LMFDB - Embedded newform 375.3.c.c.251.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [375,3,Mod(251,375)]

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, 0]))

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

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

chi := DirichletCharacter("375.251");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 375 = 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	375.c (of order $2$, degree $1$, 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			251.11
Character	$\chi$	$=$	375.251
Dual form			375.3.c.c.251.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.67701i q^{2} +(-2.99960 + 0.0488427i) q^{3} +1.18764 q^{4} +(0.0819097 + 5.03036i) q^{6} +0.986092 q^{7} -8.69972i q^{8} +(8.99523 - 0.293018i) q^{9} +O(q^{10})$	\(q-1.67701i q^{2} +(-2.99960 + 0.0488427i) q^{3} +1.18764 q^{4} +(0.0819097 + 5.03036i) q^{6} +0.986092 q^{7} -8.69972i q^{8} +(8.99523 - 0.293018i) q^{9} +10.7308i q^{11} +(-3.56246 + 0.0580078i) q^{12} +8.72887 q^{13} -1.65368i q^{14} -9.83892 q^{16} +5.40271i q^{17} +(-0.491393 - 15.0851i) q^{18} +21.2651 q^{19} +(-2.95789 + 0.0481634i) q^{21} +17.9957 q^{22} -33.8142i q^{23} +(0.424918 + 26.0957i) q^{24} -14.6384i q^{26} +(-26.9678 + 1.31829i) q^{27} +1.17113 q^{28} -35.1451i q^{29} +34.9689 q^{31} -18.2989i q^{32} +(-0.524124 - 32.1883i) q^{33} +9.06038 q^{34} +(10.6831 - 0.348001i) q^{36} +19.3152 q^{37} -35.6617i q^{38} +(-26.1831 + 0.426342i) q^{39} -52.7118i q^{41} +(0.0807705 + 4.96040i) q^{42} -29.1674 q^{43} +12.7444i q^{44} -56.7067 q^{46} +52.7420i q^{47} +(29.5129 - 0.480560i) q^{48} -48.0276 q^{49} +(-0.263883 - 16.2060i) q^{51} +10.3668 q^{52} -48.0164i q^{53} +(2.21078 + 45.2252i) q^{54} -8.57873i q^{56} +(-63.7868 + 1.03864i) q^{57} -58.9386 q^{58} -93.9152i q^{59} +28.9169 q^{61} -58.6432i q^{62} +(8.87013 - 0.288942i) q^{63} -70.0431 q^{64} +(-53.9800 + 0.878960i) q^{66} +90.9035 q^{67} +6.41649i q^{68} +(1.65158 + 101.429i) q^{69} +127.604i q^{71} +(-2.54917 - 78.2560i) q^{72} +97.8731 q^{73} -32.3918i q^{74} +25.2553 q^{76} +10.5816i q^{77} +(0.714979 + 43.9093i) q^{78} -41.7927 q^{79} +(80.8283 - 5.27152i) q^{81} -88.3981 q^{82} +97.3060i q^{83} +(-3.51292 + 0.0572010i) q^{84} +48.9139i q^{86} +(1.71658 + 105.421i) q^{87} +93.3554 q^{88} -87.7324i q^{89} +8.60747 q^{91} -40.1593i q^{92} +(-104.893 + 1.70798i) q^{93} +88.4487 q^{94} +(0.893770 + 54.8895i) q^{96} +85.0442 q^{97} +80.5427i q^{98} +(3.14433 + 96.5264i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	1.67701i		−	0.838504i	−0.907870	−	0.419252i	$-0.862292\pi$
$2$		−	1.67701i		−	0.838504i	0.907870	−	0.419252i	$-0.137708\pi$
$3$	−2.99960	+	0.0488427i	−0.999867	+	0.0162809i
$3$	−2.99960	+	0.0488427i	−0.999867	+	0.0162809i
$4$	1.18764			0.296911
$5$		0			0
$5$		0			0
$6$	0.0819097	+	5.03036i	0.0136516	+	0.838393i
$7$	0.986092			0.140870			0.0704352	−	0.997516i	$-0.477561\pi$
$7$	0.986092			0.140870			0.0704352	+	0.997516i	$0.477561\pi$
$8$		−	8.69972i		−	1.08747i
$9$	8.99523	−	0.293018i	0.999470	−	0.0325575i
$10$		0			0
$11$			10.7308i			0.975532i	0.872975	+	0.487766i	$0.162188\pi$
$11$			10.7308i			0.975532i	−0.872975	+	0.487766i	$0.837812\pi$
$12$	−3.56246	+	0.0580078i	−0.296872	+	0.00483398i
$13$	8.72887			0.671452			0.335726	−	0.941960i	$-0.391018\pi$
$13$	8.72887			0.671452			0.335726	+	0.941960i	$0.391018\pi$
$14$		−	1.65368i		−	0.118120i
$15$		0			0
$16$	−9.83892			−0.614933
$17$			5.40271i			0.317806i	0.987294	+	0.158903i	$0.0507958\pi$
$17$			5.40271i			0.317806i	−0.987294	+	0.158903i	$0.949204\pi$
$18$	−0.491393	−	15.0851i	−0.0272996	−	0.838059i
$19$	21.2651			1.11921			0.559607	−	0.828758i	$-0.310952\pi$
$19$	21.2651			1.11921			0.559607	+	0.828758i	$0.310952\pi$
$20$		0			0
$21$	−2.95789	+	0.0481634i	−0.140852	+	0.00229350i
$22$	17.9957			0.817987
$23$		−	33.8142i		−	1.47018i	−0.677968	−	0.735092i	$-0.737139\pi$
$23$		−	33.8142i		−	1.47018i	0.677968	−	0.735092i	$-0.262861\pi$
$24$	0.424918	+	26.0957i	0.0177049	+	1.08732i
$25$		0			0
$26$		−	14.6384i		−	0.563015i
$27$	−26.9678	+	1.31829i	−0.998807	+	0.0488255i
$28$	1.17113			0.0418260
$29$		−	35.1451i		−	1.21190i	−0.795503	−	0.605950i	$-0.792793\pi$
$29$		−	35.1451i		−	1.21190i	0.795503	−	0.605950i	$-0.207207\pi$
$30$		0			0
$31$	34.9689			1.12803			0.564015	−	0.825765i	$-0.309256\pi$
$31$	34.9689			1.12803			0.564015	+	0.825765i	$0.309256\pi$
$32$		−	18.2989i		−	0.571842i
$33$	−0.524124	−	32.1883i	−0.0158825	−	0.975402i
$34$	9.06038			0.266482
$35$		0			0
$36$	10.6831	−	0.348001i	0.296754	−	0.00966668i
$37$	19.3152			0.522033			0.261017	−	0.965334i	$-0.415942\pi$
$37$	19.3152			0.522033			0.261017	+	0.965334i	$0.415942\pi$
$38$		−	35.6617i		−	0.938466i
$39$	−26.1831	+	0.426342i	−0.671363	+	0.0109318i
$40$		0			0
$41$		−	52.7118i		−	1.28565i	−0.766012	−	0.642827i	$-0.777762\pi$
$41$		−	52.7118i		−	1.28565i	0.766012	−	0.642827i	$-0.222238\pi$
$42$	0.0807705	+	4.96040i	0.00192311	+	0.118105i
$43$	−29.1674			−0.678310			−0.339155	−	0.940730i	$-0.610141\pi$
$43$	−29.1674			−0.678310			−0.339155	+	0.940730i	$0.610141\pi$
$44$			12.7444i			0.289646i
$45$		0			0
$46$	−56.7067			−1.23275
$47$			52.7420i			1.12217i	0.827758	+	0.561085i	$0.189616\pi$
$47$			52.7420i			1.12217i	−0.827758	+	0.561085i	$0.810384\pi$
$48$	29.5129	−	0.480560i	0.614851	−	0.0100117i
$49$	−48.0276			−0.980156
$50$		0			0
$51$	−0.263883	−	16.2060i	−0.00517418	−	0.317764i
$52$	10.3668			0.199361
$53$		−	48.0164i		−	0.905969i	−0.891518	−	0.452985i	$-0.850359\pi$
$53$		−	48.0164i		−	0.905969i	0.891518	−	0.452985i	$-0.149641\pi$
$54$	2.21078	+	45.2252i	0.0409404	+	0.837504i
$55$		0			0
$56$		−	8.57873i		−	0.153192i
$57$	−63.7868	+	1.03864i	−1.11907	+	0.0182218i
$58$	−58.9386			−1.01618
$59$		−	93.9152i		−	1.59178i	−0.605440	−	0.795891i	$-0.707003\pi$
$59$		−	93.9152i		−	1.59178i	0.605440	−	0.795891i	$-0.292997\pi$
$60$		0			0
$61$	28.9169			0.474048			0.237024	−	0.971504i	$-0.423828\pi$
$61$	28.9169			0.474048			0.237024	+	0.971504i	$0.423828\pi$
$62$		−	58.6432i		−	0.945857i
$63$	8.87013	−	0.288942i	0.140796	−	0.00458639i
$64$	−70.0431			−1.09442
$65$		0			0
$66$	−53.9800	+	0.878960i	−0.817879	+	0.0133176i
$67$	90.9035			1.35677			0.678384	−	0.734707i	$-0.262680\pi$
$67$	90.9035			1.35677			0.678384	+	0.734707i	$0.262680\pi$
$68$			6.41649i			0.0943602i
$69$	1.65158	+	101.429i	0.0239359	+	1.46999i
$70$		0			0
$71$			127.604i			1.79724i	0.438730	+	0.898619i	$0.355429\pi$
$71$			127.604i			1.79724i	−0.438730	+	0.898619i	$0.644571\pi$
$72$	−2.54917	−	78.2560i	−0.0354052	−	1.08689i
$73$	97.8731			1.34073			0.670364	−	0.742032i	$-0.266138\pi$
