LMFDB - Embedded newform 275.2.h.c.201.4

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			201.4
Root			$-1.26407 - 0.918397i$ of defining polynomial
Character	$\chi$	$=$	275.201
Dual form			275.2.h.c.26.4

$q$-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	$-0.339143\pi$
$2$	2.07308	−	1.50618i	1.46589	−	1.06503i	0.981779	−	0.190025i	$-0.0608570\pi$
$3$	−0.553942	−	1.70486i	−0.319819	−	0.984301i	−0.973725	−	0.227726i	$-0.926871\pi$
$3$	−0.553942	−	1.70486i	−0.319819	−	0.984301i	0.653906	−	0.756575i	$-0.273129\pi$
$4$	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	$0.355079\pi$
$7$	−1.17454	+	3.61485i	−0.443933	+	1.36628i	−0.883650	+	0.468148i	$0.844921\pi$
$8$	−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	−0.964035	−	0.265776i	$-0.914372\pi$
$13$	−3.63862	+	2.64361i	−1.00917	+	0.733205i	−0.0451354	+	0.998981i	$0.514372\pi$
$14$	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	0.958476	−	0.285174i	$-0.0920512\pi$
$17$	4.05485	+	2.94602i	0.983445	+	0.714515i	0.0249691	+	0.999688i	$0.492051\pi$
$18$	−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	$-0.503509\pi$
$23$	−0.105727			−0.0220456			−0.0110228	+	0.999939i	$0.503509\pi$
$24$	−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	$-0.747710\pi$
$37$	1.73077	−	5.32675i	0.284536	−	0.875713i	0.986537	−	0.163537i	$-0.0522903\pi$
$38$	−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	$-0.389507\pi$
$43$	4.46162			0.680390			0.340195	+	0.940355i	$0.389507\pi$
$44$	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	0.918820	−	0.394676i	$-0.129143\pi$
$47$	−0.387384	−	1.19225i	−0.0565058	−	0.173907i	−0.975326	+	0.220769i	$0.929143\pi$
$48$	−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	−0.849782	−	0.527135i	$-0.823266\pi$
$53$	−4.44847	+	3.23200i	−0.611044	+	0.443949i	0.238738	+	0.971084i	$0.423266\pi$
$54$	−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	$-0.659058\pi$
$67$	−7.84414			−0.958315			−0.479157	+	0.877729i	$0.659058\pi$
$68$	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	$0.275528\pi$
$73$	−2.76651	+	8.51445i	−0.323796	+	0.996541i	−0.971981	+	0.235059i	$0.924472\pi$
$74$	−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	0.358606	−	0.933489i	$-0.383252\pi$
$83$	−3.81162	−	2.76930i	−0.418380	−	0.303971i	−0.776986	+	0.629518i	$0.783252\pi$
$84$	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	−0.755714	−	0.654902i	$-0.772710\pi$
$97$	−3.60857	+	2.62178i	−0.366394	+	0.266201i	0.389320	+	0.921103i	$0.372710\pi$
$98$	−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	$-0.598589\pi$
$103$	5.09074	−	15.6677i	0.501605	−	1.54378i	0.806403	−	0.591366i	$-0.201411\pi$
$104$	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	$-0.788306\pi$
$107$	−5.30657	−	16.3319i	−0.513005	−	1.57887i	0.273877	−	0.961765i	$-0.411694\pi$
$108$	−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	$0.135156\pi$
$113$	4.42393	+	13.6155i	0.416168	+	1.28083i	−0.495034	+	0.868874i	$0.664844\pi$
$114$	−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	0.369622	−	0.929182i	$-0.379487\pi$
$127$	−4.50622	−	3.27396i	−0.399863	−	0.290517i	−0.769485	+	0.638665i	$0.779487\pi$
$128$	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	0.188437	−	0.982085i	$-0.439658\pi$
$137$	−8.04525	−	5.84522i	−0.687352	−	0.499390i	−0.875789	+	0.482695i	$0.839658\pi$
$138$	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	0.954671	−	0.297663i	$-0.0962073\pi$
$157$	0.0922677	+	0.283971i	0.00736377	+	0.0226633i	−0.947307	+	0.320327i	$0.896207\pi$
$158$	−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	−0.0357901	−	0.999359i	$-0.511395\pi$
$163$	11.5364	−	8.38166i	0.903597	−	0.656502i	0.939387	+	0.342857i	$0.111395\pi$
$164$	4.18690			0.326942
$165$		0			0
$166$	−12.0729			−0.937037
$167$	14.5604	−	10.5788i	1.12672	−	0.818611i	0.141507	−	0.989937i	$-0.454805\pi$
$167$	14.5604	−	10.5788i	1.12672	−	0.818611i	0.985214	+	0.171326i	$0.0548053\pi$
