LMFDB - Embedded newform 153.4.l.c.19.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [153,4,Mod(19,153)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(153, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 7]))

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

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

chi := DirichletCharacter("153.19");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 153 = 3^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	153.l (of order $8$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.02729223088$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 51)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			19.10
Character	$\chi$	$=$	153.19
Dual form			153.4.l.c.145.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(3.79946 + 3.79946i) q^{2} +20.8719i q^{4} +(-4.62215 - 11.1589i) q^{5} +(-11.9634 + 28.8822i) q^{7} +(-48.9062 + 48.9062i) q^{8} +(24.8360 - 59.9594i) q^{10} +(-1.65275 - 0.684591i) q^{11} +10.2045i q^{13} +(-155.191 + 64.2823i) q^{14} -204.660 q^{16} +(69.4565 + 9.42288i) q^{17} +(73.3206 + 73.3206i) q^{19} +(232.906 - 96.4729i) q^{20} +(-3.67848 - 8.88064i) q^{22} +(-11.9071 - 4.93207i) q^{23} +(-14.7675 + 14.7675i) q^{25} +(-38.7718 + 38.7718i) q^{26} +(-602.824 - 249.698i) q^{28} +(-26.8811 - 64.8968i) q^{29} +(195.185 - 80.8484i) q^{31} +(-386.348 - 386.348i) q^{32} +(228.096 + 299.700i) q^{34} +377.588 q^{35} +(114.447 - 47.4057i) q^{37} +557.158i q^{38} +(771.789 + 319.685i) q^{40} +(132.677 - 320.311i) q^{41} +(-62.2795 + 62.2795i) q^{43} +(14.2887 - 34.4959i) q^{44} +(-26.5013 - 63.9798i) q^{46} +573.735i q^{47} +(-448.519 - 448.519i) q^{49} -112.217 q^{50} -212.988 q^{52} +(92.6502 + 92.6502i) q^{53} +21.6071i q^{55} +(-827.432 - 1997.60i) q^{56} +(144.439 - 348.707i) q^{58} +(-158.119 + 158.119i) q^{59} +(-106.746 + 257.708i) q^{61} +(1048.78 + 434.419i) q^{62} -1298.55i q^{64} +(113.871 - 47.1670i) q^{65} -304.748 q^{67} +(-196.673 + 1449.69i) q^{68} +(1434.63 + 1434.63i) q^{70} +(-517.248 + 214.251i) q^{71} +(-71.2818 - 172.090i) q^{73} +(614.955 + 254.723i) q^{74} +(-1530.34 + 1530.34i) q^{76} +(39.5449 - 39.5449i) q^{77} +(1195.22 + 495.076i) q^{79} +(945.968 + 2283.77i) q^{80} +(1721.11 - 712.909i) q^{82} +(-547.311 - 547.311i) q^{83} +(-215.890 - 818.610i) q^{85} -473.258 q^{86} +(114.310 - 47.3489i) q^{88} -35.1924i q^{89} +(-294.729 - 122.081i) q^{91} +(102.942 - 248.523i) q^{92} +(-2179.89 + 2179.89i) q^{94} +(479.275 - 1157.07i) q^{95} +(-322.475 - 778.524i) q^{97} -3408.26i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 32 q^{5} + 128 q^{10} - 112 q^{11} - 256 q^{14} - 1024 q^{16} + 112 q^{17} - 32 q^{19} + 640 q^{20} + 728 q^{22} - 208 q^{23} + 296 q^{25} - 1472 q^{26} - 328 q^{28} + 1272 q^{29} - 192 q^{31} + 960 q^{32}+ \cdots + 1008 q^{97}+O(q^{100}) $ 40 * q - 32 * q^5 + 128 * q^10 - 112 * q^11 - 256 * q^14 - 1024 * q^16 + 112 * q^17 - 32 * q^19 + 640 * q^20 + 728 * q^22 - 208 * q^23 + 296 * q^25 - 1472 * q^26 - 328 * q^28 + 1272 * q^29 - 192 * q^31 + 960 * q^32 + 24 * q^34 + 992 * q^35 - 1120 * q^37 + 2984 * q^40 + 1320 * q^41 + 672 * q^43 - 3744 * q^44 - 384 * q^46 - 2096 * q^49 + 448 * q^50 + 960 * q^52 - 2120 * q^53 - 5680 * q^56 + 1000 * q^58 + 832 * q^59 - 208 * q^61 + 4432 * q^62 + 2376 * q^65 - 2272 * q^67 + 4560 * q^68 - 4792 * q^70 - 256 * q^71 - 1416 * q^73 + 2704 * q^74 - 264 * q^76 - 6048 * q^77 + 1920 * q^79 - 1312 * q^80 + 8328 * q^82 - 4960 * q^83 + 3192 * q^85 + 15616 * q^86 - 248 * q^88 + 1232 * q^91 - 944 * q^92 - 10000 * q^94 - 4528 * q^95 + 1008 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/153\mathbb{Z}\right)^\times$.

$n$	$37$	$137$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$1$

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 $

$2$	3.79946	+	3.79946i	1.34331	+	1.34331i	0.892739	+	0.450575i	$0.148781\pi$
$2$	3.79946	+	3.79946i	1.34331	+	1.34331i	0.450575	+	0.892739i	$0.351219\pi$
$3$		0			0
$3$		0			0
$4$			20.8719i			2.60898i
$5$	−4.62215	−	11.1589i	−0.413418	−	0.998079i	−0.984213	−	0.176986i	$-0.943365\pi$
$5$	−4.62215	−	11.1589i	−0.413418	−	0.998079i	0.570796	−	0.821092i	$-0.306635\pi$
$6$		0			0
$7$	−11.9634	+	28.8822i	−0.645962	+	1.55949i	0.172551	+	0.985001i	$0.444799\pi$
$7$	−11.9634	+	28.8822i	−0.645962	+	1.55949i	−0.818512	+	0.574489i	$0.805201\pi$
$8$	−48.9062	+	48.9062i	−2.16137	+	2.16137i
$9$		0			0
$10$	24.8360	−	59.9594i	0.785383	−	1.89608i
$11$	−1.65275	−	0.684591i	−0.0453020	−	0.0187647i	0.359917	−	0.932984i	$-0.382805\pi$
$11$	−1.65275	−	0.684591i	−0.0453020	−	0.0187647i	−0.405219	+	0.914219i	$0.632805\pi$
$12$		0			0
$13$			10.2045i			0.217710i	0.994058	+	0.108855i	$0.0347184\pi$
$13$			10.2045i			0.217710i	−0.994058	+	0.108855i	$0.965282\pi$
$14$	−155.191	+	64.2823i	−2.96261	+	1.22715i
$15$		0			0
$16$	−204.660			−3.19781
$17$	69.4565	+	9.42288i	0.990922	+	0.134434i
$17$	69.4565	+	9.42288i	0.990922	+	0.134434i
$18$		0			0
$19$	73.3206	+	73.3206i	0.885310	+	0.885310i	0.994068	−	0.108758i	$-0.0346874\pi$
$19$	73.3206	+	73.3206i	0.885310	+	0.885310i	−0.108758	+	0.994068i	$0.534687\pi$
$20$	232.906	−	96.4729i	2.60397	−	1.07860i
$21$		0			0
$22$	−3.67848	−	8.88064i	−0.0356479	−	0.0860617i
$23$	−11.9071	−	4.93207i	−0.107948	−	0.0447134i	0.328056	−	0.944658i	$-0.393607\pi$
$23$	−11.9071	−	4.93207i	−0.107948	−	0.0447134i	−0.436004	+	0.899945i	$0.643607\pi$
$24$		0			0
$25$	−14.7675	+	14.7675i	−0.118140	+	0.118140i
$26$	−38.7718	+	38.7718i	−0.292453	+	0.292453i
$27$		0			0
$28$	−602.824	−	249.698i	−4.06868	−	1.68530i
$29$	−26.8811	−	64.8968i	−0.172128	−	0.415553i	0.814149	−	0.580657i	$-0.197204\pi$
$29$	−26.8811	−	64.8968i	−0.172128	−	0.415553i	−0.986276	+	0.165104i	$0.947204\pi$
$30$		0			0
$31$	195.185	−	80.8484i	1.13085	−	0.468413i	0.262779	−	0.964856i	$-0.415361\pi$
$31$	195.185	−	80.8484i	1.13085	−	0.468413i	0.868069	+	0.496443i	$0.165361\pi$
$32$	−386.348	−	386.348i	−2.13429	−	2.13429i
$33$		0			0
$34$	228.096	+	299.700i	1.15053	+	1.51171i
$35$	377.588			1.82355
$36$		0			0
$37$	114.447	−	47.4057i	0.508514	−	0.210634i	−0.113649	−	0.993521i	$-0.536254\pi$
$37$	114.447	−	47.4057i	0.508514	−	0.210634i	0.622163	+	0.782887i	$0.286254\pi$
$38$			557.158i			2.37850i
$39$		0			0
$40$	771.789	+	319.685i	3.05076	+	1.26367i
$41$	132.677	−	320.311i	0.505383	−	1.22010i	−0.441131	−	0.897443i	$-0.645423\pi$
$41$	132.677	−	320.311i	0.505383	−	1.22010i	0.946515	−	0.322661i	$-0.104577\pi$
$42$		0			0
$43$	−62.2795	+	62.2795i	−0.220873	+	0.220873i	−0.808866	−	0.587993i	$-0.799918\pi$
$43$	−62.2795	+	62.2795i	−0.220873	+	0.220873i	0.587993	+	0.808866i	$0.299918\pi$
$44$	14.2887	−	34.4959i	0.0489568	−	0.118192i
$45$		0			0
$46$	−26.5013	−	63.9798i	−0.0849435	−	0.205072i
$47$			573.735i			1.78059i	0.455382	+	0.890296i	$0.349503\pi$
$47$			573.735i			1.78059i	−0.455382	+	0.890296i	$0.650497\pi$
$48$		0			0
$49$	−448.519	−	448.519i	−1.30763	−	1.30763i
$50$	−112.217			−0.317398
$51$		0			0
$52$	−212.988			−0.568002
$53$	92.6502	+	92.6502i	0.240122	+	0.240122i	0.816901	−	0.576778i	$-0.195690\pi$
$53$	92.6502	+	92.6502i	0.240122	+	0.240122i	−0.576778	+	0.816901i	$0.695690\pi$
$54$		0			0
$55$			21.6071i			0.0529727i
$56$	−827.432	−	1997.60i	−1.97447	−	4.76679i
$57$		0			0
$58$	144.439	−	348.707i	0.326996	−	0.789439i
$59$	−158.119	+	158.119i	−0.348904	+	0.348904i	−0.859701	−	0.510797i	$-0.829350\pi$
$59$	−158.119	+	158.119i	−0.348904	+	0.348904i	0.510797	+	0.859701i	$0.329350\pi$
