LMFDB - Embedded newform 375.3.k.a.82.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [375,3,Mod(7,375)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(375, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 17]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("375.7");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 375 = 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	375.k (of order $20$, degree $8$, 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:	$10.2180099135$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 75)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			82.3
Character	$\chi$	$=$	375.82
Dual form			375.3.k.a.343.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.373594 - 2.35878i) q^{2} +(-1.54327 - 0.786335i) q^{3} +(-1.62005 + 0.526386i) q^{4} +(-1.27823 + 3.93400i) q^{6} +(5.77573 + 5.77573i) q^{7} +(-2.48998 - 4.88686i) q^{8} +(1.76336 + 2.42705i) q^{9} +O(q^{10})$	\(q+(-0.373594 - 2.35878i) q^{2} +(-1.54327 - 0.786335i) q^{3} +(-1.62005 + 0.526386i) q^{4} +(-1.27823 + 3.93400i) q^{6} +(5.77573 + 5.77573i) q^{7} +(-2.48998 - 4.88686i) q^{8} +(1.76336 + 2.42705i) q^{9} +(-14.5250 - 10.5530i) q^{11} +(2.91409 + 0.461546i) q^{12} +(0.424960 - 2.68309i) q^{13} +(11.4659 - 15.7815i) q^{14} +(-16.1092 + 11.7040i) q^{16} +(-16.4543 + 8.38387i) q^{17} +(5.06610 - 5.06610i) q^{18} +(-17.3304 - 5.63098i) q^{19} +(-4.37185 - 13.4552i) q^{21} +(-19.4658 + 38.2038i) q^{22} +(-28.3452 + 4.48944i) q^{23} +9.49970i q^{24} -6.48759 q^{26} +(-0.812857 - 5.13218i) q^{27} +(-12.3972 - 6.31670i) q^{28} +(14.4312 - 4.68898i) q^{29} +(5.10033 - 15.6972i) q^{31} +(18.1125 + 18.1125i) q^{32} +(14.1177 + 27.7076i) q^{33} +(25.9229 + 35.6799i) q^{34} +(-4.13429 - 3.00374i) q^{36} +(42.0480 + 6.65975i) q^{37} +(-6.80772 + 42.9822i) q^{38} +(-2.76564 + 3.80657i) q^{39} +(-61.0326 + 44.3428i) q^{41} +(-30.1045 + 15.3390i) q^{42} +(-18.3686 + 18.3686i) q^{43} +(29.0861 + 9.45066i) q^{44} +(21.1792 + 65.1829i) q^{46} +(32.7875 - 64.3491i) q^{47} +(34.0641 - 5.39522i) q^{48} +17.7181i q^{49} +31.9859 q^{51} +(0.723886 + 4.57043i) q^{52} +(-20.3462 - 10.3669i) q^{53} +(-11.8020 + 3.83470i) q^{54} +(13.8437 - 42.6066i) q^{56} +(22.3176 + 22.3176i) q^{57} +(-16.4517 - 32.2883i) q^{58} +(50.5873 + 69.6274i) q^{59} +(-33.2882 - 24.1853i) q^{61} +(-38.9317 - 6.16617i) q^{62} +(-3.83332 + 24.2027i) q^{63} +(-10.8592 + 14.9465i) q^{64} +(60.0819 - 43.6521i) q^{66} +(-9.58854 + 4.88560i) q^{67} +(22.2436 - 22.2436i) q^{68} +(47.2744 + 15.3604i) q^{69} +(-14.4476 - 44.4650i) q^{71} +(7.46994 - 14.6606i) q^{72} +(-32.3696 + 5.12685i) q^{73} -101.670i q^{74} +31.0401 q^{76} +(-22.9410 - 144.844i) q^{77} +(10.0121 + 5.10142i) q^{78} +(-79.3298 + 25.7758i) q^{79} +(-2.78115 + 8.55951i) q^{81} +(127.396 + 127.396i) q^{82} +(3.78135 + 7.42131i) q^{83} +(14.1652 + 19.4967i) q^{84} +(50.1898 + 36.4650i) q^{86} +(-25.9583 - 4.11140i) q^{87} +(-15.4042 + 97.2584i) q^{88} +(21.2145 - 29.1993i) q^{89} +(17.9513 - 13.0424i) q^{91} +(43.5574 - 22.1936i) q^{92} +(-20.2144 + 20.2144i) q^{93} +(-164.035 - 53.2981i) q^{94} +(-13.7100 - 42.1950i) q^{96} +(-11.3155 + 22.2079i) q^{97} +(41.7931 - 6.61938i) q^{98} -53.8616i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 4 q^{2} + 4 q^{7} + 12 q^{8}+O(q^{10}) $ 80 * q - 4 * q^2 + 4 * q^7 + 12 * q^8	$ 80 q - 4 q^{2} + 4 q^{7} + 12 q^{8} + 24 q^{12} - 32 q^{13} + 80 q^{16} + 100 q^{17} + 48 q^{18} - 100 q^{19} + 100 q^{22} + 96 q^{23} - 40 q^{26} - 196 q^{28} + 200 q^{29} - 636 q^{32} - 216 q^{33} + 100 q^{34} - 120 q^{36} + 184 q^{37} + 564 q^{38} + 160 q^{41} + 12 q^{42} + 472 q^{43} - 700 q^{44} + 288 q^{47} + 48 q^{48} - 620 q^{52} - 304 q^{53} - 72 q^{57} - 1272 q^{58} + 800 q^{59} - 240 q^{61} - 1212 q^{62} + 12 q^{63} + 100 q^{64} + 80 q^{67} - 104 q^{68} - 36 q^{72} + 116 q^{73} + 88 q^{77} + 120 q^{78} + 200 q^{79} + 180 q^{81} + 168 q^{82} + 1264 q^{83} - 1200 q^{84} + 876 q^{87} + 212 q^{88} - 1500 q^{89} + 1504 q^{92} + 648 q^{93} - 200 q^{94} + 60 q^{96} + 260 q^{97} + 92 q^{98}+O(q^{100}) $ 80 * q - 4 * q^2 + 4 * q^7 + 12 * q^8 + 24 * q^12 - 32 * q^13 + 80 * q^16 + 100 * q^17 + 48 * q^18 - 100 * q^19 + 100 * q^22 + 96 * q^23 - 40 * q^26 - 196 * q^28 + 200 * q^29 - 636 * q^32 - 216 * q^33 + 100 * q^34 - 120 * q^36 + 184 * q^37 + 564 * q^38 + 160 * q^41 + 12 * q^42 + 472 * q^43 - 700 * q^44 + 288 * q^47 + 48 * q^48 - 620 * q^52 - 304 * q^53 - 72 * q^57 - 1272 * q^58 + 800 * q^59 - 240 * q^61 - 1212 * q^62 + 12 * q^63 + 100 * q^64 + 80 * q^67 - 104 * q^68 - 36 * q^72 + 116 * q^73 + 88 * q^77 + 120 * q^78 + 200 * q^79 + 180 * q^81 + 168 * q^82 + 1264 * q^83 - 1200 * q^84 + 876 * q^87 + 212 * q^88 - 1500 * q^89 + 1504 * q^92 + 648 * q^93 - 200 * q^94 + 60 * q^96 + 260 * q^97 + 92 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/375\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{9}{20}\right)$	$1$

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 $

$2$	−0.373594	−	2.35878i	−0.186797	−	1.17939i	−0.885729	−	0.464202i	$-0.846341\pi$
$2$	−0.373594	−	2.35878i	−0.186797	−	1.17939i	0.698932	−	0.715188i	$-0.253659\pi$
$3$	−1.54327	−	0.786335i	−0.514423	−	0.262112i
$3$	−1.54327	−	0.786335i	−0.514423	−	0.262112i
$4$	−1.62005	+	0.526386i	−0.405012	+	0.131596i
$5$		0			0
$5$		0			0
$6$	−1.27823	+	3.93400i	−0.213039	+	0.655667i
$7$	5.77573	+	5.77573i	0.825104	+	0.825104i	0.986835	−	0.161731i	$-0.0517076\pi$
$7$	5.77573	+	5.77573i	0.825104	+	0.825104i	−0.161731	+	0.986835i	$0.551708\pi$
$8$	−2.48998	−	4.88686i	−0.311248	−	0.610858i
$9$	1.76336	+	2.42705i	0.195928	+	0.269672i
$10$		0			0
$11$	−14.5250	−	10.5530i	−1.32045	−	0.959365i	−0.999926	−	0.0121254i	$-0.996140\pi$
$11$	−14.5250	−	10.5530i	−1.32045	−	0.959365i	−0.320526	−	0.947240i	$-0.603860\pi$
$12$	2.91409	+	0.461546i	0.242841	+	0.0384622i
$13$	0.424960	−	2.68309i	0.0326892	−	0.206392i	−0.965938	−	0.258774i	$-0.916681\pi$
$13$	0.424960	−	2.68309i	0.0326892	−	0.206392i	0.998627	+	0.0523824i	$0.0166815\pi$
$14$	11.4659	−	15.7815i	0.818993	−	1.12725i
$15$		0			0
$16$	−16.1092	+	11.7040i	−1.00682	+	0.731500i
$17$	−16.4543	+	8.38387i	−0.967898	+	0.493169i	−0.865136	−	0.501537i	$-0.832768\pi$
$17$	−16.4543	+	8.38387i	−0.967898	+	0.493169i	−0.102762	+	0.994706i	$0.532768\pi$
$18$	5.06610	−	5.06610i	0.281450	−	0.281450i
$19$	−17.3304	−	5.63098i	−0.912124	−	0.296367i	−0.184892	−	0.982759i	$-0.559194\pi$
$19$	−17.3304	−	5.63098i	−0.912124	−	0.296367i	−0.727232	+	0.686392i	$0.759194\pi$
$20$		0			0
$21$	−4.37185	−	13.4552i	−0.208183	−	0.640722i
$22$	−19.4658	+	38.2038i	−0.884809	+	1.73654i
$23$	−28.3452	+	4.48944i	−1.23240	+	0.195193i	−0.738456	−	0.674301i	$-0.764445\pi$
$23$	−28.3452	+	4.48944i	−1.23240	+	0.195193i	−0.493943	+	0.869494i	$0.664445\pi$
$24$			9.49970i			0.395821i
$25$		0			0
$26$	−6.48759			−0.249523
$27$	−0.812857	−	5.13218i	−0.0301058	−	0.190081i
$28$	−12.3972	−	6.31670i	−0.442758	−	0.225597i
$29$	14.4312	−	4.68898i	0.497628	−	0.161689i	−0.0494405	−	0.998777i	$-0.515744\pi$
$29$	14.4312	−	4.68898i	0.497628	−	0.161689i	0.547068	+	0.837088i	$0.315744\pi$
$30$		0			0
$31$	5.10033	−	15.6972i	0.164527	−	0.506361i	−0.834474	−	0.551047i	$-0.814229\pi$
$31$	5.10033	−	15.6972i	0.164527	−	0.506361i	0.999001	+	0.0446857i	$0.0142286\pi$
$32$	18.1125	+	18.1125i	0.566017	+	0.566017i
$33$	14.1177	+	27.7076i	0.427810	+	0.839625i
$34$	25.9229	+	35.6799i	0.762439	+	1.04941i
$35$		0			0
$36$	−4.13429	−	3.00374i	−0.114841	−	0.0834371i
$37$	42.0480	+	6.65975i	1.13643	+	0.179993i	0.696171	−	0.717876i	$-0.254886\pi$
$37$	42.0480	+	6.65975i	1.13643	+	0.179993i	0.440262	+	0.897869i	$0.354886\pi$
$38$	−6.80772	+	42.9822i	−0.179150	+	1.13111i
$39$	−2.76564	+	3.80657i	−0.0709137	+	0.0976044i
$40$		0			0
$41$	−61.0326	+	44.3428i	−1.48860	+	1.08153i	−0.513942	+	0.857825i	$0.671815\pi$
$41$	−61.0326	+	44.3428i	−1.48860	+	1.08153i	−0.974657	+	0.223706i	$0.928185\pi$
$42$	−30.1045	+	15.3390i	−0.716773	+	0.365214i
$43$	−18.3686	+	18.3686i	−0.427176	+	0.427176i	−0.887665	−	0.460489i	$-0.847674\pi$
$43$	−18.3686	+	18.3686i	−0.427176	+	0.427176i	0.460489	+	0.887665i	$0.347674\pi$
$44$	29.0861	+	9.45066i	0.661049	+	0.214788i
$45$		0			0
$46$	21.1792	+	65.1829i	0.460417	+	1.41702i
$47$	32.7875	−	64.3491i	0.697606	−	1.36913i	−0.221516	−	0.975157i	$-0.571100\pi$
$47$	32.7875	−	64.3491i	0.697606	−	1.36913i	0.919122	−	0.393973i	$-0.128900\pi$
$48$	34.0641	−	5.39522i	0.709668	−	0.112400i
$49$			17.7181i			0.361594i
$50$		0			0
$51$	31.9859			0.627174
$52$	0.723886	+	4.57043i	0.0139209	+	0.0878930i
$53$	−20.3462	−	10.3669i	−0.383890	−	0.195602i	0.251386	−	0.967887i	$-0.419114\pi$
