LMFDB - Embedded newform 950.2.bb.b.243.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(143,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([27, 34]))

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

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

chi := DirichletCharacter("950.143");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.bb (of order $36$, degree $12$, 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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$4$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			243.1
Character	$\chi$	$=$	950.243
Dual form			950.2.bb.b.907.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.422618 - 0.906308i) q^{2} +(-0.284489 - 0.199201i) q^{3} +(-0.642788 + 0.766044i) q^{4} +(-0.0603074 + 0.342020i) q^{6} +(-0.127266 - 0.474963i) q^{7} +(0.965926 + 0.258819i) q^{8} +(-0.984808 - 2.70574i) q^{9} +O(q^{10})$	\(q+(-0.422618 - 0.906308i) q^{2} +(-0.284489 - 0.199201i) q^{3} +(-0.642788 + 0.766044i) q^{4} +(-0.0603074 + 0.342020i) q^{6} +(-0.127266 - 0.474963i) q^{7} +(0.965926 + 0.258819i) q^{8} +(-0.984808 - 2.70574i) q^{9} +(-2.42394 - 4.19839i) q^{11} +(0.335463 - 0.0898869i) q^{12} +(2.60862 + 3.72550i) q^{13} +(-0.376678 + 0.316070i) q^{14} +(-0.173648 - 0.984808i) q^{16} +(5.97747 - 2.78734i) q^{17} +(-2.03603 + 2.03603i) q^{18} +(-3.35080 + 2.78785i) q^{19} +(-0.0584074 + 0.160473i) q^{21} +(-2.78063 + 3.97115i) q^{22} +(0.0964329 + 1.10223i) q^{23} +(-0.223238 - 0.266044i) q^{24} +(2.27400 - 3.93868i) q^{26} +(-0.528480 + 1.97231i) q^{27} +(0.445648 + 0.207809i) q^{28} +(-5.74005 + 2.08921i) q^{29} +(-7.25316 - 4.18761i) q^{31} +(-0.819152 + 0.573576i) q^{32} +(-0.146740 + 1.67724i) q^{33} +(-5.05238 - 4.23945i) q^{34} +(2.70574 + 0.984808i) q^{36} +(-7.26449 - 7.26449i) q^{37} +(3.94276 + 1.85866i) q^{38} -1.57950i q^{39} +(5.95655 - 1.05030i) q^{41} +(0.170122 - 0.0148837i) q^{42} +(-8.97808 - 0.785480i) q^{43} +(4.77423 + 0.841826i) q^{44} +(0.958208 - 0.553221i) q^{46} +(2.11434 - 4.53422i) q^{47} +(-0.146774 + 0.314757i) q^{48} +(5.85278 - 3.37911i) q^{49} +(-2.25576 - 0.397752i) q^{51} +(-4.53069 - 0.396384i) q^{52} +(-7.76179 + 0.679069i) q^{53} +(2.01087 - 0.354570i) q^{54} -0.491718i q^{56} +(1.50861 - 0.125628i) q^{57} +(4.31931 + 4.31931i) q^{58} +(-5.32259 - 1.93726i) q^{59} +(-10.6545 - 8.94018i) q^{61} +(-0.729949 + 8.34335i) q^{62} +(-1.15979 + 0.812096i) q^{63} +(0.866025 + 0.500000i) q^{64} +(1.58211 - 0.575843i) q^{66} +(0.563946 + 0.262972i) q^{67} +(-1.70702 + 6.37068i) q^{68} +(0.192132 - 0.332782i) q^{69} +(-2.13695 - 2.54672i) q^{71} +(-0.250955 - 2.86843i) q^{72} +(-0.412181 + 0.588655i) q^{73} +(-3.51376 + 9.65397i) q^{74} +(0.0182365 - 4.35886i) q^{76} +(-1.68559 + 1.68559i) q^{77} +(-1.43152 + 0.667527i) q^{78} +(1.35213 + 7.66833i) q^{79} +(-6.07398 + 5.09667i) q^{81} +(-3.46924 - 4.95459i) q^{82} +(8.99806 - 2.41102i) q^{83} +(-0.0853859 - 0.147893i) q^{84} +(3.08241 + 8.46886i) q^{86} +(2.04915 + 0.549068i) q^{87} +(-1.25472 - 4.68269i) q^{88} +(0.290225 - 1.64595i) q^{89} +(1.43749 - 1.71313i) q^{91} +(-0.906345 - 0.634630i) q^{92} +(1.22926 + 2.63616i) q^{93} -5.00295 q^{94} +0.347296 q^{96} +(6.58259 + 14.1164i) q^{97} +(-5.53600 - 3.87635i) q^{98} +(-8.97262 + 10.6931i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 48 q^{6}+O(q^{10}) $ 48 * q - 48 * q^6	$ 48 q - 48 q^{6} - 12 q^{11} + 36 q^{21} - 72 q^{31} + 48 q^{36} + 96 q^{41} + 72 q^{46} - 48 q^{51} - 108 q^{61} + 24 q^{66} - 60 q^{71} - 48 q^{76} - 168 q^{81} - 48 q^{86} + 252 q^{91}+O(q^{100}) $ 48 * q - 48 * q^6 - 12 * q^11 + 36 * q^21 - 72 * q^31 + 48 * q^36 + 96 * q^41 + 72 * q^46 - 48 * q^51 - 108 * q^61 + 24 * q^66 - 60 * q^71 - 48 * q^76 - 168 * q^81 - 48 * q^86 + 252 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{11}{18}\right)$

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 $

$2$	−0.422618	−	0.906308i	−0.298836	−	0.640856i
$2$	−0.422618	−	0.906308i	−0.298836	−	0.640856i
$3$	−0.284489	−	0.199201i	−0.164250	−	0.115009i	0.488562	−	0.872529i	$-0.337522\pi$
$3$	−0.284489	−	0.199201i	−0.164250	−	0.115009i	−0.652811	+	0.757521i	$0.726411\pi$
$4$	−0.642788	+	0.766044i	−0.321394	+	0.383022i
$5$		0			0
$5$		0			0
$6$	−0.0603074	+	0.342020i	−0.0246204	+	0.139629i
$7$	−0.127266	−	0.474963i	−0.0481020	−	0.179519i	0.937695	−	0.347459i	$-0.112955\pi$
$7$	−0.127266	−	0.474963i	−0.0481020	−	0.179519i	−0.985797	+	0.167940i	$0.946289\pi$
$8$	0.965926	+	0.258819i	0.341506	+	0.0915064i
$9$	−0.984808	−	2.70574i	−0.328269	−	0.901912i
$10$		0			0
$11$	−2.42394	−	4.19839i	−0.730845	−	1.26586i	−0.956522	−	0.291659i	$-0.905793\pi$
$11$	−2.42394	−	4.19839i	−0.730845	−	1.26586i	0.225677	−	0.974202i	$-0.427541\pi$
$12$	0.335463	−	0.0898869i	0.0968397	−	0.0259481i
$13$	2.60862	+	3.72550i	0.723502	+	1.03327i	0.997439	+	0.0715208i	$0.0227852\pi$
$13$	2.60862	+	3.72550i	0.723502	+	1.03327i	−0.273937	+	0.961748i	$0.588326\pi$
$14$	−0.376678	+	0.316070i	−0.100671	+	0.0844733i
$15$		0			0
$16$	−0.173648	−	0.984808i	−0.0434120	−	0.246202i
$17$	5.97747	−	2.78734i	1.44975	−	0.676029i	0.471197	−	0.882028i	$-0.343822\pi$
$17$	5.97747	−	2.78734i	1.44975	−	0.676029i	0.978552	+	0.205998i	$0.0660442\pi$
$18$	−2.03603	+	2.03603i	−0.479898	+	0.479898i
$19$	−3.35080	+	2.78785i	−0.768727	+	0.639577i
$19$	−3.35080	+	2.78785i	−0.768727	+	0.639577i
$20$		0			0
$21$	−0.0584074	+	0.160473i	−0.0127455	+	0.0350181i
$22$	−2.78063	+	3.97115i	−0.592832	+	0.846652i
$23$	0.0964329	+	1.10223i	0.0201076	+	0.229831i	0.999598	+	0.0283418i	$0.00902267\pi$
$23$	0.0964329	+	1.10223i	0.0201076	+	0.229831i	−0.979491	+	0.201490i	$0.935422\pi$
$24$	−0.223238	−	0.266044i	−0.0455682	−	0.0543061i
$25$		0			0
$26$	2.27400	−	3.93868i	0.445968	−	0.772439i
$27$	−0.528480	+	1.97231i	−0.101706	+	0.379572i
$28$	0.445648	+	0.207809i	0.0842195	+	0.0392722i
$29$	−5.74005	+	2.08921i	−1.06590	+	0.387956i	−0.814642	−	0.579964i	$-0.803067\pi$
$29$	−5.74005	+	2.08921i	−1.06590	+	0.387956i	−0.251258	+	0.967920i	$0.580844\pi$
$30$		0			0
$31$	−7.25316	−	4.18761i	−1.30271	−	0.752117i	−0.321838	−	0.946795i	$-0.604301\pi$
$31$	−7.25316	−	4.18761i	−1.30271	−	0.752117i	−0.980867	+	0.194677i	$0.937634\pi$
$32$	−0.819152	+	0.573576i	−0.144807	+	0.101395i
$33$	−0.146740	+	1.67724i	−0.0255441	+	0.291971i
$34$	−5.05238	−	4.23945i	−0.866475	−	0.727059i
$35$		0			0
$36$	2.70574	+	0.984808i	0.450956	+	0.164135i
$37$	−7.26449	−	7.26449i	−1.19427	−	1.19427i	−0.975855	−	0.218420i	$-0.929910\pi$
$37$	−7.26449	−	7.26449i	−1.19427	−	1.19427i	−0.218420	−	0.975855i	$-0.570090\pi$
$38$	3.94276	+	1.85866i	0.639601	+	0.301515i
$39$		−	1.57950i		−	0.252923i
$40$		0			0
$41$	5.95655	−	1.05030i	0.930257	−	0.164029i	0.312069	−	0.950059i	$-0.398978\pi$
$41$	5.95655	−	1.05030i	0.930257	−	0.164029i	0.618188	+	0.786030i	$0.287867\pi$
$42$	0.170122	−	0.0148837i	0.0262504	−	0.00229661i
$43$	−8.97808	−	0.785480i	−1.36914	−	0.119785i	−0.621255	−	0.783608i	$-0.713377\pi$
$43$	−8.97808	−	0.785480i	−1.36914	−	0.119785i	−0.747889	+	0.663824i	$0.768933\pi$
$44$	4.77423	+	0.841826i	0.719742	+	0.126910i
$45$		0			0
$46$	0.958208	−	0.553221i	0.141280	−	0.0815681i
$47$	2.11434	−	4.53422i	0.308408	−	0.661383i	−0.689619	−	0.724173i	$-0.742222\pi$
$47$	2.11434	−	4.53422i	0.308408	−	0.661383i	0.998027	+	0.0627893i	$0.0199996\pi$
$48$	−0.146774	+	0.314757i	−0.0211850	+	0.0454313i
$49$	5.85278	−	3.37911i	0.836112	−	0.482730i
$50$		0			0
$51$	−2.25576	−	0.397752i	−0.315870	−	0.0556964i
$52$	−4.53069	−	0.396384i	−0.628294	−	0.0549686i
$53$	−7.76179	+	0.679069i	−1.06616	+	0.0932773i	−0.606709	−	0.794924i	$-0.707511\pi$
$53$	−7.76179	+	0.679069i	−1.06616	+	0.0932773i	−0.459455	+	0.888201i	$0.651955\pi$
$54$	2.01087	−	0.354570i	0.273644	−	0.0482509i
$55$		0			0
$56$		−	0.491718i		−	0.0657086i
$57$	1.50861	−	0.125628i	0.199820	−	0.0166399i
$58$	4.31931	+	4.31931i	0.567154	+	0.567154i
$59$	−5.32259	−	1.93726i	−0.692942	−	0.252210i	−0.0285475	−	0.999592i	$-0.509088\pi$
$59$	−5.32259	−	1.93726i	−0.692942	−	0.252210i	−0.664394	+	0.747382i	$0.731310\pi$
$60$		0			0
$61$	−10.6545	−	8.94018i	−1.36417	−	1.14467i	−0.974671	−	0.223645i	$-0.928204\pi$
$61$	−10.6545	−	8.94018i	−1.36417	−	1.14467i	−0.389497	−	0.921028i	$-0.627351\pi$
$62$	−0.729949	+	8.34335i	−0.0927036	+	1.05961i
$63$	−1.15979	+	0.812096i	−0.146120	+	0.102314i
$64$	0.866025	+	0.500000i	0.108253	+	0.0625000i
$65$		0			0
$66$	1.58211	−	0.575843i	0.194745	−	0.0708813i
$67$	0.563946	+	0.262972i	0.0688970	+	0.0321272i	0.456761	−	0.889589i	$-0.349009\pi$
