LMFDB - Embedded newform 825.2.bx.d.724.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [825,2,Mod(49,825)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(825, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 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("825.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	825.bx (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:	$6.58765816676$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	$\Q(\zeta_{20})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 33)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			724.1
Root			$-0.951057 - 0.309017i$ of defining polynomial
Character	$\chi$	$=$	825.724
Dual form			825.2.bx.d.49.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.48990 - 0.809017i) q^{2} +(-0.587785 - 0.809017i) q^{3} +(3.92705 + 2.85317i) q^{4} +(0.809017 + 2.48990i) q^{6} +(-0.587785 + 0.809017i) q^{7} +(-4.39201 - 6.04508i) q^{8} +(-0.309017 + 0.951057i) q^{9} +(-3.30902 - 0.224514i) q^{11} -4.85410i q^{12} +(-0.224514 - 0.0729490i) q^{13} +(2.11803 - 1.53884i) q^{14} +(3.04508 + 9.37181i) q^{16} +(1.08981 - 0.354102i) q^{17} +(1.53884 - 2.11803i) q^{18} +(4.73607 - 3.44095i) q^{19} +1.00000 q^{21} +(8.05748 + 3.23607i) q^{22} -0.236068i q^{23} +(-2.30902 + 7.10642i) q^{24} +(0.500000 + 0.363271i) q^{26} +(0.951057 - 0.309017i) q^{27} +(-4.61653 + 1.50000i) q^{28} +(-4.85410 - 3.52671i) q^{29} +(-1.88197 + 5.79210i) q^{31} -10.8541i q^{32} +(1.76336 + 2.80902i) q^{33} -3.00000 q^{34} +(-3.92705 + 2.85317i) q^{36} +(-3.66547 + 5.04508i) q^{37} +(-14.5761 + 4.73607i) q^{38} +(0.0729490 + 0.224514i) q^{39} +(-0.190983 + 0.138757i) q^{41} +(-2.48990 - 0.809017i) q^{42} +6.70820i q^{43} +(-12.3541 - 10.3229i) q^{44} +(-0.190983 + 0.587785i) q^{46} +(5.93085 + 8.16312i) q^{47} +(5.79210 - 7.97214i) q^{48} +(1.85410 + 5.70634i) q^{49} +(-0.927051 - 0.673542i) q^{51} +(-0.673542 - 0.927051i) q^{52} +(0.363271 + 0.118034i) q^{53} -2.61803 q^{54} +7.47214 q^{56} +(-5.56758 - 1.80902i) q^{57} +(9.23305 + 12.7082i) q^{58} +(5.97214 + 4.33901i) q^{59} +(-3.57295 - 10.9964i) q^{61} +(9.37181 - 12.8992i) q^{62} +(-0.587785 - 0.809017i) q^{63} +(-2.69098 + 8.28199i) q^{64} +(-2.11803 - 8.42075i) q^{66} +1.85410i q^{67} +(5.29007 + 1.71885i) q^{68} +(-0.190983 + 0.138757i) q^{69} +(3.19098 + 9.82084i) q^{71} +(7.10642 - 2.30902i) q^{72} +(3.35520 - 4.61803i) q^{73} +(13.2082 - 9.59632i) q^{74} +28.4164 q^{76} +(2.12663 - 2.54508i) q^{77} -0.618034i q^{78} +(-3.39919 + 10.4616i) q^{79} +(-0.809017 - 0.587785i) q^{81} +(0.587785 - 0.190983i) q^{82} +(1.40008 - 0.454915i) q^{83} +(3.92705 + 2.85317i) q^{84} +(5.42705 - 16.7027i) q^{86} +6.00000i q^{87} +(13.1760 + 20.9894i) q^{88} +8.23607 q^{89} +(0.190983 - 0.138757i) q^{91} +(0.673542 - 0.927051i) q^{92} +(5.79210 - 1.88197i) q^{93} +(-8.16312 - 25.1235i) q^{94} +(-8.78115 + 6.37988i) q^{96} +(7.46969 + 2.42705i) q^{97} -15.7082i q^{98} +(1.23607 - 3.07768i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 18 q^{4} + 2 q^{6} + 2 q^{9} - 22 q^{11} + 8 q^{14} + 2 q^{16} + 20 q^{19} + 8 q^{21} - 14 q^{24} + 4 q^{26} - 12 q^{29} - 24 q^{31} - 24 q^{34} - 18 q^{36} + 14 q^{39} - 6 q^{41} - 72 q^{44} - 6 q^{46}+ \cdots - 8 q^{99}+O(q^{100}) $ 8 * q + 18 * q^4 + 2 * q^6 + 2 * q^9 - 22 * q^11 + 8 * q^14 + 2 * q^16 + 20 * q^19 + 8 * q^21 - 14 * q^24 + 4 * q^26 - 12 * q^29 - 24 * q^31 - 24 * q^34 - 18 * q^36 + 14 * q^39 - 6 * q^41 - 72 * q^44 - 6 * q^46 - 12 * q^49 + 6 * q^51 - 12 * q^54 + 24 * q^56 + 12 * q^59 - 42 * q^61 - 26 * q^64 - 8 * q^66 - 6 * q^69 + 30 * q^71 + 52 * q^74 + 120 * q^76 + 22 * q^79 - 2 * q^81 + 18 * q^84 + 30 * q^86 + 48 * q^89 + 6 * q^91 - 34 * q^94 - 30 * q^96 - 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/825\mathbb{Z}\right)^\times$.

$n$	$376$	$551$	$727$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−2.48990	−	0.809017i	−1.76062	−	0.572061i	−0.763359	−	0.645974i	$-0.776451\pi$
$2$	−2.48990	−	0.809017i	−1.76062	−	0.572061i	−0.997265	+	0.0739128i	$0.976451\pi$
$3$	−0.587785	−	0.809017i	−0.339358	−	0.467086i
$3$	−0.587785	−	0.809017i	−0.339358	−	0.467086i
$4$	3.92705	+	2.85317i	1.96353	+	1.42658i
$5$		0			0
$5$		0			0
$6$	0.809017	+	2.48990i	0.330280	+	1.01650i
$7$	−0.587785	+	0.809017i	−0.222162	+	0.305780i	−0.905520	−	0.424304i	$-0.860519\pi$
$7$	−0.587785	+	0.809017i	−0.222162	+	0.305780i	0.683358	+	0.730084i	$0.260519\pi$
$8$	−4.39201	−	6.04508i	−1.55281	−	2.13726i
$9$	−0.309017	+	0.951057i	−0.103006	+	0.317019i
$10$		0			0
$11$	−3.30902	−	0.224514i	−0.997706	−	0.0676935i
$11$	−3.30902	−	0.224514i	−0.997706	−	0.0676935i
$12$		−	4.85410i		−	1.40126i
$13$	−0.224514	−	0.0729490i	−0.0622690	−	0.0202324i	0.277717	−	0.960663i	$-0.410422\pi$
$13$	−0.224514	−	0.0729490i	−0.0622690	−	0.0202324i	−0.339986	+	0.940431i	$0.610422\pi$
$14$	2.11803	−	1.53884i	0.566068	−	0.411273i
$15$		0			0
$16$	3.04508	+	9.37181i	0.761271	+	2.34295i
$17$	1.08981	−	0.354102i	0.264319	−	0.0858823i	−0.173860	−	0.984770i	$-0.555624\pi$
$17$	1.08981	−	0.354102i	0.264319	−	0.0858823i	0.438178	+	0.898888i	$0.355624\pi$
$18$	1.53884	−	2.11803i	0.362708	−	0.499225i
$19$	4.73607	−	3.44095i	1.08653	−	0.789409i	0.107719	−	0.994181i	$-0.465645\pi$
$19$	4.73607	−	3.44095i	1.08653	−	0.789409i	0.978810	+	0.204772i	$0.0656454\pi$
$20$		0			0
$21$	1.00000			0.218218
$22$	8.05748	+	3.23607i	1.71786	+	0.689932i
$23$		−	0.236068i		−	0.0492236i	−0.999697	−	0.0246118i	$-0.992165\pi$
$23$		−	0.236068i		−	0.0492236i	0.999697	−	0.0246118i	$-0.00783497\pi$
$24$	−2.30902	+	7.10642i	−0.471326	+	1.45059i
$25$		0			0
$26$	0.500000	+	0.363271i	0.0980581	+	0.0712434i
$27$	0.951057	−	0.309017i	0.183031	−	0.0594703i
$28$	−4.61653	+	1.50000i	−0.872441	+	0.283473i
$29$	−4.85410	−	3.52671i	−0.901384	−	0.654894i	0.0374370	−	0.999299i	$-0.488081\pi$
$29$	−4.85410	−	3.52671i	−0.901384	−	0.654894i	−0.938821	+	0.344405i	$0.888081\pi$
$30$		0			0
$31$	−1.88197	+	5.79210i	−0.338011	+	1.04029i	0.627209	+	0.778851i	$0.284197\pi$
$31$	−1.88197	+	5.79210i	−0.338011	+	1.04029i	−0.965220	+	0.261440i	$0.915803\pi$
$32$		−	10.8541i		−	1.91875i
$33$	1.76336	+	2.80902i	0.306961	+	0.488987i
$34$	−3.00000			−0.514496
$35$		0			0
$36$	−3.92705	+	2.85317i	−0.654508	+	0.475528i
$37$	−3.66547	+	5.04508i	−0.602599	+	0.829407i	−0.995943	−	0.0899846i	$-0.971318\pi$
$37$	−3.66547	+	5.04508i	−0.602599	+	0.829407i	0.393344	+	0.919391i	$0.371318\pi$
$38$	−14.5761	+	4.73607i	−2.36456	+	0.768292i
$39$	0.0729490	+	0.224514i	0.0116812	+	0.0359510i
$40$		0			0
$41$	−0.190983	+	0.138757i	−0.0298265	+	0.0216702i	−0.602599	−	0.798044i	$-0.705868\pi$
$41$	−0.190983	+	0.138757i	−0.0298265	+	0.0216702i	0.572772	+	0.819715i	$0.305868\pi$
$42$	−2.48990	−	0.809017i	−0.384200	−	0.124834i
$43$			6.70820i			1.02299i	0.859286	+	0.511496i	$0.170908\pi$
$43$			6.70820i			1.02299i	−0.859286	+	0.511496i	$0.829092\pi$
$44$	−12.3541	−	10.3229i	−1.86245	−	1.55623i
$45$		0			0
$46$	−0.190983	+	0.587785i	−0.0281589	+	0.0866642i
$47$	5.93085	+	8.16312i	0.865104	+	1.19071i	0.980328	+	0.197374i	$0.0632413\pi$
$47$	5.93085	+	8.16312i	0.865104	+	1.19071i	−0.115224	+	0.993339i	$0.536759\pi$
$48$	5.79210	−	7.97214i	0.836017	−	1.15068i
$49$	1.85410	+	5.70634i	0.264872	+	0.815191i
$50$		0			0
$51$	−0.927051	−	0.673542i	−0.129813	−	0.0943147i
$52$	−0.673542	−	0.927051i	−0.0934035	−	0.128559i
$53$	0.363271	+	0.118034i	0.0498991	+	0.0162132i	0.333860	−	0.942623i	$-0.391649\pi$
$53$	0.363271	+	0.118034i	0.0498991	+	0.0162132i	−0.283961	+	0.958836i	$0.591649\pi$
$54$	−2.61803			−0.356269
$55$		0			0
$56$	7.47214			0.998506
$57$	−5.56758	−	1.80902i	−0.737444	−	0.239610i
$58$	9.23305	+	12.7082i	1.21236	+	1.66867i
$59$	5.97214	+	4.33901i	0.777506	+	0.564891i	0.904229	−	0.427047i	$-0.140446\pi$
$59$	5.97214	+	4.33901i	0.777506	+	0.564891i	−0.126724	+	0.991938i	$0.540446\pi$
$60$		0			0
$61$	−3.57295	−	10.9964i	−0.457469	−	1.40795i	−0.868212	−	0.496194i	$-0.834730\pi$
$61$	−3.57295	−	10.9964i	−0.457469	−	1.40795i	0.410742	−	0.911751i	$-0.365270\pi$
$62$	9.37181	−	12.8992i	1.19022	−	1.63820i
$63$	−0.587785	−	0.809017i	−0.0740540	−	0.101927i
$64$	−2.69098	+	8.28199i	−0.336373	+	1.03525i
$65$		0			0
$66$	−2.11803	−	8.42075i	−0.260712	−	1.03652i
$67$			1.85410i			0.226515i	0.993566	+	0.113257i	$0.0361284\pi$
$67$			1.85410i			0.226515i	−0.993566	+	0.113257i	$0.963872\pi$
$68$	5.29007	+	1.71885i	0.641515	+	0.208441i
