LMFDB - Embedded newform 375.3.d.e.374.21

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			374.21
Character	$\chi$	$=$	375.374
Dual form			375.3.d.e.374.22

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

$2$	1.67701			0.838504			0.419252	−	0.907870i	$-0.362292\pi$
$2$	1.67701			0.838504			0.419252	+	0.907870i	$0.362292\pi$
$3$	0.0488427	−	2.99960i	0.0162809	−	0.999867i
$3$	0.0488427	−	2.99960i	0.0162809	−	0.999867i
$4$	−1.18764			−0.296911
$5$		0			0
$5$		0			0
$6$	0.0819097	−	5.03036i	0.0136516	−	0.838393i
$7$		−	0.986092i		−	0.140870i	−0.997516	−	0.0704352i	$-0.977561\pi$
$7$		−	0.986092i		−	0.140870i	0.997516	−	0.0704352i	$-0.0224388\pi$
$8$	−8.69972			−1.08747
$9$	−8.99523	−	0.293018i	−0.999470	−	0.0325575i
$10$		0			0
$11$		−	10.7308i		−	0.975532i	−0.872975	−	0.487766i	$-0.837812\pi$
$11$		−	10.7308i		−	0.975532i	0.872975	−	0.487766i	$-0.162188\pi$
$12$	−0.0580078	+	3.56246i	−0.00483398	+	0.296872i
$13$			8.72887i			0.671452i	0.941960	+	0.335726i	$0.108982\pi$
$13$			8.72887i			0.671452i	−0.941960	+	0.335726i	$0.891018\pi$
$14$		−	1.65368i		−	0.118120i
$15$		0			0
$16$	−9.83892			−0.614933
$17$	−5.40271			−0.317806			−0.158903	−	0.987294i	$-0.550796\pi$
$17$	−5.40271			−0.317806			−0.158903	+	0.987294i	$0.550796\pi$
$18$	−15.0851	−	0.491393i	−0.838059	−	0.0272996i
$19$	−21.2651			−1.11921			−0.559607	−	0.828758i	$-0.689048\pi$
$19$	−21.2651			−1.11921			−0.559607	+	0.828758i	$0.689048\pi$
$20$		0			0
$21$	−2.95789	−	0.0481634i	−0.140852	−	0.00229350i
$22$		−	17.9957i		−	0.817987i
$23$	−33.8142			−1.47018			−0.735092	−	0.677968i	$-0.762861\pi$
$23$	−33.8142			−1.47018			−0.735092	+	0.677968i	$0.762861\pi$
$24$	−0.424918	+	26.0957i	−0.0177049	+	1.08732i
$25$		0			0
$26$			14.6384i			0.563015i
$27$	−1.31829	+	26.9678i	−0.0488255	+	0.998807i
$28$			1.17113i			0.0418260i
$29$		−	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	$0.309256\pi$
$32$	18.2989			0.571842
$33$	−32.1883	−	0.524124i	−0.975402	−	0.0158825i
$34$	−9.06038			−0.266482
$35$		0			0
$36$	10.6831	+	0.348001i	0.296754	+	0.00966668i
$37$		−	19.3152i		−	0.522033i	−0.965334	−	0.261017i	$-0.915942\pi$
$37$		−	19.3152i		−	0.522033i	0.965334	−	0.261017i	$-0.0840578\pi$
$38$	−35.6617			−0.938466
$39$	26.1831	+	0.426342i	0.671363	+	0.0109318i
$40$		0			0
$41$			52.7118i			1.28565i	0.766012	+	0.642827i	$0.222238\pi$
$41$			52.7118i			1.28565i	−0.766012	+	0.642827i	$0.777762\pi$
$42$	−4.96040	−	0.0807705i	−0.118105	−	0.00192311i
$43$		−	29.1674i		−	0.678310i	−0.940730	−	0.339155i	$-0.889859\pi$
$43$		−	29.1674i		−	0.678310i	0.940730	−	0.339155i	$-0.110141\pi$
$44$			12.7444i			0.289646i
$45$		0			0
$46$	−56.7067			−1.23275
$47$	−52.7420			−1.12217			−0.561085	−	0.827758i	$-0.689616\pi$
$47$	−52.7420			−1.12217			−0.561085	+	0.827758i	$0.689616\pi$
$48$	−0.480560	+	29.5129i	−0.0100117	+	0.614851i
$49$	48.0276			0.980156
$50$		0			0
$51$	−0.263883	+	16.2060i	−0.00517418	+	0.317764i
$52$		−	10.3668i		−	0.199361i
$53$	−48.0164			−0.905969			−0.452985	−	0.891518i	$-0.649641\pi$
$53$	−48.0164			−0.905969			−0.452985	+	0.891518i	$0.649641\pi$
$54$	−2.21078	+	45.2252i	−0.0409404	+	0.837504i
$55$		0			0
$56$			8.57873i			0.153192i
$57$	−1.03864	+	63.7868i	−0.0182218	+	1.11907i
$58$		−	58.9386i		−	1.01618i
$59$		−	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	$0.423828\pi$
$62$	58.6432			0.945857
$63$	−0.288942	+	8.87013i	−0.00458639	+	0.140796i
$64$	70.0431			1.09442
$65$		0			0
$66$	−53.9800	−	0.878960i	−0.817879	−	0.0133176i
$67$		−	90.9035i		−	1.35677i	−0.734707	−	0.678384i	$-0.762680\pi$
$67$		−	90.9035i		−	1.35677i	0.734707	−	0.678384i	$-0.237320\pi$
$68$	6.41649			0.0943602
$69$	−1.65158	+	101.429i	−0.0239359	+	1.46999i
$70$		0			0
$71$		−	127.604i		−	1.79724i	−0.438730	−	0.898619i	$-0.644571\pi$
$71$		−	127.604i		−	1.79724i	0.438730	−	0.898619i	$-0.355429\pi$
$72$	78.2560	+	2.54917i	1.08689	+	0.0354052i
$73$			97.8731i			1.34073i	0.742032	+	0.670364i	$0.233862\pi$
$73$			97.8731i			1.34073i	−0.742032	+	0.670364i	$0.766138\pi$
$74$		−	32.3918i		−	0.437727i
$75$		0			0
$76$	25.2553			0.332307
$77$	−10.5816			−0.137423
$78$	43.9093	+	0.714979i	0.562940	+	0.00916639i
$79$	41.7927			0.529022			0.264511	−	0.964383i	$-0.414789\pi$
$79$	41.7927			0.529022			0.264511	+	0.964383i	$0.414789\pi$
$80$		0			0
$81$	80.8283	+	5.27152i	0.997880	+	0.0650805i
$82$			88.3981i			1.07803i
$83$	97.3060			1.17236			0.586181	−	0.810180i	$-0.300631\pi$
$83$	97.3060			1.17236			0.586181	+	0.810180i	$0.300631\pi$
$84$	3.51292	+	0.0572010i	0.0418204	+	0.000680965i
$85$		0			0
$86$		−	48.9139i		−	0.568766i
$87$	−105.421	−	1.71658i	−1.21174	−	0.0197308i
$88$			93.3554i			1.06086i
$89$		−	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
$92$	40.1593			0.436514
$93$	1.70798	−	104.893i	0.0183654	−	1.12788i
$94$	−88.4487			−0.940944
$95$		0			0
$96$	0.893770	−	54.8895i	0.00931010	−	0.571766i
$97$		−	85.0442i		−	0.876744i	−0.898794	−	0.438372i	$-0.855555\pi$
$97$		−	85.0442i		−	0.876744i	0.898794	−	0.438372i	$-0.144445\pi$
$98$	80.5427			0.821864
$99$	−3.14433	+	96.5264i	−0.0317609	+	0.975014i
$100$		0			0
$101$			32.4214i			0.321004i	0.987035	+	0.160502i	$0.0513114\pi$
$101$			32.4214i			0.321004i	−0.987035	+	0.160502i	$0.948689\pi$
$102$	−0.442534	+	27.1775i	−0.00433857	+	0.266447i
$103$		−	37.0251i		−	0.359467i	−0.983715	−	0.179733i	$-0.942476\pi$
$103$		−	37.0251i		−	0.359467i	0.983715	−	0.179733i	$-0.0575235\pi$
$104$		−	75.9387i		−	0.730180i
$105$		0			0
$106$	−80.5238			−0.759659
$107$	−115.551			−1.07991			−0.539957	−	0.841692i	$-0.681560\pi$
