LMFDB - Embedded newform 550.2.h.a.301.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [550,2,Mod(201,550)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(550, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 8]))

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

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

chi := DirichletCharacter("550.201");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 550 = 2 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	550.h (of order $5$, degree $4$, 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:	$4.39177211117$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			301.1
Root			$0.809017 - 0.587785i$ of defining polynomial
Character	$\chi$	$=$	550.301
Dual form			550.2.h.a.201.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.809017 - 0.587785i) q^{2} +(0.118034 - 0.363271i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-0.309017 + 0.224514i) q^{6} +(0.927051 + 2.85317i) q^{7} +(0.309017 - 0.951057i) q^{8} +(2.30902 + 1.67760i) q^{9} +(-1.23607 + 3.07768i) q^{11} +0.381966 q^{12} +(-5.04508 - 3.66547i) q^{13} +(0.927051 - 2.85317i) q^{14} +(-0.809017 + 0.587785i) q^{16} +(-3.54508 + 2.57565i) q^{17} +(-0.881966 - 2.71441i) q^{18} +(-1.80902 + 5.56758i) q^{19} +1.14590 q^{21} +(2.80902 - 1.76336i) q^{22} -1.85410 q^{23} +(-0.309017 - 0.224514i) q^{24} +(1.92705 + 5.93085i) q^{26} +(1.80902 - 1.31433i) q^{27} +(-2.42705 + 1.76336i) q^{28} +(-0.163119 - 0.502029i) q^{29} +(2.42705 + 1.76336i) q^{31} +1.00000 q^{32} +(0.972136 + 0.812299i) q^{33} +4.38197 q^{34} +(-0.881966 + 2.71441i) q^{36} +(3.26393 + 10.0453i) q^{37} +(4.73607 - 3.44095i) q^{38} +(-1.92705 + 1.40008i) q^{39} +(1.14590 - 3.52671i) q^{41} +(-0.927051 - 0.673542i) q^{42} +10.7082 q^{43} +(-3.30902 - 0.224514i) q^{44} +(1.50000 + 1.08981i) q^{46} +(-0.454915 + 1.40008i) q^{47} +(0.118034 + 0.363271i) q^{48} +(-1.61803 + 1.17557i) q^{49} +(0.517221 + 1.59184i) q^{51} +(1.92705 - 5.93085i) q^{52} +(-4.35410 - 3.16344i) q^{53} -2.23607 q^{54} +3.00000 q^{56} +(1.80902 + 1.31433i) q^{57} +(-0.163119 + 0.502029i) q^{58} +(-2.07295 - 6.37988i) q^{59} +(-7.04508 + 5.11855i) q^{61} +(-0.927051 - 2.85317i) q^{62} +(-2.64590 + 8.14324i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(-0.309017 - 1.22857i) q^{66} -0.0901699 q^{67} +(-3.54508 - 2.57565i) q^{68} +(-0.218847 + 0.673542i) q^{69} +(10.7812 - 7.83297i) q^{71} +(2.30902 - 1.67760i) q^{72} +(3.57295 + 10.9964i) q^{73} +(3.26393 - 10.0453i) q^{74} -5.85410 q^{76} +(-9.92705 - 0.673542i) q^{77} +2.38197 q^{78} +(6.28115 + 4.56352i) q^{79} +(2.38197 + 7.33094i) q^{81} +(-3.00000 + 2.17963i) q^{82} +(3.04508 - 2.21238i) q^{83} +(0.354102 + 1.08981i) q^{84} +(-8.66312 - 6.29412i) q^{86} -0.201626 q^{87} +(2.54508 + 2.12663i) q^{88} +11.1803 q^{89} +(5.78115 - 17.7926i) q^{91} +(-0.572949 - 1.76336i) q^{92} +(0.927051 - 0.673542i) q^{93} +(1.19098 - 0.865300i) q^{94} +(0.118034 - 0.363271i) q^{96} +(0.763932 + 0.555029i) q^{97} +2.00000 q^{98} +(-8.01722 + 5.03280i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{2} - 4 q^{3} - q^{4} + q^{6} - 3 q^{7} - q^{8} + 7 q^{9} + 4 q^{11} + 6 q^{12} - 9 q^{13} - 3 q^{14} - q^{16} - 3 q^{17} - 8 q^{18} - 5 q^{19} + 18 q^{21} + 9 q^{22} + 6 q^{23} + q^{24} + q^{26}+ \cdots - 3 q^{99}+O(q^{100}) $ 4 * q - q^2 - 4 * q^3 - q^4 + q^6 - 3 * q^7 - q^8 + 7 * q^9 + 4 * q^11 + 6 * q^12 - 9 * q^13 - 3 * q^14 - q^16 - 3 * q^17 - 8 * q^18 - 5 * q^19 + 18 * q^21 + 9 * q^22 + 6 * q^23 + q^24 + q^26 + 5 * q^27 - 3 * q^28 + 15 * q^29 + 3 * q^31 + 4 * q^32 - 14 * q^33 + 22 * q^34 - 8 * q^36 + 22 * q^37 + 10 * q^38 - q^39 + 18 * q^41 + 3 * q^42 + 16 * q^43 - 11 * q^44 + 6 * q^46 - 13 * q^47 - 4 * q^48 - 2 * q^49 - 27 * q^51 + q^52 - 4 * q^53 + 12 * q^56 + 5 * q^57 + 15 * q^58 - 15 * q^59 - 17 * q^61 + 3 * q^62 - 24 * q^63 - q^64 + q^66 + 22 * q^67 - 3 * q^68 - 21 * q^69 + 23 * q^71 + 7 * q^72 + 21 * q^73 + 22 * q^74 - 10 * q^76 - 33 * q^77 + 14 * q^78 + 5 * q^79 + 14 * q^81 - 12 * q^82 + q^83 - 12 * q^84 - 19 * q^86 - 50 * q^87 - q^88 + 3 * q^91 - 9 * q^92 - 3 * q^93 + 7 * q^94 - 4 * q^96 + 12 * q^97 + 8 * q^98 - 3 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/550\mathbb{Z}\right)^\times$.

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

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 $

$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$3$	0.118034	−	0.363271i	0.0681470	−	0.209735i	−0.911184	−	0.412000i	$-0.864830\pi$
$3$	0.118034	−	0.363271i	0.0681470	−	0.209735i	0.979331	+	0.202265i	$0.0648303\pi$
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$		0			0
$5$		0			0
$6$	−0.309017	+	0.224514i	−0.126156	+	0.0916575i
$7$	0.927051	+	2.85317i	0.350392	+	1.07840i	0.958633	+	0.284644i	$0.0918755\pi$
$7$	0.927051	+	2.85317i	0.350392	+	1.07840i	−0.608241	+	0.793752i	$0.708125\pi$
$8$	0.309017	−	0.951057i	0.109254	−	0.336249i
$9$	2.30902	+	1.67760i	0.769672	+	0.559200i
$10$		0			0
$11$	−1.23607	+	3.07768i	−0.372689	+	0.927957i
$11$	−1.23607	+	3.07768i	−0.372689	+	0.927957i
$12$	0.381966			0.110264
$13$	−5.04508	−	3.66547i	−1.39925	−	1.01662i	−0.994777	−	0.102070i	$-0.967453\pi$
$13$	−5.04508	−	3.66547i	−1.39925	−	1.01662i	−0.404478	−	0.914548i	$-0.632547\pi$
$14$	0.927051	−	2.85317i	0.247765	−	0.762542i
$15$		0			0
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	−3.54508	+	2.57565i	−0.859809	+	0.624688i	−0.927833	−	0.372996i	$-0.878331\pi$
$17$	−3.54508	+	2.57565i	−0.859809	+	0.624688i	0.0680237	+	0.997684i	$0.478331\pi$
$18$	−0.881966	−	2.71441i	−0.207881	−	0.639793i
$19$	−1.80902	+	5.56758i	−0.415017	+	1.27729i	0.497219	+	0.867625i	$0.334355\pi$
$19$	−1.80902	+	5.56758i	−0.415017	+	1.27729i	−0.912236	+	0.409666i	$0.865645\pi$
$20$		0			0
$21$	1.14590			0.250055
$22$	2.80902	−	1.76336i	0.598884	−	0.375949i
$23$	−1.85410			−0.386607			−0.193303	−	0.981139i	$-0.561920\pi$
$23$	−1.85410			−0.386607			−0.193303	+	0.981139i	$0.561920\pi$
$24$	−0.309017	−	0.224514i	−0.0630778	−	0.0458287i
$25$		0			0
$26$	1.92705	+	5.93085i	0.377926	+	1.16314i
$27$	1.80902	−	1.31433i	0.348145	−	0.252942i
$28$	−2.42705	+	1.76336i	−0.458670	+	0.333243i
$29$	−0.163119	−	0.502029i	−0.0302904	−	0.0932244i	0.934768	−	0.355258i	$-0.115607\pi$
$29$	−0.163119	−	0.502029i	−0.0302904	−	0.0932244i	−0.965059	+	0.262033i	$0.915607\pi$
$30$		0			0
$31$	2.42705	+	1.76336i	0.435911	+	0.316708i	0.784008	−	0.620750i	$-0.213172\pi$
$31$	2.42705	+	1.76336i	0.435911	+	0.316708i	−0.348097	+	0.937459i	$0.613172\pi$
$32$	1.00000			0.176777
$33$	0.972136	+	0.812299i	0.169227	+	0.141403i
$34$	4.38197			0.751501
$35$		0			0
$36$	−0.881966	+	2.71441i	−0.146994	+	0.452402i
$37$	3.26393	+	10.0453i	0.536587	+	1.65145i	0.740195	+	0.672393i	$0.234733\pi$
$37$	3.26393	+	10.0453i	0.536587	+	1.65145i	−0.203607	+	0.979053i	$0.565267\pi$
$38$	4.73607	−	3.44095i	0.768292	−	0.558197i
$39$	−1.92705	+	1.40008i	−0.308575	+	0.224193i
$40$		0			0
$41$	1.14590	−	3.52671i	0.178959	−	0.550780i	−0.820833	−	0.571168i	$-0.806490\pi$
$41$	1.14590	−	3.52671i	0.178959	−	0.550780i	0.999792	+	0.0203886i	$0.00649033\pi$
$42$	−0.927051	−	0.673542i	−0.143047	−	0.103930i
$43$	10.7082			1.63299			0.816493	−	0.577355i	$-0.195915\pi$
$43$	10.7082			1.63299			0.816493	+	0.577355i	$0.195915\pi$
$44$	−3.30902	−	0.224514i	−0.498853	−	0.0338468i
$45$		0			0
$46$	1.50000	+	1.08981i	0.221163	+	0.160684i
$47$	−0.454915	+	1.40008i	−0.0663562	+	0.204223i	−0.978737	−	0.205119i	$-0.934242\pi$
$47$	−0.454915	+	1.40008i	−0.0663562	+	0.204223i	0.912381	+	0.409342i	$0.134242\pi$
$48$	0.118034	+	0.363271i	0.0170367	+	0.0524337i
$49$	−1.61803	+	1.17557i	−0.231148	+	0.167939i
$50$		0			0
$51$	0.517221	+	1.59184i	0.0724254	+	0.222903i
$52$	1.92705	−	5.93085i	0.267234	−	0.822461i
$53$	−4.35410	−	3.16344i	−0.598082	−	0.434532i	0.247116	−	0.968986i	$-0.420517\pi$
$53$	−4.35410	−	3.16344i	−0.598082	−	0.434532i	−0.845198	+	0.534454i	$0.820517\pi$
$54$	−2.23607			−0.304290
$55$		0			0
$56$	3.00000			0.400892
$57$	1.80902	+	1.31433i	0.239610	+	0.174087i
$58$	−0.163119	+	0.502029i	−0.0214186	+	0.0659196i
$59$	−2.07295	−	6.37988i	−0.269875	−	0.830590i	−0.990530	−	0.137296i	$-0.956159\pi$
$59$	−2.07295	−	6.37988i	−0.269875	−	0.830590i	0.720655	−	0.693294i	$-0.243841\pi$
$60$		0			0