$67$	0.563946	+	0.262972i	0.0688970	+	0.0321272i	−0.387864	+	0.921716i	$0.626787\pi$
$68$	−1.70702	+	6.37068i	−0.207006	+	0.772558i
$69$	0.192132	−	0.332782i	0.0231299	−	0.0400622i
$70$		0			0
$71$	−2.13695	−	2.54672i	−0.253609	−	0.302240i	0.624186	−	0.781276i	$-0.285431\pi$
$71$	−2.13695	−	2.54672i	−0.253609	−	0.302240i	−0.877795	+	0.479036i	$0.840986\pi$
$72$	−0.250955	−	2.86843i	−0.0295753	−	0.338048i
$73$	−0.412181	+	0.588655i	−0.0482421	+	0.0688969i	−0.842548	−	0.538621i	$-0.818946\pi$
$73$	−0.412181	+	0.588655i	−0.0482421	+	0.0688969i	0.794306	+	0.607517i	$0.207835\pi$
$74$	−3.51376	+	9.65397i	−0.408466	+	1.12225i
$75$		0			0
$76$	0.0182365	−	4.35886i	0.00209187	−	0.499996i
$77$	−1.68559	+	1.68559i	−0.192091	+	0.192091i
$78$	−1.43152	+	0.667527i	−0.162087	+	0.0755825i
$79$	1.35213	+	7.66833i	0.152127	+	0.862755i	0.961366	+	0.275275i	$0.0887689\pi$
$79$	1.35213	+	7.66833i	0.152127	+	0.862755i	−0.809239	+	0.587480i	$0.800120\pi$
$80$		0			0
$81$	−6.07398	+	5.09667i	−0.674886	+	0.566297i
$82$	−3.46924	−	4.95459i	−0.383114	−	0.547143i
$83$	8.99806	−	2.41102i	0.987665	−	0.264644i	0.271396	−	0.962468i	$-0.412515\pi$
$83$	8.99806	−	2.41102i	0.987665	−	0.264644i	0.716270	+	0.697824i	$0.245848\pi$
$84$	−0.0853859	−	0.147893i	−0.00931637	−	0.0161364i
$85$		0			0
$86$	3.08241	+	8.46886i	0.332385	+	0.913221i
$87$	2.04915	+	0.549068i	0.219692	+	0.0588663i
$88$	−1.25472	−	4.68269i	−0.133754	−	0.499177i
$89$	0.290225	−	1.64595i	0.0307638	−	0.174470i	−0.965555	−	0.260201i	$-0.916211\pi$
$89$	0.290225	−	1.64595i	0.0307638	−	0.174470i	0.996318	+	0.0857304i	$0.0273224\pi$
$90$		0			0
$91$	1.43749	−	1.71313i	0.150690	−	0.179585i
$92$	−0.906345	−	0.634630i	−0.0944930	−	0.0661647i
$93$	1.22926	+	2.63616i	0.127469	+	0.273357i
$94$	−5.00295			−0.516015
$95$		0			0
$96$	0.347296			0.0354458
$97$	6.58259	+	14.1164i	0.668361	+	1.43331i	0.888980	+	0.457945i	$0.151414\pi$
$97$	6.58259	+	14.1164i	0.668361	+	1.43331i	−0.220619	+	0.975360i	$0.570808\pi$
$98$	−5.53600	−	3.87635i	−0.559221	−	0.391571i
$99$	−8.97262	+	10.6931i	−0.901782	+	1.07470i
$100$		0			0
$101$	0.279319	−	1.58409i	0.0277932	−	0.157623i	−0.967753	−	0.251903i	$-0.918944\pi$
$101$	0.279319	−	1.58409i	0.0277932	−	0.157623i	0.995546	+	0.0942796i	$0.0300548\pi$
$102$	0.592841	+	2.21251i	0.0587000	+	0.219071i
$103$	−10.2690	−	2.75156i	−1.01183	−	0.271119i	−0.285437	−	0.958397i	$-0.592139\pi$
$103$	−10.2690	−	2.75156i	−1.01183	−	0.271119i	−0.726395	+	0.687278i	$0.758805\pi$
$104$	1.55551	+	4.27372i	0.152530	+	0.419073i
$105$		0			0
$106$	3.89572	+	6.74759i	0.378386	+	0.655384i
$107$	−6.08889	+	1.63151i	−0.588635	+	0.157724i	−0.540829	−	0.841132i	$-0.681890\pi$
$107$	−6.08889	+	1.63151i	−0.588635	+	0.157724i	−0.0478058	+	0.998857i	$0.515223\pi$
$108$	−1.17118	−	1.67262i	−0.112697	−	0.160948i
$109$	11.9261	−	10.0072i	1.14232	−	0.958518i	0.142805	−	0.989751i	$-0.454388\pi$
$109$	11.9261	−	10.0072i	1.14232	−	0.958518i	0.999512	+	0.0312333i	$0.00994349\pi$
$110$		0			0
$111$	0.619570	+	3.51376i	0.0588070	+	0.333511i
$112$	−0.445648	+	0.207809i	−0.0421098	+	0.0196361i
$113$	−6.31645	+	6.31645i	−0.594202	+	0.594202i	−0.938764	−	0.344562i	$-0.888028\pi$
$113$	−6.31645	+	6.31645i	−0.594202	+	0.594202i	0.344562	+	0.938764i	$0.388028\pi$
$114$	−0.751423	−	1.31417i	−0.0703772	−	0.123083i
$115$		0			0
$116$	2.08921	−	5.74005i	0.193978	−	0.532950i
$117$	7.51124	−	10.7272i	0.694414	−	0.991726i
$118$	0.493666	+	5.64262i	0.0454456	+	0.519446i
$119$	−2.08461	−	2.48434i	−0.191096	−	0.227739i
$120$		0			0
$121$	−6.25097	+	10.8270i	−0.568270	+	0.984273i
$122$	−3.59977	+	13.4345i	−0.325908	+	1.21631i
$123$	−1.90379	−	0.887753i	−0.171659	−	0.0800460i
$124$	7.87014	−	2.86450i	0.706759	−	0.257239i
$125$		0			0
$126$	1.22616	+	0.707923i	0.109235	+	0.0630668i
$127$	8.96780	−	6.27932i	0.795763	−	0.557199i	−0.103489	−	0.994631i	$-0.533001\pi$
$127$	8.96780	−	6.27932i	0.795763	−	0.557199i	0.899252	+	0.437431i	$0.144112\pi$
$128$	0.0871557	−	0.996195i	0.00770355	−	0.0880520i
$129$	2.39769	+	2.01190i	0.211105	+	0.177138i
$130$		0			0
$131$	11.4787	+	4.17790i	1.00290	+	0.365025i	0.790702	−	0.612202i	$-0.209716\pi$
$131$	11.4787	+	4.17790i	1.00290	+	0.365025i	0.212197	+	0.977227i	$0.431938\pi$
$132$	−1.19052	−	1.19052i	−0.103622	−	0.103622i
$133$	1.75057	+	1.23671i	0.151794	+	0.107236i
$134$		−	0.622246i		−	0.0537539i
$135$		0			0
$136$	6.49521	−	1.14528i	0.556960	−	0.0982070i
$137$	9.17219	−	0.802462i	0.783633	−	0.0685590i	0.311685	−	0.950186i	$-0.399107\pi$
$137$	9.17219	−	0.802462i	0.783633	−	0.0685590i	0.471948	+	0.881627i	$0.343551\pi$
$138$	−0.382801	−	0.0334908i	−0.0325862	−	0.00285092i
$139$	15.2492	+	2.68884i	1.29342	+	0.228065i	0.777668	−	0.628675i	$-0.216402\pi$
$139$	15.2492	+	2.68884i	1.29342	+	0.228065i	0.515750	+	0.856739i	$0.327513\pi$
$140$		0			0
$141$	−1.50473	+	0.868754i	−0.126721	+	0.0731623i
$142$	−1.40500	+	3.01303i	−0.117905	+	0.252848i
$143$	9.31795	−	19.9824i	0.779206	−	1.67101i
$144$	−2.49362	+	1.43969i	−0.207802	+	0.119974i
$145$		0			0
$146$	0.707698	+	0.124786i	0.0585695	+	0.0103274i
$147$	−2.33817	−	0.204563i	−0.192849	−	0.0168721i
$148$	10.2344	−	0.895398i	0.841266	−	0.0736013i
$149$	2.68243	−	0.472985i	0.219754	−	0.0387485i	−0.0626872	−	0.998033i	$-0.519967\pi$
$149$	2.68243	−	0.472985i	0.219754	−	0.0387485i	0.282441	+	0.959285i	$0.408856\pi$
$150$		0			0
$151$			2.79547i			0.227492i	0.993510	+	0.113746i	$0.0362850\pi$
$151$			2.79547i			0.227492i	−0.993510	+	0.113746i	$0.963715\pi$
$152$	−3.95818	+	1.82561i	−0.321051	+	0.148076i
$153$	−13.4285	−	13.4285i	−1.08563	−	1.08563i
$154$	2.24003	+	0.815304i	0.180507	+	0.0656991i
$155$		0			0
$156$	1.20997	+	1.01529i	0.0968751	+	0.0812879i
$157$	0.382369	−	4.37050i	0.0305164	−	0.348804i	−0.965552	−	0.260212i	$-0.916208\pi$
$157$	0.382369	−	4.37050i	0.0305164	−	0.348804i	0.996068	−	0.0885921i	$-0.0282368\pi$
$158$	6.37844	−	4.46623i	0.507441	−	0.355314i
$159$	2.34341	+	1.35297i	0.185845	+	0.107297i
$160$		0			0
$161$	0.511247	−	0.186079i	0.0402919	−	0.0146651i
$162$	7.18613	+	3.35095i	0.564596	+	0.263275i
$163$	2.61661	−	9.76532i	0.204949	−	0.764879i	−0.784517	−	0.620108i	$-0.787089\pi$
$163$	2.61661	−	9.76532i	0.204949	−	0.764879i	0.989465	−	0.144771i	$-0.0462445\pi$
$164$	−3.02422	+	5.23810i	−0.236152	+	0.409027i
$165$		0			0
$166$	−5.98787	−	7.13607i	−0.464749	−	0.553866i
$167$	0.575286	+	6.57555i	0.0445170	+	0.508831i	0.985418	+	0.170150i	$0.0544252\pi$
$167$	0.575286	+	6.57555i	0.0445170	+	0.508831i	−0.940901	+	0.338681i	$0.890019\pi$
$168$	−0.0979507	+	0.139888i	−0.00755706	+	0.0107926i
$169$	−2.62818	+	7.22087i	−0.202168	+	0.555452i
$170$		0			0
$171$	10.8431	+	6.32089i	0.829192	+	0.483371i
$172$	6.37271	−	6.37271i	0.485915	−	0.485915i
$173$	7.50916	−	3.50158i	0.570911	−	0.266220i	−0.115653	−	0.993290i	$-0.536896\pi$
$173$	7.50916	−	3.50158i	0.570911	−	0.266220i	0.686564	+	0.727070i	$0.259118\pi$
$174$	−0.368384	−	2.08921i	−0.0279271	−	0.158382i
$175$		0			0
$176$	−3.71369	+	3.11616i	−0.279930	+	0.234889i
$177$	1.12831	+	1.61139i	0.0848090	+	0.121120i
$178$	−1.61439	+	0.432575i	−0.121004	+	0.0324229i
$179$	−4.47445	−	7.74997i	−0.334436	−	0.579260i	0.648940	−	0.760839i	$-0.275212\pi$
$179$	−4.47445	−	7.74997i	−0.334436	−	0.579260i	−0.983376	+	0.181579i	$0.941879\pi$
$180$		0			0
$181$	−1.57969	−	4.34015i	−0.117417	−	0.322601i	0.867037	−	0.498244i	$-0.166022\pi$
$181$	−1.57969	−	4.34015i	−0.117417	−	0.322601i	−0.984454	+	0.175643i	$0.943799\pi$
$182$	−2.16013	−	0.578805i	−0.160120	−	0.0429039i
$183$	1.25019	+	4.66576i	0.0924165	+	0.344903i
$184$	−0.192132	+	1.08963i	−0.0141641	+	0.0803289i
$185$		0			0
$186$	1.86967	−	2.22818i	0.137091	−	0.163378i
$187$	−26.1914	−	18.3394i	−1.91530	−	1.34111i
$188$	2.11434	+	4.53422i	0.154204	+	0.330692i
$189$	1.00403			0.0730327
$190$		0			0
$191$	−21.4782			−1.55411			−0.777053	−	0.629435i	$-0.783286\pi$
$191$	−21.4782			−1.55411			−0.777053	+	0.629435i	$0.783286\pi$
$192$	−0.146774	−	0.314757i	−0.0105925	−	0.0227157i
$193$	8.86548	+	6.20768i	0.638151	+	0.446838i	0.847350	−	0.531035i	$-0.178197\pi$
$193$	8.86548	+	6.20768i	0.638151	+	0.446838i	−0.209199	+	0.977873i	$0.567086\pi$
$194$	10.0119	−	11.9317i	0.718812	−	0.856647i
$195$		0			0
$196$	−1.17355	+	6.65554i	−0.0838251	+	0.475396i
$197$	3.08642	+	11.5187i	0.219898	+	0.820672i	0.984384	+	0.176032i	$0.0563261\pi$
$197$	3.08642	+	11.5187i	0.219898	+	0.820672i	−0.764486	+	0.644640i	$0.777007\pi$
$198$	13.4833	+	3.61283i	0.958215	+	0.256753i
$199$	−9.49492	−	26.0871i	−0.673077	−	1.84926i	−0.504101	−	0.863645i	$-0.668176\pi$
$199$	−9.49492	−	26.0871i	−0.673077	−	1.84926i	−0.168976	−	0.985620i	$-0.554046\pi$