$53$	−20.3462	−	10.3669i	−0.383890	−	0.195602i	−0.635276	+	0.772285i	$0.719114\pi$
$54$	−11.8020	+	3.83470i	−0.218556	+	0.0710131i
$55$		0			0
$56$	13.8437	−	42.6066i	0.247210	−	0.760833i
$57$	22.3176	+	22.3176i	0.391536	+	0.391536i
$58$	−16.4517	−	32.2883i	−0.283650	−	0.556694i
$59$	50.5873	+	69.6274i	0.857412	+	1.18013i	0.982181	+	0.187940i	$0.0601810\pi$
$59$	50.5873	+	69.6274i	0.857412	+	1.18013i	−0.124769	+	0.992186i	$0.539819\pi$
$60$		0			0
$61$	−33.2882	−	24.1853i	−0.545709	−	0.396481i	0.280492	−	0.959856i	$-0.409502\pi$
$61$	−33.2882	−	24.1853i	−0.545709	−	0.396481i	−0.826201	+	0.563376i	$0.809502\pi$
$62$	−38.9317	−	6.16617i	−0.627930	−	0.0994544i
$63$	−3.83332	+	24.2027i	−0.0608464	+	0.384169i
$64$	−10.8592	+	14.9465i	−0.169676	+	0.233539i
$65$		0			0
$66$	60.0819	−	43.6521i	0.910332	−	0.661395i
$67$	−9.58854	+	4.88560i	−0.143112	+	0.0729194i	−0.524080	−	0.851669i	$-0.675591\pi$
$67$	−9.58854	+	4.88560i	−0.143112	+	0.0729194i	0.380968	+	0.924588i	$0.375591\pi$
$68$	22.2436	−	22.2436i	0.327111	−	0.327111i
$69$	47.2744	+	15.3604i	0.685137	+	0.222614i
$70$		0			0
$71$	−14.4476	−	44.4650i	−0.203487	−	0.626268i	−0.999772	−	0.0213469i	$-0.993205\pi$
$71$	−14.4476	−	44.4650i	−0.203487	−	0.626268i	0.796285	−	0.604921i	$-0.206795\pi$
$72$	7.46994	−	14.6606i	0.103749	−	0.203619i
$73$	−32.3696	+	5.12685i	−0.443420	+	0.0702308i	−0.374152	−	0.927367i	$-0.622066\pi$
$73$	−32.3696	+	5.12685i	−0.443420	+	0.0702308i	−0.0692676	+	0.997598i	$0.522066\pi$
$74$		−	101.670i		−	1.37392i
$75$		0			0
$76$	31.0401			0.408422
$77$	−22.9410	−	144.844i	−0.297935	−	1.88109i
$78$	10.0121	+	5.10142i	0.128360	+	0.0654028i
$79$	−79.3298	+	25.7758i	−1.00418	+	0.326276i	−0.764533	−	0.644585i	$-0.777030\pi$
$79$	−79.3298	+	25.7758i	−1.00418	+	0.326276i	−0.239642	+	0.970861i	$0.577030\pi$
$80$		0			0
$81$	−2.78115	+	8.55951i	−0.0343352	+	0.105673i
$82$	127.396	+	127.396i	1.55361	+	1.55361i
$83$	3.78135	+	7.42131i	0.0455584	+	0.0894134i	0.912663	−	0.408712i	$-0.134022\pi$
$83$	3.78135	+	7.42131i	0.0455584	+	0.0894134i	−0.867105	+	0.498125i	$0.834022\pi$
$84$	14.1652	+	19.4967i	0.168633	+	0.232104i
$85$		0			0
$86$	50.1898	+	36.4650i	0.583603	+	0.424012i
$87$	−25.9583	−	4.11140i	−0.298372	−	0.0472574i
$88$	−15.4042	+	97.2584i	−0.175048	+	1.10521i
$89$	21.2145	−	29.1993i	0.238366	−	0.328082i	−0.673029	−	0.739616i	$-0.735007\pi$
$89$	21.2145	−	29.1993i	0.238366	−	0.328082i	0.911394	+	0.411534i	$0.135007\pi$
$90$		0			0
$91$	17.9513	−	13.0424i	0.197267	−	0.143323i
$92$	43.5574	−	22.1936i	0.473450	−	0.241235i
$93$	−20.2144	+	20.2144i	−0.217359	+	0.217359i
$94$	−164.035	−	53.2981i	−1.74505	−	0.567001i
$95$		0			0
$96$	−13.7100	−	42.1950i	−0.142812	−	0.439531i
$97$	−11.3155	+	22.2079i	−0.116655	+	0.228948i	−0.941950	−	0.335754i	$-0.891009\pi$
$97$	−11.3155	+	22.2079i	−0.116655	+	0.228948i	0.825295	+	0.564702i	$0.191009\pi$
$98$	41.7931	−	6.61938i	0.426461	−	0.0675447i
$99$		−	53.8616i		−	0.544056i
$100$		0			0
$101$	68.9153			0.682330			0.341165	−	0.940003i	$-0.389179\pi$
$101$	68.9153			0.682330			0.341165	+	0.940003i	$0.389179\pi$
$102$	−11.9497	−	75.4477i	−0.117154	−	0.739683i
$103$	−35.5501	−	18.1137i	−0.345146	−	0.175861i	0.272821	−	0.962065i	$-0.412043\pi$
$103$	−35.5501	−	18.1137i	−0.345146	−	0.175861i	−0.617967	+	0.786204i	$0.712043\pi$
$104$	−14.1700	+	4.60413i	−0.136250	+	0.0442704i
$105$		0			0
$106$	−16.8520	+	51.8651i	−0.158981	+	0.489294i
$107$	13.3397	+	13.3397i	0.124670	+	0.124670i	0.766689	−	0.642019i	$-0.221903\pi$
$107$	13.3397	+	13.3397i	0.124670	+	0.124670i	−0.642019	+	0.766689i	$0.721903\pi$
$108$	4.01838	+	7.88651i	0.0372072	+	0.0730232i
$109$	−32.9866	−	45.4021i	−0.302629	−	0.416533i	0.630436	−	0.776242i	$-0.282876\pi$
$109$	−32.9866	−	45.4021i	−0.302629	−	0.416533i	−0.933065	+	0.359708i	$0.882876\pi$
$110$		0			0
$111$	−59.6546	−	43.3416i	−0.537429	−	0.390465i
$112$	−160.641	−	25.4431i	−1.43430	−	0.227171i
$113$	29.9096	−	188.842i	0.264687	−	1.67116i	−0.394278	−	0.918991i	$-0.629005\pi$
$113$	29.9096	−	188.842i	0.264687	−	1.67116i	0.658965	−	0.752174i	$-0.270995\pi$
$114$	44.3045	−	60.9800i	0.388636	−	0.534912i
$115$		0			0
$116$	−20.9110	+	15.1928i	−0.180268	+	0.130972i
$117$	7.26136	−	3.69985i	0.0620629	−	0.0316226i
$118$	145.337	−	145.337i	1.23167	−	1.23167i
$119$	−143.458	−	46.6125i	−1.20553	−	0.391701i
$120$		0			0
$121$	62.2178	+	191.487i	0.514197	+	1.58254i
$122$	−44.6116	+	87.5552i	−0.365669	+	0.717665i
$123$	129.058	−	20.4408i	1.04925	−	0.166185i
$124$			28.1150i			0.226734i
$125$		0			0
$126$	58.5209			0.464451
$127$	−27.8326	−	175.728i	−0.219154	−	1.38368i	−0.814476	−	0.580197i	$-0.802975\pi$
$127$	−27.8326	−	175.728i	−0.219154	−	1.38368i	0.595322	−	0.803487i	$-0.297025\pi$
$128$	130.605	+	66.5465i	1.02035	+	0.519895i
$129$	42.7915	−	13.9038i	0.331717	−	0.107781i
$130$		0			0
$131$	44.5020	−	136.963i	0.339710	−	1.04552i	−0.624645	−	0.780909i	$-0.714756\pi$
$131$	44.5020	−	136.963i	0.339710	−	1.04552i	0.964355	−	0.264612i	$-0.0852438\pi$
$132$	−37.4563	−	37.4563i	−0.283760	−	0.283760i
$133$	−67.5725	−	132.618i	−0.508064	−	0.997131i
$134$	15.1063	+	20.7920i	0.112733	+	0.155164i
$135$		0			0
$136$	81.9416	+	59.5341i	0.602512	+	0.437751i
$137$	−155.755	−	24.6692i	−1.13690	−	0.180067i	−0.440522	−	0.897742i	$-0.645206\pi$
$137$	−155.755	−	24.6692i	−1.13690	−	0.180067i	−0.696378	+	0.717675i	$0.745206\pi$
$138$	18.5704	−	117.249i	0.134568	−	0.849627i
$139$	123.458	−	169.925i	0.888186	−	1.22248i	−0.0858994	−	0.996304i	$-0.527376\pi$
$139$	123.458	−	169.925i	0.888186	−	1.22248i	0.974086	−	0.226180i	$-0.0726236\pi$
$140$		0			0
$141$	−101.200	+	73.5260i	−0.717729	+	0.521461i
$142$	−99.4858	+	50.6905i	−0.700604	+	0.356976i
$143$	−34.4872	+	34.4872i	−0.241170	+	0.241170i
$144$	−56.8124	−	18.4595i	−0.394531	−	0.128191i
$145$		0			0
$146$	24.1862	+	74.4376i	0.165659	+	0.509846i
$147$	13.9324	−	27.3438i	0.0947780	−	0.186012i
$148$	−71.6255	+	11.3444i	−0.483956	+	0.0766511i
$149$			32.3961i			0.217424i	0.994073	+	0.108712i	$0.0346725\pi$
$149$			32.3961i			0.217424i	−0.994073	+	0.108712i	$0.965327\pi$
$150$		0			0
$151$	−276.010			−1.82788			−0.913940	−	0.405849i	$-0.866976\pi$
$151$	−276.010			−1.82788			−0.913940	+	0.405849i	$0.866976\pi$
$152$	15.6345	+	98.7121i	0.102858	+	0.649422i
$153$	−49.3628	−	25.1516i	−0.322633	−	0.164390i
$154$	−333.084	+	108.226i	−2.16288	+	0.702763i
$155$		0			0
$156$	2.47674	−	7.62262i	0.0158765	−	0.0488630i
$157$	109.925	+	109.925i	0.700162	+	0.700162i	0.964445	−	0.264283i	$-0.0851353\pi$
$157$	109.925	+	109.925i	0.700162	+	0.700162i	−0.264283	+	0.964445i	$0.585135\pi$
$158$	90.4367	+	177.492i	0.572384	+	1.12337i
$159$	23.2477	+	31.9978i	0.146212	+	0.201244i
$160$		0			0
$161$	−189.644	−	137.784i	−1.17791	−	0.855803i
$162$	21.2290	+	3.36235i	0.131043	+	0.0207552i
$163$	27.6240	−	174.411i	0.169473	−	1.07001i	−0.745504	−	0.666501i	$-0.767791\pi$
$163$	27.6240	−	174.411i	0.169473	−	1.07001i	0.914977	−	0.403507i	$-0.132209\pi$
$164$	75.5344	−	103.964i	0.460575	−	0.633928i
$165$		0			0
$166$	16.0926	−	11.6919i	0.0969431	−	0.0704333i
$167$	64.6260	−	32.9286i	0.386982	−	0.197177i	−0.249665	−	0.968332i	$-0.580321\pi$
$167$	64.6260	−	32.9286i	0.386982	−	0.197177i	0.636647	+	0.771155i	$0.280321\pi$
$168$	−54.8677	+	54.8677i	−0.326593	+	0.326593i
$169$	153.710	+	49.9435i	0.909528	+	0.295523i
$170$		0			0
$171$	−16.8929	−	51.9911i	−0.0987891	−	0.304041i
$172$	20.0890	−	39.4269i	0.116797	−	0.229226i
$173$	124.417	−	19.7057i	0.719171	−	0.113906i	0.213887	−	0.976858i	$-0.431388\pi$
$173$	124.417	−	19.7057i	0.719171	−	0.113906i	0.505284	+	0.862953i	$0.331388\pi$
$174$			62.7660i			0.360724i
$175$		0			0
$176$	357.498			2.03124
$177$	−23.3193	−	147.232i	−0.131748	−	0.831821i
$178$	−76.8004	−	39.1318i	−0.431463	−	0.219841i
$179$	−125.446	+	40.7600i	−0.700817	+	0.227709i	−0.637686	−	0.770296i	$-0.720108\pi$
$179$	−125.446	+	40.7600i	−0.700817	+	0.227709i	−0.0631306	+	0.998005i	$0.520108\pi$
$180$		0			0
$181$	30.4138	−	93.6039i	0.168032	−	0.517149i	−0.831215	−	0.555951i	$-0.812354\pi$
$181$	30.4138	−	93.6039i	0.168032	−	0.517149i	0.999247	+	0.0388022i	$0.0123542\pi$
$182$	−37.4706	−	37.4706i	−0.205882	−	0.205882i
$183$	32.3549	+	63.5001i	0.176803	+	0.346995i
$184$	92.5182	+	127.340i	0.502816	+	0.692067i
$185$		0			0
$186$	55.2334	+	40.1294i	0.296954	+	0.215749i
$187$	327.473	+	51.8666i	1.75119	+	0.277362i
$188$	−19.2449	+	121.508i	−0.102367	+	0.646317i
$189$	24.9472	−	34.3369i	0.131996	−	0.181677i
$190$		0			0
$191$	156.770	−	113.900i	0.820788	−	0.596337i	−0.0961503	−	0.995367i	$-0.530653\pi$
$191$	156.770	−	113.900i	0.820788	−	0.596337i	0.916938	+	0.399030i	$0.130653\pi$