$61$	−7.04508	+	5.11855i	−0.902031	+	0.655364i	−0.938987	−	0.343953i	$-0.888234\pi$
$61$	−7.04508	+	5.11855i	−0.902031	+	0.655364i	0.0369561	+	0.999317i	$0.488234\pi$
$62$	−0.927051	−	2.85317i	−0.117736	−	0.362353i
$63$	−2.64590	+	8.14324i	−0.333352	+	1.02595i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$		0			0
$66$	−0.309017	−	1.22857i	−0.0380374	−	0.151227i
$67$	−0.0901699			−0.0110160			−0.00550801	−	0.999985i	$-0.501753\pi$
$67$	−0.0901699			−0.0110160			−0.00550801	+	0.999985i	$0.501753\pi$
$68$	−3.54508	−	2.57565i	−0.429905	−	0.312344i
$69$	−0.218847	+	0.673542i	−0.0263461	+	0.0810849i
$70$		0			0
$71$	10.7812	−	7.83297i	1.27949	−	0.929602i	0.279950	−	0.960015i	$-0.409682\pi$
$71$	10.7812	−	7.83297i	1.27949	−	0.929602i	0.999537	+	0.0304125i	$0.00968210\pi$
$72$	2.30902	−	1.67760i	0.272120	−	0.197707i
$73$	3.57295	+	10.9964i	0.418182	+	1.28703i	0.909374	+	0.415980i	$0.136562\pi$
$73$	3.57295	+	10.9964i	0.418182	+	1.28703i	−0.491192	+	0.871052i	$0.663438\pi$
$74$	3.26393	−	10.0453i	0.379424	−	1.16775i
$75$		0			0
$76$	−5.85410			−0.671512
$77$	−9.92705	−	0.673542i	−1.13129	−	0.0767572i
$78$	2.38197			0.269705
$79$	6.28115	+	4.56352i	0.706685	+	0.513437i	0.882103	−	0.471057i	$-0.156128\pi$
$79$	6.28115	+	4.56352i	0.706685	+	0.513437i	−0.175418	+	0.984494i	$0.556128\pi$
$80$		0			0
$81$	2.38197	+	7.33094i	0.264663	+	0.814549i
$82$	−3.00000	+	2.17963i	−0.331295	+	0.240700i
$83$	3.04508	−	2.21238i	0.334241	−	0.242841i	−0.407987	−	0.912988i	$-0.633769\pi$
$83$	3.04508	−	2.21238i	0.334241	−	0.242841i	0.742228	+	0.670147i	$0.233769\pi$
$84$	0.354102	+	1.08981i	0.0386357	+	0.118908i
$85$		0			0
$86$	−8.66312	−	6.29412i	−0.934168	−	0.678713i
$87$	−0.201626			−0.0216166
$88$	2.54508	+	2.12663i	0.271307	+	0.226699i
$89$	11.1803			1.18511			0.592557	−	0.805529i	$-0.298119\pi$
$89$	11.1803			1.18511			0.592557	+	0.805529i	$0.298119\pi$
$90$		0			0
$91$	5.78115	−	17.7926i	0.606029	−	1.86517i
$92$	−0.572949	−	1.76336i	−0.0597341	−	0.183843i
$93$	0.927051	−	0.673542i	0.0961307	−	0.0698430i
$94$	1.19098	−	0.865300i	0.122841	−	0.0892489i
$95$		0			0
$96$	0.118034	−	0.363271i	0.0120468	−	0.0370762i
$97$	0.763932	+	0.555029i	0.0775655	+	0.0563547i	0.625892	−	0.779910i	$-0.284735\pi$
$97$	0.763932	+	0.555029i	0.0775655	+	0.0563547i	−0.548327	+	0.836264i	$0.684735\pi$
$98$	2.00000			0.202031
$99$	−8.01722	+	5.03280i	−0.805761	+	0.505815i
$100$		0			0
$101$	−10.6631	−	7.74721i	−1.06102	−	0.770876i	−0.0867432	−	0.996231i	$-0.527646\pi$
$101$	−10.6631	−	7.74721i	−1.06102	−	0.770876i	−0.974277	+	0.225355i	$0.927646\pi$
$102$	0.517221	−	1.59184i	0.0512125	−	0.157616i
$103$	0.218847	+	0.673542i	0.0215636	+	0.0663661i	0.961259	−	0.275646i	$-0.0888917\pi$
$103$	0.218847	+	0.673542i	0.0215636	+	0.0663661i	−0.939696	+	0.342012i	$0.888892\pi$
$104$	−5.04508	+	3.66547i	−0.494711	+	0.359429i
$105$		0			0
$106$	1.66312	+	5.11855i	0.161536	+	0.497158i
$107$	0.236068	−	0.726543i	0.0228216	−	0.0702375i	−0.938997	−	0.343925i	$-0.888243\pi$
$107$	0.236068	−	0.726543i	0.0228216	−	0.0702375i	0.961819	+	0.273687i	$0.0882434\pi$
$108$	1.80902	+	1.31433i	0.174073	+	0.126471i
$109$	−9.14590			−0.876018			−0.438009	−	0.898971i	$-0.644316\pi$
$109$	−9.14590			−0.876018			−0.438009	+	0.898971i	$0.644316\pi$
$110$		0			0
$111$	4.03444			0.382932
$112$	−2.42705	−	1.76336i	−0.229335	−	0.166621i
$113$	−1.16312	+	3.57971i	−0.109417	+	0.336751i	−0.990742	−	0.135760i	$-0.956652\pi$
$113$	−1.16312	+	3.57971i	−0.109417	+	0.336751i	0.881325	+	0.472511i	$0.156652\pi$
$114$	−0.690983	−	2.12663i	−0.0647165	−	0.199177i
$115$		0			0
$116$	0.427051	−	0.310271i	0.0396507	−	0.0288079i
$117$	−5.50000	−	16.9273i	−0.508475	−	1.56493i
$118$	−2.07295	+	6.37988i	−0.190830	+	0.587316i
$119$	−10.6353	−	7.72696i	−0.974932	−	0.708330i
$120$		0			0
$121$	−7.94427	−	7.60845i	−0.722207	−	0.691677i
$122$	8.70820			0.788404
$123$	−1.14590	−	0.832544i	−0.103322	−	0.0750679i
$124$	−0.927051	+	2.85317i	−0.0832516	+	0.256222i
$125$		0			0
$126$	6.92705	−	5.03280i	0.617111	−	0.448357i
$127$	−1.73607	+	1.26133i	−0.154051	+	0.111925i	−0.662141	−	0.749380i	$-0.730352\pi$
$127$	−1.73607	+	1.26133i	−0.154051	+	0.111925i	0.508090	+	0.861304i	$0.330352\pi$
$128$	0.309017	+	0.951057i	0.0273135	+	0.0840623i
$129$	1.26393	−	3.88998i	0.111283	−	0.342494i
$130$		0			0
$131$	−20.5623			−1.79654			−0.898269	−	0.439447i	$-0.855174\pi$
$131$	−20.5623			−1.79654			−0.898269	+	0.439447i	$0.855174\pi$
$132$	−0.472136	+	1.17557i	−0.0410942	+	0.102320i
$133$	−17.5623			−1.52285
$134$	0.0729490	+	0.0530006i	0.00630184	+	0.00457855i
$135$		0			0
$136$	1.35410	+	4.16750i	0.116113	+	0.357360i
$137$	2.57295	−	1.86936i	0.219822	−	0.159710i	−0.472425	−	0.881371i	$-0.656621\pi$
$137$	2.57295	−	1.86936i	0.219822	−	0.159710i	0.692246	+	0.721661i	$0.256621\pi$
$138$	0.572949	−	0.416272i	0.0487727	−	0.0354354i
$139$	−2.50000	−	7.69421i	−0.212047	−	0.652614i	−0.999350	−	0.0360478i	$-0.988523\pi$
$139$	−2.50000	−	7.69421i	−0.212047	−	0.652614i	0.787303	−	0.616566i	$-0.211477\pi$
$140$		0			0
$141$	0.454915	+	0.330515i	0.0383108	+	0.0278344i
$142$	−13.3262			−1.11831
$143$	17.5172	−	10.9964i	1.46486	−	0.919566i
$144$	−2.85410			−0.237842
$145$		0			0
$146$	3.57295	−	10.9964i	0.295699	−	0.910069i
$147$	0.236068	+	0.726543i	0.0194706	+	0.0599242i
$148$	−8.54508	+	6.20837i	−0.702402	+	0.510325i
$149$	17.1353	−	12.4495i	1.40377	−	1.01990i	0.409584	−	0.912273i	$-0.365674\pi$
$149$	17.1353	−	12.4495i	1.40377	−	1.01990i	0.994191	−	0.107630i	$-0.0343260\pi$
$150$		0			0
$151$	6.20820	−	19.1069i	0.505216	−	1.55490i	−0.295190	−	0.955439i	$-0.595383\pi$
$151$	6.20820	−	19.1069i	0.505216	−	1.55490i	0.800406	−	0.599458i	$-0.204617\pi$
$152$	4.73607	+	3.44095i	0.384146	+	0.279098i
$153$	−12.5066			−1.01110
$154$	7.63525	+	6.37988i	0.615266	+	0.514105i
$155$		0			0
$156$	−1.92705	−	1.40008i	−0.154288	−	0.112096i
$157$	6.09017	−	18.7436i	0.486048	−	1.49590i	−0.344408	−	0.938820i	$-0.611920\pi$
$157$	6.09017	−	18.7436i	0.486048	−	1.49590i	0.830457	−	0.557083i	$-0.188080\pi$
$158$	−2.39919	−	7.38394i	−0.190869	−	0.587435i
$159$	−1.66312	+	1.20833i	−0.131894	+	0.0958265i
$160$		0			0
$161$	−1.71885	−	5.29007i	−0.135464	−	0.416916i
$162$	2.38197	−	7.33094i	0.187145	−	0.575973i
$163$	9.85410	+	7.15942i	0.771833	+	0.560769i	0.902517	−	0.430655i	$-0.141717\pi$
$163$	9.85410	+	7.15942i	0.771833	+	0.560769i	−0.130684	+	0.991424i	$0.541717\pi$
$164$	3.70820			0.289562
$165$		0			0
$166$	−3.76393			−0.292138
$167$	4.80902	+	3.49396i	0.372133	+	0.270370i	0.758095	−	0.652144i	$-0.226130\pi$
$167$	4.80902	+	3.49396i	0.372133	+	0.270370i	−0.385962	+	0.922515i	$0.626130\pi$
$168$	0.354102	−	1.08981i	0.0273196	−	0.0840810i
$169$	8.00000	+	24.6215i	0.615385	+	1.89396i
$170$		0			0
$171$	−13.5172	+	9.82084i	−1.03369	+	0.751018i
$172$	3.30902	+	10.1841i	0.252310	+	0.776531i
$173$	−2.64590	+	8.14324i	−0.201164	+	0.619119i	0.798685	+	0.601749i	$0.205529\pi$
$173$	−2.64590	+	8.14324i	−0.201164	+	0.619119i	−0.999849	+	0.0173698i	$0.994471\pi$
$174$	0.163119	+	0.118513i	0.0123660	+	0.00898444i
$175$		0			0
$176$	−0.809017	−	3.21644i	−0.0609820	−	0.242448i
$177$	−2.56231			−0.192595
$178$	−9.04508	−	6.57164i	−0.677958	−	0.492565i
$179$	3.29180	−	10.1311i	0.246040	−	0.757234i	−0.749423	−	0.662091i	$-0.769669\pi$
$179$	3.29180	−	10.1311i	0.246040	−	0.757234i	0.995464	−	0.0951432i	$-0.0303309\pi$
$180$		0			0
$181$	−9.70820	+	7.05342i	−0.721605	+	0.524277i	−0.886897	−	0.461968i	$-0.847144\pi$
$181$	−9.70820	+	7.05342i	−0.721605	+	0.524277i	0.165292	+	0.986245i	$0.447144\pi$
$182$	−15.1353	+	10.9964i	−1.12190	+	0.815108i
$183$	1.02786	+	3.16344i	0.0759819	+	0.233848i
$184$	−0.572949	+	1.76336i	−0.0422384	+	0.129996i
$185$		0			0
$186$	−1.14590			−0.0840213
$187$	−3.54508	−	14.0943i	−0.259242	−	1.03068i
$188$	−1.47214			−0.107367
$189$	5.42705	+	3.94298i	0.394760	+	0.286810i
$190$		0			0
$191$	7.42705	+	22.8581i	0.537403	+	1.65395i	0.738400	+	0.674363i	$0.235582\pi$
$191$	7.42705	+	22.8581i	0.537403	+	1.65395i	−0.200997	+	0.979592i	$0.564418\pi$
$192$	−0.309017	+	0.224514i	−0.0223014	+	0.0162029i
$193$	1.50000	−	1.08981i	0.107972	−	0.0784465i	−0.532489	−	0.846437i	$-0.678743\pi$
$193$	1.50000	−	1.08981i	0.107972	−	0.0784465i	0.640461	+	0.767990i	$0.278743\pi$
$194$	−0.291796	−	0.898056i	−0.0209497	−	0.0644767i
