LMFDB - Embedded newform 900.2.n.a.181.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [900,2,Mod(181,900)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(900, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("900.181");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	900.n (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:	$7.18653618192$
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:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 5 $
Twist minimal:	no (minimal twist has level 300)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			181.2
Root			$0.669131 - 0.743145i$ of defining polynomial
Character	$\chi$	$=$	900.181
Dual form			900.2.n.a.721.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.233733 + 2.22382i) q^{5} -0.511170 q^{7} +O(q^{10})$	$q+(0.233733 + 2.22382i) q^{5} -0.511170 q^{7} +(0.564602 + 1.73767i) q^{11} +(1.89169 - 5.82203i) q^{13} +(2.09007 + 1.51852i) q^{17} +(3.93444 + 2.85854i) q^{19} +(2.04965 + 6.30818i) q^{23} +(-4.89074 + 1.03956i) q^{25} +(-6.46980 + 4.70059i) q^{29} +(3.95252 + 2.87167i) q^{31} +(-0.119477 - 1.13675i) q^{35} +(-2.29833 + 7.07355i) q^{37} +(-1.77084 + 5.45007i) q^{41} -2.05126 q^{43} +(6.43523 - 4.67547i) q^{47} -6.73870 q^{49} +(1.07528 - 0.781240i) q^{53} +(-3.73229 + 1.66172i) q^{55} +(3.11882 - 9.59875i) q^{59} +(1.47437 + 4.53764i) q^{61} +(13.3893 + 2.84598i) q^{65} +(11.5960 + 8.42500i) q^{67} +(-4.34421 + 3.15625i) q^{71} +(-1.07559 - 3.31031i) q^{73} +(-0.288608 - 0.888244i) q^{77} +(1.06789 - 0.775869i) q^{79} +(0.738301 + 0.536407i) q^{83} +(-2.88840 + 5.00286i) q^{85} +(-3.63893 - 11.1995i) q^{89} +(-0.966977 + 2.97605i) q^{91} +(-5.43727 + 9.41762i) q^{95} +(5.98660 - 4.34952i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 5 q^{5} - 8 q^{7}+O(q^{10}) $ 8 * q - 5 * q^5 - 8 * q^7	$ 8 q - 5 q^{5} - 8 q^{7} + 2 q^{11} - 7 q^{17} + 5 q^{19} - 7 q^{23} + 5 q^{25} - 27 q^{29} - 3 q^{31} - 20 q^{35} - 9 q^{37} - 20 q^{41} - 68 q^{43} + 7 q^{47} - 8 q^{49} + 11 q^{53} + 5 q^{55} - 2 q^{59} - 14 q^{61} + 35 q^{65} + 28 q^{67} + 15 q^{71} + 6 q^{73} - 17 q^{77} + 24 q^{79} - 2 q^{83} + 10 q^{85} + 5 q^{91} - 5 q^{95} + 34 q^{97}+O(q^{100}) $ 8 * q - 5 * q^5 - 8 * q^7 + 2 * q^11 - 7 * q^17 + 5 * q^19 - 7 * q^23 + 5 * q^25 - 27 * q^29 - 3 * q^31 - 20 * q^35 - 9 * q^37 - 20 * q^41 - 68 * q^43 + 7 * q^47 - 8 * q^49 + 11 * q^53 + 5 * q^55 - 2 * q^59 - 14 * q^61 + 35 * q^65 + 28 * q^67 + 15 * q^71 + 6 * q^73 - 17 * q^77 + 24 * q^79 - 2 * q^83 + 10 * q^85 + 5 * q^91 - 5 * q^95 + 34 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$.

$n$	$101$	$451$	$577$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{5}\right)$

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			0
$3$		0			0
$4$		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			0
$10$		0			0
$11$	0.564602	+	1.73767i	0.170234	+	0.523926i	0.999384	−	0.0351002i	$-0.0111750\pi$
$11$	0.564602	+	1.73767i	0.170234	+	0.523926i	−0.829150	+	0.559026i	$0.811175\pi$
$12$		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
$15$		0			0
$16$		0			0
$17$	2.09007	+	1.51852i	0.506916	+	0.368296i	0.811652	−	0.584141i	$-0.198568\pi$
$17$	2.09007	+	1.51852i	0.506916	+	0.368296i	−0.304736	+	0.952437i	$0.598568\pi$
$18$		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			0
$22$		0			0
$23$	2.04965	+	6.30818i	0.427382	+	1.31535i	0.900695	+	0.434453i	$0.143058\pi$
$23$	2.04965	+	6.30818i	0.427382	+	1.31535i	−0.473312	+	0.880895i	$0.656942\pi$
$24$		0			0
$25$	−4.89074	+	1.03956i	−0.978148	+	0.207912i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−6.46980	+	4.70059i	−1.20141	+	0.872877i	−0.994423	−	0.105466i	$-0.966366\pi$
$29$	−6.46980	+	4.70059i	−1.20141	+	0.872877i	−0.206989	+	0.978343i	$0.566366\pi$
$30$		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
$33$		0			0
$34$		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
$39$		0			0
$40$		0			0
$41$	−1.77084	+	5.45007i	−0.276558	+	0.851158i	0.712245	+	0.701931i	$0.247679\pi$
$41$	−1.77084	+	5.45007i	−0.276558	+	0.851158i	−0.988803	+	0.149227i	$0.952321\pi$
$42$		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
$45$		0			0
$46$		0			0
$47$	6.43523	−	4.67547i	0.938675	−	0.681987i	−0.00942623	−	0.999956i	$-0.503001\pi$