$192$	28.5117	−	14.5274i	0.148498	−	0.0756636i
$193$	−110.262	+	110.262i	−0.571306	+	0.571306i	−0.932493	−	0.361187i	$-0.882371\pi$
$193$	−110.262	+	110.262i	−0.571306	+	0.571306i	0.361187	+	0.932493i	$0.382371\pi$
$194$	56.6110	+	18.3940i	0.291809	+	0.0948146i
$195$		0			0
$196$	−9.32656	−	28.7042i	−0.0475845	−	0.146450i
$197$	−124.557	+	244.457i	−0.632271	+	1.24090i	0.323344	+	0.946281i	$0.395193\pi$
$197$	−124.557	+	244.457i	−0.632271	+	1.24090i	−0.955615	+	0.294619i	$0.904807\pi$
$198$	−127.048	+	20.1224i	−0.641655	+	0.101628i
$199$		−	299.766i		−	1.50636i	−0.657812	−	0.753182i	$-0.728518\pi$
$199$		−	299.766i		−	1.50636i	0.657812	−	0.753182i	$-0.271482\pi$
$200$		0			0
$201$	18.6394			0.0927334
$202$	−25.7464	−	162.556i	−0.127457	−	0.804734i
$203$	110.433	+	56.2684i	0.544005	+	0.277184i
$204$	−51.8187	+	16.8369i	−0.254013	+	0.0825339i
$205$		0			0
$206$	−29.4449	+	90.6219i	−0.142936	+	0.439912i
$207$	−60.8787	−	60.8787i	−0.294100	−	0.294100i
$208$	24.5572	+	48.1961i	0.118063	+	0.231712i
$209$	192.299	+	264.677i	0.920093	+	1.26640i
$210$		0			0
$211$	167.817	+	121.926i	0.795339	+	0.577848i	0.909543	−	0.415609i	$-0.136432\pi$
$211$	167.817	+	121.926i	0.795339	+	0.577848i	−0.114204	+	0.993457i	$0.536432\pi$
$212$	38.4187	+	6.08493i	0.181220	+	0.0287025i
$213$	−12.6679	+	79.9821i	−0.0594738	+	0.375503i
$214$	26.4818	−	36.4490i	0.123747	−	0.170323i
$215$		0			0
$216$	−23.0563	+	16.7513i	−0.106742	+	0.0775525i
$217$	120.121	−	61.2046i	0.553552	−	0.282049i
$218$	−94.7701	+	94.7701i	−0.434725	+	0.434725i
$219$	53.9865	+	17.5413i	0.246514	+	0.0800971i
$220$		0			0
$221$	15.5023	+	47.7111i	0.0701461	+	0.215888i
$222$	−79.9467	+	156.904i	−0.360120	+	0.706776i
$223$	−299.874	+	47.4954i	−1.34473	+	0.212984i	−0.786955	−	0.617010i	$-0.788344\pi$
$223$	−299.874	+	47.4954i	−1.34473	+	0.212984i	−0.557772	+	0.829994i	$0.688344\pi$
$224$			209.226i			0.934046i
$225$		0			0
$226$	−456.610			−2.02040
$227$	41.4802	+	261.895i	0.182732	+	1.15372i	0.893088	+	0.449882i	$0.148534\pi$
$227$	41.4802	+	261.895i	0.182732	+	1.15372i	−0.710356	+	0.703843i	$0.751466\pi$
$228$	−47.9032	−	24.4079i	−0.210102	−	0.107052i
$229$	226.534	−	73.6053i	0.989230	−	0.321420i	0.230676	−	0.973031i	$-0.425906\pi$
$229$	226.534	−	73.6053i	0.989230	−	0.321420i	0.758554	+	0.651610i	$0.225906\pi$
$230$		0			0
$231$	−78.4915	+	241.572i	−0.339790	+	1.04577i
$232$	−58.8478	−	58.8478i	−0.253654	−	0.253654i
$233$	−39.0921	−	76.7226i	−0.167777	−	0.329282i	0.791774	−	0.610814i	$-0.209157\pi$
$233$	−39.0921	−	76.7226i	−0.167777	−	0.329282i	−0.959552	+	0.281532i	$0.909157\pi$
$234$	−11.4399	−	15.7457i	−0.0488886	−	0.0672894i
$235$		0			0
$236$	−118.605	−	86.1714i	−0.502563	−	0.365133i
$237$	142.696	+	22.6008i	0.602091	+	0.0953619i
$238$	−56.3534	+	355.801i	−0.236779	+	1.49496i
$239$	−18.2516	+	25.1211i	−0.0763664	+	0.105109i	−0.845491	−	0.533989i	$-0.820692\pi$
$239$	−18.2516	+	25.1211i	−0.0763664	+	0.105109i	0.769125	+	0.639098i	$0.220692\pi$
$240$		0			0
$241$	189.951	−	138.008i	0.788180	−	0.572646i	−0.119243	−	0.992865i	$-0.538047\pi$
$241$	189.951	−	138.008i	0.788180	−	0.572646i	0.907423	+	0.420219i	$0.138047\pi$
$242$	428.431	−	218.297i	1.77038	−	0.902052i
$243$	11.0227	−	11.0227i	0.0453609	−	0.0453609i
$244$	66.6594	+	21.6590i	0.273194	+	0.0887662i
$245$		0			0
$246$	−96.4306	−	296.783i	−0.391994	−	1.20643i
$247$	−22.4731	+	44.1060i	−0.0909844	+	0.178567i
$248$	−89.4097	+	14.1611i	−0.360523	+	0.0571012i
$249$		−	14.4265i		−	0.0579377i
$250$		0			0
$251$	168.389			0.670873			0.335436	−	0.942063i	$-0.391116\pi$
$251$	168.389			0.670873			0.335436	+	0.942063i	$0.391116\pi$
$252$	−6.52976	−	41.2273i	−0.0259118	−	0.163600i
$253$	459.090	+	233.918i	1.81459	+	0.924578i
$254$	−404.106	+	131.302i	−1.59097	+	0.516936i
$255$		0			0
$256$	85.3393	−	262.647i	0.333357	−	1.02597i
$257$	55.4214	+	55.4214i	0.215647	+	0.215647i	0.806661	−	0.591014i	$-0.201272\pi$
$257$	55.4214	+	55.4214i	0.215647	+	0.215647i	−0.591014	+	0.806661i	$0.701272\pi$
$258$	−48.7827	−	95.7414i	−0.189080	−	0.371091i
$259$	204.393	+	281.323i	0.789163	+	1.08619i
$260$		0			0
$261$	36.8278	+	26.7569i	0.141102	+	0.102517i
$262$	−339.692	−	53.8019i	−1.29653	−	0.205351i
$263$	32.3760	−	204.414i	0.123103	−	0.777240i	−0.846470	−	0.532437i	$-0.821276\pi$
$263$	32.3760	−	204.414i	0.123103	−	0.777240i	0.969573	−	0.244804i	$-0.0787235\pi$
$264$	100.250	−	137.983i	0.379737	−	0.522663i
$265$		0			0
$266$	−287.573	+	208.934i	−1.08110	+	0.785467i
$267$	−55.7002	+	28.3807i	−0.208615	+	0.106295i
$268$	12.9622	−	12.9622i	0.0483664	−	0.0483664i
$269$	−134.702	−	43.7675i	−0.500753	−	0.162704i	0.0477400	−	0.998860i	$-0.484798\pi$
$269$	−134.702	−	43.7675i	−0.500753	−	0.162704i	−0.548493	+	0.836155i	$0.684798\pi$
$270$		0			0
$271$	6.01070	+	18.4990i	0.0221797	+	0.0682622i	0.961534	−	0.274687i	$-0.0885742\pi$
$271$	6.01070	+	18.4990i	0.0221797	+	0.0682622i	−0.939354	+	0.342949i	$0.888574\pi$
$272$	166.940	−	327.638i	0.613750	−	1.20455i
$273$	−37.9593	+	6.01216i	−0.139045	+	0.0220226i
$274$			376.609i			1.37449i
$275$		0			0
$276$	−84.6724			−0.306784
$277$	63.3164	+	399.764i	0.228579	+	1.44319i	0.788699	+	0.614780i	$0.210755\pi$
$277$	63.3164	+	399.764i	0.228579	+	1.44319i	−0.560119	+	0.828412i	$0.689245\pi$
$278$	−446.939	−	227.727i	−1.60770	−	0.819162i
$279$	47.0916	−	15.3010i	0.168787	−	0.0548422i
$280$		0			0
$281$	−138.832	+	427.281i	−0.494064	+	1.52057i	0.324347	+	0.945938i	$0.394855\pi$
$281$	−138.832	+	427.281i	−0.494064	+	1.52057i	−0.818411	+	0.574633i	$0.805145\pi$
$282$	211.239	+	211.239i	0.749076	+	0.749076i
$283$	−205.464	−	403.245i	−0.726020	−	1.42489i	−0.898091	−	0.439810i	$-0.855046\pi$
$283$	−205.464	−	403.245i	−0.726020	−	1.42489i	0.172071	−	0.985085i	$-0.444954\pi$
$284$	46.8115	+	64.4306i	0.164829	+	0.226868i
$285$		0			0
$286$	94.2321	+	68.4636i	0.329483	+	0.239383i
$287$	−608.619	−	96.3958i	−2.12062	−	0.335874i
$288$	−12.0212	+	75.8989i	−0.0417403	+	0.263538i
$289$	30.5839	−	42.0951i	0.105827	−	0.145658i
$290$		0			0
$291$	34.9257	−	25.3750i	0.120020	−	0.0871994i
$292$	49.7417	−	25.3447i	0.170348	−	0.0867968i
$293$	−244.581	+	244.581i	−0.834749	+	0.834749i	−0.988162	−	0.153413i	$-0.950973\pi$
$293$	−244.581	+	244.581i	−0.834749	+	0.834749i	0.153413	+	0.988162i	$0.450973\pi$
$294$	−69.7031	−	22.6479i	−0.237085	−	0.0770337i
$295$		0			0
$296$	−72.1535	−	222.066i	−0.243762	−	0.750221i
$297$	−42.3532	+	83.1229i	−0.142603	+	0.279875i
$298$	76.4153	−	12.1030i	0.256427	−	0.0406141i
$299$			77.9606i			0.260738i
$300$		0			0
$301$	−212.184			−0.704930
$302$	103.116	+	651.047i	0.341443	+	2.15578i
$303$	−106.355	−	54.1905i	−0.351006	−	0.178847i
$304$	345.083	−	112.124i	1.13514	−	0.368830i
$305$		0			0
$306$	−40.8855	+	125.833i	−0.133613	+	0.411218i
$307$	−293.569	−	293.569i	−0.956250	−	0.956250i	0.0428322	−	0.999082i	$-0.486362\pi$
$307$	−293.569	−	293.569i	−0.956250	−	0.956250i	−0.999082	+	0.0428322i	$0.986362\pi$
$308$	113.409	+	222.578i	0.368212	+	0.722656i
$309$	40.6199	+	55.9085i	0.131456	+	0.180934i
$310$		0			0
$311$	−107.626	−	78.1952i	−0.346066	−	0.251431i	0.401151	−	0.916012i	$-0.368610\pi$
$311$	−107.626	−	78.1952i	−0.346066	−	0.251431i	−0.747217	+	0.664580i	$0.768610\pi$
$312$	25.4886	+	4.03699i	0.0816941	+	0.0129391i
$313$	−42.1833	+	266.335i	−0.134771	+	0.850911i	0.823971	+	0.566632i	$0.191754\pi$
$313$	−42.1833	+	266.335i	−0.134771	+	0.850911i	−0.958742	+	0.284278i	$0.908246\pi$
$314$	218.223	−	300.358i	0.694976	−	0.956553i
$315$		0			0
$316$	114.950	−	83.5162i	0.363767	−	0.264292i
$317$	362.809	−	184.860i	1.14451	−	0.583156i	0.224274	−	0.974526i	$-0.427999\pi$
$317$	362.809	−	184.860i	1.14451	−	0.583156i	0.920233	+	0.391370i	$0.127999\pi$
$318$	66.7905	−	66.7905i	0.210033	−	0.210033i
$319$	−259.096	−	84.1854i	−0.812213	−	0.263904i
$320$		0			0
$321$	−10.0973	−	31.0762i	−0.0314556	−	0.0968105i
$322$	−254.153	+	498.804i	−0.789296	+	1.54908i
$323$	332.368	−	52.6419i	1.02900	−	0.162978i
$324$		−	15.3308i		−	0.0473172i
$325$		0			0
$326$	−421.718			−1.29361
$327$	15.2059	+	96.0062i	0.0465012	+	0.293597i
$328$	368.667	+	187.845i	1.12398	+	0.572699i
$329$	561.035	−	182.291i	1.70527	−	0.554077i
$330$		0			0
$331$	−0.0623887	+	0.192013i	−0.000188485	+	0.000580099i	−0.951151	−	0.308727i	$-0.900097\pi$
$331$	−0.0623887	+	0.192013i	−0.000188485	+	0.000580099i	0.950962	+	0.309307i	$0.100097\pi$
$332$	−10.0324	−	10.0324i	−0.0302182	−	0.0302182i
$333$	57.9821	+	113.796i	0.174120	+	0.341730i
$334$	−101.815	−	140.137i	−0.304836	−	0.419571i
$335$		0			0
$336$	227.906	+	165.583i	0.678292	+	0.492808i
$337$	152.473	+	24.1493i	0.452441	+	0.0716596i	0.378497	−	0.925603i	$-0.376441\pi$
