LMFDB - Embedded newform 833.2.j.c.373.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [833,2,Mod(67,833)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(833, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 3]))

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

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

chi := DirichletCharacter("833.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 833 = 7^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	833.j (of order $6$, degree $2$, 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:	$6.65153848837$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 12 x^{18} + 100 x^{16} - 416 x^{14} + 1248 x^{12} - 2081 x^{10} + 2420 x^{8} - 808 x^{6} + \cdots + 1 $ x^20 - 12x^18 + 100x^16 - 416x^14 + 1248x^12 - 2081x^10 + 2420x^8 - 808x^6 + 200x^4 - 16*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 119)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			373.6
Root			$0.256168 - 0.147899i$ of defining polynomial
Character	$\chi$	$=$	833.373
Dual form			833.2.j.c.67.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.147899 - 0.256168i) q^{2} +(2.67160 - 1.54245i) q^{3} +(0.956252 + 1.65628i) q^{4} +(0.654019 + 0.377598i) q^{5} -0.912504i q^{6} +1.15731 q^{8} +(3.25829 - 5.64353i) q^{9} +O(q^{10})$	\(q+(0.147899 - 0.256168i) q^{2} +(2.67160 - 1.54245i) q^{3} +(0.956252 + 1.65628i) q^{4} +(0.654019 + 0.377598i) q^{5} -0.912504i q^{6} +1.15731 q^{8} +(3.25829 - 5.64353i) q^{9} +(0.193457 - 0.111692i) q^{10} +(3.82489 - 2.20830i) q^{11} +(5.10944 + 2.94994i) q^{12} -2.34478 q^{13} +2.32970 q^{15} +(-1.74134 + 3.01609i) q^{16} +(-3.77075 - 1.66776i) q^{17} +(-0.963794 - 1.66934i) q^{18} +(-3.13589 + 5.43152i) q^{19} +1.44431i q^{20} -1.30642i q^{22} +(-2.24439 - 1.29580i) q^{23} +(3.09186 - 1.78509i) q^{24} +(-2.21484 - 3.83621i) q^{25} +(-0.346790 + 0.600659i) q^{26} -10.8483i q^{27} +6.61656i q^{29} +(0.344560 - 0.596795i) q^{30} +(-3.10867 + 1.79479i) q^{31} +(1.67239 + 2.89667i) q^{32} +(6.81238 - 11.7994i) q^{33} +(-0.984916 + 0.719286i) q^{34} +12.4630 q^{36} +(5.14815 + 2.97229i) q^{37} +(0.927588 + 1.60663i) q^{38} +(-6.26432 + 3.61671i) q^{39} +(0.756901 + 0.436997i) q^{40} +0.813118i q^{41} -0.148517 q^{43} +(7.31512 + 4.22338i) q^{44} +(4.26197 - 2.46065i) q^{45} +(-0.663884 + 0.383293i) q^{46} +(5.29320 - 9.16809i) q^{47} +10.7437i q^{48} -1.31029 q^{50} +(-12.6464 + 1.36060i) q^{51} +(-2.24220 - 3.88361i) q^{52} +(2.51349 + 4.35349i) q^{53} +(-2.77898 - 1.60445i) q^{54} +3.33540 q^{55} +19.3478i q^{57} +(1.69495 + 0.978581i) q^{58} +(-2.75520 - 4.77214i) q^{59} +(2.22778 + 3.85863i) q^{60} +(0.704181 + 0.406559i) q^{61} +1.06179i q^{62} -5.97598 q^{64} +(-1.53353 - 0.885385i) q^{65} +(-2.01508 - 3.49023i) q^{66} +(-6.26239 - 10.8468i) q^{67} +(-0.843514 - 7.84021i) q^{68} -7.99480 q^{69} -1.08120i q^{71} +(3.77085 - 6.53130i) q^{72} +(-8.66345 + 5.00185i) q^{73} +(1.52281 - 0.879195i) q^{74} +(-11.8343 - 6.83255i) q^{75} -11.9948 q^{76} +2.13962i q^{78} +(7.86005 + 4.53800i) q^{79} +(-2.27774 + 1.31505i) q^{80} +(-6.95805 - 12.0517i) q^{81} +(0.208295 + 0.120259i) q^{82} +0.344784 q^{83} +(-1.83640 - 2.51458i) q^{85} +(-0.0219655 + 0.0380454i) q^{86} +(10.2057 + 17.6768i) q^{87} +(4.42658 - 2.55569i) q^{88} +(-6.80158 + 11.7807i) q^{89} -1.45571i q^{90} -4.95644i q^{92} +(-5.53675 + 9.58994i) q^{93} +(-1.56571 - 2.71190i) q^{94} +(-4.10186 + 2.36821i) q^{95} +(8.93592 + 5.15915i) q^{96} -13.0948i q^{97} -28.7812i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 4 q^{2} - 4 q^{4} - 24 q^{8} + 6 q^{9}+O(q^{10}) $ 20 * q + 4 * q^2 - 4 * q^4 - 24 * q^8 + 6 * q^9	$ 20 q + 4 q^{2} - 4 q^{4} - 24 q^{8} + 6 q^{9} - 16 q^{13} - 16 q^{15} - 8 q^{16} - 2 q^{17} - 12 q^{18} - 4 q^{19} + 2 q^{25} - 12 q^{26} - 10 q^{30} + 18 q^{32} + 20 q^{33} + 12 q^{34} + 20 q^{36} + 4 q^{38} + 32 q^{43} + 12 q^{50} + 64 q^{52} - 8 q^{53} - 24 q^{55} - 56 q^{59} + 26 q^{60} - 72 q^{66} - 24 q^{67} + 22 q^{68} + 56 q^{69} - 10 q^{72} - 24 q^{76} - 2 q^{81} - 24 q^{83} - 40 q^{85} + 74 q^{86} + 52 q^{87} + 4 q^{89} - 32 q^{93} + 20 q^{94}+O(q^{100}) $ 20 * q + 4 * q^2 - 4 * q^4 - 24 * q^8 + 6 * q^9 - 16 * q^13 - 16 * q^15 - 8 * q^16 - 2 * q^17 - 12 * q^18 - 4 * q^19 + 2 * q^25 - 12 * q^26 - 10 * q^30 + 18 * q^32 + 20 * q^33 + 12 * q^34 + 20 * q^36 + 4 * q^38 + 32 * q^43 + 12 * q^50 + 64 * q^52 - 8 * q^53 - 24 * q^55 - 56 * q^59 + 26 * q^60 - 72 * q^66 - 24 * q^67 + 22 * q^68 + 56 * q^69 - 10 * q^72 - 24 * q^76 - 2 * q^81 - 24 * q^83 - 40 * q^85 + 74 * q^86 + 52 * q^87 + 4 * q^89 - 32 * q^93 + 20 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/833\mathbb{Z}\right)^\times$.

$n$	$52$	$785$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$

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 $

$2$	0.147899	−	0.256168i	0.104580	−	0.181138i	−0.808986	−	0.587827i	$-0.799983\pi$
$2$	0.147899	−	0.256168i	0.104580	−	0.181138i	0.913567	+	0.406689i	$0.133317\pi$
$3$	2.67160	−	1.54245i	1.54245	−	0.890533i	0.543764	−	0.839238i	$-0.316999\pi$
$3$	2.67160	−	1.54245i	1.54245	−	0.890533i	0.998684	−	0.0512947i	$-0.0163348\pi$
$4$	0.956252	+	1.65628i	0.478126	+	0.828138i
$5$	0.654019	+	0.377598i	0.292486	+	0.168867i	0.639062	−	0.769155i	$-0.279323\pi$
$5$	0.654019	+	0.377598i	0.292486	+	0.168867i	−0.346576	+	0.938022i	$0.612656\pi$
$6$		−	0.912504i		−	0.372528i
$7$		0			0
$7$		0			0
$8$	1.15731			0.409170
$9$	3.25829	−	5.64353i	1.08610	−	1.88118i
$10$	0.193457	−	0.111692i	0.0611765	−	0.0353203i
$11$	3.82489	−	2.20830i	1.15325	−	0.665828i	0.203571	−	0.979060i	$-0.434745\pi$
$11$	3.82489	−	2.20830i	1.15325	−	0.665828i	0.949677	+	0.313232i	$0.101412\pi$
$12$	5.10944	+	2.94994i	1.47497	+	0.851574i
$13$	−2.34478			−0.650326			−0.325163	−	0.945658i	$-0.605419\pi$
$13$	−2.34478			−0.650326			−0.325163	+	0.945658i	$0.605419\pi$
$14$		0			0
$15$	2.32970			0.601526
$16$	−1.74134	+	3.01609i	−0.435335	+	0.754022i
$17$	−3.77075	−	1.66776i	−0.914542	−	0.404492i
$17$	−3.77075	−	1.66776i	−0.914542	−	0.404492i
$18$	−0.963794	−	1.66934i	−0.227168	−	0.393467i
$19$	−3.13589	+	5.43152i	−0.719422	+	1.24608i	0.241807	+	0.970324i	$0.422260\pi$
$19$	−3.13589	+	5.43152i	−0.719422	+	1.24608i	−0.961229	+	0.275751i	$0.911073\pi$
$20$			1.44431i			0.322959i
$21$		0			0
$22$		−	1.30642i		−	0.278530i
$23$	−2.24439	−	1.29580i	−0.467987	−	0.270192i	0.247410	−	0.968911i	$-0.420421\pi$
$23$	−2.24439	−	1.29580i	−0.467987	−	0.270192i	−0.715397	+	0.698719i	$0.753754\pi$
$24$	3.09186	−	1.78509i	0.631124	−	0.364379i
$25$	−2.21484	−	3.83621i	−0.442968	−	0.767243i
$26$	−0.346790	+	0.600659i	−0.0680112	+	0.117799i
$27$		−	10.8483i		−	2.08775i
$28$		0			0
$29$			6.61656i			1.22866i	0.789047	+	0.614332i	$0.210575\pi$
$29$			6.61656i			1.22866i	−0.789047	+	0.614332i	$0.789425\pi$
$30$	0.344560	−	0.596795i	0.0629077	−	0.108959i
$31$	−3.10867	+	1.79479i	−0.558334	+	0.322355i	−0.752477	−	0.658619i	$-0.771141\pi$
$31$	−3.10867	+	1.79479i	−0.558334	+	0.322355i	0.194142	+	0.980973i	$0.437808\pi$
$32$	1.67239	+	2.89667i	0.295640	+	0.512063i
$33$	6.81238	−	11.7994i	1.18588	−	2.05401i
$34$	−0.984916	+	0.719286i	−0.168912	+	0.123357i
$35$		0			0
$36$	12.4630			2.07716
$37$	5.14815	+	2.97229i	0.846351	+	0.488641i	0.859418	−	0.511274i	$-0.170826\pi$
$37$	5.14815	+	2.97229i	0.846351	+	0.488641i	−0.0130668	+	0.999915i	$0.504159\pi$
$38$	0.927588	+	1.60663i	0.150475	+	0.260630i
$39$	−6.26432	+	3.61671i	−1.00309	+	0.579137i
$40$	0.756901	+	0.436997i	0.119677	+	0.0690953i
$41$			0.813118i			0.126988i	0.997982	+	0.0634939i	$0.0202243\pi$
$41$			0.813118i			0.126988i	−0.997982	+	0.0634939i	$0.979776\pi$
$42$		0			0
$43$	−0.148517			−0.0226487			−0.0113243	−	0.999936i	$-0.503605\pi$
$43$	−0.148517			−0.0226487			−0.0113243	+	0.999936i	$0.503605\pi$
$44$	7.31512	+	4.22338i	1.10280	+	0.636699i
$45$	4.26197	−	2.46065i	0.635336	−	0.366812i
$46$	−0.663884	+	0.383293i	−0.0978843	+	0.0565135i
$47$	5.29320	−	9.16809i	0.772092	−	1.33730i	−0.164322	−	0.986407i	$-0.552544\pi$
$47$	5.29320	−	9.16809i	0.772092	−	1.33730i	0.936414	−	0.350896i	$-0.114123\pi$
$48$			10.7437i			1.55072i
$49$		0			0
$50$	−1.31029			−0.185303
$51$	−12.6464	+	1.36060i	−1.77085	+	0.190522i
$52$	−2.24220	−	3.88361i	−0.310938	−	0.538560i
$53$	2.51349	+	4.35349i	0.345254	+	0.597997i	0.985400	−	0.170256i	$-0.0544595\pi$