$47$	6.43523	−	4.67547i	0.938675	−	0.681987i	0.948101	+	0.317968i	$0.103001\pi$
$48$		0			0
$49$	−6.73870			−0.962672
$50$		0			0
$51$		0			0
$52$		0			0
$53$	1.07528	−	0.781240i	0.147702	−	0.107312i	−0.511480	−	0.859295i	$-0.670903\pi$
$53$	1.07528	−	0.781240i	0.147702	−	0.107312i	0.659182	+	0.751983i	$0.270903\pi$
$54$		0			0
$55$	−3.73229	+	1.66172i	−0.503262	+	0.224067i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	3.11882	−	9.59875i	0.406036	−	1.24965i	−0.513991	−	0.857796i	$-0.671833\pi$
$59$	3.11882	−	9.59875i	0.406036	−	1.24965i	0.920027	−	0.391855i	$-0.128167\pi$
$60$		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			0
$64$		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
$69$		0			0
$70$		0			0
$71$	−4.34421	+	3.15625i	−0.515563	+	0.374578i	−0.814930	−	0.579560i	$-0.803225\pi$
$71$	−4.34421	+	3.15625i	−0.515563	+	0.374578i	0.299367	+	0.954138i	$0.403225\pi$
$72$		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
$75$		0			0
$76$		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			0
$82$		0			0
$83$	0.738301	+	0.536407i	0.0810391	+	0.0588783i	0.627567	−	0.778562i	$-0.284051\pi$
$83$	0.738301	+	0.536407i	0.0810391	+	0.0588783i	−0.546528	+	0.837441i	$0.684051\pi$
$84$		0			0
$85$	−2.88840	+	5.00286i	−0.313291	+	0.542636i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−3.63893	−	11.1995i	−0.385726	−	1.18714i	−0.935952	−	0.352127i	$-0.885459\pi$
$89$	−3.63893	−	11.1995i	−0.385726	−	1.18714i	0.550226	−	0.835016i	$-0.314541\pi$
$90$		0			0
$91$	−0.966977	+	2.97605i	−0.101367	+	0.311975i
$92$		0			0
$93$		0			0
$94$		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
$99$		0			0
$100$		0			0
$101$	−13.0962			−1.30312			−0.651561	−	0.758596i	$-0.725886\pi$
$101$	−13.0962			−1.30312			−0.651561	+	0.758596i	$0.725886\pi$
$102$		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			0
$106$		0			0
$107$	8.08083			0.781203			0.390602	−	0.920560i	$-0.372267\pi$
$107$	8.08083			0.781203			0.390602	+	0.920560i	$0.372267\pi$
$108$		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
$111$		0			0
$112$		0			0
$113$	−1.16456	+	3.58415i	−0.109553	+	0.337169i	−0.990772	−	0.135539i	$-0.956723\pi$
$113$	−1.16456	+	3.58415i	−0.109553	+	0.337169i	0.881219	+	0.472708i	$0.156723\pi$
$114$		0			0
$115$	−13.5492	+	6.03249i	−1.26347	+	0.562532i
$116$		0			0
$117$		0			0
$118$		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
$123$		0			0
$124$		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
$129$		0			0
$130$		0			0
$131$	11.9660	+	8.69382i	1.04548	+	0.759583i	0.971347	−	0.237666i	$-0.0763823\pi$
$131$	11.9660	+	8.69382i	1.04548	+	0.759583i	0.0741292	+	0.997249i	$0.476382\pi$
$132$		0			0
$133$	−2.01117	−	1.46120i	−0.174391	−	0.126702i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	0.379143	−	1.16688i	0.0323923	−	0.0996934i	−0.933553	−	0.358439i	$-0.883309\pi$
$137$	0.379143	−	1.16688i	0.0323923	−	0.0996934i	0.965946	+	0.258746i	$0.0833091\pi$
$138$		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
$141$		0			0
$142$		0			0
$143$	11.1848			0.935320
$144$		0			0
$145$	−11.9655	−	13.2890i	−0.993677	−	1.10359i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−1.90097			−0.155733			−0.0778666	−	0.996964i	$-0.524811\pi$
$149$	−1.90097			−0.155733			−0.0778666	+	0.996964i	$0.524811\pi$
$150$		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
$153$		0			0
$154$		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			0
$160$		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
$165$		0			0
$166$		0			0
$167$	−14.5925	−	10.6021i	−1.12920	−	0.820413i	−0.143624	−	0.989632i	$-0.545875\pi$
$167$	−14.5925	−	10.6021i	−1.12920	−	0.820413i	−0.985578	+	0.169219i	$0.945875\pi$
$168$		0			0
$169$	−19.8003	−	14.3858i	−1.52310	−	1.10660i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−7.91007	−	24.3447i	−0.601391	−	1.85089i	−0.519917	−	0.854217i	$-0.674037\pi$
$173$	−7.91007	−	24.3447i	−0.601391	−	1.85089i	−0.0814747	−	0.996675i	$-0.525963\pi$
$174$		0			0
$175$	2.50000	−	0.531391i	0.188982	−	0.0401694i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−6.81056	+	4.94816i	−0.509045	+	0.369843i	−0.812461	−	0.583015i	$-0.801873\pi$
