LMFDB - Embedded newform 304.4.i.e.49.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [304,4,Mod(49,304)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(304, 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("304.49");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 304 = 2^{4} \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	304.i (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$17.9365806417$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 64x^{4} + 33x^{3} + 3984x^{2} - 945x + 225 $ x^6 - x^5 + 64x^4 + 33x^3 + 3984x^2 - 945x + 225
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 38)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			49.3
Root			$-3.78825 + 6.56144i$ of defining polynomial
Character	$\chi$	$=$	304.49
Dual form			304.4.i.e.273.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.78825 - 8.29349i) q^{3} +(-7.88908 + 13.6643i) q^{5} -16.5765 q^{7} +(-32.3546 - 56.0399i) q^{9} +O(q^{10})$	\(q+(4.78825 - 8.29349i) q^{3} +(-7.88908 + 13.6643i) q^{5} -16.5765 q^{7} +(-32.3546 - 56.0399i) q^{9} -16.0285 q^{11} +(33.5522 + 58.1141i) q^{13} +(75.5497 + 130.856i) q^{15} +(-19.8025 + 34.2989i) q^{17} +(-14.7639 + 81.4925i) q^{19} +(-79.3724 + 137.477i) q^{21} +(-23.8404 - 41.2928i) q^{23} +(-61.9750 - 107.344i) q^{25} -361.123 q^{27} +(59.2021 + 102.541i) q^{29} -120.050 q^{31} +(-76.7483 + 132.932i) q^{33} +(130.773 - 226.506i) q^{35} +22.0924 q^{37} +642.624 q^{39} +(-54.5508 + 94.4847i) q^{41} +(-180.312 + 312.310i) q^{43} +1020.99 q^{45} +(96.4726 + 167.095i) q^{47} -68.2197 q^{49} +(189.638 + 328.463i) q^{51} +(-108.922 - 188.659i) q^{53} +(126.450 - 219.017i) q^{55} +(605.164 + 512.651i) q^{57} +(211.595 - 366.493i) q^{59} +(-281.960 - 488.369i) q^{61} +(536.327 + 928.945i) q^{63} -1058.78 q^{65} +(-471.426 - 816.534i) q^{67} -456.615 q^{69} +(-332.873 + 576.552i) q^{71} +(93.4728 - 161.900i) q^{73} -1187.01 q^{75} +265.696 q^{77} +(-438.177 + 758.945i) q^{79} +(-855.571 + 1481.89i) q^{81} +476.297 q^{83} +(-312.447 - 541.173i) q^{85} +1133.90 q^{87} +(482.370 + 835.489i) q^{89} +(-556.177 - 963.328i) q^{91} +(-574.827 + 995.629i) q^{93} +(-997.063 - 844.639i) q^{95} +(792.961 - 1373.45i) q^{97} +(518.595 + 898.234i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 5 q^{3} - q^{5} - 52 q^{7} - 54 q^{9}+O(q^{10}) $ 6 * q + 5 * q^3 - q^5 - 52 * q^7 - 54 * q^9	$ 6 q + 5 q^{3} - q^{5} - 52 q^{7} - 54 q^{9} - 8 q^{11} + 129 q^{13} + 77 q^{15} - 51 q^{17} - 40 q^{19} - 170 q^{21} - 47 q^{23} - 338 q^{25} - 718 q^{27} - 125 q^{29} + 100 q^{31} + 274 q^{33} + 84 q^{35} - 376 q^{37} + 1546 q^{39} + 475 q^{41} + 73 q^{43} + 3188 q^{45} + 241 q^{47} - 1354 q^{49} - 69 q^{51} + 29 q^{53} + 1838 q^{55} + 1755 q^{57} + 1065 q^{59} - 981 q^{61} + 872 q^{63} + 586 q^{65} - 877 q^{67} - 1526 q^{69} - 2135 q^{71} + 667 q^{73} - 4584 q^{75} - 492 q^{77} - 1671 q^{79} - 1287 q^{81} - 1176 q^{83} - 1929 q^{85} + 6430 q^{87} + 693 q^{89} - 1676 q^{91} - 3138 q^{93} - 4489 q^{95} - 985 q^{97} + 3184 q^{99}+O(q^{100}) $ 6 * q + 5 * q^3 - q^5 - 52 * q^7 - 54 * q^9 - 8 * q^11 + 129 * q^13 + 77 * q^15 - 51 * q^17 - 40 * q^19 - 170 * q^21 - 47 * q^23 - 338 * q^25 - 718 * q^27 - 125 * q^29 + 100 * q^31 + 274 * q^33 + 84 * q^35 - 376 * q^37 + 1546 * q^39 + 475 * q^41 + 73 * q^43 + 3188 * q^45 + 241 * q^47 - 1354 * q^49 - 69 * q^51 + 29 * q^53 + 1838 * q^55 + 1755 * q^57 + 1065 * q^59 - 981 * q^61 + 872 * q^63 + 586 * q^65 - 877 * q^67 - 1526 * q^69 - 2135 * q^71 + 667 * q^73 - 4584 * q^75 - 492 * q^77 - 1671 * q^79 - 1287 * q^81 - 1176 * q^83 - 1929 * q^85 + 6430 * q^87 + 693 * q^89 - 1676 * q^91 - 3138 * q^93 - 4489 * q^95 - 985 * q^97 + 3184 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/304\mathbb{Z}\right)^\times$.

$n$	$97$	$191$	$229$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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
$3$	4.78825	−	8.29349i	0.921499	−	1.59608i	0.124402	−	0.992232i	$-0.460299\pi$
$3$	4.78825	−	8.29349i	0.921499	−	1.59608i	0.797097	−	0.603851i	$-0.206368\pi$
$4$		0			0
$5$	−7.88908	+	13.6643i	−0.705620	+	1.22217i	0.260847	+	0.965380i	$0.415998\pi$
$5$	−7.88908	+	13.6643i	−0.705620	+	1.22217i	−0.966467	+	0.256790i	$0.917335\pi$
$6$		0			0
$7$	−16.5765			−0.895047			−0.447523	−	0.894272i	$-0.647694\pi$
$7$	−16.5765			−0.895047			−0.447523	+	0.894272i	$0.647694\pi$
$8$		0			0
$9$	−32.3546	−	56.0399i	−1.19832	−	2.07555i
$10$		0			0
$11$	−16.0285			−0.439342			−0.219671	−	0.975574i	$-0.570498\pi$
$11$	−16.0285			−0.439342			−0.219671	+	0.975574i	$0.570498\pi$
$12$		0			0
$13$	33.5522	+	58.1141i	0.715823	+	1.23984i	0.962641	+	0.270780i	$0.0872815\pi$
$13$	33.5522	+	58.1141i	0.715823	+	1.23984i	−0.246818	+	0.969062i	$0.579385\pi$
$14$		0			0
$15$	75.5497	+	130.856i	1.30046	+	2.25246i
$16$		0			0
$17$	−19.8025	+	34.2989i	−0.282518	+	0.489336i	−0.972004	−	0.234963i	$-0.924503\pi$
$17$	−19.8025	+	34.2989i	−0.282518	+	0.489336i	0.689486	+	0.724299i	$0.257836\pi$
$18$		0			0
$19$	−14.7639	+	81.4925i	−0.178267	+	0.983982i
$19$	−14.7639	+	81.4925i	−0.178267	+	0.983982i
$20$		0			0
$21$	−79.3724	+	137.477i	−0.824785	+	1.42857i
$22$		0			0
$23$	−23.8404	−	41.2928i	−0.216133	−	0.374354i	0.737489	−	0.675359i	$-0.236011\pi$
$23$	−23.8404	−	41.2928i	−0.216133	−	0.374354i	−0.953623	+	0.301005i	$0.902678\pi$
$24$		0			0
$25$	−61.9750	−	107.344i	−0.495800	−	0.858751i
$26$		0			0
$27$	−361.123			−2.57401
$28$		0			0
$29$	59.2021	+	102.541i	0.379088	+	0.656600i	0.990930	−	0.134381i	$-0.0429045\pi$
$29$	59.2021	+	102.541i	0.379088	+	0.656600i	−0.611842	+	0.790980i	$0.709571\pi$
$30$		0			0
$31$	−120.050			−0.695533			−0.347767	−	0.937581i	$-0.613060\pi$
$31$	−120.050			−0.695533			−0.347767	+	0.937581i	$0.613060\pi$
$32$		0			0
$33$	−76.7483	+	132.932i	−0.404853	+	0.701227i
$34$		0			0
$35$	130.773	−	226.506i	0.631563	−	1.09390i
$36$		0			0
$37$	22.0924			0.0981614			0.0490807	−	0.998795i	$-0.484371\pi$
$37$	22.0924			0.0981614			0.0490807	+	0.998795i	$0.484371\pi$
$38$		0			0
$39$	642.624			2.63852
$40$		0			0
$41$	−54.5508	+	94.4847i	−0.207790	+	0.359903i	−0.951018	−	0.309135i	$-0.899960\pi$
$41$	−54.5508	+	94.4847i	−0.207790	+	0.359903i	0.743228	+	0.669038i	$0.233294\pi$
$42$		0			0
$43$	−180.312	+	312.310i	−0.639473	+	1.10760i	0.346075	+	0.938207i	$0.387514\pi$
$43$	−180.312	+	312.310i	−0.639473	+	1.10760i	−0.985548	+	0.169394i	$0.945819\pi$
$44$		0			0
$45$	1020.99			3.38224
$46$		0			0
$47$	96.4726	+	167.095i	0.299404	+	0.518582i	0.976000	−	0.217772i	$-0.0698789\pi$
$47$	96.4726	+	167.095i	0.299404	+	0.518582i	−0.676596	+	0.736354i	$0.736546\pi$
$48$		0			0
$49$	−68.2197			−0.198891
$50$		0			0
