LMFDB - Embedded newform 105.3.f.a.29.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,3,Mod(29,105)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(105, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

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

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

chi := DirichletCharacter("105.29");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	105.f (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:	$2.86104277578$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			29.6
Character	$\chi$	$=$	105.29
Dual form			105.3.f.a.29.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.80814 q^{2} +(0.0756962 + 2.99904i) q^{3} +3.88565 q^{4} +(-4.04610 + 2.93753i) q^{5} +(-0.212566 - 8.42174i) q^{6} +2.64575i q^{7} +0.321110 q^{8} +(-8.98854 + 0.454033i) q^{9} +O(q^{10})$	\(q-2.80814 q^{2} +(0.0756962 + 2.99904i) q^{3} +3.88565 q^{4} +(-4.04610 + 2.93753i) q^{5} +(-0.212566 - 8.42174i) q^{6} +2.64575i q^{7} +0.321110 q^{8} +(-8.98854 + 0.454033i) q^{9} +(11.3620 - 8.24901i) q^{10} -3.59726i q^{11} +(0.294129 + 11.6532i) q^{12} -16.0798i q^{13} -7.42964i q^{14} +(-9.11607 - 11.9121i) q^{15} -16.4443 q^{16} -26.3285 q^{17} +(25.2411 - 1.27499i) q^{18} -14.4376 q^{19} +(-15.7217 + 11.4142i) q^{20} +(-7.93473 + 0.200273i) q^{21} +10.1016i q^{22} +24.0028 q^{23} +(0.0243068 + 0.963022i) q^{24} +(7.74179 - 23.7711i) q^{25} +45.1543i q^{26} +(-2.04206 - 26.9227i) q^{27} +10.2805i q^{28} +16.0230i q^{29} +(25.5992 + 33.4507i) q^{30} -11.4400 q^{31} +44.8935 q^{32} +(10.7883 - 0.272299i) q^{33} +73.9342 q^{34} +(-7.77198 - 10.7050i) q^{35} +(-34.9263 + 1.76421i) q^{36} +37.3274i q^{37} +40.5428 q^{38} +(48.2241 - 1.21718i) q^{39} +(-1.29924 + 0.943270i) q^{40} +4.38279i q^{41} +(22.2818 - 0.562396i) q^{42} +72.0574i q^{43} -13.9777i q^{44} +(35.0348 - 28.2412i) q^{45} -67.4032 q^{46} -67.7338 q^{47} +(-1.24477 - 49.3173i) q^{48} -7.00000 q^{49} +(-21.7400 + 66.7525i) q^{50} +(-1.99297 - 78.9605i) q^{51} -62.4805i q^{52} -46.0920 q^{53} +(5.73440 + 75.6026i) q^{54} +(10.5671 + 14.5549i) q^{55} +0.849576i q^{56} +(-1.09287 - 43.2990i) q^{57} -44.9948i q^{58} -69.9088i q^{59} +(-35.4219 - 46.2861i) q^{60} -35.7509 q^{61} +32.1252 q^{62} +(-1.20126 - 23.7814i) q^{63} -60.2900 q^{64} +(47.2350 + 65.0604i) q^{65} +(-30.2952 + 0.764653i) q^{66} -27.1797i q^{67} -102.304 q^{68} +(1.81692 + 71.9854i) q^{69} +(21.8248 + 30.0610i) q^{70} +23.2864i q^{71} +(-2.88631 + 0.145794i) q^{72} +126.292i q^{73} -104.821i q^{74} +(71.8766 + 21.4186i) q^{75} -56.0995 q^{76} +9.51745 q^{77} +(-135.420 + 3.41801i) q^{78} -62.5142 q^{79} +(66.5353 - 48.3057i) q^{80} +(80.5877 - 8.16218i) q^{81} -12.3075i q^{82} -66.5131 q^{83} +(-30.8316 + 0.778192i) q^{84} +(106.528 - 77.3410i) q^{85} -202.347i q^{86} +(-48.0536 + 1.21288i) q^{87} -1.15511i q^{88} -44.0836i q^{89} +(-98.3825 + 79.3052i) q^{90} +42.5432 q^{91} +93.2664 q^{92} +(-0.865967 - 34.3092i) q^{93} +190.206 q^{94} +(58.4159 - 42.4109i) q^{95} +(3.39827 + 134.638i) q^{96} +46.0554i q^{97} +19.6570 q^{98} +(1.63327 + 32.3341i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 52 q^{4} - 22 q^{9}+O(q^{10}) $ 24 * q + 52 * q^4 - 22 * q^9	$ 24 q + 52 q^{4} - 22 q^{9} - 24 q^{10} + 26 q^{15} + 4 q^{16} + 72 q^{19} + 14 q^{21} - 156 q^{24} - 64 q^{25} - 32 q^{30} - 40 q^{31} - 144 q^{34} + 36 q^{36} + 62 q^{39} - 40 q^{40} + 120 q^{45} - 104 q^{46} - 168 q^{49} + 70 q^{51} + 60 q^{54} - 16 q^{55} - 348 q^{60} + 432 q^{61} - 364 q^{64} + 284 q^{66} + 404 q^{69} + 140 q^{70} + 204 q^{75} + 152 q^{76} + 108 q^{79} - 158 q^{81} + 112 q^{84} + 196 q^{85} - 152 q^{90} - 84 q^{91} + 808 q^{94} - 516 q^{96} + 582 q^{99}+O(q^{100}) $ 24 * q + 52 * q^4 - 22 * q^9 - 24 * q^10 + 26 * q^15 + 4 * q^16 + 72 * q^19 + 14 * q^21 - 156 * q^24 - 64 * q^25 - 32 * q^30 - 40 * q^31 - 144 * q^34 + 36 * q^36 + 62 * q^39 - 40 * q^40 + 120 * q^45 - 104 * q^46 - 168 * q^49 + 70 * q^51 + 60 * q^54 - 16 * q^55 - 348 * q^60 + 432 * q^61 - 364 * q^64 + 284 * q^66 + 404 * q^69 + 140 * q^70 + 204 * q^75 + 152 * q^76 + 108 * q^79 - 158 * q^81 + 112 * q^84 + 196 * q^85 - 152 * q^90 - 84 * q^91 + 808 * q^94 - 516 * q^96 + 582 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	−2.80814			−1.40407			−0.702035	−	0.712142i	$-0.747725\pi$
$2$	−2.80814			−1.40407			−0.702035	+	0.712142i	$0.747725\pi$
$3$	0.0756962	+	2.99904i	0.0252321	+	0.999682i
$3$	0.0756962	+	2.99904i	0.0252321	+	0.999682i
$4$	3.88565			0.971413
$5$	−4.04610	+	2.93753i	−0.809219	+	0.587507i
$5$	−4.04610	+	2.93753i	−0.809219	+	0.587507i
$6$	−0.212566	−	8.42174i	−0.0354276	−	1.40362i
$7$			2.64575i			0.377964i
$7$			2.64575i			0.377964i
$8$	0.321110			0.0401387
$9$	−8.98854	+	0.454033i	−0.998727	+	0.0504481i
$10$	11.3620	−	8.24901i	1.13620	−	0.824901i
$11$		−	3.59726i		−	0.327023i	−0.986541	−	0.163512i	$-0.947718\pi$
$11$		−	3.59726i		−	0.327023i	0.986541	−	0.163512i	$-0.0522822\pi$
$12$	0.294129	+	11.6532i	0.0245108	+	0.971103i
$13$		−	16.0798i		−	1.23691i	−0.785821	−	0.618454i	$-0.787759\pi$
$13$		−	16.0798i		−	1.23691i	0.785821	−	0.618454i	$-0.212241\pi$
$14$		−	7.42964i		−	0.530689i
$15$	−9.11607	−	11.9121i	−0.607738	−	0.794138i
$16$	−16.4443			−1.02777
$17$	−26.3285			−1.54874			−0.774369	−	0.632734i	$-0.781933\pi$
$17$	−26.3285			−1.54874			−0.774369	+	0.632734i	$0.781933\pi$
$18$	25.2411	−	1.27499i	1.40228	−	0.0708326i
$19$	−14.4376			−0.759874			−0.379937	−	0.925012i	$-0.624054\pi$
$19$	−14.4376			−0.759874			−0.379937	+	0.925012i	$0.624054\pi$
$20$	−15.7217	+	11.4142i	−0.786086	+	0.570711i
$21$	−7.93473	+	0.200273i	−0.377844	+	0.00953683i
$22$			10.1016i			0.459164i
$23$	24.0028			1.04360			0.521800	−	0.853068i	$-0.325261\pi$
$23$	24.0028			1.04360			0.521800	+	0.853068i	$0.325261\pi$
$24$	0.0243068	+	0.963022i	0.00101278	+	0.0401259i
$25$	7.74179	−	23.7711i	0.309672	−	0.950844i
$26$			45.1543i			1.73671i
$27$	−2.04206	−	26.9227i	−0.0756320	−	0.997136i
$28$			10.2805i			0.367159i
$29$			16.0230i			0.552516i	0.961083	+	0.276258i	$0.0890945\pi$
$29$			16.0230i			0.552516i	−0.961083	+	0.276258i	$0.910906\pi$
$30$	25.5992	+	33.4507i	0.853307	+	1.11502i
$31$	−11.4400			−0.369033			−0.184517	−	0.982829i	$-0.559072\pi$
$31$	−11.4400			−0.369033			−0.184517	+	0.982829i	$0.559072\pi$
$32$	44.8935			1.40292
$33$	10.7883	−	0.272299i	0.326919	−	0.00825148i
$34$	73.9342			2.17454
$35$	−7.77198	−	10.7050i	−0.222057	−	0.305856i
$36$	−34.9263	+	1.76421i	−0.970176	+	0.0490059i
$37$			37.3274i			1.00885i	0.863456	+	0.504425i	$0.168295\pi$
$37$			37.3274i			1.00885i	−0.863456	+	0.504425i	$0.831705\pi$
$38$	40.5428			1.06692
$39$	48.2241	−	1.21718i	1.23651	−	0.0312098i
$40$	−1.29924	+	0.943270i	−0.0324810	+	0.0235818i
$41$			4.38279i			0.106897i	0.998571	+	0.0534487i	$0.0170214\pi$
$41$			4.38279i			0.106897i	−0.998571	+	0.0534487i	$0.982979\pi$
$42$	22.2818	−	0.562396i	0.530520	−	0.0133904i
$43$			72.0574i			1.67575i	0.545860	+	0.837876i	$0.316203\pi$
$43$			72.0574i			1.67575i	−0.545860	+	0.837876i	$0.683797\pi$
$44$		−	13.9777i		−	0.317675i
$45$	35.0348	−	28.2412i	0.778550	−	0.627582i
$46$	−67.4032			−1.46529
$47$	−67.7338			−1.44114			−0.720572	−	0.693380i	$-0.756121\pi$
$47$	−67.7338			−1.44114			−0.720572	+	0.693380i	$0.756121\pi$
$48$	−1.24477	−	49.3173i	−0.0259328	−	1.02744i
$49$	−7.00000			−0.142857
$50$	−21.7400	+	66.7525i	−0.434801	+	1.33505i
$51$	−1.99297	−	78.9605i	−0.0390779	−	1.54824i
$52$		−	62.4805i		−	1.20155i
$53$	−46.0920			−0.869660			−0.434830	−	0.900513i	$-0.643191\pi$
$53$	−46.0920			−0.869660			−0.434830	+	0.900513i	$0.643191\pi$
$54$	5.73440	+	75.6026i	0.106193	+	1.40005i
$55$	10.5671	+	14.5549i	0.192128	+	0.264634i
$56$			0.849576i			0.0151710i
$57$	−1.09287	−	43.2990i	−0.0191732	−	0.759632i
$58$		−	44.9948i		−	0.775772i
$59$		−	69.9088i		−	1.18490i	−0.805609	−	0.592448i	$-0.798162\pi$
$59$		−	69.9088i		−	1.18490i	0.805609	−	0.592448i	$-0.201838\pi$
