i	0.0187909	−	0.0325468i	−0.856477	−	0.516185i	$-0.827352\pi$
$61$	8.95247	−	15.5061i	0.0187909	−	0.0325468i	0.875268	+	0.483638i	$0.160685\pi$
$62$		0			0
$63$	114.462	−	198.254i	0.228902	−	0.396471i
$64$		0			0
$65$	1587.01			3.02837
$66$		0			0
$67$	164.655	−	285.190i	0.300236	−	0.520023i	−0.675954	−	0.736944i	$-0.736268\pi$
$67$	164.655	−	285.190i	0.300236	−	0.520023i	0.976189	+	0.216921i	$0.0696014\pi$
$68$		0			0
$69$	−716.521			−1.25013
$70$		0			0
$71$	−31.4612	−	54.4924i	−0.0525882	−	0.0910854i	0.838533	−	0.544851i	$-0.183414\pi$
$71$	−31.4612	−	54.4924i	−0.0525882	−	0.0910854i	−0.891121	+	0.453765i	$0.850080\pi$
$72$		0			0
$73$	−281.438	−	487.466i	−0.451231	−	0.781555i	0.547232	−	0.836981i	$-0.315682\pi$
$73$	−281.438	−	487.466i	−0.451231	−	0.781555i	−0.998463	+	0.0554258i	$0.982348\pi$
$74$		0			0
$75$	1434.72			2.20890
$76$		0			0
$77$	−872.965			−1.29199
$78$		0			0
$79$	−154.133	−	266.967i	−0.219511	−	0.380204i	0.735148	−	0.677907i	$-0.237113\pi$
$79$	−154.133	−	266.967i	−0.219511	−	0.380204i	−0.954658	+	0.297703i	$0.903779\pi$
$80$		0			0
$81$	455.484	+	788.922i	0.624807	+	1.08220i
$82$		0			0
$83$	−524.252			−0.693303			−0.346652	−	0.937994i	$-0.612681\pi$
$83$	−524.252			−0.693303			−0.346652	+	0.937994i	$0.612681\pi$
$84$		0			0
$85$	−448.525	+	776.867i	−0.572345	+	0.991331i
$86$		0			0
$87$	1682.07			2.07284
$88$		0			0
$89$	−298.185	+	516.471i	−0.355141	+	0.615121i	−0.987142	−	0.159846i	$-0.948900\pi$
$89$	−298.185	+	516.471i	−0.355141	+	0.615121i	0.632001	+	0.774967i	$0.282234\pi$
$90$		0			0
$91$	693.038	−	1200.38i	0.798353	−	1.38279i
$92$		0			0
$93$	391.750	+	678.531i	0.436802	+	0.756563i
$94$		0			0
$95$	−1062.25	−	1124.85i	−1.14721	−	1.21481i
$96$		0			0
$97$	275.060	+	476.417i	0.287918	+	0.498689i	0.973313	−	0.229483i	$-0.0737035\pi$
$97$	275.060	+	476.417i	0.287918	+	0.498689i	−0.685394	+	0.728172i	$0.740370\pi$
$98$		0			0
$99$	−375.351	+	650.127i	−0.381052	+	0.660002i
$100$		0			0
$101$	136.833	−	237.002i	0.134806	−	0.233491i	−0.790717	−	0.612181i	$-0.790292\pi$
$101$	136.833	−	237.002i	0.134806	−	0.233491i	0.925523	+	0.378691i	$0.123626\pi$
$102$		0			0
$103$	−997.582			−0.954317			−0.477159	−	0.878817i	$-0.658333\pi$
$103$	−997.582			−0.954317			−0.477159	+	0.878817i	$0.658333\pi$
$104$		0			0
$105$	976.195	−	1690.82i	0.907303	−	1.57150i
$106$		0			0
$107$	−590.435			−0.533453			−0.266727	−	0.963772i	$-0.585942\pi$
$107$	−590.435			−0.533453			−0.266727	+	0.963772i	$0.585942\pi$
$108$		0			0
$109$	−158.294	−	274.173i	−0.139099	−	0.240926i	0.788057	−	0.615602i	$-0.211087\pi$
$109$	−158.294	−	274.173i	−0.139099	−	0.240926i	−0.927156	+	0.374676i	$0.877754\pi$
$110$		0			0
$111$	104.411	+	180.845i	0.0892815	+	0.154640i
$112$		0			0
$113$	−1810.62			−1.50733			−0.753665	−	0.657259i	$-0.771716\pi$
$113$	−1810.62			−1.50733			−0.753665	+	0.657259i	$0.771716\pi$
$114$		0			0
$115$	−2089.66			−1.69445
$116$		0			0
$117$	−595.975	−	1032.26i	−0.470922	−	0.815661i
$118$		0			0
$119$	391.737	+	678.509i	0.301769	+	0.522679i
$120$		0			0
$121$	1531.68			1.15077
$122$		0			0
$123$	−1331.12	+	2305.57i	−0.975798	+	1.69013i
$124$		0			0
$125$	1849.09			1.32310
$126$		0			0
$127$	−616.432	+	1067.69i	−0.430705	+	0.746002i	−0.996934	−	0.0782453i	$-0.975068\pi$
$127$	−616.432	+	1067.69i	−0.430705	+	0.746002i	0.566230	+	0.824248i	$0.308402\pi$
$128$		0			0
$129$	−187.424	+	324.627i	−0.127920	+	0.221565i
$130$		0			0
$131$	−1106.71	−	1916.87i	−0.738118	−	1.27846i	−0.953342	−	0.301893i	$-0.902381\pi$
$131$	−1106.71	−	1916.87i	−0.738118	−	1.27846i	0.215224	−	0.976565i	$-0.430952\pi$
$132$		0			0
$133$	−1314.69	+	312.245i	−0.857131	+	0.203572i
$134$		0			0
$135$	775.963	+	1344.01i	0.494698	+	0.856843i
$136$		0			0
$137$	−416.403	+	721.232i	−0.259677	+	0.449774i	−0.966155	−	0.257961i	$-0.916949\pi$
$137$	−416.403	+	721.232i	−0.259677	+	0.449774i	0.706478	+	0.707735i	$0.250283\pi$
$138$		0			0
$139$	722.877	−	1252.06i	0.441106	−	0.764017i	−0.556666	−	0.830736i	$-0.687920\pi$
$139$	722.877	−	1252.06i	0.441106	−	0.764017i	0.997772	+	0.0667190i	$0.0212531\pi$
$140$		0			0
$141$	1092.31			0.652404
$142$		0			0
$143$	−2272.65	+	3936.35i	−1.32901	+	2.30192i
$144$		0			0
$145$	4905.60			2.80957
$146$		0			0
$147$	245.948	+	425.994i	0.137996	+	0.239016i
$148$		0			0
$149$	1436.08	+	2487.36i	0.789584	+	1.36760i	0.926222	+	0.376978i	$0.123037\pi$
$149$	1436.08	+	2487.36i	0.789584	+	1.36760i	−0.136638	+	0.990621i	$0.543630\pi$
$150$		0			0
$151$	−522.001			−0.281323			−0.140662	−	0.990058i	$-0.544923\pi$
$151$	−522.001			−0.281323			−0.140662	+	0.990058i	$0.544923\pi$
$152$		0			0
$153$	673.745			0.356007
$154$		0			0
$155$	1142.50	+	1978.87i	0.592050	+	1.02546i
$156$		0			0
$157$	−89.0186	−	154.185i	−0.0452513	−	0.0783776i	0.842513	−	0.538677i	$-0.181076\pi$
$157$	−89.0186	−	154.185i	−0.0452513	−	0.0783776i	−0.887764	+	0.460299i	$0.847742\pi$
$158$		0			0
$159$	−2124.52			−1.05966
$160$		0			0
$161$	−912.545	+	1580.57i	−0.446699	+	0.773706i
$162$		0			0
$163$	−425.280			−0.204359			−0.102180	−	0.994766i	$-0.532582\pi$
$163$	−425.280			−0.204359			−0.102180	+	0.994766i	$0.532582\pi$
$164$		0			0
$165$	−3201.20	+	5544.64i	−1.51038	+	2.61606i
$166$		0			0
$167$	307.877	−	533.259i	0.142660	−	0.247095i	−0.785837	−	0.618433i	$-0.787768\pi$
$167$	307.877	−	533.259i	0.142660	−	0.247095i	0.928498	+	0.371338i	$0.121101\pi$
$168$		0			0
$169$	−2509.98	−	4347.41i	−1.14246	−	1.97879i
$170$		0			0
$171$	−332.743	+	1113.35i	−0.148804	+	0.497897i
$172$		0			0
$173$	−1870.70	−	3240.15i	−0.822120	−	1.42395i	−0.904100	−	0.427320i	$-0.859458\pi$
$173$	−1870.70	−	3240.15i	−0.822120	−	1.42395i	0.0819802	−	0.996634i	$-0.473876\pi$
$174$		0			0
$175$	1827.23	−	3164.86i	0.789289	−	1.36709i
