LMFDB - Embedded newform 275.2.h.e.201.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [275,2,Mod(26,275)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("275.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 275 = 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	275.h (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.19588605559$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 10 x^{14} - 13 x^{13} + 53 x^{12} - 12 x^{11} + 136 x^{10} + 8 x^{9} + 300 x^{8} + \cdots + 16 $ x^16 - 4x^15 + 10x^14 - 13x^13 + 53x^12 - 12x^11 + 136x^10 + 8x^9 + 300x^8 - 256x^7 + 472x^6 - 48x^5 + 432x^4 + 88x^3 + 128x^2 + 64*x + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			201.1
Root			$-1.26407 - 0.918397i$ of defining polynomial
Character	$\chi$	$=$	275.201
Dual form			275.2.h.e.26.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.07308 + 1.50618i) q^{2} +(0.553942 + 1.70486i) q^{3} +(1.41105 - 4.34277i) q^{4} +(-3.71620 - 2.69998i) q^{6} +(1.17454 - 3.61485i) q^{7} +(2.03208 + 6.25410i) q^{8} +(-0.172643 + 0.125433i) q^{9} +(3.19489 - 0.890336i) q^{11} +8.18545 q^{12} +(3.63862 - 2.64361i) q^{13} +(3.00971 + 9.26295i) q^{14} +(-6.24414 - 4.53663i) q^{16} +(-4.05485 - 2.94602i) q^{17} +(0.168979 - 0.520065i) q^{18} +(-1.06936 - 3.29116i) q^{19} +6.81344 q^{21} +(-5.28226 + 6.65782i) q^{22} +0.105727 q^{23} +(-9.53671 + 6.92883i) q^{24} +(-3.56139 + 10.9608i) q^{26} +(4.04124 + 2.93613i) q^{27} +(-14.0411 - 10.2015i) q^{28} +(-0.726214 + 2.23506i) q^{29} +(-3.83900 + 2.78920i) q^{31} +6.62570 q^{32} +(3.28768 + 4.95364i) q^{33} +12.8433 q^{34} +(0.301117 + 0.926742i) q^{36} +(-1.73077 + 5.32675i) q^{37} +(7.17396 + 5.21219i) q^{38} +(6.52257 + 4.73892i) q^{39} +(0.283345 + 0.872045i) q^{41} +(-14.1248 + 10.2623i) q^{42} -4.46162 q^{43} +(0.641627 - 15.1310i) q^{44} +(-0.219181 + 0.159244i) q^{46} +(0.387384 + 1.19225i) q^{47} +(4.27543 - 13.1584i) q^{48} +(-6.02449 - 4.37704i) q^{49} +(2.77640 - 8.54487i) q^{51} +(-6.34631 - 19.5319i) q^{52} +(4.44847 - 3.23200i) q^{53} -12.8002 q^{54} +24.9944 q^{56} +(5.01860 - 3.64622i) q^{57} +(-1.86090 - 5.72727i) q^{58} +(-0.365582 + 1.12515i) q^{59} +(5.92690 + 4.30614i) q^{61} +(3.75752 - 11.5645i) q^{62} +(0.250645 + 0.771405i) q^{63} +(-1.24734 + 0.906248i) q^{64} +(-14.2767 - 5.31745i) q^{66} +7.84414 q^{67} +(-18.5155 + 13.4523i) q^{68} +(0.0585667 + 0.180250i) q^{69} +(1.76384 + 1.28150i) q^{71} +(-1.13529 - 0.824840i) q^{72} +(2.76651 - 8.51445i) q^{73} +(-4.43504 - 13.6496i) q^{74} -15.8017 q^{76} +(0.534080 - 12.5948i) q^{77} -20.6595 q^{78} +(-11.6357 + 8.45380i) q^{79} +(-2.96491 + 9.12506i) q^{81} +(-1.90086 - 1.38105i) q^{82} +(3.81162 + 2.76930i) q^{83} +(9.61410 - 29.5892i) q^{84} +(9.24930 - 6.72001i) q^{86} -4.21274 q^{87} +(12.0605 + 18.1719i) q^{88} -0.172993 q^{89} +(-5.28256 - 16.2581i) q^{91} +(0.149186 - 0.459148i) q^{92} +(-6.88177 - 4.99990i) q^{93} +(-2.59882 - 1.88815i) q^{94} +(3.67026 + 11.2959i) q^{96} +(3.60857 - 2.62178i) q^{97} +19.0819 q^{98} +(-0.439899 + 0.554454i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{3} - 2 q^{4} - 3 q^{6} - 4 q^{7} - 16 q^{8} + 8 q^{9} - 5 q^{11} + 6 q^{12} - 7 q^{13} + 3 q^{14} - 4 q^{16} - 12 q^{17} - 16 q^{18} - 13 q^{19} + 10 q^{21} - 28 q^{22} + 4 q^{23} - 43 q^{24}+ \cdots - 10 q^{99}+O(q^{100}) $ 16 * q + 2 * q^3 - 2 * q^4 - 3 * q^6 - 4 * q^7 - 16 * q^8 + 8 * q^9 - 5 * q^11 + 6 * q^12 - 7 * q^13 + 3 * q^14 - 4 * q^16 - 12 * q^17 - 16 * q^18 - 13 * q^19 + 10 * q^21 - 28 * q^22 + 4 * q^23 - 43 * q^24 - 34 * q^26 + 11 * q^27 - 47 * q^28 - 11 * q^29 - 10 * q^31 + 58 * q^32 + 34 * q^33 + 20 * q^34 + 3 * q^36 + 4 * q^37 + 36 * q^38 + 3 * q^39 + 25 * q^41 - 13 * q^42 + 28 * q^43 - q^44 + 40 * q^46 - 8 * q^47 + 106 * q^48 + 16 * q^49 + 35 * q^51 - 39 * q^52 + 22 * q^53 + 60 * q^54 - 20 * q^56 - 29 * q^57 - 6 * q^58 + 14 * q^59 + 16 * q^61 + 10 * q^62 - 73 * q^63 + 40 * q^64 - 55 * q^66 + 14 * q^67 - 83 * q^68 + 35 * q^69 - 46 * q^71 - 28 * q^72 - 7 * q^73 - 7 * q^74 - 62 * q^76 + 51 * q^77 - 34 * q^78 - 39 * q^79 - 43 * q^81 + 51 * q^82 - 28 * q^83 - 54 * q^84 + 2 * q^86 + 50 * q^87 + 76 * q^88 - 22 * q^89 - 34 * q^91 - 4 * q^92 - 3 * q^93 - 40 * q^94 + 108 * q^96 + 39 * q^97 + 52 * q^98 - 10 * q^99

Character values

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

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

Coefficient data

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

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

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

$2$	−2.07308	+	1.50618i	−1.46589	+	1.06503i	−0.484111	+	0.875006i	$0.660857\pi$
$2$	−2.07308	+	1.50618i	−1.46589	+	1.06503i	−0.981779	+	0.190025i	$0.939143\pi$
$3$	0.553942	+	1.70486i	0.319819	+	0.984301i	0.973725	+	0.227726i	$0.0731290\pi$
$3$	0.553942	+	1.70486i	0.319819	+	0.984301i	−0.653906	+	0.756575i	$0.726871\pi$
$4$	1.41105	−	4.34277i	0.705525	−	2.17138i
$5$		0			0
$5$		0			0
$6$	−3.71620	−	2.69998i	−1.51713	−	1.10226i
$7$	1.17454	−	3.61485i	0.443933	−	1.36628i	−0.439717	−	0.898136i	$-0.644921\pi$
$7$	1.17454	−	3.61485i	0.443933	−	1.36628i	0.883650	−	0.468148i	$-0.155079\pi$
$8$	2.03208	+	6.25410i	0.718449	+	2.21116i
$9$	−0.172643	+	0.125433i	−0.0575478	+	0.0418109i
$10$		0			0
$11$	3.19489	−	0.890336i	0.963295	−	0.268446i
$11$	3.19489	−	0.890336i	0.963295	−	0.268446i
$12$	8.18545			2.36294
$13$	3.63862	−	2.64361i	1.00917	−	0.733205i	0.0451354	−	0.998981i	$-0.485628\pi$
$13$	3.63862	−	2.64361i	1.00917	−	0.733205i	0.964035	+	0.265776i	$0.0856281\pi$
$14$	3.00971	+	9.26295i	0.804380	+	2.47563i
$15$		0			0
$16$	−6.24414	−	4.53663i	−1.56103	−	1.13416i
$17$	−4.05485	−	2.94602i	−0.983445	−	0.714515i	−0.0249691	−	0.999688i	$-0.507949\pi$
$17$	−4.05485	−	2.94602i	−0.983445	−	0.714515i	−0.958476	+	0.285174i	$0.907949\pi$
$18$	0.168979	−	0.520065i	0.0398288	−	0.122580i
$19$	−1.06936	−	3.29116i	−0.245329	−	0.755044i	−0.995582	−	0.0938935i	$-0.970069\pi$
$19$	−1.06936	−	3.29116i	−0.245329	−	0.755044i	0.750254	−	0.661150i	$-0.229931\pi$
$20$		0			0
$21$	6.81344			1.48681
$22$	−5.28226	+	6.65782i	−1.12618	+	1.41945i
$23$	0.105727			0.0220456			0.0110228	−	0.999939i	$-0.496491\pi$
$23$	0.105727			0.0220456			0.0110228	+	0.999939i	$0.496491\pi$
$24$	−9.53671	+	6.92883i	−1.94667	+	1.41434i
$25$		0			0
$26$	−3.56139	+	10.9608i	−0.698446	+	2.14960i
$27$	4.04124	+	2.93613i	0.777737	+	0.565059i
$28$	−14.0411	−	10.2015i	−2.65352	−	1.92790i
$29$	−0.726214	+	2.23506i	−0.134855	+	0.415040i	−0.995567	−	0.0940512i	$-0.970018\pi$
$29$	−0.726214	+	2.23506i	−0.134855	+	0.415040i	0.860713	+	0.509091i	$0.170018\pi$
$30$		0			0
$31$	−3.83900	+	2.78920i	−0.689504	+	0.500954i	−0.876497	−	0.481407i	$-0.840126\pi$
$31$	−3.83900	+	2.78920i	−0.689504	+	0.500954i	0.186993	+	0.982361i	$0.440126\pi$
$32$	6.62570			1.17127
$33$	3.28768	+	4.95364i	0.572312	+	0.862318i
$34$	12.8433			2.20260
$35$		0			0
$36$	0.301117	+	0.926742i	0.0501861	+	0.154457i
$37$	−1.73077	+	5.32675i	−0.284536	+	0.875713i	0.702001	+	0.712176i	$0.252290\pi$
$37$	−1.73077	+	5.32675i	−0.284536	+	0.875713i	−0.986537	+	0.163537i	$0.947710\pi$
$38$	7.17396	+	5.21219i	1.16377	+	0.845528i
$39$	6.52257	+	4.73892i	1.04445	+	0.758835i
$40$		0			0
$41$	0.283345	+	0.872045i	0.0442510	+	0.136191i	0.970741	−	0.240129i	$-0.0771896\pi$
$41$	0.283345	+	0.872045i	0.0442510	+	0.136191i	−0.926490	+	0.376319i	$0.877190\pi$
$42$	−14.1248	+	10.2623i	−2.17951	+	1.58350i
$43$	−4.46162			−0.680390			−0.340195	−	0.940355i	$-0.610493\pi$
$43$	−4.46162			−0.680390			−0.340195	+	0.940355i	$0.610493\pi$
$44$	0.641627	−	15.1310i	0.0967289	−	2.28108i
$45$		0			0
$46$	−0.219181	+	0.159244i	−0.0323165	+	0.0234793i
$47$	0.387384	+	1.19225i	0.0565058	+	0.173907i	0.975326	−	0.220769i	$-0.0708568\pi$
$47$	0.387384	+	1.19225i	0.0565058	+	0.173907i	−0.918820	+	0.394676i	$0.870857\pi$
$48$	4.27543	−	13.1584i	0.617105	−	1.89925i
$49$	−6.02449	−	4.37704i	−0.860641	−	0.625292i
$50$		0			0
$51$	2.77640	−	8.54487i	0.388773	−	1.19652i
$52$	−6.34631	−	19.5319i	−0.880074	−	2.70859i
$53$	4.44847	−	3.23200i	0.611044	−	0.443949i	−0.238738	−	0.971084i	$-0.576734\pi$
$53$	4.44847	−	3.23200i	0.611044	−	0.443949i	0.849782	+	0.527135i	$0.176734\pi$
$54$	−12.8002			−1.74188
$55$		0			0
$56$	24.9944			3.34002