$51$	189.638	+	328.463i	0.520680	+	0.901845i
$52$		0			0
$53$	−108.922	−	188.659i	−0.282294	−	0.488948i	0.689655	−	0.724138i	$-0.257762\pi$
$53$	−108.922	−	188.659i	−0.282294	−	0.488948i	−0.971949	+	0.235190i	$0.924429\pi$
$54$		0			0
$55$	126.450	−	219.017i	0.310009	−	0.536951i
$56$		0			0
$57$	605.164	+	512.651i	1.40624	+	1.19127i
$58$		0			0
$59$	211.595	−	366.493i	0.466903	−	0.808701i	−0.532382	−	0.846504i	$-0.678703\pi$
$59$	211.595	−	366.493i	0.466903	−	0.808701i	0.999285	+	0.0378039i	$0.0120362\pi$
$60$		0			0
$61$	−281.960	−	488.369i	−0.591824	−	1.02507i	−0.993987	−	0.109501i	$-0.965075\pi$
$61$	−281.960	−	488.369i	−0.591824	−	1.02507i	0.402162	−	0.915568i	$-0.368259\pi$
$62$		0			0
$63$	536.327	+	928.945i	1.07255	+	1.85772i
$64$		0			0
$65$	−1058.78			−2.02040
$66$		0			0
$67$	−471.426	−	816.534i	−0.859610	−	1.48889i	−0.872302	−	0.488968i	$-0.837373\pi$
$67$	−471.426	−	816.534i	−0.859610	−	1.48889i	0.0126922	−	0.999919i	$-0.495960\pi$
$68$		0			0
$69$	−456.615			−0.796667
$70$		0			0
$71$	−332.873	+	576.552i	−0.556404	+	0.963721i	0.441388	+	0.897316i	$0.354486\pi$
$71$	−332.873	+	576.552i	−0.556404	+	0.963721i	−0.997793	+	0.0664045i	$0.978847\pi$
$72$		0			0
$73$	93.4728	−	161.900i	0.149865	−	0.259574i	−0.781312	−	0.624140i	$-0.785449\pi$
$73$	93.4728	−	161.900i	0.149865	−	0.259574i	0.931178	+	0.364566i	$0.118783\pi$
$74$		0			0
$75$	−1187.01			−1.82752
$76$		0			0
$77$	265.696			0.393232
$78$		0			0
$79$	−438.177	+	758.945i	−0.624035	+	1.08086i	0.364692	+	0.931128i	$0.381174\pi$
$79$	−438.177	+	758.945i	−0.624035	+	1.08086i	−0.988727	+	0.149732i	$0.952159\pi$
$80$		0			0
$81$	−855.571	+	1481.89i	−1.17362	+	2.03277i
$82$		0			0
$83$	476.297			0.629885			0.314942	−	0.949111i	$-0.398015\pi$
$83$	476.297			0.629885			0.314942	+	0.949111i	$0.398015\pi$
$84$		0			0
$85$	−312.447	−	541.173i	−0.398701	−	0.690570i
$86$		0			0
$87$	1133.90			1.39732
$88$		0			0
$89$	482.370	+	835.489i	0.574507	+	0.995075i	0.996095	+	0.0882878i	$0.0281395\pi$
$89$	482.370	+	835.489i	0.574507	+	0.995075i	−0.421588	+	0.906787i	$0.638527\pi$
$90$		0			0
$91$	−556.177	−	963.328i	−0.640695	−	1.10972i
$92$		0			0
$93$	−574.827	+	995.629i	−0.640933	+	1.11013i
$94$		0			0
$95$	−997.063	−	844.639i	−1.07680	−	0.912191i
$96$		0			0
$97$	792.961	−	1373.45i	0.830031	−	1.43766i	−0.0679822	−	0.997687i	$-0.521656\pi$
$97$	792.961	−	1373.45i	0.830031	−	1.43766i	0.898013	−	0.439969i	$-0.145011\pi$
$98$		0			0
$99$	518.595	+	898.234i	0.526473	+	0.911878i
$100$		0			0
$101$	521.913	+	903.980i	0.514181	+	0.890588i	0.999865	+	0.0164532i	$0.00523746\pi$
$101$	521.913	+	903.980i	0.514181	+	0.890588i	−0.485683	+	0.874135i	$0.661429\pi$
$102$		0			0
$103$	−1427.83			−1.36591			−0.682954	−	0.730461i	$-0.739305\pi$
$103$	−1427.83			−1.36591			−0.682954	+	0.730461i	$0.739305\pi$
$104$		0			0
$105$	−1252.35	−	2169.13i	−1.16397	−	2.01605i
$106$		0			0
$107$	−500.924			−0.452581			−0.226290	−	0.974060i	$-0.572660\pi$
$107$	−500.924			−0.452581			−0.226290	+	0.974060i	$0.572660\pi$
$108$		0			0
$109$	−606.462	+	1050.42i	−0.532922	+	0.923048i	0.466339	+	0.884606i	$0.345573\pi$
$109$	−606.462	+	1050.42i	−0.532922	+	0.923048i	−0.999261	+	0.0384417i	$0.987761\pi$
$110$		0			0
$111$	105.784	−	183.223i	0.0904556	−	0.156674i
$112$		0			0
$113$	738.956			0.615178			0.307589	−	0.951519i	$-0.400478\pi$
$113$	738.956			0.615178			0.307589	+	0.951519i	$0.400478\pi$
$114$		0			0
$115$	752.315			0.610033
$116$		0			0
$117$	2171.14	−	3760.52i	1.71557	−	2.97145i
$118$		0			0
$119$	328.256	−	568.556i	0.252867	−	0.437978i
$120$		0			0
$121$	−1074.09			−0.806978
$122$		0			0
$123$	522.405	+	904.832i	0.382957	+	0.663301i
$124$		0			0
$125$	−16.5658			−0.0118535
$126$		0			0
$127$	119.454	+	206.900i	0.0834632	+	0.144563i	0.904735	−	0.425974i	$-0.140069\pi$
$127$	119.454	+	206.900i	0.0834632	+	0.144563i	−0.821272	+	0.570537i	$0.806735\pi$
$128$		0			0
$129$	1726.76	+	2990.84i	1.17855	+	2.04131i
$130$		0			0
$131$	132.624	−	229.712i	0.0884537	−	0.153206i	−0.818404	−	0.574643i	$-0.805141\pi$
$131$	132.624	−	229.712i	0.0884537	−	0.153206i	0.906858	+	0.421437i	$0.138474\pi$
$132$		0			0
$133$	244.734	−	1350.86i	0.159557	−	0.880710i
$134$		0			0
$135$	2848.93	−	4934.49i	1.81627	−	3.14587i
$136$		0			0
$137$	−1219.22	−	2111.76i	−0.760331	−	1.31693i	−0.942680	−	0.333698i	$-0.891703\pi$
$137$	−1219.22	−	2111.76i	−0.760331	−	1.31693i	0.182349	−	0.983234i	$-0.441630\pi$
$138$		0			0
$139$	−183.397	−	317.653i	−0.111910	−	0.193835i	0.804630	−	0.593776i	$-0.202364\pi$
$139$	−183.397	−	317.653i	−0.111910	−	0.193835i	−0.916541	+	0.399942i	$0.869030\pi$
$140$		0			0
$141$	1847.74			1.10360
$142$		0			0
$143$	−537.790	−	931.479i	−0.314491	−	0.544715i
$144$		0			0
$145$	−1868.20			−1.06997
$146$		0			0
$147$	−326.653	+	565.780i	−0.183278	+	0.317447i
$148$		0			0
$149$	1120.88	−	1941.42i	0.616281	−	1.06743i	−0.373877	−	0.927478i	$-0.621972\pi$
$149$	1120.88	−	1941.42i	0.616281	−	1.06743i	0.990158	−	0.139952i	$-0.0446949\pi$
$150$		0			0
$151$	638.195			0.343944			0.171972	−	0.985102i	$-0.444986\pi$
$151$	638.195			0.343944			0.171972	+	0.985102i	$0.444986\pi$
$152$		0			0
$153$	2562.81			1.35419
$154$		0			0
$155$	947.080	−	1640.39i	0.490782	−	0.850060i
$156$		0			0
$157$	−1063.00	+	1841.16i	−0.540358	+	0.935928i	0.458525	+	0.888682i	$0.348378\pi$
$157$	−1063.00	+	1841.16i	−0.540358	+	0.935928i	−0.998883	+	0.0472466i	$0.984955\pi$
$158$		0			0
$159$	−2086.18			−1.04054
$160$		0			0
$161$	395.191	+	684.490i	0.193450	+	0.335064i
$162$		0			0
$163$	160.043			0.0769053			0.0384526	−	0.999260i	$-0.487757\pi$
$163$	160.043			0.0769053			0.0384526	+	0.999260i	$0.487757\pi$
$164$		0			0
$165$	−1210.95	−	2097.42i	−0.571346	−	0.989600i
$166$		0			0
$167$	1051.08	+	1820.52i	0.487036	+	0.843571i	0.999889	−	0.0149055i	$-0.00474476\pi$
$167$	1051.08	+	1820.52i	0.487036	+	0.843571i	−0.512853	+	0.858476i	$0.671411\pi$
$168$		0			0
$169$	−1153.00	+	1997.05i	−0.524805	+	0.908988i
$170$		0			0
$171$	5044.51	−	1809.29i	2.25593	−	0.809123i
$172$		0			0
$173$	202.732	−	351.142i	0.0890949	−	0.154317i	−0.818034	−	0.575170i	$-0.804936\pi$
$173$	202.732	−	351.142i	0.0890949	−	0.154317i	0.907129	+	0.420853i	$0.138269\pi$
$174$		0			0
$175$	1027.33	+	1779.39i	0.443764	+	0.768623i
$176$		0			0
$177$	−2026.34	−	3509.72i	−0.860502	−	1.49043i
$178$		0			0
$179$	1628.76			0.680107			0.340053	−	0.940406i	$-0.389555\pi$
$179$	1628.76			0.680107			0.340053	+	0.940406i	$0.389555\pi$
$180$		0			0
$181$	−1418.42	−	2456.77i	−0.582487	−	1.00890i	−0.995184	−	0.0980291i	$-0.968746\pi$
$181$	−1418.42	−	2456.77i	−0.582487	−	1.00890i	0.412696	−	0.910869i	$-0.364587\pi$
$182$		0			0
$183$	−5400.38			−2.18146
