LMFDB - Embedded newform 275.2.z.c.124.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [275,2,Mod(49,275)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(275, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("275.49"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 275 = 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	275.z (of order $10$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [32,0,0,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$2.19588605559$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			124.8
Character	$\chi$	$=$	275.124
Dual form			275.2.z.c.224.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.50618 + 2.07308i) q^{2} +(-1.70486 + 0.553942i) q^{3} +(-1.41105 + 4.34277i) q^{4} +(-3.71620 - 2.69998i) q^{6} +(-3.61485 - 1.17454i) q^{7} +(-6.25410 + 2.03208i) q^{8} +(0.172643 - 0.125433i) q^{9} +(3.19489 - 0.890336i) q^{11} -8.18545i q^{12} +(2.64361 + 3.63862i) q^{13} +(-3.00971 - 9.26295i) q^{14} +(-6.24414 - 4.53663i) q^{16} +(-2.94602 + 4.05485i) q^{17} +(0.520065 + 0.168979i) q^{18} +(1.06936 + 3.29116i) q^{19} +6.81344 q^{21} +(6.65782 + 5.28226i) q^{22} +0.105727i q^{23} +(9.53671 - 6.92883i) q^{24} +(-3.56139 + 10.9608i) q^{26} +(2.93613 - 4.04124i) q^{27} +(10.2015 - 14.0411i) q^{28} +(0.726214 - 2.23506i) q^{29} +(-3.83900 + 2.78920i) q^{31} -6.62570i q^{32} +(-4.95364 + 3.28768i) q^{33} -12.8433 q^{34} +(0.301117 + 0.926742i) q^{36} +(5.32675 + 1.73077i) q^{37} +(-5.21219 + 7.17396i) q^{38} +(-6.52257 - 4.73892i) q^{39} +(0.283345 + 0.872045i) q^{41} +(10.2623 + 14.1248i) q^{42} -4.46162i q^{43} +(-0.641627 + 15.1310i) q^{44} +(-0.219181 + 0.159244i) q^{46} +(1.19225 - 0.387384i) q^{47} +(13.1584 + 4.27543i) q^{48} +(6.02449 + 4.37704i) q^{49} +(2.77640 - 8.54487i) q^{51} +(-19.5319 + 6.34631i) q^{52} +(3.23200 + 4.44847i) q^{53} +12.8002 q^{54} +24.9944 q^{56} +(-3.64622 - 5.01860i) q^{57} +(5.72727 - 1.86090i) q^{58} +(0.365582 - 1.12515i) q^{59} +(5.92690 + 4.30614i) q^{61} +(-11.5645 - 3.75752i) q^{62} +(-0.771405 + 0.250645i) q^{63} +(1.24734 - 0.906248i) q^{64} +(-14.2767 - 5.31745i) q^{66} -7.84414i q^{67} +(-13.4523 - 18.5155i) q^{68} +(-0.0585667 - 0.180250i) q^{69} +(1.76384 + 1.28150i) q^{71} +(-0.824840 + 1.13529i) q^{72} +(8.51445 + 2.76651i) q^{73} +(4.43504 + 13.6496i) q^{74} -15.8017 q^{76} +(-12.5948 - 0.534080i) q^{77} -20.6595i q^{78} +(11.6357 - 8.45380i) q^{79} +(-2.96491 + 9.12506i) q^{81} +(-1.38105 + 1.90086i) q^{82} +(-2.76930 + 3.81162i) q^{83} +(-9.61410 + 29.5892i) q^{84} +(9.24930 - 6.72001i) q^{86} +4.21274i q^{87} +(-18.1719 + 12.0605i) q^{88} +0.172993 q^{89} +(-5.28256 - 16.2581i) q^{91} +(-0.459148 - 0.149186i) q^{92} +(4.99990 - 6.88177i) q^{93} +(2.59882 + 1.88815i) q^{94} +(3.67026 + 11.2959i) q^{96} +(-2.62178 - 3.60857i) q^{97} +19.0819i q^{98} +(0.439899 - 0.554454i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 4 q^{4} - 6 q^{6} - 16 q^{9} - 10 q^{11} - 6 q^{14} - 8 q^{16} + 26 q^{19} + 20 q^{21} + 86 q^{24} - 68 q^{26} + 22 q^{29} - 20 q^{31} - 40 q^{34} + 6 q^{36} - 6 q^{39} + 50 q^{41} + 2 q^{44} + 80 q^{46}+ \cdots + 20 q^{99}+O(q^{100}) $ 32 * q + 4 * q^4 - 6 * q^6 - 16 * q^9 - 10 * q^11 - 6 * q^14 - 8 * q^16 + 26 * q^19 + 20 * q^21 + 86 * q^24 - 68 * q^26 + 22 * q^29 - 20 * q^31 - 40 * q^34 + 6 * q^36 - 6 * q^39 + 50 * q^41 + 2 * q^44 + 80 * q^46 - 32 * q^49 + 70 * q^51 - 120 * q^54 - 40 * q^56 - 28 * q^59 + 32 * q^61 - 80 * q^64 - 110 * q^66 - 70 * q^69 - 92 * q^71 + 14 * q^74 - 124 * q^76 + 78 * q^79 - 86 * q^81 + 108 * q^84 + 4 * q^86 + 44 * q^89 - 68 * q^91 + 80 * q^94 + 216 * q^96 + 20 * 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 $

$2$	1.50618	+	2.07308i	1.06503	+	1.46589i	0.875006	+	0.484111i	$0.160857\pi$
$2$	1.50618	+	2.07308i	1.06503	+	1.46589i	0.190025	+	0.981779i	$0.439143\pi$
$3$	−1.70486	+	0.553942i	−0.984301	+	0.319819i	−0.756575	−	0.653906i	$-0.773129\pi$
$3$	−1.70486	+	0.553942i	−0.984301	+	0.319819i	−0.227726	+	0.973725i	$0.573129\pi$
$4$	−1.41105	+	4.34277i	−0.705525	+	2.17138i
$5$		0			0
$5$		0			0
$6$	−3.71620	−	2.69998i	−1.51713	−	1.10226i
$7$	−3.61485	−	1.17454i	−1.36628	−	0.443933i	−0.468148	−	0.883650i	$-0.655079\pi$
$7$	−3.61485	−	1.17454i	−1.36628	−	0.443933i	−0.898136	+	0.439717i	$0.855079\pi$
$8$	−6.25410	+	2.03208i	−2.21116	+	0.718449i
$9$	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
$12$		−	8.18545i		−	2.36294i
$13$	2.64361	+	3.63862i	0.733205	+	1.00917i	0.998981	+	0.0451354i	$0.0143719\pi$
$13$	2.64361	+	3.63862i	0.733205	+	1.00917i	−0.265776	+	0.964035i	$0.585628\pi$
$14$	−3.00971	−	9.26295i	−0.804380	−	2.47563i
$15$		0			0
$16$	−6.24414	−	4.53663i	−1.56103	−	1.13416i
$17$	−2.94602	+	4.05485i	−0.714515	+	0.983445i	0.285174	+	0.958476i	$0.407949\pi$
$17$	−2.94602	+	4.05485i	−0.714515	+	0.983445i	−0.999688	+	0.0249691i	$0.992051\pi$
$18$	0.520065	+	0.168979i	0.122580	+	0.0398288i
$19$	1.06936	+	3.29116i	0.245329	+	0.755044i	0.995582	+	0.0938935i	$0.0299313\pi$
$19$	1.06936	+	3.29116i	0.245329	+	0.755044i	−0.750254	+	0.661150i	$0.770069\pi$
$20$		0			0
$21$	6.81344			1.48681
$22$	6.65782	+	5.28226i	1.41945	+	1.12618i
$23$			0.105727i			0.0220456i	0.999939	+	0.0110228i	$0.00350874\pi$
$23$			0.105727i			0.0220456i	−0.999939	+	0.0110228i	$0.996491\pi$
$24$	9.53671	−	6.92883i	1.94667	−	1.41434i
$25$		0			0
$26$	−3.56139	+	10.9608i	−0.698446	+	2.14960i
$27$	2.93613	−	4.04124i	0.565059	−	0.777737i
$28$	10.2015	−	14.0411i	1.92790	−	2.65352i
$29$	0.726214	−	2.23506i	0.134855	−	0.415040i	−0.860713	−	0.509091i	$-0.829982\pi$
$29$	0.726214	−	2.23506i	0.134855	−	0.415040i	0.995567	+	0.0940512i	$0.0299817\pi$
$30$		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	$0.440126\pi$
$32$		−	6.62570i		−	1.17127i
$33$	−4.95364	+	3.28768i	−0.862318	+	0.572312i
$34$	−12.8433			−2.20260
$35$		0			0
$36$	0.301117	+	0.926742i	0.0501861	+	0.154457i
$37$	5.32675	+	1.73077i	0.875713	+	0.284536i	0.712176	−	0.702001i	$-0.247710\pi$
$37$	5.32675	+	1.73077i	0.875713	+	0.284536i	0.163537	+	0.986537i	$0.447710\pi$
$38$	−5.21219	+	7.17396i	−0.845528	+	1.16377i
$39$	−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	$0.877190\pi$
$42$	10.2623	+	14.1248i	1.58350	+	2.17951i
$43$		−	4.46162i		−	0.680390i	−0.940355	−	0.340195i	$-0.889507\pi$
$43$		−	4.46162i		−	0.680390i	0.940355	−	0.340195i	$-0.110493\pi$
$44$	−0.641627	+	15.1310i	−0.0967289	+	2.28108i
$45$		0			0
$46$	−0.219181	+	0.159244i	−0.0323165	+	0.0234793i
$47$	1.19225	−	0.387384i	0.173907	−	0.0565058i	−0.220769	−	0.975326i	$-0.570857\pi$
$47$	1.19225	−	0.387384i	0.173907	−	0.0565058i	0.394676	+	0.918820i	$0.370857\pi$
$48$	13.1584	+	4.27543i	1.89925	+	0.617105i
$49$	6.02449	+	4.37704i	0.860641	+	0.625292i
$50$		0			0
$51$	2.77640	−	8.54487i	0.388773	−	1.19652i
$52$	−19.5319	+	6.34631i	−2.70859	+	0.880074i
$53$	3.23200	+	4.44847i	0.443949	+	0.611044i	0.971084	−	0.238738i	$-0.0767337\pi$
$53$	3.23200	+	4.44847i	0.443949	+	0.611044i	−0.527135	+	0.849782i	$0.676734\pi$
$54$	12.8002			1.74188
$55$		0			0
$56$	24.9944			3.34002
$57$	−3.64622	−	5.01860i	−0.482954	−	0.664730i
$58$	5.72727	−	1.86090i	0.752027	−	0.244348i
$59$	0.365582	−	1.12515i	0.0475947	−	0.146481i	−0.924435	−	0.381340i	$-0.875463\pi$
$59$	0.365582	−	1.12515i	0.0475947	−	0.146481i	0.972030	+	0.234859i	$0.0754627\pi$
$60$		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	$0.544614\pi$
$62$	−11.5645	−	3.75752i	−1.46869	−	0.477206i
$63$	−0.771405	+	0.250645i	−0.0971879	+	0.0315783i
$64$	1.24734	−	0.906248i	0.155918	−	0.113281i
