LMFDB - Embedded newform 448.2.z.a.271.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [448,2,Mod(47,448)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(448, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 9, 10]))

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

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

chi := DirichletCharacter("448.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 448 = 2^{6} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	448.z (of order $12$, degree $4$, not 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:	$3.57729801055$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 112)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			271.7
Character	$\chi$	$=$	448.271
Dual form			448.2.z.a.367.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.246909 + 0.0661591i) q^{3} +(-0.133797 - 0.499339i) q^{5} +(-2.45011 - 0.998472i) q^{7} +(-2.54149 - 1.46733i) q^{9} +O(q^{10})$	\(q+(0.246909 + 0.0661591i) q^{3} +(-0.133797 - 0.499339i) q^{5} +(-2.45011 - 0.998472i) q^{7} +(-2.54149 - 1.46733i) q^{9} +(-2.10325 - 0.563565i) q^{11} +(-4.30447 - 4.30447i) q^{13} -0.132143i q^{15} +(2.04492 - 1.18064i) q^{17} +(1.35963 + 5.07421i) q^{19} +(-0.538897 - 0.408629i) q^{21} +(1.78181 - 3.08619i) q^{23} +(4.09869 - 2.36638i) q^{25} +(-1.07269 - 1.07269i) q^{27} +(-5.02433 + 5.02433i) q^{29} +(-2.62224 - 4.54185i) q^{31} +(-0.482027 - 0.278298i) q^{33} +(-0.170757 + 1.35703i) q^{35} +(0.964060 - 0.258319i) q^{37} +(-0.778033 - 1.34759i) q^{39} -1.98447 q^{41} +(-2.39322 + 2.39322i) q^{43} +(-0.392650 + 1.46539i) q^{45} +(4.72113 - 8.17724i) q^{47} +(5.00611 + 4.89274i) q^{49} +(0.583019 - 0.156220i) q^{51} +(0.149454 - 0.557771i) q^{53} +1.12564i q^{55} +1.34282i q^{57} +(2.51575 - 9.38891i) q^{59} +(-3.54060 + 0.948702i) q^{61} +(4.76185 + 6.13273i) q^{63} +(-1.57346 + 2.72531i) q^{65} +(-1.34540 + 5.02111i) q^{67} +(0.644125 - 0.644125i) q^{69} -9.49052 q^{71} +(4.24351 + 7.34998i) q^{73} +(1.16856 - 0.313115i) q^{75} +(4.59050 + 3.48084i) q^{77} +(-1.71282 - 0.988896i) q^{79} +(4.20810 + 7.28864i) q^{81} +(0.925102 - 0.925102i) q^{83} +(-0.863142 - 0.863142i) q^{85} +(-1.57296 + 0.908148i) q^{87} +(7.40526 - 12.8263i) q^{89} +(6.24854 + 14.8443i) q^{91} +(-0.346970 - 1.29491i) q^{93} +(2.35183 - 1.35783i) q^{95} -10.2510i q^{97} +(4.51846 + 4.51846i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 6 q^{3} - 6 q^{5} + 8 q^{7}+O(q^{10}) $ 56 * q + 6 * q^3 - 6 * q^5 + 8 * q^7	$ 56 q + 6 q^{3} - 6 q^{5} + 8 q^{7} - 2 q^{11} - 12 q^{17} + 6 q^{19} - 10 q^{21} + 12 q^{23} - 24 q^{29} - 12 q^{33} + 2 q^{35} + 6 q^{37} + 4 q^{39} + 12 q^{45} - 8 q^{49} + 34 q^{51} + 6 q^{53} - 42 q^{59} - 6 q^{61} - 4 q^{65} - 6 q^{67} + 80 q^{71} - 24 q^{75} + 10 q^{77} - 8 q^{81} - 28 q^{85} + 12 q^{87} - 16 q^{91} + 10 q^{93} + 16 q^{99}+O(q^{100}) $ 56 * q + 6 * q^3 - 6 * q^5 + 8 * q^7 - 2 * q^11 - 12 * q^17 + 6 * q^19 - 10 * q^21 + 12 * q^23 - 24 * q^29 - 12 * q^33 + 2 * q^35 + 6 * q^37 + 4 * q^39 + 12 * q^45 - 8 * q^49 + 34 * q^51 + 6 * q^53 - 42 * q^59 - 6 * q^61 - 4 * q^65 - 6 * q^67 + 80 * q^71 - 24 * q^75 + 10 * q^77 - 8 * q^81 - 28 * q^85 + 12 * q^87 - 16 * q^91 + 10 * q^93 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/448\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{4}\right)$

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
$3$	0.246909	+	0.0661591i	0.142553	+	0.0381970i	0.329390	−	0.944194i	$-0.393157\pi$
$3$	0.246909	+	0.0661591i	0.142553	+	0.0381970i	−0.186837	+	0.982391i	$0.559824\pi$
$4$		0			0
$5$	−0.133797	−	0.499339i	−0.0598360	−	0.223311i	0.929533	−	0.368740i	$-0.120211\pi$
$5$	−0.133797	−	0.499339i	−0.0598360	−	0.223311i	−0.989369	+	0.145429i	$0.953544\pi$
$6$		0			0
$7$	−2.45011	−	0.998472i	−0.926056	−	0.377387i
$7$	−2.45011	−	0.998472i	−0.926056	−	0.377387i
$8$		0			0
$9$	−2.54149	−	1.46733i	−0.847163	−	0.489110i
$10$		0			0
$11$	−2.10325	−	0.563565i	−0.634154	−	0.169921i	−0.0726002	−	0.997361i	$-0.523130\pi$
$11$	−2.10325	−	0.563565i	−0.634154	−	0.169921i	−0.561554	+	0.827440i	$0.689796\pi$
$12$		0			0
$13$	−4.30447	−	4.30447i	−1.19385	−	1.19385i	−0.975979	−	0.217866i	$-0.930090\pi$
$13$	−4.30447	−	4.30447i	−1.19385	−	1.19385i	−0.217866	−	0.975979i	$-0.569910\pi$
$14$		0			0
$15$		−	0.132143i		−	0.0341192i
$16$		0			0
$17$	2.04492	−	1.18064i	0.495966	−	0.286346i	−0.231080	−	0.972935i	$-0.574226\pi$
$17$	2.04492	−	1.18064i	0.495966	−	0.286346i	0.727046	+	0.686589i	$0.240893\pi$
$18$		0			0
$19$	1.35963	+	5.07421i	0.311921	+	1.16410i	0.926822	+	0.375500i	$0.122529\pi$
$19$	1.35963	+	5.07421i	0.311921	+	1.16410i	−0.614902	+	0.788604i	$0.710804\pi$
$20$		0			0
$21$	−0.538897	−	0.408629i	−0.117597	−	0.0891702i
$22$		0			0
$23$	1.78181	−	3.08619i	0.371533	−	0.643515i	−0.618268	−	0.785967i	$-0.712165\pi$
$23$	1.78181	−	3.08619i	0.371533	−	0.643515i	0.989802	+	0.142453i	$0.0454988\pi$
$24$		0			0
$25$	4.09869	−	2.36638i	0.819738	−	0.473276i
$26$		0			0
$27$	−1.07269	−	1.07269i	−0.206439	−	0.206439i
$28$		0			0
$29$	−5.02433	+	5.02433i	−0.932995	+	0.932995i	−0.997892	−	0.0648973i	$-0.979328\pi$
$29$	−5.02433	+	5.02433i	−0.932995	+	0.932995i	0.0648973	+	0.997892i	$0.479328\pi$
$30$		0			0
$31$	−2.62224	−	4.54185i	−0.470968	−	0.815740i	0.528481	−	0.848945i	$-0.322762\pi$
$31$	−2.62224	−	4.54185i	−0.470968	−	0.815740i	−0.999449	+	0.0332049i	$0.989429\pi$
$32$		0			0
$33$	−0.482027	−	0.278298i	−0.0839101	−	0.0484455i
$34$		0			0
$35$	−0.170757	+	1.35703i	−0.0288632	+	0.229380i
$36$		0			0
$37$	0.964060	−	0.258319i	0.158491	−	0.0424674i	−0.178701	−	0.983903i	$-0.557190\pi$
$37$	0.964060	−	0.258319i	0.158491	−	0.0424674i	0.337192	+	0.941436i	$0.390523\pi$
$38$		0			0
$39$	−0.778033	−	1.34759i	−0.124585	−	0.215787i
$40$		0			0
$41$	−1.98447			−0.309923			−0.154961	−	0.987921i	$-0.549525\pi$
$41$	−1.98447			−0.309923			−0.154961	+	0.987921i	$0.549525\pi$
$42$		0			0
$43$	−2.39322	+	2.39322i	−0.364963	+	0.364963i	−0.865636	−	0.500673i	$-0.833086\pi$
$43$	−2.39322	+	2.39322i	−0.364963	+	0.364963i	0.500673	+	0.865636i	$0.333086\pi$
$44$		0			0
$45$	−0.392650	+	1.46539i	−0.0585327	+	0.218447i
$46$		0			0
$47$	4.72113	−	8.17724i	0.688647	−	1.19277i	−0.283628	−	0.958934i	$-0.591538\pi$
$47$	4.72113	−	8.17724i	0.688647	−	1.19277i	0.972276	−	0.233838i	$-0.0751285\pi$
$48$		0			0
$49$	5.00611	+	4.89274i	0.715158	+	0.698963i
$50$		0			0
$51$	0.583019	−	0.156220i	0.0816390	−	0.0218751i
$52$		0			0
$53$	0.149454	−	0.557771i	0.0205291	−	0.0766157i	−0.954901	−	0.296923i	$-0.904039\pi$
$53$	0.149454	−	0.557771i	0.0205291	−	0.0766157i	0.975430	+	0.220308i	$0.0707061\pi$
$54$		0			0
$55$			1.12564i			0.151781i
$56$		0			0
$57$			1.34282i			0.177861i
$58$		0			0
$59$	2.51575	−	9.38891i	0.327523	−	1.22233i	−0.584229	−	0.811589i	$-0.698603\pi$
$59$	2.51575	−	9.38891i	0.327523	−	1.22233i	0.911751	−	0.410743i	$-0.134731\pi$
$60$		0			0
$61$	−3.54060	+	0.948702i	−0.453328	+	0.121469i	−0.478256	−	0.878220i	$-0.658731\pi$
$61$	−3.54060	+	0.948702i	−0.453328	+	0.121469i	0.0249283	+	0.999689i	$0.492064\pi$
$62$		0			0