$57$	5.01860	−	3.64622i	0.664730	−	0.482954i
$58$	−1.86090	−	5.72727i	−0.244348	−	0.752027i
$59$	−0.365582	+	1.12515i	−0.0475947	+	0.146481i	−0.972030	−	0.234859i	$-0.924537\pi$
$59$	−0.365582	+	1.12515i	−0.0475947	+	0.146481i	0.924435	+	0.381340i	$0.124537\pi$
$60$		0			0
$61$	5.92690	+	4.30614i	0.758861	+	0.551345i	0.898561	−	0.438849i	$-0.144614\pi$
$61$	5.92690	+	4.30614i	0.758861	+	0.551345i	−0.139699	+	0.990194i	$0.544614\pi$
$62$	3.75752	−	11.5645i	0.477206	−	1.46869i
$63$	0.250645	+	0.771405i	0.0315783	+	0.0971879i
$64$	−1.24734	+	0.906248i	−0.155918	+	0.113281i
$65$		0			0
$66$	−14.2767	−	5.31745i	−1.75734	−	0.654533i
$67$	7.84414			0.958315			0.479157	−	0.877729i	$-0.340942\pi$
$67$	7.84414			0.958315			0.479157	+	0.877729i	$0.340942\pi$
$68$	−18.5155	+	13.4523i	−2.24533	+	1.63133i
$69$	0.0585667	+	0.180250i	0.00705060	+	0.0216995i
$70$		0			0
$71$	1.76384	+	1.28150i	0.209329	+	0.152086i	0.687510	−	0.726175i	$-0.258704\pi$
$71$	1.76384	+	1.28150i	0.209329	+	0.152086i	−0.478181	+	0.878261i	$0.658704\pi$
$72$	−1.13529	−	0.824840i	−0.133796	−	0.0972083i
$73$	2.76651	−	8.51445i	0.323796	−	0.996541i	−0.648185	−	0.761483i	$-0.724472\pi$
$73$	2.76651	−	8.51445i	0.323796	−	0.996541i	0.971981	−	0.235059i	$-0.0755282\pi$
$74$	−4.43504	−	13.6496i	−0.515563	−	1.58674i
$75$		0			0
$76$	−15.8017			−1.81257
$77$	0.534080	−	12.5948i	0.0608640	−	1.43531i
$78$	−20.6595			−2.33923
$79$	−11.6357	+	8.45380i	−1.30911	+	0.951127i	−0.309114	+	0.951025i	$0.600033\pi$
$79$	−11.6357	+	8.45380i	−1.30911	+	0.951127i	−1.00000		0.000102366i	$0.999967\pi$
$80$		0			0
$81$	−2.96491	+	9.12506i	−0.329435	+	1.01390i
$82$	−1.90086	−	1.38105i	−0.209914	−	0.152512i
$83$	3.81162	+	2.76930i	0.418380	+	0.303971i	0.776986	−	0.629518i	$-0.216748\pi$
$83$	3.81162	+	2.76930i	0.418380	+	0.303971i	−0.358606	+	0.933489i	$0.616748\pi$
$84$	9.61410	−	29.5892i	1.04898	−	3.22844i
$85$		0			0
$86$	9.24930	−	6.72001i	0.997378	−	0.724637i
$87$	−4.21274			−0.451653
$88$	12.0605	+	18.1719i	1.28566	+	1.93713i
$89$	−0.172993			−0.0183372			−0.00916862	−	0.999958i	$-0.502919\pi$
$89$	−0.172993			−0.0183372			−0.00916862	+	0.999958i	$0.502919\pi$
$90$		0			0
$91$	−5.28256	−	16.2581i	−0.553763	−	1.70431i
$92$	0.149186	−	0.459148i	0.0155537	−	0.0478695i
$93$	−6.88177	−	4.99990i	−0.713606	−	0.518465i
$94$	−2.59882	−	1.88815i	−0.268048	−	0.194748i
$95$		0			0
$96$	3.67026	+	11.2959i	0.374594	+	1.15288i
$97$	3.60857	−	2.62178i	0.366394	−	0.266201i	−0.389320	−	0.921103i	$-0.627290\pi$
$97$	3.60857	−	2.62178i	0.366394	−	0.266201i	0.755714	+	0.654902i	$0.227290\pi$
$98$	19.0819			1.92756
$99$	−0.439899	+	0.554454i	−0.0442115	+	0.0557247i
$100$		0			0
$101$	−7.12354	+	5.17556i	−0.708819	+	0.514987i	−0.882793	−	0.469763i	$-0.844339\pi$
$101$	−7.12354	+	5.17556i	−0.708819	+	0.514987i	0.173973	+	0.984750i	$0.444339\pi$
$102$	7.11444	+	21.8960i	0.704434	+	2.16803i
$103$	−5.09074	+	15.6677i	−0.501605	+	1.54378i	0.304798	+	0.952417i	$0.401411\pi$
$103$	−5.09074	+	15.6677i	−0.501605	+	1.54378i	−0.806403	+	0.591366i	$0.798589\pi$
$104$	23.9274	+	17.3843i	2.34627	+	1.70467i
$105$		0			0
$106$	−4.35406	+	13.4004i	−0.422903	+	1.30156i
$107$	5.30657	+	16.3319i	0.513005	+	1.57887i	0.786882	+	0.617103i	$0.211694\pi$
$107$	5.30657	+	16.3319i	0.513005	+	1.57887i	−0.273877	+	0.961765i	$0.588306\pi$
$108$	18.4533	−	13.4071i	1.77567	−	1.29010i
$109$	17.9060			1.71508			0.857542	−	0.514414i	$-0.171991\pi$
$109$	17.9060			1.71508			0.857542	+	0.514414i	$0.171991\pi$
$110$		0			0
$111$	−10.0401			−0.952965
$112$	−23.7332	+	17.2432i	−2.24258	+	1.62933i
$113$	−4.42393	−	13.6155i	−0.416168	−	1.28083i	−0.911202	−	0.411960i	$-0.864844\pi$
$113$	−4.42393	−	13.6155i	−0.416168	−	1.28083i	0.495034	−	0.868874i	$-0.335156\pi$
$114$	−4.91209	+	15.1178i	−0.460059	+	1.41592i
$115$		0			0
$116$	8.68161	+	6.30756i	0.806067	+	0.585642i
$117$	−0.296588	+	0.912803i	−0.0274195	+	0.0843886i
$118$	−0.936793	−	2.88315i	−0.0862388	−	0.265416i
$119$	−15.4120	+	11.1975i	−1.41281	+	1.02647i
$120$		0			0
$121$	9.41460	−	5.68904i	0.855873	−	0.517186i
$122$	−18.7728			−1.69961
$123$	−1.32976	+	0.966125i	−0.119900	+	0.0871126i
$124$	6.69581	+	20.6076i	0.601301	+	1.85061i
$125$		0			0
$126$	−1.68148	−	1.22167i	−0.149798	−	0.108835i
$127$	4.50622	+	3.27396i	0.399863	+	0.290517i	0.769485	−	0.638665i	$-0.220513\pi$
$127$	4.50622	+	3.27396i	0.399863	+	0.290517i	−0.369622	+	0.929182i	$0.620513\pi$
$128$	−2.87404	+	8.84538i	−0.254031	+	0.781828i
$129$	−2.47148	−	7.60643i	−0.217602	−	0.669709i
$130$		0			0
$131$	−13.8367			−1.20892			−0.604458	−	0.796637i	$-0.706610\pi$
$131$	−13.8367			−1.20892			−0.604458	+	0.796637i	$0.706610\pi$
$132$	26.1516	−	7.28780i	2.27620	−	0.634321i
$133$	−13.1530			−1.14051
$134$	−16.2616	+	11.8147i	−1.40478	+	1.02064i
$135$		0			0
$136$	10.1849	−	31.3460i	0.873351	−	2.68790i
$137$	8.04525	+	5.84522i	0.687352	+	0.499390i	0.875789	−	0.482695i	$-0.160342\pi$
$137$	8.04525	+	5.84522i	0.687352	+	0.499390i	−0.188437	+	0.982085i	$0.560342\pi$
$138$	−0.392903	−	0.285461i	−0.0334461	−	0.0243000i
$139$	0.627493	−	1.93122i	0.0532232	−	0.163804i	−0.920912	−	0.389771i	$-0.872554\pi$
$139$	0.627493	−	1.93122i	0.0532232	−	0.163804i	0.974135	+	0.225967i	$0.0725541\pi$
$140$		0			0
$141$	−1.81802	+	1.32087i	−0.153105	+	0.111237i
$142$	−5.58676			−0.468830
$143$	9.27126	−	11.6856i	0.775302	−	0.977201i
$144$	1.64705			0.137254
$145$		0			0
$146$	7.08911	+	21.8180i	0.586699	+	1.80567i
$147$	4.12503	−	12.6955i	0.340227	−	1.04711i
$148$	20.6907	+	15.0326i	1.70076	+	1.23568i
$149$	−8.59185	−	6.24234i	−0.703872	−	0.511393i	0.177319	−	0.984153i	$-0.443258\pi$
$149$	−8.59185	−	6.24234i	−0.703872	−	0.511393i	−0.881191	+	0.472761i	$0.843258\pi$
$150$		0			0
$151$	−1.06131	−	3.26639i	−0.0863684	−	0.265815i	0.898540	−	0.438892i	$-0.144629\pi$
$151$	−1.06131	−	3.26639i	−0.0863684	−	0.265815i	−0.984908	+	0.173077i	$0.944629\pi$
$152$	18.4102	−	13.3758i	1.49327	−	1.08492i
$153$	1.06957			0.0864696
$154$	17.8628	+	26.9144i	1.43943	+	2.16883i
$155$		0			0
$156$	29.7837	−	21.6391i	2.38460	−	1.73252i
$157$	−0.0922677	−	0.283971i	−0.00736377	−	0.0226633i	0.947307	−	0.320327i	$-0.103793\pi$
$157$	−0.0922677	−	0.283971i	−0.00736377	−	0.0226633i	−0.954671	+	0.297663i	$0.903793\pi$
$158$	11.3887	−	35.0509i	0.906038	−	2.78850i
$159$	7.97430	+	5.79367i	0.632403	+	0.459468i
$160$		0			0
$161$	0.124180	−	0.382187i	0.00978677	−	0.0301206i
$162$	−7.59750	−	23.3827i	−0.596916	−	1.83712i
$163$	−11.5364	+	8.38166i	−0.903597	+	0.656502i	−0.939387	−	0.342857i	$-0.888605\pi$
$163$	−11.5364	+	8.38166i	−0.903597	+	0.656502i	0.0357901	+	0.999359i	$0.488605\pi$
$164$	4.18690			0.326942
$165$		0			0
$166$	−12.0729			−0.937037
$167$	−14.5604	+	10.5788i	−1.12672	+	0.818611i	−0.985214	−	0.171326i	$-0.945195\pi$
$167$	−14.5604	+	10.5788i	−1.12672	+	0.818611i	−0.141507	+	0.989937i	$0.545195\pi$
$168$	13.8455	+	42.6119i	1.06820	+	3.28758i
$169$	2.23363	−	6.87441i	0.171818	−	0.528801i
$170$		0			0
$171$	0.597437	+	0.434064i	0.0456872	+	0.0331937i
$172$	−6.29557	+	19.3758i	−0.480033	+	1.47739i
$173$	−2.70499	−	8.32510i	−0.205657	−	0.632946i	−0.999686	−	0.0250663i	$-0.992020\pi$
$173$	−2.70499	−	8.32510i	−0.205657	−	0.632946i	0.794029	−	0.607880i	$-0.207980\pi$
$174$	8.73335	−	6.34515i	0.662074	−	0.481025i
$175$		0			0
$176$	−23.9884	−	8.93465i	−1.80820	−	0.673474i
$177$	−2.12073			−0.159404
$178$	0.358629	−	0.260559i	0.0268804	−	0.0195297i
$179$	−7.07647	−	21.7791i	−0.528920	−	1.62785i	−0.756431	−	0.654073i	$-0.773059\pi$
$179$	−7.07647	−	21.7791i	−0.528920	−	1.62785i	0.227511	−	0.973776i	$-0.426941\pi$
$180$		0			0
$181$	−13.9721	−	10.1513i	−1.03854	−	0.754542i	−0.0685389	−	0.997648i	$-0.521834\pi$
$181$	−13.9721	−	10.1513i	−1.03854	−	0.754542i	−0.970000	+	0.243106i	$0.921834\pi$
$182$	35.4388	+	25.7478i	2.62690	+	1.90855i
$183$	−4.05821	+	12.4899i	−0.299991	+	0.923279i
$184$	0.214846	+	0.661228i	0.0158387	+	0.0487464i
$185$		0			0
$186$	21.7972			1.59825
$187$	−15.5777	−	5.80202i	−1.13916	−	0.424286i
$188$	5.72427			0.417485
$189$	15.3603	−	11.1599i	1.11729	−	0.811762i
$190$		0			0
$191$	−5.62462	+	17.3108i	−0.406984	+	1.25257i	0.512244	+	0.858840i	$0.328814\pi$
$191$	−5.62462	+	17.3108i	−0.406984	+	1.25257i	−0.919228	+	0.393727i	$0.871186\pi$