$53$	2.51349	+	4.35349i	0.345254	+	0.597997i	−0.640146	+	0.768253i	$0.721126\pi$
$54$	−2.77898	−	1.60445i	−0.378172	−	0.218338i
$55$	3.33540			0.449745
$56$		0			0
$57$			19.3478i			2.56268i
$58$	1.69495	+	0.978581i	0.222558	+	0.128494i
$59$	−2.75520	−	4.77214i	−0.358696	−	0.621280i	0.629047	−	0.777367i	$-0.283445\pi$
$59$	−2.75520	−	4.77214i	−0.358696	−	0.621280i	−0.987743	+	0.156087i	$0.950112\pi$
$60$	2.22778	+	3.85863i	0.287605	+	0.498147i
$61$	0.704181	+	0.406559i	0.0901611	+	0.0520546i	0.544403	−	0.838824i	$-0.316756\pi$
$61$	0.704181	+	0.406559i	0.0901611	+	0.0520546i	−0.454242	+	0.890879i	$0.650090\pi$
$62$			1.06179i			0.134848i
$63$		0			0
$64$	−5.97598			−0.746998
$65$	−1.53353	−	0.885385i	−0.190211	−	0.109819i
$66$	−2.01508	−	3.49023i	−0.248040	−	0.429617i
$67$	−6.26239	−	10.8468i	−0.765073	−	1.32514i	−0.940208	−	0.340600i	$-0.889370\pi$
$67$	−6.26239	−	10.8468i	−0.765073	−	1.32514i	0.175136	−	0.984544i	$-0.443964\pi$
$68$	−0.843514	−	7.84021i	−0.102291	−	0.950765i
$69$	−7.99480			−0.962461
$70$		0			0
$71$		−	1.08120i		−	0.128315i	−0.997940	−	0.0641576i	$-0.979564\pi$
$71$		−	1.08120i		−	0.128315i	0.997940	−	0.0641576i	$-0.0204360\pi$
$72$	3.77085	−	6.53130i	0.444399	−	0.769721i
$73$	−8.66345	+	5.00185i	−1.01398	+	0.585422i	−0.912355	−	0.409401i	$-0.865738\pi$
$73$	−8.66345	+	5.00185i	−1.01398	+	0.585422i	−0.101626	+	0.994823i	$0.532404\pi$
$74$	1.52281	−	0.879195i	0.177023	−	0.102204i
$75$	−11.8343	−	6.83255i	−1.36651	−	0.788955i
$76$	−11.9948			−1.37590
$77$		0			0
$78$			2.13962i			0.242265i
$79$	7.86005	+	4.53800i	0.884325	+	0.510565i	0.872082	−	0.489360i	$-0.162770\pi$
$79$	7.86005	+	4.53800i	0.884325	+	0.510565i	0.0122427	+	0.999925i	$0.496103\pi$
$80$	−2.27774	+	1.31505i	−0.254659	+	0.147027i
$81$	−6.95805	−	12.0517i	−0.773116	−	1.33908i
$82$	0.208295	+	0.120259i	0.0230023	+	0.0132804i
$83$	0.344784			0.0378449			0.0189225	−	0.999821i	$-0.493976\pi$
$83$	0.344784			0.0378449			0.0189225	+	0.999821i	$0.493976\pi$
$84$		0			0
$85$	−1.83640	−	2.51458i	−0.199185	−	0.272744i
$86$	−0.0219655	+	0.0380454i	−0.00236860	+	0.00410254i
$87$	10.2057	+	17.6768i	1.09417	+	1.89515i
$88$	4.42658	−	2.55569i	0.471875	−	0.272437i
$89$	−6.80158	+	11.7807i	−0.720966	+	1.24875i	0.239647	+	0.970860i	$0.422968\pi$
$89$	−6.80158	+	11.7807i	−0.720966	+	1.24875i	−0.960613	+	0.277890i	$0.910365\pi$
$90$		−	1.45571i		−	0.153445i
$91$		0			0
$92$		−	4.95644i		−	0.516744i
$93$	−5.53675	+	9.58994i	−0.574134	+	0.994430i
$94$	−1.56571	−	2.71190i	−0.161491	−	0.279711i
$95$	−4.10186	+	2.36821i	−0.420842	+	0.242973i
$96$	8.93592	+	5.15915i	0.912018	+	0.526554i
$97$		−	13.0948i		−	1.32957i	−0.747033	−	0.664787i	$-0.768522\pi$
$97$		−	13.0948i		−	1.32957i	0.747033	−	0.664787i	$-0.231478\pi$
$98$		0			0
$99$		−	28.7812i		−	2.89261i
$100$	4.23589	−	7.33678i	0.423589	−	0.733678i
$101$	−0.727483	−	1.26004i	−0.0723873	−	0.125379i	0.827560	−	0.561378i	$-0.189728\pi$
$101$	−0.727483	−	1.26004i	−0.0723873	−	0.125379i	−0.899947	+	0.435999i	$0.856395\pi$
$102$	−1.52184	+	3.44083i	−0.150685	+	0.340693i
$103$	−1.34050	+	2.32181i	−0.132083	+	0.228775i	−0.924479	−	0.381232i	$-0.875500\pi$
$103$	−1.34050	+	2.32181i	−0.132083	+	0.228775i	0.792396	+	0.610007i	$0.208833\pi$
$104$	−2.71364			−0.266094
$105$		0			0
$106$	1.48697			0.144427
$107$	−8.40838	−	4.85458i	−0.812869	−	0.469310i	0.0350822	−	0.999384i	$-0.488831\pi$
$107$	−8.40838	−	4.85458i	−0.812869	−	0.469310i	−0.847951	+	0.530074i	$0.822164\pi$
$108$	17.9678	−	10.3737i	1.72895	−	0.998209i
$109$	15.6091	−	9.01189i	1.49508	−	0.863182i	0.495092	−	0.868841i	$-0.335134\pi$
$109$	15.6091	−	9.01189i	1.49508	−	0.863182i	0.999984	+	0.00565811i	$0.00180104\pi$
$110$	0.493301	−	0.854423i	0.0470344	−	0.0814660i
$111$	18.3384			1.74060
$112$		0			0
$113$			14.4126i			1.35582i	0.735144	+	0.677911i	$0.237115\pi$
$113$			14.4126i			1.35582i	−0.735144	+	0.677911i	$0.762885\pi$
$114$	4.95628	+	2.86151i	0.464198	+	0.268005i
$115$	−0.978581	−	1.69495i	−0.0912531	−	0.158055i
$116$	−10.9589	+	6.32710i	−1.01750	+	0.587456i
$117$	−7.63999	+	13.2328i	−0.706317	+	1.22338i
$118$	−1.62996			−0.150050
$119$		0			0
$120$	2.69618			0.246127
$121$	4.25319	−	7.36674i	0.386654	−	0.669704i
$122$	0.208295	−	0.120259i	0.0188581	−	0.0108877i
$123$	1.25419	+	2.17232i	0.113087	+	0.195872i
$124$	−5.94535	−	3.43255i	−0.533908	−	0.308252i
$125$		−	7.12125i		−	0.636944i
$126$		0			0
$127$	−8.99799			−0.798443			−0.399221	−	0.916855i	$-0.630720\pi$
$127$	−8.99799			−0.798443			−0.399221	+	0.916855i	$0.630720\pi$
$128$	−4.22862	+	7.32419i	−0.373761	+	0.647373i
$129$	−0.396779	+	0.229080i	−0.0349344	+	0.0201694i
$130$	−0.453615	+	0.261895i	−0.0397846	+	0.0229697i
$131$	13.1258	+	7.57820i	1.14681	+	0.662110i	0.948107	−	0.317950i	$-0.102994\pi$
$131$	13.1258	+	7.57820i	1.14681	+	0.662110i	0.198701	+	0.980060i	$0.436328\pi$
$132$	26.0574			2.26801
$133$		0			0
$134$	−3.70480			−0.320046
$135$	4.09629	−	7.09498i	0.352553	−	0.610639i
$136$	−4.36392	−	1.93011i	−0.374203	−	0.165506i
$137$	3.72304	+	6.44849i	0.318081	+	0.550932i	0.980088	−	0.198566i	$-0.0636284\pi$
$137$	3.72304	+	6.44849i	0.318081	+	0.550932i	−0.662007	+	0.749498i	$0.730295\pi$
$138$	−1.18242	+	2.04801i	−0.100654	+	0.174338i
$139$			8.75000i			0.742165i	0.928600	+	0.371082i	$0.121013\pi$
$139$			8.75000i			0.742165i	−0.928600	+	0.371082i	$0.878987\pi$
$140$		0			0
$141$		−	32.6579i		−	2.75029i
$142$	−0.276970	−	0.159909i	−0.0232428	−	0.0134192i
$143$	−8.96854	+	5.17799i	−0.749987	+	0.433005i
$144$	11.3476	+	19.6546i	0.945632	+	1.63788i
$145$	−2.49840	+	4.32735i	−0.207481	+	0.359367i
$146$			2.95907i			0.244894i
$147$		0			0
$148$			11.3690i			0.934528i
$149$	0.370056	−	0.640956i	0.0303162	−	0.0525092i	−0.850469	−	0.526025i	$-0.823682\pi$
$149$	0.370056	−	0.640956i	0.0303162	−	0.0525092i	0.880785	+	0.473516i	$0.157015\pi$
$150$	−3.50056	+	2.02105i	−0.285820	+	0.165018i
$151$	4.76784	+	8.25814i	0.388001	+	0.672038i	0.992181	−	0.124810i	$-0.0398323\pi$
$151$	4.76784	+	8.25814i	0.388001	+	0.672038i	−0.604179	+	0.796848i	$0.706499\pi$
$152$	−3.62919	+	6.28594i	−0.294366	+	0.509857i
$153$	−21.6983	+	15.8463i	−1.75420	+	1.28110i
$154$		0			0
$155$	−2.71084			−0.217740
$156$	−11.9805	−	6.91697i	−0.959211	−	0.553800i
$157$	−8.29320	−	14.3642i	−0.661869	−	1.14639i	−0.980124	−	0.198386i	$-0.936430\pi$
$157$	−8.29320	−	14.3642i	−0.661869	−	1.14639i	0.318255	−	0.948005i	$-0.396903\pi$
$158$	2.32498	−	1.34233i	0.184966	−	0.106790i
$159$	13.4301	+	7.75384i	1.06507	+	0.614920i
$160$			2.52597i			0.199695i
$161$		0			0
$162$	−4.11634			−0.323410
$163$	−0.0152261	−	0.00879078i	−0.00119260	−	0.000688547i	0.499404	−	0.866369i	$-0.333553\pi$
$163$	−0.0152261	−	0.00879078i	−0.00119260	−	0.000688547i	−0.500596	+	0.865681i	$0.666886\pi$
$164$	−1.34675	+	0.777546i	−0.105163	+	0.0607161i
$165$	8.91085	−	5.14468i	0.693708	−	0.400513i
$166$	0.0509930	−	0.0883225i	0.00395783	−	0.00685516i
$167$			0.957652i			0.0741054i	0.999313	+	0.0370527i	$0.0117969\pi$
$167$			0.957652i			0.0741054i	−0.999313	+	0.0370527i	$0.988203\pi$
$168$		0			0
$169$	−7.50199			−0.577076
$170$	−0.915755	+	0.0985243i	−0.0702352	+	0.00755647i
$171$	20.4353	+	35.3949i	1.56272	+	2.70672i
$172$	−0.142020	−	0.245986i	−0.0108289	−	0.0187563i
$173$	8.66345	+	5.00185i	0.658670	+	0.380283i	0.791770	−	0.610819i	$-0.209160\pi$
$173$	8.66345	+	5.00185i	0.658670	+	0.380283i	−0.133100	+	0.991103i	$0.542493\pi$
$174$	6.03764			0.457712
$175$		0			0
$176$			15.3816i			1.15943i
$177$	−14.7216	−	8.49949i	−1.10654	−	0.638861i
$178$	2.01189	+	3.48470i	0.150798	+	0.261189i
$179$	−8.09923	−	14.0283i	−0.605365	−	1.04852i	−0.991994	−	0.126287i	$-0.959694\pi$
$179$	−8.09923	−	14.0283i	−0.605365	−	1.04852i	0.386629	−	0.922235i	$-0.373639\pi$
$180$	8.15103	+	4.70600i	0.607542	+	0.350764i
$181$		−	10.6758i		−	0.793526i	−0.917921	−	0.396763i	$-0.870134\pi$
$181$		−	10.6758i		−	0.793526i	0.917921	−	0.396763i	$-0.129866\pi$
$182$		0			0
$183$	2.50838			0.185425
$184$	−2.59745	−	1.49964i	−0.191486	−	0.110555i
$185$	2.24466	+	3.88786i	0.165031	+	0.285841i
$186$	1.63776	+	2.83668i	0.120086	+	0.207995i
$187$	−18.1056	+	1.94795i	−1.32401	+	0.142448i
$188$	20.2465			1.47663
$189$		0			0
$190$			1.40102i			0.101641i
$191$	−4.92699	+	8.53380i	−0.356505	+	0.617484i	−0.987374	−	0.158405i	$-0.949365\pi$
$191$	−4.92699	+	8.53380i	−0.356505	+	0.617484i	0.630870	+	0.775889i	$0.282698\pi$