$69$	−0.190983	+	0.138757i	−0.0229917	+	0.0167044i
$70$		0			0
$71$	3.19098	+	9.82084i	0.378700	+	1.16552i	0.940948	+	0.338550i	$0.109937\pi$
$71$	3.19098	+	9.82084i	0.378700	+	1.16552i	−0.562248	+	0.826968i	$0.690063\pi$
$72$	7.10642	−	2.30902i	0.837500	−	0.272120i
$73$	3.35520	−	4.61803i	0.392696	−	0.540500i	−0.566196	−	0.824271i	$-0.691585\pi$
$73$	3.35520	−	4.61803i	0.392696	−	0.540500i	0.958892	+	0.283771i	$0.0915854\pi$
$74$	13.2082	−	9.59632i	1.53542	−	1.11555i
$75$		0			0
$76$	28.4164			3.25959
$77$	2.12663	−	2.54508i	0.242352	−	0.290039i
$78$		−	0.618034i		−	0.0699786i
$79$	−3.39919	+	10.4616i	−0.382438	+	1.17702i	0.555883	+	0.831260i	$0.312380\pi$
$79$	−3.39919	+	10.4616i	−0.382438	+	1.17702i	−0.938322	+	0.345764i	$0.887620\pi$
$80$		0			0
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	0.587785	−	0.190983i	0.0649100	−	0.0210905i
$83$	1.40008	−	0.454915i	0.153679	−	0.0499334i	−0.231167	−	0.972914i	$-0.574254\pi$
$83$	1.40008	−	0.454915i	0.153679	−	0.0499334i	0.384846	+	0.922981i	$0.374254\pi$
$84$	3.92705	+	2.85317i	0.428476	+	0.311306i
$85$		0			0
$86$	5.42705	−	16.7027i	0.585214	−	1.80110i
$87$			6.00000i			0.643268i
$88$	13.1760	+	20.9894i	1.40457	+	2.23747i
$89$	8.23607			0.873021			0.436511	−	0.899699i	$-0.356214\pi$
$89$	8.23607			0.873021			0.436511	+	0.899699i	$0.356214\pi$
$90$		0			0
$91$	0.190983	−	0.138757i	0.0200205	−	0.0145457i
$92$	0.673542	−	0.927051i	0.0702216	−	0.0966517i
$93$	5.79210	−	1.88197i	0.600612	−	0.195151i
$94$	−8.16312	−	25.1235i	−0.841961	−	2.59129i
$95$		0			0
$96$	−8.78115	+	6.37988i	−0.896223	+	0.651144i
$97$	7.46969	+	2.42705i	0.758433	+	0.246430i	0.662606	−	0.748968i	$-0.269451\pi$
$97$	7.46969	+	2.42705i	0.758433	+	0.246430i	0.0958268	+	0.995398i	$0.469451\pi$
$98$		−	15.7082i		−	1.58677i
$99$	1.23607	−	3.07768i	0.124230	−	0.309319i
$100$		0			0
$101$	−3.16312	+	9.73508i	−0.314742	+	0.968677i	0.661118	+	0.750282i	$0.270082\pi$
$101$	−3.16312	+	9.73508i	−0.314742	+	0.968677i	−0.975860	+	0.218395i	$0.929918\pi$
$102$	1.76336	+	2.42705i	0.174598	+	0.240314i
$103$	6.43288	−	8.85410i	0.633851	−	0.872421i	−0.364418	−	0.931235i	$-0.618732\pi$
$103$	6.43288	−	8.85410i	0.633851	−	0.872421i	0.998269	+	0.0588148i	$0.0187321\pi$
$104$	0.545085	+	1.67760i	0.0534500	+	0.164502i
$105$		0			0
$106$	−0.809017	−	0.587785i	−0.0785787	−	0.0570908i
$107$	6.74315	+	9.28115i	0.651885	+	0.897243i	0.999179	−	0.0405134i	$-0.0128994\pi$
$107$	6.74315	+	9.28115i	0.651885	+	0.897243i	−0.347294	+	0.937756i	$0.612899\pi$
$108$	4.61653	+	1.50000i	0.444225	+	0.144338i
$109$	12.0000			1.14939			0.574696	−	0.818367i	$-0.305120\pi$
$109$	12.0000			1.14939			0.574696	+	0.818367i	$0.305120\pi$
$110$		0			0
$111$	6.23607			0.591901
$112$	−9.37181	−	3.04508i	−0.885553	−	0.287733i
$113$	7.91872	+	10.8992i	0.744931	+	1.02531i	0.998320	+	0.0579448i	$0.0184547\pi$
$113$	7.91872	+	10.8992i	0.744931	+	1.02531i	−0.253389	+	0.967364i	$0.581545\pi$
$114$	12.3992	+	9.00854i	1.16129	+	0.843727i
$115$		0			0
$116$	−9.00000	−	27.6992i	−0.835629	−	2.57180i
$117$	0.138757	−	0.190983i	0.0128281	−	0.0176564i
$118$	−11.3597	−	15.6353i	−1.04574	−	1.43934i
$119$	−0.354102	+	1.08981i	−0.0324605	+	0.0999031i
$120$		0			0
$121$	10.8992	+	1.48584i	0.990835	+	0.135076i
$122$			30.2705i			2.74056i
$123$	0.224514	+	0.0729490i	0.0202437	+	0.00657759i
$124$	−23.9164	+	17.3763i	−2.14776	+	1.56044i
$125$		0			0
$126$	0.809017	+	2.48990i	0.0720730	+	0.221818i
$127$	−7.33094	+	2.38197i	−0.650516	+	0.211365i	−0.615641	−	0.788026i	$-0.711103\pi$
$127$	−7.33094	+	2.38197i	−0.650516	+	0.211365i	−0.0348741	+	0.999392i	$0.511103\pi$
$128$	0.640786	−	0.881966i	0.0566380	−	0.0779555i
$129$	5.42705	−	3.94298i	0.477825	−	0.347160i
$130$		0			0
$131$	−11.7984			−1.03083			−0.515414	−	0.856941i	$-0.672362\pi$
$131$	−11.7984			−1.03083			−0.515414	+	0.856941i	$0.672362\pi$
$132$	−1.08981	+	16.0623i	−0.0948561	+	1.39804i
$133$			5.85410i			0.507615i
$134$	1.50000	−	4.61653i	0.129580	−	0.398807i
$135$		0			0
$136$	−6.92705	−	5.03280i	−0.593990	−	0.431559i
$137$	−9.28605	+	3.01722i	−0.793361	+	0.257779i	−0.677535	−	0.735491i	$-0.736952\pi$
$137$	−9.28605	+	3.01722i	−0.793361	+	0.257779i	−0.115826	+	0.993269i	$0.536952\pi$
$138$	0.587785	−	0.190983i	0.0500356	−	0.0162576i
$139$	11.7812	+	8.55951i	0.999264	+	0.726008i	0.961930	−	0.273295i	$-0.0881134\pi$
$139$	11.7812	+	8.55951i	0.999264	+	0.726008i	0.0373340	+	0.999303i	$0.488113\pi$
$140$		0			0
$141$	3.11803	−	9.59632i	0.262586	−	0.808156i
$142$		−	27.0344i		−	2.26868i
$143$	0.726543	+	0.291796i	0.0607565	+	0.0244012i
$144$	−9.85410			−0.821175
$145$		0			0
$146$	−12.0902	+	8.78402i	−1.00059	+	0.726971i
$147$	3.52671	−	4.85410i	0.290878	−	0.400360i
$148$	−28.7890	+	9.35410i	−2.36644	+	0.768902i
$149$	1.30902	+	4.02874i	0.107239	+	0.330047i	0.990249	−	0.139306i	$-0.0444871\pi$
$149$	1.30902	+	4.02874i	0.107239	+	0.330047i	−0.883011	+	0.469353i	$0.844487\pi$
$150$		0			0
$151$	−0.854102	+	0.620541i	−0.0695058	+	0.0504989i	−0.621996	−	0.783021i	$-0.713678\pi$
$151$	−0.854102	+	0.620541i	−0.0695058	+	0.0504989i	0.552490	+	0.833520i	$0.313678\pi$
$152$	−41.6017	−	13.5172i	−3.37435	−	1.09639i
$153$			1.14590i			0.0926404i
$154$	−7.35410	+	4.61653i	−0.592610	+	0.372010i
$155$		0			0
$156$	−0.354102	+	1.08981i	−0.0283508	+	0.0872549i
$157$	−9.23305	−	12.7082i	−0.736878	−	1.01423i	−0.998792	−	0.0491340i	$-0.984354\pi$
$157$	−9.23305	−	12.7082i	−0.736878	−	1.01423i	0.261915	−	0.965091i	$-0.415646\pi$
$158$	16.9273	−	23.2984i	1.34666	−	1.85352i
$159$	−0.118034	−	0.363271i	−0.00936070	−	0.0288093i
$160$		0			0
$161$	0.190983	+	0.138757i	0.0150516	+	0.0109356i
$162$	1.53884	+	2.11803i	0.120903	+	0.166408i
$163$	4.89404	+	1.59017i	0.383331	+	0.124552i	0.494342	−	0.869267i	$-0.335409\pi$
$163$	4.89404	+	1.59017i	0.383331	+	0.124552i	−0.111011	+	0.993819i	$0.535409\pi$
$164$	−1.14590			−0.0894796
$165$		0			0
$166$	−3.85410			−0.299136
$167$	11.4454	+	3.71885i	0.885674	+	0.287773i	0.716311	−	0.697781i	$-0.245829\pi$
$167$	11.4454	+	3.71885i	0.885674	+	0.287773i	0.169363	+	0.985554i	$0.445829\pi$
$168$	−4.39201	−	6.04508i	−0.338851	−	0.466388i
$169$	−10.4721	−	7.60845i	−0.805549	−	0.585266i
$170$		0			0
$171$	1.80902	+	5.56758i	0.138339	+	0.425764i
$172$	−19.1396	+	26.3435i	−1.45938	+	2.00867i
$173$	−10.6004	−	14.5902i	−0.805932	−	1.10927i	−0.991938	−	0.126722i	$-0.959555\pi$
$173$	−10.6004	−	14.5902i	−0.805932	−	1.10927i	0.186006	−	0.982549i	$-0.440445\pi$
$174$	4.85410	−	14.9394i	0.367989	−	1.13255i
$175$		0			0
$176$	−7.97214	−	31.6951i	−0.600922	−	2.38911i
$177$		−	7.38197i		−	0.554863i
$178$	−20.5070	−	6.66312i	−1.53706	−	0.499422i
$179$	−6.89919	+	5.01255i	−0.515669	+	0.374656i	−0.814970	−	0.579503i	$-0.803247\pi$
$179$	−6.89919	+	5.01255i	−0.515669	+	0.374656i	0.299301	+	0.954159i	$0.403247\pi$
$180$		0			0
$181$	0.781153	+	2.40414i	0.0580626	+	0.178698i	0.975881	−	0.218301i	$-0.0700515\pi$
$181$	0.781153	+	2.40414i	0.0580626	+	0.178698i	−0.917819	+	0.396999i	$0.870051\pi$
$182$	−0.587785	+	0.190983i	−0.0435695	+	0.0141566i
$183$	−6.79615	+	9.35410i	−0.502386	+	0.691475i
$184$	−1.42705	+	1.03681i	−0.105204	+	0.0764349i
$185$		0			0
$186$	−15.9443			−1.16909
$187$	−3.68571	+	0.927051i	−0.269526	+	0.0677927i
$188$			48.9787i			3.57214i
$189$	−0.309017	+	0.951057i	−0.0224777	+	0.0691792i
$190$		0			0
$191$	0.663119	+	0.481784i	0.0479816	+	0.0348607i	0.611518	−	0.791231i	$-0.290559\pi$
$191$	0.663119	+	0.481784i	0.0479816	+	0.0348607i	−0.563536	+	0.826092i	$0.690559\pi$
$192$	8.28199	−	2.69098i	0.597701	−	0.194205i
$193$	−2.99193	+	0.972136i	−0.215364	+	0.0699759i	−0.414712	−	0.909953i	$-0.636118\pi$
$193$	−2.99193	+	0.972136i	−0.215364	+	0.0699759i	0.199348	+	0.979929i	$0.436118\pi$
$194$	−16.6353	−	12.0862i	−1.19434	−	0.867740i
$195$		0			0
$196$	−9.00000	+	27.6992i	−0.642857	+	1.97851i
$197$			13.0344i			0.928666i	0.885661	+	0.464333i	$0.153706\pi$
$197$			13.0344i			0.928666i	−0.885661	+	0.464333i	$0.846294\pi$
$198$	−5.56758	+	6.66312i	−0.395671	+	0.473527i
$199$	−6.70820			−0.475532			−0.237766	−	0.971322i	$-0.576415\pi$
$199$	−6.70820			−0.475532			−0.237766	+	0.971322i	$0.576415\pi$
$200$		0			0
$201$	1.50000	−	1.08981i	0.105802	−	0.0768695i
$202$	15.7517	−	21.6803i	1.10828	−	1.52542i
$203$	5.70634	−	1.85410i	0.400506	−	0.130132i
$204$	−1.71885	−	5.29007i	−0.120343	−	0.370379i
$205$		0			0