$65$		0			0
$66$	−14.2767	−	5.31745i	−1.75734	−	0.654533i
$67$		−	7.84414i		−	0.958315i	−0.877729	−	0.479157i	$-0.840942\pi$
$67$		−	7.84414i		−	0.958315i	0.877729	−	0.479157i	$-0.159058\pi$
$68$	−13.4523	−	18.5155i	−1.63133	−	2.24533i
$69$	−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	$0.658704\pi$
$72$	−0.824840	+	1.13529i	−0.0972083	+	0.133796i
$73$	8.51445	+	2.76651i	0.996541	+	0.323796i	0.761483	−	0.648185i	$-0.224472\pi$
$73$	8.51445	+	2.76651i	0.996541	+	0.323796i	0.235059	+	0.971981i	$0.424472\pi$
$74$	4.43504	+	13.6496i	0.515563	+	1.58674i
$75$		0			0
$76$	−15.8017			−1.81257
$77$	−12.5948	−	0.534080i	−1.43531	−	0.0608640i
$78$		−	20.6595i		−	2.33923i
$79$	11.6357	−	8.45380i	1.30911	−	0.951127i	0.309114	−	0.951025i	$-0.399967\pi$
$79$	11.6357	−	8.45380i	1.30911	−	0.951127i	1.00000		0.000102366i	$-3.25841e-5\pi$
$80$		0			0
$81$	−2.96491	+	9.12506i	−0.329435	+	1.01390i
$82$	−1.38105	+	1.90086i	−0.152512	+	0.209914i
$83$	−2.76930	+	3.81162i	−0.303971	+	0.418380i	−0.933489	−	0.358606i	$-0.883252\pi$
$83$	−2.76930	+	3.81162i	−0.303971	+	0.418380i	0.629518	+	0.776986i	$0.283252\pi$
$84$	−9.61410	+	29.5892i	−1.04898	+	3.22844i
$85$		0			0
$86$	9.24930	−	6.72001i	0.997378	−	0.724637i
$87$			4.21274i			0.451653i
$88$	−18.1719	+	12.0605i	−1.93713	+	1.28566i
$89$	0.172993			0.0183372			0.00916862	−	0.999958i	$-0.497081\pi$
$89$	0.172993			0.0183372			0.00916862	+	0.999958i	$0.497081\pi$
$90$		0			0
$91$	−5.28256	−	16.2581i	−0.553763	−	1.70431i
$92$	−0.459148	−	0.149186i	−0.0478695	−	0.0155537i
$93$	4.99990	−	6.88177i	0.518465	−	0.713606i
$94$	2.59882	+	1.88815i	0.268048	+	0.194748i
$95$		0			0
$96$	3.67026	+	11.2959i	0.374594	+	1.15288i
$97$	−2.62178	−	3.60857i	−0.266201	−	0.366394i	0.654902	−	0.755714i	$-0.272710\pi$
$97$	−2.62178	−	3.60857i	−0.266201	−	0.366394i	−0.921103	+	0.389320i	$0.872710\pi$
$98$			19.0819i			1.92756i
$99$	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	$0.444339\pi$
$102$	21.8960	−	7.11444i	2.16803	−	0.704434i
$103$	−15.6677	−	5.09074i	−1.54378	−	0.501605i	−0.591366	−	0.806403i	$-0.701411\pi$
$103$	−15.6677	−	5.09074i	−1.54378	−	0.501605i	−0.952417	+	0.304798i	$0.901411\pi$
$104$	−23.9274	−	17.3843i	−2.34627	−	1.70467i
$105$		0			0
$106$	−4.35406	+	13.4004i	−0.422903	+	1.30156i
$107$	16.3319	−	5.30657i	1.57887	−	0.513005i	0.617103	−	0.786882i	$-0.288306\pi$
$107$	16.3319	−	5.30657i	1.57887	−	0.513005i	0.961765	+	0.273877i	$0.0883061\pi$
$108$	13.4071	+	18.4533i	1.29010	+	1.77567i
$109$	−17.9060			−1.71508			−0.857542	−	0.514414i	$-0.828009\pi$
$109$	−17.9060			−1.71508			−0.857542	+	0.514414i	$0.828009\pi$
$110$		0			0
$111$	−10.0401			−0.952965
$112$	17.2432	+	23.7332i	1.62933	+	2.24258i
$113$	13.6155	−	4.42393i	1.28083	−	0.416168i	0.411960	−	0.911202i	$-0.364844\pi$
$113$	13.6155	−	4.42393i	1.28083	−	0.416168i	0.868874	+	0.495034i	$0.164844\pi$
$114$	4.91209	−	15.1178i	0.460059	−	1.41592i
$115$		0			0
$116$	8.68161	+	6.30756i	0.806067	+	0.585642i
$117$	0.912803	+	0.296588i	0.0843886	+	0.0274195i
$118$	2.88315	−	0.936793i	0.265416	−	0.0862388i
$119$	15.4120	−	11.1975i	1.41281	−	1.02647i
$120$		0			0
$121$	9.41460	−	5.68904i	0.855873	−	0.517186i
$122$			18.7728i			1.69961i
$123$	−0.966125	−	1.32976i	−0.0871126	−	0.119900i
$124$	−6.69581	−	20.6076i	−0.601301	−	1.85061i
$125$		0			0
$126$	−1.68148	−	1.22167i	−0.149798	−	0.108835i
$127$	3.27396	−	4.50622i	0.290517	−	0.399863i	−0.638665	−	0.769485i	$-0.720513\pi$
$127$	3.27396	−	4.50622i	0.290517	−	0.399863i	0.929182	+	0.369622i	$0.120513\pi$
$128$	−8.84538	−	2.87404i	−0.781828	−	0.254031i
$129$	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	$0.706610\pi$
$132$	−7.28780	−	26.1516i	−0.634321	−	2.27620i
$133$		−	13.1530i		−	1.14051i
$134$	16.2616	−	11.8147i	1.40478	−	1.02064i
$135$		0			0
$136$	10.1849	−	31.3460i	0.873351	−	2.68790i
$137$	5.84522	−	8.04525i	0.499390	−	0.687352i	−0.482695	−	0.875789i	$-0.660342\pi$
$137$	5.84522	−	8.04525i	0.499390	−	0.687352i	0.982085	+	0.188437i	$0.0603420\pi$
$138$	0.285461	−	0.392903i	0.0243000	−	0.0334461i
$139$	−0.627493	+	1.93122i	−0.0532232	+	0.163804i	−0.974135	−	0.225967i	$-0.927446\pi$
$139$	−0.627493	+	1.93122i	−0.0532232	+	0.163804i	0.920912	+	0.389771i	$0.127446\pi$
$140$		0			0
$141$	−1.81802	+	1.32087i	−0.153105	+	0.111237i
$142$			5.58676i			0.468830i
$143$	11.6856	+	9.27126i	0.977201	+	0.775302i
$144$	−1.64705			−0.137254
$145$		0			0
$146$	7.08911	+	21.8180i	0.586699	+	1.80567i
$147$	−12.6955	−	4.12503i	−1.04711	−	0.340227i
$148$	−15.0326	+	20.6907i	−1.23568	+	1.70076i
$149$	8.59185	+	6.24234i	0.703872	+	0.511393i	0.881191	−	0.472761i	$-0.156742\pi$
$149$	8.59185	+	6.24234i	0.703872	+	0.511393i	−0.177319	+	0.984153i	$0.556742\pi$
$150$		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	$0.944629\pi$
$152$	−13.3758	−	18.4102i	−1.08492	−	1.49327i
$153$			1.06957i			0.0864696i
$154$	−17.8628	−	26.9144i	−1.43943	−	2.16883i
$155$		0			0
$156$	29.7837	−	21.6391i	2.38460	−	1.73252i
$157$	−0.283971	+	0.0922677i	−0.0226633	+	0.00736377i	−0.320327	−	0.947307i	$-0.603793\pi$
$157$	−0.283971	+	0.0922677i	−0.0226633	+	0.00736377i	0.297663	+	0.954671i	$0.403793\pi$
$158$	35.0509	+	11.3887i	2.78850	+	0.906038i
$159$	−7.97430	−	5.79367i	−0.632403	−	0.459468i
$160$		0			0
$161$	0.124180	−	0.382187i	0.00978677	−	0.0301206i
$162$	−23.3827	+	7.59750i	−1.83712	+	0.596916i
$163$	−8.38166	−	11.5364i	−0.656502	−	0.903597i	0.342857	−	0.939387i	$-0.388605\pi$
$163$	−8.38166	−	11.5364i	−0.656502	−	0.903597i	−0.999359	+	0.0357901i	$0.988605\pi$
$164$	−4.18690			−0.326942
$165$		0			0
$166$	−12.0729			−0.937037
$167$	10.5788	+	14.5604i	0.818611	+	1.12672i	0.989937	+	0.141507i	$0.0451947\pi$
$167$	10.5788	+	14.5604i	0.818611	+	1.12672i	−0.171326	+	0.985214i	$0.554805\pi$
$168$	−42.6119	+	13.8455i	−3.28758	+	1.06820i
$169$	−2.23363	+	6.87441i	−0.171818	+	0.528801i
$170$		0			0
$171$	0.597437	+	0.434064i	0.0456872	+	0.0331937i
$172$	19.3758	+	6.29557i	1.47739	+	0.480033i
$173$	8.32510	−	2.70499i	0.632946	−	0.205657i	0.0250663	−	0.999686i	$-0.492020\pi$
$173$	8.32510	−	2.70499i	0.632946	−	0.205657i	0.607880	+	0.794029i	$0.292020\pi$
$174$	−8.73335	+	6.34515i	−0.662074	+	0.481025i
$175$		0			0
$176$	−23.9884	−	8.93465i	−1.80820	−	0.673474i
$177$			2.12073i			0.159404i
$178$	0.260559	+	0.358629i	0.0195297	+	0.0268804i
$179$	7.07647	+	21.7791i	0.528920	+	1.62785i	0.756431	+	0.654073i	$0.226941\pi$
$179$	7.07647	+	21.7791i	0.528920	+	1.62785i	−0.227511	+	0.973776i	$0.573059\pi$
$180$		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	$0.921834\pi$
$182$	25.7478	−	35.4388i	1.90855	−	2.62690i
$183$	−12.4899	−	4.05821i	−0.923279	−	0.299991i
$184$	−0.214846	−	0.661228i	−0.0158387	−	0.0487464i
$185$		0			0
$186$	21.7972			1.59825
$187$	−5.80202	+	15.5777i	−0.424286	+	1.13916i
$188$			5.72427i			0.417485i
$189$	−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	$0.871186\pi$
$192$	−1.62454	+	2.23598i	−0.117241	+	0.161368i
$193$	−6.48687	+	8.92841i	−0.466935	+	0.642681i	−0.975929	−	0.218089i	$-0.930018\pi$
$193$	−6.48687	+	8.92841i	−0.466935	+	0.642681i	0.508994	+	0.860770i	$0.330018\pi$
$194$	3.53198	−	10.8703i	0.253581	−	0.780443i
$195$		0			0
$196$	−27.5093	+	19.9867i	−1.96495	+	1.42762i
$197$			15.7213i			1.12009i	0.828461	+	0.560047i	$0.189217\pi$
$197$			15.7213i			1.12009i	−0.828461	+	0.560047i	$0.810783\pi$
$198$	1.81200	+	0.0768375i	0.128773	+	0.00546060i
$199$	−4.44523			−0.315114			−0.157557	−	0.987510i	$-0.550362\pi$
$199$	−4.44523			−0.315114			−0.157557	+	0.987510i	$0.550362\pi$
