LMFDB - Embedded newform 230.3.c.a.229.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,3,Mod(229,230)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(230, 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("230.229");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	230.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:	$6.26704608029$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			229.8
Character	$\chi$	$=$	230.229
Dual form			230.3.c.a.229.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421i q^{2} +1.47600i q^{3} -2.00000 q^{4} +(4.75172 - 1.55601i) q^{5} +2.08738 q^{6} -0.788814 q^{7} +2.82843i q^{8} +6.82142 q^{9} +O(q^{10})$	\(q-1.41421i q^{2} +1.47600i q^{3} -2.00000 q^{4} +(4.75172 - 1.55601i) q^{5} +2.08738 q^{6} -0.788814 q^{7} +2.82843i q^{8} +6.82142 q^{9} +(-2.20053 - 6.71994i) q^{10} +20.2471i q^{11} -2.95200i q^{12} -19.5253i q^{13} +1.11555i q^{14} +(2.29667 + 7.01354i) q^{15} +4.00000 q^{16} +15.2219 q^{17} -9.64694i q^{18} +2.22703i q^{19} +(-9.50344 + 3.11202i) q^{20} -1.16429i q^{21} +28.6337 q^{22} +(16.2476 - 16.2793i) q^{23} -4.17476 q^{24} +(20.1577 - 14.7875i) q^{25} -27.6129 q^{26} +23.3524i q^{27} +1.57763 q^{28} +33.2567 q^{29} +(9.91865 - 3.24799i) q^{30} +15.3208 q^{31} -5.65685i q^{32} -29.8847 q^{33} -21.5270i q^{34} +(-3.74822 + 1.22740i) q^{35} -13.6428 q^{36} +5.15939 q^{37} +3.14950 q^{38} +28.8194 q^{39} +(4.40106 + 13.4399i) q^{40} -63.8101 q^{41} -1.64655 q^{42} -16.4461 q^{43} -40.4941i q^{44} +(32.4135 - 10.6142i) q^{45} +(-23.0224 - 22.9776i) q^{46} -20.8118i q^{47} +5.90401i q^{48} -48.3778 q^{49} +(-20.9126 - 28.5072i) q^{50} +22.4675i q^{51} +39.0506i q^{52} -46.8770 q^{53} +33.0253 q^{54} +(31.5046 + 96.2083i) q^{55} -2.23110i q^{56} -3.28711 q^{57} -47.0321i q^{58} -36.3499 q^{59} +(-4.59335 - 14.0271i) q^{60} +89.3119i q^{61} -21.6669i q^{62} -5.38083 q^{63} -8.00000 q^{64} +(-30.3816 - 92.7787i) q^{65} +42.2633i q^{66} -64.3552 q^{67} -30.4437 q^{68} +(24.0282 + 23.9815i) q^{69} +(1.73581 + 5.30078i) q^{70} +28.5926 q^{71} +19.2939i q^{72} +83.5248i q^{73} -7.29648i q^{74} +(21.8263 + 29.7527i) q^{75} -4.45407i q^{76} -15.9712i q^{77} -40.7567i q^{78} -27.5144i q^{79} +(19.0069 - 6.22404i) q^{80} +26.9246 q^{81} +90.2411i q^{82} +55.6189 q^{83} +2.32858i q^{84} +(72.3300 - 23.6854i) q^{85} +23.2583i q^{86} +49.0869i q^{87} -57.2673 q^{88} +12.2070i q^{89} +(-15.0108 - 45.8396i) q^{90} +15.4018i q^{91} +(-32.4952 + 32.5586i) q^{92} +22.6135i q^{93} -29.4324 q^{94} +(3.46529 + 10.5822i) q^{95} +8.34952 q^{96} +43.7767 q^{97} +68.4165i q^{98} +138.114i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 48 q^{4} + 8 q^{6} - 96 q^{9}+O(q^{10}) $ 24 * q - 48 * q^4 + 8 * q^6 - 96 * q^9	$ 24 q - 48 q^{4} + 8 q^{6} - 96 q^{9} + 96 q^{16} - 16 q^{24} - 48 q^{25} - 32 q^{26} + 100 q^{29} - 124 q^{31} - 28 q^{35} + 192 q^{36} + 192 q^{39} - 116 q^{41} + 148 q^{46} - 76 q^{49} - 144 q^{50} - 16 q^{54} - 224 q^{55} + 84 q^{59} - 192 q^{64} - 340 q^{69} + 328 q^{70} + 196 q^{71} - 496 q^{75} + 1360 q^{81} + 316 q^{85} - 376 q^{94} - 368 q^{95} + 32 q^{96}+O(q^{100}) $ 24 * q - 48 * q^4 + 8 * q^6 - 96 * q^9 + 96 * q^16 - 16 * q^24 - 48 * q^25 - 32 * q^26 + 100 * q^29 - 124 * q^31 - 28 * q^35 + 192 * q^36 + 192 * q^39 - 116 * q^41 + 148 * q^46 - 76 * q^49 - 144 * q^50 - 16 * q^54 - 224 * q^55 + 84 * q^59 - 192 * q^64 - 340 * q^69 + 328 * q^70 + 196 * q^71 - 496 * q^75 + 1360 * q^81 + 316 * q^85 - 376 * q^94 - 368 * q^95 + 32 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$-1$	$-1$

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 $

$2$		−	1.41421i		−	0.707107i
$2$		−	1.41421i		−	0.707107i
$3$			1.47600i			0.492000i	0.969270	+	0.246000i	$0.0791164\pi$
$3$			1.47600i			0.492000i	−0.969270	+	0.246000i	$0.920884\pi$
$4$	−2.00000			−0.500000
$5$	4.75172	−	1.55601i	0.950344	−	0.311202i
$5$	4.75172	−	1.55601i	0.950344	−	0.311202i
$6$	2.08738			0.347897
$7$	−0.788814			−0.112688			−0.0563438	−	0.998411i	$-0.517944\pi$
$7$	−0.788814			−0.112688			−0.0563438	+	0.998411i	$0.517944\pi$
$8$			2.82843i			0.353553i
$9$	6.82142			0.757936
$10$	−2.20053	−	6.71994i	−0.220053	−	0.671994i
$11$			20.2471i			1.84064i	0.391164	+	0.920321i	$0.372073\pi$
$11$			20.2471i			1.84064i	−0.391164	+	0.920321i	$0.627927\pi$
$12$		−	2.95200i		−	0.246000i
$13$		−	19.5253i		−	1.50195i	−0.660333	−	0.750973i	$-0.729585\pi$
$13$		−	19.5253i		−	1.50195i	0.660333	−	0.750973i	$-0.270415\pi$
$14$			1.11555i			0.0796822i
$15$	2.29667	+	7.01354i	0.153112	+	0.467570i
$16$	4.00000			0.250000
$17$	15.2219			0.895404			0.447702	−	0.894183i	$-0.352243\pi$
$17$	15.2219			0.895404			0.447702	+	0.894183i	$0.352243\pi$
$18$		−	9.64694i		−	0.535941i
$19$			2.22703i			0.117212i	0.998281	+	0.0586062i	$0.0186656\pi$
$19$			2.22703i			0.117212i	−0.998281	+	0.0586062i	$0.981334\pi$
$20$	−9.50344	+	3.11202i	−0.475172	+	0.155601i
$21$		−	1.16429i		−	0.0554424i
$22$	28.6337			1.30153
$23$	16.2476	−	16.2793i	0.706418	−	0.707795i
$23$	16.2476	−	16.2793i	0.706418	−	0.707795i
$24$	−4.17476			−0.173948
$25$	20.1577	−	14.7875i	0.806306	−	0.591498i
$26$	−27.6129			−1.06204
$27$			23.3524i			0.864905i
$28$	1.57763			0.0563438
$29$	33.2567			1.14678			0.573391	−	0.819282i	$-0.305628\pi$
$29$	33.2567			1.14678			0.573391	+	0.819282i	$0.305628\pi$
$30$	9.91865	−	3.24799i	0.330622	−	0.108266i
$31$	15.3208			0.494219			0.247109	−	0.968988i	$-0.420519\pi$
$31$	15.3208			0.494219			0.247109	+	0.968988i	$0.420519\pi$
$32$		−	5.65685i		−	0.176777i
$33$	−29.8847			−0.905597
$34$		−	21.5270i		−	0.633146i
$35$	−3.74822	+	1.22740i	−0.107092	+	0.0350686i
$36$	−13.6428			−0.378968
$37$	5.15939			0.139443			0.0697215	−	0.997566i	$-0.477789\pi$
$37$	5.15939			0.139443			0.0697215	+	0.997566i	$0.477789\pi$
$38$	3.14950			0.0828816
$39$	28.8194			0.738958
$40$	4.40106	+	13.4399i	0.110027	+	0.335997i
$41$	−63.8101			−1.55634			−0.778172	−	0.628051i	$-0.783853\pi$
$41$	−63.8101			−1.55634			−0.778172	+	0.628051i	$0.783853\pi$
$42$	−1.64655			−0.0392037
$43$	−16.4461			−0.382468			−0.191234	−	0.981545i	$-0.561249\pi$
$43$	−16.4461			−0.382468			−0.191234	+	0.981545i	$0.561249\pi$
$44$		−	40.4941i		−	0.920321i
$45$	32.4135	−	10.6142i	0.720299	−	0.235871i
$46$	−23.0224	−	22.9776i	−0.500487	−	0.499513i
$47$		−	20.8118i		−	0.442805i	−0.975183	−	0.221402i	$-0.928937\pi$
$47$		−	20.8118i		−	0.442805i	0.975183	−	0.221402i	$-0.0710634\pi$
$48$			5.90401i			0.123000i
$49$	−48.3778			−0.987301
$50$	−20.9126	−	28.5072i	−0.418252	−	0.570145i
$51$			22.4675i			0.440539i
$52$			39.0506i			0.750973i
$53$	−46.8770			−0.884472			−0.442236	−	0.896899i	$-0.645815\pi$
$53$	−46.8770			−0.884472			−0.442236	+	0.896899i	$0.645815\pi$
$54$	33.0253			0.611580
$55$	31.5046	+	96.2083i	0.572812	+	1.74924i
$56$		−	2.23110i		−	0.0398411i
$57$	−3.28711			−0.0576685
$58$		−	47.0321i		−	0.810898i
$59$	−36.3499			−0.616100			−0.308050	−	0.951370i	$-0.599676\pi$
$59$	−36.3499			−0.616100			−0.308050	+	0.951370i	$0.599676\pi$
$60$	−4.59335	−	14.0271i	−0.0765558	−	0.233785i
$61$			89.3119i			1.46413i	0.681235	+	0.732064i	$0.261443\pi$
$61$			89.3119i			1.46413i	−0.681235	+	0.732064i	$0.738557\pi$