$195$		0			0
$196$	−1.61803	−	1.17557i	−0.115574	−	0.0839693i
$197$	−4.76393			−0.339416			−0.169708	−	0.985494i	$-0.554282\pi$
$197$	−4.76393			−0.339416			−0.169708	+	0.985494i	$0.554282\pi$
$198$	9.44427	+	0.640786i	0.671175	+	0.0455387i
$199$	−3.94427			−0.279602			−0.139801	−	0.990180i	$-0.544646\pi$
$199$	−3.94427			−0.279602			−0.139801	+	0.990180i	$0.544646\pi$
$200$		0			0
$201$	−0.0106431	+	0.0327561i	−0.000750708	+	0.00231044i
$202$	4.07295	+	12.5352i	0.286572	+	0.881977i
$203$	1.28115	−	0.930812i	0.0899193	−	0.0653302i
$204$	−1.35410	+	0.983813i	−0.0948061	+	0.0688807i
$205$		0			0
$206$	0.218847	−	0.673542i	0.0152478	−	0.0469279i
$207$	−4.28115	−	3.11044i	−0.297561	−	0.216191i
$208$	6.23607			0.432394
$209$	−14.8992	−	12.4495i	−1.03060	−	0.861149i
$210$		0			0
$211$	22.0623	+	16.0292i	1.51883	+	1.10350i	0.962063	+	0.272829i	$0.0879592\pi$
$211$	22.0623	+	16.0292i	1.51883	+	1.10350i	0.556769	+	0.830667i	$0.312041\pi$
$212$	1.66312	−	5.11855i	0.114223	−	0.351544i
$213$	−1.57295	−	4.84104i	−0.107777	−	0.331703i
$214$	−0.618034	+	0.449028i	−0.0422479	+	0.0306949i
$215$		0			0
$216$	−0.690983	−	2.12663i	−0.0470154	−	0.144699i
$217$	−2.78115	+	8.55951i	−0.188797	+	0.581057i
$218$	7.39919	+	5.37582i	0.501136	+	0.364097i
$219$	4.41641			0.298433
$220$		0			0
$221$	27.3262			1.83816
$222$	−3.26393	−	2.37139i	−0.219061	−	0.159157i
$223$	6.39919	−	19.6947i	0.428521	−	1.31885i	−0.471061	−	0.882101i	$-0.656129\pi$
$223$	6.39919	−	19.6947i	0.428521	−	1.31885i	0.899582	−	0.436752i	$-0.143871\pi$
$224$	0.927051	+	2.85317i	0.0619412	+	0.190635i
$225$		0			0
$226$	3.04508	−	2.21238i	0.202556	−	0.147166i
$227$	5.66312	+	17.4293i	0.375874	+	1.15682i	0.942887	+	0.333113i	$0.108099\pi$
$227$	5.66312	+	17.4293i	0.375874	+	1.15682i	−0.567012	+	0.823709i	$0.691901\pi$
$228$	−0.690983	+	2.12663i	−0.0457615	+	0.140839i
$229$	−0.427051	−	0.310271i	−0.0282203	−	0.0205033i	0.573586	−	0.819146i	$-0.305552\pi$
$229$	−0.427051	−	0.310271i	−0.0282203	−	0.0205033i	−0.601806	+	0.798642i	$0.705552\pi$
$230$		0			0
$231$	−1.41641	+	3.52671i	−0.0931928	+	0.232041i
$232$	−0.527864			−0.0346560
$233$	−12.4443	−	9.04129i	−0.815251	−	0.592315i	0.100097	−	0.994978i	$-0.468085\pi$
$233$	−12.4443	−	9.04129i	−0.815251	−	0.592315i	−0.915348	+	0.402663i	$0.868085\pi$
$234$	−5.50000	+	16.9273i	−0.359546	+	1.10657i
$235$		0			0
$236$	5.42705	−	3.94298i	0.353271	−	0.256666i
$237$	2.39919	−	1.74311i	0.155844	−	0.113227i
$238$	4.06231	+	12.5025i	0.263320	+	0.810416i
$239$	4.83688	−	14.8864i	0.312872	−	0.962920i	−0.663750	−	0.747955i	$-0.731036\pi$
$239$	4.83688	−	14.8864i	0.312872	−	0.962920i	0.976622	−	0.214966i	$-0.0689640\pi$
$240$		0			0
$241$	−18.0000			−1.15948			−0.579741	−	0.814801i	$-0.696846\pi$
$241$	−18.0000			−1.15948			−0.579741	+	0.814801i	$0.696846\pi$
$242$	1.95492	+	10.8249i	0.125667	+	0.695850i
$243$	9.65248			0.619207
$244$	−7.04508	−	5.11855i	−0.451015	−	0.327682i
$245$		0			0
$246$	0.437694	+	1.34708i	0.0279064	+	0.0858869i
$247$	29.5344	−	21.4580i	1.87923	−	1.36534i
$248$	2.42705	−	1.76336i	0.154118	−	0.111973i
$249$	−0.444272	−	1.36733i	−0.0281546	−	0.0866509i
$250$		0			0
$251$	11.7361	+	8.52675i	0.740774	+	0.538204i	0.892953	−	0.450149i	$-0.148629\pi$
$251$	11.7361	+	8.52675i	0.740774	+	0.538204i	−0.152179	+	0.988353i	$0.548629\pi$
$252$	−8.56231			−0.539375
$253$	2.29180	−	5.70634i	0.144084	−	0.358754i
$254$	2.14590			0.134646
$255$		0			0
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	9.80902	+	30.1891i	0.611870	+	1.88314i	0.439925	+	0.898035i	$0.355005\pi$
$257$	9.80902	+	30.1891i	0.611870	+	1.88314i	0.171945	+	0.985107i	$0.444995\pi$
$258$	−3.30902	+	2.40414i	−0.206010	+	0.149675i
$259$	−25.6353	+	18.6251i	−1.59290	+	1.15731i
$260$		0			0
$261$	0.465558	−	1.43284i	0.0288173	−	0.0886906i
$262$	16.6353	+	12.0862i	1.02773	+	0.746689i
$263$	11.0344			0.680413			0.340206	−	0.940351i	$-0.389503\pi$
$263$	11.0344			0.680413			0.340206	+	0.940351i	$0.389503\pi$
$264$	1.07295	−	0.673542i	0.0660354	−	0.0414536i
$265$		0			0
$266$	14.2082	+	10.3229i	0.871161	+	0.632935i
$267$	1.31966	−	4.06150i	0.0807619	−	0.248560i
$268$	−0.0278640	−	0.0857567i	−0.00170207	−	0.00523842i
$269$	14.6353	−	10.6331i	0.892327	−	0.648314i	−0.0441565	−	0.999025i	$-0.514060\pi$
$269$	14.6353	−	10.6331i	0.892327	−	0.648314i	0.936484	+	0.350711i	$0.114060\pi$
$270$		0			0
$271$	5.02786	+	15.4742i	0.305421	+	0.939989i	0.979520	+	0.201348i	$0.0645322\pi$
$271$	5.02786	+	15.4742i	0.305421	+	0.939989i	−0.674099	+	0.738641i	$0.735468\pi$
$272$	1.35410	−	4.16750i	0.0821045	−	0.252692i
$273$	−5.78115	−	4.20025i	−0.349891	−	0.254211i
$274$	−3.18034			−0.192131
$275$		0			0
$276$	−0.708204			−0.0426289
$277$	−5.09017	−	3.69822i	−0.305839	−	0.222205i	0.424270	−	0.905536i	$-0.360531\pi$
$277$	−5.09017	−	3.69822i	−0.305839	−	0.222205i	−0.730109	+	0.683331i	$0.760531\pi$
$278$	−2.50000	+	7.69421i	−0.149940	+	0.461468i
$279$	2.64590	+	8.14324i	0.158406	+	0.487523i
$280$		0			0
$281$	−14.7082	+	10.6861i	−0.877418	+	0.637481i	−0.932567	−	0.360997i	$-0.882437\pi$
$281$	−14.7082	+	10.6861i	−0.877418	+	0.637481i	0.0551492	+	0.998478i	$0.482437\pi$
$282$	−0.173762	−	0.534785i	−0.0103474	−	0.0318460i
$283$	−5.67376	+	17.4620i	−0.337270	+	1.03801i	0.628323	+	0.777953i	$0.283742\pi$
$283$	−5.67376	+	17.4620i	−0.337270	+	1.03801i	−0.965593	+	0.260058i	$0.916258\pi$
$284$	10.7812	+	7.83297i	0.639744	+	0.464801i
$285$		0			0
$286$	−20.6353	−	1.40008i	−1.22019	−	0.0827887i
$287$	11.1246			0.656665
$288$	2.30902	+	1.67760i	0.136060	+	0.0988535i
$289$	0.680340	−	2.09387i	0.0400200	−	0.123169i
$290$		0			0
$291$	0.291796	−	0.212002i	0.0171054	−	0.0124278i
$292$	−9.35410	+	6.79615i	−0.547407	+	0.397715i
$293$	−5.89919	−	18.1558i	−0.344634	−	1.06067i	−0.961779	−	0.273826i	$-0.911711\pi$
$293$	−5.89919	−	18.1558i	−0.344634	−	1.06067i	0.617145	−	0.786849i	$-0.288289\pi$
$294$	0.236068	−	0.726543i	0.0137678	−	0.0423728i
$295$		0			0
$296$	10.5623			0.613922
$297$	1.80902	+	7.19218i	0.104970	+	0.417333i
$298$	−21.1803			−1.22694
$299$	9.35410	+	6.79615i	0.540962	+	0.393032i
$300$		0			0
$301$	9.92705	+	30.5523i	0.572186	+	1.76101i
$302$	−16.2533	+	11.8087i	−0.935272	+	0.679515i
$303$	−4.07295	+	2.95917i	−0.233985	+	0.170000i
$304$	−1.80902	−	5.56758i	−0.103754	−	0.319323i
$305$		0			0
$306$	10.1180	+	7.35118i	0.578410	+	0.420239i
$307$	−9.56231			−0.545750			−0.272875	−	0.962050i	$-0.587974\pi$
$307$	−9.56231			−0.545750			−0.272875	+	0.962050i	$0.587974\pi$
$308$	−2.42705	−	9.64932i	−0.138294	−	0.549821i
$309$	0.270510			0.0153888
$310$		0			0
$311$	0.781153	−	2.40414i	0.0442951	−	0.136326i	−0.926463	−	0.376385i	$-0.877167\pi$
$311$	0.781153	−	2.40414i	0.0442951	−	0.136326i	0.970758	+	0.240059i	$0.0771668\pi$
$312$	0.736068	+	2.26538i	0.0416716	+	0.128252i
$313$	16.1353	−	11.7229i	0.912019	−	0.662620i	−0.0295060	−	0.999565i	$-0.509393\pi$
$313$	16.1353	−	11.7229i	0.912019	−	0.662620i	0.941525	+	0.336944i	$0.109393\pi$
$314$	−15.9443	+	11.5842i	−0.899787	+	0.653734i
$315$		0			0
$316$	−2.39919	+	7.38394i	−0.134965	+	0.415379i
$317$	−25.6803	−	18.6579i	−1.44235	−	1.04793i	−0.987545	−	0.157340i	$-0.949708\pi$
$317$	−25.6803	−	18.6579i	−1.44235	−	1.04793i	−0.454807	−	0.890590i	$-0.650292\pi$
$318$	2.05573			0.115280
$319$	1.74671	+	0.118513i	0.0977970	+	0.00663545i
$320$		0			0
$321$	−0.236068	−	0.171513i	−0.0131760	−	0.00957295i
$322$	−1.71885	+	5.29007i	−0.0957876	+	0.294804i
$323$	−7.92705	−	24.3970i	−0.441073	−	1.35748i
$324$	−6.23607	+	4.53077i	−0.346448	+	0.251709i
$325$		0			0
$326$	−3.76393	−	11.5842i	−0.208465	−	0.641589i
$327$	−1.07953	+	3.32244i	−0.0596980	+	0.183731i
$328$	−3.00000	−	2.17963i	−0.165647	−	0.120350i
$329$	−4.41641			−0.243484
$330$		0			0
$331$	12.0000			0.659580			0.329790	−	0.944054i	$-0.393022\pi$
$331$	12.0000			0.659580			0.329790	+	0.944054i	$0.393022\pi$
$332$	3.04508	+	2.21238i	0.167121	+	0.121420i
$333$	−9.31559	+	28.6705i	−0.510491	+	1.57113i
$334$	−1.83688	−	5.65334i	−0.100510	−	0.309337i
$335$		0			0
$336$	−0.927051	+	0.673542i	−0.0505748	+	0.0367447i
$337$	0.399187	+	1.22857i	0.0217451	+	0.0669245i	0.961340	−	0.275363i	$-0.0887982\pi$
$337$	0.399187	+	1.22857i	0.0217451	+	0.0669245i	−0.939595	+	0.342288i	$0.888798\pi$
$338$	8.00000	−	24.6215i	0.435143	−	1.33923i
