LMFDB - Embedded newform 375.3.d.e.374.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [375,3,Mod(374,375)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(375, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1]))

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

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

chi := DirichletCharacter("375.374");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 375 = 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	375.d (of order $2$, degree $1$, 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:	$32$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			374.19
Character	$\chi$	$=$	375.374
Dual form			375.3.d.e.374.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.654766 q^{2} +(-1.42077 - 2.64224i) q^{3} -3.57128 q^{4} +(-0.930269 - 1.73005i) q^{6} +1.39150i q^{7} -4.95742 q^{8} +(-4.96285 + 7.50800i) q^{9} +O(q^{10})$	\(q+0.654766 q^{2} +(-1.42077 - 2.64224i) q^{3} -3.57128 q^{4} +(-0.930269 - 1.73005i) q^{6} +1.39150i q^{7} -4.95742 q^{8} +(-4.96285 + 7.50800i) q^{9} +7.60997i q^{11} +(5.07395 + 9.43618i) q^{12} +1.63838i q^{13} +0.911107i q^{14} +11.0392 q^{16} +27.2825 q^{17} +(-3.24951 + 4.91599i) q^{18} -5.95062 q^{19} +(3.67667 - 1.97699i) q^{21} +4.98275i q^{22} +17.8484 q^{23} +(7.04333 + 13.0987i) q^{24} +1.07276i q^{26} +(26.8890 + 2.44594i) q^{27} -4.96943i q^{28} -33.1599i q^{29} -21.7617 q^{31} +27.0578 q^{32} +(20.1074 - 10.8120i) q^{33} +17.8636 q^{34} +(17.7237 - 26.8132i) q^{36} +61.6843i q^{37} -3.89627 q^{38} +(4.32899 - 2.32775i) q^{39} +60.0191i q^{41} +(2.40736 - 1.29447i) q^{42} +64.3754i q^{43} -27.1773i q^{44} +11.6866 q^{46} +45.9655 q^{47} +(-15.6841 - 29.1681i) q^{48} +47.0637 q^{49} +(-38.7620 - 72.0868i) q^{51} -5.85111i q^{52} +2.50611 q^{53} +(17.6060 + 1.60152i) q^{54} -6.89825i q^{56} +(8.45444 + 15.7230i) q^{57} -21.7120i q^{58} +46.7817i q^{59} -28.0694 q^{61} -14.2488 q^{62} +(-10.4474 - 6.90581i) q^{63} -26.4402 q^{64} +(13.1656 - 7.07932i) q^{66} -36.9109i q^{67} -97.4333 q^{68} +(-25.3584 - 47.1599i) q^{69} +87.9910i q^{71} +(24.6029 - 37.2203i) q^{72} -59.7906i q^{73} +40.3888i q^{74} +21.2514 q^{76} -10.5893 q^{77} +(2.83448 - 1.52413i) q^{78} -121.245 q^{79} +(-31.7402 - 74.5222i) q^{81} +39.2985i q^{82} +64.7740 q^{83} +(-13.1304 + 7.06040i) q^{84} +42.1508i q^{86} +(-87.6163 + 47.1124i) q^{87} -37.7258i q^{88} +84.8539i q^{89} -2.27980 q^{91} -63.7418 q^{92} +(30.9183 + 57.4997i) q^{93} +30.0967 q^{94} +(-38.4427 - 71.4931i) q^{96} -145.720i q^{97} +30.8157 q^{98} +(-57.1357 - 37.7672i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 68 q^{4} + 12 q^{6} + 20 q^{9}+O(q^{10}) $ 32 * q + 68 * q^4 + 12 * q^6 + 20 * q^9	$ 32 q + 68 q^{4} + 12 q^{6} + 20 q^{9} + 116 q^{16} + 40 q^{19} + 112 q^{21} + 96 q^{24} - 16 q^{31} - 64 q^{34} - 56 q^{36} - 8 q^{39} - 416 q^{46} - 468 q^{49} - 208 q^{51} - 472 q^{54} - 276 q^{61} - 136 q^{64} - 340 q^{66} - 352 q^{69} + 148 q^{76} + 580 q^{79} - 268 q^{81} + 952 q^{84} + 444 q^{91} + 936 q^{94} + 1456 q^{96} + 220 q^{99}+O(q^{100}) $ 32 * q + 68 * q^4 + 12 * q^6 + 20 * q^9 + 116 * q^16 + 40 * q^19 + 112 * q^21 + 96 * q^24 - 16 * q^31 - 64 * q^34 - 56 * q^36 - 8 * q^39 - 416 * q^46 - 468 * q^49 - 208 * q^51 - 472 * q^54 - 276 * q^61 - 136 * q^64 - 340 * q^66 - 352 * q^69 + 148 * q^76 + 580 * q^79 - 268 * q^81 + 952 * q^84 + 444 * q^91 + 936 * q^94 + 1456 * q^96 + 220 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$251$
$\chi(n)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	0.654766			0.327383			0.163692	−	0.986512i	$-0.447660\pi$
$2$	0.654766			0.327383			0.163692	+	0.986512i	$0.447660\pi$
$3$	−1.42077	−	2.64224i	−0.473588	−	0.880746i
$3$	−1.42077	−	2.64224i	−0.473588	−	0.880746i
$4$	−3.57128			−0.892820
$5$		0			0
$5$		0			0
$6$	−0.930269	−	1.73005i	−0.155045	−	0.288342i
$7$			1.39150i			0.198786i	0.995048	+	0.0993928i	$0.0316900\pi$
$7$			1.39150i			0.198786i	−0.995048	+	0.0993928i	$0.968310\pi$
$8$	−4.95742			−0.619677
$9$	−4.96285	+	7.50800i	−0.551428	+	0.834222i
$10$		0			0
$11$			7.60997i			0.691816i	0.938269	+	0.345908i	$0.112429\pi$
$11$			7.60997i			0.691816i	−0.938269	+	0.345908i	$0.887571\pi$
$12$	5.07395	+	9.43618i	0.422829	+	0.786348i
$13$			1.63838i			0.126029i	0.998013	+	0.0630146i	$0.0200715\pi$
$13$			1.63838i			0.126029i	−0.998013	+	0.0630146i	$0.979929\pi$
$14$			0.911107i			0.0650791i
$15$		0			0
$16$	11.0392			0.689948
$17$	27.2825			1.60485			0.802425	−	0.596753i	$-0.203543\pi$
$17$	27.2825			1.60485			0.802425	+	0.596753i	$0.203543\pi$
$18$	−3.24951	+	4.91599i	−0.180528	+	0.273110i
$19$	−5.95062			−0.313191			−0.156595	−	0.987663i	$-0.550052\pi$
$19$	−5.95062			−0.313191			−0.156595	+	0.987663i	$0.550052\pi$
$20$		0			0
$21$	3.67667	−	1.97699i	0.175080	−	0.0941425i
$22$			4.98275i			0.226489i
$23$	17.8484			0.776019			0.388010	−	0.921655i	$-0.373163\pi$
$23$	17.8484			0.776019			0.388010	+	0.921655i	$0.373163\pi$
$24$	7.04333	+	13.0987i	0.293472	+	0.545779i
$25$		0			0
$26$			1.07276i			0.0412598i
$27$	26.8890	+	2.44594i	0.995888	+	0.0905903i
$28$		−	4.96943i		−	0.177480i
$29$		−	33.1599i		−	1.14344i	−0.820448	−	0.571722i	$-0.806276\pi$
$29$		−	33.1599i		−	1.14344i	0.820448	−	0.571722i	$-0.193724\pi$
$30$		0			0
$31$	−21.7617			−0.701991			−0.350996	−	0.936377i	$-0.614157\pi$
$31$	−21.7617			−0.701991			−0.350996	+	0.936377i	$0.614157\pi$
$32$	27.0578			0.845555
$33$	20.1074	−	10.8120i	0.609314	−	0.327636i
$34$	17.8636			0.525401
$35$		0			0
$36$	17.7237	−	26.8132i	0.492326	−	0.744811i
$37$			61.6843i			1.66714i	0.552411	+	0.833572i	$0.313708\pi$
$37$			61.6843i			1.66714i	−0.552411	+	0.833572i	$0.686292\pi$
$38$	−3.89627			−0.102533
$39$	4.32899	−	2.32775i	0.111000	−	0.0596859i
$40$		0			0
$41$			60.0191i			1.46388i	0.681369	+	0.731940i	$0.261385\pi$
$41$			60.0191i			1.46388i	−0.681369	+	0.731940i	$0.738615\pi$
$42$	2.40736	−	1.29447i	0.0573181	−	0.0308207i
$43$			64.3754i			1.49710i	0.663077	+	0.748551i	$0.269250\pi$
$43$			64.3754i			1.49710i	−0.663077	+	0.748551i	$0.730750\pi$
$44$		−	27.1773i		−	0.617667i
$45$		0			0
$46$	11.6866			0.254056
$47$	45.9655			0.977990			0.488995	−	0.872287i	$-0.337364\pi$
$47$	45.9655			0.977990			0.488995	+	0.872287i	$0.337364\pi$
$48$	−15.6841	−	29.1681i	−0.326751	−	0.607669i
$49$	47.0637			0.960484
$50$		0			0
$51$	−38.7620	−	72.0868i	−0.760038	−	1.41347i
$52$		−	5.85111i		−	0.112521i
$53$	2.50611			0.0472851			0.0236425	−	0.999720i	$-0.492474\pi$
$53$	2.50611			0.0472851			0.0236425	+	0.999720i	$0.492474\pi$
$54$	17.6060	+	1.60152i	0.326037	+	0.0296577i
$55$		0			0
$56$		−	6.89825i		−	0.123183i
$57$	8.45444	+	15.7230i	0.148323	+	0.275842i
$58$		−	21.7120i		−	0.374344i
$59$			46.7817i			0.792911i	0.918054	+	0.396455i	$0.129760\pi$
$59$			46.7817i			0.792911i	−0.918054	+	0.396455i	$0.870240\pi$