$62$		−	21.6669i		−	0.349465i
$63$	−5.38083			−0.0854100
$64$	−8.00000			−0.125000
$65$	−30.3816	−	92.7787i	−0.467409	−	1.42737i
$66$			42.2633i			0.640354i
$67$	−64.3552			−0.960525			−0.480262	−	0.877125i	$-0.659459\pi$
$67$	−64.3552			−0.960525			−0.480262	+	0.877125i	$0.659459\pi$
$68$	−30.4437			−0.447702
$69$	24.0282	+	23.9815i	0.348235	+	0.347558i
$70$	1.73581	+	5.30078i	0.0247973	+	0.0757255i
$71$	28.5926			0.402713			0.201356	−	0.979518i	$-0.435465\pi$
$71$	28.5926			0.402713			0.201356	+	0.979518i	$0.435465\pi$
$72$			19.2939i			0.267971i
$73$			83.5248i			1.14418i	0.820192	+	0.572088i	$0.193866\pi$
$73$			83.5248i			1.14418i	−0.820192	+	0.572088i	$0.806134\pi$
$74$		−	7.29648i		−	0.0986011i
$75$	21.8263	+	29.7527i	0.291017	+	0.396703i
$76$		−	4.45407i		−	0.0586062i
$77$		−	15.9712i		−	0.207418i
$78$		−	40.7567i		−	0.522522i
$79$		−	27.5144i		−	0.348283i	−0.984721	−	0.174142i	$-0.944285\pi$
$79$		−	27.5144i		−	0.348283i	0.984721	−	0.174142i	$-0.0557151\pi$
$80$	19.0069	−	6.22404i	0.237586	−	0.0778005i
$81$	26.9246			0.332402
$82$			90.2411i			1.10050i
$83$	55.6189			0.670108			0.335054	−	0.942199i	$-0.391246\pi$
$83$	55.6189			0.670108			0.335054	+	0.942199i	$0.391246\pi$
$84$			2.32858i			0.0277212i
$85$	72.3300	−	23.6854i	0.850941	−	0.278652i
$86$			23.2583i			0.270445i
$87$			49.0869i			0.564217i
$88$	−57.2673			−0.650765
$89$			12.2070i			0.137157i	0.997646	+	0.0685785i	$0.0218464\pi$
$89$			12.2070i			0.137157i	−0.997646	+	0.0685785i	$0.978154\pi$
$90$	−15.0108	−	45.8396i	−0.166786	−	0.509329i
$91$			15.4018i			0.169251i
$92$	−32.4952	+	32.5586i	−0.353209	+	0.353898i
$93$			22.6135i			0.243156i
$94$	−29.4324			−0.313110
$95$	3.46529	+	10.5822i	0.0364767	+	0.111392i
$96$	8.34952			0.0869742
$97$	43.7767			0.451306			0.225653	−	0.974208i	$-0.427548\pi$
$97$	43.7767			0.451306			0.225653	+	0.974208i	$0.427548\pi$
$98$			68.4165i			0.698128i
$99$			138.114i			1.39509i
$100$	−40.3153	+	29.5749i	−0.403153	+	0.295749i
$101$	−108.247			−1.07176			−0.535878	−	0.844296i	$-0.680019\pi$
$101$	−108.247			−1.07176			−0.535878	+	0.844296i	$0.680019\pi$
$102$	31.7738			0.311508
$103$	−193.917			−1.88269			−0.941346	−	0.337442i	$-0.890438\pi$
$103$	−193.917			−1.88269			−0.941346	+	0.337442i	$0.890438\pi$
$104$	55.2259			0.531018
$105$	−1.81165	−	5.53238i	−0.0172538	−	0.0526893i
$106$			66.2941i			0.625416i
$107$	−137.979			−1.28952			−0.644761	−	0.764384i	$-0.723043\pi$
$107$	−137.979			−1.28952			−0.644761	+	0.764384i	$0.723043\pi$
$108$		−	46.7049i		−	0.432453i
$109$		−	171.239i		−	1.57100i	−0.618864	−	0.785498i	$-0.712407\pi$
$109$		−	171.239i		−	1.57100i	0.618864	−	0.785498i	$-0.287593\pi$
$110$	136.059	−	44.5543i	1.23690	−	0.405039i
$111$			7.61527i			0.0686060i
$112$	−3.15525			−0.0281719
$113$	151.232			1.33834			0.669168	−	0.743111i	$-0.266651\pi$
$113$	151.232			1.33834			0.669168	+	0.743111i	$0.266651\pi$
$114$			4.64867i			0.0407778i
$115$	51.8733	−	102.636i	0.451072	−	0.892487i
$116$	−66.5134			−0.573391
$117$		−	133.190i		−	1.13838i
$118$			51.4066i			0.435649i
$119$	−12.0072			−0.100901
$120$	−19.8373	+	6.49598i	−0.165311	+	0.0541331i
$121$	−288.944			−2.38796
$122$	126.306			1.03530
$123$		−	94.1838i		−	0.765722i
$124$	−30.6416			−0.247109
$125$	72.7741	−	101.631i	0.582193	−	0.813051i
$126$			7.60964i			0.0603940i
$127$		−	92.5989i		−	0.729125i	−0.931179	−	0.364563i	$-0.881219\pi$
$127$		−	92.5989i		−	0.729125i	0.931179	−	0.364563i	$-0.118781\pi$
$128$			11.3137i			0.0883883i
$129$		−	24.2745i		−	0.188174i
$130$	−131.209	+	42.9660i	−1.00930	+	0.330508i
$131$	−145.052			−1.10727			−0.553635	−	0.832760i	$-0.686760\pi$
$131$	−145.052			−1.10727			−0.553635	+	0.832760i	$0.686760\pi$
$132$	59.7694			0.452798
$133$		−	1.75672i		−	0.0132084i
$134$			91.0119i			0.679194i
$135$	36.3366	+	110.964i	0.269160	+	0.821957i
$136$			43.0539i			0.316573i
$137$	37.7211			0.275336			0.137668	−	0.990478i	$-0.456039\pi$
$137$	37.7211			0.275336			0.137668	+	0.990478i	$0.456039\pi$
$138$	33.9150	−	33.9811i	0.245761	−	0.246240i
$139$	145.263			1.04506			0.522529	−	0.852621i	$-0.324988\pi$
$139$	145.263			1.04506			0.522529	+	0.852621i	$0.324988\pi$
$140$	7.49644	−	2.45481i	0.0535460	−	0.0175343i
$141$	30.7183			0.217860
$142$		−	40.4360i		−	0.284761i
$143$	395.330			2.76455
$144$	27.2857			0.189484
$145$	158.026	−	51.7478i	1.08984	−	0.356881i
$146$	118.122			0.809054
$147$		−	71.4057i		−	0.485753i
$148$	−10.3188			−0.0697215
$149$		−	196.855i		−	1.32117i	−0.750749	−	0.660587i	$-0.770307\pi$
$149$		−	196.855i		−	1.32117i	0.750749	−	0.660587i	$-0.229693\pi$
$150$	42.0767	−	30.8670i	0.280511	−	0.205780i
$151$	112.921			0.747820			0.373910	−	0.927465i	$-0.378017\pi$
$151$	112.921			0.747820			0.373910	+	0.927465i	$0.378017\pi$
$152$	−6.29900			−0.0414408
$153$	103.835			0.678658
$154$	−22.5866			−0.146666
$155$	72.8000	−	23.8393i	0.469678	−	0.153802i
$156$	−57.6387			−0.369479
$157$	−247.403			−1.57581			−0.787907	−	0.615795i	$-0.788835\pi$
$157$	−247.403			−1.57581			−0.787907	+	0.615795i	$0.788835\pi$
$158$	−38.9112			−0.246273
$159$		−	69.1905i		−	0.435161i
$160$	−8.80213	−	26.8798i	−0.0550133	−	0.167999i
$161$	−12.8163	+	12.8413i	−0.0796046	+	0.0797598i
$162$		−	38.0771i		−	0.235044i
$163$			62.7056i			0.384697i	0.981327	+	0.192348i	$0.0616104\pi$
$163$			62.7056i			0.384697i	−0.981327	+	0.192348i	$0.938390\pi$
$164$	127.620			0.778172
$165$	−142.004	+	46.5009i	−0.860628	+	0.281824i
$166$		−	78.6570i		−	0.473838i
$167$		−	274.062i		−	1.64109i	−0.571581	−	0.820546i	$-0.693670\pi$
$167$		−	274.062i		−	1.64109i	0.571581	−	0.820546i	$-0.306330\pi$
$168$	3.29311			0.0196018
$169$	−212.237			−1.25584
$170$	−33.4962	−	102.290i	−0.197036	−	0.601706i
$171$			15.1915i			0.0888394i
$172$	32.8922			0.191234
$173$		−	4.67107i		−	0.0270004i	−0.999909	−	0.0135002i	$-0.995703\pi$
$173$		−	4.67107i		−	0.0270004i	0.999909	−	0.0135002i	$-0.00429738\pi$
$174$	69.4194			0.398962
$175$	−15.9006	+	11.6645i	−0.0908608	+	0.0666545i
$176$			80.9882i			0.460160i
$177$		−	53.6525i		−	0.303122i
$178$	17.2633			0.0969847
$179$	191.026			1.06719			0.533593	−	0.845742i	$-0.320842\pi$
$179$	191.026			1.06719			0.533593	+	0.845742i	$0.320842\pi$
$180$	−64.8269	+	21.2284i	−0.360150	+	0.117936i
$181$			237.933i			1.31454i	0.753653	+	0.657272i	$0.228290\pi$
$181$			237.933i			1.31454i	−0.753653	+	0.657272i	$0.771710\pi$
$182$	21.7815			0.119678
$183$	−131.824			−0.720352
$184$	46.0448	+	45.9552i	0.250243	+	0.249756i
$185$	24.5160	−	8.02807i	0.132519	−	0.0433950i
$186$	31.9803			0.171937
$187$			308.198i			1.64812i
$188$			41.6236i			0.221402i
$189$		−	18.4207i		−	0.0974641i
$190$	14.9655	−	4.90066i	0.0787661	−	0.0257929i
$191$			304.224i			1.59279i	0.604775	+	0.796397i	$0.293263\pi$
$191$			304.224i			1.59279i	−0.604775	+	0.796397i	$0.706737\pi$
$192$		−	11.8080i		−	0.0615001i
$193$			106.033i			0.549396i	0.961531	+	0.274698i	$0.0885778\pi$
$193$			106.033i			0.549396i	−0.961531	+	0.274698i	$0.911422\pi$
$194$		−	61.9096i		−	0.319122i
$195$	136.942	−	44.8433i	0.702264	−	0.229965i
$196$	96.7555			0.493651
$197$		−	101.263i		−	0.514025i	−0.966408	−	0.257012i	$-0.917262\pi$
$197$		−	101.263i		−	0.514025i	0.966408	−	0.257012i	$-0.0827381\pi$