$60$		0			0
$61$	−106.746	+	257.708i	−0.224057	+	0.540921i	−0.995433	−	0.0954580i	$-0.969568\pi$
$61$	−106.746	+	257.708i	−0.224057	+	0.540921i	0.771377	+	0.636379i	$0.219568\pi$
$62$	1048.78	+	434.419i	2.14831	+	0.889859i
$63$		0			0
$64$		−	1298.55i		−	2.53623i
$65$	113.871	−	47.1670i	0.217292	−	0.0900052i
$66$		0			0
$67$	−304.748			−0.555686			−0.277843	−	0.960627i	$-0.589619\pi$
$67$	−304.748			−0.555686			−0.277843	+	0.960627i	$0.589619\pi$
$68$	−196.673	+	1449.69i	−0.350737	+	2.58530i
$69$		0			0
$70$	1434.63	+	1434.63i	2.44959	+	2.44959i
$71$	−517.248	+	214.251i	−0.864592	+	0.358126i	−0.770502	−	0.637438i	$-0.779994\pi$
$71$	−517.248	+	214.251i	−0.864592	+	0.358126i	−0.0940900	+	0.995564i	$0.529994\pi$
$72$		0			0
$73$	−71.2818	−	172.090i	−0.114286	−	0.275912i	0.856378	−	0.516349i	$-0.172709\pi$
$73$	−71.2818	−	172.090i	−0.114286	−	0.275912i	−0.970665	+	0.240437i	$0.922709\pi$
$74$	614.955	+	254.723i	0.966041	+	0.400147i
$75$		0			0
$76$	−1530.34	+	1530.34i	−2.30976	+	2.30976i
$77$	39.5449	−	39.5449i	0.0585267	−	0.0585267i
$78$		0			0
$79$	1195.22	+	495.076i	1.70219	+	0.705069i	0.999976	−	0.00690127i	$-0.00219676\pi$
$79$	1195.22	+	495.076i	1.70219	+	0.705069i	0.702210	+	0.711970i	$0.252197\pi$
$80$	945.968	+	2283.77i	1.32203	+	3.19166i
$81$		0			0
$82$	1721.11	−	712.909i	2.31787	−	0.960093i
$83$	−547.311	−	547.311i	−0.723797	−	0.723797i	0.245579	−	0.969377i	$-0.421022\pi$
$83$	−547.311	−	547.311i	−0.723797	−	0.723797i	−0.969377	+	0.245579i	$0.921022\pi$
$84$		0			0
$85$	−215.890	−	818.610i	−0.275489	−	1.04460i
$86$	−473.258			−0.593403
$87$		0			0
$88$	114.310	−	47.3489i	0.138472	−	0.0573569i
$89$		−	35.1924i		−	0.0419145i	−0.999780	−	0.0209572i	$-0.993329\pi$
$89$		−	35.1924i		−	0.0419145i	0.999780	−	0.0209572i	$-0.00667138\pi$
$90$		0			0
$91$	−294.729	−	122.081i	−0.339517	−	0.140632i
$92$	102.942	−	248.523i	0.116657	−	0.281634i
$93$		0			0
$94$	−2179.89	+	2179.89i	−2.39189	+	2.39189i
$95$	479.275	−	1157.07i	0.517606	−	1.24961i
$96$		0			0
$97$	−322.475	−	778.524i	−0.337550	−	0.814919i	−0.997950	−	0.0640040i	$-0.979613\pi$
$97$	−322.475	−	778.524i	−0.337550	−	0.814919i	0.660399	−	0.750915i	$-0.270387\pi$
$98$		−	3408.26i		−	3.51313i
$99$		0			0
$100$	−308.225	−	308.225i	−0.308225	−	0.308225i
$101$	217.350			0.214130			0.107065	−	0.994252i	$-0.465855\pi$
$101$	217.350			0.214130			0.107065	+	0.994252i	$0.465855\pi$
$102$		0			0
$103$	805.483			0.770549			0.385275	−	0.922802i	$-0.374107\pi$
$103$	805.483			0.770549			0.385275	+	0.922802i	$0.374107\pi$
$104$	−499.065	−	499.065i	−0.470552	−	0.470552i
$105$		0			0
$106$			704.042i			0.645119i
$107$	2.07578	+	5.01138i	0.00187545	+	0.00452774i	0.924814	−	0.380418i	$-0.124220\pi$
$107$	2.07578	+	5.01138i	0.00187545	+	0.00452774i	−0.922939	+	0.384946i	$0.874220\pi$
$108$		0			0
$109$	449.732	−	1085.75i	0.395197	−	0.954091i	−0.593591	−	0.804767i	$-0.702290\pi$
$109$	449.732	−	1085.75i	0.395197	−	0.954091i	0.988788	−	0.149324i	$-0.0477097\pi$
$110$	−82.0953	+	82.0953i	−0.0711589	+	0.0711589i
$111$		0			0
$112$	2448.42	−	5911.01i	2.06566	−	4.98695i
$113$	326.051	+	135.055i	0.271436	+	0.112433i	0.514250	−	0.857640i	$-0.328070\pi$
$113$	326.051	+	135.055i	0.271436	+	0.112433i	−0.242814	+	0.970073i	$0.578070\pi$
$114$		0			0
$115$			155.666i			0.126226i
$116$	1354.52	−	561.059i	1.08417	−	0.449078i
$117$		0			0
$118$	−1201.53			−0.937374
$119$	−1103.09	+	1893.32i	−0.849747	+	1.45849i
$120$		0			0
$121$	−938.896	−	938.896i	−0.705407	−	0.705407i
$122$	−1384.73	+	573.575i	−1.02760	+	0.425648i
$123$		0			0
$124$	1687.46	+	4073.88i	1.22208	+	2.95036i
$125$	−1161.81	−	481.238i	−0.831324	−	0.344346i
$126$		0			0
$127$	918.768	−	918.768i	0.641949	−	0.641949i	−0.309086	−	0.951034i	$-0.600023\pi$
$127$	918.768	−	918.768i	0.641949	−	0.641949i	0.951034	+	0.309086i	$0.100023\pi$
$128$	1843.02	−	1843.02i	1.27267	−	1.27267i
$129$		0			0
$130$	611.858	+	253.440i	0.412796	+	0.170986i
$131$	−711.455	−	1717.60i	−0.474505	−	1.14556i	−0.962152	−	0.272515i	$-0.912145\pi$
$131$	−711.455	−	1717.60i	−0.474505	−	1.14556i	0.487647	−	0.873041i	$-0.337855\pi$
$132$		0			0
$133$	−2994.82	+	1240.49i	−1.95251	+	0.808755i
$134$	−1157.88	−	1157.88i	−0.746460	−	0.746460i
$135$		0			0
$136$	−3857.69	+	2936.02i	−2.43231	+	1.85119i
$137$	2263.97			1.41186			0.705928	−	0.708284i	$-0.250530\pi$
$137$	2263.97			1.41186			0.705928	+	0.708284i	$0.250530\pi$
$138$		0			0
$139$	1713.19	−	709.625i	1.04540	−	0.433019i	0.207152	−	0.978309i	$-0.433580\pi$
$139$	1713.19	−	709.625i	1.04540	−	0.433019i	0.838248	+	0.545290i	$0.183580\pi$
$140$			7880.97i			4.75760i
$141$		0			0
$142$	−2779.30	−	1151.22i	−1.64249	−	0.680343i
$143$	6.98594	−	16.8655i	0.00408527	−	0.00986271i
$144$		0			0
$145$	−599.925	+	599.925i	−0.343594	+	0.343594i
$146$	383.015	−	924.681i	0.217114	−	0.524159i
$147$		0			0
$148$	989.444	+	2388.73i	0.549539	+	1.32671i
$149$			159.296i			0.0875843i	0.999041	+	0.0437922i	$0.0139439\pi$
$149$			159.296i			0.0875843i	−0.999041	+	0.0437922i	$0.986056\pi$
$150$		0			0
$151$	−2103.98	−	2103.98i	−1.13391	−	1.13391i	−0.989522	−	0.144384i	$-0.953880\pi$
$151$	−2103.98	−	2103.98i	−1.13391	−	1.13391i	−0.144384	−	0.989522i	$-0.546120\pi$
$152$	−7171.66			−3.82696
$153$		0			0
$154$	300.499			0.157240
$155$	−1804.35	−	1804.35i	−0.935025	−	0.935025i
$156$		0			0
$157$			3909.68i			1.98743i	0.111945	+	0.993714i	$0.464292\pi$
$157$			3909.68i			1.98743i	−0.111945	+	0.993714i	$0.535708\pi$
$158$	2660.17	+	6422.22i	1.33944	+	3.23370i
$159$		0			0
$160$	−2525.44	+	6096.96i	−1.24784	+	3.01254i
$161$	284.898	−	284.898i	0.139460	−	0.139460i
$162$		0			0
$163$	701.015	−	1692.40i	0.336857	−	0.813245i	−0.661156	−	0.750248i	$-0.729934\pi$
$163$	701.015	−	1692.40i	0.336857	−	0.813245i	0.998014	−	0.0629972i	$-0.0200659\pi$
$164$	6685.50	+	2769.22i	3.18323	+	1.31854i
$165$		0			0
$166$		−	4158.98i		−	1.94457i
$167$	30.2138	−	12.5150i	0.0140001	−	0.00579902i	−0.375672	−	0.926753i	$-0.622588\pi$
$167$	30.2138	−	12.5150i	0.0140001	−	0.00579902i	0.389672	+	0.920954i	$0.372588\pi$
$168$		0			0
$169$	2092.87			0.952602
$170$	2290.01	−	3930.54i	1.03315	−	1.77329i
$171$		0			0
$172$	−1299.89	−	1299.89i	−0.576254	−	0.576254i
$173$	−958.129	+	396.870i	−0.421070	+	0.174413i	−0.583150	−	0.812365i	$-0.698180\pi$
$173$	−958.129	+	396.870i	−0.421070	+	0.174413i	0.162079	+	0.986778i	$0.448180\pi$
$174$		0			0
$175$	−249.848	−	603.187i	−0.107924	−	0.260552i
$176$	338.251	+	140.108i	0.144867	+	0.0600059i
$177$		0			0
$178$	133.712	−	133.712i	0.0563043	−	0.0563043i
$179$	−1142.50	+	1142.50i	−0.477064	+	0.477064i	−0.904191	−	0.427128i	$-0.859526\pi$
$179$	−1142.50	+	1142.50i	−0.477064	+	0.477064i	0.427128	+	0.904191i	$0.359526\pi$
$180$		0			0
$181$	−1635.33	−	677.375i	−0.671563	−	0.278171i	0.0207319	−	0.999785i	$-0.493400\pi$
$181$	−1635.33	−	677.375i	−0.671563	−	0.278171i	−0.692295	+	0.721615i	$0.743400\pi$
$182$	−655.971	−	1583.66i	−0.267164	−	0.644991i
$183$		0			0
$184$	823.539	−	341.121i	0.329957	−	0.136673i
$185$	−1057.99	−	1057.99i	−0.420458	−	0.420458i
$186$		0			0
$187$	−108.343	−	63.1229i	−0.0423682	−	0.0246845i
$188$	−11974.9			−4.64553
$189$		0			0
$190$	6217.25	−	2575.27i	2.37393	−	0.983313i
$191$		−	3969.45i		−	1.50377i	−0.659296	−	0.751883i	$-0.729146\pi$
$191$		−	3969.45i		−	1.50377i	0.659296	−	0.751883i	$-0.270854\pi$
$192$		0			0
$193$	305.738	+	126.641i	0.114028	+	0.0472321i	0.438968	−	0.898503i	$-0.355344\pi$