$206$	−23.1803	+	16.8415i	−1.61505	+	1.17340i
$207$	0.224514	+	0.0729490i	0.0156048	+	0.00507031i
$208$		−	2.32624i		−	0.161296i
$209$	−16.4443	+	10.3229i	−1.13747	+	0.714047i
$210$		0			0
$211$	1.11803	−	3.44095i	0.0769686	−	0.236885i	−0.905168	−	0.425054i	$-0.860255\pi$
$211$	1.11803	−	3.44095i	0.0769686	−	0.236885i	0.982137	+	0.188169i	$0.0602552\pi$
$212$	1.08981	+	1.50000i	0.0748487	+	0.103020i
$213$	6.06961	−	8.35410i	0.415883	−	0.572414i
$214$	−9.28115	−	28.5645i	−0.634447	−	1.95263i
$215$		0			0
$216$	−6.04508	−	4.39201i	−0.411316	−	0.298839i
$217$	−3.57971	−	4.92705i	−0.243007	−	0.334470i
$218$	−29.8788	−	9.70820i	−2.02365	−	0.657523i
$219$	−5.70820			−0.385725
$220$		0			0
$221$	−0.270510			−0.0181965
$222$	−15.5272	−	5.04508i	−1.04212	−	0.338604i
$223$	4.22050	+	5.80902i	0.282625	+	0.389001i	0.926601	−	0.376045i	$-0.122716\pi$
$223$	4.22050	+	5.80902i	0.282625	+	0.389001i	−0.643976	+	0.765046i	$0.722716\pi$
$224$	8.78115	+	6.37988i	0.586715	+	0.426274i
$225$		0			0
$226$	−10.8992	−	33.5442i	−0.725003	−	2.23133i
$227$	7.74721	−	10.6631i	0.514200	−	0.707736i	−0.470420	−	0.882443i	$-0.655898\pi$
$227$	7.74721	−	10.6631i	0.514200	−	0.707736i	0.984621	+	0.174706i	$0.0558976\pi$
$228$	−16.7027	−	22.9894i	−1.10617	−	1.52251i
$229$	−0.145898	+	0.449028i	−0.00964121	+	0.0296726i	−0.955761	−	0.294143i	$-0.904966\pi$
$229$	−0.145898	+	0.449028i	−0.00964121	+	0.0296726i	0.946120	+	0.323816i	$0.104966\pi$
$230$		0			0
$231$	−3.30902	−	0.224514i	−0.217717	−	0.0147719i
$232$			44.8328i			2.94342i
$233$	3.94298	+	1.28115i	0.258313	+	0.0839311i	0.435311	−	0.900280i	$-0.356638\pi$
$233$	3.94298	+	1.28115i	0.258313	+	0.0839311i	−0.176997	+	0.984211i	$0.556638\pi$
$234$	−0.500000	+	0.363271i	−0.0326860	+	0.0237478i
$235$		0			0
$236$	11.0729	+	34.0790i	0.720788	+	2.21836i
$237$	10.4616	−	3.39919i	0.679555	−	0.220801i
$238$	1.76336	−	2.42705i	0.114301	−	0.157322i
$239$	0.309017	−	0.224514i	0.0199886	−	0.0145226i	−0.577746	−	0.816217i	$-0.696068\pi$
$239$	0.309017	−	0.224514i	0.0199886	−	0.0145226i	0.597735	+	0.801694i	$0.296068\pi$
$240$		0			0
$241$	8.29180			0.534122			0.267061	−	0.963680i	$-0.413948\pi$
$241$	8.29180			0.534122			0.267061	+	0.963680i	$0.413948\pi$
$242$	−25.9358	−	12.5172i	−1.66722	−	0.804637i
$243$			1.00000i			0.0641500i
$244$	17.3435	−	53.3777i	1.11030	−	3.41716i
$245$		0			0
$246$	−0.500000	−	0.363271i	−0.0318788	−	0.0231613i
$247$	−1.31433	+	0.427051i	−0.0836287	+	0.0271726i
$248$	43.2793	−	14.0623i	2.74824	−	0.892957i
$249$	−1.19098	−	0.865300i	−0.0754755	−	0.0548361i
$250$		0			0
$251$	−6.79180	+	20.9030i	−0.428694	+	1.31939i	0.470718	+	0.882284i	$0.343995\pi$
$251$	−6.79180	+	20.9030i	−0.428694	+	1.31939i	−0.899412	+	0.437102i	$0.856005\pi$
$252$		−	4.85410i		−	0.305780i
$253$	−0.0530006	+	0.781153i	−0.00333212	+	0.0491107i
$254$	20.1803			1.26623
$255$		0			0
$256$	11.7812	−	8.55951i	0.736322	−	0.534969i
$257$	17.4823	−	24.0623i	1.09052	−	1.50097i	0.243125	−	0.969995i	$-0.421828\pi$
$257$	17.4823	−	24.0623i	1.09052	−	1.50097i	0.847390	−	0.530970i	$-0.178172\pi$
$258$	−16.7027	+	5.42705i	−1.03987	+	0.337873i
$259$	−1.92705	−	5.93085i	−0.119741	−	0.368525i
$260$		0			0
$261$	4.85410	−	3.52671i	0.300461	−	0.218298i
$262$	29.3768	+	9.54508i	1.81490	+	0.589697i
$263$			15.2705i			0.941620i	0.882235	+	0.470810i	$0.156038\pi$
$263$			15.2705i			0.941620i	−0.882235	+	0.470810i	$0.843962\pi$
$264$	9.23607	−	22.9969i	0.568441	−	1.41536i
$265$		0			0
$266$	4.73607	−	14.5761i	0.290387	−	0.893719i
$267$	−4.84104	−	6.66312i	−0.296267	−	0.407776i
$268$	−5.29007	+	7.28115i	−0.323142	+	0.444767i
$269$	7.85410	+	24.1724i	0.478873	+	1.47382i	0.840662	+	0.541560i	$0.182166\pi$
$269$	7.85410	+	24.1724i	0.478873	+	1.47382i	−0.361789	+	0.932260i	$0.617834\pi$
$270$		0			0
$271$	−15.0623	−	10.9434i	−0.914970	−	0.664765i	0.0272970	−	0.999627i	$-0.491310\pi$
$271$	−15.0623	−	10.9434i	−0.914970	−	0.664765i	−0.942267	+	0.334863i	$0.891310\pi$
$272$	6.63715	+	9.13525i	0.402436	+	0.553906i
$273$	−0.224514	−	0.0729490i	−0.0135882	−	0.00441508i
$274$	25.5623			1.54428
$275$		0			0
$276$	−1.14590			−0.0689750
$277$	−27.7849	−	9.02786i	−1.66943	−	0.542432i	−0.686617	−	0.727019i	$-0.740905\pi$
$277$	−27.7849	−	9.02786i	−1.66943	−	0.542432i	−0.982816	+	0.184587i	$0.940905\pi$
$278$	−22.4091	−	30.8435i	−1.34401	−	1.84987i
$279$	−4.92705	−	3.57971i	−0.294975	−	0.214312i
$280$		0			0
$281$	7.65248	+	23.5519i	0.456508	+	1.40499i	0.869355	+	0.494188i	$0.164535\pi$
$281$	7.65248	+	23.5519i	0.456508	+	1.40499i	−0.412847	+	0.910801i	$0.635465\pi$
$282$	−15.5272	+	21.3713i	−0.924630	+	1.27264i
$283$	−3.35520	−	4.61803i	−0.199446	−	0.274514i	0.697566	−	0.716521i	$-0.254267\pi$
$283$	−3.35520	−	4.61803i	−0.199446	−	0.274514i	−0.897011	+	0.442007i	$0.854267\pi$
$284$	−15.4894	+	47.6713i	−0.919124	+	2.82877i
$285$		0			0
$286$	−1.57295	−	1.31433i	−0.0930104	−	0.0777178i
$287$		−	0.236068i		−	0.0139347i
$288$	10.3229	+	3.35410i	0.608281	+	0.197642i
$289$	−12.6910	+	9.22054i	−0.746528	+	0.542385i
$290$		0			0
$291$	−2.42705	−	7.46969i	−0.142276	−	0.437881i
$292$	26.3521	−	8.56231i	1.54214	−	0.501071i
$293$	12.7270	−	17.5172i	0.743520	−	1.02337i	−0.254889	−	0.966970i	$-0.582039\pi$
$293$	12.7270	−	17.5172i	0.743520	−	1.02337i	0.998408	−	0.0563966i	$-0.0179611\pi$
$294$	−12.7082	+	9.23305i	−0.741158	+	0.538482i
$295$		0			0
$296$	46.5967			2.70838
$297$	−3.21644	+	0.809017i	−0.186637	+	0.0469439i
$298$		−	11.0902i		−	0.642436i
$299$	−0.0172209	+	0.0530006i	−0.000995912	+	0.00306510i
$300$		0			0
$301$	−5.42705	−	3.94298i	−0.312810	−	0.227270i
$302$	2.62866	−	0.854102i	0.151262	−	0.0491480i
$303$	9.73508	−	3.16312i	0.559266	−	0.181716i
$304$	46.6697	+	33.9075i	2.67669	+	1.94473i
$305$		0			0
$306$	0.927051	−	2.85317i	0.0529960	−	0.163105i
$307$			27.9787i			1.59683i	0.602108	+	0.798415i	$0.294328\pi$
$307$			27.9787i			1.59683i	−0.602108	+	0.798415i	$0.705672\pi$
$308$	15.6129	−	3.92705i	0.889629	−	0.223764i
$309$	−10.9443			−0.622598
$310$		0			0
$311$	−9.42705	+	6.84915i	−0.534559	+	0.388380i	−0.822060	−	0.569400i	$-0.807175\pi$
$311$	−9.42705	+	6.84915i	−0.534559	+	0.388380i	0.287501	+	0.957780i	$0.407175\pi$
$312$	1.03681	−	1.42705i	0.0586980	−	0.0807909i
$313$	−2.40414	+	0.781153i	−0.135890	+	0.0441534i	−0.376172	−	0.926550i	$-0.622760\pi$
$313$	−2.40414	+	0.781153i	−0.135890	+	0.0441534i	0.240282	+	0.970703i	$0.422760\pi$
$314$	12.7082	+	39.1118i	0.717165	+	2.20721i
$315$		0			0
$316$	−43.1976	+	31.3849i	−2.43005	+	1.76554i
$317$	−6.48588	−	2.10739i	−0.364283	−	0.118363i	0.121155	−	0.992634i	$-0.461340\pi$
$317$	−6.48588	−	2.10739i	−0.364283	−	0.118363i	−0.485439	+	0.874271i	$0.661340\pi$
$318$			1.00000i			0.0560772i
$319$	15.2705	+	12.7598i	0.854984	+	0.714410i
$320$		0			0
$321$	3.54508	−	10.9106i	0.197867	−	0.608973i
$322$	−0.363271	−	0.500000i	−0.0202443	−	0.0278639i
$323$	3.94298	−	5.42705i	0.219393	−	0.301969i
$324$	−1.50000	−	4.61653i	−0.0833333	−	0.256474i
$325$		0			0
$326$	−10.8992	−	7.91872i	−0.603650	−	0.438577i
$327$	−7.05342	−	9.70820i	−0.390055	−	0.536865i
$328$	1.67760	+	0.545085i	0.0926299	+	0.0300973i
$329$	−10.0902			−0.556289
$330$		0			0
$331$	16.7082			0.918366			0.459183	−	0.888342i	$-0.348142\pi$
$331$	16.7082			0.918366			0.459183	+	0.888342i	$0.348142\pi$
$332$	6.79615	+	2.20820i	0.372987	+	0.121191i
$333$	−3.66547	−	5.04508i	−0.200866	−	0.276469i
$334$	−25.4894	−	18.5191i	−1.39472	−	1.01332i
$335$		0			0
$336$	3.04508	+	9.37181i	0.166123	+	0.511274i
$337$	−10.6861	+	14.7082i	−0.582111	+	0.801207i	−0.993925	−	0.110061i	$-0.964895\pi$
$337$	−10.6861	+	14.7082i	−0.582111	+	0.801207i	0.411814	+	0.911268i	$0.364895\pi$
$338$	19.9192	+	27.4164i	1.08346	+	1.49126i
$339$	4.16312	−	12.8128i	0.226110	−	0.695894i
$340$		0			0
$341$	7.52786	−	18.7436i	0.407657	−	1.01502i
$342$		−	15.3262i		−	0.828748i
$343$	−12.3637	−	4.01722i	−0.667579	−	0.216910i
$344$	40.5517	−	29.4625i	2.18640	−	1.58851i
$345$		0			0
$346$	14.5902	+	44.9039i	0.784372	+	2.41405i
$347$	1.45309	−	0.472136i	0.0780057	−	0.0253456i	−0.269754	−	0.962929i	$-0.586942\pi$
$347$	1.45309	−	0.472136i	0.0780057	−	0.0253456i	0.347760	+	0.937584i	$0.386942\pi$
$348$	−17.1190	+	23.5623i	−0.917676	+	1.26307i
$349$	10.2812	−	7.46969i	0.550337	−	0.399844i	−0.277572	−	0.960705i	$-0.589530\pi$
$349$	10.2812	−	7.46969i	0.550337	−	0.399844i	0.827910	+	0.560861i	$0.189530\pi$
$350$		0			0