$200$		0			0
$201$	4.34521	+	13.3732i	0.306487	+	0.943270i
$202$	−21.4587	−	6.97236i	−1.50983	−	0.490573i
$203$	−5.25031	+	7.22643i	−0.368499	+	0.507196i
$204$	33.1908	+	24.1145i	2.32382	+	1.68835i
$205$		0			0
$206$	−13.0449	−	40.1480i	−0.908879	−	2.79724i
$207$	0.0132616	+	0.0182531i	0.000921747	+	0.00126868i
$208$		−	34.7131i		−	2.40692i
$209$	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	$0.325360\pi$
$212$	−23.8792	+	7.75881i	−1.64003	+	0.532877i
$213$	−3.71698	−	1.20772i	−0.254683	−	0.0827515i
$214$	35.5998	+	25.8648i	2.43355	+	1.76808i
$215$		0			0
$216$	−10.1508	+	31.2408i	−0.690671	+	2.12567i
$217$	17.1534	−	5.57348i	1.16445	−	0.378353i
$218$	−26.9697	−	37.1206i	−1.82662	−	2.51413i
$219$	−16.0484			−1.08445
$220$		0			0
$221$	−22.5422			−1.51635
$222$	−15.1222	−	20.8140i	−1.01494	−	1.39694i
$223$	−9.79327	+	3.18203i	−0.655806	+	0.213084i	−0.617972	−	0.786200i	$-0.712046\pi$
$223$	−9.79327	+	3.18203i	−0.655806	+	0.213084i	−0.0378334	+	0.999284i	$0.512046\pi$
$224$	−7.78212	+	23.9509i	−0.519965	+	1.60029i
$225$		0			0
$226$	29.6785	+	21.5627i	1.97419	+	1.43433i
$227$	6.82700	+	2.21823i	0.453124	+	0.147229i	0.526682	−	0.850062i	$-0.323436\pi$
$227$	6.82700	+	2.21823i	0.453124	+	0.147229i	−0.0735589	+	0.997291i	$0.523436\pi$
$228$	26.9396	−	8.75321i	1.78412	−	0.579696i
$229$	1.66606	−	1.21047i	0.110097	−	0.0799899i	−0.531375	−	0.847137i	$-0.678324\pi$
$229$	1.66606	−	1.21047i	0.110097	−	0.0799899i	0.641471	+	0.767147i	$0.278324\pi$
$230$		0			0
$231$	21.7682	−	6.06625i	1.43224	−	0.399130i
$232$			15.4540i			1.01461i
$233$	−10.3371	−	14.2278i	−0.677205	−	0.932093i	0.322691	−	0.946504i	$-0.395413\pi$
$233$	−10.3371	−	14.2278i	−0.677205	−	0.932093i	−0.999896	+	0.0144113i	$0.995413\pi$
$234$	0.759997	+	2.33903i	0.0496826	+	0.152907i
$235$		0			0
$236$	4.37039	+	3.17527i	0.284488	+	0.206693i
$237$	−15.1543	+	20.8580i	−0.984374	+	1.35488i
$238$	46.4265	+	15.0849i	3.00938	+	0.977808i
$239$	−5.77519	−	17.7742i	−0.373566	−	1.14972i	−0.944441	−	0.328680i	$-0.893396\pi$
$239$	−5.77519	−	17.7742i	−0.373566	−	1.14972i	0.570875	−	0.821037i	$-0.306604\pi$
$240$		0			0
$241$	30.1916			1.94481			0.972406	−	0.233296i	$-0.0749510\pi$
$241$	30.1916			1.94481			0.972406	+	0.233296i	$0.0749510\pi$
$242$	25.9740	+	10.9485i	1.66967	+	0.703797i
$243$		−	2.21359i		−	0.142002i
$244$	−27.0637	+	19.6629i	−1.73258	+	1.25879i
$245$		0			0
$246$	1.30154	−	4.00571i	0.0829829	−	0.255395i
$247$	−9.14828	+	12.5915i	−0.582091	+	0.801180i
$248$	18.3416	−	25.2451i	1.16469	−	1.60306i
$249$	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	$0.00209449\pi$
$252$		−	3.70370i		−	0.233311i
$253$	0.0941326	+	0.337786i	0.00591806	+	0.0212364i
$254$	14.2730			0.895565
$255$		0			0
$256$	−8.31752	−	25.5987i	−0.519845	−	1.59992i
$257$	−22.7699	−	7.39839i	−1.42035	−	0.461499i	−0.504635	−	0.863333i	$-0.668373\pi$
$257$	−22.7699	−	7.39839i	−1.42035	−	0.461499i	−0.915713	+	0.401834i	$0.868373\pi$
$258$	−12.0463	+	16.5803i	−0.749967	+	1.03224i
$259$	−17.2226	−	12.5129i	−1.07016	−	0.777515i
$260$		0			0
$261$	−0.154973	−	0.476959i	−0.00959260	−	0.0295230i
$262$	−20.8406	−	28.6846i	−1.28753	−	1.77214i
$263$			26.7696i			1.65069i	0.564631	+	0.825343i	$0.309018\pi$
$263$			26.7696i			1.65069i	−0.564631	+	0.825343i	$0.690982\pi$
$264$	24.2997	−	30.6277i	1.49555	−	1.88500i
$265$		0			0
$266$	27.2673	−	19.8109i	1.67187	−	1.21468i
$267$	−0.294929	+	0.0958283i	−0.0180494	+	0.00586459i
$268$	34.0653	+	11.0685i	2.08087	+	0.676115i
$269$	−4.82647	−	3.50664i	−0.294275	−	0.213803i	0.430845	−	0.902426i	$-0.358216\pi$
$269$	−4.82647	−	3.50664i	−0.294275	−	0.213803i	−0.725120	+	0.688623i	$0.758216\pi$
$270$		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	$0.173089\pi$
$272$	36.7907	−	11.9540i	2.23076	−	0.724819i
$273$	18.0121	+	24.7915i	1.09014	+	1.50045i
$274$	25.4824			1.53945
$275$		0			0
$276$	0.865424			0.0520924
$277$	0.847908	+	1.16704i	0.0509458	+	0.0701209i	0.833730	−	0.552173i	$-0.186201\pi$
$277$	0.847908	+	1.16704i	0.0509458	+	0.0701209i	−0.782784	+	0.622293i	$0.786201\pi$
$278$	−4.94871	+	1.60793i	−0.296804	+	0.0964373i
$279$	−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	$0.697728\pi$
$282$	−5.47655	−	1.77944i	−0.326124	−	0.105964i
$283$	−5.02049	+	1.63126i	−0.298437	+	0.0969680i	−0.454408	−	0.890794i	$-0.650149\pi$
$283$	−5.02049	+	1.63126i	−0.298437	+	0.0969680i	0.155971	+	0.987762i	$0.450149\pi$
$284$	−8.05414	+	5.85167i	−0.477925	+	0.347233i
$285$		0			0
$286$	−1.61942	+	38.1895i	−0.0957583	+	2.25819i
$287$		−	3.48511i		−	0.205720i
$288$	−0.831079	−	1.14388i	−0.0489718	−	0.0674039i
$289$	−2.50947	−	7.72336i	−0.147616	−	0.454315i
$290$		0			0
$291$	6.46870	+	4.69979i	0.379202	+	0.275506i
$292$	−24.0287	+	33.0726i	−1.40617	+	1.93543i
$293$	14.2619	+	4.63398i	0.833191	+	0.270720i	0.694389	−	0.719600i	$-0.255675\pi$
$293$	14.2619	+	4.63398i	0.833191	+	0.270720i	0.138802	+	0.990320i	$0.455675\pi$
$294$	−10.5703	−	32.5319i	−0.616470	−	1.89730i
$295$		0			0
$296$	−36.8311			−2.14077
$297$	5.78255	−	15.5255i	0.335538	−	0.900878i
$298$			27.2137i			1.57645i
$299$	−0.384700	+	0.279501i	−0.0222478	+	0.0161640i
$300$		0			0
$301$	−5.24033	+	16.1281i	−0.302048	+	0.929607i
$302$	5.17296	−	7.11996i	0.297670	−	0.409708i
$303$	9.27768	−	12.7696i	0.532989	−	0.733596i
$304$	8.25353	−	25.4018i	0.473372	−	1.45689i
$305$		0			0
$306$	−2.21731	+	1.61097i	−0.126755	+	0.0920929i
$307$			2.11034i			0.120443i	0.998185	+	0.0602217i	$0.0191808\pi$
$307$			2.11034i			0.120443i	−0.998185	+	0.0602217i	$0.980819\pi$
$308$	20.0912	−	53.9425i	1.14480	−	3.07366i
$309$	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	$-0.256606\pi$
$312$	50.4227	+	16.3833i	2.85462	+	0.927523i
$313$	17.0927	−	23.5261i	0.966137	−	1.32977i	0.0221632	−	0.999754i	$-0.492945\pi$
$313$	17.0927	−	23.5261i	0.966137	−	1.32977i	0.943974	−	0.330020i	$-0.107055\pi$
$314$	−0.618991	−	0.449723i	−0.0349317	−	0.0253793i
$315$		0			0
$316$	20.2944	+	62.4597i	1.14165	+	3.51363i
$317$	10.7662	+	14.8184i	0.604689	+	0.832282i	0.996127	−	0.0879217i	$-0.0280225\pi$
$317$	10.7662	+	14.8184i	0.604689	+	0.832282i	−0.391439	+	0.920204i	$0.628023\pi$
$318$		−	25.2577i		−	1.41638i
$319$	0.330221	−	7.78733i	0.0184888	−	0.436007i
$320$		0			0
$321$	−24.9041	+	18.0939i	−1.39001	+	1.00990i
$322$	0.979344	−	0.318208i	0.0545767	−	0.0177330i
$323$	−16.4955	−	5.35972i	−0.917835	−	0.298223i
$324$	−35.4444	−	25.7518i	−1.96913	−	1.43066i
$325$		0			0
$326$	11.2915	−	34.7517i	0.625379	−	1.92472i
$327$	30.5272	−	9.91890i	1.68816	−	0.548516i
$328$	−3.54413	−	4.87808i	−0.195692	−	0.269347i
$329$	−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	$0.298133\pi$
$332$	−12.6454	−	17.4048i	−0.694004	−	0.955214i
$333$	1.13672	−	0.369344i	0.0622921	−	0.0202399i
$334$	−14.2514	+	43.8614i	−0.779803	+	2.39999i
$335$		0			0
$336$	−42.5440	−	30.9101i	−2.32097	−	1.68628i
$337$	13.3732	+	4.34521i	0.728484	+	0.236699i	0.649697	−	0.760193i	$-0.274896\pi$
$337$	13.3732	+	4.34521i	0.728484	+	0.236699i	0.0787861	+	0.996892i	$0.474896\pi$
$338$	−17.6155	+	5.72362i	−0.958156	+	0.311324i
$339$	−20.7618	+	15.0844i	−1.12763	+	0.819270i
$340$		0			0
$341$	−9.78185	+	12.3292i	−0.529717	+	0.667662i
$342$			1.89232i			0.102325i
$343$	−0.997912	−	1.37351i	−0.0538822	−	0.0741625i
$344$	9.06637	+	27.9034i	0.488826	+	1.50445i
$345$		0			0
$346$	18.1468	+	13.1844i	0.975578	+	0.708799i
$347$	−16.8399	+	23.1781i	−0.904013	+	1.24427i	0.0651572	+	0.997875i	$0.479245\pi$
$347$	−16.8399	+	23.1781i	−0.904013	+	1.24427i	−0.969170	+	0.246392i	$0.920755\pi$
