LMFDB - Embedded newform 275.2.z.c.124.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [275,2,Mod(49,275)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(275, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 4]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("275.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 275 = 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	275.z (of order $10$, degree $4$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.19588605559$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			124.5
Character	$\chi$	$=$	275.124
Dual form			275.2.z.c.224.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.122427 + 0.168506i) q^{2} +(1.80155 - 0.585361i) q^{3} +(0.604628 - 1.86085i) q^{4} +(0.319195 + 0.231909i) q^{6} +(-1.22573 - 0.398265i) q^{7} +(0.783769 - 0.254662i) q^{8} +(0.475901 - 0.345762i) q^{9} +O(q^{10})$	\(q+(0.122427 + 0.168506i) q^{2} +(1.80155 - 0.585361i) q^{3} +(0.604628 - 1.86085i) q^{4} +(0.319195 + 0.231909i) q^{6} +(-1.22573 - 0.398265i) q^{7} +(0.783769 - 0.254662i) q^{8} +(0.475901 - 0.345762i) q^{9} +(0.898964 - 3.19247i) q^{11} -3.70635i q^{12} +(3.20351 + 4.40926i) q^{13} +(-0.0829527 - 0.255302i) q^{14} +(-3.02701 - 2.19925i) q^{16} +(-2.31083 + 3.18058i) q^{17} +(0.116526 + 0.0378616i) q^{18} +(-0.693894 - 2.13559i) q^{19} -2.44136 q^{21} +(0.648008 - 0.239363i) q^{22} +0.711128i q^{23} +(1.26293 - 0.917575i) q^{24} +(-0.350791 + 1.07962i) q^{26} +(-2.68530 + 3.69600i) q^{27} +(-1.48223 + 2.04011i) q^{28} +(-1.13043 + 3.47910i) q^{29} +(5.22959 - 3.79952i) q^{31} -2.42752i q^{32} +(-0.249213 - 6.27763i) q^{33} -0.818854 q^{34} +(-0.355670 - 1.09464i) q^{36} +(7.85902 + 2.55355i) q^{37} +(0.274908 - 0.378379i) q^{38} +(8.35231 + 6.06831i) q^{39} +(3.90378 + 12.0146i) q^{41} +(-0.298888 - 0.411383i) q^{42} +1.31169i q^{43} +(-5.39718 - 3.60310i) q^{44} +(-0.119829 + 0.0870611i) q^{46} +(-4.29408 + 1.39523i) q^{47} +(-6.74067 - 2.19018i) q^{48} +(-4.31931 - 3.13816i) q^{49} +(-2.30129 + 7.08265i) q^{51} +(10.1419 - 3.29531i) q^{52} +(-5.71278 - 7.86297i) q^{53} -0.951551 q^{54} -1.06212 q^{56} +(-2.50018 - 3.44120i) q^{57} +(-0.724644 + 0.235451i) q^{58} +(-2.75455 + 8.47763i) q^{59} +(1.48965 + 1.08229i) q^{61} +(1.28048 + 0.416055i) q^{62} +(-0.721033 + 0.234278i) q^{63} +(-5.64496 + 4.10130i) q^{64} +(1.02731 - 0.810544i) q^{66} -4.30232i q^{67} +(4.52140 + 6.22318i) q^{68} +(0.416266 + 1.28114i) q^{69} +(-8.21746 - 5.97033i) q^{71} +(0.284944 - 0.392192i) q^{72} +(-11.4173 - 3.70969i) q^{73} +(0.531866 + 1.63692i) q^{74} -4.39356 q^{76} +(-2.37334 + 3.55509i) q^{77} +2.15034i q^{78} +(10.3649 - 7.53052i) q^{79} +(-3.21956 + 9.90878i) q^{81} +(-1.54661 + 2.12872i) q^{82} +(-7.37274 + 10.1477i) q^{83} +(-1.47611 + 4.54301i) q^{84} +(-0.221028 + 0.160586i) q^{86} +6.92949i q^{87} +(-0.108421 - 2.73109i) q^{88} +6.28392 q^{89} +(-2.17060 - 6.68043i) q^{91} +(1.32330 + 0.429968i) q^{92} +(7.19730 - 9.90624i) q^{93} +(-0.760816 - 0.552765i) q^{94} +(-1.42098 - 4.37332i) q^{96} +(0.178336 + 0.245459i) q^{97} -1.11202i q^{98} +(-0.676018 - 1.83013i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 4 q^{4} - 6 q^{6} - 16 q^{9}+O(q^{10}) $ 32 * q + 4 * q^4 - 6 * q^6 - 16 * q^9	$ 32 q + 4 q^{4} - 6 q^{6} - 16 q^{9} - 10 q^{11} - 6 q^{14} - 8 q^{16} + 26 q^{19} + 20 q^{21} + 86 q^{24} - 68 q^{26} + 22 q^{29} - 20 q^{31} - 40 q^{34} + 6 q^{36} - 6 q^{39} + 50 q^{41} + 2 q^{44} + 80 q^{46} - 32 q^{49} + 70 q^{51} - 120 q^{54} - 40 q^{56} - 28 q^{59} + 32 q^{61} - 80 q^{64} - 110 q^{66} - 70 q^{69} - 92 q^{71} + 14 q^{74} - 124 q^{76} + 78 q^{79} - 86 q^{81} + 108 q^{84} + 4 q^{86} + 44 q^{89} - 68 q^{91} + 80 q^{94} + 216 q^{96} + 20 q^{99}+O(q^{100}) $ 32 * q + 4 * q^4 - 6 * q^6 - 16 * q^9 - 10 * q^11 - 6 * q^14 - 8 * q^16 + 26 * q^19 + 20 * q^21 + 86 * q^24 - 68 * q^26 + 22 * q^29 - 20 * q^31 - 40 * q^34 + 6 * q^36 - 6 * q^39 + 50 * q^41 + 2 * q^44 + 80 * q^46 - 32 * q^49 + 70 * q^51 - 120 * q^54 - 40 * q^56 - 28 * q^59 + 32 * q^61 - 80 * q^64 - 110 * q^66 - 70 * q^69 - 92 * q^71 + 14 * q^74 - 124 * q^76 + 78 * q^79 - 86 * q^81 + 108 * q^84 + 4 * q^86 + 44 * q^89 - 68 * q^91 + 80 * q^94 + 216 * q^96 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/275\mathbb{Z}\right)^\times$.

$n$	$101$	$177$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$-1$

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 $

$2$	0.122427	+	0.168506i	0.0865688	+	0.119152i	0.850105	−	0.526613i	$-0.176538\pi$
$2$	0.122427	+	0.168506i	0.0865688	+	0.119152i	−0.763536	+	0.645765i	$0.776538\pi$
$3$	1.80155	−	0.585361i	1.04013	−	0.337958i	0.261341	−	0.965247i	$-0.415835\pi$
$3$	1.80155	−	0.585361i	1.04013	−	0.337958i	0.778787	+	0.627288i	$0.215835\pi$
$4$	0.604628	−	1.86085i	0.302314	−	0.930427i
$5$		0			0
$5$		0			0
$6$	0.319195	+	0.231909i	0.130311	+	0.0946765i
$7$	−1.22573	−	0.398265i	−0.463284	−	0.150530i	0.0680689	−	0.997681i	$-0.478316\pi$
$7$	−1.22573	−	0.398265i	−0.463284	−	0.150530i	−0.531353	+	0.847150i	$0.678316\pi$
$8$	0.783769	−	0.254662i	0.277104	−	0.0900367i
$9$	0.475901	−	0.345762i	0.158634	−	0.115254i
$10$		0			0
$11$	0.898964	−	3.19247i	0.271048	−	0.962566i
$11$	0.898964	−	3.19247i	0.271048	−	0.962566i
$12$		−	3.70635i		−	1.06993i
$13$	3.20351	+	4.40926i	0.888494	+	1.22291i	0.973995	+	0.226569i	$0.0727510\pi$
$13$	3.20351	+	4.40926i	0.888494	+	1.22291i	−0.0855007	+	0.996338i	$0.527249\pi$
$14$	−0.0829527	−	0.255302i	−0.0221700	−	0.0682324i
$15$		0			0
$16$	−3.02701	−	2.19925i	−0.756752	−	0.549812i
$17$	−2.31083	+	3.18058i	−0.560458	+	0.771404i	−0.991385	−	0.130983i	$-0.958187\pi$
$17$	−2.31083	+	3.18058i	−0.560458	+	0.771404i	0.430927	+	0.902387i	$0.358187\pi$
$18$	0.116526	+	0.0378616i	0.0274655	+	0.00892407i
$19$	−0.693894	−	2.13559i	−0.159190	−	0.489937i	0.839371	−	0.543559i	$-0.182924\pi$
$19$	−0.693894	−	2.13559i	−0.159190	−	0.489937i	−0.998561	+	0.0536215i	$0.982924\pi$
$20$		0			0
$21$	−2.44136			−0.532748
$22$	0.648008	−	0.239363i	0.138156	−	0.0510324i
$23$			0.711128i			0.148280i	0.997248	+	0.0741402i	$0.0236212\pi$
$23$			0.711128i			0.148280i	−0.997248	+	0.0741402i	$0.976379\pi$
$24$	1.26293	−	0.917575i	0.257795	−	0.187299i
$25$		0			0
$26$	−0.350791	+	1.07962i	−0.0687957	+	0.211731i
$27$	−2.68530	+	3.69600i	−0.516786	+	0.711295i
$28$	−1.48223	+	2.04011i	−0.280115	+	0.385545i
$29$	−1.13043	+	3.47910i	−0.209915	+	0.646052i	0.789561	+	0.613673i	$0.210309\pi$
$29$	−1.13043	+	3.47910i	−0.209915	+	0.646052i	−0.999476	+	0.0323796i	$0.989691\pi$
$30$		0			0
$31$	5.22959	−	3.79952i	0.939262	−	0.682414i	−0.00898085	−	0.999960i	$-0.502859\pi$
$31$	5.22959	−	3.79952i	0.939262	−	0.682414i	0.948243	+	0.317546i	$0.102859\pi$
$32$		−	2.42752i		−	0.429130i
$33$	−0.249213	−	6.27763i	−0.0433824	−	1.09279i
$34$	−0.818854			−0.140432
$35$		0			0
$36$	−0.355670	−	1.09464i	−0.0592783	−	0.182440i
$37$	7.85902	+	2.55355i	1.29201	+	0.419801i	0.872796	−	0.488085i	$-0.162304\pi$
$37$	7.85902	+	2.55355i	1.29201	+	0.419801i	0.419218	+	0.907886i	$0.362304\pi$
$38$	0.274908	−	0.378379i	0.0445960	−	0.0613811i
$39$	8.35231	+	6.06831i	1.33744	+	0.971707i
$40$		0			0
$41$	3.90378	+	12.0146i	0.609668	+	1.87637i	0.460789	+	0.887510i	$0.347566\pi$
$41$	3.90378	+	12.0146i	0.609668	+	1.87637i	0.148879	+	0.988855i	$0.452434\pi$
$42$	−0.298888	−	0.411383i	−0.0461194	−	0.0634779i
$43$			1.31169i			0.200031i	0.994986	+	0.100015i	$0.0318892\pi$
$43$			1.31169i			0.200031i	−0.994986	+	0.100015i	$0.968111\pi$
$44$	−5.39718	−	3.60310i	−0.813656	−	0.543187i
$45$		0			0
$46$	−0.119829	+	0.0870611i	−0.0176679	+	0.0128365i
$47$	−4.29408	+	1.39523i	−0.626356	+	0.203515i	−0.604960	−	0.796256i	$-0.706811\pi$
$47$	−4.29408	+	1.39523i	−0.626356	+	0.203515i	−0.0213959	+	0.999771i	$0.506811\pi$
$48$	−6.74067	−	2.19018i	−0.972932	−	0.316125i
$49$	−4.31931	−	3.13816i	−0.617044	−	0.448309i
$50$		0			0
$51$	−2.30129	+	7.08265i	−0.322246	+	0.991770i
$52$	10.1419	−	3.29531i	1.40643	−	0.456977i
$53$	−5.71278	−	7.86297i	−0.784711	−	1.08006i	−0.994747	−	0.102369i	$-0.967358\pi$
$53$	−5.71278	−	7.86297i	−0.784711	−	1.08006i	0.210035	−	0.977694i	$-0.432642\pi$
$54$	−0.951551			−0.129490
$55$		0			0
$56$	−1.06212			−0.141931
$57$	−2.50018	−	3.44120i	−0.331157	−	0.455798i
$58$	−0.724644	+	0.235451i	−0.0951504	+	0.0309162i
$59$	−2.75455	+	8.47763i	−0.358612	+	1.10369i	0.595274	+	0.803523i	$0.297044\pi$