$107$	−115.551			−1.07991			−0.539957	+	0.841692i	$0.681560\pi$
$108$	1.56566	−	32.0281i	0.0144968	−	0.296557i
$109$	−74.6098			−0.684494			−0.342247	−	0.939610i	$-0.611188\pi$
$109$	−74.6098			−0.684494			−0.342247	+	0.939610i	$0.611188\pi$
$110$		0			0
$111$	−57.9380	−	0.943409i	−0.521964	−	0.00849918i
$112$			9.70209i			0.0866258i
$113$	162.240			1.43575			0.717876	−	0.696171i	$-0.245115\pi$
$113$	162.240			1.43575			0.717876	+	0.696171i	$0.245115\pi$
$114$	−1.74181	+	106.971i	−0.0152791	+	0.938341i
$115$		0			0
$116$			41.7399i			0.359827i
$117$	2.55771	−	78.5182i	0.0218608	−	0.671096i
$118$		−	157.496i		−	1.33472i
$119$			5.32757i			0.0447695i
$120$		0			0
$121$	5.84890			0.0483380
$122$	48.4939			0.397491
$123$	158.114	+	2.57459i	1.28548	+	0.0209316i
$124$	−41.5306			−0.334925
$125$		0			0
$126$	−0.484559	+	14.8753i	−0.00384570	+	0.118058i
$127$			233.536i			1.83887i	0.393244	+	0.919434i	$0.371353\pi$
$127$			233.536i			1.83887i	−0.393244	+	0.919434i	$0.628647\pi$
$128$	44.2672			0.345838
$129$	−87.4905	−	1.42461i	−0.678221	−	0.0110435i
$130$		0			0
$131$		−	29.4351i		−	0.224696i	−0.993669	−	0.112348i	$-0.964163\pi$
$131$		−	29.4351i		−	0.224696i	0.993669	−	0.112348i	$-0.0358371\pi$
$132$	38.2282	+	0.622473i	0.289608	+	0.00471570i
$133$			20.9693i			0.157664i
$134$		−	152.446i		−	1.13766i
$135$		0			0
$136$	47.0020			0.345603
$137$	−55.3091			−0.403716			−0.201858	−	0.979415i	$-0.564698\pi$
$137$	−55.3091			−0.403716			−0.201858	+	0.979415i	$0.564698\pi$
$138$	−2.76971	+	170.098i	−0.0200704	+	1.23259i
$139$	−183.499			−1.32014			−0.660069	−	0.751205i	$-0.729473\pi$
$139$	−183.499			−1.32014			−0.660069	+	0.751205i	$0.729473\pi$
$140$		0			0
$141$	−2.57606	+	158.205i	−0.0182700	+	1.12202i
$142$		−	213.993i		−	1.50699i
$143$	93.6682			0.655022
$144$	88.5034	+	2.88298i	0.614607	+	0.0200207i
$145$		0			0
$146$			164.134i			1.12421i
$147$	2.34580	−	144.064i	0.0159578	−	0.980026i
$148$			22.9396i			0.154998i
$149$			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	$0.510142\pi$
$152$	185.000			1.21711
$153$	48.5986	+	1.58309i	0.317638	+	0.0103470i
$154$	−17.7454			−0.115230
$155$		0			0
$156$	−31.0963	−	0.506342i	−0.199335	−	0.00324579i
$157$			231.458i			1.47425i	0.675755	+	0.737126i	$0.263818\pi$
$157$			231.458i			1.47425i	−0.675755	+	0.737126i	$0.736182\pi$
$158$	70.0868			0.443587
$159$	−2.34525	+	144.030i	−0.0147500	+	0.905849i
$160$		0			0
$161$			33.3439i			0.207105i
$162$	135.550	+	8.84038i	0.836726	+	0.0545703i
$163$			237.273i			1.45566i	0.685757	+	0.727830i	$0.259471\pi$
$163$			237.273i			1.45566i	−0.685757	+	0.727830i	$0.740529\pi$
$164$		−	62.6028i		−	0.381725i
$165$		0			0
$166$	163.183			0.983030
$167$	−54.5204			−0.326470			−0.163235	−	0.986587i	$-0.552193\pi$
$167$	−54.5204			−0.326470			−0.163235	+	0.986587i	$0.552193\pi$
$168$	25.7328	+	0.419009i	0.153171	+	0.00249410i
$169$	92.8068			0.549153
$170$		0			0
$171$	191.284	+	6.23104i	1.11862	+	0.0364388i
$172$			34.6404i			0.201398i
$173$	−207.155			−1.19743			−0.598713	−	0.800963i	$-0.704321\pi$
$173$	−207.155			−1.19743			−0.598713	+	0.800963i	$0.704321\pi$
$174$	−176.792	−	2.87872i	−1.01605	−	0.0165444i
$175$		0			0
$176$			105.580i			0.599886i
$177$	−281.708	−	4.58707i	−1.59157	−	0.0259157i
$178$		−	147.128i		−	0.826561i
$179$		−	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	$0.626242\pi$
$182$	14.4348			0.0793121
$183$	1.41238	−	86.7392i	0.00771793	−	0.473985i
$184$	294.174			1.59877
$185$		0			0
$186$	2.86429	−	175.906i	0.0153994	−	0.945732i
$187$			57.9756i			0.310030i
$188$	62.6387			0.333185
$189$	26.5927	+	1.29995i	0.140702	+	0.00687806i
$190$		0			0
$191$		−	163.827i		−	0.857732i	−0.903368	−	0.428866i	$-0.858913\pi$
$191$		−	163.827i		−	0.857732i	0.903368	−	0.428866i	$-0.141087\pi$
$192$	3.42110	−	210.102i	0.0178182	−	1.09428i
$193$		−	312.575i		−	1.61956i	−0.586732	−	0.809781i	$-0.699586\pi$
$193$		−	312.575i		−	1.61956i	0.586732	−	0.809781i	$-0.300414\pi$
$194$		−	142.620i		−	0.735154i
$195$		0			0
$196$	−57.0397			−0.291019
$197$	−203.833			−1.03469			−0.517343	−	0.855778i	$-0.673079\pi$
$197$	−203.833			−1.03469			−0.517343	+	0.855778i	$0.673079\pi$
$198$	−5.27306	+	161.876i	−0.0266316	+	0.817554i
$199$	151.879			0.763212			0.381606	−	0.924325i	$-0.375371\pi$
$199$	151.879			0.763212			0.381606	+	0.924325i	$0.375371\pi$
$200$		0			0
$201$	−272.674	−	4.43998i	−1.35659	−	0.0220894i
$202$			54.3710i			0.269163i
$203$	−34.6563			−0.170721
$204$	0.313399	−	19.2469i	0.00153627	−	0.0943477i
$205$		0			0
$206$		−	62.0914i		−	0.301414i
$207$	304.167	+	9.90816i	1.46940	+	0.0478655i
$208$		−	85.8827i		−	0.412898i
$209$			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	$0.674767\pi$
$212$	57.0264			0.268992
$213$	−382.761	−	6.23252i	−1.79700	−	0.0292607i
$214$	−193.780			−0.905513
$215$		0			0
$216$	11.4687	−	234.612i	0.0530960	−	1.08617i
$217$		−	34.4826i		−	0.158906i
$218$	−125.121			−0.573951
$219$	293.581	+	4.78039i	1.34055	+	0.0218283i
$220$		0			0
$221$		−	47.1595i		−	0.213392i
$222$	−97.1626	−	1.58210i	−0.437669	−	0.00712660i
$223$			263.520i			1.18170i	0.806781	+	0.590851i	$0.201208\pi$
$223$			263.520i			1.18170i	−0.806781	+	0.590851i	$0.798792\pi$
$224$		−	18.0444i		−	0.0805555i
$225$		0			0
$226$	272.078			1.20388
$227$	140.571			0.619257			0.309628	−	0.950858i	$-0.399795\pi$
$227$	140.571			0.619257			0.309628	+	0.950858i	$0.399795\pi$
$228$	1.23354	−	75.7560i	0.00541026	−	0.332263i
$229$	253.095			1.10522			0.552610	−	0.833440i	$-0.313632\pi$
$229$	253.095			1.10522			0.552610	+	0.833440i	$0.313632\pi$
$230$		0			0