$200$		0			0
$201$	−0.108052	−	0.187151i	−0.00762139	−	0.0132006i
$202$	−1.55372	+	0.416319i	−0.109320	+	0.0292921i
$203$	1.72281	+	2.46043i	0.120917	+	0.172688i
$204$	1.75467	−	1.47234i	0.122852	−	0.103085i
$205$		0			0
$206$	1.84609	+	10.4697i	0.128623	+	0.729459i
$207$	2.88738	−	1.34641i	0.200687	−	0.0935819i
$208$	3.21592	−	3.21592i	0.222984	−	0.222984i
$209$	19.8266	+	7.31039i	1.37144	+	0.505670i
$210$		0			0
$211$	−7.39728	+	20.3239i	−0.509250	+	1.39915i	0.372763	+	0.927927i	$0.378410\pi$
$211$	−7.39728	+	20.3239i	−0.509250	+	1.39915i	−0.882013	+	0.471226i	$0.843812\pi$
$212$	4.46899	−	6.38238i	0.306931	−	0.438343i
$213$	0.100629	+	1.15020i	0.00689499	+	0.0788101i
$214$	4.05193	+	4.82890i	0.276984	+	0.330097i
$215$		0			0
$216$	−1.02094	+	1.76833i	−0.0694665	+	0.120319i
$217$	−1.06588	+	3.97792i	−0.0723567	+	0.270039i
$218$	−14.1098	−	6.57952i	−0.955638	−	0.445621i
$219$	0.234521	−	0.0853588i	0.0158475	−	0.00576801i
$220$		0			0
$221$	25.9772	+	14.9980i	1.74742	+	1.00887i
$222$	2.92270	−	2.04650i	0.196159	−	0.137352i
$223$	1.24466	−	14.2265i	0.0833486	−	0.952679i	−0.833257	−	0.552886i	$-0.813526\pi$
$223$	1.24466	−	14.2265i	0.0833486	−	0.952679i	0.916605	−	0.399793i	$-0.130918\pi$
$224$	0.376678	+	0.316070i	0.0251678	+	0.0211183i
$225$		0			0
$226$	8.39410	+	3.05520i	0.558367	+	0.203229i
$227$	13.2466	+	13.2466i	0.879207	+	0.879207i	0.993453	−	0.114245i	$-0.0364450\pi$
$227$	13.2466	+	13.2466i	0.879207	+	0.879207i	−0.114245	+	0.993453i	$0.536445\pi$
$228$	−0.873478	+	1.23641i	−0.0578475	+	0.0818835i
$229$		−	10.8435i		−	0.716560i	−0.933614	−	0.358280i	$-0.883363\pi$
$229$		−	10.8435i		−	0.716560i	0.933614	−	0.358280i	$-0.116637\pi$
$230$		0			0
$231$	0.815304	−	0.143760i	0.0536431	−	0.00945872i
$232$	−6.08519	+	0.532385i	−0.399512	+	0.0349528i
$233$	21.0196	+	1.83898i	1.37704	+	0.120476i	0.751510	−	0.659722i	$-0.229326\pi$
$233$	21.0196	+	1.83898i	1.37704	+	0.120476i	0.625533	+	0.780198i	$0.284882\pi$
$234$	−12.8965	−	2.27400i	−0.843070	−	0.148656i
$235$		0			0
$236$	4.90532	−	2.83209i	0.319309	−	0.184353i
$237$	1.14287	−	2.45090i	0.0742376	−	0.159203i
$238$	−1.37059	+	2.93923i	−0.0888419	+	0.190522i
$239$	−5.31276	+	3.06732i	−0.343654	+	0.198409i	−0.661887	−	0.749604i	$-0.730244\pi$
$239$	−5.31276	+	3.06732i	−0.343654	+	0.198409i	0.318233	+	0.948013i	$0.396911\pi$
$240$		0			0
$241$	−2.18715	−	0.385653i	−0.140887	−	0.0248421i	0.102760	−	0.994706i	$-0.467233\pi$
$241$	−2.18715	−	0.385653i	−0.140887	−	0.0248421i	−0.243647	+	0.969864i	$0.578344\pi$
$242$	12.4544	+	1.08962i	0.800597	+	0.0700432i
$243$	8.84560	−	0.773889i	0.567445	−	0.0496450i
$244$	13.6972	−	2.41518i	0.876870	−	0.154616i
$245$		0			0
$246$			2.10060i			0.133929i
$247$	−19.1271	−	5.21097i	−1.21703	−	0.331566i
$248$	−5.92218	−	5.92218i	−0.376059	−	0.376059i
$249$	−3.04012	−	1.10651i	−0.192660	−	0.0701225i
$250$		0			0
$251$	−5.36213	−	4.49936i	−0.338455	−	0.283997i	0.457680	−	0.889117i	$-0.348681\pi$
$251$	−5.36213	−	4.49936i	−0.338455	−	0.283997i	−0.796134	+	0.605120i	$0.793125\pi$
$252$	0.123399	−	1.41046i	0.00777341	−	0.0888505i
$253$	4.39385	−	3.07661i	0.276239	−	0.193425i
$254$	−9.48095	−	5.47383i	−0.594888	−	0.343459i
$255$		0			0
$256$	−0.939693	+	0.342020i	−0.0587308	+	0.0213763i
$257$	23.7095	+	11.0559i	1.47896	+	0.689649i	0.983819	−	0.179166i	$-0.0573399\pi$
$257$	23.7095	+	11.0559i	1.47896	+	0.689649i	0.495137	+	0.868815i	$0.335118\pi$
$258$	0.810095	−	3.02331i	0.0504343	−	0.188223i
$259$	−2.52584	+	4.37489i	−0.156948	+	0.271842i
$260$		0			0
$261$	11.3057	+	13.4736i	0.699805	+	0.833995i
$262$	−1.06464	−	12.1689i	−0.0657737	−	0.751797i
$263$	8.87799	−	12.6791i	0.547440	−	0.781826i	−0.446139	−	0.894964i	$-0.647201\pi$
$263$	8.87799	−	12.6791i	0.547440	−	0.781826i	0.993579	+	0.113138i	$0.0360902\pi$
$264$	−0.575843	+	1.58211i	−0.0354407	+	0.0973724i
$265$		0			0
$266$	0.381016	−	2.10921i	0.0233616	−	0.129324i
$267$	−0.410441	+	0.410441i	−0.0251186	+	0.0251186i
$268$	−0.563946	+	0.262972i	−0.0344485	+	0.0160636i
$269$	−3.48533	−	19.7663i	−0.212504	−	1.20517i	−0.885185	−	0.465238i	$-0.845969\pi$
$269$	−3.48533	−	19.7663i	−0.212504	−	1.20517i	0.672681	−	0.739932i	$-0.265143\pi$
$270$		0			0
$271$	9.60226	−	8.05725i	0.583295	−	0.489443i	−0.302732	−	0.953076i	$-0.597899\pi$
$271$	9.60226	−	8.05725i	0.583295	−	0.489443i	0.886027	+	0.463633i	$0.153454\pi$
$272$	−3.78297	−	5.40264i	−0.229376	−	0.327583i
$273$	−0.750206	+	0.201017i	−0.0454045	+	0.0121661i
$274$	−4.60361	−	7.97369i	−0.278114	−	0.481708i
$275$		0			0
$276$	0.131426	+	0.361090i	0.00791091	+	0.0217350i
$277$	−22.1540	−	5.93615i	−1.33111	−	0.356669i	−0.477979	−	0.878371i	$-0.658631\pi$
$277$	−22.1540	−	5.93615i	−1.33111	−	0.356669i	−0.853128	+	0.521702i	$0.825297\pi$
$278$	−4.00766	−	14.9568i	−0.240364	−	0.897049i
$279$	−4.18761	+	23.7491i	−0.250706	+	1.42182i
$280$		0			0
$281$	11.5135	−	13.7212i	0.686835	−	0.818538i	−0.304134	−	0.952629i	$-0.598367\pi$
$281$	11.5135	−	13.7212i	0.686835	−	0.818538i	0.990969	+	0.134091i	$0.0428115\pi$
$282$	1.42328	+	0.996593i	0.0847553	+	0.0593463i
$283$	−3.72708	−	7.99276i	−0.221552	−	0.475120i	0.763843	−	0.645402i	$-0.223310\pi$
$283$	−3.72708	−	7.99276i	−0.221552	−	0.475120i	−0.985395	+	0.170282i	$0.945532\pi$
$284$	3.32451			0.197273
$285$		0			0
$286$	−22.0482			−1.30373
$287$	−1.25692	−	2.69548i	−0.0741937	−	0.159109i
$288$	2.35865	+	1.65155i	0.138985	+	0.0973184i
$289$	17.0335	−	20.2997i	1.00197	−	1.19410i
$290$		0			0
$291$	0.939332	−	5.32722i	0.0550646	−	0.312287i
$292$	−0.185991	−	0.694129i	−0.0108843	−	0.0406208i
$293$	9.87364	+	2.64563i	0.576824	+	0.154560i	0.535425	−	0.844583i	$-0.320152\pi$
$293$	9.87364	+	2.64563i	0.576824	+	0.154560i	0.0413997	+	0.999143i	$0.486818\pi$
$294$	0.802756	+	2.20556i	0.0468177	+	0.128631i
$295$		0			0
$296$	−5.13677	−	8.89715i	−0.298569	−	0.517136i
$297$	9.56154	−	2.56201i	0.554817	−	0.148663i
$298$	−1.56232	−	2.23122i	−0.0905025	−	0.129251i
$299$	−3.85481	+	3.23457i	−0.222930	+	0.187060i
$300$		0			0
$301$	0.769530	+	4.36422i	0.0443550	+	0.251550i
$302$	2.53356	−	1.18142i	0.145790	−	0.0679829i
$303$	−0.395016	+	0.395016i	−0.0226931	+	0.0226931i
$304$	3.32736	+	2.81579i	0.190837	+	0.161497i
$305$		0			0
$306$	−6.49521	+	17.8454i	−0.371306	+	1.02016i
$307$	−16.4640	+	23.5130i	−0.939650	+	1.34196i	6.40166e−5		1.00000i	$0.499980\pi$
$307$	−16.4640	+	23.5130i	−0.939650	+	1.34196i	−0.939715	+	0.341960i	$0.888909\pi$
$308$	−0.207761	−	2.37472i	−0.0118383	−	0.135312i
$309$	2.37329	+	2.82838i	0.135012	+	0.160901i
$310$		0			0
$311$	7.45334	−	12.9096i	0.422640	−	0.732034i	−0.573557	−	0.819166i	$-0.694437\pi$
$311$	7.45334	−	12.9096i	0.422640	−	0.732034i	0.996197	+	0.0871316i	$0.0277700\pi$
$312$	0.408806	−	1.52568i	0.0231441	−	0.0863748i
$313$	4.23764	+	1.97605i	0.239526	+	0.111693i	0.538675	−	0.842514i	$-0.318925\pi$
$313$	4.23764	+	1.97605i	0.239526	+	0.111693i	−0.299149	+	0.954206i	$0.596703\pi$
$314$	−4.12261	+	1.50051i	−0.232653	+	0.0846786i
$315$		0			0
$316$	−6.74342	−	3.89332i	−0.379347	−	0.219016i
$317$	16.3184	−	11.4263i	0.916534	−	0.641764i	−0.0171539	−	0.999853i	$-0.505461\pi$
$317$	16.3184	−	11.4263i	0.916534	−	0.641764i	0.933687	+	0.358089i	$0.116572\pi$
$318$	0.235838	−	2.69564i	0.0132251	−	0.151164i
$319$	22.6848	+	19.0348i	1.27011	+	1.06575i
$320$		0			0
$321$	2.05722	+	0.748766i	0.114823	+	0.0417921i
$322$	−0.384707	−	0.384707i	−0.0214389	−	0.0214389i
$323$	−12.2586	+	26.0041i	−0.682089	+	1.44691i
$324$		−	7.92902i		−	0.440501i
$325$		0			0
$326$	−9.95621	+	1.75555i	−0.551423	+	0.0972308i
$327$	−5.38630	+	0.471240i	−0.297863	+	0.0260596i
$328$	6.02543	+	0.527156i	0.332698	+	0.0291073i
$329$	−2.42267	−	0.427182i	−0.133566	−	0.0235513i
$330$		0			0
$331$	8.13056	−	4.69418i	0.446896	−	0.258015i	−0.259623	−	0.965710i	$-0.583598\pi$
$331$	8.13056	−	4.69418i	0.446896	−	0.258015i	0.706518	+	0.707695i	$0.250265\pi$
$332$	−3.93689	+	8.44269i	−0.216065	+	0.463353i
$333$	−12.5017	+	26.8099i	−0.685087	+	1.46917i
$334$	5.71634	−	3.30033i	0.312784	−	0.180586i
$335$		0			0
$336$	0.168177	+	0.0296542i	0.00917483	+	0.00161777i
$337$	11.3292	+	0.991177i	0.617141	+	0.0539928i	0.391440	−	0.920204i	$-0.371977\pi$
$337$	11.3292	+	0.991177i	0.617141	+	0.0539928i	0.225701	+	0.974197i	$0.427533\pi$
$338$	7.65505	−	0.669730i	0.416380	−	0.0364285i
$339$	3.05520	−	0.538715i	0.165936	−	0.0292590i
$340$		0			0
$341$			40.6021i			2.19873i
$342$	1.14619	−	12.4985i	0.0619787	−	0.675842i
$343$	−4.78369	−	4.78369i	−0.258295	−	0.258295i
$344$	−8.46886	−	3.08241i	−0.456611	−	0.166193i