$184$		0			0
$185$	−174.289	+	301.877i	−0.0692647	+	0.119970i
$186$		0			0
$187$	317.403	−	549.759i	0.124122	−	0.214986i
$188$		0			0
$189$	5986.15			2.30386
$190$		0			0
$191$	−3521.85			−1.33420			−0.667099	−	0.744969i	$-0.732464\pi$
$191$	−3521.85			−1.33420			−0.667099	+	0.744969i	$0.732464\pi$
$192$		0			0
$193$	−2367.70	+	4100.97i	−0.883060	+	1.52950i	−0.0351378	+	0.999382i	$0.511187\pi$
$193$	−2367.70	+	4100.97i	−0.883060	+	1.52950i	−0.847922	+	0.530121i	$0.822146\pi$
$194$		0			0
$195$	−5069.71	+	8781.00i	−1.86179	+	3.22472i
$196$		0			0
$197$	2357.30			0.852541			0.426270	−	0.904596i	$-0.359827\pi$
$197$	2357.30			0.852541			0.426270	+	0.904596i	$0.359827\pi$
$198$		0			0
$199$	342.578	+	593.362i	0.122034	+	0.211369i	0.920570	−	0.390579i	$-0.127725\pi$
$199$	342.578	+	593.362i	0.122034	+	0.211369i	−0.798536	+	0.601947i	$0.794392\pi$
$200$		0			0
$201$	−9029.22			−3.16852
$202$		0			0
$203$	−981.363	−	1699.77i	−0.339301	−	0.587687i
$204$		0			0
$205$	−860.710	−	1490.79i	−0.293242	−	0.507910i
$206$		0			0
$207$	−1542.70	+	2672.03i	−0.517994	+	0.897192i
$208$		0			0
$209$	236.643	−	1306.20i	0.0783203	−	0.432305i
$210$		0			0
$211$	−265.510	+	459.876i	−0.0866277	+	0.150044i	−0.906084	−	0.423099i	$-0.860942\pi$
$211$	−265.510	+	459.876i	−0.0866277	+	0.150044i	0.819456	+	0.573142i	$0.194276\pi$
$212$		0			0
$213$	3187.75	+	5521.35i	1.02545	+	1.77613i
$214$		0			0
$215$	−2844.99	−	4927.67i	−0.902451	−	1.56309i
$216$		0			0
$217$	1990.00			0.622535
$218$		0			0
$219$	−895.142	−	1550.43i	−0.276201	−	0.478395i
$220$		0			0
$221$	−2657.66			−0.808932
$222$		0			0
$223$	2425.86	−	4201.71i	0.728463	−	1.26174i	−0.229069	−	0.973410i	$-0.573568\pi$
$223$	2425.86	−	4201.71i	0.728463	−	1.26174i	0.957533	−	0.288325i	$-0.0930984\pi$
$224$		0			0
$225$	−4010.36	+	6946.15i	−1.18826	+	2.05812i
$226$		0			0
$227$	3971.88			1.16134			0.580668	−	0.814141i	$-0.302792\pi$
$227$	3971.88			1.16134			0.580668	+	0.814141i	$0.302792\pi$
$228$		0			0
$229$	−78.9844			−0.0227923			−0.0113961	−	0.999935i	$-0.503628\pi$
$229$	−78.9844			−0.0227923			−0.0113961	+	0.999935i	$0.503628\pi$
$230$		0			0
$231$	1272.22	−	2203.55i	0.362363	−	0.627631i
$232$		0			0
$233$	821.646	−	1423.13i	0.231021	−	0.400140i	−0.727088	−	0.686544i	$-0.759127\pi$
$233$	821.646	−	1423.13i	0.231021	−	0.400140i	0.958109	+	0.286405i	$0.0924601\pi$
$234$		0			0
$235$	−3044.32			−0.845061
$236$		0			0
$237$	4196.20	+	7268.03i	1.15009	+	1.99202i
$238$		0			0
$239$	6316.74			1.70961			0.854803	−	0.518952i	$-0.173678\pi$
$239$	6316.74			1.70961			0.854803	+	0.518952i	$0.173678\pi$
$240$		0			0
$241$	1747.33	+	3026.46i	0.467034	+	0.808927i	0.999291	−	0.0376561i	$-0.0119891\pi$
$241$	1747.33	+	3026.46i	0.467034	+	0.808927i	−0.532257	+	0.846583i	$0.678656\pi$
$242$		0			0
$243$	3318.21	+	5747.32i	0.875982	+	1.51724i
$244$		0			0
$245$	538.191	−	932.174i	0.140342	−	0.243079i
$246$		0			0
$247$	−5231.22	+	1876.26i	−1.34759	+	0.483334i
$248$		0			0
$249$	2280.63	−	3950.17i	0.580438	−	1.00535i
$250$		0			0
$251$	1815.19	+	3143.99i	0.456468	+	0.790626i	0.998771	−	0.0495570i	$-0.0157809\pi$
$251$	1815.19	+	3143.99i	0.456468	+	0.790626i	−0.542303	+	0.840183i	$0.682448\pi$
$252$		0			0
$253$	382.125	+	661.860i	0.0949566	+	0.164470i
$254$		0			0
$255$	−5984.29			−1.46961
$256$		0			0
$257$	774.708	+	1341.83i	0.188035	+	0.325686i	0.944595	−	0.328238i	$-0.106455\pi$
$257$	774.708	+	1341.83i	0.188035	+	0.325686i	−0.756560	+	0.653924i	$0.773122\pi$
$258$		0			0
$259$	−366.215			−0.0878590
$260$		0			0
$261$	3830.92	−	6635.36i	0.908538	−	1.57363i
$262$		0			0
$263$	−1904.91	+	3299.39i	−0.446622	+	0.773571i	−0.998164	−	0.0605757i	$-0.980706\pi$
$263$	−1904.91	+	3299.39i	−0.446622	+	0.773571i	0.551542	+	0.834147i	$0.314040\pi$
$264$		0			0
$265$	3437.18			0.796771
$266$		0			0
$267$	9238.83			2.11763
$268$		0			0
$269$	1688.20	−	2924.05i	0.382644	−	0.662759i	−0.608795	−	0.793328i	$-0.708347\pi$
$269$	1688.20	−	2924.05i	0.382644	−	0.662759i	0.991439	+	0.130568i	$0.0416801\pi$
$270$		0			0
$271$	−1762.75	+	3053.17i	−0.395127	+	0.684380i	−0.993117	−	0.117123i	$-0.962633\pi$
$271$	−1762.75	+	3053.17i	−0.395127	+	0.684380i	0.597991	+	0.801503i	$0.295966\pi$
$272$		0			0
$273$	−10652.5			−2.36160
$274$		0			0
$275$	993.365	+	1720.56i	0.217826	+	0.377286i
$276$		0			0
$277$	6557.88			1.42247			0.711236	−	0.702953i	$-0.248136\pi$
$277$	6557.88			1.42247			0.711236	+	0.702953i	$0.248136\pi$
$278$		0			0
$279$	3884.16	+	6727.56i	0.833472	+	1.44362i
$280$		0			0
$281$	−3943.90	−	6831.04i	−0.837272	−	1.45020i	−0.892167	−	0.451705i	$-0.850816\pi$
$281$	−3943.90	−	6831.04i	−0.837272	−	1.45020i	0.0548952	−	0.998492i	$-0.482518\pi$
$282$		0			0
$283$	1036.37	−	1795.04i	0.217687	−	0.377046i	−0.736413	−	0.676532i	$-0.763482\pi$
$283$	1036.37	−	1795.04i	0.217687	−	0.377046i	0.954101	+	0.299486i	$0.0968153\pi$
$284$		0			0
$285$	−11779.2	+	4224.79i	−2.44821	+	0.878087i
$286$		0			0
$287$	904.261	−	1566.23i	0.185982	−	0.322130i
$288$		0			0
$289$	1672.22	+	2896.38i	0.340367	+	0.589533i
$290$		0			0
$291$	−7593.79	−	13152.8i	−1.52974	−	2.64960i
$292$		0			0
$293$	−7820.84			−1.55938			−0.779690	−	0.626165i	$-0.784624\pi$
$293$	−7820.84			−1.55938			−0.779690	+	0.626165i	$0.784624\pi$
$294$		0			0
$295$	3338.58	+	5782.58i	0.658913	+	1.14127i
$296$		0			0
$297$	5788.25			1.13087
$298$		0			0
$299$	1599.80	−	2770.93i	0.309427	−	0.535943i
$300$		0			0
$301$	2988.95	−	5177.00i	0.572359	−	0.991354i
$302$		0			0
$303$	9996.20			1.89527
$304$		0			0
$305$	8897.62			1.67041
$306$		0			0
$307$	−2968.90	+	5142.28i	−0.551934	+	0.955978i	0.446201	+	0.894933i	$0.352777\pi$
$307$	−2968.90	+	5142.28i	−0.551934	+	0.955978i	−0.998135	+	0.0610453i	$0.980557\pi$
$308$		0			0
$309$	−6836.82	+	11841.7i	−1.25868	+	2.18010i
$310$		0			0
$311$	−1832.63			−0.334145			−0.167073	−	0.985945i	$-0.553431\pi$
$311$	−1832.63			−0.334145			−0.167073	+	0.985945i	$0.553431\pi$
$312$		0			0
$313$	469.166	+	812.619i	0.0847247	+	0.146747i	0.905274	−	0.424828i	$-0.139666\pi$
$313$	469.166	+	812.619i	0.0847247	+	0.146747i	−0.820549	+	0.571576i	$0.806332\pi$
$314$		0			0
$315$	−16924.5			−3.02726
$316$		0			0
$317$	3705.73	+	6418.51i	0.656576	+	1.13722i	0.981496	+	0.191481i	$0.0613292\pi$
$317$	3705.73	+	6418.51i	0.656576	+	1.13722i	−0.324920	+	0.945741i	$0.605337\pi$
$318$		0			0
$319$	−948.919	−	1643.58i	−0.166549	−	0.288472i
$320$		0			0
$321$	−2398.55	+	4154.41i	−0.417053	+	0.722357i
$322$		0			0
$323$	−2502.74	−	2120.14i	−0.431134	−	0.365225i
$324$		0			0
$325$	4158.79	−	7203.24i	0.709810	−	1.22943i
$326$		0			0
$327$	5807.78	+	10059.4i	0.982174	+	1.70117i
$328$		0			0
$329$	−1599.18	−	2769.86i	−0.267980	−	0.464155i