$231$	−0.516835	+	31.7406i	−0.00223738	+	0.137405i
$232$			305.753i			1.31790i
$233$	−316.754			−1.35946			−0.679730	−	0.733463i	$-0.737903\pi$
$233$	−316.754			−1.35946			−0.679730	+	0.733463i	$0.737903\pi$
$234$	4.28930	−	131.676i	0.0183304	−	0.562716i
$235$		0			0
$236$			111.538i			0.472618i
$237$	2.04127	−	125.362i	0.00861296	−	0.528952i
$238$			8.93438i			0.0375394i
$239$			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	$0.380299\pi$
$242$	9.80865			0.0405316
$243$	19.7603	−	242.195i	0.0813183	−	0.996688i
$244$	−34.3430			−0.140750
$245$		0			0
$246$	265.159	+	4.31760i	1.07788	+	0.0175512i
$247$		−	185.620i		−	0.751498i
$248$	−304.220			−1.22669
$249$	4.75269	−	291.879i	0.0190871	−	1.17221i
$250$		0			0
$251$		−	480.997i		−	1.91632i	−0.286227	−	0.958162i	$-0.592401\pi$
$251$		−	480.997i		−	1.91632i	0.286227	−	0.958162i	$-0.407599\pi$
$252$	0.343161	−	10.5346i	0.00136175	−	0.0418038i
$253$			362.855i			1.43421i
$254$			391.642i			1.54190i
$255$		0			0
$256$	−205.936			−0.804438
$257$	−228.740			−0.890037			−0.445019	−	0.895521i	$-0.646803\pi$
$257$	−228.740			−0.890037			−0.445019	+	0.895521i	$0.646803\pi$
$258$	−146.722	−	2.38909i	−0.568691	−	0.00926003i
$259$	−19.0466			−0.0735390
$260$		0			0
$261$	−10.2981	+	316.138i	−0.0394564	+	1.21126i
$262$		−	49.3630i		−	0.188408i
$263$	161.703			0.614839			0.307419	−	0.951574i	$-0.400535\pi$
$263$	161.703			0.614839			0.307419	+	0.951574i	$0.400535\pi$
$264$	280.029	+	4.55973i	1.06072	+	0.0172717i
$265$		0			0
$266$			35.1657i			0.132202i
$267$	−263.162	−	4.28509i	−0.985627	−	0.0160490i
$268$			107.961i			0.402840i
$269$		−	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	$0.527074\pi$
$272$	53.1568			0.195430
$273$	0.420413	−	25.8190i	0.00153997	−	0.0945751i
$274$	−92.7537			−0.338517
$275$		0			0
$276$	1.96149	−	120.462i	0.00710684	−	0.436456i
$277$			93.7155i			0.338323i	0.985588	+	0.169162i	$0.0541060\pi$
$277$			93.7155i			0.338323i	−0.985588	+	0.169162i	$0.945894\pi$
$278$	−307.730			−1.10694
$279$	−314.553	−	10.2465i	−1.12743	−	0.0367258i
$280$		0			0
$281$			194.543i			0.692325i	0.938175	+	0.346162i	$0.112515\pi$
$281$			194.543i			0.692325i	−0.938175	+	0.346162i	$0.887485\pi$
$282$	−4.32008	+	265.311i	−0.0153194	+	0.940819i
$283$		−	201.513i		−	0.712061i	−0.934474	−	0.356031i	$-0.884130\pi$
$283$		−	201.513i		−	0.712061i	0.934474	−	0.356031i	$-0.115870\pi$
$284$			151.548i			0.533620i
$285$		0			0
$286$	157.082			0.549239
$287$	51.9787			0.181110
$288$	−164.603	−	5.36191i	−0.571538	−	0.0186177i
$289$	−259.811			−0.898999
$290$		0			0
$291$	−255.099	−	4.15379i	−0.876628	−	0.0142742i
$292$		−	116.238i		−	0.398077i
$293$	−401.132			−1.36905			−0.684526	−	0.728988i	$-0.739991\pi$
$293$	−401.132			−1.36905			−0.684526	+	0.728988i	$0.739991\pi$
$294$	3.93393	−	241.596i	0.0133807	−	0.821755i
$295$		0			0
$296$			168.037i			0.567693i
$297$	289.387	+	14.1463i	0.974368	+	0.0476308i
$298$			116.595i			0.391258i
$299$		−	295.160i		−	0.987157i
$300$		0			0
$301$	−28.7617			−0.0955538
$302$	−16.1346			−0.0534259
$303$	97.2514	+	1.58355i	0.320962	+	0.00522624i
$304$	209.225			0.688242
$305$		0			0
$306$	81.5002	+	2.65485i	0.266341	+	0.00867598i
$307$		−	305.937i		−	0.996538i	−0.867023	−	0.498269i	$-0.833969\pi$
$307$		−	305.937i		−	0.996538i	0.867023	−	0.498269i	$-0.166031\pi$
$308$	12.5672			0.0408026
$309$	−111.061	−	1.80841i	−0.359419	−	0.00585245i
$310$		0			0
$311$			248.920i			0.800387i	0.916431	+	0.400193i	$0.131057\pi$
$311$			248.920i			0.800387i	−0.916431	+	0.400193i	$0.868943\pi$
$312$	−227.786	−	3.70906i	−0.730083	−	0.0118880i
$313$			40.3421i			0.128889i	0.997921	+	0.0644443i	$0.0205275\pi$
$313$			40.3421i			0.128889i	−0.997921	+	0.0644443i	$0.979473\pi$
$314$			388.156i			1.23617i
$315$		0			0
$316$	−49.6349			−0.157072
$317$	302.546			0.954405			0.477203	−	0.878793i	$-0.341651\pi$
$317$	302.546			0.954405			0.477203	+	0.878793i	$0.341651\pi$
$318$	−3.93300	+	241.539i	−0.0123679	+	0.759558i
$319$	−377.137			−1.18225
$320$		0			0
$321$	−5.64382	+	346.607i	−0.0175820	+	1.07977i
$322$			55.9181i			0.173659i
$323$	114.889			0.355693
$324$	−95.9952	−	6.26069i	−0.296282	−	0.0193231i
$325$		0			0
$326$			397.908i			1.22058i
$327$	−3.64415	+	223.800i	−0.0111442	+	0.684403i
$328$		−	458.578i		−	1.39810i
$329$			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	$0.503433\pi$
$332$	−115.565			−0.348087
$333$	−5.65970	+	173.745i	−0.0169961	+	0.521757i
$334$	−91.4312			−0.273746
$335$		0			0
$336$	29.1024	+	0.473877i	0.0866143	+	0.00141035i
$337$		−	65.3823i		−	0.194013i	−0.995284	−	0.0970064i	$-0.969073\pi$
$337$		−	65.3823i		−	0.194013i	0.995284	−	0.0970064i	$-0.0309267\pi$
$338$	155.638			0.460467
$339$	7.92424	−	486.655i	0.0233753	−	1.43556i
$340$		0			0
$341$		−	375.246i		−	1.10043i
$342$	320.785	+	10.4495i	0.937968	+	0.0305541i
$343$		−	95.6782i		−	0.278945i
$344$			253.748i			0.737639i
$345$		0			0
$346$	−347.400			−1.00405
$347$	110.933			0.319691			0.159845	−	0.987142i	$-0.448900\pi$
$347$	110.933			0.319691			0.159845	+	0.987142i	$0.448900\pi$
$348$	125.203	+	2.03869i	0.359779	+	0.00585830i
$349$	−0.246730			−0.000706961			−0.000353481	−	1.00000i	$-0.500113\pi$
$349$	−0.246730			−0.000706961			−0.000353481		1.00000i	$0.500113\pi$
$350$		0			0
$351$	−235.398	−	11.5072i	−0.670651	−	0.0327839i
$352$		−	196.363i		−	0.557849i
$353$	−85.7892			−0.243029			−0.121515	−	0.992590i	$-0.538775\pi$
$353$	−85.7892			−0.243029			−0.121515	+	0.992590i	$0.538775\pi$
$354$	−472.427	−	7.69256i	−1.33454	−	0.0217304i
$355$		0			0
$356$			104.195i			0.292682i
$357$	15.9806	+	0.260213i	0.0447636	+	0.000728888i