$59$	−2.75455	+	8.47763i	−0.358612	+	1.10369i	−0.953886	+	0.300171i	$0.902956\pi$
$60$		0			0
$61$	1.48965	+	1.08229i	0.190730	+	0.138574i	0.679052	−	0.734090i	$-0.262391\pi$
$61$	1.48965	+	1.08229i	0.190730	+	0.138574i	−0.488322	+	0.872663i	$0.662391\pi$
$62$	1.28048	+	0.416055i	0.162622	+	0.0528390i
$63$	−0.721033	+	0.234278i	−0.0908417	+	0.0295162i
$64$	−5.64496	+	4.10130i	−0.705620	+	0.512663i
$65$		0			0
$66$	1.02731	−	0.810544i	0.126453	−	0.0997711i
$67$		−	4.30232i		−	0.525612i	−0.964849	−	0.262806i	$-0.915352\pi$
$67$		−	4.30232i		−	0.525612i	0.964849	−	0.262806i	$-0.0846480\pi$
$68$	4.52140	+	6.22318i	0.548301	+	0.754671i
$69$	0.416266	+	1.28114i	0.0501126	+	0.154231i
$70$		0			0
$71$	−8.21746	−	5.97033i	−0.975233	−	0.708548i	−0.0185947	−	0.999827i	$-0.505919\pi$
$71$	−8.21746	−	5.97033i	−0.975233	−	0.708548i	−0.956638	+	0.291279i	$0.905919\pi$
$72$	0.284944	−	0.392192i	0.0335810	−	0.0462202i
$73$	−11.4173	−	3.70969i	−1.33629	−	0.434187i	−0.448232	−	0.893917i	$-0.647946\pi$
$73$	−11.4173	−	3.70969i	−1.33629	−	0.434187i	−0.888058	+	0.459731i	$0.847946\pi$
$74$	0.531866	+	1.63692i	0.0618282	+	0.190288i
$75$		0			0
$76$	−4.39356			−0.503976
$77$	−2.37334	+	3.55509i	−0.270467	+	0.405141i
$78$			2.15034i			0.243478i
$79$	10.3649	−	7.53052i	1.16614	−	0.847249i	0.175597	−	0.984462i	$-0.443814\pi$
$79$	10.3649	−	7.53052i	1.16614	−	0.847249i	0.990542	+	0.137213i	$0.0438143\pi$
$80$		0			0
$81$	−3.21956	+	9.90878i	−0.357729	+	1.10098i
$82$	−1.54661	+	2.12872i	−0.170794	+	0.235078i
$83$	−7.37274	+	10.1477i	−0.809263	+	1.11386i	0.182174	+	0.983266i	$0.441687\pi$
$83$	−7.37274	+	10.1477i	−0.809263	+	1.11386i	−0.991437	+	0.130589i	$0.958313\pi$
$84$	−1.47611	+	4.54301i	−0.161057	+	0.495683i
$85$		0			0
$86$	−0.221028	+	0.160586i	−0.0238340	+	0.0173164i
$87$			6.92949i			0.742920i
$88$	−0.108421	−	2.73109i	−0.0115577	−	0.291135i
$89$	6.28392			0.666095			0.333047	−	0.942910i	$-0.391923\pi$
$89$	6.28392			0.666095			0.333047	+	0.942910i	$0.391923\pi$
$90$		0			0
$91$	−2.17060	−	6.68043i	−0.227541	−	0.700299i
$92$	1.32330	+	0.429968i	0.137964	+	0.0448272i
$93$	7.19730	−	9.90624i	0.746326	−	1.02723i
$94$	−0.760816	−	0.552765i	−0.0784722	−	0.0570134i
$95$		0			0
$96$	−1.42098	−	4.37332i	−0.145028	−	0.446350i
$97$	0.178336	+	0.245459i	0.0181073	+	0.0249226i	0.817975	−	0.575254i	$-0.195097\pi$
$97$	0.178336	+	0.245459i	0.0181073	+	0.0249226i	−0.799867	+	0.600177i	$0.795097\pi$
$98$		−	1.11202i		−	0.112331i
$99$	−0.676018	−	1.83013i	−0.0679423	−	0.183935i
$100$		0			0
$101$	4.99821	−	3.63141i	0.497340	−	0.361339i	−0.310660	−	0.950521i	$-0.600550\pi$
$101$	4.99821	−	3.63141i	0.497340	−	0.361339i	0.808000	+	0.589182i	$0.200550\pi$
$102$	−1.47521	+	0.479325i	−0.146068	+	0.0474602i
$103$	−7.58828	−	2.46558i	−0.747695	−	0.242941i	−0.0897061	−	0.995968i	$-0.528593\pi$
$103$	−7.58828	−	2.46558i	−0.747695	−	0.242941i	−0.657989	+	0.753027i	$0.728593\pi$
$104$	3.63369	+	2.64003i	0.356312	+	0.258876i
$105$		0			0
$106$	0.625561	−	1.92528i	0.0607598	−	0.187000i
$107$	−9.55358	+	3.10415i	−0.923580	+	0.300089i	−0.731934	−	0.681375i	$-0.761382\pi$
$107$	−9.55358	+	3.10415i	−0.923580	+	0.300089i	−0.191645	+	0.981464i	$0.561382\pi$
$108$	5.25410	+	7.23165i	0.505576	+	0.695866i
$109$	−7.63832			−0.731619			−0.365809	−	0.930690i	$-0.619208\pi$
$109$	−7.63832			−0.731619			−0.365809	+	0.930690i	$0.619208\pi$
$110$		0			0
$111$	15.6532			1.48574
$112$	2.83442	+	3.90125i	0.267828	+	0.368633i
$113$	18.6436	−	6.05767i	1.75384	−	0.569858i	0.757309	−	0.653057i	$-0.226514\pi$
$113$	18.6436	−	6.05767i	1.75384	−	0.569858i	0.996533	+	0.0831991i	$0.0265137\pi$
$114$	0.273774	−	0.842590i	0.0256413	−	0.0789158i
$115$		0			0
$116$	5.79060	+	4.20712i	0.537644	+	0.390621i
$117$	3.04911	+	0.990715i	0.281890	+	0.0915916i
$118$	−1.76576	+	0.573731i	−0.162552	+	0.0528162i
$119$	4.09918	−	2.97823i	0.375771	−	0.273013i
$120$		0			0
$121$	−9.38373	−	5.73983i	−0.853066	−	0.521803i
$122$			0.383517i			0.0347220i
$123$	14.0657	+	19.3598i	1.26827	+	1.74562i
$124$	−3.90839	−	12.0288i	−0.350984	−	1.08022i
$125$		0			0
$126$	−0.127751	−	0.0928166i	−0.0113810	−	0.00826876i
$127$	10.0894	−	13.8869i	0.895293	−	1.23226i	−0.0766526	−	0.997058i	$-0.524423\pi$
$127$	10.0894	−	13.8869i	0.895293	−	1.23226i	0.971945	−	0.235207i	$-0.0755768\pi$
$128$	−5.99961	−	1.94939i	−0.530296	−	0.172304i
$129$	0.767812	+	2.36308i	0.0676020	+	0.208058i
$130$		0			0
$131$	10.0223			0.875655			0.437828	−	0.899059i	$-0.355748\pi$
$131$	10.0223			0.875655			0.437828	+	0.899059i	$0.355748\pi$
$132$	−11.8324	−	3.33188i	−1.02988	−	0.290003i
$133$			2.89402i			0.250943i
$134$	0.724967	−	0.526720i	0.0626276	−	0.0455016i
$135$		0			0
$136$	−1.00118	+	3.08132i	−0.0858506	+	0.264221i
$137$	2.07331	−	2.85366i	0.177134	−	0.243805i	−0.711213	−	0.702977i	$-0.751854\pi$
$137$	2.07331	−	2.85366i	0.177134	−	0.243805i	0.888347	+	0.459172i	$0.151854\pi$
$138$	−0.164917	+	0.226989i	−0.0140387	+	0.0193226i
$139$	2.71237	−	8.34781i	0.230060	−	0.708052i	−0.767679	−	0.640835i	$-0.778588\pi$
$139$	2.71237	−	8.34781i	0.230060	−	0.708052i	0.997738	−	0.0672164i	$-0.0214118\pi$
$140$		0			0
$141$	−6.91931	+	5.02717i	−0.582711	+	0.423364i
$142$		−	2.11562i		−	0.177539i
$143$	16.9563	−	6.26335i	1.41795	−	0.523768i
$144$	−2.20097			−0.183414
$145$		0			0
$146$	−0.772674	−	2.37805i	−0.0639469	−	0.196808i
$147$	−9.61843	−	3.12522i	−0.793314	−	0.257763i
$148$	9.50356	−	13.0805i	0.781188	−	1.07521i
$149$	−6.79312	−	4.93549i	−0.556514	−	0.404331i	0.273667	−	0.961824i	$-0.411763\pi$
$149$	−6.79312	−	4.93549i	−0.556514	−	0.404331i	−0.830181	+	0.557493i	$0.811763\pi$
$150$		0			0
$151$	−2.63804	−	8.11906i	−0.214681	−	0.660720i	−0.999176	−	0.0405849i	$-0.987078\pi$
$151$	−2.63804	−	8.11906i	−0.214681	−	0.660720i	0.784495	−	0.620135i	$-0.212922\pi$
$152$	−1.08771	−	1.49710i	−0.0882247	−	0.121431i
$153$			2.31264i			0.186966i
$154$	−0.889616	+	0.0353165i	−0.0716873	+	0.00284588i
$155$		0			0
$156$	16.3423	−	11.8734i	1.30843	−	0.950629i
$157$	12.0304	−	3.90892i	0.960131	−	0.311966i	0.213306	−	0.976986i	$-0.431577\pi$
$157$	12.0304	−	3.90892i	0.960131	−	0.311966i	0.746826	+	0.665020i	$0.231577\pi$
$158$	2.53788	+	0.824606i	0.201903	+	0.0656021i
$159$	−14.8946	−	10.8215i	−1.18122	−	0.858204i
$160$		0			0
$161$	0.283218	−	0.871654i	0.0223207	−	0.0686960i
$162$	−2.06385	+	0.670585i	−0.162151	+	0.0526862i
$163$	4.94275	+	6.80311i	0.387146	+	0.532860i	0.957460	−	0.288566i	$-0.0931785\pi$
$163$	4.94275	+	6.80311i	0.387146	+	0.532860i	−0.570314	+	0.821427i	$0.693179\pi$
$164$	24.7177			1.93013
$165$		0			0
$166$	−2.61257			−0.202775
$167$	−11.2414	−	15.4725i	−0.869888	−	1.19730i	−0.979120	−	0.203281i	$-0.934839\pi$
$167$	−11.2414	−	15.4725i	−0.869888	−	1.19730i	0.109233	−	0.994016i	$-0.465161\pi$
$168$	−1.91346	+	0.621721i	−0.147627	+	0.0479668i
$169$	−5.16183	+	15.8865i	−0.397064	+	1.22204i
$170$		0			0
$171$	−1.06863	−	0.776405i	−0.0817202	−	0.0593732i
$172$	2.44086	+	0.793085i	0.186114	+	0.0604721i
$173$	−11.6397	+	3.78197i	−0.884950	+	0.287538i	−0.716011	−	0.698089i	$-0.754034\pi$
$173$	−11.6397	+	3.78197i	−0.884950	+	0.287538i	−0.168939	+	0.985626i	$0.554034\pi$
$174$	−1.16766	+	0.848356i	−0.0885202	+	0.0643137i
$175$		0			0
$176$	−9.74221	+	7.68658i	−0.734347	+	0.579398i
$177$			16.8853i			1.26918i
$178$	0.769321	+	1.05888i	0.0576630	+	0.0793664i
$179$	−0.988945	−	3.04366i	−0.0739172	−	0.227494i	0.907271	−	0.420546i	$-0.138161\pi$
$179$	−0.988945	−	3.04366i	−0.0739172	−	0.227494i	−0.981189	+	0.193052i	$0.938161\pi$
$180$		0			0
$181$	−1.75310	−	1.27370i	−0.130307	−	0.0946734i	0.520723	−	0.853726i	$-0.325663\pi$
$181$	−1.75310	−	1.27370i	−0.130307	−	0.0946734i	−0.651029	+	0.759053i	$0.725663\pi$
$182$	0.859952	−	1.18362i	0.0637439	−	0.0877360i
$183$	3.31722	+	1.07783i	0.245216	+	0.0796754i
$184$	0.181097	+	0.557360i	0.0133507	+	0.0410891i
$185$		0			0
$186$	2.55040			0.187005
$187$	8.07655	+	10.2365i	0.590616	+	0.748565i
$188$			8.83425i			0.644304i
$189$	4.76345	−	3.46085i	0.346490	−	0.251740i
$190$		0			0
$191$	0.544810	−	1.67675i	0.0394211	−	0.121326i	−0.929409	−	0.369051i	$-0.879683\pi$
$191$	0.544810	−	1.67675i	0.0394211	−	0.121326i	0.968830	+	0.247725i	$0.0796829\pi$
$192$	−7.76896	+	10.6931i	−0.560677	+	0.771705i
$193$	−9.05616	+	12.4647i	−0.651877	+	0.897231i	−0.999179	−	0.0405221i	$-0.987098\pi$
$193$	−9.05616	+	12.4647i	−0.651877	+	0.897231i	0.347302	+	0.937753i	$0.387098\pi$