$198$	195.322			0.986476
$199$			94.9533i			0.477152i	0.971124	+	0.238576i	$0.0766806\pi$
$199$			94.9533i			0.477152i	−0.971124	+	0.238576i	$0.923319\pi$
$200$	41.8252	+	57.0145i	0.209126	+	0.285072i
$201$		−	94.9883i		−	0.472579i
$202$			153.085i			0.757845i
$203$	−26.2333			−0.129228
$204$		−	44.9350i		−	0.220270i
$205$	−303.208	+	99.2892i	−1.47906	+	0.484338i
$206$			274.241i			1.33126i
$207$	110.832	−	111.048i	0.535419	−	0.536463i
$208$		−	78.1012i		−	0.375487i
$209$	−45.0909			−0.215746
$210$	−7.82397	+	2.56206i	−0.0372570	+	0.0122003i
$211$	226.422			1.07309			0.536546	−	0.843871i	$-0.319729\pi$
$211$	226.422			1.07309			0.536546	+	0.843871i	$0.319729\pi$
$212$	93.7540			0.442236
$213$			42.2027i			0.198135i
$214$			195.131i			0.911829i
$215$	−78.1473	+	25.5903i	−0.363476	+	0.119025i
$216$	−66.0507			−0.305790
$217$	−12.0852			−0.0556923
$218$	−242.168			−1.11086
$219$	−123.283			−0.562935
$220$	−63.0093	−	192.417i	−0.286406	−	0.874621i
$221$		−	297.211i		−	1.34485i
$222$	10.7696			0.0485118
$223$			169.196i			0.758724i	0.925248	+	0.379362i	$0.123857\pi$
$223$			169.196i			0.758724i	−0.925248	+	0.379362i	$0.876143\pi$
$224$			4.46220i			0.0199206i
$225$	137.504	−	100.871i	0.611128	−	0.448317i
$226$		−	213.874i		−	0.946347i
$227$	−174.986			−0.770862			−0.385431	−	0.922737i	$-0.625947\pi$
$227$	−174.986			−0.770862			−0.385431	+	0.922737i	$0.625947\pi$
$228$	6.57421			0.0288343
$229$			142.594i			0.622682i	0.950298	+	0.311341i	$0.100778\pi$
$229$			142.594i			0.622682i	−0.950298	+	0.311341i	$0.899222\pi$
$230$	−145.149	−	73.3600i	−0.631084	−	0.318956i
$231$	23.5735			0.102050
$232$			94.0641i			0.405449i
$233$		−	345.944i		−	1.48474i	−0.669991	−	0.742369i	$-0.733702\pi$
$233$		−	345.944i		−	1.48474i	0.669991	−	0.742369i	$-0.266298\pi$
$234$	−188.359			−0.804955
$235$	−32.3834	−	98.8919i	−0.137802	−	0.420817i
$236$	72.6999			0.308050
$237$	40.6113			0.171356
$238$			16.9808i			0.0713478i
$239$	161.957			0.677645			0.338822	−	0.940850i	$-0.389971\pi$
$239$	161.957			0.677645			0.338822	+	0.940850i	$0.389971\pi$
$240$	9.18670	+	28.0542i	0.0382779	+	0.116892i
$241$		−	435.407i		−	1.80667i	−0.428940	−	0.903333i	$-0.641113\pi$
$241$		−	435.407i		−	1.80667i	0.428940	−	0.903333i	$-0.358887\pi$
$242$			408.628i			1.68854i
$243$			249.913i			1.02845i
$244$		−	178.624i		−	0.732064i
$245$	−229.878	+	75.2763i	−0.938276	+	0.307250i
$246$	−133.196			−0.541447
$247$	43.4835			0.176047
$248$			43.3337i			0.174733i
$249$			82.0936i			0.329693i
$250$	−143.728	−	102.918i	−0.574914	−	0.411672i
$251$		−	156.282i		−	0.622636i	−0.950306	−	0.311318i	$-0.899230\pi$
$251$		−	156.282i		−	0.622636i	0.950306	−	0.311318i	$-0.100770\pi$
$252$	10.7617			0.0427050
$253$	329.608	+	328.966i	1.30280	+	1.30026i
$254$	−130.955			−0.515569
$255$	34.9597	+	106.759i	0.137097	+	0.418663i
$256$	16.0000			0.0625000
$257$		−	161.556i		−	0.628622i	−0.949320	−	0.314311i	$-0.898227\pi$
$257$		−	161.556i		−	0.628622i	0.949320	−	0.314311i	$-0.101773\pi$
$258$	−34.3293			−0.133059
$259$	−4.06980			−0.0157135
$260$	60.7632	+	185.557i	0.233704	+	0.713683i
$261$	226.858			0.869187
$262$			205.135i			0.782958i
$263$	−339.547			−1.29105			−0.645526	−	0.763738i	$-0.723362\pi$
$263$	−339.547			−1.29105			−0.645526	+	0.763738i	$0.723362\pi$
$264$		−	84.5267i		−	0.320177i
$265$	−222.746	+	72.9411i	−0.840552	+	0.275250i
$266$	−2.48437			−0.00933974
$267$	−18.0175			−0.0674813
$268$	128.710			0.480262
$269$	94.9480			0.352967			0.176483	−	0.984304i	$-0.443528\pi$
$269$	94.9480			0.352967			0.176483	+	0.984304i	$0.443528\pi$
$270$	156.927	−	51.3878i	0.581211	−	0.190325i
$271$	−492.708			−1.81811			−0.909056	−	0.416674i	$-0.863196\pi$
$271$	−492.708			−1.81811			−0.909056	+	0.416674i	$0.863196\pi$
$272$	60.8875			0.223851
$273$	−22.7331			−0.0832715
$274$		−	53.3457i		−	0.194692i
$275$	299.402	+	408.133i	1.08874	+	1.48412i
$276$	−48.0565	−	47.9630i	−0.174118	−	0.173779i
$277$			293.370i			1.05910i	0.848279	+	0.529550i	$0.177639\pi$
$277$			293.370i			1.05910i	−0.848279	+	0.529550i	$0.822361\pi$
$278$		−	205.433i		−	0.738968i
$279$	104.509			0.374586
$280$	−3.47162	−	10.6016i	−0.0123986	−	0.0378627i
$281$			164.629i			0.585869i	0.956133	+	0.292935i	$0.0946318\pi$
$281$			164.629i			0.585869i	−0.956133	+	0.292935i	$0.905368\pi$
$282$		−	43.4422i		−	0.154050i
$283$	−345.547			−1.22101			−0.610507	−	0.792011i	$-0.709034\pi$
$283$	−345.547			−1.22101			−0.610507	+	0.792011i	$0.709034\pi$
$284$	−57.1852			−0.201356
$285$	−15.6194	+	5.11477i	−0.0548049	+	0.0179466i
$286$		−	559.081i		−	1.95483i
$287$	50.3343			0.175381
$288$		−	38.5878i		−	0.133985i
$289$	−57.2949			−0.198252
$290$	−73.1824	−	223.483i	−0.252353	−	0.770631i
$291$			64.6145i			0.222043i
$292$		−	167.050i		−	0.572088i
$293$	133.605			0.455991			0.227995	−	0.973662i	$-0.426783\pi$
$293$	133.605			0.455991			0.227995	+	0.973662i	$0.426783\pi$
$294$	−100.983			−0.343479
$295$	−172.725	+	56.5609i	−0.585507	+	0.191732i
$296$			14.5930i			0.0493005i
$297$	−472.818			−1.59198
$298$	−278.395			−0.934211
$299$	−317.858	−	317.239i	−1.06307	−	1.06100i
$300$	−43.6526	−	59.5055i	−0.145509	−	0.198352i
$301$	12.9729			0.0430994
$302$		−	159.694i		−	0.528789i
$303$		−	159.773i		−	0.527304i
$304$			8.90814i			0.0293031i
$305$	138.970	+	424.385i	0.455640	+	1.39143i
$306$		−	146.844i		−	0.479884i
$307$		−	110.193i		−	0.358934i	−0.983764	−	0.179467i	$-0.942563\pi$
$307$		−	110.193i		−	0.358934i	0.983764	−	0.179467i	$-0.0574373\pi$
$308$			31.9423i			0.103709i
$309$		−	286.222i		−	0.926286i
$310$	−33.7139	−	102.955i	−0.108754	−	0.332112i
$311$	157.966			0.507929			0.253965	−	0.967214i	$-0.418265\pi$
$311$	157.966			0.507929			0.253965	+	0.967214i	$0.418265\pi$
$312$			81.5135i			0.261261i
$313$	86.7840			0.277265			0.138633	−	0.990344i	$-0.455729\pi$
$313$	86.7840			0.277265			0.138633	+	0.990344i	$0.455729\pi$
$314$			349.880i			1.11427i
$315$	−25.5682	+	8.37263i	−0.0811689	+	0.0265798i
$316$			55.0288i			0.174142i
$317$		−	64.3675i		−	0.203052i	−0.994833	−	0.101526i	$-0.967628\pi$
$317$		−	64.3675i		−	0.203052i	0.994833	−	0.101526i	$-0.0323725\pi$
$318$	−97.8502			−0.307705
$319$			673.350i			2.11082i
$320$	−38.0137	+	12.4481i	−0.118793	+	0.0389003i
$321$		−	203.657i		−	0.634445i
$322$	18.1604	+	18.1250i	0.0563987	+	0.0562889i
$323$			33.8996i			0.104952i
$324$	−53.8491			−0.166201
$325$	−288.729	−	393.584i	−0.888398	−	1.21103i
$326$	88.6791			0.272022
$327$	252.748			0.772931
$328$		−	180.482i		−	0.550251i
$329$			16.4166i			0.0498986i
$330$	65.7622	+	200.823i	0.199279	+	0.608556i
$331$	489.272			1.47816			0.739081	−	0.673616i	$-0.235260\pi$
$331$	489.272			1.47816			0.739081	+	0.673616i	$0.235260\pi$
$332$	−111.238			−0.335054
$333$	35.1944			0.105689
$334$	−387.583			−1.16043
$335$	−305.798	+	100.137i	−0.912829	+	0.298917i
$336$		−	4.65716i		−	0.0138606i
$337$	−294.147			−0.872841			−0.436420	−	0.899743i	$-0.643754\pi$
$337$	−294.147			−0.872841			−0.436420	+	0.899743i	$0.643754\pi$
$338$			300.149i			0.888015i
$339$			223.219i			0.658462i
$340$	−144.660	+	47.3708i	−0.425471	+	0.139326i
$341$			310.201i			0.909680i
$342$	21.4841			0.0628189
$343$	76.8129			0.223944
