LMFDB - Embedded newform 300.2.m.a.181.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [300,2,Mod(61,300)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(300, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 8]))

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

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

chi := DirichletCharacter("300.61");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	300.m (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:	$2.39551206064$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	$\Q(\zeta_{15})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1 $ x^8 - x^7 + x^5 - x^4 + x^3 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			181.1
Root			$0.669131 - 0.743145i$ of defining polynomial
Character	$\chi$	$=$	300.181
Dual form			300.2.m.a.121.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 + 0.587785i) q^{3} +(-0.233733 - 2.22382i) q^{5} -0.511170 q^{7} +(0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(-0.809017 + 0.587785i) q^{3} +(-0.233733 - 2.22382i) q^{5} -0.511170 q^{7} +(0.309017 - 0.951057i) q^{9} +(-0.564602 - 1.73767i) q^{11} +(1.89169 - 5.82203i) q^{13} +(1.49622 + 1.66172i) q^{15} +(-2.09007 - 1.51852i) q^{17} +(3.93444 + 2.85854i) q^{19} +(0.413545 - 0.300458i) q^{21} +(-2.04965 - 6.30818i) q^{23} +(-4.89074 + 1.03956i) q^{25} +(0.309017 + 0.951057i) q^{27} +(6.46980 - 4.70059i) q^{29} +(3.95252 + 2.87167i) q^{31} +(1.47815 + 1.07394i) q^{33} +(0.119477 + 1.13675i) q^{35} +(-2.29833 + 7.07355i) q^{37} +(1.89169 + 5.82203i) q^{39} +(1.77084 - 5.45007i) q^{41} -2.05126 q^{43} +(-2.18720 - 0.464905i) q^{45} +(-6.43523 + 4.67547i) q^{47} -6.73870 q^{49} +2.58347 q^{51} +(-1.07528 + 0.781240i) q^{53} +(-3.73229 + 1.66172i) q^{55} -4.86324 q^{57} +(-3.11882 + 9.59875i) q^{59} +(1.47437 + 4.53764i) q^{61} +(-0.157960 + 0.486152i) q^{63} +(-13.3893 - 2.84598i) q^{65} +(11.5960 + 8.42500i) q^{67} +(5.36606 + 3.89867i) q^{69} +(4.34421 - 3.15625i) q^{71} +(-1.07559 - 3.31031i) q^{73} +(3.34565 - 3.71572i) q^{75} +(0.288608 + 0.888244i) q^{77} +(1.06789 - 0.775869i) q^{79} +(-0.809017 - 0.587785i) q^{81} +(-0.738301 - 0.536407i) q^{83} +(-2.88840 + 5.00286i) q^{85} +(-2.47124 + 7.60571i) q^{87} +(3.63893 + 11.1995i) q^{89} +(-0.966977 + 2.97605i) q^{91} -4.88558 q^{93} +(5.43727 - 9.41762i) q^{95} +(5.98660 - 4.34952i) q^{97} -1.82709 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{3} + 5 q^{5} - 8 q^{7} - 2 q^{9}+O(q^{10}) $ 8 * q - 2 * q^3 + 5 * q^5 - 8 * q^7 - 2 * q^9	$ 8 q - 2 q^{3} + 5 q^{5} - 8 q^{7} - 2 q^{9} - 2 q^{11} - 5 q^{15} + 7 q^{17} + 5 q^{19} - 3 q^{21} + 7 q^{23} + 5 q^{25} - 2 q^{27} + 27 q^{29} - 3 q^{31} + 3 q^{33} + 20 q^{35} - 9 q^{37} + 20 q^{41} - 68 q^{43} - 5 q^{45} - 7 q^{47} - 8 q^{49} - 8 q^{51} - 11 q^{53} + 5 q^{55} - 10 q^{57} + 2 q^{59} - 14 q^{61} + 7 q^{63} - 35 q^{65} + 28 q^{67} + 2 q^{69} - 15 q^{71} + 6 q^{73} + 5 q^{75} + 17 q^{77} + 24 q^{79} - 2 q^{81} + 2 q^{83} + 10 q^{85} - 23 q^{87} + 5 q^{91} - 18 q^{93} + 5 q^{95} + 34 q^{97} - 2 q^{99}+O(q^{100}) $ 8 * q - 2 * q^3 + 5 * q^5 - 8 * q^7 - 2 * q^9 - 2 * q^11 - 5 * q^15 + 7 * q^17 + 5 * q^19 - 3 * q^21 + 7 * q^23 + 5 * q^25 - 2 * q^27 + 27 * q^29 - 3 * q^31 + 3 * q^33 + 20 * q^35 - 9 * q^37 + 20 * q^41 - 68 * q^43 - 5 * q^45 - 7 * q^47 - 8 * q^49 - 8 * q^51 - 11 * q^53 + 5 * q^55 - 10 * q^57 + 2 * q^59 - 14 * q^61 + 7 * q^63 - 35 * q^65 + 28 * q^67 + 2 * q^69 - 15 * q^71 + 6 * q^73 + 5 * q^75 + 17 * q^77 + 24 * q^79 - 2 * q^81 + 2 * q^83 + 10 * q^85 - 23 * q^87 + 5 * q^91 - 18 * q^93 + 5 * q^95 + 34 * q^97 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$277$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{5}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i
$4$		0			0
$5$	−0.233733	−	2.22382i	−0.104528	−	0.994522i
$5$	−0.233733	−	2.22382i	−0.104528	−	0.994522i
$6$		0			0
$7$	−0.511170			−0.193204			−0.0966021	−	0.995323i	$-0.530797\pi$
$7$	−0.511170			−0.193204			−0.0966021	+	0.995323i	$0.530797\pi$
$8$		0			0
$9$	0.309017	−	0.951057i	0.103006	−	0.317019i
$10$		0			0
$11$	−0.564602	−	1.73767i	−0.170234	−	0.523926i	0.829150	−	0.559026i	$-0.188825\pi$
$11$	−0.564602	−	1.73767i	−0.170234	−	0.523926i	−0.999384	+	0.0351002i	$0.988825\pi$
$12$		0			0
$13$	1.89169	−	5.82203i	0.524661	−	1.61474i	−0.240323	−	0.970693i	$-0.577254\pi$
$13$	1.89169	−	5.82203i	0.524661	−	1.61474i	0.764985	−	0.644048i	$-0.222746\pi$
$14$		0			0
$15$	1.49622	+	1.66172i	0.386323	+	0.429055i
$16$		0			0
$17$	−2.09007	−	1.51852i	−0.506916	−	0.368296i	0.304736	−	0.952437i	$-0.401432\pi$
$17$	−2.09007	−	1.51852i	−0.506916	−	0.368296i	−0.811652	+	0.584141i	$0.801432\pi$
$18$		0			0
$19$	3.93444	+	2.85854i	0.902623	+	0.655794i	0.939138	−	0.343539i	$-0.111626\pi$
$19$	3.93444	+	2.85854i	0.902623	+	0.655794i	−0.0365153	+	0.999333i	$0.511626\pi$
$20$		0			0
$21$	0.413545	−	0.300458i	0.0902430	−	0.0655654i
$22$		0			0
$23$	−2.04965	−	6.30818i	−0.427382	−	1.31535i	−0.900695	−	0.434453i	$-0.856942\pi$
$23$	−2.04965	−	6.30818i	−0.427382	−	1.31535i	0.473312	−	0.880895i	$-0.343058\pi$
$24$		0			0
$25$	−4.89074	+	1.03956i	−0.978148	+	0.207912i
$26$		0			0
$27$	0.309017	+	0.951057i	0.0594703	+	0.183031i
$28$		0			0
$29$	6.46980	−	4.70059i	1.20141	−	0.872877i	0.206989	−	0.978343i	$-0.433634\pi$
$29$	6.46980	−	4.70059i	1.20141	−	0.872877i	0.994423	+	0.105466i	$0.0336336\pi$
$30$		0			0
$31$	3.95252	+	2.87167i	0.709893	+	0.515767i	0.883139	−	0.469111i	$-0.155426\pi$
$31$	3.95252	+	2.87167i	0.709893	+	0.515767i	−0.173246	+	0.984879i	$0.555426\pi$
$32$		0			0
$33$	1.47815	+	1.07394i	0.257312	+	0.186948i
$34$		0			0
$35$	0.119477	+	1.13675i	0.0201953	+	0.192146i
$36$		0			0
$37$	−2.29833	+	7.07355i	−0.377844	+	1.16288i	0.563696	+	0.825982i	$0.309379\pi$
$37$	−2.29833	+	7.07355i	−0.377844	+	1.16288i	−0.941540	+	0.336902i	$0.890621\pi$
$38$		0			0
$39$	1.89169	+	5.82203i	0.302913	+	0.932271i
$40$		0			0
$41$	1.77084	−	5.45007i	0.276558	−	0.851158i	−0.712245	−	0.701931i	$-0.752321\pi$
$41$	1.77084	−	5.45007i	0.276558	−	0.851158i	0.988803	−	0.149227i	$-0.0476786\pi$
$42$		0			0
$43$	−2.05126			−0.312814			−0.156407	−	0.987693i	$-0.549991\pi$
$43$	−2.05126			−0.312814			−0.156407	+	0.987693i	$0.549991\pi$
$44$		0			0
$45$	−2.18720	−	0.464905i	−0.326049	−	0.0693039i
$46$		0			0
$47$	−6.43523	+	4.67547i	−0.938675	+	0.681987i	−0.948101	−	0.317968i	$-0.896999\pi$
$47$	−6.43523	+	4.67547i	−0.938675	+	0.681987i	0.00942623	+	0.999956i	$0.496999\pi$
$48$		0			0
$49$	−6.73870			−0.962672
$50$		0			0
$51$	2.58347			0.361758
$52$		0			0
$53$	−1.07528	+	0.781240i	−0.147702	+	0.107312i	−0.659182	−	0.751983i	$-0.729097\pi$
$53$	−1.07528	+	0.781240i	−0.147702	+	0.107312i	0.511480	+	0.859295i	$0.329097\pi$
$54$		0			0
$55$	−3.73229	+	1.66172i	−0.503262	+	0.224067i
$56$		0			0
$57$	−4.86324			−0.644152
$58$		0			0
$59$	−3.11882	+	9.59875i	−0.406036	+	1.24965i	0.513991	+	0.857796i	$0.328167\pi$