$60$		0			0
$61$	−28.0694			−0.460154			−0.230077	−	0.973172i	$-0.573898\pi$
$61$	−28.0694			−0.460154			−0.230077	+	0.973172i	$0.573898\pi$
$62$	−14.2488			−0.229820
$63$	−10.4474	−	6.90581i	−0.165831	−	0.109616i
$64$	−26.4402			−0.413128
$65$		0			0
$66$	13.1656	−	7.07932i	0.199479	−	0.107262i
$67$		−	36.9109i		−	0.550909i	−0.961314	−	0.275454i	$-0.911172\pi$
$67$		−	36.9109i		−	0.550909i	0.961314	−	0.275454i	$-0.0888283\pi$
$68$	−97.4333			−1.43284
$69$	−25.3584	−	47.1599i	−0.367514	−	0.683476i
$70$		0			0
$71$			87.9910i			1.23931i	0.784874	+	0.619655i	$0.212727\pi$
$71$			87.9910i			1.23931i	−0.784874	+	0.619655i	$0.787273\pi$
$72$	24.6029	−	37.2203i	0.341708	−	0.516949i
$73$		−	59.7906i		−	0.819050i	−0.912299	−	0.409525i	$-0.865694\pi$
$73$		−	59.7906i		−	0.819050i	0.912299	−	0.409525i	$-0.134306\pi$
$74$			40.3888i			0.545795i
$75$		0			0
$76$	21.2514			0.279623
$77$	−10.5893			−0.137523
$78$	2.83448	−	1.52413i	0.0363394	−	0.0195402i
$79$	−121.245			−1.53475			−0.767375	−	0.641198i	$-0.778438\pi$
$79$	−121.245			−1.53475			−0.767375	+	0.641198i	$0.778438\pi$
$80$		0			0
$81$	−31.7402	−	74.5222i	−0.391854	−	0.920027i
$82$			39.2985i			0.479250i
$83$	64.7740			0.780410			0.390205	−	0.920728i	$-0.372404\pi$
$83$	64.7740			0.780410			0.390205	+	0.920728i	$0.372404\pi$
$84$	−13.1304	+	7.06040i	−0.156315	+	0.0840524i
$85$		0			0
$86$			42.1508i			0.490126i
$87$	−87.6163	+	47.1124i	−1.00708	+	0.541522i
$88$		−	37.7258i		−	0.428703i
$89$			84.8539i			0.953415i	0.879062	+	0.476708i	$0.158170\pi$
$89$			84.8539i			0.953415i	−0.879062	+	0.476708i	$0.841830\pi$
$90$		0			0
$91$	−2.27980			−0.0250528
$92$	−63.7418			−0.692846
$93$	30.9183	+	57.4997i	0.332455	+	0.618276i
$94$	30.0967			0.320177
$95$		0			0
$96$	−38.4427	−	71.4931i	−0.400445	−	0.744719i
$97$		−	145.720i		−	1.50226i	−0.660153	−	0.751131i	$-0.729508\pi$
$97$		−	145.720i		−	1.50226i	0.660153	−	0.751131i	$-0.270492\pi$
$98$	30.8157			0.314446
$99$	−57.1357	−	37.7672i	−0.577128	−	0.381487i
$100$		0			0
$101$			32.2054i			0.318865i	0.987209	+	0.159433i	$0.0509664\pi$
$101$			32.2054i			0.318865i	−0.987209	+	0.159433i	$0.949034\pi$
$102$	−25.3800	−	47.2000i	−0.248824	−	0.462745i
$103$			172.279i			1.67261i	0.548262	+	0.836307i	$0.315290\pi$
$103$			172.279i			1.67261i	−0.548262	+	0.836307i	$0.684710\pi$
$104$		−	8.12213i		−	0.0780974i
$105$		0			0
$106$	1.64092			0.0154803
$107$	−188.606			−1.76267			−0.881337	−	0.472488i	$-0.843356\pi$
$107$	−188.606			−1.76267			−0.881337	+	0.472488i	$0.843356\pi$
$108$	−96.0281	−	8.73513i	−0.889149	−	0.0808809i
$109$	2.01893			0.0185223			0.00926114	−	0.999957i	$-0.497052\pi$
$109$	2.01893			0.0185223			0.00926114	+	0.999957i	$0.497052\pi$
$110$		0			0
$111$	162.985	−	87.6390i	1.46833	−	0.789540i
$112$			15.3610i			0.137152i
$113$	144.926			1.28253			0.641266	−	0.767319i	$-0.278409\pi$
$113$	144.926			1.28253			0.641266	+	0.767319i	$0.278409\pi$
$114$	5.53568	+	10.2949i	0.0485586	+	0.0903059i
$115$		0			0
$116$			118.423i			1.02089i
$117$	−12.3009	−	8.13103i	−0.105136	−	0.0694960i
$118$			30.6311i			0.259586i
$119$			37.9635i			0.319021i
$120$		0			0
$121$	63.0883			0.521391
$122$	−18.3789			−0.150647
$123$	158.585	−	85.2730i	1.28931	−	0.693277i
$124$	77.7172			0.626752
$125$		0			0
$126$	−6.84059	−	4.52169i	−0.0542904	−	0.0358864i
$127$		−	176.391i		−	1.38890i	−0.719539	−	0.694452i	$-0.755647\pi$
$127$		−	176.391i		−	1.38890i	0.719539	−	0.694452i	$-0.244353\pi$
$128$	−125.543			−0.980806
$129$	170.095	−	91.4623i	1.31857	−	0.709010i
$130$		0			0
$131$			182.848i			1.39579i	0.716202	+	0.697893i	$0.245879\pi$
$131$			182.848i			1.39579i	−0.716202	+	0.697893i	$0.754121\pi$
$132$	−71.8090	+	38.6126i	−0.544008	+	0.292520i
$133$		−	8.28029i		−	0.0622578i
$134$		−	24.1680i		−	0.180358i
$135$		0			0
$136$	−135.251			−0.994490
$137$	−119.724			−0.873899			−0.436949	−	0.899486i	$-0.643941\pi$
$137$	−119.724			−0.873899			−0.436949	+	0.899486i	$0.643941\pi$
$138$	−16.6039	−	30.8787i	−0.120318	−	0.223759i
$139$	37.8562			0.272347			0.136173	−	0.990685i	$-0.456520\pi$
$139$	37.8562			0.272347			0.136173	+	0.990685i	$0.456520\pi$
$140$		0			0
$141$	−65.3062	−	121.452i	−0.463165	−	0.861361i
$142$			57.6135i			0.405729i
$143$	−12.4680			−0.0871889
$144$	−54.7858	+	82.8821i	−0.380457	+	0.575570i
$145$		0			0
$146$		−	39.1489i		−	0.268143i
$147$	−66.8665	−	124.354i	−0.454874	−	0.845943i
$148$		−	220.292i		−	1.48846i
$149$		−	152.876i		−	1.02601i	−0.858385	−	0.513007i	$-0.828532\pi$
$149$		−	152.876i		−	1.02601i	0.858385	−	0.513007i	$-0.171468\pi$
$150$		0			0
$151$	101.495			0.672155			0.336077	−	0.941834i	$-0.390900\pi$
$151$	101.495			0.672155			0.336077	+	0.941834i	$0.390900\pi$
$152$	29.4997			0.194077
$153$	−135.399	+	204.837i	−0.884960	+	1.33880i
$154$	−6.93350			−0.0450227
$155$		0			0
$156$	−15.4600	+	8.31305i	−0.0991028	+	0.0532888i
$157$			169.446i			1.07927i	0.841899	+	0.539636i	$0.181438\pi$
$157$			169.446i			1.07927i	−0.841899	+	0.539636i	$0.818562\pi$
$158$	−79.3873			−0.502452
$159$	−3.56059	−	6.62174i	−0.0223937	−	0.0416461i
$160$		0			0
$161$			24.8361i			0.154261i
$162$	−20.7824	−	48.7946i	−0.128286	−	0.301201i
$163$		−	168.899i		−	1.03619i	−0.855324	−	0.518094i	$-0.826642\pi$
$163$		−	168.899i		−	1.03619i	0.855324	−	0.518094i	$-0.173358\pi$
$164$		−	214.345i		−	1.30698i
$165$		0			0
$166$	42.4118			0.255493
$167$	−69.1778			−0.414238			−0.207119	−	0.978316i	$-0.566409\pi$
$167$	−69.1778			−0.414238			−0.207119	+	0.978316i	$0.566409\pi$
$168$	−18.2268	+	9.80079i	−0.108493	+	0.0583380i
$169$	166.316			0.984117
$170$		0			0
$171$	29.5321	−	44.6773i	0.172702	−	0.261271i
$172$		−	229.903i		−	1.33664i
$173$	59.5429			0.344178			0.172089	−	0.985081i	$-0.444948\pi$
$173$	59.5429			0.344178			0.172089	+	0.985081i	$0.444948\pi$
$174$	−57.3682	+	30.8476i	−0.329702	+	0.177285i
$175$		0			0
$176$			84.0078i			0.477317i
$177$	123.609	−	66.4659i	0.698353	−	0.375513i
$178$			55.5595i			0.312132i
$179$			208.232i			1.16331i	0.813437	+	0.581653i	$0.197594\pi$
$179$			208.232i			1.16331i	−0.813437	+	0.581653i	$0.802406\pi$
$180$		0			0
$181$	154.979			0.856239			0.428119	−	0.903722i	$-0.359176\pi$
$181$	154.979			0.856239			0.428119	+	0.903722i	$0.359176\pi$
$182$	−1.49274			−0.00820186
$183$	39.8800	+	74.1660i	0.217923	+	0.405279i
$184$	−88.4822			−0.480882
$185$		0			0
$186$	20.2443	+	37.6489i	0.108840	+	0.202413i
$187$			207.619i			1.11026i
$188$	−164.156			−0.873169
$189$	−3.40352	+	37.4160i	−0.0180081	+	0.197968i
$190$		0			0
$191$		−	291.125i		−	1.52421i	−0.647452	−	0.762106i	$-0.724165\pi$
$191$		−	291.125i		−	1.52421i	0.647452	−	0.762106i	$-0.275835\pi$
$192$	37.5653	+	69.8613i	0.195653	+	0.363861i
$193$			152.200i			0.788600i	0.918982	+	0.394300i	$0.129013\pi$
$193$			152.200i			0.788600i	−0.918982	+	0.394300i	$0.870987\pi$
$194$		−	95.4122i		−	0.491816i