$73$	97.8731			1.34073			0.670364	+	0.742032i	$0.266138\pi$
$74$		−	32.3918i		−	0.437727i
$75$		0			0
$76$	25.2553			0.332307
$77$			10.5816i			0.137423i
$78$	0.714979	+	43.9093i	0.00916639	+	0.562940i
$79$	−41.7927			−0.529022			−0.264511	−	0.964383i	$-0.585211\pi$
$79$	−41.7927			−0.529022			−0.264511	+	0.964383i	$0.585211\pi$
$80$		0			0
$81$	80.8283	−	5.27152i	0.997880	−	0.0650805i
$82$	−88.3981			−1.07803
$83$			97.3060i			1.17236i	0.810180	+	0.586181i	$0.199369\pi$
$83$			97.3060i			1.17236i	−0.810180	+	0.586181i	$0.800631\pi$
$84$	−3.51292	+	0.0572010i	−0.0418204	+	0.000680965i
$85$		0			0
$86$			48.9139i			0.568766i
$87$	1.71658	+	105.421i	0.0197308	+	1.21174i
$88$	93.3554			1.06086
$89$		−	87.7324i		−	0.985757i	−0.870098	−	0.492879i	$-0.835945\pi$
$89$		−	87.7324i		−	0.985757i	0.870098	−	0.492879i	$-0.164055\pi$
$90$		0			0
$91$	8.60747			0.0945876
$92$		−	40.1593i		−	0.436514i
$93$	−104.893	+	1.70798i	−1.12788	+	0.0183654i
$94$	88.4487			0.940944
$95$		0			0
$96$	0.893770	+	54.8895i	0.00931010	+	0.571766i
$97$	85.0442			0.876744			0.438372	−	0.898794i	$-0.355555\pi$
$97$	85.0442			0.876744			0.438372	+	0.898794i	$0.355555\pi$
$98$			80.5427i			0.821864i
$99$	3.14433	+	96.5264i	0.0317609	+	0.975014i
$100$		0			0
$101$		−	32.4214i		−	0.321004i	−0.987035	−	0.160502i	$-0.948689\pi$
$101$		−	32.4214i		−	0.321004i	0.987035	−	0.160502i	$-0.0513114\pi$
$102$	−27.1775	+	0.442534i	−0.266447	+	0.00433857i
$103$	−37.0251			−0.359467			−0.179733	−	0.983715i	$-0.557524\pi$
$103$	−37.0251			−0.359467			−0.179733	+	0.983715i	$0.557524\pi$
$104$		−	75.9387i		−	0.730180i
$105$		0			0
$106$	−80.5238			−0.759659
$107$			115.551i			1.07991i	0.841692	+	0.539957i	$0.181560\pi$
$107$			115.551i			1.07991i	−0.841692	+	0.539957i	$0.818440\pi$
$108$	−32.0281	+	1.56566i	−0.296557	+	0.0144968i
$109$	74.6098			0.684494			0.342247	−	0.939610i	$-0.388812\pi$
$109$	74.6098			0.684494			0.342247	+	0.939610i	$0.388812\pi$
$110$		0			0
$111$	−57.9380	+	0.943409i	−0.521964	+	0.00849918i
$112$	−9.70209			−0.0866258
$113$			162.240i			1.43575i	0.696171	+	0.717876i	$0.254885\pi$
$113$			162.240i			1.43575i	−0.696171	+	0.717876i	$0.745115\pi$
$114$	1.74181	+	106.971i	0.0152791	+	0.938341i
$115$		0			0
$116$		−	41.7399i		−	0.359827i
$117$	78.5182	−	2.55771i	0.671096	−	0.0218608i
$118$	−157.496			−1.33472
$119$			5.32757i			0.0447695i
$120$		0			0
$121$	5.84890			0.0483380
$122$		−	48.4939i		−	0.397491i
$123$	2.57459	+	158.114i	0.0209316	+	1.28548i
$124$	41.5306			0.334925
$125$		0			0
$126$	−0.484559	−	14.8753i	−0.00384570	−	0.118058i
$127$	−233.536			−1.83887			−0.919434	−	0.393244i	$-0.871353\pi$
$127$	−233.536			−1.83887			−0.919434	+	0.393244i	$0.871353\pi$
$128$			44.2672i			0.345838i
$129$	87.4905	−	1.42461i	0.678221	−	0.0110435i
$130$		0			0
$131$			29.4351i			0.224696i	0.993669	+	0.112348i	$0.0358371\pi$
$131$			29.4351i			0.224696i	−0.993669	+	0.112348i	$0.964163\pi$
$132$	−0.622473	−	38.2282i	−0.00471570	−	0.289608i
$133$	20.9693			0.157664
$134$		−	152.446i		−	1.13766i
$135$		0			0
$136$	47.0020			0.345603
$137$			55.3091i			0.403716i	0.979415	+	0.201858i	$0.0646979\pi$
$137$			55.3091i			0.403716i	−0.979415	+	0.201858i	$0.935302\pi$
$138$	170.098	−	2.76971i	1.23259	−	0.0200704i
$139$	183.499			1.32014			0.660069	−	0.751205i	$-0.270527\pi$
$139$	183.499			1.32014			0.660069	+	0.751205i	$0.270527\pi$
$140$		0			0
$141$	−2.57606	−	158.205i	−0.0182700	−	1.12202i
$142$	213.993			1.50699
$143$			93.6682i			0.655022i
$144$	−88.5034	+	2.88298i	−0.614607	+	0.0200207i
$145$		0			0
$146$		−	164.134i		−	1.12421i
$147$	144.064	−	2.34580i	0.980026	−	0.0159578i
$148$	22.9396			0.154998
$149$			69.5256i			0.466615i	0.972403	+	0.233307i	$0.0749548\pi$
$149$			69.5256i			0.466615i	−0.972403	+	0.233307i	$0.925045\pi$
$150$		0			0
$151$	−9.62107			−0.0637157			−0.0318578	−	0.999492i	$-0.510142\pi$
$151$	−9.62107			−0.0637157			−0.0318578	+	0.999492i	$0.510142\pi$
$152$		−	185.000i		−	1.21711i
$153$	1.58309	+	48.5986i	0.0103470	+	0.317638i
$154$	17.7454			0.115230
$155$		0			0
$156$	−31.0963	+	0.506342i	−0.199335	+	0.00324579i
$157$	−231.458			−1.47425			−0.737126	−	0.675755i	$-0.763818\pi$
$157$	−231.458			−1.47425			−0.737126	+	0.675755i	$0.763818\pi$
$158$			70.0868i			0.443587i
$159$	2.34525	+	144.030i	0.0147500	+	0.905849i
$160$		0			0
$161$		−	33.3439i		−	0.207105i
$162$	−8.84038	−	135.550i	−0.0545703	−	0.836726i
$163$	237.273			1.45566			0.727830	−	0.685757i	$-0.240529\pi$
$163$	237.273			1.45566			0.727830	+	0.685757i	$0.240529\pi$
$164$		−	62.6028i		−	0.381725i
$165$		0			0
$166$	163.183			0.983030
$167$			54.5204i			0.326470i	0.986587	+	0.163235i	$0.0521928\pi$
$167$			54.5204i			0.326470i	−0.986587	+	0.163235i	$0.947807\pi$
$168$	0.419009	+	25.7328i	0.00249410	+	0.153171i
$169$	−92.8068			−0.549153
$170$		0			0
$171$	191.284	−	6.23104i	1.11862	−	0.0364388i
$172$	−34.6404			−0.201398
$173$		−	207.155i		−	1.19743i	−0.800963	−	0.598713i	$-0.795679\pi$
$173$		−	207.155i		−	1.19743i	0.800963	−	0.598713i	$-0.204321\pi$
$174$	176.792	−	2.87872i	1.01605	−	0.0165444i
$175$		0			0
$176$		−	105.580i		−	0.599886i
$177$	4.58707	+	281.708i	0.0259157	+	1.59157i
$178$	−147.128			−0.826561
$179$		−	62.7827i		−	0.350741i	−0.984502	−	0.175371i	$-0.943888\pi$
$179$		−	62.7827i		−	0.350741i	0.984502	−	0.175371i	$-0.0561124\pi$
$180$		0			0
$181$	−139.836			−0.772574			−0.386287	−	0.922379i	$-0.626242\pi$
$181$	−139.836			−0.772574			−0.386287	+	0.922379i	$0.626242\pi$
$182$		−	14.4348i		−	0.0793121i
$183$	−86.7392	+	1.41238i	−0.473985	+	0.00771793i
$184$	−294.174			−1.59877
$185$		0			0
$186$	2.86429	+	175.906i	0.0153994	+	0.945732i
$187$	−57.9756			−0.310030
$188$			62.6387i			0.333185i
$189$	−26.5927	+	1.29995i	−0.140702	+	0.00687806i
$190$		0			0
$191$			163.827i			0.857732i	0.903368	+	0.428866i	$0.141087\pi$
$191$			163.827i			0.857732i	−0.903368	+	0.428866i	$0.858913\pi$
$192$	210.102	−	3.42110i	1.09428	−	0.0178182i
$193$	−312.575			−1.61956			−0.809781	−	0.586732i	$-0.800414\pi$
$193$	−312.575			−1.61956			−0.809781	+	0.586732i	$0.800414\pi$
$194$		−	142.620i		−	0.735154i
$195$		0			0
$196$	−57.0397			−0.291019
$197$			203.833i			1.03469i	0.855778	+	0.517343i	$0.173079\pi$
$197$			203.833i			1.03469i	−0.855778	+	0.517343i	$0.826921\pi$
$198$	161.876	−	5.27306i	0.817554	−	0.0266316i
$199$	−151.879			−0.763212			−0.381606	−	0.924325i	$-0.624629\pi$
$199$	−151.879			−0.763212			−0.381606	+	0.924325i	$0.624629\pi$
$200$		0			0
$201$	−272.674	+	4.43998i	−1.35659	+	0.0220894i
$202$	−54.3710			−0.269163
$203$		−	34.6563i		−	0.170721i
$204$	−0.313399	−	19.2469i	−0.00153627	−	0.0943477i
$205$		0			0
$206$			62.0914i			0.301414i