$348$	−18.2949	−	5.94439i	−0.980712	−	0.318653i
$349$	5.53826	+	17.0450i	0.296456	+	0.912399i	0.982728	+	0.185054i	$0.0592459\pi$
$349$	5.53826	+	17.0450i	0.296456	+	0.912399i	−0.686272	+	0.727345i	$0.740754\pi$
$350$		0			0
$351$	22.4665			1.19917
$352$	−5.89910	−	21.1684i	−0.314423	−	1.12828i
$353$			24.7757i			1.31868i	0.751845	+	0.659339i	$0.229164\pi$
$353$			24.7757i			1.31868i	−0.751845	+	0.659339i	$0.770836\pi$
$354$	−4.39644	+	3.19420i	−0.233668	+	0.169770i
$355$		0			0
$356$	−0.244102	+	0.751269i	−0.0129374	+	0.0398172i
$357$	−20.0725	+	27.6274i	−1.06235	+	1.46220i
$358$	−34.4915	+	47.4735i	−1.82293	+	2.50905i
$359$	3.22994	−	9.94073i	0.170470	−	0.524652i	−0.828928	−	0.559355i	$-0.811049\pi$
$359$	3.22994	−	9.94073i	0.170470	−	0.524652i	0.999398	+	0.0347037i	$0.0110487\pi$
$360$		0			0
$361$	5.68314	−	4.12904i	0.299112	−	0.217318i
$362$		−	44.2551i		−	2.32600i
$363$	−12.8992	+	14.9142i	−0.677031	+	0.782791i
$364$	78.0589			4.09140
$365$		0			0
$366$	−10.3990	−	32.0050i	−0.543567	−	1.67293i
$367$	14.4514	+	4.69553i	0.754355	+	0.245105i	0.660854	−	0.750514i	$-0.270194\pi$
$367$	14.4514	+	4.69553i	0.754355	+	0.245105i	0.0935010	+	0.995619i	$0.470194\pi$
$368$	0.479645	−	0.660174i	0.0250032	−	0.0344140i
$369$	0.158300	+	0.115012i	0.00824079	+	0.00598729i
$370$		0			0
$371$	−6.45831	−	19.8766i	−0.335299	−	1.03194i
$372$	22.8308	+	31.4239i	1.18372	+	1.62925i
$373$		−	21.1774i		−	1.09653i	−0.836306	−	0.548263i	$-0.815289\pi$
$373$		−	21.1774i		−	1.09653i	0.836306	−	0.548263i	$-0.184711\pi$
$374$	−41.0328	+	11.4348i	−2.12176	+	0.591281i
$375$		0			0
$376$	−6.66924	+	4.84548i	−0.343940	+	0.249887i
$377$	10.0523	−	3.26620i	0.517722	−	0.168218i
$378$	−46.2707	−	15.0343i	−2.37991	−	0.773279i
$379$	−28.4486	−	20.6691i	−1.46131	−	1.06170i	−0.983020	−	0.183498i	$-0.941258\pi$
$379$	−28.4486	−	20.6691i	−1.46131	−	1.06170i	−0.478287	−	0.878204i	$-0.658742\pi$
$380$		0			0
$381$	−3.08546	+	9.49606i	−0.158073	+	0.486498i
$382$	−44.3584	+	14.4129i	−2.26958	+	0.737430i
$383$	1.16961	+	1.60983i	0.0597642	+	0.0822584i	0.837853	−	0.545896i	$-0.183811\pi$
$383$	1.16961	+	1.60983i	0.0597642	+	0.0822584i	−0.778089	+	0.628154i	$0.783811\pi$
$384$	16.6722			0.850799
$385$		0			0
$386$	−28.2797			−1.43940
$387$	−0.559633	−	0.770268i	−0.0284477	−	0.0391549i
$388$	19.3706	−	6.29390i	0.983394	−	0.319524i
$389$	1.87218	−	5.76197i	0.0949231	−	0.292143i	−0.892311	−	0.451422i	$-0.850917\pi$
$389$	1.87218	−	5.76197i	0.0949231	−	0.292143i	0.987234	+	0.159279i	$0.0509169\pi$
$390$		0			0
$391$	−0.428707	−	0.311474i	−0.0216807	−	0.0157519i
$392$	−46.5723	−	15.1322i	−2.35226	−	0.764294i
$393$	23.5896	−	7.66473i	1.18994	−	0.386634i
$394$	−32.5915	+	23.6791i	−1.64194	+	1.19294i
$395$		0			0
$396$	1.78714	+	2.69274i	0.0898074	+	0.135315i
$397$		−	35.0663i		−	1.75993i	−0.475040	−	0.879964i	$-0.657566\pi$
$397$		−	35.0663i		−	1.75993i	0.475040	−	0.879964i	$-0.342434\pi$
$398$	−6.69533	−	9.21534i	−0.335607	−	0.461923i
$399$	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	$0.834944\pi$
$402$	−21.1790	+	29.1504i	−1.05631	+	1.45389i
$403$	−20.2976	−	6.59510i	−1.01110	−	0.328525i
$404$	−12.4246	−	38.2389i	−0.618145	−	1.90245i
$405$		0			0
$406$	−22.8889			−1.13596
$407$	18.5593	+	0.787007i	0.919952	+	0.0390105i
$408$			59.0824i			2.92501i
$409$	3.48714	−	2.53356i	0.172428	−	0.125276i	−0.498224	−	0.867048i	$-0.666014\pi$
$409$	3.48714	−	2.53356i	0.172428	−	0.125276i	0.670652	+	0.741772i	$0.266014\pi$
$410$		0			0
$411$	−5.50867	+	16.9539i	−0.271722	+	0.836276i
$412$	44.2158	−	60.8578i	2.17836	−	2.99825i
$413$	−2.64305	+	3.63784i	−0.130056	+	0.179007i
$414$	−0.0178657	+	0.0549849i	−0.000878050	+	0.00270236i
$415$		0			0
$416$	24.1084	−	17.5158i	1.18201	−	0.858781i
$417$		−	3.64006i		−	0.178255i
$418$	−10.2651	+	27.5606i	−0.502083	+	1.34803i
$419$	18.7114			0.914110			0.457055	−	0.889438i	$-0.348904\pi$
$419$	18.7114			0.914110			0.457055	+	0.889438i	$0.348904\pi$
$420$		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	$-0.366802\pi$
$422$	−5.63477	−	1.83085i	−0.274297	−	0.0891244i
$423$	0.157243	−	0.216426i	0.00764540	−	0.0105230i
$424$	−29.2529	−	21.2535i	−1.42065	−	1.03216i
$425$		0			0
$426$	−3.09474	−	9.52464i	−0.149941	−	0.461470i
$427$	−16.3671	−	22.5274i	−0.792061	−	1.09018i
$428$			78.4136i			3.79027i
$429$	−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	$0.364166\pi$
$432$	−36.6673	+	11.9139i	−1.76415	+	0.573208i
$433$	−26.1062	−	8.48242i	−1.25458	−	0.407639i	−0.395023	−	0.918671i	$-0.629263\pi$
$433$	−26.1062	−	8.48242i	−1.25458	−	0.407639i	−0.859561	+	0.511032i	$0.829263\pi$
$434$	37.3905	+	27.1658i	1.79480	+	1.30400i
$435$		0			0
$436$	25.2663	−	77.7616i	1.21004	−	3.72411i
$437$	−0.347964	+	0.113061i	−0.0166454	+	0.00540842i
$438$	−24.1719	−	33.2697i	−1.15498	−	1.58969i
$439$	23.1527			1.10502			0.552510	−	0.833506i	$-0.313670\pi$
$439$	23.1527			1.10502			0.552510	+	0.833506i	$0.313670\pi$
$440$		0			0
$441$	1.58911			0.0756720
$442$	−33.9526	−	46.7317i	−1.61496	−	2.22280i
$443$	19.1957	−	6.23705i	0.912013	−	0.296331i	0.184827	−	0.982771i	$-0.440828\pi$
$443$	19.1957	−	6.23705i	0.912013	−	0.296331i	0.727186	+	0.686440i	$0.240828\pi$
$444$	14.1671	−	43.6019i	0.672341	−	2.06925i
$445$		0			0
$446$	−21.3471	−	15.5095i	−1.01081	−	0.734398i
$447$	−18.1058	−	5.88293i	−0.856375	−	0.278253i
$448$	−5.57338	+	1.81090i	−0.263317	+	0.0855570i
$449$	11.3539	−	8.24906i	0.535822	−	0.389297i	−0.286709	−	0.958018i	$-0.592561\pi$
$449$	11.3539	−	8.24906i	0.535822	−	0.389297i	0.822531	+	0.568720i	$0.192561\pi$
$450$		0			0
$451$	1.68167	+	2.53381i	0.0791866	+	0.119313i
$452$			65.3711i			3.07480i
$453$	3.61878	+	4.98082i	0.170025	+	0.234019i
$454$	5.68414	+	17.4940i	0.266770	+	0.821033i
$455$		0			0
$456$	33.0021	+	23.9774i	1.54546	+	1.12285i
$457$	9.18334	−	12.6398i	0.429579	−	0.591264i	−0.538278	−	0.842767i	$-0.680925\pi$
$457$	9.18334	−	12.6398i	0.429579	−	0.591264i	0.967856	+	0.251503i	$0.0809249\pi$
$458$	5.01879	+	1.63071i	0.234513	+	0.0761979i
$459$	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	$0.257832\pi$
$462$	45.3626	+	35.9903i	2.11046	+	1.67442i
$463$			1.31629i			0.0611730i	0.999532	+	0.0305865i	$0.00973751\pi$
$463$			1.31629i			0.0611730i	−0.999532	+	0.0305865i	$0.990262\pi$
$464$	−14.6742	+	10.6614i	−0.681233	+	0.494945i
$465$		0			0
$466$	13.9258	−	42.8593i	0.645101	−	1.98542i
$467$	−7.11191	+	9.78870i	−0.329100	+	0.452967i	−0.941218	−	0.337799i	$-0.890318\pi$
$467$	−7.11191	+	9.78870i	−0.329100	+	0.452967i	0.612118	+	0.790766i	$0.290318\pi$
$468$	−2.57602	+	3.54559i	−0.119077	+	0.163895i
$469$	−9.21323	+	28.3554i	−0.425427	+	1.30933i
$470$		0			0
$471$	0.433019	−	0.314607i	0.0199525	−	0.0144963i
$472$			7.77967i			0.358088i
$473$	−3.97234	−	14.2544i	−0.182648	−	0.655416i
$474$	−66.0655			−3.03449
$475$		0			0
$476$	26.8809	+	82.7308i	1.23208	+	3.79196i
$477$	1.11597	+	0.362599i	0.0510966	+	0.0166023i
$478$	28.1489	−	38.7436i	1.28750	−	1.77209i
$479$	2.47074	+	1.79509i	0.112891	+	0.0820200i	0.642798	−	0.766036i	$-0.277773\pi$
$479$	2.47074	+	1.79509i	0.112891	+	0.0820200i	−0.529907	+	0.848055i	$0.677773\pi$
$480$		0			0
$481$	7.78426	+	23.9575i	0.354932	+	1.09237i
$482$	45.4741	+	62.5897i	2.07129	+	2.85088i
$483$			0.720365i			0.0327777i
$484$	11.4217	+	48.9130i	0.519168	+	2.22332i
$485$		0			0
$486$	4.58896	−	3.33408i	0.208160	−	0.151237i
$487$	−23.0534	+	7.49051i	−1.04465	+	0.339427i	−0.780566	−	0.625073i	$-0.785069\pi$
$487$	−23.0534	+	7.49051i	−1.04465	+	0.339427i	−0.264083	+	0.964500i	$0.585069\pi$