$345$		0			0
$346$	−6.34702	−	5.32578i	−0.341218	−	0.286316i
$347$	2.30886	−	26.3904i	0.123946	−	1.41671i	−0.638483	−	0.769636i	$-0.720438\pi$
$347$	2.30886	−	26.3904i	0.123946	−	1.41671i	0.762429	−	0.647072i	$-0.224007\pi$
$348$	−1.73778	+	1.21681i	−0.0931547	+	0.0652276i
$349$	−4.29302	−	2.47857i	−0.229800	−	0.132675i	0.380680	−	0.924707i	$-0.375690\pi$
$349$	−4.29302	−	2.47857i	−0.229800	−	0.132675i	−0.610480	+	0.792032i	$0.709023\pi$
$350$		0			0
$351$	−8.72646	+	3.17617i	−0.465784	+	0.169532i
$352$	4.39367	+	2.04880i	0.234184	+	0.109202i
$353$	−7.13947	+	26.6449i	−0.379996	+	1.41816i	0.465911	+	0.884832i	$0.345727\pi$
$353$	−7.13947	+	26.6449i	−0.379996	+	1.41816i	−0.845906	+	0.533331i	$0.820940\pi$
$354$	0.983574	−	1.70360i	0.0522764	−	0.0905454i
$355$		0			0
$356$	1.07432	+	1.28032i	0.0569387	+	0.0678569i
$357$	0.0981644	+	1.12202i	0.00519541	+	0.0593838i
$358$	−5.13288	+	7.33051i	−0.271281	+	0.387429i
$359$	−12.8628	+	35.3403i	−0.678873	+	1.86519i	−0.224156	+	0.974553i	$0.571962\pi$
$359$	−12.8628	+	35.3403i	−0.678873	+	1.86519i	−0.454718	+	0.890636i	$0.650260\pi$
$360$		0			0
$361$	3.45577	−	18.6831i	0.181882	−	0.983320i
$362$	−3.26591	+	3.26591i	−0.171652	+	0.171652i
$363$	3.93508	−	1.83496i	0.206538	−	0.0963103i
$364$	0.388335	+	2.20236i	0.0203543	+	0.115435i
$365$		0			0
$366$	3.70027	−	3.10489i	0.193416	−	0.162295i
$367$	−9.68528	−	13.8320i	−0.505567	−	0.722025i	0.482526	−	0.875882i	$-0.339719\pi$
$367$	−9.68528	−	13.8320i	−0.505567	−	0.722025i	−0.988093	+	0.153857i	$0.950831\pi$
$368$	1.06874	−	0.286368i	0.0557120	−	0.0149280i
$369$	−8.70790	−	15.0825i	−0.453315	−	0.785165i
$370$		0			0
$371$	1.31035	+	3.60014i	0.0680297	+	0.186910i
$372$	−2.80957	−	0.752823i	−0.145670	−	0.0390321i
$373$	1.69157	+	6.31301i	0.0875859	+	0.326875i	0.995791	−	0.0916496i	$-0.0292140\pi$
$373$	1.69157	+	6.31301i	0.0875859	+	0.326875i	−0.908205	+	0.418525i	$0.862547\pi$
$374$	−5.55218	+	31.4880i	−0.287097	+	1.62821i
$375$		0			0
$376$	3.21584	−	3.83249i	0.165844	−	0.197645i
$377$	−22.7570	−	15.9346i	−1.17204	−	0.820674i
$378$	−0.424323	−	0.909963i	−0.0218248	−	0.0468035i
$379$	−34.9551			−1.79553			−0.897763	−	0.440480i	$-0.854808\pi$
$379$	−34.9551			−1.79553			−0.897763	+	0.440480i	$0.854808\pi$
$380$		0			0
$381$	−3.80208			−0.194787
$382$	9.07707	+	19.4658i	0.464423	+	0.995959i
$383$	10.5368	+	7.37793i	0.538404	+	0.376995i	0.810920	−	0.585157i	$-0.198967\pi$
$383$	10.5368	+	7.37793i	0.538404	+	0.376995i	−0.272516	+	0.962151i	$0.587856\pi$
$384$	−0.223238	+	0.266044i	−0.0113921	+	0.0135765i
$385$		0			0
$386$	1.87935	−	10.6583i	0.0956565	−	0.542495i
$387$	6.71638	+	25.0659i	0.341413	+	1.27417i
$388$	−15.0450	−	4.03130i	−0.763795	−	0.204658i
$389$	1.24094	+	3.40944i	0.0629179	+	0.172866i	0.967168	−	0.254137i	$-0.0817916\pi$
$389$	1.24094	+	3.40944i	0.0629179	+	0.172866i	−0.904250	+	0.427003i	$0.859569\pi$
$390$		0			0
$391$	3.64872	+	6.31977i	0.184524	+	0.319605i
$392$	6.52793	−	1.74915i	0.329710	−	0.0883456i
$393$	−2.43332	−	3.47513i	−0.122745	−	0.175297i
$394$	9.13509	−	7.66525i	0.460219	−	0.386170i
$395$		0			0
$396$	−2.42394	−	13.7468i	−0.121808	−	0.690805i
$397$	−3.39901	+	1.58498i	−0.170591	+	0.0795481i	−0.506038	−	0.862511i	$-0.668891\pi$
$397$	−3.39901	+	1.58498i	−0.170591	+	0.0795481i	0.335447	+	0.942059i	$0.391113\pi$
$398$	−19.6302	+	19.6302i	−0.983973	+	0.983973i
$399$	−0.251663	−	0.700545i	−0.0125989	−	0.0350711i
$400$		0			0
$401$	6.91176	−	18.9899i	0.345157	−	0.948311i	−0.638716	−	0.769443i	$-0.720534\pi$
$401$	6.91176	−	18.9899i	0.345157	−	0.948311i	0.983873	−	0.178869i	$-0.0572437\pi$
$402$	−0.123952	+	0.177022i	−0.00618216	+	0.00882905i
$403$	−3.31981	−	37.9456i	−0.165371	−	1.89020i
$404$	1.03394	+	1.23221i	0.0514407	+	0.0613046i
$405$		0			0
$406$	1.50181	−	2.60122i	0.0745337	−	0.129096i
$407$	−12.8905	+	48.1078i	−0.638956	+	2.38462i
$408$	−2.07595	−	0.968033i	−0.102775	−	0.0479248i
$409$	2.06176	−	0.750419i	0.101947	−	0.0371058i	−0.290543	−	0.956862i	$-0.593836\pi$
$409$	2.06176	−	0.750419i	0.101947	−	0.0371058i	0.392490	+	0.919756i	$0.371614\pi$
$410$		0			0
$411$	−2.76923	−	1.59882i	−0.136596	−	0.0788638i
$412$	8.70859	−	6.09782i	0.429041	−	0.300418i
$413$	−0.242744	+	2.77458i	−0.0119447	+	0.136528i
$414$	−2.44052	−	2.04784i	−0.119945	−	0.100646i
$415$		0			0
$416$	−4.27372	−	1.55551i	−0.209536	−	0.0762650i
$417$	−3.80260	−	3.80260i	−0.186214	−	0.186214i
$418$	−1.75364	−	21.0585i	−0.0857732	−	1.03001i
$419$			2.60931i			0.127473i	0.997967	+	0.0637365i	$0.0203017\pi$
$419$			2.60931i			0.127473i	−0.997967	+	0.0637365i	$0.979698\pi$
$420$		0			0
$421$	2.53311	−	0.446655i	0.123456	−	0.0217687i	−0.111579	−	0.993756i	$-0.535591\pi$
$421$	2.53311	−	0.446655i	0.123456	−	0.0217687i	0.235035	+	0.971987i	$0.424480\pi$
$422$	21.5459	−	1.88502i	1.04884	−	0.0917614i
$423$	−14.3506	−	1.25552i	−0.697751	−	0.0610453i
$424$	−7.67307	−	1.35297i	−0.372637	−	0.0657060i
$425$		0			0
$426$	0.999903	−	0.577294i	0.0484455	−	0.0279700i
$427$	−2.89030	+	6.19827i	−0.139871	+	0.299955i
$428$	2.66405	−	5.71308i	0.128772	−	0.276152i
$429$	−6.63137	+	3.82862i	−0.320165	+	0.184848i
$430$		0			0
$431$	27.6139	+	4.86907i	1.33011	+	0.234535i	0.793127	−	0.609056i	$-0.208451\pi$
$431$	27.6139	+	4.86907i	1.33011	+	0.234535i	0.536986	+	0.843591i	$0.319563\pi$
$432$	2.03412	+	0.177962i	0.0978666	+	0.00856222i
$433$	−14.0549	+	1.22964i	−0.675435	+	0.0590929i	−0.419712	−	0.907657i	$-0.637869\pi$
$433$	−14.0549	+	1.22964i	−0.675435	+	0.0590929i	−0.255723	+	0.966750i	$0.582313\pi$
$434$	4.05568	−	0.715126i	0.194679	−	0.0343272i
$435$		0			0
$436$			15.5685i			0.745594i
$437$	−3.39599	−	3.42452i	−0.162452	−	0.163817i
$438$	−0.176474	−	0.176474i	−0.00843227	−	0.00843227i
$439$	1.73043	+	0.629824i	0.0825888	+	0.0300599i	0.382984	−	0.923755i	$-0.374896\pi$
$439$	1.73043	+	0.629824i	0.0825888	+	0.0300599i	−0.300395	+	0.953815i	$0.597119\pi$
$440$		0			0
$441$	−14.9068	−	12.5083i	−0.709850	−	0.595635i
$442$	2.61432	−	29.8818i	0.124350	−	1.42133i
$443$	−4.23636	+	2.96633i	−0.201276	+	0.140935i	−0.669869	−	0.742479i	$-0.733650\pi$
$443$	−4.23636	+	2.96633i	−0.201276	+	0.140935i	0.468594	+	0.883414i	$0.344761\pi$
$444$	−3.08995	−	1.78398i	−0.146642	−	0.0846640i
$445$		0			0
$446$	−13.4196	+	4.88435i	−0.635438	+	0.231281i
$447$	−0.857341	−	0.399785i	−0.0405508	−	0.0189092i
$448$	0.127266	−	0.474963i	0.00601275	−	0.0224399i
$449$	4.27643	−	7.40699i	0.201817	−	0.349558i	−0.747297	−	0.664490i	$-0.768649\pi$
$449$	4.27643	−	7.40699i	0.201817	−	0.349558i	0.949114	+	0.314933i	$0.101982\pi$
$450$		0			0
$451$	−18.8479	−	22.4621i	−0.887513	−	1.05770i
$452$	−0.778546	−	8.89882i	−0.0366197	−	0.418565i
$453$	0.556860	−	0.795279i	0.0261636	−	0.0373655i
$454$	6.40724	−	17.6037i	0.300707	−	0.826185i
$455$		0			0
$456$	1.48972	+	0.269109i	0.0697625	+	0.0126022i
$457$	−22.6983	+	22.6983i	−1.06178	+	1.06178i	−0.0638200	+	0.997961i	$0.520328\pi$
$457$	−22.6983	+	22.6983i	−1.06178	+	1.06178i	−0.997961	+	0.0638200i	$0.979672\pi$
$458$	−9.82757	+	4.58267i	−0.459212	+	0.214134i
$459$	2.33854	+	13.2625i	0.109154	+	0.619040i
$460$		0			0
$461$	−16.9302	+	14.2061i	−0.788516	+	0.661643i	−0.945378	−	0.325977i	$-0.894307\pi$
$461$	−16.9302	+	14.2061i	−0.788516	+	0.661643i	0.156862	+	0.987621i	$0.449862\pi$
$462$	−0.474853	−	0.678161i	−0.0220922	−	0.0315509i
$463$	−9.00836	+	2.41378i	−0.418654	+	0.112178i	−0.461995	−	0.886882i	$-0.652866\pi$
$463$	−9.00836	+	2.41378i	−0.418654	+	0.112178i	0.0433414	+	0.999060i	$0.486200\pi$
$464$	3.05422	+	5.29006i	0.141788	+	0.245585i
$465$		0			0
$466$	−7.21660	−	19.8275i	−0.334303	−	0.918489i
$467$	27.1793	+	7.28267i	1.25771	+	0.337002i	0.825309	−	0.564681i	$-0.191001\pi$
$467$	27.1793	+	7.28267i	1.25771	+	0.337002i	0.432399	+	0.901683i	$0.357667\pi$
$468$	3.38935	+	12.6492i	0.156673	+	0.584711i
$469$	0.0531310	−	0.301321i	0.00245336	−	0.0139137i
$470$		0			0
$471$	−0.979387	+	1.16719i	−0.0451278	+	0.0537812i
$472$	−4.63982	−	3.24884i	−0.213565	−	0.149540i
$473$	18.4646	+	39.5974i	0.849002	+	1.82069i
$474$	−2.70427			−0.124211
$475$		0			0
$476$	3.24308			0.148646
$477$	9.48126	+	20.3326i	0.434117	+	0.930967i
$478$	5.02521	+	3.51869i	0.229848	+	0.160941i
$479$	−0.558033	+	0.665038i	−0.0254972	+	0.0303863i	−0.778642	−	0.627468i	$-0.784091\pi$
$479$	−0.558033	+	0.665038i	−0.0254972	+	0.0303863i	0.753145	+	0.657854i	$0.228536\pi$
$480$		0			0
$481$	8.11354	−	46.0142i	0.369946	−	2.09807i
$482$	0.574809	+	2.14521i	0.0261818	+	0.0977119i
$483$	−0.182511	−	0.0489037i	−0.00830454	−	0.00222519i
$484$	−4.27592	−	11.7480i	−0.194360	−	0.533999i