$351$	−0.236068			−0.0126004
$352$	−2.43690	+	35.9164i	−0.129887	+	1.91435i
$353$			12.0000i			0.638696i	0.947638	+	0.319348i	$0.103464\pi$
$353$			12.0000i			0.638696i	−0.947638	+	0.319348i	$0.896536\pi$
$354$	−5.97214	+	18.3803i	−0.317415	+	0.976904i
$355$		0			0
$356$	32.3435	+	23.4989i	1.71420	+	1.24544i
$357$	1.08981	−	0.354102i	0.0576791	−	0.0187411i
$358$	21.2335	−	6.89919i	1.12223	−	0.364633i
$359$	−7.85410	−	5.70634i	−0.414524	−	0.301169i	0.360907	−	0.932602i	$-0.382467\pi$
$359$	−7.85410	−	5.70634i	−0.414524	−	0.301169i	−0.775431	+	0.631433i	$0.782467\pi$
$360$		0			0
$361$	4.71885	−	14.5231i	0.248360	−	0.764375i
$362$		−	6.61803i		−	0.347836i
$363$	−5.20431	−	9.69098i	−0.273155	−	0.508645i
$364$	1.14590			0.0600614
$365$		0			0
$366$	24.4894	−	17.7926i	1.28008	−	0.930032i
$367$	13.0170	−	17.9164i	0.679484	−	0.935229i	−0.320444	−	0.947267i	$-0.603832\pi$
$367$	13.0170	−	17.9164i	0.679484	−	0.935229i	0.999928	+	0.0120386i	$0.00383209\pi$
$368$	2.21238	−	0.718847i	0.115328	−	0.0374725i
$369$	−0.0729490	−	0.224514i	−0.00379757	−	0.0116877i
$370$		0			0
$371$	−0.309017	+	0.224514i	−0.0160434	+	0.0116562i
$372$	28.1154	+	9.13525i	1.45772	+	0.473641i
$373$		−	0.888544i		−	0.0460071i	−0.999735	−	0.0230035i	$-0.992677\pi$
$373$		−	0.888544i		−	0.0460071i	0.999735	−	0.0230035i	$-0.00732290\pi$
$374$	9.92705	+	0.673542i	0.513316	+	0.0348280i
$375$		0			0
$376$	23.2984	−	71.7050i	1.20152	−	3.69790i
$377$	0.832544	+	1.14590i	0.0428782	+	0.0590168i
$378$	1.53884	−	2.11803i	0.0791495	−	0.108940i
$379$	7.69098	+	23.6704i	0.395059	+	1.21587i	0.928915	+	0.370292i	$0.120742\pi$
$379$	7.69098	+	23.6704i	0.395059	+	1.21587i	−0.533856	+	0.845575i	$0.679258\pi$
$380$		0			0
$381$	6.23607	+	4.53077i	0.319483	+	0.232118i
$382$	−1.26133	−	1.73607i	−0.0645351	−	0.0888250i
$383$	12.0862	+	3.92705i	0.617577	+	0.200663i	0.601064	−	0.799201i	$-0.294744\pi$
$383$	12.0862	+	3.92705i	0.617577	+	0.200663i	0.0165128	+	0.999864i	$0.494744\pi$
$384$	−1.09017			−0.0556325
$385$		0			0
$386$	8.23607			0.419205
$387$	−6.37988	−	2.07295i	−0.324308	−	0.105374i
$388$	22.4091	+	30.8435i	1.13765	+	1.56584i
$389$	−29.7254	−	21.5968i	−1.50714	−	1.09500i	−0.967427	−	0.253151i	$-0.918533\pi$
$389$	−29.7254	−	21.5968i	−1.50714	−	1.09500i	−0.539712	−	0.841850i	$-0.681467\pi$
$390$		0			0
$391$	−0.0835921	−	0.257270i	−0.00422744	−	0.0130107i
$392$	26.3521	−	36.2705i	1.33098	−	1.83194i
$393$	6.93491	+	9.54508i	0.349820	+	0.481486i
$394$	10.5451	−	32.4544i	0.531254	−	1.63503i
$395$		0			0
$396$	13.6353	−	8.55951i	0.685197	−	0.430131i
$397$		−	18.7082i		−	0.938938i	−0.882949	−	0.469469i	$-0.844445\pi$
$397$		−	18.7082i		−	0.938938i	0.882949	−	0.469469i	$-0.155555\pi$
$398$	16.7027	+	5.42705i	0.837233	+	0.272033i
$399$	4.73607	−	3.44095i	0.237100	−	0.172263i
$400$		0			0
$401$	−9.79180	−	30.1360i	−0.488979	−	1.50492i	−0.826134	−	0.563473i	$-0.809465\pi$
$401$	−9.79180	−	30.1360i	−0.488979	−	1.50492i	0.337155	−	0.941449i	$-0.390535\pi$
$402$	−4.61653	+	1.50000i	−0.230251	+	0.0748132i
$403$	0.845055	−	1.16312i	0.0420952	−	0.0579391i
$404$	−40.1976	+	29.2052i	−1.99990	+	1.45301i
$405$		0			0
$406$	−15.7082			−0.779585
$407$	13.2618	−	15.8713i	0.657363	−	0.786712i
$408$			8.56231i			0.423897i
$409$	2.00000	−	6.15537i	0.0988936	−	0.304363i	−0.889355	−	0.457217i	$-0.848846\pi$
$409$	2.00000	−	6.15537i	0.0988936	−	0.304363i	0.988249	+	0.152854i	$0.0488463\pi$
$410$		0			0
$411$	7.89919	+	5.73910i	0.389638	+	0.283089i
$412$	50.5245	−	16.4164i	2.48916	−	0.808778i
$413$	−7.02067	+	2.28115i	−0.345464	+	0.112248i
$414$	−0.500000	−	0.363271i	−0.0245737	−	0.0178538i
$415$		0			0
$416$	−0.791796	+	2.43690i	−0.0388210	+	0.119479i
$417$		−	14.5623i		−	0.713119i
$418$	49.2959	−	12.3992i	2.41114	−	0.606464i
$419$	−31.4508			−1.53647			−0.768237	−	0.640165i	$-0.778866\pi$
$419$	−31.4508			−1.53647			−0.768237	+	0.640165i	$0.778866\pi$
$420$		0			0
$421$	−8.50000	+	6.17561i	−0.414265	+	0.300981i	−0.775326	−	0.631561i	$-0.782414\pi$
$421$	−8.50000	+	6.17561i	−0.414265	+	0.300981i	0.361061	+	0.932542i	$0.382414\pi$
$422$	−5.56758	+	7.66312i	−0.271026	+	0.373035i
$423$	−9.59632	+	3.11803i	−0.466589	+	0.151604i
$424$	−0.881966	−	2.71441i	−0.0428321	−	0.131824i
$425$		0			0
$426$	−21.8713	+	15.8904i	−1.05967	+	0.769895i
$427$	10.9964	+	3.57295i	0.532153	+	0.172907i
$428$			55.6869i			2.69173i
$429$	−0.190983	−	0.759299i	−0.00922075	−	0.0366593i
$430$		0			0
$431$	−1.82624	+	5.62058i	−0.0879668	+	0.270734i	−0.985357	−	0.170504i	$-0.945460\pi$
$431$	−1.82624	+	5.62058i	−0.0879668	+	0.270734i	0.897390	+	0.441238i	$0.145460\pi$
$432$	5.79210	+	7.97214i	0.278672	+	0.383560i
$433$	−20.7517	+	28.5623i	−0.997264	+	1.37262i	−0.0702758	+	0.997528i	$0.522388\pi$
$433$	−20.7517	+	28.5623i	−0.997264	+	1.37262i	−0.926989	+	0.375089i	$0.877612\pi$
$434$	4.92705	+	15.1639i	0.236506	+	0.727891i
$435$		0			0
$436$	47.1246	+	34.2380i	2.25686	+	1.63970i
$437$	−0.812299	−	1.11803i	−0.0388575	−	0.0534828i
$438$	14.2128	+	4.61803i	0.679116	+	0.220658i
$439$	−23.2918			−1.11166			−0.555828	−	0.831297i	$-0.687599\pi$
$439$	−23.2918			−1.11166			−0.555828	+	0.831297i	$0.687599\pi$
$440$		0			0
$441$	−6.00000			−0.285714
$442$	0.673542	+	0.218847i	0.0320371	+	0.0104095i
$443$	−18.5721	−	25.5623i	−0.882387	−	1.21450i	−0.975754	−	0.218870i	$-0.929763\pi$
$443$	−18.5721	−	25.5623i	−0.882387	−	1.21450i	0.0933668	−	0.995632i	$-0.470237\pi$
$444$	24.4894	+	17.7926i	1.16221	+	0.844397i
$445$		0			0
$446$	−5.80902	−	17.8783i	−0.275065	−	0.846563i
$447$	2.48990	−	3.42705i	0.117768	−	0.162094i
$448$	−5.11855	−	7.04508i	−0.241829	−	0.332849i
$449$	2.79837	−	8.61251i	0.132063	−	0.406449i	−0.863058	−	0.505104i	$-0.831454\pi$
$449$	2.79837	−	8.61251i	0.132063	−	0.406449i	0.995122	+	0.0986549i	$0.0314540\pi$
$450$		0			0
$451$	0.663119	−	0.416272i	0.0312251	−	0.0196015i
$452$			65.3951i			3.07593i
$453$	1.00406	+	0.326238i	0.0471747	+	0.0153280i
$454$	−27.9164	+	20.2825i	−1.31018	+	0.951903i
$455$		0			0
$456$	13.5172	+	41.6017i	0.633002	+	1.94818i
$457$	−22.8051	+	7.40983i	−1.06678	+	0.346617i	−0.789232	−	0.614095i	$-0.789521\pi$
$457$	−22.8051	+	7.40983i	−1.06678	+	0.346617i	−0.277546	+	0.960712i	$0.589521\pi$
$458$	0.726543	−	1.00000i	0.0339491	−	0.0467269i
$459$	0.927051	−	0.673542i	0.0432710	−	0.0314382i
$460$		0			0
$461$	9.27051			0.431771			0.215885	−	0.976419i	$-0.430736\pi$
$461$	9.27051			0.431771			0.215885	+	0.976419i	$0.430736\pi$
$462$	8.05748	+	3.23607i	0.374868	+	0.150556i
$463$		−	1.72949i		−	0.0803762i	−0.999192	−	0.0401881i	$-0.987204\pi$
$463$		−	1.72949i		−	0.0803762i	0.999192	−	0.0401881i	$-0.0127957\pi$
$464$	18.2705	−	56.2308i	0.848187	−	2.61045i
$465$		0			0
$466$	−8.78115	−	6.37988i	−0.406779	−	0.295542i
$467$	−19.8662	+	6.45492i	−0.919297	+	0.298698i	−0.730179	−	0.683256i	$-0.760563\pi$
$467$	−19.8662	+	6.45492i	−0.919297	+	0.298698i	−0.189119	+	0.981954i	$0.560563\pi$
$468$	1.08981	−	0.354102i	0.0503767	−	0.0163684i
$469$	−1.50000	−	1.08981i	−0.0692636	−	0.0503229i
$470$		0			0
$471$	−4.85410	+	14.9394i	−0.223665	+	0.688371i
$472$		−	55.1591i		−	2.53890i
$473$	1.50609	−	22.1976i	0.0692499	−	1.02064i
$474$	−28.7984			−1.32275
$475$		0			0
$476$	−4.50000	+	3.26944i	−0.206257	+	0.149855i
$477$	−0.224514	+	0.309017i	−0.0102798	+	0.0141489i
$478$	−0.951057	+	0.309017i	−0.0435003	+	0.0141341i
$479$	8.77051	+	26.9929i	0.400735	+	1.23333i	0.924405	+	0.381414i	$0.124563\pi$
$479$	8.77051	+	26.9929i	0.400735	+	1.23333i	−0.523670	+	0.851921i	$0.675437\pi$
$480$		0			0
$481$	1.19098	−	0.865300i	0.0543042	−	0.0394543i
$482$	−20.6457	−	6.70820i	−0.940387	−	0.305550i
$483$		−	0.236068i		−	0.0107415i
$484$	38.5623	+	36.9322i	1.75283	+	1.67874i
$485$		0			0
$486$	0.809017	−	2.48990i	0.0366978	−	0.112944i
$487$	7.46969	+	10.2812i	0.338484	+	0.465884i	0.943998	−	0.329951i	$-0.107032\pi$
$487$	7.46969	+	10.2812i	0.338484	+	0.465884i	−0.605514	+	0.795835i	$0.707032\pi$
$488$	−50.7818	+	69.8951i	−2.29878	+	3.16400i
$489$	−1.59017	−	4.89404i	−0.0719100	−	0.221316i
$490$		0			0
$491$	14.4894	+	10.5271i	0.653896	+	0.475083i	0.864596	−	0.502468i	$-0.167574\pi$
$491$	14.4894	+	10.5271i	0.653896	+	0.475083i	−0.210700	+	0.977551i	$0.567574\pi$
$492$	0.673542	+	0.927051i	0.0303656	+	0.0417947i
$493$	−6.53888	−	2.12461i	−0.294496	−	0.0956877i
$494$	3.61803			0.162783
$495$		0			0
$496$	−60.0132			−2.69467
$497$	−9.82084	−	3.19098i	−0.440525	−	0.143135i