$63$	4.76185	+	6.13273i	0.599936	+	0.772651i
$64$		0			0
$65$	−1.57346	+	2.72531i	−0.195164	+	0.338034i
$66$		0			0
$67$	−1.34540	+	5.02111i	−0.164367	+	0.613427i	0.833753	+	0.552138i	$0.186188\pi$
$67$	−1.34540	+	5.02111i	−0.164367	+	0.613427i	−0.998120	+	0.0612889i	$0.980479\pi$
$68$		0			0
$69$	0.644125	−	0.644125i	0.0775435	−	0.0775435i
$70$		0			0
$71$	−9.49052			−1.12632			−0.563159	−	0.826349i	$-0.690414\pi$
$71$	−9.49052			−1.12632			−0.563159	+	0.826349i	$0.690414\pi$
$72$		0			0
$73$	4.24351	+	7.34998i	0.496666	+	0.860250i	0.999993	−	0.00384589i	$-0.00122419\pi$
$73$	4.24351	+	7.34998i	0.496666	+	0.860250i	−0.503327	+	0.864096i	$0.667891\pi$
$74$		0			0
$75$	1.16856	−	0.313115i	0.134934	−	0.0361554i
$76$		0			0
$77$	4.59050	+	3.48084i	0.523136	+	0.396678i
$78$		0			0
$79$	−1.71282	−	0.988896i	−0.192707	−	0.111260i	0.400542	−	0.916278i	$-0.368822\pi$
$79$	−1.71282	−	0.988896i	−0.192707	−	0.111260i	−0.593249	+	0.805019i	$0.702155\pi$
$80$		0			0
$81$	4.20810	+	7.28864i	0.467567	+	0.809849i
$82$		0			0
$83$	0.925102	−	0.925102i	0.101543	−	0.101543i	−0.654510	−	0.756053i	$-0.727125\pi$
$83$	0.925102	−	0.925102i	0.101543	−	0.101543i	0.756053	+	0.654510i	$0.227125\pi$
$84$		0			0
$85$	−0.863142	−	0.863142i	−0.0936209	−	0.0936209i
$86$		0			0
$87$	−1.57296	+	0.908148i	−0.168639	+	0.0973636i
$88$		0			0
$89$	7.40526	−	12.8263i	0.784956	−	1.35958i	−0.144070	−	0.989567i	$-0.546019\pi$
$89$	7.40526	−	12.8263i	0.784956	−	1.35958i	0.929026	−	0.370015i	$-0.120648\pi$
$90$		0			0
$91$	6.24854	+	14.8443i	0.655025	+	1.55611i
$92$		0			0
$93$	−0.346970	−	1.29491i	−0.0359791	−	0.134276i
$94$		0			0
$95$	2.35183	−	1.35783i	0.241293	−	0.139311i
$96$		0			0
$97$		−	10.2510i		−	1.04083i	−0.853914	−	0.520414i	$-0.825778\pi$
$97$		−	10.2510i		−	1.04083i	0.853914	−	0.520414i	$-0.174222\pi$
$98$		0			0
$99$	4.51846	+	4.51846i	0.454122	+	0.454122i
$100$		0			0
$101$	−8.59094	−	2.30194i	−0.854831	−	0.229051i	−0.195314	−	0.980741i	$-0.562572\pi$
$101$	−8.59094	−	2.30194i	−0.854831	−	0.229051i	−0.659517	+	0.751690i	$0.729239\pi$
$102$		0			0
$103$	16.6175	+	9.59413i	1.63737	+	0.945337i	0.981733	+	0.190263i	$0.0609340\pi$
$103$	16.6175	+	9.59413i	1.63737	+	0.945337i	0.655639	+	0.755074i	$0.272399\pi$
$104$		0			0
$105$	−0.131941	+	0.323766i	−0.0128761	+	0.0315963i
$106$		0			0
$107$	2.99921	+	11.1932i	0.289944	+	1.08209i	0.945150	+	0.326637i	$0.105915\pi$
$107$	2.99921	+	11.1932i	0.289944	+	1.08209i	−0.655206	+	0.755451i	$0.727418\pi$
$108$		0			0
$109$	13.6656	+	3.66169i	1.30893	+	0.350726i	0.844819	−	0.535053i	$-0.179708\pi$
$109$	13.6656	+	3.66169i	1.30893	+	0.350726i	0.464108	+	0.885779i	$0.346375\pi$
$110$		0			0
$111$	0.255125			0.0242154
$112$		0			0
$113$	−8.82256			−0.829956			−0.414978	−	0.909831i	$-0.636211\pi$
$113$	−8.82256			−0.829956			−0.414978	+	0.909831i	$0.636211\pi$
$114$		0			0
$115$	−1.77945	−	0.476803i	−0.165935	−	0.0444621i
$116$		0			0
$117$	4.62369	+	17.2558i	0.427460	+	1.59530i
$118$		0			0
$119$	−6.18912	+	0.850894i	−0.567356	+	0.0780014i
$120$		0			0
$121$	−5.42022	−	3.12936i	−0.492747	−	0.284488i
$122$		0			0
$123$	−0.489985	−	0.131291i	−0.0441804	−	0.0118381i
$124$		0			0
$125$	−3.55772	−	3.55772i	−0.318213	−	0.318213i
$126$		0			0
$127$			8.06202i			0.715389i	0.933839	+	0.357694i	$0.116437\pi$
$127$			8.06202i			0.715389i	−0.933839	+	0.357694i	$0.883563\pi$
$128$		0			0
$129$	−0.749242	+	0.432575i	−0.0659671	+	0.0380861i
$130$		0			0
$131$	−5.16223	−	19.2657i	−0.451026	−	1.68325i	−0.699515	−	0.714617i	$-0.746601\pi$
$131$	−5.16223	−	19.2657i	−0.451026	−	1.68325i	0.248489	−	0.968635i	$-0.420066\pi$
$132$		0			0
$133$	1.73521	−	13.7899i	0.150462	−	1.19574i
$134$		0			0
$135$	−0.392112	+	0.679158i	−0.0337476	+	0.0584526i
$136$		0			0
$137$	−0.573618	+	0.331179i	−0.0490075	+	0.0282945i	−0.524304	−	0.851531i	$-0.675674\pi$
$137$	−0.573618	+	0.331179i	−0.0490075	+	0.0282945i	0.475296	+	0.879826i	$0.342341\pi$
$138$		0			0
$139$	−6.39898	−	6.39898i	−0.542754	−	0.542754i	0.381581	−	0.924335i	$-0.375380\pi$
$139$	−6.39898	−	6.39898i	−0.542754	−	0.542754i	−0.924335	+	0.381581i	$0.875380\pi$
$140$		0			0
$141$	1.70669	−	1.70669i	0.143729	−	0.143729i
$142$		0			0
$143$	6.62754	+	11.4792i	0.554222	+	0.959941i
$144$		0			0
$145$	3.18108	+	1.83660i	0.264175	+	0.152521i
$146$		0			0
$147$	0.912354	+	1.53926i	0.0752497	+	0.126956i
$148$		0			0
$149$	14.3722	−	3.85103i	1.17742	−	0.315489i	0.383517	−	0.923534i	$-0.374713\pi$
$149$	14.3722	−	3.85103i	1.17742	−	0.315489i	0.793903	+	0.608045i	$0.208046\pi$
$150$		0			0
$151$	3.73903	+	6.47620i	0.304278	+	0.527025i	0.977100	−	0.212779i	$-0.0682514\pi$
$151$	3.73903	+	6.47620i	0.304278	+	0.527025i	−0.672822	+	0.739804i	$0.734918\pi$
$152$		0			0
$153$	−6.92953			−0.560219
$154$		0			0
$155$	−1.91707	+	1.91707i	−0.153983	+	0.153983i
$156$		0			0
$157$	1.51511	−	5.65448i	0.120919	−	0.451277i	−0.878742	−	0.477297i	$-0.841617\pi$
$157$	1.51511	−	5.65448i	0.120919	−	0.451277i	0.999661	+	0.0260200i	$0.00828337\pi$
$158$		0			0
$159$	0.0738032	−	0.127831i	0.00585297	−	0.0101376i
$160$		0			0
$161$	−7.44711	+	5.78242i	−0.586915	+	0.455719i
$162$		0			0
$163$	−4.50473	+	1.20704i	−0.352838	+	0.0945427i	−0.430885	−	0.902407i	$-0.641798\pi$
$163$	−4.50473	+	1.20704i	−0.352838	+	0.0945427i	0.0780465	+	0.996950i	$0.475132\pi$
$164$		0			0
$165$	−0.0744712	+	0.277930i	−0.00579757	+	0.0216368i
$166$		0			0
$167$		−	9.03976i		−	0.699518i	−0.936840	−	0.349759i	$-0.886264\pi$
$167$		−	9.03976i		−	0.699518i	0.936840	−	0.349759i	$-0.113736\pi$
$168$		0			0
$169$			24.0569i			1.85053i
$170$		0			0
$171$	3.99005	−	14.8911i	0.305127	−	1.13875i
$172$		0			0
$173$	17.8505	−	4.78302i	1.35715	−	0.363646i	0.494378	−	0.869247i	$-0.335396\pi$
$173$	17.8505	−	4.78302i	1.35715	−	0.363646i	0.862768	+	0.505601i	$0.168729\pi$
$174$		0			0
$175$	−12.4050	+	1.70547i	−0.937731	+	0.128921i
$176$		0			0
$177$	1.24232	−	2.15177i	0.0933787	−	0.161737i
$178$		0			0
$179$	4.27373	−	15.9498i	0.319434	−	1.19214i	−0.600357	−	0.799732i	$-0.704975\pi$
$179$	4.27373	−	15.9498i	0.319434	−	1.19214i	0.919790	−	0.392410i	$-0.128359\pi$
$180$		0			0
$181$	−14.1744	+	14.1744i	−1.05358	+	1.05358i	−0.0550958	+	0.998481i	$0.517546\pi$
$181$	−14.1744	+	14.1744i	−1.05358	+	1.05358i	−0.998481	+	0.0550958i	$0.982454\pi$
$182$		0			0
$183$	−0.936972			−0.0692630
$184$		0			0
$185$	−0.257977	−	0.446830i	−0.0189669	−	0.0328516i
$186$		0			0
$187$	−4.96635	+	1.33073i	−0.363175	+	0.0973125i
$188$		0			0
$189$	1.55716	+	3.69926i	0.113267	+	0.269082i
$190$		0			0
$191$	−13.1853	−	7.61255i	−0.954057	−	0.550825i	−0.0597182	−	0.998215i	$-0.519020\pi$
$191$	−13.1853	−	7.61255i	−0.954057	−	0.550825i	−0.894339	+	0.447390i	$0.852354\pi$
$192$		0			0
$193$	−8.10289	−	14.0346i	−0.583259	−	1.01023i	−0.995090	−	0.0989740i	$-0.968444\pi$
$193$	−8.10289	−	14.0346i	−0.583259	−	1.01023i	0.411831	−	0.911260i	$-0.364889\pi$
$194$		0			0
$195$	−0.568806	+	0.568806i	−0.0407330	+	0.0407330i
$196$		0			0
$197$	−4.72370	−	4.72370i	−0.336549	−	0.336549i	0.518518	−	0.855067i	$-0.326484\pi$
$197$	−4.72370	−	4.72370i	−0.336549	−	0.336549i	−0.855067	+	0.518518i	$0.826484\pi$