$485$		0			0
$486$	−4.43969	−	7.68977i	−0.201389	−	0.348815i
$487$	8.43295	−	2.25960i	0.382133	−	0.102392i	−0.0626383	−	0.998036i	$-0.519951\pi$
$487$	8.43295	−	2.25960i	0.382133	−	0.102392i	0.444772	+	0.895644i	$0.353285\pi$
$488$	−7.97756	−	11.3931i	−0.361127	−	0.515743i
$489$	−2.68966	+	2.25689i	−0.121630	+	0.102060i
$490$		0			0
$491$	−6.24117	−	35.3954i	−0.281660	−	1.59737i	−0.716978	−	0.697096i	$-0.754475\pi$
$491$	−6.24117	−	35.3954i	−0.281660	−	1.59737i	0.435318	−	0.900277i	$-0.356636\pi$
$492$	1.90379	−	0.887753i	0.0858296	−	0.0400230i
$493$	−28.4876	+	28.4876i	−1.28302	+	1.28302i
$494$	3.36074	+	19.5373i	0.151207	+	0.879026i
$495$		0			0
$496$	−2.86450	+	7.87014i	−0.128620	+	0.353380i
$497$	−0.937637	+	1.33908i	−0.0420587	+	0.0600661i
$498$	0.281969	+	3.22292i	0.0126353	+	0.144423i
$499$	20.2509	+	24.1341i	0.906555	+	1.08039i	0.996429	+	0.0844366i	$0.0269090\pi$
$499$	20.2509	+	24.1341i	0.906555	+	1.08039i	−0.0898742	+	0.995953i	$0.528647\pi$
$500$		0			0
$501$	1.14619	−	1.98527i	0.0512082	−	0.0886951i
$502$	−1.81167	+	6.76125i	−0.0808589	+	0.301770i
$503$	−10.0044	−	4.66512i	−0.446073	−	0.208007i	0.186584	−	0.982439i	$-0.440258\pi$
$503$	−10.0044	−	4.66512i	−0.446073	−	0.208007i	−0.632658	+	0.774432i	$0.718036\pi$
$504$	−1.33046	+	0.484248i	−0.0592634	+	0.0215701i
$505$		0			0
$506$	−4.64528	−	2.68195i	−0.206508	−	0.119227i
$507$	2.18609	−	1.53072i	0.0970878	−	0.0679816i
$508$	−0.954151	+	10.9060i	−0.0423336	+	0.483876i
$509$	20.2408	+	16.9841i	0.897159	+	0.752806i	0.969633	−	0.244565i	$-0.0786450\pi$
$509$	20.2408	+	16.9841i	0.897159	+	0.752806i	−0.0724742	+	0.997370i	$0.523089\pi$
$510$		0			0
$511$	0.332046	+	0.120855i	0.0146889	+	0.00534630i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−3.72769	−	8.08216i	−0.164581	−	0.356836i
$514$		−	26.1605i		−	1.15389i
$515$		0			0
$516$	−3.08241	+	0.543513i	−0.135696	+	0.0239268i
$517$	−24.1614	+	2.11385i	−1.06262	+	0.0929671i
$518$	5.03246	+	0.440283i	0.221114	+	0.0193449i
$519$	−2.83379	−	0.499673i	−0.124390	−	0.0219332i
$520$		0			0
$521$	−6.14077	+	3.54537i	−0.269032	+	0.155326i	−0.628448	−	0.777852i	$-0.716309\pi$
$521$	−6.14077	+	3.54537i	−0.269032	+	0.155326i	0.359416	+	0.933178i	$0.382976\pi$
$522$	7.43323	−	15.9406i	0.325344	−	0.697702i
$523$	−0.534646	+	1.14655i	−0.0233784	+	0.0501352i	−0.917650	−	0.397389i	$-0.869916\pi$
$523$	−0.534646	+	1.14655i	−0.0233784	+	0.0501352i	0.894272	+	0.447524i	$0.147694\pi$
$524$	−10.5788	+	6.10769i	−0.462138	+	0.266816i
$525$		0			0
$526$	−15.2432	−	2.68778i	−0.664633	−	0.117193i
$527$	−55.0278	−	4.81431i	−2.39705	−	0.209715i
$528$	1.67724	−	0.146740i	0.0729927	−	0.00638603i
$529$	21.4450	−	3.78133i	0.932390	−	0.164405i
$530$		0			0
$531$			16.3094i			0.707766i
$532$	−2.07262	+	0.546073i	−0.0898594	+	0.0236753i
$533$	19.4513	+	19.4513i	0.842530	+	0.842530i
$534$	0.545445	+	0.198526i	0.0236037	+	0.00859105i
$535$		0			0
$536$	0.476668	+	0.399972i	0.0205889	+	0.0172762i
$537$	−0.270873	+	3.09609i	−0.0116890	+	0.133606i
$538$	−16.4414	+	11.5124i	−0.708837	+	0.496333i
$539$	−28.3736	−	16.3815i	−1.22214	−	0.705601i
$540$		0			0
$541$	12.9164	−	4.70118i	0.555319	−	0.202119i	−0.0490893	−	0.998794i	$-0.515632\pi$
$541$	12.9164	−	4.70118i	0.555319	−	0.202119i	0.604408	+	0.796675i	$0.293410\pi$
$542$	−11.3604	−	5.29746i	−0.487973	−	0.227545i
$543$	−0.415160	+	1.54940i	−0.0178162	+	0.0664910i
$544$	−3.29770	+	5.71179i	−0.141388	+	0.244891i
$545$		0			0
$546$	0.499234	+	0.594964i	0.0213652	+	0.0254621i
$547$	−1.47252	−	16.8309i	−0.0629602	−	0.719638i	−0.960423	−	0.278547i	$-0.910147\pi$
$547$	−1.47252	−	16.8309i	−0.0629602	−	0.719638i	0.897462	−	0.441091i	$-0.145408\pi$
$548$	−5.28105	+	7.54211i	−0.225595	+	0.322183i
$549$	−13.6972	+	37.6326i	−0.584580	+	1.60612i
$550$		0			0
$551$	13.4094	−	23.0029i	0.571259	−	0.979958i
$552$	0.271715	−	0.271715i	0.0115650	−	0.0115650i
$553$	3.47010	−	1.61813i	0.147563	−	0.0688100i
$554$	3.98271	+	22.5871i	0.169209	+	0.959634i
$555$		0			0
$556$	−11.8618	+	9.95319i	−0.503050	+	0.422109i
$557$	−15.6314	−	22.3240i	−0.662326	−	0.945899i	−0.999989	−	0.00463220i	$-0.998526\pi$
$557$	−15.6314	−	22.3240i	−0.662326	−	0.945899i	0.337664	−	0.941267i	$-0.390363\pi$
$558$	23.2938	−	6.24155i	0.986104	−	0.264226i
$559$	−20.4941	−	35.4969i	−0.866810	−	1.50136i
$560$		0			0
$561$	3.79792	+	10.4347i	0.160348	+	0.440553i
$562$	−17.3014	−	4.63590i	−0.729817	−	0.195554i
$563$	−4.13775	−	15.4423i	−0.174385	−	0.650814i	−0.996656	−	0.0817174i	$-0.973960\pi$
$563$	−4.13775	−	15.4423i	−0.174385	−	0.650814i	0.822270	−	0.569097i	$-0.192707\pi$
$564$	0.301715	−	1.71111i	0.0127045	−	0.0720508i
$565$		0			0
$566$	−5.66877	+	6.75577i	−0.238276	+	0.283966i
$567$	3.19374	+	2.23628i	0.134125	+	0.0939150i
$568$	−1.40500	−	3.01303i	−0.0589524	−	0.126424i
$569$	−20.1120			−0.843138			−0.421569	−	0.906796i	$-0.638520\pi$
$569$	−20.1120			−0.843138			−0.421569	+	0.906796i	$0.638520\pi$
$570$		0			0
$571$	−15.4379			−0.646054			−0.323027	−	0.946390i	$-0.604701\pi$
$571$	−15.4379			−0.646054			−0.323027	+	0.946390i	$0.604701\pi$
$572$	9.31795	+	19.9824i	0.389603	+	0.835507i
$573$	6.11029	+	4.27847i	0.255261	+	0.178736i
$574$	−1.91173	+	2.27831i	−0.0797942	+	0.0950950i
$575$		0			0
$576$	0.500000	−	2.83564i	0.0208333	−	0.118152i
$577$	7.04644	+	26.2977i	0.293347	+	1.09479i	0.942521	+	0.334146i	$0.108448\pi$
$577$	7.04644	+	26.2977i	0.293347	+	1.09479i	−0.649174	+	0.760640i	$0.724885\pi$
$578$	−25.5965	−	6.85856i	−1.06467	−	0.285278i
$579$	−1.28555	−	3.53203i	−0.0534257	−	0.146786i
$580$		0			0
$581$	−2.29029	−	3.96691i	−0.0950174	−	0.164575i
$582$	−5.22508	+	1.40006i	−0.216586	+	0.0580342i
$583$	21.6651	+	30.9410i	0.897278	+	1.28145i
$584$	−0.550491	+	0.461917i	−0.0227795	+	0.0191143i
$585$		0			0
$586$	−1.77502	−	10.0666i	−0.0733255	−	0.415849i
$587$	33.7512	−	15.7385i	1.39306	−	0.649595i	0.426138	−	0.904658i	$-0.359874\pi$
$587$	33.7512	−	15.7385i	1.39306	−	0.649595i	0.966924	+	0.255063i	$0.0820962\pi$
$588$	1.65965	−	1.65965i	0.0684429	−	0.0684429i
$589$	35.9783	−	6.18886i	1.48246	−	0.255008i
$590$		0			0
$591$	1.41648	−	3.89175i	0.0582663	−	0.160085i
$592$	−5.89266	+	8.41559i	−0.242187	+	0.345879i
$593$	−0.933271	−	10.6673i	−0.0383249	−	0.438055i	−0.990981	−	0.134004i	$-0.957216\pi$
$593$	−0.933271	−	10.6673i	−0.0383249	−	0.438055i	0.952656	−	0.304051i	$-0.0983392\pi$
$594$	−6.36285	−	7.58295i	−0.261071	−	0.311132i
$595$		0			0
$596$	−1.36191	+	2.35889i	−0.0557859	+	0.0966240i
$597$	−2.49538	+	9.31288i	−0.102129	+	0.381151i
$598$	4.56063	+	2.12666i	0.186498	+	0.0869655i
$599$	−19.9214	+	7.25078i	−0.813964	+	0.296259i	−0.715260	−	0.698858i	$-0.753692\pi$
$599$	−19.9214	+	7.25078i	−0.813964	+	0.296259i	−0.0987040	+	0.995117i	$0.531470\pi$
$600$		0			0
$601$	7.24299	+	4.18174i	0.295448	+	0.170577i	0.640396	−	0.768045i	$-0.278770\pi$
$601$	7.24299	+	4.18174i	0.295448	+	0.170577i	−0.344948	+	0.938622i	$0.612104\pi$
$602$	3.63011	−	2.54183i	0.147952	−	0.103597i
$603$	0.156156	−	1.78487i	0.00635915	−	0.0726854i
$604$	−2.14145	−	1.79689i	−0.0871345	−	0.0731145i
$605$		0			0
$606$	0.524947	+	0.191065i	0.0213245	+	0.00776149i
$607$	−16.5554	−	16.5554i	−0.671962	−	0.671962i	0.286206	−	0.958168i	$-0.407606\pi$
$607$	−16.5554	−	16.5554i	−0.671962	−	0.671962i	−0.958168	+	0.286206i	$0.907606\pi$
$608$	1.14577	−	4.20562i	0.0464672	−	0.170560i
$609$		−	1.04315i		−	0.0422705i
$610$		0			0
$611$	22.4078	−	3.95109i	0.906521	−	0.159844i
$612$	18.9185	−	1.65515i	0.764733	−	0.0669055i
$613$	−31.8600	−	2.78739i	−1.28681	−	0.112581i	−0.576867	−	0.816838i	$-0.695725\pi$
$613$	−31.8600	−	2.78739i	−1.28681	−	0.112581i	−0.709945	+	0.704257i	$0.751280\pi$
$614$	28.2680	+	4.98442i	1.14081	+	0.201155i
$615$		0			0
$616$	−2.06442	+	1.19190i	−0.0831780	+	0.0480228i
$617$	5.85076	−	12.5470i	0.235543	−	0.505123i	−0.752634	−	0.658439i	$-0.771217\pi$
$617$	5.85076	−	12.5470i	0.235543	−	0.505123i	0.988177	+	0.153315i	$0.0489950\pi$
$618$	1.56038	−	3.34626i	0.0627679	−	0.134606i
$619$	28.6968	−	16.5681i	1.15342	−	0.665928i	0.203702	−	0.979033i	$-0.434703\pi$
$619$	28.6968	−	16.5681i	1.15342	−	0.665928i	0.949719	+	0.313105i	$0.101369\pi$
$620$		0			0
$621$	−2.22491	−	0.392312i	−0.0892826	−	0.0157429i
$622$	−14.8500	−	1.29920i	−0.595429	−	0.0520933i
$623$	−0.818701	+	0.0716271i	−0.0328006	+	0.00286968i
$624$	−1.55551	+	0.274278i	−0.0622701	+	0.0109799i
$625$		0			0
$626$		−	4.67572i		−	0.186879i
$627$	−4.18421	−	6.02921i	−0.167101	−	0.240783i
$628$	3.10221	+	3.10221i	0.123792	+	0.123792i
$629$	−63.6719	−	23.1747i	−2.53876	−	0.924035i
$630$		0			0