$339$	1.16312	+	0.845055i	0.0631720	+	0.0458971i
$340$		0			0
$341$	−8.42705	+	5.29007i	−0.456350	+	0.286473i
$342$	16.7082			0.903476
$343$	12.1353	+	8.81678i	0.655242	+	0.476061i
$344$	3.30902	−	10.1841i	0.178410	−	0.549090i
$345$		0			0
$346$	6.92705	−	5.03280i	0.372401	−	0.270565i
$347$	11.7812	−	8.55951i	0.632445	−	0.459498i	−0.224801	−	0.974405i	$-0.572173\pi$
$347$	11.7812	−	8.55951i	0.632445	−	0.459498i	0.857247	+	0.514906i	$0.172173\pi$
$348$	−0.0623059	−	0.191758i	−0.00333995	−	0.0102793i
$349$	−2.23607	+	6.88191i	−0.119694	+	0.368380i	−0.992897	−	0.118976i	$-0.962039\pi$
$349$	−2.23607	+	6.88191i	−0.119694	+	0.368380i	0.873203	+	0.487356i	$0.162039\pi$
$350$		0			0
$351$	−13.9443			−0.744290
$352$	−1.23607	+	3.07768i	−0.0658826	+	0.164041i
$353$	−23.5623			−1.25410			−0.627048	−	0.778981i	$-0.715737\pi$
$353$	−23.5623			−1.25410			−0.627048	+	0.778981i	$0.715737\pi$
$354$	2.07295	+	1.50609i	0.110176	+	0.0800475i
$355$		0			0
$356$	3.45492	+	10.6331i	0.183110	+	0.563555i
$357$	−4.06231	+	2.95144i	−0.215000	+	0.156207i
$358$	−8.61803	+	6.26137i	−0.455477	+	0.330924i
$359$	2.76393	+	8.50651i	0.145875	+	0.448956i	0.997122	−	0.0758078i	$-0.0241535\pi$
$359$	2.76393	+	8.50651i	0.145875	+	0.448956i	−0.851248	+	0.524764i	$0.824154\pi$
$360$		0			0
$361$	−12.3541	−	8.97578i	−0.650216	−	0.472409i
$362$	12.0000			0.630706
$363$	−3.70163	+	1.98787i	−0.194285	+	0.104336i
$364$	18.7082			0.980576
$365$		0			0
$366$	1.02786	−	3.16344i	0.0537273	−	0.165356i
$367$	3.00000	+	9.23305i	0.156599	+	0.481961i	0.998319	−	0.0579520i	$-0.0184570\pi$
$367$	3.00000	+	9.23305i	0.156599	+	0.481961i	−0.841721	+	0.539913i	$0.818457\pi$
$368$	1.50000	−	1.08981i	0.0781929	−	0.0568105i
$369$	8.56231	−	6.22088i	0.445736	−	0.323846i
$370$		0			0
$371$	4.98936	−	15.3557i	0.259035	−	0.797226i
$372$	0.927051	+	0.673542i	0.0480654	+	0.0349215i
$373$	29.9787			1.55224			0.776119	−	0.630586i	$-0.217185\pi$
$373$	29.9787			1.55224			0.776119	+	0.630586i	$0.217185\pi$
$374$	−5.41641	+	13.4863i	−0.280076	+	0.697360i
$375$		0			0
$376$	1.19098	+	0.865300i	0.0614203	+	0.0446244i
$377$	−1.01722	+	3.13068i	−0.0523895	+	0.161238i
$378$	−2.07295	−	6.37988i	−0.106621	−	0.328146i
$379$	6.54508	−	4.75528i	0.336198	−	0.244262i	−0.406858	−	0.913492i	$-0.633376\pi$
$379$	6.54508	−	4.75528i	0.336198	−	0.244262i	0.743056	+	0.669229i	$0.233376\pi$
$380$		0			0
$381$	0.253289	+	0.779543i	0.0129764	+	0.0399372i
$382$	7.42705	−	22.8581i	0.380001	−	1.16952i
$383$	−5.14590	−	3.73871i	−0.262943	−	0.191039i	0.448500	−	0.893783i	$-0.351958\pi$
$383$	−5.14590	−	3.73871i	−0.262943	−	0.191039i	−0.711444	+	0.702743i	$0.751958\pi$
$384$	0.381966			0.0194921
$385$		0			0
$386$	−1.85410			−0.0943713
$387$	24.7254	+	17.9641i	1.25686	+	0.913165i
$388$	−0.291796	+	0.898056i	−0.0148137	+	0.0455919i
$389$	−7.92705	−	24.3970i	−0.401917	−	1.23697i	−0.923442	−	0.383738i	$-0.874636\pi$
$389$	−7.92705	−	24.3970i	−0.401917	−	1.23697i	0.521524	−	0.853236i	$-0.325364\pi$
$390$		0			0
$391$	6.57295	−	4.77553i	0.332408	−	0.241509i
$392$	0.618034	+	1.90211i	0.0312154	+	0.0960712i
$393$	−2.42705	+	7.46969i	−0.122429	+	0.376796i
$394$	3.85410	+	2.80017i	0.194167	+	0.141070i
$395$		0			0
$396$	−7.26393	−	6.06961i	−0.365026	−	0.305009i
$397$	6.41641			0.322030			0.161015	−	0.986952i	$-0.448523\pi$
$397$	6.41641			0.322030			0.161015	+	0.986952i	$0.448523\pi$
$398$	3.19098	+	2.31838i	0.159950	+	0.116210i
$399$	−2.07295	+	6.37988i	−0.103777	+	0.319394i
$400$		0			0
$401$	12.4894	−	9.07405i	0.623689	−	0.453136i	−0.230519	−	0.973068i	$-0.574042\pi$
$401$	12.4894	−	9.07405i	0.623689	−	0.453136i	0.854208	+	0.519931i	$0.174042\pi$
$402$	0.0278640	−	0.0202444i	0.00138973	−	0.00100970i
$403$	−5.78115	−	17.7926i	−0.287980	−	0.886311i
$404$	4.07295	−	12.5352i	0.202637	−	0.623652i
$405$		0			0
$406$	−1.58359			−0.0785924
$407$	−34.9508	−	2.37139i	−1.73245	−	0.117545i
$408$	1.67376			0.0828636
$409$	16.4443	+	11.9475i	0.813117	+	0.590764i	0.914733	−	0.404060i	$-0.132401\pi$
$409$	16.4443	+	11.9475i	0.813117	+	0.590764i	−0.101616	+	0.994824i	$0.532401\pi$
$410$		0			0
$411$	−0.375388	−	1.15533i	−0.0185165	−	0.0569880i
$412$	−0.572949	+	0.416272i	−0.0282272	+	0.0205082i
$413$	16.2812	−	11.8290i	0.801143	−	0.582065i
$414$	1.63525	+	5.03280i	0.0803684	+	0.247348i
$415$		0			0
$416$	−5.04508	−	3.66547i	−0.247356	−	0.179714i
$417$	−3.09017			−0.151326
$418$	4.73607	+	18.8294i	0.231649	+	0.920975i
$419$	−23.9443			−1.16975			−0.584877	−	0.811122i	$-0.698857\pi$
$419$	−23.9443			−1.16975			−0.584877	+	0.811122i	$0.698857\pi$
$420$		0			0
$421$	−1.39261	+	4.28601i	−0.0678716	+	0.208887i	−0.979240	−	0.202704i	$-0.935027\pi$
$421$	−1.39261	+	4.28601i	−0.0678716	+	0.208887i	0.911368	+	0.411592i	$0.135027\pi$
$422$	−8.42705	−	25.9358i	−0.410222	−	1.26253i
$423$	−3.39919	+	2.46965i	−0.165274	+	0.120079i
$424$	−4.35410	+	3.16344i	−0.211454	+	0.153630i
$425$		0			0
$426$	−1.57295	+	4.84104i	−0.0762096	+	0.234549i
$427$	−21.1353	−	15.3557i	−1.02281	−	0.743113i
$428$	0.763932			0.0369260
$429$	−1.92705	−	7.66145i	−0.0930389	−	0.369898i
$430$		0			0
$431$	−19.6074	−	14.2456i	−0.944455	−	0.686187i	0.00503407	−	0.999987i	$-0.498398\pi$
$431$	−19.6074	−	14.2456i	−0.944455	−	0.686187i	−0.949489	+	0.313801i	$0.898398\pi$
$432$	−0.690983	+	2.12663i	−0.0332449	+	0.102317i
$433$	−3.56231	−	10.9637i	−0.171193	−	0.526879i	0.828246	−	0.560365i	$-0.189339\pi$
$433$	−3.56231	−	10.9637i	−0.171193	−	0.526879i	−0.999439	+	0.0334857i	$0.989339\pi$
$434$	7.28115	−	5.29007i	0.349507	−	0.253931i
$435$		0			0
$436$	−2.82624	−	8.69827i	−0.135352	−	0.416571i
$437$	3.35410	−	10.3229i	0.160448	−	0.493810i
$438$	−3.57295	−	2.59590i	−0.170722	−	0.124037i
$439$	−3.94427			−0.188250			−0.0941249	−	0.995560i	$-0.530005\pi$
$439$	−3.94427			−0.188250			−0.0941249	+	0.995560i	$0.530005\pi$
$440$		0			0
$441$	−5.70820			−0.271819
$442$	−22.1074	−	16.0620i	−1.05154	−	0.763990i
$443$	−5.37132	+	16.5312i	−0.255199	+	0.785423i	0.738591	+	0.674154i	$0.235491\pi$
$443$	−5.37132	+	16.5312i	−0.255199	+	0.785423i	−0.993790	+	0.111269i	$0.964509\pi$
$444$	1.24671	+	3.83698i	0.0591663	+	0.182095i
$445$		0			0
$446$	−16.7533	+	12.1720i	−0.793291	+	0.576360i
$447$	−2.50000	−	7.69421i	−0.118246	−	0.363924i
$448$	0.927051	−	2.85317i	0.0437990	−	0.134800i
$449$	21.1803	+	15.3884i	0.999562	+	0.726224i	0.961994	−	0.273070i	$-0.0880390\pi$
$449$	21.1803	+	15.3884i	0.999562	+	0.726224i	0.0375678	+	0.999294i	$0.488039\pi$
$450$		0			0
$451$	9.43769	+	7.88597i	0.444404	+	0.371336i
$452$	−3.76393			−0.177040
$453$	−6.20820	−	4.51052i	−0.291687	−	0.211923i
$454$	5.66312	−	17.4293i	0.265783	−	0.817997i
$455$		0			0
$456$	1.80902	−	1.31433i	0.0847150	−	0.0615490i
$457$	5.13525	−	3.73098i	0.240217	−	0.174528i	−0.461163	−	0.887315i	$-0.652568\pi$
$457$	5.13525	−	3.73098i	0.240217	−	0.174528i	0.701380	+	0.712788i	$0.252568\pi$
$458$	0.163119	+	0.502029i	0.00762205	+	0.0234583i
$459$	−3.02786	+	9.31881i	−0.141329	+	0.434965i
$460$		0			0
$461$	−7.47214			−0.348012			−0.174006	−	0.984745i	$-0.555671\pi$
$461$	−7.47214			−0.348012			−0.174006	+	0.984745i	$0.555671\pi$
$462$	3.21885	−	2.02063i	0.149754	−	0.0940080i
$463$	−4.41641			−0.205248			−0.102624	−	0.994720i	$-0.532724\pi$
$463$	−4.41641			−0.205248			−0.102624	+	0.994720i	$0.532724\pi$
$464$	0.427051	+	0.310271i	0.0198253	+	0.0144040i
$465$		0			0
$466$	4.75329	+	14.6291i	0.220192	+	0.677681i
$467$	−12.3262	+	8.95554i	−0.570390	+	0.414413i	−0.835247	−	0.549875i	$-0.814675\pi$
$467$	−12.3262	+	8.95554i	−0.570390	+	0.414413i	0.264857	+	0.964288i	$0.414675\pi$
$468$	14.3992	−	10.4616i	0.665603	−	0.483589i
$469$	−0.0835921	−	0.257270i	−0.00385993	−	0.0118796i
$470$		0			0
$471$	−6.09017	−	4.42477i	−0.280620	−	0.203883i
$472$	−6.70820			−0.308770
$473$	−13.2361	+	32.9565i	−0.608595	+	1.51534i
$474$	−2.96556			−0.136213
$475$		0			0
$476$	4.06231	−	12.5025i	0.186195	−	0.573051i
$477$	−4.74671	−	14.6089i	−0.217337	−	0.668894i
$478$	−12.6631	+	9.20029i	−0.579198	+	0.420812i
$479$	20.7533	−	15.0781i	0.948242	−	0.688938i	−0.00214844	−	0.999998i	$-0.500684\pi$
$479$	20.7533	−	15.0781i	0.948242	−	0.688938i	0.950390	+	0.311060i	$0.100684\pi$
$480$		0			0
$481$	20.3541	−	62.6435i	0.928067	−	2.85630i
$482$	14.5623	+	10.5801i	0.663295	+	0.481912i
$483$	−2.12461			−0.0966732