$179$	−6.81056	+	4.94816i	−0.509045	+	0.369843i	0.303416	+	0.952858i	$0.401873\pi$
$180$		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
$183$		0			0
$184$		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			0
$190$		0			0
$191$	−1.19381	+	3.67416i	−0.0863808	+	0.265853i	−0.984912	−	0.173057i	$-0.944635\pi$
$191$	−1.19381	+	3.67416i	−0.0863808	+	0.265853i	0.898531	+	0.438910i	$0.144635\pi$
$192$		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
$195$		0			0
$196$		0			0
$197$	−3.36909	+	2.44778i	−0.240037	+	0.174397i	−0.701300	−	0.712866i	$-0.747397\pi$
$197$	−3.36909	+	2.44778i	−0.240037	+	0.174397i	0.461263	+	0.887264i	$0.347397\pi$
$198$		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
$201$		0			0
$202$		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
$207$		0			0
$208$		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
$213$		0			0
$214$		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
$219$		0			0
$220$		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			0
$226$		0			0
$227$	5.95154	+	18.3170i	0.395018	+	1.21574i	0.928948	+	0.370211i	$0.120714\pi$
$227$	5.95154	+	18.3170i	0.395018	+	1.21574i	−0.533930	+	0.845529i	$0.679286\pi$
$228$		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			0
$232$		0			0
$233$	−12.7508	−	9.26399i	−0.835332	−	0.606904i	0.0857308	−	0.996318i	$-0.472677\pi$
$233$	−12.7508	−	9.26399i	−0.835332	−	0.606904i	−0.921063	+	0.389414i	$0.872677\pi$
$234$		0			0
$235$	11.9015	+	13.2180i	0.776370	+	0.862246i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−5.67518	−	17.4664i	−0.367097	−	1.12981i	−0.948658	−	0.316305i	$-0.897558\pi$
$239$	−5.67518	−	17.4664i	−0.367097	−	1.12981i	0.581561	−	0.813503i	$-0.302442\pi$
$240$		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
$243$		0			0
$244$		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			0
$250$		0			0
$251$	17.4297			1.10015			0.550076	−	0.835115i	$-0.314599\pi$
$251$	17.4297			1.10015			0.550076	+	0.835115i	$0.314599\pi$
$252$		0			0
$253$	−9.80428	+	7.12323i	−0.616390	+	0.447834i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	29.6169			1.84745			0.923727	−	0.383052i	$-0.125127\pi$
$257$	29.6169			1.84745			0.923727	+	0.383052i	$0.125127\pi$
$258$		0			0
$259$	1.17484	−	3.61579i	0.0730010	−	0.224674i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	5.17140	−	15.9159i	0.318882	−	0.981419i	−0.655244	−	0.755417i	$-0.727434\pi$
$263$	5.17140	−	15.9159i	0.318882	−	0.981419i	0.974127	−	0.226002i	$-0.0725656\pi$
$264$		0			0
$265$	1.98866	+	2.20864i	0.122163	+	0.135675i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−10.3471	−	7.51758i	−0.630872	−	0.458355i	0.225830	−	0.974167i	$-0.427491\pi$
$269$	−10.3471	−	7.51758i	−0.630872	−	0.458355i	−0.856702	+	0.515811i	$0.827491\pi$
$270$		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			0
$274$		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
$279$		0			0
$280$		0			0
$281$	−5.19975	−	3.77784i	−0.310191	−	0.225367i	0.421787	−	0.906695i	$-0.361403\pi$
$281$	−5.19975	−	3.77784i	−0.310191	−	0.225367i	−0.731979	+	0.681328i	$0.761403\pi$
$282$		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
$285$		0			0
$286$		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
$291$		0			0
$292$		0			0
$293$	−4.63761			−0.270932			−0.135466	−	0.990782i	$-0.543253\pi$
$293$	−4.63761			−0.270932			−0.135466	+	0.990782i	$0.543253\pi$
$294$		0			0
$295$	22.0749	+	4.69216i	1.28525	+	0.273188i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	40.6038			2.34818
$300$		0			0
$301$	1.04854			0.0604371
$302$		0			0
$303$		0			0
$304$		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
$309$		0			0
$310$		0			0
$311$	−5.67507	−	17.4661i	−0.321803	−	0.990409i	−0.972863	−	0.231382i	$-0.925675\pi$
$311$	−5.67507	−	17.4661i	−0.321803	−	0.990409i	0.651059	−	0.759027i	$-0.274325\pi$
$312$		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
$315$		0			0
$316$		0			0
$317$	−19.1343	−	13.9019i	−1.07469	−	0.780808i	−0.0979401	−	0.995192i	$-0.531225\pi$
$317$	−19.1343	−	13.9019i	−1.07469	−	0.780808i	−0.976749	+	0.214385i	$0.931225\pi$
$318$		0			0
$319$	−11.8209	−	8.58840i	−0.661844	−	0.480858i
$320$		0			0
$321$		0			0
$322$		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
