LMFDB - Embedded newform 704.2.m.i.577.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [704,2,Mod(257,704)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(704, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("704.257");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 704 = 2^{6} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	704.m (of order $5$, 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:	$5.62146830230$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.682515625.5
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 5x^{6} + 2x^{5} + 19x^{4} + 28x^{3} + 100x^{2} + 88x + 121 $ x^8 - 3x^7 + 5x^6 + 2x^5 + 19x^4 + 28x^3 + 100x^2 + 88*x + 121
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 88)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			577.2
Root			$-1.20316 - 0.874145i$ of defining polynomial
Character	$\chi$	$=$	704.577
Dual form			704.2.m.i.449.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.743592 + 0.540251i) q^{3} +(1.24359 - 3.82738i) q^{5} +(-3.01217 + 2.18847i) q^{7} +(-0.665993 - 2.04972i) q^{9} +(-1.97174 - 2.66688i) q^{11} +(-0.324462 - 0.998590i) q^{13} +(2.99248 - 2.17416i) q^{15} +(-0.291947 + 0.898521i) q^{17} +(-1.92705 - 1.40008i) q^{19} -3.42216 q^{21} +1.73830 q^{23} +(-9.05726 - 6.58048i) q^{25} +(1.46422 - 4.50639i) q^{27} +(-2.22389 + 1.61575i) q^{29} +(-1.47966 - 4.55393i) q^{31} +(-0.0253858 - 3.04831i) q^{33} +(4.63021 + 14.2503i) q^{35} +(1.71108 - 1.24317i) q^{37} +(0.298223 - 0.917835i) q^{39} +(7.38598 + 5.36623i) q^{41} +0.431946 q^{43} -8.67327 q^{45} +(5.11739 + 3.71800i) q^{47} +(2.12066 - 6.52673i) q^{49} +(-0.702517 + 0.510409i) q^{51} +(-0.0976943 - 0.300672i) q^{53} +(-12.6592 + 4.23010i) q^{55} +(-0.676543 - 2.08218i) q^{57} +(-6.54508 + 4.75528i) q^{59} +(4.21270 - 12.9654i) q^{61} +(6.49184 + 4.71659i) q^{63} -4.22549 q^{65} +5.68178 q^{67} +(1.29259 + 0.939120i) q^{69} +(3.97664 - 12.2388i) q^{71} +(2.84881 - 2.06978i) q^{73} +(-3.17979 - 9.78640i) q^{75} +(11.7756 + 3.71800i) q^{77} +(2.73078 + 8.40447i) q^{79} +(-1.70741 + 1.24051i) q^{81} +(4.53227 - 13.9489i) q^{83} +(3.07592 + 2.23479i) q^{85} -2.52658 q^{87} +2.43195 q^{89} +(3.16272 + 2.29785i) q^{91} +(1.36000 - 4.18565i) q^{93} +(-7.75513 + 5.63443i) q^{95} +(0.457940 + 1.40940i) q^{97} +(-4.15318 + 5.81763i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - q^{3} + 3 q^{5} - 7 q^{7} - 13 q^{9} + 7 q^{11} - 7 q^{13} + 13 q^{15} + q^{17} - 2 q^{19} + 2 q^{21} + 4 q^{23} - 33 q^{25} - 22 q^{27} - 17 q^{29} + 13 q^{31} + 16 q^{33} + 11 q^{35} - q^{37}+ \cdots - 27 q^{99}+O(q^{100}) $ 8 * q - q^3 + 3 * q^5 - 7 * q^7 - 13 * q^9 + 7 * q^11 - 7 * q^13 + 13 * q^15 + q^17 - 2 * q^19 + 2 * q^21 + 4 * q^23 - 33 * q^25 - 22 * q^27 - 17 * q^29 + 13 * q^31 + 16 * q^33 + 11 * q^35 - q^37 - 39 * q^39 + 9 * q^41 + 6 * q^43 - 44 * q^45 + q^47 + 3 * q^49 + 38 * q^51 + 33 * q^53 - 13 * q^55 - 6 * q^57 - 30 * q^59 + 9 * q^61 + 10 * q^63 - 10 * q^65 - 10 * q^67 + 38 * q^69 + 25 * q^71 - 7 * q^73 - 6 * q^75 + 7 * q^77 + q^79 + 14 * q^81 - 39 * q^85 + 6 * q^87 + 22 * q^89 + 7 * q^91 + 5 * q^93 - 7 * q^95 + 8 * q^97 - 27 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/704\mathbb{Z}\right)^\times$.

$n$	$133$	$321$	$639$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.743592	+	0.540251i	0.429313	+	0.311914i	0.781374	−	0.624063i	$-0.214519\pi$
$3$	0.743592	+	0.540251i	0.429313	+	0.311914i	−0.352061	+	0.935977i	$0.614519\pi$
$4$		0			0
$5$	1.24359	−	3.82738i	0.556151	−	1.71166i	−0.136732	−	0.990608i	$-0.543660\pi$
$5$	1.24359	−	3.82738i	0.556151	−	1.71166i	0.692883	−	0.721050i	$-0.256340\pi$
$6$		0			0
$7$	−3.01217	+	2.18847i	−1.13850	+	0.827165i	−0.986909	−	0.161279i	$-0.948438\pi$
$7$	−3.01217	+	2.18847i	−1.13850	+	0.827165i	−0.151586	+	0.988444i	$0.548438\pi$
$8$		0			0
$9$	−0.665993	−	2.04972i	−0.221998	−	0.683239i
$10$		0			0
$11$	−1.97174	−	2.66688i	−0.594502	−	0.804094i
$11$	−1.97174	−	2.66688i	−0.594502	−	0.804094i
$12$		0			0
$13$	−0.324462	−	0.998590i	−0.0899895	−	0.276959i	0.895926	−	0.444203i	$-0.146513\pi$
$13$	−0.324462	−	0.998590i	−0.0899895	−	0.276959i	−0.985916	+	0.167244i	$0.946513\pi$
$14$		0			0
$15$	2.99248	−	2.17416i	0.772654	−	0.561366i
$16$		0			0
$17$	−0.291947	+	0.898521i	−0.0708076	+	0.217923i	−0.980198	−	0.198020i	$-0.936549\pi$
$17$	−0.291947	+	0.898521i	−0.0708076	+	0.217923i	0.909390	+	0.415944i	$0.136549\pi$
$18$		0			0
$19$	−1.92705	−	1.40008i	−0.442096	−	0.321201i	0.344371	−	0.938834i	$-0.388092\pi$
$19$	−1.92705	−	1.40008i	−0.442096	−	0.321201i	−0.786467	+	0.617632i	$0.788092\pi$
$20$		0			0
$21$	−3.42216			−0.746776
$22$		0			0
$23$	1.73830			0.362461			0.181230	−	0.983441i	$-0.441992\pi$
$23$	1.73830			0.362461			0.181230	+	0.983441i	$0.441992\pi$
$24$		0			0
$25$	−9.05726	−	6.58048i	−1.81145	−	1.31610i
$26$		0			0
$27$	1.46422	−	4.50639i	0.281788	−	0.867256i
$28$		0			0
$29$	−2.22389	+	1.61575i	−0.412967	+	0.300038i	−0.774802	−	0.632204i	$-0.782150\pi$
$29$	−2.22389	+	1.61575i	−0.412967	+	0.300038i	0.361835	+	0.932242i	$0.382150\pi$
$30$		0			0