$176$		0			0
$177$	2269.48	−	3930.86i	0.963756	−	1.66927i
$178$		0			0
$179$	2075.12			0.866490			0.433245	−	0.901276i	$-0.357368\pi$
$179$	2075.12			0.866490			0.433245	+	0.901276i	$0.357368\pi$
$180$		0			0
$181$	−99.2561	+	171.917i	−0.0407605	+	0.0705992i	−0.885686	−	0.464285i	$-0.846311\pi$
$181$	−99.2561	+	171.917i	−0.0407605	+	0.0705992i	0.844925	+	0.534884i	$0.179645\pi$
$182$		0			0
$183$	−114.691			−0.0463288
$184$		0			0
$185$	304.504	+	527.416i	0.121014	+	0.209602i
$186$		0			0
$187$	−1284.61	−	2225.01i	−0.502353	−	0.870100i
$188$		0			0
$189$	1355.44			0.521659
$190$		0			0
$191$	2866.38			1.08589			0.542943	−	0.839769i	$-0.317310\pi$
$191$	2866.38			1.08589			0.542943	+	0.839769i	$0.317310\pi$
$192$		0			0
$193$	−1611.94	−	2791.96i	−0.601191	−	1.04129i	−0.992641	−	0.121093i	$-0.961360\pi$
$193$	−1611.94	−	2791.96i	−0.601191	−	1.04129i	0.391451	−	0.920199i	$-0.371973\pi$
$194$		0			0
$195$	−5082.80	−	8803.67i	−1.86660	−	3.23305i
$196$		0			0
$197$	2579.50			0.932904			0.466452	−	0.884547i	$-0.345532\pi$
$197$	2579.50			0.932904			0.466452	+	0.884547i	$0.345532\pi$
$198$		0			0
$199$	1719.97	−	2979.08i	0.612691	−	1.06121i	−0.378093	−	0.925767i	$-0.623420\pi$
$199$	1719.97	−	2979.08i	0.612691	−	1.06121i	0.990785	−	0.135445i	$-0.0432465\pi$
$200$		0			0
$201$	−2109.40			−0.740227
$202$		0			0
$203$	2142.25	−	3710.49i	0.740673	−	1.28288i
$204$		0			0
$205$	−3882.08	+	6723.95i	−1.32261	+	2.29084i
$206$		0			0
$207$	784.738	+	1359.21i	0.263493	+	0.456383i
$208$		0			0
$209$	4311.23	−	1023.93i	1.42686	−	0.338885i
$210$		0			0
$211$	1693.81	+	2933.77i	0.552640	+	0.957200i	0.998083	+	0.0618898i	$0.0197127\pi$
$211$	1693.81	+	2933.77i	0.552640	+	0.957200i	−0.445443	+	0.895310i	$0.646954\pi$
$212$		0			0
$213$	−201.526	+	349.053i	−0.0648277	+	0.112285i
$214$		0			0
$215$	−546.602	+	946.743i	−0.173386	+	0.300313i
$216$		0			0
$217$	1995.70			0.624317
$218$		0			0
$219$	−1802.76	+	3122.47i	−0.556253	+	0.963458i
$220$		0			0
$221$	4079.36			1.24166
$222$		0			0
$223$	−473.899	−	820.816i	−0.142308	−	0.246484i	0.786058	−	0.618153i	$-0.212119\pi$
$223$	−473.899	−	820.816i	−0.142308	−	0.246484i	−0.928365	+	0.371669i	$0.878786\pi$
$224$		0			0
$225$	−1571.32	−	2721.60i	−0.465575	−	0.806400i
$226$		0			0
$227$	665.913			0.194706			0.0973529	−	0.995250i	$-0.468962\pi$
$227$	665.913			0.194706			0.0973529	+	0.995250i	$0.468962\pi$
$228$		0			0
$229$	−6486.13			−1.87168			−0.935842	−	0.352420i	$-0.885359\pi$
$229$	−6486.13			−1.87168			−0.935842	+	0.352420i	$0.885359\pi$
$230$		0			0
$231$	2795.90	+	4842.64i	0.796349	+	1.37932i
$232$		0			0
$233$	−436.526	−	756.085i	−0.122737	−	0.212587i	0.798109	−	0.602513i	$-0.205834\pi$
$233$	−436.526	−	756.085i	−0.122737	−	0.212587i	−0.920846	+	0.389926i	$0.872501\pi$
$234$		0			0
$235$	3185.61			0.884281
$236$		0			0
$237$	−987.305	+	1710.06i	−0.270601	+	0.468694i
$238$		0			0
$239$	2858.59			0.773668			0.386834	−	0.922149i	$-0.373569\pi$
$239$	2858.59			0.773668			0.386834	+	0.922149i	$0.373569\pi$
$240$		0			0
$241$	2608.36	−	4517.81i	0.697176	−	1.20754i	−0.272266	−	0.962222i	$-0.587773\pi$
$241$	2608.36	−	4517.81i	0.697176	−	1.20754i	0.969442	−	0.245322i	$-0.0788936\pi$
$242$		0			0
$243$	1796.10	−	3110.94i	0.474157	−	0.821264i
$244$		0			0
$245$	717.281	+	1242.37i	0.187043	+	0.323967i
$246$		0			0
$247$	−2014.67	+	6741.08i	−0.518990	+	1.73654i
$248$		0			0
$249$	1679.06	+	2908.21i	0.427333	+	0.740162i
$250$		0			0
$251$	112.255	−	194.432i	0.0282291	−	0.0488942i	−0.851566	−	0.524248i	$-0.824347\pi$
$251$	112.255	−	194.432i	0.0282291	−	0.0488942i	0.879795	+	0.475354i	$0.157680\pi$
$252$		0			0
$253$	2992.47	−	5183.12i	0.743617	−	1.28798i
$254$		0			0
$255$	5746.07			1.41111
$256$		0			0
$257$	922.346	−	1597.55i	0.223869	−	0.387753i	−0.732110	−	0.681186i	$-0.761465\pi$
$257$	922.346	−	1597.55i	0.223869	−	0.387753i	0.955980	+	0.293433i	$0.0947979\pi$
$258$		0			0
$259$	531.902			0.127609
$260$		0			0
$261$	−1842.22	−	3190.82i	−0.436899	−	0.756731i
$262$		0			0
$263$	−3071.85	−	5320.61i	−0.720223	−	1.24746i	−0.960910	−	0.276860i	$-0.910706\pi$
$263$	−3071.85	−	5320.61i	−0.720223	−	1.24746i	0.240687	−	0.970603i	$-0.422627\pi$
$264$		0			0
$265$	−6195.95			−1.43628
$266$		0			0
$267$	3820.06			0.875595
$268$		0			0
$269$	1832.50	+	3173.98i	0.415351	+	0.719409i	0.995465	−	0.0951264i	$-0.0303255\pi$
$269$	1832.50	+	3173.98i	0.415351	+	0.719409i	−0.580114	+	0.814535i	$0.696992\pi$
$270$		0			0
$271$	−4278.15	−	7409.98i	−0.958964	−	1.66097i	−0.725024	−	0.688724i	$-0.758171\pi$
$271$	−4278.15	−	7409.98i	−0.958964	−	1.66097i	−0.233941	−	0.972251i	$-0.575162\pi$
$272$		0			0
$273$	−8878.55			−1.96833
$274$		0			0
$275$	−5991.97	+	10378.4i	−1.31392	+	2.27578i
$276$		0			0
$277$	−2067.11			−0.448377			−0.224188	−	0.974546i	$-0.571973\pi$
$277$	−2067.11			−0.448377			−0.224188	+	0.974546i	$0.571973\pi$
$278$		0			0
$279$	858.095	−	1486.26i	0.184132	−	0.318926i
$280$		0			0
$281$	−176.376	+	305.492i	−0.0374438	+	0.0648546i	−0.884140	−	0.467222i	$-0.845255\pi$
$281$	−176.376	+	305.492i	−0.0374438	+	0.0648546i	0.846696	+	0.532077i	$0.178588\pi$
$282$		0			0
$283$	−1030.12	−	1784.22i	−0.216375	−	0.374772i	0.737322	−	0.675541i	$-0.236090\pi$
$283$	−1030.12	−	1784.22i	−0.216375	−	0.374772i	−0.953697	+	0.300769i	$0.902757\pi$
$284$		0			0
$285$	−2837.81	+	9495.30i	−0.589816	+	1.97352i
$286$		0			0
$287$	3390.57	+	5872.64i	0.697349	+	1.20784i
$288$		0			0
$289$	1303.58	−	2257.87i	0.265333	−	0.459570i
$290$		0			0
$291$	1761.90	−	3051.70i	0.354930	−	0.614756i
$292$		0			0
$293$	1740.17			0.346968			0.173484	−	0.984837i	$-0.444497\pi$
$293$	1740.17			0.346968			0.173484	+	0.984837i	$0.444497\pi$
$294$		0			0
$295$	6618.72	−	11464.0i	1.30629	−	2.26257i