$327$		0			0
$328$		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
$333$		0			0
$334$		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
$339$		0			0
$340$		0			0
$341$	−2.75841	+	8.48951i	−0.149376	+	0.459733i
$342$		0			0
$343$	7.02282			0.379197
$344$		0			0
$345$		0			0
$346$		0			0
$347$	2.70449	−	1.96493i	0.145185	−	0.105483i	−0.512822	−	0.858495i	$-0.671400\pi$
$347$	2.70449	−	1.96493i	0.145185	−	0.105483i	0.658007	+	0.753012i	$0.271400\pi$
$348$		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
$351$		0			0
$352$		0			0
$353$	16.4521	−	11.9531i	0.875656	−	0.636201i	−0.0564426	−	0.998406i	$-0.517976\pi$
$353$	16.4521	−	11.9531i	0.875656	−	0.636201i	0.932099	+	0.362204i	$0.117976\pi$
$354$		0			0
$355$	−8.03432	−	8.92301i	−0.426417	−	0.473584i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−11.4959	+	35.3806i	−0.606729	+	1.86732i	−0.122289	+	0.992494i	$0.539024\pi$
$359$	−11.4959	+	35.3806i	−0.606729	+	1.86732i	−0.484439	+	0.874825i	$0.660976\pi$
$360$		0			0
$361$	1.43727	+	4.42345i	0.0756456	+	0.232813i
$362$		0			0
$363$		0			0
$364$		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
$369$		0			0
$370$		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
$375$		0			0
$376$		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
$381$		0			0
$382$		0			0
$383$	−1.99777	−	1.45146i	−0.102081	−	0.0741663i	0.535574	−	0.844488i	$-0.320095\pi$
$383$	−1.99777	−	1.45146i	−0.102081	−	0.0741663i	−0.637655	+	0.770322i	$0.720095\pi$
$384$		0			0
$385$	1.90784	−	0.849423i	0.0972323	−	0.0432906i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−4.50293	−	13.8586i	−0.228307	−	0.702658i	−0.997939	−	0.0641697i	$-0.979560\pi$
$389$	−4.50293	−	13.8586i	−0.228307	−	0.702658i	0.769632	−	0.638488i	$-0.220440\pi$
$390$		0			0
$391$	−5.29521	+	16.2970i	−0.267790	+	0.824174i
$392$		0			0
$393$		0			0
$394$		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
$399$		0			0
$400$		0			0
$401$	−6.50743			−0.324966			−0.162483	−	0.986711i	$-0.551950\pi$
$401$	−6.50743			−0.324966			−0.162483	+	0.986711i	$0.551950\pi$
$402$		0			0
$403$	24.1959	−	17.5794i	1.20528	−	0.875690i
$404$		0			0
$405$		0			0
$406$		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			0
$412$		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
$417$		0			0
$418$		0			0
$419$	15.0550	+	10.9381i	0.735483	+	0.534360i	0.891293	−	0.453427i	$-0.149799\pi$
$419$	15.0550	+	10.9381i	0.735483	+	0.534360i	−0.155810	+	0.987787i	$0.549799\pi$
$420$		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
$423$		0			0
$424$		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
$429$		0			0
$430$		0			0
$431$	27.6903	+	20.1182i	1.33379	+	0.969058i	0.999648	+	0.0265371i	$0.00844800\pi$
$431$	27.6903	+	20.1182i	1.33379	+	0.969058i	0.334146	+	0.942521i	$0.391552\pi$
$432$		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
$435$		0			0
$436$		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
$441$		0			0
$442$		0			0
$443$	1.68124			0.0798779			0.0399390	−	0.999202i	$-0.487284\pi$
$443$	1.68124			0.0798779			0.0399390	+	0.999202i	$0.487284\pi$
$444$		0			0
$445$	24.0551	−	10.7100i	1.14032	−	0.507703i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	14.1334			0.666997			0.333499	−	0.942751i	$-0.391771\pi$
$449$	14.1334			0.666997			0.333499	+	0.942751i	$0.391771\pi$
$450$		0			0
$451$	−10.4702			−0.493024
$452$		0			0
$453$		0			0
$454$		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			0
$460$		0			0
$461$	10.4642	+	32.2054i	0.487365	+	1.49996i	0.828526	+	0.559951i	$0.189180\pi$
$461$	10.4642	+	32.2054i	0.487365	+	1.49996i	−0.341161	+	0.940005i	$0.610820\pi$
$462$		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
$465$		0			0
$466$		0			0
$467$	−28.0538	−	20.3823i	−1.29817	−	0.943179i	−0.298239	−	0.954491i	$-0.596399\pi$
$467$	−28.0538	−	20.3823i	−1.29817	−	0.943179i	−0.999936	+	0.0113121i	$0.996399\pi$
$468$		0			0
$469$	−5.92754	−	4.30661i	−0.273708	−	0.198861i
$470$		0			0
$471$		0			0
$472$		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			0
$478$		0			0
$479$	4.41726	−	3.20933i	0.201830	−	0.146638i	−0.482280	−	0.876017i	$-0.660191\pi$
$479$	4.41726	−	3.20933i	0.201830	−	0.146638i	0.684109	+	0.729379i	$0.260191\pi$