$195$		0			0
$196$	−168.078			−0.857540
$197$	301.130			1.52858			0.764290	−	0.644872i	$-0.223089\pi$
$197$	301.130			1.52858			0.764290	+	0.644872i	$0.223089\pi$
$198$	−37.4105	−	24.7287i	−0.188942	−	0.124892i
$199$	−108.407			−0.544760			−0.272380	−	0.962190i	$-0.587811\pi$
$199$	−108.407			−0.544760			−0.272380	+	0.962190i	$0.587811\pi$
$200$		0			0
$201$	−97.5274	+	52.4417i	−0.485211	+	0.260904i
$202$			21.0870i			0.104391i
$203$	46.1419			0.227300
$204$	138.430	+	257.442i	0.678578	+	1.26197i
$205$		0			0
$206$			112.803i			0.547585i
$207$	−88.5792	+	134.006i	−0.427919	+	0.647373i
$208$			18.0863i			0.0869536i
$209$		−	45.2841i		−	0.216670i
$210$		0			0
$211$	−223.223			−1.05793			−0.528964	−	0.848644i	$-0.677420\pi$
$211$	−223.223			−1.05793			−0.528964	+	0.848644i	$0.677420\pi$
$212$	−8.95002			−0.0422171
$213$	232.493	−	125.015i	1.09152	−	0.586923i
$214$	−123.493			−0.577070
$215$		0			0
$216$	−133.300	−	12.1255i	−0.617130	−	0.0561368i
$217$		−	30.2814i		−	0.139546i
$218$	1.32193			0.00606388
$219$	−157.981	+	84.9485i	−0.721375	+	0.387893i
$220$		0			0
$221$			44.6990i			0.202258i
$222$	106.717	−	57.3830i	0.480707	−	0.258482i
$223$		−	142.421i		−	0.638661i	−0.947643	−	0.319331i	$-0.896542\pi$
$223$		−	142.421i		−	0.638661i	0.947643	−	0.319331i	$-0.103458\pi$
$224$			37.6508i			0.168084i
$225$		0			0
$226$	94.8928			0.419879
$227$	42.4237			0.186888			0.0934442	−	0.995625i	$-0.470212\pi$
$227$	42.4237			0.186888			0.0934442	+	0.995625i	$0.470212\pi$
$228$	−30.1932	−	56.1511i	−0.132426	−	0.246277i
$229$	−147.482			−0.644024			−0.322012	−	0.946736i	$-0.604359\pi$
$229$	−147.482			−0.644024			−0.322012	+	0.946736i	$0.604359\pi$
$230$		0			0
$231$	15.0449	+	27.9794i	0.0651293	+	0.121123i
$232$			164.387i			0.708566i
$233$	222.924			0.956755			0.478378	−	0.878154i	$-0.341225\pi$
$233$	222.924			0.956755			0.478378	+	0.878154i	$0.341225\pi$
$234$	−8.05425	−	5.32393i	−0.0344199	−	0.0227518i
$235$		0			0
$236$		−	167.071i		−	0.707927i
$237$	172.261	+	320.359i	0.726840	+	1.35173i
$238$			24.8572i			0.104442i
$239$			97.3179i			0.407188i	0.979055	+	0.203594i	$0.0652623\pi$
$239$			97.3179i			0.407188i	−0.979055	+	0.203594i	$0.934738\pi$
$240$		0			0
$241$	37.9673			0.157541			0.0787704	−	0.996893i	$-0.474901\pi$
$241$	37.9673			0.157541			0.0787704	+	0.996893i	$0.474901\pi$
$242$	41.3081			0.170695
$243$	−151.810	+	189.744i	−0.624733	+	0.780838i
$244$	100.244			0.410835
$245$		0			0
$246$	103.836	−	55.8339i	0.422097	−	0.226967i
$247$		−	9.74937i		−	0.0394712i
$248$	107.882			0.435008
$249$	−92.0286	−	171.148i	−0.369593	−	0.687343i
$250$		0			0
$251$			16.7456i			0.0667157i	0.999443	+	0.0333579i	$0.0106201\pi$
$251$			16.7456i			0.0667157i	−0.999443	+	0.0333579i	$0.989380\pi$
$252$	37.3105	+	24.6626i	0.148058	+	0.0978674i
$253$			135.826i			0.536862i
$254$		−	115.495i		−	0.454704i
$255$		0			0
$256$	23.5593			0.0920285
$257$	480.276			1.86878			0.934388	−	0.356256i	$-0.115947\pi$
$257$	480.276			1.86878			0.934388	+	0.356256i	$0.115947\pi$
$258$	111.373	−	59.8864i	0.431677	−	0.232118i
$259$	−85.8337			−0.331404
$260$		0			0
$261$	248.964	+	164.568i	0.953886	+	0.630527i
$262$			119.723i			0.456957i
$263$	23.9672			0.0911301			0.0455650	−	0.998961i	$-0.485491\pi$
$263$	23.9672			0.0911301			0.0455650	+	0.998961i	$0.485491\pi$
$264$	−99.6806	+	53.5995i	−0.377578	+	0.203029i
$265$		0			0
$266$		−	5.42165i		−	0.0203822i
$267$	224.204	−	120.558i	0.839717	−	0.451526i
$268$			131.819i			0.491862i
$269$			372.819i			1.38594i	0.720965	+	0.692971i	$0.243699\pi$
$269$			372.819i			1.38594i	−0.720965	+	0.692971i	$0.756301\pi$
$270$		0			0
$271$	−232.814			−0.859091			−0.429545	−	0.903045i	$-0.641326\pi$
$271$	−232.814			−0.859091			−0.429545	+	0.903045i	$0.641326\pi$
$272$	301.176			1.10726
$273$	3.23906	+	6.02378i	0.0118647	+	0.0220651i
$274$	−78.3913			−0.286100
$275$		0			0
$276$	90.5621	+	168.421i	0.328124	+	0.610221i
$277$		−	65.8639i		−	0.237776i	−0.992908	−	0.118888i	$-0.962067\pi$
$277$		−	65.8639i		−	0.237776i	0.992908	−	0.118888i	$-0.0379329\pi$
$278$	24.7870			0.0891617
$279$	108.000	−	163.387i	0.387098	−	0.585617i
$280$		0			0
$281$		−	410.671i		−	1.46146i	−0.682665	−	0.730731i	$-0.739179\pi$
$281$		−	410.671i		−	1.46146i	0.682665	−	0.730731i	$-0.260821\pi$
$282$	−42.7603	−	79.5226i	−0.151632	−	0.281995i
$283$		−	157.017i		−	0.554829i	−0.960750	−	0.277414i	$-0.910522\pi$
$283$		−	157.017i		−	0.554829i	0.960750	−	0.277414i	$-0.0894775\pi$
$284$		−	314.241i		−	1.10648i
$285$		0			0
$286$	−8.16364			−0.0285442
$287$	−83.5165			−0.290998
$288$	−134.284	+	203.150i	−0.466263	+	0.705381i
$289$	455.332			1.57554
$290$		0			0
$291$	−385.026	+	207.033i	−1.32311	+	0.711454i
$292$			213.529i			0.731264i
$293$	−364.902			−1.24540			−0.622700	−	0.782461i	$-0.713964\pi$
$293$	−364.902			−1.24540			−0.622700	+	0.782461i	$0.713964\pi$
$294$	−43.7819	−	81.4226i	−0.148918	−	0.276947i
$295$		0			0
$296$		−	305.795i		−	1.03309i
$297$	−18.6135	+	204.624i	−0.0626718	+	0.688971i
$298$		−	100.098i		−	0.335900i
$299$			29.2425i			0.0978010i
$300$		0			0
$301$	−89.5783			−0.297602
$302$	66.4558			0.220052
$303$	85.0943	−	45.7563i	0.280839	−	0.151011i
$304$	−65.6900			−0.216085
$305$		0			0
$306$	−88.6546	+	134.120i	−0.289721	+	0.438301i
$307$		−	168.298i		−	0.548202i	−0.961701	−	0.274101i	$-0.911620\pi$
$307$		−	168.298i		−	0.548202i	0.961701	−	0.274101i	$-0.0883803\pi$
$308$	37.8173			0.122783
$309$	455.203	−	244.768i	1.47315	−	0.792130i
$310$		0			0
$311$			125.184i			0.402520i	0.979538	+	0.201260i	$0.0645036\pi$
$311$			125.184i			0.402520i	−0.979538	+	0.201260i	$0.935496\pi$
$312$	−21.4606	+	11.5396i	−0.0687840	+	0.0369860i
$313$		−	23.8145i		−	0.0760848i	−0.999276	−	0.0380424i	$-0.987888\pi$
$313$		−	23.8145i		−	0.0760848i	0.999276	−	0.0380424i	$-0.0121122\pi$
$314$			110.947i			0.353335i
$315$		0			0
$316$	433.001			1.37026
$317$	175.103			0.552375			0.276188	−	0.961104i	$-0.410929\pi$
$317$	175.103			0.552375			0.276188	+	0.961104i	$0.410929\pi$
$318$	−2.33136	−	4.33569i	−0.00733131	−	0.0136342i
$319$	252.346			0.791052
$320$		0			0
$321$	267.965	+	498.343i	0.834782	+	1.55247i
$322$			16.2618i			0.0505026i
$323$	−162.348			−0.502624
$324$	113.353	+	266.140i	0.349855	+	0.821419i
$325$		0			0
$326$		−	110.589i		−	0.339231i
$327$	−2.86842	−	5.33449i	−0.00877194	−	0.0163134i
$328$		−	297.540i		−	0.907133i
$329$			63.9610i			0.194410i
$330$		0			0
$331$	330.952			0.999856			0.499928	−	0.866067i	$-0.333360\pi$
$331$	330.952			0.999856			0.499928	+	0.866067i	$0.333360\pi$
$332$	−231.326			−0.696766
$333$	−463.126	−	306.130i	−1.39077	−	0.919310i
$334$	−45.2953			−0.135615
$335$		0			0
$336$	40.5874	−	21.8244i	0.120796	−	0.0649535i
$337$			320.640i			0.951455i	0.879593	+	0.475728i	$0.157815\pi$
$337$			320.640i			0.951455i	−0.879593	+	0.475728i	$0.842185\pi$