$31$	−1.47966	−	4.55393i	−0.265755	−	0.817909i	−0.991519	−	0.129965i	$-0.958513\pi$
$31$	−1.47966	−	4.55393i	−0.265755	−	0.817909i	0.725764	−	0.687944i	$-0.241487\pi$
$32$		0			0
$33$	−0.0253858	−	3.04831i	−0.00441911	−	0.530642i
$34$		0			0
$35$	4.63021	+	14.2503i	0.782648	+	2.40874i
$36$		0			0
$37$	1.71108	−	1.24317i	0.281299	−	0.204376i	−0.438185	−	0.898885i	$-0.644378\pi$
$37$	1.71108	−	1.24317i	0.281299	−	0.204376i	0.719484	+	0.694509i	$0.244378\pi$
$38$		0			0
$39$	0.298223	−	0.917835i	0.0477538	−	0.146971i
$40$		0			0
$41$	7.38598	+	5.36623i	1.15350	+	0.838064i	0.988942	−	0.148304i	$-0.0473816\pi$
$41$	7.38598	+	5.36623i	1.15350	+	0.838064i	0.164554	+	0.986368i	$0.447382\pi$
$42$		0			0
$43$	0.431946			0.0658711			0.0329356	−	0.999457i	$-0.489514\pi$
$43$	0.431946			0.0658711			0.0329356	+	0.999457i	$0.489514\pi$
$44$		0			0
$45$	−8.67327			−1.29294
$46$		0			0
$47$	5.11739	+	3.71800i	0.746449	+	0.542327i	0.894724	−	0.446619i	$-0.147372\pi$
$47$	5.11739	+	3.71800i	0.746449	+	0.542327i	−0.148275	+	0.988946i	$0.547372\pi$
$48$		0			0
$49$	2.12066	−	6.52673i	0.302952	−	0.932390i
$50$		0			0
$51$	−0.702517	+	0.510409i	−0.0983721	+	0.0714715i
$52$		0			0
$53$	−0.0976943	−	0.300672i	−0.0134194	−	0.0413005i	0.944123	−	0.329594i	$-0.106912\pi$
$53$	−0.0976943	−	0.300672i	−0.0134194	−	0.0413005i	−0.957542	+	0.288294i	$0.906912\pi$
$54$		0			0
$55$	−12.6592	+	4.23010i	−1.70697	+	0.570386i
$56$		0			0
$57$	−0.676543	−	2.08218i	−0.0896103	−	0.275792i
$58$		0			0
$59$	−6.54508	+	4.75528i	−0.852097	+	0.619085i	−0.925724	−	0.378201i	$-0.876543\pi$
$59$	−6.54508	+	4.75528i	−0.852097	+	0.619085i	0.0736261	+	0.997286i	$0.476543\pi$
$60$		0			0
$61$	4.21270	−	12.9654i	0.539381	−	1.66005i	−0.194606	−	0.980882i	$-0.562343\pi$
$61$	4.21270	−	12.9654i	0.539381	−	1.66005i	0.733987	−	0.679164i	$-0.237657\pi$
$62$		0			0
$63$	6.49184	+	4.71659i	0.817894	+	0.594235i
$64$		0			0
$65$	−4.22549			−0.524107
$66$		0			0
$67$	5.68178			0.694140			0.347070	−	0.937839i	$-0.387177\pi$
$67$	5.68178			0.694140			0.347070	+	0.937839i	$0.387177\pi$
$68$		0			0
$69$	1.29259	+	0.939120i	0.155609	+	0.113057i
$70$		0			0
$71$	3.97664	−	12.2388i	0.471940	−	1.45248i	−0.378101	−	0.925764i	$-0.623423\pi$
$71$	3.97664	−	12.2388i	0.471940	−	1.45248i	0.850041	−	0.526717i	$-0.176577\pi$
$72$		0			0
$73$	2.84881	−	2.06978i	0.333428	−	0.242250i	−0.408456	−	0.912778i	$-0.633933\pi$
$73$	2.84881	−	2.06978i	0.333428	−	0.242250i	0.741884	+	0.670528i	$0.233933\pi$
$74$		0			0
$75$	−3.17979	−	9.78640i	−0.367171	−	1.13004i
$76$		0			0
$77$	11.7756	+	3.71800i	1.34196	+	0.423706i
$78$		0			0
$79$	2.73078	+	8.40447i	0.307236	+	0.945577i	0.978833	+	0.204660i	$0.0656088\pi$
$79$	2.73078	+	8.40447i	0.307236	+	0.945577i	−0.671597	+	0.740917i	$0.734391\pi$
$80$		0			0
$81$	−1.70741	+	1.24051i	−0.189712	+	0.137834i
$82$		0			0
$83$	4.53227	−	13.9489i	0.497481	−	1.53109i	−0.315573	−	0.948901i	$-0.602197\pi$
$83$	4.53227	−	13.9489i	0.497481	−	1.53109i	0.813054	−	0.582188i	$-0.197803\pi$
$84$		0			0
$85$	3.07592	+	2.23479i	0.333631	+	0.242397i
$86$		0			0
$87$	−2.52658			−0.270878
$88$		0			0
$89$	2.43195			0.257786			0.128893	−	0.991659i	$-0.458858\pi$
$89$	2.43195			0.257786			0.128893	+	0.991659i	$0.458858\pi$
$90$		0			0
$91$	3.16272	+	2.29785i	0.331543	+	0.240880i
$92$		0			0
$93$	1.36000	−	4.18565i	0.141026	−	0.434032i
$94$		0			0
$95$	−7.75513	+	5.63443i	−0.795659	+	0.578080i
$96$		0			0
$97$	0.457940	+	1.40940i	0.0464968	+	0.143102i	0.971610	−	0.236590i	$-0.0760298\pi$
$97$	0.457940	+	1.40940i	0.0464968	+	0.143102i	−0.925113	+	0.379692i	$0.876030\pi$
$98$		0			0
$99$	−4.15318	+	5.81763i	−0.417410	+	0.584694i
$100$		0			0
$101$	1.34355	+	4.13503i	0.133688	+	0.411451i	0.995384	−	0.0959754i	$-0.0305970\pi$
$101$	1.34355	+	4.13503i	0.133688	+	0.411451i	−0.861695	+	0.507426i	$0.830597\pi$
$102$		0			0
$103$	8.97150	−	6.51817i	0.883988	−	0.642255i	−0.0503157	−	0.998733i	$-0.516023\pi$
$103$	8.97150	−	6.51817i	0.883988	−	0.642255i	0.934303	+	0.356479i	$0.116023\pi$
$104$		0			0
$105$	−4.25577	+	13.0979i	−0.415320	+	1.27822i
$106$		0			0
$107$	−7.72854	−	5.61512i	−0.747147	−	0.542834i	0.147795	−	0.989018i	$-0.452783\pi$
$107$	−7.72854	−	5.61512i	−0.747147	−	0.542834i	−0.894941	+	0.446184i	$0.852783\pi$
$108$		0			0
$109$	−4.14866			−0.397369			−0.198685	−	0.980063i	$-0.563667\pi$
$109$	−4.14866			−0.397369			−0.198685	+	0.980063i	$0.563667\pi$
$110$		0			0
$111$	1.94397			0.184513
$112$		0			0
$113$	7.51945	+	5.46320i	0.707371	+	0.513935i	0.882324	−	0.470642i	$-0.155978\pi$
$113$	7.51945	+	5.46320i	0.707371	+	0.513935i	−0.174954	+	0.984577i	$0.555978\pi$
$114$		0			0
$115$	2.16174	−	6.65315i	0.201583	−	0.620409i
$116$		0			0
$117$	−1.83074	+	1.33011i	−0.169252	+	0.122969i
$118$		0			0
$119$	−1.08699	−	3.34542i	−0.0996445	−	0.306674i
$120$		0			0
$121$	−3.22448	+	10.5168i	−0.293135	+	0.956071i
$122$		0			0
$123$	2.59304	+	7.98057i	0.233807	+	0.719584i
$124$		0			0
$125$	−20.1707	+	14.6549i	−1.80413	+	1.31077i
$126$		0			0
$127$	−2.45856	+	7.56667i	−0.218162	+	0.671434i	0.780752	+	0.624841i	$0.214836\pi$