$631$	2.72050	+	2.28277i	0.108302	+	0.0908758i	0.695330	−	0.718690i	$-0.255258\pi$
$631$	2.72050	+	2.28277i	0.108302	+	0.0908758i	−0.587029	+	0.809566i	$0.699702\pi$
$632$	−0.678650	+	7.75700i	−0.0269952	+	0.308557i
$633$	6.15297	−	4.30836i	0.244559	−	0.171242i
$634$	−17.2522	−	9.96055i	−0.685172	−	0.395584i
$635$		0			0
$636$	−2.54275	+	0.925486i	−0.100827	+	0.0366979i
$637$	27.8566	+	12.9897i	1.10372	+	0.514672i
$638$	7.66440	−	28.6039i	0.303436	−	1.13244i
$639$	−4.78627	+	8.29006i	−0.189342	+	0.327950i
$640$		0			0
$641$	−20.6635	−	24.6258i	−0.816158	−	0.972660i	0.183789	−	0.982966i	$-0.441164\pi$
$641$	−20.6635	−	24.6258i	−0.816158	−	0.972660i	−0.999947	+	0.0103062i	$0.996719\pi$
$642$	−0.190805	−	2.18091i	−0.00753049	−	0.0860738i
$643$	−6.80194	+	9.71417i	−0.268242	+	0.383090i	−0.930564	−	0.366130i	$-0.880682\pi$
$643$	−6.80194	+	9.71417i	−0.268242	+	0.383090i	0.662321	+	0.749220i	$0.269571\pi$
$644$	−0.186079	+	0.511247i	−0.00733253	+	0.0201460i
$645$		0			0
$646$	28.7485	+	0.120277i	1.13109	+	0.00473225i
$647$	12.4650	−	12.4650i	0.490051	−	0.490051i	−0.418271	−	0.908322i	$-0.637364\pi$
$647$	12.4650	−	12.4650i	0.490051	−	0.490051i	0.908322	+	0.418271i	$0.137364\pi$
$648$	−7.18613	+	3.35095i	−0.282298	+	0.131638i
$649$	4.76825	+	27.0421i	0.187170	+	1.06149i
$650$		0			0
$651$	1.09564	−	0.919349i	0.0429414	−	0.0360321i
$652$	5.79874	+	8.28146i	0.227096	+	0.324327i
$653$	−35.9380	+	9.62956i	−1.40636	+	0.376834i	−0.880626	−	0.473813i	$-0.842877\pi$
$653$	−35.9380	+	9.62956i	−1.40636	+	0.376834i	−0.525738	+	0.850647i	$0.676211\pi$
$654$	2.70344	+	4.68249i	0.105713	+	0.183100i
$655$		0			0
$656$	−2.06869	−	5.68368i	−0.0807687	−	0.221910i
$657$	1.99866	+	0.535541i	0.0779753	+	0.0208934i
$658$	0.636706	+	2.37622i	0.0248214	+	0.0926346i
$659$	8.77297	−	49.7540i	0.341747	−	1.93814i	−0.00447948	−	0.999990i	$-0.501426\pi$
$659$	8.77297	−	49.7540i	0.341747	−	1.93814i	0.346226	−	0.938151i	$-0.387463\pi$
$660$		0			0
$661$	−6.23730	+	7.43333i	−0.242603	+	0.289123i	−0.873582	−	0.486677i	$-0.838209\pi$
$661$	−6.23730	+	7.43333i	−0.242603	+	0.289123i	0.630979	+	0.775800i	$0.282653\pi$
$662$	−7.69049	−	5.38494i	−0.298899	−	0.209292i
$663$	−4.40261	−	9.44144i	−0.170983	−	0.366675i
$664$	9.31548			0.361511
$665$		0			0
$666$	29.5815			1.14626
$667$	−2.85632	−	6.12540i	−0.110597	−	0.237176i
$668$	−5.40695	−	3.78599i	−0.209201	−	0.146484i
$669$	−3.18803	+	3.79935i	−0.123256	+	0.146891i
$670$		0			0
$671$	−11.7085	+	66.4022i	−0.452001	+	2.56343i
$672$	−0.0441990	−	0.164953i	−0.00170501	−	0.00636320i
$673$	41.5583	+	11.1355i	1.60195	+	0.429242i	0.945632	−	0.325238i	$-0.105445\pi$
$673$	41.5583	+	11.1355i	1.60195	+	0.429242i	0.656322	+	0.754481i	$0.272111\pi$
$674$	−3.88962	−	10.6866i	−0.149822	−	0.411634i
$675$		0			0
$676$	−3.84215	−	6.65479i	−0.147775	−	0.255954i
$677$	12.2349	−	3.27833i	0.470225	−	0.125996i	−0.0159225	−	0.999873i	$-0.505069\pi$
$677$	12.2349	−	3.27833i	0.470225	−	0.125996i	0.486147	+	0.873877i	$0.338402\pi$
$678$	−1.77943	−	2.54128i	−0.0683384	−	0.0975974i
$679$	5.86704	−	4.92303i	0.225156	−	0.188929i
$680$		0			0
$681$	−1.12977	−	6.40724i	−0.0432928	−	0.245526i
$682$	36.7980	−	17.1592i	1.40907	−	0.657059i
$683$	26.9751	−	26.9751i	1.03217	−	1.03217i	0.0327076	−	0.999465i	$-0.489587\pi$
$683$	26.9751	−	26.9751i	1.03217	−	1.03217i	0.999465	−	0.0327076i	$-0.0104130\pi$
$684$	−11.8119	+	4.24330i	−0.451639	+	0.162247i
$685$		0			0
$686$	−2.31382	+	6.35717i	−0.0883421	+	0.242718i
$687$	−2.16004	+	3.08486i	−0.0824107	+	0.117695i
$688$	0.785480	+	8.97808i	0.0299462	+	0.342286i
$689$	−22.7775	−	27.1451i	−0.867753	−	1.03415i
$690$		0			0
$691$	−4.70982	+	8.15765i	−0.179170	+	0.310332i	−0.941597	−	0.336743i	$-0.890675\pi$
$691$	−4.70982	+	8.15765i	−0.179170	+	0.310332i	0.762426	+	0.647075i	$0.224008\pi$
$692$	−2.14443	+	8.00312i	−0.0815190	+	0.304233i
$693$	6.22076	+	2.90079i	0.236307	+	0.110192i
$694$	−24.8936	+	9.06051i	−0.944946	+	0.343932i
$695$		0			0
$696$	1.83722	+	1.06072i	0.0696396	+	0.0402064i
$697$	32.6776	−	22.8811i	1.23775	−	0.866683i
$698$	−0.432044	+	4.93828i	−0.0163531	+	0.186917i
$699$	−5.61352	−	4.71030i	−0.212323	−	0.178160i
$700$		0			0
$701$	38.8055	+	14.1241i	1.46566	+	0.533458i	0.946919	−	0.321471i	$-0.104177\pi$
$701$	38.8055	+	14.1241i	1.46566	+	0.533458i	0.518745	+	0.854929i	$0.326400\pi$
$702$	6.56655	+	6.56655i	0.247839	+	0.247839i
$703$	44.5942	+	4.08956i	1.68190	+	0.154241i
$704$		−	4.84788i		−	0.182711i
$705$		0			0
$706$	27.1657	−	4.79005i	1.02240	−	0.180276i
$707$	−0.787934	+	0.0689353i	−0.0296333	+	0.00259258i
$708$	−1.95966	−	0.171448i	−0.0736486	−	0.00644342i
$709$	17.6686	+	3.11545i	0.663558	+	0.117003i	0.495276	−	0.868736i	$-0.335067\pi$
$709$	17.6686	+	3.11545i	0.663558	+	0.117003i	0.168282	+	0.985739i	$0.446178\pi$
$710$		0			0
$711$	19.4169	−	11.2104i	0.728191	−	0.420421i
$712$	0.706339	−	1.51475i	0.0264712	−	0.0567676i
$713$	3.91628	−	8.39849i	0.146666	−	0.314526i
$714$	0.975413	−	0.563155i	0.0365039	−	0.0210756i
$715$		0			0
$716$	8.81295	+	1.55396i	0.329355	+	0.0580742i
$717$	2.12243	+	0.185689i	0.0792637	+	0.00693468i
$718$	37.4652	−	3.27778i	1.39819	−	0.122326i
$719$	28.3016	−	4.99034i	1.05547	−	0.186108i	0.381126	−	0.924523i	$-0.375537\pi$
$719$	28.3016	−	4.99034i	1.05547	−	0.186108i	0.674346	+	0.738415i	$0.264425\pi$
$720$		0			0
$721$			5.22756i			0.194685i
$722$	−18.3931	+	4.76383i	−0.684520	+	0.177291i
$723$	0.545396	+	0.545396i	0.0202835	+	0.0202835i
$724$	4.34015	+	1.57969i	0.161300	+	0.0587085i
$725$		0			0
$726$	−3.32607	−	2.79091i	−0.123442	−	0.103580i
$727$	−3.70442	+	42.3418i	−0.137390	+	1.57037i	0.544403	+	0.838824i	$0.316756\pi$
$727$	−3.70442	+	42.3418i	−0.137390	+	1.57037i	−0.681793	+	0.731545i	$0.738799\pi$
$728$	1.83190	−	1.28271i	0.0678946	−	0.0475403i
$729$	17.9296	+	10.3516i	0.664058	+	0.383394i
$730$		0			0
$731$	−55.8556	+	20.3298i	−2.06589	+	0.751924i
$732$	−4.37779	−	2.04140i	−0.161808	−	0.0754522i
$733$	−3.84520	+	14.3505i	−0.142026	+	0.530047i	0.857844	+	0.513910i	$0.171803\pi$
$733$	−3.84520	+	14.3505i	−0.142026	+	0.530047i	−0.999870	+	0.0161368i	$0.994863\pi$
$734$	−8.44288	+	14.6235i	−0.311632	+	0.539763i
$735$		0			0
$736$	−0.711208	−	0.847584i	−0.0262155	−	0.0312424i
$737$	−0.262912	−	3.00509i	−0.00968448	−	0.110694i
$738$	−9.98929	+	14.2662i	−0.367711	+	0.525145i
$739$	−17.6051	+	48.3697i	−0.647615	+	1.77931i	−0.0212567	+	0.999774i	$0.506767\pi$
$739$	−17.6051	+	48.3697i	−0.647615	+	1.77931i	−0.626359	+	0.779535i	$0.715456\pi$
$740$		0			0
$741$	4.40342	+	5.29261i	0.161764	+	0.194429i
$742$	2.70906	−	2.70906i	0.0994528	−	0.0994528i
$743$	−15.4437	+	7.20152i	−0.566575	+	0.264198i	−0.684730	−	0.728797i	$-0.740080\pi$
$743$	−15.4437	+	7.20152i	−0.566575	+	0.264198i	0.118155	+	0.992995i	$0.462302\pi$
$744$	0.505088	+	2.86450i	0.0185174	+	0.105018i
$745$		0			0
$746$	5.00664	−	4.20107i	0.183306	−	0.153812i
$747$	−15.3850	−	21.9720i	−0.562906	−	0.803913i
$748$	30.8843	−	8.27542i	1.12924	−	0.302579i
$749$	1.54982	+	2.68436i	0.0566291	+	0.0980844i
$750$		0			0
$751$	−5.72972	−	15.7423i	−0.209080	−	0.574444i	0.790181	−	0.612874i	$-0.209987\pi$
$751$	−5.72972	−	15.7423i	−0.209080	−	0.574444i	−0.999261	+	0.0384299i	$0.987764\pi$
$752$	−4.83248	−	1.29486i	−0.176223	−	0.0472187i
$753$	0.629187	+	2.34816i	0.0229289	+	0.0855717i
$754$	−4.82414	+	27.3591i	−0.175685	+	0.996359i
$755$		0			0
$756$	−0.645380	+	0.769134i	−0.0234723	+	0.0279731i
$757$	−43.7095	−	30.6057i	−1.58865	−	1.11238i	−0.934470	−	0.356043i	$-0.884126\pi$
$757$	−43.7095	−	30.6057i	−1.58865	−	1.11238i	−0.654178	−	0.756340i	$-0.726985\pi$
$758$	14.7727	+	31.6801i	0.536568	+	1.15067i
$759$	−1.86286			−0.0676177
$760$		0			0
$761$	−28.1609			−1.02083			−0.510416	−	0.859928i	$-0.670509\pi$
$761$	−28.1609			−1.02083			−0.510416	+	0.859928i	$0.670509\pi$
$762$	1.60683	+	3.44586i	0.0582093	+	0.124830i
$763$	−6.27085	−	4.39090i	−0.227020	−	0.158961i
$764$	13.8059	−	16.4532i	0.499480	−	0.595257i
$765$		0			0
$766$	2.23364	−	12.6676i	0.0807047	−	0.457699i
$767$	−6.66735	−	24.8829i	−0.240744	−	0.898470i
$768$	0.335463	+	0.0898869i	0.0121050	+	0.00324351i
$769$	2.51591	+	6.91240i	0.0907260	+	0.249268i	0.976754	−	0.214365i	$-0.0687681\pi$
$769$	2.51591	+	6.91240i	0.0907260	+	0.249268i	−0.886028	+	0.463632i	$0.846546\pi$
$770$		0			0
$771$	−4.54272	−	7.86823i	−0.163602	−	0.283367i
$772$	−10.4540	+	2.80114i	−0.376247	+	0.100815i
$773$	−1.49851	−	2.14009i	−0.0538976	−	0.0769738i	0.791299	−	0.611430i	$-0.209405\pi$
$773$	−1.49851	−	2.14009i	−0.0538976	−	0.0769738i	−0.845196	+	0.534456i	$0.820516\pi$