$192$	−2.23598	−	1.62454i	−0.161368	−	0.117241i
$193$	8.92841	+	6.48687i	0.642681	+	0.466935i	0.860770	−	0.508994i	$-0.169982\pi$
$193$	8.92841	+	6.48687i	0.642681	+	0.466935i	−0.218089	+	0.975929i	$0.569982\pi$
$194$	−3.53198	+	10.8703i	−0.253581	+	0.780443i
$195$		0			0
$196$	−27.5093	+	19.9867i	−1.96495	+	1.42762i
$197$	−15.7213			−1.12009			−0.560047	−	0.828461i	$-0.689217\pi$
$197$	−15.7213			−1.12009			−0.560047	+	0.828461i	$0.689217\pi$
$198$	0.0768375	−	1.81200i	0.00546060	−	0.128773i
$199$	4.44523			0.315114			0.157557	−	0.987510i	$-0.449638\pi$
$199$	4.44523			0.315114			0.157557	+	0.987510i	$0.449638\pi$
$200$		0			0
$201$	4.34521	+	13.3732i	0.306487	+	0.943270i
$202$	6.97236	−	21.4587i	0.490573	−	1.50983i
$203$	7.22643	+	5.25031i	0.507196	+	0.368499i
$204$	−33.1908	−	24.1145i	−2.32382	−	1.68835i
$205$		0			0
$206$	−13.0449	−	40.1480i	−0.908879	−	2.79724i
$207$	−0.0182531	+	0.0132616i	−0.00126868	+	0.000921747i
$208$	−34.7131			−2.40692
$209$	−6.34673	−	9.56279i	−0.439012	−	0.661472i
$210$		0			0
$211$	−1.87055	+	1.35903i	−0.128774	+	0.0935597i	−0.650308	−	0.759671i	$-0.725360\pi$
$211$	−1.87055	+	1.35903i	−0.128774	+	0.0935597i	0.521534	+	0.853231i	$0.325360\pi$
$212$	−7.75881	−	23.8792i	−0.532877	−	1.64003i
$213$	−1.20772	+	3.71698i	−0.0827515	+	0.254683i
$214$	−35.5998	−	25.8648i	−2.43355	−	1.76808i
$215$		0			0
$216$	−10.1508	+	31.2408i	−0.690671	+	2.12567i
$217$	5.57348	+	17.1534i	0.378353	+	1.16445i
$218$	−37.1206	+	26.9697i	−2.51413	+	1.82662i
$219$	16.0484			1.08445
$220$		0			0
$221$	−22.5422			−1.51635
$222$	20.8140	−	15.1222i	1.39694	−	1.01494i
$223$	3.18203	+	9.79327i	0.213084	+	0.655806i	0.999284	+	0.0378334i	$0.0120456\pi$
$223$	3.18203	+	9.79327i	0.213084	+	0.655806i	−0.786200	+	0.617972i	$0.787954\pi$
$224$	7.78212	−	23.9509i	0.519965	−	1.60029i
$225$		0			0
$226$	29.6785	+	21.5627i	1.97419	+	1.43433i
$227$	−2.21823	+	6.82700i	−0.147229	+	0.453124i	−0.997291	−	0.0735589i	$-0.976564\pi$
$227$	−2.21823	+	6.82700i	−0.147229	+	0.453124i	0.850062	+	0.526682i	$0.176564\pi$
$228$	−8.75321	−	26.9396i	−0.579696	−	1.78412i
$229$	−1.66606	+	1.21047i	−0.110097	+	0.0799899i	−0.641471	−	0.767147i	$-0.721676\pi$
$229$	−1.66606	+	1.21047i	−0.110097	+	0.0799899i	0.531375	+	0.847137i	$0.321676\pi$
$230$		0			0
$231$	21.7682	−	6.06625i	1.43224	−	0.399130i
$232$	−15.4540			−1.01461
$233$	−14.2278	+	10.3371i	−0.932093	+	0.677205i	−0.946504	−	0.322691i	$-0.895413\pi$
$233$	−14.2278	+	10.3371i	−0.932093	+	0.677205i	0.0144113	+	0.999896i	$0.495413\pi$
$234$	−0.759997	−	2.33903i	−0.0496826	−	0.152907i
$235$		0			0
$236$	4.37039	+	3.17527i	0.284488	+	0.206693i
$237$	−20.8580	−	15.1543i	−1.35488	−	0.984374i
$238$	15.0849	−	46.4265i	0.977808	−	3.00938i
$239$	5.77519	+	17.7742i	0.373566	+	1.14972i	0.944441	+	0.328680i	$0.106604\pi$
$239$	5.77519	+	17.7742i	0.373566	+	1.14972i	−0.570875	+	0.821037i	$0.693396\pi$
$240$		0			0
$241$	30.1916			1.94481			0.972406	−	0.233296i	$-0.0749510\pi$
$241$	30.1916			1.94481			0.972406	+	0.233296i	$0.0749510\pi$
$242$	−10.9485	+	25.9740i	−0.703797	+	1.66967i
$243$	−2.21359			−0.142002
$244$	27.0637	−	19.6629i	1.73258	−	1.25879i
$245$		0			0
$246$	1.30154	−	4.00571i	0.0829829	−	0.255395i
$247$	−12.5915	−	9.14828i	−0.801180	−	0.582091i
$248$	−25.2451	−	18.3416i	−1.60306	−	1.16469i
$249$	−2.60986	+	8.03231i	−0.165393	+	0.509027i
$250$		0			0
$251$	20.6391	−	14.9952i	1.30273	−	0.946489i	0.302752	−	0.953069i	$-0.402094\pi$
$251$	20.6391	−	14.9952i	1.30273	−	0.946489i	0.999978	+	0.00657998i	$0.00209449\pi$
$252$	3.70370			0.233311
$253$	0.337786	−	0.0941326i	0.0212364	−	0.00591806i
$254$	−14.2730			−0.895565
$255$		0			0
$256$	−8.31752	−	25.5987i	−0.519845	−	1.59992i
$257$	7.39839	−	22.7699i	0.461499	−	1.42035i	−0.401834	−	0.915713i	$-0.631627\pi$
$257$	7.39839	−	22.7699i	0.461499	−	1.42035i	0.863333	−	0.504635i	$-0.168373\pi$
$258$	16.5803	+	12.0463i	1.03224	+	0.749967i
$259$	17.2226	+	12.5129i	1.07016	+	0.777515i
$260$		0			0
$261$	−0.154973	−	0.476959i	−0.00959260	−	0.0295230i
$262$	28.6846	−	20.8406i	1.77214	−	1.28753i
$263$	26.7696			1.65069			0.825343	−	0.564631i	$-0.190982\pi$
$263$	26.7696			1.65069			0.825343	+	0.564631i	$0.190982\pi$
$264$	−24.2997	+	30.6277i	−1.49555	+	1.88500i
$265$		0			0
$266$	27.2673	−	19.8109i	1.67187	−	1.21468i
$267$	−0.0958283	−	0.294929i	−0.00586459	−	0.0180494i
$268$	11.0685	−	34.0653i	0.676115	−	2.08087i
$269$	4.82647	+	3.50664i	0.294275	+	0.213803i	0.725120	−	0.688623i	$-0.241784\pi$
$269$	4.82647	+	3.50664i	0.294275	+	0.213803i	−0.430845	+	0.902426i	$0.641784\pi$
$270$		0			0
$271$	−2.31566	+	7.12688i	−0.140667	+	0.432927i	−0.996428	−	0.0844429i	$-0.973089\pi$
$271$	−2.31566	+	7.12688i	−0.140667	+	0.432927i	0.855762	+	0.517370i	$0.173089\pi$
$272$	11.9540	+	36.7907i	0.724819	+	2.23076i
$273$	24.7915	−	18.0121i	1.50045	−	1.09014i
$274$	−25.4824			−1.53945
$275$		0			0
$276$	0.865424			0.0520924
$277$	−1.16704	+	0.847908i	−0.0701209	+	0.0509458i	−0.622293	−	0.782784i	$-0.713799\pi$
$277$	−1.16704	+	0.847908i	−0.0701209	+	0.0509458i	0.552173	+	0.833730i	$0.313799\pi$
$278$	1.60793	+	4.94871i	0.0964373	+	0.296804i
$279$	0.312921	−	0.963072i	0.0187341	−	0.0576576i
$280$		0			0
$281$	0.193576	+	0.140641i	0.0115478	+	0.00838994i	0.593544	−	0.804801i	$-0.297728\pi$
$281$	0.193576	+	0.140641i	0.0115478	+	0.00838994i	−0.581996	+	0.813191i	$0.697728\pi$
$282$	1.77944	−	5.47655i	0.105964	−	0.326124i
$283$	1.63126	+	5.02049i	0.0969680	+	0.298437i	0.987762	−	0.155971i	$-0.0498507\pi$
$283$	1.63126	+	5.02049i	0.0969680	+	0.298437i	−0.890794	+	0.454408i	$0.849851\pi$
$284$	8.05414	−	5.85167i	0.477925	−	0.347233i
$285$		0			0
$286$	−1.61942	+	38.1895i	−0.0957583	+	2.25819i
$287$	3.48511			0.205720
$288$	−1.14388	+	0.831079i	−0.0674039	+	0.0489718i
$289$	2.50947	+	7.72336i	0.147616	+	0.454315i
$290$		0			0
$291$	6.46870	+	4.69979i	0.379202	+	0.275506i
$292$	−33.0726	−	24.0287i	−1.93543	−	1.40617i
$293$	4.63398	−	14.2619i	0.270720	−	0.833191i	−0.719600	−	0.694389i	$-0.755675\pi$
$293$	4.63398	−	14.2619i	0.270720	−	0.833191i	0.990320	−	0.138802i	$-0.0443252\pi$
$294$	10.5703	+	32.5319i	0.616470	+	1.89730i
$295$		0			0
$296$	−36.8311			−2.14077
$297$	15.5255	+	5.78255i	0.900878	+	0.335538i
$298$	27.2137			1.57645
$299$	0.384700	−	0.279501i	0.0222478	−	0.0161640i
$300$		0			0
$301$	−5.24033	+	16.1281i	−0.302048	+	0.929607i
$302$	7.11996	+	5.17296i	0.409708	+	0.297670i
$303$	−12.7696	−	9.27768i	−0.733596	−	0.532989i
$304$	−8.25353	+	25.4018i	−0.473372	+	1.45689i
$305$		0			0
$306$	−2.21731	+	1.61097i	−0.126755	+	0.0920929i
$307$	−2.11034			−0.120443			−0.0602217	−	0.998185i	$-0.519181\pi$
$307$	−2.11034			−0.120443			−0.0602217	+	0.998185i	$0.519181\pi$
$308$	−53.9425	−	20.0912i	−3.07366	−	1.14480i
$309$	−29.5312			−1.67997
$310$		0			0
$311$	−5.14858	−	15.8457i	−0.291949	−	0.898528i	−0.984229	−	0.176898i	$-0.943394\pi$
$311$	−5.14858	−	15.8457i	−0.291949	−	0.898528i	0.692280	−	0.721629i	$-0.256606\pi$
$312$	−16.3833	+	50.4227i	−0.927523	+	2.85462i
$313$	−23.5261	−	17.0927i	−1.32977	−	0.966137i	−0.999754	−	0.0221632i	$-0.992945\pi$
$313$	−23.5261	−	17.0927i	−1.32977	−	0.966137i	−0.330020	−	0.943974i	$-0.607055\pi$
$314$	0.618991	+	0.449723i	0.0349317	+	0.0253793i
$315$		0			0
$316$	20.2944	+	62.4597i	1.14165	+	3.51363i
$317$	−14.8184	+	10.7662i	−0.832282	+	0.604689i	−0.920204	−	0.391439i	$-0.871977\pi$
$317$	−14.8184	+	10.7662i	−0.832282	+	0.604689i	0.0879217	+	0.996127i	$0.471977\pi$
$318$	−25.2577			−1.41638
$319$	−0.330221	+	7.78733i	−0.0184888	+	0.436007i
$320$		0			0
$321$	−24.9041	+	18.0939i	−1.39001	+	1.00990i
$322$	0.318208	+	0.979344i	0.0177330	+	0.0545767i
$323$	−5.35972	+	16.4955i	−0.298223	+	0.917835i
$324$	35.4444	+	25.7518i	1.96913	+	1.43066i
$325$		0			0
$326$	11.2915	−	34.7517i	0.625379	−	1.92472i
$327$	9.91890	+	30.5272i	0.548516	+	1.68816i
$328$	−4.87808	+	3.54413i	−0.269347	+	0.195692i
$329$	4.76479			0.262691
$330$		0			0
$331$	21.5599			1.18504			0.592520	−	0.805556i	$-0.298133\pi$
$331$	21.5599			1.18504			0.592520	+	0.805556i	$0.298133\pi$
$332$	17.4048	−	12.6454i	0.955214	−	0.694004i
$333$	−0.369344	−	1.13672i	−0.0202399	−	0.0622921i
$334$	14.2514	−	43.8614i	0.779803	−	2.39999i
$335$		0			0
$336$	−42.5440	−	30.9101i	−2.32097	−	1.68628i