$344$		−	46.5166i		−	0.135223i
$345$	151.491	+	76.5651i	0.439104	+	0.221928i
$346$	−6.60590			−0.0190922
$347$			611.322i			1.76173i	0.473364	+	0.880867i	$0.343040\pi$
$347$			611.322i			1.76173i	−0.473364	+	0.880867i	$0.656960\pi$
$348$		−	98.1738i		−	0.282109i
$349$	584.229			1.67401			0.837005	−	0.547196i	$-0.184305\pi$
$349$	584.229			1.67401			0.837005	+	0.547196i	$0.184305\pi$
$350$	16.4962	+	22.4869i	0.0471319	+	0.0642483i
$351$	455.963			1.29904
$352$	114.535			0.325383
$353$			308.472i			0.873857i	0.899496	+	0.436928i	$0.143934\pi$
$353$			308.472i			0.873857i	−0.899496	+	0.436928i	$0.856066\pi$
$354$	−75.8762			−0.214339
$355$	135.864	−	44.4904i	0.382715	−	0.125325i
$356$		−	24.4140i		−	0.0685785i
$357$		−	17.7227i		−	0.0496433i
$358$		−	270.152i		−	0.754614i
$359$		−	553.604i		−	1.54207i	−0.636791	−	0.771036i	$-0.719739\pi$
$359$		−	553.604i		−	1.54207i	0.636791	−	0.771036i	$-0.280261\pi$
$360$	30.0215	+	91.6791i	0.0833931	+	0.254664i
$361$	356.040			0.986261
$362$	336.487			0.929523
$363$		−	426.481i		−	1.17488i
$364$		−	30.8036i		−	0.0846254i
$365$	129.966	+	396.887i	0.356070	+	1.08736i
$366$			186.428i			0.509366i
$367$	144.977			0.395033			0.197517	−	0.980300i	$-0.436712\pi$
$367$	144.977			0.395033			0.197517	+	0.980300i	$0.436712\pi$
$368$	64.9904	−	65.1171i	0.176604	−	0.176949i
$369$	−435.275			−1.17961
$370$	−11.3534	−	34.6708i	−0.0306849	−	0.0937049i
$371$	36.9772			0.0996691
$372$		−	45.2270i		−	0.121578i
$373$	227.735			0.610549			0.305274	−	0.952264i	$-0.401252\pi$
$373$	227.735			0.610549			0.305274	+	0.952264i	$0.401252\pi$
$374$	435.858			1.16540
$375$	150.008	+	107.415i	0.400021	+	0.286439i
$376$	58.8647			0.156555
$377$		−	649.347i		−	1.72241i
$378$	−26.0508			−0.0689176
$379$			168.747i			0.445242i	0.974905	+	0.222621i	$0.0714613\pi$
$379$			168.747i			0.445242i	−0.974905	+	0.222621i	$0.928539\pi$
$380$	−6.93058	−	21.1645i	−0.0182384	−	0.0556960i
$381$	136.676			0.358730
$382$	430.237			1.12628
$383$	−475.906			−1.24258			−0.621288	−	0.783583i	$-0.713390\pi$
$383$	−475.906			−1.24258			−0.621288	+	0.783583i	$0.713390\pi$
$384$	−16.6990			−0.0434871
$385$	−24.8513	−	75.8905i	−0.0645488	−	0.197118i
$386$	149.954			0.388481
$387$	−112.186			−0.289886
$388$	−87.5535			−0.225653
$389$			441.941i			1.13610i	0.822996	+	0.568048i	$0.192301\pi$
$389$			441.941i			1.13610i	−0.822996	+	0.568048i	$0.807699\pi$
$390$	−63.4179	−	193.665i	−0.162610	−	0.496576i
$391$	247.319	−	247.801i	0.632529	−	0.633762i
$392$		−	136.833i		−	0.349064i
$393$		−	214.097i		−	0.544777i
$394$	−143.207			−0.363470
$395$	−42.8127	−	130.741i	−0.108387	−	0.330989i
$396$		−	276.227i		−	0.697544i
$397$		−	104.945i		−	0.264345i	−0.991227	−	0.132172i	$-0.957805\pi$
$397$		−	104.945i		−	0.264345i	0.991227	−	0.132172i	$-0.0421952\pi$
$398$	134.284			0.337397
$399$	2.59291			0.00649853
$400$	80.6306	−	59.1498i	0.201577	−	0.147875i
$401$		−	299.122i		−	0.745940i	−0.927843	−	0.372970i	$-0.878339\pi$
$401$		−	299.122i		−	0.745940i	0.927843	−	0.372970i	$-0.121661\pi$
$402$	−134.334			−0.334164
$403$		−	299.143i		−	0.742290i
$404$	216.495			0.535878
$405$	127.938	−	41.8949i	0.315896	−	0.103444i
$406$			37.0995i			0.0913782i
$407$			104.462i			0.256665i
$408$	−63.5477			−0.155754
$409$	−49.3689			−0.120706			−0.0603532	−	0.998177i	$-0.519223\pi$
$409$	−49.3689			−0.120706			−0.0603532	+	0.998177i	$0.519223\pi$
$410$	140.416	+	428.800i	0.342478	+	1.04585i
$411$			55.6764i			0.135466i
$412$	387.835			0.941346
$413$	28.6733			0.0694269
$414$	−157.045	−	156.740i	−0.379337	−	0.378599i
$415$	264.285	−	86.5437i	0.636832	−	0.208539i
$416$	−110.452			−0.265509
$417$			214.409i			0.514169i
$418$			63.7682i			0.152555i
$419$			318.438i			0.759996i	0.924987	+	0.379998i	$0.124075\pi$
$419$			318.438i			0.759996i	−0.924987	+	0.379998i	$0.875925\pi$
$420$	3.62330	+	11.0648i	0.00862690	+	0.0263447i
$421$			637.905i			1.51521i	0.652711	+	0.757607i	$0.273632\pi$
$421$			637.905i			1.51521i	−0.652711	+	0.757607i	$0.726368\pi$
$422$		−	320.209i		−	0.758790i
$423$		−	141.966i		−	0.335617i
$424$		−	132.588i		−	0.312708i
$425$	306.837	−	225.093i	0.721970	−	0.529630i
$426$	59.6837			0.140102
$427$		−	70.4504i		−	0.164989i
$428$	275.958			0.644761
$429$			583.508i			1.36016i
$430$	36.1902	+	110.517i	0.0841632	+	0.257016i
$431$		−	471.387i		−	1.09371i	−0.837229	−	0.546853i	$-0.815826\pi$
$431$		−	471.387i		−	1.09371i	0.837229	−	0.546853i	$-0.184174\pi$
$432$			93.4097i			0.216226i
$433$	−165.667			−0.382602			−0.191301	−	0.981531i	$-0.561271\pi$
$433$	−165.667			−0.382602			−0.191301	+	0.981531i	$0.561271\pi$
$434$			17.0911i			0.0393804i
$435$	76.3798	+	233.247i	0.175586	+	0.536200i
$436$			342.477i			0.785498i
$437$	36.2545	+	36.1840i	0.0829623	+	0.0828009i
$438$			174.348i			0.398055i
$439$	−439.047			−1.00011			−0.500053	−	0.865995i	$-0.666686\pi$
$439$	−439.047			−1.00011			−0.500053	+	0.865995i	$0.666686\pi$
$440$	−272.118	+	89.1086i	−0.618451	+	0.202520i
$441$	−330.005			−0.748311
$442$	−420.320			−0.950951
$443$		−	403.614i		−	0.911092i	−0.890212	−	0.455546i	$-0.849444\pi$
$443$		−	403.614i		−	0.911092i	0.890212	−	0.455546i	$-0.150556\pi$
$444$		−	15.2305i		−	0.0343030i
$445$	18.9942	+	58.0041i	0.0426836	+	0.130346i
$446$	239.279			0.536499
$447$	290.558			0.650018
$448$	6.31051			0.0140860
$449$	−80.7694			−0.179887			−0.0899437	−	0.995947i	$-0.528669\pi$
$449$	−80.7694			−0.179887			−0.0899437	+	0.995947i	$0.528669\pi$
$450$	−142.654	−	194.460i	−0.317008	−	0.432133i
$451$		−	1291.97i		−	2.86467i
$452$	−302.464			−0.669168
$453$			166.671i			0.367928i
$454$			247.467i			0.545082i
$455$	23.9654	+	73.1851i	0.0526712	+	0.160846i
$456$		−	9.29734i		−	0.0203889i
$457$	716.340			1.56748			0.783741	−	0.621087i	$-0.213309\pi$
$457$	716.340			1.56748			0.783741	+	0.621087i	$0.213309\pi$
$458$	201.659			0.440303
$459$			355.468i			0.774439i
$460$	−103.747	+	205.272i	−0.225536	+	0.446244i
$461$	−170.054			−0.368881			−0.184440	−	0.982844i	$-0.559047\pi$
$461$	−170.054			−0.368881			−0.184440	+	0.982844i	$0.559047\pi$
$462$		−	33.3379i		−	0.0721600i
$463$		−	26.3084i		−	0.0568216i	−0.999596	−	0.0284108i	$-0.990955\pi$
$463$		−	26.3084i		−	0.0568216i	0.999596	−	0.0284108i	$-0.00904466\pi$
$464$	133.027			0.286696
$465$	35.1868	+	107.453i	0.0756706	+	0.231082i
$466$	−489.239			−1.04987
$467$	−251.462			−0.538463			−0.269231	−	0.963076i	$-0.586770\pi$
$467$	−251.462			−0.538463			−0.269231	+	0.963076i	$0.586770\pi$
$468$			266.381i			0.569189i
$469$	50.7642			0.108239
$470$	−139.854	+	45.7971i	−0.297562	+	0.0974405i
$471$		−	365.167i		−	0.775301i
$472$		−	102.813i		−	0.217824i
$473$		−	332.985i		−	0.703986i
$474$		−	57.4330i		−	0.121167i
$475$	32.9322	+	44.8918i	0.0693309	+	0.0945091i
$476$	24.0144			0.0504505
$477$	−319.768			−0.670373
$478$		−	229.042i		−	0.479167i
$479$		−	714.965i		−	1.49262i	−0.665598	−	0.746310i	$-0.731824\pi$
$479$		−	714.965i		−	1.49262i	0.665598	−	0.746310i	$-0.268176\pi$
$480$	39.6746	−	12.9920i	0.0826554	−	0.0270666i
$481$		−	100.739i		−	0.209436i
$482$	−615.758			−1.27751
$483$	−18.9538	−	18.9169i	−0.0392418	−	0.0391655i
$484$	577.887			1.19398
$485$	208.015	−	68.1171i	0.428896	−	0.140448i