$194$	−0.0195282	+	0.0601015i	−0.00140204	+	0.00431503i
$195$		0			0
$196$	−8.45123	+	6.14018i	−0.603660	+	0.438584i
$197$			1.78727i			0.127338i	0.997971	+	0.0636689i	$0.0202801\pi$
$197$			1.78727i			0.127338i	−0.997971	+	0.0636689i	$0.979720\pi$
$198$	0.225625	−	0.337970i	0.0160345	−	0.0240185i
$199$	19.6066			1.38988			0.694938	−	0.719070i	$-0.255432\pi$
$199$	19.6066			1.38988			0.694938	+	0.719070i	$0.255432\pi$
$200$		0			0
$201$	−2.51841	−	7.75087i	−0.177635	−	0.546704i
$202$	1.22383	+	0.397646i	0.0861083	+	0.0279783i
$203$	2.77121	−	3.81424i	0.194501	−	0.267707i
$204$	11.7884	+	8.56474i	0.825350	+	0.599652i
$205$		0			0
$206$	−0.513544	−	1.58052i	−0.0357803	−	0.110120i
$207$	0.245881	+	0.338426i	0.0170899	+	0.0235223i
$208$		−	20.3922i		−	1.41394i
$209$	−7.44159	+	0.295420i	−0.514745	+	0.0204347i
$210$		0			0
$211$	13.5246	−	9.82620i	0.931072	−	0.676464i	−0.0151828	−	0.999885i	$-0.504833\pi$
$211$	13.5246	−	9.82620i	0.931072	−	0.676464i	0.946255	+	0.323421i	$0.104833\pi$
$212$	−18.0860	+	5.87648i	−1.24215	+	0.403598i
$213$	−18.2990	−	5.94570i	−1.25383	−	0.407393i
$214$	−1.69268	−	1.22981i	−0.115709	−	0.0840678i
$215$		0			0
$216$	−1.16343	+	3.58065i	−0.0791611	+	0.243633i
$217$	−7.92331	+	2.57444i	−0.537869	+	0.174764i
$218$	−0.935136	−	1.28710i	−0.0633354	−	0.0871737i
$219$	−22.7403			−1.53665
$220$		0			0
$221$	−21.4267			−1.44132
$222$	1.91637	+	2.63766i	0.128618	+	0.177028i
$223$	−5.68876	+	1.84839i	−0.380947	+	0.123777i	−0.493230	−	0.869899i	$-0.664184\pi$
$223$	−5.68876	+	1.84839i	−0.380947	+	0.123777i	0.112283	+	0.993676i	$0.464184\pi$
$224$	−0.966799	+	2.97550i	−0.0645970	+	0.198809i
$225$		0			0
$226$	3.30323	+	2.39994i	0.219728	+	0.159641i
$227$	21.1602	+	6.87537i	1.40445	+	0.456334i	0.910628	−	0.413227i	$-0.135599\pi$
$227$	21.1602	+	6.87537i	1.40445	+	0.456334i	0.493825	+	0.869562i	$0.335599\pi$
$228$	−7.91525	+	2.57182i	−0.524200	+	0.170323i
$229$	4.83195	−	3.51062i	0.319305	−	0.231988i	−0.416574	−	0.909102i	$-0.636769\pi$
$229$	4.83195	−	3.51062i	0.319305	−	0.231988i	0.735879	+	0.677113i	$0.236769\pi$
$230$		0			0
$231$	−2.19469	+	7.79396i	−0.144400	+	0.512805i
$232$			3.01469i			0.197924i
$233$	−10.4243	−	14.3479i	−0.682921	−	0.939960i	0.317044	−	0.948411i	$-0.397310\pi$
$233$	−10.4243	−	14.3479i	−0.682921	−	0.939960i	−0.999964	+	0.00845137i	$0.997310\pi$
$234$	0.206351	+	0.635083i	0.0134896	+	0.0415167i
$235$		0			0
$236$	14.1102	+	10.2516i	0.918493	+	0.667324i
$237$	14.2648	−	19.6338i	0.926599	−	1.27535i
$238$	1.00370	+	0.326121i	0.0650601	+	0.0211393i
$239$	5.90708	+	18.1801i	0.382097	+	1.17597i	0.938564	+	0.345104i	$0.112156\pi$
$239$	5.90708	+	18.1801i	0.382097	+	1.17597i	−0.556467	+	0.830870i	$0.687844\pi$
$240$		0			0
$241$	−1.79437			−0.115586			−0.0577929	−	0.998329i	$-0.518406\pi$
$241$	−1.79437			−0.115586			−0.0577929	+	0.998329i	$0.518406\pi$
$242$	−0.181623	−	2.28392i	−0.0116752	−	0.146816i
$243$			6.03029i			0.386843i
$244$	2.91468	−	2.11764i	0.186593	−	0.135568i
$245$		0			0
$246$	−1.54023	+	4.74033i	−0.0982012	+	0.302232i
$247$	7.19345	−	9.90094i	0.457708	−	0.629982i
$248$	3.13120	−	4.30973i	0.198831	−	0.273668i
$249$	−7.34232	+	22.5973i	−0.465301	+	1.43205i
$250$		0			0
$251$	−8.55143	+	6.21298i	−0.539761	+	0.392160i	−0.823996	−	0.566595i	$-0.808260\pi$
$251$	−8.55143	+	6.21298i	−0.539761	+	0.392160i	0.284235	+	0.958755i	$0.408260\pi$
$252$			1.48339i			0.0934447i
$253$	2.27025	+	0.639278i	0.142730	+	0.0401911i
$254$	3.57525			0.224331
$255$		0			0
$256$	3.90634	+	12.0225i	0.244146	+	0.751404i
$257$	−4.27900	−	1.39033i	−0.266917	−	0.0867265i	0.172501	−	0.985009i	$-0.444815\pi$
$257$	−4.27900	−	1.39033i	−0.266917	−	0.0867265i	−0.439418	+	0.898283i	$0.644815\pi$
$258$	−0.304193	+	0.418686i	−0.0189382	+	0.0260662i
$259$	−8.61608	−	6.25995i	−0.535377	−	0.388974i
$260$		0			0
$261$	0.664969	+	2.04656i	0.0411606	+	0.126679i
$262$	1.22700	+	1.68882i	0.0758045	+	0.104336i
$263$			8.87966i			0.547543i	0.961795	+	0.273772i	$0.0882712\pi$
$263$			8.87966i			0.547543i	−0.961795	+	0.273772i	$0.911729\pi$
$264$	−1.79400	−	4.85675i	−0.110413	−	0.298912i
$265$		0			0
$266$	−0.487660	+	0.354305i	−0.0299003	+	0.0217239i
$267$	11.3208	−	3.67836i	0.692824	−	0.225112i
$268$	−8.00599	−	2.60130i	−0.489044	−	0.158900i
$269$	−13.5968	−	9.87862i	−0.829009	−	0.602310i	0.0902701	−	0.995917i	$-0.471227\pi$
$269$	−13.5968	−	9.87862i	−0.829009	−	0.602310i	−0.919279	+	0.393607i	$0.871227\pi$
$270$		0			0
$271$	−4.18182	+	12.8703i	−0.254028	+	0.781817i	0.739992	+	0.672616i	$0.234829\pi$
$271$	−4.18182	+	12.8703i	−0.254028	+	0.781817i	−0.994020	+	0.109201i	$0.965171\pi$
$272$	13.9898	−	4.54555i	0.848255	−	0.275615i
$273$	−7.82092	−	10.7646i	−0.473343	−	0.651501i
$274$	0.734688			0.0443841
$275$		0			0
$276$	2.63569			0.158650
$277$	−12.0310	−	16.5592i	−0.722870	−	0.994946i	−0.999424	−	0.0339471i	$-0.989192\pi$
$277$	−12.0310	−	16.5592i	−0.722870	−	0.994946i	0.276553	−	0.960999i	$-0.410808\pi$
$278$	1.73872	−	0.564945i	0.104282	−	0.0338832i
$279$	1.17504	−	3.61639i	0.0703476	−	0.216508i
$280$		0			0
$281$	8.09848	+	5.88389i	0.483115	+	0.351004i	0.802530	−	0.596611i	$-0.203487\pi$
$281$	8.09848	+	5.88389i	0.483115	+	0.351004i	−0.319415	+	0.947615i	$0.603487\pi$
$282$	−1.69422	−	0.550485i	−0.100889	−	0.0327809i
$283$	−2.54683	+	0.827516i	−0.151394	+	0.0491907i	−0.383733	−	0.923444i	$-0.625362\pi$
$283$	−2.54683	+	0.827516i	−0.151394	+	0.0491907i	0.232340	+	0.972635i	$0.425362\pi$
$284$	−16.0784	+	11.6817i	−0.954079	+	0.693179i
$285$		0			0
$286$	3.13131	+	2.09043i	0.185158	+	0.123610i
$287$		−	16.2815i		−	0.961064i
$288$	−0.839346	−	1.15526i	−0.0494589	−	0.0680744i
$289$	0.477120	+	1.46843i	0.0280659	+	0.0863780i
$290$		0			0
$291$	0.464964	+	0.337816i	0.0272567	+	0.0198031i
$292$	−13.8064	+	19.0029i	−0.807958	+	1.11206i
$293$	−24.0525	−	7.81514i	−1.40516	−	0.456565i	−0.494306	−	0.869288i	$-0.664578\pi$
$293$	−24.0525	−	7.81514i	−1.40516	−	0.456565i	−0.910857	+	0.412723i	$0.864578\pi$
$294$	−0.650936	−	2.00337i	−0.0379633	−	0.116839i
$295$		0			0
$296$	6.80995			0.395820
$297$	9.38538	+	11.8953i	0.544595	+	0.690236i
$298$		−	1.74892i		−	0.101312i
$299$	−3.13554	+	2.27811i	−0.181333	+	0.131746i
$300$		0			0
$301$	0.522401	−	1.60778i	0.0301107	−	0.0926711i
$302$	1.04514	−	1.43852i	0.0601413	−	0.0827774i
$303$	6.87886	−	9.46794i	0.395180	−	0.543919i
$304$	−2.59627	+	7.99049i	−0.148906	+	0.458286i
$305$		0			0
$306$	−0.389693	+	0.283129i	−0.0222773	+	0.0161854i
$307$		−	8.53224i		−	0.486960i	−0.969906	−	0.243480i	$-0.921711\pi$
$307$		−	8.53224i		−	0.486960i	0.969906	−	0.243480i	$-0.0782891\pi$
$308$	5.18052	+	6.56595i	0.295188	+	0.374130i
$309$	−15.1140			−0.859803
$310$		0			0
$311$	−0.341159	−	1.04998i	−0.0193454	−	0.0595389i	0.940918	−	0.338635i	$-0.109965\pi$
$311$	−0.341159	−	1.04998i	−0.0193454	−	0.0595389i	−0.960263	+	0.279096i	$0.909965\pi$
$312$	8.09165	+	2.62914i	0.458099	+	0.148846i
$313$	−3.28657	+	4.52358i	−0.185768	+	0.255688i	−0.891736	−	0.452556i	$-0.850512\pi$
$313$	−3.28657	+	4.52358i	−0.185768	+	0.255688i	0.705968	+	0.708244i	$0.250512\pi$
$314$	2.13152	+	1.54864i	0.120289	+	0.0873949i
$315$		0			0
$316$	−7.74630	−	23.8407i	−0.435764	−	1.34114i
$317$	16.6632	+	22.9349i	0.935897	+	1.28815i	0.957514	+	0.288385i	$0.0931184\pi$
$317$	16.6632	+	22.9349i	0.935897	+	1.28815i	−0.0216175	+	0.999766i	$0.506882\pi$
$318$		−	3.83467i		−	0.215038i
$319$	10.0907	+	6.73644i	0.564971	+	0.377168i
$320$		0			0
$321$	−15.3943	+	11.1846i	−0.859223	+	0.624262i
$322$	0.181552	−	0.0589900i	0.0101175	−	0.00328738i
$323$	8.39588	+	2.72799i	0.467159	+	0.151789i
$324$	16.4921	+	11.9822i	0.916231	+	0.665680i
$325$		0			0
$326$	−0.541240	+	1.66577i	−0.0299765	+	0.0922582i
$327$	−13.7609	+	4.47117i	−0.760977	+	0.247256i
$328$	6.11933	+	8.42253i	0.337883	+	0.465056i
$329$	5.81908			0.320816
$330$		0			0
$331$	18.6052			1.02263			0.511317	−	0.859392i	$-0.329158\pi$
$331$	18.6052			1.02263			0.511317	+	0.859392i	$0.329158\pi$
$332$	14.4256	+	19.8552i	0.791709	+	1.08969i
$333$	4.62303	−	1.50211i	0.253341	−	0.0823154i
$334$	1.23096	−	3.78850i	0.0673550	−	0.207297i
$335$		0			0
$336$	7.39000	+	5.36915i	0.403158	+	0.292911i
$337$	−28.0308	−	9.10777i	−1.52694	−	0.496132i	−0.579200	−	0.815186i	$-0.696635\pi$
$337$	−28.0308	−	9.10777i	−1.52694	−	0.496132i	−0.947737	+	0.319054i	$0.896635\pi$
$338$	−3.30891	+	1.07513i	−0.179981	+	0.0584794i