$198$		0			0
$199$	6.13578	−	3.54249i	0.434954	−	0.251121i	−0.266501	−	0.963835i	$-0.585868\pi$
$199$	6.13578	−	3.54249i	0.434954	−	0.251121i	0.701455	+	0.712714i	$0.252534\pi$
$200$		0			0
$201$	−0.664385	+	1.15075i	−0.0468621	+	0.0811675i
$202$		0			0
$203$	17.3268	−	7.29352i	1.21611	−	0.511905i
$204$		0			0
$205$	0.265517	+	0.990925i	0.0185445	+	0.0692092i
$206$		0			0
$207$	−9.05691	+	5.22901i	−0.629499	+	0.363441i
$208$		0			0
$209$		−	11.4386i		−	0.791223i
$210$		0			0
$211$	−11.4688	−	11.4688i	−0.789545	−	0.789545i	0.191874	−	0.981420i	$-0.438543\pi$
$211$	−11.4688	−	11.4688i	−0.789545	−	0.789545i	−0.981420	+	0.191874i	$0.938543\pi$
$212$		0			0
$213$	−2.34329	−	0.627884i	−0.160560	−	0.0430219i
$214$		0			0
$215$	1.51524	+	0.874822i	0.103338	+	0.0596624i
$216$		0			0
$217$	1.88987	+	13.7463i	0.128293	+	0.933158i
$218$		0			0
$219$	0.561494	+	2.09552i	0.0379422	+	0.141602i
$220$		0			0
$221$	−13.8843	−	3.72029i	−0.933960	−	0.250254i
$222$		0			0
$223$	−8.27735			−0.554293			−0.277146	−	0.960828i	$-0.589389\pi$
$223$	−8.27735			−0.554293			−0.277146	+	0.960828i	$0.589389\pi$
$224$		0			0
$225$	−13.8890			−0.925936
$226$		0			0
$227$	6.69231	+	1.79320i	0.444184	+	0.119019i	0.473977	−	0.880537i	$-0.342818\pi$
$227$	6.69231	+	1.79320i	0.444184	+	0.119019i	−0.0297926	+	0.999556i	$0.509485\pi$
$228$		0			0
$229$	0.547125	+	2.04190i	0.0361550	+	0.134932i	0.981644	−	0.190721i	$-0.0610825\pi$
$229$	0.547125	+	2.04190i	0.0361550	+	0.134932i	−0.945489	+	0.325653i	$0.894416\pi$
$230$		0			0
$231$	0.903148	+	1.16315i	0.0594227	+	0.0765299i
$232$		0			0
$233$	−16.7919	−	9.69482i	−1.10008	−	0.635129i	−0.163835	−	0.986488i	$-0.552386\pi$
$233$	−16.7919	−	9.69482i	−1.10008	−	0.635129i	−0.936241	+	0.351359i	$0.885720\pi$
$234$		0			0
$235$	−4.71488	−	1.26335i	−0.307565	−	0.0824118i
$236$		0			0
$237$	−0.357486	−	0.357486i	−0.0232212	−	0.0232212i
$238$		0			0
$239$			12.1419i			0.785396i	0.919668	+	0.392698i	$0.128458\pi$
$239$			12.1419i			0.785396i	−0.919668	+	0.392698i	$0.871542\pi$
$240$		0			0
$241$	10.8672	−	6.27418i	0.700018	−	0.404156i	−0.107336	−	0.994223i	$-0.534232\pi$
$241$	10.8672	−	6.27418i	0.700018	−	0.404156i	0.807354	+	0.590067i	$0.200899\pi$
$242$		0			0
$243$	1.73470	+	6.47400i	0.111281	+	0.415307i
$244$		0			0
$245$	1.77333	−	3.15438i	0.113294	−	0.201526i
$246$		0			0
$247$	15.9893	−	27.6943i	1.01737	−	1.76214i
$248$		0			0
$249$	0.289620	−	0.167212i	0.0183539	−	0.0105966i
$250$		0			0
$251$	−18.2170	−	18.2170i	−1.14985	−	1.14985i	−0.986582	−	0.163266i	$-0.947797\pi$
$251$	−18.2170	−	18.2170i	−1.14985	−	1.14985i	−0.163266	−	0.986582i	$-0.552203\pi$
$252$		0			0
$253$	−5.48686	+	5.48686i	−0.344956	+	0.344956i
$254$		0			0
$255$	−0.156013	−	0.270222i	−0.00976990	−	0.0169220i
$256$		0			0
$257$	−16.5971	−	9.58232i	−1.03530	−	0.597729i	−0.116799	−	0.993156i	$-0.537263\pi$
$257$	−16.5971	−	9.58232i	−1.03530	−	0.597729i	−0.918497	+	0.395427i	$0.870597\pi$
$258$		0			0
$259$	−2.61998	−	0.329676i	−0.162798	−	0.0204851i
$260$		0			0
$261$	20.1416	−	5.39693i	1.24674	−	0.334062i
$262$		0			0
$263$	4.71812	+	8.17202i	0.290932	+	0.503909i	0.974030	−	0.226418i	$-0.0727014\pi$
$263$	4.71812	+	8.17202i	0.290932	+	0.503909i	−0.683099	+	0.730326i	$0.739368\pi$
$264$		0			0
$265$	−0.298513			−0.0183375
$266$		0			0
$267$	2.67700	−	2.67700i	0.163830	−	0.163830i
$268$		0			0
$269$	4.77027	−	17.8029i	0.290848	−	1.08546i	−0.653611	−	0.756831i	$-0.726747\pi$
$269$	4.77027	−	17.8029i	0.290848	−	1.08546i	0.944459	−	0.328629i	$-0.106587\pi$
$270$		0			0
$271$	3.81382	−	6.60573i	0.231673	−	0.401269i	−0.726628	−	0.687032i	$-0.758913\pi$
$271$	3.81382	−	6.60573i	0.231673	−	0.401269i	0.958301	+	0.285762i	$0.0922467\pi$
$272$		0			0
$273$	0.560735	+	4.07860i	0.0339372	+	0.246848i
$274$		0			0
$275$	−9.95419	+	2.66722i	−0.600260	+	0.160839i
$276$		0			0
$277$	−4.58537	+	17.1128i	−0.275508	+	1.02821i	0.679992	+	0.733219i	$0.261983\pi$
$277$	−4.58537	+	17.1128i	−0.275508	+	1.02821i	−0.955500	+	0.294990i	$0.904684\pi$
$278$		0			0
$279$			15.3908i			0.921420i
$280$		0			0
$281$		−	14.1841i		−	0.846155i	−0.906094	−	0.423077i	$-0.860950\pi$
$281$		−	14.1841i		−	0.846155i	0.906094	−	0.423077i	$-0.139050\pi$
$282$		0			0
$283$	−1.39051	+	5.18945i	−0.0826571	+	0.308481i	−0.994860	−	0.101258i	$-0.967713\pi$
$283$	−1.39051	+	5.18945i	−0.0826571	+	0.308481i	0.912203	+	0.409738i	$0.134380\pi$
$284$		0			0
$285$	0.670522	−	0.179666i	0.0397183	−	0.0106425i
$286$		0			0
$287$	4.86219	+	1.98144i	0.287006	+	0.116961i
$288$		0			0
$289$	−5.71220	+	9.89382i	−0.336012	+	0.581989i
$290$		0			0
$291$	0.678195	−	2.53106i	0.0397565	−	0.148373i
$292$		0			0
$293$	8.22483	−	8.22483i	0.480500	−	0.480500i	−0.424791	−	0.905291i	$-0.639653\pi$
$293$	8.22483	−	8.22483i	0.480500	−	0.480500i	0.905291	+	0.424791i	$0.139653\pi$
$294$		0			0
$295$	−5.02484			−0.292558
$296$		0			0
$297$	1.65161	+	2.86067i	0.0958359	+	0.165993i
$298$		0			0
$299$	−20.9542	+	5.61465i	−1.21181	+	0.324703i
$300$		0			0
$301$	8.25324	−	3.47410i	0.475709	−	0.200244i
$302$		0			0
$303$	−1.96889	−	1.13674i	−0.113110	−	0.0653039i
$304$		0			0
$305$	0.947447	+	1.64103i	0.0542506	+	0.0939649i
$306$		0			0
$307$	10.1445	−	10.1445i	0.578977	−	0.578977i	−0.355644	−	0.934621i	$-0.615739\pi$
$307$	10.1445	−	10.1445i	0.578977	−	0.578977i	0.934621	+	0.355644i	$0.115739\pi$
$308$		0			0
$309$	3.46828	+	3.46828i	0.197303	+	0.197303i
$310$		0			0
$311$	−23.9697	+	13.8389i	−1.35920	+	0.784734i	−0.989516	−	0.144424i	$-0.953867\pi$
$311$	−23.9697	+	13.8389i	−1.35920	+	0.784734i	−0.369683	+	0.929158i	$0.620534\pi$
$312$		0			0
$313$	10.1166	−	17.5225i	0.571826	−	0.990431i	−0.424553	−	0.905403i	$-0.639569\pi$
$313$	10.1166	−	17.5225i	0.571826	−	0.990431i	0.996379	−	0.0850279i	$-0.0270979\pi$
$314$		0			0
$315$	2.42518	−	3.19832i	0.136644	−	0.180205i
$316$		0			0
$317$	2.36566	+	8.82875i	0.132868	+	0.495872i	0.999998	−	0.00221166i	$-0.000703994\pi$
$317$	2.36566	+	8.82875i	0.132868	+	0.495872i	−0.867129	+	0.498083i	$0.834037\pi$
$318$		0			0
$319$	13.3990	−	7.73590i	0.750198	−	0.433127i
$320$		0			0
$321$			2.96213i			0.165330i
$322$		0			0
$323$	8.77113	+	8.77113i	0.488039	+	0.488039i
$324$		0			0
$325$	−27.8287	−	7.45668i	−1.54366	−	0.413622i
$326$		0			0
$327$	3.13191	+	1.80821i	0.173195	+	0.0999941i
$328$		0			0
$329$	−19.7320	+	15.3212i	−1.08786	+	0.844687i
$330$		0			0
$331$	7.22999	+	26.9827i	0.397396	+	1.48310i	0.817661	+	0.575701i	$0.195271\pi$
$331$	7.22999	+	26.9827i	0.397396	+	1.48310i	−0.420264	+	0.907402i	$0.638063\pi$
$332$		0			0
$333$	−2.82919	−	0.758079i	−0.155039	−	0.0415424i
$334$		0			0
$335$	2.68725			0.146820
$336$		0			0
$337$	36.5503			1.99102			0.995510	−	0.0946549i	$-0.0301748\pi$
$337$	36.5503			1.99102			0.995510	+	0.0946549i	$0.0301748\pi$
$338$		0			0
$339$	−2.17837	−	0.583692i	−0.118313	−	0.0317018i
$340$		0			0
$341$	2.95560	+	11.0305i	0.160055	+	0.597333i
$342$		0			0
$343$	−7.38027	−	16.9862i	−0.398497	−	0.917170i
$344$		0			0
$345$	−0.407818	−	0.235454i	−0.0219562	−	0.0126764i
$346$		0			0