$127$	−2.45856	+	7.56667i	−0.218162	+	0.671434i	−0.998914	+	0.0465926i	$0.985164\pi$
$128$		0			0
$129$	0.321192	+	0.233359i	0.0282794	+	0.0205462i
$130$		0			0
$131$	12.2670			1.07177			0.535885	−	0.844291i	$-0.319978\pi$
$131$	12.2670			1.07177			0.535885	+	0.844291i	$0.319978\pi$
$132$		0			0
$133$	8.86866			0.769010
$134$		0			0
$135$	−15.4268	−	11.2082i	−1.32773	−	0.964651i
$136$		0			0
$137$	−0.778128	+	2.39483i	−0.0664799	+	0.204604i	−0.978778	−	0.204922i	$-0.934306\pi$
$137$	−0.778128	+	2.39483i	−0.0664799	+	0.204604i	0.912298	+	0.409526i	$0.134306\pi$
$138$		0			0
$139$	−11.4034	+	8.28509i	−0.967227	+	0.702732i	−0.954818	−	0.297191i	$-0.903950\pi$
$139$	−11.4034	+	8.28509i	−0.967227	+	0.702732i	−0.0124093	+	0.999923i	$0.503950\pi$
$140$		0			0
$141$	1.79660	+	5.52936i	0.151301	+	0.465656i
$142$		0			0
$143$	−2.02336	+	2.83426i	−0.169202	+	0.237013i
$144$		0			0
$145$	3.41849	+	10.5210i	0.283890	+	0.873724i
$146$		0			0
$147$	5.10299	−	3.70754i	0.420887	−	0.305792i
$148$		0			0
$149$	−3.29883	+	10.1528i	−0.270251	+	0.831746i	0.720186	+	0.693781i	$0.244056\pi$
$149$	−3.29883	+	10.1528i	−0.270251	+	0.831746i	−0.990437	+	0.137966i	$0.955944\pi$
$150$		0			0
$151$	−16.3778	−	11.8992i	−1.33281	−	0.968341i	−0.999676	−	0.0254609i	$-0.991895\pi$
$151$	−16.3778	−	11.8992i	−1.33281	−	0.968341i	−0.333132	−	0.942880i	$-0.608105\pi$
$152$		0			0
$153$	2.03615			0.164613
$154$		0			0
$155$	−19.2697			−1.54778
$156$		0			0
$157$	15.7033	+	11.4091i	1.25326	+	0.910544i	0.998406	−	0.0564365i	$-0.0179738\pi$
$157$	15.7033	+	11.4091i	1.25326	+	0.910544i	0.254850	+	0.966981i	$0.417974\pi$
$158$		0			0
$159$	0.0897939	−	0.276357i	0.00712112	−	0.0219165i
$160$		0			0
$161$	−5.23607	+	3.80423i	−0.412660	+	0.299815i
$162$		0			0
$163$	5.83236	+	17.9502i	0.456826	+	1.40597i	0.868978	+	0.494850i	$0.164777\pi$
$163$	5.83236	+	17.9502i	0.456826	+	1.40597i	−0.412152	+	0.911115i	$0.635223\pi$
$164$		0			0
$165$	−11.6986	−	3.69369i	−0.910735	−	0.287553i
$166$		0			0
$167$	5.48945	+	16.8948i	0.424786	+	1.30736i	0.903199	+	0.429223i	$0.141212\pi$
$167$	5.48945	+	16.8948i	0.424786	+	1.30736i	−0.478412	+	0.878135i	$0.658788\pi$
$168$		0			0
$169$	9.62531	−	6.99320i	0.740409	−	0.537938i
$170$		0			0
$171$	−1.58637	+	4.88235i	−0.121313	+	0.373363i
$172$		0			0
$173$	−5.14174	−	3.73569i	−0.390919	−	0.284020i	0.374913	−	0.927060i	$-0.377673\pi$
$173$	−5.14174	−	3.73569i	−0.390919	−	0.284020i	−0.765832	+	0.643040i	$0.777673\pi$
$174$		0			0
$175$	41.6833			3.15096
$176$		0			0
$177$	−7.43592			−0.558918
$178$		0			0
$179$	1.13877	+	0.827364i	0.0851156	+	0.0618401i	0.629529	−	0.776977i	$-0.283248\pi$
$179$	1.13877	+	0.827364i	0.0851156	+	0.0618401i	−0.544414	+	0.838817i	$0.683248\pi$
$180$		0			0
$181$	−5.35860	+	16.4921i	−0.398302	+	1.22585i	0.528059	+	0.849208i	$0.322920\pi$
$181$	−5.35860	+	16.4921i	−0.398302	+	1.22585i	−0.926360	+	0.376639i	$0.877080\pi$
$182$		0			0
$183$	10.1371	−	7.36503i	0.749355	−	0.544439i
$184$		0			0
$185$	−2.63021	−	8.09495i	−0.193377	−	0.595153i
$186$		0			0
$187$	2.97189	−	0.993063i	0.217326	−	0.0726199i
$188$		0			0
$189$	5.45165	+	16.7784i	0.396549	+	1.22045i
$190$		0			0
$191$	−5.65456	+	4.10828i	−0.409149	+	0.297264i	−0.773257	−	0.634092i	$-0.781374\pi$
$191$	−5.65456	+	4.10828i	−0.409149	+	0.297264i	0.364108	+	0.931357i	$0.381374\pi$
$192$		0			0
$193$	7.21221	−	22.1969i	0.519147	−	1.59777i	−0.256462	−	0.966554i	$-0.582557\pi$
$193$	7.21221	−	22.1969i	0.519147	−	1.59777i	0.775608	−	0.631214i	$-0.217443\pi$
$194$		0			0
$195$	−3.14204	−	2.28283i	−0.225006	−	0.163477i
$196$		0			0
$197$	10.8142			0.770481			0.385240	−	0.922816i	$-0.374119\pi$
$197$	10.8142			0.770481			0.385240	+	0.922816i	$0.374119\pi$
$198$		0			0
$199$	−9.07433			−0.643262			−0.321631	−	0.946865i	$-0.604231\pi$
$199$	−9.07433			−0.643262			−0.321631	+	0.946865i	$0.604231\pi$
$200$		0			0
$201$	4.22493	+	3.06959i	0.298004	+	0.216512i
$202$		0			0
$203$	3.16272	−	9.73386i	0.221980	−	0.683183i
$204$		0			0
$205$	29.7237	−	21.5956i	2.07600	−	1.50830i
$206$		0			0
$207$	−1.15770	−	3.56302i	−0.0804655	−	0.247647i
$208$		0			0
$209$	0.0657885	+	7.89981i	0.00455068	+	0.546442i
$210$		0			0
$211$	−0.737448	−	2.26963i	−0.0507680	−	0.156248i	0.922458	−	0.386097i	$-0.126177\pi$
$211$	−0.737448	−	2.26963i	−0.0507680	−	0.156248i	−0.973226	+	0.229849i	$0.926177\pi$
$212$		0			0
$213$	9.56904	−	6.95231i	0.655660	−	0.476365i
$214$		0			0
$215$	0.537165	−	1.65322i	0.0366343	−	0.112749i
$216$		0			0
$217$	14.4231	+	10.4790i	0.979107	+	0.711363i
$218$		0			0
$219$	3.23656			0.218706
$220$		0			0
$221$	0.991980			0.0667278
$222$		0			0
$223$	−12.4428	−	9.04025i	−0.833234	−	0.605380i	0.0872383	−	0.996187i	$-0.472196\pi$
$223$	−12.4428	−	9.04025i	−0.833234	−	0.605380i	−0.920472	+	0.390807i	$0.872196\pi$
$224$		0			0
$225$	−7.45605	+	22.9474i	−0.497070	+	1.52982i
$226$		0			0
$227$	10.1460	−	7.37150i	0.673414	−	0.489264i	−0.197753	−	0.980252i	$-0.563364\pi$
$227$	10.1460	−	7.37150i	0.673414	−	0.489264i	0.871166	+	0.490988i	$0.163364\pi$
$228$		0			0