$339$	30.0415	−	21.8264i	1.63163	−	1.18545i
$340$		0			0
$341$	−7.42864	−	20.1109i	−0.402283	−	1.08907i
$342$		−	0.275124i		−	0.0148770i
$343$	9.34733	+	12.8655i	0.504708	+	0.694671i
$344$	0.334038	+	1.02806i	0.0180101	+	0.0554294i
$345$		0			0
$346$	−2.06230	−	1.49835i	−0.110870	−	0.0805516i
$347$	−10.4020	+	14.3171i	−0.558408	+	0.768583i	−0.991123	−	0.132948i	$-0.957556\pi$
$347$	−10.4020	+	14.3171i	−0.558408	+	0.768583i	0.432715	+	0.901531i	$0.357556\pi$
$348$	12.8948	+	4.18977i	0.691232	+	0.224595i
$349$	−0.483116	−	1.48688i	−0.0258606	−	0.0795908i	0.937293	−	0.348542i	$-0.113323\pi$
$349$	−0.483116	−	1.48688i	−0.0258606	−	0.0795908i	−0.963154	+	0.268951i	$0.913323\pi$
$350$		0			0
$351$	−24.8990			−1.32901
$352$	−7.74980	−	2.18226i	−0.413066	−	0.116315i
$353$		−	1.66213i		−	0.0884663i	−0.999021	−	0.0442331i	$-0.985916\pi$
$353$		−	1.66213i		−	0.0884663i	0.999021	−	0.0442331i	$-0.0140844\pi$
$354$	−2.84528	+	2.06722i	−0.151225	+	0.109871i
$355$		0			0
$356$	3.79944	−	11.6935i	0.201370	−	0.619752i
$357$	5.64155	−	7.76493i	0.298583	−	0.410964i
$358$	0.391802	−	0.539269i	0.0207074	−	0.0285012i
$359$	9.64641	−	29.6886i	0.509118	−	1.56690i	−0.284617	−	0.958641i	$-0.591866\pi$
$359$	9.64641	−	29.6886i	0.509118	−	1.56690i	0.793735	−	0.608263i	$-0.208134\pi$
$360$		0			0
$361$	11.2921	−	8.20418i	0.594320	−	0.431799i
$362$		−	0.451343i		−	0.0237220i
$363$	−20.2652	−	4.84776i	−1.06365	−	0.254441i
$364$	−13.7437			−0.720366
$365$		0			0
$366$	0.224496	+	0.690927i	0.0117346	+	0.0361153i
$367$	8.87177	+	2.88261i	0.463103	+	0.150471i	0.531270	−	0.847203i	$-0.321715\pi$
$367$	8.87177	+	2.88261i	0.463103	+	0.150471i	−0.0681670	+	0.997674i	$0.521715\pi$
$368$	1.56395	−	2.15259i	0.0815264	−	0.112211i
$369$	6.01201	+	4.36798i	0.312973	+	0.227388i
$370$		0			0
$371$	3.87081	+	11.9131i	0.200962	+	0.618499i
$372$	−14.0824	−	19.3827i	−0.730137	−	1.00495i
$373$			9.77497i			0.506129i	0.967449	+	0.253064i	$0.0814384\pi$
$373$			9.77497i			0.506129i	−0.967449	+	0.253064i	$0.918562\pi$
$374$	−0.736121	+	2.61417i	−0.0380639	+	0.135175i
$375$		0			0
$376$	−3.01026	+	2.18708i	−0.155242	+	0.112790i
$377$	−18.9616	+	6.16099i	−0.976571	+	0.317307i
$378$	1.16635	+	0.378970i	0.0599905	+	0.0194921i
$379$	10.8852	+	7.90855i	0.559135	+	0.406235i	0.831142	−	0.556060i	$-0.187688\pi$
$379$	10.8852	+	7.90855i	0.559135	+	0.406235i	−0.272007	+	0.962295i	$0.587688\pi$
$380$		0			0
$381$	10.0478	−	30.9240i	0.514765	−	1.58428i
$382$	0.349242	−	0.113476i	0.0178688	−	0.00580592i
$383$	2.30076	+	3.16673i	0.117563	+	0.161812i	0.863743	−	0.503933i	$-0.168114\pi$
$383$	2.30076	+	3.16673i	0.117563	+	0.161812i	−0.746180	+	0.665745i	$0.768114\pi$
$384$	−11.9497			−0.609807
$385$		0			0
$386$	−3.20910			−0.163339
$387$	0.453533	+	0.624234i	0.0230544	+	0.0317316i
$388$	0.564590	−	0.183446i	0.0286627	−	0.00931308i
$389$	4.11854	−	12.6755i	0.208818	−	0.642676i	−0.790717	−	0.612182i	$-0.790292\pi$
$389$	4.11854	−	12.6755i	0.208818	−	0.642676i	0.999535	−	0.0304938i	$-0.00970800\pi$
$390$		0			0
$391$	−2.26180	−	1.64329i	−0.114384	−	0.0831049i
$392$	−4.18451	−	1.35963i	−0.211350	−	0.0686717i
$393$	18.0558	−	5.86668i	0.910794	−	0.295935i
$394$	−0.301166	+	0.218810i	−0.0151725	+	0.0110235i
$395$		0			0
$396$	−3.81434	+	0.151424i	−0.191678	+	0.00760933i
$397$			8.80209i			0.441764i	0.975300	+	0.220882i	$0.0708936\pi$
$397$			8.80209i			0.441764i	−0.975300	+	0.220882i	$0.929106\pi$
$398$	2.40038	+	3.30383i	0.120320	+	0.165606i
$399$	1.69404	+	5.21373i	0.0848083	+	0.261013i
$400$		0			0
$401$	−13.2728	−	9.64323i	−0.662810	−	0.481560i	0.204801	−	0.978804i	$-0.434345\pi$
$401$	−13.2728	−	9.64323i	−0.662810	−	0.481560i	−0.867611	+	0.497244i	$0.834345\pi$
$402$	0.997747	−	1.37328i	0.0497631	−	0.0684931i
$403$	33.5061	+	10.8868i	1.66906	+	0.542310i
$404$	−3.73547	−	11.4966i	−0.185846	−	0.571976i
$405$		0			0
$406$	0.981993			0.0487355
$407$	15.2171	−	22.7941i	0.754284	−	1.12986i
$408$			6.13722i			0.303838i
$409$	−9.55575	+	6.94266i	−0.472501	+	0.343292i	−0.798415	−	0.602107i	$-0.794328\pi$
$409$	−9.55575	+	6.94266i	−0.472501	+	0.343292i	0.325914	+	0.945399i	$0.394328\pi$
$410$		0			0
$411$	2.06475	−	6.35466i	0.101847	−	0.313452i
$412$	−9.17617	+	12.6299i	−0.452078	+	0.622231i
$413$	6.75269	−	9.29429i	0.332278	−	0.457342i
$414$	−0.0269244	+	0.0828649i	−0.00132326	+	0.00407259i
$415$		0			0
$416$	10.7036	−	7.77660i	0.524786	−	0.381279i
$417$		−	16.6267i		−	0.814215i
$418$	−0.960830	−	1.21778i	−0.0469957	−	0.0595638i
$419$	−26.3901			−1.28924			−0.644620	−	0.764503i	$-0.722985\pi$
$419$	−26.3901			−1.28924			−0.644620	+	0.764503i	$0.722985\pi$
$420$		0			0
$421$	3.51334	+	10.8130i	0.171230	+	0.526991i	0.999441	−	0.0334246i	$-0.0106414\pi$
$421$	3.51334	+	10.8130i	0.171230	+	0.526991i	−0.828211	+	0.560416i	$0.810641\pi$
$422$	3.31155	+	1.07599i	0.161204	+	0.0523783i
$423$	−1.56114	+	2.14872i	−0.0759052	+	0.104474i
$424$	−6.47991	−	4.70793i	−0.314692	−	0.228637i
$425$		0			0
$426$	−1.23840	−	3.81141i	−0.0600007	−	0.184663i
$427$	−1.39488	−	1.91988i	−0.0675028	−	0.0929096i
$428$			19.6547i			0.950044i
$429$	26.8813	−	21.2093i	1.29784	−	1.02399i
$430$		0			0
$431$	−14.5688	+	10.5849i	−0.701756	+	0.509856i	−0.880504	−	0.474039i	$-0.842795\pi$
$431$	−14.5688	+	10.5849i	−0.701756	+	0.509856i	0.178747	+	0.983895i	$0.442795\pi$
$432$	16.2568	−	5.28217i	0.782158	−	0.254138i
$433$	36.3883	+	11.8233i	1.74871	+	0.568191i	0.995934	−	0.0900851i	$-0.0287139\pi$
$433$	36.3883	+	11.8233i	1.74871	+	0.568191i	0.752777	+	0.658276i	$0.228714\pi$
$434$	−1.40383	−	1.01995i	−0.0673862	−	0.0489589i
$435$		0			0
$436$	−4.61834	+	14.2138i	−0.221179	+	0.680718i
$437$	1.51868	−	0.493448i	0.0726481	−	0.0236048i
$438$	−2.78403	−	3.83189i	−0.133026	−	0.183095i
$439$	8.67958			0.414254			0.207127	−	0.978314i	$-0.433589\pi$
$439$	8.67958			0.414254			0.207127	+	0.978314i	$0.433589\pi$
$440$		0			0
$441$	−3.14062			−0.149553
$442$	−2.62321	−	3.61054i	−0.124773	−	0.171736i
$443$	−12.7400	+	4.13947i	−0.605295	+	0.196672i	−0.595601	−	0.803281i	$-0.703086\pi$
$443$	−12.7400	+	4.13947i	−0.605295	+	0.196672i	−0.00969443	+	0.999953i	$0.503086\pi$
$444$	9.46436	−	29.1283i	0.449159	−	1.38237i
$445$		0			0
$446$	−1.00792	−	0.732298i	−0.0477264	−	0.0346753i
$447$	−15.1272	−	4.91513i	−0.715493	−	0.232478i
$448$	8.55263	−	2.77892i	0.404074	−	0.131292i
$449$	−15.8011	+	11.4802i	−0.745700	+	0.541783i	−0.894491	−	0.447086i	$-0.852462\pi$
$449$	−15.8011	+	11.4802i	−0.745700	+	0.541783i	0.148791	+	0.988869i	$0.452462\pi$
$450$		0			0
$451$	41.8656	−	1.66201i	1.97137	−	0.0782608i
$452$		−	38.3556i		−	1.80410i
$453$	−9.50515	−	13.0827i	−0.446591	−	0.614680i
$454$	1.43204	+	4.40735i	0.0672088	+	0.206847i
$455$		0			0
$456$	−2.83591	−	2.06041i	−0.132803	−	0.0964874i
$457$	−15.1535	+	20.8569i	−0.708849	+	0.975647i	0.290972	+	0.956731i	$0.406021\pi$
$457$	−15.1535	+	20.8569i	−0.708849	+	0.975647i	−0.999821	+	0.0189151i	$0.993979\pi$
$458$	1.18312	+	0.384420i	0.0552836	+	0.0179627i
$459$	−5.55016	−	17.0816i	−0.259059	−	0.797302i
$460$		0			0
$461$	19.0542			0.887441			0.443720	−	0.896165i	$-0.353658\pi$
$461$	19.0542			0.887441			0.443720	+	0.896165i	$0.353658\pi$
$462$	−1.58202	+	0.584371i	−0.0736022	+	0.0271874i
$463$		−	20.0792i		−	0.933161i	−0.884479	−	0.466580i	$-0.845486\pi$
$463$		−	20.0792i		−	0.933161i	0.884479	−	0.466580i	$-0.154514\pi$
$464$	11.0732	−	8.04516i	0.514061	−	0.373487i
$465$		0			0
$466$	1.14148	−	3.51313i	0.0528782	−	0.162742i
$467$	9.70181	−	13.3534i	0.448946	−	0.617921i	−0.523225	−	0.852195i	$-0.675271\pi$
$467$	9.70181	−	13.3534i	0.448946	−	0.617921i	0.972171	+	0.234273i	$0.0752711\pi$
$468$	3.68715	−	5.07493i	0.170439	−	0.234589i
$469$	−1.71347	+	5.27350i	−0.0791205	+	0.243508i
$470$		0			0
$471$	19.3853	−	14.0843i	0.893228	−	0.648968i
$472$			7.34599i			0.338127i
$473$	4.18753	+	1.17916i	0.192543	+	0.0542179i
$474$	5.05481			0.232175
$475$		0			0
$476$	−3.06356	−	9.42868i	−0.140418	−	0.432163i
$477$	−5.43744	−	1.76673i	−0.248963	−	0.0808930i
$478$	−2.34028	+	3.22111i	−0.107042	+	0.147330i
$479$	4.15087	+	3.01578i	0.189658	+	0.137795i	0.678562	−	0.734543i	$-0.262603\pi$
$479$	4.15087	+	3.01578i	0.189658	+	0.137795i	−0.488904	+	0.872337i	$0.662603\pi$
$480$		0			0
$481$	13.9172	+	42.8327i	0.634570	+	1.95300i
$482$	−0.219680	−	0.302363i	−0.0100061	−	0.0137723i
$483$		−	1.73612i		−	0.0789960i