$337$	152.473	+	24.1493i	0.452441	+	0.0716596i	0.0739446	+	0.997262i	$0.476441\pi$
$338$	60.3805	−	381.227i	0.178640	−	1.12789i
$339$	−194.651	+	267.914i	−0.574192	+	0.790308i
$340$		0			0
$341$	−239.735	+	174.178i	−0.703035	+	0.510785i
$342$	−116.324	+	59.2703i	−0.340130	+	0.173305i
$343$	180.676	−	180.676i	0.526751	−	0.526751i
$344$	135.502	+	44.0273i	0.393901	+	0.127986i
$345$		0			0
$346$	−92.9627	−	286.110i	−0.268678	−	0.826907i
$347$	−163.335	+	320.562i	−0.470705	+	0.923811i	0.526577	+	0.850128i	$0.323475\pi$
$347$	−163.335	+	320.562i	−0.470705	+	0.923811i	−0.997282	+	0.0736830i	$0.976525\pi$
$348$	44.2180	−	7.00344i	0.127063	−	0.0201248i
$349$		−	332.528i		−	0.952804i	−0.879228	−	0.476402i	$-0.841941\pi$
$349$		−	332.528i		−	0.952804i	0.879228	−	0.476402i	$-0.158059\pi$
$350$		0			0
$351$	−14.1155			−0.0402152
$352$	−71.9423	−	454.226i	−0.204382	−	1.29042i
$353$	−428.726	−	218.447i	−1.21452	−	0.618830i	−0.275041	−	0.961432i	$-0.588691\pi$
$353$	−428.726	−	218.447i	−1.21452	−	0.618830i	−0.939480	+	0.342603i	$0.888691\pi$
$354$	−338.577	+	110.010i	−0.956432	+	0.310764i
$355$		0			0
$356$	−18.9985	+	58.4714i	−0.0533666	+	0.164245i
$357$	184.742	+	184.742i	0.517484	+	0.517484i
$358$	143.010	+	280.673i	0.399469	+	0.784002i
$359$	−300.051	−	412.985i	−0.835796	−	1.15037i	−0.986816	−	0.161844i	$-0.948256\pi$
$359$	−300.051	−	412.985i	−0.835796	−	1.15037i	0.151020	−	0.988531i	$-0.451744\pi$
$360$		0			0
$361$	−23.4216	−	17.0168i	−0.0648797	−	0.0471379i
$362$	−232.154	−	36.7695i	−0.641308	−	0.101573i
$363$	54.5539	−	344.440i	0.150286	−	0.948869i
$364$	−22.2166	+	30.5786i	−0.0610347	+	0.0840070i
$365$		0			0
$366$	137.695	−	100.041i	0.376217	−	0.273337i
$367$	169.022	−	86.1210i	0.460551	−	0.234662i	−0.208291	−	0.978067i	$-0.566790\pi$
$367$	169.022	−	86.1210i	0.460551	−	0.234662i	0.668842	+	0.743405i	$0.266790\pi$
$368$	404.073	−	404.073i	1.09803	−	1.09803i
$369$	−215.244	−	69.9371i	−0.583318	−	0.189531i
$370$		0			0
$371$	−57.6376	−	177.390i	−0.155357	−	0.478141i
$372$	22.1078	−	43.3889i	0.0594295	−	0.116637i
$373$	326.019	−	51.6363i	0.874045	−	0.138435i	0.296735	−	0.954960i	$-0.404102\pi$
$373$	326.019	−	51.6363i	0.874045	−	0.138435i	0.577310	+	0.816525i	$0.304102\pi$
$374$		−	791.814i		−	2.11715i
$375$		0			0
$376$	−396.105			−1.05347
$377$	−6.44829	−	40.7129i	−0.0171042	−	0.107992i
$378$	−90.3134	−	46.0170i	−0.238924	−	0.121738i
$379$	−458.598	+	149.007i	−1.21002	+	0.393160i	−0.843438	−	0.537226i	$-0.819472\pi$
$379$	−458.598	+	149.007i	−1.21002	+	0.393160i	−0.366582	+	0.930386i	$0.619472\pi$
$380$		0			0
$381$	−95.2278	+	293.081i	−0.249942	+	0.769242i
$382$	−327.235	−	327.235i	−0.856635	−	0.856635i
$383$	−91.6581	−	179.889i	−0.239316	−	0.469684i	0.739843	−	0.672780i	$-0.234900\pi$
$383$	−91.6581	−	179.889i	−0.239316	−	0.469684i	−0.979159	+	0.203095i	$0.934900\pi$
$384$	−149.231	−	205.398i	−0.388621	−	0.534891i
$385$		0			0
$386$	301.277	+	218.891i	0.780511	+	0.567075i
$387$	−76.9718	−	12.1911i	−0.198894	−	0.0315016i
$388$	6.64173	−	41.9342i	0.0171179	−	0.108078i
$389$	−277.352	+	381.742i	−0.712987	+	0.981343i	0.286740	+	0.958008i	$0.407428\pi$
$389$	−277.352	+	381.742i	−0.712987	+	0.981343i	−0.999728	+	0.0233346i	$0.992572\pi$
$390$		0			0
$391$	428.761	−	311.513i	1.09657	−	0.796708i
$392$	86.5859	−	44.1177i	0.220883	−	0.112545i
$393$	−176.378	+	176.378i	−0.448798	+	0.448798i
$394$	623.156	+	202.476i	1.58161	+	0.513897i
$395$		0			0
$396$	28.3520	+	87.2584i	0.0715959	+	0.220350i
$397$	146.446	−	287.417i	0.368882	−	0.723972i	−0.629720	−	0.776822i	$-0.716831\pi$
$397$	146.446	−	287.417i	0.368882	−	0.723972i	0.998602	+	0.0528501i	$0.0168306\pi$
$398$	−707.083	+	111.991i	−1.77659	+	0.281384i
$399$			257.801i			0.646117i
$400$		0			0
$401$	502.077			1.25206			0.626031	−	0.779798i	$-0.284678\pi$
$401$	502.077			1.25206			0.626031	+	0.779798i	$0.284678\pi$
$402$	−6.96357	−	43.9663i	−0.0173223	−	0.109369i
$403$	−39.9496	−	20.3553i	−0.0991305	−	0.0505095i
$404$	−111.646	+	36.2761i	−0.276352	+	0.0897922i
$405$		0			0
$406$	91.4678	−	281.509i	0.225290	−	0.693372i
$407$	−540.466	−	540.466i	−1.32793	−	1.32793i
$408$	−79.6442	−	156.311i	−0.195206	−	0.383114i
$409$	−24.4376	−	33.6355i	−0.0597497	−	0.0822384i	0.778097	−	0.628145i	$-0.216185\pi$
$409$	−24.4376	−	33.6355i	−0.0597497	−	0.0822384i	−0.837846	+	0.545906i	$0.816185\pi$
$410$		0			0
$411$	220.974	+	160.547i	0.537650	+	0.390625i
$412$	67.1276	+	10.6320i	0.162931	+	0.0258057i
$413$	−109.971	+	694.328i	−0.266273	+	1.68118i
$414$	−120.856	+	166.344i	−0.291922	+	0.401796i
$415$		0			0
$416$	56.2947	−	40.9005i	0.135324	−	0.0983185i
$417$	−324.147	+	165.161i	−0.777330	+	0.396070i
$418$	552.474	−	552.474i	1.32171	−	1.32171i
$419$	−113.394	−	36.8440i	−0.270631	−	0.0879333i	0.170558	−	0.985348i	$-0.445443\pi$
$419$	−113.394	−	36.8440i	−0.270631	−	0.0879333i	−0.441189	+	0.897414i	$0.645443\pi$
$420$		0			0
$421$	−12.5000	−	38.4712i	−0.0296913	−	0.0913804i	0.935113	−	0.354350i	$-0.115298\pi$
$421$	−12.5000	−	38.4712i	−0.0296913	−	0.0913804i	−0.964804	+	0.262970i	$0.915298\pi$
$422$	224.901	−	441.393i	0.532941	−	1.04596i
$423$	213.995	−	33.8934i	0.505897	−	0.0801263i
$424$			125.242i			0.295382i
$425$		0			0
$426$	193.393			0.453974
$427$	−52.5760	−	331.952i	−0.123129	−	0.777405i
$428$	−28.6328	−	14.5891i	−0.0668990	−	0.0340867i
$429$	80.3416	−	26.1046i	0.187276	−	0.0608498i
$430$		0			0
$431$	−22.9936	+	70.7669i	−0.0533493	+	0.164192i	−0.974181	−	0.225767i	$-0.927511\pi$
$431$	−22.9936	+	70.7669i	−0.0533493	+	0.164192i	0.920832	+	0.389960i	$0.127511\pi$
$432$	73.1615	+	73.1615i	0.169355	+	0.169355i
$433$	141.805	+	278.309i	0.327495	+	0.642745i	0.994778	−	0.102059i	$-0.0325429\pi$
$433$	141.805	+	278.309i	0.327495	+	0.642745i	−0.667283	+	0.744804i	$0.732543\pi$
$434$	−189.245	−	260.473i	−0.436048	−	0.600168i
$435$		0			0
$436$	77.3389	+	56.1900i	0.177383	+	0.128876i
$437$	516.512	+	81.8075i	1.18195	+	0.187203i
$438$	21.2070	−	133.896i	0.0484178	−	0.305698i
$439$	−182.989	+	251.863i	−0.416831	+	0.573719i	−0.964868	−	0.262735i	$-0.915375\pi$
$439$	−182.989	+	251.863i	−0.416831	+	0.573719i	0.548037	+	0.836454i	$0.315375\pi$
$440$		0			0
$441$	−43.0028	+	31.2433i	−0.0975119	+	0.0708465i
$442$	106.749	−	54.3911i	0.241513	−	0.123057i
$443$	−393.848	+	393.848i	−0.889047	+	0.889047i	−0.994432	−	0.105385i	$-0.966393\pi$
$443$	−393.848	+	393.848i	−0.889047	+	0.889047i	0.105385	+	0.994432i	$0.466393\pi$
$444$	119.458	+	38.8142i	0.269049	+	0.0874194i
$445$		0			0
$446$	224.063	+	689.593i	0.502382	+	1.54617i
$447$	25.4742	−	49.9959i	0.0569892	−	0.111848i
$448$	−149.047	+	23.6067i	−0.332694	+	0.0526935i
$449$			310.377i			0.691262i	0.938371	+	0.345631i	$0.112335\pi$
$449$			310.377i			0.691262i	−0.938371	+	0.345631i	$0.887665\pi$
$450$		0			0
$451$	1354.45			3.00321
$452$	50.9486	+	321.677i	0.112718	+	0.711674i
$453$	425.957	+	217.036i	0.940303	+	0.479108i
$454$	602.257	−	195.685i	1.32656	−	0.431025i
$455$		0			0
$456$	53.4926	−	164.633i	0.117308	−	0.361038i
$457$	225.209	+	225.209i	0.492798	+	0.492798i	0.909187	−	0.416388i	$-0.136704\pi$
$457$	225.209	+	225.209i	0.492798	+	0.492798i	−0.416388	+	0.909187i	$0.636704\pi$
$458$	−258.250	−	506.845i	−0.563866	−	1.10665i
$459$	56.4025	+	77.6314i	0.122881	+	0.169132i
$460$		0			0
$461$	−455.660	−	331.057i	−0.988417	−	0.718127i	−0.0288435	−	0.999584i	$-0.509182\pi$
$461$	−455.660	−	331.057i	−0.988417	−	0.718127i	−0.959574	+	0.281457i	$0.909182\pi$
$462$	599.140	+	94.8944i	1.29684	+	0.205399i
$463$	33.1683	−	209.416i	0.0716377	−	0.452303i	−0.925630	−	0.378430i	$-0.876464\pi$
$463$	33.1683	−	209.416i	0.0716377	−	0.452303i	0.997268	−	0.0738729i	$-0.0235359\pi$
$464$	−177.595	+	244.439i	−0.382748	+	0.526807i
$465$		0			0
$466$	−166.367	+	120.873i	−0.357011	+	0.259384i
$467$	233.668	−	119.060i	0.500359	−	0.254946i	−0.185547	−	0.982635i	$-0.559406\pi$
$467$	233.668	−	119.060i	0.500359	−	0.254946i	0.685907	+	0.727690i	$0.259406\pi$
$468$	−9.81621	+	9.81621i	−0.0209748	+	0.0209748i
$469$	−83.5987	−	27.1629i	−0.178249	−	0.0579166i
$470$		0			0
$471$	−83.2063	−	256.083i	−0.176659	−	0.543700i
$472$	214.298	−	420.584i	0.454022	−	0.891068i
$473$	460.647	−	72.9593i	0.973884	−	0.154248i
$474$		−	345.031i		−	0.727914i
$475$		0			0
$476$	256.946			0.539802
$477$	−10.7166	−	67.6616i	−0.0224666	−	0.141848i
$478$	66.0740	+	33.6664i	0.138230	+	0.0704317i
$479$	−227.892	+	74.0466i	−0.475766	+	0.154586i	−0.537077	−	0.843533i	$-0.680472\pi$
$479$	−227.892	+	74.0466i	−0.475766	+	0.154586i	0.0613115	+	0.998119i	$0.480472\pi$
$480$		0			0
$481$	35.7375	−	109.989i	0.0742983	−	0.228667i
$482$	−396.495	−	396.495i	−0.822603	−	0.822603i
$483$	184.327	+	361.762i	0.381629	+	0.748989i