$207$	−9.90816	−	304.167i	−0.0478655	−	1.46940i
$208$	−85.8827			−0.412898
$209$			228.192i			1.09183i
$210$		0			0
$211$	−220.231			−1.04375			−0.521875	−	0.853022i	$-0.674767\pi$
$211$	−220.231			−1.04375			−0.521875	+	0.853022i	$0.674767\pi$
$212$		−	57.0264i		−	0.268992i
$213$	−6.23252	−	382.761i	−0.0292607	−	1.79700i
$214$	193.780			0.905513
$215$		0			0
$216$	11.4687	+	234.612i	0.0530960	+	1.08617i
$217$	34.4826			0.158906
$218$		−	125.121i		−	0.573951i
$219$	−293.581	+	4.78039i	−1.34055	+	0.0218283i
$220$		0			0
$221$			47.1595i			0.213392i
$222$	1.58210	+	97.1626i	0.00712660	+	0.437669i
$223$	263.520			1.18170			0.590851	−	0.806781i	$-0.298792\pi$
$223$	263.520			1.18170			0.590851	+	0.806781i	$0.298792\pi$
$224$		−	18.0444i		−	0.0805555i
$225$		0			0
$226$	272.078			1.20388
$227$		−	140.571i		−	0.619257i	−0.950858	−	0.309628i	$-0.899795\pi$
$227$		−	140.571i		−	0.619257i	0.950858	−	0.309628i	$-0.100205\pi$
$228$	−75.7560	+	1.23354i	−0.332263	+	0.00541026i
$229$	−253.095			−1.10522			−0.552610	−	0.833440i	$-0.686368\pi$
$229$	−253.095			−1.10522			−0.552610	+	0.833440i	$0.686368\pi$
$230$		0			0
$231$	−0.516835	−	31.7406i	−0.00223738	−	0.137405i
$232$	−305.753			−1.31790
$233$		−	316.754i		−	1.35946i	−0.733463	−	0.679730i	$-0.762097\pi$
$233$		−	316.754i		−	1.35946i	0.733463	−	0.679730i	$-0.237903\pi$
$234$	−4.28930	−	131.676i	−0.0183304	−	0.562716i
$235$		0			0
$236$		−	111.538i		−	0.472618i
$237$	125.362	−	2.04127i	0.528952	−	0.00861296i
$238$	8.93438			0.0375394
$239$			65.1454i			0.272575i	0.990669	+	0.136287i	$0.0435171\pi$
$239$			65.1454i			0.272575i	−0.990669	+	0.136287i	$0.956483\pi$
$240$		0			0
$241$	177.015			0.734501			0.367250	−	0.930122i	$-0.380299\pi$
$241$	177.015			0.734501			0.367250	+	0.930122i	$0.380299\pi$
$242$		−	9.80865i		−	0.0405316i
$243$	−242.195	+	19.7603i	−0.996688	+	0.0813183i
$244$	34.3430			0.140750
$245$		0			0
$246$	265.159	−	4.31760i	1.07788	−	0.0175512i
$247$	185.620			0.751498
$248$		−	304.220i		−	1.22669i
$249$	−4.75269	−	291.879i	−0.0190871	−	1.17221i
$250$		0			0
$251$			480.997i			1.91632i	0.286227	+	0.958162i	$0.407599\pi$
$251$			480.997i			1.91632i	−0.286227	+	0.958162i	$0.592401\pi$
$252$	10.5346	−	0.343161i	0.0418038	−	0.00136175i
$253$	362.855			1.43421
$254$			391.642i			1.54190i
$255$		0			0
$256$	−205.936			−0.804438
$257$			228.740i			0.890037i	0.895521	+	0.445019i	$0.146803\pi$
$257$			228.740i			0.890037i	−0.895521	+	0.445019i	$0.853197\pi$
$258$	−2.38909	−	146.722i	−0.00926003	−	0.568691i
$259$	19.0466			0.0735390
$260$		0			0
$261$	−10.2981	−	316.138i	−0.0394564	−	1.21126i
$262$	49.3630			0.188408
$263$			161.703i			0.614839i	0.951574	+	0.307419i	$0.0994654\pi$
$263$			161.703i			0.614839i	−0.951574	+	0.307419i	$0.900535\pi$
$264$	−280.029	+	4.55973i	−1.06072	+	0.0172717i
$265$		0			0
$266$		−	35.1657i		−	0.132202i
$267$	4.28509	+	263.162i	0.0160490	+	0.985627i
$268$	107.961			0.402840
$269$		−	27.1313i		−	0.100860i	−0.998728	−	0.0504299i	$-0.983941\pi$
$269$		−	27.1313i		−	0.100860i	0.998728	−	0.0504299i	$-0.0160591\pi$
$270$		0			0
$271$	−46.0453			−0.169909			−0.0849544	−	0.996385i	$-0.527074\pi$
$271$	−46.0453			−0.169909			−0.0849544	+	0.996385i	$0.527074\pi$
$272$		−	53.1568i		−	0.195430i
$273$	−25.8190	+	0.420413i	−0.0945751	+	0.00153997i
$274$	92.7537			0.338517
$275$		0			0
$276$	1.96149	+	120.462i	0.00710684	+	0.436456i
$277$	−93.7155			−0.338323			−0.169162	−	0.985588i	$-0.554106\pi$
$277$	−93.7155			−0.338323			−0.169162	+	0.985588i	$0.554106\pi$
$278$		−	307.730i		−	1.10694i
$279$	314.553	−	10.2465i	1.12743	−	0.0367258i
$280$		0			0
$281$		−	194.543i		−	0.692325i	−0.938175	−	0.346162i	$-0.887485\pi$
$281$		−	194.543i		−	0.692325i	0.938175	−	0.346162i	$-0.112515\pi$
$282$	−265.311	+	4.32008i	−0.940819	+	0.0153194i
$283$	−201.513			−0.712061			−0.356031	−	0.934474i	$-0.615870\pi$
$283$	−201.513			−0.712061			−0.356031	+	0.934474i	$0.615870\pi$
$284$			151.548i			0.533620i
$285$		0			0
$286$	157.082			0.549239
$287$		−	51.9787i		−	0.181110i
$288$	−5.36191	−	164.603i	−0.0186177	−	0.571538i
$289$	259.811			0.898999
$290$		0			0
$291$	−255.099	+	4.15379i	−0.876628	+	0.0142742i
$292$	116.238			0.398077
$293$		−	401.132i		−	1.36905i	−0.728988	−	0.684526i	$-0.760009\pi$
$293$		−	401.132i		−	1.36905i	0.728988	−	0.684526i	$-0.239991\pi$
$294$	−3.93393	−	241.596i	−0.0133807	−	0.821755i
$295$		0			0
$296$		−	168.037i		−	0.567693i
$297$	−14.1463	−	289.387i	−0.0476308	−	0.974368i
$298$	116.595			0.391258
$299$		−	295.160i		−	0.987157i
$300$		0			0
$301$	−28.7617			−0.0955538
$302$			16.1346i			0.0534259i
$303$	1.58355	+	97.2514i	0.00522624	+	0.320962i
$304$	−209.225			−0.688242
$305$		0			0
$306$	81.5002	−	2.65485i	0.266341	−	0.00867598i
$307$	305.937			0.996538			0.498269	−	0.867023i	$-0.333969\pi$
$307$	305.937			0.996538			0.498269	+	0.867023i	$0.333969\pi$
$308$			12.5672i			0.0408026i
$309$	111.061	−	1.80841i	0.359419	−	0.00585245i
$310$		0			0
$311$		−	248.920i		−	0.800387i	−0.916431	−	0.400193i	$-0.868943\pi$
$311$		−	248.920i		−	0.800387i	0.916431	−	0.400193i	$-0.131057\pi$
$312$	3.70906	+	227.786i	0.0118880	+	0.730083i
$313$	40.3421			0.128889			0.0644443	−	0.997921i	$-0.479473\pi$
$313$	40.3421			0.128889			0.0644443	+	0.997921i	$0.479473\pi$
$314$			388.156i			1.23617i
$315$		0			0
$316$	−49.6349			−0.157072
$317$		−	302.546i		−	0.954405i	−0.878793	−	0.477203i	$-0.841651\pi$
$317$		−	302.546i		−	0.954405i	0.878793	−	0.477203i	$-0.158349\pi$
$318$	241.539	−	3.93300i	0.759558	−	0.0123679i
$319$	377.137			1.18225
$320$		0			0
$321$	−5.64382	−	346.607i	−0.0175820	−	1.07977i
$322$	−55.9181			−0.173659
$323$			114.889i			0.355693i
$324$	95.9952	−	6.26069i	0.296282	−	0.0193231i
$325$		0			0
$326$		−	397.908i		−	1.22058i
$327$	−223.800	+	3.64415i	−0.684403	+	0.0111442i
$328$	−458.578			−1.39810
$329$			52.0085i			0.158080i
$330$		0			0
$331$	−7.13884			−0.0215675			−0.0107837	−	0.999942i	$-0.503433\pi$
$331$	−7.13884			−0.0215675			−0.0107837	+	0.999942i	$0.503433\pi$
$332$			115.565i			0.348087i
$333$	173.745	−	5.65970i	0.521757	−	0.0169961i
$334$	91.4312			0.273746
$335$		0			0
$336$	29.1024	−	0.473877i	0.0866143	−	0.00141035i
$337$	65.3823			0.194013			0.0970064	−	0.995284i	$-0.469073\pi$
$337$	65.3823			0.194013			0.0970064	+	0.995284i	$0.469073\pi$
$338$			155.638i			0.460467i
$339$	−7.92424	−	486.655i	−0.0233753	−	1.43556i
$340$		0			0
$341$			375.246i			1.10043i
$342$	−10.4495	−	320.785i	−0.0305541	−	0.937968i
$343$	−95.6782			−0.278945
$344$			253.748i			0.737639i
$345$		0			0
$346$	−347.400			−1.00405
$347$		−	110.933i		−	0.319691i	−0.987142	−	0.159845i	$-0.948900\pi$