$774$	19.8789	−	16.6804i	0.714533	−	0.599565i
$775$		0			0
$776$	2.70470	+	15.3391i	0.0970931	+	0.550642i
$777$	1.59005	−	0.741455i	0.0570429	−	0.0265995i
$778$	2.56556	−	2.56556i	0.0919799	−	0.0919799i
$779$	−17.0312	+	20.1253i	−0.610204	+	0.721065i
$780$		0			0
$781$	−5.51227	+	15.1448i	−0.197245	+	0.541925i
$782$	4.18564	−	5.97772i	0.149678	−	0.213763i
$783$	−1.08707	−	12.4253i	−0.0388487	−	0.444043i
$784$	−4.34410	−	5.17709i	−0.155146	−	0.184896i
$785$		0			0
$786$	−2.12118	+	3.67399i	−0.0756599	+	0.131047i
$787$	−8.25214	+	30.7974i	−0.294157	+	1.09781i	0.647728	+	0.761872i	$0.275719\pi$
$787$	−8.25214	+	30.7974i	−0.294157	+	1.09781i	−0.941885	+	0.335937i	$0.890947\pi$
$788$	−10.8077	−	5.03973i	−0.385010	−	0.179533i
$789$	−5.05137	+	1.83855i	−0.179834	+	0.0654541i
$790$		0			0
$791$	3.80395	+	2.19621i	0.135253	+	0.0780883i
$792$	−11.4345	+	8.00651i	−0.406306	+	0.284499i
$793$	5.51309	−	63.0149i	0.195776	−	2.23773i
$794$	2.87297	+	2.41071i	0.101958	+	0.0855527i
$795$		0			0
$796$	26.0871	+	9.49492i	0.924632	+	0.336539i
$797$	6.20196	+	6.20196i	0.219685	+	0.219685i	0.808366	−	0.588681i	$-0.200352\pi$
$797$	6.20196	+	6.20196i	0.219685	+	0.219685i	−0.588681	+	0.808366i	$0.700352\pi$
$798$	−0.528552	+	0.524147i	−0.0187105	+	0.0185546i
$799$		−	32.9965i		−	1.16733i
$800$		0			0
$801$	−4.73932	+	0.835670i	−0.167456	+	0.0295270i
$802$	−20.1317	+	1.76130i	−0.710877	+	0.0621936i
$803$	3.47050	+	0.303630i	0.122471	+	0.0107149i
$804$	0.212821	+	0.0375260i	0.00750560	+	0.00132344i
$805$		0			0
$806$	−32.9874	+	19.0453i	−1.16193	+	0.670841i
$807$	−2.94593	+	6.31756i	−0.103701	+	0.222389i
$808$	0.679795	−	1.45783i	0.0239151	−	0.0512861i
$809$	40.6815	−	23.4875i	1.43029	−	0.825776i	0.433143	−	0.901325i	$-0.357404\pi$
$809$	40.6815	−	23.4875i	1.43029	−	0.825776i	0.997142	+	0.0755496i	$0.0240711\pi$
$810$		0			0
$811$	26.5575	+	4.68280i	0.932559	+	0.164435i	0.619230	−	0.785210i	$-0.287445\pi$
$811$	26.5575	+	4.68280i	0.932559	+	0.164435i	0.313329	+	0.949645i	$0.398556\pi$
$812$	−2.99220	−	0.261783i	−0.105005	−	0.00918679i
$813$	−4.33674	+	0.379416i	−0.152096	+	0.0133067i
$814$	49.0482	−	8.64853i	1.71914	−	0.303131i
$815$		0			0
$816$			2.29056i			0.0801857i
$817$	32.2736	−	22.3976i	1.12911	−	0.783592i
$818$	−1.55145	−	1.55145i	−0.0542451	−	0.0542451i
$819$	−6.05093	−	2.20236i	−0.211437	−	0.0769566i
$820$		0			0
$821$	10.9297	+	9.17113i	0.381450	+	0.320075i	0.813271	−	0.581884i	$-0.197684\pi$
$821$	10.9297	+	9.17113i	0.381450	+	0.320075i	−0.431821	+	0.901959i	$0.642129\pi$
$822$	−0.278692	+	3.18547i	−0.00972051	+	0.111106i
$823$	−2.93075	+	2.05213i	−0.102160	+	0.0715329i	−0.623540	−	0.781791i	$-0.714306\pi$
$823$	−2.93075	+	2.05213i	−0.102160	+	0.0715329i	0.521380	+	0.853324i	$0.325417\pi$
$824$	−9.20691	−	5.31561i	−0.320738	−	0.185178i
$825$		0			0
$826$	2.61721	−	0.952587i	0.0910644	−	0.0331447i
$827$	11.3690	+	5.30146i	0.395340	+	0.184350i	0.610114	−	0.792314i	$-0.291124\pi$
$827$	11.3690	+	5.30146i	0.395340	+	0.184350i	−0.214774	+	0.976664i	$0.568902\pi$
$828$	−0.824565	+	3.07732i	−0.0286556	+	0.106944i
$829$	9.20326	−	15.9405i	0.319642	−	0.553637i	−0.660771	−	0.750588i	$-0.729771\pi$
$829$	9.20326	−	15.9405i	0.319642	−	0.553637i	0.980413	+	0.196951i	$0.0631039\pi$
$830$		0			0
$831$	5.12008	+	6.10187i	0.177614	+	0.211672i
$832$	0.396384	+	4.53069i	0.0137421	+	0.157073i
$833$	25.5661	−	36.5122i	0.885814	−	1.26507i
$834$	−1.83928	+	5.05337i	−0.0636889	+	0.174984i
$835$		0			0
$836$	−18.3444	+	10.4891i	−0.634454	+	0.362772i
$837$	12.0924	−	12.0924i	0.417976	−	0.417976i
$838$	2.36484	−	1.10274i	0.0816919	−	0.0380935i
$839$	−2.43674	−	13.8194i	−0.0841256	−	0.477100i	−0.997542	−	0.0700733i	$-0.977677\pi$
$839$	−2.43674	−	13.8194i	−0.0841256	−	0.477100i	0.913416	−	0.407027i	$-0.133434\pi$
$840$		0			0
$841$	6.36808	−	5.34346i	0.219589	−	0.184257i
$842$	−1.47535	−	2.10701i	−0.0508438	−	0.0726124i
$843$	−6.00872	+	1.61003i	−0.206951	+	0.0554525i
$844$	−10.8141	−	18.7306i	−0.372237	−	0.644733i
$845$		0			0
$846$	4.92695	+	13.5367i	0.169392	+	0.465401i
$847$	5.93796	+	1.59107i	0.204031	+	0.0546699i
$848$	2.01657	+	7.52596i	0.0692494	+	0.258442i
$849$	−0.531853	+	3.01629i	−0.0182531	+	0.103519i
$850$		0			0
$851$	7.30662	−	8.70769i	0.250468	−	0.298496i
$852$	−0.945784	−	0.662245i	−0.0324020	−	0.0226881i
$853$	−17.8287	−	38.2338i	−0.610444	−	1.30910i	−0.932085	−	0.362239i	$-0.882012\pi$
$853$	−17.8287	−	38.2338i	−0.610444	−	1.30910i	0.321641	−	0.946862i	$-0.395765\pi$
$854$	6.83904			0.234027
$855$		0			0
$856$	−6.30368			−0.215455
$857$	19.8676	+	42.6062i	0.678664	+	1.45540i	0.879561	+	0.475786i	$0.157836\pi$
$857$	19.8676	+	42.6062i	0.678664	+	1.45540i	−0.200897	+	0.979612i	$0.564386\pi$
$858$	6.27245	+	4.39201i	0.214138	+	0.149941i
$859$	−13.6182	+	16.2296i	−0.464648	+	0.553746i	−0.946583	−	0.322461i	$-0.895490\pi$
$859$	−13.6182	+	16.2296i	−0.464648	+	0.553746i	0.481935	+	0.876207i	$0.339934\pi$
$860$		0			0
$861$	−0.179362	+	1.01721i	−0.00611264	+	0.0346665i
$862$	−7.25725	−	27.0844i	−0.247183	−	0.922499i
$863$	0.554662	+	0.148621i	0.0188809	+	0.00505912i	0.268247	−	0.963350i	$-0.413556\pi$
$863$	0.554662	+	0.148621i	0.0188809	+	0.00505912i	−0.249366	+	0.968409i	$0.580222\pi$
$864$	−0.698367	−	1.91875i	−0.0237589	−	0.0652771i
$865$		0			0
$866$	7.05429	+	12.2184i	0.239715	+	0.415198i
$867$	−8.88956	+	2.38195i	−0.301905	+	0.0808953i
$868$	−2.36213	−	3.37347i	−0.0801759	−	0.114503i
$869$	28.9172	−	24.2644i	0.980947	−	0.823112i
$870$		0			0
$871$	0.491420	+	2.78698i	0.0166511	+	0.0944332i
$872$	14.1098	−	6.57952i	0.477819	−	0.222811i
$873$	31.7127	−	31.7127i	1.07331	−	1.07331i
$874$	−1.66847	+	4.52508i	−0.0564367	+	0.153063i
$875$		0			0
$876$	−0.0853588	+	0.234521i	−0.00288401	+	0.00792374i
$877$	8.16054	−	11.6545i	0.275562	−	0.393543i	−0.657386	−	0.753554i	$-0.728338\pi$
$877$	8.16054	−	11.6545i	0.275562	−	0.393543i	0.932948	+	0.360011i	$0.117227\pi$
$878$	−0.160496	−	1.83448i	−0.00541647	−	0.0619106i
$879$	−2.28192	−	2.71949i	−0.0769674	−	0.0917262i
$880$		0			0
$881$	5.14870	−	8.91781i	0.173464	−	0.300449i	−0.766165	−	0.642644i	$-0.777837\pi$
$881$	5.14870	−	8.91781i	0.173464	−	0.300449i	0.939629	+	0.342196i	$0.111171\pi$
$882$	−5.03649	+	18.7964i	−0.169587	+	0.632909i
$883$	−2.34607	−	1.09399i	−0.0789517	−	0.0368158i	0.382741	−	0.923856i	$-0.374980\pi$
$883$	−2.34607	−	1.09399i	−0.0789517	−	0.0368158i	−0.461693	+	0.887040i	$0.652758\pi$
$884$	−28.1869	+	10.2592i	−0.948029	+	0.345054i
$885$		0			0
$886$	4.47877	+	2.58582i	0.150467	+	0.0868723i
$887$	44.9550	−	31.4779i	1.50944	−	1.05692i	0.531745	−	0.846905i	$-0.321536\pi$
$887$	44.9550	−	31.4779i	1.50944	−	1.05692i	0.977697	−	0.210018i	$-0.0673524\pi$
$888$	−0.310968	+	3.55439i	−0.0104354	+	0.119277i
$889$	−4.12374	−	3.46023i	−0.138306	−	0.116052i
$890$		0			0
$891$	36.1208	+	13.1469i	1.21009	+	0.440437i
$892$	10.0981	+	10.0981i	0.338110	+	0.338110i
$893$	5.55599	+	21.0877i	0.185924	+	0.705674i
$894$			0.945971i			0.0316380i
$895$		0			0
$896$	−0.484248	+	0.0853859i	−0.0161776	+	0.00285254i
$897$	1.74098	−	0.152316i	0.0581296	−	0.00508568i
$898$	−8.52031	−	0.745431i	−0.284326	−	0.0248753i
$899$	50.3823	+	8.88375i	1.68034	+	0.296290i
$900$		0			0
$901$	−44.5031	+	25.6939i	−1.48261	+	0.855987i
$902$	−12.3921	+	26.5749i	−0.412611	+	0.884846i
$903$	0.650435	−	1.39486i	0.0216451	−	0.0464181i
$904$	−7.73604	+	4.46641i	−0.257297	+	0.148551i
$905$		0			0
$906$	−0.956107	−	0.168587i	−0.0317645	−	0.00560094i
$907$	2.19380	+	0.191932i	0.0728438	+	0.00637300i	0.123519	−	0.992342i	$-0.460582\pi$
$907$	2.19380	+	0.191932i	0.0728438	+	0.00637300i	−0.0506756	+	0.998715i	$0.516137\pi$
$908$	−18.6622	+	1.63273i	−0.619328	+	0.0541842i
$909$	−4.56122	+	0.804266i	−0.151286	+	0.0266758i
$910$		0			0
$911$		−	26.3886i		−	0.874294i	−0.899390	−	0.437147i	$-0.855989\pi$
$911$		−	26.3886i		−	0.874294i	0.899390	−	0.437147i	$-0.144011\pi$
$912$	−0.385687	−	1.46387i	−0.0127714	−	0.0484737i
$913$	−31.9332	−	31.9332i	−1.05683	−	1.05683i
$914$	30.1644	+	10.9789i	0.997748	+	0.363151i
$915$		0			0
$916$	8.30662	+	6.97008i	0.274458	+	0.230298i
$917$	0.523503	−	5.98366i	0.0172876	−	0.197598i
$918$	11.0316	−	7.72441i	0.364097	−	0.254943i
$919$	37.1063	+	21.4233i	1.22402	+	0.706690i	0.965773	−	0.259388i	$-0.0835207\pi$
$919$	37.1063	+	21.4233i	1.22402	+	0.706690i	0.258250	+	0.966078i	$0.416854\pi$
$920$		0			0
$921$	9.36764	−	3.40954i	0.308674	−	0.112348i
$922$	20.0301	+	9.34018i	0.659655	+	0.307602i
$923$	3.91330	−	14.6047i	0.128808	−	0.480718i
$924$	−0.413941	+	0.716966i	−0.0136177	+	0.0235865i
$925$		0			0