$484$	−16.3547	+	13.9913i	−0.743393	+	0.635967i
$485$		0			0
$486$	−1.01614	+	0.738269i	−0.0460930	+	0.0334886i
$487$	−15.9201	+	5.17276i	−0.721409	+	0.234400i	−0.646634	−	0.762800i	$-0.723824\pi$
$487$	−15.9201	+	5.17276i	−0.721409	+	0.234400i	−0.0747753	+	0.997200i	$0.523824\pi$
$488$	1.44316	+	0.468912i	0.0653289	+	0.0212266i
$489$	12.8869	+	9.36288i	0.582766	+	0.423404i
$490$		0			0
$491$	−0.238396	+	0.733708i	−0.0107587	+	0.0331118i	−0.956292	−	0.292414i	$-0.905541\pi$
$491$	−0.238396	+	0.733708i	−0.0107587	+	0.0331118i	0.945533	+	0.325526i	$0.105541\pi$
$492$	44.5304	−	14.4688i	2.00758	−	0.652304i
$493$	−8.45333	−	11.6350i	−0.380719	−	0.524014i
$494$	2.54904			0.114687
$495$		0			0
$496$	−24.1861			−1.08599
$497$	7.69465	+	10.5908i	0.345152	+	0.475061i
$498$	−4.70669	+	1.52930i	−0.210912	+	0.0685294i
$499$	−5.40385	+	16.6313i	−0.241909	+	0.744521i	0.754220	+	0.656622i	$0.228015\pi$
$499$	−5.40385	+	16.6313i	−0.241909	+	0.744521i	−0.996129	+	0.0878988i	$0.971985\pi$
$500$		0			0
$501$	−29.3090	−	21.2943i	−1.30943	−	0.951357i
$502$	−2.09385	−	0.680333i	−0.0934530	−	0.0303647i
$503$	37.2553	−	12.1050i	1.66113	−	0.539734i	0.680021	−	0.733193i	$-0.261971\pi$
$503$	37.2553	−	12.1050i	1.66113	−	0.539734i	0.981108	+	0.193459i	$0.0619706\pi$
$504$	−0.505462	+	0.367240i	−0.0225151	+	0.0163582i
$505$		0			0
$506$	0.170218	+	0.460816i	0.00756710	+	0.0204858i
$507$			31.6419i			1.40526i
$508$	−19.7412	−	27.1714i	−0.875873	−	1.20554i
$509$	−1.00212	−	3.08420i	−0.0444181	−	0.136705i	0.926388	−	0.376570i	$-0.122897\pi$
$509$	−1.00212	−	3.08420i	−0.0444181	−	0.136705i	−0.970806	+	0.239865i	$0.922897\pi$
$510$		0			0
$511$	12.5171	+	9.09420i	0.553724	+	0.402304i
$512$	−8.96355	+	12.3373i	−0.396137	+	0.545235i
$513$	9.75644	+	3.17006i	0.430757	+	0.139962i
$514$	−0.289585	−	0.891252i	−0.0127731	−	0.0393114i
$515$		0			0
$516$	4.86159			0.214020
$517$	0.594010	+	14.9630i	0.0261245	+	0.658072i
$518$		−	2.21825i		−	0.0974642i
$519$	−18.7557	+	13.6268i	−0.823286	+	0.598152i
$520$		0			0
$521$	3.60355	−	11.0906i	0.157874	−	0.485887i	−0.840567	−	0.541708i	$-0.817778\pi$
$521$	3.60355	−	11.0906i	0.157874	−	0.485887i	0.998441	+	0.0558215i	$0.0177778\pi$
$522$	−0.263449	+	0.362606i	−0.0115308	+	0.0158708i
$523$	−3.00403	+	4.13469i	−0.131357	+	0.180797i	−0.869629	−	0.493706i	$-0.835642\pi$
$523$	−3.00403	+	4.13469i	−0.131357	+	0.180797i	0.738272	+	0.674503i	$0.235642\pi$
$524$	6.05978	−	18.6501i	0.264723	−	0.814733i
$525$		0			0
$526$	−1.49628	+	1.08711i	−0.0652407	+	0.0474002i
$527$			25.4132i			1.10701i
$528$	−13.0517	+	19.5505i	−0.568002	+	0.850826i
$529$	22.4943			0.978013
$530$		0			0
$531$	1.62035	+	4.98693i	0.0703173	+	0.216414i
$532$	5.38534	+	1.74980i	0.233484	+	0.0758636i
$533$	−40.4696	+	55.7017i	−1.75293	+	2.41271i
$534$	2.00580	+	1.45730i	0.0867994	+	0.0630635i
$535$		0			0
$536$	−1.09564	−	3.37203i	−0.0473244	−	0.145649i
$537$	−3.56328	−	4.90443i	−0.153767	−	0.211642i
$538$		−	3.50054i		−	0.150919i
$539$	−13.9014	+	10.9682i	−0.598775	+	0.472432i
$540$		0			0
$541$	−29.3114	+	21.2960i	−1.26019	+	0.915585i	−0.998767	−	0.0496388i	$-0.984193\pi$
$541$	−29.3114	+	21.2960i	−1.26019	+	0.915585i	−0.261427	+	0.965223i	$0.584193\pi$
$542$	−2.68070	+	0.871011i	−0.115146	+	0.0374131i
$543$	−3.90388	−	1.26845i	−0.167531	−	0.0544342i
$544$	7.72093	+	5.60959i	0.331032	+	0.240509i
$545$		0			0
$546$	0.856405	−	2.63574i	0.0366508	−	0.112799i
$547$	−18.2177	+	5.91930i	−0.778934	+	0.253091i	−0.671385	−	0.741109i	$-0.734300\pi$
$547$	−18.2177	+	5.91930i	−0.778934	+	0.253091i	−0.107549	+	0.994200i	$0.534300\pi$
$548$	−4.05667	−	5.58352i	−0.173292	−	0.238516i
$549$	1.08314			0.0462274
$550$		0			0
$551$	8.21432			0.349942
$552$	0.652513	+	0.898108i	0.0277728	+	0.0382260i
$553$	−15.7037	+	5.10245i	−0.667790	+	0.216978i
$554$	1.31741	−	4.05458i	0.0559715	−	0.172263i
$555$		0			0
$556$	−13.8941	−	10.0946i	−0.589240	−	0.428108i
$557$	25.3841	+	8.24779i	1.07556	+	0.349470i	0.792650	−	0.609677i	$-0.208701\pi$
$557$	25.3841	+	8.24779i	1.07556	+	0.349470i	0.282908	+	0.959147i	$0.408701\pi$
$558$	0.753239	−	0.244742i	0.0318872	−	0.0103608i
$559$	−5.78358	+	4.20201i	−0.244619	+	0.177726i
$560$		0			0
$561$	20.5424	+	13.7139i	0.867300	+	0.579000i
$562$			2.08499i			0.0879500i
$563$	−20.0359	−	27.5770i	−0.844412	−	1.16223i	−0.985066	−	0.172174i	$-0.944921\pi$
$563$	−20.0359	−	27.5770i	−0.844412	−	1.16223i	0.140655	−	0.990059i	$-0.455079\pi$
$564$	5.17122	+	15.9154i	0.217748	+	0.670159i
$565$		0			0
$566$	−0.451242	−	0.327847i	−0.0189671	−	0.0137804i
$567$	7.89265	−	10.8633i	0.331460	−	0.456215i
$568$	−7.96101	−	2.58669i	−0.334037	−	0.108535i
$569$	7.05363	+	21.7088i	0.295703	+	0.910082i	0.982984	+	0.183690i	$0.0588042\pi$
$569$	7.05363	+	21.7088i	0.295703	+	0.910082i	−0.687281	+	0.726392i	$0.741196\pi$
$570$		0			0
$571$	−36.9818			−1.54764			−0.773820	−	0.633406i	$-0.781656\pi$
$571$	−36.9818			−1.54764			−0.773820	+	0.633406i	$0.781656\pi$
$572$	−1.40295	−	35.3401i	−0.0586604	−	1.47764i
$573$		−	3.33967i		−	0.139517i
$574$	2.74352	−	1.99329i	0.114512	−	0.0831982i
$575$		0			0
$576$	−1.26837	+	3.90363i	−0.0528486	+	0.162651i
$577$	−16.9984	+	23.3962i	−0.707651	+	0.973999i	0.292193	+	0.956359i	$0.405615\pi$
$577$	−16.9984	+	23.3962i	−0.707651	+	0.973999i	−0.999844	+	0.0176392i	$0.994385\pi$
$578$	−0.189026	+	0.260172i	−0.00786246	+	0.0108217i
$579$	−9.01880	+	27.7570i	−0.374809	+	1.15354i
$580$		0			0
$581$	13.0785	−	9.50209i	0.542588	−	0.394213i
$582$			0.119707i			0.00496202i
$583$	−30.2379	+	11.1694i	−1.25233	+	0.462588i
$584$	−9.89322			−0.409385
$585$		0			0
$586$	−1.62778	−	5.00978i	−0.0672428	−	0.206952i
$587$	−6.87011	−	2.23223i	−0.283560	−	0.0921341i	0.163784	−	0.986496i	$-0.447630\pi$
$587$	−6.87011	−	2.23223i	−0.283560	−	0.0921341i	−0.447344	+	0.894362i	$0.647630\pi$
$588$	−11.6311	+	16.0089i	−0.479660	+	0.660195i
$589$	−11.7430	−	8.53178i	−0.483861	−	0.351546i
$590$		0			0
$591$	1.04620	+	3.21986i	0.0430348	+	0.132448i
$592$	−18.1734	−	25.0135i	−0.746922	−	1.02805i
$593$		−	10.9657i		−	0.450308i	−0.974323	−	0.225154i	$-0.927711\pi$
$593$		−	10.9657i		−	0.450308i	0.974323	−	0.225154i	$-0.0722886\pi$
$594$	−0.855410	+	3.03780i	−0.0350979	+	0.124642i
$595$		0			0
$596$	−13.2915	+	9.65687i	−0.544442	+	0.395561i
$597$	35.3224	−	11.4769i	1.44565	−	0.469720i
$598$	−0.767749	−	0.249457i	−0.0313956	−	0.0102011i
$599$	4.69066	+	3.40797i	0.191655	+	0.139246i	0.679475	−	0.733699i	$-0.262208\pi$
$599$	4.69066	+	3.40797i	0.191655	+	0.139246i	−0.487820	+	0.872944i	$0.662208\pi$
$600$		0			0
$601$	−2.51599	+	7.74343i	−0.102629	+	0.315861i	−0.989167	−	0.146796i	$-0.953104\pi$
$601$	−2.51599	+	7.74343i	−0.102629	+	0.315861i	0.886537	+	0.462657i	$0.153104\pi$
$602$	0.334877	−	0.108808i	0.0136486	−	0.00443469i
$603$	−1.48758	−	2.04748i	−0.0605789	−	0.0833798i
$604$	−16.7034			−0.679652
$605$		0			0
$606$	2.43756			0.0990192
$607$	15.6720	+	21.5706i	0.636106	+	0.875525i	0.998400	−	0.0565387i	$-0.0180064\pi$
$607$	15.6720	+	21.5706i	0.636106	+	0.875525i	−0.362294	+	0.932064i	$0.618006\pi$
$608$	−5.18419	+	1.68445i	−0.210247	+	0.0683133i
$609$	2.75978	−	8.49372i	0.111832	−	0.344183i
$610$		0			0
$611$	−19.9081	−	14.4641i	−0.805395	−	0.585153i
$612$	4.30348	+	1.39829i	0.173958	+	0.0565223i
$613$	9.81873	−	3.19030i	0.396575	−	0.128855i	−0.103939	−	0.994584i	$-0.533145\pi$
$613$	9.81873	−	3.19030i	0.396575	−	0.128855i	0.500513	+	0.865729i	$0.333145\pi$
$614$	1.43773	−	1.04457i	0.0580222	−	0.0421556i
$615$		0			0
$616$	−0.954805	+	3.39078i	−0.0384702	+	0.136618i
$617$		−	8.79766i		−	0.354180i	−0.984195	−	0.177090i	$-0.943332\pi$
$617$		−	8.79766i		−	0.354180i	0.984195	−	0.177090i	$-0.0566684\pi$
$618$	−1.85035	−	2.54679i	−0.0744321	−	0.102447i
$619$	4.20736	+	12.9489i	0.169108	+	0.520461i	0.999315	−	0.0369937i	$-0.0117781\pi$
$619$	4.20736	+	12.9489i	0.169108	+	0.520461i	−0.830208	+	0.557454i	$0.811778\pi$
$620$		0			0
$621$	−2.62833	−	1.90959i	−0.105471	−	0.0766293i
$622$	0.135161	−	0.186033i	0.00541946	−	0.00745925i
$623$	−7.70242	−	2.50267i	−0.308591	−	0.100267i
$624$	−11.9368	−	36.7376i	−0.477853	−	1.47068i
$625$		0			0
$626$	−1.16462			−0.0465474
$627$	−13.2335	+	4.88823i	−0.528495	+	0.195217i
$628$		−	24.7503i		−	0.987643i
$629$	−26.2826	+	19.0954i	−1.04796	+	0.761384i
$630$		0			0
$631$	−8.10923	+	24.9576i	−0.322823	+	0.993548i	0.649590	+	0.760285i	$0.274941\pi$