$347$		−	110.933i		−	0.319691i	0.987142	−	0.159845i	$-0.0510996\pi$
$348$	2.03869	+	125.203i	0.00585830	+	0.359779i
$349$	0.246730			0.000706961			0.000353481	−	1.00000i	$-0.499887\pi$
$349$	0.246730			0.000706961			0.000353481		1.00000i	$0.499887\pi$
$350$		0			0
$351$	−235.398	+	11.5072i	−0.670651	+	0.0327839i
$352$	196.363			0.557849
$353$		−	85.7892i		−	0.243029i	−0.992590	−	0.121515i	$-0.961225\pi$
$353$		−	85.7892i		−	0.243029i	0.992590	−	0.121515i	$-0.0387751\pi$
$354$	472.427	−	7.69256i	1.33454	−	0.0217304i
$355$		0			0
$356$		−	104.195i		−	0.292682i
$357$	−0.260213	−	15.9806i	−0.000728888	−	0.0447636i
$358$	−105.287			−0.294098
$359$			638.603i			1.77884i	0.457091	+	0.889420i	$0.348891\pi$
$359$			638.603i			1.77884i	−0.457091	+	0.889420i	$0.651109\pi$
$360$		0			0
$361$	91.2034			0.252641
$362$			234.506i			0.647806i
$363$	−17.5444	+	0.285676i	−0.0483316	+	0.000786987i
$364$	10.2226			0.0280841
$365$		0			0
$366$	2.36857	+	145.462i	0.00647151	+	0.397438i
$367$	−254.118			−0.692419			−0.346209	−	0.938157i	$-0.612531\pi$
$367$	−254.118			−0.692419			−0.346209	+	0.938157i	$0.612531\pi$
$368$			332.695i			0.904064i
$369$	−15.4455	−	474.155i	−0.0418577	−	1.28497i
$370$		0			0
$371$		−	47.3486i		−	0.127624i
$372$	−124.575	+	2.02847i	−0.334880	+	0.00545288i
$373$	−436.515			−1.17028			−0.585141	−	0.810932i	$-0.698961\pi$
$373$	−436.515			−1.17028			−0.585141	+	0.810932i	$0.698961\pi$
$374$			97.2256i			0.259961i
$375$		0			0
$376$	458.841			1.22032
$377$		−	306.777i		−	0.813732i
$378$	2.18003	+	44.5962i	0.00576728	+	0.117979i
$379$	−269.326			−0.710624			−0.355312	−	0.934748i	$-0.615625\pi$
$379$	−269.326			−0.710624			−0.355312	+	0.934748i	$0.615625\pi$
$380$		0			0
$381$	700.516	−	11.4065i	1.83862	−	0.0299384i
$382$	274.739			0.719211
$383$			630.454i			1.64609i	0.567974	+	0.823047i	$0.307727\pi$
$383$			630.454i			1.64609i	−0.567974	+	0.823047i	$0.692273\pi$
$384$	−2.16213	−	132.784i	−0.00563055	−	0.345792i
$385$		0			0
$386$			524.191i			1.35801i
$387$	−262.367	+	8.54655i	−0.677951	+	0.0220841i
$388$	101.002			0.260315
$389$			61.9695i			0.159305i	0.996823	+	0.0796523i	$0.0253810\pi$
$389$			61.9695i			0.159305i	−0.996823	+	0.0796523i	$0.974619\pi$
$390$		0			0
$391$	182.688			0.467233
$392$			417.827i			1.06588i
$393$	−1.43769	−	88.2937i	−0.00365825	−	0.224666i
$394$	341.830			0.867588
$395$		0			0
$396$	3.73434	+	114.639i	0.00943016	+	0.289493i
$397$	511.967			1.28959			0.644794	−	0.764356i	$-0.276943\pi$
$397$	511.967			1.28959			0.644794	+	0.764356i	$0.276943\pi$
$398$			254.703i			0.639956i
$399$	−62.8997	+	1.02420i	−0.157643	+	0.00256692i
$400$		0			0
$401$			403.443i			1.00609i	0.864260	+	0.503046i	$0.167787\pi$
$401$			403.443i			1.00609i	−0.864260	+	0.503046i	$0.832213\pi$
$402$	7.44588	+	457.277i	0.0185221	+	1.13751i
$403$	305.239			0.757417
$404$		−	38.5051i		−	0.0953097i
$405$		0			0
$406$	−58.1189			−0.143150
$407$			207.269i			0.509260i
$408$	−140.987	+	2.29571i	−0.345557	+	0.00562674i
$409$	203.296			0.497057			0.248528	−	0.968625i	$-0.420053\pi$
$409$	203.296			0.497057			0.248528	+	0.968625i	$0.420053\pi$
$410$		0			0
$411$	−2.70145	−	165.905i	−0.00657286	−	0.403662i
$412$	−43.9726			−0.106730
$413$		−	92.6090i		−	0.224235i
$414$	−510.090	+	16.6161i	−1.23210	+	0.0401354i
$415$		0			0
$416$		−	159.729i		−	0.383964i
$417$	−550.424	+	8.96260i	−1.31996	+	0.0214930i
$418$	382.680			0.915503
$419$		−	63.4056i		−	0.151326i	−0.997133	−	0.0756630i	$-0.975893\pi$
$419$		−	63.4056i		−	0.151326i	0.997133	−	0.0756630i	$-0.0241073\pi$
$420$		0			0
$421$	−666.311			−1.58269			−0.791344	−	0.611371i	$-0.790618\pi$
$421$	−666.311			−1.58269			−0.791344	+	0.611371i	$0.790618\pi$
$422$			369.329i			0.875188i
$423$	15.4543	+	474.426i	0.0365351	+	1.12158i
$424$	−417.729			−0.985210
$425$		0			0
$426$	−641.893	+	10.4520i	−1.50679	+	0.0245352i
$427$	28.5147			0.0667793
$428$			137.233i			0.320639i
$429$	−4.57501	−	280.967i	−0.0106644	−	0.654935i
$430$		0			0
$431$			582.760i			1.35211i	0.736851	+	0.676055i	$0.236312\pi$
$431$			582.760i			1.35211i	−0.736851	+	0.676055i	$0.763688\pi$
$432$	265.334	−	12.9705i	0.614199	−	0.0300244i
$433$	756.314			1.74668			0.873341	−	0.487109i	$-0.161949\pi$
$433$	756.314			1.74668			0.873341	+	0.487109i	$0.161949\pi$
$434$		−	57.8276i		−	0.133243i
$435$		0			0
$436$	88.6099			0.203234
$437$		−	719.062i		−	1.64545i
$438$	8.01676	+	492.337i	0.0183031	+	1.12406i
$439$	−243.610			−0.554921			−0.277461	−	0.960737i	$-0.589493\pi$
$439$	−243.610			−0.554921			−0.277461	+	0.960737i	$0.589493\pi$
$440$		0			0
$441$	−432.019	+	14.0729i	−0.979636	+	0.0319114i
$442$	79.0869			0.178930
$443$			719.320i			1.62375i	0.583833	+	0.811874i	$0.301552\pi$
$443$			719.320i			1.62375i	−0.583833	+	0.811874i	$0.698448\pi$
$444$	−68.8098	+	1.12043i	−0.154977	+	0.00252350i
$445$		0			0
$446$		−	441.924i		−	0.990862i
$447$	−3.39582	−	208.549i	−0.00759692	−	0.466553i
$448$	−69.0690			−0.154172
$449$			509.284i			1.13426i	0.823628	+	0.567131i	$0.191947\pi$
$449$			509.284i			1.13426i	−0.823628	+	0.567131i	$0.808053\pi$
$450$		0			0
$451$	565.642			1.25420
$452$			192.683i			0.426290i
$453$	28.8594	−	0.469919i	0.0637073	−	0.00103735i
$454$	−235.739			−0.519249
$455$		0			0
$456$	9.03592	+	554.927i	0.0198156	+	1.21695i
$457$	220.079			0.481573			0.240786	−	0.970578i	$-0.422595\pi$
$457$	220.079			0.481573			0.240786	+	0.970578i	$0.422595\pi$
$458$			424.443i			0.926731i
$459$	−7.12232	−	145.699i	−0.0155170	−	0.317427i
$460$		0			0
$461$			75.3071i			0.163356i	0.996659	+	0.0816779i	$0.0260279\pi$
$461$			75.3071i			0.163356i	−0.996659	+	0.0816779i	$0.973972\pi$
$462$	−53.2293	+	0.866736i	−0.115215	+	0.00187605i
$463$	−832.748			−1.79859			−0.899295	−	0.437342i	$-0.855920\pi$
$463$	−832.748			−1.79859			−0.899295	+	0.437342i	$0.855920\pi$
$464$			345.790i			0.745237i
$465$		0			0
$466$	−531.199			−1.13991
$467$		−	322.907i		−	0.691451i	−0.938336	−	0.345725i	$-0.887633\pi$
$467$		−	322.907i		−	0.691451i	0.938336	−	0.345725i	$-0.112367\pi$
$468$	93.2517	−	3.03765i	0.199256	−	0.00649071i
$469$	89.6393			0.191129
$470$		0			0
$471$	694.281	−	11.3050i	1.47406	−	0.0240022i
$472$	−817.036			−1.73101
$473$		−	312.990i		−	0.661713i
$474$	−3.42323	−	210.232i	−0.00722200	−	0.443528i
$475$		0			0
$476$			6.32726i			0.0132926i
$477$	−14.0696	−	431.918i	−0.0294961	−	0.905489i
$478$	109.249			0.228555
$479$		−	12.5420i		−	0.0261836i	−0.999914	−	0.0130918i	$-0.995833\pi$
$479$		−	12.5420i		−	0.0261836i	0.999914	−	0.0130918i	$-0.00416737\pi$
$480$		0			0
$481$	168.600			0.350520
$482$		−	296.855i		−	0.615882i
$483$	1.62861	+	100.019i	0.00337186	+	0.207078i
$484$	6.94641			0.0143521
$485$		0			0