$296$		0			0
$297$	−4444.84			−0.868403
$298$		0			0
$299$	4751.39	+	8229.65i	0.918997	+	1.59175i
$300$		0			0
$301$	477.398	+	826.877i	0.0914177	+	0.158340i
$302$		0			0
$303$	−1752.98			−0.332362
$304$		0			0
$305$	−334.483			−0.0627949
$306$		0			0
$307$	1274.07	+	2206.75i	0.236856	+	0.410247i	0.959811	−	0.280649i	$-0.0905496\pi$
$307$	1274.07	+	2206.75i	0.236856	+	0.410247i	−0.722954	+	0.690896i	$0.757216\pi$
$308$		0			0
$309$	3195.02	+	5533.93i	0.588214	+	1.01882i
$310$		0			0
$311$	−7899.32			−1.44029			−0.720144	−	0.693825i	$-0.755924\pi$
$311$	−7899.32			−1.44029			−0.720144	+	0.693825i	$0.755924\pi$
$312$		0			0
$313$	−3295.44	+	5707.87i	−0.595109	+	1.03076i	0.398422	+	0.917202i	$0.369558\pi$
$313$	−3295.44	+	5707.87i	−0.595109	+	1.03076i	−0.993531	+	0.113557i	$0.963775\pi$
$314$		0			0
$315$	−4276.54			−0.764939
$316$		0			0
$317$	3605.13	−	6244.27i	0.638752	−	1.10635i	−0.346955	−	0.937882i	$-0.612784\pi$
$317$	3605.13	−	6244.27i	0.638752	−	1.10635i	0.985707	−	0.168469i	$-0.0538825\pi$
$318$		0			0
$319$	−7025.01	+	12167.7i	−1.23299	+	2.13561i
$320$		0			0
$321$	1891.02	+	3275.35i	0.328806	+	0.569508i
$322$		0			0
$323$	−2730.49	−	2891.40i	−0.470366	−	0.498087i
$324$		0			0
$325$	−9513.93	−	16478.6i	−1.62381	−	2.81252i
$326$		0			0
$327$	−1013.95	+	1756.22i	−0.171473	+	0.297000i
$328$		0			0
$329$	1391.14	−	2409.53i	0.233119	−	0.403774i
$330$		0			0
$331$	1423.88			0.236445			0.118223	−	0.992987i	$-0.462280\pi$
$331$	1423.88			0.236445			0.118223	+	0.992987i	$0.462280\pi$
$332$		0			0
$333$	228.703	−	396.125i	0.0376362	−	0.0651878i
$334$		0			0
$335$	−6151.85			−1.00332
$336$		0			0
$337$	4525.32	+	7838.08i	0.731483	+	1.26697i	0.956249	+	0.292553i	$0.0945048\pi$
$337$	4525.32	+	7838.08i	0.731483	+	1.26697i	−0.224766	+	0.974413i	$0.572162\pi$
$338$		0			0
$339$	5798.97	+	10044.1i	0.929076	+	1.60921i
$340$		0			0
$341$	−6544.41			−1.03930
$342$		0			0
$343$	6849.28			1.07821
$344$		0			0
$345$	6692.68	+	11592.1i	1.04441	+	1.80897i
$346$		0			0
$347$	1792.31	+	3104.37i	0.277280	+	0.480264i	0.970708	−	0.240263i	$-0.0772336\pi$
$347$	1792.31	+	3104.37i	0.277280	+	0.480264i	−0.693428	+	0.720526i	$0.743900\pi$
$348$		0			0
$349$	−5531.39			−0.848391			−0.424195	−	0.905571i	$-0.639443\pi$
$349$	−5531.39			−0.848391			−0.424195	+	0.905571i	$0.639443\pi$
$350$		0			0
$351$	3528.72	−	6111.91i	0.536606	−	0.929430i
$352$		0			0
$353$	8194.29			1.23552			0.617759	−	0.786367i	$-0.288041\pi$
$353$	8194.29			1.23552			0.617759	+	0.786367i	$0.288041\pi$
$354$		0			0
$355$	−587.729	+	1017.98i	−0.0878687	+	0.152193i
$356$		0			0
$357$	2509.28	−	4346.21i	0.372004	−	0.644330i
$358$		0			0
$359$	−3155.69	−	5465.82i	−0.463931	−	0.803551i	0.535222	−	0.844711i	$-0.320228\pi$
$359$	−3155.69	−	5465.82i	−0.463931	−	0.803551i	−0.999153	+	0.0411601i	$0.986895\pi$
$360$		0			0
$361$	6126.51	−	3084.11i	0.893208	−	0.449645i
$362$		0			0
$363$	−4905.61	−	8496.76i	−0.709305	−	1.22855i
$364$		0			0
$365$	−5257.57	+	9106.38i	−0.753955	+	1.30589i
$366$		0			0
$367$	−979.255	+	1696.12i	−0.139283	+	0.241244i	−0.927225	−	0.374504i	$-0.877813\pi$
$367$	−979.255	+	1696.12i	−0.139283	+	0.241244i	0.787943	+	0.615749i	$0.211146\pi$
$368$		0			0
$369$	5831.41			0.822686
$370$		0			0
$371$	−2705.75	+	4686.49i	−0.378640	+	0.655823i
$372$		0			0
$373$	−7125.83			−0.989173			−0.494587	−	0.869128i	$-0.664681\pi$
$373$	−7125.83			−0.989173			−0.494587	+	0.869128i	$0.664681\pi$
$374$		0			0
$375$	−5922.19	−	10257.5i	−0.815521	−	1.41252i
$376$		0			0
$377$	−11154.2	−	19319.6i	−1.52379	−	2.63928i
$378$		0			0
$379$	2438.86			0.330543			0.165271	−	0.986248i	$-0.447150\pi$
$379$	2438.86			0.330543			0.165271	+	0.986248i	$0.447150\pi$
$380$		0			0
$381$	7897.14			1.06190
$382$		0			0
$383$	2877.47	+	4983.92i	0.383895	+	0.664926i	0.991615	−	0.129225i	$-0.0412491\pi$
$383$	2877.47	+	4983.92i	0.383895	+	0.664926i	−0.607720	+	0.794151i	$0.707916\pi$
$384$		0			0
$385$	8153.95	+	14123.1i	1.07939	+	1.86955i
$386$		0			0
$387$	821.071			0.107849
$388$		0			0
$389$	−2976.47	+	5155.40i	−0.387951	+	0.671951i	−0.992174	−	0.124864i	$-0.960150\pi$
$389$	−2976.47	+	5155.40i	−0.387951	+	0.671951i	0.604223	+	0.796816i	$0.293484\pi$
$390$		0			0
$391$	−5371.41			−0.694742
$392$		0			0
$393$	−7089.04	+	12278.6i	−0.909910	+	1.57601i
$394$		0			0
$395$	−2879.37	+	4987.22i	−0.366777	+	0.635277i
$396$		0			0
$397$	232.192	+	402.169i	0.0293536	+	0.0508420i	0.880329	−	0.474364i	$-0.157322\pi$
$397$	232.192	+	402.169i	0.0293536	+	0.0508420i	−0.850975	+	0.525206i	$0.823988\pi$
$398$		0			0
$399$	5942.79	+	6293.02i	0.745643	+	0.789586i
$400$		0			0
$401$	−97.2349	−	168.416i	−0.0121089	−	0.0209733i	0.859907	−	0.510450i	$-0.170521\pi$
$401$	−97.2349	−	168.416i	−0.0121089	−	0.0209733i	−0.872016	+	0.489477i	$0.837188\pi$
$402$		0			0
$403$	5195.55	−	8998.95i	0.642205	−	1.11233i
$404$		0			0
$405$	8508.93	−	14737.9i	1.04398	−	1.80823i
$406$		0			0
$407$	−1744.24			−0.212430
$408$		0			0
$409$	2144.34	−	3714.11i	0.259244	−	0.449024i	−0.706795	−	0.707418i	$-0.749860\pi$
$409$	2144.34	−	3714.11i	0.259244	−	0.449024i	0.966040	+	0.258394i	$0.0831932\pi$
$410$		0			0
$411$	5334.56			0.640230
$412$		0			0
$413$	−5780.73	−	10012.5i	−0.688744	−	1.19294i
$414$		0			0
$415$	4896.79	+	8481.49i	0.579215	+	1.00323i
$416$		0			0
$417$	−9260.82			−1.08754
$418$		0			0
$419$	10474.9			1.22132			0.610660	−	0.791893i	$-0.290904\pi$
$419$	10474.9			1.22132			0.610660	+	0.791893i	$0.290904\pi$
$420$		0			0
$421$	6444.88	+	11162.9i	0.746091	+	1.29227i	0.949683	+	0.313211i	$0.101405\pi$
$421$	6444.88	+	11162.9i	0.746091	+	1.29227i	−0.203593	+	0.979056i	$0.565262\pi$
$422$		0			0
$423$	−1196.30	−	2072.06i	−0.137509	−	0.238173i
$424$		0			0
$425$	10755.4			1.22756