$338$	108.898			0.322183
$339$	−205.906	−	382.930i	−0.607392	−	1.12959i
$340$		0			0
$341$		−	165.606i		−	0.485648i
$342$	19.3366	−	29.2532i	0.0565398	−	0.0855356i
$343$			133.673i			0.389716i
$344$		−	319.136i		−	0.927721i
$345$		0			0
$346$	38.9867			0.112678
$347$	−466.651			−1.34482			−0.672408	−	0.740180i	$-0.734740\pi$
$347$	−466.651			−1.34482			−0.672408	+	0.740180i	$0.734740\pi$
$348$	312.902	−	168.252i	0.899145	−	0.483481i
$349$	158.835			0.455114			0.227557	−	0.973765i	$-0.426926\pi$
$349$	158.835			0.455114			0.227557	+	0.973765i	$0.426926\pi$
$350$		0			0
$351$	−4.00737	+	44.0543i	−0.0114170	+	0.125511i
$352$			205.909i			0.584968i
$353$	−121.203			−0.343352			−0.171676	−	0.985153i	$-0.554918\pi$
$353$	−121.203			−0.343352			−0.171676	+	0.985153i	$0.554918\pi$
$354$	80.9347	−	43.5196i	0.228629	−	0.122937i
$355$		0			0
$356$		−	303.037i		−	0.851228i
$357$	100.309	−	53.9372i	0.280977	−	0.151085i
$358$			136.343i			0.380846i
$359$			479.208i			1.33484i	0.744681	+	0.667420i	$0.232601\pi$
$359$			479.208i			1.33484i	−0.744681	+	0.667420i	$0.767399\pi$
$360$		0			0
$361$	−325.590			−0.901912
$362$	101.475			0.280318
$363$	−89.6337	−	166.694i	−0.246925	−	0.459213i
$364$	8.14182			0.0223676
$365$		0			0
$366$	26.1121	+	48.5614i	0.0713445	+	0.132681i
$367$		−	538.114i		−	1.46625i	−0.680094	−	0.733125i	$-0.738061\pi$
$367$		−	538.114i		−	1.46625i	0.680094	−	0.733125i	$-0.261939\pi$
$368$	197.032			0.535413
$369$	−450.623	−	297.866i	−1.22120	−	0.807225i
$370$		0			0
$371$			3.48725i			0.00939959i
$372$	−110.418	−	205.348i	−0.296822	−	0.552010i
$373$			395.678i			1.06080i	0.847748	+	0.530399i	$0.177958\pi$
$373$			395.678i			1.06080i	−0.847748	+	0.530399i	$0.822042\pi$
$374$			135.942i			0.363481i
$375$		0			0
$376$	−227.870			−0.606038
$377$	54.3284			0.144107
$378$	−2.22851	+	24.4987i	−0.00589553	+	0.0648115i
$379$	−410.468			−1.08303			−0.541514	−	0.840692i	$-0.682149\pi$
$379$	−410.468			−1.08303			−0.541514	+	0.840692i	$0.682149\pi$
$380$		0			0
$381$	−466.067	+	250.610i	−1.22327	+	0.657769i
$382$		−	190.619i		−	0.499002i
$383$	27.0650			0.0706659			0.0353330	−	0.999376i	$-0.488751\pi$
$383$	27.0650			0.0706659			0.0353330	+	0.999376i	$0.488751\pi$
$384$	178.367	+	331.715i	0.464498	+	0.863841i
$385$		0			0
$386$			99.6553i			0.258174i
$387$	−483.331	−	319.486i	−1.24892	−	0.825544i
$388$			520.405i			1.34125i
$389$		−	6.81165i		−	0.0175107i	−0.999962	−	0.00875533i	$-0.997213\pi$
$389$		−	6.81165i		−	0.0175107i	0.999962	−	0.00875533i	$-0.00278694\pi$
$390$		0			0
$391$	486.949			1.24539
$392$	−233.315			−0.595190
$393$	483.128	−	259.784i	1.22933	−	0.661028i
$394$	197.170			0.500432
$395$		0			0
$396$	204.048	+	134.877i	0.515272	+	0.340599i
$397$			398.817i			1.00458i	0.864700	+	0.502289i	$0.167508\pi$
$397$			398.817i			1.00458i	−0.864700	+	0.502289i	$0.832492\pi$
$398$	−70.9814			−0.178345
$399$	−21.8785	+	11.7643i	−0.0548333	+	0.0294846i
$400$		0			0
$401$		−	421.444i		−	1.05098i	−0.850799	−	0.525491i	$-0.823882\pi$
$401$		−	421.444i		−	1.05098i	0.850799	−	0.525491i	$-0.176118\pi$
$402$	−63.8576	+	34.3370i	−0.158850	+	0.0854155i
$403$		−	35.6539i		−	0.0884713i
$404$		−	115.014i		−	0.284689i
$405$		0			0
$406$	30.2122			0.0744142
$407$	−469.416			−1.15336
$408$	192.159	+	357.364i	0.470979	+	0.875893i
$409$	−737.811			−1.80394			−0.901969	−	0.431800i	$-0.857879\pi$
$409$	−737.811			−1.80394			−0.901969	+	0.431800i	$0.857879\pi$
$410$		0			0
$411$	170.100	+	316.340i	0.413868	+	0.769683i
$412$		−	615.257i		−	1.49334i
$413$	−65.0967			−0.157619
$414$	−57.9987	+	87.7427i	−0.140093	+	0.211939i
$415$		0			0
$416$			44.3309i			0.106565i
$417$	−53.7847	−	100.025i	−0.128980	−	0.239868i
$418$		−	29.6505i		−	0.0709342i
$419$			56.2843i			0.134330i	0.997742	+	0.0671651i	$0.0213954\pi$
$419$			56.2843i			0.134330i	−0.997742	+	0.0671651i	$0.978605\pi$
$420$		0			0
$421$	−335.771			−0.797555			−0.398777	−	0.917048i	$-0.630565\pi$
$421$	−335.771			−0.797555			−0.398777	+	0.917048i	$0.630565\pi$
$422$	−146.159			−0.346348
$423$	−228.120	+	345.109i	−0.539291	+	0.815861i
$424$	−12.4238			−0.0293015
$425$		0			0
$426$	152.229	−	81.8553i	0.357344	−	0.192149i
$427$		−	39.0585i		−	0.0914719i
$428$	673.566			1.57375
$429$	17.7141	+	32.9435i	0.0412917	+	0.0767913i
$430$		0			0
$431$		−	269.813i		−	0.626017i	−0.949750	−	0.313009i	$-0.898663\pi$
$431$		−	269.813i		−	0.626017i	0.949750	−	0.313009i	$-0.101337\pi$
$432$	296.832	+	27.0011i	0.687111	+	0.0625026i
$433$		−	241.828i		−	0.558495i	−0.960219	−	0.279247i	$-0.909915\pi$
$433$		−	241.828i		−	0.558495i	0.960219	−	0.279247i	$-0.0900849\pi$
$434$		−	19.8273i		−	0.0456849i
$435$		0			0
$436$	−7.21016			−0.0165371
$437$	−106.209			−0.243042
$438$	−103.441	+	55.6214i	−0.236166	+	0.126989i
$439$	157.224			0.358142			0.179071	−	0.983836i	$-0.442691\pi$
$439$	157.224			0.358142			0.179071	+	0.983836i	$0.442691\pi$
$440$		0			0
$441$	−233.570	+	353.355i	−0.529638	+	0.801257i
$442$			29.2674i			0.0662158i
$443$	38.3345			0.0865338			0.0432669	−	0.999064i	$-0.486223\pi$
$443$	38.3345			0.0865338			0.0432669	+	0.999064i	$0.486223\pi$
$444$	−582.064	+	312.983i	−1.31096	+	0.704917i
$445$		0			0
$446$		−	93.2528i		−	0.209087i
$447$	−403.935	+	217.201i	−0.903658	+	0.485908i
$448$		−	36.7915i		−	0.0821239i
$449$			652.180i			1.45252i	0.687422	+	0.726258i	$0.258742\pi$
$449$			652.180i			1.45252i	−0.687422	+	0.726258i	$0.741258\pi$
$450$		0			0
$451$	−456.743			−1.01273
$452$	−517.572			−1.14507
$453$	−144.201	−	268.175i	−0.318325	−	0.591998i
$454$	27.7776			0.0611841
$455$		0			0
$456$	−41.9122	−	77.9454i	−0.0919127	−	0.170933i
$457$		−	235.891i		−	0.516172i	−0.966122	−	0.258086i	$-0.916908\pi$
$457$		−	235.891i		−	0.516172i	0.966122	−	0.258086i	$-0.0830919\pi$
$458$	−96.5660			−0.210843
$459$	733.597	+	66.7312i	1.59825	+	0.145384i
$460$		0			0
$461$		−	585.877i		−	1.27088i	−0.772149	−	0.635442i	$-0.780818\pi$
$461$		−	585.877i		−	1.27088i	0.772149	−	0.635442i	$-0.219182\pi$
$462$	9.85087	+	18.3200i	0.0213222	+	0.0396536i
$463$		−	372.852i		−	0.805296i	−0.915355	−	0.402648i	$-0.868090\pi$
$463$		−	372.852i		−	0.805296i	0.915355	−	0.402648i	$-0.131910\pi$
$464$		−	366.057i		−	0.788917i
$465$		0			0
$466$	145.963			0.313226
$467$	−279.458			−0.598412			−0.299206	−	0.954189i	$-0.596722\pi$
$467$	−279.458			−0.598412			−0.299206	+	0.954189i	$0.596722\pi$
$468$	43.9301	+	29.0382i	0.0938678	+	0.0620474i
$469$	51.3615			0.109513
$470$		0			0
$471$	447.716	−	240.742i	0.950564	−	0.511130i
$472$		−	231.917i		−	0.491349i
$473$	−489.895			−1.03572
$474$	112.791	+	209.760i	0.237955	+	0.442532i
$475$		0			0
$476$		−	135.578i		−	0.284829i
$477$	−12.4374	+	18.8159i	−0.0260743	+	0.0394463i
$478$			63.7205i			0.133306i
$479$		−	732.583i		−	1.52940i	−0.644386	−	0.764700i	$-0.722887\pi$
$479$		−	732.583i		−	1.52940i	0.644386	−	0.764700i	$-0.277113\pi$