$486$	33.1382	+	406.163i	0.0681857	+	0.835727i
$487$	391.799			0.804515			0.402258	−	0.915526i	$-0.368226\pi$
$487$	391.799			0.804515			0.402258	+	0.915526i	$0.368226\pi$
$488$		−	251.569i		−	0.515510i
$489$	−711.724	+	11.5890i	−1.45547	+	0.0236995i
$490$		0			0
$491$		−	501.930i		−	1.02226i	−0.859503	−	0.511130i	$-0.829227\pi$
$491$		−	501.930i		−	1.02226i	0.859503	−	0.511130i	$-0.170773\pi$
$492$	3.05769	+	187.784i	0.00621482	+	0.381674i
$493$	189.879			0.385149
$494$		−	311.286i		−	0.630134i
$495$		0			0
$496$	−344.057			−0.693662
$497$			125.829i			0.253178i
$498$	−489.484	+	7.97030i	−0.982900	+	0.0160046i
$499$	−444.402			−0.890585			−0.445293	−	0.895385i	$-0.646900\pi$
$499$	−444.402			−0.890585			−0.445293	+	0.895385i	$0.646900\pi$
$500$		0			0
$501$	−2.66293	−	163.540i	−0.00531522	−	0.326426i
$502$	806.636			1.60685
$503$			624.696i			1.24194i	0.783834	+	0.620971i	$0.213261\pi$
$503$			624.696i			1.24194i	−0.783834	+	0.620971i	$0.786739\pi$
$504$	−2.51372	−	77.1676i	−0.00498754	−	0.153110i
$505$		0			0
$506$		−	608.511i		−	1.20259i
$507$	278.384	−	4.53294i	0.549080	−	0.00894071i
$508$	−277.358			−0.545980
$509$		−	127.740i		−	0.250962i	−0.992096	−	0.125481i	$-0.959953\pi$
$509$		−	127.740i		−	0.250962i	0.992096	−	0.125481i	$-0.0400474\pi$
$510$		0			0
$511$	96.5120			0.188869
$512$			522.425i			1.02036i
$513$	−573.472	+	28.0335i	−1.11788	+	0.0546462i
$514$	383.598			0.746300
$515$		0			0
$516$	103.908	−	1.69193i	0.201371	−	0.00327894i
$517$	−565.966			−1.09471
$518$		−	31.9413i		−	0.0616628i
$519$	10.1180	+	621.382i	0.0194952	+	1.19727i
$520$		0			0
$521$			813.374i			1.56118i	0.625044	+	0.780589i	$0.285081\pi$
$521$			813.374i			1.56118i	−0.625044	+	0.780589i	$0.714919\pi$
$522$	−530.166	+	17.2700i	−1.01564	+	0.0330844i
$523$	−170.814			−0.326605			−0.163303	−	0.986576i	$-0.552215\pi$
$523$	−170.814			−0.326605			−0.163303	+	0.986576i	$0.552215\pi$
$524$			34.9585i			0.0667146i
$525$		0			0
$526$	271.177			0.515545
$527$			188.927i			0.358495i
$528$	5.15682	+	316.698i	0.00976670	+	0.599807i
$529$	−614.401			−1.16144
$530$		0			0
$531$	−27.5188	−	844.788i	−0.0518245	−	1.59094i
$532$	24.9041			0.0468122
$533$		−	460.114i		−	0.863254i
$534$	441.325	−	7.18613i	0.826452	−	0.0134572i
$535$		0			0
$536$		−	790.835i		−	1.47544i
$537$	3.06648	+	188.323i	0.00571038	+	0.350695i
$538$	−45.4993			−0.0845713
$539$		−	515.377i		−	0.956173i
$540$		0			0
$541$	418.188			0.772990			0.386495	−	0.922291i	$-0.373686\pi$
$541$	418.188			0.772990			0.386495	+	0.922291i	$0.373686\pi$
$542$			77.2183i			0.142469i
$543$	419.452	−	6.82996i	0.772471	−	0.0125782i
$544$	98.8637			0.181735
$545$		0			0
$546$	0.705035	+	43.2987i	0.00129127	+	0.0793016i
$547$	−515.125			−0.941728			−0.470864	−	0.882206i	$-0.656058\pi$
$547$	−515.125			−0.941728			−0.470864	+	0.882206i	$0.656058\pi$
$548$			65.6875i			0.119868i
$549$	260.114	−	8.47316i	0.473796	−	0.0154338i
$550$		0			0
$551$		−	747.363i		−	1.35638i
$552$	882.406	−	14.3683i	1.59856	−	0.0260295i
$553$	−41.2115			−0.0745235
$554$			157.162i			0.283685i
$555$		0			0
$556$	217.932			0.391963
$557$		−	688.047i		−	1.23527i	−0.786464	−	0.617637i	$-0.788090\pi$
$557$		−	688.047i		−	1.23527i	0.786464	−	0.617637i	$-0.211910\pi$
$558$	−17.1835	−	527.509i	−0.0307948	−	0.945356i
$559$	−254.598			−0.455453
$560$		0			0
$561$	173.904	−	2.83169i	0.309989	−	0.00504757i
$562$	−326.251			−0.580517
$563$			523.680i			0.930159i	0.885269	+	0.465079i	$0.153974\pi$
$563$			523.680i			0.930159i	−0.885269	+	0.465079i	$0.846026\pi$
$564$	−3.05945	−	187.891i	−0.00542455	−	0.333141i
$565$		0			0
$566$			337.939i			0.597066i
$567$	79.7042	−	5.19821i	0.140572	−	0.00916791i
$568$	1110.12			1.95443
$569$			1008.79i			1.77291i	0.462811	+	0.886457i	$0.346841\pi$
$569$			1008.79i			1.77291i	−0.462811	+	0.886457i	$0.653159\pi$
$570$		0			0
$571$	−142.897			−0.250257			−0.125129	−	0.992141i	$-0.539934\pi$
$571$	−142.897			−0.250257			−0.125129	+	0.992141i	$0.539934\pi$
$572$			111.244i			0.194483i
$573$	−8.00175	−	491.415i	−0.0139647	−	0.857618i
$574$	−87.1687			−0.151862
$575$		0			0
$576$	−630.054	+	20.5239i	−1.09384	+	0.0356317i
$577$	−175.636			−0.304394			−0.152197	−	0.988350i	$-0.548635\pi$
$577$	−175.636			−0.304394			−0.152197	+	0.988350i	$0.548635\pi$
$578$		−	435.705i		−	0.753814i
$579$	937.602	−	15.2670i	1.61935	−	0.0263679i
$580$		0			0
$581$			95.9527i			0.165151i
$582$	6.96594	+	427.803i	0.0119690	+	0.735056i
$583$	515.256			0.883802
$584$		−	851.469i		−	1.45799i
$585$		0			0
$586$	−672.702			−1.14796
$587$		−	523.786i		−	0.892311i	−0.894955	−	0.446155i	$-0.852793\pi$
$587$		−	523.786i		−	0.892311i	0.894955	−	0.446155i	$-0.147207\pi$
$588$	171.096	−	2.78598i	0.290980	−	0.00473805i
$589$	743.617			1.26251
$590$		0			0
$591$	−9.95576	−	611.418i	−0.0168456	−	1.03455i
$592$	−190.041			−0.321016
$593$		−	649.656i		−	1.09554i	−0.836629	−	0.547771i	$-0.815477\pi$
$593$		−	649.656i		−	1.09554i	0.836629	−	0.547771i	$-0.184523\pi$
$594$	−485.305	+	23.7235i	−0.817012	+	0.0399386i
$595$		0			0
$596$			82.5717i			0.138543i
$597$	455.577	−	7.41819i	0.763111	−	0.0124258i
$598$	−494.985			−0.827735
$599$		−	26.1406i		−	0.0436405i	−0.999762	−	0.0218202i	$-0.993054\pi$
$599$		−	26.1406i		−	0.0436405i	0.999762	−	0.0218202i	$-0.00694614\pi$
$600$		0			0
$601$	233.697			0.388847			0.194423	−	0.980918i	$-0.437716\pi$
$601$	233.697			0.388847			0.194423	+	0.980918i	$0.437716\pi$
$602$			48.2336i			0.0801223i
$603$	817.698	−	26.6363i	1.35605	−	0.0441730i
$604$	−11.4264			−0.0189179
$605$		0			0
$606$	163.091	−	2.65563i	0.269128	−	0.00438223i
$607$	623.998			1.02800			0.514001	−	0.857789i	$-0.328163\pi$
$607$	623.998			1.02800			0.514001	+	0.857789i	$0.328163\pi$
$608$		−	389.128i		−	0.640013i
$609$	1.69271	+	103.955i	0.00277949	+	0.170698i
$610$		0			0
$611$			460.378i			0.753483i
$612$	1.88015	+	57.7178i	0.00307213	+	0.0943102i
$613$	−947.803			−1.54617			−0.773086	−	0.634302i	$-0.781288\pi$
$613$	−947.803			−1.54617			−0.773086	+	0.634302i	$0.781288\pi$
$614$		−	513.059i		−	0.835601i
$615$		0			0
$616$	92.0570			0.149443
$617$			429.729i			0.696482i	0.937405	+	0.348241i	$0.113221\pi$
$617$			429.729i			0.696482i	−0.937405	+	0.348241i	$0.886779\pi$
$618$	−3.03271	−	186.249i	−0.00490730	−	0.301374i
$619$	687.130			1.11006			0.555032	−	0.831829i	$-0.312706\pi$
$619$	687.130			1.11006			0.555032	+	0.831829i	$0.312706\pi$
$620$		0			0
$621$	44.5769	+	911.895i	0.0717824	+	1.46843i
$622$	−417.441			−0.671128
$623$		−	86.5123i		−	0.138864i
$624$	257.614	−	4.19475i	0.412843	−	0.00672235i
$625$		0			0
$626$		−	67.6541i		−	0.108074i
$627$	−11.1455	−	684.486i	−0.0177760	−	1.09168i