$358$		−	105.287i		−	0.294098i
$359$			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
$362$	−234.506			−0.647806
$363$	0.285676	−	17.5444i	0.000786987	−	0.0483316i
$364$	−10.2226			−0.0280841
$365$		0			0
$366$	2.36857	−	145.462i	0.00647151	−	0.397438i
$367$			254.118i			0.692419i	0.938157	+	0.346209i	$0.112531\pi$
$367$			254.118i			0.692419i	−0.938157	+	0.346209i	$0.887469\pi$
$368$	332.695			0.904064
$369$	15.4455	−	474.155i	0.0418577	−	1.28497i
$370$		0			0
$371$			47.3486i			0.127624i
$372$	−2.02847	+	124.575i	−0.00545288	+	0.334880i
$373$		−	436.515i		−	1.17028i	−0.810932	−	0.585141i	$-0.801039\pi$
$373$		−	436.515i		−	1.17028i	0.810932	−	0.585141i	$-0.198961\pi$
$374$			97.2256i			0.259961i
$375$		0			0
$376$	458.841			1.22032
$377$	306.777			0.813732
$378$	44.5962	+	2.18003i	0.117979	+	0.00576728i
$379$	269.326			0.710624			0.355312	−	0.934748i	$-0.384375\pi$
$379$	269.326			0.710624			0.355312	+	0.934748i	$0.384375\pi$
$380$		0			0
$381$	700.516	+	11.4065i	1.83862	+	0.0299384i
$382$		−	274.739i		−	0.719211i
$383$	630.454			1.64609			0.823047	−	0.567974i	$-0.192273\pi$
$383$	630.454			1.64609			0.823047	+	0.567974i	$0.192273\pi$
$384$	2.16213	−	132.784i	0.00563055	−	0.345792i
$385$		0			0
$386$		−	524.191i		−	1.35801i
$387$	−8.54655	+	262.367i	−0.0220841	+	0.677951i
$388$			101.002i			0.260315i
$389$			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
$392$	−417.827			−1.06588
$393$	−88.2937	−	1.43769i	−0.224666	−	0.00365825i
$394$	−341.830			−0.867588
$395$		0			0
$396$	3.73434	−	114.639i	0.00943016	−	0.289493i
$397$		−	511.967i		−	1.28959i	−0.764356	−	0.644794i	$-0.776943\pi$
$397$		−	511.967i		−	1.28959i	0.764356	−	0.644794i	$-0.223057\pi$
$398$	254.703			0.639956
$399$	62.8997	+	1.02420i	0.157643	+	0.00256692i
$400$		0			0
$401$		−	403.443i		−	1.00609i	−0.864260	−	0.503046i	$-0.832213\pi$
$401$		−	403.443i		−	1.00609i	0.864260	−	0.503046i	$-0.167787\pi$
$402$	−457.277	−	7.44588i	−1.13751	−	0.0185221i
$403$			305.239i			0.757417i
$404$		−	38.5051i		−	0.0953097i
$405$		0			0
$406$	−58.1189			−0.143150
$407$	−207.269			−0.509260
$408$	2.29571	−	140.987i	0.00562674	−	0.345557i
$409$	−203.296			−0.497057			−0.248528	−	0.968625i	$-0.579947\pi$
$409$	−203.296			−0.497057			−0.248528	+	0.968625i	$0.579947\pi$
$410$		0			0
$411$	−2.70145	+	165.905i	−0.00657286	+	0.403662i
$412$			43.9726i			0.106730i
$413$	−92.6090			−0.224235
$414$	510.090	+	16.6161i	1.23210	+	0.0401354i
$415$		0			0
$416$			159.729i			0.383964i
$417$	−8.96260	+	550.424i	−0.0214930	+	1.31996i
$418$			382.680i			0.915503i
$419$		−	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	$0.790618\pi$
$422$	−369.329			−0.875188
$423$	474.426	+	15.4543i	1.12158	+	0.0365351i
$424$	417.729			0.985210
$425$		0			0
$426$	−641.893	−	10.4520i	−1.50679	−	0.0245352i
$427$		−	28.5147i		−	0.0667793i
$428$	137.233			0.320639
$429$	4.57501	−	280.967i	0.0106644	−	0.654935i
$430$		0			0
$431$		−	582.760i		−	1.35211i	−0.736851	−	0.676055i	$-0.763688\pi$
$431$		−	582.760i		−	1.35211i	0.736851	−	0.676055i	$-0.236312\pi$
$432$	12.9705	−	265.334i	0.0300244	−	0.614199i
$433$			756.314i			1.74668i	0.487109	+	0.873341i	$0.338051\pi$
$433$			756.314i			1.74668i	−0.487109	+	0.873341i	$0.661949\pi$
$434$		−	57.8276i		−	0.133243i
$435$		0			0
$436$	88.6099			0.203234
$437$	719.062			1.64545
$438$	492.337	+	8.01676i	1.12406	+	0.0183031i
$439$	243.610			0.554921			0.277461	−	0.960737i	$-0.410507\pi$
$439$	243.610			0.554921			0.277461	+	0.960737i	$0.410507\pi$
$440$		0			0
$441$	−432.019	−	14.0729i	−0.979636	−	0.0319114i
$442$		−	79.0869i		−	0.178930i
$443$	719.320			1.62375			0.811874	−	0.583833i	$-0.198448\pi$
$443$	719.320			1.62375			0.811874	+	0.583833i	$0.198448\pi$
$444$	68.8098	+	1.12043i	0.154977	+	0.00252350i
$445$		0			0
$446$			441.924i			0.990862i
$447$	208.549	+	3.39582i	0.466553	+	0.00759692i
$448$		−	69.0690i		−	0.154172i
$449$			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
$452$	−192.683			−0.426290
$453$	−0.469919	+	28.8594i	−0.00103735	+	0.0637073i
$454$	235.739			0.519249
$455$		0			0
$456$	9.03592	−	554.927i	0.0198156	−	1.21695i
$457$		−	220.079i		−	0.481573i	−0.970578	−	0.240786i	$-0.922595\pi$
$457$		−	220.079i		−	0.481573i	0.970578	−	0.240786i	$-0.0774053\pi$
$458$	424.443			0.926731
$459$	7.12232	−	145.699i	0.0155170	−	0.317427i
$460$		0			0
$461$		−	75.3071i		−	0.163356i	−0.996659	−	0.0816779i	$-0.973972\pi$
$461$		−	75.3071i		−	0.163356i	0.996659	−	0.0816779i	$-0.0260279\pi$
$462$	−0.866736	+	53.2293i	−0.00187605	+	0.115215i
$463$		−	832.748i		−	1.79859i	−0.437342	−	0.899295i	$-0.644080\pi$
$463$		−	832.748i		−	1.79859i	0.437342	−	0.899295i	$-0.355920\pi$
$464$			345.790i			0.745237i
$465$		0			0
$466$	−531.199			−1.13991
$467$	322.907			0.691451			0.345725	−	0.938336i	$-0.387633\pi$
$467$	322.907			0.691451			0.345725	+	0.938336i	$0.387633\pi$
$468$	−3.03765	+	93.2517i	−0.00649071	+	0.199256i
$469$	−89.6393			−0.191129
$470$		0			0
$471$	694.281	+	11.3050i	1.47406	+	0.0240022i
$472$			817.036i			1.73101i
$473$	−312.990			−0.661713
$474$	3.42323	−	210.232i	0.00722200	−	0.443528i
$475$		0			0
$476$		−	6.32726i		−	0.0132926i
$477$	431.918	+	14.0696i	0.905489	+	0.0294961i
$478$			109.249i			0.228555i
$479$		−	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
$482$	296.855			0.615882
$483$	100.019	+	1.62861i	0.207078	+	0.00337186i
$484$	−6.94641			−0.0143521
$485$		0			0
$486$	33.1382	−	406.163i	0.0681857	−	0.835727i
$487$		−	391.799i		−	0.804515i	−0.915526	−	0.402258i	$-0.868226\pi$
$487$		−	391.799i		−	0.804515i	0.915526	−	0.402258i	$-0.131774\pi$