$426$		0			0
$427$	−146.067	+	252.996i	−0.0165543	+	0.0286729i
$428$		0			0
$429$	29115.1			3.27667
$430$		0			0
$431$	579.967	−	1004.53i	0.0648168	−	0.112266i	−0.831796	−	0.555082i	$-0.812687\pi$
$431$	579.967	−	1004.53i	0.0648168	−	0.112266i	0.896613	+	0.442816i	$0.146020\pi$
$432$		0			0
$433$	−3080.16	+	5334.99i	−0.341855	+	0.592110i	−0.984777	−	0.173822i	$-0.944388\pi$
$433$	−3080.16	+	5334.99i	−0.341855	+	0.592110i	0.642923	+	0.765931i	$0.277722\pi$
$434$		0			0
$435$	−15711.5	−	27213.1i	−1.73174	−	2.99946i
$436$		0			0
$437$	2652.78	−	8876.19i	0.290388	−	0.971638i
$438$		0			0
$439$	−4890.12	−	8469.94i	−0.531647	−	0.920839i	−0.999318	−	0.0369363i	$-0.988240\pi$
$439$	−4890.12	−	8469.94i	−0.531647	−	0.920839i	0.467671	−	0.883903i	$-0.345093\pi$
$440$		0			0
$441$	538.727	−	933.103i	0.0581716	−	0.100756i
$442$		0			0
$443$	−5444.99	+	9430.99i	−0.583971	+	1.01147i	0.411032	+	0.911621i	$0.365168\pi$
$443$	−5444.99	+	9430.99i	−0.583971	+	1.01147i	−0.995003	+	0.0998462i	$0.968165\pi$
$444$		0			0
$445$	11140.8			1.18680
$446$		0			0
$447$	9198.82	−	15932.8i	0.973354	−	1.68590i
$448$		0			0
$449$	−17403.0			−1.82917			−0.914584	−	0.404396i	$-0.867482\pi$
$449$	−17403.0			−1.82917			−0.914584	+	0.404396i	$0.867482\pi$
$450$		0			0
$451$	−11118.6	−	19257.9i	−1.16087	−	2.01069i
$452$		0			0
$453$	1671.85	+	2895.72i	0.173400	+	0.300337i
$454$		0			0
$455$	−25893.4			−2.66791
$456$		0			0
$457$	−2823.09			−0.288969			−0.144484	−	0.989507i	$-0.546152\pi$
$457$	−2823.09			−0.288969			−0.144484	+	0.989507i	$0.546152\pi$
$458$		0			0
$459$	1994.59	+	3454.74i	0.202831	+	0.351314i
$460$		0			0
$461$	−7839.87	−	13579.1i	−0.792059	−	1.37189i	−0.924690	−	0.380721i	$-0.875676\pi$
$461$	−7839.87	−	13579.1i	−0.792059	−	1.37189i	0.132631	−	0.991165i	$-0.457657\pi$
$462$		0			0
$463$	5027.29			0.504617			0.252309	−	0.967647i	$-0.418810\pi$
$463$	5027.29			0.504617			0.252309	+	0.967647i	$0.418810\pi$
$464$		0			0
$465$	7318.31	−	12675.7i	0.729846	−	1.26413i
$466$		0			0
$467$	7868.25			0.779656			0.389828	−	0.920888i	$-0.372534\pi$
$467$	7868.25			0.779656			0.389828	+	0.920888i	$0.372534\pi$
$468$		0			0
$469$	−2686.49	+	4653.13i	−0.264500	+	0.458127i
$470$		0			0
$471$	−570.211	+	987.634i	−0.0557833	+	0.0966195i
$472$		0			0
$473$	−1565.51	−	2711.55i	−0.152182	−	0.263588i
$474$		0			0
$475$	−5311.78	+	17773.2i	−0.513098	+	1.71682i
$476$		0			0
$477$	2326.79	+	4030.12i	0.223347	+	0.386848i
$478$		0			0
$479$	−1020.82	+	1768.11i	−0.0973744	+	0.168657i	−0.910597	−	0.413295i	$-0.864378\pi$
$479$	−1020.82	+	1768.11i	−0.0973744	+	0.168657i	0.813223	+	0.581953i	$0.197711\pi$
$480$		0			0
$481$	1384.74	−	2398.44i	0.131265	−	0.227358i
$482$		0			0
$483$	11690.7			1.10133
$484$		0			0
$485$	5138.41	−	8899.98i	0.481078	−	0.833252i
$486$		0			0
$487$	−8699.63			−0.809482			−0.404741	−	0.914431i	$-0.632638\pi$
$487$	−8699.63			−0.809482			−0.404741	+	0.914431i	$0.632638\pi$
$488$		0			0
$489$	1362.07	+	2359.18i	0.125961	+	0.218171i
$490$		0			0
$491$	−6529.44	−	11309.3i	−0.600141	−	1.03948i	−0.992799	−	0.119791i	$-0.961778\pi$
$491$	−6529.44	−	11309.3i	−0.600141	−	1.03948i	0.392658	−	0.919685i	$-0.371556\pi$
$492$		0			0
$493$	12609.7			1.15195
$494$		0			0
$495$	14023.9			1.27339
$496$		0			0
$497$	513.317	+	889.091i	0.0463288	+	0.0802439i
$498$		0			0
$499$	4086.77	+	7078.50i	0.366632	+	0.635024i	0.989037	−	0.147671i	$-0.0471776\pi$
$499$	4086.77	+	7078.50i	0.366632	+	0.635024i	−0.622405	+	0.782695i	$0.713844\pi$
$500$		0			0
$501$	−3944.23			−0.351727
$502$		0			0
$503$	10026.6	−	17366.7i	0.888799	−	1.53945i	0.0475029	−	0.998871i	$-0.484874\pi$
$503$	10026.6	−	17366.7i	0.888799	−	1.53945i	0.841296	−	0.540574i	$-0.181793\pi$
$504$		0			0
$505$	−5112.37			−0.450490
$506$		0			0
$507$	−16077.7	+	27847.4i	−1.40836	+	2.43935i
$508$		0			0
$509$	3411.92	−	5909.62i	0.297113	−	0.514615i	−0.678361	−	0.734729i	$-0.737309\pi$
$509$	3411.92	−	5909.62i	0.297113	−	0.514615i	0.975474	+	0.220113i	$0.0706427\pi$
$510$		0			0
$511$	4591.91	+	7953.43i	0.397523	+	0.688530i
$512$		0			0
$513$	−6693.98	+	1589.85i	−0.576113	+	0.136829i
$514$		0			0
$515$	9317.94	+	16139.2i	0.797277	+	1.38092i
$516$		0			0
$517$	−4561.92	+	7901.47i	−0.388071	+	0.672159i
$518$		0			0
$519$	−11982.8	+	20754.9i	−1.01346	+	1.75537i
$520$		0			0
$521$	8668.43			0.728926			0.364463	−	0.931218i	$-0.381253\pi$
$521$	8668.43			0.728926			0.364463	+	0.931218i	$0.381253\pi$
$522$		0			0
$523$	2521.77	−	4367.84i	0.210840	−	0.365186i	−0.741138	−	0.671353i	$-0.765713\pi$
$523$	2521.77	−	4367.84i	0.210840	−	0.365186i	0.951978	+	0.306167i	$0.0990467\pi$
$524$		0			0
$525$	−23408.7			−1.94598
$526$		0			0
$527$	2936.76	+	5086.63i	0.242747	+	0.420449i
$528$		0			0
$529$	−172.803	−	299.304i	−0.0142026	−	0.0245997i
$530$		0			0
$531$	−9942.22			−0.812534
$532$		0			0
$533$	35307.7			2.86932
$534$		0			0
$535$	5514.98	+	9552.22i	0.445670	+	0.771922i
$536$		0			0
$537$	−6646.11	−	11511.4i	−0.534080	−	0.925054i
$538$		0			0
$539$	−4108.70			−0.328338
$540$		0			0
$541$	121.909	−	211.153i	0.00968813	−	0.0167803i	−0.861141	−	0.508367i	$-0.830249\pi$
$541$	121.909	−	211.153i	0.00968813	−	0.0167803i	0.870829	+	0.491586i	$0.163583\pi$
$542$		0			0
$543$	1271.57			0.100494
$544$		0			0
$545$	−2957.09	+	5121.83i	−0.232418	+	0.402560i
$546$		0			0
$547$	10711.1	−	18552.1i	0.837245	−	1.45015i	−0.0549453	−	0.998489i	$-0.517498\pi$
$547$	10711.1	−	18552.1i	0.837245	−	1.45015i	0.892190	−	0.451661i	$-0.149168\pi$
$548$		0			0
$549$	125.610	+	217.563i	0.00976484	+	0.0169132i
$550$		0			0
$551$	−6227.56	+	20837.4i	−0.481494	+	1.61108i
$552$		0			0
$553$	2514.82	+	4355.79i	0.193383	+	0.334950i
$554$		0			0
$555$	1950.51	−	3378.37i	0.149179	−	0.258386i
$556$		0			0