$488$	−45.8179	−	14.8871i	−2.07408	−	0.673909i
$489$	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	$0.836051\pi$
$492$	7.13808	−	2.31930i	0.321809	−	0.104562i
$493$	6.92337	+	9.52921i	0.311813	+	0.429174i
$494$	−39.8823			−1.79439
$495$		0			0
$496$	36.6248			1.64450
$497$	−4.87084	−	6.70413i	−0.218487	−	0.300721i
$498$	20.5826	−	6.68768i	0.922327	−	0.299682i
$499$	9.27234	−	28.5373i	0.415087	−	1.27751i	−0.497086	−	0.867701i	$-0.665597\pi$
$499$	9.27234	−	28.5373i	0.415087	−	1.27751i	0.912173	−	0.409805i	$-0.134403\pi$
$500$		0			0
$501$	−26.1010	−	18.9635i	−1.16611	−	0.847226i
$502$	62.1726	+	20.2011i	2.77490	+	0.901619i
$503$	12.8883	−	4.18767i	0.574662	−	0.186719i	−0.00724562	−	0.999974i	$-0.502306\pi$
$503$	12.8883	−	4.18767i	0.574662	−	0.186719i	0.581908	+	0.813255i	$0.302306\pi$
$504$	4.31512	−	3.13512i	0.192211	−	0.139649i
$505$		0			0
$506$	−0.558477	+	0.703912i	−0.0248273	+	0.0312927i
$507$		−	12.9572i		−	0.575450i
$508$	14.9497	+	20.5766i	0.663288	+	0.912937i
$509$	−11.7687	−	36.2203i	−0.521638	−	1.60544i	−0.770870	−	0.636993i	$-0.780178\pi$
$509$	−11.7687	−	36.2203i	−0.521638	−	1.60544i	0.249232	−	0.968444i	$-0.419822\pi$
$510$		0			0
$511$	−27.5291	−	20.0011i	−1.21782	−	0.884795i
$512$	29.6070	−	40.7506i	1.30846	−	1.80094i
$513$	16.4402	+	5.34173i	0.725851	+	0.235843i
$514$	−18.9582	−	58.3472i	−0.836209	−	2.57359i
$515$		0			0
$516$	−36.5203			−1.60772
$517$	3.46419	−	2.29915i	0.152355	−	0.101116i
$518$		−	54.5505i		−	2.39681i
$519$	−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	$0.0845932\pi$
$522$	0.755356	−	1.03966i	0.0330610	−	0.0455046i
$523$	1.41222	−	1.94375i	0.0617521	−	0.0849944i	−0.777024	−	0.629471i	$-0.783272\pi$
$523$	1.41222	−	1.94375i	0.0617521	−	0.0849944i	0.838776	+	0.544477i	$0.183272\pi$
$524$	19.5243	−	60.0895i	0.852921	−	2.62502i
$525$		0			0
$526$	−55.4957	+	40.3200i	−2.41973	+	1.75803i
$527$		−	23.7836i		−	1.03603i
$528$	45.8462	+	1.94410i	1.99520	+	0.0846063i
$529$	22.9888			0.999514
$530$		0			0
$531$	−0.0780148	−	0.240105i	−0.00338555	−	0.0104197i
$532$	57.1206	+	18.5596i	2.47649	+	0.804661i
$533$	−2.42398	+	3.33633i	−0.104994	+	0.144512i
$534$	−0.642877	−	0.467077i	−0.0278200	−	0.0202124i
$535$		0			0
$536$	15.9399	+	49.0581i	0.688501	+	2.11899i
$537$	−24.1288	−	33.2104i	−1.04123	−	1.43314i
$538$		−	15.2873i		−	0.659083i
$539$	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	$0.131349\pi$
$542$	−18.2624	+	5.93382i	−0.784438	+	0.254879i
$543$	29.4437	+	9.56685i	1.26355	+	0.410553i
$544$	26.8662	+	19.5194i	1.15188	+	0.836889i
$545$		0			0
$546$	−24.2653	+	74.6810i	−1.03846	+	3.19605i
$547$	1.34503	−	0.437026i	0.0575093	−	0.0186859i	−0.280121	−	0.959965i	$-0.590375\pi$
$547$	1.34503	−	0.437026i	0.0575093	−	0.0186859i	0.337630	+	0.941279i	$0.390375\pi$
$548$	26.6907	+	36.7367i	1.14017	+	1.56931i
$549$	1.56337			0.0667230
$550$		0			0
$551$	8.13251			0.346457
$552$	0.732565	+	1.00829i	0.0311800	+	0.0429156i
$553$	−51.9905	+	16.8927i	−2.21086	+	0.718352i
$554$	−1.14228	+	3.51556i	−0.0485307	+	0.149362i
$555$		0			0
$556$	−7.50143	−	5.45011i	−0.318132	−	0.231136i
$557$	−4.72163	−	1.53415i	−0.200062	−	0.0650041i	0.207272	−	0.978283i	$-0.433542\pi$
$557$	−4.72163	−	1.53415i	−0.200062	−	0.0650041i	−0.407334	+	0.913279i	$0.633542\pi$
$558$	−2.46784	+	0.801851i	−0.104472	+	0.0339451i
$559$	16.2341	−	11.7948i	0.686630	−	0.498866i
$560$		0			0
$561$	1.26247	−	29.7718i	0.0533016	−	1.25697i
$562$			0.613129i			0.0258633i
$563$	−9.75863	−	13.4316i	−0.411277	−	0.566075i	0.552252	−	0.833677i	$-0.313769\pi$
$563$	−9.75863	−	13.4316i	−0.411277	−	0.566075i	−0.963529	+	0.267603i	$0.913769\pi$
$564$	−3.17091	−	9.75907i	−0.133520	−	0.410931i
$565$		0			0
$566$	−10.9435	−	7.95091i	−0.459989	−	0.334202i
$567$	21.4354	−	29.5033i	0.900203	−	1.23902i
$568$	−13.6353	−	4.43039i	−0.572126	−	0.185895i
$569$	8.37027	+	25.7610i	0.350900	+	1.07996i	0.958349	+	0.285600i	$0.0921929\pi$
$569$	8.37027	+	25.7610i	0.350900	+	1.07996i	−0.607449	+	0.794359i	$0.707807\pi$
$570$		0			0
$571$	−25.9648			−1.08659			−0.543296	−	0.839541i	$-0.682824\pi$
$571$	−25.9648			−1.08659			−0.543296	+	0.839541i	$0.682824\pi$
$572$	−56.7519	+	37.6657i	−2.37292	+	1.57488i
$573$		−	32.6282i		−	1.36306i
$574$	7.22492	−	5.24921i	0.301562	−	0.219098i
$575$		0			0
$576$	0.101672	−	0.312915i	0.00423635	−	0.0130381i
$577$	0.438786	−	0.603937i	0.0182669	−	0.0251422i	−0.799786	−	0.600285i	$-0.795054\pi$
$577$	0.438786	−	0.603937i	0.0182669	−	0.0251422i	0.818053	+	0.575143i	$0.195054\pi$
$578$	12.2314	−	16.8351i	0.508761	−	0.700249i
$579$	6.11338	−	18.8150i	0.254063	−	0.781926i
$580$		0			0
$581$	14.4875	−	10.5258i	0.601043	−	0.436683i
$582$			20.4889i			0.849291i
$583$	14.2865	+	11.3348i	0.591687	+	0.469439i
$584$	−58.8721			−2.43614
$585$		0			0
$586$	11.8744	+	36.5458i	0.490529	+	1.50969i
$587$	−17.0241	−	5.53146i	−0.702659	−	0.228308i	−0.0641701	−	0.997939i	$-0.520440\pi$
$587$	−17.0241	−	5.53146i	−0.702659	−	0.228308i	−0.638488	+	0.769631i	$0.720440\pi$
$588$	35.8281	−	49.3131i	1.47753	−	2.03364i
$589$	−13.2850	−	9.65209i	−0.547397	−	0.397708i
$590$		0			0
$591$	−8.70868	−	26.8026i	−0.358227	−	1.10251i
$592$	−25.4091	−	34.9727i	−1.04431	−	1.43737i
$593$			11.1992i			0.459895i	0.973203	+	0.229948i	$0.0738555\pi$
$593$			11.1992i			0.459895i	−0.973203	+	0.229948i	$0.926145\pi$
$594$	40.8951	−	11.3965i	1.67795	−	0.467602i
$595$		0			0
$596$	−39.2326	+	28.5041i	−1.60703	+	1.16758i
$597$	7.57850	−	2.46240i	0.310167	−	0.100780i
$598$	−1.15886	−	0.376535i	−0.0473892	−	0.0153977i
$599$	−1.46910	−	1.06736i	−0.0600257	−	0.0436112i	0.557368	−	0.830266i	$-0.311811\pi$
$599$	−1.46910	−	1.06736i	−0.0600257	−	0.0436112i	−0.617393	+	0.786654i	$0.711811\pi$
$600$		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	$-0.303889\pi$
$602$	−41.3277	+	13.4282i	−1.68439	+	0.547292i
$603$	−0.983912	−	1.35424i	−0.0400680	−	0.0551489i
$604$	15.6827			0.638121
$605$		0			0
$606$	40.4464			1.64302
$607$	19.3381	+	26.6166i	0.784908	+	1.08033i	0.994723	+	0.102593i	$0.0327138\pi$
$607$	19.3381	+	26.6166i	0.784908	+	1.08033i	−0.209815	+	0.977741i	$0.567286\pi$
$608$	21.8062	−	7.08527i	0.884359	−	0.287346i
$609$	4.94801	−	15.2284i	0.200504	−	0.617087i
$610$		0			0
$611$	4.56137	+	3.31403i	0.184533	+	0.134071i
$612$	−4.64489	−	1.50922i	−0.187759	−	0.0610065i
$613$	−14.1574	+	4.60003i	−0.571813	+	0.185793i	−0.580630	−	0.814168i	$-0.697194\pi$
$613$	−14.1574	+	4.60003i	−0.571813	+	0.185793i	0.00881636	+	0.999961i	$0.497194\pi$
$614$	−4.37490	+	3.17855i	−0.176557	+	0.128276i
$615$		0			0
$616$	79.8543	−	22.2534i	3.21742	−	0.896615i
$617$		−	37.4741i		−	1.50865i	−0.656502	−	0.754324i	$-0.727965\pi$
$617$		−	37.4741i		−	1.50865i	0.656502	−	0.754324i	$-0.272035\pi$
$618$	44.4793	+	61.2206i	1.78922	+	2.46265i
$619$	3.82934	+	11.7855i	0.153914	+	0.473700i	0.998049	−	0.0624311i	$-0.0198854\pi$
$619$	3.82934	+	11.7855i	0.153914	+	0.473700i	−0.844135	+	0.536131i	$0.819885\pi$
$620$		0			0
$621$	0.427269	+	0.310429i	0.0171457	+	0.0124571i
$622$	25.0948	−	34.5400i	1.00621	−	1.38493i
$623$	−0.625344	−	0.203187i	−0.0250539	−	0.00814050i
$624$	19.2291	+	59.1810i	0.769778	+	2.36913i
$625$		0			0
$626$	74.5163			2.97827
$627$	−16.1175	−	12.7875i	−0.643671	−	0.510683i
$628$		−	1.36341i		−	0.0544061i
$629$	−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	$0.0902236\pi$
$632$	−55.5918	+	76.5156i	−2.21132	+	3.04363i
$633$	2.43620	−	3.35314i	0.0968301	−	0.133275i
$634$	−14.5039	+	44.6383i	−0.576022	+	1.77281i