$484$	4.78115	−	9.90659i	0.217325	−	0.450300i
$485$		0			0
$486$	−7.80902	−	5.67358i	−0.354224	−	0.257359i
$487$	−2.69098	+	8.28199i	−0.121940	+	0.375293i	−0.993331	−	0.115296i	$-0.963218\pi$
$487$	−2.69098	+	8.28199i	−0.121940	+	0.375293i	0.871391	+	0.490589i	$0.163218\pi$
$488$	2.69098	+	8.28199i	0.121815	+	0.374908i
$489$	3.76393	−	2.73466i	0.170211	−	0.123665i
$490$		0			0
$491$	−8.52786	−	26.2461i	−0.384857	−	1.18447i	−0.936584	−	0.350443i	$-0.886031\pi$
$491$	−8.52786	−	26.2461i	−0.384857	−	1.18447i	0.551727	−	0.834025i	$-0.313969\pi$
$492$	0.437694	−	1.34708i	0.0197328	−	0.0607312i
$493$	1.87132	+	1.35960i	0.0842801	+	0.0612331i
$494$	−36.5066			−1.64251
$495$		0			0
$496$	−3.00000			−0.134704
$497$	32.3435	+	23.4989i	1.45080	+	1.05407i
$498$	−0.444272	+	1.36733i	−0.0199083	+	0.0612714i
$499$	7.46149	+	22.9641i	0.334022	+	1.02801i	0.967202	+	0.254010i	$0.0817496\pi$
$499$	7.46149	+	22.9641i	0.334022	+	1.02801i	−0.633179	+	0.774005i	$0.718250\pi$
$500$		0			0
$501$	1.83688	−	1.33457i	0.0820658	−	0.0596243i
$502$	−4.48278	−	13.7966i	−0.200076	−	0.615771i
$503$	−2.77051	+	8.52675i	−0.123531	+	0.380189i	−0.993631	−	0.112687i	$-0.964054\pi$
$503$	−2.77051	+	8.52675i	−0.123531	+	0.380189i	0.870100	+	0.492876i	$0.164054\pi$
$504$	6.92705	+	5.03280i	0.308555	+	0.224179i
$505$		0			0
$506$	−5.20820	+	3.26944i	−0.231533	+	0.145344i
$507$	9.88854			0.439166
$508$	−1.73607	−	1.26133i	−0.0770256	−	0.0559623i
$509$	−0.0623059	+	0.191758i	−0.00276166	+	0.00849952i	−0.952428	−	0.304764i	$-0.901422\pi$
$509$	−0.0623059	+	0.191758i	−0.00276166	+	0.00849952i	0.949666	+	0.313264i	$0.101422\pi$
$510$		0			0
$511$	−28.0623	+	20.3885i	−1.24140	+	0.901932i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$	4.04508	+	12.4495i	0.178595	+	0.549658i
$514$	9.80902	−	30.1891i	0.432657	−	1.33158i
$515$		0			0
$516$	4.09017			0.180060
$517$	−3.74671	−	3.13068i	−0.164780	−	0.137687i
$518$	31.6869			1.39224
$519$	2.64590	+	1.92236i	0.116142	+	0.0843821i
$520$		0			0
$521$	−5.46149	−	16.8087i	−0.239272	−	0.736405i	−0.996526	−	0.0832835i	$-0.973459\pi$
$521$	−5.46149	−	16.8087i	−0.239272	−	0.736405i	0.757254	−	0.653121i	$-0.226541\pi$
$522$	−1.21885	+	0.885544i	−0.0533475	+	0.0387592i
$523$	2.78115	−	2.02063i	0.121611	−	0.0883558i	−0.525317	−	0.850907i	$-0.676053\pi$
$523$	2.78115	−	2.02063i	0.121611	−	0.0883558i	0.646928	+	0.762551i	$0.276053\pi$
$524$	−6.35410	−	19.5559i	−0.277580	−	0.854304i
$525$		0			0
$526$	−8.92705	−	6.48588i	−0.389238	−	0.282798i
$527$	−13.1459			−0.572644
$528$	−1.26393	−	0.0857567i	−0.0550056	−	0.00373208i
$529$	−19.5623			−0.850535
$530$		0			0
$531$	5.91641	−	18.2088i	0.256750	−	0.790196i
$532$	−5.42705	−	16.7027i	−0.235293	−	0.724156i
$533$	−18.7082	+	13.5923i	−0.810342	+	0.588748i
$534$	−3.45492	+	2.51014i	−0.149509	+	0.108624i
$535$		0			0
$536$	−0.0278640	+	0.0857567i	−0.00120354	+	0.00370413i
$537$	−3.29180	−	2.39163i	−0.142051	−	0.103206i
$538$	−18.0902			−0.779923
$539$	−1.61803	−	6.43288i	−0.0696937	−	0.277084i
$540$		0			0
$541$	3.11803	+	2.26538i	0.134055	+	0.0973965i	0.652792	−	0.757537i	$-0.273598\pi$
$541$	3.11803	+	2.26538i	0.134055	+	0.0973965i	−0.518737	+	0.854934i	$0.673598\pi$
$542$	5.02786	−	15.4742i	0.215965	−	0.664673i
$543$	1.41641	+	4.35926i	0.0607839	+	0.187074i
$544$	−3.54508	+	2.57565i	−0.151994	+	0.110430i
$545$		0			0
$546$	2.20820	+	6.79615i	0.0945024	+	0.290848i
$547$	−0.656541	+	2.02063i	−0.0280717	+	0.0863957i	−0.964111	−	0.265500i	$-0.914463\pi$
$547$	−0.656541	+	2.02063i	−0.0280717	+	0.0863957i	0.936039	+	0.351896i	$0.114463\pi$
$548$	2.57295	+	1.86936i	0.109911	+	0.0798550i
$549$	−24.8541			−1.06075
$550$		0			0
$551$	3.09017			0.131646
$552$	0.572949	+	0.416272i	0.0243863	+	0.0177177i
$553$	−7.19756	+	22.1518i	−0.306071	+	0.941991i
$554$	1.94427	+	5.98385i	0.0826042	+	0.254230i
$555$		0			0
$556$	6.54508	−	4.75528i	0.277573	−	0.201669i
$557$	−0.291796	−	0.898056i	−0.0123638	−	0.0380519i	0.944684	−	0.327981i	$-0.106368\pi$
$557$	−0.291796	−	0.898056i	−0.0123638	−	0.0380519i	−0.957048	+	0.289929i	$0.906368\pi$
$558$	2.64590	−	8.14324i	0.112010	−	0.344731i
$559$	−54.0238	−	39.2506i	−2.28496	−	1.66012i
$560$		0			0
$561$	−5.53851	−	0.375783i	−0.233836	−	0.0158656i
$562$	18.1803			0.766891
$563$	28.9615	+	21.0418i	1.22058	+	0.886804i	0.996148	−	0.0876852i	$-0.0279470\pi$
$563$	28.9615	+	21.0418i	1.22058	+	0.886804i	0.224433	+	0.974489i	$0.427947\pi$
$564$	−0.173762	+	0.534785i	−0.00731670	+	0.0225185i
$565$		0			0
$566$	14.8541	−	10.7921i	0.624364	−	0.453627i
$567$	−18.7082	+	13.5923i	−0.785671	+	0.570823i
$568$	−4.11803	−	12.6740i	−0.172789	−	0.531789i
$569$	−12.8262	+	39.4751i	−0.537704	+	1.65488i	0.200029	+	0.979790i	$0.435896\pi$
$569$	−12.8262	+	39.4751i	−0.537704	+	1.65488i	−0.737733	+	0.675092i	$0.764104\pi$
$570$		0			0
$571$	18.7082			0.782914			0.391457	−	0.920196i	$-0.371971\pi$
$571$	18.7082			0.782914			0.391457	+	0.920196i	$0.371971\pi$
$572$	15.8713	+	13.2618i	0.663613	+	0.554503i
$573$	9.18034			0.383514
$574$	−9.00000	−	6.53888i	−0.375653	−	0.272928i
$575$		0			0
$576$	−0.881966	−	2.71441i	−0.0367486	−	0.113101i
$577$	23.2254	−	16.8743i	0.966887	−	0.702485i	0.0121471	−	0.999926i	$-0.496133\pi$
$577$	23.2254	−	16.8743i	0.966887	−	0.702485i	0.954740	+	0.297442i	$0.0961334\pi$
$578$	−1.78115	+	1.29408i	−0.0740862	+	0.0538268i
$579$	−0.218847	−	0.673542i	−0.00909497	−	0.0279914i
$580$		0			0
$581$	9.13525	+	6.63715i	0.378994	+	0.275355i
$582$	−0.360680			−0.0149507
$583$	15.1180	−	9.49032i	0.626125	−	0.393049i
$584$	11.5623			0.478452
$585$		0			0
$586$	−5.89919	+	18.1558i	−0.243693	+	0.750010i
$587$	6.84346	+	21.0620i	0.282460	+	0.869322i	0.987149	+	0.159805i	$0.0510866\pi$
$587$	6.84346	+	21.0620i	0.282460	+	0.869322i	−0.704689	+	0.709517i	$0.748913\pi$
$588$	−0.618034	+	0.449028i	−0.0254873	+	0.0185176i
$589$	−14.2082	+	10.3229i	−0.585439	+	0.425346i
$590$		0			0
$591$	−0.562306	+	1.73060i	−0.0231302	+	0.0711874i
$592$	−8.54508	−	6.20837i	−0.351201	−	0.255162i
$593$	38.3951			1.57670			0.788349	−	0.615228i	$-0.210936\pi$
$593$	38.3951			1.57670			0.788349	+	0.615228i	$0.210936\pi$
$594$	2.76393	−	6.88191i	0.113406	−	0.282368i
$595$		0			0
$596$	17.1353	+	12.4495i	0.701887	+	0.509951i
$597$	−0.465558	+	1.43284i	−0.0190540	+	0.0586423i
$598$	−3.57295	−	10.9964i	−0.146109	−	0.449676i
$599$	−7.23607	+	5.25731i	−0.295658	+	0.214808i	−0.725718	−	0.687992i	$-0.758492\pi$
$599$	−7.23607	+	5.25731i	−0.295658	+	0.214808i	0.430060	+	0.902800i	$0.358492\pi$
$600$		0			0
$601$	−6.02786	−	18.5519i	−0.245882	−	0.756746i	−0.995490	−	0.0948646i	$-0.969758\pi$
$601$	−6.02786	−	18.5519i	−0.245882	−	0.756746i	0.749608	−	0.661881i	$-0.230242\pi$
$602$	9.92705	−	30.5523i	0.404596	−	1.24522i
$603$	−0.208204	−	0.151269i	−0.00847872	−	0.00616015i
$604$	20.0902			0.817457
$605$		0			0
$606$	5.03444			0.204510
$607$	−16.2082	−	11.7759i	−0.657871	−	0.477971i	0.208072	−	0.978113i	$-0.433281\pi$
$607$	−16.2082	−	11.7759i	−0.657871	−	0.477971i	−0.865943	+	0.500142i	$0.833281\pi$
$608$	−1.80902	+	5.56758i	−0.0733653	+	0.225795i
$609$	−0.186918	−	0.575274i	−0.00757429	−	0.0233113i
$610$		0			0
$611$	7.42705	−	5.39607i	0.300466	−	0.218302i
$612$	−3.86475	−	11.8945i	−0.156223	−	0.480805i
$613$	6.39919	−	19.6947i	0.258461	−	0.795460i	−0.734667	−	0.678428i	$-0.762662\pi$
$613$	6.39919	−	19.6947i	0.258461	−	0.795460i	0.993128	−	0.117033i	$-0.0373383\pi$
$614$	7.73607	+	5.62058i	0.312202	+	0.226828i
$615$		0			0
$616$	−3.70820	+	9.23305i	−0.149408	+	0.372010i
$617$	−48.6312			−1.95782			−0.978909	−	0.204297i	$-0.934509\pi$
$617$	−48.6312			−1.95782			−0.978909	+	0.204297i	$0.934509\pi$
$618$	−0.218847	−	0.159002i	−0.00880332	−	0.00639599i
$619$	9.83688	−	30.2748i	0.395378	−	1.21685i	−0.533289	−	0.845933i	$-0.679044\pi$
$619$	9.83688	−	30.2748i	0.395378	−	1.21685i	0.928667	−	0.370914i	$-0.120956\pi$
$620$		0			0
$621$	−3.35410	+	2.43690i	−0.134595	+	0.0977893i
$622$	−2.04508	+	1.48584i	−0.0820004	+	0.0595768i
$623$	10.3647	+	31.8994i	0.415255	+	1.27802i
$624$	0.736068	−	2.26538i	0.0294663	−	0.0906880i
$625$		0			0
$626$	−19.9443			−0.797133
$627$	−6.28115	+	3.94298i	−0.250845	+	0.157468i
$628$	19.7082			0.786443
$629$	−37.4443	−	27.2049i	−1.49300	−	1.08473i
$630$		0			0
$631$	−6.12868	−	18.8621i	−0.243979	−	0.750889i	−0.995803	−	0.0915256i	$-0.970826\pi$