$60$	−35.4219	−	46.2861i	−0.590364	−	0.771435i
$61$	−35.7509			−0.586080			−0.293040	−	0.956100i	$-0.594667\pi$
$61$	−35.7509			−0.586080			−0.293040	+	0.956100i	$0.594667\pi$
$62$	32.1252			0.518148
$63$	−1.20126	−	23.7814i	−0.0190676	−	0.377483i
$64$	−60.2900			−0.942031
$65$	47.2350	+	65.0604i	0.726692	+	1.00093i
$66$	−30.2952	+	0.764653i	−0.459018	+	0.0115857i
$67$		−	27.1797i		−	0.405667i	−0.979213	−	0.202834i	$-0.934985\pi$
$67$		−	27.1797i		−	0.405667i	0.979213	−	0.202834i	$-0.0650151\pi$
$68$	−102.304			−1.50446
$69$	1.81692	+	71.9854i	0.0263322	+	1.04327i
$70$	21.8248	+	30.0610i	0.311783	+	0.429443i
$71$			23.2864i			0.327977i	0.986462	+	0.163989i	$0.0524361\pi$
$71$			23.2864i			0.327977i	−0.986462	+	0.163989i	$0.947564\pi$
$72$	−2.88631	+	0.145794i	−0.0400876	+	0.00202492i
$73$			126.292i			1.73003i	0.501745	+	0.865016i	$0.332692\pi$
$73$			126.292i			1.73003i	−0.501745	+	0.865016i	$0.667308\pi$
$74$		−	104.821i		−	1.41650i
$75$	71.8766	+	21.4186i	0.958354	+	0.285581i
$76$	−56.0995			−0.738151
$77$	9.51745			0.123603
$78$	−135.420	+	3.41801i	−1.73615	+	0.0438207i
$79$	−62.5142			−0.791319			−0.395659	−	0.918397i	$-0.629484\pi$
$79$	−62.5142			−0.791319			−0.395659	+	0.918397i	$0.629484\pi$
$80$	66.5353	−	48.3057i	0.831691	−	0.603822i
$81$	80.5877	−	8.16218i	0.994910	−	0.100768i
$82$		−	12.3075i		−	0.150091i
$83$	−66.5131			−0.801363			−0.400681	−	0.916217i	$-0.631227\pi$
$83$	−66.5131			−0.801363			−0.400681	+	0.916217i	$0.631227\pi$
$84$	−30.8316	+	0.778192i	−0.367043	+	0.00926420i
$85$	106.528	−	77.3410i	1.25327	−	0.909894i
$86$		−	202.347i		−	2.35287i
$87$	−48.0536	+	1.21288i	−0.552340	+	0.0139411i
$88$		−	1.15511i		−	0.0131263i
$89$		−	44.0836i		−	0.495322i	−0.968847	−	0.247661i	$-0.920338\pi$
$89$		−	44.0836i		−	0.495322i	0.968847	−	0.247661i	$-0.0796618\pi$
$90$	−98.3825	+	79.3052i	−1.09314	+	0.881169i
$91$	42.5432			0.467507
$92$	93.2664			1.01377
$93$	−0.865967	−	34.3092i	−0.00931147	−	0.368916i
$94$	190.206			2.02347
$95$	58.4159	−	42.4109i	0.614904	−	0.446431i
$96$	3.39827	+	134.638i	0.0353986	+	1.40248i
$97$			46.0554i			0.474798i	0.971412	+	0.237399i	$0.0762948\pi$
$97$			46.0554i			0.474798i	−0.971412	+	0.237399i	$0.923705\pi$
$98$	19.6570			0.200581
$99$	1.63327	+	32.3341i	0.0164977	+	0.326607i
$100$	30.0819	−	92.3661i	0.300819	−	0.923661i
$101$			175.773i			1.74032i	0.492766	+	0.870162i	$0.335986\pi$
$101$			175.773i			1.74032i	−0.492766	+	0.870162i	$0.664014\pi$
$102$	5.59654	+	221.732i	0.0548681	+	2.17384i
$103$		−	104.183i		−	1.01148i	−0.862685	−	0.505742i	$-0.831219\pi$
$103$		−	104.183i		−	1.01148i	0.862685	−	0.505742i	$-0.168781\pi$
$104$		−	5.16338i		−	0.0496479i
$105$	31.5164	−	24.1189i	0.300156	−	0.229703i
$106$	129.433			1.22106
$107$	−15.8591			−0.148216			−0.0741081	−	0.997250i	$-0.523611\pi$
$107$	−15.8591			−0.148216			−0.0741081	+	0.997250i	$0.523611\pi$
$108$	−7.93474	−	104.612i	−0.0734699	−	0.968630i
$109$	−98.5537			−0.904163			−0.452081	−	0.891977i	$-0.649318\pi$
$109$	−98.5537			−0.904163			−0.452081	+	0.891977i	$0.649318\pi$
$110$	−29.6738	−	40.8721i	−0.269762	−	0.371564i
$111$	−111.947	+	2.82555i	−1.00853	+	0.0254554i
$112$		−	43.5076i		−	0.388461i
$113$	125.379			1.10955			0.554777	−	0.831999i	$-0.312804\pi$
$113$	125.379			1.10955			0.554777	+	0.831999i	$0.312804\pi$
$114$	3.06894	+	121.590i	0.0269205	+	1.06658i
$115$	−97.1176	+	70.5090i	−0.844500	+	0.613121i
$116$			62.2597i			0.536721i
$117$	7.30076	+	144.534i	0.0623996	+	1.23533i
$118$			196.314i			1.66368i
$119$		−	69.6588i		−	0.585368i
$120$	−2.92726	−	3.82508i	−0.0243938	−	0.0318757i
$121$	108.060			0.893056
$122$	100.394			0.822898
$123$	−13.1442	+	0.331761i	−0.106863	+	0.00269724i
$124$	−44.4519			−0.358483
$125$	38.5043	+	118.922i	0.308035	+	0.951375i
$126$	3.37330	+	66.7816i	0.0267722	+	0.530013i
$127$		−	193.048i		−	1.52006i	−0.649886	−	0.760032i	$-0.725183\pi$
$127$		−	193.048i		−	1.52006i	0.649886	−	0.760032i	$-0.274817\pi$
$128$	−10.2713			−0.0802446
$129$	−216.103	+	5.45447i	−1.67522	+	0.0422827i
$130$	−132.642	−	182.699i	−1.02033	−	1.40538i
$131$			145.120i			1.10779i	0.832587	+	0.553894i	$0.186859\pi$
$131$			145.120i			1.10779i	−0.832587	+	0.553894i	$0.813141\pi$
$132$	41.9197	−	1.05806i	0.317574	−	0.00801559i
$133$		−	38.1983i		−	0.287205i
$134$			76.3244i			0.569585i
$135$	87.3486	+	102.933i	0.647027	+	0.762467i
$136$	−8.45435			−0.0621643
$137$	15.5198			0.113283			0.0566416	−	0.998395i	$-0.481961\pi$
$137$	15.5198			0.113283			0.0566416	+	0.998395i	$0.481961\pi$
$138$	−5.10217	−	202.145i	−0.0369722	−	1.46482i
$139$	56.1606			0.404033			0.202016	−	0.979382i	$-0.435251\pi$
$139$	56.1606			0.404033			0.202016	+	0.979382i	$0.435251\pi$
$140$	−30.1992	−	41.5958i	−0.215709	−	0.297113i
$141$	−5.12719	−	203.137i	−0.0363631	−	1.44069i
$142$		−	65.3915i		−	0.460503i
$143$	−57.8432			−0.404498
$144$	147.810	−	7.46626i	1.02646	−	0.0518490i
$145$	−47.0680	−	64.8305i	−0.324607	−	0.447107i
$146$		−	354.646i		−	2.42909i
$147$	−0.529874	−	20.9933i	−0.00360458	−	0.142812i
$148$			145.041i			0.980009i
$149$			20.1726i			0.135387i	0.997706	+	0.0676934i	$0.0215640\pi$
$149$			20.1726i			0.135387i	−0.997706	+	0.0676934i	$0.978436\pi$
$150$	−201.840	−	60.1464i	−1.34560	−	0.400976i
$151$	−77.8789			−0.515754			−0.257877	−	0.966178i	$-0.583023\pi$
$151$	−77.8789			−0.515754			−0.257877	+	0.966178i	$0.583023\pi$
$152$	−4.63605			−0.0305003
$153$	236.655	−	11.9540i	1.54677	−	0.0781309i
$154$	−26.7263			−0.173548
$155$	46.2875	−	33.6055i	0.298629	−	0.216809i
$156$	187.382	−	4.72954i	1.20117	−	0.0303176i
$157$			3.27506i			0.0208602i	0.999946	+	0.0104301i	$0.00332007\pi$
$157$			3.27506i			0.0208602i	−0.999946	+	0.0104301i	$0.996680\pi$
$158$	175.549			1.11107
$159$	−3.48899	−	138.232i	−0.0219433	−	0.869383i
$160$	−181.644	+	131.876i	−1.13527	+	0.824226i
$161$			63.5054i			0.394443i
$162$	−226.302	+	22.9206i	−1.39692	+	0.141485i
$163$			156.100i			0.957670i	0.877905	+	0.478835i	$0.158941\pi$
$163$			156.100i			0.957670i	−0.877905	+	0.478835i	$0.841059\pi$
$164$			17.0300i			0.103841i
$165$	−42.8508	+	32.7929i	−0.259702	+	0.198745i
$166$	186.778			1.12517
$167$	−238.098			−1.42573			−0.712867	−	0.701299i	$-0.752604\pi$
$167$	−238.098			−1.42573			−0.712867	+	0.701299i	$0.752604\pi$
$168$	−2.54792	+	0.0643097i	−0.0151662	+	0.000382796i
$169$	−89.5602			−0.529942
$170$	−299.145	+	217.184i	−1.75968	+	1.27755i
$171$	129.773	−	6.55514i	0.758906	−	0.0383342i
$172$			279.990i			1.62785i
$173$	263.981			1.52590			0.762952	−	0.646455i	$-0.223749\pi$
$173$	263.981			1.52590			0.762952	+	0.646455i	$0.223749\pi$
$174$	134.941	−	3.40593i	0.775525	−	0.0195743i
$175$	62.8924	+	20.4829i	0.359385	+	0.117045i
$176$			59.1545i			0.336105i
$177$	209.660	−	5.29184i	1.18452	−	0.0298974i
$178$			123.793i			0.695466i
$179$			208.009i			1.16206i	0.813881	+	0.581031i	$0.197351\pi$
$179$			208.009i			1.16206i	−0.813881	+	0.581031i	$0.802649\pi$
$180$	136.133	−	109.735i	0.756294	−	0.609641i
$181$	233.113			1.28791			0.643957	−	0.765061i	$-0.277291\pi$
$181$	233.113			1.28791			0.643957	+	0.765061i	$0.277291\pi$
$182$	−119.467			−0.656413
$183$	−2.70621	−	107.219i	−0.0147880	−	0.585894i
$184$	7.70752			0.0418887
$185$	−109.651	−	151.030i	−0.592706	−	0.816381i
$186$	2.43176	+	96.3449i	0.0130740	+	0.517983i
$187$			94.7106i			0.506474i
$188$	−263.190			−1.39995
$189$	71.2307	−	5.40279i	0.376882	−	0.0285862i
$190$	−164.040	+	119.096i	−0.863369	+	0.626820i
$191$		−	361.005i		−	1.89008i	−0.326958	−	0.945039i	$-0.606024\pi$
$191$		−	361.005i		−	1.89008i	0.326958	−	0.945039i	$-0.393976\pi$
$192$	−4.56373	−	180.812i	−0.0237694	−	0.941731i
$193$		−	193.089i		−	1.00046i	−0.865893	−	0.500230i	$-0.833249\pi$
$193$		−	193.089i		−	1.00046i	0.865893	−	0.500230i	$-0.166751\pi$
$194$		−	129.330i		−	0.666649i
$195$	−191.544	+	146.585i	−0.982275	+	0.751716i
$196$	−27.1996			−0.138773