$635$		0			0
$636$	36.4127	−	26.4554i	1.44386	−	1.04902i
$637$			33.4920i			1.32700i
$638$	16.6411	−	11.0446i	0.658829	−	0.437258i
$639$	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	$0.688549\pi$
$642$	−75.0203	−	24.3756i	−2.96082	−	0.962027i
$643$	11.9428	−	16.4378i	0.470978	−	0.648245i	−0.505762	−	0.862673i	$-0.668789\pi$
$643$	11.9428	−	16.4378i	0.470978	−	0.648245i	0.976740	+	0.214428i	$0.0687886\pi$
$644$	1.48453	+	1.07857i	0.0584985	+	0.0425017i
$645$		0			0
$646$	−13.7341	−	42.2693i	−0.540361	−	1.66306i
$647$	−13.0304	−	17.9348i	−0.512279	−	0.705092i	0.472023	−	0.881586i	$-0.343524\pi$
$647$	−13.0304	−	17.9348i	−0.512279	−	0.705092i	−0.984302	+	0.176495i	$0.943524\pi$
$648$		−	63.0940i		−	2.47857i
$649$	0.166236	−	3.92020i	0.00652533	−	0.153881i
$650$		0			0
$651$	−26.1568	+	19.0040i	−1.02516	+	0.744826i
$652$	61.9267	−	20.1212i	2.42524	−	0.788007i
$653$	−11.2908	−	3.66862i	−0.441845	−	0.143564i	0.0796417	−	0.996824i	$-0.474622\pi$
$653$	−11.2908	−	3.66862i	−0.441845	−	0.143564i	−0.521487	+	0.853259i	$0.674622\pi$
$654$	66.5423	+	48.3458i	2.60201	+	1.89047i
$655$		0			0
$656$	2.18690	−	6.73060i	0.0853843	−	0.262786i
$657$	1.81697	−	0.590371i	0.0708869	−	0.0230326i
$658$	−7.17664	−	9.87780i	−0.279774	−	0.385077i
$659$	−13.3368			−0.519527			−0.259764	−	0.965672i	$-0.583645\pi$
$659$	−13.3368			−0.519527			−0.259764	+	0.965672i	$0.583645\pi$
$660$		0			0
$661$	−44.8817			−1.74570			−0.872848	−	0.487992i	$-0.837730\pi$
$661$	−44.8817			−1.74570			−0.872848	+	0.487992i	$0.837730\pi$
$662$	32.4732	+	44.6955i	1.26211	+	1.73714i
$663$	38.4312	−	12.4871i	1.49254	−	0.484957i
$664$	9.57400	−	29.4657i	0.371543	−	1.14349i
$665$		0			0
$666$	2.47779	+	1.80022i	0.0960125	+	0.0697572i
$667$	0.236306	+	0.0767805i	0.00914980	+	0.00297295i
$668$	−78.1598	+	25.3957i	−3.02409	+	0.982588i
$669$	14.9335	−	10.8498i	0.577362	−	0.419478i
$670$		0			0
$671$	22.7697	+	8.48071i	0.879014	+	0.327394i
$672$		−	45.1438i		−	1.74146i
$673$	−3.45897	−	4.76086i	−0.133333	−	0.183518i	0.737130	−	0.675751i	$-0.236181\pi$
$673$	−3.45897	−	4.76086i	−0.133333	−	0.183518i	−0.870463	+	0.492233i	$0.836181\pi$
$674$	11.1345	+	34.2684i	0.428884	+	1.31997i
$675$		0			0
$676$	−26.7022	−	19.4003i	−1.02701	−	0.746165i
$677$	−17.3989	+	23.9475i	−0.668694	+	0.920379i	−0.999730	−	0.0232393i	$-0.992602\pi$
$677$	−17.3989	+	23.9475i	−0.668694	+	0.920379i	0.331035	+	0.943618i	$0.392602\pi$
$678$	−62.5422	−	20.3212i	−2.40192	−	0.780431i
$679$	5.23894	+	16.1238i	0.201052	+	0.618774i
$680$		0			0
$681$	−12.8678			−0.493097
$682$	−40.2926	−	1.70860i	−1.54288	−	0.0654258i
$683$			13.1257i			0.502239i	0.967956	+	0.251120i	$0.0807988\pi$
$683$			13.1257i			0.502239i	−0.967956	+	0.251120i	$0.919201\pi$
$684$	−2.72805	+	1.98204i	−0.104310	+	0.0757854i
$685$		0			0
$686$	1.34436	−	4.13751i	0.0513278	−	0.157971i
$687$	−2.16988	+	2.98658i	−0.0827860	+	0.113945i
$688$	−20.2407	+	27.8590i	−0.771670	+	1.06211i
$689$	−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	$0.257231\pi$
$692$			39.9709i			1.51946i
$693$	−2.24139	+	1.48759i	−0.0851435	+	0.0565089i
$694$	−73.4141			−2.78676
$695$		0			0
$696$	−8.56063	−	26.3469i	−0.324490	−	0.998677i
$697$	−4.37075	−	1.42014i	−0.165554	−	0.0537917i
$698$	−26.9941	+	37.1542i	−1.02174	+	1.40631i
$699$	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	$0.583847\pi$
$702$	33.8387	+	46.5749i	1.27716	+	1.75786i
$703$			19.3820i			0.731006i
$704$	3.17826	−	4.00591i	0.119785	−	0.150979i
$705$		0			0
$706$	−51.3621	+	37.3168i	−1.93304	+	1.40443i
$707$	31.8294	−	10.3420i	1.19707	−	0.388951i
$708$	−9.20982	−	2.99245i	−0.346126	−	0.112463i
$709$	−15.7889	−	11.4713i	−0.592963	−	0.430813i	0.250411	−	0.968140i	$-0.419434\pi$
$709$	−15.7889	−	11.4713i	−0.592963	−	0.430813i	−0.843374	+	0.537327i	$0.819434\pi$
$710$		0			0
$711$	0.948436	−	2.91899i	0.0355691	−	0.109471i
$712$	−1.08192	+	0.351536i	−0.0405466	+	0.0131744i
$713$	−0.294893	−	0.405886i	−0.0110438	−	0.0152006i
$714$	−87.5068			−3.27486
$715$		0			0
$716$	−104.567			−3.90785
$717$	19.6918	+	27.1034i	0.735402	+	1.01219i
$718$	25.4728	−	8.27662i	0.950638	−	0.308881i
$719$	−14.6482	+	45.0824i	−0.546284	+	1.68129i	0.171634	+	0.985161i	$0.445095\pi$
$719$	−14.6482	+	45.0824i	−0.546284	+	1.68129i	−0.717918	+	0.696128i	$0.754905\pi$
$720$		0			0
$721$	50.6571	+	36.8045i	1.88657	+	1.37067i
$722$	17.1197	+	5.56252i	0.637128	+	0.207016i
$723$	−51.4724	+	16.7244i	−1.91428	+	0.621987i
$724$	63.8002	−	46.3536i	2.37112	−	1.72272i
$725$		0			0
$726$	−50.3468	−	4.27760i	−1.86855	−	0.158756i
$727$			37.2483i			1.38146i	0.723112	+	0.690731i	$0.242711\pi$
$727$			37.2483i			1.38146i	−0.723112	+	0.690731i	$0.757289\pi$
$728$	66.0754	+	90.9450i	2.44892	+	3.37065i
$729$	−7.66853	−	23.6013i	−0.284020	−	0.874123i
$730$		0			0
$731$	18.0912	+	13.1440i	0.669126	+	0.486149i
$732$	35.2477	−	48.5143i	1.30279	−	1.79314i
$733$	−11.0521	−	3.59105i	−0.408219	−	0.132638i	0.0977073	−	0.995215i	$-0.468849\pi$
$733$	−11.0521	−	3.59105i	−0.408219	−	0.132638i	−0.505926	+	0.862577i	$0.668849\pi$
$734$	12.0322	+	37.0312i	0.444115	+	1.36685i
$735$		0			0
$736$	0.700516			0.0258214
$737$	−6.98392	−	25.0612i	−0.257256	−	0.923140i
$738$			0.501399i			0.0184568i
$739$	30.7265	−	22.3241i	1.13029	−	0.821207i	0.144556	−	0.989497i	$-0.453824\pi$
$739$	30.7265	−	22.3241i	1.13029	−	0.821207i	0.985738	+	0.168290i	$0.0538245\pi$
$740$		0			0
$741$	8.62156	−	26.5344i	0.316721	−	0.974766i
$742$	31.4785	−	43.3265i	1.15561	−	1.59056i
$743$	4.53596	−	6.24321i	0.166408	−	0.229041i	−0.717666	−	0.696387i	$-0.754790\pi$
$743$	4.53596	−	6.24321i	0.166408	−	0.229041i	0.884075	+	0.467346i	$0.154790\pi$
$744$	−17.2856	+	53.1995i	−0.633720	+	1.95039i
$745$		0			0
$746$	43.9025	−	31.8971i	1.60739	−	1.16783i
$747$			1.00541i			0.0367861i
$748$	−59.4635	−	47.1778i	−2.17420	−	1.72499i
$749$	−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	$0.805534\pi$
$752$	−9.20197	−	2.98990i	−0.335561	−	0.109030i
$753$	−26.8803	+	36.9976i	−0.979574	+	1.34827i
$754$	21.9118	+	15.9198i	0.797979	+	0.579766i
$755$		0			0
$756$	−26.7907	−	82.4532i	−0.974367	−	2.99879i
$757$	3.74775	+	5.15833i	0.136214	+	0.187483i	0.871675	−	0.490085i	$-0.163034\pi$
$757$	3.74775	+	5.15833i	0.136214	+	0.187483i	−0.735461	+	0.677568i	$0.763034\pi$
$758$		−	90.1078i		−	3.27286i
$759$	−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	$0.207161\pi$
$762$	−24.3334	+	7.90640i	−0.881506	+	0.286419i
$763$	64.7275	+	21.0312i	2.34329	+	0.761382i
$764$	−67.2402	−	48.8529i	−2.43267	−	1.76743i
$765$		0			0
$766$	−1.57566	+	4.84939i	−0.0569310	+	0.175216i
$767$	5.06043	−	1.64423i	0.182721	−	0.0593698i
$768$	28.3604	+	39.0348i	1.02337	+	1.40855i
$769$	51.7503			1.86616			0.933082	−	0.359663i	$-0.117108\pi$
$769$	51.7503			1.86616			0.933082	+	0.359663i	$0.117108\pi$
$770$		0			0
$771$	42.9178			1.54565
$772$	−29.6207	−	40.7694i	−1.06607	−	1.46732i
$773$	9.21198	−	2.99315i	0.331332	−	0.107656i	−0.138627	−	0.990345i	$-0.544269\pi$
$773$	9.21198	−	2.99315i	0.331332	−	0.107656i	0.469959	+	0.882688i	$0.344269\pi$
$774$	0.753921	−	2.32033i	0.0270991	−	0.0834025i
$775$		0			0
$776$	23.7298	+	17.2407i	0.851849	+	0.618905i
$777$	36.2935	+	11.7925i	1.30202	+	0.423053i
$778$	14.7649	−	4.79740i	0.529346	−	0.171995i
$779$	−2.56704	+	1.86506i	−0.0919737	+	0.0668228i
$780$		0			0
$781$	6.77623	+	2.52385i	0.242473	+	0.0903105i
$782$		−	1.35788i		−	0.0485578i
$783$	−6.90014	−	9.49723i	−0.246591	−	0.339403i
$784$	−17.7607	−	54.6617i	−0.634310	−	1.95221i
$785$		0			0