$484$	−201.592	−	277.467i	−0.416512	−	0.573280i
$485$		0			0
$486$	−30.1182	−	21.8821i	−0.0619715	−	0.0450250i
$487$	−57.3791	−	9.08795i	−0.117821	−	0.0186611i	0.0972452	−	0.995260i	$-0.468997\pi$
$487$	−57.3791	−	9.08795i	−0.117821	−	0.0186611i	−0.215067	+	0.976599i	$0.568997\pi$
$488$	−35.3033	+	222.896i	−0.0723427	+	0.456754i
$489$	−179.777	+	247.442i	−0.367642	+	0.506016i
$490$		0			0
$491$	66.1686	−	48.0743i	0.134763	−	0.0979110i	−0.518362	−	0.855162i	$-0.673458\pi$
$491$	66.1686	−	48.0743i	0.134763	−	0.0979110i	0.653124	+	0.757251i	$0.273458\pi$
$492$	−198.320	+	101.049i	−0.403090	+	0.205385i
$493$	−198.143	+	198.143i	−0.401913	+	0.401913i
$494$	112.432	+	36.5315i	0.227596	+	0.0739503i
$495$		0			0
$496$	101.558	+	312.563i	0.204754	+	0.630168i
$497$	173.373	−	340.263i	0.348839	−	0.684634i
$498$	−34.0289	+	5.38965i	−0.0683311	+	0.0108226i
$499$		−	232.716i		−	0.466365i	−0.972433	−	0.233183i	$-0.925086\pi$
$499$		−	232.716i		−	0.466365i	0.972433	−	0.233183i	$-0.0749140\pi$
$500$		0			0
$501$	−125.628			−0.250755
$502$	−62.9092	−	397.193i	−0.125317	−	0.791221i
$503$	468.444	+	238.684i	0.931300	+	0.474521i	0.852709	−	0.522386i	$-0.174958\pi$
$503$	468.444	+	238.684i	0.931300	+	0.474521i	0.0785911	+	0.996907i	$0.474958\pi$
$504$	127.820	−	41.5312i	0.253611	−	0.0824032i
$505$		0			0
$506$	380.248	−	1170.28i	0.751479	−	2.31281i
$507$	−197.944	−	197.944i	−0.390422	−	0.390422i
$508$	137.591	+	270.037i	0.270848	+	0.531569i
$509$	−135.466	−	186.453i	−0.266141	−	0.366312i	0.654941	−	0.755680i	$-0.272693\pi$
$509$	−135.466	−	186.453i	−0.266141	−	0.366312i	−0.921082	+	0.389368i	$0.872693\pi$
$510$		0			0
$511$	−216.570	−	157.347i	−0.423815	−	0.307920i
$512$	−72.3030	−	11.4517i	−0.141217	−	0.0223665i
$513$	−14.8121	+	93.5197i	−0.0288734	+	0.182300i
$514$	110.022	−	151.432i	0.214050	−	0.294615i
$515$		0			0
$516$	−62.0055	+	45.0497i	−0.120166	+	0.0873056i
$517$	−1155.31	+	588.662i	−2.23465	+	1.13861i
$518$	587.219	−	587.219i	1.13363	−	1.13363i
$519$	−207.504	−	67.4220i	−0.399814	−	0.129907i
$520$		0			0
$521$	171.171	+	526.809i	0.328543	+	1.01115i	0.969816	+	0.243838i	$0.0784064\pi$
$521$	171.171	+	526.809i	0.328543	+	1.01115i	−0.641274	+	0.767312i	$0.721594\pi$
$522$	49.3551	−	96.8648i	0.0945500	−	0.185565i
$523$	180.305	−	28.5575i	0.344752	−	0.0546033i	0.0183423	−	0.999832i	$-0.494161\pi$
$523$	180.305	−	28.5575i	0.344752	−	0.0546033i	0.326410	+	0.945228i	$0.394161\pi$
$524$			245.312i			0.468153i
$525$		0			0
$526$	−494.264			−0.939665
$527$	47.6811	+	301.046i	0.0904764	+	0.571245i
$528$	−551.715	−	281.113i	−1.04492	−	0.532411i
$529$	280.186	−	91.0378i	0.529651	−	0.172094i
$530$		0			0
$531$	−79.7859	+	245.556i	−0.150256	+	0.462440i
$532$	179.279	+	179.279i	0.336991	+	0.336991i
$533$	93.0393	+	182.600i	0.174558	+	0.342589i
$534$	87.7530	+	120.782i	0.164331	+	0.226183i
$535$		0			0
$536$	47.7505	+	34.6928i	0.0890868	+	0.0647254i
$537$	225.648	+	35.7392i	0.420202	+	0.0665534i
$538$	−52.9138	+	334.085i	−0.0983529	+	0.620976i
$539$	186.979	−	257.355i	0.346901	−	0.477468i
$540$		0			0
$541$	736.024	−	534.753i	1.36049	−	0.988453i	0.362075	−	0.932149i	$-0.382068\pi$
$541$	736.024	−	534.753i	1.36049	−	0.988453i	0.998414	−	0.0563041i	$-0.0179316\pi$
$542$	41.3896	−	21.0891i	0.0763646	−	0.0389097i
$543$	−120.541	+	120.541i	−0.221990	+	0.221990i
$544$	−449.882	−	146.175i	−0.826989	−	0.268705i
$545$		0			0
$546$	28.3627	+	87.2915i	0.0519464	+	0.159875i
$547$	21.0507	−	41.3143i	0.0384839	−	0.0755290i	−0.870964	−	0.491347i	$-0.836505\pi$
$547$	21.0507	−	41.3143i	0.0384839	−	0.0755290i	0.909448	+	0.415818i	$0.136505\pi$
$548$	265.317	−	42.0220i	0.484155	−	0.0766826i
$549$		−	123.440i		−	0.224844i
$550$		0			0
$551$	−276.502			−0.501818
$552$	−42.6483	−	269.271i	−0.0772614	−	0.487809i
$553$	−607.062	−	309.314i	−1.09776	−	0.559337i
$554$	919.301	−	298.699i	1.65939	−	0.539168i
$555$		0			0
$556$	−110.562	+	340.274i	−0.198852	+	0.612003i
$557$	254.601	+	254.601i	0.457094	+	0.457094i	0.897700	−	0.440606i	$-0.145237\pi$
$557$	254.601	+	254.601i	0.457094	+	0.457094i	−0.440606	+	0.897700i	$0.645237\pi$
$558$	−53.6848	−	105.362i	−0.0962093	−	0.188821i
$559$	41.4787	+	57.0905i	0.0742015	+	0.102130i
$560$		0			0
$561$	−464.594	−	337.548i	−0.828154	−	0.601689i
$562$	1059.73	+	167.844i	1.88564	+	0.298656i
$563$	88.7328	−	560.237i	0.157607	−	0.995093i	−0.774411	−	0.632682i	$-0.781954\pi$
$563$	88.7328	−	560.237i	0.157607	−	0.995093i	0.932019	−	0.362410i	$-0.118046\pi$
$564$	125.246	−	172.386i	0.222067	−	0.305649i
$565$		0			0
$566$	−874.407	+	635.294i	−1.54489	+	1.12243i
$567$	−65.5006	+	33.3742i	−0.115521	+	0.0588611i
$568$	−181.320	+	181.320i	−0.319226	+	0.319226i
$569$	68.3828	+	22.2189i	0.120181	+	0.0390491i	0.368490	−	0.929632i	$-0.379875\pi$
$569$	68.3828	+	22.2189i	0.120181	+	0.0390491i	−0.248309	+	0.968681i	$0.579875\pi$
$570$		0			0
$571$	26.6887	+	82.1395i	0.0467404	+	0.143852i	0.971703	−	0.236206i	$-0.0759040\pi$
$571$	26.6887	+	82.1395i	0.0467404	+	0.143852i	−0.924963	+	0.380058i	$0.875904\pi$
$572$	37.7174	−	74.0246i	0.0659396	−	0.129414i
$573$	−331.503	+	52.5049i	−0.578539	+	0.0916316i
$574$			1471.61i			2.56379i
$575$		0			0
$576$	−55.4246			−0.0962232
$577$	−8.31247	−	52.4829i	−0.0144064	−	0.0909582i	0.979438	−	0.201748i	$-0.0646621\pi$
$577$	−8.31247	−	52.4829i	−0.0144064	−	0.0909582i	−0.993844	+	0.110789i	$0.964662\pi$
$578$	−110.719	−	56.4142i	−0.191555	−	0.0976024i
$579$	256.867	−	83.4611i	0.443639	−	0.144147i
$580$		0			0
$581$	−21.0235	+	64.7035i	−0.0361849	+	0.111366i
$582$	−72.9021	−	72.9021i	−0.125261	−	0.125261i
$583$	186.126	+	365.292i	0.319255	+	0.626573i
$584$	105.654	+	145.420i	0.180914	+	0.249007i
$585$		0			0
$586$	668.288	+	485.540i	1.14042	+	0.828566i
$587$	−634.141	−	100.438i	−1.08031	−	0.171104i	−0.409187	−	0.912451i	$-0.634188\pi$
$587$	−634.141	−	100.438i	−1.08031	−	0.171104i	−0.671122	+	0.741347i	$0.734188\pi$
$588$	−8.17772	+	51.6321i	−0.0139077	+	0.0878097i
$589$	−176.781	+	243.318i	−0.300138	+	0.413104i
$590$		0			0
$591$	384.451	−	279.320i	0.650509	−	0.472622i
$592$	−755.305	+	384.847i	−1.27585	+	0.650080i
$593$	−336.039	+	336.039i	−0.566676	+	0.566676i	−0.931196	−	0.364520i	$-0.881233\pi$
$593$	−336.039	+	336.039i	−0.566676	+	0.566676i	0.364520	+	0.931196i	$0.381233\pi$
$594$	211.892	+	68.8478i	0.356720	+	0.115905i
$595$		0			0
$596$	−17.0529	−	52.4833i	−0.0286122	−	0.0880592i
$597$	−235.717	+	462.620i	−0.394835	+	0.774908i
$598$	183.892	−	29.1256i	0.307512	−	0.0487051i
$599$			763.402i			1.27446i	0.770673	+	0.637230i	$0.219920\pi$
$599$			763.402i			1.27446i	−0.770673	+	0.637230i	$0.780080\pi$
$600$		0			0
$601$	−1140.68			−1.89796			−0.948982	−	0.315330i	$-0.897885\pi$
$601$	−1140.68			−1.89796			−0.948982	+	0.315330i	$0.897885\pi$
$602$	79.2706	+	500.495i	0.131679	+	0.831387i
$603$	−28.7656	−	14.6568i	−0.0477042	−	0.0243065i
$604$	447.150	−	145.288i	0.740314	−	0.240543i
$605$		0			0
$606$	−88.0900	+	271.113i	−0.145363	+	0.447381i
$607$	377.961	+	377.961i	0.622670	+	0.622670i	0.946213	−	0.323543i	$-0.104874\pi$
$607$	377.961	+	377.961i	0.622670	+	0.622670i	−0.323543	+	0.946213i	$0.604874\pi$
$608$	−211.906	−	415.888i	−0.348529	−	0.684026i
$609$	−126.182	−	173.675i	−0.207195	−	0.285180i
$610$		0			0
$611$	−158.721	−	115.318i	−0.259773	−	0.188736i
$612$	93.2097	+	14.7630i	0.152303	+	0.0241225i
$613$	97.3279	−	614.504i	0.158773	−	1.00245i	−0.771671	−	0.636021i	$-0.780579\pi$
$613$	97.3279	−	614.504i	0.158773	−	1.00245i	0.930445	−	0.366433i	$-0.119421\pi$
$614$	−582.789	+	802.140i	−0.949168	+	1.30642i
$615$		0			0
$616$	−650.709	+	472.767i	−1.05635	+	0.767480i
$617$	−607.650	+	309.613i	−0.984846	+	0.501804i	−0.870782	−	0.491669i	$-0.836387\pi$
$617$	−607.650	+	309.613i	−0.984846	+	0.501804i	−0.114064	+	0.993473i	$0.536387\pi$
$618$	116.700	−	116.700i	0.188836	−	0.188836i
$619$	−419.900	−	136.434i	−0.678352	−	0.220410i	−0.0504785	−	0.998725i	$-0.516075\pi$
$619$	−419.900	−	136.434i	−0.678352	−	0.220410i	−0.627874	+	0.778315i	$0.716075\pi$
$620$		0			0
$621$	46.0812	+	141.823i	0.0742048	+	0.228379i
$622$	−144.237	+	283.080i	−0.231892	+	0.455113i
$623$	291.177	−	46.1179i	0.467379	−	0.0740255i
$624$		−	93.6898i		−	0.150144i
$625$		0			0
$626$	643.986			1.02873
$627$	−88.6446	−	559.680i	−0.141379	−	0.892631i
$628$	−235.948	−	120.221i	−0.375713	−	0.191435i
$629$	−747.704	+	242.944i	−1.18872	+	0.386238i
$630$		0			0
$631$	−191.435	+	589.175i	−0.303383	+	0.933717i	0.676893	+	0.736082i	$0.263326\pi$
$631$	−191.435	+	589.175i	−0.303383	+	0.933717i	−0.980276	+	0.197635i	$0.936674\pi$
$632$	323.493	+	323.493i	0.511855	+	0.511855i
$633$	−163.112	−	320.124i	−0.257680	−	0.505726i