$168$	−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	$0.00797969\pi$
$173$	2.70499	+	8.32510i	0.205657	+	0.632946i	−0.794029	+	0.607880i	$0.792020\pi$
$174$	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	0.218089	−	0.975929i	$-0.430018\pi$
$193$	−8.92841	−	6.48687i	−0.642681	−	0.466935i	−0.860770	+	0.508994i	$0.830018\pi$
$194$	−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	$-0.310783\pi$
$197$	15.7213			1.12009			0.560047	+	0.828461i	$0.310783\pi$
$198$	−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	$-0.987954\pi$
$223$	−3.18203	−	9.79327i	−0.213084	−	0.655806i	0.786200	−	0.617972i	$-0.212046\pi$
$224$	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	−0.850062	−	0.526682i	$-0.823436\pi$
$227$	2.21823	−	6.82700i	0.147229	−	0.453124i	0.997291	+	0.0735589i	$0.0234357\pi$
$228$	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	−0.0144113	−	0.999896i	$-0.504587\pi$
$233$	14.2278	−	10.3371i	0.932093	−	0.677205i	0.946504	+	0.322691i	$0.104587\pi$
$234$	−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	$0.368373\pi$
$257$	−7.39839	+	22.7699i	−0.461499	+	1.42035i	−0.863333	+	0.504635i	$0.831627\pi$
$258$	−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	$-0.809018\pi$
$263$	−26.7696			−1.65069			−0.825343	+	0.564631i	$0.809018\pi$
$264$	−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	−0.552173	−	0.833730i	$-0.686201\pi$
$277$	1.16704	−	0.847908i	0.0701209	−	0.0509458i	0.622293	+	0.782784i	$0.286201\pi$
$278$	−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	0.890794	−	0.454408i	$-0.150149\pi$
$283$	−1.63126	−	5.02049i	−0.0969680	−	0.298437i	−0.987762	+	0.155971i	$0.950149\pi$
$284$	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	$0.244325\pi$
$293$	−4.63398	+	14.2619i	−0.270720	+	0.833191i	−0.990320	+	0.138802i	$0.955675\pi$
$294$	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	$-0.480819\pi$
$307$	2.11034			0.120443			0.0602217	+	0.998185i	$0.480819\pi$
$308$	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	$0.00705535\pi$
$313$	23.5261	+	17.0927i	1.32977	+	0.966137i	0.330020	+	0.943974i	$0.392945\pi$
$314$	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	−0.0879217	−	0.996127i	$-0.528023\pi$
$317$	14.8184	−	10.7662i	0.832282	−	0.604689i	0.920204	+	0.391439i	$0.128023\pi$
$318$	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	$-0.774896\pi$
$337$	4.34521	−	13.3732i	0.236699	−	0.728484i	0.996892	−	0.0787861i	$-0.0251044\pi$
$338$	−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	0.997875	−	0.0651572i	$-0.0207549\pi$
$347$	23.1781	+	16.8399i	1.24427	+	0.904013i	0.246392	+	0.969170i	$0.420755\pi$
$348$	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	$-0.729164\pi$
$353$	−24.7757			−1.31868			−0.659339	+	0.751845i	$0.729164\pi$
$354$	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	$-0.770194\pi$
$367$	4.69553	−	14.4514i	0.245105	−	0.754355i	0.995619	−	0.0935010i	$-0.0298058\pi$
$368$	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	$-0.315289\pi$
$373$	21.1774			1.09653			0.548263	+	0.836306i	$0.315289\pi$
$374$	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	−0.628154	−	0.778089i	$-0.716189\pi$
$383$	−1.60983	+	1.16961i	−0.0822584	+	0.0597642i	0.545896	+	0.837853i	$0.316189\pi$
$384$	−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	$-0.842434\pi$
$397$	−35.0663			−1.75993			−0.879964	+	0.475040i	$0.842434\pi$
$398$	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	$-0.670737\pi$
$433$	8.48242	−	26.1062i	0.407639	−	1.25458i	0.918671	−	0.395023i	$-0.129263\pi$
$434$	−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	$0.0591724\pi$
$443$	6.23705	+	19.1957i	0.296331	+	0.912013i	−0.686440	+	0.727186i	$0.740828\pi$
$444$	−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	0.251503	−	0.967856i	$-0.419075\pi$
$457$	−12.6398	−	9.18334i	−0.591264	−	0.429579i	−0.842767	+	0.538278i	$0.819075\pi$
$458$	−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	$-0.509738\pi$