$193$	305.738	+	126.641i	0.114028	+	0.0472321i	−0.324940	+	0.945735i	$0.605344\pi$
$194$	1732.74	−	4183.21i	0.641255	−	1.54813i
$195$		0			0
$196$	9361.42	−	9361.42i	3.41159	−	3.41159i
$197$	−850.106	+	2052.34i	−0.307449	+	0.742248i	0.692337	+	0.721574i	$0.256581\pi$
$197$	−850.106	+	2052.34i	−0.307449	+	0.742248i	−0.999786	+	0.0206740i	$0.993419\pi$
$198$		0			0
$199$	576.145	+	1390.94i	0.205235	+	0.495482i	0.992661	−	0.120927i	$-0.0385867\pi$
$199$	576.145	+	1390.94i	0.205235	+	0.495482i	−0.787426	+	0.616409i	$0.788587\pi$
$200$		−	1444.44i		−	0.510688i
$201$		0			0
$202$	825.815	+	825.815i	0.287644	+	0.287644i
$203$	2195.95			0.759238
$204$		0			0
$205$	−4187.57			−1.42669
$206$	3060.40	+	3060.40i	1.03509	+	1.03509i
$207$		0			0
$208$		−	2088.46i		−	0.696195i
$209$	−70.9858	−	171.375i	−0.0234938	−	0.0567189i
$210$		0			0
$211$	−1506.35	+	3636.65i	−0.491475	+	1.18653i	0.462494	+	0.886622i	$0.346955\pi$
$211$	−1506.35	+	3636.65i	−0.491475	+	1.18653i	−0.953969	+	0.299904i	$0.903045\pi$
$212$	−1933.78	+	1933.78i	−0.626475	+	0.626475i
$213$		0			0
$214$	−11.1537	+	26.9274i	−0.00356286	+	0.00860150i
$215$	982.833	+	407.103i	0.311761	+	0.129136i
$216$		0			0
$217$			6604.59i			2.06612i
$218$	5834.01	−	2416.52i	1.81252	−	0.750769i
$219$		0			0
$220$	−450.980			−0.138205
$221$	−96.1562	+	708.772i	−0.0292677	+	0.215734i
$222$		0			0
$223$	2595.93	+	2595.93i	0.779536	+	0.779536i	0.979752	−	0.200216i	$-0.0641643\pi$
$223$	2595.93	+	2595.93i	0.779536	+	0.779536i	−0.200216	+	0.979752i	$0.564164\pi$
$224$	15780.6	−	6536.53i	4.70707	−	1.94973i
$225$		0			0
$226$	725.683	+	1751.95i	0.213592	+	0.515656i
$227$	−409.359	−	169.562i	−0.119692	−	0.0495781i	0.322034	−	0.946728i	$-0.395634\pi$
$227$	−409.359	−	169.562i	−0.119692	−	0.0495781i	−0.441726	+	0.897150i	$0.645634\pi$
$228$		0			0
$229$	457.635	−	457.635i	0.132058	−	0.132058i	−0.637988	−	0.770046i	$-0.720233\pi$
$229$	457.635	−	457.635i	0.132058	−	0.132058i	0.770046	+	0.637988i	$0.220233\pi$
$230$	−591.448	+	591.448i	−0.169561	+	0.169561i
$231$		0			0
$232$	4488.51	+	1859.20i	1.27019	+	0.526131i
$233$	84.0334	+	202.875i	0.0236275	+	0.0570419i	0.935253	−	0.353980i	$-0.115172\pi$
$233$	84.0334	+	202.875i	0.0236275	+	0.0570419i	−0.911625	+	0.411022i	$0.865172\pi$
$234$		0			0
$235$	6402.23	−	2651.89i	1.77717	−	0.736128i
$236$	−3300.23	−	3300.23i	−0.910284	−	0.910284i
$237$		0			0
$238$	−11384.8	+	3002.48i	−3.10069	+	0.817738i
$239$	5907.10			1.59874			0.799370	−	0.600840i	$-0.205167\pi$
$239$	5907.10			1.59874			0.799370	+	0.600840i	$0.205167\pi$
$240$		0			0
$241$	2766.01	−	1145.72i	0.739312	−	0.306233i	0.0189395	−	0.999821i	$-0.493971\pi$
$241$	2766.01	−	1145.72i	0.739312	−	0.306233i	0.720372	+	0.693588i	$0.243971\pi$
$242$		−	7134.61i		−	1.89516i
$243$		0			0
$244$	−5378.85	−	2227.99i	−1.41125	−	0.584560i
$245$	−2931.83	+	7078.08i	−0.764523	+	1.84572i
$246$		0			0
$247$	−748.203	+	748.203i	−0.192741	+	0.192741i
$248$	−5591.78	+	13499.7i	−1.43177	+	3.45659i
$249$		0			0
$250$	−2585.81	−	6242.71i	−0.654165	−	1.57929i
$251$			496.659i			0.124896i	0.998048	+	0.0624479i	$0.0198907\pi$
$251$			496.659i			0.124896i	−0.998048	+	0.0624479i	$0.980109\pi$
$252$		0			0
$253$	16.3030	+	16.3030i	0.00405122	+	0.00405122i
$254$	6981.65			1.72468
$255$		0			0
$256$	3616.56			0.882949
$257$	−212.203	−	212.203i	−0.0515052	−	0.0515052i	0.680885	−	0.732390i	$-0.261595\pi$
$257$	−212.203	−	212.203i	−0.0515052	−	0.0515052i	−0.732390	+	0.680885i	$0.761595\pi$
$258$		0			0
$259$			3872.62i			0.929084i
$260$	984.462	+	2376.70i	0.234822	+	0.566911i
$261$		0			0
$262$	3822.83	−	9229.12i	0.901432	−	2.17625i
$263$	2190.44	−	2190.44i	0.513568	−	0.513568i	−0.402050	−	0.915618i	$-0.631702\pi$
$263$	2190.44	−	2190.44i	0.513568	−	0.513568i	0.915618	+	0.402050i	$0.131702\pi$
$264$		0			0
$265$	605.627	−	1462.11i	0.140390	−	0.338932i
$266$	−16091.9	−	6665.49i	−3.70924	−	1.53642i
$267$		0			0
$268$		−	6360.67i		−	1.44977i
$269$	1789.74	−	741.334i	0.405659	−	0.168030i	−0.170518	−	0.985355i	$-0.554544\pi$
$269$	1789.74	−	741.334i	0.405659	−	0.168030i	0.576177	+	0.817325i	$0.304544\pi$
$270$		0			0
$271$	4708.60			1.05545			0.527725	−	0.849415i	$-0.323045\pi$
$271$	4708.60			1.05545			0.527725	+	0.849415i	$0.323045\pi$
$272$	−14215.0	−	1928.48i	−3.16878	−	0.429895i
$273$		0			0
$274$	8601.88	+	8601.88i	1.89656	+	1.89656i
$275$	34.5167	−	14.2973i	0.00756885	−	0.00313512i
$276$		0			0
$277$	−2718.84	−	6563.85i	−0.589744	−	1.42377i	−0.883748	−	0.467964i	$-0.844988\pi$
$277$	−2718.84	−	6563.85i	−0.589744	−	1.42377i	0.294004	−	0.955804i	$-0.405012\pi$
$278$	9205.39	+	3813.00i	1.98598	+	0.822620i
$279$		0			0
$280$	−18466.4	+	18466.4i	−3.94135	+	3.94135i
$281$	2138.46	−	2138.46i	0.453985	−	0.453985i	−0.442690	−	0.896675i	$-0.645976\pi$
$281$	2138.46	−	2138.46i	0.453985	−	0.453985i	0.896675	+	0.442690i	$0.145976\pi$
$282$		0			0
$283$	−6811.77	−	2821.53i	−1.43080	−	0.592658i	−0.473254	−	0.880926i	$-0.656921\pi$
$283$	−6811.77	−	2821.53i	−1.43080	−	0.592658i	−0.957550	+	0.288267i	$0.906921\pi$
$284$	−4471.82	−	10795.9i	−0.934343	−	2.25570i
$285$		0			0
$286$	90.6229	−	37.5372i	0.0187365	−	0.00776092i
$287$	7664.01	+	7664.01i	1.57628	+	1.57628i
$288$		0			0
$289$	4735.42	+	1308.96i	0.963855	+	0.266428i
$290$	−4558.79			−0.923108
$291$		0			0
$292$	3591.83	−	1487.78i	0.719849	−	0.298171i
$293$			8058.39i			1.60675i	0.595477	+	0.803373i	$0.296963\pi$
$293$			8058.39i			1.60675i	−0.595477	+	0.803373i	$0.703037\pi$
$294$		0			0
$295$	2495.27	+	1033.58i	0.492476	+	0.203990i
$296$	−3278.75	+	7915.61i	−0.643830	+	1.55434i
$297$		0			0
$298$	−605.241	+	605.241i	−0.117653	+	0.117653i
$299$	50.3296	−	121.506i	0.00973457	−	0.0235013i
$300$		0			0
$301$	−1053.69	−	2543.84i	−0.201774	−	0.487124i
$302$		−	15988.0i		−	3.04638i
$303$		0			0
$304$	−15005.8	−	15005.8i	−2.83105	−	2.83105i
$305$	3369.13			0.632511
$306$		0			0
$307$	726.313			0.135026			0.0675128	−	0.997718i	$-0.478494\pi$
$307$	726.313			0.135026			0.0675128	+	0.997718i	$0.478494\pi$
$308$	825.376	+	825.376i	0.152695	+	0.152695i
$309$		0			0
$310$		−	13711.1i		−	2.51206i
$311$	2929.36	+	7072.10i	0.534112	+	1.28946i	0.928778	+	0.370635i	$0.120860\pi$
$311$	2929.36	+	7072.10i	0.534112	+	1.28946i	−0.394667	+	0.918824i	$0.629140\pi$
$312$		0			0
$313$	−2412.82	+	5825.07i	−0.435722	+	1.05193i	0.541690	+	0.840579i	$0.317785\pi$
$313$	−2412.82	+	5825.07i	−0.435722	+	1.05193i	−0.977411	+	0.211347i	$0.932215\pi$
$314$	−14854.7	+	14854.7i	−2.66974	+	2.66974i
$315$		0			0
$316$	−10333.2	+	24946.5i	−1.83951	+	4.44097i
$317$	−1300.28	−	538.592i	−0.230381	−	0.0954269i	0.264507	−	0.964384i	$-0.414791\pi$
$317$	−1300.28	−	538.592i	−0.230381	−	0.0954269i	−0.494888	+	0.868957i	$0.664791\pi$
$318$		0			0
$319$			125.661i			0.0220553i
$320$	−14490.4	+	6002.10i	−2.53136	+	1.04852i
$321$		0			0
$322$	2164.92			0.374678
$323$	4401.70	+	5783.48i	0.758258	+	0.996290i
$324$		0			0
$325$	−150.696	−	150.696i	−0.0257203	−	0.0257203i
$326$	9093.69	−	3766.73i	1.54495	−	0.639938i
$327$		0			0
$328$	9176.47	+	22154.0i	1.54477	+	3.72941i
$329$	−16570.7	−	6863.81i	−2.77681	−	1.15019i
$330$		0			0
$331$	918.583	−	918.583i	0.152537	−	0.152537i	−0.626713	−	0.779250i	$-0.715600\pi$
$331$	918.583	−	918.583i	0.152537	−	0.152537i	0.779250	+	0.626713i	$0.215600\pi$
$332$	11423.4	−	11423.4i	1.88837	−	1.88837i
$333$		0			0
$334$	162.346	+	67.2460i	0.0265964	+	0.0110166i
$335$	1408.59	+	3400.64i	0.229730	+	0.554618i
$336$		0			0