$347$	25.7539	+	6.90075i	1.38254	+	0.370452i	0.872045	−	0.489426i	$-0.162794\pi$
$347$	25.7539	+	6.90075i	1.38254	+	0.370452i	0.510500	+	0.859878i	$0.329460\pi$
$348$		0			0
$349$	−1.81441	−	1.81441i	−0.0971229	−	0.0971229i	0.656876	−	0.753999i	$-0.271878\pi$
$349$	−1.81441	−	1.81441i	−0.0971229	−	0.0971229i	−0.753999	+	0.656876i	$0.771878\pi$
$350$		0			0
$351$			9.23472i			0.492913i
$352$		0			0
$353$	12.0310	−	6.94611i	0.640346	−	0.369704i	−0.144402	−	0.989519i	$-0.546126\pi$
$353$	12.0310	−	6.94611i	0.640346	−	0.369704i	0.784748	+	0.619815i	$0.212792\pi$
$354$		0			0
$355$	1.26981	+	4.73898i	0.0673943	+	0.251519i
$356$		0			0
$357$	−1.58444	−	0.199373i	−0.0838577	−	0.0105519i
$358$		0			0
$359$	−1.13190	+	1.96051i	−0.0597393	+	0.103472i	−0.894348	−	0.447371i	$-0.852360\pi$
$359$	−1.13190	+	1.96051i	−0.0597393	+	0.103472i	0.834609	+	0.550843i	$0.185694\pi$
$360$		0			0
$361$	−7.44453	+	4.29810i	−0.391817	+	0.226216i
$362$		0			0
$363$	−1.13126	−	1.13126i	−0.0593760	−	0.0593760i
$364$		0			0
$365$	3.10236	−	3.10236i	0.162385	−	0.162385i
$366$		0			0
$367$	3.26744	+	5.65938i	0.170559	+	0.295417i	0.938615	−	0.344965i	$-0.112109\pi$
$367$	3.26744	+	5.65938i	0.170559	+	0.295417i	−0.768056	+	0.640382i	$0.778776\pi$
$368$		0			0
$369$	5.04352	+	2.91188i	0.262555	+	0.151586i
$370$		0			0
$371$	−0.923098	+	1.21738i	−0.0479249	+	0.0632030i
$372$		0			0
$373$	−3.40480	+	0.912313i	−0.176294	+	0.0472378i	−0.345886	−	0.938277i	$-0.612422\pi$
$373$	−3.40480	+	0.912313i	−0.176294	+	0.0472378i	0.169592	+	0.985514i	$0.445755\pi$
$374$		0			0
$375$	−0.643059	−	1.11381i	−0.0332074	−	0.0575169i
$376$		0			0
$377$	43.2542			2.22770
$378$		0			0
$379$	−4.04684	+	4.04684i	−0.207872	+	0.207872i	−0.803362	−	0.595490i	$-0.796958\pi$
$379$	−4.04684	+	4.04684i	−0.207872	+	0.207872i	0.595490	+	0.803362i	$0.296958\pi$
$380$		0			0
$381$	−0.533376	+	1.99059i	−0.0273257	+	0.101981i
$382$		0			0
$383$	5.28313	−	9.15066i	0.269956	−	0.467577i	−0.698895	−	0.715225i	$-0.746324\pi$
$383$	5.28313	−	9.15066i	0.269956	−	0.467577i	0.968850	+	0.247648i	$0.0796577\pi$
$384$		0			0
$385$	1.12392	−	2.75794i	0.0572802	−	0.140558i
$386$		0			0
$387$	9.59400	−	2.57071i	0.487691	−	0.130676i
$388$		0			0
$389$	3.13038	−	11.6827i	0.158717	−	0.592339i	−0.840042	−	0.542522i	$-0.817470\pi$
$389$	3.13038	−	11.6827i	0.158717	−	0.592339i	0.998758	−	0.0498169i	$-0.0158638\pi$
$390$		0			0
$391$		−	8.41468i		−	0.425549i
$392$		0			0
$393$		−	5.09840i		−	0.257180i
$394$		0			0
$395$	−0.264623	+	0.987588i	−0.0133147	+	0.0496910i
$396$		0			0
$397$	−12.4921	+	3.34726i	−0.626963	+	0.167994i	−0.558291	−	0.829645i	$-0.688543\pi$
$397$	−12.4921	+	3.34726i	−0.626963	+	0.167994i	−0.0686717	+	0.997639i	$0.521876\pi$
$398$		0			0
$399$	1.34077	−	3.29006i	0.0671224	−	0.164709i
$400$		0			0
$401$	−14.8962	+	25.8009i	−0.743880	+	1.28844i	0.206837	+	0.978376i	$0.433683\pi$
$401$	−14.8962	+	25.8009i	−0.743880	+	1.28844i	−0.950716	+	0.310062i	$0.899650\pi$
$402$		0			0
$403$	−8.26291	+	30.8376i	−0.411605	+	1.53613i
$404$		0			0
$405$	3.07647	−	3.07647i	0.152871	−	0.152871i
$406$		0			0
$407$	−2.17324			−0.107724
$408$		0			0
$409$	0.946108	+	1.63871i	0.0467820	+	0.0810289i	0.888468	−	0.458938i	$-0.151770\pi$
$409$	0.946108	+	1.63871i	0.0467820	+	0.0810289i	−0.841686	+	0.539967i	$0.818437\pi$
$410$		0			0
$411$	−0.163542	+	0.0438210i	−0.00806693	+	0.00216153i
$412$		0			0
$413$	−15.5384	+	20.4920i	−0.764596	+	1.00834i
$414$		0			0
$415$	−0.585716	−	0.338163i	−0.0287516	−	0.0165998i
$416$		0			0
$417$	−1.15661	−	2.00332i	−0.0566397	−	0.0981028i
$418$		0			0
$419$	−12.0009	+	12.0009i	−0.586284	+	0.586284i	−0.936623	−	0.350339i	$-0.886066\pi$
$419$	−12.0009	+	12.0009i	−0.586284	+	0.586284i	0.350339	+	0.936623i	$0.386066\pi$
$420$		0			0
$421$	−15.6668	−	15.6668i	−0.763554	−	0.763554i	0.213409	−	0.976963i	$-0.431543\pi$
$421$	−15.6668	−	15.6668i	−0.763554	−	0.763554i	−0.976963	+	0.213409i	$0.931543\pi$
$422$		0			0
$423$	−23.9974	+	13.8549i	−1.16679	+	0.673648i
$424$		0			0
$425$	5.58766	−	9.67812i	0.271042	−	0.469458i
$426$		0			0
$427$	9.62213	+	1.21077i	0.465648	+	0.0585931i
$428$		0			0
$429$	0.876944	+	3.27280i	0.0423392	+	0.158012i
$430$		0			0
$431$	20.0635	−	11.5837i	0.966427	−	0.557967i	0.0682816	−	0.997666i	$-0.478248\pi$
$431$	20.0635	−	11.5837i	0.966427	−	0.557967i	0.898145	+	0.439699i	$0.144915\pi$
$432$		0			0
$433$			32.5292i			1.56325i	0.623746	+	0.781627i	$0.285610\pi$
$433$			32.5292i			1.56325i	−0.623746	+	0.781627i	$0.714390\pi$
$434$		0			0
$435$	0.663931	+	0.663931i	0.0318330	+	0.0318330i
$436$		0			0
$437$	18.0826	+	4.84521i	0.865007	+	0.231778i
$438$		0			0
$439$	25.4654	+	14.7025i	1.21540	+	0.701711i	0.963930	−	0.266154i	$-0.0857530\pi$
$439$	25.4654	+	14.7025i	1.21540	+	0.701711i	0.251469	+	0.967865i	$0.419086\pi$
$440$		0			0
$441$	−5.54371	−	19.7805i	−0.263986	−	0.941926i
$442$		0			0
$443$	−3.68306	−	13.7454i	−0.174987	−	0.653062i	−0.996554	−	0.0829491i	$-0.973566\pi$
$443$	−3.68306	−	13.7454i	−0.174987	−	0.653062i	0.821566	−	0.570113i	$-0.193101\pi$
$444$		0			0
$445$	−7.39546	−	1.98161i	−0.350578	−	0.0939372i
$446$		0			0
$447$	3.80342			0.179895
$448$		0			0
$449$	4.02168			0.189795			0.0948974	−	0.995487i	$-0.469748\pi$
$449$	4.02168			0.189795			0.0948974	+	0.995487i	$0.469748\pi$
$450$		0			0
$451$	4.17385	+	1.11838i	0.196539	+	0.0526625i
$452$		0			0
$453$	0.494742	+	1.84640i	0.0232450	+	0.0867516i
$454$		0			0
$455$	6.57631	−	5.10627i	0.308302	−	0.239386i
$456$		0			0
$457$	14.8376	+	8.56651i	0.694075	+	0.400724i	0.805137	−	0.593089i	$-0.202092\pi$
$457$	14.8376	+	8.56651i	0.694075	+	0.400724i	−0.111062	+	0.993813i	$0.535425\pi$
$458$		0			0
$459$	−3.46002	−	0.927110i	−0.161500	−	0.0432738i
$460$		0			0
$461$	17.5096	+	17.5096i	0.815505	+	0.815505i	0.985453	−	0.169948i	$-0.0543600\pi$
$461$	17.5096	+	17.5096i	0.815505	+	0.815505i	−0.169948	+	0.985453i	$0.554360\pi$
$462$		0			0
$463$		−	29.8874i		−	1.38899i	−0.719499	−	0.694494i	$-0.755628\pi$
$463$		−	29.8874i		−	1.38899i	0.719499	−	0.694494i	$-0.244372\pi$
$464$		0			0
$465$	−0.600174	+	0.346511i	−0.0278324	+	0.0160691i
$466$		0			0
$467$	3.64227	+	13.5931i	0.168544	+	0.629015i	0.997562	+	0.0697924i	$0.0222337\pi$
$467$	3.64227	+	13.5931i	0.168544	+	0.629015i	−0.829017	+	0.559223i	$0.811100\pi$
$468$		0			0
$469$	8.30983	−	10.9589i	0.383712	−	0.506037i
$470$		0			0
$471$	0.748191	−	1.29590i	0.0344748	−	0.0597121i
$472$		0			0
$473$	6.38229	−	3.68482i	0.293458	−	0.169428i
$474$		0			0
$475$	17.5802	+	17.5802i	0.806635	+	0.806635i
$476$		0			0
$477$	−1.19827	+	1.19827i	−0.0548650	+	0.0548650i
$478$		0			0
$479$	4.61606	+	7.99525i	0.210913	+	0.365312i	0.952001	−	0.306096i	$-0.0990229\pi$
$479$	4.61606	+	7.99525i	0.210913	+	0.365312i	−0.741087	+	0.671409i	$0.765690\pi$
$480$		0			0
$481$	−5.26169	−	3.03784i	−0.239913	−	0.138514i
$482$		0			0
$483$	−2.22132	+	0.935038i	−0.101073	+	0.0425457i
$484$		0			0
$485$	−5.11871	+	1.37155i	−0.232428	+	0.0622790i
$486$		0			0
$487$	−6.64586	−	11.5110i	−0.301153	−	0.521612i	0.675245	−	0.737594i	$-0.264038\pi$