$337$	−4.34521	+	13.3732i	−0.236699	+	0.728484i	0.760193	+	0.649697i	$0.225104\pi$
$337$	−4.34521	+	13.3732i	−0.236699	+	0.728484i	−0.996892	+	0.0787861i	$0.974896\pi$
$338$	5.72362	+	17.6155i	0.311324	+	0.958156i
$339$	20.7618	−	15.0844i	1.12763	−	0.819270i
$340$		0			0
$341$	−9.78185	+	12.3292i	−0.529717	+	0.667662i
$342$	−1.89232			−0.102325
$343$	−1.37351	+	0.997912i	−0.0741625	+	0.0538822i
$344$	−9.06637	−	27.9034i	−0.488826	−	1.50445i
$345$		0			0
$346$	18.1468	+	13.1844i	0.975578	+	0.708799i
$347$	−23.1781	−	16.8399i	−1.24427	−	0.904013i	−0.246392	−	0.969170i	$-0.579245\pi$
$347$	−23.1781	−	16.8399i	−1.24427	−	0.904013i	−0.997875	+	0.0651572i	$0.979245\pi$
$348$	−5.94439	+	18.2949i	−0.318653	+	0.980712i
$349$	−5.53826	−	17.0450i	−0.296456	−	0.912399i	−0.982728	−	0.185054i	$-0.940754\pi$
$349$	−5.53826	−	17.0450i	−0.296456	−	0.912399i	0.686272	−	0.727345i	$-0.259246\pi$
$350$		0			0
$351$	22.4665			1.19917
$352$	21.1684	−	5.89910i	1.12828	−	0.314423i
$353$	24.7757			1.31868			0.659339	−	0.751845i	$-0.270836\pi$
$353$	24.7757			1.31868			0.659339	+	0.751845i	$0.270836\pi$
$354$	4.39644	−	3.19420i	0.233668	−	0.169770i
$355$		0			0
$356$	−0.244102	+	0.751269i	−0.0129374	+	0.0398172i
$357$	−27.6274	−	20.0725i	−1.46220	−	1.06235i
$358$	47.4735	+	34.4915i	2.50905	+	1.82293i
$359$	−3.22994	+	9.94073i	−0.170470	+	0.524652i	−0.999398	−	0.0347037i	$-0.988951\pi$
$359$	−3.22994	+	9.94073i	−0.170470	+	0.524652i	0.828928	+	0.559355i	$0.188951\pi$
$360$		0			0
$361$	5.68314	−	4.12904i	0.299112	−	0.217318i
$362$	44.2551			2.32600
$363$	14.9142	+	12.8992i	0.782791	+	0.677031i
$364$	−78.0589			−4.09140
$365$		0			0
$366$	−10.3990	−	32.0050i	−0.543567	−	1.67293i
$367$	−4.69553	+	14.4514i	−0.245105	+	0.754355i	0.750514	+	0.660854i	$0.229806\pi$
$367$	−4.69553	+	14.4514i	−0.245105	+	0.754355i	−0.995619	+	0.0935010i	$0.970194\pi$
$368$	−0.660174	−	0.479645i	−0.0344140	−	0.0250032i
$369$	−0.158300	−	0.115012i	−0.00824079	−	0.00598729i
$370$		0			0
$371$	−6.45831	−	19.8766i	−0.335299	−	1.03194i
$372$	−31.4239	+	22.8308i	−1.62925	+	1.18372i
$373$	−21.1774			−1.09653			−0.548263	−	0.836306i	$-0.684711\pi$
$373$	−21.1774			−1.09653			−0.548263	+	0.836306i	$0.684711\pi$
$374$	41.0328	−	11.4348i	2.12176	−	0.591281i
$375$		0			0
$376$	−6.66924	+	4.84548i	−0.343940	+	0.249887i
$377$	3.26620	+	10.0523i	0.168218	+	0.517722i
$378$	−15.0343	+	46.2707i	−0.773279	+	2.37991i
$379$	28.4486	+	20.6691i	1.46131	+	1.06170i	0.983020	+	0.183498i	$0.0587422\pi$
$379$	28.4486	+	20.6691i	1.46131	+	1.06170i	0.478287	+	0.878204i	$0.341258\pi$
$380$		0			0
$381$	−3.08546	+	9.49606i	−0.158073	+	0.486498i
$382$	−14.4129	−	44.3584i	−0.737430	−	2.26958i
$383$	1.60983	−	1.16961i	0.0822584	−	0.0597642i	−0.545896	−	0.837853i	$-0.683811\pi$
$383$	1.60983	−	1.16961i	0.0822584	−	0.0597642i	0.628154	+	0.778089i	$0.283811\pi$
$384$	−16.6722			−0.850799
$385$		0			0
$386$	−28.2797			−1.43940
$387$	0.770268	−	0.559633i	0.0391549	−	0.0284477i
$388$	−6.29390	−	19.3706i	−0.319524	−	0.983394i
$389$	−1.87218	+	5.76197i	−0.0949231	+	0.292143i	−0.987234	−	0.159279i	$-0.949083\pi$
$389$	−1.87218	+	5.76197i	−0.0949231	+	0.292143i	0.892311	+	0.451422i	$0.149083\pi$
$390$		0			0
$391$	−0.428707	−	0.311474i	−0.0216807	−	0.0157519i
$392$	15.1322	−	46.5723i	0.764294	−	2.35226i
$393$	−7.66473	−	23.5896i	−0.386634	−	1.18994i
$394$	32.5915	−	23.6791i	1.64194	−	1.19294i
$395$		0			0
$396$	1.78714	+	2.69274i	0.0898074	+	0.135315i
$397$	35.0663			1.75993			0.879964	−	0.475040i	$-0.157566\pi$
$397$	35.0663			1.75993			0.879964	+	0.475040i	$0.157566\pi$
$398$	−9.21534	+	6.69533i	−0.461923	+	0.335607i
$399$	−7.28603	−	22.4241i	−0.364758	−	1.12261i
$400$		0			0
$401$	−13.3283	−	9.68359i	−0.665585	−	0.483576i	0.202960	−	0.979187i	$-0.434944\pi$
$401$	−13.3283	−	9.68359i	−0.665585	−	0.483576i	−0.868544	+	0.495612i	$0.834944\pi$
$402$	−29.1504	−	21.1790i	−1.45389	−	1.05631i
$403$	−6.59510	+	20.2976i	−0.328525	+	1.01110i
$404$	12.4246	+	38.2389i	0.618145	+	1.90245i
$405$		0			0
$406$	−22.8889			−1.13596
$407$	−0.787007	+	18.5593i	−0.0390105	+	0.919952i
$408$	59.0824			2.92501
$409$	−3.48714	+	2.53356i	−0.172428	+	0.125276i	−0.670652	−	0.741772i	$-0.733986\pi$
$409$	−3.48714	+	2.53356i	−0.172428	+	0.125276i	0.498224	+	0.867048i	$0.333986\pi$
$410$		0			0
$411$	−5.50867	+	16.9539i	−0.271722	+	0.836276i
$412$	60.8578	+	44.2158i	2.99825	+	2.17836i
$413$	3.63784	+	2.64305i	0.179007	+	0.130056i
$414$	0.0178657	−	0.0549849i	0.000878050	−	0.00270236i
$415$		0			0
$416$	24.1084	−	17.5158i	1.18201	−	0.858781i
$417$	3.64006			0.178255
$418$	27.5606	+	10.2651i	1.34803	+	0.502083i
$419$	−18.7114			−0.914110			−0.457055	−	0.889438i	$-0.651096\pi$
$419$	−18.7114			−0.914110			−0.457055	+	0.889438i	$0.651096\pi$
$420$		0			0
$421$	−9.42742	−	29.0146i	−0.459465	−	1.41409i	−0.865813	−	0.500368i	$-0.833198\pi$
$421$	−9.42742	−	29.0146i	−0.459465	−	1.41409i	0.406348	−	0.913718i	$-0.366802\pi$
$422$	1.83085	−	5.63477i	0.0891244	−	0.274297i
$423$	−0.216426	−	0.157243i	−0.0105230	−	0.00764540i
$424$	29.2529	+	21.2535i	1.42065	+	1.03216i
$425$		0			0
$426$	−3.09474	−	9.52464i	−0.149941	−	0.461470i
$427$	22.5274	−	16.3671i	1.09018	−	0.792061i
$428$	78.4136			3.79027
$429$	25.0581	+	9.33304i	1.20982	+	0.450604i
$430$		0			0
$431$	−6.72568	+	4.88649i	−0.323965	+	0.235374i	−0.737865	−	0.674948i	$-0.764166\pi$
$431$	−6.72568	+	4.88649i	−0.323965	+	0.235374i	0.413901	+	0.910322i	$0.364166\pi$
$432$	−11.9139	−	36.6673i	−0.573208	−	1.76415i
$433$	−8.48242	+	26.1062i	−0.407639	+	1.25458i	0.511032	+	0.859561i	$0.329263\pi$
$433$	−8.48242	+	26.1062i	−0.407639	+	1.25458i	−0.918671	+	0.395023i	$0.870737\pi$
$434$	−37.3905	−	27.1658i	−1.79480	−	1.30400i
$435$		0			0
$436$	25.2663	−	77.7616i	1.21004	−	3.72411i
$437$	−0.113061	−	0.347964i	−0.00540842	−	0.0166454i
$438$	−33.2697	+	24.1719i	−1.58969	+	1.15498i
$439$	−23.1527			−1.10502			−0.552510	−	0.833506i	$-0.686330\pi$
$439$	−23.1527			−1.10502			−0.552510	+	0.833506i	$0.686330\pi$
$440$		0			0
$441$	1.58911			0.0756720
$442$	46.7317	−	33.9526i	2.22280	−	1.61496i
$443$	−6.23705	−	19.1957i	−0.296331	−	0.912013i	−0.982771	−	0.184827i	$-0.940828\pi$
$443$	−6.23705	−	19.1957i	−0.296331	−	0.912013i	0.686440	−	0.727186i	$-0.259172\pi$
$444$	−14.1671	+	43.6019i	−0.672341	+	2.06925i
$445$		0			0
$446$	−21.3471	−	15.5095i	−1.01081	−	0.734398i
$447$	5.88293	−	18.1058i	0.278253	−	0.856375i
$448$	1.81090	+	5.57338i	0.0855570	+	0.263317i
$449$	−11.3539	+	8.24906i	−0.535822	+	0.389297i	−0.822531	−	0.568720i	$-0.807439\pi$
$449$	−11.3539	+	8.24906i	−0.535822	+	0.389297i	0.286709	+	0.958018i	$0.407439\pi$
$450$		0			0
$451$	1.68167	+	2.53381i	0.0791866	+	0.119313i
$452$	−65.3711			−3.07480
$453$	4.98082	−	3.61878i	0.234019	−	0.170025i
$454$	−5.68414	−	17.4940i	−0.266770	−	0.821033i
$455$		0			0
$456$	33.0021	+	23.9774i	1.54546	+	1.12285i
$457$	12.6398	+	9.18334i	0.591264	+	0.429579i	0.842767	−	0.538278i	$-0.180925\pi$
$457$	12.6398	+	9.18334i	0.591264	+	0.429579i	−0.251503	+	0.967856i	$0.580925\pi$
$458$	1.63071	−	5.01879i	0.0761979	−	0.234513i
$459$	−7.73671	−	23.8111i	−0.361119	−	1.11141i
$460$		0			0
$461$	29.6082			1.37899			0.689496	−	0.724289i	$-0.257832\pi$
$461$	29.6082			1.37899			0.689496	+	0.724289i	$0.257832\pi$
$462$	−35.9903	+	45.3626i	−1.67442	+	2.11046i
$463$	1.31629			0.0611730			0.0305865	−	0.999532i	$-0.490262\pi$
$463$	1.31629			0.0611730			0.0305865	+	0.999532i	$0.490262\pi$
$464$	14.6742	−	10.6614i	0.681233	−	0.494945i
$465$		0			0
$466$	13.9258	−	42.8593i	0.645101	−	1.98542i
$467$	−9.78870	−	7.11191i	−0.452967	−	0.329100i	0.337799	−	0.941218i	$-0.390318\pi$
$467$	−9.78870	−	7.11191i	−0.452967	−	0.329100i	−0.790766	+	0.612118i	$0.790318\pi$
$468$	3.54559	+	2.57602i	0.163895	+	0.119077i
$469$	9.21323	−	28.3554i	0.425427	−	1.30933i
$470$		0			0
$471$	0.433019	−	0.314607i	0.0199525	−	0.0144963i
$472$	−7.77967			−0.358088
$473$	−14.2544	+	3.97234i	−0.655416	+	0.182648i
$474$	66.0655			3.03449
$475$		0			0
$476$	26.8809	+	82.7308i	1.23208	+	3.79196i
$477$	−0.362599	+	1.11597i	−0.0166023	+	0.0510966i
$478$	−38.7436	−	28.1489i	−1.77209	−	1.28750i
$479$	−2.47074	−	1.79509i	−0.112891	−	0.0820200i	0.529907	−	0.848055i	$-0.322227\pi$
$479$	−2.47074	−	1.79509i	−0.112891	−	0.0820200i	−0.642798	+	0.766036i	$0.722227\pi$