$192$	−15.9654	+	9.21764i	−1.15220	+	0.665226i
$193$	10.8783	−	6.28057i	0.783035	−	0.452085i	−0.0544701	−	0.998515i	$-0.517347\pi$
$193$	10.8783	−	6.28057i	0.783035	−	0.452085i	0.837505	+	0.546430i	$0.184014\pi$
$194$	−3.35446	−	1.93670i	−0.240836	−	0.139047i
$195$	−5.46264			−0.391188
$196$		0			0
$197$		−	4.48842i		−	0.319787i	−0.987134	−	0.159893i	$-0.948885\pi$
$197$		−	4.48842i		−	0.319787i	0.987134	−	0.159893i	$-0.0511150\pi$
$198$	−7.37281	−	4.25669i	−0.523963	−	0.302510i
$199$	22.3355	−	12.8954i	1.58332	−	0.914133i	0.588955	−	0.808166i	$-0.299540\pi$
$199$	22.3355	−	12.8954i	1.58332	−	0.914133i	0.994370	−	0.105967i	$-0.0337937\pi$
$200$	−2.56325	−	4.43968i	−0.181249	−	0.313933i
$201$	−33.4612	−	19.3188i	−2.36017	−	1.36264i
$202$	−0.430375			−0.0302811
$203$		0			0
$204$	−14.3466	−	19.6448i	−1.00447	−	1.37541i
$205$	−0.307032	+	0.531794i	−0.0214440	+	0.0371421i
$206$	0.396516	+	0.686785i	0.0276266	+	0.0478506i
$207$	−14.6257	+	8.44417i	−1.01656	+	0.586910i
$208$	4.08306	−	7.07208i	0.283110	−	0.490360i
$209$			27.6999i			1.91605i
$210$		0			0
$211$		−	18.0965i		−	1.24581i	−0.782296	−	0.622907i	$-0.785951\pi$
$211$		−	18.0965i		−	1.24581i	0.782296	−	0.622907i	$-0.214049\pi$
$212$	−4.80705	+	8.32606i	−0.330150	+	0.571836i
$213$	−1.66770	−	2.88854i	−0.114269	−	0.197920i
$214$	−2.48718	+	1.43597i	−0.170020	+	0.0981610i
$215$	−0.0971332	−	0.0560799i	−0.00662443	−	0.00382462i
$216$		−	12.5548i		−	0.854247i
$217$		0			0
$218$		−	5.33139i		−	0.361087i
$219$	−15.4302	+	26.7258i	−1.04267	+	1.80597i
$220$	3.18948	+	5.52435i	0.215035	+	0.372451i
$221$	8.84160	+	3.91054i	0.594750	+	0.263051i
$222$	2.71222	−	4.69771i	0.182033	−	0.315290i
$223$	−12.9476			−0.867034			−0.433517	−	0.901145i	$-0.642728\pi$
$223$	−12.9476			−0.867034			−0.433517	+	0.901145i	$0.642728\pi$
$224$		0			0
$225$	−28.8664			−1.92442
$226$	3.69204	+	2.13160i	0.245591	+	0.141792i
$227$	−1.38010	+	0.796801i	−0.0916004	+	0.0528855i	−0.545100	−	0.838371i	$-0.683509\pi$
$227$	−1.38010	+	0.796801i	−0.0916004	+	0.0528855i	0.453500	+	0.891256i	$0.350175\pi$
$228$	−32.0453	+	18.5014i	−2.12225	+	1.22528i
$229$	−6.11451	+	10.5906i	−0.404058	+	0.699850i	−0.994211	−	0.107442i	$-0.965734\pi$
$229$	−6.11451	+	10.5906i	−0.404058	+	0.699850i	0.590153	+	0.807291i	$0.299067\pi$
$230$	−0.578923			−0.0381731
$231$		0			0
$232$			7.65740i			0.502733i
$233$	18.3262	+	10.5807i	1.20059	+	0.693162i	0.960687	−	0.277635i	$-0.0895506\pi$
$233$	18.3262	+	10.5807i	1.20059	+	0.693162i	0.239904	+	0.970797i	$0.422884\pi$
$234$	2.25989	+	3.91424i	0.147733	+	0.255882i
$235$	6.92370	−	3.99740i	0.451652	−	0.260762i
$236$	5.26932	−	9.12673i	0.343004	−	0.594100i
$237$	27.9985			1.81870
$238$		0			0
$239$	27.6877			1.79097			0.895484	−	0.445094i	$-0.146830\pi$
$239$	27.6877			1.79097			0.895484	+	0.445094i	$0.146830\pi$
$240$	−4.05680	+	7.02658i	−0.261865	+	0.453564i
$241$	−12.7926	+	7.38580i	−0.824042	+	0.475761i	−0.851808	−	0.523854i	$-0.824494\pi$
$241$	−12.7926	+	7.38580i	−0.824042	+	0.475761i	0.0277663	+	0.999614i	$0.491161\pi$
$242$	−1.25808	−	2.17906i	−0.0808726	−	0.140075i
$243$	−8.99353	−	5.19242i	−0.576935	−	0.333094i
$244$			1.55509i			0.0995545i
$245$		0			0
$246$	0.741974			0.0473065
$247$	7.35298	−	12.7357i	0.467859	−	0.810356i
$248$	−3.59769	+	2.07713i	−0.228454	+	0.131898i
$249$	0.921123	−	0.531811i	0.0583738	−	0.0337021i
$250$	−1.82424	−	1.05322i	−0.115375	−	0.0666117i
$251$	−8.26776			−0.521857			−0.260928	−	0.965358i	$-0.584029\pi$
$251$	−8.26776			−0.521857			−0.260928	+	0.965358i	$0.584029\pi$
$252$		0			0
$253$	−11.4460			−0.719607
$254$	−1.33079	+	2.30500i	−0.0835013	+	0.144628i
$255$	−8.78472	−	3.88538i	−0.550121	−	0.243312i
$256$	−4.72516	−	8.18423i	−0.295323	−	0.511514i
$257$	12.2290	−	21.1812i	0.762823	−	1.32125i	−0.178567	−	0.983928i	$-0.557146\pi$
$257$	12.2290	−	21.1812i	0.762823	−	1.32125i	0.941390	−	0.337320i	$-0.109521\pi$
$258$			0.135523i			0.00843728i
$259$		0			0
$260$		−	3.38661i		−	0.210028i
$261$	37.3407	+	21.5587i	2.31133	+	1.33445i
$262$	3.88258	−	2.24161i	0.239867	−	0.138487i
$263$	8.76139	+	15.1752i	0.540250	+	0.935741i	0.998889	+	0.0471182i	$0.0150037\pi$
$263$	8.76139	+	15.1752i	0.540250	+	0.935741i	−0.458639	+	0.888623i	$0.651663\pi$
$264$	7.88402	−	13.6555i	0.485228	−	0.840440i
$265$			3.79635i			0.233208i
$266$		0			0
$267$			41.9643i			2.56818i
$268$	11.9768	−	20.7445i	0.731602	−	1.26717i
$269$	−17.1610	+	9.90790i	−1.04632	+	0.604095i	−0.921618	−	0.388099i	$-0.873132\pi$
$269$	−17.1610	+	9.90790i	−1.04632	+	0.604095i	−0.124706	+	0.992194i	$0.539799\pi$
$270$	−1.21167	−	2.09868i	−0.0737400	−	0.127721i
$271$	−5.05268	+	8.75150i	−0.306928	+	0.531616i	−0.977689	−	0.210059i	$-0.932635\pi$
$271$	−5.05268	+	8.75150i	−0.306928	+	0.531616i	0.670760	+	0.741674i	$0.265968\pi$
$272$	11.5963	−	8.46878i	0.703128	−	0.513495i
$273$		0			0
$274$	2.20253			0.133060
$275$	−16.9430	−	9.78207i	−1.02170	−	0.589881i
$276$	−7.64504	−	13.2416i	−0.460177	−	0.797051i
$277$	−27.0551	+	15.6203i	−1.62559	+	0.938533i	−0.640198	+	0.768210i	$0.721148\pi$
$277$	−27.0551	+	15.6203i	−1.62559	+	0.938533i	−0.985388	+	0.170323i	$0.945519\pi$
$278$	2.24147	+	1.29411i	0.134434	+	0.0776157i
$279$			23.3918i			1.40043i
$280$		0			0
$281$	−23.5665			−1.40586			−0.702930	−	0.711259i	$-0.748125\pi$
$281$	−23.5665			−1.40586			−0.702930	+	0.711259i	$0.748125\pi$
$282$	−8.36591	−	4.83006i	−0.498183	−	0.287626i
$283$	6.12556	−	3.53659i	0.364127	−	0.210229i	−0.306763	−	0.951786i	$-0.599246\pi$
$283$	6.12556	−	3.53659i	0.364127	−	0.210229i	0.670889	+	0.741557i	$0.265913\pi$
$284$	1.79077	−	1.03390i	0.106263	−	0.0613508i
$285$	−7.30568	+	12.6538i	−0.432751	+	0.749547i
$286$			3.06327i			0.181135i
$287$		0			0
$288$	21.7966			1.28437
$289$	11.4371	+	12.5774i	0.672773	+	0.739849i
$290$	0.739020	+	1.28002i	0.0433967	+	0.0751654i
$291$	−20.1980	−	34.9840i	−1.18403	−	2.05080i
$292$	−16.5689	−	9.56605i	−0.969621	−	0.559811i
$293$	−6.26841			−0.366204			−0.183102	−	0.983094i	$-0.558614\pi$
$293$	−6.26841			−0.366204			−0.183102	+	0.983094i	$0.558614\pi$
$294$		0			0
$295$		−	4.16142i		−	0.242287i
$296$	5.95800	+	3.43985i	0.346302	+	0.199937i
$297$	−23.9563	−	41.4935i	−1.39008	−	2.40770i
$298$	−0.109462	−	0.189593i	−0.00634094	−	0.0109828i
$299$	5.26260	+	3.03836i	0.304344	+	0.175713i
$300$		−	26.1346i		−	1.50888i
$301$		0			0
$302$	2.82063			0.162309
$303$	−3.88709	−	2.24421i	−0.223307	−	0.128927i
$304$	−10.9213	−	18.9162i	−0.626379	−	1.08492i
$305$	0.307032	+	0.531794i	0.0175806	+	0.0304505i
$306$	0.850166	+	7.90204i	0.0486008	+	0.451730i
$307$	−3.56954			−0.203724			−0.101862	−	0.994799i	$-0.532480\pi$
$307$	−3.56954			−0.203724			−0.101862	+	0.994799i	$0.532480\pi$
$308$		0			0
$309$			8.27059i			0.470497i
$310$	−0.400930	+	0.694431i	−0.0227713	+	0.0394410i
$311$	19.3523	−	11.1730i	1.09737	−	0.633565i	0.161838	−	0.986817i	$-0.448258\pi$
$311$	19.3523	−	11.1730i	1.09737	−	0.633565i	0.935528	+	0.353253i	$0.114924\pi$
$312$	−7.24975	+	4.18564i	−0.410436	+	0.236965i
$313$	3.18532	+	1.83905i	0.180045	+	0.103949i	0.587314	−	0.809359i	$-0.300185\pi$
$313$	3.18532	+	1.83905i	0.180045	+	0.103949i	−0.407269	+	0.913308i	$0.633519\pi$
$314$	−4.90621			−0.276874
$315$		0			0
$316$			17.3579i			0.976458i
$317$	−14.1956	−	8.19582i	−0.797303	−	0.460323i	0.0452243	−	0.998977i	$-0.485600\pi$
$317$	−14.1956	−	8.19582i	−0.797303	−	0.460323i	−0.842527	+	0.538654i	$0.818933\pi$
$318$	3.97257	−	2.29357i	0.222771	−	0.128617i
$319$	14.6114	+	25.3076i	0.818079	+	1.41695i
$320$	−3.90840	−	2.25652i	−0.218486	−	0.126143i
$321$	−29.9518			−1.67174
$322$		0			0
$323$	20.8831	−	15.2510i	1.16197	−	0.848588i
$324$	13.3073	−	23.0489i	0.739294	−	1.28049i
$325$	5.19332	+	8.99509i	0.288074	+	0.498958i
$326$	−0.00450384	+	0.00260029i	−0.000249444	+	0.000144017i
$327$	27.8007	−	48.1523i	1.53738	−	2.66283i
$328$			0.941028i			0.0519596i
$329$		0			0
$330$		−	3.04356i		−	0.167543i
$331$	1.95396	−	3.38436i	0.107400	−	0.186021i	−0.807316	−	0.590119i	$-0.799081\pi$
$331$	1.95396	−	3.38436i	0.107400	−	0.186021i	0.914716	+	0.404097i	$0.132414\pi$
$332$	0.329700	+	0.571057i	0.0180946	+	0.0313408i
$333$	33.5484	−	19.3692i	1.83844	−	1.06142i
$334$	0.245320	+	0.141636i	0.0134233	+	0.00774995i
$335$		−	9.45866i		−	0.516782i
$336$		0			0
$337$		−	22.1822i		−	1.20834i	−0.796855	−	0.604170i	$-0.793505\pi$