$486$	353.430			0.727222
$487$		−	469.844i		−	0.964773i	−0.875958	−	0.482387i	$-0.839770\pi$
$487$		−	469.844i		−	0.964773i	0.875958	−	0.482387i	$-0.160230\pi$
$488$	−252.612			−0.517648
$489$	−92.5536			−0.189271
$490$	106.457	+	325.096i	0.217259	+	0.663461i
$491$	−205.376			−0.418281			−0.209141	−	0.977886i	$-0.567067\pi$
$491$	−205.376			−0.418281			−0.209141	+	0.977886i	$0.567067\pi$
$492$			188.368i			0.382861i
$493$	506.229			1.02683
$494$		−	61.4950i		−	0.124484i
$495$	214.906	+	656.278i	0.434154	+	1.32581i
$496$	61.2831			0.123555
$497$	−22.5542			−0.0453808
$498$	116.098			0.233128
$499$	−775.458			−1.55402			−0.777012	−	0.629486i	$-0.783266\pi$
$499$	−775.458			−1.55402			−0.777012	+	0.629486i	$0.783266\pi$
$500$	−145.548	+	203.263i	−0.291096	+	0.406525i
$501$	404.516			0.807418
$502$	−221.016			−0.440270
$503$	110.501			0.219684			0.109842	−	0.993949i	$-0.464965\pi$
$503$	110.501			0.219684			0.109842	+	0.993949i	$0.464965\pi$
$504$		−	15.2193i		−	0.0301970i
$505$	−514.361	+	168.434i	−1.01854	+	0.333533i
$506$	465.229	−	466.136i	0.919424	−	0.921217i
$507$		−	313.263i		−	0.617875i
$508$			185.198i			0.364563i
$509$	566.938			1.11383			0.556913	−	0.830571i	$-0.311986\pi$
$509$	566.938			1.11383			0.556913	+	0.830571i	$0.311986\pi$
$510$	150.980	−	49.4404i	0.296040	−	0.0969420i
$511$		−	65.8855i		−	0.128935i
$512$		−	22.6274i		−	0.0441942i
$513$	−52.0067			−0.101378
$514$	−228.474			−0.444503
$515$	−921.441	+	301.737i	−1.78921	+	0.585898i
$516$			48.5489i			0.0940871i
$517$	421.378			0.815045
$518$			5.75556i			0.0111111i
$519$	6.89451			0.0132842
$520$	262.418	−	85.9321i	0.504650	−	0.165254i
$521$			368.951i			0.708160i	0.935215	+	0.354080i	$0.115206\pi$
$521$			368.951i			0.708160i	−0.935215	+	0.354080i	$0.884794\pi$
$522$		−	320.825i		−	0.614608i
$523$	−401.116			−0.766952			−0.383476	−	0.923551i	$-0.625273\pi$
$523$	−401.116			−0.766952			−0.383476	+	0.923551i	$0.625273\pi$
$524$	290.105			0.553635
$525$	−17.2169	−	23.4694i	−0.0327941	−	0.0447036i
$526$			480.191i			0.912911i
$527$	233.211			0.442525
$528$	−119.539			−0.226399
$529$	−1.03035	−	528.999i	−0.00194773	−	0.999998i
$530$	103.154	+	315.011i	0.194631	+	0.594360i
$531$	−247.958			−0.466964
$532$			3.51343i			0.00660419i
$533$			1245.91i			2.33754i
$534$			25.4806i			0.0477165i
$535$	−655.636	+	214.697i	−1.22549	+	0.401302i
$536$		−	182.024i		−	0.339597i
$537$			281.955i			0.525056i
$538$		−	134.277i		−	0.249585i
$539$		−	979.508i		−	1.81727i
$540$	−72.6733	−	221.928i	−0.134580	−	0.410979i
$541$	37.4575			0.0692374			0.0346187	−	0.999401i	$-0.488978\pi$
$541$	37.4575			0.0692374			0.0346187	+	0.999401i	$0.488978\pi$
$542$			696.795i			1.28560i
$543$	−351.189			−0.646756
$544$		−	86.1079i		−	0.158287i
$545$	−266.449	−	813.678i	−0.488898	−	1.49299i
$546$			32.1495i			0.0588818i
$547$			745.614i			1.36310i	0.731773	+	0.681548i	$0.238693\pi$
$547$			745.614i			1.36310i	−0.731773	+	0.681548i	$0.761307\pi$
$548$	−75.4422			−0.137668
$549$			609.234i			1.10972i
$550$	577.188	−	423.419i	1.04943	−	0.769853i
$551$			74.0638i			0.134417i
$552$	−67.8299	+	67.9621i	−0.122880	+	0.123120i
$553$			21.7037i			0.0392472i
$554$	414.888			0.748896
$555$	11.8494	+	36.1856i	0.0213503	+	0.0651993i
$556$	−290.526			−0.522529
$557$	−343.596			−0.616869			−0.308435	−	0.951246i	$-0.599805\pi$
$557$	−343.596			−0.616869			−0.308435	+	0.951246i	$0.599805\pi$
$558$		−	147.799i		−	0.264872i
$559$			321.115i			0.574446i
$560$	−14.9929	+	4.90961i	−0.0267730	+	0.00876716i
$561$	−454.901			−0.810875
$562$	232.821			0.414272
$563$	703.332			1.24926			0.624629	−	0.780922i	$-0.285250\pi$
$563$	703.332			1.24926			0.624629	+	0.780922i	$0.285250\pi$
$564$	−61.4365			−0.108930
$565$	718.612	−	235.319i	1.27188	−	0.416493i
$566$			488.677i			0.863388i
$567$	−21.2385			−0.0374576
$568$			80.8721i			0.142380i
$569$		−	914.870i		−	1.60786i	−0.594727	−	0.803928i	$-0.702740\pi$
$569$		−	914.870i		−	1.60786i	0.594727	−	0.803928i	$-0.297260\pi$
$570$	7.23338	+	22.0892i	0.0126901	+	0.0387529i
$571$			861.857i			1.50938i	0.656080	+	0.754691i	$0.272213\pi$
$571$			861.857i			1.50938i	−0.656080	+	0.754691i	$0.727787\pi$
$572$	−790.660			−1.38227
$573$	−449.034			−0.783655
$574$		−	71.1834i		−	0.124013i
$575$	86.7846	−	568.413i	0.150930	−	0.988544i
$576$	−54.5714			−0.0947419
$577$		−	493.733i		−	0.855690i	−0.903852	−	0.427845i	$-0.859273\pi$
$577$		−	493.733i		−	0.855690i	0.903852	−	0.427845i	$-0.140727\pi$
$578$			81.0272i			0.140186i
$579$	−156.505			−0.270303
$580$	−316.053	+	103.496i	−0.544919	+	0.178441i
$581$	−43.8730			−0.0755129
$582$	91.3787			0.157008
$583$		−	949.122i		−	1.62800i
$584$	−236.244			−0.404527
$585$	−207.246	−	632.883i	−0.354266	−	1.08185i
$586$		−	188.946i		−	0.322434i
$587$			7.33491i			0.0124956i	0.999980	+	0.00624779i	$0.00198875\pi$
$587$			7.33491i			0.0124956i	−0.999980	+	0.00624779i	$0.998011\pi$
$588$			142.811i			0.242876i
$589$			34.1199i			0.0579285i
$590$	79.9892	+	244.270i	0.135575	+	0.414016i
$591$	149.464			0.252900
$592$	20.6376			0.0348607
$593$			607.334i			1.02417i	0.858934	+	0.512086i	$0.171127\pi$
$593$			607.334i			1.02417i	−0.858934	+	0.512086i	$0.828873\pi$
$594$			668.666i			1.12570i
$595$	−57.0549	+	18.6834i	−0.0958906	+	0.0314006i
$596$			393.710i			0.660587i
$597$	−140.151			−0.234759
$598$	−448.644	+	449.519i	−0.750241	+	0.751704i
$599$	155.874			0.260223			0.130112	−	0.991499i	$-0.458466\pi$
$599$	155.874			0.260223			0.130112	+	0.991499i	$0.458466\pi$
$600$	−84.1534	+	61.7341i	−0.140256	+	0.102890i
$601$	285.755			0.475466			0.237733	−	0.971330i	$-0.423596\pi$
$601$	285.755			0.475466			0.237733	+	0.971330i	$0.423596\pi$
$602$		−	18.3465i		−	0.0304759i
$603$	−438.994			−0.728016
$604$	−225.842			−0.373910
$605$	−1372.98	+	449.599i	−2.26939	+	0.743139i
$606$	−225.953			−0.372860
$607$			465.939i			0.767610i	0.923414	+	0.383805i	$0.125387\pi$
$607$			465.939i			0.767610i	−0.923414	+	0.383805i	$0.874613\pi$
$608$	12.5980			0.0207204
$609$		−	38.7204i		−	0.0635803i
$610$	600.171	−	196.534i	0.983887	−	0.322186i
$611$	−406.357			−0.665069
$612$	−207.669			−0.339329
$613$	−562.032			−0.916855			−0.458427	−	0.888732i	$-0.651587\pi$
$613$	−562.032			−0.916855			−0.458427	+	0.888732i	$0.651587\pi$
$614$	−155.836			−0.253804
$615$	−146.551	−	447.535i	−0.238294	−	0.727699i
$616$	45.1733			0.0733332
$617$	595.966			0.965909			0.482954	−	0.875645i	$-0.339564\pi$
$617$	595.966			0.965909			0.482954	+	0.875645i	$0.339564\pi$
$618$	−404.779			−0.654983
$619$			125.836i			0.203288i	0.994821	+	0.101644i	$0.0324103\pi$
$619$			125.836i			0.203288i	−0.994821	+	0.101644i	$0.967590\pi$
$620$	−145.600	+	47.6786i	−0.234839	+	0.0769010i
$621$	380.161	+	379.421i	0.612176	+	0.610984i
$622$		−	223.398i		−	0.359160i
$623$		−	9.62903i		−	0.0154559i
$624$	115.277			0.184740
$625$	187.663	−	596.161i	0.300260	−	0.953857i
$626$		−	122.731i		−	0.196056i
$627$		−	66.5542i		−	0.106147i
$628$	494.805			0.787907
$629$	78.5355			0.124858
$630$	11.8407	+	36.1589i	0.0187947	+	0.0573950i
$631$			43.2972i			0.0686169i	0.999411	+	0.0343084i	$0.0109229\pi$
$631$			43.2972i			0.0686169i	−0.999411	+	0.0343084i	$0.989077\pi$