$480$		0			0
$481$	−101.062			−0.210109
$482$	24.8597			0.0515762
$483$	65.6229	−	35.2863i	0.135865	−	0.0730564i
$484$	−225.306			−0.465509
$485$		0			0
$486$	−99.4002	+	124.238i	−0.204527	+	0.255633i
$487$		−	694.558i		−	1.42620i	−0.701064	−	0.713098i	$-0.747291\pi$
$487$		−	694.558i		−	1.42620i	0.701064	−	0.713098i	$-0.252709\pi$
$488$	139.152			0.285147
$489$	−446.271	+	239.965i	−0.912619	+	0.490727i
$490$		0			0
$491$			238.779i			0.486311i	0.969987	+	0.243156i	$0.0781826\pi$
$491$			238.779i			0.486311i	−0.969987	+	0.243156i	$0.921817\pi$
$492$	−566.351	+	304.534i	−1.15112	+	0.618971i
$493$		−	904.682i		−	1.83506i
$494$		−	6.38356i		−	0.0129222i
$495$		0			0
$496$	−240.231			−0.484338
$497$	−122.439			−0.246357
$498$	−60.2573	−	112.062i	−0.120999	−	0.225025i
$499$	280.345			0.561814			0.280907	−	0.959735i	$-0.409365\pi$
$499$	280.345			0.561814			0.280907	+	0.959735i	$0.409365\pi$
$500$		0			0
$501$	98.2854	+	182.784i	0.196179	+	0.364839i
$502$			10.9645i			0.0218416i
$503$	−577.859			−1.14883			−0.574413	−	0.818566i	$-0.694770\pi$
$503$	−577.859			−1.14883			−0.574413	+	0.818566i	$0.694770\pi$
$504$	51.7920	+	34.2350i	0.102762	+	0.0679266i
$505$		0			0
$506$			88.9344i			0.175760i
$507$	−236.296	−	439.446i	−0.466066	−	0.866757i
$508$			629.941i			1.24004i
$509$		−	217.726i		−	0.427752i	−0.976861	−	0.213876i	$-0.931391\pi$
$509$		−	217.726i		−	0.427752i	0.976861	−	0.213876i	$-0.0686089\pi$
$510$		0			0
$511$	83.1986			0.162815
$512$	517.599			1.01093
$513$	−160.006	−	14.5549i	−0.311903	−	0.0283721i
$514$	314.468			0.611806
$515$		0			0
$516$	−607.458	+	326.638i	−1.17724	+	0.633019i
$517$			349.796i			0.676588i
$518$	−56.2010			−0.108496
$519$	−84.5964	−	157.326i	−0.162999	−	0.303134i
$520$		0			0
$521$			10.5452i			0.0202404i	0.999949	+	0.0101202i	$0.00322141\pi$
$521$			10.5452i			0.0202404i	−0.999949	+	0.0101202i	$0.996779\pi$
$522$	163.013	+	107.753i	0.312286	+	0.206424i
$523$			820.342i			1.56853i	0.620426	+	0.784265i	$0.286960\pi$
$523$			820.342i			1.56853i	−0.620426	+	0.784265i	$0.713040\pi$
$524$		−	653.001i		−	1.24619i
$525$		0			0
$526$	15.6929			0.0298344
$527$	−593.713			−1.12659
$528$	221.969	−	119.355i	0.420395	−	0.226052i
$529$	−210.433			−0.397794
$530$		0			0
$531$	−351.237	−	232.171i	−0.661464	−	0.437233i
$532$			29.5712i			0.0555850i
$533$	−98.3340			−0.184492
$534$	146.801	−	78.9370i	0.274909	−	0.147822i
$535$		0			0
$536$			182.983i			0.341386i
$537$	550.198	−	295.848i	1.02458	−	0.550928i
$538$			244.109i			0.453734i
$539$			358.154i			0.664478i
$540$		0			0
$541$	807.407			1.49243			0.746217	−	0.665703i	$-0.231868\pi$
$541$	807.407			1.49243			0.746217	+	0.665703i	$0.231868\pi$
$542$	−152.438			−0.281252
$543$	−220.189	−	409.492i	−0.405505	−	0.754129i
$544$	738.202			1.35699
$545$		0			0
$546$	2.12083	+	3.94417i	0.00388430	+	0.00722376i
$547$			627.774i			1.14767i	0.818972	+	0.573834i	$0.194545\pi$
$547$			627.774i			1.14767i	−0.818972	+	0.573834i	$0.805455\pi$
$548$	427.568			0.780234
$549$	139.304	−	210.745i	0.253742	−	0.383870i
$550$		0			0
$551$			197.322i			0.358116i
$552$	125.712	+	233.791i	0.227740	+	0.423535i
$553$		−	168.713i		−	0.305086i
$554$		−	43.1254i		−	0.0778437i
$555$		0			0
$556$	−135.195			−0.243157
$557$	560.466			1.00622			0.503111	−	0.864222i	$-0.332189\pi$
$557$	560.466			1.00622			0.503111	+	0.864222i	$0.332189\pi$
$558$	70.7149	−	106.980i	0.126729	−	0.191721i
$559$	−105.471			−0.188678
$560$		0			0
$561$	548.578	−	294.977i	0.977858	−	0.525806i
$562$		−	268.893i		−	0.478458i
$563$	−281.793			−0.500521			−0.250261	−	0.968179i	$-0.580516\pi$
$563$	−281.793			−0.500521			−0.250261	+	0.968179i	$0.580516\pi$
$564$	233.227	+	433.739i	0.413523	+	0.769040i
$565$		0			0
$566$		−	102.809i		−	0.181642i
$567$	103.698	−	44.1664i	0.182888	−	0.0778949i
$568$		−	436.208i		−	0.767972i
$569$		−	573.846i		−	1.00852i	−0.863553	−	0.504259i	$-0.831766\pi$
$569$		−	573.846i		−	1.00852i	0.863553	−	0.504259i	$-0.168234\pi$
$570$		0			0
$571$	−518.101			−0.907356			−0.453678	−	0.891166i	$-0.649888\pi$
$571$	−518.101			−0.907356			−0.453678	+	0.891166i	$0.649888\pi$
$572$	44.5268			0.0778440
$573$	−769.221	+	413.620i	−1.34244	+	0.721849i
$574$	−54.6838			−0.0952679
$575$		0			0
$576$	131.219	−	198.513i	0.227810	−	0.344641i
$577$			83.1972i			0.144189i	0.997398	+	0.0720947i	$0.0229684\pi$
$577$			83.1972i			0.144189i	−0.997398	+	0.0720947i	$0.977032\pi$
$578$	298.136			0.515807
$579$	402.148	−	216.240i	0.694556	−	0.373472i
$580$		0			0
$581$			90.1330i			0.155134i
$582$	−252.102	+	135.558i	−0.433165	+	0.232918i
$583$			19.0714i			0.0327125i
$584$			296.407i			0.507547i
$585$		0			0
$586$	−238.925			−0.407723
$587$	325.684			0.554827			0.277414	−	0.960751i	$-0.410523\pi$
$587$	325.684			0.554827			0.277414	+	0.960751i	$0.410523\pi$
$588$	238.799	+	444.102i	0.406121	+	0.755275i
$589$	129.496			0.219857
$590$		0			0
$591$	−427.835	−	795.658i	−0.723918	−	1.34629i
$592$			680.944i			1.15024i
$593$	676.740			1.14121			0.570607	−	0.821223i	$-0.306708\pi$
$593$	676.740			1.14121			0.570607	+	0.821223i	$0.306708\pi$
$594$	−12.1875	+	133.981i	−0.0205177	+	0.225558i
$595$		0			0
$596$			545.963i			0.916046i
$597$	154.021	+	286.438i	0.257992	+	0.479795i
$598$			19.1470i			0.0320184i
$599$		−	360.639i		−	0.602068i	−0.953613	−	0.301034i	$-0.902668\pi$
$599$		−	360.639i		−	0.602068i	0.953613	−	0.301034i	$-0.0973317\pi$
$600$		0			0
$601$	658.435			1.09556			0.547782	−	0.836621i	$-0.315472\pi$
$601$	658.435			1.09556			0.547782	+	0.836621i	$0.315472\pi$
$602$	−58.6529			−0.0974300
$603$	277.127	+	183.183i	0.459580	+	0.303787i
$604$	−362.469			−0.600113
$605$		0			0
$606$	55.7169	−	29.9597i	0.0919420	−	0.0494384i
$607$		−	78.8724i		−	0.129938i	−0.997887	−	0.0649690i	$-0.979305\pi$
$607$		−	78.8724i		−	0.129938i	0.997887	−	0.0649690i	$-0.0206948\pi$
$608$	−161.011			−0.264820
$609$	−65.5568	−	121.918i	−0.107647	−	0.200194i
$610$		0			0
$611$			75.3089i			0.123255i
$612$	483.547	−	731.529i	0.790110	−	1.19531i
$613$		−	364.090i		−	0.593948i	−0.954886	−	0.296974i	$-0.904023\pi$
$613$		−	364.090i		−	0.593948i	0.954886	−	0.296974i	$-0.0959774\pi$
$614$		−	110.196i		−	0.179472i
$615$		0			0
$616$	52.4955			0.0852199
$617$	1108.31			1.79628			0.898141	−	0.439708i	$-0.144918\pi$
$617$	1108.31			1.79628			0.898141	+	0.439708i	$0.144918\pi$
$618$	298.051	−	160.266i	0.482284	−	0.259330i
$619$	353.346			0.570834			0.285417	−	0.958403i	$-0.407868\pi$
$619$	353.346			0.570834			0.285417	+	0.958403i	$0.407868\pi$
$620$		0			0
$621$	479.927	+	43.6562i	0.772829	+	0.0702998i
$622$			81.9661i			0.131778i
$623$	−118.074			−0.189525
$624$	47.7884	−	25.6964i	0.0765840	−	0.0411802i
$625$		0			0
$626$		−	15.5930i		−	0.0249089i
$627$	−119.651	+	64.3380i	−0.190832	+	0.102612i
$628$		−	605.138i		−	0.963596i
$629$			1682.90i			2.67552i
$630$		0			0
