LMFDB - Embedded newform 230.3.c.a.229.7

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			229.7
Character	$\chi$	$=$	230.229
Dual form			230.3.c.a.229.17

$q$-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	$-0.482056\pi$
$7$	0.788814			0.112688			0.0563438	+	0.998411i	$0.482056\pi$
$8$			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	$-0.627927\pi$
$11$		−	20.2471i		−	1.84064i	0.391164	−	0.920321i	$-0.372073\pi$
$12$		−	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	$-0.647757\pi$
$17$	−15.2219			−0.895404			−0.447702	+	0.894183i	$0.647757\pi$
$18$		−	9.64694i		−	0.535941i
$19$		−	2.22703i		−	0.117212i	−0.998281	−	0.0586062i	$-0.981334\pi$
$19$		−	2.22703i		−	0.117212i	0.998281	−	0.0586062i	$-0.0186656\pi$
$20$	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	$-0.522211\pi$
$37$	−5.15939			−0.139443			−0.0697215	+	0.997566i	$0.522211\pi$
$38$	−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	$-0.438751\pi$
$43$	16.4461			0.382468			0.191234	+	0.981545i	$0.438751\pi$
$44$			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	$-0.354185\pi$
$53$	46.8770			0.884472			0.442236	+	0.896899i	$0.354185\pi$
$54$	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	$-0.738557\pi$
$61$		−	89.3119i		−	1.46413i	0.681235	−	0.732064i	$-0.261443\pi$
$62$		−	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	$-0.340541\pi$
$67$	64.3552			0.960525			0.480262	+	0.877125i	$0.340541\pi$
$68$	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	$0.0557151\pi$
$79$			27.5144i			0.348283i	−0.984721	+	0.174142i	$0.944285\pi$
$80$	−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	$-0.608754\pi$
$83$	−55.6189			−0.670108			−0.335054	+	0.942199i	$0.608754\pi$
$84$		−	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	$-0.978154\pi$
$89$		−	12.2070i		−	0.137157i	0.997646	−	0.0685785i	$-0.0218464\pi$
$90$	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	$-0.572452\pi$
$97$	−43.7767			−0.451306			−0.225653	+	0.974208i	$0.572452\pi$
$98$			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	$-0.109562\pi$
$103$	193.917			1.88269			0.941346	+	0.337442i	$0.109562\pi$
$104$	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	$-0.276957\pi$
$107$	137.979			1.28952			0.644761	+	0.764384i	$0.276957\pi$
$108$		−	46.7049i		−	0.432453i
$109$			171.239i			1.57100i	0.618864	+	0.785498i	$0.287593\pi$
$109$			171.239i			1.57100i	−0.618864	+	0.785498i	$0.712407\pi$
$110$	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	$-0.733349\pi$
$113$	−151.232			−1.33834			−0.669168	+	0.743111i	$0.733349\pi$
$114$		−	4.64867i		−	0.0407778i
$115$	102.535	+	52.0731i	0.891607	+	0.452810i
$116$	−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	$-0.543961\pi$
$137$	−37.7211			−0.275336			−0.137668	+	0.990478i	$0.543961\pi$
$138$	−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	$0.229693\pi$
$149$			196.855i			1.32117i	−0.750749	+	0.660587i	$0.770307\pi$
$150$	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	$-0.211165\pi$
$157$	247.403			1.57581			0.787907	+	0.615795i	$0.211165\pi$
$158$	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	$-0.771710\pi$
$181$		−	237.933i		−	1.31454i	0.753653	−	0.657272i	$-0.228290\pi$
$182$	−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	$-0.706737\pi$
$191$		−	304.224i		−	1.59279i	0.604775	−	0.796397i	$-0.293263\pi$
$192$		−	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	$-0.923319\pi$
$199$		−	94.9533i		−	0.477152i	0.971124	−	0.238576i	$-0.0766806\pi$
$200$	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	$-0.374053\pi$
$227$	174.986			0.770862			0.385431	+	0.922737i	$0.374053\pi$
$228$	−6.57421			−0.0288343
$229$		−	142.594i		−	0.622682i	−0.950298	−	0.311341i	$-0.899222\pi$
$229$		−	142.594i		−	0.622682i	0.950298	−	0.311341i	$-0.100778\pi$
$230$	73.6425	−	145.006i	0.320185	−	0.630461i
$231$	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	$0.358887\pi$
$241$			435.407i			1.80667i	−0.428940	+	0.903333i	$0.641113\pi$
$242$			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	$0.100770\pi$
$251$			156.282i			0.622636i	−0.950306	+	0.311318i	$0.899230\pi$
$252$	−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	$-0.276638\pi$
$263$	339.547			1.29105			0.645526	+	0.763738i	$0.276638\pi$
$264$			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	$-0.905368\pi$
$281$		−	164.629i		−	0.585869i	0.956133	−	0.292935i	$-0.0946318\pi$
$282$		−	43.4422i		−	0.154050i
$283$	345.547			1.22101			0.610507	−	0.792011i	$-0.290966\pi$
$283$	345.547			1.22101			0.610507	+	0.792011i	$0.290966\pi$