$631$	−6.12868	−	18.8621i	−0.243979	−	0.750889i	0.751824	−	0.659364i	$-0.229174\pi$
$632$	6.28115	−	4.56352i	0.249851	−	0.181527i
$633$	8.42705	−	6.12261i	0.334945	−	0.243352i
$634$	9.80902	+	30.1891i	0.389566	+	1.19896i
$635$		0			0
$636$	−1.66312	−	1.20833i	−0.0659470	−	0.0479133i
$637$	12.4721			0.494164
$638$	−1.34346	−	1.12257i	−0.0531880	−	0.0444430i
$639$	38.0344			1.50462
$640$		0			0
$641$	−8.52786	+	26.2461i	−0.336830	+	1.03666i	0.628983	+	0.777419i	$0.283471\pi$
$641$	−8.52786	+	26.2461i	−0.336830	+	1.03666i	−0.965813	+	0.259238i	$0.916529\pi$
$642$	0.0901699	+	0.277515i	0.00355872	+	0.0109526i
$643$	−11.7533	+	8.53926i	−0.463504	+	0.336756i	−0.794904	−	0.606735i	$-0.792479\pi$
$643$	−11.7533	+	8.53926i	−0.463504	+	0.336756i	0.331400	+	0.943490i	$0.392479\pi$
$644$	4.50000	−	3.26944i	0.177325	−	0.128834i
$645$		0			0
$646$	−7.92705	+	24.3970i	−0.311886	+	0.959885i
$647$	35.0344	+	25.4540i	1.37735	+	1.00070i	0.997123	+	0.0758058i	$0.0241529\pi$
$647$	35.0344	+	25.4540i	1.37735	+	1.00070i	0.380223	+	0.924895i	$0.375847\pi$
$648$	7.70820			0.302807
$649$	22.1976	+	1.50609i	0.871330	+	0.0591190i
$650$		0			0
$651$	2.78115	+	2.02063i	0.109002	+	0.0791946i
$652$	−3.76393	+	11.5842i	−0.147407	+	0.453672i
$653$	5.70820	+	17.5680i	0.223379	+	0.687491i	0.998452	+	0.0556188i	$0.0177132\pi$
$653$	5.70820	+	17.5680i	0.223379	+	0.687491i	−0.775073	+	0.631872i	$0.782287\pi$
$654$	2.82624	−	2.05338i	0.110515	−	0.0802936i
$655$		0			0
$656$	1.14590	+	3.52671i	0.0447398	+	0.137695i
$657$	−10.1976	+	31.3849i	−0.397845	+	1.22444i
$658$	3.57295	+	2.59590i	0.139288	+	0.101199i
$659$	45.4508			1.77051			0.885257	−	0.465102i	$-0.153983\pi$
$659$	45.4508			1.77051			0.885257	+	0.465102i	$0.153983\pi$
$660$		0			0
$661$	30.2918			1.17821			0.589107	−	0.808055i	$-0.299480\pi$
$661$	30.2918			1.17821			0.589107	+	0.808055i	$0.299480\pi$
$662$	−9.70820	−	7.05342i	−0.377320	−	0.274139i
$663$	3.22542	−	9.92684i	0.125265	−	0.385526i
$664$	−1.16312	−	3.57971i	−0.0451378	−	0.138920i
$665$		0			0
$666$	24.3885	−	17.7193i	0.945037	−	0.686609i
$667$	0.302439	+	0.930812i	0.0117105	+	0.0360412i
$668$	−1.83688	+	5.65334i	−0.0710711	+	0.218734i
$669$	−6.39919	−	4.64928i	−0.247407	−	0.179752i
$670$		0			0
$671$	−7.04508	−	28.0094i	−0.271972	−	1.08129i
$672$	1.14590			0.0442040
$673$	19.7533	+	14.3516i	0.761433	+	0.553214i	0.899350	−	0.437230i	$-0.144040\pi$
$673$	19.7533	+	14.3516i	0.761433	+	0.553214i	−0.137916	+	0.990444i	$0.544040\pi$
$674$	0.399187	−	1.22857i	0.0153761	−	0.0473228i
$675$		0			0
$676$	−20.9443	+	15.2169i	−0.805549	+	0.585266i
$677$	9.70820	−	7.05342i	0.373117	−	0.271085i	−0.385386	−	0.922756i	$-0.625932\pi$
$677$	9.70820	−	7.05342i	0.373117	−	0.271085i	0.758502	+	0.651671i	$0.225932\pi$
$678$	−0.444272	−	1.36733i	−0.0170622	−	0.0525119i
$679$	−0.875388	+	2.69417i	−0.0335943	+	0.103393i
$680$		0			0
$681$	7.00000			0.268241
$682$	9.92705	+	0.673542i	0.380126	+	0.0257913i
$683$	−33.8885			−1.29671			−0.648355	−	0.761339i	$-0.724543\pi$
$683$	−33.8885			−1.29671			−0.648355	+	0.761339i	$0.724543\pi$
$684$	−13.5172	−	9.82084i	−0.516844	−	0.375509i
$685$		0			0
$686$	−4.63525	−	14.2658i	−0.176975	−	0.544673i
$687$	−0.163119	+	0.118513i	−0.00622338	+	0.00452155i
$688$	−8.66312	+	6.29412i	−0.330278	+	0.239961i
$689$	10.3713	+	31.9196i	0.395116	+	1.21604i
$690$		0			0
$691$	0.0278640	+	0.0202444i	0.00106000	+	0.000770134i	0.588315	−	0.808632i	$-0.299791\pi$
$691$	0.0278640	+	0.0202444i	0.00106000	+	0.000770134i	−0.587255	+	0.809402i	$0.699791\pi$
$692$	−8.56231			−0.325490
$693$	−21.7918	−	18.2088i	−0.827802	−	0.691696i
$694$	−14.5623			−0.552778
$695$		0			0
$696$	−0.0623059	+	0.191758i	−0.00236170	+	0.00726856i
$697$	5.02129	+	15.4539i	0.190195	+	0.585359i
$698$	5.85410	−	4.25325i	0.221581	−	0.160988i
$699$	−4.75329	+	3.45347i	−0.179786	+	0.130622i
$700$		0			0
$701$	−4.07953	+	12.5555i	−0.154082	+	0.474214i	−0.998067	−	0.0621522i	$-0.980204\pi$
$701$	−4.07953	+	12.5555i	−0.154082	+	0.474214i	0.843985	+	0.536367i	$0.180204\pi$
$702$	11.2812	+	8.19624i	0.425780	+	0.309347i
$703$	−61.8328			−2.33207
$704$	2.80902	−	1.76336i	0.105869	−	0.0664590i
$705$		0			0
$706$	19.0623	+	13.8496i	0.717419	+	0.521236i
$707$	12.2188	−	37.6057i	0.459537	−	1.41431i
$708$	−0.791796	−	2.43690i	−0.0297575	−	0.0915842i
$709$	5.42705	−	3.94298i	0.203817	−	0.148082i	−0.481195	−	0.876614i	$-0.659797\pi$
$709$	5.42705	−	3.94298i	0.203817	−	0.148082i	0.685012	+	0.728532i	$0.259797\pi$
$710$		0			0
$711$	6.84752	+	21.0745i	0.256802	+	0.790356i
$712$	3.45492	−	10.6331i	0.129478	−	0.398494i
$713$	−4.50000	−	3.26944i	−0.168526	−	0.122442i
$714$	5.02129			0.187917
$715$		0			0
$716$	10.6525			0.398102
$717$	−4.83688	−	3.51420i	−0.180637	−	0.131240i
$718$	2.76393	−	8.50651i	0.103149	−	0.317460i
$719$	14.1074	+	43.4181i	0.526117	+	1.61922i	0.762097	+	0.647463i	$0.224170\pi$
$719$	14.1074	+	43.4181i	0.526117	+	1.61922i	−0.235980	+	0.971758i	$0.575830\pi$
$720$		0			0
$721$	−1.71885	+	1.24882i	−0.0640132	+	0.0465083i
$722$	4.71885	+	14.5231i	0.175617	+	0.540494i
$723$	−2.12461	+	6.53888i	−0.0790152	+	0.243184i
$724$	−9.70820	−	7.05342i	−0.360803	−	0.262138i
$725$		0			0
$726$	4.16312	+	0.567541i	0.154508	+	0.0210634i
$727$	−14.7639			−0.547564			−0.273782	−	0.961792i	$-0.588275\pi$
$727$	−14.7639			−0.547564			−0.273782	+	0.961792i	$0.588275\pi$
$728$	−15.1353	−	10.9964i	−0.560950	−	0.407554i
$729$	−6.00658	+	18.4863i	−0.222466	+	0.684679i
$730$		0			0
$731$	−37.9615	+	27.5806i	−1.40406	+	1.02011i
$732$	−2.69098	+	1.95511i	−0.0994616	+	0.0722631i
$733$	−11.3647	−	34.9771i	−0.419766	−	1.29191i	−0.907917	−	0.419149i	$-0.862328\pi$
$733$	−11.3647	−	34.9771i	−0.419766	−	1.29191i	0.488151	−	0.872759i	$-0.337672\pi$
$734$	3.00000	−	9.23305i	0.110732	−	0.340798i
$735$		0			0
$736$	−1.85410			−0.0683431
$737$	0.111456	−	0.277515i	0.00410554	−	0.0102224i
$738$	−10.5836			−0.389587
$739$	−17.5623	−	12.7598i	−0.646040	−	0.469375i	0.215880	−	0.976420i	$-0.430738\pi$
$739$	−17.5623	−	12.7598i	−0.646040	−	0.469375i	−0.861920	+	0.507044i	$0.830738\pi$
$740$		0			0
$741$	−4.30902	−	13.2618i	−0.158296	−	0.487184i
$742$	−13.0623	+	9.49032i	−0.479532	+	0.348401i
$743$	27.3156	−	19.8459i	1.00211	−	0.728077i	0.0395720	−	0.999217i	$-0.487401\pi$
$743$	27.3156	−	19.8459i	1.00211	−	0.728077i	0.962540	+	0.271140i	$0.0874006\pi$
$744$	−0.354102	−	1.08981i	−0.0129820	−	0.0399545i
$745$		0			0
$746$	−24.2533	−	17.6210i	−0.887976	−	0.645152i
$747$	10.7426			0.393053
$748$	12.3090	−	7.72696i	0.450062	−	0.282526i
$749$	2.29180			0.0837404
$750$		0			0
$751$	3.15654	−	9.71483i	0.115184	−	0.354499i	−0.876802	−	0.480853i	$-0.840327\pi$
$751$	3.15654	−	9.71483i	0.115184	−	0.354499i	0.991985	+	0.126353i	$0.0403272\pi$
$752$	−0.454915	−	1.40008i	−0.0165890	−	0.0510558i
$753$	4.48278	−	3.25693i	0.163362	−	0.118689i
$754$	2.66312	−	1.93487i	0.0969851	−	0.0704638i
$755$		0			0
$756$	−2.07295	+	6.37988i	−0.0753924	+	0.232034i
$757$	−12.4894	−	9.07405i	−0.453933	−	0.329802i	0.337213	−	0.941428i	$-0.390516\pi$
$757$	−12.4894	−	9.07405i	−0.453933	−	0.329802i	−0.791147	+	0.611626i	$0.790516\pi$
$758$	−8.09017			−0.293848
$759$	−1.80244	−	1.50609i	−0.0654244	−	0.0546674i
$760$		0			0
$761$	19.9894	+	14.5231i	0.724614	+	0.526463i	0.887855	−	0.460124i	$-0.152195\pi$
$761$	19.9894	+	14.5231i	0.724614	+	0.526463i	−0.163241	+	0.986586i	$0.552195\pi$
$762$	0.253289	−	0.779543i	0.00917569	−	0.0282399i
$763$	−8.47871	−	26.0948i	−0.306950	−	0.944695i
$764$	−19.4443	+	14.1271i	−0.703469	+	0.511100i
$765$		0			0
$766$	1.96556	+	6.04937i	0.0710185	+	0.218572i
$767$	−12.9271	+	39.7854i	−0.466769	+	1.43657i
$768$	−0.309017	−	0.224514i	−0.0111507	−	0.00810145i
$769$	12.2361			0.441244			0.220622	−	0.975359i	$-0.429191\pi$
$769$	12.2361			0.441244			0.220622	+	0.975359i	$0.429191\pi$
$770$		0			0
$771$	12.1246			0.436657
$772$	1.50000	+	1.08981i	0.0539862	+	0.0392233i
$773$	8.79837	−	27.0786i	0.316456	−	0.973950i	−0.658696	−	0.752409i	$-0.728892\pi$
$773$	8.79837	−	27.0786i	0.316456	−	0.973950i	0.975151	−	0.221540i	$-0.0711085\pi$
$774$	−9.44427	−	29.0665i	−0.339467	−	1.04477i
$775$		0			0
$776$	0.763932	−	0.555029i	0.0274236	−	0.0199244i
$777$	3.74013	+	11.5109i	0.134177	+	0.412953i