$59$	−3.11882	+	9.59875i	−0.406036	+	1.24965i	−0.920027	+	0.391855i	$0.871833\pi$
$60$		0			0
$61$	1.47437	+	4.53764i	0.188774	+	0.580985i	0.999993	−	0.00375653i	$-0.00119574\pi$
$61$	1.47437	+	4.53764i	0.188774	+	0.580985i	−0.811219	+	0.584742i	$0.801196\pi$
$62$		0			0
$63$	−0.157960	+	0.486152i	−0.0199011	+	0.0612494i
$64$		0			0
$65$	−13.3893	−	2.84598i	−1.66074	−	0.353001i
$66$		0			0
$67$	11.5960	+	8.42500i	1.41668	+	1.02928i	0.992309	+	0.123789i	$0.0395045\pi$
$67$	11.5960	+	8.42500i	1.41668	+	1.02928i	0.424370	+	0.905489i	$0.360495\pi$
$68$		0			0
$69$	5.36606	+	3.89867i	0.645998	+	0.469345i
$70$		0			0
$71$	4.34421	−	3.15625i	0.515563	−	0.374578i	−0.299367	−	0.954138i	$-0.596775\pi$
$71$	4.34421	−	3.15625i	0.515563	−	0.374578i	0.814930	+	0.579560i	$0.196775\pi$
$72$		0			0
$73$	−1.07559	−	3.31031i	−0.125888	−	0.387443i	0.868174	−	0.496260i	$-0.165294\pi$
$73$	−1.07559	−	3.31031i	−0.125888	−	0.387443i	−0.994062	+	0.108817i	$0.965294\pi$
$74$		0			0
$75$	3.34565	−	3.71572i	0.386323	−	0.429055i
$76$		0			0
$77$	0.288608	+	0.888244i	0.0328899	+	0.101225i
$78$		0			0
$79$	1.06789	−	0.775869i	0.120147	−	0.0872921i	−0.526089	−	0.850430i	$-0.676342\pi$
$79$	1.06789	−	0.775869i	0.120147	−	0.0872921i	0.646236	+	0.763137i	$0.276342\pi$
$80$		0			0
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$		0			0
$83$	−0.738301	−	0.536407i	−0.0810391	−	0.0588783i	0.546528	−	0.837441i	$-0.315949\pi$
$83$	−0.738301	−	0.536407i	−0.0810391	−	0.0588783i	−0.627567	+	0.778562i	$0.715949\pi$
$84$		0			0
$85$	−2.88840	+	5.00286i	−0.313291	+	0.542636i
$86$		0			0
$87$	−2.47124	+	7.60571i	−0.264945	+	0.815417i
$88$		0			0
$89$	3.63893	+	11.1995i	0.385726	+	1.18714i	0.935952	+	0.352127i	$0.114541\pi$
$89$	3.63893	+	11.1995i	0.385726	+	1.18714i	−0.550226	+	0.835016i	$0.685459\pi$
$90$		0			0
$91$	−0.966977	+	2.97605i	−0.101367	+	0.311975i
$92$		0			0
$93$	−4.88558			−0.506611
$94$		0			0
$95$	5.43727	−	9.41762i	0.557852	−	0.966228i
$96$		0			0
$97$	5.98660	−	4.34952i	0.607847	−	0.441627i	−0.240809	−	0.970573i	$-0.577413\pi$
$97$	5.98660	−	4.34952i	0.607847	−	0.441627i	0.848655	+	0.528946i	$0.177413\pi$
$98$		0			0
$99$	−1.82709			−0.183630
$100$		0			0
$101$	13.0962			1.30312			0.651561	−	0.758596i	$-0.274114\pi$
$101$	13.0962			1.30312			0.651561	+	0.758596i	$0.274114\pi$
$102$		0			0
$103$	8.92360	−	6.48337i	0.879268	−	0.638826i	−0.0537897	−	0.998552i	$-0.517130\pi$
$103$	8.92360	−	6.48337i	0.879268	−	0.638826i	0.933058	+	0.359727i	$0.117130\pi$
$104$		0			0
$105$	−0.764824	−	0.849423i	−0.0746392	−	0.0828952i
$106$		0			0
$107$	−8.08083			−0.781203			−0.390602	−	0.920560i	$-0.627733\pi$
$107$	−8.08083			−0.781203			−0.390602	+	0.920560i	$0.627733\pi$
$108$		0			0
$109$	3.49904	−	10.7690i	0.335148	−	1.03148i	−0.631502	−	0.775375i	$-0.717561\pi$
$109$	3.49904	−	10.7690i	0.335148	−	1.03148i	0.966649	−	0.256104i	$-0.0824390\pi$
$110$		0			0
$111$	−2.29833	−	7.07355i	−0.218148	−	0.671391i
$112$		0			0
$113$	1.16456	−	3.58415i	0.109553	−	0.337169i	−0.881219	−	0.472708i	$-0.843277\pi$
$113$	1.16456	−	3.58415i	0.109553	−	0.337169i	0.990772	+	0.135539i	$0.0432766\pi$
$114$		0			0
$115$	−13.5492	+	6.03249i	−1.26347	+	0.562532i
$116$		0			0
$117$	−4.95252	−	3.59821i	−0.457860	−	0.332655i
$118$		0			0
$119$	1.06838	+	0.776224i	0.0979383	+	0.0711563i
$120$		0			0
$121$	6.19848	−	4.50346i	0.563498	−	0.409405i
$122$		0			0
$123$	1.77084	+	5.45007i	0.159671	+	0.491416i
$124$		0			0
$125$	3.45492	+	10.6331i	0.309017	+	0.951057i
$126$		0			0
$127$	−1.28920	−	3.96774i	−0.114398	−	0.352080i	0.877423	−	0.479717i	$-0.159261\pi$
$127$	−1.28920	−	3.96774i	−0.114398	−	0.352080i	−0.991821	+	0.127637i	$0.959261\pi$
$128$		0			0
$129$	1.65951	−	1.20570i	0.146111	−	0.106156i
$130$		0			0
$131$	−11.9660	−	8.69382i	−1.04548	−	0.759583i	−0.0741292	−	0.997249i	$-0.523618\pi$
$131$	−11.9660	−	8.69382i	−1.04548	−	0.759583i	−0.971347	+	0.237666i	$0.923618\pi$
$132$		0			0
$133$	−2.01117	−	1.46120i	−0.174391	−	0.126702i
$134$		0			0
$135$	2.04275	−	0.909491i	0.175812	−	0.0782765i
$136$		0			0
$137$	−0.379143	+	1.16688i	−0.0323923	+	0.0996934i	−0.965946	−	0.258746i	$-0.916691\pi$
$137$	−0.379143	+	1.16688i	−0.0323923	+	0.0996934i	0.933553	+	0.358439i	$0.116691\pi$
$138$		0			0
$139$	2.80764	+	8.64102i	0.238141	+	0.732922i	0.996689	+	0.0813051i	$0.0259088\pi$
$139$	2.80764	+	8.64102i	0.238141	+	0.732922i	−0.758549	+	0.651616i	$0.774091\pi$
$140$		0			0
$141$	2.45804	−	7.56507i	0.207004	−	0.637094i
$142$		0			0
$143$	−11.1848			−0.935320
$144$		0			0
$145$	−11.9655	−	13.2890i	−0.993677	−	1.10359i
$146$		0			0
$147$	5.45173	−	3.96091i	0.449651	−	0.326690i
$148$		0			0
$149$	1.90097			0.155733			0.0778666	−	0.996964i	$-0.475189\pi$
$149$	1.90097			0.155733			0.0778666	+	0.996964i	$0.475189\pi$
$150$		0			0
$151$	−4.60292			−0.374580			−0.187290	−	0.982305i	$-0.559970\pi$
$151$	−4.60292			−0.374580			−0.187290	+	0.982305i	$0.559970\pi$
$152$		0			0
$153$	−2.09007	+	1.51852i	−0.168972	+	0.122765i
$154$		0			0
$155$	5.46224	−	9.46088i	0.438738	−	0.759916i
$156$		0			0
$157$	3.96076			0.316103			0.158052	−	0.987431i	$-0.449479\pi$
$157$	3.96076			0.316103			0.158052	+	0.987431i	$0.449479\pi$
$158$		0			0
$159$	0.410722	−	1.26407i	0.0325724	−	0.100247i
$160$		0			0
$161$	1.04772	+	3.22456i	0.0825721	+	0.254131i
$162$		0			0
$163$	6.48302	−	19.9527i	0.507789	−	1.56281i	−0.288241	−	0.957558i	$-0.593071\pi$
$163$	6.48302	−	19.9527i	0.507789	−	1.56281i	0.796031	−	0.605256i	$-0.206929\pi$
$164$		0			0
$165$	2.04275	−	3.53815i	0.159028	−	0.275444i
$166$		0			0
$167$	14.5925	+	10.6021i	1.12920	+	0.820413i	0.985578	−	0.169219i	$-0.0541246\pi$
$167$	14.5925	+	10.6021i	1.12920	+	0.820413i	0.143624	+	0.989632i	$0.454125\pi$
$168$		0			0
$169$	−19.8003	−	14.3858i	−1.52310	−	1.10660i
$170$		0			0
$171$	3.93444	−	2.85854i	0.300874	−	0.218598i
$172$		0			0
$173$	7.91007	+	24.3447i	0.601391	+	1.85089i	0.519917	+	0.854217i	$0.325963\pi$
$173$	7.91007	+	24.3447i	0.601391	+	1.85089i	0.0814747	+	0.996675i	$0.474037\pi$
$174$		0			0
$175$	2.50000	−	0.531391i	0.188982	−	0.0401694i
$176$		0			0
$177$	−3.11882	−	9.59875i	−0.234425	−	0.721486i
$178$		0			0
$179$	6.81056	−	4.94816i	0.509045	−	0.369843i	−0.303416	−	0.952858i	$-0.598127\pi$
$179$	6.81056	−	4.94816i	0.509045	−	0.369843i	0.812461	+	0.583015i	$0.198127\pi$
$180$		0			0
$181$	16.2350	+	11.7955i	1.20674	+	0.876749i	0.994931	−	0.100561i	$-0.0320639\pi$
$181$	16.2350	+	11.7955i	1.20674	+	0.876749i	0.211811	+	0.977311i	$0.432064\pi$
$182$		0			0
$183$	−3.85995	−	2.80442i	−0.285336	−	0.207308i
$184$		0			0
$185$	16.2675	+	3.45776i	1.19601	+	0.254220i
$186$		0			0
$187$	−1.45863	+	4.48920i	−0.106666	+	0.328283i
$188$		0			0
$189$	−0.157960	−	0.486152i	−0.0114899	−	0.0353623i
$190$		0			0
$191$	1.19381	−	3.67416i	0.0863808	−	0.265853i	−0.898531	−	0.438910i	$-0.855365\pi$
$191$	1.19381	−	3.67416i	0.0863808	−	0.265853i	0.984912	+	0.173057i	$0.0553646\pi$
$192$		0			0
$193$	10.6925			0.769662			0.384831	−	0.922987i	$-0.374260\pi$