$284$	−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	$-0.573217\pi$
$293$	−133.605			−0.455991			−0.227995	+	0.973662i	$0.573217\pi$
$294$	−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	$-0.544271\pi$
$313$	−86.7840			−0.277265			−0.138633	+	0.990344i	$0.544271\pi$
$314$		−	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	$-0.356246\pi$
$337$	294.147			0.872841			0.436420	+	0.899743i	$0.356246\pi$
$338$			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
$345$	−76.8600	+	151.342i	−0.222783	+	0.438671i
$346$	−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	$0.280261\pi$
$359$			553.604i			1.54207i	−0.636791	+	0.771036i	$0.719739\pi$
$360$	−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	$-0.563288\pi$
$367$	−144.977			−0.395033			−0.197517	+	0.980300i	$0.563288\pi$
$368$	−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	$-0.598748\pi$
$373$	−227.735			−0.610549			−0.305274	+	0.952264i	$0.598748\pi$
$374$	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	$-0.928539\pi$
$379$		−	168.747i		−	0.445242i	0.974905	−	0.222621i	$-0.0714613\pi$
$380$	−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	$-0.286610\pi$
$383$	475.906			1.24258			0.621288	+	0.783583i	$0.286610\pi$
$384$	−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	$-0.807699\pi$
$389$		−	441.941i		−	1.13610i	0.822996	−	0.568048i	$-0.192301\pi$
$390$	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	$0.121661\pi$
$401$			299.122i			0.745940i	−0.927843	+	0.372970i	$0.878339\pi$
$402$	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	$-0.875925\pi$
$419$		−	318.438i		−	0.759996i	0.924987	−	0.379998i	$-0.124075\pi$
$420$	3.62330	+	11.0648i	0.00862690	+	0.0263447i
$421$		−	637.905i		−	1.51521i	−0.652711	−	0.757607i	$-0.726368\pi$
$421$		−	637.905i		−	1.51521i	0.652711	−	0.757607i	$-0.273632\pi$
$422$		−	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	$0.184174\pi$
$431$			471.387i			1.09371i	−0.837229	+	0.546853i	$0.815826\pi$
$432$			93.4097i			0.216226i
$433$	165.667			0.382602			0.191301	−	0.981531i	$-0.438729\pi$
$433$	165.667			0.382602			0.191301	+	0.981531i	$0.438729\pi$
$434$		−	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	$-0.786691\pi$
$457$	−716.340			−1.56748			−0.783741	+	0.621087i	$0.786691\pi$
$458$	−201.659			−0.440303
$459$		−	355.468i		−	0.774439i
$460$	−205.070	−	104.146i	−0.445804	−	0.226405i
$461$	−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	$-0.413230\pi$
$467$	251.462			0.538463			0.269231	+	0.963076i	$0.413230\pi$
$468$			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	$0.268176\pi$
$479$			714.965i			1.49262i	−0.665598	+	0.746310i	$0.731824\pi$
$480$	−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	$-0.535035\pi$
$503$	−110.501			−0.219684			−0.109842	+	0.993949i	$0.535035\pi$
$504$			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	$-0.884794\pi$
$521$		−	368.951i		−	0.708160i	0.935215	−	0.354080i	$-0.115206\pi$
$522$		−	320.825i		−	0.614608i
$523$	401.116			0.766952			0.383476	−	0.923551i	$-0.374727\pi$
$523$	401.116			0.766952			0.383476	+	0.923551i	$0.374727\pi$
$524$	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	$-0.400195\pi$
$557$	343.596			0.616869			0.308435	+	0.951246i	$0.400195\pi$
$558$		−	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	$-0.714750\pi$
$563$	−703.332			−1.24926			−0.624629	+	0.780922i	$0.714750\pi$
$564$	−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	$0.297260\pi$
$569$			914.870i			1.60786i	−0.594727	+	0.803928i	$0.702740\pi$
$570$	7.23338	+	22.0892i	0.0126901	+	0.0387529i
$571$		−	861.857i		−	1.50938i	−0.656080	−	0.754691i	$-0.727787\pi$
$571$		−	861.857i		−	1.50938i	0.656080	−	0.754691i	$-0.272213\pi$
$572$	790.660			1.38227
$573$	449.034			0.783655
$574$			71.1834i			0.124013i
$575$	−568.243	−	87.8916i	−0.988249	−	0.152855i
$576$	−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	$-0.348413\pi$
$613$	562.032			0.916855			0.458427	+	0.888732i	$0.348413\pi$
$614$	−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	$-0.660436\pi$
$617$	−595.966			−0.965909			−0.482954	+	0.875645i	$0.660436\pi$
$618$	404.779			0.654983
$619$		−	125.836i		−	0.203288i	−0.994821	−	0.101644i	$-0.967590\pi$
$619$		−	125.836i		−	0.203288i	0.994821	−	0.101644i	$-0.0324103\pi$
$620$	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	$-0.989077\pi$
$631$		−	43.2972i		−	0.0686169i	0.999411	−	0.0343084i	$-0.0109229\pi$
$632$	−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	$-0.977659\pi$
$641$		−	89.9061i		−	0.140259i	0.997538	−	0.0701296i	$-0.0223413\pi$