$480$		0			0
$481$	36.8347	+	26.7620i	1.67952	+	1.22024i
$482$		0			0
$483$		0			0
$484$		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
$489$		0			0
$490$		0			0
$491$	−4.07930	+	12.5548i	−0.184096	+	0.566590i	−0.999932	−	0.0116942i	$-0.996278\pi$
$491$	−4.07930	+	12.5548i	−0.184096	+	0.566590i	0.815835	+	0.578284i	$0.196278\pi$
$492$		0			0
$493$	−20.6603			−0.930492
$494$		0			0
$495$		0			0
$496$		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
$501$		0			0
$502$		0			0
$503$	−23.6136	+	17.1563i	−1.05288	+	0.764960i	−0.972757	−	0.231826i	$-0.925530\pi$
$503$	−23.6136	+	17.1563i	−1.05288	+	0.764960i	−0.0801193	+	0.996785i	$0.525530\pi$
$504$		0			0
$505$	−3.06101	−	29.1236i	−0.136213	−	1.29598i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−8.87540	+	27.3157i	−0.393395	+	1.21075i	0.536809	+	0.843704i	$0.319630\pi$
$509$	−8.87540	+	27.3157i	−0.393395	+	1.21075i	−0.930204	+	0.367042i	$0.880370\pi$
$510$		0			0
$511$	0.549808	+	1.69213i	0.0243221	+	0.0748556i
$512$		0			0
$513$		0			0
$514$		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
$519$		0			0
$520$		0			0
$521$	27.6502	−	20.0890i	1.21138	−	0.880116i	0.216021	−	0.976389i	$-0.430692\pi$
$521$	27.6502	−	20.0890i	1.21138	−	0.880116i	0.995355	+	0.0962724i	$0.0306920\pi$
$522$		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
$525$		0			0
$526$		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
$531$		0			0
$532$		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
$537$		0			0
$538$		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
$543$		0			0
$544$		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
$549$		0			0
$550$		0			0
$551$	−38.8919			−1.65685
$552$		0			0
$553$	−0.545875	+	0.396601i	−0.0232130	+	0.0168652i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	24.3856			1.03325			0.516625	−	0.856212i	$-0.327188\pi$
$557$	24.3856			1.03325			0.516625	+	0.856212i	$0.327188\pi$
$558$		0			0
$559$	−3.88036	+	11.9425i	−0.164122	+	0.505114i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	8.88197	−	27.3359i	0.374330	−	1.15207i	−0.569599	−	0.821923i	$-0.692902\pi$
$563$	8.88197	−	27.3359i	0.374330	−	1.15207i	0.943929	−	0.330147i	$-0.107098\pi$
$564$		0			0
$565$	−8.24270	−	1.75204i	−0.346773	−	0.0737089i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	14.1571	+	10.2858i	0.593498	+	0.431202i	0.843565	−	0.537027i	$-0.180453\pi$
$569$	14.1571	+	10.2858i	0.593498	+	0.431202i	−0.250067	+	0.968229i	$0.580453\pi$
$570$		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
$573$		0			0
$574$		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
$579$		0			0
$580$		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
$585$		0			0
$586$		0			0
$587$	5.47068	−	16.8370i	0.225799	−	0.694938i	−0.772411	−	0.635123i	$-0.780949\pi$
$587$	5.47068	−	16.8370i	0.225799	−	0.694938i	0.998210	−	0.0598141i	$-0.0190508\pi$
$588$		0			0
$589$	7.34216	+	22.5969i	0.302529	+	0.931087i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−25.8975			−1.06348			−0.531742	−	0.846907i	$-0.678462\pi$
$593$	−25.8975			−1.06348			−0.531742	+	0.846907i	$0.678462\pi$
$594$		0			0
$595$	1.47647	−	2.55731i	0.0605292	−	0.104840i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−10.0259			−0.409646			−0.204823	−	0.978799i	$-0.565662\pi$
$599$	−10.0259			−0.409646			−0.204823	+	0.978799i	$0.565662\pi$
$600$		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
$603$		0			0
$604$		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
$609$		0			0
$610$		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
$615$		0			0
$616$		0			0
$617$	−8.04174	−	5.84267i	−0.323748	−	0.235217i	0.414025	−	0.910266i	$-0.364123\pi$
$617$	−8.04174	−	5.84267i	−0.323748	−	0.235217i	−0.737773	+	0.675049i	$0.764123\pi$
$618$		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
$621$		0			0
$622$		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
$627$		0			0
$628$		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
$633$		0			0
$634$		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
$639$		0			0
$640$		0			0
$641$	−4.53631	+	13.9613i	−0.179174	+	0.551440i	−0.999799	−	0.0200262i	$-0.993625\pi$