$628$	−274.889			−0.437722
$629$			104.355i			0.165906i
$630$		0			0
$631$	−1137.47			−1.80265			−0.901326	−	0.433141i	$-0.857405\pi$
$631$	−1137.47			−1.80265			−0.901326	+	0.433141i	$0.857405\pi$
$632$			363.585i			0.575293i
$633$	660.606	−	10.7567i	1.04361	−	0.0169932i
$634$	−507.373			−0.800273
$635$		0			0
$636$	2.78532	+	171.056i	0.00437944	+	0.268957i
$637$	−419.227			−0.658127
$638$		−	632.461i		−	0.991319i
$639$	37.3902	+	1147.83i	0.0585136	+	1.79629i
$640$		0			0
$641$		−	344.531i		−	0.537490i	−0.963211	−	0.268745i	$-0.913391\pi$
$641$		−	344.531i		−	0.537490i	0.963211	−	0.268745i	$-0.0866089\pi$
$642$	−581.262	+	9.46473i	−0.905393	+	0.0147426i
$643$	−444.434			−0.691189			−0.345594	−	0.938384i	$-0.612323\pi$
$643$	−444.434			−0.691189			−0.345594	+	0.938384i	$0.612323\pi$
$644$		−	39.6007i		−	0.0614918i
$645$		0			0
$646$	192.670			0.298250
$647$		−	203.910i		−	0.315162i	−0.987506	−	0.157581i	$-0.949630\pi$
$647$		−	203.910i		−	0.315162i	0.987506	−	0.157581i	$-0.0503696\pi$
$648$	−45.8608	−	703.183i	−0.0707728	−	1.08516i
$649$	1007.79			1.55283
$650$		0			0
$651$	−103.434	+	1.68422i	−0.158885	+	0.00258713i
$652$	281.796			0.432202
$653$		−	587.575i		−	0.899809i	−0.893077	−	0.449904i	$-0.851458\pi$
$653$		−	587.575i		−	0.899809i	0.893077	−	0.449904i	$-0.148542\pi$
$654$	6.11127	+	375.314i	0.00934444	+	0.573875i
$655$		0			0
$656$			518.627i			0.790590i
$657$	880.391	−	28.6786i	1.34002	−	0.0436508i
$658$	87.2186			0.132551
$659$		−	1001.62i		−	1.51991i	−0.649977	−	0.759954i	$-0.725221\pi$
$659$		−	1001.62i		−	1.51991i	0.649977	−	0.759954i	$-0.274779\pi$
$660$		0			0
$661$	809.420			1.22454			0.612269	−	0.790650i	$-0.290257\pi$
$661$	809.420			1.22454			0.612269	+	0.790650i	$0.290257\pi$
$662$			11.9719i			0.0180844i
$663$	−2.30340	−	141.460i	−0.00347421	−	0.213363i
$664$	846.535			1.27490
$665$		0			0
$666$	−9.49137	−	291.372i	−0.0142513	−	0.437495i
$667$	−1188.40			−1.78172
$668$			64.7509i			0.0969325i
$669$	−790.454	+	12.8710i	−1.18155	+	0.0192392i
$670$		0			0
$671$			310.303i			0.462449i
$672$	0.881340	+	54.1261i	0.00131152	+	0.0805448i
$673$	−627.941			−0.933047			−0.466523	−	0.884509i	$-0.654494\pi$
$673$	−627.941			−0.933047			−0.466523	+	0.884509i	$0.654494\pi$
$674$		−	109.647i		−	0.162680i
$675$		0			0
$676$	−110.221			−0.163050
$677$			592.236i			0.874794i	0.899268	+	0.437397i	$0.144100\pi$
$677$			592.236i			0.874794i	−0.899268	+	0.437397i	$0.855900\pi$
$678$	−816.125	+	13.2890i	−1.20372	+	0.0196003i
$679$	83.8615			0.123507
$680$		0			0
$681$	6.86588	+	421.658i	0.0100821	+	0.619175i
$682$	629.291			0.922714
$683$		−	668.583i		−	0.978891i	−0.872034	−	0.489446i	$-0.837199\pi$
$683$		−	668.583i		−	0.978891i	0.872034	−	0.489446i	$-0.162801\pi$
$684$	227.178	−	7.40026i	0.332131	−	0.0108191i
$685$		0			0
$686$			160.453i			0.233897i
$687$	759.185	−	12.3619i	1.10507	−	0.0179940i
$688$	286.975			0.417115
$689$		−	419.129i		−	0.608314i
$690$		0			0
$691$	754.280			1.09158			0.545789	−	0.837923i	$-0.316230\pi$
$691$	754.280			1.09158			0.545789	+	0.837923i	$0.316230\pi$
$692$		−	246.026i		−	0.355529i
$693$	3.10060	+	95.1840i	0.00447417	+	0.137351i
$694$	−186.035			−0.268062
$695$		0			0
$696$	917.136	−	14.9338i	1.31772	−	0.0214566i
$697$	284.786			0.408589
$698$		−	0.413767i		−	0.000592790i
$699$	15.4711	+	950.136i	0.0221332	+	1.35928i
$700$		0			0
$701$			682.125i			0.973074i	0.873660	+	0.486537i	$0.161740\pi$
$701$			682.125i			0.973074i	−0.873660	+	0.486537i	$0.838260\pi$
$702$	19.2976	+	394.765i	0.0274895	+	0.562343i
$703$	410.740			0.584267
$704$		−	751.622i		−	1.06765i
$705$		0			0
$706$	−143.869			−0.203781
$707$		−	31.9705i		−	0.0452200i
$708$	5.44781	+	334.569i	0.00769465	+	0.472555i
$709$	−106.898			−0.150773			−0.0753867	−	0.997154i	$-0.524019\pi$
$709$	−106.898			−0.150773			−0.0753867	+	0.997154i	$0.524019\pi$
$710$		0			0
$711$	−375.935	+	12.2460i	−0.528742	+	0.0172236i
$712$	−763.247			−1.07198
$713$		−	1182.45i		−	1.65841i
$714$	−26.7996	+	0.436379i	−0.0375344	+	0.000611175i
$715$		0			0
$716$		−	74.5635i		−	0.104139i
$717$	−3.18188	−	195.410i	−0.00443777	−	0.272539i
$718$	1070.94			1.49156
$719$		−	172.195i		−	0.239492i	−0.992805	−	0.119746i	$-0.961792\pi$
$719$		−	172.195i		−	0.239492i	0.992805	−	0.119746i	$-0.0382081\pi$
$720$		0			0
$721$	−36.5102			−0.0506382
$722$		−	152.949i		−	0.211841i
$723$	−530.974	+	8.64588i	−0.734404	+	0.0119583i
$724$	−166.075			−0.229386
$725$		0			0
$726$	0.479081	+	29.4221i	0.000659892	+	0.0405263i
$727$	−501.862			−0.690319			−0.345160	−	0.938544i	$-0.612175\pi$
$727$	−501.862			−0.690319			−0.345160	+	0.938544i	$0.612175\pi$
$728$		−	74.8826i		−	0.102861i
$729$	725.524	−	71.1026i	0.995232	−	0.0975345i
$730$		0			0
$731$		−	157.583i		−	0.215571i
$732$	−103.015	+	1.67741i	−0.140731	+	0.00229154i
$733$	102.508			0.139847			0.0699237	−	0.997552i	$-0.477724\pi$
$733$	102.508			0.139847			0.0699237	+	0.997552i	$0.477724\pi$
$734$			426.157i			0.580596i
$735$		0			0
$736$	−618.764			−0.840712
$737$			975.472i			1.32357i
$738$	−795.161	+	25.9022i	−1.07745	+	0.0350978i
$739$	−228.683			−0.309449			−0.154724	−	0.987958i	$-0.549449\pi$
$739$	−228.683			−0.309449			−0.154724	+	0.987958i	$0.549449\pi$
$740$		0			0
$741$	−556.786	+	9.06619i	−0.751399	+	0.0122351i
$742$	−79.4039			−0.107013
$743$		−	597.078i		−	0.803605i	−0.915726	−	0.401802i	$-0.868384\pi$
$743$		−	597.078i		−	0.803605i	0.915726	−	0.401802i	$-0.131616\pi$
$744$	14.8589	+	912.539i	0.0199717	+	1.22653i
$745$		0			0
$746$			732.040i			0.981286i
$747$	28.5124	+	875.290i	0.0381692	+	1.17174i
$748$	−68.8544			−0.0920514
$749$			113.944i			0.152128i
$750$		0			0
$751$	339.769			0.452422			0.226211	−	0.974078i	$-0.427366\pi$
$751$	339.769			0.452422			0.226211	+	0.974078i	$0.427366\pi$
$752$		−	518.924i		−	0.690059i
$753$	−23.4932	−	1442.80i	−0.0311995	−	1.91607i
$754$	−514.468			−0.682318
$755$		0			0
$756$	−31.5827	+	1.54388i	−0.0417761	+	0.00204217i
$757$	244.894			0.323506			0.161753	−	0.986831i	$-0.448285\pi$
$757$	244.894			0.323506			0.161753	+	0.986831i	$0.448285\pi$
$758$			451.662i			0.595861i
$759$	−1088.42	+	17.7228i	−1.43402	+	0.0233502i
$760$		0			0
$761$			551.072i			0.724142i	0.932151	+	0.362071i	$0.117930\pi$
$761$			551.072i			0.724142i	−0.932151	+	0.362071i	$0.882070\pi$
$762$	−19.1289	−	1174.77i	−0.0251035	−	1.54169i
$763$	73.5722			0.0964249
$764$			194.568i			0.254670i
$765$		0			0
$766$	1057.28			1.38026
$767$		−	819.773i		−	1.06880i
$768$	617.727	−	10.0585i	0.804331	−	0.0130970i
$769$	−903.877			−1.17539			−0.587696	−	0.809082i	$-0.699965\pi$
$769$	−903.877			−1.17539			−0.587696	+	0.809082i	$0.699965\pi$
$770$		0			0