$631$	−8.10923	+	24.9576i	−0.322823	+	0.993548i	−0.972414	+	0.233264i	$0.925059\pi$
$632$	6.20593	−	8.54173i	0.246859	−	0.339772i
$633$	18.6134	−	25.6192i	0.739818	−	1.01827i
$634$	−1.82465	+	5.61569i	−0.0724661	+	0.223028i
$635$		0			0
$636$	−29.1430	+	21.1736i	−1.15559	+	0.839588i
$637$		−	29.0981i		−	1.15291i
$638$	0.100242	+	2.52507i	0.00396860	+	0.0999683i
$639$	−5.97501			−0.236368
$640$		0			0
$641$	12.3908	+	38.1350i	0.489407	+	1.50624i	0.825495	+	0.564410i	$0.190896\pi$
$641$	12.3908	+	38.1350i	0.489407	+	1.50624i	−0.336087	+	0.941831i	$0.609104\pi$
$642$	−3.76934	−	1.22473i	−0.148764	−	0.0483363i
$643$	1.54059	−	2.12044i	0.0607548	−	0.0836218i	−0.777558	−	0.628811i	$-0.783542\pi$
$643$	1.54059	−	2.12044i	0.0607548	−	0.0836218i	0.838313	+	0.545189i	$0.183542\pi$
$644$	−1.45078	−	1.05405i	−0.0571687	−	0.0415355i
$645$		0			0
$646$	0.568198	+	1.74873i	0.0223555	+	0.0688031i
$647$	17.7459	+	24.4251i	0.697662	+	0.960250i	0.999975	+	0.00704095i	$0.00224122\pi$
$647$	17.7459	+	24.4251i	0.697662	+	0.960250i	−0.302313	+	0.953209i	$0.597759\pi$
$648$			8.58610i			0.337294i
$649$	24.5883	+	16.4149i	0.965177	+	0.644341i
$650$		0			0
$651$	−12.7673	+	9.27598i	−0.500390	+	0.363554i
$652$	15.6481	−	5.08438i	0.612827	−	0.199120i
$653$	34.6286	+	11.2515i	1.35512	+	0.440305i	0.894411	−	0.447246i	$-0.147595\pi$
$653$	34.6286	+	11.2515i	1.35512	+	0.440305i	0.460709	+	0.887551i	$0.347595\pi$
$654$	−2.43812	−	1.77140i	−0.0953380	−	0.0692671i
$655$		0			0
$656$	14.6063	−	44.9537i	0.570281	−	1.75515i
$657$	−6.71616	+	2.18221i	−0.262022	+	0.0851362i
$658$	0.712411	+	0.980550i	0.0277727	+	0.0382258i
$659$	32.9001			1.28161			0.640803	−	0.767706i	$-0.278602\pi$
$659$	32.9001			1.28161			0.640803	+	0.767706i	$0.278602\pi$
$660$		0			0
$661$	31.0455			1.20753			0.603766	−	0.797162i	$-0.293666\pi$
$661$	31.0455			1.20753			0.603766	+	0.797162i	$0.293666\pi$
$662$	2.27778	+	3.13509i	0.0885283	+	0.121849i
$663$	−38.6015	+	12.5424i	−1.49916	+	0.487105i
$664$	−3.19429	+	9.83102i	−0.123963	+	0.381517i
$665$		0			0
$666$	0.819099	+	0.595110i	0.0317394	+	0.0230601i
$667$	−2.47408	−	0.803878i	−0.0957969	−	0.0311263i
$668$	−35.5889	+	11.5635i	−1.37698	+	0.447407i
$669$	−9.16663	+	6.65995i	−0.354402	+	0.257488i
$670$		0			0
$671$	4.79433	−	3.78272i	0.185083	−	0.146030i
$672$			5.92645i			0.228618i
$673$	−2.72189	−	3.74637i	−0.104921	−	0.144412i	0.753328	−	0.657645i	$-0.228447\pi$
$673$	−2.72189	−	3.74637i	−0.104921	−	0.144412i	−0.858249	+	0.513234i	$0.828447\pi$
$674$	−1.89701	−	5.83840i	−0.0730701	−	0.224887i
$675$		0			0
$676$	26.4414	+	19.2108i	1.01698	+	0.738877i
$677$	13.0396	−	17.9475i	0.501154	−	0.689780i	−0.481242	−	0.876588i	$-0.659814\pi$
$677$	13.0396	−	17.9475i	0.501154	−	0.689780i	0.982396	+	0.186808i	$0.0598142\pi$
$678$	7.35578	+	2.39004i	0.282497	+	0.0917888i
$679$	−0.120835	−	0.371892i	−0.00463723	−	0.0142719i
$680$		0			0
$681$	42.1458			1.61503
$682$	2.47935	−	3.71389i	0.0949393	−	0.142212i
$683$		−	42.5540i		−	1.62828i	−0.580665	−	0.814142i	$-0.697207\pi$
$683$		−	42.5540i		−	1.62828i	0.580665	−	0.814142i	$-0.302793\pi$
$684$	−2.09090	+	1.51913i	−0.0799476	+	0.0580853i
$685$		0			0
$686$	−1.02355	+	3.15016i	−0.0390793	+	0.120274i
$687$	6.65005	−	9.15301i	0.253715	−	0.349209i
$688$	2.88473	−	3.97050i	0.109979	−	0.151374i
$689$	16.3689	−	50.3783i	0.623605	−	1.91926i
$690$		0			0
$691$	3.05397	−	2.21884i	0.116178	−	0.0844086i	−0.528179	−	0.849133i	$-0.677125\pi$
$691$	3.05397	−	2.21884i	0.116178	−	0.0844086i	0.644357	+	0.764725i	$0.277125\pi$
$692$			23.9465i			0.910308i
$693$	0.0997421	+	2.51248i	0.00378889	+	0.0954414i
$694$	−3.68600			−0.139919
$695$		0			0
$696$	1.76468	+	5.43112i	0.0668900	+	0.205866i
$697$	−47.2343	−	15.3474i	−1.78913	−	0.581323i
$698$	0.191402	−	0.263442i	0.00724466	−	0.00997143i
$699$	−27.1787	−	19.7465i	−1.02799	−	0.746880i
$700$		0			0
$701$	−0.265067	−	0.815792i	−0.0100114	−	0.0308120i	0.945926	−	0.324382i	$-0.105156\pi$
$701$	−0.265067	−	0.815792i	−0.0100114	−	0.0308120i	−0.955937	+	0.293570i	$0.905156\pi$
$702$	−3.04830	−	4.19563i	−0.115051	−	0.158354i
$703$		−	18.5555i		−	0.699834i
$704$	8.01867	+	21.7083i	0.302215	+	0.818162i
$705$		0			0
$706$	0.280079	−	0.203489i	0.0105409	−	0.00765842i
$707$	−7.57274	+	2.46053i	−0.284802	+	0.0925378i
$708$	31.4211	+	10.2093i	1.18088	+	0.383690i
$709$	20.0202	+	14.5455i	0.751874	+	0.546269i	0.896407	−	0.443231i	$-0.146168\pi$
$709$	20.0202	+	14.5455i	0.751874	+	0.546269i	−0.144533	+	0.989500i	$0.546168\pi$
$710$		0			0
$711$	2.32888	−	7.16756i	0.0873399	−	0.268804i
$712$	4.92515	−	1.60028i	0.184578	−	0.0599729i
$713$	2.70194	+	3.71891i	0.101189	+	0.139274i
$714$	1.99912			0.0748150
$715$		0			0
$716$	−6.26175			−0.234012
$717$	21.2838	+	29.2947i	0.794860	+	1.09403i
$718$	6.18369	−	2.00920i	0.230773	−	0.0749828i
$719$	5.40434	−	16.6329i	0.201548	−	0.620301i	−0.798289	−	0.602274i	$-0.794261\pi$
$719$	5.40434	−	16.6329i	0.201548	−	0.620301i	0.999837	−	0.0180271i	$-0.00573851\pi$
$720$		0			0
$721$	8.31926	+	6.04430i	0.309826	+	0.225101i
$722$	2.76491	+	0.898373i	0.102899	+	0.0334340i
$723$	−3.23266	+	1.05036i	−0.120224	+	0.0390632i
$724$	−3.43014	+	2.49214i	−0.127480	+	0.0926198i
$725$		0			0
$726$	−1.66412	−	4.00830i	−0.0617614	−	0.148762i
$727$			13.8835i			0.514909i	0.966290	+	0.257455i	$0.0828838\pi$
$727$			13.8835i			0.514909i	−0.966290	+	0.257455i	$0.917116\pi$
$728$	−3.40250	−	4.68314i	−0.126105	−	0.173569i
$729$	−6.12878	−	18.8624i	−0.226992	−	0.698609i
$730$		0			0
$731$	−4.17194	−	3.03109i	−0.154305	−	0.112109i
$732$	4.01137	−	5.52117i	0.148264	−	0.204068i
$733$	28.7684	+	9.34742i	1.06259	+	0.345255i	0.787596	−	0.616192i	$-0.211326\pi$
$733$	28.7684	+	9.34742i	1.06259	+	0.345255i	0.274990	+	0.961447i	$0.411326\pi$
$734$	0.600405	+	1.84786i	0.0221614	+	0.0682056i
$735$		0			0
$736$	1.72628			0.0636315
$737$	−13.7350	−	3.86763i	−0.505936	−	0.142466i
$738$			1.54782i			0.0569759i
$739$	−19.8185	+	14.3990i	−0.729037	+	0.529676i	−0.889259	−	0.457405i	$-0.848779\pi$
$739$	−19.8185	+	14.3990i	−0.729037	+	0.529676i	0.160222	+	0.987081i	$0.448779\pi$
$740$		0			0
$741$	7.16378	−	22.0478i	0.263168	−	0.809948i
$742$	−1.53354	+	2.11074i	−0.0562981	+	0.0774877i
$743$	−3.90607	+	5.37625i	−0.143300	+	0.197235i	−0.874634	−	0.484784i	$-0.838898\pi$
$743$	−3.90607	+	5.37625i	−0.143300	+	0.197235i	0.731334	+	0.682020i	$0.238898\pi$
$744$	3.11828	−	9.59709i	0.114322	−	0.351846i
$745$		0			0
$746$	−1.64714	+	1.19672i	−0.0603061	+	0.0438150i
$747$			7.37851i			0.269966i
$748$	23.9319	−	8.84003i	0.875036	−	0.323223i
$749$	12.9464			0.473052
$750$		0			0
$751$	−5.58167	−	17.1786i	−0.203678	−	0.626857i	−0.999765	−	0.0216746i	$-0.993100\pi$
$751$	−5.58167	−	17.1786i	−0.203678	−	0.626857i	0.796087	−	0.605182i	$-0.206900\pi$
$752$	16.0667	+	5.22038i	0.585891	+	0.190368i
$753$	−11.7690	+	16.1987i	−0.428887	+	0.590313i
$754$	−3.35957	−	2.44087i	−0.122348	−	0.0888912i
$755$		0			0
$756$	−3.56002	−	10.9566i	−0.129477	−	0.398488i
$757$	−6.22154	−	8.56321i	−0.226126	−	0.311235i	0.680846	−	0.732426i	$-0.261612\pi$
$757$	−6.22154	−	8.56321i	−0.226126	−	0.311235i	−0.906972	+	0.421191i	$0.861612\pi$
$758$			2.80244i			0.101789i
$759$	4.46419	−	0.177222i	0.162040	−	0.00643276i
$760$		0			0
$761$	−6.26922	+	4.55485i	−0.227259	+	0.165113i	−0.695588	−	0.718441i	$-0.744856\pi$
$761$	−6.26922	+	4.55485i	−0.227259	+	0.165113i	0.468329	+	0.883554i	$0.344856\pi$
$762$	6.44100	−	2.09281i	0.233333	−	0.0758145i
$763$	9.36256	+	3.04208i	0.338947	+	0.110131i
$764$	−2.79078	−	2.02762i	−0.100967	−	0.0733569i
$765$		0			0
$766$	−0.251938	+	0.775384i	−0.00910288	+	0.0280158i
$767$	−46.2043	+	15.0127i	−1.66834	+	0.542076i
$768$	14.0750	+	19.3725i	0.507886	+	0.699046i
$769$	23.9339			0.863078			0.431539	−	0.902094i	$-0.357971\pi$
$769$	23.9339			0.863078			0.431539	+	0.902094i	$0.357971\pi$
$770$		0			0
$771$	−8.52270			−0.306938
$772$	17.7194	+	24.3887i	0.637737	+	0.877769i
$773$	33.0476	−	10.7378i	1.18864	−	0.386212i	0.353069	−	0.935597i	$-0.385138\pi$
$773$	33.0476	−	10.7378i	1.18864	−	0.386212i	0.835569	+	0.549385i	$0.185138\pi$
$774$	−0.0496627	+	0.152846i	−0.00178509	+	0.00549394i
$775$		0			0
$776$	0.202284	+	0.146968i	0.00726156	+	0.00527583i
$777$	−19.1867	−	6.23413i	−0.688318	−	0.223648i
$778$	2.64013	−	0.857829i	0.0946531	−	0.0307547i
$779$	22.9494	−	16.6737i	0.822248	−	0.597398i
$780$		0			0
$781$	−26.4473	+	20.8669i	−0.946359	+	0.746675i