$337$		−	22.1822i		−	1.20834i	0.796855	−	0.604170i	$-0.206495\pi$
$338$	−1.10953	+	1.92177i	−0.0603507	+	0.104530i
$339$	22.2307	+	38.5046i	1.20740	+	2.09129i
$340$	2.40877	−	5.44615i	0.130634	−	0.295359i
$341$	−7.92689	+	13.7298i	−0.429265	+	0.743509i
$342$	12.0894			0.653720
$343$		0			0
$344$	−0.171880			−0.00926717
$345$	−5.22875	−	3.01882i	−0.281506	−	0.162528i
$346$	2.56263	−	1.47953i	0.137768	−	0.0795402i
$347$	8.22289	−	4.74749i	0.441428	−	0.254859i	−0.262775	−	0.964857i	$-0.584638\pi$
$347$	8.22289	−	4.74749i	0.441428	−	0.254859i	0.704203	+	0.709998i	$0.251304\pi$
$348$	−19.5184	+	33.8069i	−1.04630	+	1.81224i
$349$	−4.92745			−0.263761			−0.131880	−	0.991266i	$-0.542101\pi$
$349$	−4.92745			−0.263761			−0.131880	+	0.991266i	$0.542101\pi$
$350$		0			0
$351$			25.4369i			1.35772i
$352$	12.7934	+	7.38629i	0.681892	+	0.393691i
$353$	11.7607	+	20.3702i	0.625962	+	1.08420i	0.988354	+	0.152172i	$0.0486266\pi$
$353$	11.7607	+	20.3702i	0.625962	+	1.08420i	−0.362393	+	0.932026i	$0.618040\pi$
$354$	−4.35460	+	2.51413i	−0.231444	+	0.133624i
$355$	0.408260	−	0.707127i	0.0216682	−	0.0375304i
$356$	−26.0161			−1.37885
$357$		0			0
$358$	−4.79146			−0.253236
$359$	−9.36856	+	16.2268i	−0.494454	+	0.856419i	−0.999980	−	0.00639257i	$-0.997965\pi$
$359$	−9.36856	+	16.2268i	−0.494454	+	0.856419i	0.505526	+	0.862811i	$0.331299\pi$
$360$	4.93241	−	2.84773i	0.259961	−	0.150088i
$361$	−10.1676	−	17.6108i	−0.535137	−	0.926884i
$362$	−2.73480	−	1.57894i	−0.143738	−	0.0829870i
$363$		−	26.2413i		−	1.37731i
$364$		0			0
$365$	−7.55475			−0.395433
$366$	0.370987	−	0.642568i	0.0193918	−	0.0335876i
$367$	19.7328	−	11.3927i	1.03004	−	0.594696i	0.113047	−	0.993590i	$-0.463939\pi$
$367$	19.7328	−	11.3927i	1.03004	−	0.594696i	0.916997	+	0.398893i	$0.130606\pi$
$368$	7.81648	−	4.51285i	0.407462	−	0.235248i
$369$	4.58885	+	2.64938i	0.238886	+	0.137921i
$370$	1.32793			0.0690357
$371$		0			0
$372$	−21.1781			−1.09803
$373$	18.5310	−	32.0966i	0.959496	−	1.66190i	0.235771	−	0.971809i	$-0.424238\pi$
$373$	18.5310	−	32.0966i	0.959496	−	1.66190i	0.723726	−	0.690088i	$-0.242428\pi$
$374$	−2.17880	+	4.92618i	−0.112663	+	0.254727i
$375$	−10.9842	−	19.0251i	−0.567220	−	0.982453i
$376$	6.12586	−	10.6103i	0.315917	−	0.547185i
$377$		−	15.5144i		−	0.799033i
$378$		0			0
$379$			5.06862i			0.260357i	0.991491	+	0.130179i	$0.0415551\pi$
$379$			5.06862i			0.260357i	−0.991491	+	0.130179i	$0.958445\pi$
$380$	−7.84482	−	4.52921i	−0.402431	−	0.232344i
$381$	−24.0390	+	13.8789i	−1.23156	+	0.711039i
$382$	1.45739	+	2.52427i	0.0745666	+	0.129153i
$383$	−3.14869	+	5.45370i	−0.160891	+	0.278671i	−0.935188	−	0.354151i	$-0.884770\pi$
$383$	−3.14869	+	5.45370i	−0.160891	+	0.278671i	0.774298	+	0.632822i	$0.218103\pi$
$384$			26.0897i			1.33139i
$385$		0			0
$386$		−	3.71555i		−	0.189117i
$387$	−0.483913	+	0.838162i	−0.0245987	+	0.0426062i
$388$	21.6886	−	12.5219i	1.10107	−	0.635704i
$389$	0.629332	+	1.09003i	0.0319084	+	0.0552669i	0.881539	−	0.472112i	$-0.156508\pi$
$389$	0.629332	+	1.09003i	0.0319084	+	0.0552669i	−0.849630	+	0.527379i	$0.823175\pi$
$390$	−0.807918	+	1.39935i	−0.0409105	+	0.0708591i
$391$	6.30194	+	8.62923i	0.318703	+	0.436399i
$392$		0			0
$393$	46.7559			2.35852
$394$	−1.14979	−	0.663832i	−0.0579256	−	0.0334433i
$395$	3.42708	+	5.93588i	0.172435	+	0.298666i
$396$	47.6696	−	27.5220i	2.39549	−	1.38303i
$397$	16.2390	+	9.37559i	0.815012	+	0.470547i	0.848693	−	0.528885i	$-0.177390\pi$
$397$	16.2390	+	9.37559i	0.815012	+	0.470547i	−0.0336813	+	0.999433i	$0.510723\pi$
$398$		−	7.62887i		−	0.382401i
$399$		0			0
$400$	15.4272			0.771358
$401$	1.12372	+	0.648778i	0.0561157	+	0.0323984i	0.527795	−	0.849372i	$-0.323019\pi$
$401$	1.12372	+	0.648778i	0.0561157	+	0.0323984i	−0.471680	+	0.881770i	$0.656352\pi$
$402$	−9.89773	+	5.71446i	−0.493654	+	0.285011i
$403$	7.28917	−	4.20840i	0.363099	−	0.209636i
$404$	1.39132	−	2.40983i	0.0692205	−	0.119893i
$405$		−	10.5094i		−	0.522215i
$406$		0			0
$407$	26.2548			1.30140
$408$	−14.6357	+	1.57463i	−0.724577	+	0.0779559i
$409$	−3.30814	−	5.72986i	−0.163577	−	0.283323i	0.772572	−	0.634927i	$-0.218970\pi$
$409$	−3.30814	−	5.72986i	−0.163577	−	0.283323i	−0.936149	+	0.351604i	$0.885636\pi$
$410$	0.0908191	+	0.157303i	0.00448524	+	0.00776866i
$411$	19.8929	+	11.4852i	0.981245	+	0.566522i
$412$	−5.12741			−0.252610
$413$		0			0
$414$			4.99553i			0.245517i
$415$	0.225495	+	0.130190i	0.0110691	+	0.00639075i
$416$	−3.92140	−	6.79206i	−0.192262	−	0.333008i
$417$	13.4964	+	23.3765i	0.660922	+	1.14475i
$418$	7.09584	+	4.09679i	0.347069	+	0.200380i
$419$			6.77679i			0.331068i	0.986204	+	0.165534i	$0.0529347\pi$
$419$			6.77679i			0.331068i	−0.986204	+	0.165534i	$0.947065\pi$
$420$		0			0
$421$	12.5941			0.613799			0.306899	−	0.951742i	$-0.400708\pi$
$421$	12.5941			0.613799			0.306899	+	0.951742i	$0.400708\pi$
$422$	−4.63574	−	2.67645i	−0.225664	−	0.130287i
$423$	−34.4936	−	59.7446i	−1.67713	−	2.90488i
$424$	2.90888	+	5.03833i	0.141268	+	0.244683i
$425$	1.95372	+	18.1592i	0.0947693	+	0.880853i
$426$	−0.986602			−0.0478010
$427$		0			0
$428$		−	18.5688i		−	0.897557i
$429$	−15.9736	+	27.6670i	−0.771211	+	1.33578i
$430$	−0.0287317	+	0.0165883i	−0.00138557	+	0.000799958i
$431$	11.5801	−	6.68578i	0.557794	−	0.322043i	−0.194465	−	0.980909i	$-0.562297\pi$
$431$	11.5801	−	6.68578i	0.557794	−	0.322043i	0.752260	+	0.658867i	$0.228964\pi$
$432$	32.7194	+	18.8906i	1.57421	+	0.908872i
$433$	0.994338			0.0477849			0.0238924	−	0.999715i	$-0.492394\pi$
$433$	0.994338			0.0477849			0.0238924	+	0.999715i	$0.492394\pi$
$434$		0			0
$435$			15.4146i			0.739074i
$436$	29.8524	+	17.2353i	1.42967	+	0.825420i
$437$	14.0763	−	8.12695i	0.673361	−	0.388765i
$438$	4.56420	+	7.90543i	0.218086	+	0.377736i
$439$	14.3896	+	8.30785i	0.686779	+	0.396512i	0.802404	−	0.596781i	$-0.203554\pi$
$439$	14.3896	+	8.30785i	0.686779	+	0.396512i	−0.115625	+	0.993293i	$0.536887\pi$
$440$	3.86009			0.184022
$441$		0			0
$442$	2.30942	−	1.68657i	0.109848	−	0.0802220i
$443$	10.4884	−	18.1665i	0.498320	−	0.863115i	−0.501678	−	0.865054i	$-0.667284\pi$
$443$	10.4884	−	18.1665i	0.498320	−	0.863115i	0.999998	+	0.00193888i	$0.000617165\pi$
$444$	17.5361	+	30.3735i	0.832228	+	1.44146i
$445$	−8.89672	+	5.13653i	−0.421745	+	0.243495i
$446$	−1.91493	+	3.31675i	−0.0906745	+	0.157053i
$447$		−	2.28317i		−	0.107990i
$448$		0			0
$449$		−	0.787831i		−	0.0371800i	−0.999827	−	0.0185900i	$-0.994082\pi$
$449$		−	0.787831i		−	0.0371800i	0.999827	−	0.0185900i	$-0.00591773\pi$
$450$	−4.26930	+	7.39464i	−0.201257	+	0.348587i
$451$	1.79561	+	3.11009i	0.0845520	+	0.146448i
$452$	−23.8712	+	13.7821i	−1.12281	+	0.648254i
$453$	25.4755	+	14.7083i	1.19694	+	0.691056i
$454$			0.471383i			0.0221231i
$455$		0			0
$456$			22.3913i			1.04857i
$457$	7.72411	−	13.3786i	0.361319	−	0.625822i	−0.626859	−	0.779132i	$-0.715660\pi$
$457$	7.72411	−	13.3786i	0.361319	−	0.625822i	0.988178	+	0.153310i	$0.0489933\pi$
$458$	1.80866	+	3.13268i	0.0845130	+	0.146381i
$459$	−18.0924	+	40.9062i	−0.844479	+	1.90934i
$460$	1.87154	−	3.24160i	0.0872610	−	0.151140i
$461$	22.7334			1.05880			0.529400	−	0.848372i	$-0.322417\pi$
$461$	22.7334			1.05880			0.529400	+	0.848372i	$0.322417\pi$
$462$		0			0
$463$	−0.105969			−0.00492481			−0.00246240	−	0.999997i	$-0.500784\pi$
$463$	−0.105969			−0.00492481			−0.00246240	+	0.999997i	$0.500784\pi$
$464$	−19.9561	−	11.5217i	−0.926440	−	0.534881i
$465$	−7.24228	+	4.18133i	−0.335853	+	0.193905i
$466$	5.42085	−	3.12973i	0.251116	−	0.144982i
$467$	9.35481	−	16.2030i	0.432889	−	0.749786i	−0.564232	−	0.825617i	$-0.690828\pi$
$467$	9.35481	−	16.2030i	0.432889	−	0.749786i	0.997121	+	0.0758307i	$0.0241608\pi$
$468$	−29.2230			−1.35083
$469$		0			0
$470$		−	2.36484i		−	0.109082i
$471$	−44.3122	−	25.5836i	−2.04180	−	1.17883i
$472$	−3.18861	−	5.52284i	−0.146768	−	0.254209i
$473$	−0.568063	+	0.327971i	−0.0261196	+	0.0150801i
$474$	4.14094	−	7.17233i	0.190200	−	0.329436i
$475$	27.7820			1.27472
$476$		0			0
$477$	32.7587			1.49992
$478$	4.09497	−	7.09270i	0.187300	−	0.324412i
$479$	−14.4569	+	8.34667i	−0.660551	+	0.381369i	−0.792487	−	0.609889i	$-0.791214\pi$
$479$	−14.4569	+	8.34667i	−0.660551	+	0.381369i	0.131936	+	0.991258i	$0.457881\pi$
$480$	3.89617	+	6.74837i	0.177835	+	0.308019i
$481$	−12.0713	−	6.96937i	−0.550404	−	0.317776i
$482$			4.36940i			0.199021i
$483$		0			0
$484$	16.2685			0.739476