$631$	1153.93			1.82873			0.914365	−	0.404890i	$-0.132690\pi$
$631$	1153.93			1.82873			0.914365	+	0.404890i	$0.132690\pi$
$632$	601.064			0.951050
$633$	317.147	+	589.808i	0.501023	+	0.931767i
$634$	114.652			0.180838
$635$		0			0
$636$	12.7159	+	23.6481i	0.0199935	+	0.0371825i
$637$			77.1082i			0.121049i
$638$	165.227			0.258977
$639$	−660.636	−	436.686i	−1.03386	−	0.683390i
$640$		0			0
$641$			706.832i			1.10270i	0.834273	+	0.551351i	$0.185888\pi$
$641$			706.832i			1.10270i	−0.834273	+	0.551351i	$0.814112\pi$
$642$	175.455	+	326.298i	0.273294	+	0.508252i
$643$		−	683.915i		−	1.06363i	−0.846860	−	0.531816i	$-0.821510\pi$
$643$		−	683.915i		−	1.06363i	0.846860	−	0.531816i	$-0.178490\pi$
$644$		−	88.6967i		−	0.137728i
$645$		0			0
$646$	−106.300			−0.164551
$647$	−320.944			−0.496049			−0.248025	−	0.968754i	$-0.579781\pi$
$647$	−320.944			−0.496049			−0.248025	+	0.968754i	$0.579781\pi$
$648$	157.349	+	369.438i	0.242823	+	0.570120i
$649$	−356.008			−0.548548
$650$		0			0
$651$	−80.0108	+	43.0228i	−0.122904	+	0.0660872i
$652$			603.185i			0.925130i
$653$	30.7467			0.0470853			0.0235426	−	0.999723i	$-0.492505\pi$
$653$	30.7467			0.0470853			0.0235426	+	0.999723i	$0.492505\pi$
$654$	−1.87815	−	3.49285i	−0.00287179	−	0.00534074i
$655$		0			0
$656$			662.561i			1.01000i
$657$	448.908	+	296.732i	0.683270	+	0.451647i
$658$			41.8795i			0.0636466i
$659$			17.4285i			0.0264470i	0.999913	+	0.0132235i	$0.00420929\pi$
$659$			17.4285i			0.0264470i	−0.999913	+	0.0132235i	$0.995791\pi$
$660$		0			0
$661$	−620.887			−0.939314			−0.469657	−	0.882849i	$-0.655622\pi$
$661$	−620.887			−0.939314			−0.469657	+	0.882849i	$0.655622\pi$
$662$	216.696			0.327336
$663$	118.105	−	63.5068i	0.178138	−	0.0957870i
$664$	−321.112			−0.483602
$665$		0			0
$666$	−303.239	−	200.444i	−0.455314	−	0.300967i
$667$		−	591.852i		−	0.887334i
$668$	247.053			0.369841
$669$	−376.312	+	202.347i	−0.562499	+	0.302463i
$670$		0			0
$671$		−	213.607i		−	0.318341i
$672$	99.4825	−	53.4930i	0.148039	−	0.0796027i
$673$			1105.88i			1.64321i	0.570058	+	0.821604i	$0.306921\pi$
$673$			1105.88i			1.64321i	−0.570058	+	0.821604i	$0.693079\pi$
$674$			209.945i			0.311490i
$675$		0			0
$676$	−593.960			−0.878639
$677$	1184.47			1.74959			0.874793	−	0.484497i	$-0.160997\pi$
$677$	1184.47			1.74959			0.874793	+	0.484497i	$0.160997\pi$
$678$	−134.820	−	250.729i	−0.198850	−	0.369807i
$679$	202.769			0.298628
$680$		0			0
$681$	−60.2741	−	112.094i	−0.0885082	−	0.164601i
$682$		−	108.433i		−	0.158993i
$683$	−491.782			−0.720032			−0.360016	−	0.932946i	$-0.617229\pi$
$683$	−491.782			−0.720032			−0.360016	+	0.932946i	$0.617229\pi$
$684$	−105.467	+	159.555i	−0.154192	+	0.233268i
$685$		0			0
$686$			87.5243i			0.127586i
$687$	209.537	+	389.682i	0.305002	+	0.567222i
$688$			710.651i			1.03292i
$689$			4.10595i			0.00595930i
$690$		0			0
$691$	−433.719			−0.627669			−0.313834	−	0.949478i	$-0.601614\pi$
$691$	−433.719			−0.627669			−0.313834	+	0.949478i	$0.601614\pi$
$692$	−212.644			−0.307289
$693$	52.5530	−	79.5042i	0.0758340	−	0.114725i
$694$	−305.548			−0.440270
$695$		0			0
$696$	434.351	−	233.556i	0.624067	−	0.335569i
$697$			1637.47i			2.34931i
$698$	104.000			0.148997
$699$	−316.723	−	589.018i	−0.453108	−	0.842659i
$700$		0			0
$701$			176.492i			0.251772i	0.992045	+	0.125886i	$0.0401774\pi$
$701$			176.492i			0.251772i	−0.992045	+	0.125886i	$0.959823\pi$
$702$	−2.62389	+	28.8453i	−0.00373774	+	0.0410902i
$703$		−	367.060i		−	0.522134i
$704$		−	201.209i		−	0.285808i
$705$		0			0
$706$	−79.3598			−0.112408
$707$	−44.8137			−0.0633858
$708$	−441.441	+	237.368i	−0.623504	+	0.335266i
$709$	−1265.27			−1.78458			−0.892291	−	0.451460i	$-0.850903\pi$
$709$	−1265.27			−1.78458			−0.892291	+	0.451460i	$0.850903\pi$
$710$		0			0
$711$	601.723	−	910.310i	0.846305	−	1.28032i
$712$		−	420.657i		−	0.590810i
$713$	−388.413			−0.544759
$714$	65.6787	−	35.3163i	0.0919870	−	0.0494626i
$715$		0			0
$716$		−	743.654i		−	1.03862i
$717$	257.137	−	138.266i	0.358629	−	0.192839i
$718$			313.769i			0.437004i
$719$			1225.73i			1.70478i	0.522910	+	0.852388i	$0.324846\pi$
$719$			1225.73i			1.70478i	−0.522910	+	0.852388i	$0.675154\pi$
$720$		0			0
$721$	−239.726			−0.332491
$722$	−213.185			−0.295271
$723$	−53.9427	−	100.319i	−0.0746095	−	0.138753i
$724$	−553.474			−0.764467
$725$		0			0
$726$	−58.6891	−	109.146i	−0.0808390	−	0.150339i
$727$			757.105i			1.04141i	0.853737	+	0.520705i	$0.174331\pi$
$727$			757.105i			1.04141i	−0.853737	+	0.520705i	$0.825669\pi$
$728$	11.3019			0.0155246
$729$	717.035	+	131.538i	0.983587	+	0.180436i
$730$		0			0
$731$			1756.32i			2.40263i
$732$	−142.423	−	264.868i	−0.194566	−	0.361841i
$733$		−	483.548i		−	0.659683i	−0.944036	−	0.329842i	$-0.893005\pi$
$733$		−	483.548i		−	0.659683i	0.944036	−	0.329842i	$-0.106995\pi$
$734$		−	352.339i		−	0.480026i
$735$		0			0
$736$	482.939			0.656167
$737$	280.891			0.381127
$738$	−295.053	−	195.033i	−0.399801	−	0.264272i
$739$	462.179			0.625411			0.312705	−	0.949850i	$-0.398765\pi$
$739$	462.179			0.625411			0.312705	+	0.949850i	$0.398765\pi$
$740$		0			0
$741$	−25.7602	+	13.8516i	−0.0347641	+	0.0186931i
$742$			2.28333i			0.00307727i
$743$	747.203			1.00566			0.502828	−	0.864386i	$-0.332293\pi$
$743$	747.203			1.00566			0.502828	+	0.864386i	$0.332293\pi$
$744$	−153.275	−	285.050i	−0.206015	−	0.383132i
$745$		0			0
$746$			259.076i			0.347287i
$747$	−321.464	+	486.323i	−0.430340	+	0.651035i
$748$		−	741.465i		−	0.991263i
$749$		−	262.445i		−	0.350394i
$750$		0			0
$751$	1153.67			1.53618			0.768090	−	0.640342i	$-0.221207\pi$
$751$	1153.67			1.53618			0.768090	+	0.640342i	$0.221207\pi$
$752$	507.421			0.674762
$753$	44.2460	−	23.7916i	0.0587596	−	0.0315958i
$754$	35.5724			0.0471783
$755$		0			0
$756$	12.1549	−	133.623i	0.0160780	−	0.176750i
$757$		−	714.489i		−	0.943843i	−0.881640	−	0.471922i	$-0.843561\pi$
$757$		−	714.489i		−	0.943843i	0.881640	−	0.471922i	$-0.156439\pi$
$758$	−268.760			−0.354565
$759$	358.885	−	192.977i	0.472840	−	0.254252i
$760$		0			0
$761$		−	43.0757i		−	0.0566040i	−0.999599	−	0.0283020i	$-0.990990\pi$
$761$		−	43.0757i		−	0.0566040i	0.999599	−	0.0283020i	$-0.00901001\pi$
$762$	−305.165	+	164.091i	−0.400479	+	0.215342i
$763$			2.80934i			0.00368196i
$764$			1039.69i			1.36085i
$765$		0			0
$766$	17.7213			0.0231348
$767$	−76.6462			−0.0999298
$768$	−33.4722	−	62.2493i	−0.0435836	−	0.0810537i
$769$	607.301			0.789728			0.394864	−	0.918740i	$-0.370792\pi$
$769$	607.301			0.789728			0.394864	+	0.918740i	$0.370792\pi$
$770$		0			0
$771$	−682.359	−	1269.00i	−0.885031	−	1.64592i
$772$		−	543.548i		−	0.704078i
$773$	−1085.11			−1.40376			−0.701882	−	0.712293i	$-0.747657\pi$
$773$	−1085.11			−1.40376			−0.701882	+	0.712293i	$0.747657\pi$
$774$	−316.469	−	209.188i	−0.408874	−	0.270269i
$775$		0			0
$776$			722.393i			0.930918i