$786$	51.4199	+	37.3587i	1.83409	+	1.33254i
$787$	−10.7110	+	14.7424i	−0.381805	+	0.525510i	−0.956062	−	0.293166i	$-0.905291\pi$
$787$	−10.7110	+	14.7424i	−0.381805	+	0.525510i	0.574256	+	0.818675i	$0.305291\pi$
$788$	−68.2739	−	22.1835i	−2.43216	−	0.790255i
$789$	−14.8288	−	45.6385i	−0.527921	−	1.62477i
$790$		0			0
$791$	−54.4139			−1.93473
$792$	−1.62448	+	4.36152i	−0.0577233	+	0.154980i
$793$			32.9495i			1.17007i
$794$	72.6954	−	52.8163i	2.57986	−	1.87438i
$795$		0			0
$796$	6.27245	−	19.3046i	0.222321	−	0.684234i
$797$	−11.7634	+	16.1910i	−0.416682	+	0.573514i	−0.964832	−	0.262866i	$-0.915332\pi$
$797$	−11.7634	+	16.1910i	−0.416682	+	0.573514i	0.548150	+	0.836380i	$0.315332\pi$
$798$	−35.5129	+	48.8793i	−1.25714	+	1.73031i
$799$	−1.94160	+	5.97562i	−0.0686887	+	0.211402i
$800$		0			0
$801$	0.0298661	−	0.0216990i	0.00105527	−	0.000766696i
$802$		−	42.2160i		−	1.49070i
$803$	29.6658	+	1.25798i	1.04688	+	0.0443930i
$804$	−64.2079			−2.26444
$805$		0			0
$806$	−16.8997	−	52.0121i	−0.595268	−	1.83205i
$807$	10.1709	+	3.30474i	0.358034	+	0.116332i
$808$	34.0342	−	46.8441i	1.19732	−	1.64797i
$809$	−25.7317	−	18.6952i	−0.904679	−	0.657288i	0.0349842	−	0.999388i	$-0.488862\pi$
$809$	−25.7317	−	18.6952i	−0.904679	−	0.657288i	−0.939664	+	0.342100i	$0.888862\pi$
$810$		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	$0.879560\pi$
$812$	−23.9742	−	32.9977i	−0.841331	−	1.15799i
$813$		−	13.4331i		−	0.471119i
$814$	26.3222	+	39.6604i	0.922593	+	1.39010i
$815$		0			0
$816$	−56.1012	+	40.7599i	−1.96393	+	1.42688i
$817$	14.6839	−	4.77108i	0.513724	−	0.166919i
$818$	10.5045	+	3.41313i	0.367283	+	0.119337i
$819$	−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	$0.0227705\pi$
$822$	−43.4440	+	14.1158i	−1.51528	+	0.492345i
$823$	−23.8500	−	32.8267i	−0.831358	−	1.14427i	−0.987669	−	0.156558i	$-0.949960\pi$
$823$	−23.8500	−	32.8267i	−0.831358	−	1.14427i	0.156311	−	0.987708i	$-0.450040\pi$
$824$	108.332			3.77393
$825$		0			0
$826$	−11.5225			−0.400918
$827$	−9.12955	−	12.5658i	−0.317466	−	0.436954i	0.620226	−	0.784423i	$-0.287041\pi$
$827$	−9.12955	−	12.5658i	−0.317466	−	0.436954i	−0.937691	+	0.347469i	$0.887041\pi$
$828$	−0.0979817	+	0.0318362i	−0.00340510	+	0.00110638i
$829$	9.00201	−	27.7053i	0.312653	−	0.962247i	−0.664057	−	0.747682i	$-0.731167\pi$
$829$	9.00201	−	27.7053i	0.312653	−	0.962247i	0.976710	−	0.214565i	$-0.0688332\pi$
$830$		0			0
$831$	−2.09204	−	1.51996i	−0.0725720	−	0.0527267i
$832$	6.59497	+	2.14284i	0.228640	+	0.0742895i
$833$	−35.4965	+	11.5335i	−1.22988	+	0.399612i
$834$	7.54615	−	5.48260i	0.261302	−	0.189847i
$835$		0			0
$836$	−50.4845	+	14.0688i	−1.74604	+	0.486579i
$837$			23.7038i			0.819322i
$838$	28.1827	+	38.7902i	0.973557	+	1.33999i
$839$	−6.73139	−	20.7171i	−0.232393	−	0.715233i	−0.997456	−	0.0712779i	$-0.977292\pi$
$839$	−6.73139	−	20.7171i	−0.232393	−	0.715233i	0.765063	−	0.643955i	$-0.222708\pi$
$840$		0			0
$841$	18.9934	+	13.7995i	0.654945	+	0.475845i
$842$	45.9503	−	63.2451i	1.58355	−	2.17957i
$843$	−0.407927	−	0.132543i	−0.0140497	−	0.00456504i
$844$	−3.26253	−	10.0410i	−0.112301	−	0.345626i
$845$		0			0
$846$	0.685505			0.0235681
$847$	−40.7144	+	9.50725i	−1.39896	+	0.326673i
$848$		−	42.4392i		−	1.45737i
$849$	7.65560	−	5.56212i	0.262740	−	0.190892i
$850$		0			0
$851$	−0.182989	+	0.563182i	−0.00627278	+	0.0193056i
$852$	10.4897	−	14.4378i	0.359371	−	0.494631i
$853$	−5.14484	+	7.08127i	−0.176156	+	0.242458i	−0.887961	−	0.459920i	$-0.847878\pi$
$853$	−5.14484	+	7.08127i	−0.176156	+	0.242458i	0.711804	+	0.702378i	$0.247878\pi$
$854$	22.0493	−	67.8608i	0.754512	−	2.32215i
$855$		0			0
$856$	−91.3583	+	66.3757i	−3.12256	+	2.26867i
$857$			14.0273i			0.479163i	0.970876	+	0.239582i	$0.0770103\pi$
$857$			14.0273i			0.479163i	−0.970876	+	0.239582i	$0.922990\pi$
$858$	−18.3939	−	66.0047i	−0.627957	−	2.25336i
$859$	−31.8774			−1.08764			−0.543822	−	0.839201i	$-0.683023\pi$
$859$	−31.8774			−1.08764			−0.543822	+	0.839201i	$0.683023\pi$
$860$		0			0
$861$	1.93055	+	5.94162i	0.0657930	+	0.202490i
$862$	−20.2602	−	6.58294i	−0.690065	−	0.224216i
$863$	−2.03681	+	2.80343i	−0.0693338	+	0.0954298i	−0.842276	−	0.539047i	$-0.818784\pi$
$863$	−2.03681	+	2.80343i	−0.0693338	+	0.0954298i	0.772942	+	0.634477i	$0.218784\pi$
$864$	−26.7761	−	19.4539i	−0.910940	−	0.661836i
$865$		0			0
$866$	−21.7360	−	66.8964i	−0.738618	−	2.27323i
$867$	8.55659	+	11.7771i	0.290597	+	0.399973i
$868$			82.3577i			2.79540i
$869$	29.6479	−	37.3686i	1.00574	−	1.26764i
$870$		0			0
$871$	28.5418	−	20.7368i	0.967103	−	0.702641i
$872$	111.986	−	36.3865i	3.79233	−	1.23220i
$873$	−0.905265	−	0.294138i	−0.0306386	−	0.00995507i
$874$	−0.758482	−	0.551069i	−0.0256560	−	0.0186402i
$875$		0			0
$876$	22.6452	−	69.6946i	0.765109	−	2.35476i
$877$	−18.8084	+	6.11122i	−0.635114	+	0.206361i	−0.608839	−	0.793294i	$-0.708365\pi$
$877$	−18.8084	+	6.11122i	−0.635114	+	0.206361i	−0.0262750	+	0.999655i	$0.508365\pi$
$878$	34.8723	+	47.9975i	1.17688	+	1.61984i
$879$	−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	$0.0860025\pi$
$882$	2.39349	+	3.29436i	0.0805931	+	0.110927i
$883$	54.4396	−	17.6885i	1.83204	−	0.595265i	0.832915	−	0.553402i	$-0.186671\pi$
$883$	54.4396	−	17.6885i	1.83204	−	0.595265i	0.999123	−	0.0418636i	$-0.0133295\pi$
$884$	31.8081	−	97.8953i	1.06982	−	3.29258i
$885$		0			0
$886$	41.8421	+	30.4000i	1.40571	+	1.02131i
$887$	−37.7809	−	12.2757i	−1.26856	−	0.412179i	−0.404021	−	0.914750i	$-0.632388\pi$
$887$	−37.7809	−	12.2757i	−1.26856	−	0.412179i	−0.864536	+	0.502571i	$0.832388\pi$
$888$	62.7919	−	20.4023i	2.10716	−	0.684657i
$889$	−17.1276	+	12.4439i	−0.574441	+	0.417356i
$890$		0			0
$891$	−1.34819	+	31.7933i	−0.0451661	+	1.06512i
$892$		−	47.0199i		−	1.57434i
$893$	2.54989	+	3.50962i	0.0853287	+	0.117445i
$894$	−15.0748	−	46.3956i	−0.504178	−	1.55170i
$895$		0			0
$896$	28.5990	+	20.7784i	0.955427	+	0.694158i
$897$	0.501032	−	0.689612i	0.0167290	−	0.0230255i
$898$	34.2020	+	11.1129i	1.14133	+	0.370842i
$899$	3.44608	+	10.6059i	0.114933	+	0.353728i
$900$		0			0
$901$	−27.5594			−0.918136
$902$	−2.71991	+	7.30262i	−0.0905630	+	0.243151i
$903$		−	30.3989i		−	1.01161i
$904$	−76.1627	+	55.3354i	−2.53313	+	1.84043i
$905$		0			0
$906$	−4.87511	+	15.0041i	−0.161965	+	0.498476i
$907$	15.6421	−	21.5295i	0.519387	−	0.714875i	−0.466080	−	0.884743i	$-0.654334\pi$
$907$	15.6421	−	21.5295i	0.519387	−	0.714875i	0.985467	+	0.169867i	$0.0543339\pi$
$908$	−19.2665	+	26.5180i	−0.639380	+	0.880032i
$909$	−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	$0.341180\pi$
$912$			47.8784i			1.58541i
$913$	−5.45399	+	14.6433i	−0.180501	+	0.484623i
$914$	40.0351			1.32424
$915$		0			0
$916$	2.90587	+	8.94336i	0.0960128	+	0.295497i
$917$	50.0175	+	16.2517i	1.65172	+	0.536678i
$918$	−37.7096	+	51.9028i	−1.24460	+	1.71305i
$919$	−12.9266	−	9.39169i	−0.426408	−	0.309803i	0.353803	−	0.935320i	$-0.384888\pi$
$919$	−12.9266	−	9.39169i	−0.426408	−	0.309803i	−0.780211	+	0.625517i	$0.784888\pi$
$920$		0			0
$921$	−1.16901	−	3.59783i	−0.0385201	−	0.118553i
$922$	44.5954	+	61.3803i	1.46867	+	2.02145i
$923$			9.80572i			0.322759i
$924$	−4.37168	+	103.094i	−0.143818	+	3.39154i
$925$		0			0
$926$	−2.72877	+	1.98257i	−0.0896730	+	0.0651512i
$927$	−3.34347	+	1.08636i	−0.109814	+	0.0356807i
$928$	−14.8088	−	4.81167i	−0.486123	−	0.157951i
$929$	8.02976	+	5.83396i	0.263448	+	0.191406i	0.711666	−	0.702518i	$-0.247941\pi$
$929$	8.02976	+	5.83396i	0.263448	+	0.191406i	−0.448218	+	0.893924i	$0.647941\pi$
$930$		0			0
$931$	−7.96319	+	24.5082i	−0.260983	+	0.803223i