$487$	−6.64586	−	11.5110i	−0.301153	−	0.521612i	−0.976397	+	0.215982i	$0.930705\pi$
$488$		0			0
$489$	−1.19212			−0.0539094
$490$		0			0
$491$	15.8754	−	15.8754i	0.716445	−	0.716445i	−0.251430	−	0.967875i	$-0.580901\pi$
$491$	15.8754	−	15.8754i	0.716445	−	0.716445i	0.967875	+	0.251430i	$0.0809009\pi$
$492$		0			0
$493$	−4.34245	+	16.2063i	−0.195574	+	0.729893i
$494$		0			0
$495$	1.65168	−	2.86080i	0.0742376	−	0.128583i
$496$		0			0
$497$	23.2528	+	9.47601i	1.04303	+	0.425057i
$498$		0			0
$499$	30.2224	−	8.09807i	1.35294	−	0.362519i	0.491721	−	0.870753i	$-0.336368\pi$
$499$	30.2224	−	8.09807i	1.35294	−	0.362519i	0.861219	+	0.508234i	$0.169701\pi$
$500$		0			0
$501$	0.598062	−	2.23200i	0.0267194	−	0.0997183i
$502$		0			0
$503$			19.6757i			0.877298i	0.898659	+	0.438649i	$0.144543\pi$
$503$			19.6757i			0.877298i	−0.898659	+	0.438649i	$0.855457\pi$
$504$		0			0
$505$			4.59778i			0.204599i
$506$		0			0
$507$	−1.59158	+	5.93987i	−0.0706847	+	0.263799i
$508$		0			0
$509$	−30.9137	+	8.28331i	−1.37023	+	0.367151i	−0.867562	−	0.497330i	$-0.834314\pi$
$509$	−30.9137	+	8.28331i	−1.37023	+	0.367151i	−0.502665	+	0.864481i	$0.667647\pi$
$510$		0			0
$511$	−3.05834	−	22.2453i	−0.135293	−	0.984075i
$512$		0			0
$513$	3.98459	−	6.90151i	0.175924	−	0.304709i
$514$		0			0
$515$	2.56734	−	9.58143i	0.113130	−	0.422208i
$516$		0			0
$517$	−14.5381	+	14.5381i	−0.639386	+	0.639386i
$518$		0			0
$519$	4.72388			0.207355
$520$		0			0
$521$	5.17549	+	8.96421i	0.226742	+	0.392729i	0.956841	−	0.290613i	$-0.0938591\pi$
$521$	5.17549	+	8.96421i	0.226742	+	0.392729i	−0.730098	+	0.683342i	$0.760526\pi$
$522$		0			0
$523$	−33.3679	+	8.94091i	−1.45908	+	0.390959i	−0.899171	−	0.437597i	$-0.855830\pi$
$523$	−33.3679	+	8.94091i	−1.45908	+	0.390959i	−0.559907	+	0.828556i	$0.689163\pi$
$524$		0			0
$525$	−3.17574	−	0.399608i	−0.138601	−	0.0174403i
$526$		0			0
$527$	−10.7245	−	6.19182i	−0.467168	−	0.269720i
$528$		0			0
$529$	5.15030	+	8.92058i	0.223926	+	0.387851i
$530$		0			0
$531$	−20.1704	+	20.1704i	−0.875320	+	0.875320i
$532$		0			0
$533$	8.54211	+	8.54211i	0.370000	+	0.370000i
$534$		0			0
$535$	5.18791	−	2.99524i	0.224293	−	0.129496i
$536$		0			0
$537$	2.11045	−	3.65540i	0.0910725	−	0.157742i
$538$		0			0
$539$	−7.77173	−	13.1119i	−0.334752	−	0.564771i
$540$		0			0
$541$	−0.909894	−	3.39577i	−0.0391194	−	0.145996i	0.943604	−	0.331077i	$-0.107412\pi$
$541$	−0.909894	−	3.39577i	−0.0391194	−	0.145996i	−0.982723	+	0.185081i	$0.940745\pi$
$542$		0			0
$543$	−4.43756	+	2.56203i	−0.190434	+	0.109947i
$544$		0			0
$545$		−	7.31368i		−	0.313284i
$546$		0			0
$547$	−1.41889	−	1.41889i	−0.0606674	−	0.0606674i	0.676122	−	0.736790i	$-0.263659\pi$
$547$	−1.41889	−	1.41889i	−0.0606674	−	0.0606674i	−0.736790	+	0.676122i	$0.763659\pi$
$548$		0			0
$549$	10.3905	+	2.78412i	0.443454	+	0.118823i
$550$		0			0
$551$	−32.3257	−	18.6633i	−1.37712	−	0.795082i
$552$		0			0
$553$	3.20921	+	4.13311i	0.136470	+	0.175758i
$554$		0			0
$555$	−0.0341351	−	0.127394i	−0.00144895	−	0.00540757i
$556$		0			0
$557$	−16.0307	−	4.29542i	−0.679243	−	0.182003i	−0.0973282	−	0.995252i	$-0.531030\pi$
$557$	−16.0307	−	4.29542i	−0.679243	−	0.182003i	−0.581915	+	0.813250i	$0.697696\pi$
$558$		0			0
$559$	20.6031			0.871419
$560$		0			0
$561$	−1.31428			−0.0554888
$562$		0			0
$563$	18.1600	+	4.86597i	0.765355	+	0.205076i	0.620318	−	0.784350i	$-0.287003\pi$
$563$	18.1600	+	4.86597i	0.765355	+	0.205076i	0.145036	+	0.989426i	$0.453670\pi$
$564$		0			0
$565$	1.18043	+	4.40544i	0.0496613	+	0.185338i
$566$		0			0
$567$	−3.03281	−	22.0597i	−0.127366	−	0.926419i
$568$		0			0
$569$	−26.3651	−	15.2219i	−1.10528	−	0.638135i	−0.167679	−	0.985842i	$-0.553627\pi$
$569$	−26.3651	−	15.2219i	−1.10528	−	0.638135i	−0.937603	+	0.347707i	$0.886961\pi$
$570$		0			0
$571$	−27.8263	−	7.45604i	−1.16450	−	0.312026i	−0.375736	−	0.926727i	$-0.622610\pi$
$571$	−27.8263	−	7.45604i	−1.16450	−	0.312026i	−0.788760	+	0.614701i	$0.789277\pi$
$572$		0			0
$573$	−2.75194	−	2.75194i	−0.114964	−	0.114964i
$574$		0			0
$575$		−	16.8658i		−	0.703351i
$576$		0			0
$577$	−4.00919	+	2.31471i	−0.166905	+	0.0963626i	−0.581126	−	0.813814i	$-0.697387\pi$
$577$	−4.00919	+	2.31471i	−0.166905	+	0.0963626i	0.414221	+	0.910176i	$0.364054\pi$
$578$		0			0
$579$	−1.07216	−	4.00136i	−0.0445574	−	0.166291i
$580$		0			0
$581$	−3.19029	+	1.34292i	−0.132356	+	0.0557136i
$582$		0			0
$583$	−0.628680	+	1.08890i	−0.0260372	+	0.0450978i
$584$		0			0
$585$	7.99787	−	4.61757i	0.330671	−	0.190913i
$586$		0			0
$587$	11.6498	+	11.6498i	0.480838	+	0.480838i	0.905399	−	0.424562i	$-0.139572\pi$
$587$	11.6498	+	11.6498i	0.480838	+	0.480838i	−0.424562	+	0.905399i	$0.639572\pi$
$588$		0			0
$589$	19.4810	−	19.4810i	0.802702	−	0.802702i
$590$		0			0
$591$	−0.853808	−	1.47884i	−0.0351210	−	0.0608313i
$592$		0			0
$593$	−3.92435	−	2.26572i	−0.161154	−	0.0930421i	0.417254	−	0.908790i	$-0.362992\pi$
$593$	−3.92435	−	2.26572i	−0.161154	−	0.0930421i	−0.578408	+	0.815748i	$0.696326\pi$
$594$		0			0
$595$	1.25297	+	2.97662i	0.0513668	+	0.122029i
$596$		0			0
$597$	1.74935	−	0.468736i	0.0715960	−	0.0191841i
$598$		0			0
$599$	−2.76430	−	4.78791i	−0.112946	−	0.195629i	0.804011	−	0.594615i	$-0.202695\pi$
$599$	−2.76430	−	4.78791i	−0.112946	−	0.195629i	−0.916957	+	0.398986i	$0.869362\pi$
$600$		0			0
$601$	−7.12419			−0.290602			−0.145301	−	0.989388i	$-0.546415\pi$
$601$	−7.12419			−0.290602			−0.145301	+	0.989388i	$0.546415\pi$
$602$		0			0
$603$	10.7870	−	10.7870i	0.439279	−	0.439279i
$604$		0			0
$605$	−0.837401	+	3.12522i	−0.0340452	+	0.127058i
$606$		0			0
$607$	−14.7666	+	25.5765i	−0.599357	+	1.03812i	0.393559	+	0.919299i	$0.371244\pi$
$607$	−14.7666	+	25.5765i	−0.599357	+	1.03812i	−0.992916	+	0.118818i	$0.962090\pi$
$608$		0			0
$609$	4.76068	−	0.654510i	0.192913	−	0.0265221i
$610$		0			0
$611$	−55.5206	+	14.8767i	−2.24612	+	0.601847i
$612$		0			0
$613$	2.97664	−	11.1090i	0.120225	−	0.448687i	−0.879399	−	0.476085i	$-0.842056\pi$
$613$	2.97664	−	11.1090i	0.120225	−	0.448687i	0.999625	+	0.0273982i	$0.00872222\pi$
$614$		0			0
$615$			0.262235i			0.0105743i
$616$		0			0
$617$		−	3.58264i		−	0.144232i	−0.997396	−	0.0721158i	$-0.977025\pi$
$617$		−	3.58264i		−	0.144232i	0.997396	−	0.0721158i	$-0.0229751\pi$
$618$		0			0
$619$	4.47703	−	16.7085i	0.179947	−	0.671571i	−0.815709	−	0.578463i	$-0.803653\pi$
$619$	4.47703	−	16.7085i	0.179947	−	0.671571i	0.995656	−	0.0931089i	$-0.0296805\pi$
$620$		0			0
$621$	−5.22185	+	1.39919i	−0.209546	+	0.0561476i
$622$		0			0
$623$	−30.9504	+	24.0319i	−1.24000	+	0.962817i
$624$		0			0
$625$	10.5314	−	18.2409i	0.421256	−	0.729637i
$626$		0			0
$627$	0.756766	−	2.82429i	0.0302223	−	0.112791i
$628$		0			0
$629$	1.66645	−	1.66645i	0.0664455	−	0.0664455i
$630$		0			0
$631$	−0.128219			−0.00510432			−0.00255216	−	0.999997i	$-0.500812\pi$
$631$	−0.128219			−0.00510432			−0.00255216	+	0.999997i	$0.500812\pi$
$632$		0			0
$633$	−2.07299	−	3.59052i	−0.0823938	−	0.142710i
$634$		0			0
$635$	4.02568	−	1.07868i	0.159754	−	0.0428060i
$636$		0			0
$637$	−0.487994	−	42.6093i	−0.0193350	−	1.68824i
$638$		0			0
$639$	24.1200	+	13.9257i	0.954174	+	0.550893i