$634$	−571.588	−	786.724i	−0.901559	−	1.24089i
$635$		0			0
$636$	−54.5056	−	39.6007i	−0.0857007	−	0.0622652i
$637$	47.5393	+	7.52949i	0.0746300	+	0.0118202i
$638$	−101.778	+	642.602i	−0.159527	+	1.00721i
$639$	82.4427	−	113.473i	0.129018	−	0.177579i
$640$		0			0
$641$	−727.318	+	528.427i	−1.13466	+	0.824379i	−0.986366	−	0.164564i	$-0.947378\pi$
$641$	−727.318	+	528.427i	−1.13466	+	0.824379i	−0.148295	+	0.988943i	$0.547378\pi$
$642$	−69.5296	+	35.4271i	−0.108302	+	0.0551824i
$643$	−495.654	+	495.654i	−0.770846	+	0.770846i	−0.978255	−	0.207408i	$-0.933497\pi$
$643$	−495.654	+	495.654i	−0.770846	+	0.770846i	0.207408	+	0.978255i	$0.433497\pi$
$644$	379.760	+	123.392i	0.589690	+	0.191602i
$645$		0			0
$646$	−248.341	−	764.316i	−0.384429	−	1.18315i
$647$	88.4035	−	173.502i	0.136636	−	0.268163i	−0.812542	−	0.582902i	$-0.801917\pi$
$647$	88.4035	−	173.502i	0.136636	−	0.268163i	0.949178	+	0.314739i	$0.101917\pi$
$648$	48.7542	−	7.72190i	0.0752379	−	0.0119165i
$649$		−	1545.19i		−	2.38087i
$650$		0			0
$651$	−233.506			−0.358688
$652$	47.0554	+	297.096i	0.0721708	+	0.455668i
$653$	628.339	+	320.155i	0.962234	+	0.490283i	0.863234	−	0.504805i	$-0.168435\pi$
$653$	628.339	+	320.155i	0.962234	+	0.490283i	0.0990006	+	0.995087i	$0.468435\pi$
$654$	220.777	−	71.7347i	0.337579	−	0.109686i
$655$		0			0
$656$	464.197	−	1428.65i	0.707617	−	2.17782i
$657$	−69.5223	−	69.5223i	−0.105818	−	0.105818i
$658$	−639.584	−	1255.26i	−0.972013	−	1.90768i
$659$	−288.885	−	397.617i	−0.438369	−	0.603363i	0.531480	−	0.847071i	$-0.321636\pi$
$659$	−288.885	−	397.617i	−0.438369	−	0.603363i	−0.969849	+	0.243708i	$0.921636\pi$
$660$		0			0
$661$	−736.083	−	534.795i	−1.11359	−	0.809070i	−0.130364	−	0.991466i	$-0.541615\pi$
$661$	−736.083	−	534.795i	−1.11359	−	0.809070i	−0.983225	+	0.182396i	$0.941615\pi$
$662$	0.476224	+	0.0754264i	0.000719371	+	0.000113937i
$663$	13.5927	−	85.8211i	0.0205018	−	0.129444i
$664$	26.8514	−	36.9578i	0.0404389	−	0.0556594i
$665$		0			0
$666$	246.759	−	179.281i	0.370508	−	0.269190i
$667$	−388.004	+	197.698i	−0.581716	+	0.296399i
$668$	−87.3641	+	87.3641i	−0.130785	+	0.130785i
$669$	500.134	+	162.503i	0.747584	+	0.242905i
$670$		0			0
$671$	228.283	+	702.583i	0.340213	+	1.04707i
$672$	164.522	−	322.892i	0.244824	−	0.480494i
$673$	−420.027	+	66.5258i	−0.624112	+	0.0988496i	−0.460478	−	0.887671i	$-0.652322\pi$
$673$	−420.027	+	66.5258i	−0.624112	+	0.0988496i	−0.163635	+	0.986521i	$0.552322\pi$
$674$		−	368.672i		−	0.546991i
$675$		0			0
$676$	−275.308			−0.407260
$677$	129.929	+	820.342i	0.191919	+	1.21173i	0.875995	+	0.482320i	$0.160206\pi$
$677$	129.929	+	820.342i	0.191919	+	1.21173i	−0.684076	+	0.729411i	$0.739794\pi$
$678$	704.672	+	359.048i	1.03934	+	0.529570i
$679$	−193.622	+	62.9117i	−0.285158	+	0.0926534i
$680$		0			0
$681$	141.922	−	436.792i	0.208403	−	0.641399i
$682$	500.410	+	500.410i	0.733739	+	0.733739i
$683$	284.079	+	557.537i	0.415929	+	0.816306i	0.999989	+	0.00459594i	$0.00146294\pi$
$683$	284.079	+	557.537i	0.415929	+	0.816306i	−0.584061	+	0.811710i	$0.698537\pi$
$684$	54.7347	+	75.3359i	0.0800216	+	0.110140i
$685$		0			0
$686$	−493.674	−	358.675i	−0.719641	−	0.522850i
$687$	−407.481	−	64.5386i	−0.593131	−	0.0939427i
$688$	80.9168	−	510.888i	0.117612	−	0.742570i
$689$	−36.4616	+	50.1851i	−0.0529196	+	0.0728376i
$690$		0			0
$691$	−585.791	+	425.602i	−0.847744	+	0.615922i	−0.924523	−	0.381126i	$-0.875536\pi$
$691$	−585.791	+	425.602i	−0.847744	+	0.615922i	0.0767791	+	0.997048i	$0.475536\pi$
$692$	−191.188	+	97.4153i	−0.276284	+	0.140774i
$693$	311.090	−	311.090i	0.448903	−	0.448903i
$694$	817.157	+	265.510i	1.17746	+	0.382580i
$695$		0			0
$696$	44.5439	+	137.092i	0.0639999	+	0.196971i
$697$	632.483	−	1241.32i	0.907435	−	1.78094i
$698$	−784.362	+	124.231i	−1.12373	+	0.177981i
$699$			149.143i			0.213366i
$700$		0			0
$701$	668.428			0.953535			0.476768	−	0.879029i	$-0.341808\pi$
$701$	668.428			0.953535			0.476768	+	0.879029i	$0.341808\pi$
$702$	5.27348	+	33.2955i	0.00751209	+	0.0474294i
$703$	−691.207	−	352.187i	−0.983224	−	0.500978i
$704$	315.461	−	102.499i	0.448098	−	0.145596i
$705$		0			0
$706$	−355.099	+	1092.88i	−0.502973	+	1.54799i
$707$	398.036	+	398.036i	0.562993	+	0.562993i
$708$	115.279	+	226.249i	0.162824	+	0.319560i
$709$	127.787	+	175.884i	0.180235	+	0.248073i	0.889570	−	0.456799i	$-0.151004\pi$
$709$	127.787	+	175.884i	0.180235	+	0.248073i	−0.709334	+	0.704872i	$0.751004\pi$
$710$		0			0
$711$	−202.446	−	147.086i	−0.284734	−	0.206871i
$712$	−195.517	−	30.9668i	−0.274602	−	0.0434927i
$713$	−74.0982	+	467.837i	−0.103924	+	0.656153i
$714$	366.747	−	504.784i	0.513651	−	0.706980i
$715$		0			0
$716$	181.774	−	132.066i	0.253874	−	0.184450i
$717$	47.9207	−	24.4168i	0.0668350	−	0.0340541i
$718$	−862.043	+	862.043i	−1.20062	+	1.20062i
$719$	763.200	+	247.979i	1.06147	+	0.344894i	0.787162	−	0.616747i	$-0.211550\pi$
$719$	763.200	+	247.979i	1.06147	+	0.344894i	0.274312	+	0.961641i	$0.411550\pi$
$720$		0			0
$721$	−100.708	−	309.947i	−0.139678	−	0.429885i
$722$	−31.3887	+	61.6038i	−0.0434746	+	0.0853238i
$723$	−401.666	+	63.6177i	−0.555555	+	0.0879913i
$724$			167.652i			0.231564i
$725$		0			0
$726$	−832.839			−1.14716
$727$	110.811	+	699.630i	0.152422	+	0.962352i	0.938764	+	0.344561i	$0.111972\pi$
$727$	110.811	+	699.630i	0.152422	+	0.962352i	−0.786342	+	0.617791i	$0.788028\pi$
$728$	−108.435	−	55.2502i	−0.148949	−	0.0758931i
$729$	−25.6785	+	8.34346i	−0.0352243	+	0.0114451i
$730$		0			0
$731$	148.242	−	456.241i	0.202793	−	0.624133i
$732$	−85.8422	−	85.8422i	−0.117271	−	0.117271i
$733$	96.8506	+	190.080i	0.132129	+	0.259318i	0.947587	−	0.319499i	$-0.103515\pi$
$733$	96.8506	+	190.080i	0.132129	+	0.259318i	−0.815458	+	0.578817i	$0.803515\pi$
$734$	−266.286	−	366.512i	−0.362788	−	0.499335i
$735$		0			0
$736$	−594.718	−	432.088i	−0.808041	−	0.587076i
$737$	190.831	+	30.2247i	0.258930	+	0.0410104i
$738$	−84.5523	+	533.842i	−0.114569	+	0.723363i
$739$	−536.040	+	737.796i	−0.725359	+	0.998371i	0.273970	+	0.961738i	$0.411663\pi$
$739$	−536.040	+	737.796i	−0.725359	+	0.998371i	−0.999329	+	0.0366329i	$0.988337\pi$
$740$		0			0
$741$	69.3642	−	50.3960i	0.0936089	−	0.0680108i
$742$	−396.892	+	202.226i	−0.534894	+	0.272542i
$743$	784.715	−	784.715i	1.05614	−	1.05614i	0.0578172	−	0.998327i	$-0.481586\pi$
$743$	784.715	−	784.715i	1.05614	−	1.05614i	0.998327	−	0.0578172i	$-0.0184141\pi$
$744$	149.119	+	48.4516i	0.200428	+	0.0651231i
$745$		0			0
$746$	−243.597	−	749.716i	−0.326538	−	1.00498i
$747$	−11.3440	+	22.2639i	−0.0151861	+	0.0298045i
$748$	−557.824	+	88.3507i	−0.745755	+	0.118116i
$749$			154.093i			0.205731i
$750$		0			0
$751$	1381.08			1.83898			0.919492	−	0.393108i	$-0.128600\pi$
$751$	1381.08			1.83898			0.919492	+	0.393108i	$0.128600\pi$
$752$	224.962	+	1420.36i	0.299152	+	1.88877i
$753$	−259.870	−	132.410i	−0.345112	−	0.175843i
$754$	−93.6237	+	30.4202i	−0.124169	+	0.0403451i
$755$		0			0
$756$	−22.3413	+	68.7594i	−0.0295520	+	0.0909516i
$757$	−18.1580	−	18.1580i	−0.0239868	−	0.0239868i	0.695012	−	0.718998i	$-0.255399\pi$
$757$	−18.1580	−	18.1580i	−0.0239868	−	0.0239868i	−0.718998	+	0.695012i	$0.755399\pi$
$758$	522.806	+	1026.06i	0.689717	+	1.35365i
$759$	−524.562	−	721.997i	−0.691122	−	0.951248i
$760$		0			0
$761$	443.977	+	322.568i	0.583413	+	0.423874i	0.839953	−	0.542659i	$-0.182582\pi$
$761$	443.977	+	322.568i	0.583413	+	0.423874i	−0.256540	+	0.966534i	$0.582582\pi$
$762$	726.891	+	115.128i	0.953925	+	0.151087i
$763$	71.7089	−	452.752i	0.0939828	−	0.593384i
$764$	−194.020	+	267.046i	−0.253953	+	0.349537i
$765$		0			0
$766$	−390.076	+	283.407i	−0.509238	+	0.369983i
$767$	208.314	−	106.141i	0.271596	−	0.138385i
$768$	−338.230	+	338.230i	−0.440404	+	0.440404i
$769$	969.691	+	315.072i	1.26098	+	0.409716i	0.861842	−	0.507176i	$-0.169311\pi$
$769$	969.691	+	315.072i	1.26098	+	0.409716i	0.399134	+	0.916892i	$0.369311\pi$
$770$		0			0
$771$	−41.9503	−	129.110i	−0.0544103	−	0.167458i
$772$	120.590	−	236.670i	0.156204	−	0.306568i
$773$	−390.983	+	61.9256i	−0.505799	+	0.0801107i	−0.404119	−	0.914706i	$-0.632422\pi$
$773$	−390.983	+	61.9256i	−0.505799	+	0.0801107i	−0.101680	+	0.994817i	$0.532422\pi$
$774$			186.114i			0.240458i
$775$		0			0
$776$	136.702			0.176163
$777$	−94.2195	−	594.878i	−0.121261	−	0.765609i
$778$	1004.06	+	511.596i	1.29057	+	0.657579i
$779$	1307.41	−	424.803i	1.67832	−	0.545318i
$780$		0			0
$781$	−259.390	+	798.319i	−0.332125	+	1.02218i
$782$	−894.973	−	894.973i	−1.14447	−	1.14447i
$783$	−35.7952	−	70.2521i	−0.0457155	−	0.0897217i
$784$	−207.373	−	285.424i	−0.264506	−	0.364061i
$785$		0			0
$786$	481.930	+	350.142i	0.613142	+	0.445474i