$488$	−251.569			−0.515510
$489$	711.724	+	11.5890i	1.45547	+	0.0236995i
$490$		0			0
$491$			501.930i			1.02226i	0.859503	+	0.511130i	$0.170773\pi$
$491$			501.930i			1.02226i	−0.859503	+	0.511130i	$0.829227\pi$
$492$	−187.784	−	3.05769i	−0.381674	−	0.00621482i
$493$			189.879i			0.385149i
$494$		−	311.286i		−	0.630134i
$495$		0			0
$496$	−344.057			−0.693662
$497$	−125.829			−0.253178
$498$	7.97030	−	489.484i	0.0160046	−	0.982900i
$499$	444.402			0.890585			0.445293	−	0.895385i	$-0.353100\pi$
$499$	444.402			0.890585			0.445293	+	0.895385i	$0.353100\pi$
$500$		0			0
$501$	−2.66293	+	163.540i	−0.00531522	+	0.326426i
$502$		−	806.636i		−	1.60685i
$503$	624.696			1.24194			0.620971	−	0.783834i	$-0.286739\pi$
$503$	624.696			1.24194			0.620971	+	0.783834i	$0.286739\pi$
$504$	2.51372	−	77.1676i	0.00498754	−	0.153110i
$505$		0			0
$506$			608.511i			1.20259i
$507$	4.53294	−	278.384i	0.00894071	−	0.549080i
$508$		−	277.358i		−	0.545980i
$509$		−	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
$512$	−522.425			−1.02036
$513$	28.0335	−	573.472i	0.0546462	−	1.11788i
$514$	−383.598			−0.746300
$515$		0			0
$516$	103.908	+	1.69193i	0.201371	+	0.00327894i
$517$			565.966i			1.09471i
$518$	−31.9413			−0.0616628
$519$	−10.1180	+	621.382i	−0.0194952	+	1.19727i
$520$		0			0
$521$		−	813.374i		−	1.56118i	−0.625044	−	0.780589i	$-0.714919\pi$
$521$		−	813.374i		−	1.56118i	0.625044	−	0.780589i	$-0.285081\pi$
$522$	−17.2700	+	530.166i	−0.0330844	+	1.01564i
$523$		−	170.814i		−	0.326605i	−0.986576	−	0.163303i	$-0.947785\pi$
$523$		−	170.814i		−	0.326605i	0.986576	−	0.163303i	$-0.0522147\pi$
$524$			34.9585i			0.0667146i
$525$		0			0
$526$	271.177			0.515545
$527$	−188.927			−0.358495
$528$	316.698	+	5.15682i	0.599807	+	0.00976670i
$529$	614.401			1.16144
$530$		0			0
$531$	−27.5188	+	844.788i	−0.0518245	+	1.59094i
$532$		−	24.9041i		−	0.0468122i
$533$	−460.114			−0.863254
$534$	−441.325	−	7.18613i	−0.826452	−	0.0134572i
$535$		0			0
$536$			790.835i			1.47544i
$537$	−188.323	−	3.06648i	−0.350695	−	0.00571038i
$538$		−	45.4993i		−	0.0845713i
$539$		−	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	$0.373686\pi$
$542$	−77.2183			−0.142469
$543$	−6.82996	+	419.452i	−0.0125782	+	0.772471i
$544$	−98.8637			−0.181735
$545$		0			0
$546$	0.705035	−	43.2987i	0.00129127	−	0.0793016i
$547$			515.125i			0.941728i	0.882206	+	0.470864i	$0.156058\pi$
$547$			515.125i			0.941728i	−0.882206	+	0.470864i	$0.843942\pi$
$548$	65.6875			0.119868
$549$	−260.114	−	8.47316i	−0.473796	−	0.0154338i
$550$		0			0
$551$			747.363i			1.35638i
$552$	14.3683	−	882.406i	0.0260295	−	1.59856i
$553$		−	41.2115i		−	0.0745235i
$554$			157.162i			0.283685i
$555$		0			0
$556$	217.932			0.391963
$557$	688.047			1.23527			0.617637	−	0.786464i	$-0.288090\pi$
$557$	688.047			1.23527			0.617637	+	0.786464i	$0.288090\pi$
$558$	−527.509	−	17.1835i	−0.945356	−	0.0307948i
$559$	254.598			0.455453
$560$		0			0
$561$	173.904	+	2.83169i	0.309989	+	0.00504757i
$562$			326.251i			0.580517i
$563$	523.680			0.930159			0.465079	−	0.885269i	$-0.346026\pi$
$563$	523.680			0.930159			0.465079	+	0.885269i	$0.346026\pi$
$564$	3.05945	−	187.891i	0.00542455	−	0.333141i
$565$		0			0
$566$		−	337.939i		−	0.597066i
$567$	5.19821	−	79.7042i	0.00916791	−	0.140572i
$568$			1110.12i			1.95443i
$569$			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	$0.539934\pi$
$572$	−111.244			−0.194483
$573$	−491.415	−	8.00175i	−0.857618	−	0.0139647i
$574$	87.1687			0.151862
$575$		0			0
$576$	−630.054	−	20.5239i	−1.09384	−	0.0356317i
$577$			175.636i			0.304394i	0.988350	+	0.152197i	$0.0486349\pi$
$577$			175.636i			0.304394i	−0.988350	+	0.152197i	$0.951365\pi$
$578$	−435.705			−0.753814
$579$	−937.602	−	15.2670i	−1.61935	−	0.0263679i
$580$		0			0
$581$		−	95.9527i		−	0.165151i
$582$	−427.803	−	6.96594i	−0.735056	−	0.0119690i
$583$			515.256i			0.883802i
$584$		−	851.469i		−	1.45799i
$585$		0			0
$586$	−672.702			−1.14796
$587$	523.786			0.892311			0.446155	−	0.894955i	$-0.352793\pi$
$587$	523.786			0.892311			0.446155	+	0.894955i	$0.352793\pi$
$588$	−2.78598	+	171.096i	−0.00473805	+	0.290980i
$589$	−743.617			−1.26251
$590$		0			0
$591$	−9.95576	+	611.418i	−0.0168456	+	1.03455i
$592$			190.041i			0.321016i
$593$	−649.656			−1.09554			−0.547771	−	0.836629i	$-0.684523\pi$
$593$	−649.656			−1.09554			−0.547771	+	0.836629i	$0.684523\pi$
$594$	485.305	+	23.7235i	0.817012	+	0.0399386i
$595$		0			0
$596$		−	82.5717i		−	0.138543i
$597$	7.41819	−	455.577i	0.0124258	−	0.763111i
$598$		−	494.985i		−	0.827735i
$599$		−	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	$0.437716\pi$
$602$	−48.2336			−0.0801223
$603$	−26.6363	+	817.698i	−0.0441730	+	1.35605i
$604$	11.4264			0.0189179
$605$		0			0
$606$	163.091	+	2.65563i	0.269128	+	0.00438223i
$607$		−	623.998i		−	1.02800i	−0.857789	−	0.514001i	$-0.828163\pi$
$607$		−	623.998i		−	1.02800i	0.857789	−	0.514001i	$-0.171837\pi$
$608$	−389.128			−0.640013
$609$	−1.69271	+	103.955i	−0.00277949	+	0.170698i
$610$		0			0
$611$		−	460.378i		−	0.753483i
$612$	−57.7178	−	1.88015i	−0.0943102	−	0.00307213i
$613$		−	947.803i		−	1.54617i	−0.634302	−	0.773086i	$-0.718712\pi$
$613$		−	947.803i		−	1.54617i	0.634302	−	0.773086i	$-0.281288\pi$
$614$		−	513.059i		−	0.835601i
$615$		0			0
$616$	92.0570			0.149443
$617$	−429.729			−0.696482			−0.348241	−	0.937405i	$-0.613221\pi$
$617$	−429.729			−0.696482			−0.348241	+	0.937405i	$0.613221\pi$
$618$	−186.249	−	3.03271i	−0.301374	−	0.00490730i
$619$	−687.130			−1.11006			−0.555032	−	0.831829i	$-0.687294\pi$