$557$	−2979.56	+	5160.74i	−0.226657	+	0.392581i	−0.956815	−	0.290697i	$-0.906113\pi$
$557$	−2979.56	+	5160.74i	−0.226657	+	0.392581i	0.730158	+	0.683278i	$0.239446\pi$
$558$		0			0
$559$	4971.38			0.376148
$560$		0			0
$561$	−8228.60	+	14252.4i	−0.619272	+	1.07261i
$562$		0			0
$563$	−2542.88			−0.190354			−0.0951771	−	0.995460i	$-0.530342\pi$
$563$	−2542.88			−0.190354			−0.0951771	+	0.995460i	$0.530342\pi$
$564$		0			0
$565$	16912.1	+	29292.6i	1.25929	+	2.18115i
$566$		0			0
$567$	−7431.62	−	12871.9i	−0.550439	−	0.953388i
$568$		0			0
$569$	11766.3			0.866908			0.433454	−	0.901176i	$-0.357295\pi$
$569$	11766.3			0.866908			0.433454	+	0.901176i	$0.357295\pi$
$570$		0			0
$571$	−17847.7			−1.30806			−0.654032	−	0.756467i	$-0.726924\pi$
$571$	−17847.7			−1.30806			−0.654032	+	0.756467i	$0.726924\pi$
$572$		0			0
$573$	−9180.35	−	15900.8i	−0.669310	−	1.15928i
$574$		0			0
$575$	12527.3	+	21697.9i	0.908563	+	1.57368i
$576$		0			0
$577$	−469.766			−0.0338936			−0.0169468	−	0.999856i	$-0.505395\pi$
$577$	−469.766			−0.0338936			−0.0169468	+	0.999856i	$0.505395\pi$
$578$		0			0
$579$	−10325.3	+	17884.0i	−0.741114	+	1.28365i
$580$		0			0
$581$	8553.63			0.610782
$582$		0			0
$583$	8872.85	−	15368.2i	0.630319	−	1.09174i
$584$		0			0
$585$	−11133.4	+	19283.7i	−0.786857	+	1.36288i
$586$		0			0
$587$	−9424.24	−	16323.3i	−0.662658	−	1.14776i	−0.979915	−	0.199417i	$-0.936095\pi$
$587$	−9424.24	−	16323.3i	−0.662658	−	1.14776i	0.317257	−	0.948340i	$-0.397238\pi$
$588$		0			0
$589$	−9855.96	+	2340.83i	−0.689487	+	0.163756i
$590$		0			0
$591$	−8261.54	−	14309.4i	−0.575016	−	0.995957i
$592$		0			0
$593$	−8306.48	+	14387.2i	−0.575221	+	0.996312i	0.420797	+	0.907155i	$0.361751\pi$
$593$	−8306.48	+	14387.2i	−0.575221	+	0.996312i	−0.996018	+	0.0891571i	$0.971583\pi$
$594$		0			0
$595$	7318.07	−	12675.3i	0.504221	−	0.873337i
$596$		0			0
$597$	−22034.6			−1.51058
$598$		0			0
$599$	−2122.62	+	3676.48i	−0.144788	+	0.250780i	−0.929294	−	0.369341i	$-0.879583\pi$
$599$	−2122.62	+	3676.48i	−0.144788	+	0.250780i	0.784506	+	0.620121i	$0.212917\pi$
$600$		0			0
$601$	−22313.6			−1.51446			−0.757230	−	0.653148i	$-0.773448\pi$
$601$	−22313.6			−1.51446			−0.757230	+	0.653148i	$0.773448\pi$
$602$		0			0
$603$	2310.23	+	4001.44i	0.156020	+	0.270234i
$604$		0			0
$605$	−14306.7	−	24779.9i	−0.961405	−	1.66520i
$606$		0			0
$607$	−6593.84			−0.440915			−0.220458	−	0.975397i	$-0.570755\pi$
$607$	−6593.84			−0.440915			−0.220458	+	0.975397i	$0.570755\pi$
$608$		0			0
$609$	−27444.5			−1.82612
$610$		0			0
$611$	−7243.32	−	12545.8i	−0.479596	−	0.830685i
$612$		0			0
$613$	−11681.2	−	20232.4i	−0.769657	−	1.33308i	−0.937749	−	0.347313i	$-0.887094\pi$
$613$	−11681.2	−	20232.4i	−0.769657	−	1.33308i	0.168092	−	0.985771i	$-0.446239\pi$
$614$		0			0
$615$	49733.5			3.26089
$616$		0			0
$617$	−6713.50	+	11628.1i	−0.438047	+	0.758720i	−0.997539	−	0.0701159i	$-0.977663\pi$
$617$	−6713.50	+	11628.1i	−0.438047	+	0.758720i	0.559492	+	0.828836i	$0.310996\pi$
$618$		0			0
$619$	21161.5			1.37408			0.687039	−	0.726621i	$-0.258910\pi$
$619$	21161.5			1.37408			0.687039	+	0.726621i	$0.258910\pi$
$620$		0			0
$621$	−4646.37	+	8047.74i	−0.300245	+	0.520040i
$622$		0			0
$623$	4865.14	−	8426.67i	0.312870	−	0.541906i
$624$		0			0
$625$	−3272.58	−	5668.28i	−0.209445	−	0.362770i
$626$		0			0
$627$	−19488.0	−	20636.5i	−1.24127	−	1.31442i
$628$		0			0
$629$	782.719	+	1355.71i	0.0496169	+	0.0859390i
$630$		0			0
$631$	−6605.23	+	11440.6i	−0.416719	+	0.721779i	−0.995607	−	0.0936280i	$-0.970154\pi$
$631$	−6605.23	+	11440.6i	−0.416719	+	0.721779i	0.578888	+	0.815407i	$0.303487\pi$
$632$		0			0
$633$	10849.8	−	18792.3i	0.681263	−	1.17998i
$634$		0			0
$635$	23031.2			1.43932
$636$		0			0
$637$	3261.86	−	5649.70i	0.202888	−	0.351412i
$638$		0			0
$639$	882.849			0.0546557
$640$		0			0
$641$	−4058.44	−	7029.42i	−0.250076	−	0.433144i	0.713471	−	0.700685i	$-0.247122\pi$
$641$	−4058.44	−	7029.42i	−0.250076	−	0.433144i	−0.963546	+	0.267541i	$0.913789\pi$
$642$		0			0
$643$	5100.58	+	8834.47i	0.312826	+	0.541831i	0.978973	−	0.203990i	$-0.0653909\pi$
$643$	5100.58	+	8834.47i	0.312826	+	0.541831i	−0.666147	+	0.745821i	$0.732058\pi$
$644$		0			0
$645$	7002.55			0.427481
$646$		0			0
$647$	22261.3			1.35268			0.676338	−	0.736591i	$-0.263566\pi$
$647$	22261.3			1.35268			0.676338	+	0.736591i	$0.263566\pi$
$648$		0			0
$649$	18956.5	+	32833.7i	1.14655	+	1.98588i
$650$		0			0
$651$	−6391.74	−	11070.8i	−0.384811	−	0.666513i
$652$		0			0
$653$	−25907.6			−1.55259			−0.776295	−	0.630370i	$-0.782903\pi$
$653$	−25907.6			−1.55259			−0.776295	+	0.630370i	$0.782903\pi$
$654$		0			0
$655$	−20674.5	+	35809.2i	−1.23331	+	2.13616i
$656$		0			0
$657$	7897.59			0.468971
$658$		0			0
$659$	16265.9	−	28173.3i	0.961501	−	1.66537i	0.242765	−	0.970085i	$-0.421945\pi$
$659$	16265.9	−	28173.3i	0.961501	−	1.66537i	0.718736	−	0.695283i	$-0.244721\pi$
$660$		0			0
$661$	−12609.7	+	21840.6i	−0.741997	+	1.28518i	0.209588	+	0.977790i	$0.432788\pi$
$661$	−12609.7	+	21840.6i	−0.741997	+	1.28518i	−0.951585	+	0.307387i	$0.900545\pi$
$662$		0			0
$663$	−13065.2	−	22629.6i	−0.765326	−	1.32558i
$664$		0			0
$665$	17331.5	+	18352.9i	1.01066	+	1.07022i
$666$		0			0
$667$	14687.0	+	25438.7i	0.852601	+	1.47675i
$668$		0			0
$669$	−3035.57	+	5257.76i	−0.175429	+	0.303852i
$670$		0			0
$671$	478.993	−	829.640i	0.0275579	−	0.0477316i
$672$		0			0
$673$	−12578.8			−0.720471			−0.360235	−	0.932861i	$-0.617304\pi$
$673$	−12578.8			−0.720471			−0.360235	+	0.932861i	$0.617304\pi$
$674$		0			0
$675$	9303.63	−	16114.4i	0.530514	−	0.918877i
$676$		0			0
$677$	30360.9			1.72358			0.861790	−	0.507265i	$-0.169343\pi$
$677$	30360.9			1.72358			0.861790	+	0.507265i	$0.169343\pi$
$678$		0			0