$229$	−4.12253	−	12.6879i	−0.272425	−	0.838437i	−0.989889	−	0.141842i	$-0.954698\pi$
$229$	−4.12253	−	12.6879i	−0.272425	−	0.838437i	0.717465	−	0.696595i	$-0.245302\pi$
$230$		0			0
$231$	6.74760	+	9.12647i	0.443960	+	0.600478i
$232$		0			0
$233$	−7.25552	−	22.3302i	−0.475325	−	1.46290i	−0.845519	−	0.533946i	$-0.820709\pi$
$233$	−7.25552	−	22.3302i	−0.475325	−	1.46290i	0.370194	−	0.928955i	$-0.379291\pi$
$234$		0			0
$235$	20.5942	−	14.9625i	1.34342	−	0.976049i
$236$		0			0
$237$	−2.50994	+	7.72480i	−0.163038	+	0.501780i
$238$		0			0
$239$	3.02068	+	2.19466i	0.195392	+	0.141960i	0.681180	−	0.732116i	$-0.261467\pi$
$239$	3.02068	+	2.19466i	0.195392	+	0.141960i	−0.485788	+	0.874077i	$0.661467\pi$
$240$		0			0
$241$	15.9621			1.02821			0.514104	−	0.857728i	$-0.328125\pi$
$241$	15.9621			1.02821			0.514104	+	0.857728i	$0.328125\pi$
$242$		0			0
$243$	−16.1547			−1.03633
$244$		0			0
$245$	−22.3431	−	16.2332i	−1.42745	−	1.03710i
$246$		0			0
$247$	−0.772857	+	2.37861i	−0.0491757	+	0.151347i
$248$		0			0
$249$	10.9061	−	7.92372i	0.691144	−	0.502146i
$250$		0			0
$251$	−3.42442	−	10.5393i	−0.216148	−	0.665234i	−0.999070	−	0.0431147i	$-0.986272\pi$
$251$	−3.42442	−	10.5393i	−0.216148	−	0.665234i	0.782923	−	0.622119i	$-0.213728\pi$
$252$		0			0
$253$	−3.42748	−	4.63584i	−0.215484	−	0.291453i
$254$		0			0
$255$	1.07988	+	3.32354i	0.0676250	+	0.208128i
$256$		0			0
$257$	−12.1230	+	8.80787i	−0.756212	+	0.549420i	−0.897746	−	0.440513i	$-0.854796\pi$
$257$	−12.1230	+	8.80787i	−0.756212	+	0.549420i	0.141534	+	0.989933i	$0.454796\pi$
$258$		0			0
$259$	−2.43342	+	7.48930i	−0.151205	+	0.465362i
$260$		0			0
$261$	4.79293	+	3.48227i	0.296675	+	0.215547i
$262$		0			0
$263$	−8.96129			−0.552577			−0.276288	−	0.961075i	$-0.589104\pi$
$263$	−8.96129			−0.552577			−0.276288	+	0.961075i	$0.589104\pi$
$264$		0			0
$265$	−1.27228			−0.0781555
$266$		0			0
$267$	1.80838	+	1.31386i	0.110671	+	0.0804071i
$268$		0			0
$269$	−0.324462	+	0.998590i	−0.0197828	+	0.0608851i	−0.960461	−	0.278416i	$-0.910191\pi$
$269$	−0.324462	+	0.998590i	−0.0197828	+	0.0608851i	0.940678	+	0.339301i	$0.110191\pi$
$270$		0			0
$271$	14.6960	−	10.6773i	0.892720	−	0.648599i	−0.0438656	−	0.999037i	$-0.513967\pi$
$271$	14.6960	−	10.6773i	0.892720	−	0.648599i	0.936586	+	0.350438i	$0.113967\pi$
$272$		0			0
$273$	1.11036	+	3.41733i	0.0672019	+	0.206826i
$274$		0			0
$275$	0.309210	+	37.1296i	0.0186461	+	2.23900i
$276$		0			0
$277$	−6.16272	−	18.9669i	−0.370282	−	1.13961i	−0.946607	−	0.322390i	$-0.895514\pi$
$277$	−6.16272	−	18.9669i	−0.370282	−	1.13961i	0.576325	−	0.817221i	$-0.304486\pi$
$278$		0			0
$279$	−8.34881	+	6.06577i	−0.499830	+	0.363148i
$280$		0			0
$281$	−6.49159	+	19.9791i	−0.387256	+	1.19185i	0.547575	+	0.836757i	$0.315551\pi$
$281$	−6.49159	+	19.9791i	−0.387256	+	1.19185i	−0.934831	+	0.355094i	$0.884449\pi$
$282$		0			0
$283$	−5.29615	−	3.84788i	−0.314823	−	0.228733i	0.419140	−	0.907922i	$-0.362332\pi$
$283$	−5.29615	−	3.84788i	−0.314823	−	0.228733i	−0.733963	+	0.679189i	$0.762332\pi$
$284$		0			0
$285$	−8.81066			−0.521899
$286$		0			0
$287$	−33.9917			−2.00647
$288$		0			0
$289$	13.0312	+	9.46771i	0.766540	+	0.556924i
$290$		0			0
$291$	−0.420907	+	1.29542i	−0.0246740	+	0.0759388i
$292$		0			0
$293$	−12.9630	+	9.41816i	−0.757306	+	0.550215i	−0.898083	−	0.439826i	$-0.855040\pi$
$293$	−12.9630	+	9.41816i	−0.757306	+	0.550215i	0.140777	+	0.990041i	$0.455040\pi$
$294$		0			0
$295$	10.0609	+	30.9642i	0.585767	+	1.80280i
$296$		0			0
$297$	−14.9051	+	4.98055i	−0.864879	+	0.289001i
$298$		0			0
$299$	−0.564012	−	1.73585i	−0.0326177	−	0.100387i
$300$		0			0
$301$	−1.30110	+	0.945302i	−0.0749940	+	0.0544863i
$302$		0			0
$303$	−1.23490	+	3.80063i	−0.0709432	+	0.218341i
$304$		0			0
$305$	−44.3845	−	32.2473i	−2.54145	−	1.84647i
$306$		0			0
$307$	10.8016			0.616478			0.308239	−	0.951309i	$-0.400260\pi$
$307$	10.8016			0.616478			0.308239	+	0.951309i	$0.400260\pi$
$308$		0			0
$309$	10.1926			0.579836
$310$		0			0
$311$	2.58023	+	1.87465i	0.146311	+	0.106301i	0.658533	−	0.752552i	$-0.271177\pi$
$311$	2.58023	+	1.87465i	0.146311	+	0.106301i	−0.512222	+	0.858853i	$0.671177\pi$
$312$		0			0
$313$	4.65232	−	14.3184i	0.262965	−	0.809323i	−0.729190	−	0.684311i	$-0.760103\pi$
$313$	4.65232	−	14.3184i	0.262965	−	0.809323i	0.992155	−	0.125012i	$-0.0398969\pi$
$314$		0			0
$315$	26.1254	−	18.9812i	1.47200	−	1.06947i
$316$		0			0
$317$	−4.09444	−	12.6014i	−0.229967	−	0.707765i	−0.997749	−	0.0670547i	$-0.978640\pi$
$317$	−4.09444	−	12.6014i	−0.229967	−	0.707765i	0.767782	−	0.640711i	$-0.221360\pi$
$318$		0			0
$319$	8.69396	+	2.74501i	0.486768	+	0.153691i
$320$		0			0
$321$	−2.71331	−	8.35071i	−0.151442	−	0.466091i
$322$		0			0
$323$	1.82060	−	1.32275i	0.101301	−	0.0735995i
$324$		0			0
$325$	−3.63247	+	11.1796i	−0.201493	+	0.620133i
$326$		0			0
$327$	−3.08491	−	2.24132i	−0.170596	−	0.123945i
$328$		0			0
$329$	−23.5512			−1.29842
$330$		0			0
$331$	−33.5540			−1.84429			−0.922147	−	0.386839i	$-0.873567\pi$
$331$	−33.5540			−1.84429			−0.922147	+	0.386839i	$0.873567\pi$
$332$		0			0