$619$	−687.130			−1.11006			−0.555032	+	0.831829i	$0.687294\pi$
$620$		0			0
$621$	44.5769	−	911.895i	0.0717824	−	1.46843i
$622$			417.441i			0.671128i
$623$	−86.5123			−0.138864
$624$	−257.614	−	4.19475i	−0.412843	−	0.00672235i
$625$		0			0
$626$			67.6541i			0.108074i
$627$	684.486	+	11.1455i	1.09168	+	0.0177760i
$628$		−	274.889i		−	0.437722i
$629$			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	$0.857405\pi$
$632$	−363.585			−0.575293
$633$	−10.7567	+	660.606i	−0.0169932	+	1.04361i
$634$	507.373			0.800273
$635$		0			0
$636$	2.78532	−	171.056i	0.00437944	−	0.268957i
$637$			419.227i			0.658127i
$638$	−632.461			−0.991319
$639$	−37.3902	+	1147.83i	−0.0585136	+	1.79629i
$640$		0			0
$641$			344.531i			0.537490i	0.963211	+	0.268745i	$0.0866089\pi$
$641$			344.531i			0.537490i	−0.963211	+	0.268745i	$0.913391\pi$
$642$	−9.46473	+	581.262i	−0.0147426	+	0.905393i
$643$		−	444.434i		−	0.691189i	−0.938384	−	0.345594i	$-0.887677\pi$
$643$		−	444.434i		−	0.691189i	0.938384	−	0.345594i	$-0.112323\pi$
$644$		−	39.6007i		−	0.0614918i
$645$		0			0
$646$	192.670			0.298250
$647$	203.910			0.315162			0.157581	−	0.987506i	$-0.449630\pi$
$647$	203.910			0.315162			0.157581	+	0.987506i	$0.449630\pi$
$648$	−703.183	−	45.8608i	−1.08516	−	0.0707728i
$649$	−1007.79			−1.55283
$650$		0			0
$651$	−103.434	−	1.68422i	−0.158885	−	0.00258713i
$652$		−	281.796i		−	0.432202i
$653$	−587.575			−0.899809			−0.449904	−	0.893077i	$-0.648542\pi$
$653$	−587.575			−0.899809			−0.449904	+	0.893077i	$0.648542\pi$
$654$	−6.11127	+	375.314i	−0.00934444	+	0.573875i
$655$		0			0
$656$		−	518.627i		−	0.790590i
$657$	28.6786	−	880.391i	0.0436508	−	1.34002i
$658$			87.2186i			0.132551i
$659$		−	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	$0.290257\pi$
$662$	−11.9719			−0.0180844
$663$	−141.460	−	2.30340i	−0.213363	−	0.00347421i
$664$	−846.535			−1.27490
$665$		0			0
$666$	−9.49137	+	291.372i	−0.0142513	+	0.437495i
$667$			1188.40i			1.78172i
$668$	64.7509			0.0969325
$669$	790.454	+	12.8710i	1.18155	+	0.0192392i
$670$		0			0
$671$		−	310.303i		−	0.462449i
$672$	−54.1261	−	0.881340i	−0.0805448	−	0.00131152i
$673$		−	627.941i		−	0.933047i	−0.884509	−	0.466523i	$-0.845506\pi$
$673$		−	627.941i		−	0.933047i	0.884509	−	0.466523i	$-0.154494\pi$
$674$		−	109.647i		−	0.162680i
$675$		0			0
$676$	−110.221			−0.163050
$677$	−592.236			−0.874794			−0.437397	−	0.899268i	$-0.644100\pi$
$677$	−592.236			−0.874794			−0.437397	+	0.899268i	$0.644100\pi$
$678$	13.2890	−	816.125i	0.0196003	−	1.20372i
$679$	−83.8615			−0.123507
$680$		0			0
$681$	6.86588	−	421.658i	0.0100821	−	0.619175i
$682$		−	629.291i		−	0.922714i
$683$	−668.583			−0.978891			−0.489446	−	0.872034i	$-0.662801\pi$
$683$	−668.583			−0.978891			−0.489446	+	0.872034i	$0.662801\pi$
$684$	−227.178	−	7.40026i	−0.332131	−	0.0108191i
$685$		0			0
$686$		−	160.453i		−	0.233897i
$687$	12.3619	−	759.185i	0.0179940	−	1.10507i
$688$			286.975i			0.417115i
$689$		−	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	$0.316230\pi$
$692$	246.026			0.355529
$693$	95.1840	+	3.10060i	0.137351	+	0.00447417i
$694$	186.035			0.268062
$695$		0			0
$696$	917.136	+	14.9338i	1.31772	+	0.0214566i
$697$		−	284.786i		−	0.408589i
$698$	−0.413767			−0.000592790
$699$	−15.4711	+	950.136i	−0.0221332	+	1.35928i
$700$		0			0
$701$		−	682.125i		−	0.973074i	−0.873660	−	0.486537i	$-0.838260\pi$
$701$		−	682.125i		−	0.973074i	0.873660	−	0.486537i	$-0.161740\pi$
$702$	−394.765	−	19.2976i	−0.562343	−	0.0274895i
$703$			410.740i			0.584267i
$704$		−	751.622i		−	1.06765i
$705$		0			0
$706$	−143.869			−0.203781
$707$	31.9705			0.0452200
$708$	334.569	+	5.44781i	0.472555	+	0.00769465i
$709$	106.898			0.150773			0.0753867	−	0.997154i	$-0.475981\pi$
$709$	106.898			0.150773			0.0753867	+	0.997154i	$0.475981\pi$
$710$		0			0
$711$	−375.935	−	12.2460i	−0.528742	−	0.0172236i
$712$			763.247i			1.07198i
$713$	−1182.45			−1.65841
$714$	26.7996	+	0.436379i	0.0375344	+	0.000611175i
$715$		0			0
$716$			74.5635i			0.104139i
$717$	195.410	+	3.18188i	0.272539	+	0.00443777i
$718$			1070.94i			1.49156i
$719$		−	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
$722$	152.949			0.211841
$723$	8.64588	−	530.974i	0.0119583	−	0.734404i
$724$	166.075			0.229386
$725$		0			0
$726$	0.479081	−	29.4221i	0.000659892	−	0.0405263i
$727$			501.862i			0.690319i	0.938544	+	0.345160i	$0.112175\pi$
$727$			501.862i			0.690319i	−0.938544	+	0.345160i	$0.887825\pi$
$728$	−74.8826			−0.102861
$729$	−725.524	−	71.1026i	−0.995232	−	0.0975345i
$730$		0			0
$731$			157.583i			0.215571i
$732$	−1.67741	+	103.015i	−0.00229154	+	0.140731i
$733$			102.508i			0.139847i	0.997552	+	0.0699237i	$0.0222756\pi$
$733$			102.508i			0.139847i	−0.997552	+	0.0699237i	$0.977724\pi$
$734$			426.157i			0.580596i
$735$		0			0
$736$	−618.764			−0.840712
$737$	−975.472			−1.32357
$738$	25.9022	−	795.161i	0.0350978	−	1.07745i
$739$	228.683			0.309449			0.154724	−	0.987958i	$-0.450551\pi$
$739$	228.683			0.309449			0.154724	+	0.987958i	$0.450551\pi$
$740$		0			0
$741$	−556.786	−	9.06619i	−0.751399	−	0.0122351i
$742$			79.4039i			0.107013i
$743$	−597.078			−0.803605			−0.401802	−	0.915726i	$-0.631616\pi$
$743$	−597.078			−0.803605			−0.401802	+	0.915726i	$0.631616\pi$
$744$	−14.8589	+	912.539i	−0.0199717	+	1.22653i
$745$		0			0
$746$		−	732.040i		−	0.981286i
$747$	−875.290	−	28.5124i	−1.17174	−	0.0381692i
$748$		−	68.8544i		−	0.0920514i
$749$			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	$0.427366\pi$
$752$	518.924			0.690059
$753$	−1442.80	−	23.4932i	−1.91607	−	0.0311995i
$754$	514.468			0.682318