$485$	4.94456	−	8.56423i	0.224521	−	0.388882i
$486$	−2.66026	+	1.53590i	−0.120672	+	0.0696700i
$487$	−24.0174	+	13.8665i	−1.08833	+	0.628350i	−0.933132	−	0.359533i	$-0.882936\pi$
$487$	−24.0174	+	13.8665i	−1.08833	+	0.628350i	−0.155201	+	0.987883i	$0.549603\pi$
$488$	0.814954	+	0.470514i	0.0368913	+	0.0212992i
$489$	−0.0542373			−0.00245270
$490$		0			0
$491$	−12.9752			−0.585563			−0.292782	−	0.956179i	$-0.594581\pi$
$491$	−12.9752			−0.585563			−0.292782	+	0.956179i	$0.594581\pi$
$492$	−2.39865	+	4.15458i	−0.108139	+	0.187303i
$493$	11.0348	−	24.9494i	0.496985	−	1.12366i
$494$	−2.17499	−	3.76720i	−0.0978575	−	0.169494i
$495$	10.8677	−	18.8234i	0.488467	−	0.846049i
$496$		−	12.5014i		−	0.561329i
$497$		0			0
$498$		−	0.314616i		−	0.0140983i
$499$	−12.9079	−	7.45237i	−0.577836	−	0.333614i	0.182437	−	0.983218i	$-0.441601\pi$
$499$	−12.9079	−	7.45237i	−0.577836	−	0.333614i	−0.760273	+	0.649604i	$0.774935\pi$
$500$	11.7948	−	6.80971i	0.527478	−	0.304540i
$501$	1.47713	+	2.55846i	0.0659933	+	0.114304i
$502$	−1.22279	+	2.11794i	−0.0545758	+	0.0945281i
$503$		−	10.9124i		−	0.486560i	−0.969956	−	0.243280i	$-0.921777\pi$
$503$		−	10.9124i		−	0.486560i	0.969956	−	0.243280i	$-0.0782234\pi$
$504$		0			0
$505$		−	1.09878i		−	0.0488953i
$506$	−1.69285	+	2.93211i	−0.0752566	+	0.130348i
$507$	−20.0423	+	11.5714i	−0.890110	+	0.513905i
$508$	−8.60435	−	14.9032i	−0.381756	−	0.661221i
$509$	5.01498	−	8.68620i	0.222285	−	0.385009i	−0.733216	−	0.679995i	$-0.761982\pi$
$509$	5.01498	−	8.68620i	0.222285	−	0.385009i	0.955501	+	0.294986i	$0.0953151\pi$
$510$	−2.29456	+	1.67572i	−0.101605	+	0.0742022i
$511$		0			0
$512$	−19.7099			−0.871062
$513$	58.9227	+	34.0190i	2.60150	+	1.50198i
$514$	−3.61730	−	6.26535i	−0.159552	−	0.276353i
$515$	−1.75342	+	1.01234i	−0.0772650	+	0.0446089i
$516$	−0.758841	−	0.438117i	−0.0334061	−	0.0192870i
$517$		−	46.7559i		−	2.05632i
$518$		0			0
$519$	30.8603			1.35462
$520$	−1.77477	−	1.02466i	−0.0778288	−	0.0449345i
$521$	31.0983	−	17.9546i	1.36244	−	0.786606i	0.372493	−	0.928035i	$-0.378503\pi$
$521$	31.0983	−	17.9546i	1.36244	−	0.786606i	0.989948	+	0.141429i	$0.0451696\pi$
$522$	11.0453	−	6.37700i	0.483439	−	0.279114i
$523$	−7.13069	+	12.3507i	−0.311803	+	0.540059i	−0.978753	−	0.205044i	$-0.934266\pi$
$523$	−7.13069	+	12.3507i	−0.311803	+	0.540059i	0.666950	+	0.745103i	$0.267600\pi$
$524$			28.9867i			1.26629i
$525$		0			0
$526$	5.18319			0.225998
$527$	14.7153	−	1.58319i	0.641010	−	0.0689650i
$528$	23.7253	+	41.0935i	1.03251	+	1.78836i
$529$	−8.14182	−	14.1020i	−0.353992	−	0.613132i
$530$	0.972503	+	0.561475i	0.0422428	+	0.0243889i
$531$	−35.9089			−1.55831
$532$		0			0
$533$		−	1.90659i		−	0.0825834i
$534$	10.7499	+	6.20647i	0.465195	+	0.268580i
$535$	−3.66616	−	6.34997i	−0.158502	−	0.274533i
$536$	−7.24751	−	12.5531i	−0.313045	−	0.542210i
$537$	−43.2758	−	24.9853i	−1.86749	−	1.07819i
$538$			5.86146i			0.252705i
$539$		0			0
$540$	15.6683			0.674258
$541$	−22.0107	−	12.7079i	−0.946315	−	0.546355i	−0.0543806	−	0.998520i	$-0.517318\pi$
$541$	−22.0107	−	12.7079i	−0.946315	−	0.546355i	−0.891934	+	0.452165i	$0.850652\pi$
$542$	1.49457	+	2.58867i	0.0641972	+	0.111193i
$543$	−16.4669	−	28.5214i	−0.706660	−	1.22397i
$544$	−1.47522	−	13.7118i	−0.0632497	−	0.587887i
$545$	13.6115			0.583052
$546$		0			0
$547$		−	0.552855i		−	0.0236384i	−0.999930	−	0.0118192i	$-0.996238\pi$
$547$		−	0.552855i		−	0.0236384i	0.999930	−	0.0118192i	$-0.00376225\pi$
$548$	−7.12032	+	12.3328i	−0.304165	+	0.526829i
$549$	4.58885	−	2.64938i	0.195847	−	0.113073i
$550$	−5.01171	+	2.89351i	−0.213700	+	0.123380i
$551$	−35.9380	−	20.7488i	−1.53101	−	0.883929i
$552$	−9.25245			−0.393810
$553$		0			0
$554$			9.24088i			0.392608i
$555$	11.9937	+	6.92454i	0.509102	+	0.293930i
$556$	−14.4924	+	8.36720i	−0.614615	+	0.354848i
$557$	−17.8883	−	30.9835i	−0.757953	−	1.31281i	−0.943893	−	0.330252i	$-0.892866\pi$
$557$	−17.8883	−	30.9835i	−0.757953	−	1.31281i	0.185939	−	0.982561i	$-0.440467\pi$
$558$	5.99224	+	3.45962i	0.253672	+	0.146457i
$559$	0.348241			0.0147290
$560$		0			0
$561$	−45.3664	+	33.1311i	−1.91537	+	1.39880i
$562$	−3.48546	+	6.03699i	−0.147025	+	0.254655i
$563$	3.35632	+	5.81332i	0.141452	+	0.245002i	0.928044	−	0.372472i	$-0.121490\pi$
$563$	3.35632	+	5.81332i	0.141452	+	0.245002i	−0.786592	+	0.617474i	$0.788156\pi$
$564$	54.0906	−	31.2292i	2.27762	−	1.31499i
$565$	−5.44216	+	9.42610i	−0.228954	+	0.396559i
$566$		−	2.09223i		−	0.0879429i
$567$		0			0
$568$		−	1.25129i		−	0.0525028i
$569$	4.80793	−	8.32758i	0.201559	−	0.349110i	−0.747472	−	0.664293i	$-0.768733\pi$
$569$	4.80793	−	8.32758i	0.201559	−	0.349110i	0.949031	+	0.315183i	$0.102066\pi$
$570$	2.16100	+	3.74296i	0.0905144	+	0.156775i
$571$	6.39059	−	3.68961i	0.267438	−	0.154405i	−0.360285	−	0.932842i	$-0.617320\pi$
$571$	6.39059	−	3.68961i	0.267438	−	0.154405i	0.627723	+	0.778437i	$0.283987\pi$
$572$	−17.1524	−	9.90292i	−0.717177	−	0.414062i
$573$			30.3985i			1.26992i
$574$		0			0
$575$			11.4799i			0.478746i
$576$	−19.4715	+	33.7256i	−0.811312	+	1.40523i
$577$	−5.01867	−	8.69260i	−0.208930	−	0.361878i	0.742448	−	0.669904i	$-0.233665\pi$
$577$	−5.01867	−	8.69260i	−0.208930	−	0.361878i	−0.951378	+	0.308026i	$0.900331\pi$
$578$	4.91347	−	1.06964i	0.204374	−	0.0444913i
$579$	19.3749	−	33.5583i	0.805193	−	1.39464i
$580$	−9.55640			−0.396808
$581$		0			0
$582$	−11.9490			−0.495304
$583$	19.2276	+	11.1011i	0.796327	+	0.459759i
$584$	−10.0263	+	5.78868i	−0.414891	+	0.239537i
$585$	−9.99339	+	5.76969i	−0.413176	+	0.238547i
$586$	−0.927089	+	1.60577i	−0.0382977	+	0.0663335i
$587$	23.8774			0.985526			0.492763	−	0.870164i	$-0.335987\pi$
$587$	23.8774			0.985526			0.492763	+	0.870164i	$0.335987\pi$
$588$		0			0
$589$		−	22.5131i		−	0.927636i
$590$	−1.06602	−	0.615469i	−0.0438875	−	0.0253385i
$591$	−6.92316	−	11.9913i	−0.284781	−	0.493254i
$592$	−17.9294	+	10.3515i	−0.736892	+	0.425445i
$593$	4.54110	−	7.86542i	0.186481	−	0.322994i	−0.757594	−	0.652726i	$-0.773625\pi$
$593$	4.54110	−	7.86542i	0.186481	−	0.322994i	0.944074	+	0.329732i	$0.106959\pi$
$594$	−14.1724			−0.581501
$595$		0			0
$596$	1.41547			0.0579798
$597$	39.7811	−	68.9028i	1.62813	−	2.82000i
$598$	1.55666	−	0.898740i	0.0636567	−	0.0367522i
$599$	9.05229	+	15.6790i	0.369866	+	0.640628i	0.989544	−	0.144229i	$-0.0460701\pi$
$599$	9.05229	+	15.6790i	0.369866	+	0.640628i	−0.619678	+	0.784856i	$0.712737\pi$
$600$	−13.6960	−	7.90737i	−0.559135	−	0.322817i
$601$		−	17.9862i		−	0.733674i	−0.930285	−	0.366837i	$-0.880441\pi$
$601$		−	17.9862i		−	0.733674i	0.930285	−	0.366837i	$-0.119559\pi$
$602$		0			0
$603$	−81.6187			−3.32377
$604$	−9.11851	+	15.7937i	−0.371027	+	0.642638i
$605$	5.56333	−	3.21199i	0.226182	−	0.130586i
$606$	−1.14979	+	0.663832i	−0.0467070	+	0.0269663i
$607$	−5.89495	−	3.40345i	−0.239268	−	0.138142i	0.375572	−	0.926793i	$-0.377446\pi$
$607$	−5.89495	−	3.40345i	−0.239268	−	0.138142i	−0.614840	+	0.788652i	$0.710780\pi$
$608$	−20.9777			−0.850760
$609$		0			0
$610$	0.181638			0.00735432
$611$	−12.4114	+	21.4972i	−0.502112	+	0.869683i
$612$	−46.9948	−	20.7853i	−1.89965	−	0.840196i
$613$	−6.98551	−	12.0993i	−0.282142	−	0.488685i	0.689770	−	0.724029i	$-0.257712\pi$
$613$	−6.98551	−	12.0993i	−0.282142	−	0.488685i	−0.971912	+	0.235344i	$0.924378\pi$
$614$	−0.527930	+	0.914402i	−0.0213055	+	0.0369022i
$615$			1.89432i			0.0763864i
$616$		0			0
$617$			38.1175i			1.53455i	0.641316	+	0.767277i	$0.278389\pi$
$617$			38.1175i			1.53455i	−0.641316	+	0.767277i	$0.721611\pi$
$618$	2.11866	+	1.22321i	0.0852250	+	0.0492047i
$619$	9.99527	−	5.77077i	0.401744	−	0.231947i	−0.285492	−	0.958381i	$-0.592157\pi$
$619$	9.99527	−	5.77077i	0.401744	−	0.231947i	0.687236	+	0.726434i	$0.258824\pi$
$620$	−2.59225	−	4.48990i	−0.104107	−	0.180319i
$621$	−14.0572	+	24.3478i	−0.564095	+	0.977042i
$622$		−	6.60991i		−	0.265033i
$623$		0			0
$624$		−	25.1917i		−	1.00847i
$625$	−8.38523	+	14.5236i	−0.335409	+	0.580946i
$626$	0.942209	−	0.543985i	0.0376583	−	0.0217420i
$627$	42.7257	+	74.0031i	1.70630	+	2.95540i
$628$	15.8608	−	27.4717i	0.632914	−	1.09624i
$629$	−14.4553	−	19.7937i	−0.576372	−	0.789225i
$630$		0			0
$631$	−0.585114			−0.0232930			−0.0116465	−	0.999932i	$-0.503707\pi$
$631$	−0.585114			−0.0232930			−0.0116465	+	0.999932i	$0.503707\pi$
$632$	9.09650	+	5.25187i	0.361839	+	0.208908i
$633$	−27.9129	−	48.3466i	−1.10944	−	1.92160i