$197$	−75.9883			−0.385727			−0.192864	−	0.981226i	$-0.561778\pi$
$197$	−75.9883			−0.385727			−0.192864	+	0.981226i	$0.561778\pi$
$198$	−4.58646	−	90.7987i	−0.0231639	−	0.458579i
$199$	−8.99113			−0.0451816			−0.0225908	−	0.999745i	$-0.507191\pi$
$199$	−8.99113			−0.0451816			−0.0225908	+	0.999745i	$0.507191\pi$
$200$	2.48596	−	7.63313i	0.0124298	−	0.0381656i
$201$	81.5132	−	2.05740i	0.405538	−	0.0102358i
$202$		−	493.594i		−	2.44354i
$203$	−42.3928			−0.208832
$204$	−7.74399	−	306.813i	−0.0379607	−	1.50398i
$205$	−12.8746	−	17.7332i	−0.0628029	−	0.0865034i
$206$			292.560i			1.42019i
$207$	−215.750	+	10.8980i	−1.04227	+	0.0526476i
$208$			264.422i			1.27126i
$209$			51.9358i			0.248497i
$210$	−88.5024	+	67.7291i	−0.421440	+	0.322520i
$211$	54.8329			0.259872			0.129936	−	0.991522i	$-0.458523\pi$
$211$	54.8329			0.259872			0.129936	+	0.991522i	$0.458523\pi$
$212$	−179.097			−0.844798
$213$	−69.8370	+	1.76269i	−0.327873	+	0.00827555i
$214$	44.5346			0.208106
$215$	−211.671	−	291.551i	−0.984516	−	1.35605i
$216$	−0.655726	−	8.64513i	−0.00303577	−	0.0400237i
$217$		−	30.2675i		−	0.139481i
$218$	276.753			1.26951
$219$	−378.756	+	9.55985i	−1.72948	+	0.0436523i
$220$	41.0599	+	56.5551i	0.186636	+	0.257069i
$221$			423.358i			1.91565i
$222$	314.362	−	7.93453i	1.41604	−	0.0357411i
$223$		−	21.8991i		−	0.0982021i	−0.998794	−	0.0491011i	$-0.984364\pi$
$223$		−	21.8991i		−	0.0982021i	0.998794	−	0.0491011i	$-0.0156356\pi$
$224$			118.777i			0.530255i
$225$	−58.7946	+	217.182i	−0.261309	+	0.965255i
$226$	−352.083			−1.55789
$227$	314.948			1.38743			0.693717	−	0.720247i	$-0.255972\pi$
$227$	314.948			1.38743			0.693717	+	0.720247i	$0.255972\pi$
$228$	−4.24652	−	168.245i	−0.0186251	−	0.737916i
$229$	−215.213			−0.939794			−0.469897	−	0.882721i	$-0.655709\pi$
$229$	−215.213			−0.939794			−0.469897	+	0.882721i	$0.655709\pi$
$230$	272.720	−	197.999i	1.18574	−	0.860865i
$231$	0.720435	+	28.5433i	0.00311877	+	0.123564i
$232$			5.14513i			0.0221773i
$233$	−7.50423			−0.0322070			−0.0161035	−	0.999870i	$-0.505126\pi$
$233$	−7.50423			−0.0322070			−0.0161035	+	0.999870i	$0.505126\pi$
$234$	−20.5016	−	405.872i	−0.0876135	−	1.73449i
$235$	274.058	−	198.970i	1.16620	−	0.846682i
$236$		−	271.641i		−	1.15102i
$237$	−4.73209	−	187.483i	−0.0199666	−	0.791067i
$238$			195.612i			0.821897i
$239$			150.775i			0.630858i	0.948949	+	0.315429i	$0.102148\pi$
$239$			150.775i			0.630858i	−0.948949	+	0.315429i	$0.897852\pi$
$240$	149.908	+	195.886i	0.624615	+	0.816191i
$241$	25.3748			0.105290			0.0526449	−	0.998613i	$-0.483235\pi$
$241$	25.3748			0.105290			0.0526449	+	0.998613i	$0.483235\pi$
$242$	−303.447			−1.25391
$243$	30.5789	+	241.068i	0.125839	+	0.992051i
$244$	−138.916			−0.569326
$245$	28.3227	−	20.5627i	0.115603	−	0.0839295i
$246$	36.9107	−	0.931631i	0.150044	−	0.00378712i
$247$			232.154i			0.939894i
$248$	−3.67350			−0.0148125
$249$	−5.03479	−	199.476i	−0.0202200	−	0.801108i
$250$	−108.126	−	333.949i	−0.432502	−	1.33580i
$251$			109.276i			0.435364i	0.976020	+	0.217682i	$0.0698495\pi$
$251$			109.276i			0.435364i	−0.976020	+	0.217682i	$0.930151\pi$
$252$	−4.66767	−	92.4064i	−0.0185225	−	0.366692i
$253$		−	86.3442i		−	0.341281i
$254$			542.106i			2.13428i
$255$	240.013	+	313.627i	0.941227	+	1.22991i
$256$	270.003			1.05470
$257$	156.675			0.609630			0.304815	−	0.952412i	$-0.401405\pi$
$257$	156.675			0.609630			0.304815	+	0.952412i	$0.401405\pi$
$258$	606.848	−	15.3169i	2.35212	−	0.0593679i
$259$	−98.7591			−0.381309
$260$	183.539	+	252.802i	0.705918	+	0.972316i
$261$	−7.27496	−	144.023i	−0.0278734	−	0.551813i
$262$		−	407.518i		−	1.55541i
$263$	−315.001			−1.19772			−0.598862	−	0.800853i	$-0.704380\pi$
$263$	−315.001			−1.19772			−0.598862	+	0.800853i	$0.704380\pi$
$264$	3.46424	−	0.0874378i	0.0131221	−	0.000331204i
$265$	186.493	−	135.397i	0.703745	−	0.510931i
$266$			107.266i			0.403256i
$267$	132.209	−	3.33696i	0.495164	−	0.0124980i
$268$		−	105.611i		−	0.394070i
$269$			361.371i			1.34339i	0.740829	+	0.671694i	$0.234433\pi$
$269$			361.371i			1.34339i	−0.740829	+	0.671694i	$0.765567\pi$
$270$	−245.287	−	289.050i	−0.908471	−	1.07056i
$271$	63.2390			0.233354			0.116677	−	0.993170i	$-0.462776\pi$
$271$	63.2390			0.233354			0.116677	+	0.993170i	$0.462776\pi$
$272$	432.955			1.59175
$273$	3.22036	+	127.589i	0.0117962	+	0.467358i
$274$	−43.5818			−0.159058
$275$	−85.5107	−	27.8492i	−0.310948	−	0.101270i
$276$	7.05992	+	279.710i	0.0255794	+	1.01344i
$277$			495.461i			1.78867i	0.447400	+	0.894334i	$0.352350\pi$
$277$			495.461i			1.78867i	−0.447400	+	0.894334i	$0.647650\pi$
$278$	−157.707			−0.567291
$279$	102.829	−	5.19415i	0.368563	−	0.0186170i
$280$	−2.49566	−	3.43747i	−0.00891307	−	0.0122767i
$281$		−	409.194i		−	1.45621i	−0.685467	−	0.728104i	$-0.740402\pi$
$281$		−	409.194i		−	1.45621i	0.685467	−	0.728104i	$-0.259598\pi$
$282$	14.3979	+	570.436i	0.0510563	+	2.02282i
$283$		−	339.701i		−	1.20036i	−0.799866	−	0.600179i	$-0.795096\pi$
$283$		−	339.701i		−	1.20036i	0.799866	−	0.600179i	$-0.204904\pi$
$284$			90.4828i			0.318601i
$285$	131.614	+	171.982i	0.461804	+	0.603444i
$286$	162.432			0.567943
$287$	−11.5958			−0.0404034
$288$	−403.527	+	20.3831i	−1.40114	+	0.0707748i
$289$	404.192			1.39859
$290$	132.174	+	182.053i	0.455771	+	0.627769i
$291$	−138.122	+	3.48622i	−0.474647	+	0.0119801i
$292$			490.728i			1.68057i
$293$	−576.774			−1.96851			−0.984256	−	0.176751i	$-0.943441\pi$
$293$	−576.774			−1.96851			−0.984256	+	0.176751i	$0.943441\pi$
$294$	1.48796	+	58.9522i	0.00506109	+	0.200518i
$295$	205.360	+	282.858i	0.696134	+	0.958841i
$296$			11.9862i			0.0404939i
$297$	−96.8478	+	7.34583i	−0.326087	+	0.0247334i
$298$		−	56.6476i		−	0.190093i
$299$		−	385.960i		−	1.29084i
$300$	279.287	+	83.2252i	0.930958	+	0.277417i
$301$	−190.646			−0.633375
$302$	218.695			0.724155
$303$	−527.150	+	13.3053i	−1.73977	+	0.0439120i
$304$	237.417			0.780975
$305$	144.652	−	105.019i	0.474268	−	0.344326i
$306$	−664.561	+	33.5686i	−2.17177	+	0.109701i
$307$		−	191.371i		−	0.623358i	−0.950187	−	0.311679i	$-0.899109\pi$
$307$		−	191.371i		−	0.623358i	0.950187	−	0.311679i	$-0.100891\pi$
$308$	36.9815			0.120070
$309$	312.449	−	7.88624i	1.01116	−	0.0255218i
$310$	−129.982	+	94.3688i	−0.419296	+	0.304416i
$311$		−	66.5906i		−	0.214118i	−0.994253	−	0.107059i	$-0.965857\pi$
$311$		−	66.5906i		−	0.214118i	0.994253	−	0.107059i	$-0.0341433\pi$
$312$	15.4852	−	0.390848i	0.0496321	−	0.00125272i
$313$		−	145.842i		−	0.465950i	−0.972483	−	0.232975i	$-0.925154\pi$
$313$		−	145.842i		−	0.465950i	0.972483	−	0.232975i	$-0.0748461\pi$
$314$		−	9.19682i		−	0.0292892i
$315$	74.7192	+	92.6933i	0.237204	+	0.294264i
$316$	−242.908			−0.768697
$317$	−96.6461			−0.304877			−0.152439	−	0.988313i	$-0.548713\pi$
$317$	−96.6461			−0.304877			−0.152439	+	0.988313i	$0.548713\pi$
$318$	9.79757	+	388.174i	0.0308100	+	1.22067i
$319$	57.6388			0.180686
$320$	243.939	−	177.104i	0.762310	−	0.553450i
$321$	−1.20048	−	47.5622i	−0.00373980	−	0.148169i
$322$		−	178.332i		−	0.553826i
$323$	380.121			1.17685
$324$	313.136	−	31.7154i	0.966468	−	0.0978870i
$325$	−382.234	−	124.487i	−1.17611	−	0.383036i
$326$		−	438.351i		−	1.34464i
$327$	−7.46014	−	295.567i	−0.0228139	−	0.903875i
$328$			1.40736i			0.00429072i
$329$		−	179.207i		−	0.544702i
$330$	120.331	−	92.0869i	0.364639	−	0.279051i
$331$	7.88340			0.0238169			0.0119085	−	0.999929i	$-0.496209\pi$
$331$	7.88340			0.0238169			0.0119085	+	0.999929i	$0.496209\pi$
$332$	−258.447			−0.778454
$333$	−16.9479	−	335.519i	−0.0508945	−	1.00757i
$334$	668.611			2.00183
$335$	79.8413	+	109.972i	0.238332	+	0.328274i
$336$	130.481	−	3.29336i	0.388337	−	0.00980167i
$337$			226.672i			0.672616i	0.941752	+	0.336308i	$0.109178\pi$
$337$			226.672i			0.672616i	−0.941752	+	0.336308i	$0.890822\pi$
$338$	251.497			0.744075
$339$	9.49075	+	376.019i	0.0279963	+	1.10920i
$340$	413.930	−	300.520i	1.21744	−	0.883882i