$337$	−6734.89	+	2789.68i	−1.08864	+	0.450931i	−0.853534	−	0.521038i	$-0.825545\pi$
$337$	−6734.89	+	2789.68i	−1.08864	+	0.450931i	−0.235110	+	0.971969i	$0.575545\pi$
$338$	7951.77	+	7951.77i	1.27964	+	1.27964i
$339$		0			0
$340$	17085.9	−	4506.02i	2.72533	−	0.718746i
$341$	−377.940			−0.0600194
$342$		0			0
$343$	8413.40	−	3484.94i	1.32443	−	0.548599i
$344$		−	6091.71i		−	0.954775i
$345$		0			0
$346$	−5148.27	−	2132.48i	−0.799921	−	0.331338i
$347$	−1607.98	+	3882.02i	−0.248764	+	0.600570i	−0.998100	−	0.0616209i	$-0.980373\pi$
$347$	−1607.98	+	3882.02i	−0.248764	+	0.600570i	0.749336	+	0.662190i	$0.230373\pi$
$348$		0			0
$349$	−2168.42	+	2168.42i	−0.332587	+	0.332587i	−0.853568	−	0.520981i	$-0.825566\pi$
$349$	−2168.42	+	2168.42i	−0.332587	+	0.332587i	0.520981	+	0.853568i	$0.325566\pi$
$350$	1342.50	−	3241.07i	0.205027	−	0.494979i
$351$		0			0
$352$	374.045	+	903.026i	0.0566383	+	0.136737i
$353$		−	3349.30i		−	0.505000i	−0.967597	−	0.252500i	$-0.918747\pi$
$353$		−	3349.30i		−	0.505000i	0.967597	−	0.252500i	$-0.0812528\pi$
$354$		0			0
$355$	4781.59	+	4781.59i	0.714875	+	0.714875i
$356$	734.531			0.109354
$357$		0			0
$358$	−8681.77			−1.28169
$359$	−6531.15	−	6531.15i	−0.960170	−	0.960170i	0.0390667	−	0.999237i	$-0.487562\pi$
$359$	−6531.15	−	6531.15i	−0.960170	−	0.960170i	−0.999237	+	0.0390667i	$0.987562\pi$
$360$		0			0
$361$			3892.81i			0.567548i
$362$	−3639.71	−	8787.03i	−0.528450	−	1.27579i
$363$		0			0
$364$	2548.05	−	6151.55i	0.366908	−	0.885793i
$365$	−1590.85	+	1590.85i	−0.228134	+	0.228134i
$366$		0			0
$367$	−956.804	+	2309.93i	−0.136089	+	0.328549i	−0.977202	−	0.212311i	$-0.931901\pi$
$367$	−956.804	+	2309.93i	−0.136089	+	0.328549i	0.841113	+	0.540860i	$0.181901\pi$
$368$	2436.90	+	1009.40i	0.345196	+	0.142985i
$369$		0			0
$370$		−	8039.56i		−	1.12961i
$371$	−3784.35	+	1567.53i	−0.529578	+	0.219358i
$372$		0			0
$373$	−6885.53			−0.955816			−0.477908	−	0.878410i	$-0.658605\pi$
$373$	−6885.53			−0.955816			−0.477908	+	0.878410i	$0.658605\pi$
$374$	−171.813	−	651.480i	−0.0237547	−	0.0900728i
$375$		0			0
$376$	−28059.2	−	28059.2i	−3.84851	−	3.84851i
$377$	662.242	−	274.310i	0.0904701	−	0.0374739i
$378$		0			0
$379$	−2871.64	−	6932.75i	−0.389198	−	0.939608i	−0.990110	−	0.140293i	$-0.955196\pi$
$379$	−2871.64	−	6932.75i	−0.389198	−	0.939608i	0.600912	−	0.799315i	$-0.294804\pi$
$380$	24150.3	+	10003.4i	3.26022	+	1.35043i
$381$		0			0
$382$	15081.8	−	15081.8i	2.02003	−	2.02003i
$383$	6890.93	−	6890.93i	0.919348	−	0.919348i	−0.0776340	−	0.996982i	$-0.524737\pi$
$383$	6890.93	−	6890.93i	0.919348	−	0.919348i	0.996982	+	0.0776340i	$0.0247366\pi$
$384$		0			0
$385$	−624.058	−	258.493i	−0.0826103	−	0.0342183i
$386$	680.472	+	1642.81i	0.0897283	+	0.216623i
$387$		0			0
$388$	16249.2	−	6730.65i	2.12611	−	0.880663i
$389$	−8709.15	−	8709.15i	−1.13515	−	1.13515i	−0.989309	−	0.145837i	$-0.953413\pi$
$389$	−8709.15	−	8709.15i	−1.13515	−	1.13515i	−0.145837	−	0.989309i	$-0.546587\pi$
$390$		0			0
$391$	−780.550	−	454.764i	−0.100957	−	0.0588194i
$392$	43870.7			5.65256
$393$		0			0
$394$	−11027.7	+	4567.83i	−1.41007	+	0.584071i
$395$		−	15625.6i		−	1.99040i
$396$		0			0
$397$	11254.7	+	4661.86i	1.42282	+	0.589351i	0.955567	−	0.294774i	$-0.0952444\pi$
$397$	11254.7	+	4661.86i	1.42282	+	0.589351i	0.467251	+	0.884125i	$0.345244\pi$
$398$	−3095.77	+	7473.86i	−0.389892	+	0.941283i
$399$		0			0
$400$	3022.31	−	3022.31i	0.377789	−	0.377789i
$401$	2293.09	−	5536.01i	0.285565	−	0.689415i	−0.714382	−	0.699756i	$-0.753292\pi$
$401$	2293.09	−	5536.01i	0.285565	−	0.689415i	0.999947	+	0.0103417i	$0.00329194\pi$
$402$		0			0
$403$	825.021	+	1991.78i	0.101978	+	0.246197i
$404$			4536.51i			0.558663i
$405$		0			0
$406$	8343.43	+	8343.43i	1.01989	+	1.01989i
$407$	−221.606			−0.0269892
$408$		0			0
$409$	−10892.4			−1.31686			−0.658431	−	0.752641i	$-0.728780\pi$
$409$	−10892.4			−1.31686			−0.658431	+	0.752641i	$0.728780\pi$
$410$	−15910.5	−	15910.5i	−1.91650	−	1.91650i
$411$		0			0
$412$			16811.9i			2.01035i
$413$	−2675.18	−	6458.45i	−0.318733	−	0.769490i
$414$		0			0
$415$	−3577.61	+	8637.12i	−0.423176	+	1.02164i
$416$	3942.50	−	3942.50i	0.464657	−	0.464657i
$417$		0			0
$418$	381.425	−	920.841i	0.0446318	−	0.107751i
$419$	3703.73	+	1534.13i	0.431835	+	0.178872i	0.588003	−	0.808859i	$-0.299914\pi$
$419$	3703.73	+	1534.13i	0.431835	+	0.178872i	−0.156168	+	0.987730i	$0.549914\pi$
$420$		0			0
$421$		−	7417.88i		−	0.858730i	−0.903131	−	0.429365i	$-0.858737\pi$
$421$		−	7417.88i		−	0.858730i	0.903131	−	0.429365i	$-0.141263\pi$
$422$	−19540.6	+	8093.99i	−2.25408	+	0.933671i
$423$		0			0
$424$	−9062.33			−1.03799
$425$	−1164.85	+	886.547i	−0.132950	+	0.101186i
$426$		0			0
$427$	−6166.12	−	6166.12i	−0.698828	−	0.698828i
$428$	−104.597	+	43.3254i	−0.0118128	+	0.00489302i
$429$		0			0
$430$	2187.47	+	5281.01i	0.245323	+	0.592263i
$431$	−3268.31	−	1353.78i	−0.365264	−	0.151297i	0.192500	−	0.981297i	$-0.438341\pi$
$431$	−3268.31	−	1353.78i	−0.365264	−	0.151297i	−0.557764	+	0.830000i	$0.688341\pi$
$432$		0			0
$433$	4020.07	−	4020.07i	0.446171	−	0.446171i	−0.447908	−	0.894080i	$-0.647831\pi$
$433$	4020.07	−	4020.07i	0.446171	−	0.446171i	0.894080	+	0.447908i	$0.147831\pi$
$434$	−25093.9	+	25093.9i	−2.77545	+	2.77545i
$435$		0			0
$436$	22661.6	+	9386.74i	2.48921	+	1.03106i
$437$	−511.411	−	1234.66i	−0.0559820	−	0.135152i
$438$		0			0
$439$	5772.10	−	2390.88i	0.627534	−	0.259933i	−0.0461710	−	0.998934i	$-0.514702\pi$
$439$	5772.10	−	2390.88i	0.627534	−	0.259933i	0.673705	+	0.739001i	$0.264702\pi$
$440$	−1056.72	−	1056.72i	−0.114493	−	0.114493i
$441$		0			0
$442$	−3058.30	+	2327.61i	−0.329114	+	0.250483i
$443$	−9234.56			−0.990400			−0.495200	−	0.868779i	$-0.664905\pi$
$443$	−9234.56			−0.990400			−0.495200	+	0.868779i	$0.664905\pi$
$444$		0			0
$445$	−392.707	+	162.665i	−0.0418339	+	0.0173282i
$446$			19726.3i			2.09432i
$447$		0			0
$448$	37505.0	+	15535.1i	3.95523	+	1.63831i
$449$	−917.097	+	2214.07i	−0.0963931	+	0.232713i	−0.964720	−	0.263280i	$-0.915196\pi$
$449$	−917.097	+	2214.07i	−0.0963931	+	0.232713i	0.868327	+	0.495993i	$0.165196\pi$
$450$		0			0
$451$	−438.564	+	438.564i	−0.0457898	+	0.0457898i
$452$	−2818.84	+	6805.29i	−0.293335	+	0.708172i
$453$		0			0
$454$	−911.100	−	2199.59i	−0.0941851	−	0.227383i
$455$			3853.12i			0.397004i
$456$		0			0
$457$	3365.78	+	3365.78i	0.344518	+	0.344518i	0.858063	−	0.513545i	$-0.171668\pi$
$457$	3365.78	+	3365.78i	0.344518	+	0.344518i	−0.513545	+	0.858063i	$0.671668\pi$
$458$	3477.54			0.354792
$459$		0			0
$460$	−3249.04			−0.329321
$461$	13656.2	+	13656.2i	1.37968	+	1.37968i	0.845154	+	0.534523i	$0.179509\pi$
$461$	13656.2	+	13656.2i	1.37968	+	1.37968i	0.534523	+	0.845154i	$0.320491\pi$
$462$		0			0
$463$			6618.40i			0.664326i	0.943222	+	0.332163i	$0.107778\pi$
$463$			6618.40i			0.664326i	−0.943222	+	0.332163i	$0.892222\pi$
$464$	5501.48	+	13281.8i	0.550431	+	1.32886i
$465$		0			0
$466$	−451.533	+	1090.10i	−0.0448859	+	0.108364i
$467$	10395.5	−	10395.5i	1.03008	−	1.03008i	0.0305483	−	0.999533i	$-0.490275\pi$
$467$	10395.5	−	10395.5i	1.03008	−	1.03008i	0.999533	−	0.0305483i	$-0.00972534\pi$
$468$		0			0
$469$	3645.82	−	8801.79i	0.358952	−	0.866586i
$470$	34400.8	+	14249.3i	3.37615	+	1.39845i
$471$		0			0
$472$		−	15466.0i		−	1.50822i
$473$	145.568	−	60.2964i	0.0141506	−	0.00586137i
$474$		0			0
$475$	−2165.52			−0.209181
$476$	−39517.2	−	23023.5i	−3.80518	−	2.21698i
$477$		0			0