$634$	−4.19901	+	2.42430i	−0.166764	+	0.0962813i
$635$	−5.88486	−	3.39762i	−0.233533	−	0.134831i
$636$			29.6585i			1.17604i
$637$		0			0
$638$	8.64400			0.342219
$639$	−6.10180	−	3.52287i	−0.241383	−	0.139363i
$640$	−5.53120	+	3.19344i	−0.218640	+	0.126232i
$641$	−34.9898	+	20.2014i	−1.38201	+	0.797906i	−0.992398	−	0.123071i	$-0.960726\pi$
$641$	−34.9898	+	20.2014i	−1.38201	+	0.797906i	−0.389616	+	0.920977i	$0.627392\pi$
$642$	−4.42982	+	7.67268i	−0.174831	+	0.302817i
$643$		−	2.67695i		−	0.105569i	−0.998606	−	0.0527843i	$-0.983190\pi$
$643$		−	2.67695i		−	0.105569i	0.998606	−	0.0527843i	$-0.0168096\pi$
$644$		0			0
$645$	−0.346001			−0.0136238
$646$	−0.818229	−	7.60519i	−0.0321928	−	0.299222i
$647$	21.6519	+	37.5022i	0.851223	+	1.47436i	0.880105	+	0.474779i	$0.157472\pi$
$647$	21.6519	+	37.5022i	0.851223	+	1.47436i	−0.0288820	+	0.999583i	$0.509195\pi$
$648$	−8.05261	−	13.9475i	−0.316336	−	0.547910i
$649$	−21.0766	−	12.1686i	−0.827331	−	0.477660i
$650$	3.07234			0.120507
$651$		0			0
$652$		−	0.0336248i		−	0.00131685i
$653$	8.86388	+	5.11756i	0.346870	+	0.200266i	0.663306	−	0.748348i	$-0.269153\pi$
$653$	8.86388	+	5.11756i	0.346870	+	0.200266i	−0.316436	+	0.948614i	$0.602486\pi$
$654$	−8.22338	−	14.2433i	−0.321560	−	0.556958i
$655$	5.72302	+	9.91256i	0.223617	+	0.387316i
$656$	−2.45244	−	1.41591i	−0.0957516	−	0.0552822i
$657$			65.1899i			2.54330i
$658$		0			0
$659$	−10.5288			−0.410144			−0.205072	−	0.978747i	$-0.565743\pi$
$659$	−10.5288			−0.410144			−0.205072	+	0.978747i	$0.565743\pi$
$660$	17.0420	+	9.83922i	0.663360	+	0.382991i
$661$	13.5857	+	23.5310i	0.528421	+	0.915252i	0.999451	+	0.0331345i	$0.0105490\pi$
$661$	13.5857	+	23.5310i	0.528421	+	0.915252i	−0.471030	+	0.882117i	$0.656118\pi$
$662$	−0.577977	−	1.00109i	−0.0224637	−	0.0389083i
$663$	29.6530	−	3.19031i	1.15163	−	0.123901i
$664$	0.399021			0.0154850
$665$		0			0
$666$		−	11.4587i		−	0.444015i
$667$	8.57372	−	14.8501i	0.331976	−	0.574999i
$668$	−1.58614	+	0.915757i	−0.0613695	+	0.0354317i
$669$	−34.5907	+	19.9710i	−1.33735	+	0.772122i
$670$	−2.42301	−	1.39892i	−0.0936089	−	0.0540451i
$671$	3.59122			0.138637
$672$		0			0
$673$		−	22.9759i		−	0.885656i	−0.896607	−	0.442828i	$-0.853975\pi$
$673$		−	22.9759i		−	0.885656i	0.896607	−	0.442828i	$-0.146025\pi$
$674$	−5.68236	−	3.28071i	−0.218876	−	0.126368i
$675$	−41.6164	+	24.0272i	−1.60181	+	0.924808i
$676$	−7.17379	−	12.4254i	−0.275915	−	0.477899i
$677$	11.1923	+	6.46185i	0.430153	+	0.248349i	0.699412	−	0.714719i	$-0.253445\pi$
$677$	11.1923	+	6.46185i	0.430153	+	0.248349i	−0.269259	+	0.963068i	$0.586779\pi$
$678$	13.1515			0.505082
$679$		0			0
$680$	−2.12528	−	2.91014i	−0.0815008	−	0.111599i
$681$	−2.45805	+	4.25746i	−0.0941926	+	0.163146i
$682$	2.34475	+	4.06123i	0.0897852	+	0.155513i
$683$	−23.3956	+	13.5075i	−0.895209	+	0.516849i	−0.875643	−	0.482960i	$-0.839562\pi$
$683$	−23.3956	+	13.5075i	−0.895209	+	0.516849i	−0.0195661	+	0.999809i	$0.506228\pi$
$684$	−39.0825	+	67.6930i	−1.49436	+	2.58830i
$685$			5.62324i			0.214853i
$686$		0			0
$687$			37.7253i			1.43931i
$688$	0.258619	−	0.447942i	0.00985977	−	0.0170776i
$689$	−5.89358	−	10.2080i	−0.224528	−	0.388893i
$690$	−1.54665	+	0.892959i	−0.0588799	+	0.0339944i
$691$	−20.9182	−	12.0771i	−0.795765	−	0.459435i	0.0462234	−	0.998931i	$-0.485281\pi$
$691$	−20.9182	−	12.0771i	−0.795765	−	0.459435i	−0.841988	+	0.539496i	$0.818615\pi$
$692$			19.1321i			0.727293i
$693$		0			0
$694$		−	2.80859i		−	0.106613i
$695$	−3.30398	+	5.72266i	−0.125327	+	0.217073i
$696$	11.8111	+	20.4575i	0.447700	+	0.775439i
$697$	1.35609	−	3.06607i	0.0513655	−	0.116136i
$698$	−0.728764	+	1.26226i	−0.0275841	+	0.0477771i
$699$	65.2804			2.46913
$700$		0			0
$701$	21.5620			0.814384			0.407192	−	0.913343i	$-0.366508\pi$
$701$	21.5620			0.814384			0.407192	+	0.913343i	$0.366508\pi$
$702$	6.51612	+	3.76208i	0.245935	+	0.141991i
$703$	−32.2881	+	18.6415i	−1.21777	+	0.703079i
$704$	−22.8575	+	13.1968i	−0.861473	+	0.497372i
$705$	12.3316	−	21.3589i	0.464433	−	0.804422i
$706$	6.95760			0.261853
$707$		0			0
$708$		−	32.5106i		−	1.22182i
$709$	6.92370	+	3.99740i	0.260025	+	0.150125i	0.624346	−	0.781148i	$-0.285366\pi$
$709$	6.92370	+	3.99740i	0.260025	+	0.150125i	−0.364321	+	0.931273i	$0.618699\pi$
$710$	−0.120762	−	0.209166i	−0.00453213	−	0.00784987i
$711$	51.2207	−	29.5723i	1.92092	−	1.10905i
$712$	−7.87153	+	13.6339i	−0.294998	+	0.510951i
$713$	9.30276			0.348391
$714$		0			0
$715$	−7.82079			−0.292481
$716$	15.4898	−	26.8291i	0.578881	−	1.00265i
$717$	73.9704	−	42.7068i	2.76247	−	1.59492i
$718$	2.77119	+	4.79985i	0.103420	+	0.179129i
$719$	30.3163	+	17.5031i	1.13061	+	0.652755i	0.944087	−	0.329696i	$-0.106946\pi$
$719$	30.3163	+	17.5031i	1.13061	+	0.652755i	0.186518	+	0.982451i	$0.440280\pi$
$720$			17.1393i			0.638744i
$721$		0			0
$722$	−6.01510			−0.223859
$723$	−22.7844	+	39.4638i	−0.847361	+	1.46767i
$724$	17.6821	−	10.2087i	0.657149	−	0.379405i
$725$	25.3826	−	14.6546i	0.942684	−	0.544259i
$726$	−6.72218	−	3.88105i	−0.249483	−	0.144039i
$727$	−3.31262			−0.122858			−0.0614291	−	0.998111i	$-0.519566\pi$
$727$	−3.31262			−0.122858			−0.0614291	+	0.998111i	$0.519566\pi$
$728$		0			0
$729$	9.71215			0.359709
$730$	−1.11734	+	1.93528i	−0.0413545	+	0.0716281i
$731$	0.560022	+	0.247692i	0.0207132	+	0.00916121i
$732$	2.39865	+	4.15458i	0.0886566	+	0.153558i
$733$	−16.8821	+	29.2406i	−0.623554	+	1.08003i	0.365264	+	0.930904i	$0.380979\pi$
$733$	−16.8821	+	29.2406i	−0.623554	+	1.08003i	−0.988819	+	0.149124i	$0.952355\pi$
$734$		−	6.73989i		−	0.248774i
$735$		0			0
$736$		−	8.66832i		−	0.319519i
$737$	−47.9059	−	27.6585i	−1.76464	−	1.01881i
$738$	1.35737	−	0.783678i	0.0499655	−	0.0288476i
$739$	10.2062	+	17.6776i	0.375440	+	0.650282i	0.990393	−	0.138282i	$-0.0441582\pi$
$739$	10.2062	+	17.6776i	0.375440	+	0.650282i	−0.614953	+	0.788564i	$0.710825\pi$
$740$	−4.29292	+	7.43555i	−0.157811	+	0.273336i
$741$		−	45.3664i		−	1.66657i
$742$		0			0
$743$		−	19.8386i		−	0.727807i	−0.931437	−	0.363903i	$-0.881444\pi$
$743$		−	19.8386i		−	0.727807i	0.931437	−	0.363903i	$-0.118556\pi$
$744$	−6.40773	+	11.0985i	−0.234919	+	0.406891i
$745$	0.484047	−	0.279465i	0.0177341	−	0.0102388i
$746$	−5.48141	−	9.49408i	−0.200689	−	0.347603i
$747$	1.12341	−	1.94580i	0.0411033	−	0.0711929i
$748$	−20.5399	−	28.1252i	−0.751013	−	1.02836i
$749$		0			0
$750$	−6.49817			−0.237280
$751$	−27.6523	−	15.9651i	−1.00905	−	0.582574i	−0.0981351	−	0.995173i	$-0.531288\pi$
$751$	−27.6523	−	15.9651i	−1.00905	−	0.582574i	−0.910913	+	0.412599i	$0.864621\pi$
$752$	18.4345	+	31.9295i	0.672237	+	1.16435i
$753$	−22.0881	+	12.7526i	−0.804937	+	0.464730i
$754$	−3.97429	−	2.29456i	−0.144735	−	0.0835629i
$755$			7.20130i			0.262082i
$756$		0			0
$757$	8.10112			0.294440			0.147220	−	0.989104i	$-0.452967\pi$
$757$	8.10112			0.294440			0.147220	+	0.989104i	$0.452967\pi$
$758$	1.29842	+	0.749642i	0.0471607	+	0.0272282i
$759$	−30.5792	+	17.6549i	−1.10996	+	0.640833i
$760$	−4.74712	+	2.74075i	−0.172196	+	0.0994174i
$761$	23.2919	−	40.3427i	0.844329	−	1.46242i	−0.0418728	−	0.999123i	$-0.513332\pi$
$761$	23.2919	−	40.3427i	0.844329	−	1.46242i	0.886202	−	0.463299i	$-0.153334\pi$
$762$			8.21070i			0.297442i
$763$		0			0
$764$	−18.8458			−0.681816
$765$	−20.1746	+	2.17055i	−0.729414	+	0.0784763i
$766$	0.931375	+	1.61319i	0.0336519	+	0.0582869i
$767$	6.46034	+	11.1896i	0.233269	+	0.404034i
$768$	−25.2475	−	14.5766i	−0.911040	−	0.525989i
$769$	−2.01175			−0.0725455			−0.0362728	−	0.999342i	$-0.511549\pi$
$769$	−2.01175			−0.0725455			−0.0362728	+	0.999342i	$0.511549\pi$
$770$		0			0
$771$		−	75.4503i		−	2.71728i
$772$	20.8047	+	12.0116i	0.748778	+	0.432307i
$773$	−13.2699	−	22.9842i	−0.477286	−	0.826683i	0.522375	−	0.852716i	$-0.325046\pi$
$773$	−13.2699	−	22.9842i	−0.477286	−	0.826683i	−0.999661	+	0.0260325i	$0.991713\pi$
$774$	0.143140	+	0.247926i	0.00514507	+	0.00891152i
$775$	13.7704	+	7.95036i	0.494648	+	0.285585i
$776$		−	15.1547i		−	0.544022i
$777$		0			0
$778$	0.372309			0.0133479
$779$	−4.41647	−	2.54985i	−0.158236	−	0.0913578i
$780$	−5.22366	−	9.04765i	−0.187037	−	0.323958i
$781$	−2.38762	−	4.13548i	−0.0854358	−	0.147979i
$782$	3.14258	−	0.338105i	0.112379	−	0.0120906i
$783$	71.7784			2.56515
$784$		0			0
$785$		−	12.5260i		−	0.447071i
$786$	6.91513	−	11.9774i	0.246655	−	0.427218i