$642$	288.014			0.448620
$643$	−553.559			−0.860901			−0.430450	−	0.902614i	$-0.641645\pi$
$643$	−553.559			−0.860901			−0.430450	+	0.902614i	$0.641645\pi$
$644$	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	$0.0316790\pi$
$659$			130.954i			0.198717i	−0.995052	+	0.0993583i	$0.968321\pi$
$660$	284.007	−	93.0018i	0.430314	−	0.140912i
$661$			363.722i			0.550259i	0.961407	+	0.275130i	$0.0887208\pi$
$661$			363.722i			0.550259i	−0.961407	+	0.275130i	$0.911279\pi$
$662$		−	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	$-0.408480\pi$
$677$	383.957			0.567145			0.283573	+	0.958951i	$0.408480\pi$
$678$	−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
$690$	214.029	+	108.696i	0.310187	+	0.157531i
$691$	−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	$-0.890691\pi$
$701$		−	472.046i		−	0.673390i	0.941614	−	0.336695i	$-0.109309\pi$
$702$		−	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	$-0.680759\pi$
$709$		−	1195.44i		−	1.68610i	0.537839	−	0.843048i	$-0.319241\pi$
$710$	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	$-0.478670\pi$
$727$	97.3614			0.133922			0.0669611	+	0.997756i	$0.478670\pi$
$728$	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	$-0.687179\pi$
$733$	−813.236			−1.10946			−0.554731	+	0.832030i	$0.687179\pi$
$734$			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	$-0.387806\pi$
$743$	512.991			0.690432			0.345216	+	0.938523i	$0.387806\pi$
$744$	−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	$-0.606476\pi$
$751$		−	1418.75i		−	1.88915i	0.328301	−	0.944573i	$-0.393524\pi$
$752$		−	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	$-0.657567\pi$
$757$	−719.211			−0.950081			−0.475040	+	0.879964i	$0.657567\pi$
$758$	−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	$-0.900348\pi$
$769$		−	473.670i		−	0.615956i	0.951394	−	0.307978i	$-0.0996522\pi$
$770$	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	$-0.360753\pi$
$773$	654.945			0.847277			0.423638	+	0.905831i	$0.360753\pi$
$774$		−	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	$-0.766280\pi$
$787$	−1168.43			−1.48466			−0.742331	+	0.670034i	$0.766280\pi$
$788$			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	$-0.704248\pi$
$797$	−954.055			−1.19706			−0.598529	+	0.801101i	$0.704248\pi$
$798$		−	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
$805$	80.8809	+	41.0760i	0.100473	+	0.0510261i
$806$	−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	$-0.526237\pi$
$827$	−136.178			−0.164665			−0.0823327	+	0.996605i	$0.526237\pi$
$828$	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	$0.284355\pi$
$839$			1307.43i			1.55832i	−0.626824	+	0.779161i	$0.715645\pi$
$840$	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	$-0.913100\pi$
$881$		−	475.083i		−	0.539254i	0.962965	−	0.269627i	$-0.0869005\pi$
$882$			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	$-0.753206\pi$
$907$	−1295.54			−1.42838			−0.714192	+	0.699950i	$0.753206\pi$
$908$	−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	$-0.819662\pi$
$911$		−	977.910i		−	1.07345i	0.843758	−	0.536724i	$-0.180338\pi$
$912$	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	$0.0924078\pi$
$919$			526.122i			0.572494i	−0.958156	+	0.286247i	$0.907592\pi$
$920$	−147.285	+	290.012i	−0.160092	+	0.315231i
$921$	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	$-0.225927\pi$
$937$	1421.45			1.51702			0.758511	+	0.651660i	$0.225927\pi$
$938$		−	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	$0.0731432\pi$
$941$			428.662i			0.455539i	−0.973715	+	0.227769i	$0.926857\pi$
$942$	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	$-0.664564\pi$
$953$	−942.074			−0.988536			−0.494268	+	0.869310i	$0.664564\pi$
$954$		−	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	$-0.845107\pi$
$971$		−	908.141i		−	0.935264i	0.883923	−	0.467632i	$-0.154893\pi$
$972$		−	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	$-0.402373\pi$
$977$	589.947			0.603835			0.301917	+	0.953334i	$0.402373\pi$
$978$			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	$-0.134984\pi$
$983$	1791.86			1.82285			0.911424	+	0.411469i	$0.134984\pi$
$984$	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.229.7	✓	24
5.2	odd	4		1150.3.d.e.551.18		24
5.3	odd	4		1150.3.d.e.551.7		24
5.4	even	2	inner	230.3.c.a.229.18	yes	24
23.22	odd	2	inner	230.3.c.a.229.8	yes	24
115.22	even	4		1150.3.d.e.551.19		24
115.68	even	4		1150.3.d.e.551.6		24
115.114	odd	2	inner	230.3.c.a.229.17	yes	24

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