$478$	22443.8	+	22443.8i	2.14761	+	2.14761i
$479$	−10915.0	+	4521.13i	−1.04117	+	0.431265i	−0.836730	−	0.547615i	$-0.815536\pi$
$479$	−10915.0	+	4521.13i	−1.04117	+	0.431265i	−0.204435	+	0.978880i	$0.565536\pi$
$480$		0			0
$481$	483.753	+	1167.88i	0.0458571	+	0.110709i
$482$	14862.5	+	6156.23i	1.40449	+	0.581761i
$483$		0			0
$484$	19596.5	−	19596.5i	1.84039	−	1.84039i
$485$	−7196.91	+	7196.91i	−0.673804	+	0.673804i
$486$		0			0
$487$	−6489.26	−	2687.94i	−0.603812	−	0.250107i	0.0597682	−	0.998212i	$-0.480964\pi$
$487$	−6489.26	−	2687.94i	−0.603812	−	0.250107i	−0.663580	+	0.748105i	$0.730964\pi$
$488$	−7382.98	−	17824.1i	−0.684860	−	1.65340i
$489$		0			0
$490$	−38032.3	+	15753.5i	−3.50638	+	1.45239i
$491$	9843.17	+	9843.17i	0.904717	+	0.904717i	0.995840	−	0.0911225i	$-0.0290455\pi$
$491$	9843.17	+	9843.17i	0.904717	+	0.904717i	−0.0911225	+	0.995840i	$0.529045\pi$
$492$		0			0
$493$	−1255.56	−	4760.80i	−0.114701	−	0.434921i
$494$	−5685.54			−0.517823
$495$		0			0
$496$	−39946.5	+	16546.4i	−3.61624	+	1.49789i
$497$		−	17502.4i		−	1.57966i
$498$		0			0
$499$	−16520.2	−	6842.89i	−1.48206	−	0.613887i	−0.512484	−	0.858697i	$-0.671275\pi$
$499$	−16520.2	−	6842.89i	−1.48206	−	0.613887i	−0.969571	+	0.244810i	$0.921275\pi$
$500$	10044.3	−	24249.2i	0.898392	−	2.16891i
$501$		0			0
$502$	−1887.04	+	1887.04i	−0.167774	+	0.167774i
$503$	−606.562	+	1464.37i	−0.0537679	+	0.129807i	−0.948481	−	0.316834i	$-0.897380\pi$
$503$	−606.562	+	1464.37i	−0.0537679	+	0.129807i	0.894713	+	0.446642i	$0.147380\pi$
$504$		0			0
$505$	−1004.63	−	2425.38i	−0.0885253	−	0.213719i
$506$			123.885i			0.0108841i
$507$		0			0
$508$	19176.4	+	19176.4i	1.67483	+	1.67483i
$509$	−20663.8			−1.79943			−0.899713	−	0.436482i	$-0.856224\pi$
$509$	−20663.8			−1.79943			−0.899713	+	0.436482i	$0.856224\pi$
$510$		0			0
$511$	5823.09			0.504106
$512$	−1003.17	−	1003.17i	−0.0865901	−	0.0865901i
$513$		0			0
$514$		−	1612.51i		−	0.138375i
$515$	−3723.06	−	8988.27i	−0.318559	−	0.769069i
$516$		0			0
$517$	392.773	−	948.239i	0.0334123	−	0.0806644i
$518$	−14713.9	+	14713.9i	−1.24805	+	1.24805i
$519$		0			0
$520$	−3262.24	+	7875.76i	−0.275113	+	0.664182i
$521$	4720.05	+	1955.11i	0.396908	+	0.164405i	0.572204	−	0.820111i	$-0.306088\pi$
$521$	4720.05	+	1955.11i	0.396908	+	0.164405i	−0.175296	+	0.984516i	$0.556088\pi$
$522$		0			0
$523$		−	19709.6i		−	1.64788i	−0.566679	−	0.823938i	$-0.691772\pi$
$523$		−	19709.6i		−	1.64788i	0.566679	−	0.823938i	$-0.308228\pi$
$524$	35849.6	−	14849.4i	2.98873	−	1.23797i
$525$		0			0
$526$	16645.0			1.37977
$527$	14318.7	−	3776.24i	1.18355	−	0.312136i
$528$		0			0
$529$	−8485.91	−	8485.91i	−0.697453	−	0.697453i
$530$	7856.31	−	3254.19i	0.643880	−	0.266704i
$531$		0			0
$532$	−25891.4	−	62507.4i	−2.11003	−	5.09406i
$533$	3268.63	+	1353.91i	0.265629	+	0.110027i
$534$		0			0
$535$	46.3267	−	46.3267i	0.00374370	−	0.00374370i
$536$	14904.1	−	14904.1i	1.20104	−	1.20104i
$537$		0			0
$538$	9616.72	+	3983.38i	0.770644	+	0.319211i
$539$	434.237	+	1048.34i	0.0347011	+	0.0837759i
$540$		0			0
$541$	4756.67	−	1970.28i	0.378013	−	0.156578i	−0.185583	−	0.982629i	$-0.559417\pi$
$541$	4756.67	−	1970.28i	0.378013	−	0.156578i	0.563596	+	0.826050i	$0.309417\pi$
$542$	17890.1	+	17890.1i	1.41780	+	1.41780i
$543$		0			0
$544$	−23193.9	−	30474.9i	−1.82799	−	2.40184i
$545$	−14194.5			−1.11564
$546$		0			0
$547$	8574.26	−	3551.57i	0.670217	−	0.277613i	−0.0215135	−	0.999769i	$-0.506848\pi$
$547$	8574.26	−	3551.57i	0.670217	−	0.277613i	0.691731	+	0.722155i	$0.256848\pi$
$548$			47253.3i			3.68351i
$549$		0			0
$550$	185.467	+	76.8229i	0.0143788	+	0.00595589i
$551$	2787.33	−	6729.21i	0.215507	−	0.520279i
$552$		0			0
$553$	−28597.7	+	28597.7i	−2.19909	+	2.19909i
$554$	14609.0	−	35269.3i	1.12036	−	2.70478i
$555$		0			0
$556$	14811.2	+	35757.4i	1.12974	+	2.72743i
$557$			6892.53i			0.524319i	0.965025	+	0.262159i	$0.0844347\pi$
$557$			6892.53i			0.524319i	−0.965025	+	0.262159i	$0.915565\pi$
$558$		0			0
$559$	−635.534	−	635.534i	−0.0480863	−	0.0480863i
$560$	−77277.1			−5.83135
$561$		0			0
$562$	16250.0			1.21969
$563$	1892.65	+	1892.65i	0.141680	+	0.141680i	0.774389	−	0.632709i	$-0.218057\pi$
$563$	1892.65	+	1892.65i	0.141680	+	0.141680i	−0.632709	+	0.774389i	$0.718057\pi$
$564$		0			0
$565$		−	4262.60i		−	0.317396i
$566$	−15160.8	−	36601.4i	−1.12589	−	2.71814i
$567$		0			0
$568$	14818.4	−	35774.8i	1.09466	−	2.64274i
$569$	3661.33	−	3661.33i	0.269756	−	0.269756i	−0.559246	−	0.829002i	$-0.688909\pi$
$569$	3661.33	−	3661.33i	0.269756	−	0.269756i	0.829002	+	0.559246i	$0.188909\pi$
$570$		0			0
$571$	4983.44	−	12031.1i	0.365237	−	0.881761i	−0.629279	−	0.777179i	$-0.716650\pi$
$571$	4983.44	−	12031.1i	0.365237	−	0.881761i	0.994516	−	0.104581i	$-0.0333503\pi$
$572$	352.015	+	145.810i	0.0257316	+	0.0106584i
$573$		0			0
$574$			58238.3i			4.23488i
$575$	248.672	−	103.003i	0.0180354	−	0.00747051i
$576$		0			0
$577$	5485.73			0.395795			0.197898	−	0.980223i	$-0.436589\pi$
$577$	5485.73			0.395795			0.197898	+	0.980223i	$0.436589\pi$
$578$	13018.7	+	22965.4i	0.936863	+	1.65266i
$579$		0			0
$580$	−12521.6	−	12521.6i	−0.896430	−	0.896430i
$581$	22355.2	−	9259.83i	1.59630	−	0.661209i
$582$		0			0
$583$	−89.7000	−	216.555i	−0.00637220	−	0.0153839i
$584$	11902.4	+	4930.12i	0.843362	+	0.349332i
$585$		0			0
$586$	−30617.6	+	30617.6i	−2.15836	+	2.15836i
$587$	−12590.9	+	12590.9i	−0.885315	+	0.885315i	−0.994069	−	0.108753i	$-0.965314\pi$
$587$	−12590.9	+	12590.9i	−0.885315	+	0.885315i	0.108753	+	0.994069i	$0.465314\pi$
$588$		0			0
$589$	20238.9	+	8383.24i	1.41584	+	0.586461i
$590$	5553.67	+	13407.7i	0.387527	+	0.935573i
$591$		0			0
$592$	−23422.8	+	9702.03i	−1.62613	+	0.673566i
$593$	−417.771	−	417.771i	−0.0289305	−	0.0289305i	0.692494	−	0.721424i	$-0.256512\pi$
$593$	−417.771	−	417.771i	−0.0289305	−	0.0289305i	−0.721424	+	0.692494i	$0.756512\pi$
$594$		0			0
$595$	26226.0	+	3557.97i	1.80699	+	0.245147i
$596$	−3324.81			−0.228506
$597$		0			0
$598$	652.885	−	270.434i	0.0446462	−	0.0184931i
$599$			20309.7i			1.38537i	0.721243	+	0.692683i	$0.243571\pi$
$599$			20309.7i			1.38537i	−0.721243	+	0.692683i	$0.756429\pi$
$600$		0			0
$601$	−21675.3	−	8978.19i	−1.47114	−	0.609364i	−0.504017	−	0.863693i	$-0.668145\pi$
$601$	−21675.3	−	8978.19i	−1.47114	−	0.609364i	−0.967118	+	0.254329i	$0.918145\pi$
$602$	5661.76	−	13668.7i	0.383316	−	0.925406i
$603$		0			0
$604$	43914.0	−	43914.0i	2.95834	−	2.95834i
$605$	−6137.29	+	14816.7i	−0.412424	+	0.995679i
$606$		0			0
$607$	226.222	+	546.148i	0.0151270	+	0.0365197i	0.931263	−	0.364349i	$-0.118708\pi$
$607$	226.222	+	546.148i	0.0151270	+	0.0365197i	−0.916136	+	0.400869i	$0.868708\pi$
$608$		−	56654.5i		−	3.77902i
$609$		0			0
$610$	12800.9	+	12800.9i	0.849660	+	0.849660i
$611$	−5854.70			−0.387653
$612$		0			0
$613$	20834.7			1.37277			0.686383	−	0.727241i	$-0.259198\pi$
$613$	20834.7			1.37277			0.686383	+	0.727241i	$0.259198\pi$
$614$	2759.60	+	2759.60i	0.181382	+	0.181382i
$615$		0			0
$616$			3867.98i			0.252996i
$617$	−1305.29	−	3151.24i	−0.0851684	−	0.205615i	0.875557	−	0.483114i	$-0.160494\pi$
$617$	−1305.29	−	3151.24i	−0.0851684	−	0.205615i	−0.960726	+	0.277499i	$0.910494\pi$
$618$		0			0
$619$	5112.48	−	12342.6i	0.331967	−	0.801440i	−0.666469	−	0.745533i	$-0.732195\pi$
$619$	5112.48	−	12342.6i	0.331967	−	0.801440i	0.998436	−	0.0559069i	$-0.0178050\pi$
$620$	37660.2	−	37660.2i	2.43947	−	2.43947i
$621$		0			0
$622$	−15740.2	+	38000.2i	−1.01467	+	2.44963i