$330$		0			0
$331$	5412.69			0.898817			0.449408	−	0.893326i	$-0.351635\pi$
$331$	5412.69			0.898817			0.449408	+	0.893326i	$0.351635\pi$
$332$		0			0
$333$	−714.792	−	1238.06i	−0.117629	−	0.203739i
$334$		0			0
$335$	14876.5			2.42623
$336$		0			0
$337$	−4636.79	+	8031.15i	−0.749501	+	1.29817i	0.198561	+	0.980088i	$0.436373\pi$
$337$	−4636.79	+	8031.15i	−0.749501	+	1.29817i	−0.948062	+	0.318085i	$0.896960\pi$
$338$		0			0
$339$	3538.31	−	6128.52i	0.566886	−	0.981875i
$340$		0			0
$341$	1924.21			0.305577
$342$		0			0
$343$	6816.58			1.07306
$344$		0			0
$345$	3602.27	−	6239.32i	0.562145	−	0.973663i
$346$		0			0
$347$	−4837.24	+	8378.35i	−0.748348	+	1.29618i	0.200266	+	0.979741i	$0.435819\pi$
$347$	−4837.24	+	8378.35i	−0.748348	+	1.29618i	−0.948614	+	0.316435i	$0.897514\pi$
$348$		0			0
$349$	1300.56			0.199477			0.0997387	−	0.995014i	$-0.468199\pi$
$349$	1300.56			0.199477			0.0997387	+	0.995014i	$0.468199\pi$
$350$		0			0
$351$	−12116.5	−	20986.3i	−1.84253	−	3.19136i
$352$		0			0
$353$	11985.4			1.80713			0.903564	−	0.428454i	$-0.140942\pi$
$353$	11985.4			1.80713			0.903564	+	0.428454i	$0.140942\pi$
$354$		0			0
$355$	−5252.11	−	9096.93i	−0.785221	−	1.36004i
$356$		0			0
$357$	−3143.54	−	5444.77i	−0.466033	−	0.807193i
$358$		0			0
$359$	−2203.95	+	3817.35i	−0.324011	+	0.561204i	−0.981312	−	0.192425i	$-0.938365\pi$
$359$	−2203.95	+	3817.35i	−0.324011	+	0.561204i	0.657301	+	0.753628i	$0.271698\pi$
$360$		0			0
$361$	−6423.05	−	2406.30i	−0.936442	−	0.350823i
$362$		0			0
$363$	−5143.00	+	8907.94i	−0.743630	+	1.28800i
$364$		0			0
$365$	1474.83	+	2554.48i	0.211496	+	0.366322i
$366$		0			0
$367$	3130.04	+	5421.39i	0.445196	+	0.771102i	0.998066	−	0.0621658i	$-0.0198008\pi$
$367$	3130.04	+	5421.39i	0.445196	+	0.771102i	−0.552870	+	0.833267i	$0.686467\pi$
$368$		0			0
$369$	7059.88			0.995997
$370$		0			0
$371$	1805.55	+	3127.30i	0.252667	+	0.437631i
$372$		0			0
$373$	−2745.24			−0.381081			−0.190541	−	0.981679i	$-0.561024\pi$
$373$	−2745.24			−0.381081			−0.190541	+	0.981679i	$0.561024\pi$
$374$		0			0
$375$	−79.3212	+	137.388i	−0.0109230	+	0.0189192i
$376$		0			0
$377$	−3972.72	+	6880.95i	−0.542720	+	0.940018i
$378$		0			0
$379$	−10772.3			−1.45998			−0.729992	−	0.683455i	$-0.760476\pi$
$379$	−10772.3			−1.45998			−0.729992	+	0.683455i	$0.760476\pi$
$380$		0			0
$381$	2287.90			0.307645
$382$		0			0
$383$	−1689.97	+	2927.12i	−0.225466	+	0.390519i	−0.956459	−	0.291866i	$-0.905724\pi$
$383$	−1689.97	+	2927.12i	−0.225466	+	0.390519i	0.730993	+	0.682385i	$0.239057\pi$
$384$		0			0
$385$	−2096.09	+	3630.54i	−0.277472	+	0.480596i
$386$		0			0
$387$	23335.8			3.06518
$388$		0			0
$389$	−2351.28	−	4072.54i	−0.306464	−	0.530812i	0.671122	−	0.741347i	$-0.265813\pi$
$389$	−2351.28	−	4072.54i	−0.306464	−	0.530812i	−0.977586	+	0.210535i	$0.932479\pi$
$390$		0			0
$391$	1888.40			0.244246
$392$		0			0
$393$	−1270.08	−	2199.84i	−0.163020	−	0.282359i
$394$		0			0
$395$	−6913.62	−	11974.7i	−0.880663	−	1.52535i
$396$		0			0
$397$	−125.749	+	217.804i	−0.0158972	+	0.0275347i	−0.873865	−	0.486169i	$-0.838394\pi$
$397$	−125.749	+	217.804i	−0.0158972	+	0.0275347i	0.857967	+	0.513704i	$0.171727\pi$
$398$		0			0
$399$	−10031.5	−	8497.95i	−1.25865	−	1.06624i
$400$		0			0
$401$	3225.16	−	5586.15i	0.401638	−	0.695658i	−0.592285	−	0.805728i	$-0.701774\pi$
$401$	3225.16	−	5586.15i	0.401638	−	0.695658i	0.993924	+	0.110070i	$0.0351075\pi$
$402$		0			0
$403$	−4027.92	−	6976.56i	−0.497879	−	0.862351i
$404$		0			0
$405$	−13499.3	−	23381.5i	−1.65626	−	2.86873i
$406$		0			0
$407$	−354.108			−0.0431264
$408$		0			0
$409$	−1007.96	−	1745.84i	−0.121859	−	0.211066i	0.798642	−	0.601807i	$-0.205552\pi$
$409$	−1007.96	−	1745.84i	−0.121859	−	0.211066i	−0.920501	+	0.390741i	$0.872219\pi$
$410$		0			0
$411$	−23351.8			−2.80258
$412$		0			0
$413$	−3507.50	+	6075.17i	−0.417900	+	0.723825i
$414$		0			0
$415$	−3757.55	+	6508.26i	−0.444460	+	0.769827i
$416$		0			0
$417$	−3512.61			−0.412501
$418$		0			0
$419$	10124.5			1.18046			0.590232	−	0.807234i	$-0.299036\pi$
$419$	10124.5			1.18046			0.590232	+	0.807234i	$0.299036\pi$
$420$		0			0
$421$	−1573.13	+	2724.75i	−0.182114	+	0.315430i	−0.942600	−	0.333924i	$-0.891627\pi$
$421$	−1573.13	+	2724.75i	−0.182114	+	0.315430i	0.760487	+	0.649354i	$0.224961\pi$
$422$		0			0
$423$	6242.67	−	10812.6i	0.717563	−	1.24286i
$424$		0			0
$425$	4909.04			0.560290
$426$		0			0
$427$	4673.91	+	8095.45i	0.529710	+	0.917485i
$428$		0			0
$429$	−10300.3			−1.15921
$430$		0			0
$431$	5831.16	+	10099.9i	0.651687	+	1.12875i	0.982713	+	0.185133i	$0.0592717\pi$
$431$	5831.16	+	10099.9i	0.651687	+	1.12875i	−0.331027	+	0.943621i	$0.607395\pi$
$432$		0			0
$433$	4484.52	+	7767.42i	0.497719	+	0.862074i	0.999997	−	0.00263209i	$-0.000837820\pi$
$433$	4484.52	+	7767.42i	0.497719	+	0.862074i	−0.502278	+	0.864706i	$0.667504\pi$
$434$		0			0
$435$	−8945.40	+	15493.9i	−0.985975	+	1.70776i
$436$		0			0
$437$	3717.03	−	1333.17i	0.406887	−	0.145936i
$438$		0			0
$439$	49.1536	−	85.1366i	0.00534391	−	0.00925592i	−0.863341	−	0.504621i	$-0.831632\pi$
$439$	49.1536	−	85.1366i	0.00534391	−	0.00925592i	0.868685	+	0.495365i	$0.164966\pi$
$440$		0			0
$441$	2207.23	+	3823.03i	0.238336	+	0.412809i
$442$		0			0
$443$	−4660.23	−	8071.75i	−0.499806	−	0.865690i	0.500194	−	0.865914i	$-0.333262\pi$
$443$	−4660.23	−	8071.75i	−0.499806	−	0.865690i	−1.00000		0.000223670i	$0.999929\pi$
$444$		0			0
$445$	−15221.8			−1.62154
$446$		0			0
$447$	−10734.1	−	18592.0i	−1.13580	−	1.96727i
$448$		0			0
$449$	9992.53			1.05028			0.525141	−	0.851015i	$-0.324013\pi$
$449$	9992.53			1.05028			0.525141	+	0.851015i	$0.324013\pi$
$450$		0			0
$451$	874.365	−	1514.44i	0.0912910	−	0.158121i
$452$		0			0
$453$	3055.84	−	5292.86i	0.316944	−	0.548963i
$454$		0			0
$455$	17550.9			1.80835
$456$		0			0
$457$	−1536.89			−0.157314			−0.0786572	−	0.996902i	$-0.525063\pi$
$457$	−1536.89			−0.157314			−0.0786572	+	0.996902i	$0.525063\pi$
$458$		0			0
$459$	7151.13	−	12386.1i	0.727203	−	1.25955i
$460$		0			0
$461$	8312.46	−	14397.6i	0.839804	−	1.45458i	−0.0502537	−	0.998736i	$-0.516003\pi$
$461$	8312.46	−	14397.6i	0.839804	−	1.45458i	0.890058	−	0.455847i	$-0.150664\pi$
$462$		0			0
$463$	−7191.48			−0.721850			−0.360925	−	0.932595i	$-0.617539\pi$
$463$	−7191.48			−0.721850			−0.360925	+	0.932595i	$0.617539\pi$
$464$		0			0
$465$	−9069.71	−	15709.2i	−0.904511	−	1.56666i
$466$		0			0
$467$	7001.51			0.693772			0.346886	−	0.937907i	$-0.387239\pi$
$467$	7001.51			0.693772			0.346886	+	0.937907i	$0.387239\pi$
$468$		0			0
$469$	7814.59	+	13535.3i	0.769391	+	1.33262i
$470$		0			0
$471$	10179.8	+	17631.9i	0.995879	+	1.72491i
$472$		0			0