$333$	−3.68771	−	2.67928i	−0.202085	−	0.146824i
$334$		0			0
$335$	7.06582	−	21.7464i	0.386047	−	1.18813i
$336$		0			0
$337$	−5.58656	+	4.05887i	−0.304319	+	0.221101i	−0.729455	−	0.684029i	$-0.760226\pi$
$337$	−5.58656	+	4.05887i	−0.304319	+	0.221101i	0.425136	+	0.905129i	$0.360226\pi$
$338$		0			0
$339$	2.63991	+	8.12479i	0.143380	+	0.441278i
$340$		0			0
$341$	−9.22726	+	12.9252i	−0.499684	+	0.699941i
$342$		0			0
$343$	−0.158073	−	0.486498i	−0.00853513	−	0.0262684i
$344$		0			0
$345$	5.20182	−	3.77935i	0.280057	−	0.203473i
$346$		0			0
$347$	−6.39637	+	19.6860i	−0.343375	+	1.05680i	0.619072	+	0.785334i	$0.287509\pi$
$347$	−6.39637	+	19.6860i	−0.343375	+	1.05680i	−0.962448	+	0.271467i	$0.912491\pi$
$348$		0			0
$349$	−8.94507	−	6.49898i	−0.478819	−	0.347882i	0.322049	−	0.946723i	$-0.395628\pi$
$349$	−8.94507	−	6.49898i	−0.478819	−	0.347882i	−0.800868	+	0.598841i	$0.795628\pi$
$350$		0			0
$351$	−4.97512			−0.265552
$352$		0			0
$353$	13.5005			0.718557			0.359279	−	0.933230i	$-0.383023\pi$
$353$	13.5005			0.718557			0.359279	+	0.933230i	$0.383023\pi$
$354$		0			0
$355$	−41.8974	−	30.4402i	−2.22368	−	1.61560i
$356$		0			0
$357$	0.999089	−	3.07488i	0.0528774	−	0.162740i
$358$		0			0
$359$	27.0425	−	19.6475i	1.42725	−	1.03696i	0.436726	−	0.899595i	$-0.356138\pi$
$359$	27.0425	−	19.6475i	1.42725	−	1.03696i	0.990521	−	0.137361i	$-0.0438621\pi$
$360$		0			0
$361$	−4.11803	−	12.6740i	−0.216739	−	0.667053i
$362$		0			0
$363$	−8.07941	+	6.07817i	−0.424059	+	0.319021i
$364$		0			0
$365$	−4.37909	−	13.4775i	−0.229212	−	0.705442i
$366$		0			0
$367$	16.2563	−	11.8109i	0.848570	−	0.616522i	−0.0761814	−	0.997094i	$-0.524273\pi$
$367$	16.2563	−	11.8109i	0.848570	−	0.616522i	0.924751	+	0.380572i	$0.124273\pi$
$368$		0			0
$369$	6.08023	−	18.7130i	0.316524	−	0.974161i
$370$		0			0
$371$	0.952286	+	0.691876i	0.0494402	+	0.0359204i
$372$		0			0
$373$	26.4379			1.36890			0.684451	−	0.729059i	$-0.260042\pi$
$373$	26.4379			1.36890			0.684451	+	0.729059i	$0.260042\pi$
$374$		0			0
$375$	−22.9161			−1.18338
$376$		0			0
$377$	2.33504	+	1.69651i	0.120261	+	0.0873746i
$378$		0			0
$379$	6.26005	−	19.2665i	0.321557	−	0.989652i	−0.651413	−	0.758723i	$-0.725824\pi$
$379$	6.26005	−	19.2665i	0.321557	−	0.989652i	0.972971	−	0.230929i	$-0.0741764\pi$
$380$		0			0
$381$	−5.91607	+	4.29828i	−0.303090	+	0.220208i
$382$		0			0
$383$	1.42442	+	4.38392i	0.0727845	+	0.224008i	0.980831	−	0.194863i	$-0.0624261\pi$
$383$	1.42442	+	4.38392i	0.0727845	+	0.224008i	−0.908046	+	0.418870i	$0.862426\pi$
$384$		0			0
$385$	28.8743	−	40.4461i	1.47157	−	2.06133i
$386$		0			0
$387$	−0.287673	−	0.885366i	−0.0146232	−	0.0450057i
$388$		0			0
$389$	24.9393	−	18.1195i	1.26447	−	0.918694i	0.265506	−	0.964109i	$-0.414461\pi$
$389$	24.9393	−	18.1195i	1.26447	−	0.918694i	0.998968	+	0.0454151i	$0.0144611\pi$
$390$		0			0
$391$	−0.507492	+	1.56190i	−0.0256650	+	0.0789887i
$392$		0			0
$393$	9.12162	+	6.62724i	0.460125	+	0.334300i
$394$		0			0
$395$	35.5631			1.78937
$396$		0			0
$397$	−15.9382			−0.799916			−0.399958	−	0.916533i	$-0.630975\pi$
$397$	−15.9382			−0.799916			−0.399958	+	0.916533i	$0.630975\pi$
$398$		0			0
$399$	6.59467	+	4.79131i	0.330146	+	0.239865i
$400$		0			0
$401$	7.12841	−	21.9390i	0.355976	−	1.09558i	−0.599466	−	0.800401i	$-0.704620\pi$
$401$	7.12841	−	21.9390i	0.355976	−	1.09558i	0.955441	−	0.295181i	$-0.0953799\pi$
$402$		0			0
$403$	−4.06741	+	2.95515i	−0.202612	+	0.147206i
$404$		0			0
$405$	2.62457	+	8.07761i	0.130416	+	0.401380i
$406$		0			0
$407$	−6.68919	−	2.11203i	−0.331571	−	0.104689i
$408$		0			0
$409$	4.49146	+	13.8233i	0.222088	+	0.683518i	0.998574	+	0.0533829i	$0.0170004\pi$
$409$	4.49146	+	13.8233i	0.222088	+	0.683518i	−0.776486	+	0.630135i	$0.783000\pi$
$410$		0			0
$411$	−1.87242	+	1.36039i	−0.0923597	+	0.0671033i
$412$		0			0
$413$	9.30813	−	28.6475i	0.458023	−	1.40965i
$414$		0			0
$415$	−47.7515	−	34.6935i	−2.34403	−	1.70304i
$416$		0			0
$417$	−12.9555			−0.634436
$418$		0			0
$419$	7.34710			0.358929			0.179465	−	0.983764i	$-0.442563\pi$
$419$	7.34710			0.358929			0.179465	+	0.983764i	$0.442563\pi$
$420$		0			0
$421$	1.43035	+	1.03921i	0.0697111	+	0.0506481i	0.622095	−	0.782942i	$-0.286282\pi$
$421$	1.43035	+	1.03921i	0.0697111	+	0.0506481i	−0.552384	+	0.833590i	$0.686282\pi$
$422$		0			0
$423$	4.21270	−	12.9654i	0.204829	−	0.630398i
$424$		0			0
$425$	8.55695	−	6.21699i	0.415073	−	0.301568i
$426$		0			0
$427$	15.6850	+	48.2733i	0.759048	+	2.33611i
$428$		0			0
$429$	−3.03577	+	1.01441i	−0.146568	+	0.0489761i
$430$		0			0
$431$	5.03267	+	15.4890i	0.242415	+	0.746077i	0.996051	+	0.0887844i	$0.0282982\pi$
$431$	5.03267	+	15.4890i	0.242415	+	0.746077i	−0.753636	+	0.657292i	$0.771702\pi$
$432$		0			0
$433$	1.81976	−	1.32213i	0.0874521	−	0.0635376i	−0.543200	−	0.839603i	$-0.682787\pi$
$433$	1.81976	−	1.32213i	0.0874521	−	0.0635376i	0.630652	+	0.776066i	$0.282787\pi$
$434$		0			0
$435$	−3.14204	+	9.67020i	−0.150649	+	0.463651i
$436$		0			0
$437$	−3.34980	−	2.43377i	−0.160242	−	0.116423i
$438$		0			0
$439$	8.85337			0.422549			0.211274	−	0.977427i	$-0.432239\pi$