$193$	10.6925			0.769662			0.384831	+	0.922987i	$0.374260\pi$
$194$		0			0
$195$	12.5050	−	5.56758i	0.895501	−	0.398703i
$196$		0			0
$197$	3.36909	−	2.44778i	0.240037	−	0.174397i	−0.461263	−	0.887264i	$-0.652603\pi$
$197$	3.36909	−	2.44778i	0.240037	−	0.174397i	0.701300	+	0.712866i	$0.252603\pi$
$198$		0			0
$199$	−27.5965			−1.95627			−0.978134	−	0.207978i	$-0.933312\pi$
$199$	−27.5965			−1.95627			−0.978134	+	0.207978i	$0.933312\pi$
$200$		0			0
$201$	−14.3335			−1.01100
$202$		0			0
$203$	−3.30717	+	2.40280i	−0.232118	+	0.168643i
$204$		0			0
$205$	−12.5339	−	2.66416i	−0.875404	−	0.186073i
$206$		0			0
$207$	−6.63282			−0.461013
$208$		0			0
$209$	2.74580	−	8.45069i	0.189931	−	0.584546i
$210$		0			0
$211$	0.597913	+	1.84019i	0.0411621	+	0.126684i	0.969526	−	0.244989i	$-0.0787843\pi$
$211$	0.597913	+	1.84019i	0.0411621	+	0.126684i	−0.928364	+	0.371673i	$0.878784\pi$
$212$		0			0
$213$	−1.65934	+	5.10692i	−0.113696	+	0.349921i
$214$		0			0
$215$	0.479447	+	4.56163i	0.0326980	+	0.311101i
$216$		0			0
$217$	−2.02041	−	1.46791i	−0.137154	−	0.0996484i
$218$		0			0
$219$	2.81592	+	2.04589i	0.190282	+	0.138248i
$220$		0			0
$221$	−12.7947	+	9.29586i	−0.860662	+	0.625307i
$222$		0			0
$223$	−5.68828	−	17.5067i	−0.380916	−	1.17234i	−0.939400	−	0.342823i	$-0.888617\pi$
$223$	−5.68828	−	17.5067i	−0.380916	−	1.17234i	0.558485	−	0.829515i	$-0.311383\pi$
$224$		0			0
$225$	−0.522642	+	4.97261i	−0.0348428	+	0.331507i
$226$		0			0
$227$	−5.95154	−	18.3170i	−0.395018	−	1.21574i	−0.928948	−	0.370211i	$-0.879286\pi$
$227$	−5.95154	−	18.3170i	−0.395018	−	1.21574i	0.533930	−	0.845529i	$-0.320714\pi$
$228$		0			0
$229$	21.3918	−	15.5420i	1.41361	−	1.02705i	0.420824	−	0.907142i	$-0.361741\pi$
$229$	21.3918	−	15.5420i	1.41361	−	1.02705i	0.992785	−	0.119905i	$-0.0382589\pi$
$230$		0			0
$231$	−0.755585	−	0.548965i	−0.0497139	−	0.0361192i
$232$		0			0
$233$	12.7508	+	9.26399i	0.835332	+	0.606904i	0.921063	−	0.389414i	$-0.127323\pi$
$233$	12.7508	+	9.26399i	0.835332	+	0.606904i	−0.0857308	+	0.996318i	$0.527323\pi$
$234$		0			0
$235$	11.9015	+	13.2180i	0.776370	+	0.862246i
$236$		0			0
$237$	−0.407899	+	1.25538i	−0.0264959	+	0.0815459i
$238$		0			0
$239$	5.67518	+	17.4664i	0.367097	+	1.12981i	0.948658	+	0.316305i	$0.102442\pi$
$239$	5.67518	+	17.4664i	0.367097	+	1.12981i	−0.581561	+	0.813503i	$0.697558\pi$
$240$		0			0
$241$	−7.81517	+	24.0526i	−0.503419	+	1.54936i	0.299993	+	0.953941i	$0.403016\pi$
$241$	−7.81517	+	24.0526i	−0.503419	+	1.54936i	−0.803412	+	0.595423i	$0.796984\pi$
$242$		0			0
$243$	1.00000			0.0641500
$244$		0			0
$245$	1.57506	+	14.9857i	0.100627	+	0.957399i
$246$		0			0
$247$	24.0853	−	17.4990i	1.53251	−	1.11343i
$248$		0			0
$249$	0.912590			0.0578331
$250$		0			0
$251$	−17.4297			−1.10015			−0.550076	−	0.835115i	$-0.685401\pi$
$251$	−17.4297			−1.10015			−0.550076	+	0.835115i	$0.685401\pi$
$252$		0			0
$253$	−9.80428	+	7.12323i	−0.616390	+	0.447834i
$254$		0			0
$255$	−0.603841	−	5.74516i	−0.0378140	−	0.359776i
$256$		0			0
$257$	−29.6169			−1.84745			−0.923727	−	0.383052i	$-0.874873\pi$
$257$	−29.6169			−1.84745			−0.923727	+	0.383052i	$0.874873\pi$
$258$		0			0
$259$	1.17484	−	3.61579i	0.0730010	−	0.224674i
$260$		0			0
$261$	−2.47124	−	7.60571i	−0.152966	−	0.470781i
$262$		0			0
$263$	−5.17140	+	15.9159i	−0.318882	+	0.981419i	0.655244	+	0.755417i	$0.272566\pi$
$263$	−5.17140	+	15.9159i	−0.318882	+	0.981419i	−0.974127	+	0.226002i	$0.927434\pi$
$264$		0			0
$265$	1.98866	+	2.20864i	0.122163	+	0.135675i
$266$		0			0
$267$	−9.52685	−	6.92166i	−0.583034	−	0.423599i
$268$		0			0
$269$	10.3471	+	7.51758i	0.630872	+	0.458355i	0.856702	−	0.515811i	$-0.172509\pi$
$269$	10.3471	+	7.51758i	0.630872	+	0.458355i	−0.225830	+	0.974167i	$0.572509\pi$
$270$		0			0
$271$	−23.1964	+	16.8532i	−1.40908	+	1.02376i	−0.415628	+	0.909535i	$0.636438\pi$
$271$	−23.1964	+	16.8532i	−1.40908	+	1.02376i	−0.993455	+	0.114224i	$0.963562\pi$
$272$		0			0
$273$	−0.966977	−	2.97605i	−0.0585241	−	0.180119i
$274$		0			0
$275$	4.56773	+	7.91154i	0.275444	+	0.477084i
$276$		0			0
$277$	1.64932	+	5.07610i	0.0990983	+	0.304993i	0.988300	−	0.152522i	$-0.0487395\pi$
$277$	1.64932	+	5.07610i	0.0990983	+	0.304993i	−0.889202	+	0.457515i	$0.848739\pi$
$278$		0			0
$279$	3.95252	−	2.87167i	0.236631	−	0.171922i
$280$		0			0
$281$	5.19975	+	3.77784i	0.310191	+	0.225367i	0.731979	−	0.681328i	$-0.238597\pi$
$281$	5.19975	+	3.77784i	0.310191	+	0.225367i	−0.421787	+	0.906695i	$0.638597\pi$
$282$		0			0
$283$	8.46527	+	6.15038i	0.503208	+	0.365602i	0.810241	−	0.586097i	$-0.199336\pi$
$283$	8.46527	+	6.15038i	0.503208	+	0.365602i	−0.307033	+	0.951699i	$0.599336\pi$
$284$		0			0
$285$	1.13670	+	10.8150i	0.0673322	+	0.640623i
$286$		0			0
$287$	−0.905199	+	2.78591i	−0.0534322	+	0.164447i
$288$		0			0
$289$	−3.19082	−	9.82033i	−0.187695	−	0.577666i
$290$		0			0
$291$	−2.28668	+	7.03767i	−0.134047	+	0.412555i
$292$		0			0
$293$	4.63761			0.270932			0.135466	−	0.990782i	$-0.456747\pi$
$293$	4.63761			0.270932			0.135466	+	0.990782i	$0.456747\pi$
$294$		0			0
$295$	22.0749	+	4.69216i	1.28525	+	0.273188i
$296$		0			0
$297$	1.47815	−	1.07394i	0.0857708	−	0.0623162i
$298$		0			0
$299$	−40.6038			−2.34818
$300$		0			0
$301$	1.04854			0.0604371
$302$		0			0
$303$	−10.5951	+	7.69776i	−0.608670	+	0.442225i
$304$		0			0
$305$	9.74628	−	4.33932i	0.558071	−	0.248469i
$306$		0			0
$307$	17.5664			1.00257			0.501285	−	0.865282i	$-0.332861\pi$
$307$	17.5664			1.00257			0.501285	+	0.865282i	$0.332861\pi$
$308$		0			0
$309$	−3.40851	+	10.4903i	−0.193903	+	0.596773i
$310$		0			0
$311$	5.67507	+	17.4661i	0.321803	+	0.990409i	0.972863	+	0.231382i	$0.0743249\pi$
$311$	5.67507	+	17.4661i	0.321803	+	0.990409i	−0.651059	+	0.759027i	$0.725675\pi$
$312$		0			0
$313$	−7.83472	+	24.1128i	−0.442845	+	1.36294i	0.441986	+	0.897022i	$0.354274\pi$
$313$	−7.83472	+	24.1128i	−0.442845	+	1.36294i	−0.884830	+	0.465914i	$0.845726\pi$
$314$		0			0
$315$	1.11803	+	0.237645i	0.0629941	+	0.0133898i
$316$		0			0
$317$	19.1343	+	13.9019i	1.07469	+	0.780808i	0.976749	−	0.214385i	$-0.0687747\pi$
$317$	19.1343	+	13.9019i	1.07469	+	0.780808i	0.0979401	+	0.995192i	$0.468775\pi$
$318$		0			0
$319$	−11.8209	−	8.58840i	−0.661844	−	0.480858i
$320$		0			0
$321$	6.53753	−	4.74979i	0.364889	−	0.265108i
$322$		0			0
$323$	−3.88249	−	11.9491i	−0.216028	−	0.664865i
$324$		0			0
$325$	−3.19943	+	30.4406i	−0.177473	+	1.68854i
$326$		0			0
$327$	3.49904	+	10.7690i	0.193498	+	0.595524i
$328$		0			0
$329$	3.28950	−	2.38996i	0.181356	−	0.131763i
$330$		0			0
$331$	−26.6188	−	19.3397i	−1.46310	−	1.06301i	−0.982541	−	0.186045i	$-0.940433\pi$
$331$	−26.6188	−	19.3397i	−1.46310	−	1.06301i	−0.480561	−	0.876961i	$-0.659567\pi$
$332$		0			0
$333$	6.01712	+	4.37169i	0.329736	+	0.239567i
$334$		0			0
$335$	16.0253	−	27.7566i	0.875556	−	1.51651i
$336$		0			0
$337$	1.60814	−	4.94935i	0.0876011	−	0.269608i	−0.897654	−	0.440701i	$-0.854730\pi$