$787$	1278.74	+	202.532i	1.62482	+	0.257347i	0.901377	−	0.433035i	$-0.142557\pi$
$787$	1278.74	+	202.532i	1.62482	+	0.257347i	0.723446	+	0.690381i	$0.242557\pi$
$788$	73.1100	−	461.598i	0.0927792	−	0.585785i
$789$	−210.703	+	290.008i	−0.267050	+	0.367563i
$790$		0			0
$791$	1263.45	−	917.949i	1.59728	−	1.16049i
$792$	−263.214	+	134.114i	−0.332341	+	0.169336i
$793$	−79.0376	+	79.0376i	−0.0996691	+	0.0996691i
$794$	−732.665	−	238.057i	−0.922751	−	0.299820i
$795$		0			0
$796$	157.793	+	485.636i	0.198232	+	0.610096i
$797$	225.198	−	441.976i	0.282557	−	0.554549i	−0.705487	−	0.708723i	$-0.749272\pi$
$797$	225.198	−	441.976i	0.282557	−	0.554549i	0.988044	+	0.154174i	$0.0492716\pi$
$798$	608.095	−	96.3128i	0.762024	−	0.120693i
$799$			1333.70i			1.66922i
$800$		0			0
$801$	108.277			0.135177
$802$	−187.573	−	1184.29i	−0.233881	−	1.47667i
$803$	524.272	+	267.130i	0.652892	+	0.332665i
$804$	−30.1968	+	9.81152i	−0.0375581	+	0.0122034i
$805$		0			0
$806$	−33.0888	+	101.837i	−0.0410531	+	0.126349i
$807$	173.466	+	173.466i	0.214952	+	0.214952i
$808$	−171.598	−	336.780i	−0.212374	−	0.416807i
$809$	411.446	+	566.307i	0.508586	+	0.700009i	0.983680	−	0.179926i	$-0.0575859\pi$
$809$	411.446	+	566.307i	0.508586	+	0.700009i	−0.475094	+	0.879935i	$0.657586\pi$
$810$		0			0
$811$	232.424	+	168.866i	0.286590	+	0.208220i	0.721787	−	0.692116i	$-0.243321\pi$
$811$	232.424	+	168.866i	0.286590	+	0.208220i	−0.435197	+	0.900335i	$0.643321\pi$
$812$	−208.526	−	33.0273i	−0.256805	−	0.0406740i
$813$	5.27031	−	33.2754i	0.00648254	−	0.0409292i
$814$	−1072.93	+	1476.76i	−1.31809	+	1.81420i
$815$		0			0
$816$	−515.266	+	374.363i	−0.631454	+	0.458778i
$817$	421.767	−	214.901i	0.516239	−	0.263037i
$818$	−70.2090	+	70.2090i	−0.0858301	+	0.0858301i
$819$	63.3090	+	20.5703i	0.0773003	+	0.0251164i
$820$		0			0
$821$	92.2636	+	283.958i	0.112380	+	0.345869i	0.991391	−	0.130931i	$-0.0417967\pi$
$821$	92.2636	+	283.958i	0.112380	+	0.345869i	−0.879012	+	0.476800i	$0.841797\pi$
$822$	296.141	−	581.209i	0.360268	−	0.707067i
$823$	−118.797	+	18.8156i	−0.144346	+	0.0228622i	−0.228189	−	0.973617i	$-0.573281\pi$
$823$	−118.797	+	18.8156i	−0.144346	+	0.0228622i	0.0838432	+	0.996479i	$0.473281\pi$
$824$			218.831i			0.265571i
$825$		0			0
$826$	1678.85			2.03251
$827$	−164.303	−	1037.37i	−0.198674	−	1.25438i	−0.862333	−	0.506342i	$-0.830997\pi$
$827$	−164.303	−	1037.37i	−0.198674	−	1.25438i	0.663659	−	0.748035i	$-0.269003\pi$
$828$	130.672	+	66.5808i	0.157817	+	0.0804116i
$829$	−434.073	+	141.039i	−0.523610	+	0.170131i	−0.558883	−	0.829246i	$-0.688770\pi$
$829$	−434.073	+	141.039i	−0.523610	+	0.170131i	0.0352728	+	0.999378i	$0.488770\pi$
$830$		0			0
$831$	216.634	−	666.731i	0.260691	−	0.802324i
$832$	35.4880	+	35.4880i	0.0426539	+	0.0426539i
$833$	−148.546	−	291.539i	−0.178327	−	0.349986i
$834$	510.678	+	702.888i	0.612324	+	0.842791i
$835$		0			0
$836$	−450.857	−	327.567i	−0.539302	−	0.391826i
$837$	−84.7066	−	13.4162i	−0.101203	−	0.0160289i
$838$	−44.5436	+	281.237i	−0.0531546	+	0.335605i
$839$	266.156	−	366.333i	0.317231	−	0.436630i	−0.620389	−	0.784295i	$-0.713025\pi$
$839$	266.156	−	366.333i	0.317231	−	0.436630i	0.937619	+	0.347664i	$0.113025\pi$
$840$		0			0
$841$	−494.110	+	358.992i	−0.587527	+	0.426863i
$842$	−86.0751	+	43.8574i	−0.102227	+	0.0520872i
$843$	550.240	−	550.240i	0.652717	−	0.652717i
$844$	−336.051	−	109.190i	−0.398165	−	0.129372i
$845$		0			0
$846$	−159.894	−	492.104i	−0.189000	−	0.581683i
$847$	−746.623	+	1465.33i	−0.881491	+	1.73002i
$848$	449.094	−	71.1295i	0.529592	−	0.0838791i
$849$			783.879i			0.923296i
$850$		0			0
$851$	−1221.76			−1.43567
$852$	−21.5788	−	136.243i	−0.0253272	−	0.159910i
$853$	−924.507	−	471.060i	−1.08383	−	0.552239i	−0.181547	−	0.983382i	$-0.558110\pi$
$853$	−924.507	−	471.060i	−1.08383	−	0.552239i	−0.902283	+	0.431143i	$0.858110\pi$
$854$	−763.359	+	248.031i	−0.893863	+	0.290434i
$855$		0			0
$856$	31.9736	−	98.4047i	0.0373524	−	0.114959i
$857$	−389.202	−	389.202i	−0.454144	−	0.454144i	0.442583	−	0.896727i	$-0.354062\pi$
$857$	−389.202	−	389.202i	−0.454144	−	0.454144i	−0.896727	+	0.442583i	$0.854062\pi$
$858$	−91.5901	−	179.756i	−0.106748	−	0.209506i
$859$	−415.076	−	571.303i	−0.483209	−	0.665080i	0.495909	−	0.868375i	$-0.334835\pi$
$859$	−415.076	−	571.303i	−0.483209	−	0.665080i	−0.979118	+	0.203295i	$0.934835\pi$
$860$		0			0
$861$	863.464	+	627.343i	1.00286	+	0.728621i
$862$	175.514	+	27.7987i	0.203612	+	0.0322490i
$863$	59.3118	−	374.480i	0.0687274	−	0.433928i	−0.929200	−	0.369577i	$-0.879502\pi$
$863$	59.3118	−	374.480i	0.0687274	−	0.433928i	0.997927	−	0.0643504i	$-0.0204975\pi$
$864$	78.2339	−	107.680i	0.0905485	−	0.124629i
$865$		0			0
$866$	603.492	−	438.462i	0.696873	−	0.506308i
$867$	−80.3000	+	40.9149i	−0.0926182	+	0.0471913i
$868$	−162.384	+	162.384i	−0.187079	+	0.187079i
$869$	1424.28	+	462.776i	1.63898	+	0.532538i
$870$		0			0
$871$	9.03378	+	27.8031i	0.0103717	+	0.0319209i
$872$	−139.738	+	274.251i	−0.160250	+	0.314508i
$873$	−73.8530	+	11.6972i	−0.0845968	+	0.0133988i
$874$		−	1248.90i		−	1.42895i
$875$		0			0
$876$	−96.6942			−0.110382
$877$	88.9800	+	561.798i	0.101460	+	0.640590i	0.985042	+	0.172315i	$0.0551245\pi$
$877$	88.9800	+	561.798i	0.101460	+	0.640590i	−0.883582	+	0.468276i	$0.844875\pi$
$878$	662.452	+	337.536i	0.754502	+	0.384438i
$879$	569.778	−	185.132i	0.648211	−	0.210617i
$880$		0			0
$881$	−180.637	+	555.945i	−0.205037	+	0.631039i	0.794675	+	0.607035i	$0.207641\pi$
$881$	−180.637	+	555.945i	−0.205037	+	0.631039i	−0.999712	+	0.0240035i	$0.992359\pi$
$882$	89.7617	+	89.7617i	0.101771	+	0.101771i
$883$	302.370	+	593.435i	0.342435	+	0.672067i	0.996429	−	0.0844330i	$-0.0269079\pi$
$883$	302.370	+	593.435i	0.342435	+	0.672067i	−0.653994	+	0.756500i	$0.726908\pi$
$884$	−50.2289	−	69.1342i	−0.0568201	−	0.0782061i
$885$		0			0
$886$	1076.14	+	781.861i	1.21460	+	0.882462i
$887$	−366.886	−	58.1090i	−0.413625	−	0.0655118i	−0.0538460	−	0.998549i	$-0.517148\pi$
$887$	−366.886	−	58.1090i	−0.413625	−	0.0655118i	−0.359779	+	0.933037i	$0.617148\pi$
$888$	−63.2656	+	399.444i	−0.0712451	+	0.449824i
$889$	854.204	−	1175.71i	0.960859	−	1.32251i
$890$		0			0
$891$	130.725	−	94.9771i	0.146717	−	0.106596i
$892$	460.810	−	234.794i	0.516603	−	0.263222i
$893$	−930.567	+	930.567i	−1.04207	+	1.04207i
$894$	−127.446	−	41.4098i	−0.142557	−	0.0463197i
$895$		0			0
$896$	369.984	+	1138.69i	0.412928	+	1.27086i
$897$	61.3031	−	120.314i	0.0683424	−	0.134129i
$898$	732.111	−	115.955i	0.815268	−	0.129126i
$899$		−	250.445i		−	0.278581i
$900$		0			0
$901$	421.696			0.468031
$902$	−506.013	−	3194.84i	−0.560990	−	3.54195i
$903$	327.457	+	166.847i	0.362632	+	0.184770i
$904$	−997.317	+	324.048i	−1.10323	+	0.358460i
$905$		0			0
$906$	352.805	−	1085.82i	0.389410	−	1.19848i
$907$	−418.645	−	418.645i	−0.461571	−	0.461571i	0.437599	−	0.899170i	$-0.355829\pi$
$907$	−418.645	−	418.645i	−0.461571	−	0.461571i	−0.899170	+	0.437599i	$0.855829\pi$
$908$	−205.058	−	402.449i	−0.225835	−	0.443226i
$909$	121.522	+	167.261i	0.133688	+	0.184006i
$910$		0			0
$911$	−461.236	−	335.108i	−0.506296	−	0.367846i	0.305120	−	0.952314i	$-0.401303\pi$
$911$	−461.236	−	335.108i	−0.506296	−	0.367846i	−0.811417	+	0.584468i	$0.801303\pi$
$912$	−620.723	−	98.3128i	−0.680617	−	0.107799i
$913$	23.3932	−	147.699i	0.0256224	−	0.161773i
$914$	447.082	−	615.355i	0.489148	−	0.673255i
$915$		0			0
$916$	−328.251	+	238.488i	−0.358353	+	0.260358i
$917$	1048.09	−	534.031i	1.14296	−	0.582367i
$918$	162.044	−	162.044i	0.176518	−	0.176518i
$919$	−1157.04	−	375.944i	−1.25902	−	0.409079i	−0.397873	−	0.917440i	$-0.630252\pi$
$919$	−1157.04	−	375.944i	−1.25902	−	0.409079i	−0.861144	+	0.508361i	$0.830252\pi$
$920$		0			0
$921$	222.212	+	683.899i	0.241273	+	0.742561i
$922$	−610.658	+	1198.48i	−0.662319	+	1.29987i
$923$	−125.443	+	19.8683i	−0.135908	+	0.0215258i
$924$		−	432.675i		−	0.468263i
$925$		0			0
$926$	−506.358			−0.546823
$927$	−18.7246	−	118.223i	−0.0201992	−	0.127532i
$928$	346.315	+	176.456i	0.373184	+	0.190147i
$929$	429.309	−	139.491i	0.462120	−	0.150152i	−0.0686985	−	0.997637i	$-0.521885\pi$
$929$	429.309	−	139.491i	0.462120	−	0.150152i	0.530818	+	0.847486i	$0.321885\pi$
$930$		0			0
$931$	99.7702	−	307.061i	0.107165	−	0.329819i
$932$	103.717	+	103.717i	0.111284	+	0.111284i
$933$	104.609	+	205.307i	0.112121	+	0.220050i
$934$	−368.133	−	506.691i	−0.394146	−	0.542496i
$935$		0			0
$936$	−36.1613	−	26.2727i	−0.0386338	−	0.0280691i
$937$	−10.3768	−	1.64353i	−0.0110745	−	0.00175403i	0.150895	−	0.988550i	$-0.451785\pi$
$937$	−10.3768	−	1.64353i	−0.0110745	−	0.00175403i	−0.161969	+	0.986796i	$0.551785\pi$
$938$	−32.8393	+	207.339i	−0.0350099	+	0.221044i