$771$	−11.1723	−	686.128i	−0.0144906	−	0.889919i
$772$	−371.228			−0.480866
$773$			438.057i			0.566697i	0.959017	+	0.283349i	$0.0914453\pi$
$773$			438.057i			0.566697i	−0.959017	+	0.283349i	$0.908555\pi$
$774$	14.3326	+	439.992i	0.0185176	+	0.568465i
$775$		0			0
$776$		−	739.861i		−	0.953429i
$777$	−57.1323	+	0.930289i	−0.0735293	+	0.00119728i
$778$	103.923			0.133578
$779$		−	1120.92i		−	1.43892i
$780$		0			0
$781$	−1369.30			−1.75326
$782$		−	306.370i		−	0.391777i
$783$	46.3314	+	947.786i	0.0591716	+	1.21045i
$784$	472.540			0.602730
$785$		0			0
$786$	−148.069	+	2.41102i	−0.188383	+	0.00306746i
$787$	678.254			0.861822			0.430911	−	0.902394i	$-0.358192\pi$
$787$	678.254			0.861822			0.430911	+	0.902394i	$0.358192\pi$
$788$			242.081i			0.307210i
$789$	−7.89800	−	485.043i	−0.0100101	−	0.614757i
$790$		0			0
$791$			159.984i			0.202255i
$792$	839.753	−	27.3548i	1.06029	−	0.0345388i
$793$	252.412			0.318300
$794$		−	858.572i		−	1.08133i
$795$		0			0
$796$	−180.378			−0.226606
$797$		−	1248.06i		−	1.56595i	−0.622056	−	0.782973i	$-0.713702\pi$
$797$		−	1248.06i		−	1.56595i	0.622056	−	0.782973i	$-0.286298\pi$
$798$	1.71759	+	105.483i	0.00215237	+	0.132184i
$799$	−284.950			−0.356633
$800$		0			0
$801$	−25.7071	−	789.173i	−0.0320938	−	0.985235i
$802$	676.577			0.843612
$803$			1050.26i			1.30792i
$804$	−323.840	+	5.27311i	−0.402786	+	0.00655860i
$805$		0			0
$806$		−	511.889i		−	0.635098i
$807$	1.32517	+	81.3830i	0.00164209	+	0.100846i
$808$	−282.057			−0.349081
$809$		−	351.882i		−	0.434959i	−0.976065	−	0.217479i	$-0.930216\pi$
$809$		−	351.882i		−	0.434959i	0.976065	−	0.217479i	$-0.0697835\pi$
$810$		0			0
$811$	−715.833			−0.882654			−0.441327	−	0.897346i	$-0.645492\pi$
$811$	−715.833			−0.882654			−0.441327	+	0.897346i	$0.645492\pi$
$812$		−	41.1594i		−	0.0506889i
$813$	138.118	−	2.24898i	0.169886	−	0.00276627i
$814$	347.592			0.427017
$815$		0			0
$816$	2.59632	+	159.449i	0.00318177	+	0.195404i
$817$	−620.246			−0.759175
$818$		−	340.929i		−	0.416784i
$819$	77.4262	−	2.52214i	0.0945375	−	0.00307954i
$820$		0			0
$821$		−	1391.14i		−	1.69445i	−0.531238	−	0.847223i	$-0.678273\pi$
$821$		−	1391.14i		−	1.69445i	0.531238	−	0.847223i	$-0.321727\pi$
$822$	−278.224	+	4.53035i	−0.338472	+	0.00551137i
$823$	−140.224			−0.170382			−0.0851910	−	0.996365i	$-0.527150\pi$
$823$	−140.224			−0.170382			−0.0851910	+	0.996365i	$0.527150\pi$
$824$			322.108i			0.390908i
$825$		0			0
$826$	−155.306			−0.188022
$827$			926.931i			1.12084i	0.828210	+	0.560418i	$0.189359\pi$
$827$			926.931i			1.12084i	−0.828210	+	0.560418i	$0.810641\pi$
$828$	−11.7674	−	361.242i	−0.0142118	−	0.436282i
$829$	−1423.22			−1.71679			−0.858394	−	0.512991i	$-0.828537\pi$
$829$	−1423.22			−1.71679			−0.858394	+	0.512991i	$0.828537\pi$
$830$		0			0
$831$	281.109	−	4.57732i	0.338278	−	0.00550821i
$832$	−611.398			−0.734853
$833$		−	259.479i		−	0.311500i
$834$	15.0304	+	923.066i	0.0180220	+	1.10679i
$835$		0			0
$836$			271.011i			0.324176i
$837$	−943.035	+	46.0991i	−1.12668	+	0.0550766i
$838$	−106.332			−0.126888
$839$		−	24.8412i		−	0.0296081i	−0.999890	−	0.0148040i	$-0.995288\pi$
$839$		−	24.8412i		−	0.0296081i	0.999890	−	0.0148040i	$-0.00471244\pi$
$840$		0			0
$841$	−394.178			−0.468702
$842$			1117.41i			1.32709i
$843$	9.50202	+	583.552i	0.0112717	+	0.692233i
$844$	−261.556			−0.309901
$845$		0			0
$846$	795.617	−	25.9170i	0.940445	−	0.0306348i
$847$	5.76756			0.00680939
$848$			472.429i			0.557110i
$849$	604.460	−	9.84246i	0.711967	−	0.0115930i
$850$		0			0
$851$		−	653.130i		−	0.767485i
$852$	−7.40202	−	454.584i	−0.00868782	−	0.533549i
$853$	559.803			0.656275			0.328138	−	0.944630i	$-0.393579\pi$
$853$	559.803			0.656275			0.328138	+	0.944630i	$0.393579\pi$
$854$		−	47.8195i		−	0.0559947i
$855$		0			0
$856$	1005.26			1.17437
$857$			733.960i			0.856429i	0.903677	+	0.428214i	$0.140857\pi$
$857$			733.960i			0.856429i	−0.903677	+	0.428214i	$0.859143\pi$
$858$	−471.184	+	7.67233i	−0.549166	+	0.00894211i
$859$	−359.689			−0.418730			−0.209365	−	0.977838i	$-0.567140\pi$
$859$	−359.689			−0.418730			−0.209365	+	0.977838i	$0.567140\pi$
$860$		0			0
$861$	2.53878	+	155.915i	0.00294864	+	0.181086i
$862$	977.292			1.13375
$863$			867.952i			1.00574i	0.864362	+	0.502869i	$0.167722\pi$
$863$			867.952i			1.00574i	−0.864362	+	0.502869i	$0.832278\pi$
$864$	24.1233	+	493.482i	0.0279204	+	0.571159i
$865$		0			0
$866$		−	1268.34i		−	1.46460i
$867$	−779.329	+	12.6899i	−0.898880	+	0.0146365i
$868$	40.9530			0.0471809
$869$		−	448.472i		−	0.516078i
$870$		0			0
$871$	793.485			0.911005
$872$		−	649.085i		−	0.744363i
$873$	764.992	−	24.9194i	0.876280	−	0.0285446i
$874$	−1205.87			−1.37972
$875$		0			0
$876$	−348.669	+	5.67740i	−0.398024	+	0.00648106i
$877$	441.711			0.503661			0.251831	−	0.967771i	$-0.418967\pi$
$877$	441.711			0.503661			0.251831	+	0.967771i	$0.418967\pi$
$878$			408.537i			0.465304i
$879$	19.5924	+	1203.24i	0.0222894	+	1.36887i
$880$		0			0
$881$			610.857i			0.693368i	0.937982	+	0.346684i	$0.112692\pi$
$881$			610.857i			0.693368i	−0.937982	+	0.346684i	$0.887308\pi$
$882$	23.6004	+	724.500i	0.0267579	+	0.821429i
$883$	−145.758			−0.165071			−0.0825356	−	0.996588i	$-0.526302\pi$
$883$	−145.758			−0.165071			−0.0825356	+	0.996588i	$0.526302\pi$
$884$			56.0087i			0.0633583i
$885$		0			0
$886$	1206.31			1.36152
$887$			1104.66i			1.24539i	0.782466	+	0.622693i	$0.213961\pi$
$887$			1104.66i			1.24539i	−0.782466	+	0.622693i	$0.786039\pi$
$888$	8.20740	+	504.045i	0.00924256	+	0.567618i
$889$	−230.288			−0.259042
$890$		0			0
$891$	56.5679	+	867.356i	0.0634881	+	0.973464i
$892$	312.967			0.350860
$893$			1121.56i			1.25595i
$894$	−349.739	+	5.69482i	−0.391207	+	0.00637004i
$895$		0			0
$896$			43.6516i			0.0487183i
$897$	14.4164	+	885.362i	0.0160718	+	0.987026i
$898$	854.073			0.951083
$899$		−	1228.99i		−	1.36706i
$900$		0			0
$901$	259.418			0.287923
$902$		−	948.586i		−	1.05165i
$903$	86.2737	−	1.40480i	0.0955412	−	0.00155570i
$904$	1411.44			1.56133
$905$		0			0
$906$	−0.788059	−	48.3974i	−0.000869822	−	0.0534188i
$907$	438.512			0.483475			0.241737	−	0.970342i	$-0.422283\pi$
$907$	438.512			0.483475			0.241737	+	0.970342i	$0.422283\pi$
$908$		−	166.949i		−	0.183864i
$909$	−9.50005	−	291.638i	−0.0104511	−	0.320834i
$910$		0			0
$911$		−	870.840i		−	0.955917i	−0.878383	−	0.477958i	$-0.841377\pi$
$911$		−	870.840i		−	0.955917i	0.878383	−	0.477958i	$-0.158623\pi$
$912$	627.593	−	10.2191i	0.688150	−	0.0112052i
$913$	−1044.18			−1.14368
$914$		−	369.074i		−	0.403801i
$915$		0			0
$916$	−300.587			−0.328152
$917$			29.0258i			0.0316530i
$918$	−244.339	+	11.9442i	−0.266164	+	0.0130111i