$679$	−4487.84	−	7773.17i	−0.253649	−	0.439332i
$680$		0			0
$681$	−2132.76	−	3694.05i	−0.120011	−	0.207865i
$682$		0			0
$683$	2426.04			0.135915			0.0679574	−	0.997688i	$-0.478352\pi$
$683$	2426.04			0.135915			0.0679574	+	0.997688i	$0.478352\pi$
$684$		0			0
$685$	15557.7			0.867780
$686$		0			0
$687$	20773.5	+	35980.8i	1.15365	+	1.99819i
$688$		0			0
$689$	14088.1	+	24401.4i	0.778978	+	1.34923i
$690$		0			0
$691$	−30357.6			−1.67129			−0.835643	−	0.549273i	$-0.814905\pi$
$691$	−30357.6			−1.67129			−0.835643	+	0.549273i	$0.814905\pi$
$692$		0			0
$693$	6124.17	−	10607.4i	0.335697	−	0.581445i
$694$		0			0
$695$	−27008.2			−1.47407
$696$		0			0
$697$	−9978.78	+	17283.8i	−0.542286	+	0.939267i
$698$		0			0
$699$	−2796.18	+	4843.12i	−0.151303	+	0.262065i
$700$		0			0
$701$	−9467.93	−	16398.9i	−0.510127	−	0.883565i	−0.999931	−	0.0117329i	$-0.996265\pi$
$701$	−9467.93	−	16398.9i	−0.510127	−	0.883565i	0.489805	−	0.871832i	$-0.337068\pi$
$702$		0			0
$703$	−2626.85	+	623.888i	−0.140930	+	0.0334714i
$704$		0			0
$705$	−10202.7	−	17671.7i	−0.545046	−	0.944048i
$706$		0			0
$707$	−2232.55	+	3866.89i	−0.118761	+	0.205699i
$708$		0			0
$709$	6928.63	−	12000.7i	0.367010	−	0.635680i	−0.622087	−	0.782948i	$-0.713715\pi$
$709$	6928.63	−	12000.7i	0.367010	−	0.635680i	0.989097	+	0.147268i	$0.0470481\pi$
$710$		0			0
$711$	4325.21			0.228141
$712$		0			0
$713$	−6841.14	+	11849.2i	−0.359330	+	0.622378i
$714$		0			0
$715$	84911.2			4.44126
$716$		0			0
$717$	−9155.38	−	15857.6i	−0.476867	−	0.825959i
$718$		0			0
$719$	7967.10	+	13799.4i	0.413244	+	0.715760i	0.995242	−	0.0974301i	$-0.0310622\pi$
$719$	7967.10	+	13799.4i	0.413244	+	0.715760i	−0.581998	+	0.813190i	$0.697729\pi$
$720$		0			0
$721$	16276.4			0.840729
$722$		0			0
$723$	−33415.8			−1.71888
$724$		0			0
$725$	−29408.5	−	50937.1i	−1.50649	−	2.60932i
$726$		0			0
$727$	4654.92	+	8062.56i	0.237471	+	0.411312i	0.959988	−	0.280041i	$-0.0903481\pi$
$727$	4654.92	+	8062.56i	0.237471	+	0.411312i	−0.722517	+	0.691353i	$0.757015\pi$
$728$		0			0
$729$	1586.16			0.0805852
$730$		0			0
$731$	−1405.03	+	2433.58i	−0.0710900	+	0.123132i
$732$		0			0
$733$	12311.8			0.620391			0.310195	−	0.950673i	$-0.399606\pi$
$733$	12311.8			0.620391			0.310195	+	0.950673i	$0.399606\pi$
$734$		0			0
$735$	4594.56	−	7958.02i	0.230576	−	0.399369i
$736$		0			0
$737$	8809.69	−	15258.8i	0.440311	−	0.762641i
$738$		0			0
$739$	19313.1	+	33451.3i	0.961360	+	1.66512i	0.719092	+	0.694915i	$0.244558\pi$
$739$	19313.1	+	33451.3i	0.961360	+	1.66512i	0.242268	+	0.970209i	$0.422109\pi$
$740$		0			0
$741$	43847.6	−	10414.0i	2.17380	−	0.516286i
$742$		0			0
$743$	−14569.3	−	25234.7i	−0.719373	−	1.24599i	−0.961248	−	0.275684i	$-0.911096\pi$
$743$	−14569.3	−	25234.7i	−0.719373	−	1.24599i	0.241875	−	0.970307i	$-0.422238\pi$
$744$		0			0
$745$	26827.4	−	46466.5i	1.31930	−	2.28510i
$746$		0			0
$747$	3677.83	−	6370.18i	0.180140	−	0.312012i
$748$		0			0
$749$	9633.46			0.469959
$750$		0			0
$751$	5352.16	−	9270.22i	0.260057	−	0.450433i	−0.706199	−	0.708013i	$-0.749592\pi$
$751$	5352.16	−	9270.22i	0.260057	−	0.450433i	0.966257	+	0.257580i	$0.0829252\pi$
$752$		0			0
$753$	−1438.11			−0.0695985
$754$		0			0
$755$	4875.77	+	8445.07i	0.235029	+	0.407083i
$756$		0			0
$757$	−2276.73	−	3943.41i	−0.109312	−	0.189334i	0.806180	−	0.591671i	$-0.201531\pi$
$757$	−2276.73	−	3943.41i	−0.109312	−	0.189334i	−0.915492	+	0.402337i	$0.868198\pi$
$758$		0			0
$759$	−38336.7			−1.83338
$760$		0			0
$761$	−37730.0			−1.79726			−0.898628	−	0.438711i	$-0.855435\pi$
$761$	−37730.0			−1.79726			−0.898628	+	0.438711i	$0.855435\pi$
$762$		0			0
$763$	2582.70	+	4473.36i	0.122543	+	0.212250i
$764$		0			0
$765$	−6293.14	−	10900.0i	−0.297423	−	0.515152i
$766$		0			0
$767$	−60197.6			−2.83391
$768$		0			0
$769$	6998.33	−	12121.5i	0.328175	−	0.568415i	−0.653975	−	0.756516i	$-0.726900\pi$
$769$	6998.33	−	12121.5i	0.328175	−	0.568415i	0.982150	+	0.188101i	$0.0602332\pi$
$770$		0			0
$771$	−11816.2			−0.551946
$772$		0			0
$773$	8178.21	−	14165.1i	0.380530	−	0.659098i	−0.610608	−	0.791933i	$-0.709075\pi$
$773$	8178.21	−	14165.1i	0.380530	−	0.659098i	0.991138	+	0.132835i	$0.0424081\pi$
$774$		0			0
$775$	13698.3	−	23726.2i	0.634914	−	1.09970i
$776$		0			0
$777$	−1703.55	−	2950.64i	−0.0786547	−	0.136234i
$778$		0			0
$779$	−23632.9	−	25025.7i	−1.08696	−	1.15101i
$780$		0			0
$781$	−1683.30	−	2915.56i	−0.0771233	−	0.133581i
$782$		0			0
$783$	10907.6	−	18892.6i	0.497837	−	0.862280i
$784$		0			0
$785$	−1662.96	+	2880.33i	−0.0756098	+	0.130960i
$786$		0			0
$787$	−40574.2			−1.83776			−0.918878	−	0.394541i	$-0.870904\pi$
$787$	−40574.2			−1.83776			−0.918878	+	0.394541i	$0.870904\pi$
$788$		0			0
$789$	−19676.8	+	34081.3i	−0.887851	+	1.53780i
$790$		0			0
$791$	29541.8			1.32792
$792$		0			0
$793$	760.536	+	1317.29i	0.0340573	+	0.0589890i
$794$		0			0
$795$	19844.2	+	34371.1i	0.885283	+	1.53336i
$796$		0			0
$797$	5182.09			0.230313			0.115156	−	0.993347i	$-0.463263\pi$
$797$	5182.09			0.230313			0.115156	+	0.993347i	$0.463263\pi$
$798$		0			0
$799$	8188.52			0.362565
$800$		0			0
$801$	−4183.75	−	7246.47i	−0.184551	−	0.319652i
$802$		0			0
$803$	−15058.1	−	26081.4i	−0.661754	−	1.14619i
$804$		0			0
$805$	34094.6			1.49277
$806$		0			0
$807$	11738.1	−	20331.0i	0.512021	−	0.886847i
$808$		0			0
$809$	13663.9			0.593816			0.296908	−	0.954906i	$-0.404045\pi$
$809$	13663.9			0.593816			0.296908	+	0.954906i	$0.404045\pi$
$810$		0			0
$811$	−1512.46	+	2619.65i	−0.0654865	+	0.113426i	−0.896910	−	0.442214i	$-0.854193\pi$
$811$	−1512.46	+	2619.65i	−0.0654865	+	0.113426i	0.831423	+	0.555640i	$0.187527\pi$
$812$		0			0
$813$	−27403.8	+	47464.8i	−1.18216	+	2.04756i
$814$		0			0
$815$	3972.34	+	6880.30i	0.170730	+	0.295713i