$439$	8.85337			0.422549			0.211274	+	0.977427i	$0.432239\pi$
$440$		0			0
$441$	−14.7903			−0.704300
$442$		0			0
$443$	−12.9159	−	9.38396i	−0.613654	−	0.445845i	0.237045	−	0.971499i	$-0.423821\pi$
$443$	−12.9159	−	9.38396i	−0.613654	−	0.445845i	−0.850699	+	0.525653i	$0.823821\pi$
$444$		0			0
$445$	3.02435	−	9.30799i	0.143368	−	0.441241i
$446$		0			0
$447$	−7.93803	+	5.76732i	−0.375456	+	0.272785i
$448$		0			0
$449$	7.35448	+	22.6348i	0.347079	+	1.06820i	0.960461	+	0.278414i	$0.0898086\pi$
$449$	7.35448	+	22.6348i	0.347079	+	1.06820i	−0.613382	+	0.789786i	$0.710191\pi$
$450$		0			0
$451$	−0.252153	−	30.2783i	−0.0118734	−	1.42575i
$452$		0			0
$453$	−5.74987	−	17.6963i	−0.270152	−	0.831443i
$454$		0			0
$455$	12.7279	−	9.24736i	0.596693	−	0.433523i
$456$		0			0
$457$	9.16009	−	28.1919i	0.428491	−	1.31876i	−0.471120	−	0.882069i	$-0.656150\pi$
$457$	9.16009	−	28.1919i	0.428491	−	1.31876i	0.899612	−	0.436691i	$-0.143850\pi$
$458$		0			0
$459$	3.62162	+	2.63126i	0.169043	+	0.122817i
$460$		0			0
$461$	−9.00605			−0.419454			−0.209727	−	0.977760i	$-0.567257\pi$
$461$	−9.00605			−0.419454			−0.209727	+	0.977760i	$0.567257\pi$
$462$		0			0
$463$	−16.0634			−0.746528			−0.373264	−	0.927725i	$-0.621761\pi$
$463$	−16.0634			−0.746528			−0.373264	+	0.927725i	$0.621761\pi$
$464$		0			0
$465$	−14.3288	−	10.4105i	−0.664483	−	0.482775i
$466$		0			0
$467$	−1.25913	+	3.87521i	−0.0582656	+	0.179323i	−0.975953	−	0.217979i	$-0.930054\pi$
$467$	−1.25913	+	3.87521i	−0.0582656	+	0.179323i	0.917688	+	0.397302i	$0.130054\pi$
$468$		0			0
$469$	−17.1145	+	12.4344i	−0.790275	+	0.574168i
$470$		0			0
$471$	5.51305	+	16.9674i	0.254028	+	0.781817i
$472$		0			0
$473$	−0.851685	−	1.15195i	−0.0391605	−	0.0529666i
$474$		0			0
$475$	8.24057	+	25.3619i	0.378103	+	1.16368i
$476$		0			0
$477$	−0.551229	+	0.400491i	−0.0252390	+	0.0183372i
$478$		0			0
$479$	−0.107974	+	0.332309i	−0.00493344	+	0.0151836i	−0.953493	−	0.301415i	$-0.902541\pi$
$479$	−0.107974	+	0.332309i	−0.00493344	+	0.0151836i	0.948559	+	0.316599i	$0.102541\pi$
$480$		0			0
$481$	−1.79660	−	1.30530i	−0.0819178	−	0.0595168i
$482$		0			0
$483$	−5.94874			−0.270677
$484$		0			0
$485$	5.96379			0.270802
$486$		0			0
$487$	31.6732	+	23.0119i	1.43525	+	1.04277i	0.989009	+	0.147855i	$0.0472368\pi$
$487$	31.6732	+	23.0119i	1.43525	+	1.04277i	0.446239	+	0.894914i	$0.352763\pi$
$488$		0			0
$489$	−5.36070	+	16.4985i	−0.242419	+	0.746090i
$490$		0			0
$491$	7.10844	−	5.16458i	0.320799	−	0.233074i	−0.415717	−	0.909494i	$-0.636469\pi$
$491$	7.10844	−	5.16458i	0.320799	−	0.233074i	0.736516	+	0.676420i	$0.236469\pi$
$492$		0			0
$493$	−0.802529	−	2.46993i	−0.0361441	−	0.111240i
$494$		0			0
$495$	17.1014	+	23.1306i	0.768653	+	1.03964i
$496$		0			0
$497$	14.8060	+	45.5682i	0.664141	+	2.04401i
$498$		0			0
$499$	20.8304	−	15.1342i	0.932497	−	0.677499i	−0.0141058	−	0.999901i	$-0.504490\pi$
$499$	20.8304	−	15.1342i	0.932497	−	0.677499i	0.946603	+	0.322402i	$0.104490\pi$
$500$		0			0
$501$	−5.04552	+	15.5285i	−0.225417	+	0.693763i
$502$		0			0
$503$	12.0267	+	8.73793i	0.536246	+	0.389605i	0.822689	−	0.568492i	$-0.192473\pi$
$503$	12.0267	+	8.73793i	0.536246	+	0.389605i	−0.286443	+	0.958097i	$0.592473\pi$
$504$		0			0
$505$	17.4972			0.778614
$506$		0			0
$507$	10.9354			0.485658
$508$		0			0
$509$	2.78541	+	2.02372i	0.123461	+	0.0896997i	0.647802	−	0.761809i	$-0.275688\pi$
$509$	2.78541	+	2.02372i	0.123461	+	0.0896997i	−0.524341	+	0.851508i	$0.675688\pi$
$510$		0			0
$511$	−4.05145	+	12.4691i	−0.179226	+	0.551600i
$512$		0			0
$513$	−9.13095	+	6.63402i	−0.403141	+	0.292899i
$514$		0			0
$515$	−13.7907	−	42.4433i	−0.607689	−	1.87028i
$516$		0			0
$517$	−0.174705	−	20.9784i	−0.00768352	−	0.922629i
$518$		0			0
$519$	−1.80515	−	5.55567i	−0.0792371	−	0.243867i
$520$		0			0
$521$	−32.5393	+	23.6412i	−1.42557	+	1.03574i	−0.434755	+	0.900549i	$0.643165\pi$
$521$	−32.5393	+	23.6412i	−1.42557	+	1.03574i	−0.990820	+	0.135191i	$0.956835\pi$
$522$		0			0
$523$	−10.6385	+	32.7419i	−0.465189	+	1.43170i	0.393556	+	0.919301i	$0.371245\pi$
$523$	−10.6385	+	32.7419i	−0.465189	+	1.43170i	−0.858745	+	0.512403i	$0.828755\pi$
$524$		0			0
$525$	30.9954	+	22.5194i	1.35275	+	0.982829i
$526$		0			0
$527$	4.52378			0.197059
$528$		0			0
$529$	−19.9783			−0.868622
$530$		0			0
$531$	14.1060	+	10.2486i	0.612146	+	0.444750i
$532$		0			0
$533$	2.96219	−	9.11670i	0.128307	−	0.394888i
$534$		0			0
$535$	−31.1024	+	22.5972i	−1.34467	+	0.976962i
$536$		0			0
$537$	0.399795	+	1.23044i	0.0172524	+	0.0530976i
$538$		0			0
$539$	−21.5874	+	7.21347i	−0.929835	+	0.310706i
$540$		0			0
$541$	5.84779	+	17.9977i	0.251416	+	0.773780i	0.994515	+	0.104598i	$0.0333555\pi$
$541$	5.84779	+	17.9977i	0.251416	+	0.773780i	−0.743098	+	0.669182i	$0.766645\pi$
$542$		0			0
$543$	−12.8945	+	9.36839i	−0.553355	+	0.402036i
$544$		0			0
$545$	−5.15924	+	15.8785i	−0.220998	+	0.680161i
$546$		0			0
$547$	−26.5669	−	19.3020i	−1.13592	−	0.825292i	−0.149372	−	0.988781i	$-0.547725\pi$
$547$	−26.5669	−	19.3020i	−1.13592	−	0.825292i	−0.986545	+	0.163489i	$0.947725\pi$
$548$		0			0
$549$	−29.3809			−1.25395