$919$	916.817			0.997625			0.498812	−	0.866710i	$-0.333770\pi$
$919$	916.817			0.997625			0.498812	+	0.866710i	$0.333770\pi$
$920$		0			0
$921$	−917.689	+	14.9428i	−0.996406	+	0.0162245i
$922$	126.291			0.136975
$923$			1113.84i			1.20676i
$924$	−0.613816	−	37.6966i	−0.000664303	−	0.0407971i
$925$		0			0
$926$			1396.52i			1.50813i
$927$	−333.049	+	10.8490i	−0.359276	+	0.0117033i
$928$	−643.118			−0.693015
$929$			237.632i			0.255793i	0.991788	+	0.127896i	$0.0408225\pi$
$929$			237.632i			0.255793i	−0.991788	+	0.127896i	$0.959177\pi$
$930$		0			0
$931$	−1021.31			−1.09700
$932$		−	376.191i		−	0.403639i
$933$	12.1580	+	746.662i	0.0130310	+	0.800281i
$934$	−541.518			−0.579784
$935$		0			0
$936$	−22.2514	−	683.086i	−0.0237728	−	0.729793i
$937$	−649.421			−0.693085			−0.346542	−	0.938034i	$-0.612644\pi$
$937$	−649.421			−0.693085			−0.346542	+	0.938034i	$0.612644\pi$
$938$		−	150.326i		−	0.160262i
$939$	−121.010	+	1.97042i	−0.128872	+	0.00209842i
$940$		0			0
$941$			87.3770i			0.0928555i	0.998922	+	0.0464277i	$0.0147837\pi$
$941$			87.3770i			0.0928555i	−0.998922	+	0.0464277i	$0.985216\pi$
$942$	−18.9586	−	1164.31i	−0.0201259	−	1.23600i
$943$	−1782.41			−1.89015
$944$			924.024i			0.978839i
$945$		0			0
$946$	−524.887			−0.554849
$947$		−	152.556i		−	0.161094i	−0.996751	−	0.0805470i	$-0.974333\pi$
$947$		−	152.556i		−	0.161094i	0.996751	−	0.0805470i	$-0.0256667\pi$
$948$	148.885	−	2.42430i	0.157052	−	0.00255728i
$949$	854.322			0.900234
$950$		0			0
$951$	14.7772	+	907.519i	0.0155386	+	0.954279i
$952$	46.3484			0.0486853
$953$			940.275i			0.986647i	0.869846	+	0.493323i	$0.164218\pi$
$953$			940.275i			0.986647i	−0.869846	+	0.493323i	$0.835782\pi$
$954$	−724.330	+	23.5949i	−0.759256	+	0.0247326i
$955$		0			0
$956$			77.3695i			0.0809305i
$957$	−1131.26	+	18.4204i	−1.18209	+	0.0192481i
$958$	−21.0330			−0.0219551
$959$			54.5399i			0.0568716i
$960$		0			0
$961$	261.826			0.272451
$962$		−	282.744i		−	0.293913i
$963$	33.8584	+	1039.41i	0.0351593	+	1.07934i
$964$	210.231			0.218081
$965$		0			0
$966$	167.732	−	2.73119i	0.173636	−	0.00282732i
$967$	569.336			0.588765			0.294383	−	0.955688i	$-0.404886\pi$
$967$	569.336			0.588765			0.294383	+	0.955688i	$0.404886\pi$
$968$		−	50.8838i		−	0.0525659i
$969$	−5.61149	−	344.621i	−0.00579101	−	0.355646i
$970$		0			0
$971$			733.809i			0.755725i	0.925862	+	0.377862i	$0.123341\pi$
$971$			733.809i			0.755725i	−0.925862	+	0.377862i	$0.876659\pi$
$972$	−287.642	+	23.4683i	−0.295928	+	0.0241443i
$973$	180.947			0.185968
$974$		−	657.050i		−	0.674589i
$975$		0			0
$976$	−284.511			−0.291507
$977$			917.699i			0.939303i	0.882852	+	0.469652i	$0.155621\pi$
$977$			917.699i			0.939303i	−0.882852	+	0.469652i	$0.844379\pi$
$978$	19.4349	+	1193.57i	0.0198721	+	1.22042i
$979$	941.443			0.961637
$980$		0			0
$981$	671.133	−	21.8620i	0.684131	−	0.0222854i
$982$	−841.740			−0.857169
$983$		−	629.515i		−	0.640402i	−0.947350	−	0.320201i	$-0.896250\pi$
$983$		−	629.515i		−	0.640402i	0.947350	−	0.320201i	$-0.103750\pi$
$984$	1375.55	−	22.3982i	1.39792	−	0.0227624i
$985$		0			0
$986$		−	318.428i		−	0.322949i
$987$	−2.54024	−	156.005i	−0.00257369	−	0.158060i
$988$	220.451			0.223128
$989$			986.271i			0.997241i
$990$		0			0
$991$	−367.381			−0.370717			−0.185359	−	0.982671i	$-0.559345\pi$
$991$	−367.381			−0.370717			−0.185359	+	0.982671i	$0.559345\pi$
$992$		−	639.894i		−	0.645054i
$993$	21.4137	−	0.348680i	0.0215646	−	0.000351138i
$994$	211.017			0.212290
$995$		0			0
$996$	−5.64451	−	346.649i	−0.00566718	−	0.348041i
$997$	1777.46			1.78281			0.891403	−	0.453212i	$-0.149722\pi$
$997$	1777.46			1.78281			0.891403	+	0.453212i	$0.149722\pi$
$998$			745.266i			0.746759i
$999$	−520.889	+	25.4630i	−0.521411	+	0.0254885i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	375.3.c.c.251.11	✓	32
3.2	odd	2	inner	375.3.c.c.251.21	yes	32
5.2	odd	4		375.3.d.e.374.22		32
5.3	odd	4		375.3.d.e.374.11		32
5.4	even	2	inner	375.3.c.c.251.22	yes	32
15.2	even	4		375.3.d.e.374.12		32
15.8	even	4		375.3.d.e.374.21		32
15.14	odd	2	inner	375.3.c.c.251.12	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
375.3.c.c.251.11	✓	32	1.1	even	1	trivial
375.3.c.c.251.12	yes	32	15.14	odd	2	inner
375.3.c.c.251.21	yes	32	3.2	odd	2	inner
375.3.c.c.251.22	yes	32	5.4	even	2	inner
375.3.d.e.374.11		32	5.3	odd	4
375.3.d.e.374.12		32	15.2	even	4
375.3.d.e.374.21		32	15.8	even	4
375.3.d.e.374.22		32	5.2	odd	4

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.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.67701i q^{2} +(-2.99960 + 0.0488427i) q^{3} +1.18764 q^{4} +(0.0819097 + 5.03036i) q^{6} +0.986092 q^{7} -8.69972i q^{8} +(8.99523 - 0.293018i) q^{9} +O(q^{10})\)	\(q-1.67701i q^{2} +(-2.99960 + 0.0488427i) q^{3} +1.18764 q^{4} +(0.0819097 + 5.03036i) q^{6} +0.986092 q^{7} -8.69972i q^{8} +(8.99523 - 0.293018i) q^{9} +10.7308i q^{11} +(-3.56246 + 0.0580078i) q^{12} +8.72887 q^{13} -1.65368i q^{14} -9.83892 q^{16} +5.40271i q^{17} +(-0.491393 - 15.0851i) q^{18} +21.2651 q^{19} +(-2.95789 + 0.0481634i) q^{21} +17.9957 q^{22} -33.8142i q^{23} +(0.424918 + 26.0957i) q^{24} -14.6384i q^{26} +(-26.9678 + 1.31829i) q^{27} +1.17113 q^{28} -35.1451i q^{29} +34.9689 q^{31} -18.2989i q^{32} +(-0.524124 - 32.1883i) q^{33} +9.06038 q^{34} +(10.6831 - 0.348001i) q^{36} +19.3152 q^{37} -35.6617i q^{38} +(-26.1831 + 0.426342i) q^{39} -52.7118i q^{41} +(0.0807705 + 4.96040i) q^{42} -29.1674 q^{43} +12.7444i q^{44} -56.7067 q^{46} +52.7420i q^{47} +(29.5129 - 0.480560i) q^{48} -48.0276 q^{49} +(-0.263883 - 16.2060i) q^{51} +10.3668 q^{52} -48.0164i q^{53} +(2.21078 + 45.2252i) q^{54} -8.57873i q^{56} +(-63.7868 + 1.03864i) q^{57} -58.9386 q^{58} -93.9152i q^{59} +28.9169 q^{61} -58.6432i q^{62} +(8.87013 - 0.288942i) q^{63} -70.0431 q^{64} +(-53.9800 + 0.878960i) q^{66} +90.9035 q^{67} +6.41649i q^{68} +(1.65158 + 101.429i) q^{69} +127.604i q^{71} +(-2.54917 - 78.2560i) q^{72} +97.8731 q^{73} -32.3918i q^{74} +25.2553 q^{76} +10.5816i q^{77} +(0.714979 + 43.9093i) q^{78} -41.7927 q^{79} +(80.8283 - 5.27152i) q^{81} -88.3981 q^{82} +97.3060i q^{83} +(-3.51292 + 0.0572010i) q^{84} +48.9139i q^{86} +(1.71658 + 105.421i) q^{87} +93.3554 q^{88} -87.7324i q^{89} +8.60747 q^{91} -40.1593i q^{92} +(-104.893 + 1.70798i) q^{93} +88.4487 q^{94} +(0.893770 + 54.8895i) q^{96} +85.0442 q^{97} +80.5427i q^{98} +(3.14433 + 96.5264i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 68 q^{4} + 12 q^{6} - 20 q^{9}+O(q^{10}) \) 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

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Representations

Groups

Database

Properties

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