$341$			41.1527i			0.120682i
$342$	−364.421	+	18.4078i	−1.06556	+	0.0538239i
$343$		−	18.5203i		−	0.0539949i
$344$			23.1383i			0.0672625i
$345$	−218.811	−	285.923i	−0.634235	−	0.828761i
$346$	−741.297			−2.14248
$347$	510.911			1.47237			0.736183	−	0.676782i	$-0.236626\pi$
$347$	510.911			1.47237			0.736183	+	0.676782i	$0.236626\pi$
$348$	−186.720	+	4.71282i	−0.536550	+	0.0135426i
$349$	−541.756			−1.55231			−0.776154	−	0.630543i	$-0.782832\pi$
$349$	−541.756			−1.55231			−0.776154	+	0.630543i	$0.782832\pi$
$350$	−176.611	−	57.5187i	−0.504602	−	0.164339i
$351$	−432.911	+	32.8360i	−1.23337	+	0.0935498i
$352$		−	161.494i		−	0.458789i
$353$	−373.717			−1.05869			−0.529345	−	0.848407i	$-0.677562\pi$
$353$	−373.717			−1.05869			−0.529345	+	0.848407i	$0.677562\pi$
$354$	−588.754	+	14.8602i	−1.66315	+	0.0419780i
$355$	−68.4046	−	94.2190i	−0.192689	−	0.265406i
$356$		−	171.294i		−	0.481162i
$357$	208.910	−	5.27291i	0.585182	−	0.0147700i
$358$		−	584.119i		−	1.63162i
$359$		−	505.480i		−	1.40802i	−0.710190	−	0.704011i	$-0.751391\pi$
$359$		−	505.480i		−	1.40802i	0.710190	−	0.704011i	$-0.248609\pi$
$360$	11.2500	−	9.06852i	0.0312500	−	0.0251903i
$361$	−152.556			−0.422592
$362$	−654.613			−1.80832
$363$	8.17971	+	324.076i	0.0225336	+	0.892771i
$364$	165.308			0.454143
$365$	−370.988	−	510.991i	−1.01641	−	1.39997i
$366$	7.59941	+	301.085i	0.0207634	+	0.822636i
$367$		−	135.116i		−	0.368164i	−0.982911	−	0.184082i	$-0.941069\pi$
$367$		−	135.116i		−	0.368164i	0.982911	−	0.184082i	$-0.0589311\pi$
$368$	−394.709			−1.07258
$369$	−1.98993	−	39.3949i	−0.00539277	−	0.106761i
$370$	307.914	+	424.115i	0.832201	+	1.14626i
$371$		−	121.948i		−	0.328700i
$372$	−3.36484	−	133.313i	−0.00904528	−	0.358369i
$373$			122.340i			0.327989i	0.986461	+	0.163994i	$0.0524379\pi$
$373$			122.340i			0.327989i	−0.986461	+	0.163994i	$0.947562\pi$
$374$		−	265.961i		−	0.711124i
$375$	−353.737	+	124.478i	−0.943300	+	0.331942i
$376$	−21.7500			−0.0578457
$377$	257.646			0.683412
$378$	−200.026	+	15.1718i	−0.529169	+	0.0401370i
$379$	−259.772			−0.685413			−0.342707	−	0.939442i	$-0.611344\pi$
$379$	−259.772			−0.685413			−0.342707	+	0.939442i	$0.611344\pi$
$380$	226.984	−	164.794i	0.597326	−	0.433669i
$381$	578.960	−	14.6130i	1.51958	−	0.0383544i
$382$			1013.75i			2.65380i
$383$	320.383			0.836509			0.418254	−	0.908330i	$-0.362642\pi$
$383$	320.383			0.836509			0.418254	+	0.908330i	$0.362642\pi$
$384$	−0.777499	−	30.8041i	−0.00202474	−	0.0802191i
$385$	−38.5085	+	27.9578i	−0.100022	+	0.0726177i
$386$			542.220i			1.40472i
$387$	−32.7164	−	647.690i	−0.0845385	−	1.67362i
$388$			178.955i			0.461225i
$389$		−	67.6100i		−	0.173805i	−0.996217	−	0.0869023i	$-0.972303\pi$
$389$		−	67.6100i		−	0.173805i	0.996217	−	0.0869023i	$-0.0276968\pi$
$390$	537.882	−	411.630i	1.37918	−	1.05546i
$391$	−631.958			−1.61626
$392$	−2.24777			−0.00573410
$393$	−435.222	+	10.9851i	−1.10744	+	0.0279518i
$394$	213.386			0.541588
$395$	252.938	−	183.637i	0.640350	−	0.464905i
$396$	6.34633	+	125.639i	0.0160261	+	0.317270i
$397$			128.847i			0.324553i	0.986745	+	0.162276i	$0.0518836\pi$
$397$			128.847i			0.324553i	−0.986745	+	0.162276i	$0.948116\pi$
$398$	25.2484			0.0634381
$399$	114.558	−	2.89147i	0.287114	−	0.00724678i
$400$	−127.309	+	390.899i	−0.318271	+	0.977249i
$401$			509.137i			1.26967i	0.772648	+	0.634834i	$0.218932\pi$
$401$			509.137i			1.26967i	−0.772648	+	0.634834i	$0.781068\pi$
$402$	−228.900	+	5.77747i	−0.569404	+	0.0143718i
$403$			183.953i			0.456460i
$404$			682.991i			1.69057i
$405$	−302.089	+	269.754i	−0.745899	+	0.666059i
$406$	119.045			0.293214
$407$	134.276			0.329917
$408$	−0.639962	−	25.3550i	−0.00156854	−	0.0621445i
$409$	−44.4377			−0.108650			−0.0543248	−	0.998523i	$-0.517301\pi$
$409$	−44.4377			−0.108650			−0.0543248	+	0.998523i	$0.517301\pi$
$410$	36.1537	+	49.7973i	0.0881797	+	0.121457i
$411$	1.17479	+	46.5446i	0.00285837	+	0.113247i
$412$		−	404.818i		−	0.982568i
$413$	184.961			0.447848
$414$	605.856	−	30.6032i	1.46342	−	0.0739209i
$415$	269.118	−	195.384i	0.648478	−	0.470806i
$416$		−	721.879i		−	1.73529i
$417$	4.25114	+	168.428i	0.0101946	+	0.403904i
$418$		−	145.843i		−	0.348906i
$419$		−	299.257i		−	0.714218i	−0.934063	−	0.357109i	$-0.883762\pi$
$419$		−	299.257i		−	0.714218i	0.934063	−	0.357109i	$-0.116238\pi$
$420$	122.462	−	93.7174i	0.291575	−	0.223137i
$421$	153.710			0.365107			0.182554	−	0.983196i	$-0.441564\pi$
$421$	153.710			0.365107			0.182554	+	0.983196i	$0.441564\pi$
$422$	−153.979			−0.364878
$423$	608.828	−	30.7534i	1.43931	−	0.0727030i
$424$	−14.8006			−0.0349070
$425$	−203.830	+	625.858i	−0.479600	+	1.47261i
$426$	196.112	−	4.94989i	0.460357	−	0.0116195i
$427$		−	94.5880i		−	0.221518i
$428$	−61.6230			−0.143979
$429$	−4.37851	−	173.474i	−0.0102063	−	0.404369i
$430$	594.401	+	818.716i	1.38233	+	1.90399i
$431$		−	83.8187i		−	0.194475i	−0.995261	−	0.0972375i	$-0.968999\pi$
$431$		−	83.8187i		−	0.194475i	0.995261	−	0.0972375i	$-0.0310006\pi$
$432$	33.5803	+	442.725i	0.0777323	+	1.02483i
$433$			690.606i			1.59493i	0.603363	+	0.797467i	$0.293827\pi$
$433$			690.606i			1.59493i	−0.603363	+	0.797467i	$0.706173\pi$
$434$			84.9953i			0.195842i
$435$	190.867	−	146.067i	0.438774	−	0.335785i
$436$	−382.945			−0.878315
$437$	−346.542			−0.793003
$438$	1063.60	−	26.8454i	2.42831	−	0.0612909i
$439$	201.984			0.460101			0.230050	−	0.973179i	$-0.426111\pi$
$439$	201.984			0.460101			0.230050	+	0.973179i	$0.426111\pi$
$440$	3.39319	+	4.67370i	0.00771179	+	0.0106221i
$441$	62.9198	−	3.17823i	0.142675	−	0.00720687i
$442$		−	1188.85i		−	2.68970i
$443$	884.029			1.99555			0.997775	−	0.0666696i	$-0.0212374\pi$
$443$	884.029			1.99555			0.997775	+	0.0666696i	$0.0212374\pi$
$444$	−434.986	+	10.9791i	−0.979697	+	0.0247277i
$445$	129.497	+	178.367i	0.291005	+	0.400824i
$446$			61.4957i			0.137883i
$447$	−60.4987	+	1.52699i	−0.135344	+	0.00341609i
$448$		−	159.512i		−	0.356054i
$449$			183.991i			0.409779i	0.978785	+	0.204890i	$0.0656835\pi$
$449$			183.991i			0.409779i	−0.978785	+	0.204890i	$0.934316\pi$
$450$	165.103	−	609.879i	0.366896	−	1.35529i
$451$	15.7660			0.0349580
$452$	487.181			1.07783
$453$	−5.89514	−	233.562i	−0.0130135	−	0.515590i
$454$	−884.417			−1.94806
$455$	−172.134	+	124.972i	−0.378316	+	0.274664i
$456$	−0.350932	−	13.9037i	−0.000769587	−	0.0304906i
$457$		−	97.9893i		−	0.214419i	−0.994236	−	0.107209i	$-0.965809\pi$
$457$		−	97.9893i		−	0.214419i	0.994236	−	0.107209i	$-0.0341915\pi$
$458$	604.348			1.31954
$459$	53.7646	+	708.835i	0.117134	+	1.54430i
$460$	−377.365	+	273.973i	−0.820358	+	0.595594i
$461$			443.155i			0.961290i	0.876915	+	0.480645i	$0.159597\pi$
$461$			443.155i			0.961290i	−0.876915	+	0.480645i	$0.840403\pi$
$462$	−2.02308	−	80.1535i	−0.00437897	−	0.173492i
$463$			351.262i			0.758664i	0.925261	+	0.379332i	$0.123846\pi$
$463$			351.262i			0.758664i	−0.925261	+	0.379332i	$0.876154\pi$
$464$		−	263.487i		−	0.567860i
$465$	104.288	+	136.274i	0.224275	+	0.293063i
$466$	21.0729			0.0452209
$467$	215.999			0.462524			0.231262	−	0.972892i	$-0.425715\pi$
$467$	215.999			0.462524			0.231262	+	0.972892i	$0.425715\pi$
$468$	28.3682	+	561.609i	0.0606158	+	1.20002i
$469$	71.9108			0.153328
$470$	−769.592	+	558.737i	−1.63743	+	1.18880i
$471$	−9.82205	+	0.247910i	−0.0208536	+	0.000526347i
$472$		−	22.4484i		−	0.0475602i
$473$	259.209			0.548010
$474$	13.2884	+	526.478i	0.0280345	+	1.11071i
$475$	−111.773	+	343.197i	−0.235311	+	0.722521i
$476$		−	270.670i		−	0.568634i
$477$	414.299	−	20.9273i	0.868552	−	0.0438727i
$478$		−	423.398i		−	0.885769i
$479$		−	328.120i		−	0.685010i	−0.939516	−	0.342505i	$-0.888725\pi$
$479$		−	328.120i		−	0.685010i	0.939516	−	0.342505i	$-0.111275\pi$
$480$	−409.252	−	534.775i	−0.852609	−	1.11411i
$481$	600.218			1.24785
$482$	−71.2561			−0.147834
$483$	−190.455	+	4.80712i	−0.394318	+	0.00995262i
$484$	419.882			0.867526
$485$	−135.289	−	186.345i	−0.278947	−	0.384216i