$498$	2.26538	+	3.11803i	0.101514	+	0.139722i
$499$	−14.6803	−	10.6659i	−0.657182	−	0.477471i	0.208528	−	0.978016i	$-0.433133\pi$
$499$	−14.6803	−	10.6659i	−0.657182	−	0.477471i	−0.865710	+	0.500546i	$0.833133\pi$
$500$		0			0
$501$	−3.71885	−	11.4454i	−0.166146	−	0.511344i
$502$	33.8218	−	46.5517i	1.50954	−	2.07770i
$503$	5.08580	+	7.00000i	0.226765	+	0.312115i	0.907205	−	0.420689i	$-0.138212\pi$
$503$	5.08580	+	7.00000i	0.226765	+	0.312115i	−0.680441	+	0.732803i	$0.738212\pi$
$504$	−2.30902	+	7.10642i	−0.102852	+	0.316545i
$505$		0			0
$506$	0.763932	−	1.90211i	0.0339609	−	0.0845592i
$507$			12.9443i			0.574875i
$508$	−35.5851	−	11.5623i	−1.57883	−	0.512994i
$509$	31.3435	−	22.7724i	1.38927	−	1.00937i	0.393330	−	0.919397i	$-0.371323\pi$
$509$	31.3435	−	22.7724i	1.38927	−	1.00937i	0.995945	−	0.0899695i	$-0.0286770\pi$
$510$		0			0
$511$	1.76393	+	5.42882i	0.0780318	+	0.240157i
$512$	−38.3323	+	12.4549i	−1.69406	+	0.550435i
$513$	3.44095	−	4.73607i	0.151922	−	0.209103i
$514$	−62.9959	+	45.7692i	−2.77863	+	2.01879i
$515$		0			0
$516$	32.5623			1.43348
$517$	−17.7926	−	28.3435i	−0.782516	−	1.24654i
$518$			16.3262i			0.717334i
$519$	−5.57295	+	17.1518i	−0.244625	+	0.752879i
$520$		0			0
$521$	−7.23607	−	5.25731i	−0.317018	−	0.230327i	0.417884	−	0.908500i	$-0.362772\pi$
$521$	−7.23607	−	5.25731i	−0.317018	−	0.230327i	−0.734902	+	0.678173i	$0.762772\pi$
$522$	−14.9394	+	4.85410i	−0.653879	+	0.212458i
$523$	17.3763	−	5.64590i	0.759812	−	0.246878i	0.0966140	−	0.995322i	$-0.469199\pi$
$523$	17.3763	−	5.64590i	0.759812	−	0.246878i	0.663198	+	0.748444i	$0.269199\pi$
$524$	−46.3328	−	33.6628i	−2.02406	−	1.47056i
$525$		0			0
$526$	12.3541	−	38.0220i	0.538664	−	1.65784i
$527$			6.97871i			0.303998i
$528$	−20.9560	+	25.0795i	−0.911993	+	1.09145i
$529$	22.9443			0.997577
$530$		0			0
$531$	−5.97214	+	4.33901i	−0.259169	+	0.188297i
$532$	−16.7027	+	22.9894i	−0.724156	+	0.996715i
$533$	0.0530006	−	0.0172209i	0.00229571	−	0.000745921i
$534$	6.66312	+	20.5070i	0.288341	+	0.887423i
$535$		0			0
$536$	11.2082	−	8.14324i	0.484121	−	0.351734i
$537$	8.11048	+	2.63525i	0.349993	+	0.113720i
$538$		−	66.5410i		−	2.86879i
$539$	−4.85410	−	19.2986i	−0.209081	−	0.831251i
$540$		0			0
$541$	−2.31559	+	7.12667i	−0.0995552	+	0.306399i	−0.988414	−	0.151782i	$-0.951499\pi$
$541$	−2.31559	+	7.12667i	−0.0995552	+	0.306399i	0.888859	+	0.458181i	$0.151499\pi$
$542$	28.6502	+	39.4336i	1.23063	+	1.69382i
$543$	1.48584	−	2.04508i	0.0637635	−	0.0877630i
$544$	−3.84346	−	11.8290i	−0.164787	−	0.507162i
$545$		0			0
$546$	0.500000	+	0.363271i	0.0213980	+	0.0155466i
$547$	18.0701	+	24.8713i	0.772621	+	1.06342i	0.996058	+	0.0887027i	$0.0282721\pi$
$547$	18.0701	+	24.8713i	0.772621	+	1.06342i	−0.223438	+	0.974718i	$0.571728\pi$
$548$	−45.0754	−	14.6459i	−1.92553	−	0.625642i
$549$	11.5623			0.493467
$550$		0			0
$551$	−35.1246			−1.49636
$552$	1.67760	+	0.545085i	0.0714034	+	0.0232004i
$553$	−6.46564	−	8.89919i	−0.274947	−	0.378432i
$554$	61.8779	+	44.9569i	2.62894	+	1.91004i
$555$		0			0
$556$	21.8435	+	67.2273i	0.926369	+	2.85107i
$557$	22.1191	−	30.4443i	0.937215	−	1.28997i	−0.0197634	−	0.999805i	$-0.506291\pi$
$557$	22.1191	−	30.4443i	0.937215	−	1.28997i	0.956978	−	0.290161i	$-0.0937087\pi$
$558$	9.37181	+	12.8992i	0.396740	+	0.546066i
$559$	0.489357	−	1.50609i	0.0206976	−	0.0637006i
$560$		0			0
$561$	2.91641	+	2.43690i	0.123131	+	0.102886i
$562$		−	64.8328i		−	2.73481i
$563$	−38.6098	−	12.5451i	−1.62721	−	0.528712i	−0.653582	−	0.756856i	$-0.726734\pi$
$563$	−38.6098	−	12.5451i	−1.62721	−	0.528712i	−0.973627	+	0.228144i	$0.926734\pi$
$564$	39.6246	−	28.7890i	1.66850	−	1.21223i
$565$		0			0
$566$	4.61803	+	14.2128i	0.194110	+	0.597411i
$567$	0.951057	−	0.309017i	0.0399406	−	0.0129775i
$568$	45.3530	−	62.4230i	1.90297	−	2.61921i
$569$	27.6525	−	20.0907i	1.15925	−	0.842246i	0.169569	−	0.985518i	$-0.445763\pi$
$569$	27.6525	−	20.0907i	1.15925	−	0.842246i	0.989683	+	0.143272i	$0.0457625\pi$
$570$		0			0
$571$	−9.09017			−0.380412			−0.190206	−	0.981744i	$-0.560916\pi$
$571$	−9.09017			−0.380412			−0.190206	+	0.981744i	$0.560916\pi$
$572$	2.02063	+	3.21885i	0.0844866	+	0.134587i
$573$		−	0.819660i		−	0.0342418i
$574$	−0.190983	+	0.587785i	−0.00797148	+	0.0245337i
$575$		0			0
$576$	−7.04508	−	5.11855i	−0.293545	−	0.213273i
$577$	−30.1563	+	9.79837i	−1.25542	+	0.407912i	−0.859861	−	0.510528i	$-0.829450\pi$
$577$	−30.1563	+	9.79837i	−1.25542	+	0.407912i	−0.395562	+	0.918439i	$0.629450\pi$
$578$	39.0588	−	12.6910i	1.62463	−	0.527875i
$579$	2.54508	+	1.84911i	0.105770	+	0.0768465i
$580$		0			0
$581$	−0.454915	+	1.40008i	−0.0188731	+	0.0580853i
$582$			20.5623i			0.852335i
$583$	−1.17557	−	0.472136i	−0.0486872	−	0.0195539i
$584$	−42.6525			−1.76497
$585$		0			0
$586$	−45.8607	+	33.3197i	−1.89449	+	1.37643i
$587$	−1.24882	+	1.71885i	−0.0515441	+	0.0709444i	−0.834011	−	0.551748i	$-0.813961\pi$
$587$	−1.24882	+	1.71885i	−0.0515441	+	0.0709444i	0.782467	+	0.622692i	$0.213961\pi$
$588$	27.6992	−	9.00000i	1.14229	−	0.371154i
$589$	11.0172	+	33.9075i	0.453957	+	1.39714i
$590$		0			0
$591$	10.5451	−	7.66145i	0.433767	−	0.315150i
$592$	−58.4432	−	18.9894i	−2.40200	−	0.780458i
$593$			14.0344i			0.576325i	0.957581	+	0.288163i	$0.0930444\pi$
$593$			14.0344i			0.576325i	−0.957581	+	0.288163i	$0.906956\pi$
$594$	8.66312	+	0.587785i	0.355452	+	0.0241171i
$595$		0			0
$596$	−6.35410	+	19.5559i	−0.260274	+	0.801041i
$597$	3.94298	+	5.42705i	0.161376	+	0.222114i
$598$	0.0857567	−	0.118034i	0.00350685	−	0.00482677i
$599$	−3.90983	−	12.0332i	−0.159751	−	0.491664i	0.838860	−	0.544347i	$-0.183223\pi$
$599$	−3.90983	−	12.0332i	−0.159751	−	0.491664i	−0.998611	+	0.0526833i	$0.983223\pi$
$600$		0			0
$601$	5.57295	+	4.04898i	0.227325	+	0.165162i	0.695618	−	0.718412i	$-0.255131\pi$
$601$	5.57295	+	4.04898i	0.227325	+	0.165162i	−0.468293	+	0.883573i	$0.655131\pi$
$602$	10.3229	+	14.2082i	0.420729	+	0.579083i
$603$	−1.76336	−	0.572949i	−0.0718094	−	0.0233323i
$604$	−5.12461			−0.208517
$605$		0			0
$606$	−26.7984			−1.08861
$607$	−15.7517	−	5.11803i	−0.639341	−	0.207735i	−0.0286327	−	0.999590i	$-0.509115\pi$
$607$	−15.7517	−	5.11803i	−0.639341	−	0.207735i	−0.610709	+	0.791855i	$0.709115\pi$
$608$	−37.3485	−	51.4058i	−1.51468	−	2.08478i
$609$	−4.85410	−	3.52671i	−0.196698	−	0.142910i
$610$		0			0
$611$	−0.736068	−	2.26538i	−0.0297781	−	0.0916476i
$612$	−3.26944	+	4.50000i	−0.132159	+	0.181902i
$613$	−8.40051	−	11.5623i	−0.339293	−	0.466997i	0.604942	−	0.796270i	$-0.293196\pi$
$613$	−8.40051	−	11.5623i	−0.339293	−	0.466997i	−0.944235	+	0.329273i	$0.893196\pi$
$614$	22.6353	−	69.6642i	0.913485	−	2.81142i
$615$		0			0
$616$	−24.7254	−	1.67760i	−0.996216	−	0.0675924i
$617$			11.1803i			0.450104i	0.974347	+	0.225052i	$0.0722551\pi$
$617$			11.1803i			0.450104i	−0.974347	+	0.225052i	$0.927745\pi$
$618$	27.2501	+	8.85410i	1.09616	+	0.356164i
$619$	19.5172	−	14.1801i	0.784463	−	0.569946i	−0.121852	−	0.992548i	$-0.538883\pi$
$619$	19.5172	−	14.1801i	0.784463	−	0.569946i	0.906315	+	0.422602i	$0.138883\pi$
$620$		0			0
$621$	−0.0729490	−	0.224514i	−0.00292734	−	0.00900944i
$622$	29.0135	−	9.42705i	1.16333	−	0.377990i
$623$	−4.84104	+	6.66312i	−0.193952	+	0.266952i
$624$	−1.88197	+	1.36733i	−0.0753389	+	0.0547369i
$625$		0			0
$626$	6.61803			0.264510
$627$	18.0171	+	7.23607i	0.719533	+	0.288981i
$628$		−	76.2492i		−	3.04268i
$629$	−2.20820	+	6.79615i	−0.0880469	+	0.270980i
$630$		0			0
$631$	−15.5451	−	11.2942i	−0.618840	−	0.449614i	0.233676	−	0.972314i	$-0.424924\pi$
$631$	−15.5451	−	11.2942i	−0.618840	−	0.449614i	−0.852516	+	0.522701i	$0.824924\pi$
$632$	78.1707	−	25.3992i	3.10946	−	1.01033i
$633$	−3.44095	+	1.11803i	−0.136766	+	0.0444379i
$634$	14.4443	+	10.4944i	0.573655	+	0.416785i
$635$		0			0
$636$	0.572949	−	1.76336i	0.0227189	−	0.0699216i
$637$		−	1.41641i		−	0.0561201i
$638$	−27.6992	−	44.1246i	−1.09662	−	1.74691i
$639$	−10.3262			−0.408500
$640$		0			0
$641$	20.2984	−	14.7476i	0.801738	−	0.582496i	−0.109686	−	0.993966i	$-0.534984\pi$
$641$	20.2984	−	14.7476i	0.801738	−	0.582496i	0.911423	+	0.411470i	$0.134984\pi$
$642$	−17.6538	+	24.2984i	−0.696740	+	0.958980i
$643$	19.8334	−	6.44427i	0.782154	−	0.254137i	0.109394	−	0.993998i	$-0.465109\pi$
$643$	19.8334	−	6.44427i	0.782154	−	0.254137i	0.672760	+	0.739861i	$0.265109\pi$
$644$	0.354102	+	1.08981i	0.0139536	+	0.0429447i
$645$		0			0