$550$		0			0
$551$	6.54775			0.278943
$552$		0			0
$553$	−26.6185	−	19.3395i	−1.13194	−	0.822399i
$554$		0			0
$555$	2.41751	−	7.44032i	0.102617	−	0.315824i
$556$		0			0
$557$	−25.9380	+	18.8451i	−1.09903	+	0.798492i	−0.980901	−	0.194506i	$-0.937690\pi$
$557$	−25.9380	+	18.8451i	−1.09903	+	0.798492i	−0.118129	+	0.992998i	$0.537690\pi$
$558$		0			0
$559$	−0.140150	−	0.431337i	−0.00592771	−	0.0182436i
$560$		0			0
$561$	2.74638	+	0.867135i	0.115952	+	0.0366105i
$562$		0			0
$563$	0.387163	+	1.19157i	0.0163170	+	0.0502185i	0.958883	−	0.283800i	$-0.0915952\pi$
$563$	0.387163	+	1.19157i	0.0163170	+	0.0502185i	−0.942567	+	0.334019i	$0.891595\pi$
$564$		0			0
$565$	30.2609	−	21.9858i	1.27309	−	0.924951i
$566$		0			0
$567$	2.42821	−	7.47325i	0.101975	−	0.313847i
$568$		0			0
$569$	−4.17610	−	3.03411i	−0.175071	−	0.127197i	0.496799	−	0.867866i	$-0.334509\pi$
$569$	−4.17610	−	3.03411i	−0.175071	−	0.127197i	−0.671870	+	0.740669i	$0.734509\pi$
$570$		0			0
$571$	1.46767			0.0614200			0.0307100	−	0.999528i	$-0.490223\pi$
$571$	1.46767			0.0614200			0.0307100	+	0.999528i	$0.490223\pi$
$572$		0			0
$573$	−6.42419			−0.268374
$574$		0			0
$575$	−15.7442	−	11.4389i	−0.656581	−	0.477034i
$576$		0			0
$577$	−5.93354	+	18.2616i	−0.247016	+	0.760238i	0.748282	+	0.663381i	$0.230879\pi$
$577$	−5.93354	+	18.2616i	−0.247016	+	0.760238i	−0.995298	+	0.0968575i	$0.969121\pi$
$578$		0			0
$579$	17.3549	−	12.6090i	0.721243	−	0.524014i
$580$		0			0
$581$	16.8748	+	51.9353i	0.700084	+	2.15464i
$582$		0			0
$583$	−0.609229	+	0.853387i	−0.0252317	+	0.0353437i
$584$		0			0
$585$	2.81414	+	8.66105i	0.116351	+	0.358090i
$586$		0			0
$587$	4.62070	−	3.35713i	0.190717	−	0.138564i	−0.488330	−	0.872659i	$-0.662394\pi$
$587$	4.62070	−	3.35713i	0.190717	−	0.138564i	0.679046	+	0.734096i	$0.262394\pi$
$588$		0			0
$589$	−3.52450	+	10.8473i	−0.145225	+	0.446955i
$590$		0			0
$591$	8.04137	+	5.84240i	0.330778	+	0.240324i
$592$		0			0
$593$	36.3301			1.49190			0.745949	−	0.666003i	$-0.231996\pi$
$593$	36.3301			1.49190			0.745949	+	0.666003i	$0.231996\pi$
$594$		0			0
$595$	−14.1560			−0.580339
$596$		0			0
$597$	−6.74760	−	4.90242i	−0.276161	−	0.200643i
$598$		0			0
$599$	12.7458	−	39.2276i	0.520780	−	1.60280i	−0.251732	−	0.967797i	$-0.581000\pi$
$599$	12.7458	−	39.2276i	0.520780	−	1.60280i	0.772512	−	0.635000i	$-0.219000\pi$
$600$		0			0
$601$	−17.3591	+	12.6121i	−0.708091	+	0.514458i	−0.882557	−	0.470205i	$-0.844180\pi$
$601$	−17.3591	+	12.6121i	−0.708091	+	0.514458i	0.174466	+	0.984663i	$0.444180\pi$
$602$		0			0
$603$	−3.78403	−	11.6460i	−0.154097	−	0.474263i
$604$		0			0
$605$	36.2418	+	25.4199i	1.47344	+	1.03347i
$606$		0			0
$607$	−1.15092	−	3.54218i	−0.0467146	−	0.143773i	0.924979	−	0.380019i	$-0.124083\pi$
$607$	−1.15092	−	3.54218i	−0.0467146	−	0.143773i	−0.971693	+	0.236247i	$0.924083\pi$
$608$		0			0
$609$	7.61051	−	5.52936i	0.308393	−	0.224061i
$610$		0			0
$611$	2.05236	−	6.31653i	0.0830298	−	0.255539i
$612$		0			0
$613$	−11.5250	−	8.37340i	−0.465490	−	0.338198i	0.330191	−	0.943914i	$-0.392887\pi$
$613$	−11.5250	−	8.37340i	−0.465490	−	0.338198i	−0.795681	+	0.605716i	$0.792887\pi$
$614$		0			0
$615$	33.7694			1.36171
$616$		0			0
$617$	33.2403			1.33821			0.669103	−	0.743170i	$-0.266678\pi$
$617$	33.2403			1.33821			0.669103	+	0.743170i	$0.266678\pi$
$618$		0			0
$619$	12.6726	+	9.20717i	0.509354	+	0.370067i	0.812578	−	0.582852i	$-0.198063\pi$
$619$	12.6726	+	9.20717i	0.509354	+	0.370067i	−0.303224	+	0.952919i	$0.598063\pi$
$620$		0			0
$621$	2.54525	−	7.83347i	0.102137	−	0.314346i
$622$		0			0
$623$	−7.32545	+	5.32225i	−0.293488	+	0.213231i
$624$		0			0
$625$	13.7079	+	42.1887i	0.548317	+	1.68755i
$626$		0			0
$627$	−4.21897	+	5.90978i	−0.168489	+	0.236014i
$628$		0			0
$629$	0.617471	+	1.90038i	0.0246202	+	0.0757731i
$630$		0			0
$631$	6.17588	−	4.48704i	0.245858	−	0.178626i	−0.458031	−	0.888936i	$-0.651445\pi$
$631$	6.17588	−	4.48704i	0.245858	−	0.178626i	0.703889	+	0.710310i	$0.251445\pi$
$632$		0			0
$633$	0.677811	−	2.08609i	0.0269406	−	0.0829146i
$634$		0			0
$635$	25.9031	+	18.8197i	1.02793	+	0.746838i
$636$		0			0
$637$	−7.20560			−0.285496
$638$		0			0
$639$	−27.7345			−1.09716
$640$		0			0
$641$	15.3559	+	11.1567i	0.606521	+	0.440663i	0.848187	−	0.529696i	$-0.177694\pi$
$641$	15.3559	+	11.1567i	0.606521	+	0.440663i	−0.241667	+	0.970359i	$0.577694\pi$
$642$		0			0
$643$	5.09102	−	15.6686i	0.200770	−	0.617908i	−0.799090	−	0.601211i	$-0.794685\pi$
$643$	5.09102	−	15.6686i	0.200770	−	0.617908i	0.999861	−	0.0166965i	$-0.00531491\pi$
$644$		0			0
$645$	1.29259	−	0.939120i	0.0508956	−	0.0369778i
$646$		0			0
$647$	−12.3054	−	37.8720i	−0.483774	−	1.48890i	−0.833749	−	0.552144i	$-0.813810\pi$
$647$	−12.3054	−	37.8720i	−0.483774	−	1.48890i	0.349975	−	0.936759i	$-0.386190\pi$
$648$		0			0
$649$	25.5870	+	8.07877i	1.00438	+	0.317119i
$650$		0			0
$651$	5.06363	+	15.5842i	0.198459	+	0.610795i
$652$		0			0
$653$	−19.9459	+	14.4915i	−0.780542	+	0.567097i	−0.905142	−	0.425110i	$-0.860235\pi$
$653$	−19.9459	+	14.4915i	−0.780542	+	0.567097i	0.124600	+	0.992207i	$0.460235\pi$