$755$		0			0
$756$	−31.5827	−	1.54388i	−0.0417761	−	0.00204217i
$757$		−	244.894i		−	0.323506i	−0.986831	−	0.161753i	$-0.948285\pi$
$757$		−	244.894i		−	0.323506i	0.986831	−	0.161753i	$-0.0517148\pi$
$758$	451.662			0.595861
$759$	1088.42	+	17.7228i	1.43402	+	0.0233502i
$760$		0			0
$761$		−	551.072i		−	0.724142i	−0.932151	−	0.362071i	$-0.882070\pi$
$761$		−	551.072i		−	0.724142i	0.932151	−	0.362071i	$-0.117930\pi$
$762$	1174.77	+	19.1289i	1.54169	+	0.0251035i
$763$			73.5722i			0.0964249i
$764$			194.568i			0.254670i
$765$		0			0
$766$	1057.28			1.38026
$767$	819.773			1.06880
$768$	−10.0585	+	617.727i	−0.0130970	+	0.804331i
$769$	903.877			1.17539			0.587696	−	0.809082i	$-0.300035\pi$
$769$	903.877			1.17539			0.587696	+	0.809082i	$0.300035\pi$
$770$		0			0
$771$	−11.1723	+	686.128i	−0.0144906	+	0.889919i
$772$			371.228i			0.480866i
$773$	438.057			0.566697			0.283349	−	0.959017i	$-0.408555\pi$
$773$	438.057			0.566697			0.283349	+	0.959017i	$0.408555\pi$
$774$	−14.3326	+	439.992i	−0.0185176	+	0.568465i
$775$		0			0
$776$			739.861i			0.953429i
$777$	−0.930289	+	57.1323i	−0.00119728	+	0.0735293i
$778$			103.923i			0.133578i
$779$		−	1120.92i		−	1.43892i
$780$		0			0
$781$	−1369.30			−1.75326
$782$	306.370			0.391777
$783$	947.786	+	46.3314i	1.21045	+	0.0591716i
$784$	−472.540			−0.602730
$785$		0			0
$786$	−148.069	−	2.41102i	−0.188383	−	0.00306746i
$787$		−	678.254i		−	0.861822i	−0.902394	−	0.430911i	$-0.858192\pi$
$787$		−	678.254i		−	0.861822i	0.902394	−	0.430911i	$-0.141808\pi$
$788$	242.081			0.307210
$789$	7.89800	−	485.043i	0.0100101	−	0.614757i
$790$		0			0
$791$		−	159.984i		−	0.202255i
$792$	27.3548	−	839.753i	0.0345388	−	1.06029i
$793$			252.412i			0.318300i
$794$		−	858.572i		−	1.08133i
$795$		0			0
$796$	−180.378			−0.226606
$797$	1248.06			1.56595			0.782973	−	0.622056i	$-0.213702\pi$
$797$	1248.06			1.56595			0.782973	+	0.622056i	$0.213702\pi$
$798$	105.483	+	1.71759i	0.132184	+	0.00215237i
$799$	284.950			0.356633
$800$		0			0
$801$	−25.7071	+	789.173i	−0.0320938	+	0.985235i
$802$		−	676.577i		−	0.843612i
$803$	1050.26			1.30792
$804$	323.840	+	5.27311i	0.402786	+	0.00655860i
$805$		0			0
$806$			511.889i			0.635098i
$807$	−81.3830	−	1.32517i	−0.100846	−	0.00164209i
$808$		−	282.057i		−	0.349081i
$809$		−	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	$0.645492\pi$
$812$	41.1594			0.0506889
$813$	−2.24898	+	138.118i	−0.00276627	+	0.169886i
$814$	−347.592			−0.427017
$815$		0			0
$816$	2.59632	−	159.449i	0.00318177	−	0.195404i
$817$			620.246i			0.759175i
$818$	−340.929			−0.416784
$819$	−77.4262	−	2.52214i	−0.0945375	−	0.00307954i
$820$		0			0
$821$			1391.14i			1.69445i	0.531238	+	0.847223i	$0.321727\pi$
$821$			1391.14i			1.69445i	−0.531238	+	0.847223i	$0.678273\pi$
$822$	−4.53035	+	278.224i	−0.00551137	+	0.338472i
$823$		−	140.224i		−	0.170382i	−0.996365	−	0.0851910i	$-0.972850\pi$
$823$		−	140.224i		−	0.170382i	0.996365	−	0.0851910i	$-0.0271501\pi$
$824$			322.108i			0.390908i
$825$		0			0
$826$	−155.306			−0.188022
$827$	−926.931			−1.12084			−0.560418	−	0.828210i	$-0.689359\pi$
$827$	−926.931			−1.12084			−0.560418	+	0.828210i	$0.689359\pi$
$828$	−361.242	−	11.7674i	−0.436282	−	0.0142118i
$829$	1423.22			1.71679			0.858394	−	0.512991i	$-0.171463\pi$
$829$	1423.22			1.71679			0.858394	+	0.512991i	$0.171463\pi$
$830$		0			0
$831$	281.109	+	4.57732i	0.338278	+	0.00550821i
$832$			611.398i			0.734853i
$833$	−259.479			−0.311500
$834$	−15.0304	+	923.066i	−0.0180220	+	1.10679i
$835$		0			0
$836$		−	271.011i		−	0.324176i
$837$	−46.0991	+	943.035i	−0.0550766	+	1.12668i
$838$		−	106.332i		−	0.126888i
$839$		−	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
$842$	−1117.41			−1.32709
$843$	583.552	+	9.50202i	0.692233	+	0.0112717i
$844$	261.556			0.309901
$845$		0			0
$846$	795.617	+	25.9170i	0.940445	+	0.0306348i
$847$		−	5.76756i		−	0.00680939i
$848$	472.429			0.557110
$849$	−604.460	−	9.84246i	−0.711967	−	0.0115930i
$850$		0			0
$851$			653.130i			0.767485i
$852$	454.584	+	7.40202i	0.533549	+	0.00868782i
$853$			559.803i			0.656275i	0.944630	+	0.328138i	$0.106421\pi$
$853$			559.803i			0.656275i	−0.944630	+	0.328138i	$0.893579\pi$
$854$		−	47.8195i		−	0.0559947i
$855$		0			0
$856$	1005.26			1.17437
$857$	−733.960			−0.856429			−0.428214	−	0.903677i	$-0.640857\pi$
$857$	−733.960			−0.856429			−0.428214	+	0.903677i	$0.640857\pi$
$858$	7.67233	−	471.184i	0.00894211	−	0.549166i
$859$	359.689			0.418730			0.209365	−	0.977838i	$-0.432860\pi$
$859$	359.689			0.418730			0.209365	+	0.977838i	$0.432860\pi$
$860$		0			0
$861$	2.53878	−	155.915i	0.00294864	−	0.181086i
$862$		−	977.292i		−	1.13375i
$863$	867.952			1.00574			0.502869	−	0.864362i	$-0.332278\pi$
$863$	867.952			1.00574			0.502869	+	0.864362i	$0.332278\pi$
$864$	−24.1233	+	493.482i	−0.0279204	+	0.571159i
$865$		0			0
$866$			1268.34i			1.46460i
$867$	−12.6899	+	779.329i	−0.0146365	+	0.898880i
$868$			40.9530i			0.0471809i
$869$		−	448.472i		−	0.516078i
$870$		0			0
$871$	793.485			0.911005
$872$	649.085			0.744363
$873$	−24.9194	+	764.992i	−0.0285446	+	0.876280i
$874$	1205.87			1.37972
$875$		0			0
$876$	−348.669	−	5.67740i	−0.398024	−	0.00648106i
$877$		−	441.711i		−	0.503661i	−0.967771	−	0.251831i	$-0.918967\pi$
$877$		−	441.711i		−	0.503661i	0.967771	−	0.251831i	$-0.0810326\pi$
$878$	408.537			0.465304
$879$	−19.5924	+	1203.24i	−0.0222894	+	1.36887i
$880$		0			0
$881$		−	610.857i		−	0.693368i	−0.937982	−	0.346684i	$-0.887308\pi$
$881$		−	610.857i		−	0.693368i	0.937982	−	0.346684i	$-0.112692\pi$
$882$	−724.500	−	23.6004i	−0.821429	−	0.0267579i