$646$	−14.2082	+	10.3229i	−0.559014	+	0.406148i
$647$	42.8303	+	13.9164i	1.68383	+	0.547110i	0.985649	−	0.168808i	$-0.0539918\pi$
$647$	42.8303	+	13.9164i	1.68383	+	0.547110i	0.698184	+	0.715918i	$0.253992\pi$
$648$			7.47214i			0.293533i
$649$	−18.7877	−	15.6987i	−0.737483	−	0.616227i
$650$		0			0
$651$	−1.88197	+	5.79210i	−0.0737601	+	0.227010i
$652$	14.6821	+	20.2082i	0.574996	+	0.791414i
$653$	3.30220	−	4.54508i	0.129225	−	0.177863i	−0.739502	−	0.673155i	$-0.764939\pi$
$653$	3.30220	−	4.54508i	0.129225	−	0.177863i	0.868727	+	0.495292i	$0.164939\pi$
$654$	9.70820	+	29.8788i	0.379621	+	1.16835i
$655$		0			0
$656$	−1.88197	−	1.36733i	−0.0734784	−	0.0533852i
$657$	3.35520	+	4.61803i	0.130899	+	0.180167i
$658$	25.1235	+	8.16312i	0.979416	+	0.318232i
$659$	41.1246			1.60199			0.800994	−	0.598673i	$-0.204305\pi$
$659$	41.1246			1.60199			0.800994	+	0.598673i	$0.204305\pi$
$660$		0			0
$661$	36.5623			1.42211			0.711054	−	0.703137i	$-0.248218\pi$
$661$	36.5623			1.42211			0.711054	+	0.703137i	$0.248218\pi$
$662$	−41.6017	−	13.5172i	−1.61690	−	0.525362i
$663$	0.159002	+	0.218847i	0.00617511	+	0.00849932i
$664$	−8.89919	−	6.46564i	−0.345355	−	0.250915i
$665$		0			0
$666$	5.04508	+	15.5272i	0.195493	+	0.601666i
$667$	−0.832544	+	1.14590i	−0.0322362	+	0.0443693i
$668$	34.3363	+	47.2599i	1.32851	+	1.82854i
$669$	2.21885	−	6.82891i	0.0857856	−	0.264021i
$670$		0			0
$671$	9.35410	+	37.1895i	0.361111	+	1.43568i
$672$		−	10.8541i		−	0.418706i
$673$	−34.0790	−	11.0729i	−1.31365	−	0.426831i	−0.433340	−	0.901230i	$-0.642665\pi$
$673$	−34.0790	−	11.0729i	−1.31365	−	0.426831i	−0.880310	+	0.474399i	$0.842665\pi$
$674$	38.5066	−	27.9767i	1.48322	−	1.07762i
$675$		0			0
$676$	−19.4164	−	59.7576i	−0.746785	−	2.29837i
$677$	−12.8658	+	4.18034i	−0.494471	+	0.160664i	−0.545629	−	0.838027i	$-0.683709\pi$
$677$	−12.8658	+	4.18034i	−0.494471	+	0.160664i	0.0511572	+	0.998691i	$0.483709\pi$
$678$	−20.7315	+	28.5344i	−0.796188	+	1.09586i
$679$	−6.35410	+	4.61653i	−0.243848	+	0.177166i
$680$		0			0
$681$	−13.1803			−0.505072
$682$	−33.9075	+	40.5795i	−1.29839	+	1.55387i
$683$		−	9.06888i		−	0.347011i	−0.984833	−	0.173506i	$-0.944491\pi$
$683$		−	9.06888i		−	0.347011i	0.984833	−	0.173506i	$-0.0555095\pi$
$684$	−8.78115	+	27.0256i	−0.335756	+	1.03335i
$685$		0			0
$686$	27.5344	+	20.0049i	1.05127	+	0.763792i
$687$	0.449028	−	0.145898i	0.0171315	−	0.00556636i
$688$	−62.8680	+	20.4271i	−2.39682	+	0.778774i
$689$	−0.0729490	−	0.0530006i	−0.00277914	−	0.00201916i
$690$		0			0
$691$	0.416408	−	1.28157i	0.0158409	−	0.0487533i	−0.942824	−	0.333292i	$-0.891840\pi$
$691$	0.416408	−	1.28157i	0.0158409	−	0.0487533i	0.958665	+	0.284539i	$0.0918405\pi$
$692$		−	87.5410i		−	3.32781i
$693$	1.76336	+	2.80902i	0.0669843	+	0.106706i
$694$	−4.00000			−0.151838
$695$		0			0
$696$	36.2705	−	26.3521i	1.37483	−	0.998873i
$697$	−0.159002	+	0.218847i	−0.00602262	+	0.00828942i
$698$	−31.6421	+	10.2812i	−1.19767	+	0.389147i
$699$	−1.28115	−	3.94298i	−0.0484577	−	0.149137i
$700$		0			0
$701$	28.1525	−	20.4540i	1.06330	−	0.772536i	0.0886075	−	0.996067i	$-0.471758\pi$
$701$	28.1525	−	20.4540i	1.06330	−	0.772536i	0.974697	+	0.223531i	$0.0717583\pi$
$702$	0.587785	+	0.190983i	0.0221845	+	0.00720819i
$703$			36.5066i			1.37687i
$704$	10.7639	−	26.8011i	0.405681	−	1.01010i
$705$		0			0
$706$	9.70820	−	29.8788i	0.365373	−	1.12450i
$707$	−6.01661	−	8.28115i	−0.226278	−	0.311445i
$708$	21.0620	−	28.9894i	0.791558	−	1.08949i
$709$	−3.46556	−	10.6659i	−0.130152	−	0.400566i	0.864653	−	0.502370i	$-0.167538\pi$
$709$	−3.46556	−	10.6659i	−0.130152	−	0.400566i	−0.994804	+	0.101804i	$0.967538\pi$
$710$		0			0
$711$	−8.89919	−	6.46564i	−0.333746	−	0.242480i
$712$	−36.1729	−	49.7877i	−1.35564	−	1.86587i
$713$	1.36733	+	0.444272i	0.0512068	+	0.0166381i
$714$	−3.00000			−0.112272
$715$		0			0
$716$	−41.3951			−1.54701
$717$	−0.363271	−	0.118034i	−0.0135666	−	0.00440806i
$718$	14.9394	+	20.5623i	0.557533	+	0.767378i
$719$	−31.1353	−	22.6211i	−1.16115	−	0.843624i	−0.171226	−	0.985232i	$-0.554773\pi$
$719$	−31.1353	−	22.6211i	−1.16115	−	0.843624i	−0.989923	+	0.141608i	$0.954773\pi$
$720$		0			0
$721$	3.38197	+	10.4086i	0.125951	+	0.387637i
$722$	−23.4989	+	32.3435i	−0.874538	+	1.20370i
$723$	−4.87380	−	6.70820i	−0.181258	−	0.249481i
$724$	−3.79180	+	11.6699i	−0.140921	+	0.433710i
$725$		0			0
$726$	5.11803	+	28.3399i	0.189948	+	1.05179i
$727$		−	9.14590i		−	0.339203i	−0.985513	−	0.169601i	$-0.945752\pi$
$727$		−	9.14590i		−	0.339203i	0.985513	−	0.169601i	$-0.0542480\pi$
$728$	−1.67760	−	0.545085i	−0.0621760	−	0.0202022i
$729$	0.809017	−	0.587785i	0.0299636	−	0.0217698i
$730$		0			0
$731$	2.37539	+	7.31069i	0.0878569	+	0.270396i
$732$	−53.3777	+	17.3435i	−1.97290	+	0.641033i
$733$	0.237026	−	0.326238i	0.00875474	−	0.0120499i	−0.804617	−	0.593794i	$-0.797629\pi$
$733$	0.237026	−	0.326238i	0.00875474	−	0.0120499i	0.813372	+	0.581744i	$0.197629\pi$
$734$	−46.9058	+	34.0790i	−1.73132	+	1.25788i
$735$		0			0
$736$	−2.56231			−0.0944478
$737$	0.416272	−	6.13525i	0.0153336	−	0.225995i
$738$			0.618034i			0.0227501i
$739$	−0.927051	+	2.85317i	−0.0341021	+	0.104956i	−0.966659	−	0.256068i	$-0.917573\pi$
$739$	−0.927051	+	2.85317i	−0.0341021	+	0.104956i	0.932557	+	0.361024i	$0.117573\pi$
$740$		0			0
$741$	1.11803	+	0.812299i	0.0410720	+	0.0298406i
$742$	0.951057	−	0.309017i	0.0349144	−	0.0113444i
$743$	−40.7894	+	13.2533i	−1.49642	+	0.486216i	−0.938971	−	0.343996i	$-0.888219\pi$
$743$	−40.7894	+	13.2533i	−1.49642	+	0.486216i	−0.557448	+	0.830212i	$0.688219\pi$
$744$	−36.8156	−	26.7481i	−1.34973	−	0.980633i
$745$		0			0
$746$	−0.718847	+	2.21238i	−0.0263189	+	0.0810011i
$747$			1.47214i			0.0538626i
$748$	−17.1190	−	6.87539i	−0.625933	−	0.251389i
$749$	−11.4721			−0.419183
$750$		0			0
$751$	−13.0623	+	9.49032i	−0.476650	+	0.346307i	−0.800027	−	0.599963i	$-0.795182\pi$
$751$	−13.0623	+	9.49032i	−0.476650	+	0.346307i	0.323377	+	0.946270i	$0.395182\pi$
$752$	−58.4432	+	80.4402i	−2.13121	+	2.93335i
$753$	20.9030	−	6.79180i	0.761748	−	0.247507i
$754$	−1.14590	−	3.52671i	−0.0417311	−	0.128435i
$755$		0			0
$756$	−3.92705	+	2.85317i	−0.142825	+	0.103769i
$757$	4.75528	+	1.54508i	0.172834	+	0.0561571i	0.394156	−	0.919044i	$-0.371037\pi$
$757$	4.75528	+	1.54508i	0.172834	+	0.0561571i	−0.221322	+	0.975201i	$0.571037\pi$
$758$		−	65.1591i		−	2.36668i
$759$	0.663119	−	0.416272i	0.0240697	−	0.0151097i
$760$		0			0
$761$	9.05166	−	27.8582i	0.328123	−	1.00986i	−0.641889	−	0.766798i	$-0.721849\pi$
$761$	9.05166	−	27.8582i	0.328123	−	1.00986i	0.970011	−	0.243060i	$-0.0781511\pi$
$762$	−11.8617	−	16.3262i	−0.429704	−	0.591437i
$763$	−7.05342	+	9.70820i	−0.255351	+	0.351461i
$764$	1.22949	+	3.78398i	0.0444814	+	0.136900i
$765$		0			0
$766$	−26.9164	−	19.5559i	−0.972529	−	0.706584i
$767$	−1.02430	−	1.40983i	−0.0369854	−	0.0509060i
$768$	−13.8496	−	4.50000i	−0.499754	−	0.162380i
$769$	34.5066			1.24434			0.622170	−	0.782883i	$-0.286251\pi$
$769$	34.5066			1.24434			0.622170	+	0.782883i	$0.286251\pi$
$770$		0			0
$771$	−29.7426			−1.07116
$772$	−14.5231	−	4.71885i	−0.522698	−	0.169835i
$773$	15.9762	+	21.9894i	0.574624	+	0.790902i	0.993093	−	0.117329i	$-0.0374332\pi$
$773$	15.9762	+	21.9894i	0.574624	+	0.790902i	−0.418469	+	0.908231i	$0.637433\pi$
$774$	14.2082	+	10.3229i	0.510703	+	0.371048i
$775$		0			0
$776$	−18.1353	−	55.8146i	−0.651018	−	2.00363i
$777$	−3.66547	+	5.04508i	−0.131498	+	0.180991i
$778$	56.5411	+	77.8222i	2.02710	+	2.79006i
$779$	−0.427051	+	1.31433i	−0.0153007	+	0.0470907i
$780$		0			0
$781$	−8.35410	−	33.2137i	−0.298933	−	1.18848i
$782$			0.708204i			0.0253253i
$783$	−5.70634	−	1.85410i	−0.203928	−	0.0662602i
$784$	−47.8328	+	34.7526i	−1.70831	+	1.24116i
$785$		0			0
$786$	−9.54508	−	29.3768i	−0.340462	−	1.04783i
$787$	9.23305	−	3.00000i	0.329123	−	0.106938i	−0.139795	−	0.990181i	$-0.544644\pi$
$787$	9.23305	−	3.00000i	0.329123	−	0.106938i	0.468917	+	0.883242i	$0.344644\pi$
$788$	−37.1895	+	51.1869i	−1.32482	+	1.82346i
$789$	12.3541	−	8.97578i	0.439818	−	0.319546i
$790$		0			0
$791$	−13.4721			−0.479014
$792$	−24.0337	+	6.04508i	−0.854000	+	0.214803i
$793$			2.72949i			0.0969270i
$794$	−15.1353	+	46.5815i	−0.537130	+	1.65312i
$795$		0			0
$796$	−26.3435	−	19.1396i	−0.933719	−	0.678387i
$797$	−17.6336	+	5.72949i	−0.624613	+	0.202949i	−0.604187	−	0.796842i	$-0.706502\pi$