$777$	121.950	+	226.793i	0.156949	+	0.291883i
$778$		−	4.46004i		−	0.00573270i
$779$		−	357.151i		−	0.458474i
$780$		0			0
$781$	−669.609			−0.857374
$782$	318.838			0.407721
$783$	81.1070	−	891.635i	0.103585	−	1.13874i
$784$	519.545			0.662684
$785$		0			0
$786$	316.336	−	170.098i	0.402463	−	0.216409i
$787$		−	160.077i		−	0.203401i	−0.994815	−	0.101701i	$-0.967572\pi$
$787$		−	160.077i		−	0.203401i	0.994815	−	0.101701i	$-0.0324284\pi$
$788$	−1075.42			−1.36475
$789$	−34.0518	−	63.3271i	−0.0431581	−	0.0802625i
$790$		0			0
$791$			201.665i			0.254949i
$792$	283.246	+	187.228i	0.357633	+	0.236399i
$793$		−	45.9883i		−	0.0579928i
$794$			261.132i			0.328882i
$795$		0			0
$796$	387.152			0.486372
$797$	−159.221			−0.199776			−0.0998878	−	0.994999i	$-0.531848\pi$
$797$	−159.221			−0.199776			−0.0998878	+	0.994999i	$0.531848\pi$
$798$	−14.3253	+	7.70290i	−0.0179515	+	0.00965275i
$799$	1254.05			1.56953
$800$		0			0
$801$	−637.083	−	421.118i	−0.795360	−	0.525740i
$802$		−	275.947i		−	0.344074i
$803$	455.005			0.566632
$804$	348.298	−	187.284i	0.433206	−	0.232940i
$805$		0			0
$806$		−	23.3450i		−	0.0289640i
$807$	985.076	−	529.688i	1.22066	−	0.656366i
$808$		−	159.656i		−	0.197594i
$809$			345.680i			0.427293i	0.976911	+	0.213646i	$0.0685340\pi$
$809$			345.680i			0.427293i	−0.976911	+	0.213646i	$0.931466\pi$
$810$		0			0
$811$	−1374.78			−1.69517			−0.847584	−	0.530661i	$-0.821944\pi$
$811$	−1374.78			−1.69517			−0.847584	+	0.530661i	$0.821944\pi$
$812$	−164.786			−0.202938
$813$	330.773	+	615.149i	0.406855	+	0.756641i
$814$	−307.358			−0.377589
$815$		0			0
$816$	−427.900	−	795.778i	−0.524387	−	0.975218i
$817$		−	383.074i		−	0.468879i
$818$	−483.094			−0.590579
$819$	11.3143	−	17.1168i	0.0138148	−	0.0208996i
$820$		0			0
$821$		−	15.4079i		−	0.0187673i	−0.999956	−	0.00938364i	$-0.997013\pi$
$821$		−	15.4079i		−	0.0187673i	0.999956	−	0.00938364i	$-0.00298695\pi$
$822$	111.376	+	207.129i	0.135493	+	0.251981i
$823$			18.2039i			0.0221190i	0.999939	+	0.0110595i	$0.00352042\pi$
$823$			18.2039i			0.0221190i	−0.999939	+	0.0110595i	$0.996480\pi$
$824$		−	854.060i		−	1.03648i
$825$		0			0
$826$	−42.6232			−0.0516019
$827$	−585.863			−0.708420			−0.354210	−	0.935166i	$-0.615250\pi$
$827$	−585.863			−0.708420			−0.354210	+	0.935166i	$0.615250\pi$
$828$	316.341	−	478.574i	0.382055	−	0.577988i
$829$	−347.094			−0.418690			−0.209345	−	0.977842i	$-0.567133\pi$
$829$	−347.094			−0.418690			−0.209345	+	0.977842i	$0.567133\pi$
$830$		0			0
$831$	−174.028	+	93.5771i	−0.209420	+	0.112608i
$832$		−	43.3190i		−	0.0520661i
$833$	1284.01			1.54143
$834$	−35.2164	−	65.4930i	−0.0422259	−	0.0785288i
$835$		0			0
$836$			161.722i			0.193448i
$837$	−585.151	−	53.2279i	−0.699105	−	0.0635936i
$838$			36.8531i			0.0439774i
$839$		−	1413.50i		−	1.68474i	−0.538896	−	0.842372i	$-0.681158\pi$
$839$		−	1413.50i		−	1.68474i	0.538896	−	0.842372i	$-0.318842\pi$
$840$		0			0
$841$	−258.577			−0.307463
$842$	−219.851			−0.261106
$843$	−1085.09	+	583.467i	−1.28718	+	0.692131i
$844$	797.192			0.944540
$845$		0			0
$846$	−149.365	+	225.966i	−0.176555	+	0.267099i
$847$			87.7874i			0.103645i
$848$	27.6654			0.0326243
$849$	−414.875	+	223.084i	−0.488664	+	0.262761i
$850$		0			0
$851$			1100.97i			1.29374i
$852$	−830.299	+	446.462i	−0.974529	+	0.524016i
$853$		−	100.133i		−	0.117390i	−0.998276	−	0.0586948i	$-0.981306\pi$
$853$		−	100.133i		−	0.117390i	0.998276	−	0.0586948i	$-0.0186939\pi$
$854$		−	25.5742i		−	0.0299464i
$855$		0			0
$856$	935.000			1.09229
$857$	−775.192			−0.904541			−0.452271	−	0.891881i	$-0.649386\pi$
$857$	−775.192			−0.904541			−0.452271	+	0.891881i	$0.649386\pi$
$858$	11.5986	+	21.5703i	0.0135182	+	0.0251402i
$859$	75.7667			0.0882034			0.0441017	−	0.999027i	$-0.485957\pi$
$859$	75.7667			0.0882034			0.0441017	+	0.999027i	$0.485957\pi$
$860$		0			0
$861$	118.657	+	220.671i	0.137813	+	0.256296i
$862$		−	176.665i		−	0.204948i
$863$	1511.62			1.75159			0.875794	−	0.482685i	$-0.160338\pi$
$863$	1511.62			1.75159			0.875794	+	0.482685i	$0.160338\pi$
$864$	727.556	+	66.1816i	0.842078	+	0.0765991i
$865$		0			0
$866$		−	158.341i		−	0.182842i
$867$	−646.920	−	1203.10i	−0.746160	−	1.38766i
$868$			108.143i			0.124589i
$869$		−	922.673i		−	1.06176i
$870$		0			0
$871$	60.4740			0.0694305
$872$	−10.0087			−0.0114778
$873$	1094.06	+	723.185i	1.25322	+	0.828390i
$874$	−69.5423			−0.0795679
$875$		0			0
$876$	564.195	−	303.375i	0.644058	−	0.346318i
$877$		−	577.921i		−	0.658975i	−0.944160	−	0.329487i	$-0.893124\pi$
$877$		−	577.921i		−	0.658975i	0.944160	−	0.329487i	$-0.106876\pi$
$878$	102.945			0.117250
$879$	518.440	+	964.158i	0.589806	+	1.09688i
$880$		0			0
$881$		−	1195.69i		−	1.35719i	−0.734512	−	0.678596i	$-0.762589\pi$
$881$		−	1195.69i		−	1.35719i	0.734512	−	0.678596i	$-0.237411\pi$
$882$	−152.934	+	231.365i	−0.173395	+	0.262318i
$883$			619.800i			0.701925i	0.936390	+	0.350962i	$0.114146\pi$
$883$			619.800i			0.701925i	−0.936390	+	0.350962i	$0.885854\pi$
$884$		−	159.633i		−	0.180580i
$885$		0			0
$886$	25.1001			0.0283297
$887$	−870.412			−0.981298			−0.490649	−	0.871357i	$-0.663240\pi$
$887$	−870.412			−0.981298			−0.490649	+	0.871357i	$0.663240\pi$
$888$	−807.984	+	434.463i	−0.909892	+	0.489260i
$889$	245.448			0.276094
$890$		0			0
$891$	567.112	−	241.542i	0.636489	−	0.271091i
$892$			508.627i			0.570210i
$893$	−273.523			−0.306297
$894$	−264.483	+	142.216i	−0.295842	+	0.159078i
$895$		0			0
$896$		−	174.693i		−	0.194970i
$897$	77.2657	−	41.5467i	0.0861379	−	0.0463174i
$898$			427.025i			0.475529i
$899$			721.616i			0.802687i
$900$		0			0
$901$	68.3728			0.0758855
$902$	−299.060			−0.331552
$903$	127.270	+	236.687i	0.140941	+	0.262112i
$904$	−718.460			−0.794756
$905$		0			0
$906$	−94.4180	−	175.592i	−0.104214	−	0.193810i
$907$		−	92.4261i		−	0.101903i	−0.998701	−	0.0509515i	$-0.983775\pi$
$907$		−	92.4261i		−	0.101903i	0.998701	−	0.0509515i	$-0.0162254\pi$
$908$	−151.507			−0.166858
$909$	−241.798	−	159.831i	−0.266004	−	0.175831i
$910$		0			0
$911$			1500.98i			1.64761i	0.566870	+	0.823807i	$0.308154\pi$
$911$			1500.98i			1.64761i	−0.566870	+	0.823807i	$0.691846\pi$
$912$	93.3300	+	173.569i	0.102336	+	0.190316i
$913$			492.928i			0.539900i
$914$		−	154.453i		−	0.168986i
$915$		0			0
$916$	526.698			0.574998
$917$	−254.433			−0.277462
$918$	480.335	+	43.6934i	0.523241	+	0.0475962i
$919$	−340.729			−0.370761			−0.185381	−	0.982667i	$-0.559352\pi$
$919$	−340.729			−0.370761			−0.185381	+	0.982667i	$0.559352\pi$
$920$		0			0
$921$	−444.684	+	239.112i	−0.482827	+	0.259622i
$922$		−	383.613i		−	0.416066i
$923$	−144.163			−0.156189
$924$	−53.7294	−	99.9222i	−0.0581487	−	0.108141i
$925$		0			0
$926$		−	244.131i		−	0.263640i
$927$	−1293.47	−	854.996i	−1.39533	−	0.922326i
$928$		−	897.232i		−	0.966844i
$929$		−	588.289i		−	0.633250i	−0.948551	−	0.316625i	$-0.897450\pi$