$337$	1.60814	−	4.94935i	0.0876011	−	0.269608i	0.985255	+	0.171093i	$0.0547298\pi$
$338$		0			0
$339$	1.16456	+	3.58415i	0.0632503	+	0.194665i
$340$		0			0
$341$	2.75841	−	8.48951i	0.149376	−	0.459733i
$342$		0			0
$343$	7.02282			0.379197
$344$		0			0
$345$	7.41572	−	12.8444i	0.399249	−	0.691519i
$346$		0			0
$347$	−2.70449	+	1.96493i	−0.145185	+	0.105483i	−0.658007	−	0.753012i	$-0.728600\pi$
$347$	−2.70449	+	1.96493i	−0.145185	+	0.105483i	0.512822	+	0.858495i	$0.328600\pi$
$348$		0			0
$349$	−28.9138			−1.54772			−0.773859	−	0.633358i	$-0.781676\pi$
$349$	−28.9138			−1.54772			−0.773859	+	0.633358i	$0.781676\pi$
$350$		0			0
$351$	6.12165			0.326749
$352$		0			0
$353$	−16.4521	+	11.9531i	−0.875656	+	0.636201i	−0.932099	−	0.362204i	$-0.882024\pi$
$353$	−16.4521	+	11.9531i	−0.875656	+	0.636201i	0.0564426	+	0.998406i	$0.482024\pi$
$354$		0			0
$355$	−8.03432	−	8.92301i	−0.426417	−	0.473584i
$356$		0			0
$357$	−1.32059			−0.0698931
$358$		0			0
$359$	11.4959	−	35.3806i	0.606729	−	1.86732i	0.122289	−	0.992494i	$-0.460976\pi$
$359$	11.4959	−	35.3806i	0.606729	−	1.86732i	0.484439	−	0.874825i	$-0.339024\pi$
$360$		0			0
$361$	1.43727	+	4.42345i	0.0756456	+	0.232813i
$362$		0			0
$363$	−2.36761	+	7.28675i	−0.124267	+	0.382455i
$364$		0			0
$365$	−7.11014	+	3.16564i	−0.372162	+	0.165697i
$366$		0			0
$367$	−2.97782	−	2.16352i	−0.155441	−	0.112935i	0.507346	−	0.861742i	$-0.330627\pi$
$367$	−2.97782	−	2.16352i	−0.155441	−	0.112935i	−0.662787	+	0.748808i	$0.730627\pi$
$368$		0			0
$369$	−4.63611	−	3.36833i	−0.241346	−	0.175348i
$370$		0			0
$371$	0.549653	−	0.399347i	0.0285366	−	0.0207330i
$372$		0			0
$373$	6.29124	+	19.3625i	0.325748	+	1.00255i	0.971102	+	0.238666i	$0.0767101\pi$
$373$	6.29124	+	19.3625i	0.325748	+	1.00255i	−0.645353	+	0.763884i	$0.723290\pi$
$374$		0			0
$375$	−9.04508	−	6.57164i	−0.467086	−	0.339358i
$376$		0			0
$377$	−15.1281	−	46.5595i	−0.779136	−	2.39793i
$378$		0			0
$379$	5.17476	−	3.75968i	0.265809	−	0.193122i	−0.446895	−	0.894586i	$-0.647470\pi$
$379$	5.17476	−	3.75968i	0.265809	−	0.193122i	0.712704	+	0.701465i	$0.247470\pi$
$380$		0			0
$381$	3.37516	+	2.45220i	0.172915	+	0.125630i
$382$		0			0
$383$	1.99777	+	1.45146i	0.102081	+	0.0741663i	0.637655	−	0.770322i	$-0.279905\pi$
$383$	1.99777	+	1.45146i	0.102081	+	0.0741663i	−0.535574	+	0.844488i	$0.679905\pi$
$384$		0			0
$385$	1.90784	−	0.849423i	0.0972323	−	0.0432906i
$386$		0			0
$387$	−0.633875	+	1.95087i	−0.0322217	+	0.0991681i
$388$		0			0
$389$	4.50293	+	13.8586i	0.228307	+	0.702658i	0.997939	+	0.0641697i	$0.0204399\pi$
$389$	4.50293	+	13.8586i	0.228307	+	0.702658i	−0.769632	+	0.638488i	$0.779560\pi$
$390$		0			0
$391$	−5.29521	+	16.2970i	−0.267790	+	0.824174i
$392$		0			0
$393$	14.7908			0.746098
$394$		0			0
$395$	−1.97499	−	2.19345i	−0.0993727	−	0.110365i
$396$		0			0
$397$	20.0023	−	14.5325i	1.00389	−	0.729365i	0.0409675	−	0.999160i	$-0.486956\pi$
$397$	20.0023	−	14.5325i	1.00389	−	0.729365i	0.962918	+	0.269795i	$0.0869560\pi$
$398$		0			0
$399$	2.48594			0.124453
$400$		0			0
$401$	6.50743			0.324966			0.162483	−	0.986711i	$-0.448050\pi$
$401$	6.50743			0.324966			0.162483	+	0.986711i	$0.448050\pi$
$402$		0			0
$403$	24.1959	−	17.5794i	1.20528	−	0.875690i
$404$		0			0
$405$	−1.11803	+	1.93649i	−0.0555556	+	0.0962250i
$406$		0			0
$407$	13.5891			0.673587
$408$		0			0
$409$	3.41434	−	10.5082i	0.168828	−	0.519599i	−0.830470	−	0.557063i	$-0.811928\pi$
$409$	3.41434	−	10.5082i	0.168828	−	0.519599i	0.999298	+	0.0374642i	$0.0119280\pi$
$410$		0			0
$411$	−0.379143	−	1.16688i	−0.0187017	−	0.0575580i
$412$		0			0
$413$	1.59425	−	4.90660i	0.0784479	−	0.241438i
$414$		0			0
$415$	−1.02031	+	1.76722i	−0.0500849	+	0.0867496i
$416$		0			0
$417$	−7.35049	−	5.34044i	−0.359955	−	0.261523i
$418$		0			0
$419$	−15.0550	−	10.9381i	−0.735483	−	0.534360i	0.155810	−	0.987787i	$-0.450201\pi$
$419$	−15.0550	−	10.9381i	−0.735483	−	0.534360i	−0.891293	+	0.453427i	$0.850201\pi$
$420$		0			0
$421$	11.0426	−	8.02291i	0.538183	−	0.391013i	−0.285227	−	0.958460i	$-0.592069\pi$
$421$	11.0426	−	8.02291i	0.538183	−	0.391013i	0.823410	+	0.567447i	$0.192069\pi$
$422$		0			0
$423$	2.45804	+	7.56507i	0.119514	+	0.367826i
$424$		0			0
$425$	11.8006	+	5.25395i	0.572412	+	0.254854i
$426$		0			0
$427$	−0.753654	−	2.31951i	−0.0364719	−	0.112249i
$428$		0			0
$429$	9.04870	−	6.57426i	0.436875	−	0.317408i
$430$		0			0
$431$	−27.6903	−	20.1182i	−1.33379	−	0.969058i	−0.999648	−	0.0265371i	$-0.991552\pi$
$431$	−27.6903	−	20.1182i	−1.33379	−	0.969058i	−0.334146	−	0.942521i	$-0.608448\pi$
$432$		0			0
$433$	−7.29864	−	5.30277i	−0.350750	−	0.254835i	0.398434	−	0.917197i	$-0.369554\pi$
$433$	−7.29864	−	5.30277i	−0.350750	−	0.254835i	−0.749184	+	0.662362i	$0.769554\pi$
$434$		0			0
$435$	17.4913	+	3.71790i	0.838645	+	0.178259i
$436$		0			0
$437$	9.96795	−	30.6782i	0.476832	−	1.46754i
$438$		0			0
$439$	5.87343	+	18.0766i	0.280324	+	0.862747i	0.987761	+	0.155972i	$0.0498509\pi$
$439$	5.87343	+	18.0766i	0.280324	+	0.862747i	−0.707438	+	0.706776i	$0.750149\pi$
$440$		0			0
$441$	−2.08237	+	6.40889i	−0.0991607	+	0.305185i
$442$		0			0
$443$	−1.68124			−0.0798779			−0.0399390	−	0.999202i	$-0.512716\pi$
$443$	−1.68124			−0.0798779			−0.0399390	+	0.999202i	$0.512716\pi$
$444$		0			0
$445$	24.0551	−	10.7100i	1.14032	−	0.507703i
$446$		0			0
$447$	−1.53791	+	1.11736i	−0.0727408	+	0.0528493i
$448$		0			0
$449$	−14.1334			−0.666997			−0.333499	−	0.942751i	$-0.608229\pi$
$449$	−14.1334			−0.666997			−0.333499	+	0.942751i	$0.608229\pi$
$450$		0			0
$451$	−10.4702			−0.493024
$452$		0			0
$453$	3.72384	−	2.70553i	0.174961	−	0.127117i
$454$		0			0
$455$	6.84421	+	1.45478i	0.320862	+	0.0682012i
$456$		0			0
$457$	−24.8188			−1.16097			−0.580487	−	0.814269i	$-0.697138\pi$
$457$	−24.8188			−1.16097			−0.580487	+	0.814269i	$0.697138\pi$
$458$		0			0
$459$	0.798335	−	2.45702i	0.0372631	−	0.114684i
$460$		0			0
$461$	−10.4642	−	32.2054i	−0.487365	−	1.49996i	−0.828526	−	0.559951i	$-0.810820\pi$
$461$	−10.4642	−	32.2054i	−0.487365	−	1.49996i	0.341161	−	0.940005i	$-0.389180\pi$
$462$		0			0
$463$	0.846018	−	2.60378i	0.0393178	−	0.121008i	−0.929471	−	0.368895i	$-0.879736\pi$
$463$	0.846018	−	2.60378i	0.0393178	−	0.121008i	0.968789	+	0.247887i	$0.0797362\pi$
$464$		0			0
$465$	1.14192	+	10.8646i	0.0529553	+	0.503836i
$466$		0			0
$467$	28.0538	+	20.3823i	1.29817	+	0.943179i	0.999936	−	0.0113121i	$-0.00360084\pi$
$467$	28.0538	+	20.3823i	1.29817	+	0.943179i	0.298239	+	0.954491i	$0.403601\pi$
$468$		0			0
$469$	−5.92754	−	4.30661i	−0.273708	−	0.198861i
$470$		0			0
$471$	−3.20432	+	2.32808i	−0.147647	+	0.107272i
$472$		0			0
$473$	1.15815	+	3.56441i	0.0532516	+	0.163892i
$474$		0			0
$475$	−22.2139	−	9.89029i	−1.01925	−	0.453797i
$476$		0			0
$477$	0.410722	+	1.26407i	0.0188057	+	0.0578779i
$478$		0			0
$479$	−4.41726	+	3.20933i	−0.201830	+	0.146638i	−0.684109	−	0.729379i	$-0.739809\pi$
$479$	−4.41726	+	3.20933i	−0.201830	+	0.146638i	0.482280	+	0.876017i	$0.339809\pi$
$480$		0			0