$486$	−85.8699	−	676.954i	−0.176687	−	1.39291i
$487$			148.564i			0.305059i	0.988299	+	0.152530i	$0.0487419\pi$
$487$			148.564i			0.305059i	−0.988299	+	0.152530i	$0.951258\pi$
$488$	−11.4800			−0.0235245
$489$	−468.152	+	11.8162i	−0.957366	+	0.0241640i
$490$	−79.5340	+	57.7430i	−0.162314	+	0.117843i
$491$			373.029i			0.759732i	0.925041	+	0.379866i	$0.124030\pi$
$491$			373.029i			0.759732i	−0.925041	+	0.379866i	$0.875970\pi$
$492$	−51.0737	+	1.28911i	−0.103808	+	0.00262014i
$493$		−	421.862i		−	0.855703i
$494$		−	651.920i		−	1.31968i
$495$	−101.591	−	126.029i	−0.205234	−	0.254604i
$496$	188.124			0.379281
$497$	−61.6100			−0.123964
$498$	14.1384	+	560.156i	0.0283904	+	1.12481i
$499$	474.076			0.950052			0.475026	−	0.879972i	$-0.342439\pi$
$499$	474.076			0.950052			0.475026	+	0.879972i	$0.342439\pi$
$500$	149.614	+	462.089i	0.299229	+	0.924178i
$501$	−18.0231	−	714.065i	−0.0359742	−	1.42528i
$502$		−	306.863i		−	0.611281i
$503$	−490.248			−0.974648			−0.487324	−	0.873221i	$-0.662027\pi$
$503$	−490.248			−0.974648			−0.487324	+	0.873221i	$0.662027\pi$
$504$	−0.385735	−	7.63645i	−0.000765348	−	0.0151517i
$505$	−516.338	−	711.193i	−1.02245	−	1.40830i
$506$			242.467i			0.479183i
$507$	−6.77937	−	268.595i	−0.0133715	−	0.529773i
$508$		−	750.117i		−	1.47661i
$509$			217.790i			0.427879i	0.976847	+	0.213940i	$0.0686296\pi$
$509$			217.790i			0.427879i	−0.976847	+	0.213940i	$0.931370\pi$
$510$	−673.990	−	880.709i	−1.32155	−	1.72688i
$511$	−334.138			−0.653890
$512$	−717.122			−1.40063
$513$	29.4825	+	388.699i	0.0574707	+	0.757697i
$514$	−439.965			−0.855964
$515$	306.040	+	421.534i	0.594253	+	0.818512i
$516$	−839.702	+	21.1942i	−1.62733	+	0.0410740i
$517$			243.656i			0.471288i
$518$	277.329			0.535385
$519$	19.9824	+	791.692i	0.0385017	+	1.52542i
$520$	15.1676	+	20.8915i	0.0291685	+	0.0401760i
$521$		−	152.871i		−	0.293418i	−0.989180	−	0.146709i	$-0.953132\pi$
$521$		−	152.871i		−	0.293418i	0.989180	−	0.146709i	$-0.0468680\pi$
$522$	20.4291	+	404.437i	0.0391362	+	0.774784i
$523$		−	442.325i		−	0.845746i	−0.906189	−	0.422873i	$-0.861022\pi$
$523$		−	442.325i		−	0.845746i	0.906189	−	0.422873i	$-0.138978\pi$
$524$			563.887i			1.07612i
$525$	−56.6683	+	190.168i	−0.107940	+	0.362224i
$526$	884.567			1.68169
$527$	301.199			0.571536
$528$	−177.407	+	4.47777i	−0.335998	+	0.00848063i
$529$	47.1333			0.0890989
$530$	−523.697	+	380.213i	−0.988108	+	0.717383i
$531$	31.7409	+	628.378i	0.0597757	+	1.18339i
$532$		−	148.425i		−	0.278995i
$533$	70.4745			0.132222
$534$	−371.261	+	9.37066i	−0.695245	+	0.0175481i
$535$	64.1675	−	46.5867i	0.119939	−	0.0870780i
$536$		−	8.72767i		−	0.0162830i
$537$	−623.829	+	15.7455i	−1.16169	+	0.0293213i
$538$		−	1014.78i		−	1.88621i
$539$			25.1808i			0.0467176i
$540$	339.406	+	399.962i	0.628530	+	0.740670i
$541$	461.203			0.852500			0.426250	−	0.904605i	$-0.359834\pi$
$541$	461.203			0.852500			0.426250	+	0.904605i	$0.359834\pi$
$542$	−177.584			−0.327645
$543$	17.6457	+	699.115i	0.0324968	+	1.28750i
$544$	−1181.98			−2.17276
$545$	398.758	−	289.505i	0.731666	−	0.531202i
$546$	−9.04321	−	358.287i	−0.0165627	−	0.656204i
$547$			517.451i			0.945980i	0.881068	+	0.472990i	$0.156825\pi$
$547$			517.451i			0.945980i	−0.881068	+	0.472990i	$0.843175\pi$
$548$	60.3045			0.110045
$549$	321.348	−	16.2321i	0.585334	−	0.0295666i
$550$	240.126	+	78.2045i	0.436593	+	0.142190i
$551$		−	231.333i		−	0.419843i
$552$	0.583430	+	23.1152i	0.00105694	+	0.0418754i
$553$		−	165.397i		−	0.299090i
$554$		−	1391.32i		−	2.51142i
$555$	444.647	−	340.279i	0.801165	−	0.613116i
$556$	218.220			0.392483
$557$	−308.730			−0.554272			−0.277136	−	0.960831i	$-0.589385\pi$
$557$	−308.730			−0.554272			−0.277136	+	0.960831i	$0.589385\pi$
$558$	−288.759	+	14.5859i	−0.517489	+	0.0261396i
$559$	1158.67			2.07275
$560$	127.805	+	176.036i	0.228223	+	0.314350i
$561$	−284.041	+	7.16923i	−0.506312	+	0.0127794i
$562$			1149.07i			2.04462i
$563$	−147.864			−0.262636			−0.131318	−	0.991340i	$-0.541921\pi$
$563$	−147.864			−0.262636			−0.131318	+	0.991340i	$0.541921\pi$
$564$	−19.9225	−	789.318i	−0.0353236	−	1.39950i
$565$	−507.298	+	368.306i	−0.897872	+	0.651870i
$566$			953.929i			1.68539i
$567$	21.5951	+	213.215i	0.0380866	+	0.376041i
$568$			7.47749i			0.0131646i
$569$		−	353.635i		−	0.621502i	−0.950491	−	0.310751i	$-0.899419\pi$
$569$		−	353.635i		−	0.621502i	0.950491	−	0.310751i	$-0.100581\pi$
$570$	−369.591	−	482.948i	−0.648405	−	0.847278i
$571$	−756.937			−1.32563			−0.662817	−	0.748782i	$-0.730639\pi$
$571$	−756.937			−1.32563			−0.662817	+	0.748782i	$0.730639\pi$
$572$	−224.758			−0.392934
$573$	1082.67	−	27.3267i	1.88948	−	0.0476906i
$574$	32.5626			0.0567292
$575$	185.825	−	570.572i	0.323173	−	0.992299i
$576$	541.919	−	27.3736i	0.940832	−	0.0475237i
$577$		−	324.153i		−	0.561790i	−0.959739	−	0.280895i	$-0.909369\pi$
$577$		−	324.153i		−	0.561790i	0.959739	−	0.280895i	$-0.0906312\pi$
$578$	−1135.03			−1.96372
$579$	579.082	−	14.6161i	1.00014	−	0.0252437i
$580$	−182.890	−	251.909i	−0.315327	−	0.434325i
$581$		−	175.977i		−	0.302887i
$582$	387.866	−	9.78979i	0.666437	−	0.0168209i
$583$			165.805i			0.284399i
$584$			40.5537i			0.0694412i
$585$	−454.113	−	563.352i	−0.776262	−	0.962995i
$586$	1619.66			2.76393
$587$	−94.9854			−0.161815			−0.0809075	−	0.996722i	$-0.525782\pi$
$587$	−94.9854			−0.161815			−0.0809075	+	0.996722i	$0.525782\pi$
$588$	−2.05890	−	81.5727i	−0.00350154	−	0.138729i
$589$	165.167			0.280419
$590$	−576.678	−	794.305i	−0.977421	−	1.34628i
$591$	−5.75203	−	227.892i	−0.00973270	−	0.385605i
$592$		−	613.824i		−	1.03687i
$593$	−470.531			−0.793475			−0.396738	−	0.917932i	$-0.629858\pi$
$593$	−470.531			−0.793475			−0.396738	+	0.917932i	$0.629858\pi$
$594$	271.962	−	20.6281i	0.457849	−	0.0347275i
$595$	204.625	+	281.846i	0.343908	+	0.473691i
$596$			78.3838i			0.131516i
$597$	−0.680595	−	26.9648i	−0.00114002	−	0.0451672i
$598$			1083.83i			1.81242i
$599$			243.755i			0.406937i	0.979082	+	0.203468i	$0.0652214\pi$
$599$			243.755i			0.406937i	−0.979082	+	0.203468i	$0.934779\pi$
$600$	23.0803	+	6.87772i	0.0384671	+	0.0114629i
$601$	653.937			1.08808			0.544041	−	0.839059i	$-0.316894\pi$
$601$	653.937			1.08808			0.544041	+	0.839059i	$0.316894\pi$
$602$	535.360			0.889303
$603$	12.3405	+	244.306i	0.0204651	+	0.405151i
$604$	−302.610			−0.501010
$605$	−437.220	+	317.429i	−0.722678	+	0.524676i
$606$	1480.31	−	37.3632i	2.44276	−	0.0616555i
$607$			691.680i			1.13951i	0.821816	+	0.569753i	$0.192961\pi$
$607$			691.680i			1.13951i	−0.821816	+	0.569753i	$0.807039\pi$
$608$	−648.155			−1.06604
$609$	−3.20898	−	127.138i	−0.00526925	−	0.208765i
$610$	−406.202	+	294.909i	−0.665905	+	0.483458i
$611$			1089.15i			1.78256i
$612$	919.559	−	46.4491i	1.50255	−	0.0758973i
$613$		−	635.116i		−	1.03608i	−0.855357	−	0.518039i	$-0.826662\pi$
$613$		−	635.116i		−	1.03608i	0.855357	−	0.518039i	$-0.173338\pi$
$614$			537.397i			0.875239i
$615$	52.2081	−	39.9538i	0.0848912	−	0.0649656i
$616$	3.05615			0.00496127
$617$	−845.663			−1.37061			−0.685303	−	0.728258i	$-0.740330\pi$
$617$	−845.663			−1.37061			−0.685303	+	0.728258i	$0.740330\pi$
$618$	−877.400	+	22.1457i	−1.41974	+	0.0358344i
$619$	−13.6959			−0.0221258			−0.0110629	−	0.999939i	$-0.503522\pi$
$619$	−13.6959			−0.0221258			−0.0110629	+	0.999939i	$0.503522\pi$
$620$	179.857	−	130.579i	0.290092	−	0.210611i
$621$	−49.0152	−	646.219i	−0.0789295	−	1.04061i
$622$			186.996i			0.300636i
$623$	116.634			0.187214
$624$	−793.012	+	20.0157i	−1.27085	+	0.0320765i
$625$	−505.129	−	368.062i	−0.808207	−	0.588899i
$626$			409.546i			0.654227i
$627$	−155.758	+	3.93134i	−0.248417	+	0.00627008i
$628$			12.7257i			0.0202639i
$629$		−	982.777i		−	1.56244i
$630$	−209.822	−	260.296i	−0.333051	−	0.413168i
$631$	−734.501			−1.16403			−0.582013	−	0.813179i	$-0.697735\pi$
$631$	−734.501			−1.16403			−0.582013	+	0.813179i	$0.697735\pi$