$623$	1016.43	+	421.020i	0.0653652	+	0.0270751i
$624$		0			0
$625$			17799.4i			1.13916i
$626$	−31299.6	+	12964.7i	−1.99838	+	0.827755i
$627$		0			0
$628$	−81602.3			−5.18517
$629$	8395.82	−	2214.21i	0.532215	−	0.140360i
$630$		0			0
$631$	−1711.75	−	1711.75i	−0.107993	−	0.107993i	0.651045	−	0.759039i	$-0.274331\pi$
$631$	−1711.75	−	1711.75i	−0.107993	−	0.107993i	−0.759039	+	0.651045i	$0.774331\pi$
$632$	−82665.9	+	34241.3i	−5.20296	+	2.15514i
$633$		0			0
$634$	−2893.99	−	6986.71i	−0.181286	−	0.437662i
$635$	−14499.1	−	6005.72i	−0.906108	−	0.375322i
$636$		0			0
$637$	4576.93	−	4576.93i	0.284685	−	0.284685i
$638$	−477.443	+	477.443i	−0.0296272	+	0.0296272i
$639$		0			0
$640$	−29084.7	−	12047.3i	−1.79637	−	0.744079i
$641$	−738.568	−	1783.06i	−0.0455096	−	0.109870i	0.899490	−	0.436941i	$-0.143938\pi$
$641$	−738.568	−	1783.06i	−0.0455096	−	0.109870i	−0.945000	+	0.327071i	$0.893938\pi$
$642$		0			0
$643$	12138.4	−	5027.88i	0.744464	−	0.308367i	0.0219837	−	0.999758i	$-0.493002\pi$
$643$	12138.4	−	5027.88i	0.744464	−	0.308367i	0.722481	+	0.691391i	$0.243002\pi$
$644$	5946.35	+	5946.35i	0.363849	+	0.363849i
$645$		0			0
$646$	−5250.03	+	38698.2i	−0.319752	+	2.35691i
$647$	20951.6			1.27310			0.636549	−	0.771237i	$-0.280361\pi$
$647$	20951.6			1.27310			0.636549	+	0.771237i	$0.280361\pi$
$648$		0			0
$649$	369.577	−	153.084i	0.0223531	−	0.00925897i
$650$		−	1145.13i		−	0.0691008i
$651$		0			0
$652$	35323.5	+	14631.5i	2.12174	+	0.878855i
$653$	6116.19	−	14765.8i	0.366532	−	0.884886i	−0.627782	−	0.778390i	$-0.716037\pi$
$653$	6116.19	−	14765.8i	0.366532	−	0.884886i	0.994313	−	0.106496i	$-0.0339631\pi$
$654$		0			0
$655$	−15878.0	+	15878.0i	−0.947186	+	0.947186i
$656$	−27153.7	+	65554.8i	−1.61612	+	3.90166i
$657$		0			0
$658$	−36881.0	−	89038.6i	−2.18506	−	5.27520i
$659$		−	28685.6i		−	1.69565i	−0.530277	−	0.847825i	$-0.677912\pi$
$659$		−	28685.6i		−	1.69565i	0.530277	−	0.847825i	$-0.322088\pi$
$660$		0			0
$661$	−8359.02	−	8359.02i	−0.491874	−	0.491874i	0.417023	−	0.908896i	$-0.363074\pi$
$661$	−8359.02	−	8359.02i	−0.491874	−	0.491874i	−0.908896	+	0.417023i	$0.863074\pi$
$662$	6980.25			0.409811
$663$		0			0
$664$	53533.8			3.12879
$665$	27685.0	+	27685.0i	1.61440	+	1.61440i
$666$		0			0
$667$			905.311i			0.0525544i
$668$	261.210	+	630.617i	0.0151295	+	0.0365259i
$669$		0			0
$670$	−7568.73	+	18272.5i	−0.436426	+	1.05363i
$671$	352.849	−	352.849i	0.0203004	−	0.0203004i
$672$		0			0
$673$	−8493.22	+	20504.4i	−0.486463	+	1.17443i	0.470025	+	0.882653i	$0.344245\pi$
$673$	−8493.22	+	20504.4i	−0.486463	+	1.17443i	−0.956488	+	0.291772i	$0.905755\pi$
$674$	−36188.3	−	14989.7i	−2.06813	−	0.856648i
$675$		0			0
$676$			43682.0i			2.48532i
$677$	−1225.95	+	507.803i	−0.0695966	+	0.0288279i	−0.417210	−	0.908810i	$-0.636992\pi$
$677$	−1225.95	+	507.803i	−0.0695966	+	0.0288279i	0.347614	+	0.937638i	$0.386992\pi$
$678$		0			0
$679$	26343.3			1.48890
$680$	50593.4	+	29476.7i	2.85319	+	1.66232i
$681$		0			0
$682$	−1435.97	−	1435.97i	−0.0806248	−	0.0806248i
$683$	9607.17	−	3979.42i	0.538226	−	0.222940i	−0.0969760	−	0.995287i	$-0.530917\pi$
$683$	9607.17	−	3979.42i	0.538226	−	0.222940i	0.635202	+	0.772346i	$0.280917\pi$
$684$		0			0
$685$	−10464.4	−	25263.3i	−0.583686	−	1.40914i
$686$	45207.3	+	18725.5i	2.51607	+	1.04219i
$687$		0			0
$688$	12746.1	−	12746.1i	0.706309	−	0.706309i
$689$	−945.453	+	945.453i	−0.0522771	+	0.0522771i
$690$		0			0
$691$	17774.8	+	7362.56i	0.978560	+	0.405333i	0.813892	−	0.581016i	$-0.197345\pi$
$691$	17774.8	+	7362.56i	0.978560	+	0.405333i	0.164668	+	0.986349i	$0.447345\pi$
$692$	−8283.41	−	19997.9i	−0.455041	−	1.09857i
$693$		0			0
$694$	−20859.1	+	8640.11i	−1.14092	+	0.472585i
$695$	−15837.2	−	15837.2i	−0.864374	−	0.864374i
$696$		0			0
$697$	12233.6	−	20997.5i	0.664820	−	1.14109i
$698$	−16477.7			−0.893537
$699$		0			0
$700$	12589.6	−	5214.79i	0.679776	−	0.281572i
$701$			21509.8i			1.15894i	0.814994	+	0.579469i	$0.196740\pi$
$701$			21509.8i			1.15894i	−0.814994	+	0.579469i	$0.803260\pi$
$702$		0			0
$703$	11867.2	+	4915.54i	0.636669	+	0.263717i
$704$	−888.977	+	2146.18i	−0.0475917	+	0.114897i
$705$		0			0
$706$	12725.5	−	12725.5i	0.678374	−	0.678374i
$707$	−2600.25	+	6277.55i	−0.138320	+	0.333934i
$708$		0			0
$709$	−5891.43	−	14223.2i	−0.312070	−	0.753403i	−0.999628	−	0.0272737i	$-0.991317\pi$
$709$	−5891.43	−	14223.2i	−0.312070	−	0.753403i	0.687558	−	0.726129i	$-0.258683\pi$
$710$			36335.0i			1.92060i
$711$		0			0
$712$	1721.13	+	1721.13i	0.0905926	+	0.0905926i
$713$	−2722.84			−0.143017
$714$		0			0
$715$	−220.490			−0.0115327
$716$	−23846.1	−	23846.1i	−1.24465	−	1.24465i
$717$		0			0
$718$		−	49629.8i		−	2.57962i
$719$	9395.23	+	22682.1i	0.487320	+	1.17649i	0.956063	+	0.293160i	$0.0947068\pi$
$719$	9395.23	+	22682.1i	0.487320	+	1.17649i	−0.468744	+	0.883334i	$0.655293\pi$
$720$		0			0
$721$	−9636.30	+	23264.1i	−0.497745	+	1.20166i
$722$	−14790.6	+	14790.6i	−0.762395	+	0.762395i
$723$		0			0
$724$	14138.1	−	34132.3i	0.725742	−	1.75210i
$725$	1355.33	+	561.396i	0.0694286	+	0.0287583i
$726$		0			0
$727$		−	8805.07i		−	0.449191i	−0.974452	−	0.224595i	$-0.927894\pi$
$727$		−	8805.07i		−	0.449191i	0.974452	−	0.224595i	$-0.0721061\pi$
$728$	20384.6	−	8443.57i	1.03778	−	0.429862i
$729$		0			0
$730$	−12088.7			−0.612910
$731$	−4912.57	+	3738.87i	−0.248561	+	0.189175i
$732$		0			0
$733$	−17154.5	−	17154.5i	−0.864416	−	0.864416i	0.127432	−	0.991847i	$-0.459327\pi$
$733$	−17154.5	−	17154.5i	−0.864416	−	0.864416i	−0.991847	+	0.127432i	$0.959327\pi$
$734$	−12411.8	+	5141.15i	−0.624155	+	0.258533i
$735$		0			0
$736$	2694.78	+	6505.77i	0.134960	+	0.325823i
$737$	503.672	+	208.628i	0.0251737	+	0.0104273i
$738$		0			0
$739$	−27543.6	+	27543.6i	−1.37105	+	1.37105i	−0.512160	+	0.858890i	$0.671155\pi$
$739$	−27543.6	+	27543.6i	−1.37105	+	1.37105i	−0.858890	+	0.512160i	$0.828845\pi$
$740$	22082.1	−	22082.1i	1.09697	−	1.09697i
$741$		0			0
$742$	−20334.3	−	8422.72i	−1.00606	−	0.416722i
$743$	−10772.7	−	26007.7i	−0.531916	−	1.28416i	−0.930253	−	0.366919i	$-0.880413\pi$
$743$	−10772.7	−	26007.7i	−0.531916	−	1.28416i	0.398337	−	0.917239i	$-0.369587\pi$
$744$		0			0
$745$	1777.56	−	736.291i	0.0874160	−	0.0362089i
$746$	−26161.3	−	26161.3i	−1.28396	−	1.28396i
$747$		0			0
$748$	1317.49	−	2261.33i	0.0644015	−	0.110538i
$749$	−169.573			−0.00827244
$750$		0			0
$751$	−32521.4	+	13470.8i	−1.58019	+	0.654537i	−0.988444	−	0.151587i	$-0.951562\pi$
$751$	−32521.4	+	13470.8i	−1.58019	+	0.654537i	−0.591748	+	0.806123i	$0.701562\pi$
$752$		−	117420.i		−	5.69399i
$753$		0			0
$754$	3558.40	+	1473.94i	0.171869	+	0.0711904i
$755$	−13753.1	+	33203.0i	−0.662950	+	1.60050i
$756$		0			0
$757$	−17080.4	+	17080.4i	−0.820078	+	0.820078i	−0.986119	−	0.166041i	$-0.946902\pi$
$757$	−17080.4	+	17080.4i	−0.820078	+	0.820078i	0.166041	+	0.986119i	$0.446902\pi$
$758$	15430.0	−	37251.4i	0.739373	−	1.78500i
$759$		0			0
$760$	33148.5	+	80027.5i	1.58213	+	3.81961i
$761$			25612.3i			1.22003i	0.792388	+	0.610017i	$0.208837\pi$
$761$			25612.3i			1.22003i	−0.792388	+	0.610017i	$0.791163\pi$
$762$		0			0
$763$	25978.5	+	25978.5i	1.23261	+	1.23261i
$764$	82849.8			3.92330
$765$		0			0
$766$	52363.7			2.46994
$767$	−1613.53	−	1613.53i	−0.0759599	−	0.0759599i
$768$		0			0
$769$		−	1349.23i		−	0.0632699i	−0.999499	−	0.0316350i	$-0.989929\pi$
$769$		−	1349.23i		−	0.0632699i	0.999499	−	0.0316350i	$-0.0100714\pi$
$770$	−1388.95	−	3353.22i	−0.0650056	−	0.156937i
$771$		0			0