$797$	−17.6336	+	5.72949i	−0.624613	+	0.202949i	−0.0204255	+	0.999791i	$0.506502\pi$
$798$	−14.5761	+	4.73607i	−0.515989	+	0.167655i
$799$	9.35410	+	6.79615i	0.330924	+	0.240431i
$800$		0			0
$801$	−2.54508	+	7.83297i	−0.0899262	+	0.276764i
$802$			82.9574i			2.92933i
$803$	−12.1392	+	14.5279i	−0.428384	+	0.512677i
$804$	9.00000			0.317406
$805$		0			0
$806$	−3.04508	+	2.21238i	−0.107259	+	0.0779279i
$807$	14.9394	−	20.5623i	0.525891	−	0.723827i
$808$	72.7418	−	23.6353i	2.55905	−	0.831485i
$809$	−8.37132	−	25.7643i	−0.294320	−	0.905824i	−0.983449	−	0.181185i	$-0.942007\pi$
$809$	−8.37132	−	25.7643i	−0.294320	−	0.905824i	0.689129	−	0.724639i	$-0.257993\pi$
$810$		0			0
$811$	−29.5795	+	21.4908i	−1.03868	+	0.754644i	−0.970027	−	0.242997i	$-0.921869\pi$
$811$	−29.5795	+	21.4908i	−1.03868	+	0.754644i	−0.0686507	+	0.997641i	$0.521869\pi$
$812$	27.6992	+	9.00000i	0.972050	+	0.315838i
$813$			18.6180i			0.652963i
$814$	−45.8607	+	28.7890i	−1.60742	+	1.00905i
$815$		0			0
$816$	3.48936	−	10.7391i	0.122152	−	0.375945i
$817$	23.0826	+	31.7705i	0.807559	+	1.11151i
$818$	−9.95959	+	13.7082i	−0.348229	+	0.479296i
$819$	0.0729490	+	0.224514i	0.00254904	+	0.00784515i
$820$		0			0
$821$	−32.8435	−	23.8622i	−1.14624	−	0.832795i	−0.158268	−	0.987396i	$-0.550591\pi$
$821$	−32.8435	−	23.8622i	−1.14624	−	0.832795i	−0.987977	+	0.154601i	$0.950591\pi$
$822$	−15.0251	−	20.6803i	−0.524062	−	0.721310i
$823$	26.4706	+	8.60081i	0.922706	+	0.299805i	0.731577	−	0.681759i	$-0.238785\pi$
$823$	26.4706	+	8.60081i	0.922706	+	0.299805i	0.191130	+	0.981565i	$0.438785\pi$
$824$	−81.7771			−2.84884
$825$		0			0
$826$	19.3262			0.672446
$827$	−10.1311	−	3.29180i	−0.352293	−	0.114467i	0.127524	−	0.991835i	$-0.459297\pi$
$827$	−10.1311	−	3.29180i	−0.352293	−	0.114467i	−0.479817	+	0.877369i	$0.659297\pi$
$828$	0.673542	+	0.927051i	0.0234072	+	0.0322172i
$829$	−25.3992	−	18.4536i	−0.882150	−	0.640920i	0.0516692	−	0.998664i	$-0.483546\pi$
$829$	−25.3992	−	18.4536i	−0.882150	−	0.640920i	−0.933819	+	0.357745i	$0.883546\pi$
$830$		0			0
$831$	9.02786	+	27.7849i	0.313173	+	0.963848i
$832$	1.20833	−	1.66312i	0.0418912	−	0.0576583i
$833$	4.04125	+	5.56231i	0.140021	+	0.192722i
$834$	−11.7812	+	36.2587i	−0.407948	+	1.25553i
$835$		0			0
$836$	−94.0304	−	6.37988i	−3.25211	−	0.220653i
$837$			6.09017i			0.210507i
$838$	78.3094	+	25.4443i	2.70515	+	0.878958i
$839$	−14.4271	+	10.4819i	−0.498077	+	0.361874i	−0.808282	−	0.588796i	$-0.799602\pi$
$839$	−14.4271	+	10.4819i	−0.498077	+	0.361874i	0.310205	+	0.950670i	$0.399602\pi$
$840$		0			0
$841$	2.16312	+	6.65740i	0.0745903	+	0.229565i
$842$	26.1603	−	8.50000i	0.901544	−	0.292929i
$843$	14.5559	−	20.0344i	0.501331	−	0.690023i
$844$	14.2082	−	10.3229i	0.489067	−	0.355328i
$845$		0			0
$846$	26.4164			0.908215
$847$	−7.60845	+	7.94427i	−0.261430	+	0.272968i
$848$			3.76393i			0.129254i
$849$	−1.76393	+	5.42882i	−0.0605380	+	0.186317i
$850$		0			0
$851$	1.19098	+	0.865300i	0.0408264	+	0.0296621i
$852$	47.6713	−	15.4894i	1.63319	−	0.530657i
$853$	−53.1002	+	17.2533i	−1.81811	+	0.590741i	−0.818241	+	0.574876i	$0.805050\pi$
$853$	−53.1002	+	17.2533i	−1.81811	+	0.590741i	−0.999874	+	0.0158658i	$0.994950\pi$
$854$	−24.4894	−	17.7926i	−0.838009	−	0.608849i
$855$		0			0
$856$	26.4894	−	81.5259i	0.905388	−	2.78650i
$857$			27.7639i			0.948398i	0.880418	+	0.474199i	$0.157262\pi$
$857$			27.7639i			0.948398i	−0.880418	+	0.474199i	$0.842738\pi$
$858$	−0.138757	+	2.04508i	−0.00473710	+	0.0698180i
$859$	34.4164			1.17427			0.587136	−	0.809488i	$-0.300255\pi$
$859$	34.4164			1.17427			0.587136	+	0.809488i	$0.300255\pi$
$860$		0			0
$861$	−0.190983	+	0.138757i	−0.00650868	+	0.00472884i
$862$	9.09429	−	12.5172i	0.309753	−	0.426338i
$863$	0.106001	−	0.0344419i	0.00360832	−	0.00117241i	−0.307212	−	0.951641i	$-0.599396\pi$
$863$	0.106001	−	0.0344419i	0.00360832	−	0.00117241i	0.310821	+	0.950469i	$0.399396\pi$
$864$	−3.35410	−	10.3229i	−0.114109	−	0.351191i
$865$		0			0
$866$	74.7771	−	54.3287i	2.54103	−	1.84617i
$867$	14.9191	+	4.84752i	0.506681	+	0.164631i
$868$		−	29.5623i		−	1.00341i
$869$	13.5967	−	33.8545i	0.461238	−	1.14844i
$870$		0			0
$871$	0.135255	−	0.416272i	0.00458294	−	0.0141048i
$872$	−52.7041	−	72.5410i	−1.78479	−	2.45655i
$873$	−4.61653	+	6.35410i	−0.156246	+	0.215054i
$874$	1.11803	+	3.44095i	0.0378181	+	0.116392i
$875$		0			0
$876$	−22.4164	−	16.2865i	−0.757380	−	0.550269i
$877$	34.0588	+	46.8779i	1.15008	+	1.58295i	0.742590	+	0.669746i	$0.233597\pi$
$877$	34.0588	+	46.8779i	1.15008	+	1.58295i	0.407493	+	0.913208i	$0.366403\pi$
$878$	57.9942	+	18.8435i	1.95721	+	0.635936i
$879$	−21.6525			−0.730320
$880$		0			0
$881$	6.20163			0.208938			0.104469	−	0.994528i	$-0.466686\pi$
$881$	6.20163			0.208938			0.104469	+	0.994528i	$0.466686\pi$
$882$	14.9394	+	4.85410i	0.503035	+	0.163446i
$883$	0.620541	+	0.854102i	0.0208829	+	0.0287428i	0.819331	−	0.573321i	$-0.194345\pi$
$883$	0.620541	+	0.854102i	0.0208829	+	0.0287428i	−0.798448	+	0.602064i	$0.794345\pi$
$884$	−1.06231	−	0.771810i	−0.0357292	−	0.0259588i
$885$		0			0
$886$	25.5623	+	78.6727i	0.858782	+	2.64306i
$887$	−32.0257	+	44.0795i	−1.07532	+	1.48005i	−0.210741	+	0.977542i	$0.567588\pi$
$887$	−32.0257	+	44.0795i	−1.07532	+	1.48005i	−0.864575	+	0.502504i	$0.832412\pi$
$888$	−27.3889	−	37.6976i	−0.919111	−	1.26505i
$889$	2.38197	−	7.33094i	0.0798886	−	0.245872i
$890$		0			0
$891$	2.54508	+	2.12663i	0.0852636	+	0.0712447i
$892$			34.8541i			1.16700i
$893$	56.1778	+	18.2533i	1.87992	+	0.610823i
$894$	−8.97214	+	6.51864i	−0.300073	+	0.218016i
$895$		0			0
$896$	0.336881	+	1.03681i	0.0112544	+	0.0346375i
$897$	0.0530006	−	0.0172209i	0.00176964	−	0.000574990i
$898$	−13.9353	+	19.1803i	−0.465028	+	0.640056i
$899$	29.5623	−	21.4783i	0.985958	−	0.716340i
$900$		0			0
$901$	0.437694			0.0145817
$902$	−1.98787	+	0.500000i	−0.0661888	+	0.0166482i
$903$			6.70820i			0.223235i
$904$	31.1074	−	95.7387i	1.03462	−	3.18422i
$905$		0			0
$906$	−2.23607	−	1.62460i	−0.0742884	−	0.0539737i
$907$	40.3202	−	13.1008i	1.33881	−	0.435005i	0.449896	−	0.893081i	$-0.351461\pi$
$907$	40.3202	−	13.1008i	1.33881	−	0.435005i	0.888913	+	0.458076i	$0.151461\pi$
$908$	60.8474	−	19.7705i	2.01929	−	0.656107i
$909$	−8.28115	−	6.01661i	−0.274669	−	0.199558i
$910$		0			0
$911$	11.9271	−	36.7077i	0.395161	−	1.21618i	−0.533675	−	0.845689i	$-0.679190\pi$
$911$	11.9271	−	36.7077i	0.395161	−	1.21618i	0.928836	−	0.370491i	$-0.120810\pi$
$912$		−	57.6869i		−	1.91020i
$913$	−4.73504	+	1.19098i	−0.156707	+	0.0394158i
$914$	62.7771			2.07648
$915$		0			0
$916$	−1.85410	+	1.34708i	−0.0612613	+	0.0445089i
$917$	6.93491	−	9.54508i	0.229011	−	0.315206i
$918$	−2.85317	+	0.927051i	−0.0941686	+	0.0305972i
$919$	−7.92705	−	24.3970i	−0.261489	−	0.804781i	−0.992481	−	0.122395i	$-0.960942\pi$
$919$	−7.92705	−	24.3970i	−0.261489	−	0.804781i	0.730992	−	0.682386i	$-0.239058\pi$
$920$		0			0
$921$	22.6353	−	16.4455i	0.745857	−	0.541897i
$922$	−23.0826	−	7.50000i	−0.760186	−	0.246999i
$923$		−	2.43769i		−	0.0802377i
$924$	−12.3541	−	10.3229i	−0.406420	−	0.339597i
$925$		0			0
$926$	−1.39919	+	4.30625i	−0.0459801	+	0.141512i
$927$	6.43288	+	8.85410i	0.211284	+	0.290807i
$928$	−38.2793	+	52.6869i	−1.25658	+	1.72953i
$929$	3.92705	+	12.0862i	0.128842	+	0.396536i	0.994582	−	0.103959i	$-0.0331512\pi$
$929$	3.92705	+	12.0862i	0.128842	+	0.396536i	−0.865739	+	0.500495i	$0.833151\pi$
$930$		0			0
$931$	28.4164	+	20.6457i	0.931310	+	0.676636i
$932$	11.8290	+	16.2812i	0.387470	+	0.533307i
$933$	11.0822	+	3.60081i	0.362814	+	0.117885i
$934$	54.6869			1.78941
$935$		0			0
$936$	−1.76393			−0.0576559
$937$	39.6139	+	12.8713i	1.29413	+	0.420488i	0.873535	−	0.486761i	$-0.161822\pi$
$937$	39.6139	+	12.8713i	1.29413	+	0.420488i	0.420593	+	0.907249i	$0.361822\pi$
$938$	2.85317	+	3.92705i	0.0931593	+	0.128223i
$939$	2.04508	+	1.48584i	0.0667388	+	0.0484886i
$940$		0			0
$941$	−4.46556	−	13.7436i	−0.145573	−	0.448028i	0.851511	−	0.524336i	$-0.175687\pi$
$941$	−4.46556	−	13.7436i	−0.145573	−	0.448028i	−0.997084	+	0.0763087i	$0.975687\pi$
$942$	24.1724	−	33.2705i	0.787581	−	1.08401i
$943$	0.0327561	+	0.0450850i	0.00106669	+	0.00146817i
$944$	−22.4787	+	69.1824i	−0.731620	+	2.25169i
$945$		0			0
$946$	−21.7082	+	54.0512i	−0.705795	+	1.75736i
$947$		−	32.3951i		−	1.05270i	−0.850268	−	0.526350i	$-0.823560\pi$
$947$		−	32.3951i		−	1.05270i	0.850268	−	0.526350i	$-0.176440\pi$
$948$	50.7818	+	16.5000i	1.64932	+	0.535895i