$883$		−	145.758i		−	0.165071i	−0.996588	−	0.0825356i	$-0.973698\pi$
$883$		−	145.758i		−	0.165071i	0.996588	−	0.0825356i	$-0.0263018\pi$
$884$			56.0087i			0.0633583i
$885$		0			0
$886$	1206.31			1.36152
$887$	−1104.66			−1.24539			−0.622693	−	0.782466i	$-0.713961\pi$
$887$	−1104.66			−1.24539			−0.622693	+	0.782466i	$0.713961\pi$
$888$	504.045	+	8.20740i	0.567618	+	0.00924256i
$889$	230.288			0.259042
$890$		0			0
$891$	56.5679	−	867.356i	0.0634881	−	0.973464i
$892$		−	312.967i		−	0.350860i
$893$	1121.56			1.25595
$894$	349.739	+	5.69482i	0.391207	+	0.00637004i
$895$		0			0
$896$		−	43.6516i		−	0.0487183i
$897$	−885.362	−	14.4164i	−0.987026	−	0.0160718i
$898$			854.073i			0.951083i
$899$		−	1228.99i		−	1.36706i
$900$		0			0
$901$	259.418			0.287923
$902$	948.586			1.05165
$903$	−1.40480	+	86.2737i	−0.00155570	+	0.0955412i
$904$	−1411.44			−1.56133
$905$		0			0
$906$	−0.788059	+	48.3974i	−0.000869822	+	0.0534188i
$907$		−	438.512i		−	0.483475i	−0.970342	−	0.241737i	$-0.922283\pi$
$907$		−	438.512i		−	0.483475i	0.970342	−	0.241737i	$-0.0777172\pi$
$908$	−166.949			−0.183864
$909$	9.50005	−	291.638i	0.0104511	−	0.320834i
$910$		0			0
$911$			870.840i			0.955917i	0.878383	+	0.477958i	$0.158623\pi$
$911$			870.840i			0.955917i	−0.878383	+	0.477958i	$0.841377\pi$
$912$	10.2191	−	627.593i	0.0112052	−	0.688150i
$913$		−	1044.18i		−	1.14368i
$914$		−	369.074i		−	0.403801i
$915$		0			0
$916$	−300.587			−0.328152
$917$	−29.0258			−0.0316530
$918$	11.9442	−	244.339i	0.0130111	−	0.266164i
$919$	−916.817			−0.997625			−0.498812	−	0.866710i	$-0.666230\pi$
$919$	−916.817			−0.997625			−0.498812	+	0.866710i	$0.666230\pi$
$920$		0			0
$921$	−917.689	−	14.9428i	−0.996406	−	0.0162245i
$922$		−	126.291i		−	0.136975i
$923$	1113.84			1.20676
$924$	0.613816	−	37.6966i	0.000664303	−	0.0407971i
$925$		0			0
$926$		−	1396.52i		−	1.50813i
$927$	−10.8490	+	333.049i	−0.0117033	+	0.359276i
$928$		−	643.118i		−	0.693015i
$929$			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
$932$	376.191			0.403639
$933$	746.662	+	12.1580i	0.800281	+	0.0130310i
$934$	541.518			0.579784
$935$		0			0
$936$	−22.2514	+	683.086i	−0.0237728	+	0.729793i
$937$			649.421i			0.693085i	0.938034	+	0.346542i	$0.112644\pi$
$937$			649.421i			0.693085i	−0.938034	+	0.346542i	$0.887356\pi$
$938$	−150.326			−0.160262
$939$	121.010	+	1.97042i	0.128872	+	0.00209842i
$940$		0			0
$941$		−	87.3770i		−	0.0928555i	−0.998922	−	0.0464277i	$-0.985216\pi$
$941$		−	87.3770i		−	0.0928555i	0.998922	−	0.0464277i	$-0.0147837\pi$
$942$	1164.31	+	18.9586i	1.23600	+	0.0201259i
$943$		−	1782.41i		−	1.89015i
$944$			924.024i			0.978839i
$945$		0			0
$946$	−524.887			−0.554849
$947$	152.556			0.161094			0.0805470	−	0.996751i	$-0.474333\pi$
$947$	152.556			0.161094			0.0805470	+	0.996751i	$0.474333\pi$
$948$	−2.42430	+	148.885i	−0.00255728	+	0.157052i
$949$	−854.322			−0.900234
$950$		0			0
$951$	14.7772	−	907.519i	0.0155386	−	0.954279i
$952$		−	46.3484i		−	0.0486853i
$953$	940.275			0.986647			0.493323	−	0.869846i	$-0.335782\pi$
$953$	940.275			0.986647			0.493323	+	0.869846i	$0.335782\pi$
$954$	724.330	+	23.5949i	0.759256	+	0.0247326i
$955$		0			0
$956$		−	77.3695i		−	0.0809305i
$957$	−18.4204	+	1131.26i	−0.0192481	+	1.18209i
$958$		−	21.0330i		−	0.0219551i
$959$			54.5399i			0.0568716i
$960$		0			0
$961$	261.826			0.272451
$962$	282.744			0.293913
$963$	1039.41	+	33.8584i	1.07934	+	0.0351593i
$964$	−210.231			−0.218081
$965$		0			0
$966$	167.732	+	2.73119i	0.173636	+	0.00282732i
$967$		−	569.336i		−	0.588765i	−0.955688	−	0.294383i	$-0.904886\pi$
$967$		−	569.336i		−	0.588765i	0.955688	−	0.294383i	$-0.0951140\pi$
$968$	−50.8838			−0.0525659
$969$	5.61149	−	344.621i	0.00579101	−	0.355646i
$970$		0			0
$971$		−	733.809i		−	0.755725i	−0.925862	−	0.377862i	$-0.876659\pi$
$971$		−	733.809i		−	0.755725i	0.925862	−	0.377862i	$-0.123341\pi$
$972$	−23.4683	+	287.642i	−0.0241443	+	0.295928i
$973$			180.947i			0.185968i
$974$		−	657.050i		−	0.674589i
$975$		0			0
$976$	−284.511			−0.291507
$977$	−917.699			−0.939303			−0.469652	−	0.882852i	$-0.655621\pi$
$977$	−917.699			−0.939303			−0.469652	+	0.882852i	$0.655621\pi$
$978$	1193.57	+	19.4349i	1.22042	+	0.0198721i
$979$	−941.443			−0.961637
$980$		0			0
$981$	671.133	+	21.8620i	0.684131	+	0.0222854i
$982$			841.740i			0.857169i
$983$	−629.515			−0.640402			−0.320201	−	0.947350i	$-0.603750\pi$
$983$	−629.515			−0.640402			−0.320201	+	0.947350i	$0.603750\pi$
$984$	−1375.55	−	22.3982i	−1.39792	−	0.0227624i
$985$		0			0
$986$			318.428i			0.322949i
$987$	156.005	+	2.54024i	0.158060	+	0.00257369i
$988$			220.451i			0.223128i
$989$			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	$0.559345\pi$
$992$	639.894			0.645054
$993$	−0.348680	+	21.4137i	−0.000351138	+	0.0215646i
$994$	−211.017			−0.212290
$995$		0			0
$996$	−5.64451	+	346.649i	−0.00566718	+	0.348041i
$997$		−	1777.46i		−	1.78281i	−0.453212	−	0.891403i	$-0.649722\pi$
$997$		−	1777.46i		−	1.78281i	0.453212	−	0.891403i	$-0.350278\pi$
$998$	745.266			0.746759
$999$	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.d.e.374.21		32
3.2	odd	2	inner	375.3.d.e.374.11		32
5.2	odd	4		375.3.c.c.251.21	yes	32
5.3	odd	4		375.3.c.c.251.12	yes	32
5.4	even	2	inner	375.3.d.e.374.12		32
15.2	even	4		375.3.c.c.251.11	✓	32
15.8	even	4		375.3.c.c.251.22	yes	32
15.14	odd	2	inner	375.3.d.e.374.22		32

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

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

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Database

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