$926$	5.99473	+	7.14424i	0.196999	+	0.234774i
$927$	2.66796	+	30.4949i	0.0876272	+	1.00158i
$928$	3.50365	−	5.00373i	0.115013	−	0.164256i
$929$	−8.29606	+	22.7932i	−0.272185	+	0.747821i	0.726006	+	0.687689i	$0.241375\pi$
$929$	−8.29606	+	22.7932i	−0.272185	+	0.747821i	−0.998190	+	0.0601327i	$0.980848\pi$
$930$		0			0
$931$	−10.1911	+	27.6394i	−0.333999	+	0.905845i
$932$	−14.9199	+	14.9199i	−0.488718	+	0.488718i
$933$	−4.69199	+	2.18791i	−0.153609	+	0.0716290i
$934$	−4.88613	−	27.7106i	−0.159879	−	0.906719i
$935$		0			0
$936$	10.0317	−	8.41759i	0.327896	−	0.275137i
$937$	16.0136	+	22.8698i	0.523142	+	0.747124i	0.990585	−	0.136899i	$-0.0437137\pi$
$937$	16.0136	+	22.8698i	0.523142	+	0.747124i	−0.467443	+	0.884023i	$0.654825\pi$
$938$	−0.295544	+	0.0791907i	−0.00964985	+	0.00258567i
$939$	−0.811931	−	1.40630i	−0.0264964	−	0.0458930i
$940$		0			0
$941$	13.7656	+	37.8206i	0.448745	+	1.23292i	0.933599	+	0.358321i	$0.116651\pi$
$941$	13.7656	+	37.8206i	0.448745	+	1.23292i	−0.484854	+	0.874595i	$0.661127\pi$
$942$	1.47174	+	0.394351i	0.0479518	+	0.0128487i
$943$	1.73208	+	6.46422i	0.0564044	+	0.210504i
$944$	−0.983574	+	5.57813i	−0.0320126	+	0.181553i
$945$		0			0
$946$	28.0840	−	33.4692i	0.913089	−	1.08818i
$947$	−23.6175	−	16.5371i	−0.767464	−	0.537384i	0.123017	−	0.992405i	$-0.460743\pi$
$947$	−23.6175	−	16.5371i	−0.767464	−	0.537384i	−0.890481	+	0.455020i	$0.849632\pi$
$948$	1.14287	+	2.45090i	0.0371188	+	0.0796015i
$949$	−3.26826			−0.106092
$950$		0			0
$951$	−6.91853			−0.224349
$952$	−1.37059	−	2.93923i	−0.0444209	−	0.0952610i
$953$	−20.5563	−	14.3937i	−0.665883	−	0.466256i	0.191121	−	0.981567i	$-0.438788\pi$
$953$	−20.5563	−	14.3937i	−0.665883	−	0.466256i	−0.857004	+	0.515310i	$0.827677\pi$
$954$	14.4207	−	17.1859i	0.466886	−	0.556413i
$955$		0			0
$956$	1.06527	−	6.04145i	0.0344533	−	0.195394i
$957$	−2.66182	−	9.93403i	−0.0860443	−	0.321122i
$958$	0.838564	+	0.224692i	0.0270928	+	0.00725948i
$959$	−1.54845	−	4.25432i	−0.0500020	−	0.137379i
$960$		0			0
$961$	19.5722	+	33.9000i	0.631361	+	1.09355i
$962$	−45.1320	+	12.0931i	−1.45511	+	0.389896i
$963$	10.4108	+	14.8682i	0.335484	+	0.479121i
$964$	1.70130	−	1.42756i	0.0547952	−	0.0459786i
$965$		0			0
$966$	0.0328107	+	0.186079i	0.00105567	+	0.00598699i
$967$	29.5811	−	13.7939i	0.951264	−	0.443582i	0.115889	−	0.993262i	$-0.463028\pi$
$967$	29.5811	−	13.7939i	0.951264	−	0.443582i	0.835375	+	0.549681i	$0.185251\pi$
$968$	−8.84021	+	8.84021i	−0.284135	+	0.284135i
$969$	8.66749	−	4.95594i	0.278440	−	0.159208i
$970$		0			0
$971$	−14.0386	+	38.5708i	−0.450520	+	1.23779i	0.481838	+	0.876260i	$0.339969\pi$
$971$	−14.0386	+	38.5708i	−0.450520	+	1.23779i	−0.932359	+	0.361535i	$0.882253\pi$
$972$	−5.09301	+	7.27357i	−0.163358	+	0.233300i
$973$	−0.663601	−	7.58499i	−0.0212741	−	0.243164i
$974$	−5.61181	−	6.68790i	−0.179814	−	0.214294i
$975$		0			0
$976$	−6.95423	+	12.0451i	−0.222599	+	0.385553i
$977$	−1.26160	+	4.70837i	−0.0403623	+	0.150634i	−0.983166	−	0.182714i	$-0.941512\pi$
$977$	−1.26160	+	4.70837i	−0.0403623	+	0.150634i	0.942804	+	0.333348i	$0.108178\pi$
$978$	3.18213	+	1.48385i	0.101753	+	0.0474484i
$979$	−7.61382	+	2.77120i	−0.243339	+	0.0885681i
$980$		0			0
$981$	−38.8219	−	22.4138i	−1.23949	−	0.715618i
$982$	−29.4415	+	20.6152i	−0.939516	+	0.657856i
$983$	−1.04948	+	11.9956i	−0.0334732	+	0.382600i	0.960918	+	0.276834i	$0.0892851\pi$
$983$	−1.04948	+	11.9956i	−0.0334732	+	0.382600i	−0.994391	+	0.105766i	$0.966270\pi$
$984$	−1.60915	−	1.35024i	−0.0512980	−	0.0430441i
$985$		0			0
$986$	37.8580	+	13.7792i	1.20564	+	0.438818i
$987$	0.604126	+	0.604126i	0.0192296	+	0.0192296i
$988$	16.2865	−	11.3027i	0.518143	−	0.359587i
$989$		−	9.97168i		−	0.317081i
$990$		0			0
$991$	−32.2731	+	5.69063i	−1.02519	+	0.180769i	−0.660866	−	0.750504i	$-0.729811\pi$
$991$	−32.2731	+	5.69063i	−1.02519	+	0.180769i	−0.364324	+	0.931272i	$0.618700\pi$
$992$	8.34335	−	0.729949i	0.264902	−	0.0231759i
$993$	−3.24813	−	0.284175i	−0.103076	−	0.00901802i
$994$	1.60988	+	0.283866i	0.0510624	+	0.00900368i
$995$		0			0
$996$	2.80179	−	1.61762i	0.0887782	−	0.0512561i
$997$	−15.3449	+	32.9072i	−0.485977	+	1.04218i	0.498535	+	0.866869i	$0.333871\pi$
$997$	−15.3449	+	32.9072i	−0.485977	+	1.04218i	−0.984513	+	0.175313i	$0.943906\pi$
$998$	13.3145	−	28.5530i	0.421463	−	0.903831i
$999$	18.1670	−	10.4887i	0.574778	−	0.331848i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.bb.b.243.1	✓	48
5.2	odd	4	inner	950.2.bb.b.357.4	yes	48
5.3	odd	4	inner	950.2.bb.b.357.1	yes	48
5.4	even	2	inner	950.2.bb.b.243.4	yes	48
19.14	odd	18	inner	950.2.bb.b.793.4	yes	48
95.14	odd	18	inner	950.2.bb.b.793.1	yes	48
95.33	even	36	inner	950.2.bb.b.907.4	yes	48
95.52	even	36	inner	950.2.bb.b.907.1	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.bb.b.243.1	✓	48	1.1	even	1	trivial
950.2.bb.b.243.4	yes	48	5.4	even	2	inner
950.2.bb.b.357.1	yes	48	5.3	odd	4	inner
950.2.bb.b.357.4	yes	48	5.2	odd	4	inner
950.2.bb.b.793.1	yes	48	95.14	odd	18	inner
950.2.bb.b.793.4	yes	48	19.14	odd	18	inner
950.2.bb.b.907.1	yes	48	95.52	even	36	inner
950.2.bb.b.907.4	yes	48	95.33	even	36	inner

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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.bb (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.422618 - 0.906308i) q^{2} +(-0.284489 - 0.199201i) q^{3} +(-0.642788 + 0.766044i) q^{4} +(-0.0603074 + 0.342020i) q^{6} +(-0.127266 - 0.474963i) q^{7} +(0.965926 + 0.258819i) q^{8} +(-0.984808 - 2.70574i) q^{9} +O(q^{10})\)	\(q+(-0.422618 - 0.906308i) q^{2} +(-0.284489 - 0.199201i) q^{3} +(-0.642788 + 0.766044i) q^{4} +(-0.0603074 + 0.342020i) q^{6} +(-0.127266 - 0.474963i) q^{7} +(0.965926 + 0.258819i) q^{8} +(-0.984808 - 2.70574i) q^{9} +(-2.42394 - 4.19839i) q^{11} +(0.335463 - 0.0898869i) q^{12} +(2.60862 + 3.72550i) q^{13} +(-0.376678 + 0.316070i) q^{14} +(-0.173648 - 0.984808i) q^{16} +(5.97747 - 2.78734i) q^{17} +(-2.03603 + 2.03603i) q^{18} +(-3.35080 + 2.78785i) q^{19} +(-0.0584074 + 0.160473i) q^{21} +(-2.78063 + 3.97115i) q^{22} +(0.0964329 + 1.10223i) q^{23} +(-0.223238 - 0.266044i) q^{24} +(2.27400 - 3.93868i) q^{26} +(-0.528480 + 1.97231i) q^{27} +(0.445648 + 0.207809i) q^{28} +(-5.74005 + 2.08921i) q^{29} +(-7.25316 - 4.18761i) q^{31} +(-0.819152 + 0.573576i) q^{32} +(-0.146740 + 1.67724i) q^{33} +(-5.05238 - 4.23945i) q^{34} +(2.70574 + 0.984808i) q^{36} +(-7.26449 - 7.26449i) q^{37} +(3.94276 + 1.85866i) q^{38} -1.57950i q^{39} +(5.95655 - 1.05030i) q^{41} +(0.170122 - 0.0148837i) q^{42} +(-8.97808 - 0.785480i) q^{43} +(4.77423 + 0.841826i) q^{44} +(0.958208 - 0.553221i) q^{46} +(2.11434 - 4.53422i) q^{47} +(-0.146774 + 0.314757i) q^{48} +(5.85278 - 3.37911i) q^{49} +(-2.25576 - 0.397752i) q^{51} +(-4.53069 - 0.396384i) q^{52} +(-7.76179 + 0.679069i) q^{53} +(2.01087 - 0.354570i) q^{54} -0.491718i q^{56} +(1.50861 - 0.125628i) q^{57} +(4.31931 + 4.31931i) q^{58} +(-5.32259 - 1.93726i) q^{59} +(-10.6545 - 8.94018i) q^{61} +(-0.729949 + 8.34335i) q^{62} +(-1.15979 + 0.812096i) q^{63} +(0.866025 + 0.500000i) q^{64} +(1.58211 - 0.575843i) q^{66} +(0.563946 + 0.262972i) q^{67} +(-1.70702 + 6.37068i) q^{68} +(0.192132 - 0.332782i) q^{69} +(-2.13695 - 2.54672i) q^{71} +(-0.250955 - 2.86843i) q^{72} +(-0.412181 + 0.588655i) q^{73} +(-3.51376 + 9.65397i) q^{74} +(0.0182365 - 4.35886i) q^{76} +(-1.68559 + 1.68559i) q^{77} +(-1.43152 + 0.667527i) q^{78} +(1.35213 + 7.66833i) q^{79} +(-6.07398 + 5.09667i) q^{81} +(-3.46924 - 4.95459i) q^{82} +(8.99806 - 2.41102i) q^{83} +(-0.0853859 - 0.147893i) q^{84} +(3.08241 + 8.46886i) q^{86} +(2.04915 + 0.549068i) q^{87} +(-1.25472 - 4.68269i) q^{88} +(0.290225 - 1.64595i) q^{89} +(1.43749 - 1.71313i) q^{91} +(-0.906345 - 0.634630i) q^{92} +(1.22926 + 2.63616i) q^{93} -5.00295 q^{94} +0.347296 q^{96} +(6.58259 + 14.1164i) q^{97} +(-5.53600 - 3.87635i) q^{98} +(-8.97262 + 10.6931i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 48 q^{6}+O(q^{10}) \) 48 * q - 48 * q^6	\( 48 q - 48 q^{6} - 12 q^{11} + 36 q^{21} - 72 q^{31} + 48 q^{36} + 96 q^{41} + 72 q^{46} - 48 q^{51} - 108 q^{61} + 24 q^{66} - 60 q^{71} - 48 q^{76} - 168 q^{81} - 48 q^{86} + 252 q^{91}+O(q^{100}) \) 48 * q - 48 * q^6 - 12 * q^11 + 36 * q^21 - 72 * q^31 + 48 * q^36 + 96 * q^41 + 72 * q^46 - 48 * q^51 - 108 * q^61 + 24 * q^66 - 60 * q^71 - 48 * q^76 - 168 * q^81 - 48 * q^86 + 252 * q^91

Introduction

L-functions

Modular forms

Varieties

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Database

Properties

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