$473$	2890.13	−	5005.85i	0.280948	−	0.486616i
$474$		0			0
$475$	9662.72	−	3465.68i	0.933381	−	0.334772i
$476$		0			0
$477$	−7048.27	+	12208.0i	−0.676558	+	1.17183i
$478$		0			0
$479$	955.918	+	1655.70i	0.0911837	+	0.157935i	0.908009	−	0.418950i	$-0.137602\pi$
$479$	955.918	+	1655.70i	0.0911837	+	0.157935i	−0.816826	+	0.576884i	$0.804268\pi$
$480$		0			0
$481$	741.248	+	1283.88i	0.0702661	+	0.121705i
$482$		0			0
$483$	7569.08			0.713054
$484$		0			0
$485$	12511.5	+	21670.5i	1.17137	+	2.02888i
$486$		0			0
$487$	6061.32			0.563993			0.281997	−	0.959415i	$-0.409003\pi$
$487$	6061.32			0.563993			0.281997	+	0.959415i	$0.409003\pi$
$488$		0			0
$489$	766.327	−	1327.32i	0.0708681	−	0.122747i
$490$		0			0
$491$	3219.51	−	5576.36i	0.295916	−	0.512541i	−0.679282	−	0.733877i	$-0.737709\pi$
$491$	3219.51	−	5576.36i	0.295916	−	0.512541i	0.975197	+	0.221337i	$0.0710420\pi$
$492$		0			0
$493$	−4689.39			−0.428397
$494$		0			0
$495$	−16365.0			−1.48596
$496$		0			0
$497$	5517.86	−	9557.22i	0.498008	−	0.862575i
$498$		0			0
$499$	8229.07	−	14253.2i	0.738244	−	1.27868i	−0.215041	−	0.976605i	$-0.568989\pi$
$499$	8229.07	−	14253.2i	0.738244	−	1.27868i	0.953285	−	0.302071i	$-0.0976780\pi$
$500$		0			0
$501$	20131.3			1.79521
$502$		0			0
$503$	−1362.42	−	2359.78i	−0.120770	−	0.209179i	0.799302	−	0.600930i	$-0.205203\pi$
$503$	−1362.42	−	2359.78i	−0.120770	−	0.209179i	−0.920071	+	0.391751i	$0.871870\pi$
$504$		0			0
$505$	−16469.7			−1.45127
$506$		0			0
$507$	11041.7	+	19124.7i	0.967214	+	1.67526i
$508$		0			0
$509$	−2730.41	−	4729.20i	−0.237767	−	0.411824i	0.722307	−	0.691573i	$-0.243082\pi$
$509$	−2730.41	−	4729.20i	−0.237767	−	0.411824i	−0.960073	+	0.279749i	$0.909749\pi$
$510$		0			0
$511$	−1549.45	+	2683.73i	−0.134136	+	0.232331i
$512$		0			0
$513$	5331.59	−	29428.8i	0.458861	−	2.53278i
$514$		0			0
$515$	11264.3	−	19510.3i	0.963813	−	1.66937i
$516$		0			0
$517$	−1546.31	−	2678.28i	−0.131541	−	0.227835i
$518$		0			0
$519$	−1941.46	−	3362.71i	−0.164202	−	0.284406i
$520$		0			0
$521$	7411.04			0.623193			0.311596	−	0.950215i	$-0.399136\pi$
$521$	7411.04			0.623193			0.311596	+	0.950215i	$0.399136\pi$
$522$		0			0
$523$	−399.710	−	692.318i	−0.0334189	−	0.0578833i	0.848832	−	0.528662i	$-0.177306\pi$
$523$	−399.710	−	692.318i	−0.0334189	−	0.0578833i	−0.882251	+	0.470779i	$0.843973\pi$
$524$		0			0
$525$	19676.4			1.63571
$526$		0			0
$527$	2377.28	−	4117.57i	0.196501	−	0.340349i
$528$		0			0
$529$	4946.77	−	8568.06i	0.406573	−	0.704204i
$530$		0			0
$531$	−27384.3			−2.23800
$532$		0			0
$533$	−7321.19			−0.594964
$534$		0			0
$535$	3951.83	−	6844.77i	0.319350	−	0.553131i
$536$		0			0
$537$	7798.90	−	13508.1i	0.626717	−	1.08551i
$538$		0			0
$539$	1093.46			0.0873814
$540$		0			0
$541$	−2947.56	−	5105.33i	−0.234243	−	0.405721i	0.724809	−	0.688950i	$-0.241928\pi$
$541$	−2947.56	−	5105.33i	−0.234243	−	0.405721i	−0.959052	+	0.283228i	$0.908595\pi$
$542$		0			0
$543$	−27167.0			−2.14705
$544$		0			0
$545$	−9568.84	−	16573.7i	−0.752081	−	1.30264i
$546$		0			0
$547$	5745.64	+	9951.74i	0.449115	+	0.777890i	0.998329	−	0.0577920i	$-0.0184060\pi$
$547$	5745.64	+	9951.74i	0.449115	+	0.777890i	−0.549214	+	0.835682i	$0.685073\pi$
$548$		0			0
$549$	−18245.4	+	31602.0i	−1.41839	+	2.45672i
$550$		0			0
$551$	−9230.38	+	3310.62i	−0.713661	+	0.255966i
$552$		0			0
$553$	7263.44	−	12580.6i	0.558540	−	0.967420i
$554$		0			0
$555$	1669.08	+	2890.92i	0.127655	+	0.221104i
$556$		0			0
$557$	1122.30	+	1943.88i	0.0853740	+	0.147872i	0.905551	−	0.424238i	$-0.139458\pi$
$557$	1122.30	+	1943.88i	0.0853740	+	0.147872i	−0.820176	+	0.572111i	$0.806125\pi$
$558$		0			0
$559$	−24199.5			−1.83100
$560$		0			0
$561$	−3039.61	−	5264.76i	−0.228757	−	0.396218i
$562$		0			0
$563$	19529.8			1.46196			0.730978	−	0.682401i	$-0.239064\pi$
$563$	19529.8			1.46196			0.730978	+	0.682401i	$0.239064\pi$
$564$		0			0
$565$	−5829.68	+	10097.3i	−0.434082	+	0.751853i
$566$		0			0
$567$	14182.4	−	24564.6i	1.05045	−	1.81943i
$568$		0			0
$569$	−3300.68			−0.243184			−0.121592	−	0.992580i	$-0.538800\pi$
$569$	−3300.68			−0.243184			−0.121592	+	0.992580i	$0.538800\pi$
$570$		0			0
$571$	−3080.76			−0.225789			−0.112895	−	0.993607i	$-0.536012\pi$
$571$	−3080.76			−0.225789			−0.112895	+	0.993607i	$0.536012\pi$
$572$		0			0
$573$	−16863.5	+	29208.4i	−1.22946	+	2.12949i
$574$		0			0
$575$	−2955.02	+	5118.25i	−0.214318	+	0.371210i
$576$		0			0
$577$	4946.52			0.356892			0.178446	−	0.983950i	$-0.442893\pi$
$577$	4946.52			0.356892			0.178446	+	0.983950i	$0.442893\pi$
$578$		0			0
$579$	22674.2	+	39272.9i	1.62748	+	2.81887i
$580$		0			0
$581$	−7895.34			−0.563776
$582$		0			0
$583$	1745.85	+	3023.91i	0.124024	+	0.214816i
$584$		0			0
$585$	34256.5	+	59334.1i	2.42108	+	4.19344i
$586$		0			0
$587$	7278.01	−	12605.9i	0.511748	−	0.886373i	−0.488160	−	0.872754i	$-0.662332\pi$
$587$	7278.01	−	12605.9i	0.511748	−	0.886373i	0.999907	−	0.0136184i	$-0.00433502\pi$
$588$		0			0
$589$	1772.40	−	9783.13i	0.123991	−	0.684392i
$590$		0			0
$591$	11287.3	−	19550.2i	0.785615	−	1.36073i
$592$		0			0
$593$	10308.6	+	17855.1i	0.713869	+	1.23646i	0.963394	+	0.268089i	$0.0863921\pi$
$593$	10308.6	+	17855.1i	0.713869	+	1.23646i	−0.249525	+	0.968368i	$0.580275\pi$
$594$		0			0
$595$	5179.27	+	8970.76i	0.356856	+	0.618093i
$596$		0			0
$597$	6561.39			0.449816
$598$		0			0
$599$	10652.2	+	18450.2i	0.726608	+	1.25852i	0.958309	+	0.285735i	$0.0922378\pi$
$599$	10652.2	+	18450.2i	0.726608	+	1.25852i	−0.231700	+	0.972787i	$0.574429\pi$
$600$		0			0
$601$	−26351.4			−1.78852			−0.894258	−	0.447553i	$-0.852296\pi$
$601$	−26351.4			−1.78852			−0.894258	+	0.447553i	$0.852296\pi$
$602$		0			0
$603$	−30505.6	+	52837.3i	−2.06018	+	3.56833i
$604$		0			0
$605$	8473.56	−	14676.6i	0.569420	−	0.986265i
$606$		0			0
$607$	−24027.8			−1.60669			−0.803344	−	0.595516i	$-0.796948\pi$
$607$	−24027.8			−1.60669			−0.803344	+	0.595516i	$0.796948\pi$
$608$		0			0
$609$	−18796.0			−1.25066
$610$		0			0
$611$	−6473.73	+	11212.8i	−0.428640	+	0.742426i
$612$		0			0
$613$	−7619.00	+	13196.5i	−0.502004	+	0.869497i	0.497993	+	0.867181i	$0.334070\pi$
$613$	−7619.00	+	13196.5i	−0.502004	+	0.869497i	−0.999997	+	0.00231571i	$0.999263\pi$
$614$		0			0
$615$	−16485.2			−1.08089
$616$		0			0
$617$	14065.4	+	24362.0i	0.917751	+	1.58959i	0.802822	+	0.596218i	$0.203331\pi$
$617$	14065.4	+	24362.0i	0.917751	+	1.58959i	0.114929	+	0.993374i	$0.463336\pi$
$618$		0			0
$619$	−9482.23			−0.615708			−0.307854	−	0.951434i	$-0.599611\pi$
$619$	−9482.23			−0.615708			−0.307854	+	0.951434i	$0.599611\pi$
$620$		0			0
$621$	8609.32	+	14911.8i	0.556329	+	0.963590i
$622$		0			0
$623$	−7996.01	−	13849.5i	−0.514211	−	0.890639i
$624$		0			0