$480$		0			0
$481$	7.78426	+	23.9575i	0.354932	+	1.09237i
$482$	−62.5897	+	45.4741i	−2.85088	+	2.07129i
$483$	0.720365			0.0327777
$484$	−11.4217	−	48.9130i	−0.519168	−	2.22332i
$485$		0			0
$486$	4.58896	−	3.33408i	0.208160	−	0.151237i
$487$	−7.49051	−	23.0534i	−0.339427	−	1.04465i	−0.964500	−	0.264083i	$-0.914931\pi$
$487$	−7.49051	−	23.0534i	−0.339427	−	1.04465i	0.625073	−	0.780566i	$-0.285069\pi$
$488$	−14.8871	+	45.8179i	−0.673909	+	2.07408i
$489$	−20.6800	−	15.0249i	−0.935183	−	0.679450i
$490$		0			0
$491$	−10.0985	+	31.0801i	−0.455741	+	1.40263i	0.414522	+	0.910039i	$0.363949\pi$
$491$	−10.0985	+	31.0801i	−0.455741	+	1.40263i	−0.870263	+	0.492587i	$0.836051\pi$
$492$	2.31930	+	7.13808i	0.104562	+	0.321809i
$493$	9.52921	−	6.92337i	0.429174	−	0.311813i
$494$	39.8823			1.79439
$495$		0			0
$496$	36.6248			1.64450
$497$	6.70413	−	4.87084i	0.300721	−	0.218487i
$498$	−6.68768	−	20.5826i	−0.299682	−	0.922327i
$499$	−9.27234	+	28.5373i	−0.415087	+	1.27751i	0.497086	+	0.867701i	$0.334403\pi$
$499$	−9.27234	+	28.5373i	−0.415087	+	1.27751i	−0.912173	+	0.409805i	$0.865597\pi$
$500$		0			0
$501$	−26.1010	−	18.9635i	−1.16611	−	0.847226i
$502$	−20.2011	+	62.1726i	−0.901619	+	2.77490i
$503$	−4.18767	−	12.8883i	−0.186719	−	0.574662i	0.813255	−	0.581908i	$-0.197694\pi$
$503$	−4.18767	−	12.8883i	−0.186719	−	0.574662i	−0.999974	+	0.00724562i	$0.997694\pi$
$504$	−4.31512	+	3.13512i	−0.192211	+	0.139649i
$505$		0			0
$506$	−0.558477	+	0.703912i	−0.0248273	+	0.0312927i
$507$	12.9572			0.575450
$508$	20.5766	−	14.9497i	0.912937	−	0.663288i
$509$	11.7687	+	36.2203i	0.521638	+	1.60544i	0.770870	+	0.636993i	$0.219822\pi$
$509$	11.7687	+	36.2203i	0.521638	+	1.60544i	−0.249232	+	0.968444i	$0.580178\pi$
$510$		0			0
$511$	−27.5291	−	20.0011i	−1.21782	−	0.884795i
$512$	40.7506	+	29.6070i	1.80094	+	1.30846i
$513$	5.34173	−	16.4402i	0.235843	−	0.725851i
$514$	18.9582	+	58.3472i	0.836209	+	2.57359i
$515$		0			0
$516$	−36.5203			−1.60772
$517$	2.29915	+	3.46419i	0.101116	+	0.152355i
$518$	−54.5505			−2.39681
$519$	12.6947	−	9.22326i	0.557237	−	0.404856i
$520$		0			0
$521$	0.682532	−	2.10062i	0.0299023	−	0.0920298i	−0.934992	−	0.354670i	$-0.884593\pi$
$521$	0.682532	−	2.10062i	0.0299023	−	0.0920298i	0.964894	+	0.262640i	$0.0845932\pi$
$522$	1.03966	+	0.755356i	0.0455046	+	0.0330610i
$523$	−1.94375	−	1.41222i	−0.0849944	−	0.0617521i	0.544477	−	0.838776i	$-0.316728\pi$
$523$	−1.94375	−	1.41222i	−0.0849944	−	0.0617521i	−0.629471	+	0.777024i	$0.716728\pi$
$524$	−19.5243	+	60.0895i	−0.852921	+	2.62502i
$525$		0			0
$526$	−55.4957	+	40.3200i	−2.41973	+	1.75803i
$527$	23.7836			1.03603
$528$	1.94410	−	45.8462i	0.0846063	−	1.99520i
$529$	−22.9888			−0.999514
$530$		0			0
$531$	−0.0780148	−	0.240105i	−0.00338555	−	0.0104197i
$532$	−18.5596	+	57.1206i	−0.804661	+	2.47649i
$533$	3.33633	+	2.42398i	0.144512	+	0.104994i
$534$	0.642877	+	0.467077i	0.0278200	+	0.0202124i
$535$		0			0
$536$	15.9399	+	49.0581i	0.688501	+	2.11899i
$537$	33.2104	−	24.1288i	1.43314	−	1.04123i
$538$	−15.2873			−0.659083
$539$	−23.1446	−	8.62035i	−0.996908	−	0.371305i
$540$		0			0
$541$	19.0200	−	13.8189i	0.817735	−	0.594119i	−0.0983277	−	0.995154i	$-0.531349\pi$
$541$	19.0200	−	13.8189i	0.817735	−	0.594119i	0.916063	+	0.401035i	$0.131349\pi$
$542$	−5.93382	−	18.2624i	−0.254879	−	0.784438i
$543$	9.56685	−	29.4437i	0.410553	−	1.26355i
$544$	−26.8662	−	19.5194i	−1.15188	−	0.836889i
$545$		0			0
$546$	−24.2653	+	74.6810i	−1.03846	+	3.19605i
$547$	0.437026	+	1.34503i	0.0186859	+	0.0575093i	0.959965	−	0.280121i	$-0.0903746\pi$
$547$	0.437026	+	1.34503i	0.0186859	+	0.0575093i	−0.941279	+	0.337630i	$0.890375\pi$
$548$	36.7367	−	26.6907i	1.56931	−	1.14017i
$549$	−1.56337			−0.0667230
$550$		0			0
$551$	8.13251			0.346457
$552$	−1.00829	+	0.732565i	−0.0429156	+	0.0311800i
$553$	16.8927	+	51.9905i	0.718352	+	2.21086i
$554$	1.14228	−	3.51556i	0.0485307	−	0.149362i
$555$		0			0
$556$	−7.50143	−	5.45011i	−0.318132	−	0.231136i
$557$	1.53415	−	4.72163i	0.0650041	−	0.200062i	−0.913279	−	0.407334i	$-0.866458\pi$
$557$	1.53415	−	4.72163i	0.0650041	−	0.200062i	0.978283	+	0.207272i	$0.0664585\pi$
$558$	0.801851	+	2.46784i	0.0339451	+	0.104472i
$559$	−16.2341	+	11.7948i	−0.686630	+	0.498866i
$560$		0			0
$561$	1.26247	−	29.7718i	0.0533016	−	1.25697i
$562$	−0.613129			−0.0258633
$563$	−13.4316	+	9.75863i	−0.566075	+	0.411277i	−0.833677	−	0.552252i	$-0.813769\pi$
$563$	−13.4316	+	9.75863i	−0.566075	+	0.411277i	0.267603	+	0.963529i	$0.413769\pi$
$564$	3.17091	+	9.75907i	0.133520	+	0.410931i
$565$		0			0
$566$	−10.9435	−	7.95091i	−0.459989	−	0.334202i
$567$	29.5033	+	21.4354i	1.23902	+	0.900203i
$568$	−4.43039	+	13.6353i	−0.185895	+	0.572126i
$569$	−8.37027	−	25.7610i	−0.350900	−	1.07996i	−0.958349	−	0.285600i	$-0.907807\pi$
$569$	−8.37027	−	25.7610i	−0.350900	−	1.07996i	0.607449	−	0.794359i	$-0.292193\pi$
$570$		0			0
$571$	−25.9648			−1.08659			−0.543296	−	0.839541i	$-0.682824\pi$
$571$	−25.9648			−1.08659			−0.543296	+	0.839541i	$0.682824\pi$
$572$	−37.6657	−	56.7519i	−1.57488	−	2.37292i
$573$	−32.6282			−1.36306
$574$	−7.22492	+	5.24921i	−0.301562	+	0.219098i
$575$		0			0
$576$	0.101672	−	0.312915i	0.00423635	−	0.0130381i
$577$	0.603937	+	0.438786i	0.0251422	+	0.0182669i	0.600285	−	0.799786i	$-0.295054\pi$
$577$	0.603937	+	0.438786i	0.0251422	+	0.0182669i	−0.575143	+	0.818053i	$0.695054\pi$
$578$	−16.8351	−	12.2314i	−0.700249	−	0.508761i
$579$	−6.11338	+	18.8150i	−0.254063	+	0.781926i
$580$		0			0
$581$	14.4875	−	10.5258i	0.601043	−	0.436683i
$582$	−20.4889			−0.849291
$583$	11.3348	−	14.2865i	0.469439	−	0.591687i
$584$	58.8721			2.43614
$585$		0			0
$586$	11.8744	+	36.5458i	0.490529	+	1.50969i
$587$	5.53146	−	17.0241i	0.228308	−	0.702659i	−0.769631	−	0.638488i	$-0.779560\pi$
$587$	5.53146	−	17.0241i	0.228308	−	0.702659i	0.997939	−	0.0641701i	$-0.0204400\pi$
$588$	−49.3131	−	35.8281i	−2.03364	−	1.47753i
$589$	13.2850	+	9.65209i	0.547397	+	0.397708i
$590$		0			0
$591$	−8.70868	−	26.8026i	−0.358227	−	1.10251i
$592$	34.9727	−	25.4091i	1.43737	−	1.04431i
$593$	11.1992			0.459895			0.229948	−	0.973203i	$-0.426145\pi$
$593$	11.1992			0.459895			0.229948	+	0.973203i	$0.426145\pi$
$594$	−40.8951	+	11.3965i	−1.67795	+	0.467602i
$595$		0			0
$596$	−39.2326	+	28.5041i	−1.60703	+	1.16758i
$597$	2.46240	+	7.57850i	0.100780	+	0.310167i
$598$	−0.376535	+	1.15886i	−0.0153977	+	0.0473892i
$599$	1.46910	+	1.06736i	0.0600257	+	0.0436112i	0.617393	−	0.786654i	$-0.288189\pi$
$599$	1.46910	+	1.06736i	0.0600257	+	0.0436112i	−0.557368	+	0.830266i	$0.688189\pi$
$600$		0			0
$601$	14.4659	−	44.5214i	0.590075	−	1.81606i	0.0122187	−	0.999925i	$-0.496111\pi$
$601$	14.4659	−	44.5214i	0.590075	−	1.81606i	0.577856	−	0.816139i	$-0.303889\pi$
$602$	−13.4282	−	41.3277i	−0.547292	−	1.68439i
$603$	−1.35424	+	0.983912i	−0.0551489	+	0.0400680i
$604$	−15.6827			−0.638121
$605$		0			0
$606$	40.4464			1.64302
$607$	−26.6166	+	19.3381i	−1.08033	+	0.784908i	−0.977741	−	0.209815i	$-0.932714\pi$
$607$	−26.6166	+	19.3381i	−1.08033	+	0.784908i	−0.102593	+	0.994723i	$0.532714\pi$
$608$	−7.08527	−	21.8062i	−0.287346	−	0.884359i
$609$	−4.94801	+	15.2284i	−0.200504	+	0.617087i
$610$		0			0
$611$	4.56137	+	3.31403i	0.184533	+	0.134071i
$612$	1.50922	−	4.64489i	0.0610065	−	0.187759i
$613$	4.60003	+	14.1574i	0.185793	+	0.571813i	0.999961	−	0.00881636i	$-0.00280637\pi$
$613$	4.60003	+	14.1574i	0.185793	+	0.571813i	−0.814168	+	0.580630i	$0.802806\pi$
$614$	4.37490	−	3.17855i	0.176557	−	0.128276i
$615$		0			0
$616$	79.8543	−	22.2534i	3.21742	−	0.896615i
$617$	37.4741			1.50865			0.754324	−	0.656502i	$-0.227965\pi$
$617$	37.4741			1.50865			0.754324	+	0.656502i	$0.227965\pi$
$618$	61.2206	−	44.4793i	2.46265	−	1.78922i
$619$	−3.82934	−	11.7855i	−0.153914	−	0.473700i	0.844135	−	0.536131i	$-0.180115\pi$
$619$	−3.82934	−	11.7855i	−0.153914	−	0.473700i	−0.998049	+	0.0624311i	$0.980115\pi$
$620$		0			0
$621$	0.427269	+	0.310429i	0.0171457	+	0.0124571i
$622$	34.5400	+	25.0948i	1.38493	+	1.00621i
$623$	−0.203187	+	0.625344i	−0.00814050	+	0.0250539i
$624$	−19.2291	−	59.1810i	−0.769778	−	2.36913i
$625$		0			0
$626$	74.5163			2.97827
$627$	12.7875	−	16.1175i	0.510683	−	0.643671i
$628$	−1.36341			−0.0544061
$629$	22.7107	−	16.5003i	0.905536	−	0.657910i
$630$		0			0