$463$	−1.31629			−0.0611730			−0.0305865	+	0.999532i	$0.509738\pi$
$464$	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	0.790766	−	0.612118i	$-0.209682\pi$
$467$	9.78870	+	7.11191i	0.452967	+	0.329100i	−0.337799	+	0.941218i	$0.609682\pi$
$468$	−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	$0.0850693\pi$
$487$	7.49051	+	23.0534i	0.339427	+	1.04465i	−0.625073	+	0.780566i	$0.714931\pi$
$488$	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	0.999974	−	0.00724562i	$-0.00230637\pi$
$503$	4.18767	+	12.8883i	0.186719	+	0.574662i	−0.813255	+	0.581908i	$0.802306\pi$
$504$	−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	0.629471	−	0.777024i	$-0.283272\pi$
$523$	1.94375	+	1.41222i	0.0849944	+	0.0617521i	−0.544477	+	0.838776i	$0.683272\pi$
$524$	−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	0.941279	−	0.337630i	$-0.109625\pi$
$547$	−0.437026	−	1.34503i	−0.0186859	−	0.0575093i	−0.959965	+	0.280121i	$0.909625\pi$
$548$	−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	−0.978283	−	0.207272i	$-0.933542\pi$
$557$	−1.53415	+	4.72163i	−0.0650041	+	0.200062i	0.913279	+	0.407334i	$0.133542\pi$
$558$	−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	−0.267603	−	0.963529i	$-0.586231\pi$
$563$	13.4316	−	9.75863i	0.566075	−	0.411277i	0.833677	+	0.552252i	$0.186231\pi$
$564$	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	0.575143	−	0.818053i	$-0.304946\pi$
$577$	−0.603937	−	0.438786i	−0.0251422	−	0.0182669i	−0.600285	+	0.799786i	$0.704946\pi$
$578$	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	$0.220440\pi$
$587$	−5.53146	+	17.0241i	−0.228308	+	0.702659i	−0.997939	+	0.0641701i	$0.979560\pi$
$588$	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	$-0.573855\pi$
$593$	−11.1992			−0.459895			−0.229948	+	0.973203i	$0.573855\pi$
$594$	−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	0.102593	−	0.994723i	$-0.467286\pi$
$607$	26.6166	−	19.3381i	1.08033	−	0.784908i	0.977741	+	0.209815i	$0.0672862\pi$
$608$	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	0.814168	−	0.580630i	$-0.197194\pi$
$613$	−4.60003	−	14.1574i	−0.185793	−	0.571813i	−0.999961	+	0.00881636i	$0.997194\pi$
$614$	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	$-0.772035\pi$
$617$	−37.4741			−1.50865			−0.754324	+	0.656502i	$0.772035\pi$
$618$	−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	0.862673	−	0.505762i	$-0.168789\pi$
$643$	16.4378	+	11.9428i	0.648245	+	0.470978i	−0.214428	+	0.976740i	$0.568789\pi$
$644$	−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	−0.881586	−	0.472023i	$-0.843524\pi$
$647$	−17.9348	+	13.0304i	−0.705092	+	0.512279i	0.176495	+	0.984302i	$0.443524\pi$
$648$	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	−0.853259	−	0.521487i	$-0.825378\pi$
$653$	3.66862	−	11.2908i	0.143564	−	0.441845i	0.996824	+	0.0796417i	$0.0253776\pi$
$654$	−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	−0.492233	−	0.870463i	$-0.663819\pi$
$673$	4.76086	−	3.45897i	0.183518	−	0.133333i	0.675751	+	0.737130i	$0.263819\pi$
$674$	−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	0.943618	−	0.331035i	$-0.107398\pi$
$677$	23.9475	+	17.3989i	0.920379	+	0.668694i	−0.0232393	+	0.999730i	$0.507398\pi$
$678$	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	$-0.580799\pi$
$683$	−13.1257			−0.502239			−0.251120	+	0.967956i	$0.580799\pi$
$684$	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	$-0.257289\pi$
$727$	37.2483			1.38146			0.690731	+	0.723112i	$0.257289\pi$
$728$	−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	−0.862577	−	0.505926i	$-0.831151\pi$
$733$	3.59105	−	11.0521i	0.132638	−	0.408219i	0.995215	+	0.0977073i	$0.0311509\pi$
$734$	−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	0.696387	−	0.717666i	$-0.254790\pi$
$743$	6.24321	+	4.53596i	0.229041	+	0.166408i	−0.467346	+	0.884075i	$0.654790\pi$
$744$	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	−0.490085	−	0.871675i	$-0.663034\pi$