$939$	274.529	−	377.856i	0.292363	−	0.402403i
$940$		0			0
$941$	86.5028	−	62.8480i	0.0919265	−	0.0667885i	−0.540873	−	0.841105i	$-0.681906\pi$
$941$	86.5028	−	62.8480i	0.0919265	−	0.0667885i	0.632799	+	0.774316i	$0.281906\pi$
$942$	−572.958	+	291.936i	−0.608235	+	0.309911i
$943$	1530.91	−	1530.91i	1.62344	−	1.62344i
$944$	−1629.84	−	529.567i	−1.72652	−	0.560982i
$945$		0			0
$946$	−344.190	−	1059.31i	−0.363837	−	1.11978i
$947$	407.602	−	799.964i	0.430414	−	0.844735i	−0.569330	−	0.822109i	$-0.692797\pi$
$947$	407.602	−	799.964i	0.430414	−	0.844735i	0.999744	−	0.0226259i	$-0.00720266\pi$
$948$	−243.071	+	38.4986i	−0.256404	+	0.0406104i
$949$			89.0295i			0.0938140i
$950$		0			0
$951$	−705.274			−0.741613
$952$	129.420	+	817.126i	0.135945	+	0.858325i
$953$	−362.634	−	184.771i	−0.380519	−	0.193884i	0.253260	−	0.967398i	$-0.418497\pi$
$953$	−362.634	−	184.771i	−0.380519	−	0.193884i	−0.633779	+	0.773514i	$0.718497\pi$
$954$	−155.595	+	50.5560i	−0.163098	+	0.0529937i
$955$		0			0
$956$	16.3450	−	50.3049i	0.0170973	−	0.0526202i
$957$	333.657	+	333.657i	0.348649	+	0.348649i
$958$	259.799	+	509.884i	0.271189	+	0.532238i
$959$	−757.118	−	1042.08i	−0.789487	−	1.08664i
$960$		0			0
$961$	557.077	+	404.740i	0.579685	+	0.421165i
$962$	−272.790	−	43.2057i	−0.283566	−	0.0449124i
$963$	−8.85348	+	55.8987i	−0.00919365	+	0.0580464i
$964$	−235.085	+	323.567i	−0.243864	+	0.335650i
$965$		0			0
$966$	784.453	−	569.939i	0.812064	−	0.589999i
$967$	70.0847	−	35.7099i	0.0724764	−	0.0369286i	−0.417377	−	0.908734i	$-0.637050\pi$
$967$	70.0847	−	35.7099i	0.0724764	−	0.0369286i	0.489853	+	0.871805i	$0.337050\pi$
$968$	780.848	−	780.848i	0.806662	−	0.806662i
$969$	−554.327	−	180.112i	−0.572061	−	0.185874i
$970$		0			0
$971$	48.4946	+	149.251i	0.0499430	+	0.153709i	0.972918	−	0.231152i	$-0.0742495\pi$
$971$	48.4946	+	149.251i	0.0499430	+	0.153709i	−0.922975	+	0.384861i	$0.874249\pi$
$972$	−12.0551	+	23.6595i	−0.0124024	+	0.0243411i
$973$	1694.50	−	268.383i	1.74152	−	0.275830i
$974$			138.740i			0.142443i
$975$		0			0
$976$	819.311			0.839458
$977$	208.840	+	1318.57i	0.213757	+	1.34961i	0.828105	+	0.560573i	$0.189419\pi$
$977$	208.840	+	1318.57i	0.213757	+	1.34961i	−0.614348	+	0.789035i	$0.710581\pi$
$978$	650.825	+	331.612i	0.665465	+	0.339071i
$979$	−616.282	+	200.242i	−0.629501	+	0.204537i
$980$		0			0
$981$	52.0262	−	160.120i	0.0530339	−	0.163221i
$982$	−138.117	−	138.117i	−0.140649	−	0.140649i
$983$	−585.873	−	1149.84i	−0.596005	−	1.16973i	−0.970184	−	0.242369i	$-0.922076\pi$
$983$	−585.873	−	1149.84i	−0.596005	−	1.16973i	0.374179	−	0.927356i	$-0.377924\pi$
$984$	−421.243	−	579.791i	−0.428092	−	0.589218i
$985$		0			0
$986$	541.402	+	393.351i	0.549089	+	0.398936i
$987$	−1009.17	−	159.837i	−1.02246	−	0.161942i
$988$	13.1908	−	83.2835i	0.0133510	−	0.0842950i
$989$	438.196	−	603.125i	0.443070	−	0.609833i
$990$		0			0
$991$	62.2028	−	45.1930i	0.0627677	−	0.0456034i	−0.555959	−	0.831210i	$-0.687649\pi$
$991$	62.2028	−	45.1930i	0.0627677	−	0.0456034i	0.618727	+	0.785606i	$0.287649\pi$
$992$	376.696	−	191.936i	0.379734	−	0.193484i
$993$	0.247269	−	0.247269i	0.000249012	−	0.000249012i
$994$	−867.378	−	281.828i	−0.872613	−	0.283529i
$995$		0			0
$996$	7.59390	+	23.3716i	0.00762439	+	0.0234655i
$997$	93.8876	−	184.265i	0.0941702	−	0.184819i	−0.839116	−	0.543952i	$-0.816927\pi$
$997$	93.8876	−	184.265i	0.0941702	−	0.184819i	0.933287	+	0.359133i	$0.116927\pi$
$998$	−548.927	+	86.9415i	−0.550027	+	0.0871157i
$999$		−	221.211i		−	0.221433i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	375.3.k.a.82.3		80
5.2	odd	4		375.3.k.c.43.8		80
5.3	odd	4		375.3.k.b.43.3		80
5.4	even	2		75.3.k.a.37.8	✓	80
15.14	odd	2		225.3.r.b.37.3		80
25.2	odd	20		75.3.k.a.73.8	yes	80
25.11	even	5		375.3.k.b.157.3		80
25.14	even	10		375.3.k.c.157.8		80
25.23	odd	20	inner	375.3.k.a.343.3		80
75.2	even	20		225.3.r.b.73.3		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.3.k.a.37.8	✓	80	5.4	even	2
75.3.k.a.73.8	yes	80	25.2	odd	20
225.3.r.b.37.3		80	15.14	odd	2
225.3.r.b.73.3		80	75.2	even	20
375.3.k.a.82.3		80	1.1	even	1	trivial
375.3.k.a.343.3		80	25.23	odd	20	inner
375.3.k.b.43.3		80	5.3	odd	4
375.3.k.b.157.3		80	25.11	even	5
375.3.k.c.43.8		80	5.2	odd	4
375.3.k.c.157.8		80	25.14	even	10

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:	\( N \)	\(=\)	\( 375 = 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	375.k (of order \(20\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.373594 - 2.35878i) q^{2} +(-1.54327 - 0.786335i) q^{3} +(-1.62005 + 0.526386i) q^{4} +(-1.27823 + 3.93400i) q^{6} +(5.77573 + 5.77573i) q^{7} +(-2.48998 - 4.88686i) q^{8} +(1.76336 + 2.42705i) q^{9} +O(q^{10})\)	\(q+(-0.373594 - 2.35878i) q^{2} +(-1.54327 - 0.786335i) q^{3} +(-1.62005 + 0.526386i) q^{4} +(-1.27823 + 3.93400i) q^{6} +(5.77573 + 5.77573i) q^{7} +(-2.48998 - 4.88686i) q^{8} +(1.76336 + 2.42705i) q^{9} +(-14.5250 - 10.5530i) q^{11} +(2.91409 + 0.461546i) q^{12} +(0.424960 - 2.68309i) q^{13} +(11.4659 - 15.7815i) q^{14} +(-16.1092 + 11.7040i) q^{16} +(-16.4543 + 8.38387i) q^{17} +(5.06610 - 5.06610i) q^{18} +(-17.3304 - 5.63098i) q^{19} +(-4.37185 - 13.4552i) q^{21} +(-19.4658 + 38.2038i) q^{22} +(-28.3452 + 4.48944i) q^{23} +9.49970i q^{24} -6.48759 q^{26} +(-0.812857 - 5.13218i) q^{27} +(-12.3972 - 6.31670i) q^{28} +(14.4312 - 4.68898i) q^{29} +(5.10033 - 15.6972i) q^{31} +(18.1125 + 18.1125i) q^{32} +(14.1177 + 27.7076i) q^{33} +(25.9229 + 35.6799i) q^{34} +(-4.13429 - 3.00374i) q^{36} +(42.0480 + 6.65975i) q^{37} +(-6.80772 + 42.9822i) q^{38} +(-2.76564 + 3.80657i) q^{39} +(-61.0326 + 44.3428i) q^{41} +(-30.1045 + 15.3390i) q^{42} +(-18.3686 + 18.3686i) q^{43} +(29.0861 + 9.45066i) q^{44} +(21.1792 + 65.1829i) q^{46} +(32.7875 - 64.3491i) q^{47} +(34.0641 - 5.39522i) q^{48} +17.7181i q^{49} +31.9859 q^{51} +(0.723886 + 4.57043i) q^{52} +(-20.3462 - 10.3669i) q^{53} +(-11.8020 + 3.83470i) q^{54} +(13.8437 - 42.6066i) q^{56} +(22.3176 + 22.3176i) q^{57} +(-16.4517 - 32.2883i) q^{58} +(50.5873 + 69.6274i) q^{59} +(-33.2882 - 24.1853i) q^{61} +(-38.9317 - 6.16617i) q^{62} +(-3.83332 + 24.2027i) q^{63} +(-10.8592 + 14.9465i) q^{64} +(60.0819 - 43.6521i) q^{66} +(-9.58854 + 4.88560i) q^{67} +(22.2436 - 22.2436i) q^{68} +(47.2744 + 15.3604i) q^{69} +(-14.4476 - 44.4650i) q^{71} +(7.46994 - 14.6606i) q^{72} +(-32.3696 + 5.12685i) q^{73} -101.670i q^{74} +31.0401 q^{76} +(-22.9410 - 144.844i) q^{77} +(10.0121 + 5.10142i) q^{78} +(-79.3298 + 25.7758i) q^{79} +(-2.78115 + 8.55951i) q^{81} +(127.396 + 127.396i) q^{82} +(3.78135 + 7.42131i) q^{83} +(14.1652 + 19.4967i) q^{84} +(50.1898 + 36.4650i) q^{86} +(-25.9583 - 4.11140i) q^{87} +(-15.4042 + 97.2584i) q^{88} +(21.2145 - 29.1993i) q^{89} +(17.9513 - 13.0424i) q^{91} +(43.5574 - 22.1936i) q^{92} +(-20.2144 + 20.2144i) q^{93} +(-164.035 - 53.2981i) q^{94} +(-13.7100 - 42.1950i) q^{96} +(-11.3155 + 22.2079i) q^{97} +(41.7931 - 6.61938i) q^{98} -53.8616i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 4 q^{2} + 4 q^{7} + 12 q^{8}+O(q^{10}) \) 80 * q - 4 * q^2 + 4 * q^7 + 12 * q^8	\( 80 q - 4 q^{2} + 4 q^{7} + 12 q^{8} + 24 q^{12} - 32 q^{13} + 80 q^{16} + 100 q^{17} + 48 q^{18} - 100 q^{19} + 100 q^{22} + 96 q^{23} - 40 q^{26} - 196 q^{28} + 200 q^{29} - 636 q^{32} - 216 q^{33} + 100 q^{34} - 120 q^{36} + 184 q^{37} + 564 q^{38} + 160 q^{41} + 12 q^{42} + 472 q^{43} - 700 q^{44} + 288 q^{47} + 48 q^{48} - 620 q^{52} - 304 q^{53} - 72 q^{57} - 1272 q^{58} + 800 q^{59} - 240 q^{61} - 1212 q^{62} + 12 q^{63} + 100 q^{64} + 80 q^{67} - 104 q^{68} - 36 q^{72} + 116 q^{73} + 88 q^{77} + 120 q^{78} + 200 q^{79} + 180 q^{81} + 168 q^{82} + 1264 q^{83} - 1200 q^{84} + 876 q^{87} + 212 q^{88} - 1500 q^{89} + 1504 q^{92} + 648 q^{93} - 200 q^{94} + 60 q^{96} + 260 q^{97} + 92 q^{98}+O(q^{100}) \) 80 * q - 4 * q^2 + 4 * q^7 + 12 * q^8 + 24 * q^12 - 32 * q^13 + 80 * q^16 + 100 * q^17 + 48 * q^18 - 100 * q^19 + 100 * q^22 + 96 * q^23 - 40 * q^26 - 196 * q^28 + 200 * q^29 - 636 * q^32 - 216 * q^33 + 100 * q^34 - 120 * q^36 + 184 * q^37 + 564 * q^38 + 160 * q^41 + 12 * q^42 + 472 * q^43 - 700 * q^44 + 288 * q^47 + 48 * q^48 - 620 * q^52 - 304 * q^53 - 72 * q^57 - 1272 * q^58 + 800 * q^59 - 240 * q^61 - 1212 * q^62 + 12 * q^63 + 100 * q^64 + 80 * q^67 - 104 * q^68 - 36 * q^72 + 116 * q^73 + 88 * q^77 + 120 * q^78 + 200 * q^79 + 180 * q^81 + 168 * q^82 + 1264 * q^83 - 1200 * q^84 + 876 * q^87 + 212 * q^88 - 1500 * q^89 + 1504 * q^92 + 648 * q^93 - 200 * q^94 + 60 * q^96 + 260 * q^97 + 92 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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