$772$	−2643.23	+	6381.31i	−0.123228	+	0.297498i
$773$	2254.38	−	2254.38i	0.104896	−	0.104896i	−0.652711	−	0.757607i	$-0.726369\pi$
$773$	2254.38	−	2254.38i	0.104896	−	0.104896i	0.757607	+	0.652711i	$0.226369\pi$
$774$		0			0
$775$	−1688.47	+	4076.33i	−0.0782602	+	0.188937i
$776$	53845.6	+	22303.6i	2.49091	+	1.03177i
$777$		0			0
$778$		−	66180.2i		−	3.04971i
$779$	33213.4	−	13757.4i	1.52759	−	0.632749i
$780$		0			0
$781$	1001.55			0.0458879
$782$	−1237.81	−	4693.53i	−0.0566038	−	0.214630i
$783$		0			0
$784$	91793.7	+	91793.7i	4.18156	+	4.18156i
$785$	43627.5	−	18071.1i	1.98361	−	0.821638i
$786$		0			0
$787$	−1041.32	−	2513.97i	−0.0471652	−	0.113867i	0.898541	−	0.438890i	$-0.144628\pi$
$787$	−1041.32	−	2513.97i	−0.0471652	−	0.113867i	−0.945706	+	0.325023i	$0.894628\pi$
$788$	−42836.1	−	17743.3i	−1.93651	−	0.802130i
$789$		0			0
$790$	59368.9	−	59368.9i	2.67374	−	2.67374i
$791$	−7801.34	+	7801.34i	−0.350675	+	0.350675i
$792$		0			0
$793$	−2629.80	−	1089.30i	−0.117764	−	0.0487794i
$794$	25049.4	+	60474.5i	1.11961	+	2.70297i
$795$		0			0
$796$	−29031.5	+	12025.2i	−1.29270	+	0.535456i
$797$	22381.4	+	22381.4i	0.994716	+	0.994716i	0.999986	−	0.00526978i	$-0.00167743\pi$
$797$	22381.4	+	22381.4i	0.994716	+	0.994716i	−0.00526978	+	0.999986i	$0.501677\pi$
$798$		0			0
$799$	−5406.24	+	39849.6i	−0.239373	+	1.76443i
$800$	11410.8			0.504290
$801$		0			0
$802$	29746.4	−	12321.4i	1.30970	−	0.542497i
$803$			333.220i			0.0146439i
$804$		0			0
$805$	−4495.98	−	1862.29i	−0.196848	−	0.0815369i
$806$	−4433.05	+	10702.3i	−0.193731	+	0.467709i
$807$		0			0
$808$	−10629.8	+	10629.8i	−0.462815	+	0.462815i
$809$	−12127.9	+	29279.4i	−0.527064	+	1.27244i	0.406375	+	0.913706i	$0.366793\pi$
$809$	−12127.9	+	29279.4i	−0.527064	+	1.27244i	−0.933438	+	0.358738i	$0.883207\pi$
$810$		0			0
$811$	−13033.1	−	31464.7i	−0.564309	−	1.36236i	−0.906290	−	0.422656i	$-0.861098\pi$
$811$	−13033.1	−	31464.7i	−0.564309	−	1.36236i	0.341981	−	0.939707i	$-0.388902\pi$
$812$			45833.5i			1.98084i
$813$		0			0
$814$	−841.985	−	841.985i	−0.0362550	−	0.0362550i
$815$	−22125.4			−0.950945
$816$		0			0
$817$	−9132.74			−0.391082
$818$	−41385.5	−	41385.5i	−1.76896	−	1.76896i
$819$		0			0
$820$		−	87402.3i		−	3.72222i
$821$	−14611.3	−	35274.8i	−0.621117	−	1.49951i	−0.850393	−	0.526148i	$-0.823636\pi$
$821$	−14611.3	−	35274.8i	−0.621117	−	1.49951i	0.229275	−	0.973362i	$-0.426364\pi$
$822$		0			0
$823$	−7680.56	+	18542.5i	−0.325307	+	0.785360i	0.673621	+	0.739077i	$0.264738\pi$
$823$	−7680.56	+	18542.5i	−0.325307	+	0.785360i	−0.998928	+	0.0462837i	$0.985262\pi$
$824$	−39393.1	+	39393.1i	−1.66544	+	1.66544i
$825$		0			0
$826$	14374.4	−	34702.9i	0.605508	−	1.46183i
$827$	−1706.74	−	706.956i	−0.0717645	−	0.0297258i	0.346512	−	0.938045i	$-0.387366\pi$
$827$	−1706.74	−	706.956i	−0.0717645	−	0.0297258i	−0.418277	+	0.908320i	$0.637366\pi$
$828$		0			0
$829$		−	3383.13i		−	0.141738i	−0.997486	−	0.0708691i	$-0.977423\pi$
$829$		−	3383.13i		−	0.141738i	0.997486	−	0.0708691i	$-0.0225773\pi$
$830$	−46409.4	+	19223.4i	−1.94084	+	0.803921i
$831$		0			0
$832$	13251.1			0.552164
$833$	−26926.2	−	35378.9i	−1.11997	−	1.47156i
$834$		0			0
$835$	−279.305	−	279.305i	−0.0115758	−	0.0115758i
$836$	3576.92	−	1481.61i	0.147979	−	0.0612948i
$837$		0			0
$838$	8243.29	+	19901.1i	0.339809	+	0.820371i
$839$	−33283.7	−	13786.6i	−1.36958	−	0.567300i	−0.427908	−	0.903822i	$-0.640749\pi$
$839$	−33283.7	−	13786.6i	−1.36958	−	0.567300i	−0.941676	+	0.336522i	$0.890749\pi$
$840$		0			0
$841$	13756.6	−	13756.6i	0.564051	−	0.564051i
$842$	28184.0	−	28184.0i	1.15354	−	1.15354i
$843$		0			0
$844$	−75903.6	−	31440.3i	−3.09563	−	1.28225i
$845$	−9673.55	−	23354.0i	−0.393823	−	0.950772i
$846$		0			0
$847$	38349.7	−	15885.0i	1.55574	−	0.644409i
$848$	−18961.8	−	18961.8i	−0.767865	−	0.767865i
$849$		0			0
$850$	−7794.22	−	1057.41i	−0.314517	−	0.0426692i
$851$	−1596.54			−0.0643111
$852$		0			0
$853$	24460.9	−	10132.0i	0.981859	−	0.406699i	0.166745	−	0.986000i	$-0.446674\pi$
$853$	24460.9	−	10132.0i	0.981859	−	0.406699i	0.815114	+	0.579301i	$0.196674\pi$
$854$		−	46855.9i		−	1.87749i
$855$		0			0
$856$	−346.606	−	143.569i	−0.0138397	−	0.00573258i
$857$	14988.5	−	36185.4i	0.597429	−	1.44232i	−0.278763	−	0.960360i	$-0.589924\pi$
$857$	14988.5	−	36185.4i	0.597429	−	1.44232i	0.876192	−	0.481962i	$-0.160076\pi$
$858$		0			0
$859$	−9624.53	+	9624.53i	−0.382287	+	0.382287i	−0.871926	−	0.489638i	$-0.837129\pi$
$859$	−9624.53	+	9624.53i	−0.382287	+	0.382287i	0.489638	+	0.871926i	$0.337129\pi$
$860$	−8497.00	+	20513.6i	−0.336913	+	0.813380i
$861$		0			0
$862$	−7274.20	−	17561.5i	−0.287425	−	0.693905i
$863$		−	27577.7i		−	1.08778i	−0.839156	−	0.543892i	$-0.816950\pi$
$863$		−	27577.7i		−	1.08778i	0.839156	−	0.543892i	$-0.183050\pi$
$864$		0			0
$865$	8857.23	+	8857.23i	0.348156	+	0.348156i
$866$	30548.2			1.19870
$867$		0			0
$868$	−137850.			−5.39048
$869$	−1636.47	−	1636.47i	−0.0638821	−	0.0638821i
$870$		0			0
$871$		−	3109.82i		−	0.120978i
$872$	31105.2	+	75094.5i	1.20797	+	2.91631i
$873$		0			0
$874$	2747.94	−	6634.12i	0.106351	−	0.256754i
$875$	27798.4	−	27798.4i	1.07401	−	1.07401i
$876$		0			0
$877$	−336.298	+	811.895i	−0.0129487	+	0.0312608i	−0.930222	−	0.366998i	$-0.880385\pi$
$877$	−336.298	+	811.895i	−0.0129487	+	0.0312608i	0.917273	+	0.398259i	$0.130385\pi$
$878$	31015.0	+	12846.8i	1.19215	+	0.493803i
$879$		0			0
$880$		−	4422.09i		−	0.169396i
$881$	−9639.60	+	3992.85i	−0.368634	+	0.152693i	−0.559307	−	0.828960i	$-0.688933\pi$
$881$	−9639.60	+	3992.85i	−0.368634	+	0.152693i	0.190674	+	0.981653i	$0.438933\pi$
$882$		0			0
$883$	26952.0			1.02719			0.513595	−	0.858033i	$-0.328313\pi$
$883$	26952.0			1.02719			0.513595	+	0.858033i	$0.328313\pi$
$884$	−14793.4	−	2006.96i	−0.562846	−	0.0763590i
$885$		0			0
$886$	−35086.4	−	35086.4i	−1.33042	−	1.33042i
$887$	−15399.1	+	6378.52i	−0.582922	+	0.241454i	−0.654602	−	0.755974i	$-0.727164\pi$
$887$	−15399.1	+	6378.52i	−0.582922	+	0.241454i	0.0716804	+	0.997428i	$0.477164\pi$
$888$		0			0
$889$	15544.4	+	37527.6i	0.586438	+	1.41579i
$890$	−2110.12	−	874.038i	−0.0794733	−	0.0329189i
$891$		0			0
$892$	−54182.0	+	54182.0i	−2.03380	+	2.03380i
$893$	−42066.6	+	42066.6i	−1.57638	+	1.57638i
$894$		0			0
$895$	18029.8	+	7468.18i	0.673374	+	0.278921i
$896$	31181.6	+	75279.1i	1.16262	+	2.80681i
$897$		0			0
$898$	−11896.8	+	4927.80i	−0.442093	+	0.183121i
$899$	−10493.6	−	10493.6i	−0.389300	−	0.389300i
$900$		0			0
$901$	5562.13	+	7308.19i	0.205662	+	0.270223i
$902$	−3332.62			−0.123020
$903$		0			0
$904$	−22550.9	+	9340.90i	−0.829682	+	0.343665i
$905$			21379.3i			0.785274i
$906$		0			0
$907$	−30759.4	−	12740.9i	−1.12607	−	0.466435i	−0.259628	−	0.965709i	$-0.583600\pi$
$907$	−30759.4	−	12740.9i	−1.12607	−	0.466435i	−0.866444	+	0.499274i	$0.833600\pi$
$908$	3539.07	−	8544.08i	0.129348	−	0.312274i
$909$		0			0
$910$	−14639.8	+	14639.8i	−0.533301	+	0.533301i
$911$	−8045.04	+	19422.5i	−0.292584	+	0.706361i	−1.00000		0.000437010i	$-0.999861\pi$
$911$	−8045.04	+	19422.5i	−0.292584	+	0.706361i	0.707416	+	0.706798i	$0.249861\pi$
$912$		0			0
$913$	529.883	+	1279.25i	0.0192076	+	0.0463713i
$914$			25576.3i			0.925591i
$915$		0			0
$916$	9551.70	+	9551.70i	0.344538	+	0.344538i
$917$	58119.5			2.09299
$918$		0			0
$919$	−47653.1			−1.71048			−0.855240	−	0.518232i	$-0.826590\pi$
$919$	−47653.1			−1.71048			−0.855240	+	0.518232i	$0.826590\pi$
$920$	−7613.04	−	7613.04i	−0.272820	−	0.272820i
$921$		0			0