$640$		0			0
$641$	−1.21974	−	2.11264i	−0.0481767	−	0.0834444i	0.840931	−	0.541142i	$-0.182008\pi$
$641$	−1.21974	−	2.11264i	−0.0481767	−	0.0834444i	−0.889108	+	0.457697i	$0.848674\pi$
$642$		0			0
$643$	32.3912	−	32.3912i	1.27738	−	1.27738i	0.335259	−	0.942126i	$-0.391176\pi$
$643$	32.3912	−	32.3912i	1.27738	−	1.27738i	0.942126	−	0.335259i	$-0.108824\pi$
$644$		0			0
$645$	0.316248	+	0.316248i	0.0124523	+	0.0124523i
$646$		0			0
$647$	19.1676	−	11.0664i	0.753555	−	0.435065i	−0.0734221	−	0.997301i	$-0.523392\pi$
$647$	19.1676	−	11.0664i	0.753555	−	0.435065i	0.826977	+	0.562236i	$0.190059\pi$
$648$		0			0
$649$	−10.5825	+	18.3295i	−0.415400	+	0.719494i
$650$		0			0
$651$	−0.442815	+	3.51911i	−0.0173553	+	0.137925i
$652$		0			0
$653$	−0.00473248	−	0.0176619i	−0.000185196	−	0.000691162i	0.965833	−	0.259165i	$-0.0834472\pi$
$653$	−0.00473248	−	0.0176619i	−0.000185196	−	0.000691162i	−0.966018	+	0.258473i	$0.916781\pi$
$654$		0			0
$655$	−8.92941	+	5.15540i	−0.348901	+	0.201438i
$656$		0			0
$657$		−	24.9065i		−	0.971696i
$658$		0			0
$659$	12.7235	+	12.7235i	0.495639	+	0.495639i	0.910077	−	0.414439i	$-0.136022\pi$
$659$	12.7235	+	12.7235i	0.495639	+	0.495639i	−0.414439	+	0.910077i	$0.636022\pi$
$660$		0			0
$661$	−36.9272	−	9.89461i	−1.43630	−	0.384856i	−0.545064	−	0.838394i	$-0.683495\pi$
$661$	−36.9272	−	9.89461i	−1.43630	−	0.384856i	−0.891237	+	0.453539i	$0.850161\pi$
$662$		0			0
$663$	−3.18203	−	1.83715i	−0.123580	−	0.0713488i
$664$		0			0
$665$	−7.11801	+	0.978601i	−0.276025	+	0.0379485i
$666$		0			0
$667$	6.55362	+	24.4584i	0.253757	+	0.947034i
$668$		0			0
$669$	−2.04375	−	0.547622i	−0.0790161	−	0.0211723i
$670$		0			0
$671$	7.98144			0.308120
$672$		0			0
$673$	−0.347088			−0.0133793			−0.00668963	−	0.999978i	$-0.502129\pi$
$673$	−0.347088			−0.0133793			−0.00668963	+	0.999978i	$0.502129\pi$
$674$		0			0
$675$	−6.93501	−	1.85823i	−0.266929	−	0.0715233i
$676$		0			0
$677$	−1.94067	−	7.24267i	−0.0745859	−	0.278358i	0.918553	−	0.395297i	$-0.129358\pi$
$677$	−1.94067	−	7.24267i	−0.0745859	−	0.278358i	−0.993139	+	0.116939i	$0.962692\pi$
$678$		0			0
$679$	−10.2353	+	25.1160i	−0.392795	+	0.963865i
$680$		0			0
$681$	1.53376	+	0.885514i	0.0587736	+	0.0339330i
$682$		0			0
$683$	−22.7306	−	6.09066i	−0.869764	−	0.233053i	−0.203778	−	0.979017i	$-0.565322\pi$
$683$	−22.7306	−	6.09066i	−0.869764	−	0.233053i	−0.665986	+	0.745965i	$0.731989\pi$
$684$		0			0
$685$	0.242119	+	0.242119i	0.00925089	+	0.00925089i
$686$		0			0
$687$			0.540360i			0.0206160i
$688$		0			0
$689$	−3.04423	+	1.75759i	−0.115976	+	0.0669587i
$690$		0			0
$691$	−4.76409	−	17.7798i	−0.181235	−	0.676377i	−0.995405	−	0.0957513i	$-0.969475\pi$
$691$	−4.76409	−	17.7798i	−0.181235	−	0.676377i	0.814171	−	0.580626i	$-0.197192\pi$
$692$		0			0
$693$	−6.55918	−	15.5823i	−0.249163	−	0.591922i
$694$		0			0
$695$	−2.33909	+	4.05142i	−0.0887267	+	0.153679i
$696$		0			0
$697$	−4.05809	+	2.34294i	−0.153711	+	0.0887452i
$698$		0			0
$699$	−3.50468	−	3.50468i	−0.132559	−	0.132559i
$700$		0			0
$701$	15.5894	−	15.5894i	0.588803	−	0.588803i	−0.348504	−	0.937307i	$-0.613310\pi$
$701$	15.5894	−	15.5894i	0.588803	−	0.588803i	0.937307	+	0.348504i	$0.113310\pi$
$702$		0			0
$703$	2.62153	+	4.54062i	0.0988729	+	0.171253i
$704$		0			0
$705$	−1.08057	−	0.623865i	−0.0406964	−	0.0234961i
$706$		0			0
$707$	18.7504	+	14.2178i	0.705180	+	0.534716i
$708$		0			0
$709$	13.3669	−	3.58166i	0.502006	−	0.134512i	0.00107497	−	0.999999i	$-0.499658\pi$
$709$	13.3669	−	3.58166i	0.502006	−	0.134512i	0.500931	+	0.865487i	$0.332991\pi$
$710$		0			0
$711$	2.90207	+	5.02654i	0.108836	+	0.188510i
$712$		0			0
$713$	−18.6893			−0.699921
$714$		0			0
$715$	4.84527	−	4.84527i	0.181203	−	0.181203i
$716$		0			0
$717$	−0.803299	+	2.99795i	−0.0299997	+	0.111961i
$718$		0			0
$719$	−0.515281	+	0.892493i	−0.0192167	+	0.0332844i	−0.875474	−	0.483265i	$-0.839451\pi$
$719$	−0.515281	+	0.892493i	−0.0192167	+	0.0332844i	0.856257	+	0.516550i	$0.172784\pi$
$720$		0			0
$721$	−31.1353	−	40.0988i	−1.15954	−	1.49336i
$722$		0			0
$723$	3.09831	−	0.830188i	0.115227	−	0.0308750i
$724$		0			0
$725$	−8.70370	+	32.4826i	−0.323247	+	1.20638i
$726$		0			0
$727$		−	3.68053i		−	0.136503i	−0.997668	−	0.0682517i	$-0.978258\pi$
$727$		−	3.68053i		−	0.136503i	0.997668	−	0.0682517i	$-0.0217421\pi$
$728$		0			0
$729$		−	23.5353i		−	0.871679i
$730$		0			0
$731$	−2.06843	+	7.71948i	−0.0765036	+	0.285515i
$732$		0			0
$733$	7.65019	−	2.04986i	0.282566	−	0.0757134i	−0.114752	−	0.993394i	$-0.536607\pi$
$733$	7.65019	−	2.04986i	0.282566	−	0.0757134i	0.397319	+	0.917681i	$0.369941\pi$
$734$		0			0
$735$	0.646542	−	0.661523i	0.0238480	−	0.0244006i
$736$		0			0
$737$	5.65945	−	9.80245i	0.208468	−	0.361078i
$738$		0			0
$739$	1.87174	−	6.98543i	0.0688531	−	0.256963i	−0.922916	−	0.385001i	$-0.874201\pi$
$739$	1.87174	−	6.98543i	0.0688531	−	0.256963i	0.991769	+	0.128038i	$0.0408678\pi$
$740$		0			0
$741$	5.78013	−	5.78013i	0.212338	−	0.212338i
$742$		0			0
$743$	48.0436			1.76255			0.881274	−	0.472605i	$-0.156686\pi$
$743$	48.0436			1.76255			0.881274	+	0.472605i	$0.156686\pi$
$744$		0			0
$745$	−3.84594	−	6.66136i	−0.140904	−	0.244053i
$746$		0			0
$747$	−3.70857	+	0.993708i	−0.135689	+	0.0363579i
$748$		0			0
$749$	3.82770	−	30.4192i	0.139861	−	1.11149i
$750$		0			0
$751$	−23.9552	−	13.8306i	−0.874138	−	0.504684i	−0.00541712	−	0.999985i	$-0.501724\pi$
$751$	−23.9552	−	13.8306i	−0.874138	−	0.504684i	−0.868721	+	0.495301i	$0.835058\pi$
$752$		0			0
$753$	−3.29273	−	5.70317i	−0.119994	−	0.207835i
$754$		0			0
$755$	2.73354	−	2.73354i	0.0994837	−	0.0994837i
$756$		0			0
$757$	11.4412	+	11.4412i	0.415836	+	0.415836i	0.883766	−	0.467930i	$-0.155000\pi$
$757$	11.4412	+	11.4412i	0.415836	+	0.415836i	−0.467930	+	0.883766i	$0.655000\pi$
$758$		0			0
$759$	−1.71776	+	0.991751i	−0.0623508	+	0.0359983i
$760$		0			0
$761$	−21.0572	+	36.4722i	−0.763324	+	1.32212i	0.177804	+	0.984066i	$0.443101\pi$
$761$	−21.0572	+	36.4722i	−0.763324	+	1.32212i	−0.941128	+	0.338050i	$0.890233\pi$
$762$		0			0
$763$	−29.8262	−	22.6163i	−1.07978	−	0.818764i
$764$		0			0
$765$	0.927152	+	3.46018i	0.0335213	+	0.125103i
$766$		0			0
$767$	−51.2432	+	29.5853i	−1.85029	+	1.06826i
$768$		0			0
$769$			24.9820i			0.900875i	0.892808	+	0.450438i	$0.148732\pi$
$769$			24.9820i			0.900875i	−0.892808	+	0.450438i	$0.851268\pi$
$770$		0			0
$771$	−3.46401	−	3.46401i	−0.124753	−	0.124753i
$772$		0			0
$773$	28.4576	+	7.62520i	1.02355	+	0.274259i	0.731281	−	0.682077i	$-0.238923\pi$
$773$	28.4576	+	7.62520i	1.02355	+	0.274259i	0.292270	+	0.956336i	$0.405590\pi$
$774$		0			0
$775$	−21.4955	−	12.4104i	−0.772141	−	0.445796i
$776$		0			0
$777$	−0.625086	−	0.254735i	−0.0224248	−	0.00913858i
$778$		0			0
$779$	−2.69815	−	10.0696i	−0.0966713	−	0.360782i
$780$		0			0
$781$	19.9609	+	5.34852i	0.714259	+	0.191385i
$782$		0			0
$783$	10.7791			0.385213
$784$		0			0
$785$	−3.02622			−0.108010
$786$		0			0
$787$	−52.5631	−	14.0842i	−1.87367	−	0.502049i	−0.999876	−	0.0157543i	$-0.994985\pi$
$787$	−52.5631	−	14.0842i	−1.87367	−	0.502049i	−0.873795	−	0.486294i	$-0.838348\pi$