$632$	−20.0739			−0.0317625
$633$	4.15065	+	164.446i	0.00655710	+	0.259789i
$634$	271.396			0.428069
$635$	567.085	+	781.091i	0.893048	+	1.23006i
$636$	−13.5570	−	537.121i	−0.0213160	−	0.844529i
$637$			112.559i			0.176701i
$638$	−161.858			−0.253696
$639$	−10.5728	−	209.311i	−0.0165458	−	0.327560i
$640$	41.5587	−	30.1723i	0.0649355	−	0.0471442i
$641$		−	923.554i		−	1.44080i	−0.693558	−	0.720401i	$-0.743958\pi$
$641$		−	923.554i		−	1.44080i	0.693558	−	0.720401i	$-0.256042\pi$
$642$	3.37110	+	133.561i	0.00525094	+	0.208040i
$643$		−	826.161i		−	1.28485i	−0.766347	−	0.642427i	$-0.777928\pi$
$643$		−	826.161i		−	1.28485i	0.766347	−	0.642427i	$-0.222072\pi$
$644$			246.760i			0.383167i
$645$	858.352	−	656.880i	1.33078	−	1.01842i
$646$	−1067.43			−1.65237
$647$	717.041			1.10826			0.554128	−	0.832432i	$-0.313052\pi$
$647$	717.041			1.10826			0.554128	+	0.832432i	$0.313052\pi$
$648$	25.8775	−	2.62096i	0.0399344	−	0.00404469i
$649$	−251.480			−0.387489
$650$	1073.37	+	349.576i	1.65134	+	0.537809i
$651$	90.7735	−	2.29113i	0.139437	−	0.00351941i
$652$			606.551i			0.930293i
$653$	−353.997			−0.542108			−0.271054	−	0.962564i	$-0.587372\pi$
$653$	−353.997			−0.542108			−0.271054	+	0.962564i	$0.587372\pi$
$654$	20.9491	+	829.994i	0.0320323	+	1.26910i
$655$	−426.296	−	587.171i	−0.650833	−	0.896444i
$656$		−	72.0721i		−	0.109866i
$657$	−57.3408	−	1135.18i	−0.0872768	−	1.72783i
$658$			503.238i			0.764799i
$659$			1195.73i			1.81446i	0.420637	+	0.907229i	$0.361807\pi$
$659$			1195.73i			1.81446i	−0.420637	+	0.907229i	$0.638193\pi$
$660$	−166.503	+	127.422i	−0.252277	+	0.193063i
$661$	817.579			1.23688			0.618441	−	0.785831i	$-0.287764\pi$
$661$	817.579			1.23688			0.618441	+	0.785831i	$0.287764\pi$
$662$	−22.1377			−0.0334406
$663$	−1269.67	+	32.0466i	−1.91504	+	0.0483357i
$664$	−21.3580			−0.0321657
$665$	112.209	+	154.554i	0.168735	+	0.232412i
$666$	47.5920	+	942.185i	0.0714595	+	1.41469i
$667$			384.596i			0.576606i
$668$	−925.164			−1.38498
$669$	65.6763	−	1.65768i	0.0981709	−	0.00247784i
$670$	−224.206	−	308.816i	−0.334635	−	0.460919i
$671$			128.605i			0.191662i
$672$	−356.218	+	8.99098i	−0.530086	+	0.0133794i
$673$			986.717i			1.46615i	0.680149	+	0.733074i	$0.261915\pi$
$673$			986.717i			1.46615i	−0.680149	+	0.733074i	$0.738085\pi$
$674$		−	636.526i		−	0.944400i
$675$	−655.790	−	159.888i	−0.971541	−	0.236871i
$676$	−348.000			−0.514792
$677$	169.920			0.250989			0.125495	−	0.992094i	$-0.459948\pi$
$677$	169.920			0.250989			0.125495	+	0.992094i	$0.459948\pi$
$678$	−26.6514	−	1055.91i	−0.0393088	−	1.55739i
$679$	−121.851			−0.179457
$680$	34.2071	−	24.8349i	0.0503046	−	0.0365220i
$681$	23.8403	+	944.542i	0.0350079	+	1.38699i
$682$		−	115.563i		−	0.169447i
$683$	744.119			1.08949			0.544743	−	0.838603i	$-0.316627\pi$
$683$	744.119			1.08949			0.544743	+	0.838603i	$0.316627\pi$
$684$	504.252	−	25.4710i	0.737211	−	0.0372383i
$685$	−62.7946	+	45.5899i	−0.0916710	+	0.0665547i
$686$			52.0075i			0.0758127i
$687$	−16.2908	−	645.433i	−0.0237130	−	0.939495i
$688$		−	1184.93i		−	1.72229i
$689$			741.150i			1.07569i
$690$	614.452	+	802.911i	0.890510	+	1.16364i
$691$	−731.677			−1.05887			−0.529433	−	0.848352i	$-0.677595\pi$
$691$	−731.677			−1.05887			−0.529433	+	0.848352i	$0.677595\pi$
$692$	1025.74			1.48228
$693$	−85.5480	+	4.32123i	−0.123446	+	0.00623555i
$694$	−1434.71			−2.06731
$695$	−227.231	+	164.974i	−0.326951	+	0.237372i
$696$	−15.4305	+	0.389467i	−0.0221702	+	0.000559579i
$697$		−	115.393i		−	0.165556i
$698$	1521.33			2.17955
$699$	−0.568042	−	22.5055i	−0.000812649	−	0.0321967i
$700$	244.378	+	79.5892i	0.349111	+	0.113699i
$701$		−	785.104i		−	1.11998i	−0.828500	−	0.559989i	$-0.810805\pi$
$701$		−	785.104i		−	1.11998i	0.828500	−	0.559989i	$-0.189195\pi$
$702$	1215.68	−	92.2080i	1.73173	−	0.131350i
$703$		−	538.919i		−	0.766598i
$704$			216.879i			0.308066i
$705$	617.466	+	806.850i	0.875838	+	1.14447i
$706$	1049.45			1.48647
$707$	−465.051			−0.657781
$708$	814.665	−	20.5622i	1.15066	−	0.0290427i
$709$	−962.545			−1.35761			−0.678804	−	0.734319i	$-0.737502\pi$
$709$	−962.545			−1.35761			−0.678804	+	0.734319i	$0.737502\pi$
$710$	192.090	+	264.580i	0.270549	+	0.372648i
$711$	561.911	−	28.3835i	0.790311	−	0.0399205i
$712$		−	14.1557i		−	0.0198816i
$713$	−274.592			−0.385123
$714$	−586.648	+	14.8071i	−0.821636	+	0.0207382i
$715$	234.039	−	169.916i	0.327328	−	0.237645i
$716$			808.251i			1.12884i
$717$	−452.181	+	11.4131i	−0.630657	+	0.0159179i
$718$			1419.46i			1.97696i
$719$		−	601.146i		−	0.836086i	−0.908427	−	0.418043i	$-0.862716\pi$
$719$		−	601.146i		−	0.836086i	0.908427	−	0.418043i	$-0.137284\pi$
$720$	−576.123	+	464.407i	−0.800171	+	0.645010i
$721$	275.642			0.382305
$722$	428.398			0.593349
$723$	1.92078	+	76.1003i	0.00265668	+	0.105256i
$724$	905.794			1.25110
$725$	380.884	+	124.047i	0.525357	+	0.171099i
$726$	−22.9698	−	910.051i	−0.0316388	−	1.25351i
$727$			65.8049i			0.0905156i	0.998975	+	0.0452578i	$0.0144109\pi$
$727$			65.8049i			0.0905156i	−0.998975	+	0.0452578i	$0.985589\pi$
$728$	13.6610			0.0187651
$729$	−720.660	+	109.956i	−0.988560	+	0.150831i
$730$	1041.79	+	1434.93i	1.42710	+	1.96566i
$731$		−	1897.17i		−	2.59530i
$732$	−10.5154	−	416.614i	−0.0143653	−	0.569145i
$733$		−	641.162i		−	0.874709i	−0.899289	−	0.437354i	$-0.855916\pi$
$733$		−	641.162i		−	0.874709i	0.899289	−	0.437354i	$-0.144084\pi$
$734$			379.425i			0.516927i
$735$	63.8125	+	83.3845i	0.0868197	+	0.113448i
$736$	1077.57			1.46409
$737$	−97.7724			−0.132663
$738$	5.58801	+	110.626i	0.00757183	+	0.149900i
$739$	−251.721			−0.340624			−0.170312	−	0.985390i	$-0.554478\pi$
$739$	−251.721			−0.340624			−0.170312	+	0.985390i	$0.554478\pi$
$740$	−426.064	−	586.851i	−0.575762	−	0.793042i
$741$	−696.240	+	17.5732i	−0.939595	+	0.0237155i
$742$			342.447i			0.461518i
$743$	−768.311			−1.03407			−0.517033	−	0.855966i	$-0.672964\pi$
$743$	−768.311			−1.03407			−0.517033	+	0.855966i	$0.672964\pi$
$744$	−0.278070	−	11.0170i	−0.000373750	−	0.0148078i
$745$	−59.2578	−	81.6205i	−0.0795407	−	0.109558i
$746$		−	343.548i		−	0.460520i
$747$	597.856	−	30.1991i	0.800342	−	0.0404272i
$748$			368.012i			0.491995i
$749$		−	41.9593i		−	0.0560204i
$750$	993.344	−	349.552i	1.32446	−	0.466069i
$751$	30.1616			0.0401619			0.0200809	−	0.999798i	$-0.493608\pi$
$751$	30.1616			0.0401619			0.0200809	+	0.999798i	$0.493608\pi$
$752$	1113.84			1.48117
$753$	−327.724	+	8.27180i	−0.435225	+	0.0109851i
$754$	−723.507			−0.959558
$755$	315.105	−	228.772i	0.417358	−	0.303009i
$756$	276.778	−	20.9934i	0.366108	−	0.0277690i
$757$		−	118.277i		−	0.156244i	−0.996944	−	0.0781220i	$-0.975108\pi$
$757$		−	118.277i		−	0.156244i	0.996944	−	0.0781220i	$-0.0248924\pi$
$758$	729.475			0.962369
$759$	258.950	−	6.53593i	0.341173	−	0.00861124i
$760$	18.7579	−	13.6186i	0.0246815	−	0.0179192i
$761$			703.506i			0.924450i	0.886763	+	0.462225i	$0.152949\pi$
$761$			703.506i			0.924450i	−0.886763	+	0.462225i	$0.847051\pi$
$762$	−1625.80	+	41.0354i	−2.13360	+	0.0538522i
$763$		−	260.749i		−	0.341741i
$764$		−	1402.74i		−	1.83605i
$765$	−922.414	+	743.550i	−1.20577	+	0.971960i
$766$	−899.680			−1.17452
$767$	−1124.12			−1.46561
$768$	20.4382	+	809.752i	0.0266123	+	1.05436i
$769$	846.031			1.10017			0.550085	−	0.835109i	$-0.314595\pi$
$769$	846.031			1.10017			0.550085	+	0.835109i	$0.314595\pi$
$770$	108.137	−	78.5095i	0.140438	−	0.101960i
$771$	11.8597	+	469.875i	0.0153822	+	0.609436i
$772$		−	750.275i		−	0.971859i
$773$	−559.073			−0.723250			−0.361625	−	0.932324i	$-0.617778\pi$
$773$	−559.073			−0.723250			−0.361625	+	0.932324i	$0.617778\pi$
$774$	91.8722	+	1818.81i	0.118698	+	2.34988i
$775$	−88.5663	+	271.942i	−0.114279	+	0.350893i
$776$			14.7888i			0.0190578i
$777$	−7.47569	−	296.183i	−0.00962123	−	0.381188i
$778$			189.858i			0.244034i
$779$		−	63.2770i		−	0.0812285i
$780$	−744.272	+	569.577i	−0.954195	+	0.730226i
$781$	83.7672			0.107256