$641$	−4.53631	+	13.9613i	−0.179174	+	0.551440i	0.820626	+	0.571466i	$0.193625\pi$
$642$		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
$645$		0			0
$646$		0			0
$647$	30.9405	−	22.4796i	1.21640	−	0.883764i	0.220600	−	0.975364i	$-0.429198\pi$
$647$	30.9405	−	22.4796i	1.21640	−	0.883764i	0.995796	+	0.0916006i	$0.0291983\pi$
$648$		0			0
$649$	18.4403			0.723846
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−6.79344	+	4.93572i	−0.265848	+	0.193150i	−0.712721	−	0.701448i	$-0.752537\pi$
$653$	−6.79344	+	4.93572i	−0.265848	+	0.193150i	0.446873	+	0.894597i	$0.352537\pi$
$654$		0			0
$655$	−16.5366	+	28.6423i	−0.646140	+	1.11915i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	14.5953	−	44.9197i	0.568552	−	1.74982i	−0.0886012	−	0.996067i	$-0.528240\pi$
$659$	14.5953	−	44.9197i	0.568552	−	1.74982i	0.657153	−	0.753757i	$-0.271760\pi$
$660$		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
$663$		0			0
$664$		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
$669$		0			0
$670$		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
$675$		0			0
$676$		0			0
$677$	−10.6671	−	32.8299i	−0.409970	−	1.26176i	−0.916674	−	0.399637i	$-0.869136\pi$
$677$	−10.6671	−	32.8299i	−0.409970	−	1.26176i	0.506704	−	0.862120i	$-0.330864\pi$
$678$		0			0
$679$	−3.06017	+	2.22334i	−0.117439	+	0.0853241i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	20.2580	+	14.7183i	0.775152	+	0.563181i	0.903520	−	0.428546i	$-0.140974\pi$
$683$	20.2580	+	14.7183i	0.775152	+	0.563181i	−0.128368	+	0.991727i	$0.540974\pi$
$684$		0			0
$685$	2.68355	+	0.570406i	0.102533	+	0.0217941i
$686$		0			0
$687$		0			0
$688$		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			0
$694$		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
$699$		0			0
$700$		0			0
$701$	5.38643			0.203443			0.101721	−	0.994813i	$-0.467565\pi$
$701$	5.38643			0.203443			0.101721	+	0.994813i	$0.467565\pi$
$702$		0			0
$703$	−29.2627	+	21.2606i	−1.10366	+	0.801858i
$704$		0			0
$705$		0			0
$706$		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			0
$712$		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
$717$		0			0
$718$		0			0
$719$	−27.6232	−	20.0694i	−1.03017	−	0.748464i	−0.0618291	−	0.998087i	$-0.519693\pi$
$719$	−27.6232	−	20.0694i	−1.03017	−	0.748464i	−0.968343	+	0.249623i	$0.919693\pi$
$720$		0			0
$721$	−4.56148	+	3.31411i	−0.169878	+	0.123424i
$722$		0			0
$723$		0			0
$724$		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			0
$730$		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
$735$		0			0
$736$		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
$741$		0			0
$742$		0			0
$743$	−18.9855			−0.696512			−0.348256	−	0.937400i	$-0.613226\pi$
$743$	−18.9855			−0.696512			−0.348256	+	0.937400i	$0.613226\pi$
$744$		0			0
$745$	−0.444318	−	4.22740i	−0.0162786	−	0.154880i
$746$		0			0
$747$		0			0
$748$		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
$753$		0			0
$754$		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
$759$		0			0
$760$		0			0
$761$	−6.40922	−	19.7255i	−0.232334	−	0.715050i	−0.997464	−	0.0711744i	$-0.977325\pi$
$761$	−6.40922	−	19.7255i	−0.232334	−	0.715050i	0.765130	−	0.643876i	$-0.222675\pi$
$762$		0			0
$763$	−1.78861	+	5.50477i	−0.0647520	+	0.199286i
$764$		0			0
$765$		0			0
$766$		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
$771$		0			0
$772$		0			0
$773$	8.30485	+	25.5597i	0.298705	+	0.919318i	0.981952	+	0.189131i	$0.0605671\pi$
$773$	8.30485	+	25.5597i	0.298705	+	0.919318i	−0.683247	+	0.730187i	$0.739433\pi$
$774$		0			0
$775$	−22.3160	−	9.93572i	−0.801614	−	0.356902i
$776$		0			0
$777$		0			0
$778$		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
$783$		0			0
$784$		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
$789$		0			0
$790$		0			0
$791$	0.595290	−	1.83211i	0.0211661	−	0.0651424i
$792$		0			0
$793$	29.2074			1.03718
$794$		0			0
$795$		0			0
$796$		0			0
$797$	39.9915	−	29.0555i	1.41657	−	1.02920i	0.424247	−	0.905547i	$-0.360539\pi$
$797$	39.9915	−	29.0555i	1.41657	−	1.02920i	0.992325	−	0.123653i	$-0.0394611\pi$
$798$		0			0
$799$	20.5499			0.727003
$800$		0			0
$801$		0			0
$802$		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
$807$		0			0
$808$		0			0