$631$	0.476748	−	1.46728i	0.0189790	−	0.0584114i	−0.941118	−	0.338077i	$-0.890224\pi$
$631$	0.476748	−	1.46728i	0.0189790	−	0.0584114i	0.960097	+	0.279666i	$0.0902236\pi$
$632$	−76.5156	−	55.5918i	−3.04363	−	2.21132i
$633$	−3.35314	−	2.43620i	−0.133275	−	0.0968301i
$634$	14.5039	−	44.6383i	0.576022	−	1.77281i
$635$		0			0
$636$	36.4127	−	26.4554i	1.44386	−	1.04902i
$637$	−33.4920			−1.32700
$638$	−11.0446	−	16.6411i	−0.437258	−	0.658829i
$639$	−0.465257			−0.0184053
$640$		0			0
$641$	9.64663	+	29.6893i	0.381019	+	1.17266i	0.939327	+	0.343023i	$0.111451\pi$
$641$	9.64663	+	29.6893i	0.381019	+	1.17266i	−0.558308	+	0.829634i	$0.688549\pi$
$642$	24.3756	−	75.0203i	0.962027	−	2.96082i
$643$	−16.4378	−	11.9428i	−0.648245	−	0.470978i	0.214428	−	0.976740i	$-0.431211\pi$
$643$	−16.4378	−	11.9428i	−0.648245	−	0.470978i	−0.862673	+	0.505762i	$0.831211\pi$
$644$	−1.48453	−	1.07857i	−0.0584985	−	0.0425017i
$645$		0			0
$646$	−13.7341	−	42.2693i	−0.540361	−	1.66306i
$647$	17.9348	−	13.0304i	0.705092	−	0.512279i	−0.176495	−	0.984302i	$-0.556476\pi$
$647$	17.9348	−	13.0304i	0.705092	−	0.512279i	0.881586	+	0.472023i	$0.156476\pi$
$648$	−63.0940			−2.47857
$649$	−0.166236	+	3.92020i	−0.00652533	+	0.153881i
$650$		0			0
$651$	−26.1568	+	19.0040i	−1.02516	+	0.744826i
$652$	20.1212	+	61.9267i	0.788007	+	2.42524i
$653$	−3.66862	+	11.2908i	−0.143564	+	0.441845i	−0.996824	−	0.0796417i	$-0.974622\pi$
$653$	−3.66862	+	11.2908i	−0.143564	+	0.441845i	0.853259	+	0.521487i	$0.174622\pi$
$654$	−66.5423	−	48.3458i	−2.60201	−	1.89047i
$655$		0			0
$656$	2.18690	−	6.73060i	0.0853843	−	0.262786i
$657$	0.590371	+	1.81697i	0.0230326	+	0.0708869i
$658$	−9.87780	+	7.17664i	−0.385077	+	0.279774i
$659$	13.3368			0.519527			0.259764	−	0.965672i	$-0.416355\pi$
$659$	13.3368			0.519527			0.259764	+	0.965672i	$0.416355\pi$
$660$		0			0
$661$	−44.8817			−1.74570			−0.872848	−	0.487992i	$-0.837730\pi$
$661$	−44.8817			−1.74570			−0.872848	+	0.487992i	$0.837730\pi$
$662$	−44.6955	+	32.4732i	−1.73714	+	1.26211i
$663$	−12.4871	−	38.4312i	−0.484957	−	1.49254i
$664$	−9.57400	+	29.4657i	−0.371543	+	1.14349i
$665$		0			0
$666$	2.47779	+	1.80022i	0.0960125	+	0.0697572i
$667$	−0.0767805	+	0.236306i	−0.00297295	+	0.00914980i
$668$	25.3957	+	78.1598i	0.982588	+	3.02409i
$669$	−14.9335	+	10.8498i	−0.577362	+	0.419478i
$670$		0			0
$671$	22.7697	+	8.48071i	0.879014	+	0.327394i
$672$	45.1438			1.74146
$673$	−4.76086	+	3.45897i	−0.183518	+	0.133333i	−0.675751	−	0.737130i	$-0.736181\pi$
$673$	−4.76086	+	3.45897i	−0.183518	+	0.133333i	0.492233	+	0.870463i	$0.336181\pi$
$674$	−11.1345	−	34.2684i	−0.428884	−	1.31997i
$675$		0			0
$676$	−26.7022	−	19.4003i	−1.02701	−	0.746165i
$677$	−23.9475	−	17.3989i	−0.920379	−	0.668694i	0.0232393	−	0.999730i	$-0.492602\pi$
$677$	−23.9475	−	17.3989i	−0.920379	−	0.668694i	−0.943618	+	0.331035i	$0.892602\pi$
$678$	−20.3212	+	62.5422i	−0.780431	+	2.40192i
$679$	−5.23894	−	16.1238i	−0.201052	−	0.618774i
$680$		0			0
$681$	−12.8678			−0.493097
$682$	1.70860	−	40.2926i	0.0654258	−	1.54288i
$683$	13.1257			0.502239			0.251120	−	0.967956i	$-0.419201\pi$
$683$	13.1257			0.502239			0.251120	+	0.967956i	$0.419201\pi$
$684$	2.72805	−	1.98204i	0.104310	−	0.0757854i
$685$		0			0
$686$	1.34436	−	4.13751i	0.0513278	−	0.157971i
$687$	−2.98658	−	2.16988i	−0.113945	−	0.0827860i
$688$	27.8590	+	20.2407i	1.06211	+	0.771670i
$689$	7.64211	−	23.5200i	0.291141	−	0.896041i
$690$		0			0
$691$	5.69772	−	4.13963i	0.216751	−	0.157479i	−0.474112	−	0.880465i	$-0.657231\pi$
$691$	5.69772	−	4.13963i	0.216751	−	0.157479i	0.690863	+	0.722986i	$0.257231\pi$
$692$	−39.9709			−1.51946
$693$	1.48759	+	2.24139i	0.0565089	+	0.0851435i
$694$	73.4141			2.78676
$695$		0			0
$696$	−8.56063	−	26.3469i	−0.324490	−	0.998677i
$697$	1.42014	−	4.37075i	0.0537917	−	0.165554i
$698$	37.1542	+	26.9941i	1.40631	+	1.02174i
$699$	−25.5047	−	18.5302i	−0.964675	−	0.700877i
$700$		0			0
$701$	13.7090	+	42.1921i	0.517783	+	1.59357i	0.778161	+	0.628065i	$0.216153\pi$
$701$	13.7090	+	42.1921i	0.517783	+	1.59357i	−0.260377	+	0.965507i	$0.583847\pi$
$702$	−46.5749	+	33.8387i	−1.75786	+	1.27716i
$703$	19.3820			0.731006
$704$	−3.17826	+	4.00591i	−0.119785	+	0.150979i
$705$		0			0
$706$	−51.3621	+	37.3168i	−1.93304	+	1.40443i
$707$	10.3420	+	31.8294i	0.388951	+	1.19707i
$708$	−2.99245	+	9.20982i	−0.112463	+	0.346126i
$709$	15.7889	+	11.4713i	0.592963	+	0.430813i	0.843374	−	0.537327i	$-0.180566\pi$
$709$	15.7889	+	11.4713i	0.592963	+	0.430813i	−0.250411	+	0.968140i	$0.580566\pi$
$710$		0			0
$711$	0.948436	−	2.91899i	0.0355691	−	0.109471i
$712$	−0.351536	−	1.08192i	−0.0131744	−	0.0405466i
$713$	−0.405886	+	0.294893i	−0.0152006	+	0.0110438i
$714$	87.5068			3.27486
$715$		0			0
$716$	−104.567			−3.90785
$717$	−27.1034	+	19.6918i	−1.01219	+	0.735402i
$718$	−8.27662	−	25.4728i	−0.308881	−	0.950638i
$719$	14.6482	−	45.0824i	0.546284	−	1.68129i	−0.171634	−	0.985161i	$-0.554905\pi$
$719$	14.6482	−	45.0824i	0.546284	−	1.68129i	0.717918	−	0.696128i	$-0.245095\pi$
$720$		0			0
$721$	50.6571	+	36.8045i	1.88657	+	1.37067i
$722$	−5.56252	+	17.1197i	−0.207016	+	0.637128i
$723$	16.7244	+	51.4724i	0.621987	+	1.91428i
$724$	−63.8002	+	46.3536i	−2.37112	+	1.72272i
$725$		0			0
$726$	−50.3468	−	4.27760i	−1.86855	−	0.158756i
$727$	−37.2483			−1.38146			−0.690731	−	0.723112i	$-0.742711\pi$
$727$	−37.2483			−1.38146			−0.690731	+	0.723112i	$0.742711\pi$
$728$	90.9450	−	66.0754i	3.37065	−	2.44892i
$729$	7.66853	+	23.6013i	0.284020	+	0.874123i
$730$		0			0
$731$	18.0912	+	13.1440i	0.669126	+	0.486149i
$732$	48.5143	+	35.2477i	1.79314	+	1.30279i
$733$	−3.59105	+	11.0521i	−0.132638	+	0.408219i	−0.995215	−	0.0977073i	$-0.968849\pi$
$733$	−3.59105	+	11.0521i	−0.132638	+	0.408219i	0.862577	+	0.505926i	$0.168849\pi$
$734$	−12.0322	−	37.0312i	−0.444115	−	1.36685i
$735$		0			0
$736$	0.700516			0.0258214
$737$	25.0612	−	6.98392i	0.923140	−	0.257256i
$738$	0.501399			0.0184568
$739$	−30.7265	+	22.3241i	−1.13029	+	0.821207i	−0.985738	−	0.168290i	$-0.946176\pi$
$739$	−30.7265	+	22.3241i	−1.13029	+	0.821207i	−0.144556	+	0.989497i	$0.546176\pi$
$740$		0			0
$741$	8.62156	−	26.5344i	0.316721	−	0.974766i
$742$	43.3265	+	31.4785i	1.59056	+	1.15561i
$743$	−6.24321	−	4.53596i	−0.229041	−	0.166408i	0.467346	−	0.884075i	$-0.345210\pi$
$743$	−6.24321	−	4.53596i	−0.229041	−	0.166408i	−0.696387	+	0.717666i	$0.745210\pi$
$744$	17.2856	−	53.1995i	0.633720	−	1.95039i
$745$		0			0
$746$	43.9025	−	31.8971i	1.60739	−	1.16783i
$747$	−1.00541			−0.0367861
$748$	−47.1778	+	59.4635i	−1.72499	+	2.17420i
$749$	65.2703			2.38492
$750$		0			0
$751$	4.95293	+	15.2435i	0.180735	+	0.556245i	0.999849	−	0.0173860i	$-0.00553442\pi$
$751$	4.95293	+	15.2435i	0.180735	+	0.556245i	−0.819114	+	0.573631i	$0.805534\pi$
$752$	2.98990	−	9.20197i	0.109030	−	0.335561i
$753$	36.9976	+	26.8803i	1.34827	+	0.979574i
$754$	−21.9118	−	15.9198i	−0.797979	−	0.579766i
$755$		0			0
$756$	−26.7907	−	82.4532i	−0.974367	−	2.99879i
$757$	−5.15833	+	3.74775i	−0.187483	+	0.136214i	−0.677568	−	0.735461i	$-0.736966\pi$
$757$	−5.15833	+	3.74775i	−0.187483	+	0.136214i	0.490085	+	0.871675i	$0.336966\pi$
$758$	−90.1078			−3.27286
$759$	0.347597	+	0.523734i	0.0126170	+	0.0190103i
$760$		0			0
$761$	12.8347	−	9.32499i	0.465259	−	0.338031i	−0.330332	−	0.943865i	$-0.607161\pi$
$761$	12.8347	−	9.32499i	0.465259	−	0.338031i	0.795591	+	0.605834i	$0.207161\pi$
$762$	−7.90640	−	24.3334i	−0.286419	−	0.881506i
$763$	21.0312	−	64.7275i	0.761382	−	2.34329i
$764$	67.2402	+	48.8529i	2.43267	+	1.76743i
$765$		0			0
$766$	−1.57566	+	4.84939i	−0.0569310	+	0.175216i
$767$	1.64423	+	5.06043i	0.0593698	+	0.182721i
$768$	39.0348	−	28.3604i	1.40855	−	1.02337i
$769$	−51.7503			−1.86616			−0.933082	−	0.359663i	$-0.882892\pi$
$769$	−51.7503			−1.86616			−0.933082	+	0.359663i	$0.882892\pi$
$770$		0			0
$771$	42.9178			1.54565
$772$	40.7694	−	29.6207i	1.46732	−	1.06607i
$773$	−2.99315	−	9.21198i	−0.107656	−	0.331332i	0.882688	−	0.469959i	$-0.155731\pi$
$773$	−2.99315	−	9.21198i	−0.107656	−	0.331332i	−0.990345	+	0.138627i	$0.955731\pi$
$774$	−0.753921	+	2.32033i	−0.0270991	+	0.0834025i
$775$		0			0
$776$	23.7298	+	17.2407i	0.851849	+	0.618905i
$777$	−11.7925	+	36.2935i	−0.423053	+	1.30202i
$778$	−4.79740	−	14.7649i	−0.171995	−	0.529346i