$787$	12.4779	−	7.20414i	0.444791	−	0.256800i	−0.260837	−	0.965383i	$-0.583999\pi$
$787$	12.4779	−	7.20414i	0.444791	−	0.256800i	0.705628	+	0.708583i	$0.250665\pi$
$788$	7.43407	−	4.29206i	0.264828	−	0.152898i
$789$	46.8138	+	27.0280i	1.66662	+	0.962221i
$790$	2.02744			0.0721331
$791$		0			0
$792$		−	33.3087i		−	1.18357i
$793$	−1.65115	−	0.953293i	−0.0586341	−	0.0338524i
$794$	4.80345	−	2.77327i	0.170468	−	0.0984198i
$795$	5.85567	+	10.1423i	0.207679	+	0.359711i
$796$	42.7168	+	24.6626i	1.51406	+	0.874141i
$797$	1.97503			0.0699593			0.0349796	−	0.999388i	$-0.488863\pi$
$797$	1.97503			0.0699593			0.0349796	+	0.999388i	$0.488863\pi$
$798$		0			0
$799$	−35.2495	+	25.7428i	−1.24704	+	0.910714i
$800$	7.40816	−	12.8313i	0.261918	−	0.453655i
$801$	44.3231	+	76.7698i	1.56608	+	2.71253i
$802$	0.332392	−	0.191907i	0.0117372	−	0.00677647i
$803$	−22.0912	+	38.2630i	−0.779580	+	1.35027i
$804$		−	73.8946i		−	2.60606i
$805$		0			0
$806$		−	2.48967i		−	0.0876949i
$807$	−30.5648	+	52.9398i	−1.07593	+	1.86357i
$808$	−0.841923	−	1.45825i	−0.0296187	−	0.0513012i
$809$	−5.95561	+	3.43847i	−0.209388	+	0.120890i	−0.601027	−	0.799229i	$-0.705242\pi$
$809$	−5.95561	+	3.43847i	−0.209388	+	0.120890i	0.391639	+	0.920119i	$0.371908\pi$
$810$	−2.69217	−	1.55432i	−0.0945931	−	0.0546133i
$811$			47.9854i			1.68500i	0.538700	+	0.842498i	$0.318916\pi$
$811$			47.9854i			1.68500i	−0.538700	+	0.842498i	$0.681084\pi$
$812$		0			0
$813$			31.1740i			1.09332i
$814$	3.88305	−	6.72565i	0.136101	−	0.235734i
$815$	−0.00663876	−	0.0114987i	−0.000232546	−	0.000402781i
$816$	17.9179	−	40.5118i	0.627253	−	1.41820i
$817$	0.465734	−	0.806675i	0.0162940	−	0.0282220i
$818$	−1.95708			−0.0684275
$819$		0			0
$820$	−1.17440			−0.0410118
$821$	0.382966	+	0.221105i	0.0133656	+	0.00771663i	0.506668	−	0.862141i	$-0.330877\pi$
$821$	0.382966	+	0.221105i	0.0133656	+	0.00771663i	−0.493302	+	0.869858i	$0.664210\pi$
$822$	5.88427	−	3.39729i	0.205238	−	0.118494i
$823$	32.1813	−	18.5799i	1.12177	−	0.647654i	0.179918	−	0.983682i	$-0.442417\pi$
$823$	32.1813	−	18.5799i	1.12177	−	0.647654i	0.941852	+	0.336028i	$0.109084\pi$
$824$	−1.55137	+	2.68705i	−0.0540445	+	0.0936078i
$825$	−60.3533			−2.10123
$826$		0			0
$827$		−	46.0180i		−	1.60020i	−0.599865	−	0.800101i	$-0.704779\pi$
$827$		−	46.0180i		−	1.60020i	0.599865	−	0.800101i	$-0.295221\pi$
$828$	−27.9718	−	16.1495i	−0.972086	−	0.561234i
$829$	22.3477	+	38.7073i	0.776167	+	1.34436i	0.934136	+	0.356917i	$0.116172\pi$
$829$	22.3477	+	38.7073i	0.776167	+	1.34436i	−0.157969	+	0.987444i	$0.550495\pi$
$830$	0.0667008	−	0.0385097i	0.00231522	−	0.00133669i
$831$	−48.1870	+	83.4623i	−1.67159	+	2.89528i
$832$	14.0124			0.485792
$833$		0			0
$834$	7.98441			0.276477
$835$	−0.361608	+	0.626323i	−0.0125139	+	0.0216748i
$836$	−45.8788	+	26.4881i	−1.58675	+	0.916111i
$837$	19.4704	+	33.7238i	0.672997	+	1.16566i
$838$	1.73600	+	1.00228i	0.0599690	+	0.0346231i
$839$			44.3895i			1.53250i	0.642545	+	0.766248i	$0.277879\pi$
$839$			44.3895i			1.53250i	−0.642545	+	0.766248i	$0.722121\pi$
$840$		0			0
$841$	−14.7789			−0.509617
$842$	1.86265	−	3.22621i	0.0641912	−	0.111182i
$843$	−62.9603	+	36.3501i	−2.16847	+	1.25196i
$844$	29.9728	−	17.3048i	1.03171	−	0.595656i
$845$	−4.90644	−	2.83274i	−0.168787	−	0.0974491i
$846$	−20.4062			−0.701580
$847$		0			0
$848$	−17.5073			−0.601204
$849$	10.9100	−	18.8967i	0.374431	−	0.648533i
$850$	4.94077	+	2.18525i	0.169467	+	0.0749534i
$851$	−7.70297	−	13.3419i	−0.264054	−	0.457355i
$852$	3.18948	−	5.52435i	0.109270	−	0.189261i
$853$			39.1942i			1.34198i	0.741465	+	0.670992i	$0.234131\pi$
$853$			39.1942i			1.34198i	−0.741465	+	0.670992i	$0.765869\pi$
$854$		0			0
$855$			30.8653i			1.05557i
$856$	−9.73109	−	5.61825i	−0.332602	−	0.192028i
$857$	27.5579	−	15.9106i	0.941361	−	0.543495i	0.0509741	−	0.998700i	$-0.483767\pi$
$857$	27.5579	−	15.9106i	0.941361	−	0.543495i	0.890387	+	0.455205i	$0.150434\pi$
$858$	4.72494	+	8.18383i	0.161307	+	0.279391i
$859$	3.85953	−	6.68491i	0.131686	−	0.228086i	−0.792641	−	0.609689i	$-0.791294\pi$
$859$	3.85953	−	6.68491i	0.131686	−	0.228086i	0.924326	+	0.381603i	$0.124628\pi$
$860$		−	0.214506i		−	0.00731459i
$861$		0			0
$862$		−	3.95527i		−	0.134717i
$863$	−16.8716	+	29.2224i	−0.574315	+	0.994743i	0.421801	+	0.906689i	$0.361398\pi$
$863$	−16.8716	+	29.2224i	−0.574315	+	0.994743i	−0.996116	+	0.0880542i	$0.971935\pi$
$864$	31.4239	−	18.1426i	1.06906	−	0.617223i
$865$	3.77737	+	6.54260i	0.128435	+	0.222455i
$866$	0.147061	−	0.254718i	0.00499735	−	0.00865566i
$867$	49.9555	+	15.9606i	1.69658	+	0.542052i
$868$		0			0
$869$	40.0851			1.35979
$870$	3.94873	+	2.27980i	0.133874	+	0.0772924i
$871$	14.6839	+	25.4333i	0.497547	+	0.861776i
$872$	18.0645	−	10.4295i	0.611741	−	0.353189i
$873$	−73.9007	−	42.6666i	−2.50116	−	1.44405i
$874$		−	4.80786i		−	0.162628i
$875$		0			0
$876$	−59.0205			−1.99412
$877$	−2.51818	−	1.45387i	−0.0850331	−	0.0490939i	0.456881	−	0.889528i	$-0.348967\pi$
$877$	−2.51818	−	1.45387i	−0.0850331	−	0.0490939i	−0.541914	+	0.840434i	$0.682300\pi$
$878$	4.25641	−	2.45744i	0.143647	−	0.0829346i
$879$	−16.7467	+	9.66869i	−0.564851	+	0.326117i
$880$	−5.80806	+	10.0599i	−0.195790	+	0.339118i
$881$		−	33.0566i		−	1.11371i	−0.830611	−	0.556853i	$-0.812009\pi$
$881$		−	33.0566i		−	1.11371i	0.830611	−	0.556853i	$-0.187991\pi$
$882$		0			0
$883$	−8.51675			−0.286612			−0.143306	−	0.989678i	$-0.545773\pi$
$883$	−8.51675			−0.286612			−0.143306	+	0.989678i	$0.545773\pi$
$884$	1.97786	+	18.3836i	0.0665225	+	0.618307i
$885$	−6.41878	−	11.1177i	−0.215765	−	0.373716i
$886$	−3.10245	−	5.37360i	−0.104229	−	0.180529i
$887$	46.7220	+	26.9750i	1.56877	+	0.905731i	0.996313	+	0.0857975i	$0.0273438\pi$
$887$	46.7220	+	26.9750i	1.56877	+	0.905731i	0.572459	+	0.819933i	$0.305990\pi$
$888$	21.2232			0.712203
$889$		0			0
$890$			3.03874i			0.101859i
$891$	−53.2275	−	30.7309i	−1.78319	−	1.02952i
$892$	−12.3811	−	21.4448i	−0.414551	−	0.718024i
$893$	33.1978	+	57.5002i	1.11092	+	1.92417i
$894$	−0.584875	−	0.337678i	−0.0195611	−	0.0112936i
$895$		−	12.2330i		−	0.408904i
$896$		0			0
$897$	18.7461			0.625913
$898$	−0.201817	−	0.116519i	−0.00673472	−	0.00388829i
$899$	−11.8754	−	20.5687i	−0.396066	−	0.686006i
$900$	−27.6035	−	47.8107i	−0.920117	−	1.59369i
$901$	−2.21716	−	20.6078i	−0.0738642	−	0.686546i
$902$	1.06227			0.0353698
$903$		0			0
$904$			16.6798i			0.554762i
$905$	4.03116	−	6.98217i	0.134000	−	0.232095i
$906$	7.53559	−	4.35067i	0.250353	−	0.144541i
$907$	3.91766	−	2.26186i	0.130084	−	0.0751040i	−0.433546	−	0.901131i	$-0.642738\pi$
$907$	3.91766	−	2.26186i	0.130084	−	0.0751040i	0.563630	+	0.826028i	$0.309404\pi$
$908$	−2.63945	−	1.52388i	−0.0875931	−	0.0505719i
$909$	−9.48141			−0.314479
$910$		0			0
$911$		−	12.4415i		−	0.412206i	−0.978530	−	0.206103i	$-0.933922\pi$
$911$		−	12.4415i		−	0.412206i	0.978530	−	0.206103i	$-0.0660781\pi$
$912$	−58.3546	−	33.6911i	−1.93231	−	1.11562i
$913$	1.31876	−	0.761386i	0.0436446	−	0.0251982i
$914$	−2.28477	−	3.95734i	−0.0755735	−	0.130897i
$915$	1.64053	+	0.947161i	0.0542343	+	0.0313122i
$916$	−23.3881			−0.772763
$917$		0			0
$918$	7.80303	+	10.6847i	0.257538	+	0.352646i
$919$	11.3375	−	19.6372i	0.373991	−	0.647772i	−0.616184	−	0.787602i	$-0.711322\pi$
$919$	11.3375	−	19.6372i	0.373991	−	0.647772i	0.990175	+	0.139830i	$0.0446557\pi$
$920$	−1.13252	−	1.96158i	−0.0373381	−	0.0646714i
$921$	−9.53637	+	5.50583i	−0.314234	+	0.181423i
$922$	3.36224	−	5.82357i	0.110729	−	0.191789i
$923$			2.53519i			0.0834467i
$924$		0			0
$925$		−	26.3326i		−	0.865809i
$926$	−0.0156727	+	0.0271459i	−0.000515037	+	0.000892071i
$927$	8.73546	+	15.1303i	0.286910	+	0.496943i
$928$	−19.1660	+	11.0655i	−0.629154	+	0.363242i
$929$	−32.9314	−	19.0129i	−1.08044	−	0.623794i	−0.149427	−	0.988773i	$-0.547743\pi$
$929$	−32.9314	−	19.0129i	−1.08044	−	0.623794i	−0.931016	+	0.364979i	$0.881076\pi$
$930$			2.47365i			0.0811143i
$931$		0			0
$932$			40.4711i			1.32567i
$933$	34.4676	−	59.6997i	1.12842	−	1.95448i
$934$	−2.76713	−	4.79281i	−0.0905432	−	0.156825i
$935$	−12.5770	−	5.56265i	−0.411311	−	0.181918i
$936$	−8.84182	+	15.3145i	−0.289004	+	0.500570i
$937$	35.1574			1.14854			0.574271	−	0.818665i	$-0.305286\pi$
$937$	35.1574			1.14854			0.574271	+	0.818665i	$0.305286\pi$
$938$		0			0
$939$	11.3465			0.370280
$940$	13.2416	+	7.64504i	0.431893	+	0.249354i
$941$	−14.4576	+	8.34712i	−0.471306	+	0.272108i	−0.716786	−	0.697293i	$-0.754388\pi$