$782$		−	0.582310i		−	0.0208234i
$783$	−9.82320	−	13.5205i	−0.351053	−	0.483183i
$784$	6.17298	+	18.9985i	0.220463	+	0.678517i
$785$		0			0
$786$	3.19908	+	2.32427i	0.114108	+	0.0829040i
$787$	5.16087	−	7.10333i	0.183965	−	0.253206i	−0.707067	−	0.707147i	$-0.749982\pi$
$787$	5.16087	−	7.10333i	0.183965	−	0.253206i	0.891032	+	0.453940i	$0.149982\pi$
$788$	3.32585	+	1.08063i	0.118478	+	0.0384960i
$789$	5.19780	+	15.9972i	0.185047	+	0.569515i
$790$		0			0
$791$	−25.2647			−0.898308
$792$	−0.995906	−	1.26224i	−0.0353880	−	0.0448518i
$793$			10.0354i			0.356367i
$794$	−1.48321	+	1.07761i	−0.0526370	+	0.0382430i
$795$		0			0
$796$	11.8547	−	36.4850i	0.420179	−	1.29318i
$797$	29.1149	−	40.0732i	1.03130	−	1.41946i	0.127336	−	0.991860i	$-0.459357\pi$
$797$	29.1149	−	40.0732i	1.03130	−	1.41946i	0.903966	−	0.427605i	$-0.140643\pi$
$798$	−0.671149	+	0.923757i	−0.0237584	+	0.0327007i
$799$	5.48523	−	16.8818i	0.194054	−	0.597235i
$800$		0			0
$801$	2.99052	−	2.17274i	0.105665	−	0.0767701i
$802$		−	3.41713i		−	0.120663i
$803$	−22.1068	+	33.1144i	−0.780132	+	1.16858i
$804$	−15.9459			−0.562370
$805$		0			0
$806$	2.26756	+	6.97882i	0.0798712	+	0.245818i
$807$	−30.2778	−	9.83787i	−1.06583	−	0.346309i
$808$	2.99266	−	4.11904i	0.105281	−	0.144907i
$809$	−32.0568	−	23.2906i	−1.12706	−	0.818854i	−0.141792	−	0.989896i	$-0.545286\pi$
$809$	−32.0568	−	23.2906i	−1.12706	−	0.818854i	−0.985264	+	0.171042i	$0.945286\pi$
$810$		0			0
$811$	−15.4557	−	47.5676i	−0.542722	−	1.67033i	−0.726346	−	0.687329i	$-0.758783\pi$
$811$	−15.4557	−	47.5676i	−0.542722	−	1.67033i	0.183624	−	0.982997i	$-0.441217\pi$
$812$	−5.42219	−	7.46301i	−0.190282	−	0.261900i
$813$			25.6345i			0.899040i
$814$	5.70393	−	0.226438i	0.199923	−	0.00793665i
$815$		0			0
$816$	22.5426	−	16.3781i	0.789147	−	0.573349i
$817$	2.80123	−	0.910175i	0.0980026	−	0.0318430i
$818$	−2.33976	−	0.760234i	−0.0818078	−	0.0265810i
$819$	−3.34283	−	2.42871i	−0.116808	−	0.0848659i
$820$		0			0
$821$	12.5676	−	38.6792i	0.438613	−	1.34991i	−0.450725	−	0.892663i	$-0.648834\pi$
$821$	12.5676	−	38.6792i	0.438613	−	1.34991i	0.889338	−	0.457250i	$-0.151166\pi$
$822$	1.32358	−	0.430057i	0.0461651	−	0.0150000i
$823$	17.4851	+	24.0661i	0.609491	+	0.838892i	0.996535	−	0.0831687i	$-0.0265040\pi$
$823$	17.4851	+	24.0661i	0.609491	+	0.838892i	−0.387045	+	0.922061i	$0.626504\pi$
$824$	−6.57535			−0.229063
$825$		0			0
$826$	2.39285			0.0832581
$827$	−27.1475	−	37.3653i	−0.944011	−	1.29932i	−0.954137	−	0.299371i	$-0.903223\pi$
$827$	−27.1475	−	37.3653i	−0.944011	−	1.29932i	0.0101260	−	0.999949i	$-0.496777\pi$
$828$	0.778428	−	0.252927i	0.0270523	−	0.00878981i
$829$	15.1310	−	46.5683i	0.525520	−	1.61738i	−0.237766	−	0.971323i	$-0.576415\pi$
$829$	15.1310	−	46.5683i	0.525520	−	1.61738i	0.763285	−	0.646061i	$-0.223585\pi$
$830$		0			0
$831$	−31.3675	−	22.7898i	−1.08813	−	0.790571i
$832$	−36.1674	−	11.7515i	−1.25388	−	0.407410i
$833$	19.9623	−	6.48616i	0.691654	−	0.224732i
$834$	2.80171	−	2.03556i	0.0970152	−	0.0704856i
$835$		0			0
$836$	−3.94966	+	14.0263i	−0.136602	+	0.485110i
$837$			29.5314i			1.02075i
$838$	−3.23086	−	4.44689i	−0.111608	−	0.153615i
$839$	14.2351	+	43.8112i	0.491451	+	1.51253i	0.822415	+	0.568889i	$0.192626\pi$
$839$	14.2351	+	43.8112i	0.491451	+	1.51253i	−0.330963	+	0.943644i	$0.607374\pi$
$840$		0			0
$841$	12.6352	+	9.18004i	0.435698	+	0.316553i
$842$	−1.39192	+	1.91582i	−0.0479688	+	0.0660233i
$843$	18.0341	+	5.85962i	0.621126	+	0.201816i
$844$	−10.1078	−	31.1085i	−0.347924	−	1.07080i
$845$		0			0
$846$	−0.553198			−0.0190193
$847$	9.21598	+	10.7727i	0.316665	+	0.370155i
$848$			36.3651i			1.24878i
$849$	−4.10386	+	2.98163i	−0.140844	+	0.102329i
$850$		0			0
$851$	−1.81590	+	5.58877i	−0.0622482	+	0.191580i
$852$	−22.1282	+	30.4568i	−0.758099	+	1.04343i
$853$	12.5780	−	17.3122i	0.430663	−	0.592757i	−0.537442	−	0.843301i	$-0.680609\pi$
$853$	12.5780	−	17.3122i	0.430663	−	0.592757i	0.968105	+	0.250543i	$0.0806093\pi$
$854$	0.152742	−	0.470090i	0.00522671	−	0.0160862i
$855$		0			0
$856$	−6.69730	+	4.86587i	−0.228909	+	0.166312i
$857$		−	10.0178i		−	0.342201i	−0.985254	−	0.171100i	$-0.945268\pi$
$857$		−	10.0178i		−	0.342201i	0.985254	−	0.171100i	$-0.0547323\pi$
$858$	6.86489	+	1.93308i	0.234363	+	0.0659941i
$859$	31.7860			1.08452			0.542261	−	0.840210i	$-0.317568\pi$
$859$	31.7860			1.08452			0.542261	+	0.840210i	$0.317568\pi$
$860$		0			0
$861$	−9.53052	−	29.3319i	−0.324799	−	0.999629i
$862$	−3.56723	−	1.15906i	−0.121500	−	0.0394779i
$863$	16.1711	−	22.2577i	0.550472	−	0.757660i	−0.439604	−	0.898192i	$-0.644881\pi$
$863$	16.1711	−	22.2577i	0.550472	−	0.757660i	0.990076	+	0.140532i	$0.0448812\pi$
$864$	8.97213	+	6.51863i	0.305238	+	0.221768i
$865$		0			0
$866$	2.46261	+	7.57914i	0.0836830	+	0.257550i
$867$	1.71912	+	2.36616i	0.0583843	+	0.0803590i
$868$			16.3007i			0.553282i
$869$	−14.7233	−	39.8592i	−0.499454	−	1.35213i
$870$		0			0
$871$	18.9700	−	13.7825i	0.642775	−	0.467003i
$872$	−5.98668	+	1.94519i	−0.202735	+	0.0658725i
$873$	0.169741	+	0.0551521i	0.00574485	+	0.00186662i
$874$	0.269076	+	0.195495i	0.00910162	+	0.00661271i
$875$		0			0
$876$	−13.7494	+	42.3164i	−0.464551	+	1.42974i
$877$	26.0002	−	8.44797i	0.877964	−	0.285268i	0.164852	−	0.986318i	$-0.447285\pi$
$877$	26.0002	−	8.44797i	0.877964	−	0.285268i	0.713112	+	0.701050i	$0.247285\pi$
$878$	1.06261	+	1.46256i	0.0358615	+	0.0493591i
$879$	−47.9066			−1.61585
$880$		0			0
$881$	−48.8428			−1.64555			−0.822777	−	0.568364i	$-0.807576\pi$
$881$	−48.8428			−1.64555			−0.822777	+	0.568364i	$0.807576\pi$
$882$	−0.384496	−	0.529214i	−0.0129467	−	0.0178195i
$883$	−45.7961	+	14.8801i	−1.54116	+	0.500754i	−0.951697	−	0.307039i	$-0.900662\pi$
$883$	−45.7961	+	14.8801i	−1.54116	+	0.500754i	−0.589466	+	0.807793i	$0.700662\pi$
$884$	−12.9552	+	39.8720i	−0.435731	+	1.34104i
$885$		0			0
$886$	−2.25724	−	1.63998i	−0.0758335	−	0.0550963i
$887$	55.5232	+	18.0406i	1.86429	+	0.605744i	0.993464	+	0.114148i	$0.0364138\pi$
$887$	55.5232	+	18.0406i	1.86429	+	0.605744i	0.870824	+	0.491596i	$0.163586\pi$
$888$	12.2685	−	3.98628i	0.411704	−	0.133771i
$889$	−17.8977	+	13.0034i	−0.600268	+	0.436120i
$890$		0			0
$891$	28.7392	+	19.1860i	0.962800	+	0.642754i
$892$			11.7035i			0.391863i
$893$	5.95928	+	8.20224i	0.199420	+	0.274478i
$894$	−1.02375	−	3.15077i	−0.0342392	−	0.105378i
$895$		0			0
$896$	6.57756	+	4.77888i	0.219741	+	0.159651i
$897$	−4.31534	+	5.93956i	−0.144085	+	0.198316i
$898$	−3.86896	−	1.25710i	−0.129109	−	0.0419500i
$899$	7.30723	+	22.4893i	0.243710	+	0.750061i
$900$		0			0
$901$	38.2101			1.27296
$902$	5.40553	+	6.85113i	0.179985	+	0.228118i
$903$		−	3.20230i		−	0.106566i
$904$	13.0696	−	9.49563i	0.434689	−	0.315820i
$905$		0			0
$906$	1.04083	−	3.20335i	0.0345793	−	0.106424i
$907$	26.4814	−	36.4485i	0.879299	−	1.21025i	−0.0973150	−	0.995254i	$-0.531025\pi$
$907$	26.4814	−	36.4485i	0.879299	−	1.21025i	0.976614	−	0.214998i	$-0.0689746\pi$
$908$	25.5881	−	35.2190i	0.849171	−	1.16878i
$909$	1.12305	−	3.45638i	0.0372491	−	0.114641i
$910$		0			0
$911$	−5.00639	+	3.63735i	−0.165869	+	0.120511i	−0.667623	−	0.744499i	$-0.732688\pi$
$911$	−5.00639	+	3.63735i	−0.165869	+	0.120511i	0.501754	+	0.865010i	$0.332688\pi$
$912$			15.9150i			0.527000i
$913$	25.7684	+	32.6597i	0.852810	+	1.08088i
$914$	−5.36971			−0.177614
$915$		0			0
$916$	−3.61122	−	11.1142i	−0.119318	−	0.367223i
$917$	−12.2847	−	3.99155i	−0.405677	−	0.131813i
$918$	2.19887	−	3.02648i	0.0725735	−	0.0998889i
$919$	6.73240	+	4.89138i	0.222081	+	0.161352i	0.693263	−	0.720685i	$-0.256172\pi$
$919$	6.73240	+	4.89138i	0.222081	+	0.161352i	−0.471182	+	0.882036i	$0.656172\pi$
$920$		0			0
$921$	−4.99444	−	15.3713i	−0.164572	−	0.506501i
$922$	2.33274	+	3.21074i	0.0768247	+	0.105740i
$923$		−	55.3589i		−	1.82216i
$924$	13.1764	+	8.79645i	0.433473	+	0.289382i
$925$		0			0
$926$	3.38347	−	2.45824i	0.111188	−	0.0807826i
$927$	−4.46377	+	1.45037i	−0.146610	+	0.0476363i
$928$	8.44559	+	2.74414i	0.277240	+	0.0900808i
$929$	8.60810	+	6.25415i	0.282423	+	0.205192i	0.719973	−	0.694002i	$-0.244154\pi$
$929$	8.60810	+	6.25415i	0.282423	+	0.205192i	−0.437551	+	0.899194i	$0.644154\pi$
$930$		0			0
$931$	−3.70467	+	11.4018i	−0.121416	+	0.373679i
$932$	−33.0021	+	10.7230i	−1.08102	+	0.351245i
$933$	−1.22923	−	1.69190i	−0.0402433	−	0.0553902i
$934$	3.43789			0.112491
$935$		0			0
$936$	2.64210			0.0863596