$782$	1774.63			2.26934
$783$	431.381	−	32.7199i	0.550934	−	0.0417879i
$784$	115.110			0.146824
$785$	−9.62059	−	13.2512i	−0.0122555	−	0.0168805i
$786$	1222.17	−	30.8476i	1.55492	−	0.0392463i
$787$			836.040i			1.06231i	0.847274	+	0.531156i	$0.178242\pi$
$787$			836.040i			1.06231i	−0.847274	+	0.531156i	$0.821758\pi$
$788$	−295.264			−0.374700
$789$	−23.8444	−	944.703i	−0.0302210	−	1.19734i
$790$	−710.286	+	515.680i	−0.899097	+	0.652759i
$791$			331.723i			0.419372i
$792$	0.524460	+	10.3828i	0.000662197	+	0.0131096i
$793$			574.868i			0.724928i
$794$		−	361.822i		−	0.455695i
$795$	420.177	+	549.050i	0.528525	+	0.690629i
$796$	−34.9364			−0.0438899
$797$	−35.0825			−0.0440182			−0.0220091	−	0.999758i	$-0.507006\pi$
$797$	−35.0825			−0.0440182			−0.0220091	+	0.999758i	$0.507006\pi$
$798$	−321.696	+	8.11964i	−0.403128	+	0.0101750i
$799$	1783.33			2.23196
$800$	347.556	−	1067.17i	0.434446	−	1.33396i
$801$	20.0154	+	396.247i	0.0249880	+	0.494691i
$802$		−	1429.73i		−	1.78270i
$803$	454.306			0.565761
$804$	316.732	−	7.99434i	0.393945	−	0.00994321i
$805$	−186.549	−	256.949i	−0.231738	−	0.319191i
$806$		−	516.567i		−	0.640902i
$807$	−1083.77	+	27.3544i	−1.34296	+	0.0338965i
$808$			56.4423i			0.0698543i
$809$			557.385i			0.688980i	0.938790	+	0.344490i	$0.111948\pi$
$809$			557.385i			0.688980i	−0.938790	+	0.344490i	$0.888052\pi$
$810$	848.308	−	757.507i	1.04729	−	0.935194i
$811$	−386.517			−0.476593			−0.238297	−	0.971192i	$-0.576589\pi$
$811$	−386.517			−0.476593			−0.238297	+	0.971192i	$0.576589\pi$
$812$	−164.724			−0.202862
$813$	4.78695	+	189.656i	0.00588801	+	0.233280i
$814$	−377.067			−0.463227
$815$	−458.550	−	631.597i	−0.562638	−	0.774965i
$816$	32.7731	+	1298.45i	0.0401631	+	1.59124i
$817$		−	1040.34i		−	1.27336i
$818$	124.787			0.152552
$819$	−382.401	+	19.3160i	−0.466912	+	0.0235849i
$820$	−50.0262	−	68.9050i	−0.0610076	−	0.0840305i
$821$			589.251i			0.717724i	0.933391	+	0.358862i	$0.116835\pi$
$821$			589.251i			0.717724i	−0.933391	+	0.358862i	$0.883165\pi$
$822$	−3.29898	−	130.704i	−0.00401335	−	0.159007i
$823$		−	957.094i		−	1.16293i	−0.813570	−	0.581466i	$-0.802479\pi$
$823$		−	957.094i		−	1.16293i	0.813570	−	0.581466i	$-0.197521\pi$
$824$		−	33.4541i		−	0.0405996i
$825$	77.0483	−	258.559i	0.0933918	−	0.313404i
$826$	−519.398			−0.628811
$827$	−1191.52			−1.44078			−0.720389	−	0.693570i	$-0.756037\pi$
$827$	−1191.52			−1.44078			−0.720389	+	0.693570i	$0.756037\pi$
$828$	−838.329	+	42.3460i	−1.01247	+	0.0511425i
$829$	−109.610			−0.132220			−0.0661100	−	0.997812i	$-0.521059\pi$
$829$	−109.610			−0.132220			−0.0661100	+	0.997812i	$0.521059\pi$
$830$	−755.722	+	548.667i	−0.910509	+	0.661045i
$831$	−1485.91	+	37.5045i	−1.78810	+	0.0451318i
$832$			969.452i			1.16521i
$833$	184.300			0.221248
$834$	−11.9378	−	472.970i	−0.0143139	−	0.567110i
$835$	963.366	−	699.420i	1.15373	−	0.837628i
$836$			201.804i			0.241393i
$837$	23.3613	+	307.996i	0.0279107	+	0.367976i
$838$			840.356i			1.00281i
$839$			130.962i			0.156093i	0.996950	+	0.0780464i	$0.0248682\pi$
$839$			130.962i			0.156093i	−0.996950	+	0.0780464i	$0.975132\pi$
$840$	10.1202	−	7.74480i	0.0120479	−	0.00922000i
$841$	584.264			0.694726
$842$	−431.640			−0.512636
$843$	1227.19	−	30.9745i	1.45574	−	0.0367431i
$844$	213.062			0.252443
$845$	362.369	−	263.086i	0.428839	−	0.311344i
$846$	−1709.67	+	86.3598i	−2.02089	+	0.102080i
$847$			285.899i			0.337543i
$848$	757.951			0.893810
$849$	1018.78	−	25.7141i	1.19998	−	0.0302875i
$850$	572.384	−	1757.50i	0.673393	−	2.06764i
$851$			895.962i			1.05283i
$852$	−271.362	+	6.84921i	−0.318500	+	0.00803898i
$853$			942.633i			1.10508i	0.833487	+	0.552540i	$0.186341\pi$
$853$			942.633i			1.10508i	−0.833487	+	0.552540i	$0.813659\pi$
$854$			265.616i			0.311026i
$855$	−505.818	+	407.735i	−0.591600	+	0.476883i
$856$	−5.09252			−0.00594920
$857$	−725.685			−0.846774			−0.423387	−	0.905949i	$-0.639159\pi$
$857$	−725.685			−0.846774			−0.423387	+	0.905949i	$0.639159\pi$
$858$	12.2955	+	487.140i	0.0143304	+	0.567763i
$859$	−115.679			−0.134667			−0.0673336	−	0.997731i	$-0.521449\pi$
$859$	−115.679			−0.134667			−0.0673336	+	0.997731i	$0.521449\pi$
$860$	−822.479	−	1132.87i	−0.956371	−	1.31729i
$861$	−0.877757	−	34.7763i	−0.00101946	−	0.0403906i
$862$			235.375i			0.273056i
$863$	445.017			0.515662			0.257831	−	0.966190i	$-0.416992\pi$
$863$	445.017			0.515662			0.257831	+	0.966190i	$0.416992\pi$
$864$	−91.6754	−	1208.65i	−0.106106	−	1.39890i
$865$	−1068.09	+	775.454i	−1.23479	+	0.896479i
$866$		−	1939.32i		−	2.23940i
$867$	30.5958	+	1212.19i	0.0352893	+	1.39814i
$868$		−	117.609i		−	0.135494i
$869$			224.880i			0.258780i
$870$	−535.980	+	410.175i	−0.616070	+	0.471466i
$871$	−437.045			−0.501773
$872$	−31.6465			−0.0362919
$873$	−20.9107	−	413.971i	−0.0239526	−	0.474193i
$874$	973.140			1.11343
$875$	−314.638	+	101.873i	−0.359586	+	0.116426i
$876$	−1471.71	+	37.1462i	−1.68004	+	0.0424044i
$877$		−	1089.65i		−	1.24247i	−0.783624	−	0.621235i	$-0.786631\pi$
$877$		−	1089.65i		−	1.24247i	0.783624	−	0.621235i	$-0.213369\pi$
$878$	−567.200			−0.646014
$879$	−43.6596	−	1729.77i	−0.0496696	−	1.96788i
$880$	−173.768	−	239.345i	−0.197464	−	0.271983i
$881$		−	1029.75i		−	1.16884i	−0.811451	−	0.584420i	$-0.801322\pi$
$881$		−	1029.75i		−	1.16884i	0.811451	−	0.584420i	$-0.198678\pi$
$882$	−176.688	+	8.92491i	−0.200326	+	0.0101189i
$883$		−	1414.53i		−	1.60196i	−0.598688	−	0.800982i	$-0.704311\pi$
$883$		−	1414.53i		−	1.60196i	0.598688	−	0.800982i	$-0.295689\pi$
$884$			1645.02i			1.86088i
$885$	−832.759	+	637.294i	−0.940970	+	0.720106i
$886$	−2482.48			−2.80189
$887$	−859.783			−0.969315			−0.484658	−	0.874704i	$-0.661056\pi$
$887$	−859.783			−0.969315			−0.484658	+	0.874704i	$0.661056\pi$
$888$	−35.9472	+	0.907310i	−0.0404810	+	0.00102175i
$889$	510.757			0.574530
$890$	−363.646	−	500.878i	−0.408591	−	0.562785i
$891$	−29.3615	−	289.895i	−0.0329534	−	0.325359i
$892$		−	85.0921i		−	0.0953948i
$893$	977.914			1.09509
$894$	169.889	−	4.28801i	0.190032	−	0.00479643i
$895$	−611.034	−	841.626i	−0.682720	−	0.940364i
$896$		−	27.1753i		−	0.0303296i
$897$	1157.51	−	29.2157i	1.29043	−	0.0325705i
$898$		−	516.672i		−	0.575359i
$899$		−	183.303i		−	0.203897i
$900$	−228.455	+	843.895i	−0.253839	+	0.937661i
$901$	1213.53			1.34687
$902$	−44.2732			−0.0490834
$903$	−14.4312	−	571.755i	−0.0159814	−	0.633173i
$904$	40.2606			0.0445360
$905$	−943.196	+	684.776i	−1.04221	+	0.756659i
$906$	16.5544	+	655.876i	0.0182719	+	0.723924i
$907$			94.7102i			0.104421i	0.998636	+	0.0522107i	$0.0166267\pi$
$907$			94.7102i			0.104421i	−0.998636	+	0.0522107i	$0.983373\pi$
$908$	1223.78			1.34777
$909$	−79.8066	−	1579.94i	−0.0877960	−	1.73811i
$910$	483.376	−	350.939i	0.531182	−	0.385647i
$911$		−	688.550i		−	0.755818i	−0.925843	−	0.377909i	$-0.876643\pi$
$911$		−	688.550i		−	0.755818i	0.925843	−	0.377909i	$-0.123357\pi$
$912$	17.9715	+	712.023i	0.0197056	+	0.780727i
$913$			239.265i			0.262064i
$914$			275.168i			0.301059i
$915$	325.908	+	425.867i	0.356183	+	0.465429i
$916$	−836.242			−0.912928
$917$	−383.952			−0.418705
$918$	−150.978	−	1990.51i	−0.164464	−	2.16831i
$919$	−279.085			−0.303683			−0.151842	−	0.988405i	$-0.548520\pi$
$919$	−279.085			−0.303683			−0.151842	+	0.988405i	$0.548520\pi$
$920$	−31.1854	+	22.6411i	−0.0338972	+	0.0246099i
$921$	573.930	−	14.4861i	0.623160	−	0.0157286i
$922$		−	1244.44i		−	1.34972i
$923$	374.441			0.405678
$924$	2.79936	+	110.909i	0.00302961	+	0.120032i
$925$	887.314	+	288.981i	0.959258	+	0.312412i
$926$		−	986.392i		−	1.06522i
$927$	47.3024	+	936.451i	0.0510274	+	1.01020i
$928$			719.328i			0.775138i
$929$			217.641i			0.234275i	0.993116	+	0.117137i	$0.0373718\pi$
$929$			217.641i			0.234275i	−0.993116	+	0.117137i	$0.962628\pi$
$930$	−292.856	−	382.677i	−0.314898	−	0.411481i
$931$	101.063			0.108553
$932$	−29.1588			−0.0312863
$933$	199.708	−	5.04066i	0.214050	−	0.00540264i