$632$	77.8224			0.123137
$633$			334.200i			0.527961i
$634$	−91.0293			−0.143579
$635$	−144.085	−	440.004i	−0.226905	−	0.692920i
$636$			138.381i			0.217580i
$637$			944.591i			1.48287i
$638$	952.261			1.49257
$639$	195.042			0.305230
$640$	17.6043	+	53.7596i	0.0275066	+	0.0839993i
$641$			89.9061i			0.140259i	0.997538	+	0.0701296i	$0.0223413\pi$
$641$			89.9061i			0.140259i	−0.997538	+	0.0701296i	$0.977659\pi$
$642$	−288.014			−0.448620
$643$	553.559			0.860901			0.430450	−	0.902614i	$-0.358355\pi$
$643$	553.559			0.860901			0.430450	+	0.902614i	$0.358355\pi$
$644$	25.6327	−	25.6826i	0.0398023	−	0.0398799i
$645$	−37.7713	−	115.345i	−0.0585602	−	0.178830i
$646$	47.9413			0.0742125
$647$			682.623i			1.05506i	0.849537	+	0.527529i	$0.176882\pi$
$647$			682.623i			1.05506i	−0.849537	+	0.527529i	$0.823118\pi$
$648$			76.1541i			0.117522i
$649$		−	735.979i		−	1.13402i
$650$	−556.612	+	408.325i	−0.856327	+	0.628192i
$651$		−	17.8378i		−	0.0274007i
$652$		−	125.411i		−	0.192348i
$653$			961.817i			1.47292i	0.676481	+	0.736460i	$0.263504\pi$
$653$			961.817i			1.47292i	−0.676481	+	0.736460i	$0.736496\pi$
$654$		−	357.440i		−	0.546545i
$655$	−689.248	+	225.703i	−1.05229	+	0.344585i
$656$	−255.240			−0.389086
$657$			569.758i			0.867212i
$658$	23.2166			0.0352837
$659$		−	130.954i		−	0.198717i	−0.995052	−	0.0993583i	$-0.968321\pi$
$659$		−	130.954i		−	0.198717i	0.995052	−	0.0993583i	$-0.0316790\pi$
$660$	284.007	−	93.0018i	0.430314	−	0.140912i
$661$		−	363.722i		−	0.550259i	−0.961407	−	0.275130i	$-0.911279\pi$
$661$		−	363.722i		−	0.550259i	0.961407	−	0.275130i	$-0.0887208\pi$
$662$		−	691.935i		−	1.04522i
$663$	438.684			0.661666
$664$			157.314i			0.236919i
$665$	−2.73347	−	8.34742i	−0.00411048	−	0.0125525i
$666$		−	49.7724i		−	0.0747333i
$667$	540.342	−	541.395i	0.810107	−	0.811687i
$668$			548.124i			0.820546i
$669$	−249.733			−0.373293
$670$	141.616	+	432.463i	0.211367	+	0.645467i
$671$	−1808.30			−2.69494
$672$	−6.58622			−0.00980092
$673$			57.2239i			0.0850280i	0.999096	+	0.0425140i	$0.0135367\pi$
$673$			57.2239i			0.0850280i	−0.999096	+	0.0425140i	$0.986463\pi$
$674$			415.987i			0.617192i
$675$	345.323	+	470.730i	0.511590	+	0.697379i
$676$	424.475			0.627921
$677$	−383.957			−0.567145			−0.283573	−	0.958951i	$-0.591520\pi$
$677$	−383.957			−0.567145			−0.283573	+	0.958951i	$0.591520\pi$
$678$	315.679			0.465603
$679$	−34.5317			−0.0508567
$680$	66.9924	+	204.580i	0.0985182	+	0.300853i
$681$		−	258.279i		−	0.379264i
$682$	438.690			0.643241
$683$		−	852.643i		−	1.24838i	−0.781273	−	0.624190i	$-0.785429\pi$
$683$		−	852.643i		−	1.24838i	0.781273	−	0.624190i	$-0.214571\pi$
$684$		−	30.3831i		−	0.0444197i
$685$	179.240	−	58.6944i	0.261664	−	0.0856853i
$686$		−	108.630i		−	0.158353i
$687$	−210.469			−0.306360
$688$	−65.7844			−0.0956169
$689$			915.288i			1.32843i
$690$	108.279	−	214.241i	0.156927	−	0.310494i
$691$	−0.117064			−0.000169412			−8.47060e−5	−	1.00000i	$-0.500027\pi$
$691$	−0.117064			−0.000169412			−8.47060e−5		1.00000i	$0.500027\pi$
$692$			9.34215i			0.0135002i
$693$		−	108.946i		−	0.157209i
$694$	864.539			1.24573
$695$	690.250	−	226.031i	0.993165	−	0.325225i
$696$	−138.839			−0.199481
$697$	−971.308			−1.39356
$698$		−	826.225i		−	1.18370i
$699$	510.614			0.730492
$700$	31.8013	−	23.3291i	0.0454304	−	0.0333273i
$701$			472.046i			0.673390i	0.941614	+	0.336695i	$0.109309\pi$
$701$			472.046i			0.673390i	−0.941614	+	0.336695i	$0.890691\pi$
$702$		−	644.830i		−	0.918561i
$703$			11.4901i			0.0163444i
$704$		−	161.976i		−	0.230080i
$705$	145.965	−	47.7980i	0.207042	−	0.0677985i
$706$	436.245			0.617910
$707$	85.3869			0.120774
$708$			107.305i			0.151561i
$709$			1195.44i			1.68610i	0.537839	+	0.843048i	$0.319241\pi$
$709$			1195.44i			1.68610i	−0.537839	+	0.843048i	$0.680759\pi$
$710$	−62.9189	−	192.141i	−0.0886182	−	0.270621i
$711$		−	187.687i		−	0.263976i
$712$	−34.5265			−0.0484923
$713$	248.926	−	249.411i	0.349125	−	0.349806i
$714$	−25.0636			−0.0351031
$715$	1878.50	−	615.138i	2.62727	−	0.860332i
$716$	−382.052			−0.533593
$717$			239.049i			0.333401i
$718$	−782.914			−1.09041
$719$	453.685			0.630994			0.315497	−	0.948927i	$-0.397829\pi$
$719$	453.685			0.630994			0.315497	+	0.948927i	$0.397829\pi$
$720$	129.654	−	42.4568i	0.180075	−	0.0589678i
$721$	152.965			0.212156
$722$		−	503.517i		−	0.697392i
$723$	642.661			0.888880
$724$		−	475.865i		−	0.657272i
$725$	670.377	−	491.782i	0.924658	−	0.678320i
$726$	−603.135			−0.830765
$727$	−97.3614			−0.133922			−0.0669611	−	0.997756i	$-0.521330\pi$
$727$	−97.3614			−0.133922			−0.0669611	+	0.997756i	$0.521330\pi$
$728$	−43.5629			−0.0598392
$729$	−126.550			−0.173594
$730$	561.282	−	183.799i	0.768880	−	0.251780i
$731$	−250.340			−0.342463
$732$	263.649			0.360176
$733$	813.236			1.10946			0.554731	−	0.832030i	$-0.312821\pi$
$733$	813.236			1.10946			0.554731	+	0.832030i	$0.312821\pi$
$734$		−	205.029i		−	0.279331i
$735$	−111.108	−	339.300i	−0.151167	−	0.461632i
$736$	−92.0896	−	91.9104i	−0.125122	−	0.124878i
$737$		−	1303.00i		−	1.76798i
$738$			615.572i			0.834109i
$739$	−221.757			−0.300077			−0.150039	−	0.988680i	$-0.547940\pi$
$739$	−221.757			−0.300077			−0.150039	+	0.988680i	$0.547940\pi$
$740$	−49.0319	+	16.0561i	−0.0662594	+	0.0216975i
$741$			64.1817i			0.0866150i
$742$		−	52.2937i		−	0.0704767i
$743$	−512.991			−0.690432			−0.345216	−	0.938523i	$-0.612194\pi$
$743$	−512.991			−0.690432			−0.345216	+	0.938523i	$0.612194\pi$
$744$	−63.9606			−0.0859686
$745$	−306.308	−	935.399i	−0.411152	−	1.25557i
$746$		−	322.065i		−	0.431723i
$747$	379.400			0.507898
$748$		−	616.396i		−	0.824059i
$749$	108.840			0.145313
$750$	151.907	−	212.143i	0.202543	−	0.282858i
$751$			1418.75i			1.88915i	0.328301	+	0.944573i	$0.393524\pi$
$751$			1418.75i			1.88915i	−0.328301	+	0.944573i	$0.606476\pi$
$752$		−	83.2473i		−	0.110701i
$753$	230.672			0.306337
$754$	−918.315			−1.21792
$755$	536.568	−	175.706i	0.710686	−	0.232723i
$756$			36.8414i			0.0487321i
$757$	719.211			0.950081			0.475040	−	0.879964i	$-0.342433\pi$
$757$	719.211			0.950081			0.475040	+	0.879964i	$0.342433\pi$
$758$	238.644			0.314834
$759$	−485.555	+	486.501i	−0.639730	+	0.640977i
$760$	−29.9311	+	9.80132i	−0.0393830	+	0.0128965i
$761$	−752.173			−0.988401			−0.494200	−	0.869348i	$-0.664539\pi$
$761$	−752.173			−0.988401			−0.494200	+	0.869348i	$0.664539\pi$
$762$		−	193.289i		−	0.253660i
$763$			135.075i			0.177032i
$764$		−	608.447i		−	0.796397i
$765$	493.393	−	161.568i	0.644959	−	0.211200i
$766$			673.033i			0.878634i
$767$			709.743i			0.925350i
$768$			23.6160i			0.0307500i
$769$			473.670i			0.615956i	0.951394	+	0.307978i	$0.0996522\pi$
$769$			473.670i			0.615956i	−0.951394	+	0.307978i	$0.900348\pi$
$770$	−107.325	+	35.1450i	−0.139384	+	0.0456429i
$771$	238.457			0.309282
$772$		−	212.067i		−	0.274698i
$773$	−654.945			−0.847277			−0.423638	−	0.905831i	$-0.639247\pi$
$773$	−654.945			−0.847277			−0.423638	+	0.905831i	$0.639247\pi$
$774$			158.655i			0.204980i
$775$	308.831	−	226.555i	0.398492	−	0.292329i
$776$			123.819i			0.159561i
$777$		−	6.00703i		−	0.00773105i
$778$	624.999			0.803341
$779$		−	142.107i		−	0.182423i
$780$	−273.883	+	89.6865i	−0.351132	+	0.114983i