$937$	−22.4382	−	30.8835i	−0.733023	−	1.00892i	−0.998990	−	0.0449375i	$-0.985691\pi$
$937$	−22.4382	−	30.8835i	−0.733023	−	1.00892i	0.265967	−	0.963982i	$-0.414309\pi$
$938$	−1.09839	+	0.356889i	−0.0358638	+	0.0116528i
$939$	−3.27302	+	10.0733i	−0.106811	+	0.328730i
$940$		0			0
$941$	32.7729	+	23.8109i	1.06837	+	0.776213i	0.975618	−	0.219476i	$-0.0704349\pi$
$941$	32.7729	+	23.8109i	1.06837	+	0.776213i	0.0927480	+	0.995690i	$0.470435\pi$
$942$	4.74656	+	1.54225i	0.154651	+	0.0502493i
$943$	−8.54391	+	2.77609i	−0.278228	+	0.0904018i
$944$	26.9825	−	19.6039i	0.878204	−	0.638053i
$945$		0			0
$946$	0.313970	+	0.849986i	0.0102081	+	0.0276354i
$947$		−	25.2006i		−	0.818909i	−0.912330	−	0.409455i	$-0.865719\pi$
$947$		−	25.2006i		−	0.818909i	0.912330	−	0.409455i	$-0.134281\pi$
$948$	−27.9108	−	38.4159i	−0.906500	−	1.24769i
$949$	−20.2184	−	62.2257i	−0.656316	−	2.01993i
$950$		0			0
$951$	43.4448	+	31.5645i	1.40879	+	1.02355i
$952$	2.45437	−	3.37815i	0.0795465	−	0.109486i
$953$	−19.3852	−	6.29862i	−0.627947	−	0.204032i	−0.0222813	−	0.999752i	$-0.507093\pi$
$953$	−19.3852	−	6.29862i	−0.627947	−	0.204032i	−0.605665	+	0.795720i	$0.707093\pi$
$954$	−0.367983	−	1.13254i	−0.0119139	−	0.0366672i
$955$		0			0
$956$	37.4021			1.20967
$957$	22.1222	+	6.22937i	0.715109	+	0.201367i
$958$			1.06866i			0.0345268i
$959$	−3.67784	+	2.67211i	−0.118764	+	0.0862868i
$960$		0			0
$961$	3.33274	−	10.2571i	0.107508	−	0.330874i
$962$	−5.51374	+	7.58901i	−0.177770	+	0.244680i
$963$	−3.47326	+	4.78053i	−0.111924	+	0.154051i
$964$	−1.08493	+	3.33907i	−0.0349432	+	0.107544i
$965$		0			0
$966$	0.292546	−	0.212547i	0.00941252	−	0.00683860i
$967$		−	4.49928i		−	0.144687i	−0.997380	−	0.0723436i	$-0.976952\pi$
$967$		−	4.49928i		−	0.144687i	0.997380	−	0.0723436i	$-0.0230478\pi$
$968$	−8.81640	−	2.10902i	−0.283370	−	0.0677866i
$969$	16.7225			0.537204
$970$		0			0
$971$	10.5776	+	32.5546i	0.339452	+	1.04473i	0.964487	+	0.264129i	$0.0850845\pi$
$971$	10.5776	+	32.5546i	0.339452	+	1.04473i	−0.625035	+	0.780596i	$0.714915\pi$
$972$	11.2215	+	3.64608i	0.359929	+	0.116948i
$973$	−6.64928	+	9.15195i	−0.213166	+	0.293398i
$974$	−2.82069	−	2.04935i	−0.0903808	−	0.0656655i
$975$		0			0
$976$	−2.12895	−	6.55222i	−0.0681459	−	0.209732i
$977$	25.7833	+	35.4877i	0.824881	+	1.13535i	0.988854	+	0.148887i	$0.0475690\pi$
$977$	25.7833	+	35.4877i	0.824881	+	1.13535i	−0.163973	+	0.986465i	$0.552431\pi$
$978$			3.31779i			0.106091i
$979$	5.64902	−	20.0612i	0.180544	−	0.641160i
$980$		0			0
$981$	−3.63508	+	2.64104i	−0.116059	+	0.0843220i
$982$	−0.152820	+	0.0496543i	−0.00487669	+	0.00158453i
$983$	−17.0632	−	5.54416i	−0.544231	−	0.176831i	0.0239829	−	0.999712i	$-0.492365\pi$
$983$	−17.0632	−	5.54416i	−0.544231	−	0.176831i	−0.568214	+	0.822881i	$0.692365\pi$
$984$	15.9545	+	11.5916i	0.508611	+	0.369528i
$985$		0			0
$986$	0.925655	−	2.84887i	0.0294789	−	0.0907266i
$987$	10.4834	−	3.40626i	0.333690	−	0.108422i
$988$	−14.0748	−	19.3723i	−0.447780	−	0.616316i
$989$	−0.932779			−0.0296607
$990$		0			0
$991$	−33.5351			−1.06528			−0.532638	−	0.846343i	$-0.678799\pi$
$991$	−33.5351			−1.06528			−0.532638	+	0.846343i	$0.678799\pi$
$992$	−9.22343	−	12.6950i	−0.292844	−	0.403065i
$993$	33.5183	−	10.8908i	1.06367	−	0.345608i
$994$	−0.842578	+	2.59319i	−0.0267250	+	0.0822510i
$995$		0			0
$996$	37.6110	+	27.3260i	1.19175	+	0.865857i
$997$	−21.1100	−	6.85905i	−0.668560	−	0.217228i	−0.0449802	−	0.998988i	$-0.514322\pi$
$997$	−21.1100	−	6.85905i	−0.668560	−	0.217228i	−0.623580	+	0.781759i	$0.714322\pi$
$998$	−3.46406	+	1.12554i	−0.109653	+	0.0356283i
$999$	−30.5417	+	22.1899i	−0.966298	+	0.702056i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	275.2.z.c.124.5		32
5.2	odd	4		275.2.h.c.201.2	yes	16
5.3	odd	4		275.2.h.e.201.3	yes	16
5.4	even	2	inner	275.2.z.c.124.4		32
11.4	even	5	inner	275.2.z.c.224.4		32
55.2	even	20		3025.2.a.bm.1.3		8
55.4	even	10	inner	275.2.z.c.224.5		32
55.13	even	20		3025.2.a.bj.1.6		8
55.37	odd	20		275.2.h.c.26.2	✓	16
55.42	odd	20		3025.2.a.bi.1.6		8
55.48	odd	20		275.2.h.e.26.3	yes	16
55.53	odd	20		3025.2.a.bn.1.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
275.2.h.c.26.2	✓	16	55.37	odd	20
275.2.h.c.201.2	yes	16	5.2	odd	4
275.2.h.e.26.3	yes	16	55.48	odd	20
275.2.h.e.201.3	yes	16	5.3	odd	4
275.2.z.c.124.4		32	5.4	even	2	inner
275.2.z.c.124.5		32	1.1	even	1	trivial
275.2.z.c.224.4		32	11.4	even	5	inner
275.2.z.c.224.5		32	55.4	even	10	inner
3025.2.a.bi.1.6		8	55.42	odd	20
3025.2.a.bj.1.6		8	55.13	even	20
3025.2.a.bm.1.3		8	55.2	even	20
3025.2.a.bn.1.3		8	55.53	odd	20

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:	\( N \)	\(=\)	\( 275 = 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	275.z (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.122427 + 0.168506i) q^{2} +(1.80155 - 0.585361i) q^{3} +(0.604628 - 1.86085i) q^{4} +(0.319195 + 0.231909i) q^{6} +(-1.22573 - 0.398265i) q^{7} +(0.783769 - 0.254662i) q^{8} +(0.475901 - 0.345762i) q^{9} +O(q^{10})\)	\(q+(0.122427 + 0.168506i) q^{2} +(1.80155 - 0.585361i) q^{3} +(0.604628 - 1.86085i) q^{4} +(0.319195 + 0.231909i) q^{6} +(-1.22573 - 0.398265i) q^{7} +(0.783769 - 0.254662i) q^{8} +(0.475901 - 0.345762i) q^{9} +(0.898964 - 3.19247i) q^{11} -3.70635i q^{12} +(3.20351 + 4.40926i) q^{13} +(-0.0829527 - 0.255302i) q^{14} +(-3.02701 - 2.19925i) q^{16} +(-2.31083 + 3.18058i) q^{17} +(0.116526 + 0.0378616i) q^{18} +(-0.693894 - 2.13559i) q^{19} -2.44136 q^{21} +(0.648008 - 0.239363i) q^{22} +0.711128i q^{23} +(1.26293 - 0.917575i) q^{24} +(-0.350791 + 1.07962i) q^{26} +(-2.68530 + 3.69600i) q^{27} +(-1.48223 + 2.04011i) q^{28} +(-1.13043 + 3.47910i) q^{29} +(5.22959 - 3.79952i) q^{31} -2.42752i q^{32} +(-0.249213 - 6.27763i) q^{33} -0.818854 q^{34} +(-0.355670 - 1.09464i) q^{36} +(7.85902 + 2.55355i) q^{37} +(0.274908 - 0.378379i) q^{38} +(8.35231 + 6.06831i) q^{39} +(3.90378 + 12.0146i) q^{41} +(-0.298888 - 0.411383i) q^{42} +1.31169i q^{43} +(-5.39718 - 3.60310i) q^{44} +(-0.119829 + 0.0870611i) q^{46} +(-4.29408 + 1.39523i) q^{47} +(-6.74067 - 2.19018i) q^{48} +(-4.31931 - 3.13816i) q^{49} +(-2.30129 + 7.08265i) q^{51} +(10.1419 - 3.29531i) q^{52} +(-5.71278 - 7.86297i) q^{53} -0.951551 q^{54} -1.06212 q^{56} +(-2.50018 - 3.44120i) q^{57} +(-0.724644 + 0.235451i) q^{58} +(-2.75455 + 8.47763i) q^{59} +(1.48965 + 1.08229i) q^{61} +(1.28048 + 0.416055i) q^{62} +(-0.721033 + 0.234278i) q^{63} +(-5.64496 + 4.10130i) q^{64} +(1.02731 - 0.810544i) q^{66} -4.30232i q^{67} +(4.52140 + 6.22318i) q^{68} +(0.416266 + 1.28114i) q^{69} +(-8.21746 - 5.97033i) q^{71} +(0.284944 - 0.392192i) q^{72} +(-11.4173 - 3.70969i) q^{73} +(0.531866 + 1.63692i) q^{74} -4.39356 q^{76} +(-2.37334 + 3.55509i) q^{77} +2.15034i q^{78} +(10.3649 - 7.53052i) q^{79} +(-3.21956 + 9.90878i) q^{81} +(-1.54661 + 2.12872i) q^{82} +(-7.37274 + 10.1477i) q^{83} +(-1.47611 + 4.54301i) q^{84} +(-0.221028 + 0.160586i) q^{86} +6.92949i q^{87} +(-0.108421 - 2.73109i) q^{88} +6.28392 q^{89} +(-2.17060 - 6.68043i) q^{91} +(1.32330 + 0.429968i) q^{92} +(7.19730 - 9.90624i) q^{93} +(-0.760816 - 0.552765i) q^{94} +(-1.42098 - 4.37332i) q^{96} +(0.178336 + 0.245459i) q^{97} -1.11202i q^{98} +(-0.676018 - 1.83013i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 4 q^{4} - 6 q^{6} - 16 q^{9}+O(q^{10}) \) 32 * q + 4 * q^4 - 6 * q^6 - 16 * q^9	\( 32 q + 4 q^{4} - 6 q^{6} - 16 q^{9} - 10 q^{11} - 6 q^{14} - 8 q^{16} + 26 q^{19} + 20 q^{21} + 86 q^{24} - 68 q^{26} + 22 q^{29} - 20 q^{31} - 40 q^{34} + 6 q^{36} - 6 q^{39} + 50 q^{41} + 2 q^{44} + 80 q^{46} - 32 q^{49} + 70 q^{51} - 120 q^{54} - 40 q^{56} - 28 q^{59} + 32 q^{61} - 80 q^{64} - 110 q^{66} - 70 q^{69} - 92 q^{71} + 14 q^{74} - 124 q^{76} + 78 q^{79} - 86 q^{81} + 108 q^{84} + 4 q^{86} + 44 q^{89} - 68 q^{91} + 80 q^{94} + 216 q^{96} + 20 q^{99}+O(q^{100}) \) 32 * q + 4 * q^4 - 6 * q^6 - 16 * q^9 - 10 * q^11 - 6 * q^14 - 8 * q^16 + 26 * q^19 + 20 * q^21 + 86 * q^24 - 68 * q^26 + 22 * q^29 - 20 * q^31 - 40 * q^34 + 6 * q^36 - 6 * q^39 + 50 * q^41 + 2 * q^44 + 80 * q^46 - 32 * q^49 + 70 * q^51 - 120 * q^54 - 40 * q^56 - 28 * q^59 + 32 * q^61 - 80 * q^64 - 110 * q^66 - 70 * q^69 - 92 * q^71 + 14 * q^74 - 124 * q^76 + 78 * q^79 - 86 * q^81 + 108 * q^84 + 4 * q^86 + 44 * q^89 - 68 * q^91 + 80 * q^94 + 216 * q^96 + 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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