$757$	5.15833	−	3.74775i	0.187483	−	0.136214i	0.677568	+	0.735461i	$0.263034\pi$
$758$	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	0.990345	−	0.138627i	$-0.0442688\pi$
$773$	2.99315	+	9.21198i	0.107656	+	0.331332i	−0.882688	+	0.469959i	$0.844269\pi$
$774$	−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	0.818675	−	0.574256i	$-0.194709\pi$
$787$	14.7424	+	10.7110i	0.525510	+	0.381805i	−0.293166	+	0.956062i	$0.594709\pi$
$788$	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	0.836380	−	0.548150i	$-0.184668\pi$
$797$	16.1910	+	11.7634i	0.573514	+	0.416682i	−0.262866	+	0.964832i	$0.584668\pi$
$798$	−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	0.156558	−	0.987669i	$-0.449960\pi$
$823$	32.8267	−	23.8500i	1.14427	−	0.831358i	0.987708	+	0.156311i	$0.0499602\pi$
$824$	−108.332			−3.77393
$825$		0			0
$826$	−11.5225			−0.400918
$827$	−12.5658	+	9.12955i	−0.436954	+	0.317466i	−0.784423	−	0.620226i	$-0.787041\pi$
$827$	−12.5658	+	9.12955i	−0.436954	+	0.317466i	0.347469	+	0.937691i	$0.387041\pi$
$828$	−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	0.459920	−	0.887961i	$-0.347878\pi$
$853$	−7.08127	−	5.14484i	−0.242458	−	0.176156i	−0.702378	+	0.711804i	$0.747878\pi$
$854$	−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	$-0.422990\pi$
$857$	14.0273			0.479163			0.239582	+	0.970876i	$0.422990\pi$
$858$	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	0.539047	−	0.842276i	$-0.318784\pi$
$863$	−2.80343	−	2.03681i	−0.0954298	−	0.0693338i	−0.634477	+	0.772942i	$0.718784\pi$
$864$	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	$0.00836456\pi$
$877$	6.11122	+	18.8084i	0.206361	+	0.635114i	−0.793294	+	0.608839i	$0.791635\pi$
$878$	−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	$0.313329\pi$
$883$	17.6885	+	54.4396i	0.595265	+	1.83204i	0.0418636	+	0.999123i	$0.486671\pi$
$884$	−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	$0.332388\pi$
$887$	−12.2757	+	37.7809i	−0.412179	+	1.26856i	−0.914750	+	0.404021i	$0.867612\pi$
$888$	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	0.169867	−	0.985467i	$-0.445666\pi$
$907$	−21.5295	−	15.6421i	−0.714875	−	0.519387i	−0.884743	+	0.466080i	$0.845666\pi$
$908$	−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	−0.699365	−	0.714764i	$-0.746534\pi$
$937$	−7.21488	+	5.24192i	−0.235700	+	0.171246i	0.463666	+	0.886010i	$0.346534\pi$
$938$	−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	$-0.491615\pi$
$947$	1.62118			0.0526814			0.0263407	+	0.999653i	$0.491615\pi$
$948$	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	$0.234630\pi$
$953$	−7.83110	+	24.1017i	−0.253674	+	0.780729i	−0.994088	+	0.108578i	$0.965370\pi$
$954$	−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	$-0.465612\pi$
$967$	6.70594			0.215648			0.107824	+	0.994170i	$0.465612\pi$
$968$	−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	−0.518014	−	0.855372i	$-0.673328\pi$
$977$	4.23279	−	3.07530i	0.135419	−	0.0983875i	0.653432	+	0.756985i	$0.273328\pi$
$978$	−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	−0.851327	−	0.524636i	$-0.824201\pi$
$983$	4.57075	−	14.0673i	0.145784	−	0.448678i	0.997111	+	0.0759580i	$0.0242015\pi$
$984$	−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	−0.997039	−	0.0768969i	$-0.975499\pi$
$997$	−4.58532	+	14.1122i	−0.145219	+	0.446937i	0.851820	+	0.523834i	$0.175499\pi$
$998$	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.c.201.4	yes	16
5.2	odd	4		275.2.z.c.124.8		32
5.3	odd	4		275.2.z.c.124.1		32
5.4	even	2		275.2.h.e.201.1	yes	16
11.2	odd	10		3025.2.a.bm.1.7		8
11.4	even	5	inner	275.2.h.c.26.4	✓	16
11.9	even	5		3025.2.a.bi.1.2		8
55.4	even	10		275.2.h.e.26.1	yes	16
55.9	even	10		3025.2.a.bn.1.7		8
55.24	odd	10		3025.2.a.bj.1.2		8
55.37	odd	20		275.2.z.c.224.1		32
55.48	odd	20		275.2.z.c.224.8		32

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

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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