$949$	−1.09017	+	0.792055i	−0.0353884	+	0.0257112i
$950$		0			0
$951$	2.10739	+	6.48588i	0.0683368	+	0.210319i
$952$	8.14324	−	2.64590i	0.263924	−	0.0857540i
$953$	−6.66991	+	9.18034i	−0.216059	+	0.297380i	−0.903265	−	0.429082i	$-0.858837\pi$
$953$	−6.66991	+	9.18034i	−0.216059	+	0.297380i	0.687206	+	0.726463i	$0.258837\pi$
$954$	0.809017	−	0.587785i	0.0261929	−	0.0190303i
$955$		0			0
$956$	1.85410			0.0599659
$957$	1.34708	−	19.8541i	0.0435450	−	0.641792i
$958$		−	74.3050i		−	2.40068i
$959$	3.01722	−	9.28605i	0.0974311	−	0.299862i
$960$		0			0
$961$	−4.92705	−	3.57971i	−0.158937	−	0.115475i
$962$	−3.66547	+	1.19098i	−0.118179	+	0.0383988i
$963$	−10.9106	+	3.54508i	−0.351591	+	0.114239i
$964$	32.5623	+	23.6579i	1.04876	+	0.761970i
$965$		0			0
$966$	−0.190983	+	0.587785i	−0.00614478	+	0.0189117i
$967$			43.9230i			1.41247i	0.707978	+	0.706234i	$0.249607\pi$
$967$			43.9230i			1.41247i	−0.707978	+	0.706234i	$0.750393\pi$
$968$	−38.8873	−	72.4123i	−1.24989	−	2.32742i
$969$	−6.70820			−0.215499
$970$		0			0
$971$	33.9787	−	24.6870i	1.09043	−	0.792243i	0.110957	−	0.993825i	$-0.464608\pi$
$971$	33.9787	−	24.6870i	1.09043	−	0.792243i	0.979472	+	0.201582i	$0.0646083\pi$
$972$	−2.85317	+	3.92705i	−0.0915155	+	0.125960i
$973$	−13.8496	+	4.50000i	−0.443997	+	0.144263i
$974$	−10.2812	−	31.6421i	−0.329429	−	1.01388i
$975$		0			0
$976$	92.1763	−	66.9700i	2.95049	−	2.14366i
$977$	−0.567541	−	0.184405i	−0.0181572	−	0.00589964i	0.299924	−	0.953963i	$-0.403039\pi$
$977$	−0.567541	−	0.184405i	−0.0181572	−	0.00589964i	−0.318082	+	0.948063i	$0.603039\pi$
$978$			13.4721i			0.430791i
$979$	−27.2533	−	1.84911i	−0.871019	−	0.0590979i
$980$		0			0
$981$	−3.70820	+	11.4127i	−0.118394	+	0.364379i
$982$	−27.5604	−	37.9336i	−0.879488	−	1.21051i
$983$	4.76779	−	6.56231i	0.152069	−	0.209305i	−0.726185	−	0.687499i	$-0.758708\pi$
$983$	4.76779	−	6.56231i	0.152069	−	0.209305i	0.878254	+	0.478194i	$0.158708\pi$
$984$	−0.545085	−	1.67760i	−0.0173767	−	0.0534799i
$985$		0			0
$986$	14.5623	+	10.5801i	0.463758	+	0.336940i
$987$	5.93085	+	8.16312i	0.188781	+	0.259835i
$988$	−6.37988	−	2.07295i	−0.202971	−	0.0659493i
$989$	1.58359			0.0503553
$990$		0			0
$991$	3.74265			0.118889			0.0594445	−	0.998232i	$-0.481067\pi$
$991$	3.74265			0.118889			0.0594445	+	0.998232i	$0.481067\pi$
$992$	62.8680	+	20.4271i	1.99606	+	0.648560i
$993$	−9.82084	−	13.5172i	−0.311655	−	0.428956i
$994$	21.8713	+	15.8904i	0.693716	+	0.504014i
$995$		0			0
$996$	−2.20820	−	6.79615i	−0.0699696	−	0.215344i
$997$	−12.4620	+	17.1525i	−0.394676	+	0.543224i	−0.959398	−	0.282057i	$-0.908983\pi$
$997$	−12.4620	+	17.1525i	−0.394676	+	0.543224i	0.564722	+	0.825281i	$0.308983\pi$
$998$	27.9237	+	38.4336i	0.883908	+	1.21660i
$999$	−1.92705	+	5.93085i	−0.0609692	+	0.187644i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.2.bx.d.724.1		8
5.2	odd	4		825.2.n.c.526.1		4
5.3	odd	4		33.2.e.b.31.1	yes	4
5.4	even	2	inner	825.2.bx.d.724.2		8
11.5	even	5	inner	825.2.bx.d.49.2		8
15.8	even	4		99.2.f.a.64.1		4
20.3	even	4		528.2.y.b.97.1		4
45.13	odd	12		891.2.n.c.460.1		8
45.23	even	12		891.2.n.b.460.1		8
45.38	even	12		891.2.n.b.757.1		8
45.43	odd	12		891.2.n.c.757.1		8
55.3	odd	20		363.2.e.k.202.1		4
55.7	even	20		9075.2.a.u.1.1		2
55.8	even	20		363.2.e.b.202.1		4
55.13	even	20		363.2.e.b.124.1		4
55.18	even	20		363.2.a.i.1.2		2
55.27	odd	20		825.2.n.c.676.1		4
55.28	even	20		363.2.e.f.148.1		4
55.37	odd	20		9075.2.a.cb.1.2		2
55.38	odd	20		33.2.e.b.16.1	✓	4
55.43	even	4		363.2.e.f.130.1		4
55.48	odd	20		363.2.a.d.1.1		2
55.49	even	10	inner	825.2.bx.d.49.1		8
55.53	odd	20		363.2.e.k.124.1		4
165.38	even	20		99.2.f.a.82.1		4
165.128	odd	20		1089.2.a.l.1.1		2
165.158	even	20		1089.2.a.t.1.2		2
220.103	even	20		5808.2.a.cj.1.1		2
220.183	odd	20		5808.2.a.ci.1.1		2
220.203	even	20		528.2.y.b.49.1		4
495.38	even	60		891.2.n.b.676.1		8
495.148	odd	60		891.2.n.c.379.1		8
495.203	even	60		891.2.n.b.379.1		8
495.313	odd	60		891.2.n.c.676.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.2.e.b.16.1	✓	4	55.38	odd	20
33.2.e.b.31.1	yes	4	5.3	odd	4
99.2.f.a.64.1		4	15.8	even	4
99.2.f.a.82.1		4	165.38	even	20
363.2.a.d.1.1		2	55.48	odd	20
363.2.a.i.1.2		2	55.18	even	20
363.2.e.b.124.1		4	55.13	even	20
363.2.e.b.202.1		4	55.8	even	20
363.2.e.f.130.1		4	55.43	even	4
363.2.e.f.148.1		4	55.28	even	20
363.2.e.k.124.1		4	55.53	odd	20
363.2.e.k.202.1		4	55.3	odd	20
528.2.y.b.49.1		4	220.203	even	20
528.2.y.b.97.1		4	20.3	even	4
825.2.n.c.526.1		4	5.2	odd	4
825.2.n.c.676.1		4	55.27	odd	20
825.2.bx.d.49.1		8	55.49	even	10	inner
825.2.bx.d.49.2		8	11.5	even	5	inner
825.2.bx.d.724.1		8	1.1	even	1	trivial
825.2.bx.d.724.2		8	5.4	even	2	inner
891.2.n.b.379.1		8	495.203	even	60
891.2.n.b.460.1		8	45.23	even	12
891.2.n.b.676.1		8	495.38	even	60
891.2.n.b.757.1		8	45.38	even	12
891.2.n.c.379.1		8	495.148	odd	60
891.2.n.c.460.1		8	45.13	odd	12
891.2.n.c.676.1		8	495.313	odd	60
891.2.n.c.757.1		8	45.43	odd	12
1089.2.a.l.1.1		2	165.128	odd	20
1089.2.a.t.1.2		2	165.158	even	20
5808.2.a.ci.1.1		2	220.183	odd	20
5808.2.a.cj.1.1		2	220.103	even	20
9075.2.a.u.1.1		2	55.7	even	20
9075.2.a.cb.1.2		2	55.37	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:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	825.bx (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.48990 - 0.809017i) q^{2} +(-0.587785 - 0.809017i) q^{3} +(3.92705 + 2.85317i) q^{4} +(0.809017 + 2.48990i) q^{6} +(-0.587785 + 0.809017i) q^{7} +(-4.39201 - 6.04508i) q^{8} +(-0.309017 + 0.951057i) q^{9} +(-3.30902 - 0.224514i) q^{11} -4.85410i q^{12} +(-0.224514 - 0.0729490i) q^{13} +(2.11803 - 1.53884i) q^{14} +(3.04508 + 9.37181i) q^{16} +(1.08981 - 0.354102i) q^{17} +(1.53884 - 2.11803i) q^{18} +(4.73607 - 3.44095i) q^{19} +1.00000 q^{21} +(8.05748 + 3.23607i) q^{22} -0.236068i q^{23} +(-2.30902 + 7.10642i) q^{24} +(0.500000 + 0.363271i) q^{26} +(0.951057 - 0.309017i) q^{27} +(-4.61653 + 1.50000i) q^{28} +(-4.85410 - 3.52671i) q^{29} +(-1.88197 + 5.79210i) q^{31} -10.8541i q^{32} +(1.76336 + 2.80902i) q^{33} -3.00000 q^{34} +(-3.92705 + 2.85317i) q^{36} +(-3.66547 + 5.04508i) q^{37} +(-14.5761 + 4.73607i) q^{38} +(0.0729490 + 0.224514i) q^{39} +(-0.190983 + 0.138757i) q^{41} +(-2.48990 - 0.809017i) q^{42} +6.70820i q^{43} +(-12.3541 - 10.3229i) q^{44} +(-0.190983 + 0.587785i) q^{46} +(5.93085 + 8.16312i) q^{47} +(5.79210 - 7.97214i) q^{48} +(1.85410 + 5.70634i) q^{49} +(-0.927051 - 0.673542i) q^{51} +(-0.673542 - 0.927051i) q^{52} +(0.363271 + 0.118034i) q^{53} -2.61803 q^{54} +7.47214 q^{56} +(-5.56758 - 1.80902i) q^{57} +(9.23305 + 12.7082i) q^{58} +(5.97214 + 4.33901i) q^{59} +(-3.57295 - 10.9964i) q^{61} +(9.37181 - 12.8992i) q^{62} +(-0.587785 - 0.809017i) q^{63} +(-2.69098 + 8.28199i) q^{64} +(-2.11803 - 8.42075i) q^{66} +1.85410i q^{67} +(5.29007 + 1.71885i) q^{68} +(-0.190983 + 0.138757i) q^{69} +(3.19098 + 9.82084i) q^{71} +(7.10642 - 2.30902i) q^{72} +(3.35520 - 4.61803i) q^{73} +(13.2082 - 9.59632i) q^{74} +28.4164 q^{76} +(2.12663 - 2.54508i) q^{77} -0.618034i q^{78} +(-3.39919 + 10.4616i) q^{79} +(-0.809017 - 0.587785i) q^{81} +(0.587785 - 0.190983i) q^{82} +(1.40008 - 0.454915i) q^{83} +(3.92705 + 2.85317i) q^{84} +(5.42705 - 16.7027i) q^{86} +6.00000i q^{87} +(13.1760 + 20.9894i) q^{88} +8.23607 q^{89} +(0.190983 - 0.138757i) q^{91} +(0.673542 - 0.927051i) q^{92} +(5.79210 - 1.88197i) q^{93} +(-8.16312 - 25.1235i) q^{94} +(-8.78115 + 6.37988i) q^{96} +(7.46969 + 2.42705i) q^{97} -15.7082i q^{98} +(1.23607 - 3.07768i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 18 q^{4} + 2 q^{6} + 2 q^{9} - 22 q^{11} + 8 q^{14} + 2 q^{16} + 20 q^{19} + 8 q^{21} - 14 q^{24} + 4 q^{26} - 12 q^{29} - 24 q^{31} - 24 q^{34} - 18 q^{36} + 14 q^{39} - 6 q^{41} - 72 q^{44} - 6 q^{46}+ \cdots - 8 q^{99}+O(q^{100}) \) 8 * q + 18 * q^4 + 2 * q^6 + 2 * q^9 - 22 * q^11 + 8 * q^14 + 2 * q^16 + 20 * q^19 + 8 * q^21 - 14 * q^24 + 4 * q^26 - 12 * q^29 - 24 * q^31 - 24 * q^34 - 18 * q^36 + 14 * q^39 - 6 * q^41 - 72 * q^44 - 6 * q^46 - 12 * q^49 + 6 * q^51 - 12 * q^54 + 24 * q^56 + 12 * q^59 - 42 * q^61 - 26 * q^64 - 8 * q^66 - 6 * q^69 + 30 * q^71 + 52 * q^74 + 120 * q^76 + 22 * q^79 - 2 * q^81 + 18 * q^84 + 30 * q^86 + 48 * q^89 + 6 * q^91 - 34 * q^94 - 30 * q^96 - 8 * q^99

Introduction

L-functions

Modular forms

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