$929$		−	588.289i		−	0.633250i	0.948551	−	0.316625i	$-0.102550\pi$
$930$		0			0
$931$	−280.059			−0.300815
$932$	−796.124			−0.854210
$933$	330.765	−	177.857i	0.354518	−	0.190629i
$934$	−182.980			−0.195910
$935$		0			0
$936$	60.9810	+	40.3089i	0.0651506	+	0.0430651i
$937$			1317.14i			1.40570i	0.711338	+	0.702851i	$0.248090\pi$
$937$			1317.14i			1.40570i	−0.711338	+	0.702851i	$0.751910\pi$
$938$	33.6298			0.0358526
$939$	−62.9237	+	33.8349i	−0.0670114	+	0.0360329i
$940$		0			0
$941$			381.659i			0.405589i	0.979221	+	0.202794i	$0.0650023\pi$
$941$			381.659i			0.405589i	−0.979221	+	0.202794i	$0.934998\pi$
$942$	293.149	−	157.630i	0.311199	−	0.167335i
$943$			1071.25i			1.13600i
$944$			516.432i			0.547067i
$945$		0			0
$946$	−320.767			−0.339077
$947$	−736.967			−0.778212			−0.389106	−	0.921193i	$-0.627216\pi$
$947$	−736.967			−0.778212			−0.389106	+	0.921193i	$0.627216\pi$
$948$	−615.193	−	1144.09i	−0.648938	−	1.20685i
$949$	97.9597			0.103224
$950$		0			0
$951$	−248.780	−	462.664i	−0.261598	−	0.486502i
$952$		−	188.201i		−	0.197690i
$953$	718.725			0.754171			0.377086	−	0.926178i	$-0.376926\pi$
$953$	718.725			0.754171			0.377086	+	0.926178i	$0.376926\pi$
$954$	−8.14362	+	12.3200i	−0.00853629	+	0.0129140i
$955$		0			0
$956$		−	347.550i		−	0.363546i
$957$	−358.524	−	666.757i	−0.374633	−	0.696716i
$958$		−	479.670i		−	0.500700i
$959$		−	166.596i		−	0.173718i
$960$		0			0
$961$	−487.427			−0.507208
$962$	−66.1722			−0.0687861
$963$	936.025	−	1416.06i	0.971988	−	1.47046i
$964$	−135.592			−0.140656
$965$		0			0
$966$	42.9677	−	23.1043i	0.0444800	−	0.0239174i
$967$		−	1101.42i		−	1.13901i	−0.821987	−	0.569506i	$-0.807134\pi$
$967$		−	1101.42i		−	1.13901i	0.821987	−	0.569506i	$-0.192866\pi$
$968$	−312.755			−0.323094
$969$	230.658	+	428.961i	0.238037	+	0.442684i
$970$		0			0
$971$			354.427i			0.365012i	0.983205	+	0.182506i	$0.0584209\pi$
$971$			354.427i			0.365012i	−0.983205	+	0.182506i	$0.941579\pi$
$972$	542.157	−	677.628i	0.557775	−	0.697148i
$973$			52.6768i			0.0541386i
$974$		−	454.773i		−	0.466913i
$975$		0			0
$976$	−309.863			−0.317482
$977$	−149.462			−0.152980			−0.0764902	−	0.997070i	$-0.524371\pi$
$977$	−149.462			−0.152980			−0.0764902	+	0.997070i	$0.524371\pi$
$978$	−292.203	+	157.121i	−0.298776	+	0.160656i
$979$	−645.736			−0.659587
$980$		0			0
$981$	−10.0196	+	15.1581i	−0.0102137	+	0.0154517i
$982$			156.344i			0.159210i
$983$	−179.415			−0.182518			−0.0912589	−	0.995827i	$-0.529089\pi$
$983$	−179.415			−0.182518			−0.0912589	+	0.995827i	$0.529089\pi$
$984$	−786.171	+	422.734i	−0.798954	+	0.429608i
$985$		0			0
$986$		−	592.356i		−	0.600766i
$987$	169.000	−	90.8735i	0.171226	−	0.0920704i
$988$			34.8178i			0.0352406i
$989$			1149.00i			1.16178i
$990$		0			0
$991$	−8.59572			−0.00867378			−0.00433689	−	0.999991i	$-0.501380\pi$
$991$	−8.59572			−0.00867378			−0.00433689	+	0.999991i	$0.501380\pi$
$992$	−588.824			−0.593572
$993$	−470.205	−	874.455i	−0.473520	−	0.880619i
$994$	−80.1692			−0.0806531
$995$		0			0
$996$	328.660	+	611.219i	0.329980	+	0.613674i
$997$		−	872.069i		−	0.874693i	−0.899293	−	0.437347i	$-0.855918\pi$
$997$		−	872.069i		−	0.874693i	0.899293	−	0.437347i	$-0.144082\pi$
$998$	183.561			0.183929
$999$	−150.876	+	1658.63i	−0.151027	+	1.66029i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	375.3.d.e.374.19		32
3.2	odd	2	inner	375.3.d.e.374.13		32
5.2	odd	4		375.3.c.c.251.19	yes	32
5.3	odd	4		375.3.c.c.251.14	yes	32
5.4	even	2	inner	375.3.d.e.374.14		32
15.2	even	4		375.3.c.c.251.13	✓	32
15.8	even	4		375.3.c.c.251.20	yes	32
15.14	odd	2	inner	375.3.d.e.374.20		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
375.3.c.c.251.13	✓	32	15.2	even	4
375.3.c.c.251.14	yes	32	5.3	odd	4
375.3.c.c.251.19	yes	32	5.2	odd	4
375.3.c.c.251.20	yes	32	15.8	even	4
375.3.d.e.374.13		32	3.2	odd	2	inner
375.3.d.e.374.14		32	5.4	even	2	inner
375.3.d.e.374.19		32	1.1	even	1	trivial
375.3.d.e.374.20		32	15.14	odd	2	inner

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.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+0.654766 q^{2} +(-1.42077 - 2.64224i) q^{3} -3.57128 q^{4} +(-0.930269 - 1.73005i) q^{6} +1.39150i q^{7} -4.95742 q^{8} +(-4.96285 + 7.50800i) q^{9} +O(q^{10})\)	\(q+0.654766 q^{2} +(-1.42077 - 2.64224i) q^{3} -3.57128 q^{4} +(-0.930269 - 1.73005i) q^{6} +1.39150i q^{7} -4.95742 q^{8} +(-4.96285 + 7.50800i) q^{9} +7.60997i q^{11} +(5.07395 + 9.43618i) q^{12} +1.63838i q^{13} +0.911107i q^{14} +11.0392 q^{16} +27.2825 q^{17} +(-3.24951 + 4.91599i) q^{18} -5.95062 q^{19} +(3.67667 - 1.97699i) q^{21} +4.98275i q^{22} +17.8484 q^{23} +(7.04333 + 13.0987i) q^{24} +1.07276i q^{26} +(26.8890 + 2.44594i) q^{27} -4.96943i q^{28} -33.1599i q^{29} -21.7617 q^{31} +27.0578 q^{32} +(20.1074 - 10.8120i) q^{33} +17.8636 q^{34} +(17.7237 - 26.8132i) q^{36} +61.6843i q^{37} -3.89627 q^{38} +(4.32899 - 2.32775i) q^{39} +60.0191i q^{41} +(2.40736 - 1.29447i) q^{42} +64.3754i q^{43} -27.1773i q^{44} +11.6866 q^{46} +45.9655 q^{47} +(-15.6841 - 29.1681i) q^{48} +47.0637 q^{49} +(-38.7620 - 72.0868i) q^{51} -5.85111i q^{52} +2.50611 q^{53} +(17.6060 + 1.60152i) q^{54} -6.89825i q^{56} +(8.45444 + 15.7230i) q^{57} -21.7120i q^{58} +46.7817i q^{59} -28.0694 q^{61} -14.2488 q^{62} +(-10.4474 - 6.90581i) q^{63} -26.4402 q^{64} +(13.1656 - 7.07932i) q^{66} -36.9109i q^{67} -97.4333 q^{68} +(-25.3584 - 47.1599i) q^{69} +87.9910i q^{71} +(24.6029 - 37.2203i) q^{72} -59.7906i q^{73} +40.3888i q^{74} +21.2514 q^{76} -10.5893 q^{77} +(2.83448 - 1.52413i) q^{78} -121.245 q^{79} +(-31.7402 - 74.5222i) q^{81} +39.2985i q^{82} +64.7740 q^{83} +(-13.1304 + 7.06040i) q^{84} +42.1508i q^{86} +(-87.6163 + 47.1124i) q^{87} -37.7258i q^{88} +84.8539i q^{89} -2.27980 q^{91} -63.7418 q^{92} +(30.9183 + 57.4997i) q^{93} +30.0967 q^{94} +(-38.4427 - 71.4931i) q^{96} -145.720i q^{97} +30.8157 q^{98} +(-57.1357 - 37.7672i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 68 q^{4} + 12 q^{6} + 20 q^{9}+O(q^{10}) \) 32 * q + 68 * q^4 + 12 * q^6 + 20 * q^9	\( 32 q + 68 q^{4} + 12 q^{6} + 20 q^{9} + 116 q^{16} + 40 q^{19} + 112 q^{21} + 96 q^{24} - 16 q^{31} - 64 q^{34} - 56 q^{36} - 8 q^{39} - 416 q^{46} - 468 q^{49} - 208 q^{51} - 472 q^{54} - 276 q^{61} - 136 q^{64} - 340 q^{66} - 352 q^{69} + 148 q^{76} + 580 q^{79} - 268 q^{81} + 952 q^{84} + 444 q^{91} + 936 q^{94} + 1456 q^{96} + 220 q^{99}+O(q^{100}) \) 32 * q + 68 * q^4 + 12 * q^6 + 20 * q^9 + 116 * q^16 + 40 * q^19 + 112 * q^21 + 96 * q^24 - 16 * q^31 - 64 * q^34 - 56 * q^36 - 8 * q^39 - 416 * q^46 - 468 * q^49 - 208 * q^51 - 472 * q^54 - 276 * q^61 - 136 * q^64 - 340 * q^66 - 352 * q^69 + 148 * q^76 + 580 * q^79 - 268 * q^81 + 952 * q^84 + 444 * q^91 + 936 * q^94 + 1456 * q^96 + 220 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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