$778$	−7.92705	+	24.3970i	−0.284199	+	0.874673i
$779$	17.5623	+	12.7598i	0.629235	+	0.457166i
$780$		0			0
$781$	10.7812	+	42.8631i	0.385780	+	1.53376i
$782$	−8.12461			−0.290536
$783$	−0.954915	−	0.693786i	−0.0341259	−	0.0247939i
$784$	0.618034	−	1.90211i	0.0220726	−	0.0679326i
$785$		0			0
$786$	6.35410	−	4.61653i	0.226643	−	0.164666i
$787$	20.5623	−	14.9394i	0.732967	−	0.532532i	−0.157534	−	0.987514i	$-0.550354\pi$
$787$	20.5623	−	14.9394i	0.732967	−	0.532532i	0.890501	+	0.454982i	$0.150354\pi$
$788$	−1.47214	−	4.53077i	−0.0524427	−	0.161402i
$789$	1.30244	−	4.00850i	0.0463681	−	0.142706i
$790$		0			0
$791$	−11.2918			−0.401490
$792$	2.30902	+	9.18005i	0.0820473	+	0.326199i
$793$	54.3050			1.92843
$794$	−5.19098	−	3.77147i	−0.184221	−	0.133844i
$795$		0			0
$796$	−1.21885	−	3.75123i	−0.0432009	−	0.132959i
$797$	15.9894	−	11.6169i	0.566372	−	0.411493i	−0.267413	−	0.963582i	$-0.586169\pi$
$797$	15.9894	−	11.6169i	0.566372	−	0.411493i	0.833786	+	0.552088i	$0.186169\pi$
$798$	5.42705	−	3.94298i	0.192116	−	0.139580i
$799$	−1.99342	−	6.13512i	−0.0705222	−	0.217045i
$800$		0			0
$801$	25.8156	+	18.7561i	0.912149	+	0.662715i
$802$	−15.4377			−0.545124
$803$	−38.2599	−	2.59590i	−1.35016	−	0.0916073i
$804$	−0.0344419			−0.00121467
$805$		0			0
$806$	−5.78115	+	17.7926i	−0.203632	+	0.626716i
$807$	−2.13525	−	6.57164i	−0.0751645	−	0.231333i
$808$	−10.6631	+	7.74721i	−0.375127	+	0.272546i
$809$	−15.2254	+	11.0619i	−0.535297	+	0.388916i	−0.822336	−	0.569003i	$-0.807329\pi$
$809$	−15.2254	+	11.0619i	−0.535297	+	0.388916i	0.287038	+	0.957919i	$0.407329\pi$
$810$		0			0
$811$	−13.3647	+	41.1325i	−0.469300	+	1.44436i	0.384194	+	0.923252i	$0.374479\pi$
$811$	−13.3647	+	41.1325i	−0.469300	+	1.44436i	−0.853494	+	0.521103i	$0.825521\pi$
$812$	1.28115	+	0.930812i	0.0449597	+	0.0326651i
$813$	6.21478			0.217962
$814$	26.8820	+	22.4621i	0.942212	+	0.787296i
$815$		0			0
$816$	−1.35410	−	0.983813i	−0.0474031	−	0.0344403i
$817$	−19.3713	+	59.6188i	−0.677717	+	2.08580i
$818$	−6.28115	−	19.3314i	−0.219615	−	0.675907i
$819$	43.1976	−	31.3849i	1.50944	−	1.09668i
$820$		0			0
$821$	9.07295	+	27.9237i	0.316648	+	0.974543i	0.975071	+	0.221894i	$0.0712240\pi$
$821$	9.07295	+	27.9237i	0.316648	+	0.974543i	−0.658423	+	0.752648i	$0.728776\pi$
$822$	−0.375388	+	1.15533i	−0.0130932	+	0.0402966i
$823$	−32.7705	−	23.8092i	−1.14231	−	0.829935i	−0.154869	−	0.987935i	$-0.549496\pi$
$823$	−32.7705	−	23.8092i	−1.14231	−	0.829935i	−0.987439	+	0.158000i	$0.949496\pi$
$824$	0.708204			0.0246715
$825$		0			0
$826$	−20.1246			−0.700225
$827$	12.0451	+	8.75127i	0.418849	+	0.304311i	0.777174	−	0.629285i	$-0.216652\pi$
$827$	12.0451	+	8.75127i	0.418849	+	0.304311i	−0.358326	+	0.933597i	$0.616652\pi$
$828$	1.63525	−	5.03280i	0.0568290	−	0.174902i
$829$	1.50658	+	4.63677i	0.0523256	+	0.161042i	0.973805	−	0.227387i	$-0.0730181\pi$
$829$	1.50658	+	4.63677i	0.0523256	+	0.161042i	−0.921479	+	0.388428i	$0.873018\pi$
$830$		0			0
$831$	−1.94427	+	1.41260i	−0.0674460	+	0.0490024i
$832$	1.92705	+	5.93085i	0.0668085	+	0.205615i
$833$	2.70820	−	8.33499i	0.0938337	−	0.288790i
$834$	2.50000	+	1.81636i	0.0865679	+	0.0628953i
$835$		0			0
$836$	7.23607	−	18.0171i	0.250265	−	0.623134i
$837$	6.70820			0.231869
$838$	19.3713	+	14.0741i	0.669171	+	0.486181i
$839$	−15.1631	+	46.6673i	−0.523489	+	1.61113i	0.243796	+	0.969827i	$0.421607\pi$
$839$	−15.1631	+	46.6673i	−0.523489	+	1.61113i	−0.767285	+	0.641307i	$0.778393\pi$
$840$		0			0
$841$	23.2361	−	16.8820i	0.801244	−	0.582138i
$842$	3.64590	−	2.64890i	0.125646	−	0.0912871i
$843$	2.14590	+	6.60440i	0.0739087	+	0.227467i
$844$	−8.42705	+	25.9358i	−0.290071	+	0.892747i
$845$		0			0
$846$	4.20163			0.144455
$847$	14.3435	−	29.7198i	0.492847	−	1.02118i
$848$	5.38197			0.184817
$849$	5.67376	+	4.12223i	0.194723	+	0.141475i
$850$		0			0
$851$	−6.05166	−	18.6251i	−0.207448	−	0.638460i
$852$	4.11803	−	2.99193i	0.141082	−	0.102502i
$853$	−12.7082	+	9.23305i	−0.435121	+	0.316134i	−0.783693	−	0.621148i	$-0.786667\pi$
$853$	−12.7082	+	9.23305i	−0.435121	+	0.316134i	0.348573	+	0.937282i	$0.386667\pi$
$854$	8.07295	+	24.8460i	0.276251	+	0.850212i
$855$		0			0
$856$	−0.618034	−	0.449028i	−0.0211240	−	0.0153475i
$857$	41.3394			1.41213			0.706063	−	0.708149i	$-0.250469\pi$
$857$	41.3394			1.41213			0.706063	+	0.708149i	$0.250469\pi$
$858$	−2.94427	+	7.33094i	−0.100516	+	0.250274i
$859$	−6.30495			−0.215122			−0.107561	−	0.994198i	$-0.534304\pi$
$859$	−6.30495			−0.215122			−0.107561	+	0.994198i	$0.534304\pi$
$860$		0			0
$861$	1.31308	−	4.04125i	0.0447497	−	0.137725i
$862$	7.48936	+	23.0499i	0.255089	+	0.785082i
$863$	−11.4271	+	8.30224i	−0.388981	+	0.282611i	−0.765038	−	0.643985i	$-0.777280\pi$
$863$	−11.4271	+	8.30224i	−0.388981	+	0.282611i	0.376057	+	0.926597i	$0.377280\pi$
$864$	1.80902	−	1.31433i	0.0615440	−	0.0447143i
$865$		0			0
$866$	−3.56231	+	10.9637i	−0.121052	+	0.372560i
$867$	−0.680340	−	0.494296i	−0.0231056	−	0.0167872i
$868$	−9.00000			−0.305480
$869$	−21.8090	+	13.6906i	−0.739820	+	0.464421i
$870$		0			0
$871$	0.454915	+	0.330515i	0.0154142	+	0.0111991i
$872$	−2.82624	+	8.69827i	−0.0957085	+	0.294560i
$873$	0.832816	+	2.56314i	0.0281865	+	0.0867493i
$874$	−8.78115	+	6.37988i	−0.297027	+	0.215803i
$875$		0			0
$876$	1.36475	+	4.20025i	0.0461105	+	0.141913i
$877$	−6.79837	+	20.9232i	−0.229565	+	0.706528i	0.768231	+	0.640172i	$0.221137\pi$
$877$	−6.79837	+	20.9232i	−0.229565	+	0.706528i	−0.997796	+	0.0663553i	$0.978863\pi$
$878$	3.19098	+	2.31838i	0.107690	+	0.0782417i
$879$	−7.29180			−0.245946
$880$		0			0
$881$	−42.7984			−1.44191			−0.720957	−	0.692980i	$-0.756297\pi$
$881$	−42.7984			−1.44191			−0.720957	+	0.692980i	$0.756297\pi$
$882$	4.61803	+	3.35520i	0.155497	+	0.112975i
$883$	14.9787	−	46.0997i	0.504074	−	1.55138i	−0.298248	−	0.954488i	$-0.596402\pi$
$883$	14.9787	−	46.0997i	0.504074	−	1.55138i	0.802322	−	0.596891i	$-0.203598\pi$
$884$	8.44427	+	25.9888i	0.284012	+	0.874098i
$885$		0			0
$886$	14.0623	−	10.2169i	0.472432	−	0.343242i
$887$	−11.5344	−	35.4994i	−0.387289	−	1.19195i	−0.934806	−	0.355158i	$-0.884427\pi$
$887$	−11.5344	−	35.4994i	−0.387289	−	1.19195i	0.547518	−	0.836794i	$-0.315573\pi$
$888$	1.24671	−	3.83698i	0.0418369	−	0.128761i
$889$	−5.20820	−	3.78398i	−0.174678	−	0.126911i
$890$		0			0
$891$	−25.5066	−	1.73060i	−0.854503	−	0.0579773i
$892$	20.7082			0.693362
$893$	−6.97214	−	5.06555i	−0.233314	−	0.169512i
$894$	−2.50000	+	7.69421i	−0.0836125	+	0.257333i
$895$		0			0
$896$	−2.42705	+	1.76336i	−0.0810821	+	0.0589096i
$897$	3.57295	−	2.59590i	0.119297	−	0.0866746i
$898$	−8.09017	−	24.8990i	−0.269972	−	0.830890i
$899$	0.489357	−	1.50609i	0.0163210	−	0.0502308i
$900$		0			0
$901$	23.5836			0.785683
$902$	−3.00000	−	11.9272i	−0.0998891	−	0.397133i
$903$	12.2705			0.408337
$904$	3.04508	+	2.21238i	0.101278	+	0.0735828i
$905$		0			0
$906$	2.37132	+	7.29818i	0.0787819	+	0.242466i
$907$	−34.0344	+	24.7275i	−1.13010	+	0.821062i	−0.985709	−	0.168459i	$-0.946121\pi$
$907$	−34.0344	+	24.7275i	−1.13010	+	0.821062i	−0.144386	+	0.989521i	$0.546121\pi$
$908$	−14.8262	+	10.7719i	−0.492026	+	0.357478i
$909$	−11.6246	−	35.7769i	−0.385564	−	1.18664i
$910$		0			0
$911$	43.8328	+	31.8464i	1.45225	+	1.05512i	0.985300	+	0.170833i	$0.0546457\pi$
$911$	43.8328	+	31.8464i	1.45225	+	1.05512i	0.466946	+	0.884286i	$0.345354\pi$
$912$	−2.23607			−0.0740436
$913$	3.04508	+	12.1065i	0.100778	+	0.400665i
$914$	−6.34752			−0.209957
$915$		0			0
$916$	0.163119	−	0.502029i	0.00538960	−	0.0165875i
$917$	−19.0623	−	58.6677i	−0.629493	−	1.93738i
$918$	7.92705	−	5.75934i	0.261632	−	0.190087i
$919$	29.0066	−	21.0745i	0.956839	−	0.695184i	0.00442432	−	0.999990i	$-0.498592\pi$
$919$	29.0066	−	21.0745i	0.956839	−	0.695184i	0.952414	+	0.304806i	$0.0985917\pi$
$920$		0			0
$921$	−1.12868	+	3.47371i	−0.0371912	+	0.114463i
$922$	6.04508	+	4.39201i	0.199084	+	0.144643i
$923$	−83.1033			−2.73538
$924$	−3.79180	−	0.257270i	−0.124741	−	0.00846357i
$925$		0			0
$926$	3.57295	+	2.59590i	0.117414	+	0.0853065i
$927$	−0.624612	+	1.92236i	−0.0205149	+	0.0631385i
$928$	−0.163119	−	0.502029i	−0.00535464	−	0.0164799i
$929$	4.47214	−	3.24920i	0.146726	−	0.106603i	−0.512001	−	0.858985i	$-0.671095\pi$
$929$	4.47214	−	3.24920i	0.146726	−	0.106603i	0.658727	+	0.752382i	$0.271095\pi$
$930$		0			0