$788$		0			0
$789$	0.624293	+	2.32989i	0.0222254	+	0.0829464i
$790$		0			0
$791$	21.6163	+	8.80908i	0.768586	+	0.313215i
$792$		0			0
$793$	19.3241	+	11.1568i	0.686218	+	0.396188i
$794$		0			0
$795$	−0.0737055	−	0.0197493i	−0.00261407	−	0.000700437i
$796$		0			0
$797$	7.86246	+	7.86246i	0.278503	+	0.278503i	0.832511	−	0.554008i	$-0.186902\pi$
$797$	7.86246	+	7.86246i	0.278503	+	0.278503i	−0.554008	+	0.832511i	$0.686902\pi$
$798$		0			0
$799$		−	22.2957i		−	0.788766i
$800$		0			0
$801$	−37.6408	+	21.7319i	−1.32997	+	0.767859i
$802$		0			0
$803$	−4.78299	−	17.8504i	−0.168788	−	0.629925i
$804$		0			0
$805$	3.88379	+	2.94496i	0.136886	+	0.103796i
$806$		0			0
$807$	2.35564	−	4.08009i	0.0829226	−	0.143626i
$808$		0			0
$809$	−3.29250	+	1.90093i	−0.115758	+	0.0668331i	−0.556761	−	0.830673i	$-0.687956\pi$
$809$	−3.29250	+	1.90093i	−0.115758	+	0.0668331i	0.441003	+	0.897506i	$0.354623\pi$
$810$		0			0
$811$	7.73995	+	7.73995i	0.271787	+	0.271787i	0.829819	−	0.558033i	$-0.188444\pi$
$811$	7.73995	+	7.73995i	0.271787	+	0.271787i	−0.558033	+	0.829819i	$0.688444\pi$
$812$		0			0
$813$	1.37870	−	1.37870i	0.0483530	−	0.0483530i
$814$		0			0
$815$	1.20544	+	2.08789i	0.0422248	+	0.0731356i
$816$		0			0
$817$	−15.3976	−	8.88982i	−0.538695	−	0.311016i
$818$		0			0
$819$	5.90091	−	46.8954i	0.206195	−	1.63866i
$820$		0			0
$821$	−12.8658	+	3.44738i	−0.449019	+	0.120314i	−0.476240	−	0.879315i	$-0.658001\pi$
$821$	−12.8658	+	3.44738i	−0.449019	+	0.120314i	0.0272212	+	0.999629i	$0.491334\pi$
$822$		0			0
$823$	−5.00600	−	8.67064i	−0.174498	−	0.302239i	0.765489	−	0.643448i	$-0.222497\pi$
$823$	−5.00600	−	8.67064i	−0.174498	−	0.302239i	−0.939987	+	0.341209i	$0.889164\pi$
$824$		0			0
$825$	−2.63424			−0.0917124
$826$		0			0
$827$	−1.10671	+	1.10671i	−0.0384842	+	0.0384842i	−0.726087	−	0.687603i	$-0.758663\pi$
$827$	−1.10671	+	1.10671i	−0.0384842	+	0.0384842i	0.687603	+	0.726087i	$0.258663\pi$
$828$		0			0
$829$	−11.9413	+	44.5656i	−0.414739	+	1.54783i	0.370618	+	0.928785i	$0.379146\pi$
$829$	−11.9413	+	44.5656i	−0.414739	+	1.54783i	−0.785357	+	0.619043i	$0.787521\pi$
$830$		0			0
$831$	−2.26434	+	3.92195i	−0.0785490	+	0.136051i
$832$		0			0
$833$	16.0136	+	4.09487i	0.554840	+	0.141879i
$834$		0			0
$835$	−4.51390	+	1.20950i	−0.156210	+	0.0418563i
$836$		0			0
$837$	−2.05915	+	7.68484i	−0.0711745	+	0.265627i
$838$		0			0
$839$			23.6366i			0.816027i	0.912976	+	0.408013i	$0.133778\pi$
$839$			23.6366i			0.816027i	−0.912976	+	0.408013i	$0.866222\pi$
$840$		0			0
$841$		−	21.4878i		−	0.740958i
$842$		0			0
$843$	0.938409	−	3.50219i	0.0323205	−	0.120622i
$844$		0			0
$845$	12.0125	−	3.21875i	0.413244	−	0.110728i
$846$		0			0
$847$	10.1556	+	13.0792i	0.348949	+	0.449408i
$848$		0			0
$849$	−0.686658	+	1.18933i	−0.0235660	+	0.0408176i
$850$		0			0
$851$	0.920552	−	3.43555i	0.0315561	−	0.117769i
$852$		0			0
$853$	8.67274	−	8.67274i	0.296949	−	0.296949i	−0.542869	−	0.839818i	$-0.682662\pi$
$853$	8.67274	−	8.67274i	0.296949	−	0.296949i	0.839818	+	0.542869i	$0.182662\pi$
$854$		0			0
$855$	−7.96955			−0.272553
$856$		0			0
$857$	19.6513	+	34.0371i	0.671276	+	1.16268i	0.977543	+	0.210738i	$0.0675867\pi$
$857$	19.6513	+	34.0371i	0.671276	+	1.16268i	−0.306267	+	0.951946i	$0.599080\pi$
$858$		0			0
$859$	41.0276	−	10.9933i	1.39984	−	0.375087i	0.521555	−	0.853218i	$-0.325352\pi$
$859$	41.0276	−	10.9933i	1.39984	−	0.375087i	0.878289	+	0.478131i	$0.158685\pi$
$860$		0			0
$861$	1.06943	+	0.810914i	0.0364460	+	0.0276359i
$862$		0			0
$863$	37.2542	+	21.5087i	1.26815	+	0.732165i	0.974637	−	0.223790i	$-0.0718431\pi$
$863$	37.2542	+	21.5087i	1.26815	+	0.732165i	0.293510	+	0.955956i	$0.405176\pi$
$864$		0			0
$865$	−4.77669	−	8.27347i	−0.162412	−	0.281306i
$866$		0			0
$867$	−2.06496	+	2.06496i	−0.0701297	+	0.0701297i
$868$		0			0
$869$	3.04518	+	3.04518i	0.103301	+	0.103301i
$870$		0			0
$871$	27.4045	−	15.8220i	0.928565	−	0.536108i
$872$		0			0
$873$	−15.0416	+	26.0527i	−0.509080	+	0.881752i
$874$		0			0
$875$	5.16454	+	12.2691i	0.174593	+	0.414772i
$876$		0			0
$877$	−3.76697	−	14.0585i	−0.127201	−	0.474722i	0.872707	−	0.488244i	$-0.162362\pi$
$877$	−3.76697	−	14.0585i	−0.127201	−	0.474722i	−0.999909	+	0.0135219i	$0.995696\pi$
$878$		0			0
$879$	2.57493	−	1.48664i	0.0868503	−	0.0501431i
$880$		0			0
$881$			15.1419i			0.510145i	0.966922	+	0.255072i	$0.0820993\pi$
$881$			15.1419i			0.510145i	−0.966922	+	0.255072i	$0.917901\pi$
$882$		0			0
$883$	−22.0225	−	22.0225i	−0.741116	−	0.741116i	0.231677	−	0.972793i	$-0.425579\pi$
$883$	−22.0225	−	22.0225i	−0.741116	−	0.741116i	−0.972793	+	0.231677i	$0.925579\pi$
$884$		0			0
$885$	−1.24068	−	0.332439i	−0.0417050	−	0.0111748i
$886$		0			0
$887$	10.4138	+	6.01243i	0.349662	+	0.201877i	0.664536	−	0.747256i	$-0.268629\pi$
$887$	10.4138	+	6.01243i	0.349662	+	0.201877i	−0.314874	+	0.949133i	$0.601962\pi$
$888$		0			0
$889$	8.04970	−	19.7529i	0.269978	−	0.662490i
$890$		0			0
$891$	−4.74307	−	17.7014i	−0.158899	−	0.593019i
$892$		0			0
$893$	47.9120	+	12.8380i	1.60331	+	0.429607i
$894$		0			0
$895$	−8.53615			−0.285332
$896$		0			0
$897$	−5.54523			−0.185150
$898$		0			0
$899$	35.9948	+	9.64476i	1.20049	+	0.321671i
$900$		0			0
$901$	−0.352902	−	1.31705i	−0.0117569	−	0.0438772i
$902$		0			0
$903$	2.26764	−	0.311761i	0.0754624	−	0.0103748i
$904$		0			0
$905$	8.97434	+	5.18134i	0.298317	+	0.172233i
$906$		0			0
$907$	35.8938	+	9.61773i	1.19184	+	0.319351i	0.799611	−	0.600518i	$-0.205039\pi$
$907$	35.8938	+	9.61773i	1.19184	+	0.319351i	0.392224	+	0.919870i	$0.371706\pi$
$908$		0			0
$909$	18.4561	+	18.4561i	0.612150	+	0.612150i
$910$		0			0
$911$			39.6140i			1.31247i	0.754557	+	0.656234i	$0.227852\pi$
$911$			39.6140i			1.31247i	−0.754557	+	0.656234i	$0.772148\pi$
$912$		0			0
$913$	−2.46708	+	1.42437i	−0.0816484	+	0.0471397i
$914$		0			0
$915$	0.125364	+	0.467866i	0.00414442	+	0.0154672i
$916$		0			0
$917$	−6.58822	+	52.3575i	−0.217562	+	1.72900i
$918$		0			0
$919$	−17.6814	+	30.6250i	−0.583255	+	1.01023i	0.411836	+	0.911258i	$0.364888\pi$
$919$	−17.6814	+	30.6250i	−0.583255	+	1.01023i	−0.995091	+	0.0989687i	$0.968446\pi$
$920$		0			0
$921$	3.17592	−	1.83362i	0.104650	−	0.0604198i
$922$		0			0
$923$	40.8516	+	40.8516i	1.34465	+	1.34465i
$924$		0			0
$925$	3.34010	−	3.34010i	0.109822	−	0.109822i
$926$		0			0
$927$	−28.1555	−	48.7667i	−0.924748	−	1.60171i
$928$		0			0
$929$	−2.53541	−	1.46382i	−0.0831840	−	0.0480263i	0.457831	−	0.889039i	$-0.348626\pi$
$929$	−2.53541	−	1.46382i	−0.0831840	−	0.0480263i	−0.541015	+	0.841013i	$0.681960\pi$
$930$		0			0
$931$	−18.0203	+	32.0544i	−0.590592	+	1.05054i
$932$		0			0
$933$	−6.83392	+	1.83114i	−0.223732	+	0.0599489i
$934$		0			0
$935$	1.32897	+	2.30184i	0.0434619	+	0.0752782i
$936$		0			0
$937$	38.5253			1.25857			0.629283	−	0.777176i	$-0.283348\pi$
$937$	38.5253			1.25857			0.629283	+	0.777176i	$0.283348\pi$
$938$		0			0
$939$	3.65716	−	3.65716i	0.119347	−	0.119347i
$940$		0			0
$941$	0.0696597	−	0.259973i	0.00227084	−	0.00847489i	−0.964781	−	0.263054i	$-0.915270\pi$
$941$	0.0696597	−	0.259973i	0.00227084	−	0.00847489i	0.967052	+	0.254579i	$0.0819369\pi$