$941$	−14.4576	+	8.34712i	−0.471306	+	0.272108i	0.245481	+	0.969402i	$0.421054\pi$
$942$	−13.1074	+	7.56757i	−0.427063	+	0.246565i
$943$	1.05364	−	1.82495i	0.0343111	−	0.0594286i
$944$	19.1909			0.624611
$945$		0			0
$946$			0.194026i			0.00630833i
$947$	17.1909	+	9.92516i	0.558629	+	0.322524i	0.752595	−	0.658484i	$-0.228802\pi$
$947$	17.1909	+	9.92516i	0.558629	+	0.322524i	−0.193966	+	0.981008i	$0.562135\pi$
$948$	26.7736	+	46.3733i	0.869567	+	1.50614i
$949$	20.3139	−	11.7282i	0.659418	−	0.380715i
$950$	4.10892	−	7.11685i	0.133311	−	0.230901i
$951$	−50.5665			−1.63973
$952$		0			0
$953$	−44.1533			−1.43026			−0.715132	−	0.698989i	$-0.753634\pi$
$953$	−44.1533			−1.43026			−0.715132	+	0.698989i	$0.753634\pi$
$954$	4.84497	−	8.39173i	0.156862	−	0.271692i
$955$	−6.44469	+	3.72084i	−0.208545	+	0.120404i
$956$	26.4764	+	45.8585i	0.856308	+	1.48317i
$957$	78.0714	+	45.0745i	2.52369	+	1.45705i
$958$			4.93785i			0.159535i
$959$		0			0
$960$	−13.9222			−0.449338
$961$	−9.05743	+	15.6879i	−0.292175	+	0.506062i
$962$	−3.57066	+	2.06152i	−0.115123	+	0.0664661i
$963$	−54.7939	+	31.6353i	−1.76571	+	1.01943i
$964$	−24.4658	−	14.1254i	−0.787992	−	0.454947i
$965$	9.48612			0.305369
$966$		0			0
$967$	9.42477			0.303080			0.151540	−	0.988451i	$-0.451577\pi$
$967$	9.42477			0.303080			0.151540	+	0.988451i	$0.451577\pi$
$968$	4.92225	−	8.52559i	0.158207	−	0.274023i
$969$	32.2675	−	72.9557i	1.03658	−	2.34367i
$970$	−1.46259	−	2.53328i	−0.0469609	−	0.0813386i
$971$	−7.58374	+	13.1354i	−0.243374	+	0.421536i	−0.961673	−	0.274198i	$-0.911588\pi$
$971$	−7.58374	+	13.1354i	−0.243374	+	0.421536i	0.718299	+	0.695734i	$0.244921\pi$
$972$		−	19.8610i		−	0.637043i
$973$		0			0
$974$			8.20333i			0.262852i
$975$	27.7489	+	16.0209i	0.888677	+	0.513078i
$976$	−2.45244	+	1.41591i	−0.0785006	+	0.0453223i
$977$	−10.2405	−	17.7371i	−0.327623	−	0.567460i	0.654416	−	0.756134i	$-0.272914\pi$
$977$	−10.2405	−	17.7371i	−0.327623	−	0.567460i	−0.982040	+	0.188674i	$0.939581\pi$
$978$	−0.00802163	+	0.0138939i	−0.000256503	+	0.000444277i
$979$			60.0798i			1.92016i
$980$		0			0
$981$		−	117.453i		−	3.75000i
$982$	−1.91902	+	3.32383i	−0.0612383	+	0.106068i
$983$	11.1225	−	6.42156i	0.354752	−	0.204816i	−0.312024	−	0.950074i	$-0.601007\pi$
$983$	11.1225	−	6.42156i	0.354752	−	0.204816i	0.666776	+	0.745258i	$0.267674\pi$
$984$	1.45149	+	2.51405i	0.0462717	+	0.0801450i
$985$	1.69482	−	2.93551i	0.0540014	−	0.0935332i
$986$	−4.75920	−	6.51676i	−0.151564	−	0.207536i
$987$		0			0
$988$	28.1252			0.894782
$989$	0.333331	+	0.192449i	0.0105993	+	0.00611951i
$990$	−3.21464	−	5.56791i	−0.102168	−	0.176960i
$991$	0.486136	−	0.280671i	0.0154426	−	0.00891580i	−0.492259	−	0.870449i	$-0.663829\pi$
$991$	0.486136	−	0.280671i	0.0154426	−	0.00891580i	0.507701	+	0.861533i	$0.330495\pi$
$992$	−10.3978	−	6.00320i	−0.330132	−	0.190602i
$993$		−	12.0555i		−	0.382571i
$994$		0			0
$995$	19.4771			0.617467
$996$	1.76165	+	1.01709i	0.0558201	+	0.0322277i
$997$	−5.95777	+	3.43972i	−0.188685	+	0.108937i	−0.591367	−	0.806403i	$-0.701411\pi$
$997$	−5.95777	+	3.43972i	−0.188685	+	0.108937i	0.402682	+	0.915340i	$0.368078\pi$
$998$	−3.81812	+	2.20439i	−0.120860	+	0.0697788i
$999$	32.2442	−	55.8487i	1.02016	−	1.76697i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	833.2.j.c.373.6		20
7.2	even	3		119.2.b.a.50.6	yes	10
7.3	odd	6		833.2.j.d.67.6		20
7.4	even	3	inner	833.2.j.c.67.5		20
7.5	odd	6		833.2.b.a.50.5		10
7.6	odd	2		833.2.j.d.373.5		20
17.16	even	2	inner	833.2.j.c.373.5		20
21.2	odd	6		1071.2.f.c.883.6		10
28.23	odd	6		1904.2.c.i.1121.1		10
119.16	even	6		119.2.b.a.50.5	✓	10
119.30	even	12		2023.2.a.i.1.3		5
119.33	odd	6		833.2.b.a.50.6		10
119.67	even	6	inner	833.2.j.c.67.6		20
119.72	even	12		2023.2.a.h.1.3		5
119.101	odd	6		833.2.j.d.67.5		20
119.118	odd	2		833.2.j.d.373.6		20
357.254	odd	6		1071.2.f.c.883.5		10
476.135	odd	6		1904.2.c.i.1121.10		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
119.2.b.a.50.5	✓	10	119.16	even	6
119.2.b.a.50.6	yes	10	7.2	even	3
833.2.b.a.50.5		10	7.5	odd	6
833.2.b.a.50.6		10	119.33	odd	6
833.2.j.c.67.5		20	7.4	even	3	inner
833.2.j.c.67.6		20	119.67	even	6	inner
833.2.j.c.373.5		20	17.16	even	2	inner
833.2.j.c.373.6		20	1.1	even	1	trivial
833.2.j.d.67.5		20	119.101	odd	6
833.2.j.d.67.6		20	7.3	odd	6
833.2.j.d.373.5		20	7.6	odd	2
833.2.j.d.373.6		20	119.118	odd	2
1071.2.f.c.883.5		10	357.254	odd	6
1071.2.f.c.883.6		10	21.2	odd	6
1904.2.c.i.1121.1		10	28.23	odd	6
1904.2.c.i.1121.10		10	476.135	odd	6
2023.2.a.h.1.3		5	119.72	even	12
2023.2.a.i.1.3		5	119.30	even	12

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:	\( N \)	\(=\)	\( 833 = 7^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	833.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.147899 - 0.256168i) q^{2} +(2.67160 - 1.54245i) q^{3} +(0.956252 + 1.65628i) q^{4} +(0.654019 + 0.377598i) q^{5} -0.912504i q^{6} +1.15731 q^{8} +(3.25829 - 5.64353i) q^{9} +O(q^{10})\)	\(q+(0.147899 - 0.256168i) q^{2} +(2.67160 - 1.54245i) q^{3} +(0.956252 + 1.65628i) q^{4} +(0.654019 + 0.377598i) q^{5} -0.912504i q^{6} +1.15731 q^{8} +(3.25829 - 5.64353i) q^{9} +(0.193457 - 0.111692i) q^{10} +(3.82489 - 2.20830i) q^{11} +(5.10944 + 2.94994i) q^{12} -2.34478 q^{13} +2.32970 q^{15} +(-1.74134 + 3.01609i) q^{16} +(-3.77075 - 1.66776i) q^{17} +(-0.963794 - 1.66934i) q^{18} +(-3.13589 + 5.43152i) q^{19} +1.44431i q^{20} -1.30642i q^{22} +(-2.24439 - 1.29580i) q^{23} +(3.09186 - 1.78509i) q^{24} +(-2.21484 - 3.83621i) q^{25} +(-0.346790 + 0.600659i) q^{26} -10.8483i q^{27} +6.61656i q^{29} +(0.344560 - 0.596795i) q^{30} +(-3.10867 + 1.79479i) q^{31} +(1.67239 + 2.89667i) q^{32} +(6.81238 - 11.7994i) q^{33} +(-0.984916 + 0.719286i) q^{34} +12.4630 q^{36} +(5.14815 + 2.97229i) q^{37} +(0.927588 + 1.60663i) q^{38} +(-6.26432 + 3.61671i) q^{39} +(0.756901 + 0.436997i) q^{40} +0.813118i q^{41} -0.148517 q^{43} +(7.31512 + 4.22338i) q^{44} +(4.26197 - 2.46065i) q^{45} +(-0.663884 + 0.383293i) q^{46} +(5.29320 - 9.16809i) q^{47} +10.7437i q^{48} -1.31029 q^{50} +(-12.6464 + 1.36060i) q^{51} +(-2.24220 - 3.88361i) q^{52} +(2.51349 + 4.35349i) q^{53} +(-2.77898 - 1.60445i) q^{54} +3.33540 q^{55} +19.3478i q^{57} +(1.69495 + 0.978581i) q^{58} +(-2.75520 - 4.77214i) q^{59} +(2.22778 + 3.85863i) q^{60} +(0.704181 + 0.406559i) q^{61} +1.06179i q^{62} -5.97598 q^{64} +(-1.53353 - 0.885385i) q^{65} +(-2.01508 - 3.49023i) q^{66} +(-6.26239 - 10.8468i) q^{67} +(-0.843514 - 7.84021i) q^{68} -7.99480 q^{69} -1.08120i q^{71} +(3.77085 - 6.53130i) q^{72} +(-8.66345 + 5.00185i) q^{73} +(1.52281 - 0.879195i) q^{74} +(-11.8343 - 6.83255i) q^{75} -11.9948 q^{76} +2.13962i q^{78} +(7.86005 + 4.53800i) q^{79} +(-2.27774 + 1.31505i) q^{80} +(-6.95805 - 12.0517i) q^{81} +(0.208295 + 0.120259i) q^{82} +0.344784 q^{83} +(-1.83640 - 2.51458i) q^{85} +(-0.0219655 + 0.0380454i) q^{86} +(10.2057 + 17.6768i) q^{87} +(4.42658 - 2.55569i) q^{88} +(-6.80158 + 11.7807i) q^{89} -1.45571i q^{90} -4.95644i q^{92} +(-5.53675 + 9.58994i) q^{93} +(-1.56571 - 2.71190i) q^{94} +(-4.10186 + 2.36821i) q^{95} +(8.93592 + 5.15915i) q^{96} -13.0948i q^{97} -28.7812i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{2} - 4 q^{4} - 24 q^{8} + 6 q^{9}+O(q^{10}) \) 20 * q + 4 * q^2 - 4 * q^4 - 24 * q^8 + 6 * q^9	\( 20 q + 4 q^{2} - 4 q^{4} - 24 q^{8} + 6 q^{9} - 16 q^{13} - 16 q^{15} - 8 q^{16} - 2 q^{17} - 12 q^{18} - 4 q^{19} + 2 q^{25} - 12 q^{26} - 10 q^{30} + 18 q^{32} + 20 q^{33} + 12 q^{34} + 20 q^{36} + 4 q^{38} + 32 q^{43} + 12 q^{50} + 64 q^{52} - 8 q^{53} - 24 q^{55} - 56 q^{59} + 26 q^{60} - 72 q^{66} - 24 q^{67} + 22 q^{68} + 56 q^{69} - 10 q^{72} - 24 q^{76} - 2 q^{81} - 24 q^{83} - 40 q^{85} + 74 q^{86} + 52 q^{87} + 4 q^{89} - 32 q^{93} + 20 q^{94}+O(q^{100}) \) 20 * q + 4 * q^2 - 4 * q^4 - 24 * q^8 + 6 * q^9 - 16 * q^13 - 16 * q^15 - 8 * q^16 - 2 * q^17 - 12 * q^18 - 4 * q^19 + 2 * q^25 - 12 * q^26 - 10 * q^30 + 18 * q^32 + 20 * q^33 + 12 * q^34 + 20 * q^36 + 4 * q^38 + 32 * q^43 + 12 * q^50 + 64 * q^52 - 8 * q^53 - 24 * q^55 - 56 * q^59 + 26 * q^60 - 72 * q^66 - 24 * q^67 + 22 * q^68 + 56 * q^69 - 10 * q^72 - 24 * q^76 - 2 * q^81 - 24 * q^83 - 40 * q^85 + 74 * q^86 + 52 * q^87 + 4 * q^89 - 32 * q^93 + 20 * q^94

Introduction

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