$931$	−3.61803	−	11.1352i	−0.118576	−	0.364940i
$932$	4.75329	−	14.6291i	0.155699	−	0.479193i
$933$	−0.781153	−	0.567541i	−0.0255738	−	0.0185805i
$934$	15.2361			0.498539
$935$		0			0
$936$	−17.7984			−0.581758
$937$	34.0795	+	24.7602i	1.11333	+	0.808881i	0.983185	−	0.182614i	$-0.0584558\pi$
$937$	34.0795	+	24.7602i	1.11333	+	0.808881i	0.130145	+	0.991495i	$0.458456\pi$
$938$	−0.0835921	+	0.257270i	−0.00272938	+	0.00840017i
$939$	−2.35410	−	7.24518i	−0.0768232	−	0.236438i
$940$		0			0
$941$	8.60739	−	6.25364i	0.280593	−	0.203863i	−0.438583	−	0.898691i	$-0.644519\pi$
$941$	8.60739	−	6.25364i	0.280593	−	0.203863i	0.719176	+	0.694828i	$0.244519\pi$
$942$	2.32624	+	7.15942i	0.0757929	+	0.233267i
$943$	−2.12461	+	6.53888i	−0.0691869	+	0.212935i
$944$	5.42705	+	3.94298i	0.176635	+	0.128333i
$945$		0			0
$946$	30.0795	−	18.8824i	0.977970	−	0.613919i
$947$	−43.3050			−1.40722			−0.703611	−	0.710585i	$-0.748430\pi$
$947$	−43.3050			−1.40722			−0.703611	+	0.710585i	$0.748430\pi$
$948$	2.39919	+	1.74311i	0.0779220	+	0.0566136i
$949$	22.2812	−	68.5743i	0.723277	−	2.22602i
$950$		0			0
$951$	−9.80902	+	7.12667i	−0.318079	+	0.231098i
$952$	−10.6353	+	7.72696i	−0.344691	+	0.250432i
$953$	5.18034	+	15.9434i	0.167808	+	0.516459i	0.999232	−	0.0391788i	$-0.0124742\pi$
$953$	5.18034	+	15.9434i	0.167808	+	0.516459i	−0.831425	+	0.555638i	$0.812474\pi$
$954$	−4.74671	+	14.6089i	−0.153680	+	0.472980i
$955$		0			0
$956$	15.6525			0.506237
$957$	0.249224	−	0.620541i	0.00805625	−	0.0200593i
$958$	−25.6525			−0.828794
$959$	7.71885	+	5.60807i	0.249255	+	0.181094i
$960$		0			0
$961$	−6.79837	−	20.9232i	−0.219302	−	0.674943i
$962$	−53.2877	+	38.7158i	−1.71807	+	1.24825i
$963$	1.76393	−	1.28157i	0.0568419	−	0.0412981i
$964$	−5.56231	−	17.1190i	−0.179150	−	0.551366i
$965$		0			0
$966$	1.71885	+	1.24882i	0.0553030	+	0.0401800i
$967$	−13.1803			−0.423851			−0.211926	−	0.977286i	$-0.567973\pi$
$967$	−13.1803			−0.423851			−0.211926	+	0.977286i	$0.567973\pi$
$968$	−9.69098	+	5.20431i	−0.311480	+	0.167273i
$969$	−9.79837			−0.314769
$970$		0			0
$971$	−12.7599	+	39.2708i	−0.409484	+	1.26026i	0.507609	+	0.861587i	$0.330529\pi$
$971$	−12.7599	+	39.2708i	−0.409484	+	1.26026i	−0.917093	+	0.398674i	$0.869471\pi$
$972$	2.98278	+	9.18005i	0.0956727	+	0.294450i
$973$	19.6353	−	14.2658i	0.629477	−	0.457342i
$974$	7.04508	−	5.11855i	0.225739	−	0.164009i
$975$		0			0
$976$	2.69098	−	8.28199i	0.0861363	−	0.265100i
$977$	7.30902	+	5.31031i	0.233836	+	0.169892i	0.698533	−	0.715578i	$-0.253837\pi$
$977$	7.30902	+	5.31031i	0.233836	+	0.169892i	−0.464697	+	0.885470i	$0.653837\pi$
$978$	−4.65248			−0.148770
$979$	−13.8197	+	34.4095i	−0.441678	+	1.09973i
$980$		0			0
$981$	−21.1180	−	15.3431i	−0.674247	−	0.489869i
$982$	−8.52786	+	26.2461i	−0.272135	+	0.837546i
$983$	6.23607	+	19.1926i	0.198900	+	0.612150i	0.999909	+	0.0134983i	$0.00429676\pi$
$983$	6.23607	+	19.1926i	0.198900	+	0.612150i	−0.801009	+	0.598652i	$0.795703\pi$
$984$	−1.14590	+	0.832544i	−0.0365299	+	0.0265405i
$985$		0			0
$986$	−0.714782	−	2.19987i	−0.0227633	−	0.0700582i
$987$	−0.521286	+	1.60435i	−0.0165927	+	0.0510672i
$988$	29.5344	+	21.4580i	0.939616	+	0.682671i
$989$	−19.8541			−0.631324
$990$		0			0
$991$	−28.0000			−0.889449			−0.444725	−	0.895667i	$-0.646698\pi$
$991$	−28.0000			−0.889449			−0.444725	+	0.895667i	$0.646698\pi$
$992$	2.42705	+	1.76336i	0.0770589	+	0.0559866i
$993$	1.41641	−	4.35926i	0.0449483	−	0.138337i
$994$	−12.3541	−	38.0220i	−0.391848	−	1.20599i
$995$		0			0
$996$	1.16312	−	0.845055i	0.0368548	−	0.0267766i
$997$	−0.190983	−	0.587785i	−0.00604849	−	0.0186153i	0.947987	−	0.318310i	$-0.103115\pi$
$997$	−0.190983	−	0.587785i	−0.00604849	−	0.0186153i	−0.954035	+	0.299695i	$0.903115\pi$
$998$	7.46149	−	22.9641i	0.236189	−	0.726916i
$999$	19.1074	+	13.8823i	0.604531	+	0.439218i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	550.2.h.a.301.1	yes	4
5.2	odd	4		550.2.ba.d.499.2		8
5.3	odd	4		550.2.ba.d.499.1		8
5.4	even	2		550.2.h.i.301.1	yes	4
11.3	even	5	inner	550.2.h.a.201.1	✓	4
11.5	even	5		6050.2.a.cx.1.1		2
11.6	odd	10		6050.2.a.cg.1.1		2
55.3	odd	20		550.2.ba.d.399.2		8
55.14	even	10		550.2.h.i.201.1	yes	4
55.39	odd	10		6050.2.a.cj.1.2		2
55.47	odd	20		550.2.ba.d.399.1		8
55.49	even	10		6050.2.a.br.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
550.2.h.a.201.1	✓	4	11.3	even	5	inner
550.2.h.a.301.1	yes	4	1.1	even	1	trivial
550.2.h.i.201.1	yes	4	55.14	even	10
550.2.h.i.301.1	yes	4	5.4	even	2
550.2.ba.d.399.1		8	55.47	odd	20
550.2.ba.d.399.2		8	55.3	odd	20
550.2.ba.d.499.1		8	5.3	odd	4
550.2.ba.d.499.2		8	5.2	odd	4
6050.2.a.br.1.2		2	55.49	even	10
6050.2.a.cg.1.1		2	11.6	odd	10
6050.2.a.cj.1.2		2	55.39	odd	10
6050.2.a.cx.1.1		2	11.5	even	5

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:	\( N \)	\(=\)	\( 550 = 2 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	550.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 - 0.587785i) q^{2} +(0.118034 - 0.363271i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-0.309017 + 0.224514i) q^{6} +(0.927051 + 2.85317i) q^{7} +(0.309017 - 0.951057i) q^{8} +(2.30902 + 1.67760i) q^{9} +(-1.23607 + 3.07768i) q^{11} +0.381966 q^{12} +(-5.04508 - 3.66547i) q^{13} +(0.927051 - 2.85317i) q^{14} +(-0.809017 + 0.587785i) q^{16} +(-3.54508 + 2.57565i) q^{17} +(-0.881966 - 2.71441i) q^{18} +(-1.80902 + 5.56758i) q^{19} +1.14590 q^{21} +(2.80902 - 1.76336i) q^{22} -1.85410 q^{23} +(-0.309017 - 0.224514i) q^{24} +(1.92705 + 5.93085i) q^{26} +(1.80902 - 1.31433i) q^{27} +(-2.42705 + 1.76336i) q^{28} +(-0.163119 - 0.502029i) q^{29} +(2.42705 + 1.76336i) q^{31} +1.00000 q^{32} +(0.972136 + 0.812299i) q^{33} +4.38197 q^{34} +(-0.881966 + 2.71441i) q^{36} +(3.26393 + 10.0453i) q^{37} +(4.73607 - 3.44095i) q^{38} +(-1.92705 + 1.40008i) q^{39} +(1.14590 - 3.52671i) q^{41} +(-0.927051 - 0.673542i) q^{42} +10.7082 q^{43} +(-3.30902 - 0.224514i) q^{44} +(1.50000 + 1.08981i) q^{46} +(-0.454915 + 1.40008i) q^{47} +(0.118034 + 0.363271i) q^{48} +(-1.61803 + 1.17557i) q^{49} +(0.517221 + 1.59184i) q^{51} +(1.92705 - 5.93085i) q^{52} +(-4.35410 - 3.16344i) q^{53} -2.23607 q^{54} +3.00000 q^{56} +(1.80902 + 1.31433i) q^{57} +(-0.163119 + 0.502029i) q^{58} +(-2.07295 - 6.37988i) q^{59} +(-7.04508 + 5.11855i) q^{61} +(-0.927051 - 2.85317i) q^{62} +(-2.64590 + 8.14324i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(-0.309017 - 1.22857i) q^{66} -0.0901699 q^{67} +(-3.54508 - 2.57565i) q^{68} +(-0.218847 + 0.673542i) q^{69} +(10.7812 - 7.83297i) q^{71} +(2.30902 - 1.67760i) q^{72} +(3.57295 + 10.9964i) q^{73} +(3.26393 - 10.0453i) q^{74} -5.85410 q^{76} +(-9.92705 - 0.673542i) q^{77} +2.38197 q^{78} +(6.28115 + 4.56352i) q^{79} +(2.38197 + 7.33094i) q^{81} +(-3.00000 + 2.17963i) q^{82} +(3.04508 - 2.21238i) q^{83} +(0.354102 + 1.08981i) q^{84} +(-8.66312 - 6.29412i) q^{86} -0.201626 q^{87} +(2.54508 + 2.12663i) q^{88} +11.1803 q^{89} +(5.78115 - 17.7926i) q^{91} +(-0.572949 - 1.76336i) q^{92} +(0.927051 - 0.673542i) q^{93} +(1.19098 - 0.865300i) q^{94} +(0.118034 - 0.363271i) q^{96} +(0.763932 + 0.555029i) q^{97} +2.00000 q^{98} +(-8.01722 + 5.03280i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} - 4 q^{3} - q^{4} + q^{6} - 3 q^{7} - q^{8} + 7 q^{9} + 4 q^{11} + 6 q^{12} - 9 q^{13} - 3 q^{14} - q^{16} - 3 q^{17} - 8 q^{18} - 5 q^{19} + 18 q^{21} + 9 q^{22} + 6 q^{23} + q^{24} + q^{26}+ \cdots - 3 q^{99}+O(q^{100}) \) 4 * q - q^2 - 4 * q^3 - q^4 + q^6 - 3 * q^7 - q^8 + 7 * q^9 + 4 * q^11 + 6 * q^12 - 9 * q^13 - 3 * q^14 - q^16 - 3 * q^17 - 8 * q^18 - 5 * q^19 + 18 * q^21 + 9 * q^22 + 6 * q^23 + q^24 + q^26 + 5 * q^27 - 3 * q^28 + 15 * q^29 + 3 * q^31 + 4 * q^32 - 14 * q^33 + 22 * q^34 - 8 * q^36 + 22 * q^37 + 10 * q^38 - q^39 + 18 * q^41 + 3 * q^42 + 16 * q^43 - 11 * q^44 + 6 * q^46 - 13 * q^47 - 4 * q^48 - 2 * q^49 - 27 * q^51 + q^52 - 4 * q^53 + 12 * q^56 + 5 * q^57 + 15 * q^58 - 15 * q^59 - 17 * q^61 + 3 * q^62 - 24 * q^63 - q^64 + q^66 + 22 * q^67 - 3 * q^68 - 21 * q^69 + 23 * q^71 + 7 * q^72 + 21 * q^73 + 22 * q^74 - 10 * q^76 - 33 * q^77 + 14 * q^78 + 5 * q^79 + 14 * q^81 - 12 * q^82 + q^83 - 12 * q^84 - 19 * q^86 - 50 * q^87 - q^88 + 3 * q^91 - 9 * q^92 - 3 * q^93 + 7 * q^94 - 4 * q^96 + 12 * q^97 + 8 * q^98 - 3 * q^99

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