$781$			578.916i			0.741250i
$782$	−350.444	−	349.762i	−0.448138	−	0.447266i
$783$			776.625i			0.991858i
$784$	−193.511			−0.246825
$785$	−1175.59	+	384.961i	−1.49756	+	0.490397i
$786$	−302.779			−0.385215
$787$	1168.43			1.48466			0.742331	−	0.670034i	$-0.233720\pi$
$787$	1168.43			1.48466			0.742331	+	0.670034i	$0.233720\pi$
$788$			202.526i			0.257012i
$789$		−	501.171i		−	0.635198i
$790$	−184.895	+	60.5463i	−0.234044	+	0.0766408i
$791$	−119.294			−0.150814
$792$	−390.645			−0.493238
$793$	1743.84			2.19904
$794$	−148.414			−0.186920
$795$	−107.661	−	328.774i	−0.135423	−	0.413552i
$796$		−	189.907i		−	0.238576i
$797$	954.055			1.19706			0.598529	−	0.801101i	$-0.295752\pi$
$797$	954.055			1.19706			0.598529	+	0.801101i	$0.295752\pi$
$798$		−	3.66693i		−	0.00459516i
$799$		−	316.795i		−	0.396489i
$800$	−83.6505	−	114.029i	−0.104563	−	0.142536i
$801$			83.2689i			0.103956i
$802$	−423.022			−0.527459
$803$	−1691.13			−2.10602
$804$			189.977i			0.236289i
$805$	−40.9184	+	80.9607i	−0.0508303	+	0.100572i
$806$	−423.052			−0.524878
$807$			140.143i			0.173660i
$808$		−	306.170i		−	0.378923i
$809$	1223.11			1.51188			0.755942	−	0.654639i	$-0.227179\pi$
$809$	1223.11			1.51188			0.755942	+	0.654639i	$0.227179\pi$
$810$	−59.2483	−	180.932i	−0.0731461	−	0.223372i
$811$	−227.108			−0.280034			−0.140017	−	0.990149i	$-0.544716\pi$
$811$	−227.108			−0.280034			−0.140017	+	0.990149i	$0.544716\pi$
$812$	52.4667			0.0646141
$813$		−	727.238i		−	0.894512i
$814$	147.732			0.181489
$815$	97.5706	+	297.959i	0.119719	+	0.365594i
$816$			89.8700i			0.110135i
$817$		−	36.6260i		−	0.0448299i
$818$			69.8182i			0.0853524i
$819$			105.062i			0.128281i
$820$	606.415	−	198.578i	0.739531	−	0.242169i
$821$	1424.71			1.73533			0.867665	−	0.497150i	$-0.165620\pi$
$821$	1424.71			1.73533			0.867665	+	0.497150i	$0.165620\pi$
$822$	78.7383			0.0957886
$823$		−	841.908i		−	1.02297i	−0.859291	−	0.511487i	$-0.829095\pi$
$823$		−	841.908i		−	1.02297i	0.859291	−	0.511487i	$-0.170905\pi$
$824$		−	548.481i		−	0.665632i
$825$	−602.405	+	441.918i	−0.730188	+	0.535659i
$826$		−	40.5502i		−	0.0490923i
$827$	136.178			0.164665			0.0823327	−	0.996605i	$-0.473763\pi$
$827$	136.178			0.164665			0.0823327	+	0.996605i	$0.473763\pi$
$828$	−221.664	+	222.096i	−0.267710	+	0.268232i
$829$	−572.032			−0.690027			−0.345013	−	0.938598i	$-0.612126\pi$
$829$	−572.032			−0.690027			−0.345013	+	0.938598i	$0.612126\pi$
$830$	−122.391	−	373.756i	−0.147459	−	0.450309i
$831$	−433.015			−0.521077
$832$			156.202i			0.187743i
$833$	−736.400			−0.884033
$834$	303.220			0.363573
$835$	−426.444	−	1302.27i	−0.510711	−	1.55960i
$836$	90.1818			0.107873
$837$			357.777i			0.427452i
$838$	450.340			0.537398
$839$		−	1307.43i		−	1.55832i	−0.626824	−	0.779161i	$-0.715645\pi$
$839$		−	1307.43i		−	1.55832i	0.626824	−	0.779161i	$-0.284355\pi$
$840$	15.6479	−	5.12411i	0.0186285	−	0.00610014i
$841$	265.007			0.315110
$842$	902.134			1.07142
$843$	−242.993			−0.288248
$844$	−452.845			−0.536546
$845$	−1008.49	+	330.244i	−1.19348	+	0.390821i
$846$	−200.770			−0.237317
$847$	227.923			0.269094
$848$	−187.508			−0.221118
$849$		−	510.028i		−	0.600740i
$850$	−318.329	−	433.933i	−0.374505	−	0.510510i
$851$	83.8278	−	83.9912i	0.0985050	−	0.0986970i
$852$		−	84.4054i		−	0.0990674i
$853$		−	578.080i		−	0.677702i	−0.940840	−	0.338851i	$-0.889962\pi$
$853$		−	578.080i		−	0.677702i	0.940840	−	0.338851i	$-0.110038\pi$
$854$	−99.6319			−0.116665
$855$	23.6382	+	72.1859i	0.0276470	+	0.0844280i
$856$		−	390.263i		−	0.455915i
$857$			1196.62i			1.39628i	0.715959	+	0.698142i	$0.245990\pi$
$857$			1196.62i			1.39628i	−0.715959	+	0.698142i	$0.754010\pi$
$858$	825.204			0.961777
$859$	873.617			1.01702			0.508508	−	0.861057i	$-0.330197\pi$
$859$	873.617			1.01702			0.508508	+	0.861057i	$0.330197\pi$
$860$	156.295	−	51.1806i	0.181738	−	0.0595124i
$861$			74.2935i			0.0862874i
$862$	−666.642			−0.773367
$863$		−	1294.66i		−	1.50019i	−0.661332	−	0.750094i	$-0.730008\pi$
$863$		−	1294.66i		−	1.50019i	0.661332	−	0.750094i	$-0.269992\pi$
$864$	132.101			0.152895
$865$	−7.26824	−	22.1956i	−0.00840259	−	0.0256597i
$866$			234.288i			0.270541i
$867$		−	84.5673i		−	0.0975402i
$868$	24.1705			0.0278462
$869$	557.085			0.641065
$870$	329.861	−	108.017i	0.379151	−	0.124158i
$871$			1256.55i			1.44266i
$872$	484.336			0.555431
$873$	298.619			0.342061
$874$	51.1719	−	51.2717i	0.0585491	−	0.0586632i
$875$	−57.4052	+	80.1682i	−0.0656060	+	0.0916208i
$876$	246.566			0.281467
$877$			219.160i			0.249898i	0.992163	+	0.124949i	$0.0398767\pi$
$877$			219.160i			0.249898i	−0.992163	+	0.124949i	$0.960123\pi$
$878$			620.906i			0.707182i
$879$			197.202i			0.224348i
$880$	126.019	+	384.833i	0.143203	+	0.437311i
$881$			475.083i			0.539254i	0.962965	+	0.269627i	$0.0869005\pi$
$881$			475.083i			0.539254i	−0.962965	+	0.269627i	$0.913100\pi$
$882$			466.698i			0.529136i
$883$		−	197.328i		−	0.223474i	−0.993738	−	0.111737i	$-0.964359\pi$
$883$		−	197.328i		−	0.223474i	0.993738	−	0.111737i	$-0.0356415\pi$
$884$			594.423i			0.672424i
$885$	−83.4839	−	254.942i	−0.0943321	−	0.288070i
$886$	−570.796			−0.644239
$887$		−	504.739i		−	0.569040i	−0.958670	−	0.284520i	$-0.908166\pi$
$887$		−	504.739i		−	0.569040i	0.958670	−	0.284520i	$-0.0918343\pi$
$888$	−21.5392			−0.0242559
$889$			73.0433i			0.0821634i
$890$	82.0302	−	26.8618i	0.0921688	−	0.0301818i
$891$			545.143i			0.611833i
$892$		−	338.391i		−	0.379362i
$893$	46.3486			0.0519022
$894$		−	410.911i		−	0.459632i
$895$	907.703	−	297.239i	1.01419	−	0.332110i
$896$		−	8.92441i		−	0.00996028i
$897$	468.246	−	469.159i	0.522013	−	0.523031i
$898$			114.225i			0.127200i
$899$	509.518			0.566761
$900$	−275.008	+	201.743i	−0.305564	+	0.224159i
$901$	−713.555			−0.791959
$902$	−1827.12			−2.02563
$903$			19.1480i			0.0212049i
$904$			427.749i			0.473173i
$905$	370.226	+	1130.59i	0.409089	+	1.24927i
$906$	235.709			0.260164
$907$	1295.54			1.42838			0.714192	−	0.699950i	$-0.246794\pi$
$907$	1295.54			1.42838			0.714192	+	0.699950i	$0.246794\pi$
$908$	349.971			0.385431
$909$	−738.400			−0.812321
$910$	103.499	−	33.8922i	0.113736	−	0.0372442i
$911$			977.910i			1.07345i	0.843758	+	0.536724i	$0.180338\pi$
$911$			977.910i			1.07345i	−0.843758	+	0.536724i	$0.819662\pi$
$912$	−13.1484			−0.0144171
$913$			1126.12i			1.23343i
$914$		−	1013.06i		−	1.10838i
$915$	−626.393	+	205.120i	−0.684582	+	0.224175i
$916$		−	285.189i		−	0.311341i
$917$	114.419			0.124776
$918$	502.707			0.547611
$919$		−	526.122i		−	0.572494i	−0.958156	−	0.286247i	$-0.907592\pi$
$919$		−	526.122i		−	0.572494i	0.958156	−	0.286247i	$-0.0924078\pi$
$920$	290.299	+	146.720i	0.315542	+	0.159478i
$921$	162.644			0.176596
$922$			240.493i			0.260838i
$923$		−	558.279i		−	0.604853i
$924$	−47.1469			−0.0510248
$925$	104.001	−	76.2942i	0.112434	−	0.0824802i
$926$	−37.2057			−0.0401789
$927$	−1322.79			−1.42696
$928$		−	188.128i		−	0.202724i
$929$	564.705			0.607864			0.303932	−	0.952694i	$-0.401701\pi$
$929$	564.705			0.607864			0.303932	+	0.952694i	$0.401701\pi$
$930$	151.961	−	49.7617i	0.163399	−	0.0535072i
$931$		−	107.739i		−	0.115724i
$932$			691.888i			0.742369i