$922$			103772.i			3.70668i
$923$	−2186.33	−	5278.28i	−0.0779676	−	0.188230i
$924$		0			0
$925$	−990.039	+	2390.17i	−0.0351917	+	0.0849602i
$926$	−25146.4	+	25146.4i	−0.892398	+	0.892398i
$927$		0			0
$928$	−14687.3	+	35458.2i	−0.519540	+	1.25428i
$929$	−37240.7	−	15425.6i	−1.31521	−	0.544777i	−0.388808	−	0.921319i	$-0.627113\pi$
$929$	−37240.7	−	15425.6i	−1.31521	−	0.544777i	−0.926399	+	0.376542i	$0.877113\pi$
$930$		0			0
$931$		−	65771.3i		−	2.31532i
$932$	−4234.37	+	1753.93i	−0.148821	+	0.0616438i
$933$		0			0
$934$	78995.0			2.76745
$935$	−203.601	+	1500.75i	−0.00712135	+	0.0524918i
$936$		0			0
$937$	8379.91	+	8379.91i	0.292166	+	0.292166i	0.837935	−	0.545769i	$-0.183763\pi$
$937$	8379.91	+	8379.91i	0.292166	+	0.292166i	−0.545769	+	0.837935i	$0.683763\pi$
$938$	47294.3	−	19589.9i	1.64628	−	0.681912i
$939$		0			0
$940$	55349.9	+	133626.i	1.92055	+	4.63661i
$941$	5584.59	+	2313.21i	0.193467	+	0.0801367i	0.477314	−	0.878733i	$-0.341611\pi$
$941$	5584.59	+	2313.21i	0.193467	+	0.0801367i	−0.283846	+	0.958870i	$0.591611\pi$
$942$		0			0
$943$	−3159.60	+	3159.60i	−0.109110	+	0.109110i
$944$	32360.6	−	32360.6i	1.11573	−	1.11573i
$945$		0			0
$946$	782.175	+	323.988i	0.0268824	+	0.0111350i
$947$	8928.00	+	21554.1i	0.306358	+	0.739614i	0.999817	+	0.0191180i	$0.00608582\pi$
$947$	8928.00	+	21554.1i	0.306358	+	0.739614i	−0.693459	+	0.720496i	$0.743914\pi$
$948$		0			0
$949$	1756.10	−	727.399i	0.0600688	−	0.0248813i
$950$	−8227.83	−	8227.83i	−0.280996	−	0.280996i
$951$		0			0
$952$	−38647.5	−	146543.i	−1.31573	−	4.98896i
$953$	−31114.9			−1.05762			−0.528810	−	0.848740i	$-0.677362\pi$
$953$	−31114.9			−1.05762			−0.528810	+	0.848740i	$0.677362\pi$
$954$		0			0
$955$	−44294.6	+	18347.4i	−1.50088	+	0.621684i
$956$			123292.i			4.17108i
$957$		0			0
$958$	−58649.0	−	24293.2i	−1.97793	−	0.819287i
$959$	−27084.8	+	65388.4i	−0.912005	+	2.20177i
$960$		0			0
$961$	10495.4	−	10495.4i	0.352301	−	0.352301i
$962$	−2599.33	+	6275.34i	−0.0871162	+	0.210317i
$963$		0			0
$964$	23913.3	+	57731.7i	0.798956	+	1.92885i
$965$		−	3997.03i		−	0.133336i
$966$		0			0
$967$	21337.7	+	21337.7i	0.709591	+	0.709591i	0.966449	−	0.256858i	$-0.0826873\pi$
$967$	21337.7	+	21337.7i	0.709591	+	0.709591i	−0.256858	+	0.966449i	$0.582687\pi$
$968$	91835.7			3.04929
$969$		0			0
$970$	−54688.8			−1.81026
$971$	1502.19	+	1502.19i	0.0496473	+	0.0496473i	0.731495	−	0.681847i	$-0.238823\pi$
$971$	1502.19	+	1502.19i	0.0496473	+	0.0496473i	−0.681847	+	0.731495i	$0.738823\pi$
$972$		0			0
$973$			57970.0i			1.91000i
$974$	−14443.0	−	34868.4i	−0.475137	−	1.14708i
$975$		0			0
$976$	21846.7	−	52742.5i	0.716490	−	1.72976i
$977$	35415.1	−	35415.1i	1.15970	−	1.15970i	0.175165	−	0.984539i	$-0.443954\pi$
$977$	35415.1	−	35415.1i	1.15970	−	1.15970i	0.984539	−	0.175165i	$-0.0560459\pi$
$978$		0			0
$979$	−24.0924	+	58.1642i	−0.000786513	+	0.00189881i
$980$	−147733.	−	61192.8i	−4.81545	−	1.99463i
$981$		0			0
$982$			74797.6i			2.43064i
$983$	−48582.3	+	20123.4i	−1.57633	+	0.652938i	−0.987827	−	0.155556i	$-0.950283\pi$
$983$	−48582.3	+	20123.4i	−1.57633	+	0.652938i	−0.588505	+	0.808494i	$0.700283\pi$
$984$		0			0
$985$	26831.1			0.867927
$986$	13318.1	−	22858.9i	0.430156	−	0.738313i
$987$		0			0
$988$	−15616.4	−	15616.4i	−0.502858	−	0.502858i
$989$	1048.73	−	434.400i	0.0337187	−	0.0139668i
$990$		0			0
$991$	−9906.88	−	23917.3i	−0.317560	−	0.766659i	−0.999382	−	0.0351406i	$-0.988812\pi$
$991$	−9906.88	−	23917.3i	−0.317560	−	0.766659i	0.681822	−	0.731518i	$-0.261188\pi$
$992$	−106645.	−	44173.8i	−3.41329	−	1.41383i
$993$		0			0
$994$	66499.7	−	66499.7i	2.12197	−	2.12197i
$995$	12858.2	−	12858.2i	0.409682	−	0.409682i
$996$		0			0
$997$	−719.995	−	298.232i	−0.0228711	−	0.00947352i	0.371219	−	0.928546i	$-0.378940\pi$
$997$	−719.995	−	298.232i	−0.0228711	−	0.00947352i	−0.394090	+	0.919072i	$0.628940\pi$
$998$	−36768.6	−	88767.2i	−1.16622	−	2.81551i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	153.4.l.c.19.10		40
3.2	odd	2		51.4.h.a.19.1	✓	40
17.9	even	8	inner	153.4.l.c.145.10		40
51.14	even	16		867.4.a.v.1.2		20
51.20	even	16		867.4.a.w.1.2		20
51.26	odd	8		51.4.h.a.43.1	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.4.h.a.19.1	✓	40	3.2	odd	2
51.4.h.a.43.1	yes	40	51.26	odd	8
153.4.l.c.19.10		40	1.1	even	1	trivial
153.4.l.c.145.10		40	17.9	even	8	inner
867.4.a.v.1.2		20	51.14	even	16
867.4.a.w.1.2		20	51.20	even	16

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:	\( N \)	\(=\)	\( 153 = 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	153.l (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(3.79946 + 3.79946i) q^{2} +20.8719i q^{4} +(-4.62215 - 11.1589i) q^{5} +(-11.9634 + 28.8822i) q^{7} +(-48.9062 + 48.9062i) q^{8} +(24.8360 - 59.9594i) q^{10} +(-1.65275 - 0.684591i) q^{11} +10.2045i q^{13} +(-155.191 + 64.2823i) q^{14} -204.660 q^{16} +(69.4565 + 9.42288i) q^{17} +(73.3206 + 73.3206i) q^{19} +(232.906 - 96.4729i) q^{20} +(-3.67848 - 8.88064i) q^{22} +(-11.9071 - 4.93207i) q^{23} +(-14.7675 + 14.7675i) q^{25} +(-38.7718 + 38.7718i) q^{26} +(-602.824 - 249.698i) q^{28} +(-26.8811 - 64.8968i) q^{29} +(195.185 - 80.8484i) q^{31} +(-386.348 - 386.348i) q^{32} +(228.096 + 299.700i) q^{34} +377.588 q^{35} +(114.447 - 47.4057i) q^{37} +557.158i q^{38} +(771.789 + 319.685i) q^{40} +(132.677 - 320.311i) q^{41} +(-62.2795 + 62.2795i) q^{43} +(14.2887 - 34.4959i) q^{44} +(-26.5013 - 63.9798i) q^{46} +573.735i q^{47} +(-448.519 - 448.519i) q^{49} -112.217 q^{50} -212.988 q^{52} +(92.6502 + 92.6502i) q^{53} +21.6071i q^{55} +(-827.432 - 1997.60i) q^{56} +(144.439 - 348.707i) q^{58} +(-158.119 + 158.119i) q^{59} +(-106.746 + 257.708i) q^{61} +(1048.78 + 434.419i) q^{62} -1298.55i q^{64} +(113.871 - 47.1670i) q^{65} -304.748 q^{67} +(-196.673 + 1449.69i) q^{68} +(1434.63 + 1434.63i) q^{70} +(-517.248 + 214.251i) q^{71} +(-71.2818 - 172.090i) q^{73} +(614.955 + 254.723i) q^{74} +(-1530.34 + 1530.34i) q^{76} +(39.5449 - 39.5449i) q^{77} +(1195.22 + 495.076i) q^{79} +(945.968 + 2283.77i) q^{80} +(1721.11 - 712.909i) q^{82} +(-547.311 - 547.311i) q^{83} +(-215.890 - 818.610i) q^{85} -473.258 q^{86} +(114.310 - 47.3489i) q^{88} -35.1924i q^{89} +(-294.729 - 122.081i) q^{91} +(102.942 - 248.523i) q^{92} +(-2179.89 + 2179.89i) q^{94} +(479.275 - 1157.07i) q^{95} +(-322.475 - 778.524i) q^{97} -3408.26i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 32 q^{5} + 128 q^{10} - 112 q^{11} - 256 q^{14} - 1024 q^{16} + 112 q^{17} - 32 q^{19} + 640 q^{20} + 728 q^{22} - 208 q^{23} + 296 q^{25} - 1472 q^{26} - 328 q^{28} + 1272 q^{29} - 192 q^{31} + 960 q^{32}+ \cdots + 1008 q^{97}+O(q^{100}) \) 40 * q - 32 * q^5 + 128 * q^10 - 112 * q^11 - 256 * q^14 - 1024 * q^16 + 112 * q^17 - 32 * q^19 + 640 * q^20 + 728 * q^22 - 208 * q^23 + 296 * q^25 - 1472 * q^26 - 328 * q^28 + 1272 * q^29 - 192 * q^31 + 960 * q^32 + 24 * q^34 + 992 * q^35 - 1120 * q^37 + 2984 * q^40 + 1320 * q^41 + 672 * q^43 - 3744 * q^44 - 384 * q^46 - 2096 * q^49 + 448 * q^50 + 960 * q^52 - 2120 * q^53 - 5680 * q^56 + 1000 * q^58 + 832 * q^59 - 208 * q^61 + 4432 * q^62 + 2376 * q^65 - 2272 * q^67 + 4560 * q^68 - 4792 * q^70 - 256 * q^71 - 1416 * q^73 + 2704 * q^74 - 264 * q^76 - 6048 * q^77 + 1920 * q^79 - 1312 * q^80 + 8328 * q^82 - 4960 * q^83 + 3192 * q^85 + 15616 * q^86 - 248 * q^88 + 1232 * q^91 - 944 * q^92 - 10000 * q^94 - 4528 * q^95 + 1008 * q^97

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