$934$	−606.554			−0.649415
$935$	−278.215	−	383.208i	−0.297557	−	0.409848i
$936$	2.34434	+	46.4113i	0.00250464	+	0.0495847i
$937$			382.654i			0.408382i	0.978931	+	0.204191i	$0.0654564\pi$
$937$			382.654i			0.408382i	−0.978931	+	0.204191i	$0.934544\pi$
$938$	−201.935			−0.215283
$939$	437.388	−	11.0397i	0.465802	−	0.0117569i
$940$	1064.89	−	773.129i	1.13286	−	0.822478i
$941$			1130.69i			1.20158i	0.799407	+	0.600790i	$0.205147\pi$
$941$			1130.69i			1.20158i	−0.799407	+	0.600790i	$0.794853\pi$
$942$	27.5817	−	0.696165i	0.0292799	−	0.000739029i
$943$			105.199i			0.111558i
$944$			1149.60i			1.21780i
$945$	−272.335	+	231.103i	−0.288186	+	0.244553i
$946$	−727.895			−0.769445
$947$	1146.63			1.21080			0.605402	−	0.795920i	$-0.293013\pi$
$947$	1146.63			1.21080			0.605402	+	0.795920i	$0.293013\pi$
$948$	−18.3872	−	728.493i	−0.0193958	−	0.768452i
$949$	2030.76			2.13989
$950$	313.874	−	963.746i	0.330394	−	1.01447i
$951$	−7.31575	−	289.846i	−0.00769269	−	0.304780i
$952$		−	22.3681i		−	0.0234959i
$953$	813.087			0.853187			0.426593	−	0.904444i	$-0.359714\pi$
$953$	813.087			0.853187			0.426593	+	0.904444i	$0.359714\pi$
$954$	−1163.41	+	58.7667i	−1.21951	+	0.0616003i
$955$	1060.46	+	1460.66i	1.11043	+	1.52949i
$956$			585.859i			0.612824i
$957$	4.36304	+	172.861i	0.00455908	+	0.180628i
$958$			921.406i			0.961801i
$959$			41.0615i			0.0428170i
$960$	549.608	+	718.178i	0.572508	+	0.748103i
$961$	−830.126			−0.863815
$962$	−1685.50			−1.75207
$963$	142.550	−	7.20056i	0.148027	−	0.00747722i
$964$	98.5978			0.102280
$965$	567.205	+	781.256i	0.587777	+	0.809591i
$966$	534.826	−	13.4991i	0.553650	−	0.0139742i
$967$		−	238.373i		−	0.246508i	−0.992375	−	0.123254i	$-0.960667\pi$
$967$		−	238.373i		−	0.246508i	0.992375	−	0.123254i	$-0.0393329\pi$
$968$	34.6990			0.0358461
$969$	28.7737	+	1140.00i	0.0296942	+	1.17647i
$970$	379.911	+	523.282i	0.391661	+	0.539466i
$971$		−	469.438i		−	0.483458i	−0.970344	−	0.241729i	$-0.922285\pi$
$971$		−	469.438i		−	0.483458i	0.970344	−	0.241729i	$-0.0777145\pi$
$972$	118.819	+	936.707i	0.122242	+	0.963690i
$973$			148.587i			0.152710i
$974$		−	417.188i		−	0.428324i
$975$	344.407	−	1155.76i	0.353238	−	1.18540i
$976$	587.899			0.602356
$977$	1525.56			1.56148			0.780739	−	0.624857i	$-0.214843\pi$
$977$	1525.56			1.56148			0.780739	+	0.624857i	$0.214843\pi$
$978$	1314.64	−	33.1816i	1.34421	−	0.0339280i
$979$	−158.580			−0.161982
$980$	110.052	−	79.8996i	0.112298	−	0.0815302i
$981$	885.854	−	44.7466i	0.903011	−	0.0456133i
$982$		−	1047.52i		−	1.06672i
$983$	30.5714			0.0311001			0.0155500	−	0.999879i	$-0.495050\pi$
$983$	30.5714			0.0311001			0.0155500	+	0.999879i	$0.495050\pi$
$984$	−4.22073	+	0.106532i	−0.00428936	+	0.000108264i
$985$	307.456	−	223.218i	0.312138	−	0.226617i
$986$			1184.65i			1.20147i
$987$	537.449	−	13.5653i	0.544528	−	0.0137440i
$988$			902.069i			0.913025i
$989$			1729.58i			1.74881i
$990$	285.281	+	353.907i	0.288163	+	0.357482i
$991$	−728.776			−0.735395			−0.367697	−	0.929945i	$-0.619854\pi$
$991$	−728.776			−0.735395			−0.367697	+	0.929945i	$0.619854\pi$
$992$	−513.583			−0.517725
$993$	0.596743	+	23.6427i	0.000600950	+	0.0238093i
$994$	173.010			0.174054
$995$	36.3790	−	26.4118i	0.0365618	−	0.0265445i
$996$	−19.5634	−	775.093i	−0.0196420	−	0.778206i
$997$			1775.86i			1.78120i	0.454785	+	0.890601i	$0.349716\pi$
$997$			1775.86i			1.78120i	−0.454785	+	0.890601i	$0.650284\pi$
$998$	−1331.27			−1.33394
$999$	1004.95	−	76.2250i	1.00596	−	0.0763013i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.3.f.a.29.6	yes	24
3.2	odd	2	inner	105.3.f.a.29.20	yes	24
5.2	odd	4		525.3.c.e.176.6		24
5.3	odd	4		525.3.c.e.176.19		24
5.4	even	2	inner	105.3.f.a.29.19	yes	24
15.2	even	4		525.3.c.e.176.20		24
15.8	even	4		525.3.c.e.176.5		24
15.14	odd	2	inner	105.3.f.a.29.5	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.f.a.29.5	✓	24	15.14	odd	2	inner
105.3.f.a.29.6	yes	24	1.1	even	1	trivial
105.3.f.a.29.19	yes	24	5.4	even	2	inner
105.3.f.a.29.20	yes	24	3.2	odd	2	inner
525.3.c.e.176.5		24	15.8	even	4
525.3.c.e.176.6		24	5.2	odd	4
525.3.c.e.176.19		24	5.3	odd	4
525.3.c.e.176.20		24	15.2	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:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	105.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.80814 q^{2} +(0.0756962 + 2.99904i) q^{3} +3.88565 q^{4} +(-4.04610 + 2.93753i) q^{5} +(-0.212566 - 8.42174i) q^{6} +2.64575i q^{7} +0.321110 q^{8} +(-8.98854 + 0.454033i) q^{9} +O(q^{10})\)	\(q-2.80814 q^{2} +(0.0756962 + 2.99904i) q^{3} +3.88565 q^{4} +(-4.04610 + 2.93753i) q^{5} +(-0.212566 - 8.42174i) q^{6} +2.64575i q^{7} +0.321110 q^{8} +(-8.98854 + 0.454033i) q^{9} +(11.3620 - 8.24901i) q^{10} -3.59726i q^{11} +(0.294129 + 11.6532i) q^{12} -16.0798i q^{13} -7.42964i q^{14} +(-9.11607 - 11.9121i) q^{15} -16.4443 q^{16} -26.3285 q^{17} +(25.2411 - 1.27499i) q^{18} -14.4376 q^{19} +(-15.7217 + 11.4142i) q^{20} +(-7.93473 + 0.200273i) q^{21} +10.1016i q^{22} +24.0028 q^{23} +(0.0243068 + 0.963022i) q^{24} +(7.74179 - 23.7711i) q^{25} +45.1543i q^{26} +(-2.04206 - 26.9227i) q^{27} +10.2805i q^{28} +16.0230i q^{29} +(25.5992 + 33.4507i) q^{30} -11.4400 q^{31} +44.8935 q^{32} +(10.7883 - 0.272299i) q^{33} +73.9342 q^{34} +(-7.77198 - 10.7050i) q^{35} +(-34.9263 + 1.76421i) q^{36} +37.3274i q^{37} +40.5428 q^{38} +(48.2241 - 1.21718i) q^{39} +(-1.29924 + 0.943270i) q^{40} +4.38279i q^{41} +(22.2818 - 0.562396i) q^{42} +72.0574i q^{43} -13.9777i q^{44} +(35.0348 - 28.2412i) q^{45} -67.4032 q^{46} -67.7338 q^{47} +(-1.24477 - 49.3173i) q^{48} -7.00000 q^{49} +(-21.7400 + 66.7525i) q^{50} +(-1.99297 - 78.9605i) q^{51} -62.4805i q^{52} -46.0920 q^{53} +(5.73440 + 75.6026i) q^{54} +(10.5671 + 14.5549i) q^{55} +0.849576i q^{56} +(-1.09287 - 43.2990i) q^{57} -44.9948i q^{58} -69.9088i q^{59} +(-35.4219 - 46.2861i) q^{60} -35.7509 q^{61} +32.1252 q^{62} +(-1.20126 - 23.7814i) q^{63} -60.2900 q^{64} +(47.2350 + 65.0604i) q^{65} +(-30.2952 + 0.764653i) q^{66} -27.1797i q^{67} -102.304 q^{68} +(1.81692 + 71.9854i) q^{69} +(21.8248 + 30.0610i) q^{70} +23.2864i q^{71} +(-2.88631 + 0.145794i) q^{72} +126.292i q^{73} -104.821i q^{74} +(71.8766 + 21.4186i) q^{75} -56.0995 q^{76} +9.51745 q^{77} +(-135.420 + 3.41801i) q^{78} -62.5142 q^{79} +(66.5353 - 48.3057i) q^{80} +(80.5877 - 8.16218i) q^{81} -12.3075i q^{82} -66.5131 q^{83} +(-30.8316 + 0.778192i) q^{84} +(106.528 - 77.3410i) q^{85} -202.347i q^{86} +(-48.0536 + 1.21288i) q^{87} -1.15511i q^{88} -44.0836i q^{89} +(-98.3825 + 79.3052i) q^{90} +42.5432 q^{91} +93.2664 q^{92} +(-0.865967 - 34.3092i) q^{93} +190.206 q^{94} +(58.4159 - 42.4109i) q^{95} +(3.39827 + 134.638i) q^{96} +46.0554i q^{97} +19.6570 q^{98} +(1.63327 + 32.3341i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 52 q^{4} - 22 q^{9}+O(q^{10}) \) 24 * q + 52 * q^4 - 22 * q^9	\( 24 q + 52 q^{4} - 22 q^{9} - 24 q^{10} + 26 q^{15} + 4 q^{16} + 72 q^{19} + 14 q^{21} - 156 q^{24} - 64 q^{25} - 32 q^{30} - 40 q^{31} - 144 q^{34} + 36 q^{36} + 62 q^{39} - 40 q^{40} + 120 q^{45} - 104 q^{46} - 168 q^{49} + 70 q^{51} + 60 q^{54} - 16 q^{55} - 348 q^{60} + 432 q^{61} - 364 q^{64} + 284 q^{66} + 404 q^{69} + 140 q^{70} + 204 q^{75} + 152 q^{76} + 108 q^{79} - 158 q^{81} + 112 q^{84} + 196 q^{85} - 152 q^{90} - 84 q^{91} + 808 q^{94} - 516 q^{96} + 582 q^{99}+O(q^{100}) \) 24 * q + 52 * q^4 - 22 * q^9 - 24 * q^10 + 26 * q^15 + 4 * q^16 + 72 * q^19 + 14 * q^21 - 156 * q^24 - 64 * q^25 - 32 * q^30 - 40 * q^31 - 144 * q^34 + 36 * q^36 + 62 * q^39 - 40 * q^40 + 120 * q^45 - 104 * q^46 - 168 * q^49 + 70 * q^51 + 60 * q^54 - 16 * q^55 - 348 * q^60 + 432 * q^61 - 364 * q^64 + 284 * q^66 + 404 * q^69 + 140 * q^70 + 204 * q^75 + 152 * q^76 + 108 * q^79 - 158 * q^81 + 112 * q^84 + 196 * q^85 - 152 * q^90 - 84 * q^91 + 808 * q^94 - 516 * q^96 + 582 * q^99

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