$816$		0			0
$817$	−3327.55	−	3523.66i	−0.142492	−	0.150890i
$818$		0			0
$819$	9723.85	+	16842.2i	0.414870	+	0.718576i
$820$		0			0
$821$	8134.69	−	14089.7i	0.345801	−	0.598945i	−0.639698	−	0.768626i	$-0.720941\pi$
$821$	8134.69	−	14089.7i	0.345801	−	0.598945i	0.985499	+	0.169681i	$0.0542739\pi$
$822$		0			0
$823$	19967.1	−	34584.0i	0.845697	−	1.46479i	−0.0393174	−	0.999227i	$-0.512518\pi$
$823$	19967.1	−	34584.0i	0.845697	−	1.46479i	0.885014	−	0.465563i	$-0.154148\pi$
$824$		0			0
$825$	76763.4			3.23946
$826$		0			0
$827$	−1334.93	+	2312.17i	−0.0561307	+	0.0972213i	−0.892725	−	0.450601i	$-0.851210\pi$
$827$	−1334.93	+	2312.17i	−0.0561307	+	0.0972213i	0.836595	+	0.547822i	$0.184543\pi$
$828$		0			0
$829$	−2680.10			−0.112284			−0.0561421	−	0.998423i	$-0.517880\pi$
$829$	−2680.10			−0.112284			−0.0561421	+	0.998423i	$0.517880\pi$
$830$		0			0
$831$	6620.45	+	11467.0i	0.276367	+	0.478681i
$832$		0			0
$833$	1843.75	+	3193.47i	0.0766894	+	0.132830i
$834$		0			0
$835$	−11502.9			−0.476738
$836$		0			0
$837$	10161.4			0.419629
$838$		0			0
$839$	−15390.4	−	26657.0i	−0.633296	−	1.09690i	−0.986873	−	0.161496i	$-0.948368\pi$
$839$	−15390.4	−	26657.0i	−0.633296	−	1.09690i	0.353577	−	0.935405i	$-0.384965\pi$
$840$		0			0
$841$	−22284.2	−	38597.4i	−0.913700	−	1.58257i
$842$		0			0
$843$	2259.56			0.0923173
$844$		0			0
$845$	−46889.0	+	81214.2i	−1.90891	+	3.30634i
$846$		0			0
$847$	−24990.7			−1.01380
$848$		0			0
$849$	−6598.44	+	11428.8i	−0.266735	+	0.461998i
$850$		0			0
$851$	−1823.33	+	3158.10i	−0.0734464	+	0.127213i
$852$		0			0
$853$	18597.3	+	32211.4i	0.746493	+	1.29296i	0.949494	+	0.313785i	$0.101597\pi$
$853$	18597.3	+	32211.4i	0.746493	+	1.29296i	−0.203002	+	0.979178i	$0.565070\pi$
$854$		0			0
$855$	21120.1	−	5016.12i	0.844788	−	0.200641i
$856$		0			0
$857$	22055.4	+	38201.0i	0.879110	+	1.52266i	0.852319	+	0.523022i	$0.175196\pi$
$857$	22055.4	+	38201.0i	0.879110	+	1.52266i	0.0267913	+	0.999641i	$0.491471\pi$
$858$		0			0
$859$	−18976.3	+	32868.0i	−0.753741	+	1.30552i	0.192257	+	0.981345i	$0.438419\pi$
$859$	−18976.3	+	32868.0i	−0.753741	+	1.30552i	−0.945998	+	0.324173i	$0.894914\pi$
$860$		0			0
$861$	21718.4	−	37617.4i	0.859652	−	1.48896i
$862$		0			0
$863$	10039.5			0.396001			0.198001	−	0.980202i	$-0.436555\pi$
$863$	10039.5			0.396001			0.198001	+	0.980202i	$0.436555\pi$
$864$		0			0
$865$	−34946.7	+	60529.4i	−1.37367	+	2.37926i
$866$		0			0
$867$	−16700.2			−0.654174
$868$		0			0
$869$	−8246.75	−	14283.8i	−0.321924	−	0.557589i
$870$		0			0
$871$	13987.9	+	24227.7i	0.544157	+	0.942507i
$872$		0			0
$873$	−7718.59			−0.299238
$874$		0			0
$875$	−30169.5			−1.16562
$876$		0			0
$877$	7066.59	+	12239.7i	0.272089	+	0.471271i	0.969396	−	0.245500i	$-0.0789523\pi$
$877$	7066.59	+	12239.7i	0.272089	+	0.471271i	−0.697308	+	0.716772i	$0.745619\pi$
$878$		0			0
$879$	−5573.34	−	9653.31i	−0.213861	−	0.370419i
$880$		0			0
$881$	5550.33			0.212253			0.106127	−	0.994353i	$-0.466155\pi$
$881$	5550.33			0.212253			0.106127	+	0.994353i	$0.466155\pi$
$882$		0			0
$883$	−8728.39	+	15118.0i	−0.332654	+	0.576174i	−0.983031	−	0.183437i	$-0.941278\pi$
$883$	−8728.39	+	15118.0i	−0.332654	+	0.576174i	0.650377	+	0.759612i	$0.274611\pi$
$884$		0			0
$885$	−84792.7			−3.22065
$886$		0			0
$887$	−5559.59	+	9629.49i	−0.210454	+	0.364517i	−0.951857	−	0.306543i	$-0.900828\pi$
$887$	−5559.59	+	9629.49i	−0.210454	+	0.364517i	0.741403	+	0.671060i	$0.234161\pi$
$888$		0			0
$889$	10057.6	−	17420.3i	0.379440	−	0.657209i
$890$		0			0
$891$	24370.2	+	42210.5i	0.916311	+	1.58710i
$892$		0			0
$893$	−4044.07	+	13531.4i	−0.151545	+	0.507068i
$894$		0			0
$895$	−19382.7	−	33571.8i	−0.723902	−	1.25384i
$896$		0			0
$897$	30435.2	−	52715.2i	1.13289	−	1.96222i
$898$		0			0
$899$	16060.0	−	27816.7i	0.595807	−	1.03197i
$900$		0			0
$901$	−15926.5			−0.588890
$902$		0			0
$903$	3057.98	−	5296.58i	0.112695	−	0.195193i
$904$		0			0
$905$	3708.42			0.136212
$906$		0			0
$907$	4460.08	+	7725.08i	0.163279	+	0.282808i	0.936043	−	0.351886i	$-0.114459\pi$
$907$	4460.08	+	7725.08i	0.163279	+	0.282808i	−0.772763	+	0.634694i	$0.781126\pi$
$908$		0			0
$909$	1919.87	+	3325.31i	0.0700529	+	0.121335i
$910$		0			0
$911$	15263.9			0.555123			0.277561	−	0.960708i	$-0.410474\pi$
$911$	15263.9			0.555123			0.277561	+	0.960708i	$0.410474\pi$
$912$		0			0
$913$	−28049.6			−1.01676
$914$		0			0
$915$	1071.27	+	1855.49i	0.0387050	+	0.0670391i
$916$		0			0
$917$	18056.9	+	31275.5i	0.650263	+	1.12629i
$918$		0			0
$919$	−5357.59			−0.192307			−0.0961537	−	0.995366i	$-0.530654\pi$
$919$	−5357.59			−0.192307			−0.0961537	+	0.995366i	$0.530654\pi$
$920$		0			0
$921$	8161.08	−	14135.4i	0.291983	−	0.505730i
$922$		0			0
$923$	5345.43			0.190625
$924$		0			0
$925$	3650.93	−	6323.60i	0.129775	−	0.224777i
$926$		0			0
$927$	6998.41	−	12121.6i	0.247959	−	0.429478i
$928$		0			0
$929$	14658.5	+	25389.2i	0.517685	+	0.896656i	0.999789	+	0.0205423i	$0.00653926\pi$
$929$	14658.5	+	25389.2i	0.517685	+	0.896656i	−0.482104	+	0.876114i	$0.660127\pi$
$930$		0			0
$931$	−6187.75	+	1469.62i	−0.217825	+	0.0517344i
$932$		0			0
$933$	25299.7	+	43820.3i	0.887753	+	1.53763i
$934$		0			0
$935$	−23997.9	+	41565.5i	−0.839373	+	1.45384i
$936$		0			0
$937$	−7522.09	+	13028.6i	−0.262258	+	0.454245i	−0.966842	−	0.255376i	$-0.917801\pi$
$937$	−7522.09	+	13028.6i	−0.262258	+	0.454245i	0.704583	+	0.709621i	$0.251134\pi$
$938$		0			0
$939$	42218.0			1.46723
$940$		0			0
$941$	21063.4	−	36482.9i	0.729701	−	1.26388i	−0.227309	−	0.973823i	$-0.572993\pi$
$941$	21063.4	−	36482.9i	0.729701	−	1.26388i	0.957010	−	0.290056i	$-0.0936739\pi$
$942$		0			0
$943$	−46490.7			−1.60546
$944$		0			0
$945$	−12660.5	−	21928.7i	−0.435816	−	0.754856i
$946$		0			0