$625$	7877.57	−	13644.3i	0.504164	−	0.873238i
$626$		0			0
$627$	−9699.85	−	8217.01i	−0.617822	−	0.523374i
$628$		0			0
$629$	−437.485	+	757.746i	−0.0277324	+	0.0480339i
$630$		0			0
$631$	−850.702	−	1473.46i	−0.0536702	−	0.0929595i	0.837942	−	0.545759i	$-0.183759\pi$
$631$	−850.702	−	1473.46i	−0.0536702	−	0.0929595i	−0.891612	+	0.452800i	$0.850425\pi$
$632$		0			0
$633$	2542.65	+	4404.01i	0.159655	+	0.276530i
$634$		0			0
$635$	−3769.53			−0.235573
$636$		0			0
$637$	−2288.92	−	3964.53i	−0.142371	−	0.246594i
$638$		0			0
$639$	43079.9			2.66700
$640$		0			0
$641$	−10815.8	+	18733.5i	−0.666454	+	1.15433i	0.312435	+	0.949939i	$0.398855\pi$
$641$	−10815.8	+	18733.5i	−0.666454	+	1.15433i	−0.978889	+	0.204393i	$0.934478\pi$
$642$		0			0
$643$	−2722.31	+	4715.17i	−0.166963	+	0.289189i	−0.937351	−	0.348387i	$-0.886729\pi$
$643$	−2722.31	+	4715.17i	−0.166963	+	0.289189i	0.770388	+	0.637576i	$0.220063\pi$
$644$		0			0
$645$	−54490.2			−3.32643
$646$		0			0
$647$	−27393.8			−1.66454			−0.832272	−	0.554367i	$-0.812960\pi$
$647$	−27393.8			−1.66454			−0.832272	+	0.554367i	$0.812960\pi$
$648$		0			0
$649$	−3391.54	+	5874.32i	−0.205130	+	0.355296i
$650$		0			0
$651$	9528.62	−	16504.0i	0.573665	−	0.993617i
$652$		0			0
$653$	−23390.6			−1.40175			−0.700875	−	0.713284i	$-0.747207\pi$
$653$	−23390.6			−1.40175			−0.700875	+	0.713284i	$0.747207\pi$
$654$		0			0
$655$	2092.57	+	3624.43i	0.124830	+	0.216211i
$656$		0			0
$657$	−12097.1			−0.718346
$658$		0			0
$659$	−10029.5	−	17371.6i	−0.592860	−	1.02686i	−0.993845	−	0.110779i	$-0.964666\pi$
$659$	−10029.5	−	17371.6i	−0.592860	−	1.02686i	0.400985	−	0.916084i	$-0.368668\pi$
$660$		0			0
$661$	−11618.9	−	20124.5i	−0.683696	−	1.18420i	−0.973845	−	0.227214i	$-0.927038\pi$
$661$	−11618.9	−	20124.5i	−0.683696	−	1.18420i	0.290149	−	0.956981i	$-0.406295\pi$
$662$		0			0
$663$	−12725.6	+	22041.3i	−0.745430	+	1.29112i
$664$		0			0
$665$	16527.8	+	14001.2i	0.963791	+	0.816453i
$666$		0			0
$667$	2822.80	−	4889.24i	0.163867	−	0.283826i
$668$		0			0
$669$	−23231.2	−	40237.6i	−1.34256	−	2.32538i
$670$		0			0
$671$	4519.39	+	7827.81i	0.260013	+	0.450356i
$672$		0			0
$673$	−10185.3			−0.583378			−0.291689	−	0.956513i	$-0.594217\pi$
$673$	−10185.3			−0.583378			−0.291689	+	0.956513i	$0.594217\pi$
$674$		0			0
$675$	22380.6	+	38764.4i	1.27619	+	2.21043i
$676$		0			0
$677$	3202.89			0.181827			0.0909136	−	0.995859i	$-0.471021\pi$
$677$	3202.89			0.181827			0.0909136	+	0.995859i	$0.471021\pi$
$678$		0			0
$679$	−13144.5	+	22767.0i	−0.742916	+	1.28677i
$680$		0			0
$681$	19018.4	−	32940.8i	1.07017	−	1.85359i
$682$		0			0
$683$	−1625.51			−0.0910662			−0.0455331	−	0.998963i	$-0.514499\pi$
$683$	−1625.51			−0.0910662			−0.0455331	+	0.998963i	$0.514499\pi$
$684$		0			0
$685$	38474.2			2.14602
$686$		0			0
$687$	−378.197	+	655.056i	−0.0210031	+	0.0363784i
$688$		0			0
$689$	7309.15	−	12659.8i	0.404146	−	0.700001i
$690$		0			0
$691$	−839.130			−0.0461968			−0.0230984	−	0.999733i	$-0.507353\pi$
$691$	−839.130			−0.0461968			−0.0230984	+	0.999733i	$0.507353\pi$
$692$		0			0
$693$	−8596.50	−	14889.6i	−0.471218	−	0.816173i
$694$		0			0
$695$	5787.34			0.315865
$696$		0			0
$697$	−2160.48	−	3742.06i	−0.117409	−	0.203358i
$698$		0			0
$699$	−7868.49	−	13628.6i	−0.425771	−	0.737457i
$700$		0			0
$701$	729.064	−	1262.78i	0.0392816	−	0.0680377i	−0.845716	−	0.533633i	$-0.820826\pi$
$701$	729.064	−	1262.78i	0.0392816	−	0.0680377i	0.884998	+	0.465595i	$0.154160\pi$
$702$		0			0
$703$	−326.171	+	1800.37i	−0.0174989	+	0.0965890i
$704$		0			0
$705$	−14577.0	+	25248.0i	−0.778723	+	1.34879i
$706$		0			0
$707$	−8651.49	−	14984.8i	−0.460216	−	0.797118i
$708$		0			0
$709$	16159.9	+	27989.8i	0.855993	+	1.48262i	0.875721	+	0.482818i	$0.160387\pi$
$709$	16159.9	+	27989.8i	0.855993	+	1.48262i	−0.0197278	+	0.999805i	$0.506280\pi$
$710$		0			0
$711$	56708.2			2.99117
$712$		0			0
$713$	2862.03	+	4957.18i	0.150328	+	0.260376i
$714$		0			0
$715$	16970.7			0.887646
$716$		0			0
$717$	30246.1	−	52387.8i	1.57540	−	2.72867i
$718$		0			0
$719$	−2885.84	+	4998.42i	−0.149685	+	0.259262i	−0.931111	−	0.364736i	$-0.881159\pi$
$719$	−2885.84	+	4998.42i	−0.149685	+	0.259262i	0.781426	+	0.623998i	$0.214493\pi$
$720$		0			0
$721$	23668.5			1.22255
$722$		0			0
$723$	33466.6			1.72149
$724$		0			0
$725$	7338.10	−	12710.0i	0.375904	−	0.651085i
$726$		0			0
$727$	2726.16	−	4721.84i	0.139075	−	0.240885i	−0.788072	−	0.615583i	$-0.788920\pi$
$727$	2726.16	−	4721.84i	0.139075	−	0.240885i	0.927147	+	0.374698i	$0.122254\pi$
$728$		0			0
$729$	17352.9			0.881618
$730$		0			0
$731$	−7141.26	−	12369.0i	−0.361326	−	0.625834i
$732$		0			0
$733$	9558.30			0.481643			0.240821	−	0.970569i	$-0.422583\pi$
$733$	9558.30			0.481643			0.240821	+	0.970569i	$0.422583\pi$
$734$		0			0
$735$	−5153.98	−	8926.96i	−0.258650	−	0.447994i
$736$		0			0
$737$	7556.23	+	13087.8i	0.377663	+	0.654131i
$738$		0			0
$739$	6476.74	−	11218.0i	0.322396	−	0.558406i	−0.658586	−	0.752506i	$-0.728845\pi$
$739$	6476.74	−	11218.0i	0.322396	−	0.558406i	0.980982	+	0.194099i	$0.0621784\pi$
$740$		0			0
$741$	−9487.66	+	52369.1i	−0.470361	+	2.59626i
$742$		0			0
$743$	−91.9794	+	159.313i	−0.00454158	+	0.00786625i	−0.868287	−	0.496062i	$-0.834779\pi$
$743$	−91.9794	+	159.313i	−0.00454158	+	0.00786625i	0.863746	+	0.503928i	$0.168112\pi$
$744$		0			0
$745$	17685.4	+	30632.0i	0.869721	+	1.50640i
$746$		0			0
$747$	−15410.4	−	26691.7i	−0.754804	−	1.30736i
$748$		0			0
$749$	8303.57			0.405081
$750$		0			0
$751$	5247.19	+	9088.39i	0.254957	+	0.441598i	0.964884	−	0.262677i	$-0.0846054\pi$
$751$	5247.19	+	9088.39i	0.254957	+	0.441598i	−0.709927	+	0.704275i	$0.751272\pi$
$752$		0			0
$753$	34766.2			1.68254
$754$		0			0
$755$	−5034.77	+	8720.47i	−0.242694	+	0.420358i
$756$		0			0
$757$	4731.24	−	8194.75i	0.227160	−	0.393452i	−0.729805	−	0.683655i	$-0.760389\pi$
$757$	4731.24	−	8194.75i	0.227160	−	0.393452i	0.956965	+	0.290203i	$0.0937227\pi$
$758$		0			0
$759$	7318.84			0.350009
$760$		0			0
$761$	−38400.1			−1.82918			−0.914588	−	0.404388i	$-0.867485\pi$
$761$	−38400.1			−1.82918			−0.914588	+	0.404388i	$0.867485\pi$
$762$		0			0
$763$	10053.0	−	17412.3i	0.476990	−	0.826171i
$764$		0			0
$765$	−20218.2	+	35018.9i	−0.955543	+	1.65505i
$766$		0			0
$767$	28397.9			1.33688
$768$		0			0
$769$	1535.93	+	2660.31i	0.0720249	+	0.124751i	0.899789	−	0.436326i	$-0.143721\pi$
$769$	1535.93	+	2660.31i	0.0720249	+	0.124751i	−0.827764	+	0.561077i	$0.810387\pi$
$770$		0			0
$771$	14838.0			0.693095
$772$		0			0
$773$	−3588.67	−	6215.75i	−0.166980	−	0.289218i	0.770377	−	0.637589i	$-0.220068\pi$
$773$	−3588.67	−	6215.75i	−0.166980	−	0.289218i	−0.937357	+	0.348371i	$0.886735\pi$