$942$		0			0
$943$	−3.53596	+	6.12446i	−0.115147	+	0.199440i
$944$		0			0
$945$	1.63884	−	1.27250i	0.0533115	−	0.0413945i
$946$		0			0
$947$	42.3504	−	11.3478i	1.37620	−	0.368753i	0.506463	−	0.862261i	$-0.330953\pi$
$947$	42.3504	−	11.3478i	1.37620	−	0.368753i	0.869741	+	0.493509i	$0.164286\pi$
$948$		0			0
$949$	13.3717	−	49.9038i	0.434064	−	1.61995i
$950$		0			0
$951$			2.33641i			0.0757632i
$952$		0			0
$953$			40.1902i			1.30189i	0.759125	+	0.650945i	$0.225627\pi$
$953$			40.1902i			1.30189i	−0.759125	+	0.650945i	$0.774373\pi$
$954$		0			0
$955$	−2.03708	+	7.60248i	−0.0659183	+	0.246011i
$956$		0			0
$957$	3.82013	−	1.02360i	0.123487	−	0.0330883i
$958$		0			0
$959$	1.73610	−	0.238683i	0.0560617	−	0.00770749i
$960$		0			0
$961$	1.74773	−	3.02716i	0.0563783	−	0.0976502i
$962$		0			0
$963$	8.80165	−	32.8482i	0.283629	−	1.05852i
$964$		0			0
$965$	−5.92388	+	5.92388i	−0.190697	+	0.190697i
$966$		0			0
$967$	13.9779			0.449498			0.224749	−	0.974417i	$-0.427844\pi$
$967$	13.9779			0.449498			0.224749	+	0.974417i	$0.427844\pi$
$968$		0			0
$969$	1.58538	+	2.74596i	0.0509298	+	0.0882130i
$970$		0			0
$971$	8.02262	−	2.14965i	0.257458	−	0.0689857i	−0.127781	−	0.991802i	$-0.540786\pi$
$971$	8.02262	−	2.14965i	0.257458	−	0.0689857i	0.385239	+	0.922817i	$0.374119\pi$
$972$		0			0
$973$	9.28902	+	22.0674i	0.297792	+	0.707449i
$974$		0			0
$975$	−6.37783	−	3.68224i	−0.204254	−	0.117926i
$976$		0			0
$977$	2.64300	+	4.57781i	0.0845570	+	0.146457i	0.905202	−	0.424981i	$-0.139719\pi$
$977$	2.64300	+	4.57781i	0.0845570	+	0.146457i	−0.820645	+	0.571438i	$0.806386\pi$
$978$		0			0
$979$	−22.8036	+	22.8036i	−0.728805	+	0.728805i
$980$		0			0
$981$	−29.3581	−	29.3581i	−0.937331	−	0.937331i
$982$		0			0
$983$	3.47962	−	2.00896i	0.110982	−	0.0640758i	−0.443481	−	0.896284i	$-0.646257\pi$
$983$	3.47962	−	2.00896i	0.110982	−	0.0640758i	0.554464	+	0.832208i	$0.312923\pi$
$984$		0			0
$985$	−1.72671	+	2.99074i	−0.0550174	+	0.0952929i
$986$		0			0
$987$	−5.88566	+	2.47750i	−0.187343	+	0.0788596i
$988$		0			0
$989$	3.12167	+	11.6502i	0.0992632	+	0.370455i
$990$		0			0
$991$	1.44893	−	0.836541i	0.0460268	−	0.0265736i	−0.476810	−	0.879006i	$-0.658207\pi$
$991$	1.44893	−	0.836541i	0.0460268	−	0.0265736i	0.522837	+	0.852433i	$0.324874\pi$
$992$		0			0
$993$			7.14060i			0.226600i
$994$		0			0
$995$	−2.58985	−	2.58985i	−0.0821039	−	0.0821039i
$996$		0			0
$997$	4.81753	+	1.29085i	0.152573	+	0.0408817i	0.334297	−	0.942468i	$-0.391501\pi$
$997$	4.81753	+	1.29085i	0.152573	+	0.0408817i	−0.181724	+	0.983350i	$0.558168\pi$
$998$		0			0
$999$	−1.31123	−	0.757041i	−0.0414856	−	0.0239517i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	448.2.z.a.271.7		56
4.3	odd	2		112.2.v.a.75.12	yes	56
7.3	odd	6	inner	448.2.z.a.143.7		56
8.3	odd	2		896.2.z.b.159.7		56
8.5	even	2		896.2.z.a.159.8		56
16.3	odd	4	inner	448.2.z.a.47.7		56
16.5	even	4		896.2.z.b.607.7		56
16.11	odd	4		896.2.z.a.607.8		56
16.13	even	4		112.2.v.a.19.2	yes	56
28.3	even	6		112.2.v.a.59.2	yes	56
28.11	odd	6		784.2.w.f.619.2		56
28.19	even	6		784.2.j.a.587.15		56
28.23	odd	6		784.2.j.a.587.16		56
28.27	even	2		784.2.w.f.411.12		56
56.3	even	6		896.2.z.b.31.7		56
56.45	odd	6		896.2.z.a.31.8		56
112.3	even	12	inner	448.2.z.a.367.7		56
112.13	odd	4		784.2.w.f.19.2		56
112.45	odd	12		112.2.v.a.3.12	✓	56
112.59	even	12		896.2.z.a.479.8		56
112.61	odd	12		784.2.j.a.195.16		56
112.93	even	12		784.2.j.a.195.15		56
112.101	odd	12		896.2.z.b.479.7		56
112.109	even	12		784.2.w.f.227.12		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.v.a.3.12	✓	56	112.45	odd	12
112.2.v.a.19.2	yes	56	16.13	even	4
112.2.v.a.59.2	yes	56	28.3	even	6
112.2.v.a.75.12	yes	56	4.3	odd	2
448.2.z.a.47.7		56	16.3	odd	4	inner
448.2.z.a.143.7		56	7.3	odd	6	inner
448.2.z.a.271.7		56	1.1	even	1	trivial
448.2.z.a.367.7		56	112.3	even	12	inner
784.2.j.a.195.15		56	112.93	even	12
784.2.j.a.195.16		56	112.61	odd	12
784.2.j.a.587.15		56	28.19	even	6
784.2.j.a.587.16		56	28.23	odd	6
784.2.w.f.19.2		56	112.13	odd	4
784.2.w.f.227.12		56	112.109	even	12
784.2.w.f.411.12		56	28.27	even	2
784.2.w.f.619.2		56	28.11	odd	6
896.2.z.a.31.8		56	56.45	odd	6
896.2.z.a.159.8		56	8.5	even	2
896.2.z.a.479.8		56	112.59	even	12
896.2.z.a.607.8		56	16.11	odd	4
896.2.z.b.31.7		56	56.3	even	6
896.2.z.b.159.7		56	8.3	odd	2
896.2.z.b.479.7		56	112.101	odd	12
896.2.z.b.607.7		56	16.5	even	4

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:	\( N \)	\(=\)	\( 448 = 2^{6} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	448.z (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.246909 + 0.0661591i) q^{3} +(-0.133797 - 0.499339i) q^{5} +(-2.45011 - 0.998472i) q^{7} +(-2.54149 - 1.46733i) q^{9} +O(q^{10})\)	\(q+(0.246909 + 0.0661591i) q^{3} +(-0.133797 - 0.499339i) q^{5} +(-2.45011 - 0.998472i) q^{7} +(-2.54149 - 1.46733i) q^{9} +(-2.10325 - 0.563565i) q^{11} +(-4.30447 - 4.30447i) q^{13} -0.132143i q^{15} +(2.04492 - 1.18064i) q^{17} +(1.35963 + 5.07421i) q^{19} +(-0.538897 - 0.408629i) q^{21} +(1.78181 - 3.08619i) q^{23} +(4.09869 - 2.36638i) q^{25} +(-1.07269 - 1.07269i) q^{27} +(-5.02433 + 5.02433i) q^{29} +(-2.62224 - 4.54185i) q^{31} +(-0.482027 - 0.278298i) q^{33} +(-0.170757 + 1.35703i) q^{35} +(0.964060 - 0.258319i) q^{37} +(-0.778033 - 1.34759i) q^{39} -1.98447 q^{41} +(-2.39322 + 2.39322i) q^{43} +(-0.392650 + 1.46539i) q^{45} +(4.72113 - 8.17724i) q^{47} +(5.00611 + 4.89274i) q^{49} +(0.583019 - 0.156220i) q^{51} +(0.149454 - 0.557771i) q^{53} +1.12564i q^{55} +1.34282i q^{57} +(2.51575 - 9.38891i) q^{59} +(-3.54060 + 0.948702i) q^{61} +(4.76185 + 6.13273i) q^{63} +(-1.57346 + 2.72531i) q^{65} +(-1.34540 + 5.02111i) q^{67} +(0.644125 - 0.644125i) q^{69} -9.49052 q^{71} +(4.24351 + 7.34998i) q^{73} +(1.16856 - 0.313115i) q^{75} +(4.59050 + 3.48084i) q^{77} +(-1.71282 - 0.988896i) q^{79} +(4.20810 + 7.28864i) q^{81} +(0.925102 - 0.925102i) q^{83} +(-0.863142 - 0.863142i) q^{85} +(-1.57296 + 0.908148i) q^{87} +(7.40526 - 12.8263i) q^{89} +(6.24854 + 14.8443i) q^{91} +(-0.346970 - 1.29491i) q^{93} +(2.35183 - 1.35783i) q^{95} -10.2510i q^{97} +(4.51846 + 4.51846i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 6 q^{3} - 6 q^{5} + 8 q^{7}+O(q^{10}) \) 56 * q + 6 * q^3 - 6 * q^5 + 8 * q^7	\( 56 q + 6 q^{3} - 6 q^{5} + 8 q^{7} - 2 q^{11} - 12 q^{17} + 6 q^{19} - 10 q^{21} + 12 q^{23} - 24 q^{29} - 12 q^{33} + 2 q^{35} + 6 q^{37} + 4 q^{39} + 12 q^{45} - 8 q^{49} + 34 q^{51} + 6 q^{53} - 42 q^{59} - 6 q^{61} - 4 q^{65} - 6 q^{67} + 80 q^{71} - 24 q^{75} + 10 q^{77} - 8 q^{81} - 28 q^{85} + 12 q^{87} - 16 q^{91} + 10 q^{93} + 16 q^{99}+O(q^{100}) \) 56 * q + 6 * q^3 - 6 * q^5 + 8 * q^7 - 2 * q^11 - 12 * q^17 + 6 * q^19 - 10 * q^21 + 12 * q^23 - 24 * q^29 - 12 * q^33 + 2 * q^35 + 6 * q^37 + 4 * q^39 + 12 * q^45 - 8 * q^49 + 34 * q^51 + 6 * q^53 - 42 * q^59 - 6 * q^61 - 4 * q^65 - 6 * q^67 + 80 * q^71 - 24 * q^75 + 10 * q^77 - 8 * q^81 - 28 * q^85 + 12 * q^87 - 16 * q^91 + 10 * q^93 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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