$481$	36.8347	+	26.7620i	1.67952	+	1.22024i
$482$		0			0
$483$	−2.74297	−	1.99289i	−0.124810	−	0.0906794i
$484$		0			0
$485$	−11.0718	−	12.2965i	−0.502745	−	0.558354i
$486$		0			0
$487$	−7.29352	+	22.4471i	−0.330501	+	1.01718i	0.638395	+	0.769709i	$0.279599\pi$
$487$	−7.29352	+	22.4471i	−0.330501	+	1.01718i	−0.968896	+	0.247468i	$0.920401\pi$
$488$		0			0
$489$	6.48302	+	19.9527i	0.293172	+	0.902291i
$490$		0			0
$491$	4.07930	−	12.5548i	0.184096	−	0.566590i	−0.815835	−	0.578284i	$-0.803722\pi$
$491$	4.07930	−	12.5548i	0.184096	−	0.566590i	0.999932	+	0.0116942i	$0.00372245\pi$
$492$		0			0
$493$	−20.6603			−0.930492
$494$		0			0
$495$	0.427051	+	4.06312i	0.0191945	+	0.182624i
$496$		0			0
$497$	−2.22063	+	1.61338i	−0.0996089	+	0.0723701i
$498$		0			0
$499$	25.5183			1.14235			0.571177	−	0.820827i	$-0.306487\pi$
$499$	25.5183			1.14235			0.571177	+	0.820827i	$0.306487\pi$
$500$		0			0
$501$	−18.0373			−0.805848
$502$		0			0
$503$	23.6136	−	17.1563i	1.05288	−	0.764960i	0.0801193	−	0.996785i	$-0.474470\pi$
$503$	23.6136	−	17.1563i	1.05288	−	0.764960i	0.972757	+	0.231826i	$0.0744699\pi$
$504$		0			0
$505$	−3.06101	−	29.1236i	−0.136213	−	1.29598i
$506$		0			0
$507$	24.4746			1.08695
$508$		0			0
$509$	8.87540	−	27.3157i	0.393395	−	1.21075i	−0.536809	−	0.843704i	$-0.680370\pi$
$509$	8.87540	−	27.3157i	0.393395	−	1.21075i	0.930204	−	0.367042i	$-0.119630\pi$
$510$		0			0
$511$	0.549808	+	1.69213i	0.0243221	+	0.0748556i
$512$		0			0
$513$	−1.50282	+	4.62521i	−0.0663513	+	0.204208i
$514$		0			0
$515$	−16.5036	−	18.3291i	−0.727235	−	0.807676i
$516$		0			0
$517$	11.7578	+	8.54251i	0.517105	+	0.375699i
$518$		0			0
$519$	−20.7088	−	15.0458i	−0.909017	−	0.660439i
$520$		0			0
$521$	−27.6502	+	20.0890i	−1.21138	+	0.880116i	−0.995355	−	0.0962724i	$-0.969308\pi$
$521$	−27.6502	+	20.0890i	−1.21138	+	0.880116i	−0.216021	+	0.976389i	$0.569308\pi$
$522$		0			0
$523$	4.65282	+	14.3199i	0.203454	+	0.626166i	0.999773	+	0.0212901i	$0.00677737\pi$
$523$	4.65282	+	14.3199i	0.203454	+	0.626166i	−0.796320	+	0.604876i	$0.793223\pi$
$524$		0			0
$525$	−1.71020	+	1.89937i	−0.0746392	+	0.0828952i
$526$		0			0
$527$	−3.90033	−	12.0040i	−0.169901	−	0.522901i
$528$		0			0
$529$	−16.9847	+	12.3401i	−0.738466	+	0.536527i
$530$		0			0
$531$	8.16519	+	5.93236i	0.354339	+	0.257442i
$532$		0			0
$533$	−28.3806	−	20.6197i	−1.22930	−	0.893139i
$534$		0			0
$535$	1.88875	+	17.9703i	0.0816580	+	0.776924i
$536$		0			0
$537$	−2.60140	+	8.00630i	−0.112259	+	0.345497i
$538$		0			0
$539$	3.80469	+	11.7096i	0.163879	+	0.504369i
$540$		0			0
$541$	13.5497	−	41.7016i	0.582546	−	1.79289i	−0.0263633	−	0.999652i	$-0.508393\pi$
$541$	13.5497	−	41.7016i	0.582546	−	1.79289i	0.608909	−	0.793240i	$-0.291607\pi$
$542$		0			0
$543$	−20.0676			−0.861184
$544$		0			0
$545$	−24.7660	−	5.26418i	−1.06086	−	0.225493i
$546$		0			0
$547$	8.39025	−	6.09587i	0.358741	−	0.260641i	−0.393786	−	0.919202i	$-0.628835\pi$
$547$	8.39025	−	6.09587i	0.358741	−	0.260641i	0.752527	+	0.658562i	$0.228835\pi$
$548$		0			0
$549$	4.77116			0.203628
$550$		0			0
$551$	38.8919			1.65685
$552$		0			0
$553$	−0.545875	+	0.396601i	−0.0232130	+	0.0168652i
$554$		0			0
$555$	−15.1931	+	6.76440i	−0.644911	+	0.287133i
$556$		0			0
$557$	−24.3856			−1.03325			−0.516625	−	0.856212i	$-0.672812\pi$
$557$	−24.3856			−1.03325			−0.516625	+	0.856212i	$0.672812\pi$
$558$		0			0
$559$	−3.88036	+	11.9425i	−0.164122	+	0.505114i
$560$		0			0
$561$	−1.45863	−	4.48920i	−0.0615834	−	0.189534i
$562$		0			0
$563$	−8.88197	+	27.3359i	−0.374330	+	1.15207i	0.569599	+	0.821923i	$0.307098\pi$
$563$	−8.88197	+	27.3359i	−0.374330	+	1.15207i	−0.943929	+	0.330147i	$0.892902\pi$
$564$		0			0
$565$	−8.24270	−	1.75204i	−0.346773	−	0.0737089i
$566$		0			0
$567$	0.413545	+	0.300458i	0.0173673	+	0.0126181i
$568$		0			0
$569$	−14.1571	−	10.2858i	−0.593498	−	0.431202i	0.250067	−	0.968229i	$-0.419547\pi$
$569$	−14.1571	−	10.2858i	−0.593498	−	0.431202i	−0.843565	+	0.537027i	$0.819547\pi$
$570$		0			0
$571$	15.5117	−	11.2699i	0.649146	−	0.471632i	−0.213834	−	0.976870i	$-0.568595\pi$
$571$	15.5117	−	11.2699i	0.649146	−	0.471632i	0.862980	+	0.505238i	$0.168595\pi$
$572$		0			0
$573$	1.19381	+	3.67416i	0.0498720	+	0.153490i
$574$		0			0
$575$	16.5820	+	28.7209i	0.691519	+	1.19775i
$576$		0			0
$577$	2.86928	+	8.83072i	0.119450	+	0.367628i	0.992849	−	0.119377i	$-0.0380896\pi$
$577$	2.86928	+	8.83072i	0.119450	+	0.367628i	−0.873400	+	0.487004i	$0.838090\pi$
$578$		0			0
$579$	−8.65040	+	6.28489i	−0.359498	+	0.261191i
$580$		0			0
$581$	0.377398	+	0.274195i	0.0156571	+	0.0113755i
$582$		0			0
$583$	1.96464	+	1.42740i	0.0813672	+	0.0591167i
$584$		0			0
$585$	−6.84421	+	11.8545i	−0.282973	+	0.490124i
$586$		0			0
$587$	−5.47068	+	16.8370i	−0.225799	+	0.694938i	0.772411	+	0.635123i	$0.219051\pi$
$587$	−5.47068	+	16.8370i	−0.225799	+	0.694938i	−0.998210	+	0.0598141i	$0.980949\pi$
$588$		0			0
$589$	7.34216	+	22.5969i	0.302529	+	0.931087i
$590$		0			0
$591$	−1.28688	+	3.96060i	−0.0529350	+	0.162917i
$592$		0			0
$593$	25.8975			1.06348			0.531742	−	0.846907i	$-0.321538\pi$
$593$	25.8975			1.06348			0.531742	+	0.846907i	$0.321538\pi$
$594$		0			0
$595$	1.47647	−	2.55731i	0.0605292	−	0.104840i
$596$		0			0
$597$	22.3261	−	16.2208i	0.913745	−	0.663875i
$598$		0			0
$599$	10.0259			0.409646			0.204823	−	0.978799i	$-0.434338\pi$
$599$	10.0259			0.409646			0.204823	+	0.978799i	$0.434338\pi$
$600$		0			0
$601$	−1.69846			−0.0692818			−0.0346409	−	0.999400i	$-0.511029\pi$
$601$	−1.69846			−0.0692818			−0.0346409	+	0.999400i	$0.511029\pi$
$602$		0			0
$603$	11.5960	−	8.42500i	0.472226	−	0.343092i
$604$		0			0
$605$	−11.4637	−	12.7317i	−0.466064	−	0.517617i
$606$		0			0
$607$	−13.3043			−0.540005			−0.270002	−	0.962860i	$-0.587024\pi$
$607$	−13.3043			−0.540005			−0.270002	+	0.962860i	$0.587024\pi$
$608$		0			0
$609$	1.26323	−	3.88781i	0.0511885	−	0.157542i
$610$		0			0
$611$	15.0473	+	46.3107i	0.608747	+	1.87353i
$612$		0			0
$613$	−2.17187	+	6.68433i	−0.0877210	+	0.269977i	−0.985288	−	0.170900i	$-0.945333\pi$
$613$	−2.17187	+	6.68433i	−0.0877210	+	0.269977i	0.897567	+	0.440877i	$0.145333\pi$
$614$		0			0
$615$	11.7061	−	5.21188i	0.472034	−	0.210163i
$616$		0			0
$617$	8.04174	+	5.84267i	0.323748	+	0.235217i	0.737773	−	0.675049i	$-0.235877\pi$
$617$	8.04174	+	5.84267i	0.323748	+	0.235217i	−0.414025	+	0.910266i	$0.635877\pi$
$618$		0			0
$619$	20.2765	+	14.7317i	0.814980	+	0.592118i	0.915270	−	0.402840i	$-0.131977\pi$
$619$	20.2765	+	14.7317i	0.814980	+	0.592118i	−0.100290	+	0.994958i	$0.531977\pi$
$620$		0			0
$621$	5.36606	−	3.89867i	0.215333	−	0.156448i
$622$		0			0
$623$	−1.86011	−	5.72484i	−0.0745239	−	0.229361i
$624$		0			0
$625$	22.8386	−	10.1684i	0.913545	−	0.406737i
$626$		0			0
$627$	2.74580	+	8.45069i	0.109656	+	0.337488i
$628$		0			0
$629$	15.5450	−	11.2941i	0.619821	−	0.450326i
$630$		0			0
$631$	−8.20614	−	5.96211i	−0.326681	−	0.237348i	0.412340	−	0.911030i	$-0.364712\pi$