$774$		0			0
$775$	7440.07	+	12886.6i	0.344846	+	0.597290i
$776$		0			0
$777$	−1753.53	+	3037.20i	−0.0809620	+	0.140230i
$778$		0			0
$779$	−6894.41	−	5840.44i	−0.317096	−	0.268621i
$780$		0			0
$781$	5335.44	−	9241.25i	0.244452	−	0.423403i
$782$		0			0
$783$	−21379.2	−	37029.9i	−0.975774	−	1.69009i
$784$		0			0
$785$	−16772.1	−	29050.1i	−0.762576	−	1.32082i
$786$		0			0
$787$	−40299.0			−1.82529			−0.912645	−	0.408754i	$-0.865963\pi$
$787$	−40299.0			−1.82529			−0.912645	+	0.408754i	$0.865963\pi$
$788$		0			0
$789$	18242.3	+	31596.6i	0.823123	+	1.42569i
$790$		0			0
$791$	−12249.3			−0.550613
$792$		0			0
$793$	18920.7	−	32771.7i	0.847283	−	1.46754i
$794$		0			0
$795$	16458.1	−	28506.2i	0.734223	−	1.27171i
$796$		0			0
$797$	−33505.8			−1.48913			−0.744565	−	0.667550i	$-0.767343\pi$
$797$	−33505.8			−1.48913			−0.744565	+	0.667550i	$0.767343\pi$
$798$		0			0
$799$	−7641.59			−0.338348
$800$		0			0
$801$	31213.8	−	54063.9i	1.37689	−	2.38484i
$802$		0			0
$803$	−1498.23	+	2595.00i	−0.0658421	+	0.114042i
$804$		0			0
$805$	−12470.8			−0.546008
$806$		0			0
$807$	−16167.0	−	28002.1i	−0.705213	−	1.22146i
$808$		0			0
$809$	−20863.7			−0.906710			−0.453355	−	0.891330i	$-0.649773\pi$
$809$	−20863.7			−0.906710			−0.453355	+	0.891330i	$0.649773\pi$
$810$		0			0
$811$	8728.82	+	15118.8i	0.377941	+	0.654613i	0.990763	−	0.135608i	$-0.0432988\pi$
$811$	8728.82	+	15118.8i	0.377941	+	0.654613i	−0.612821	+	0.790221i	$0.709966\pi$
$812$		0			0
$813$	16881.0	+	29238.7i	0.728218	+	1.26131i
$814$		0			0
$815$	−1262.59	+	2186.88i	−0.0542659	+	0.0939914i
$816$		0			0
$817$	−22788.8	−	19305.0i	−0.975862	−	0.826679i
$818$		0			0
$819$	−35989.8	+	62336.2i	−1.53552	+	2.65959i
$820$		0			0
$821$	−14635.8	−	25349.9i	−0.622158	−	1.07761i	−0.989083	−	0.147359i	$-0.952923\pi$
$821$	−14635.8	−	25349.9i	−0.622158	−	1.07761i	0.366925	−	0.930251i	$-0.380411\pi$
$822$		0			0
$823$	19338.7	+	33495.5i	0.819080	+	1.41869i	0.906361	+	0.422505i	$0.138849\pi$
$823$	19338.7	+	33495.5i	0.819080	+	1.41869i	−0.0872806	+	0.996184i	$0.527818\pi$
$824$		0			0
$825$	19025.9			0.802906
$826$		0			0
$827$	2321.06	+	4020.19i	0.0975951	+	0.169040i	0.910689	−	0.413093i	$-0.135552\pi$
$827$	2321.06	+	4020.19i	0.0975951	+	0.169040i	−0.813094	+	0.582133i	$0.802218\pi$
$828$		0			0
$829$	−7918.14			−0.331735			−0.165868	−	0.986148i	$-0.553042\pi$
$829$	−7918.14			−0.331735			−0.165868	+	0.986148i	$0.553042\pi$
$830$		0			0
$831$	31400.7	−	54387.7i	1.31081	−	2.27038i
$832$		0			0
$833$	1350.92	−	2339.86i	0.0561904	−	0.0973246i
$834$		0			0
$835$	−33168.2			−1.37465
$836$		0			0
$837$	43352.6			1.79031
$838$		0			0
$839$	4061.92	−	7035.45i	0.167143	−	0.289500i	−0.770271	−	0.637716i	$-0.779879\pi$
$839$	4061.92	−	7035.45i	0.167143	−	0.289500i	0.937414	+	0.348216i	$0.113212\pi$
$840$		0			0
$841$	5184.73	−	8980.21i	0.212585	−	0.368207i
$842$		0			0
$843$	−75537.5			−3.08618
$844$		0			0
$845$	−18192.1	−	31509.7i	−0.740626	−	1.28280i
$846$		0			0
$847$	17804.6			0.722283
$848$		0			0
$849$	−9924.75	−	17190.2i	−0.401198	−	0.694895i
$850$		0			0
$851$	−526.692	−	912.258i	−0.0212160	−	0.0367471i
$852$		0			0
$853$	−22594.4	+	39134.7i	−0.906938	+	1.57086i	−0.0886427	+	0.996063i	$0.528253\pi$
$853$	−22594.4	+	39134.7i	−0.906938	+	1.57086i	−0.818295	+	0.574799i	$0.805080\pi$
$854$		0			0
$855$	−15073.9	+	83203.3i	−0.602942	+	3.32806i
$856$		0			0
$857$	−15246.2	+	26407.1i	−0.607700	+	1.05257i	0.383918	+	0.923367i	$0.374574\pi$
$857$	−15246.2	+	26407.1i	−0.607700	+	1.05257i	−0.991618	+	0.129201i	$0.958759\pi$
$858$		0			0
$859$	−19527.3	−	33822.2i	−0.775625	−	1.34342i	−0.934443	−	0.356113i	$-0.884102\pi$
$859$	−19527.3	−	33822.2i	−0.775625	−	1.34342i	0.158818	−	0.987308i	$-0.449232\pi$
$860$		0			0
$861$	−8659.65	−	14999.0i	−0.342764	−	0.593685i
$862$		0			0
$863$	21510.4			0.848461			0.424230	−	0.905554i	$-0.360545\pi$
$863$	21510.4			0.848461			0.424230	+	0.905554i	$0.360545\pi$
$864$		0			0
$865$	3198.73	+	5540.37i	0.125734	+	0.217778i
$866$		0			0
$867$	32028.1			1.25459
$868$		0			0
$869$	7023.30	−	12164.7i	0.274165	−	0.474867i
$870$		0			0
$871$	31634.7	−	54792.9i	1.23066	−	2.13156i
$872$		0			0
$873$	−102624.			−3.97857
$874$		0			0
$875$	274.603			0.0106095
$876$		0			0
$877$	−4199.45	+	7273.66i	−0.161694	+	0.280062i	−0.935476	−	0.353390i	$-0.885029\pi$
$877$	−4199.45	+	7273.66i	−0.161694	+	0.280062i	0.773783	+	0.633451i	$0.218362\pi$
$878$		0			0
$879$	−37448.1	+	64862.1i	−1.43697	+	2.48890i
$880$		0			0
$881$	−46320.2			−1.77136			−0.885679	−	0.464298i	$-0.846307\pi$
$881$	−46320.2			−1.77136			−0.885679	+	0.464298i	$0.846307\pi$
$882$		0			0
$883$	16002.0	+	27716.2i	0.609863	+	1.05631i	0.991262	+	0.131904i	$0.0421091\pi$
$883$	16002.0	+	27716.2i	0.609863	+	1.05631i	−0.381399	+	0.924411i	$0.624558\pi$
$884$		0			0
$885$	63943.7			2.42875
$886$		0			0
$887$	−16782.7	−	29068.6i	−0.635298	−	1.10037i	−0.986452	−	0.164051i	$-0.947544\pi$
$887$	−16782.7	−	29068.6i	−0.635298	−	1.10037i	0.351154	−	0.936318i	$-0.385789\pi$
$888$		0			0
$889$	−1980.13	−	3429.68i	−0.0747035	−	0.129390i
$890$		0			0
$891$	13713.5	−	23752.5i	0.515622	−	0.893084i
$892$		0			0
$893$	−15041.3	+	5394.81i	−0.563650	+	0.202162i
$894$		0			0
$895$	−12849.4	+	22255.8i	−0.479897	+	0.831206i
$896$		0			0
$897$	−15320.4	−	26535.8i	−0.570272	−	0.987741i
$898$		0			0
$899$	−7107.18	−	12310.0i	−0.263668	−	0.456687i
$900$		0			0
$901$	8627.71			0.319013
$902$		0			0
$903$	−28623.6	−	49577.6i	−1.05486	−	1.82706i
$904$		0			0
$905$	44760.1			1.64406
$906$		0			0
$907$	19984.2	−	34613.7i	0.731604	−	1.26718i	−0.224593	−	0.974453i	$-0.572105\pi$
$907$	19984.2	−	34613.7i	0.731604	−	1.26718i	0.956197	−	0.292723i	$-0.0945614\pi$
$908$		0			0
$909$	33772.6	−	58495.9i	1.23231	−	2.13442i
$910$		0			0
$911$	−38734.2			−1.40869			−0.704347	−	0.709855i	$-0.748760\pi$
$911$	−38734.2			−1.40869			−0.704347	+	0.709855i	$0.748760\pi$
$912$		0			0
$913$	−7634.32			−0.276735
$914$		0			0
$915$	42604.0	−	73792.3i	1.53928	−	2.66612i
$916$		0			0
$917$	−2198.45	+	3807.82i	−0.0791702	+	0.137127i
$918$		0			0
$919$	−7565.87			−0.271572			−0.135786	−	0.990738i	$-0.543356\pi$
$919$	−7565.87			−0.271572			−0.135786	+	0.990738i	$0.543356\pi$
$920$		0			0
$921$	28431.6	+	49245.0i	1.01721	+	1.76187i
$922$		0			0
$923$	−44674.4			−1.59315
$924$		0			0
$925$	−1369.18	−	2371.49i	−0.0486684	−	0.0842962i
$926$		0			0
$927$	46197.0	+	80015.6i	1.63680	+	2.83501i
$928$		0			0
$929$	11858.4	−	20539.3i	0.418796	−	0.725376i	−0.577023	−	0.816728i	$-0.695786\pi$
$929$	11858.4	−	20539.3i	0.418796	−	0.725376i	0.995819	+	0.0913524i	$0.0291190\pi$
$930$		0			0
$931$	1007.19	−	5559.40i	0.0354558	−	0.195706i