$932$	76.3741	−	24.8155i	2.50172	−	0.812857i
$933$	17.5552	+	24.1627i	0.574732	+	0.791051i
$934$	−31.0046			−1.01450
$935$		0			0
$936$	−6.31145			−0.206296
$937$	−5.24192	−	7.21488i	−0.171246	−	0.235700i	0.714764	−	0.699365i	$-0.246534\pi$
$937$	−5.24192	−	7.21488i	−0.171246	−	0.235700i	−0.886010	+	0.463666i	$0.846534\pi$
$938$	−72.6599	+	23.6086i	−2.37243	+	0.770849i
$939$	−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	$0.908157\pi$
$942$	1.30441	+	0.423829i	0.0425001	+	0.0138091i
$943$	−0.0921987	+	0.0299572i	−0.00300240	+	0.000975540i
$944$	−7.38712	+	5.36705i	−0.240430	+	0.174683i
$945$		0			0
$946$	23.5674	−	29.7047i	0.766242	−	0.965782i
$947$			1.62118i			0.0526814i	0.999653	+	0.0263407i	$0.00838548\pi$
$947$			1.62118i			0.0526814i	−0.999653	+	0.0263407i	$0.991615\pi$
$948$	−69.1982	−	95.2431i	−2.24745	−	3.09335i
$949$	12.4426	+	38.2944i	0.403904	+	1.24309i
$950$		0			0
$951$	−26.5633	−	19.2994i	−0.861375	−	0.625826i
$952$	−73.6340	+	101.348i	−2.38649	+	3.28472i
$953$	24.1017	+	7.83110i	0.780729	+	0.253674i	0.672152	−	0.740414i	$-0.265370\pi$
$953$	24.1017	+	7.83110i	0.780729	+	0.253674i	0.108578	+	0.994088i	$0.465370\pi$
$954$	0.929151	+	2.85963i	0.0300824	+	0.0925840i
$955$		0			0
$956$	85.3383			2.76004
$957$	3.75075	+	13.4592i	0.121245	+	0.435075i
$958$			7.82578i			0.252839i
$959$	−30.5790	+	22.2169i	−0.987448	+	0.717423i
$960$		0			0
$961$	−2.62123	+	8.06732i	−0.0845558	+	0.260236i
$962$	−37.9413	+	52.2217i	−1.22328	+	1.68370i
$963$	2.15398	−	2.96470i	0.0694111	−	0.0955362i
$964$	−42.6019	+	131.115i	−1.37211	+	4.22293i
$965$		0			0
$966$	−1.49338	+	1.08500i	−0.0480486	+	0.0349093i
$967$			6.70594i			0.215648i	0.994170	+	0.107824i	$0.0343884\pi$
$967$			6.70594i			0.215648i	−0.994170	+	0.107824i	$0.965612\pi$
$968$	−47.3193	+	54.7111i	−1.52090	+	1.75848i
$969$	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	$0.870233\pi$
$972$	9.61312	+	3.12349i	0.308341	+	0.100186i
$973$	4.53658	−	6.24407i	0.145436	−	0.200176i
$974$	−50.2511	−	36.5095i	−1.61015	−	1.16984i
$975$		0			0
$976$	−17.4730	−	53.7763i	−0.559296	−	1.72134i
$977$	3.07530	+	4.23279i	0.0983875	+	0.135419i	0.855372	−	0.518014i	$-0.173328\pi$
$977$	3.07530	+	4.23279i	0.0983875	+	0.135419i	−0.756985	+	0.653432i	$0.773328\pi$
$978$			65.5017i			2.09451i
$979$	0.552694	−	0.154022i	0.0176642	−	0.00492256i
$980$		0			0
$981$	−3.09135	+	2.24600i	−0.0986993	+	0.0717092i
$982$	−79.6419	+	25.8772i	−2.54148	+	0.825775i
$983$	−14.0673	−	4.57075i	−0.448678	−	0.145784i	0.0759580	−	0.997111i	$-0.475799\pi$
$983$	−14.0673	−	4.57075i	−0.448678	−	0.145784i	−0.524636	+	0.851327i	$0.675799\pi$
$984$	8.74443	+	6.35320i	0.278762	+	0.202533i
$985$		0			0
$986$	−9.32696	+	28.7054i	−0.297031	+	0.914168i
$987$	8.12329	−	2.63942i	0.258567	−	0.0840136i
$988$	−41.7734	−	57.4962i	−1.32899	−	1.82920i
$989$	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	$0.370472\pi$
$992$	18.4804	+	25.4361i	0.586752	+	0.807595i
$993$	−36.7566	+	11.9430i	−1.16644	+	0.378998i
$994$	6.56185	−	20.1953i	0.208129	−	0.640556i
$995$		0			0
$996$	31.1998	+	22.6680i	0.988604	+	0.718263i
$997$	−14.1122	−	4.58532i	−0.446937	−	0.145219i	0.0768969	−	0.997039i	$-0.475499\pi$
$997$	−14.1122	−	4.58532i	−0.446937	−	0.145219i	−0.523834	+	0.851820i	$0.675499\pi$
$998$	73.1261	−	23.7601i	2.31477	−	0.752113i
$999$	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.z.c.124.8		32
5.2	odd	4		275.2.h.e.201.1	yes	16
5.3	odd	4		275.2.h.c.201.4	yes	16
5.4	even	2	inner	275.2.z.c.124.1		32
11.4	even	5	inner	275.2.z.c.224.1		32
55.2	even	20		3025.2.a.bj.1.2		8
55.4	even	10	inner	275.2.z.c.224.8		32
55.13	even	20		3025.2.a.bm.1.7		8
55.37	odd	20		275.2.h.e.26.1	yes	16
55.42	odd	20		3025.2.a.bn.1.7		8
55.48	odd	20		275.2.h.c.26.4	✓	16
55.53	odd	20		3025.2.a.bi.1.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
275.2.h.c.26.4	✓	16	55.48	odd	20
275.2.h.c.201.4	yes	16	5.3	odd	4
275.2.h.e.26.1	yes	16	55.37	odd	20
275.2.h.e.201.1	yes	16	5.2	odd	4
275.2.z.c.124.1		32	5.4	even	2	inner
275.2.z.c.124.8		32	1.1	even	1	trivial
275.2.z.c.224.1		32	11.4	even	5	inner
275.2.z.c.224.8		32	55.4	even	10	inner
3025.2.a.bi.1.2		8	55.53	odd	20
3025.2.a.bj.1.2		8	55.2	even	20
3025.2.a.bm.1.7		8	55.13	even	20
3025.2.a.bn.1.7		8	55.42	odd	20

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 275 = 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	275.z (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.50618 + 2.07308i) q^{2} +(-1.70486 + 0.553942i) q^{3} +(-1.41105 + 4.34277i) q^{4} +(-3.71620 - 2.69998i) q^{6} +(-3.61485 - 1.17454i) q^{7} +(-6.25410 + 2.03208i) q^{8} +(0.172643 - 0.125433i) q^{9} +(3.19489 - 0.890336i) q^{11} -8.18545i q^{12} +(2.64361 + 3.63862i) q^{13} +(-3.00971 - 9.26295i) q^{14} +(-6.24414 - 4.53663i) q^{16} +(-2.94602 + 4.05485i) q^{17} +(0.520065 + 0.168979i) q^{18} +(1.06936 + 3.29116i) q^{19} +6.81344 q^{21} +(6.65782 + 5.28226i) q^{22} +0.105727i q^{23} +(9.53671 - 6.92883i) q^{24} +(-3.56139 + 10.9608i) q^{26} +(2.93613 - 4.04124i) q^{27} +(10.2015 - 14.0411i) q^{28} +(0.726214 - 2.23506i) q^{29} +(-3.83900 + 2.78920i) q^{31} -6.62570i q^{32} +(-4.95364 + 3.28768i) q^{33} -12.8433 q^{34} +(0.301117 + 0.926742i) q^{36} +(5.32675 + 1.73077i) q^{37} +(-5.21219 + 7.17396i) q^{38} +(-6.52257 - 4.73892i) q^{39} +(0.283345 + 0.872045i) q^{41} +(10.2623 + 14.1248i) q^{42} -4.46162i q^{43} +(-0.641627 + 15.1310i) q^{44} +(-0.219181 + 0.159244i) q^{46} +(1.19225 - 0.387384i) q^{47} +(13.1584 + 4.27543i) q^{48} +(6.02449 + 4.37704i) q^{49} +(2.77640 - 8.54487i) q^{51} +(-19.5319 + 6.34631i) q^{52} +(3.23200 + 4.44847i) q^{53} +12.8002 q^{54} +24.9944 q^{56} +(-3.64622 - 5.01860i) q^{57} +(5.72727 - 1.86090i) q^{58} +(0.365582 - 1.12515i) q^{59} +(5.92690 + 4.30614i) q^{61} +(-11.5645 - 3.75752i) q^{62} +(-0.771405 + 0.250645i) q^{63} +(1.24734 - 0.906248i) q^{64} +(-14.2767 - 5.31745i) q^{66} -7.84414i q^{67} +(-13.4523 - 18.5155i) q^{68} +(-0.0585667 - 0.180250i) q^{69} +(1.76384 + 1.28150i) q^{71} +(-0.824840 + 1.13529i) q^{72} +(8.51445 + 2.76651i) q^{73} +(4.43504 + 13.6496i) q^{74} -15.8017 q^{76} +(-12.5948 - 0.534080i) q^{77} -20.6595i q^{78} +(11.6357 - 8.45380i) q^{79} +(-2.96491 + 9.12506i) q^{81} +(-1.38105 + 1.90086i) q^{82} +(-2.76930 + 3.81162i) q^{83} +(-9.61410 + 29.5892i) q^{84} +(9.24930 - 6.72001i) q^{86} +4.21274i q^{87} +(-18.1719 + 12.0605i) q^{88} +0.172993 q^{89} +(-5.28256 - 16.2581i) q^{91} +(-0.459148 - 0.149186i) q^{92} +(4.99990 - 6.88177i) q^{93} +(2.59882 + 1.88815i) q^{94} +(3.67026 + 11.2959i) q^{96} +(-2.62178 - 3.60857i) q^{97} +19.0819i q^{98} +(0.439899 - 0.554454i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 4 q^{4} - 6 q^{6} - 16 q^{9} - 10 q^{11} - 6 q^{14} - 8 q^{16} + 26 q^{19} + 20 q^{21} + 86 q^{24} - 68 q^{26} + 22 q^{29} - 20 q^{31} - 40 q^{34} + 6 q^{36} - 6 q^{39} + 50 q^{41} + 2 q^{44} + 80 q^{46}+ \cdots + 20 q^{99}+O(q^{100}) \) 32 * q + 4 * q^4 - 6 * q^6 - 16 * q^9 - 10 * q^11 - 6 * q^14 - 8 * q^16 + 26 * q^19 + 20 * q^21 + 86 * q^24 - 68 * q^26 + 22 * q^29 - 20 * q^31 - 40 * q^34 + 6 * q^36 - 6 * q^39 + 50 * q^41 + 2 * q^44 + 80 * q^46 - 32 * q^49 + 70 * q^51 - 120 * q^54 - 40 * q^56 - 28 * q^59 + 32 * q^61 - 80 * q^64 - 110 * q^66 - 70 * q^69 - 92 * q^71 + 14 * q^74 - 124 * q^76 + 78 * q^79 - 86 * q^81 + 108 * q^84 + 4 * q^86 + 44 * q^89 - 68 * q^91 + 80 * q^94 + 216 * q^96 + 20 * q^99

Introduction

L-functions

Modular forms

Varieties

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