$631$	−8.20614	−	5.96211i	−0.326681	−	0.237348i	−0.739021	+	0.673682i	$0.764712\pi$
$632$		0			0
$633$	−1.56536	−	1.13730i	−0.0622174	−	0.0452036i
$634$		0			0
$635$	−8.52221	+	3.79433i	−0.338194	+	0.150574i
$636$		0			0
$637$	−12.7476	+	39.2330i	−0.505077	+	1.55447i
$638$		0			0
$639$	−1.65934	−	5.10692i	−0.0656425	−	0.202027i
$640$		0			0
$641$	4.53631	−	13.9613i	0.179174	−	0.551440i	−0.820626	−	0.571466i	$-0.806375\pi$
$641$	4.53631	−	13.9613i	0.179174	−	0.551440i	0.999799	+	0.0200262i	$0.00637497\pi$
$642$		0			0
$643$	8.52311			0.336119			0.168059	−	0.985777i	$-0.446250\pi$
$643$	8.52311			0.336119			0.168059	+	0.985777i	$0.446250\pi$
$644$		0			0
$645$	−3.06914	−	3.40863i	−0.120847	−	0.134215i
$646$		0			0
$647$	−30.9405	+	22.4796i	−1.21640	+	0.883764i	−0.995796	−	0.0916006i	$-0.970802\pi$
$647$	−30.9405	+	22.4796i	−1.21640	+	0.883764i	−0.220600	+	0.975364i	$0.570802\pi$
$648$		0			0
$649$	18.4403			0.723846
$650$		0			0
$651$	2.49736			0.0978794
$652$		0			0
$653$	6.79344	−	4.93572i	0.265848	−	0.193150i	−0.446873	−	0.894597i	$-0.647463\pi$
$653$	6.79344	−	4.93572i	0.265848	−	0.193150i	0.712721	+	0.701448i	$0.247463\pi$
$654$		0			0
$655$	−16.5366	+	28.6423i	−0.646140	+	1.11915i
$656$		0			0
$657$	−3.48067			−0.135794
$658$		0			0
$659$	−14.5953	+	44.9197i	−0.568552	+	1.74982i	0.0886012	+	0.996067i	$0.471760\pi$
$659$	−14.5953	+	44.9197i	−0.568552	+	1.74982i	−0.657153	+	0.753757i	$0.728240\pi$
$660$		0			0
$661$	−7.82323	−	24.0774i	−0.304288	−	0.936503i	−0.979942	−	0.199284i	$-0.936138\pi$
$661$	−7.82323	−	24.0774i	−0.304288	−	0.936503i	0.675654	−	0.737219i	$-0.263862\pi$
$662$		0			0
$663$	4.88712	−	15.0410i	0.189800	−	0.584145i
$664$		0			0
$665$	−2.77937	+	4.81401i	−0.107779	+	0.186679i
$666$		0			0
$667$	−42.9130	−	31.1781i	−1.66160	−	1.20722i
$668$		0			0
$669$	14.8921	+	10.8198i	0.575763	+	0.418316i
$670$		0			0
$671$	7.05248	−	5.12392i	0.272258	−	0.197807i
$672$		0			0
$673$	−4.89943	−	15.0789i	−0.188859	−	0.581248i	0.811135	−	0.584860i	$-0.198850\pi$
$673$	−4.89943	−	15.0789i	−0.188859	−	0.581248i	−0.999993	+	0.00361149i	$0.998850\pi$
$674$		0			0
$675$	−2.50000	−	4.33013i	−0.0962250	−	0.166667i
$676$		0			0
$677$	10.6671	+	32.8299i	0.409970	+	1.26176i	0.916674	+	0.399637i	$0.130864\pi$
$677$	10.6671	+	32.8299i	0.409970	+	1.26176i	−0.506704	+	0.862120i	$0.669136\pi$
$678$		0			0
$679$	−3.06017	+	2.22334i	−0.117439	+	0.0853241i
$680$		0			0
$681$	15.5813	+	11.3205i	0.597078	+	0.433803i
$682$		0			0
$683$	−20.2580	−	14.7183i	−0.775152	−	0.563181i	0.128368	−	0.991727i	$-0.459026\pi$
$683$	−20.2580	−	14.7183i	−0.775152	−	0.563181i	−0.903520	+	0.428546i	$0.859026\pi$
$684$		0			0
$685$	2.68355	+	0.570406i	0.102533	+	0.0217941i
$686$		0			0
$687$	−8.17094	+	25.1476i	−0.311741	+	0.959439i
$688$		0			0
$689$	2.51430	+	7.73821i	0.0957870	+	0.294802i
$690$		0			0
$691$	−8.49860	+	26.1560i	−0.323302	+	0.995021i	0.648899	+	0.760874i	$0.275230\pi$
$691$	−8.49860	+	26.1560i	−0.323302	+	0.995021i	−0.972201	+	0.234147i	$0.924770\pi$
$692$		0			0
$693$	0.933955			0.0354780
$694$		0			0
$695$	18.5598	−	8.26336i	0.704014	−	0.313447i
$696$		0			0
$697$	−11.9772	+	8.70196i	−0.453670	+	0.329610i
$698$		0			0
$699$	−15.7608			−0.596130
$700$		0			0
$701$	−5.38643			−0.203443			−0.101721	−	0.994813i	$-0.532435\pi$
$701$	−5.38643			−0.203443			−0.101721	+	0.994813i	$0.532435\pi$
$702$		0			0
$703$	−29.2627	+	21.2606i	−1.10366	+	0.801858i
$704$		0			0
$705$	−17.3979	−	3.69803i	−0.655242	−	0.139276i
$706$		0			0
$707$	−6.69440			−0.251769
$708$		0			0
$709$	6.33013	−	19.4821i	0.237733	−	0.731667i	−0.759014	−	0.651074i	$-0.774319\pi$
$709$	6.33013	−	19.4821i	0.237733	−	0.731667i	0.996747	−	0.0805929i	$-0.0256814\pi$
$710$		0			0
$711$	−0.407899	−	1.25538i	−0.0152974	−	0.0470805i
$712$		0			0
$713$	10.0137	−	30.8191i	0.375018	−	1.15419i
$714$		0			0
$715$	2.61426	+	24.8730i	0.0977676	+	0.930197i
$716$		0			0
$717$	−14.8578	−	10.7948i	−0.554875	−	0.403141i
$718$		0			0
$719$	27.6232	+	20.0694i	1.03017	+	0.748464i	0.968343	−	0.249623i	$-0.0803066\pi$
$719$	27.6232	+	20.0694i	1.03017	+	0.748464i	0.0618291	+	0.998087i	$0.480307\pi$
$720$		0			0
$721$	−4.56148	+	3.31411i	−0.169878	+	0.123424i
$722$		0			0
$723$	−7.81517	−	24.0526i	−0.290649	−	0.894526i
$724$		0			0
$725$	−26.7556	+	29.7151i	−0.993677	+	1.10359i
$726$		0			0
$727$	−9.46652	−	29.1350i	−0.351094	−	1.08056i	−0.958240	−	0.285966i	$-0.907686\pi$
$727$	−9.46652	−	29.1350i	−0.351094	−	1.08056i	0.607146	−	0.794590i	$-0.292314\pi$
$728$		0			0
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$		0			0
$731$	4.28728	+	3.11489i	0.158571	+	0.115208i
$732$		0			0
$733$	−29.9046	−	21.7270i	−1.10455	−	0.802505i	−0.122756	−	0.992437i	$-0.539173\pi$
$733$	−29.9046	−	21.7270i	−1.10455	−	0.802505i	−0.981797	+	0.189932i	$0.939173\pi$
$734$		0			0
$735$	−10.0826	−	11.1979i	−0.371902	−	0.413039i
$736$		0			0
$737$	8.09270	−	24.9068i	0.298099	−	0.917453i
$738$		0			0
$739$	10.2391	+	31.5127i	0.376652	+	1.15922i	0.942357	+	0.334608i	$0.108604\pi$
$739$	10.2391	+	31.5127i	0.376652	+	1.15922i	−0.565706	+	0.824607i	$0.691396\pi$
$740$		0			0
$741$	−9.19975	+	28.3139i	−0.337961	+	1.04014i
$742$		0			0
$743$	18.9855			0.696512			0.348256	−	0.937400i	$-0.386774\pi$
$743$	18.9855			0.696512			0.348256	+	0.937400i	$0.386774\pi$
$744$		0			0
$745$	−0.444318	−	4.22740i	−0.0162786	−	0.154880i
$746$		0			0
$747$	−0.738301	+	0.536407i	−0.0270130	+	0.0196261i
$748$		0			0
$749$	4.13068			0.150932
$750$		0			0
$751$	−7.10651			−0.259320			−0.129660	−	0.991559i	$-0.541389\pi$
$751$	−7.10651			−0.259320			−0.129660	+	0.991559i	$0.541389\pi$
$752$		0			0
$753$	14.1009	−	10.2449i	0.513866	−	0.373345i
$754$		0			0
$755$	1.07585	+	10.2361i	0.0391543	+	0.372528i
$756$		0			0
$757$	−8.77180			−0.318817			−0.159408	−	0.987213i	$-0.550959\pi$
$757$	−8.77180			−0.318817			−0.159408	+	0.987213i	$0.550959\pi$
$758$		0			0
$759$	3.74490	−	11.5256i	0.135931	−	0.418354i
$760$		0			0
$761$	6.40922	+	19.7255i	0.232334	+	0.715050i	0.997464	+	0.0711744i	$0.0226747\pi$
$761$	6.40922	+	19.7255i	0.232334	+	0.715050i	−0.765130	+	0.643876i	$0.777325\pi$
$762$		0			0
$763$	−1.78861	+	5.50477i	−0.0647520	+	0.199286i
$764$		0			0
$765$	3.86544	+	4.29300i	0.139755	+	0.155214i
$766$		0			0
$767$	49.9844	+	36.3158i	1.80483	+	1.31129i
$768$		0			0
$769$	11.0923	+	8.05906i	0.400000	+	0.290617i	0.769541	−	0.638597i	$-0.220485\pi$
$769$	11.0923	+	8.05906i	0.400000	+	0.290617i	−0.369541	+	0.929214i	$0.620485\pi$
$770$		0			0
$771$	23.9606	−	17.4084i	0.862920	−	0.626948i
$772$		0			0
$773$	−8.30485	−	25.5597i	−0.298705	−	0.919318i	−0.981952	−	0.189131i	$-0.939433\pi$
$773$	−8.30485	−	25.5597i	−0.298705	−	0.919318i	0.683247	−	0.730187i	$-0.260567\pi$
$774$		0			0
$775$	−22.3160	−	9.93572i	−0.801614	−	0.356902i
$776$		0			0
$777$	1.17484	+	3.61579i	0.0421472	+	0.129716i
$778$		0			0
$779$	22.5465	−	16.3810i	0.807812	−	0.586910i
$780$		0			0
$781$	−7.93727	−	5.76676i	−0.284018	−	0.206351i