$932$		0			0
$933$	−8775.11	+	15198.9i	−0.307914	+	0.533323i
$934$		0			0
$935$	5008.04	+	8674.18i	0.175166	+	0.303397i
$936$		0			0
$937$	−22291.9	−	38610.8i	−0.777210	−	1.34617i	−0.933544	−	0.358463i	$-0.883301\pi$
$937$	−22291.9	−	38610.8i	−0.777210	−	1.34617i	0.156334	−	0.987704i	$-0.450032\pi$
$938$		0			0
$939$	8985.93			0.312295
$940$		0			0
$941$	20086.2	+	34790.3i	0.695846	+	1.20524i	0.969895	+	0.243525i	$0.0783037\pi$
$941$	20086.2	+	34790.3i	0.695846	+	1.20524i	−0.274049	+	0.961716i	$0.588363\pi$
$942$		0			0
$943$	5202.05			0.179642
$944$		0			0
$945$	−47225.2	+	81796.5i	−1.62565	+	2.81570i
$946$		0			0
$947$	−21487.4	+	37217.2i	−0.737324	+	1.27708i	0.216372	+	0.976311i	$0.430577\pi$
$947$	−21487.4	+	37217.2i	−0.737324	+	1.27708i	−0.953696	+	0.300772i	$0.902756\pi$
$948$		0			0
$949$	12544.9			0.429108
$950$		0			0
$951$	70975.8			2.42014
$952$		0			0
$953$	−16391.0	+	28390.0i	−0.557141	+	0.964997i	0.440592	+	0.897707i	$0.354769\pi$
$953$	−16391.0	+	28390.0i	−0.557141	+	0.964997i	−0.997733	+	0.0672898i	$0.978565\pi$
$954$		0			0
$955$	27784.1	−	48123.5i	0.941438	−	1.63062i
$956$		0			0
$957$	−18174.6			−0.613900
$958$		0			0
$959$	20210.5	+	35005.6i	0.680532	+	1.17872i
$960$		0			0
$961$	−15379.1			−0.516234
$962$		0			0
$963$	16207.2	+	28071.7i	0.542337	+	0.939355i
$964$		0			0
$965$	−37357.9	−	64705.7i	−1.24621	−	2.15850i
$966$		0			0
$967$	9881.92	−	17116.0i	0.328626	−	0.569196i	−0.653614	−	0.756828i	$-0.726748\pi$
$967$	9881.92	−	17116.0i	0.328626	−	0.569196i	0.982239	+	0.187632i	$0.0600812\pi$
$968$		0			0
$969$	−29567.1	+	10604.7i	−0.980219	+	0.351571i
$970$		0			0
$971$	6926.88	−	11997.7i	0.228933	−	0.396524i	−0.728559	−	0.684983i	$-0.759810\pi$
$971$	6926.88	−	11997.7i	0.228933	−	0.396524i	0.957492	+	0.288459i	$0.0931429\pi$
$972$		0			0
$973$	3040.08	+	5265.58i	0.100165	+	0.173491i
$974$		0			0
$975$	−39826.7	−	68981.8i	−1.30818	−	2.26583i
$976$		0			0
$977$	53113.0			1.73924			0.869620	−	0.493722i	$-0.164364\pi$
$977$	53113.0			1.73924			0.869620	+	0.493722i	$0.164364\pi$
$978$		0			0
$979$	−7731.65	−	13391.6i	−0.252405	−	0.437179i
$980$		0			0
$981$	78487.4			2.55444
$982$		0			0
$983$	−8672.89	+	15021.9i	−0.281406	+	0.487410i	−0.971731	−	0.236090i	$-0.924134\pi$
$983$	−8672.89	+	15021.9i	−0.281406	+	0.487410i	0.690325	+	0.723499i	$0.257467\pi$
$984$		0			0
$985$	−18596.9	+	32210.8i	−0.601570	+	1.04195i
$986$		0			0
$987$	−30629.0			−0.987774
$988$		0			0
$989$	17194.9			0.552847
$990$		0			0
$991$	−3316.70	+	5744.69i	−0.106315	+	0.184143i	−0.914275	−	0.405095i	$-0.867239\pi$
$991$	−3316.70	+	5744.69i	−0.106315	+	0.184143i	0.807960	+	0.589238i	$0.200572\pi$
$992$		0			0
$993$	25917.3	−	44890.1i	0.828258	−	1.43459i
$994$		0			0
$995$	−10810.5			−0.344438
$996$		0			0
$997$	10306.3	+	17851.0i	0.327386	+	0.567049i	0.981992	−	0.188921i	$-0.0604989\pi$
$997$	10306.3	+	17851.0i	0.327386	+	0.567049i	−0.654606	+	0.755970i	$0.727166\pi$
$998$		0			0
$999$	−7978.08			−0.252668

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	304.4.i.e.49.3		6
4.3	odd	2		38.4.c.c.11.1	yes	6
12.11	even	2		342.4.g.f.163.3		6
19.7	even	3	inner	304.4.i.e.273.3		6
76.7	odd	6		38.4.c.c.7.1	✓	6
76.11	odd	6		722.4.a.j.1.3		3
76.27	even	6		722.4.a.k.1.1		3
228.83	even	6		342.4.g.f.235.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.4.c.c.7.1	✓	6	76.7	odd	6
38.4.c.c.11.1	yes	6	4.3	odd	2
304.4.i.e.49.3		6	1.1	even	1	trivial
304.4.i.e.273.3		6	19.7	even	3	inner
342.4.g.f.163.3		6	12.11	even	2
342.4.g.f.235.3		6	228.83	even	6
722.4.a.j.1.3		3	76.11	odd	6
722.4.a.k.1.1		3	76.27	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 304 = 2^{4} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	304.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(4.78825 - 8.29349i) q^{3} +(-7.88908 + 13.6643i) q^{5} -16.5765 q^{7} +(-32.3546 - 56.0399i) q^{9} +O(q^{10})\)	\(q+(4.78825 - 8.29349i) q^{3} +(-7.88908 + 13.6643i) q^{5} -16.5765 q^{7} +(-32.3546 - 56.0399i) q^{9} -16.0285 q^{11} +(33.5522 + 58.1141i) q^{13} +(75.5497 + 130.856i) q^{15} +(-19.8025 + 34.2989i) q^{17} +(-14.7639 + 81.4925i) q^{19} +(-79.3724 + 137.477i) q^{21} +(-23.8404 - 41.2928i) q^{23} +(-61.9750 - 107.344i) q^{25} -361.123 q^{27} +(59.2021 + 102.541i) q^{29} -120.050 q^{31} +(-76.7483 + 132.932i) q^{33} +(130.773 - 226.506i) q^{35} +22.0924 q^{37} +642.624 q^{39} +(-54.5508 + 94.4847i) q^{41} +(-180.312 + 312.310i) q^{43} +1020.99 q^{45} +(96.4726 + 167.095i) q^{47} -68.2197 q^{49} +(189.638 + 328.463i) q^{51} +(-108.922 - 188.659i) q^{53} +(126.450 - 219.017i) q^{55} +(605.164 + 512.651i) q^{57} +(211.595 - 366.493i) q^{59} +(-281.960 - 488.369i) q^{61} +(536.327 + 928.945i) q^{63} -1058.78 q^{65} +(-471.426 - 816.534i) q^{67} -456.615 q^{69} +(-332.873 + 576.552i) q^{71} +(93.4728 - 161.900i) q^{73} -1187.01 q^{75} +265.696 q^{77} +(-438.177 + 758.945i) q^{79} +(-855.571 + 1481.89i) q^{81} +476.297 q^{83} +(-312.447 - 541.173i) q^{85} +1133.90 q^{87} +(482.370 + 835.489i) q^{89} +(-556.177 - 963.328i) q^{91} +(-574.827 + 995.629i) q^{93} +(-997.063 - 844.639i) q^{95} +(792.961 - 1373.45i) q^{97} +(518.595 + 898.234i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 5 q^{3} - q^{5} - 52 q^{7} - 54 q^{9}+O(q^{10}) \) 6 * q + 5 * q^3 - q^5 - 52 * q^7 - 54 * q^9	\( 6 q + 5 q^{3} - q^{5} - 52 q^{7} - 54 q^{9} - 8 q^{11} + 129 q^{13} + 77 q^{15} - 51 q^{17} - 40 q^{19} - 170 q^{21} - 47 q^{23} - 338 q^{25} - 718 q^{27} - 125 q^{29} + 100 q^{31} + 274 q^{33} + 84 q^{35} - 376 q^{37} + 1546 q^{39} + 475 q^{41} + 73 q^{43} + 3188 q^{45} + 241 q^{47} - 1354 q^{49} - 69 q^{51} + 29 q^{53} + 1838 q^{55} + 1755 q^{57} + 1065 q^{59} - 981 q^{61} + 872 q^{63} + 586 q^{65} - 877 q^{67} - 1526 q^{69} - 2135 q^{71} + 667 q^{73} - 4584 q^{75} - 492 q^{77} - 1671 q^{79} - 1287 q^{81} - 1176 q^{83} - 1929 q^{85} + 6430 q^{87} + 693 q^{89} - 1676 q^{91} - 3138 q^{93} - 4489 q^{95} - 985 q^{97} + 3184 q^{99}+O(q^{100}) \) 6 * q + 5 * q^3 - q^5 - 52 * q^7 - 54 * q^9 - 8 * q^11 + 129 * q^13 + 77 * q^15 - 51 * q^17 - 40 * q^19 - 170 * q^21 - 47 * q^23 - 338 * q^25 - 718 * q^27 - 125 * q^29 + 100 * q^31 + 274 * q^33 + 84 * q^35 - 376 * q^37 + 1546 * q^39 + 475 * q^41 + 73 * q^43 + 3188 * q^45 + 241 * q^47 - 1354 * q^49 - 69 * q^51 + 29 * q^53 + 1838 * q^55 + 1755 * q^57 + 1065 * q^59 - 981 * q^61 + 872 * q^63 + 586 * q^65 - 877 * q^67 - 1526 * q^69 - 2135 * q^71 + 667 * q^73 - 4584 * q^75 - 492 * q^77 - 1671 * q^79 - 1287 * q^81 - 1176 * q^83 - 1929 * q^85 + 6430 * q^87 + 693 * q^89 - 1676 * q^91 - 3138 * q^93 - 4489 * q^95 - 985 * q^97 + 3184 * q^99

Introduction

L-functions

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