$947$	16485.7	+	28554.0i	0.565694	+	0.979811i	0.996985	+	0.0775981i	$0.0247251\pi$
$947$	16485.7	+	28554.0i	0.565694	+	0.979811i	−0.431290	+	0.902213i	$0.641942\pi$
$948$		0			0
$949$	47817.9			1.63565
$950$		0			0
$951$	−46185.5			−1.57484
$952$		0			0
$953$	−22547.4	−	39053.3i	−0.766404	−	1.32745i	−0.939501	−	0.342547i	$-0.888711\pi$
$953$	−22547.4	−	39053.3i	−0.766404	−	1.32745i	0.173096	−	0.984905i	$-0.444623\pi$
$954$		0			0
$955$	−26773.6	−	46373.1i	−0.907196	−	1.57131i
$956$		0			0
$957$	89997.8			3.03993
$958$		0			0
$959$	6793.98	−	11767.5i	0.228769	−	0.396239i
$960$		0			0
$961$	−14829.7			−0.497792
$962$		0			0
$963$	4142.12	−	7174.37i	0.138606	−	0.240073i
$964$		0			0
$965$	−30112.7	+	52156.7i	−1.00452	+	1.73988i
$966$		0			0
$967$	−29521.6	−	51133.0i	−0.981750	−	1.70044i	−0.655574	−	0.755131i	$-0.727573\pi$
$967$	−29521.6	−	51133.0i	−0.981750	−	1.70044i	−0.326175	−	0.945309i	$-0.605760\pi$
$968$		0			0
$969$	−7294.52	+	24407.4i	−0.241831	+	0.809164i
$970$		0			0
$971$	25311.7	+	43841.1i	0.836551	+	1.44895i	0.892762	+	0.450529i	$0.148765\pi$
$971$	25311.7	+	43841.1i	0.836551	+	1.44895i	−0.0562108	+	0.998419i	$0.517902\pi$
$972$		0			0
$973$	−11794.4	+	20428.5i	−0.388603	+	0.673079i
$974$		0			0
$975$	−60941.7	+	105554.i	−2.00174	+	3.46712i
$976$		0			0
$977$	−23724.7			−0.776887			−0.388444	−	0.921472i	$-0.626987\pi$
$977$	−23724.7			−0.776887			−0.388444	+	0.921472i	$0.626987\pi$
$978$		0			0
$979$	−15954.1	+	27633.3i	−0.520832	+	0.902107i
$980$		0			0
$981$	4441.96			0.144568
$982$		0			0
$983$	13760.3	+	23833.5i	0.446476	+	0.773318i	0.998154	−	0.0607387i	$-0.0193456\pi$
$983$	13760.3	+	23833.5i	0.446476	+	0.773318i	−0.551678	+	0.834057i	$0.686012\pi$
$984$		0			0
$985$	−24093.9	−	41731.9i	−0.779387	−	1.34994i
$986$		0			0
$987$	−17822.0			−0.574751
$988$		0			0
$989$	−6545.97			−0.210465
$990$		0			0
$991$	19700.9	+	34122.9i	0.631502	+	1.09379i	0.987245	+	0.159210i	$0.0508945\pi$
$991$	19700.9	+	34122.9i	0.631502	+	1.09379i	−0.355743	+	0.934584i	$0.615772\pi$
$992$		0			0
$993$	−4560.34	−	7898.75i	−0.145738	−	0.252426i
$994$		0			0
$995$	−64261.8			−2.04747
$996$		0			0
$997$	−1039.58	+	1800.60i	−0.0330228	+	0.0571971i	−0.882064	−	0.471129i	$-0.843847\pi$
$997$	−1039.58	+	1800.60i	−0.0330228	+	0.0571971i	0.849042	+	0.528326i	$0.177180\pi$
$998$		0			0
$999$	2708.26			0.0857714

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	152.4.i.b.121.2	yes	16
4.3	odd	2		304.4.i.h.273.7		16
19.11	even	3	inner	152.4.i.b.49.2	✓	16
76.11	odd	6		304.4.i.h.49.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
152.4.i.b.49.2	✓	16	19.11	even	3	inner
152.4.i.b.121.2	yes	16	1.1	even	1	trivial
304.4.i.h.49.7		16	76.11	odd	6
304.4.i.h.273.7		16	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 152 = 2^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	152.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.20276 - 5.54735i) q^{3} +(-9.34053 - 16.1783i) q^{5} -16.3159 q^{7} +(-7.01538 + 12.1510i) q^{9} +O(q^{10})\)	\(q+(-3.20276 - 5.54735i) q^{3} +(-9.34053 - 16.1783i) q^{5} -16.3159 q^{7} +(-7.01538 + 12.1510i) q^{9} +53.5040 q^{11} +(-42.4763 + 73.5712i) q^{13} +(-59.8310 + 103.630i) q^{15} +(-24.0096 - 41.5858i) q^{17} +(80.5776 - 19.1375i) q^{19} +(52.2559 + 90.5098i) q^{21} +(55.9299 - 96.8734i) q^{23} +(-111.991 + 193.974i) q^{25} -83.0749 q^{27} +(-131.299 + 227.416i) q^{29} -122.316 q^{31} +(-171.361 - 296.805i) q^{33} +(152.399 + 263.963i) q^{35} -32.6003 q^{37} +544.166 q^{39} +(-207.808 - 359.934i) q^{41} +(-29.2597 - 50.6793i) q^{43} +262.109 q^{45} +(-85.2630 + 147.680i) q^{47} -76.7924 q^{49} +(-153.794 + 266.379i) q^{51} +(165.835 - 287.235i) q^{53} +(-499.756 - 865.603i) q^{55} +(-364.234 - 385.699i) q^{57} +(354.301 + 613.667i) q^{59} +(8.95247 - 15.5061i) q^{61} +(114.462 - 198.254i) q^{63} +1587.01 q^{65} +(164.655 - 285.190i) q^{67} -716.521 q^{69} +(-31.4612 - 54.4924i) q^{71} +(-281.438 - 487.466i) q^{73} +1434.72 q^{75} -872.965 q^{77} +(-154.133 - 266.967i) q^{79} +(455.484 + 788.922i) q^{81} -524.252 q^{83} +(-448.525 + 776.867i) q^{85} +1682.07 q^{87} +(-298.185 + 516.471i) q^{89} +(693.038 - 1200.38i) q^{91} +(391.750 + 678.531i) q^{93} +(-1062.25 - 1124.85i) q^{95} +(275.060 + 476.417i) q^{97} +(-375.351 + 650.127i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 5 q^{5} - 8 q^{7} - 104 q^{9}+O(q^{10}) \) 16 * q - 5 * q^5 - 8 * q^7 - 104 * q^9	\( 16 q - 5 q^{5} - 8 q^{7} - 104 q^{9} + 46 q^{11} + 21 q^{13} - 45 q^{15} - 75 q^{17} + 241 q^{19} + 80 q^{21} - 251 q^{23} - 275 q^{25} + 48 q^{27} - 69 q^{29} + 124 q^{31} + 245 q^{33} - 240 q^{35} - 224 q^{37} + 1566 q^{39} - 630 q^{41} + 249 q^{43} - 1876 q^{45} - 421 q^{47} + 624 q^{49} + 921 q^{51} - 467 q^{53} - 1220 q^{55} + 29 q^{57} + 1094 q^{59} - 253 q^{61} + 1032 q^{63} + 4326 q^{65} + 250 q^{67} - 426 q^{69} - 1113 q^{71} - 1952 q^{73} - 2930 q^{75} + 1072 q^{77} + 861 q^{79} - 688 q^{81} + 886 q^{83} - 547 q^{85} + 2394 q^{87} - 1935 q^{89} + 904 q^{91} - 866 q^{93} + 3 q^{95} - 2126 q^{97} - 682 q^{99}+O(q^{100}) \) 16 * q - 5 * q^5 - 8 * q^7 - 104 * q^9 + 46 * q^11 + 21 * q^13 - 45 * q^15 - 75 * q^17 + 241 * q^19 + 80 * q^21 - 251 * q^23 - 275 * q^25 + 48 * q^27 - 69 * q^29 + 124 * q^31 + 245 * q^33 - 240 * q^35 - 224 * q^37 + 1566 * q^39 - 630 * q^41 + 249 * q^43 - 1876 * q^45 - 421 * q^47 + 624 * q^49 + 921 * q^51 - 467 * q^53 - 1220 * q^55 + 29 * q^57 + 1094 * q^59 - 253 * q^61 + 1032 * q^63 + 4326 * q^65 + 250 * q^67 - 426 * q^69 - 1113 * q^71 - 1952 * q^73 - 2930 * q^75 + 1072 * q^77 + 861 * q^79 - 688 * q^81 + 886 * q^83 - 547 * q^85 + 2394 * q^87 - 1935 * q^89 + 904 * q^91 - 866 * q^93 + 3 * q^95 - 2126 * q^97 - 682 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more