$782$		0			0
$783$	6.46980	+	4.70059i	0.231212	+	0.167985i
$784$		0			0
$785$	−0.925760	−	8.80802i	−0.0330418	−	0.314372i
$786$		0			0
$787$	−0.449069	+	1.38209i	−0.0160076	+	0.0492662i	−0.958741	−	0.284280i	$-0.908245\pi$
$787$	−0.449069	+	1.38209i	−0.0160076	+	0.0492662i	0.942734	+	0.333546i	$0.108245\pi$
$788$		0			0
$789$	−5.17140	−	15.9159i	−0.184107	−	0.566623i
$790$		0			0
$791$	−0.595290	+	1.83211i	−0.0211661	+	0.0651424i
$792$		0			0
$793$	29.2074			1.03718
$794$		0			0
$795$	−2.90707	−	0.617916i	−0.103103	−	0.0219152i
$796$		0			0
$797$	−39.9915	+	29.0555i	−1.41657	+	1.02920i	−0.424247	+	0.905547i	$0.639461\pi$
$797$	−39.9915	+	29.0555i	−1.41657	+	1.02920i	−0.992325	+	0.123653i	$0.960539\pi$
$798$		0			0
$799$	20.5499			0.727003
$800$		0			0
$801$	11.7758			0.416078
$802$		0			0
$803$	−5.14494	+	3.73802i	−0.181561	+	0.131912i
$804$		0			0
$805$	6.92594	−	3.08363i	0.244107	−	0.108684i
$806$		0			0
$807$	−12.7897			−0.450218
$808$		0			0
$809$	−13.2003	+	40.6264i	−0.464099	+	1.42835i	0.396014	+	0.918244i	$0.370393\pi$
$809$	−13.2003	+	40.6264i	−0.464099	+	1.42835i	−0.860113	+	0.510104i	$0.829607\pi$
$810$		0			0
$811$	−10.7851	−	33.1931i	−0.378715	−	1.16557i	−0.940938	−	0.338580i	$-0.890054\pi$
$811$	−10.7851	−	33.1931i	−0.378715	−	1.16557i	0.562222	−	0.826986i	$-0.309946\pi$
$812$		0			0
$813$	8.86025	−	27.2690i	0.310743	−	0.956367i
$814$		0			0
$815$	−45.8864	−	9.75346i	−1.60733	−	0.341649i
$816$		0			0
$817$	−8.07057	−	5.86361i	−0.282354	−	0.205142i
$818$		0			0
$819$	2.53158	+	1.83930i	0.0884605	+	0.0642703i
$820$		0			0
$821$	0.210535	−	0.152962i	0.00734771	−	0.00533843i	−0.584105	−	0.811678i	$-0.698555\pi$
$821$	0.210535	−	0.152962i	0.00734771	−	0.00533843i	0.591453	+	0.806339i	$0.298555\pi$
$822$		0			0
$823$	−7.14135	−	21.9788i	−0.248932	−	0.766133i	−0.994965	−	0.100224i	$-0.968044\pi$
$823$	−7.14135	−	21.9788i	−0.248932	−	0.766133i	0.746033	−	0.665909i	$-0.231956\pi$
$824$		0			0
$825$	−8.34565	−	3.71572i	−0.290558	−	0.129365i
$826$		0			0
$827$	1.96890	+	6.05965i	0.0684654	+	0.210715i	0.979435	−	0.201758i	$-0.0646653\pi$
$827$	1.96890	+	6.05965i	0.0684654	+	0.210715i	−0.910970	+	0.412472i	$0.864665\pi$
$828$		0			0
$829$	20.3689	−	14.7989i	0.707442	−	0.513987i	−0.174905	−	0.984585i	$-0.555962\pi$
$829$	20.3689	−	14.7989i	0.707442	−	0.513987i	0.882347	+	0.470599i	$0.155962\pi$
$830$		0			0
$831$	−4.31799	−	3.13720i	−0.149789	−	0.108828i
$832$		0			0
$833$	14.0844	+	10.2329i	0.487994	+	0.354548i
$834$		0			0
$835$	20.1663	−	34.9291i	0.697885	−	1.20877i
$836$		0			0
$837$	−1.50973	+	4.64646i	−0.0521838	+	0.160605i
$838$		0			0
$839$	−12.5553	−	38.6411i	−0.433455	−	1.33404i	−0.894661	−	0.446745i	$-0.852583\pi$
$839$	−12.5553	−	38.6411i	−0.433455	−	1.33404i	0.461206	−	0.887293i	$-0.347417\pi$
$840$		0			0
$841$	10.8013	−	33.2431i	0.372460	−	1.14631i
$842$		0			0
$843$	−6.42725			−0.221366
$844$		0			0
$845$	−27.3634	+	47.3948i	−0.941329	+	1.63043i
$846$		0			0
$847$	−3.16848	+	2.30203i	−0.108870	+	0.0790988i
$848$		0			0
$849$	−10.4636			−0.359111
$850$		0			0
$851$	49.3320			1.69108
$852$		0			0
$853$	−21.1437	+	15.3618i	−0.723947	+	0.525979i	−0.887643	−	0.460532i	$-0.847659\pi$
$853$	−21.1437	+	15.3618i	−0.723947	+	0.525979i	0.163696	+	0.986511i	$0.447659\pi$
$854$		0			0
$855$	−7.27648	−	8.08135i	−0.248850	−	0.276376i
$856$		0			0
$857$	30.0649			1.02700			0.513498	−	0.858091i	$-0.328349\pi$
$857$	30.0649			1.02700			0.513498	+	0.858091i	$0.328349\pi$
$858$		0			0
$859$	3.09348	−	9.52077i	0.105548	−	0.324844i	−0.884310	−	0.466899i	$-0.845371\pi$
$859$	3.09348	−	9.52077i	0.105548	−	0.324844i	0.989859	+	0.142055i	$0.0453710\pi$
$860$		0			0
$861$	−0.905199	−	2.78591i	−0.0308491	−	0.0949437i
$862$		0			0
$863$	3.85892	−	11.8765i	0.131359	−	0.404282i	−0.863647	−	0.504097i	$-0.831825\pi$
$863$	3.85892	−	11.8765i	0.131359	−	0.404282i	0.995006	+	0.0998156i	$0.0318253\pi$
$864$		0			0
$865$	52.2893	−	23.2807i	1.77789	−	0.791568i
$866$		0			0
$867$	8.35367	+	6.06930i	0.283705	+	0.206124i
$868$		0			0
$869$	−1.95114	−	1.41758i	−0.0661878	−	0.0480882i
$870$		0			0
$871$	70.9867	−	51.5749i	2.40529	−	1.74755i
$872$		0			0
$873$	−2.28668	−	7.03767i	−0.0773923	−	0.238189i
$874$		0			0
$875$	−1.76605	−	5.43534i	−0.0597034	−	0.183748i
$876$		0			0
$877$	10.8569	+	33.4142i	0.366612	+	1.12832i	0.948965	+	0.315381i	$0.102132\pi$
$877$	10.8569	+	33.4142i	0.366612	+	1.12832i	−0.582353	+	0.812936i	$0.697868\pi$
$878$		0			0
$879$	−3.75191	+	2.72592i	−0.126549	+	0.0919430i
$880$		0			0
$881$	5.56613	+	4.04403i	0.187528	+	0.136247i	0.677588	−	0.735442i	$-0.263025\pi$
$881$	5.56613	+	4.04403i	0.187528	+	0.136247i	−0.490060	+	0.871688i	$0.663025\pi$
$882$		0			0
$883$	15.1596	+	11.0141i	0.510161	+	0.370654i	0.812885	−	0.582424i	$-0.197896\pi$
$883$	15.1596	+	11.0141i	0.510161	+	0.370654i	−0.302723	+	0.953078i	$0.597896\pi$
$884$		0			0
$885$	−20.6169	+	9.17924i	−0.693030	+	0.308557i
$886$		0			0
$887$	9.20647	−	28.3346i	0.309123	−	0.951383i	−0.668983	−	0.743277i	$-0.733270\pi$
$887$	9.20647	−	28.3346i	0.309123	−	0.951383i	0.978106	−	0.208106i	$-0.0667298\pi$
$888$		0			0
$889$	0.659000	+	2.02819i	0.0221021	+	0.0680234i
$890$		0			0
$891$	−0.564602	+	1.73767i	−0.0189149	+	0.0582140i
$892$		0			0
$893$	−38.6841			−1.29451
$894$		0			0
$895$	−12.5957	−	13.9889i	−0.421027	−	0.467598i
$896$		0			0
$897$	32.8491	−	23.8663i	1.09680	−	0.796872i
$898$		0			0
$899$	39.0705			1.30308
$900$		0			0
$901$	3.43375			0.114395
$902$		0			0
$903$	−0.848290	+	0.616319i	−0.0282293	+	0.0205098i
$904$		0			0
$905$	22.4363	−	38.8608i	0.745807	−	1.29178i
$906$		0			0
$907$	−14.5112			−0.481838			−0.240919	−	0.970545i	$-0.577449\pi$
$907$	−14.5112			−0.481838			−0.240919	+	0.970545i	$0.577449\pi$
$908$		0			0
$909$	4.04695	−	12.4552i	0.134229	−	0.413114i
$910$		0			0
$911$	10.4651	+	32.2084i	0.346726	+	1.06711i	0.960653	+	0.277750i	$0.0895886\pi$
$911$	10.4651	+	32.2084i	0.346726	+	1.06711i	−0.613928	+	0.789362i	$0.710411\pi$
$912$		0			0
$913$	−0.515250	+	1.58578i	−0.0170523	+	0.0524816i
$914$		0			0
$915$	−5.33432	+	9.23931i	−0.176347	+	0.305442i
$916$		0			0
$917$	6.11668	+	4.44402i	0.201990	+	0.146755i
$918$		0			0
$919$	25.5931	+	18.5945i	0.844239	+	0.613376i	0.923552	−	0.383474i	$-0.125272\pi$
$919$	25.5931	+	18.5945i	0.844239	+	0.613376i	−0.0793122	+	0.996850i	$0.525272\pi$
$920$		0			0
$921$	−14.2116	+	10.3253i	−0.468286	+	0.340230i
$922$		0			0
$923$	−10.1579	−	31.2628i	−0.334351	−	1.02903i
$924$		0			0
$925$	3.88719	−	36.9841i	0.127810	−	1.21603i
$926$		0			0
$927$	−3.40851	−	10.4903i	−0.111950	−	0.344547i
$928$		0			0
$929$	−35.8848	+	26.0718i	−1.17734	+	0.855389i	−0.991869	−	0.127261i	$-0.959382\pi$
$929$	−35.8848	+	26.0718i	−1.17734	+	0.855389i	−0.185472	+	0.982649i	$0.559382\pi$
$930$		0			0
$931$	−26.5130	−	19.2629i	−0.868930	−	0.631315i
$932$		0			0
$933$	−14.8575	−	10.7946i	−0.486413	−	0.353400i
$934$		0			0
$935$	10.3241	+	2.19446i	0.337634	+	0.0717664i
$936$		0			0