$779$	2.56704	−	1.86506i	0.0919737	−	0.0668228i
$780$		0			0
$781$	6.77623	+	2.52385i	0.242473	+	0.0903105i
$782$	1.35788			0.0485578
$783$	−9.49723	+	6.90014i	−0.339403	+	0.246591i
$784$	17.7607	+	54.6617i	0.634310	+	1.95221i
$785$		0			0
$786$	51.4199	+	37.3587i	1.83409	+	1.33254i
$787$	−14.7424	−	10.7110i	−0.525510	−	0.381805i	0.293166	−	0.956062i	$-0.405291\pi$
$787$	−14.7424	−	10.7110i	−0.525510	−	0.381805i	−0.818675	+	0.574256i	$0.805291\pi$
$788$	−22.1835	+	68.2739i	−0.790255	+	2.43216i
$789$	14.8288	+	45.6385i	0.527921	+	1.62477i
$790$		0			0
$791$	−54.4139			−1.93473
$792$	−4.36152	−	1.62448i	−0.154980	−	0.0577233i
$793$	32.9495			1.17007
$794$	−72.6954	+	52.8163i	−2.57986	+	1.87438i
$795$		0			0
$796$	6.27245	−	19.3046i	0.222321	−	0.684234i
$797$	−16.1910	−	11.7634i	−0.573514	−	0.416682i	0.262866	−	0.964832i	$-0.415332\pi$
$797$	−16.1910	−	11.7634i	−0.573514	−	0.416682i	−0.836380	+	0.548150i	$0.815332\pi$
$798$	48.8793	+	35.5129i	1.73031	+	1.25714i
$799$	1.94160	−	5.97562i	0.0686887	−	0.211402i
$800$		0			0
$801$	0.0298661	−	0.0216990i	0.00105527	−	0.000766696i
$802$	42.2160			1.49070
$803$	1.25798	−	29.6658i	0.0443930	−	1.04688i
$804$	64.2079			2.26444
$805$		0			0
$806$	−16.8997	−	52.0121i	−0.595268	−	1.83205i
$807$	−3.30474	+	10.1709i	−0.116332	+	0.358034i
$808$	−46.8441	−	34.0342i	−1.64797	−	1.19732i
$809$	25.7317	+	18.6952i	0.904679	+	0.657288i	0.939664	−	0.342100i	$-0.111138\pi$
$809$	25.7317	+	18.6952i	0.904679	+	0.657288i	−0.0349842	+	0.999388i	$0.511138\pi$
$810$		0			0
$811$	1.12941	+	3.47596i	0.0396589	+	0.122057i	0.968926	−	0.247351i	$-0.0795602\pi$
$811$	1.12941	+	3.47596i	0.0396589	+	0.122057i	−0.929267	+	0.369409i	$0.879560\pi$
$812$	32.9977	−	23.9742i	1.15799	−	0.841331i
$813$	−13.4331			−0.471119
$814$	−26.3222	−	39.6604i	−0.922593	−	1.39010i
$815$		0			0
$816$	−56.1012	+	40.7599i	−1.96393	+	1.42688i
$817$	4.77108	+	14.6839i	0.166919	+	0.513724i
$818$	3.41313	−	10.5045i	0.119337	−	0.367283i
$819$	2.95129	+	2.14424i	0.103126	+	0.0749258i
$820$		0			0
$821$	4.25449	−	13.0940i	0.148483	−	0.456983i	−0.848960	−	0.528458i	$-0.822770\pi$
$821$	4.25449	−	13.0940i	0.148483	−	0.456983i	0.997442	+	0.0714746i	$0.0227705\pi$
$822$	−14.1158	−	43.4440i	−0.492345	−	1.51528i
$823$	−32.8267	+	23.8500i	−1.14427	+	0.831358i	−0.987708	−	0.156311i	$-0.950040\pi$
$823$	−32.8267	+	23.8500i	−1.14427	+	0.831358i	−0.156558	+	0.987669i	$0.550040\pi$
$824$	−108.332			−3.77393
$825$		0			0
$826$	−11.5225			−0.400918
$827$	12.5658	−	9.12955i	0.436954	−	0.317466i	−0.347469	−	0.937691i	$-0.612959\pi$
$827$	12.5658	−	9.12955i	0.436954	−	0.317466i	0.784423	+	0.620226i	$0.212959\pi$
$828$	0.0318362	+	0.0979817i	0.00110638	+	0.00340510i
$829$	−9.00201	+	27.7053i	−0.312653	+	0.962247i	0.664057	+	0.747682i	$0.268833\pi$
$829$	−9.00201	+	27.7053i	−0.312653	+	0.962247i	−0.976710	+	0.214565i	$0.931167\pi$
$830$		0			0
$831$	−2.09204	−	1.51996i	−0.0725720	−	0.0527267i
$832$	−2.14284	+	6.59497i	−0.0742895	+	0.228640i
$833$	11.5335	+	35.4965i	0.399612	+	1.22988i
$834$	−7.54615	+	5.48260i	−0.261302	+	0.189847i
$835$		0			0
$836$	−50.4845	+	14.0688i	−1.74604	+	0.486579i
$837$	−23.7038			−0.819322
$838$	38.7902	−	28.1827i	1.33999	−	0.973557i
$839$	6.73139	+	20.7171i	0.232393	+	0.715233i	0.997456	+	0.0712779i	$0.0227077\pi$
$839$	6.73139	+	20.7171i	0.232393	+	0.715233i	−0.765063	+	0.643955i	$0.777292\pi$
$840$		0			0
$841$	18.9934	+	13.7995i	0.654945	+	0.475845i
$842$	63.2451	+	45.9503i	2.17957	+	1.58355i
$843$	−0.132543	+	0.407927i	−0.00456504	+	0.0140497i
$844$	3.26253	+	10.0410i	0.112301	+	0.345626i
$845$		0			0
$846$	0.685505			0.0235681
$847$	−9.50725	−	40.7144i	−0.326673	−	1.39896i
$848$	−42.4392			−1.45737
$849$	−7.65560	+	5.56212i	−0.262740	+	0.190892i
$850$		0			0
$851$	−0.182989	+	0.563182i	−0.00627278	+	0.0193056i
$852$	14.4378	+	10.4897i	0.494631	+	0.359371i
$853$	7.08127	+	5.14484i	0.242458	+	0.176156i	0.702378	−	0.711804i	$-0.252122\pi$
$853$	7.08127	+	5.14484i	0.242458	+	0.176156i	−0.459920	+	0.887961i	$0.652122\pi$
$854$	−22.0493	+	67.8608i	−0.754512	+	2.32215i
$855$		0			0
$856$	−91.3583	+	66.3757i	−3.12256	+	2.26867i
$857$	−14.0273			−0.479163			−0.239582	−	0.970876i	$-0.577010\pi$
$857$	−14.0273			−0.479163			−0.239582	+	0.970876i	$0.577010\pi$
$858$	−66.0047	+	18.3939i	−2.25336	+	0.627957i
$859$	31.8774			1.08764			0.543822	−	0.839201i	$-0.316977\pi$
$859$	31.8774			1.08764			0.543822	+	0.839201i	$0.316977\pi$
$860$		0			0
$861$	1.93055	+	5.94162i	0.0657930	+	0.202490i
$862$	6.58294	−	20.2602i	0.224216	−	0.690065i
$863$	2.80343	+	2.03681i	0.0954298	+	0.0693338i	0.634477	−	0.772942i	$-0.281216\pi$
$863$	2.80343	+	2.03681i	0.0954298	+	0.0693338i	−0.539047	+	0.842276i	$0.681216\pi$
$864$	26.7761	+	19.4539i	0.910940	+	0.661836i
$865$		0			0
$866$	−21.7360	−	66.8964i	−0.738618	−	2.27323i
$867$	−11.7771	+	8.55659i	−0.399973	+	0.290597i
$868$	82.3577			2.79540
$869$	−29.6479	+	37.3686i	−1.00574	+	1.26764i
$870$		0			0
$871$	28.5418	−	20.7368i	0.967103	−	0.702641i
$872$	36.3865	+	111.986i	1.23220	+	3.79233i
$873$	−0.294138	+	0.905265i	−0.00995507	+	0.0306386i
$874$	0.758482	+	0.551069i	0.0256560	+	0.0186402i
$875$		0			0
$876$	22.6452	−	69.6946i	0.765109	−	2.35476i
$877$	−6.11122	−	18.8084i	−0.206361	−	0.635114i	−0.999655	−	0.0262750i	$-0.991635\pi$
$877$	−6.11122	−	18.8084i	−0.206361	−	0.635114i	0.793294	−	0.608839i	$-0.208365\pi$
$878$	47.9975	−	34.8723i	1.61984	−	1.17688i
$879$	26.8816			0.906692
$880$		0			0
$881$	57.2097			1.92744			0.963722	−	0.266910i	$-0.0860025\pi$
$881$	57.2097			1.92744			0.963722	+	0.266910i	$0.0860025\pi$
$882$	−3.29436	+	2.39349i	−0.110927	+	0.0805931i
$883$	−17.6885	−	54.4396i	−0.595265	−	1.83204i	−0.553402	−	0.832915i	$-0.686671\pi$
$883$	−17.6885	−	54.4396i	−0.595265	−	1.83204i	−0.0418636	−	0.999123i	$-0.513329\pi$
$884$	−31.8081	+	97.8953i	−1.06982	+	3.29258i
$885$		0			0
$886$	41.8421	+	30.4000i	1.40571	+	1.02131i
$887$	12.2757	−	37.7809i	0.412179	−	1.26856i	−0.502571	−	0.864536i	$-0.667612\pi$
$887$	12.2757	−	37.7809i	0.412179	−	1.26856i	0.914750	−	0.404021i	$-0.132388\pi$
$888$	−20.4023	−	62.7919i	−0.684657	−	2.10716i
$889$	17.1276	−	12.4439i	0.574441	−	0.417356i
$890$		0			0
$891$	−1.34819	+	31.7933i	−0.0451661	+	1.06512i
$892$	47.0199			1.57434
$893$	3.50962	−	2.54989i	0.117445	−	0.0853287i
$894$	15.0748	+	46.3956i	0.504178	+	1.55170i
$895$		0			0
$896$	28.5990	+	20.7784i	0.955427	+	0.694158i
$897$	0.689612	+	0.501032i	0.0230255	+	0.0167290i
$898$	11.1129	−	34.2020i	0.370842	−	1.14133i
$899$	−3.44608	−	10.6059i	−0.114933	−	0.353728i
$900$		0			0
$901$	−27.5594			−0.918136
$902$	−7.30262	−	2.71991i	−0.243151	−	0.0905630i
$903$	−30.3989			−1.01161
$904$	76.1627	−	55.3354i	2.53313	−	1.84043i
$905$		0			0
$906$	−4.87511	+	15.0041i	−0.161965	+	0.498476i
$907$	21.5295	+	15.6421i	0.714875	+	0.519387i	0.884743	−	0.466080i	$-0.154334\pi$
$907$	21.5295	+	15.6421i	0.714875	+	0.519387i	−0.169867	+	0.985467i	$0.554334\pi$
$908$	26.5180	+	19.2665i	0.880032	+	0.639380i
$909$	0.580648	−	1.78705i	0.0192589	−	0.0592727i
$910$		0			0
$911$	−6.30044	+	4.57754i	−0.208743	+	0.151661i	−0.687245	−	0.726426i	$-0.741180\pi$
$911$	−6.30044	+	4.57754i	−0.208743	+	0.151661i	0.478502	+	0.878087i	$0.341180\pi$
$912$	−47.8784			−1.58541
$913$	14.6433	+	5.45399i	0.484623	+	0.180501i
$914$	−40.0351			−1.32424
$915$		0			0
$916$	2.90587	+	8.94336i	0.0960128	+	0.295497i
$917$	−16.2517	+	50.0175i	−0.536678	+	1.65172i
$918$	51.9028	+	37.7096i	1.71305	+	1.24460i
$919$	12.9266	+	9.39169i	0.426408	+	0.309803i	0.780211	−	0.625517i	$-0.215112\pi$
$919$	12.9266	+	9.39169i	0.426408	+	0.309803i	−0.353803	+	0.935320i	$0.615112\pi$
$920$		0			0
$921$	−1.16901	−	3.59783i	−0.0385201	−	0.118553i
$922$	−61.3803	+	44.5954i	−2.02145	+	1.46867i
$923$	9.80572			0.322759
$924$	4.37168	−	103.094i	0.143818	−	3.39154i
$925$		0			0
$926$	−2.72877	+	1.98257i	−0.0896730	+	0.0651512i
$927$	−1.08636	−	3.34347i	−0.0356807	−	0.109814i
$928$	−4.81167	+	14.8088i	−0.157951	+	0.486123i
$929$	−8.02976	−	5.83396i	−0.263448	−	0.191406i	0.448218	−	0.893924i	$-0.352059\pi$
$929$	−8.02976	−	5.83396i	−0.263448	−	0.191406i	−0.711666	+	0.702518i	$0.752059\pi$
$930$		0			0
$931$	−7.96319	+	24.5082i	−0.260983	+	0.803223i
$932$	24.8155	+	76.3741i	0.812857	+	2.50172i