$809$	13.2003	−	40.6264i	0.464099	−	1.42835i	−0.396014	−	0.918244i	$-0.629607\pi$
$809$	13.2003	−	40.6264i	0.464099	−	1.42835i	0.860113	−	0.510104i	$-0.170393\pi$
$810$		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
$813$		0			0
$814$		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
$819$		0			0
$820$		0			0
$821$	−0.210535	+	0.152962i	−0.00734771	+	0.00533843i	−0.591453	−	0.806339i	$-0.701445\pi$
$821$	−0.210535	+	0.152962i	−0.00734771	+	0.00533843i	0.584105	+	0.811678i	$0.301445\pi$
$822$		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
$825$		0			0
$826$		0			0
$827$	−1.96890	−	6.05965i	−0.0684654	−	0.210715i	0.910970	−	0.412472i	$-0.135335\pi$
$827$	−1.96890	−	6.05965i	−0.0684654	−	0.210715i	−0.979435	+	0.201758i	$0.935335\pi$
$828$		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
$831$		0			0
$832$		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
$837$		0			0
$838$		0			0
$839$	12.5553	+	38.6411i	0.433455	+	1.33404i	0.894661	+	0.446745i	$0.147417\pi$
$839$	12.5553	+	38.6411i	0.433455	+	1.33404i	−0.461206	+	0.887293i	$0.652583\pi$
$840$		0			0
$841$	10.8013	−	33.2431i	0.372460	−	1.14631i
$842$		0			0
$843$		0			0
$844$		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
$849$		0			0
$850$		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
$855$		0			0
$856$		0			0
$857$	−30.0649			−1.02700			−0.513498	−	0.858091i	$-0.671651\pi$
$857$	−30.0649			−1.02700			−0.513498	+	0.858091i	$0.671651\pi$
$858$		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			0
$862$		0			0
$863$	−3.85892	+	11.8765i	−0.131359	+	0.404282i	−0.995006	−	0.0998156i	$-0.968175\pi$
$863$	−3.85892	+	11.8765i	−0.131359	+	0.404282i	0.863647	+	0.504097i	$0.168175\pi$
$864$		0			0
$865$	52.2893	−	23.2807i	1.77789	−	0.791568i
$866$		0			0
$867$		0			0
$868$		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
$873$		0			0
$874$		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
$879$		0			0
$880$		0			0
$881$	−5.56613	−	4.04403i	−0.187528	−	0.136247i	0.490060	−	0.871688i	$-0.336975\pi$
$881$	−5.56613	−	4.04403i	−0.187528	−	0.136247i	−0.677588	+	0.735442i	$0.736975\pi$
$882$		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
$885$		0			0
$886$		0			0
$887$	−9.20647	+	28.3346i	−0.309123	+	0.951383i	0.668983	+	0.743277i	$0.266730\pi$
$887$	−9.20647	+	28.3346i	−0.309123	+	0.951383i	−0.978106	+	0.208106i	$0.933270\pi$
$888$		0			0
$889$	0.659000	+	2.02819i	0.0221021	+	0.0680234i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	38.6841			1.29451
$894$		0			0
$895$	−12.5957	−	13.9889i	−0.421027	−	0.467598i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−39.0705			−1.30308
$900$		0			0
$901$	3.43375			0.114395
$902$		0			0
$903$		0			0
$904$		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
$909$		0			0
$910$		0			0
$911$	−10.4651	−	32.2084i	−0.346726	−	1.06711i	−0.960653	−	0.277750i	$-0.910411\pi$
$911$	−10.4651	−	32.2084i	−0.346726	−	1.06711i	0.613928	−	0.789362i	$-0.289589\pi$
$912$		0			0
$913$	−0.515250	+	1.58578i	−0.0170523	+	0.0524816i
$914$		0			0
$915$		0			0
$916$		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
$921$		0			0
$922$		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
$927$		0			0
$928$		0			0
$929$	35.8848	−	26.0718i	1.17734	−	0.855389i	0.185472	−	0.982649i	$-0.440618\pi$
$929$	35.8848	−	26.0718i	1.17734	−	0.855389i	0.991869	+	0.127261i	$0.0406185\pi$
$930$		0			0
$931$	−26.5130	−	19.2629i	−0.868930	−	0.631315i
$932$		0			0
$933$		0			0
$934$		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
$939$		0			0
$940$		0			0
$941$	−4.60549	+	14.1742i	−0.150135	+	0.462067i	−0.997636	−	0.0687270i	$-0.978106\pi$
$941$	−4.60549	+	14.1742i	−0.150135	+	0.462067i	0.847501	+	0.530794i	$0.178106\pi$
$942$		0			0
$943$	−38.0097			−1.23776
$944$		0			0
$945$		0			0
$946$		0			0
$947$	8.53769	−	6.20300i	0.277438	−	0.201570i	−0.440361	−	0.897821i	$-0.645150\pi$
$947$	8.53769	−	6.20300i	0.277438	−	0.201570i	0.717799	+	0.696250i	$0.245150\pi$
$948$		0			0
$949$	−21.3074			−0.691668
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−21.7177	+	15.7788i	−0.703504	+	0.511126i	−0.881071	−	0.472983i	$-0.843177\pi$
$953$	−21.7177	+	15.7788i	−0.703504	+	0.511126i	0.177568	+	0.984109i	$0.443177\pi$
$954$		0			0