$937$	−8.12561	+	25.0081i	−0.265452	+	0.816978i	0.726137	+	0.687550i	$0.241314\pi$
$937$	−8.12561	+	25.0081i	−0.265452	+	0.816978i	−0.991589	+	0.129427i	$0.958686\pi$
$938$		0			0
$939$	−7.83472	−	24.1128i	−0.255676	−	0.786891i
$940$		0			0
$941$	4.60549	−	14.1742i	0.150135	−	0.462067i	−0.847501	−	0.530794i	$-0.821894\pi$
$941$	4.60549	−	14.1742i	0.150135	−	0.462067i	0.997636	+	0.0687270i	$0.0218937\pi$
$942$		0			0
$943$	−38.0097			−1.23776
$944$		0			0
$945$	−1.04419	+	0.464905i	−0.0339676	+	0.0151234i
$946$		0			0
$947$	−8.53769	+	6.20300i	−0.277438	+	0.201570i	−0.717799	−	0.696250i	$-0.754850\pi$
$947$	−8.53769	+	6.20300i	−0.277438	+	0.201570i	0.440361	+	0.897821i	$0.354850\pi$
$948$		0			0
$949$	−21.3074			−0.691668
$950$		0			0
$951$	−23.6513			−0.766946
$952$		0			0
$953$	21.7177	−	15.7788i	0.703504	−	0.511126i	−0.177568	−	0.984109i	$-0.556823\pi$
$953$	21.7177	−	15.7788i	0.703504	−	0.511126i	0.881071	+	0.472983i	$0.156823\pi$
$954$		0			0
$955$	−8.44969	−	1.79604i	−0.273426	−	0.0581184i
$956$		0			0
$957$	14.6115			0.472321
$958$		0			0
$959$	0.193806	−	0.596475i	0.00625834	−	0.0192612i
$960$		0			0
$961$	−2.20364	−	6.78209i	−0.0710850	−	0.218777i
$962$		0			0
$963$	−2.49711	+	7.68533i	−0.0804684	+	0.247656i
$964$		0			0
$965$	−2.49918	−	23.7782i	−0.0804516	−	0.765446i
$966$		0			0
$967$	−40.9100	−	29.7228i	−1.31558	−	0.955822i	−0.999976	−	0.00692933i	$-0.997794\pi$
$967$	−40.9100	−	29.7228i	−1.31558	−	0.955822i	−0.315600	−	0.948892i	$-0.602206\pi$
$968$		0			0
$969$	10.1645	+	7.38494i	0.326531	+	0.237238i
$970$		0			0
$971$	−21.3040	+	15.4782i	−0.683676	+	0.496720i	−0.874575	−	0.484890i	$-0.838860\pi$
$971$	−21.3040	+	15.4782i	−0.683676	+	0.496720i	0.190899	+	0.981610i	$0.438860\pi$
$972$		0			0
$973$	−1.43518	−	4.41703i	−0.0460098	−	0.141604i
$974$		0			0
$975$	−15.3041	−	26.5075i	−0.490124	−	0.848920i
$976$		0			0
$977$	−1.96818	−	6.05744i	−0.0629677	−	0.193795i	0.914624	−	0.404306i	$-0.132487\pi$
$977$	−1.96818	−	6.05744i	−0.0629677	−	0.193795i	−0.977591	+	0.210512i	$0.932487\pi$
$978$		0			0
$979$	17.4064	−	12.6465i	0.556311	−	0.404184i
$980$		0			0
$981$	−9.16062	−	6.65558i	−0.292476	−	0.212496i
$982$		0			0
$983$	45.9752	+	33.4030i	1.46638	+	1.06539i	0.981642	+	0.190731i	$0.0610858\pi$
$983$	45.9752	+	33.4030i	1.46638	+	1.06539i	0.484740	+	0.874658i	$0.338914\pi$
$984$		0			0
$985$	−6.23089	−	6.92011i	−0.198533	−	0.220493i
$986$		0			0
$987$	−1.25648	+	3.86704i	−0.0399941	+	0.123089i
$988$		0			0
$989$	4.20438	+	12.9397i	0.133691	+	0.411460i
$990$		0			0
$991$	4.11746	−	12.6722i	0.130795	−	0.402547i	−0.864117	−	0.503291i	$-0.832122\pi$
$991$	4.11746	−	12.6722i	0.130795	−	0.402547i	0.994912	+	0.100744i	$0.0321224\pi$
$992$		0			0
$993$	32.9027			1.04413
$994$		0			0
$995$	6.45022	+	61.3697i	0.204486	+	1.94555i
$996$		0			0
$997$	−20.7058	+	15.0437i	−0.655761	+	0.476438i	−0.865229	−	0.501378i	$-0.832827\pi$
$997$	−20.7058	+	15.0437i	−0.655761	+	0.476438i	0.209468	+	0.977815i	$0.432827\pi$
$998$		0			0
$999$	−7.43757			−0.235314

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.2.m.a.181.1	yes	8
3.2	odd	2		900.2.n.a.181.2		8
5.2	odd	4		1500.2.o.a.349.3		16
5.3	odd	4		1500.2.o.a.349.2		16
5.4	even	2		1500.2.m.b.901.2		8
25.2	odd	20		7500.2.d.d.1249.2		8
25.3	odd	20		1500.2.o.a.649.4		16
25.4	even	10		1500.2.m.b.601.2		8
25.11	even	5		7500.2.a.g.1.2		4
25.14	even	10		7500.2.a.d.1.3		4
25.21	even	5	inner	300.2.m.a.121.1	✓	8
25.22	odd	20		1500.2.o.a.649.1		16
25.23	odd	20		7500.2.d.d.1249.7		8
75.71	odd	10		900.2.n.a.721.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.m.a.121.1	✓	8	25.21	even	5	inner
300.2.m.a.181.1	yes	8	1.1	even	1	trivial
900.2.n.a.181.2		8	3.2	odd	2
900.2.n.a.721.2		8	75.71	odd	10
1500.2.m.b.601.2		8	25.4	even	10
1500.2.m.b.901.2		8	5.4	even	2
1500.2.o.a.349.2		16	5.3	odd	4
1500.2.o.a.349.3		16	5.2	odd	4
1500.2.o.a.649.1		16	25.22	odd	20
1500.2.o.a.649.4		16	25.3	odd	20
7500.2.a.d.1.3		4	25.14	even	10
7500.2.a.g.1.2		4	25.11	even	5
7500.2.d.d.1249.2		8	25.2	odd	20
7500.2.d.d.1249.7		8	25.23	odd	20

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	300.m (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 + 0.587785i) q^{3} +(-0.233733 - 2.22382i) q^{5} -0.511170 q^{7} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(-0.809017 + 0.587785i) q^{3} +(-0.233733 - 2.22382i) q^{5} -0.511170 q^{7} +(0.309017 - 0.951057i) q^{9} +(-0.564602 - 1.73767i) q^{11} +(1.89169 - 5.82203i) q^{13} +(1.49622 + 1.66172i) q^{15} +(-2.09007 - 1.51852i) q^{17} +(3.93444 + 2.85854i) q^{19} +(0.413545 - 0.300458i) q^{21} +(-2.04965 - 6.30818i) q^{23} +(-4.89074 + 1.03956i) q^{25} +(0.309017 + 0.951057i) q^{27} +(6.46980 - 4.70059i) q^{29} +(3.95252 + 2.87167i) q^{31} +(1.47815 + 1.07394i) q^{33} +(0.119477 + 1.13675i) q^{35} +(-2.29833 + 7.07355i) q^{37} +(1.89169 + 5.82203i) q^{39} +(1.77084 - 5.45007i) q^{41} -2.05126 q^{43} +(-2.18720 - 0.464905i) q^{45} +(-6.43523 + 4.67547i) q^{47} -6.73870 q^{49} +2.58347 q^{51} +(-1.07528 + 0.781240i) q^{53} +(-3.73229 + 1.66172i) q^{55} -4.86324 q^{57} +(-3.11882 + 9.59875i) q^{59} +(1.47437 + 4.53764i) q^{61} +(-0.157960 + 0.486152i) q^{63} +(-13.3893 - 2.84598i) q^{65} +(11.5960 + 8.42500i) q^{67} +(5.36606 + 3.89867i) q^{69} +(4.34421 - 3.15625i) q^{71} +(-1.07559 - 3.31031i) q^{73} +(3.34565 - 3.71572i) q^{75} +(0.288608 + 0.888244i) q^{77} +(1.06789 - 0.775869i) q^{79} +(-0.809017 - 0.587785i) q^{81} +(-0.738301 - 0.536407i) q^{83} +(-2.88840 + 5.00286i) q^{85} +(-2.47124 + 7.60571i) q^{87} +(3.63893 + 11.1995i) q^{89} +(-0.966977 + 2.97605i) q^{91} -4.88558 q^{93} +(5.43727 - 9.41762i) q^{95} +(5.98660 - 4.34952i) q^{97} -1.82709 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{3} + 5 q^{5} - 8 q^{7} - 2 q^{9}+O(q^{10}) \) 8 * q - 2 * q^3 + 5 * q^5 - 8 * q^7 - 2 * q^9	\( 8 q - 2 q^{3} + 5 q^{5} - 8 q^{7} - 2 q^{9} - 2 q^{11} - 5 q^{15} + 7 q^{17} + 5 q^{19} - 3 q^{21} + 7 q^{23} + 5 q^{25} - 2 q^{27} + 27 q^{29} - 3 q^{31} + 3 q^{33} + 20 q^{35} - 9 q^{37} + 20 q^{41} - 68 q^{43} - 5 q^{45} - 7 q^{47} - 8 q^{49} - 8 q^{51} - 11 q^{53} + 5 q^{55} - 10 q^{57} + 2 q^{59} - 14 q^{61} + 7 q^{63} - 35 q^{65} + 28 q^{67} + 2 q^{69} - 15 q^{71} + 6 q^{73} + 5 q^{75} + 17 q^{77} + 24 q^{79} - 2 q^{81} + 2 q^{83} + 10 q^{85} - 23 q^{87} + 5 q^{91} - 18 q^{93} + 5 q^{95} + 34 q^{97} - 2 q^{99}+O(q^{100}) \) 8 * q - 2 * q^3 + 5 * q^5 - 8 * q^7 - 2 * q^9 - 2 * q^11 - 5 * q^15 + 7 * q^17 + 5 * q^19 - 3 * q^21 + 7 * q^23 + 5 * q^25 - 2 * q^27 + 27 * q^29 - 3 * q^31 + 3 * q^33 + 20 * q^35 - 9 * q^37 + 20 * q^41 - 68 * q^43 - 5 * q^45 - 7 * q^47 - 8 * q^49 - 8 * q^51 - 11 * q^53 + 5 * q^55 - 10 * q^57 + 2 * q^59 - 14 * q^61 + 7 * q^63 - 35 * q^65 + 28 * q^67 + 2 * q^69 - 15 * q^71 + 6 * q^73 + 5 * q^75 + 17 * q^77 + 24 * q^79 - 2 * q^81 + 2 * q^83 + 10 * q^85 - 23 * q^87 + 5 * q^91 - 18 * q^93 + 5 * q^95 + 34 * q^97 - 2 * q^99

Introduction

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