$933$	24.1627	−	17.5552i	0.791051	−	0.574732i
$934$	31.0046			1.01450
$935$		0			0
$936$	−6.31145			−0.206296
$937$	7.21488	−	5.24192i	0.235700	−	0.171246i	−0.463666	−	0.886010i	$-0.653466\pi$
$937$	7.21488	−	5.24192i	0.235700	−	0.171246i	0.699365	+	0.714764i	$0.253466\pi$
$938$	23.6086	+	72.6599i	0.770849	+	2.37243i
$939$	16.1086	−	49.5771i	0.525683	−	1.61789i
$940$		0			0
$941$	−30.1937	−	21.9370i	−0.984287	−	0.715126i	−0.0256241	−	0.999672i	$-0.508157\pi$
$941$	−30.1937	−	21.9370i	−0.984287	−	0.715126i	−0.958663	+	0.284546i	$0.908157\pi$
$942$	−0.423829	+	1.30441i	−0.0138091	+	0.0425001i
$943$	0.0299572	+	0.0921987i	0.000975540	+	0.00300240i
$944$	7.38712	−	5.36705i	0.240430	−	0.174683i
$945$		0			0
$946$	23.5674	−	29.7047i	0.766242	−	0.965782i
$947$	−1.62118			−0.0526814			−0.0263407	−	0.999653i	$-0.508385\pi$
$947$	−1.62118			−0.0526814			−0.0263407	+	0.999653i	$0.508385\pi$
$948$	−95.2431	+	69.1982i	−3.09335	+	2.24745i
$949$	−12.4426	−	38.2944i	−0.403904	−	1.24309i
$950$		0			0
$951$	−26.5633	−	19.2994i	−0.861375	−	0.625826i
$952$	−101.348	−	73.6340i	−3.28472	−	2.38649i
$953$	7.83110	−	24.1017i	0.253674	−	0.780729i	−0.740414	−	0.672152i	$-0.765370\pi$
$953$	7.83110	−	24.1017i	0.253674	−	0.780729i	0.994088	−	0.108578i	$-0.0346297\pi$
$954$	−0.929151	−	2.85963i	−0.0300824	−	0.0925840i
$955$		0			0
$956$	85.3383			2.76004
$957$	−13.4592	+	3.75075i	−0.435075	+	0.121245i
$958$	7.82578			0.252839
$959$	30.5790	−	22.2169i	0.987448	−	0.717423i
$960$		0			0
$961$	−2.62123	+	8.06732i	−0.0845558	+	0.260236i
$962$	−52.2217	−	37.9413i	−1.68370	−	1.22328i
$963$	−2.96470	−	2.15398i	−0.0955362	−	0.0694111i
$964$	42.6019	−	131.115i	1.37211	−	4.22293i
$965$		0			0
$966$	−1.49338	+	1.08500i	−0.0480486	+	0.0349093i
$967$	−6.70594			−0.215648			−0.107824	−	0.994170i	$-0.534388\pi$
$967$	−6.70594			−0.215648			−0.107824	+	0.994170i	$0.534388\pi$
$968$	54.7111	+	47.3193i	1.75848	+	1.52090i
$969$	−31.0915			−0.998803
$970$		0			0
$971$	1.79835	+	5.53476i	0.0577119	+	0.177619i	0.975757	−	0.218857i	$-0.0702329\pi$
$971$	1.79835	+	5.53476i	0.0577119	+	0.177619i	−0.918045	+	0.396476i	$0.870233\pi$
$972$	−3.12349	+	9.61312i	−0.100186	+	0.308341i
$973$	−6.24407	−	4.53658i	−0.200176	−	0.145436i
$974$	50.2511	+	36.5095i	1.61015	+	1.16984i
$975$		0			0
$976$	−17.4730	−	53.7763i	−0.559296	−	1.72134i
$977$	−4.23279	+	3.07530i	−0.135419	+	0.0983875i	−0.653432	−	0.756985i	$-0.726672\pi$
$977$	−4.23279	+	3.07530i	−0.135419	+	0.0983875i	0.518014	+	0.855372i	$0.326672\pi$
$978$	65.5017			2.09451
$979$	−0.552694	+	0.154022i	−0.0176642	+	0.00492256i
$980$		0			0
$981$	−3.09135	+	2.24600i	−0.0986993	+	0.0717092i
$982$	−25.8772	−	79.6419i	−0.825775	−	2.54148i
$983$	−4.57075	+	14.0673i	−0.145784	+	0.448678i	−0.997111	−	0.0759580i	$-0.975799\pi$
$983$	−4.57075	+	14.0673i	−0.145784	+	0.448678i	0.851327	+	0.524636i	$0.175799\pi$
$984$	−8.74443	−	6.35320i	−0.278762	−	0.202533i
$985$		0			0
$986$	−9.32696	+	28.7054i	−0.297031	+	0.914168i
$987$	2.63942	+	8.12329i	0.0840136	+	0.258567i
$988$	−57.4962	+	41.7734i	−1.82920	+	1.32899i
$989$	−0.471714			−0.0149996
$990$		0			0
$991$	24.9189			0.791575			0.395788	−	0.918342i	$-0.370472\pi$
$991$	24.9189			0.791575			0.395788	+	0.918342i	$0.370472\pi$
$992$	−25.4361	+	18.4804i	−0.807595	+	0.586752i
$993$	11.9430	+	36.7566i	0.378998	+	1.16644i
$994$	−6.56185	+	20.1953i	−0.208129	+	0.640556i
$995$		0			0
$996$	31.1998	+	22.6680i	0.988604	+	0.718263i
$997$	4.58532	−	14.1122i	0.145219	−	0.446937i	−0.851820	−	0.523834i	$-0.824501\pi$
$997$	4.58532	−	14.1122i	0.145219	−	0.446937i	0.997039	+	0.0768969i	$0.0245012\pi$
$998$	−23.7601	−	73.1261i	−0.752113	−	2.31477i
$999$	−22.6345	+	16.4449i	−0.716124	+	0.520295i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	275.2.h.e.201.1	yes	16
5.2	odd	4		275.2.z.c.124.1		32
5.3	odd	4		275.2.z.c.124.8		32
5.4	even	2		275.2.h.c.201.4	yes	16
11.2	odd	10		3025.2.a.bj.1.2		8
11.4	even	5	inner	275.2.h.e.26.1	yes	16
11.9	even	5		3025.2.a.bn.1.7		8
55.4	even	10		275.2.h.c.26.4	✓	16
55.9	even	10		3025.2.a.bi.1.2		8
55.24	odd	10		3025.2.a.bm.1.7		8
55.37	odd	20		275.2.z.c.224.8		32
55.48	odd	20		275.2.z.c.224.1		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
275.2.h.c.26.4	✓	16	55.4	even	10
275.2.h.c.201.4	yes	16	5.4	even	2
275.2.h.e.26.1	yes	16	11.4	even	5	inner
275.2.h.e.201.1	yes	16	1.1	even	1	trivial
275.2.z.c.124.1		32	5.2	odd	4
275.2.z.c.124.8		32	5.3	odd	4
275.2.z.c.224.1		32	55.48	odd	20
275.2.z.c.224.8		32	55.37	odd	20
3025.2.a.bi.1.2		8	55.9	even	10
3025.2.a.bj.1.2		8	11.2	odd	10
3025.2.a.bm.1.7		8	55.24	odd	10
3025.2.a.bn.1.7		8	11.9	even	5

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 275 = 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	275.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.07308 + 1.50618i) q^{2} +(0.553942 + 1.70486i) q^{3} +(1.41105 - 4.34277i) q^{4} +(-3.71620 - 2.69998i) q^{6} +(1.17454 - 3.61485i) q^{7} +(2.03208 + 6.25410i) q^{8} +(-0.172643 + 0.125433i) q^{9} +(3.19489 - 0.890336i) q^{11} +8.18545 q^{12} +(3.63862 - 2.64361i) q^{13} +(3.00971 + 9.26295i) q^{14} +(-6.24414 - 4.53663i) q^{16} +(-4.05485 - 2.94602i) q^{17} +(0.168979 - 0.520065i) q^{18} +(-1.06936 - 3.29116i) q^{19} +6.81344 q^{21} +(-5.28226 + 6.65782i) q^{22} +0.105727 q^{23} +(-9.53671 + 6.92883i) q^{24} +(-3.56139 + 10.9608i) q^{26} +(4.04124 + 2.93613i) q^{27} +(-14.0411 - 10.2015i) q^{28} +(-0.726214 + 2.23506i) q^{29} +(-3.83900 + 2.78920i) q^{31} +6.62570 q^{32} +(3.28768 + 4.95364i) q^{33} +12.8433 q^{34} +(0.301117 + 0.926742i) q^{36} +(-1.73077 + 5.32675i) q^{37} +(7.17396 + 5.21219i) q^{38} +(6.52257 + 4.73892i) q^{39} +(0.283345 + 0.872045i) q^{41} +(-14.1248 + 10.2623i) q^{42} -4.46162 q^{43} +(0.641627 - 15.1310i) q^{44} +(-0.219181 + 0.159244i) q^{46} +(0.387384 + 1.19225i) q^{47} +(4.27543 - 13.1584i) q^{48} +(-6.02449 - 4.37704i) q^{49} +(2.77640 - 8.54487i) q^{51} +(-6.34631 - 19.5319i) q^{52} +(4.44847 - 3.23200i) q^{53} -12.8002 q^{54} +24.9944 q^{56} +(5.01860 - 3.64622i) q^{57} +(-1.86090 - 5.72727i) q^{58} +(-0.365582 + 1.12515i) q^{59} +(5.92690 + 4.30614i) q^{61} +(3.75752 - 11.5645i) q^{62} +(0.250645 + 0.771405i) q^{63} +(-1.24734 + 0.906248i) q^{64} +(-14.2767 - 5.31745i) q^{66} +7.84414 q^{67} +(-18.5155 + 13.4523i) q^{68} +(0.0585667 + 0.180250i) q^{69} +(1.76384 + 1.28150i) q^{71} +(-1.13529 - 0.824840i) q^{72} +(2.76651 - 8.51445i) q^{73} +(-4.43504 - 13.6496i) q^{74} -15.8017 q^{76} +(0.534080 - 12.5948i) q^{77} -20.6595 q^{78} +(-11.6357 + 8.45380i) q^{79} +(-2.96491 + 9.12506i) q^{81} +(-1.90086 - 1.38105i) q^{82} +(3.81162 + 2.76930i) q^{83} +(9.61410 - 29.5892i) q^{84} +(9.24930 - 6.72001i) q^{86} -4.21274 q^{87} +(12.0605 + 18.1719i) q^{88} -0.172993 q^{89} +(-5.28256 - 16.2581i) q^{91} +(0.149186 - 0.459148i) q^{92} +(-6.88177 - 4.99990i) q^{93} +(-2.59882 - 1.88815i) q^{94} +(3.67026 + 11.2959i) q^{96} +(3.60857 - 2.62178i) q^{97} +19.0819 q^{98} +(-0.439899 + 0.554454i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{3} - 2 q^{4} - 3 q^{6} - 4 q^{7} - 16 q^{8} + 8 q^{9} - 5 q^{11} + 6 q^{12} - 7 q^{13} + 3 q^{14} - 4 q^{16} - 12 q^{17} - 16 q^{18} - 13 q^{19} + 10 q^{21} - 28 q^{22} + 4 q^{23} - 43 q^{24}+ \cdots - 10 q^{99}+O(q^{100}) \) 16 * q + 2 * q^3 - 2 * q^4 - 3 * q^6 - 4 * q^7 - 16 * q^8 + 8 * q^9 - 5 * q^11 + 6 * q^12 - 7 * q^13 + 3 * q^14 - 4 * q^16 - 12 * q^17 - 16 * q^18 - 13 * q^19 + 10 * q^21 - 28 * q^22 + 4 * q^23 - 43 * q^24 - 34 * q^26 + 11 * q^27 - 47 * q^28 - 11 * q^29 - 10 * q^31 + 58 * q^32 + 34 * q^33 + 20 * q^34 + 3 * q^36 + 4 * q^37 + 36 * q^38 + 3 * q^39 + 25 * q^41 - 13 * q^42 + 28 * q^43 - q^44 + 40 * q^46 - 8 * q^47 + 106 * q^48 + 16 * q^49 + 35 * q^51 - 39 * q^52 + 22 * q^53 + 60 * q^54 - 20 * q^56 - 29 * q^57 - 6 * q^58 + 14 * q^59 + 16 * q^61 + 10 * q^62 - 73 * q^63 + 40 * q^64 - 55 * q^66 + 14 * q^67 - 83 * q^68 + 35 * q^69 - 46 * q^71 - 28 * q^72 - 7 * q^73 - 7 * q^74 - 62 * q^76 + 51 * q^77 - 34 * q^78 - 39 * q^79 - 43 * q^81 + 51 * q^82 - 28 * q^83 - 54 * q^84 + 2 * q^86 + 50 * q^87 + 76 * q^88 - 22 * q^89 - 34 * q^91 - 4 * q^92 - 3 * q^93 - 40 * q^94 + 108 * q^96 + 39 * q^97 + 52 * q^98 - 10 * q^99

Introduction

L-functions

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