$955$	−8.44969	−	1.79604i	−0.273426	−	0.0581184i
$956$		0			0
$957$		0			0
$958$		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
$963$		0			0
$964$		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
$969$		0			0
$970$		0			0
$971$	21.3040	−	15.4782i	0.683676	−	0.496720i	−0.190899	−	0.981610i	$-0.561140\pi$
$971$	21.3040	−	15.4782i	0.683676	−	0.496720i	0.874575	+	0.484890i	$0.161140\pi$
$972$		0			0
$973$	−1.43518	−	4.41703i	−0.0460098	−	0.141604i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	1.96818	+	6.05744i	0.0629677	+	0.193795i	0.977591	−	0.210512i	$-0.0675130\pi$
$977$	1.96818	+	6.05744i	0.0629677	+	0.193795i	−0.914624	+	0.404306i	$0.867513\pi$
$978$		0			0
$979$	17.4064	−	12.6465i	0.556311	−	0.404184i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−45.9752	−	33.4030i	−1.46638	−	1.06539i	−0.981642	−	0.190731i	$-0.938914\pi$
$983$	−45.9752	−	33.4030i	−1.46638	−	1.06539i	−0.484740	−	0.874658i	$-0.661086\pi$
$984$		0			0
$985$	−6.23089	−	6.92011i	−0.198533	−	0.220493i
$986$		0			0
$987$		0			0
$988$		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
$993$		0			0
$994$		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
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.2.n.a.181.2		8
3.2	odd	2		300.2.m.a.181.1	yes	8
15.2	even	4		1500.2.o.a.349.3		16
15.8	even	4		1500.2.o.a.349.2		16
15.14	odd	2		1500.2.m.b.901.2		8
25.21	even	5	inner	900.2.n.a.721.2		8
75.2	even	20		7500.2.d.d.1249.2		8
75.11	odd	10		7500.2.a.g.1.2		4
75.14	odd	10		7500.2.a.d.1.3		4
75.23	even	20		7500.2.d.d.1249.7		8
75.29	odd	10		1500.2.m.b.601.2		8
75.47	even	20		1500.2.o.a.649.1		16
75.53	even	20		1500.2.o.a.649.4		16
75.71	odd	10		300.2.m.a.121.1	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.m.a.121.1	✓	8	75.71	odd	10
300.2.m.a.181.1	yes	8	3.2	odd	2
900.2.n.a.181.2		8	1.1	even	1	trivial
900.2.n.a.721.2		8	25.21	even	5	inner
1500.2.m.b.601.2		8	75.29	odd	10
1500.2.m.b.901.2		8	15.14	odd	2
1500.2.o.a.349.2		16	15.8	even	4
1500.2.o.a.349.3		16	15.2	even	4
1500.2.o.a.649.1		16	75.47	even	20
1500.2.o.a.649.4		16	75.53	even	20
7500.2.a.d.1.3		4	75.14	odd	10
7500.2.a.g.1.2		4	75.11	odd	10
7500.2.d.d.1249.2		8	75.2	even	20
7500.2.d.d.1249.7		8	75.23	even	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:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	900.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.233733 + 2.22382i) q^{5} -0.511170 q^{7} +O(q^{10})\)	\(q+(0.233733 + 2.22382i) q^{5} -0.511170 q^{7} +(0.564602 + 1.73767i) q^{11} +(1.89169 - 5.82203i) q^{13} +(2.09007 + 1.51852i) q^{17} +(3.93444 + 2.85854i) q^{19} +(2.04965 + 6.30818i) q^{23} +(-4.89074 + 1.03956i) q^{25} +(-6.46980 + 4.70059i) q^{29} +(3.95252 + 2.87167i) q^{31} +(-0.119477 - 1.13675i) q^{35} +(-2.29833 + 7.07355i) q^{37} +(-1.77084 + 5.45007i) q^{41} -2.05126 q^{43} +(6.43523 - 4.67547i) q^{47} -6.73870 q^{49} +(1.07528 - 0.781240i) q^{53} +(-3.73229 + 1.66172i) q^{55} +(3.11882 - 9.59875i) q^{59} +(1.47437 + 4.53764i) q^{61} +(13.3893 + 2.84598i) q^{65} +(11.5960 + 8.42500i) q^{67} +(-4.34421 + 3.15625i) q^{71} +(-1.07559 - 3.31031i) q^{73} +(-0.288608 - 0.888244i) q^{77} +(1.06789 - 0.775869i) q^{79} +(0.738301 + 0.536407i) q^{83} +(-2.88840 + 5.00286i) q^{85} +(-3.63893 - 11.1995i) q^{89} +(-0.966977 + 2.97605i) q^{91} +(-5.43727 + 9.41762i) q^{95} +(5.98660 - 4.34952i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 5 q^{5} - 8 q^{7}+O(q^{10}) \) 8 * q - 5 * q^5 - 8 * q^7	\( 8 q - 5 q^{5} - 8 q^{7} + 2 q^{11} - 7 q^{17} + 5 q^{19} - 7 q^{23} + 5 q^{25} - 27 q^{29} - 3 q^{31} - 20 q^{35} - 9 q^{37} - 20 q^{41} - 68 q^{43} + 7 q^{47} - 8 q^{49} + 11 q^{53} + 5 q^{55} - 2 q^{59} - 14 q^{61} + 35 q^{65} + 28 q^{67} + 15 q^{71} + 6 q^{73} - 17 q^{77} + 24 q^{79} - 2 q^{83} + 10 q^{85} + 5 q^{91} - 5 q^{95} + 34 q^{97}+O(q^{100}) \) 8 * q - 5 * q^5 - 8 * q^7 + 2 * q^11 - 7 * q^17 + 5 * q^19 - 7 * q^23 + 5 * q^25 - 27 * q^29 - 3 * q^31 - 20 * q^35 - 9 * q^37 - 20 * q^41 - 68 * q^43 + 7 * q^47 - 8 * q^49 + 11 * q^53 + 5 * q^55 - 2 * q^59 - 14 * q^61 + 35 * q^65 + 28 * q^67 + 15 * q^71 + 6 * q^73 - 17 * q^77 + 24 * q^79 - 2 * q^83 + 10 * q^85 + 5 * q^91 - 5 * q^95 + 34 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more