$933$			233.158i			0.249901i
$934$			355.621i			0.380751i
$935$	479.559	+	1464.47i	0.512898	+	1.56628i
$936$	376.719			0.402478
$937$	−1421.45			−1.51702			−0.758511	−	0.651660i	$-0.774073\pi$
$937$	−1421.45			−1.51702			−0.758511	+	0.651660i	$0.774073\pi$
$938$		−	71.7915i		−	0.0765367i
$939$			128.093i			0.136415i
$940$	64.7668	+	197.784i	0.0689009	+	0.210408i
$941$		−	428.662i		−	0.455539i	−0.973715	−	0.227769i	$-0.926857\pi$
$941$		−	428.662i		−	0.455539i	0.973715	−	0.227769i	$-0.0731432\pi$
$942$	−516.424			−0.548221
$943$	−1036.76	+	1038.78i	−1.09943	+	1.10157i
$944$	−145.400			−0.154025
$945$	−28.6628	−	87.5301i	−0.0303311	−	0.0926244i
$946$	−470.912			−0.497793
$947$		−	294.836i		−	0.311337i	−0.987809	−	0.155668i	$-0.950247\pi$
$947$		−	294.836i		−	0.311337i	0.987809	−	0.155668i	$-0.0497531\pi$
$948$	−81.2225			−0.0856778
$949$	1630.85			1.71849
$950$	63.4866	−	46.5731i	0.0668280	−	0.0490243i
$951$	95.0064			0.0999016
$952$		−	33.9615i		−	0.0356739i
$953$	942.074			0.988536			0.494268	−	0.869310i	$-0.335436\pi$
$953$	942.074			0.988536			0.494268	+	0.869310i	$0.335436\pi$
$954$			452.220i			0.474025i
$955$	473.375	+	1445.58i	0.495681	+	1.51370i
$956$	−323.914			−0.338822
$957$	−993.866			−1.03852
$958$	−1011.11			−1.05544
$959$	−29.7549			−0.0310270
$960$	−18.3734	−	56.1083i	−0.0191390	−	0.0584462i
$961$	−726.274			−0.755748
$962$	−142.466			−0.148093
$963$	−941.211			−0.977374
$964$			870.813i			0.903333i
$965$	164.989	+	503.841i	0.170973	+	0.522115i
$966$	−26.7526	+	26.8047i	−0.0276942	+	0.0277482i
$967$		−	149.443i		−	0.154543i	−0.997010	−	0.0772714i	$-0.975379\pi$
$967$		−	149.443i		−	0.154543i	0.997010	−	0.0772714i	$-0.0246208\pi$
$968$		−	817.256i		−	0.844272i
$969$	−50.0359			−0.0516366
$970$	−96.3321	−	294.177i	−0.0993114	−	0.303275i
$971$			908.141i			0.935264i	0.883923	+	0.467632i	$0.154893\pi$
$971$			908.141i			0.935264i	−0.883923	+	0.467632i	$0.845107\pi$
$972$		−	499.825i		−	0.514223i
$973$	−114.586			−0.117765
$974$	−664.460			−0.682198
$975$	580.931	−	426.165i	0.595827	−	0.437092i
$976$			357.247i			0.366032i
$977$	−589.947			−0.603835			−0.301917	−	0.953334i	$-0.597627\pi$
$977$	−589.947			−0.603835			−0.301917	+	0.953334i	$0.597627\pi$
$978$			130.890i			0.133835i
$979$	−247.155			−0.252457
$980$	459.755	−	150.553i	0.469138	−	0.153625i
$981$		−	1168.09i		−	1.19071i
$982$			290.446i			0.295770i
$983$	−1791.86			−1.82285			−0.911424	−	0.411469i	$-0.865016\pi$
$983$	−1791.86			−1.82285			−0.911424	+	0.411469i	$0.865016\pi$
$984$	266.392			0.270724
$985$	−157.566	−	481.173i	−0.159966	−	0.488500i
$986$		−	715.916i		−	0.726081i
$987$	−24.2310			−0.0245501
$988$	−86.9670			−0.0880233
$989$	−267.210	+	267.731i	−0.270182	+	0.270709i
$990$	928.117	−	303.924i	0.937491	−	0.306994i
$991$	−322.623			−0.325553			−0.162777	−	0.986663i	$-0.552045\pi$
$991$	−322.623			−0.325553			−0.162777	+	0.986663i	$0.552045\pi$
$992$		−	86.6674i		−	0.0873663i
$993$			722.166i			0.727257i
$994$			31.8965i			0.0320890i
$995$	147.748	+	451.191i	0.148491	+	0.453458i
$996$		−	164.187i		−	0.164847i
$997$		−	1259.49i		−	1.26328i	−0.775261	−	0.631641i	$-0.782382\pi$
$997$		−	1259.49i		−	1.26328i	0.775261	−	0.631641i	$-0.217618\pi$
$998$			1096.66i			1.09886i
$999$			120.484i			0.120605i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.3.c.a.229.8	yes	24
5.2	odd	4		1150.3.d.e.551.19		24
5.3	odd	4		1150.3.d.e.551.6		24
5.4	even	2	inner	230.3.c.a.229.17	yes	24
23.22	odd	2	inner	230.3.c.a.229.7	✓	24
115.22	even	4		1150.3.d.e.551.18		24
115.68	even	4		1150.3.d.e.551.7		24
115.114	odd	2	inner	230.3.c.a.229.18	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.3.c.a.229.7	✓	24	23.22	odd	2	inner
230.3.c.a.229.8	yes	24	1.1	even	1	trivial
230.3.c.a.229.17	yes	24	5.4	even	2	inner
230.3.c.a.229.18	yes	24	115.114	odd	2	inner
1150.3.d.e.551.6		24	5.3	odd	4
1150.3.d.e.551.7		24	115.68	even	4
1150.3.d.e.551.18		24	115.22	even	4
1150.3.d.e.551.19		24	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:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	230.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.41421i q^{2} +1.47600i q^{3} -2.00000 q^{4} +(4.75172 - 1.55601i) q^{5} +2.08738 q^{6} -0.788814 q^{7} +2.82843i q^{8} +6.82142 q^{9} +O(q^{10})\)	\(q-1.41421i q^{2} +1.47600i q^{3} -2.00000 q^{4} +(4.75172 - 1.55601i) q^{5} +2.08738 q^{6} -0.788814 q^{7} +2.82843i q^{8} +6.82142 q^{9} +(-2.20053 - 6.71994i) q^{10} +20.2471i q^{11} -2.95200i q^{12} -19.5253i q^{13} +1.11555i q^{14} +(2.29667 + 7.01354i) q^{15} +4.00000 q^{16} +15.2219 q^{17} -9.64694i q^{18} +2.22703i q^{19} +(-9.50344 + 3.11202i) q^{20} -1.16429i q^{21} +28.6337 q^{22} +(16.2476 - 16.2793i) q^{23} -4.17476 q^{24} +(20.1577 - 14.7875i) q^{25} -27.6129 q^{26} +23.3524i q^{27} +1.57763 q^{28} +33.2567 q^{29} +(9.91865 - 3.24799i) q^{30} +15.3208 q^{31} -5.65685i q^{32} -29.8847 q^{33} -21.5270i q^{34} +(-3.74822 + 1.22740i) q^{35} -13.6428 q^{36} +5.15939 q^{37} +3.14950 q^{38} +28.8194 q^{39} +(4.40106 + 13.4399i) q^{40} -63.8101 q^{41} -1.64655 q^{42} -16.4461 q^{43} -40.4941i q^{44} +(32.4135 - 10.6142i) q^{45} +(-23.0224 - 22.9776i) q^{46} -20.8118i q^{47} +5.90401i q^{48} -48.3778 q^{49} +(-20.9126 - 28.5072i) q^{50} +22.4675i q^{51} +39.0506i q^{52} -46.8770 q^{53} +33.0253 q^{54} +(31.5046 + 96.2083i) q^{55} -2.23110i q^{56} -3.28711 q^{57} -47.0321i q^{58} -36.3499 q^{59} +(-4.59335 - 14.0271i) q^{60} +89.3119i q^{61} -21.6669i q^{62} -5.38083 q^{63} -8.00000 q^{64} +(-30.3816 - 92.7787i) q^{65} +42.2633i q^{66} -64.3552 q^{67} -30.4437 q^{68} +(24.0282 + 23.9815i) q^{69} +(1.73581 + 5.30078i) q^{70} +28.5926 q^{71} +19.2939i q^{72} +83.5248i q^{73} -7.29648i q^{74} +(21.8263 + 29.7527i) q^{75} -4.45407i q^{76} -15.9712i q^{77} -40.7567i q^{78} -27.5144i q^{79} +(19.0069 - 6.22404i) q^{80} +26.9246 q^{81} +90.2411i q^{82} +55.6189 q^{83} +2.32858i q^{84} +(72.3300 - 23.6854i) q^{85} +23.2583i q^{86} +49.0869i q^{87} -57.2673 q^{88} +12.2070i q^{89} +(-15.0108 - 45.8396i) q^{90} +15.4018i q^{91} +(-32.4952 + 32.5586i) q^{92} +22.6135i q^{93} -29.4324 q^{94} +(3.46529 + 10.5822i) q^{95} +8.34952 q^{96} +43.7767 q^{97} +68.4165i q^{98} +138.114i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 48 q^{4} + 8 q^{6} - 96 q^{9}+O(q^{10}) \) 24 * q - 48 * q^4 + 8 * q^6 - 96 * q^9	\( 24 q - 48 q^{4} + 8 q^{6} - 96 q^{9} + 96 q^{16} - 16 q^{24} - 48 q^{25} - 32 q^{26} + 100 q^{29} - 124 q^{31} - 28 q^{35} + 192 q^{36} + 192 q^{39} - 116 q^{41} + 148 q^{46} - 76 q^{49} - 144 q^{50} - 16 q^{54} - 224 q^{55} + 84 q^{59} - 192 q^{64} - 340 q^{69} + 328 q^{70} + 196 q^{71} - 496 q^{75} + 1360 q^{81} + 316 q^{85} - 376 q^{94} - 368 q^{95} + 32 q^{96}+O(q^{100}) \) 24 * q - 48 * q^4 + 8 * q^6 - 96 * q^9 + 96 * q^16 - 16 * q^24 - 48 * q^25 - 32 * q^26 + 100 * q^29 - 124 * q^31 - 28 * q^35 + 192 * q^36 + 192 * q^39 - 116 * q^41 + 148 * q^46 - 76 * q^49 - 144 * q^50 - 16 * q^54 - 224 * q^55 + 84 * q^59 - 192 * q^64 - 340 * q^69 + 328 * q^70 + 196 * q^71 - 496 * q^75 + 1360 * q^81 + 316 * q^85 - 376 * q^94 - 368 * q^95 + 32 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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