$654$		0			0
$655$	15.2551	−	46.9504i	0.596066	−	1.83450i
$656$		0			0
$657$	−6.13975	−	4.46079i	−0.239535	−	0.174032i
$658$		0			0
$659$	−11.3599			−0.442518			−0.221259	−	0.975215i	$-0.571017\pi$
$659$	−11.3599			−0.442518			−0.221259	+	0.975215i	$0.571017\pi$
$660$		0			0
$661$	5.05889			0.196768			0.0983841	−	0.995149i	$-0.468633\pi$
$661$	5.05889			0.196768			0.0983841	+	0.995149i	$0.468633\pi$
$662$		0			0
$663$	0.737629	+	0.535919i	0.0286471	+	0.0208134i
$664$		0			0
$665$	11.0290	−	33.9438i	0.427686	−	1.31628i
$666$		0			0
$667$	−3.86580	+	2.80867i	−0.149684	+	0.108752i
$668$		0			0
$669$	−4.36839	−	13.4445i	−0.168892	−	0.519795i
$670$		0			0
$671$	−42.8834	+	14.3296i	−1.65550	+	0.553187i
$672$		0			0
$673$	−12.4707	−	38.3809i	−0.480710	−	1.47947i	−0.838099	−	0.545518i	$-0.816333\pi$
$673$	−12.4707	−	38.3809i	−0.480710	−	1.47947i	0.357389	−	0.933956i	$-0.383667\pi$
$674$		0			0
$675$	−42.9160	+	31.1803i	−1.65184	+	1.20013i
$676$		0			0
$677$	−9.72753	+	29.9382i	−0.373859	+	1.15062i	0.570386	+	0.821377i	$0.306794\pi$
$677$	−9.72753	+	29.9382i	−0.373859	+	1.15062i	−0.944245	+	0.329244i	$0.893206\pi$
$678$		0			0
$679$	−4.46382	−	3.24315i	−0.171306	−	0.124461i
$680$		0			0
$681$	11.5269			0.441714
$682$		0			0
$683$	40.0582			1.53279			0.766393	−	0.642372i	$-0.222050\pi$
$683$	40.0582			1.53279			0.766393	+	0.642372i	$0.222050\pi$
$684$		0			0
$685$	8.19826	+	5.95639i	0.313240	+	0.227582i
$686$		0			0
$687$	3.78915	−	11.6618i	0.144565	−	0.444925i
$688$		0			0
$689$	−0.268550	+	0.195113i	−0.0102310	+	0.00743322i
$690$		0			0
$691$	−4.00915	−	12.3389i	−0.152515	−	0.469394i	0.845385	−	0.534157i	$-0.179371\pi$
$691$	−4.00915	−	12.3389i	−0.152515	−	0.469394i	−0.997901	+	0.0647632i	$0.979371\pi$
$692$		0			0
$693$	−0.221628	−	26.6128i	−0.00841894	−	1.01094i
$694$		0			0
$695$	17.5290	+	53.9486i	0.664912	+	2.04639i
$696$		0			0
$697$	−6.97798	+	5.06980i	−0.264310	+	0.192032i
$698$		0			0
$699$	6.66877	−	20.5244i	0.252236	−	0.776303i
$700$		0			0
$701$	10.6664	+	7.74961i	0.402865	+	0.292699i	0.770707	−	0.637190i	$-0.219903\pi$
$701$	10.6664	+	7.74961i	0.402865	+	0.292699i	−0.367842	+	0.929888i	$0.619903\pi$
$702$		0			0
$703$	−5.03788			−0.190007
$704$		0			0
$705$	23.3972			0.881190
$706$		0			0
$707$	−13.0964	−	9.51510i	−0.492541	−	0.357852i
$708$		0			0
$709$	−5.05048	+	15.5438i	−0.189675	+	0.583758i	−0.999998	−	0.00222523i	$-0.999292\pi$
$709$	−5.05048	+	15.5438i	−0.189675	+	0.583758i	0.810323	+	0.585984i	$0.199292\pi$
$710$		0			0
$711$	15.4081	−	11.1946i	0.577849	−	0.419832i
$712$		0			0
$713$	−2.57210	−	7.91610i	−0.0963257	−	0.296460i
$714$		0			0
$715$	8.33156	+	11.2689i	0.311583	+	0.421431i
$716$		0			0
$717$	1.06049	+	3.26386i	0.0396048	+	0.121891i
$718$		0			0
$719$	−4.53222	+	3.29285i	−0.169023	+	0.122803i	−0.669081	−	0.743189i	$-0.733312\pi$
$719$	−4.53222	+	3.29285i	−0.169023	+	0.122803i	0.500058	+	0.865992i	$0.333312\pi$
$720$		0			0
$721$	−12.7589	+	39.2678i	−0.475165	+	1.46241i
$722$		0			0
$723$	11.8693	+	8.62354i	0.441423	+	0.320713i
$724$		0			0
$725$	30.7748			1.14295
$726$		0			0
$727$	29.1822			1.08231			0.541155	−	0.840923i	$-0.317987\pi$
$727$	29.1822			1.08231			0.541155	+	0.840923i	$0.317987\pi$
$728$		0			0
$729$	−6.89028	−	5.00608i	−0.255196	−	0.185410i
$730$		0			0
$731$	−0.126105	+	0.388113i	−0.00466418	+	0.0143549i
$732$		0			0
$733$	20.0564	−	14.5718i	0.740800	−	0.538223i	−0.152161	−	0.988356i	$-0.548623\pi$
$733$	20.0564	−	14.5718i	0.740800	−	0.538223i	0.892962	+	0.450133i	$0.148623\pi$
$734$		0			0
$735$	−7.84413	−	24.1417i	−0.289335	−	0.890482i
$736$		0			0
$737$	−11.2030	−	15.1526i	−0.412668	−	0.558154i
$738$		0			0
$739$	8.26632	+	25.4411i	0.304081	+	0.935866i	0.980018	+	0.198907i	$0.0637391\pi$
$739$	8.26632	+	25.4411i	0.304081	+	0.935866i	−0.675937	+	0.736959i	$0.736261\pi$
$740$		0			0
$741$	−1.85974	+	1.35118i	−0.0683191	+	0.0496368i
$742$		0			0
$743$	−11.3483	+	34.9265i	−0.416330	+	1.28133i	0.494727	+	0.869049i	$0.335268\pi$
$743$	−11.3483	+	34.9265i	−0.416330	+	1.28133i	−0.911056	+	0.412282i	$0.864732\pi$
$744$		0			0
$745$	34.7561	+	25.2518i	1.27337	+	0.925154i
$746$		0			0
$747$	−31.6097			−1.15654
$748$		0			0
$749$	35.5683			1.29964
$750$		0			0
$751$	−18.4555	−	13.4087i	−0.673451	−	0.489290i	0.197728	−	0.980257i	$-0.436644\pi$
$751$	−18.4555	−	13.4087i	−0.673451	−	0.489290i	−0.871178	+	0.490966i	$0.836644\pi$
$752$		0			0
$753$	3.14749	−	9.68698i	0.114701	−	0.353013i
$754$		0			0
$755$	−65.9100	+	47.8864i	−2.39871	+	1.74277i
$756$		0			0
$757$	8.25614	+	25.4098i	0.300075	+	0.923535i	0.981469	+	0.191619i	$0.0613737\pi$
$757$	8.25614	+	25.4098i	0.300075	+	0.923535i	−0.681395	+	0.731916i	$0.738626\pi$
$758$		0			0
$759$	−0.0441282	−	5.29888i	−0.00160175	−	0.192337i
$760$		0			0
$761$	6.71252	+	20.6590i	0.243329	+	0.748889i	0.995907	+	0.0903857i	$0.0288100\pi$
$761$	6.71252	+	20.6590i	0.243329	+	0.748889i	−0.752578	+	0.658503i	$0.771190\pi$
$762$		0			0
$763$	12.4965	−	9.07923i	0.452403	−	0.328690i
$764$		0			0
$765$	2.53214	−	7.79312i	0.0915497	−	0.281761i
$766$		0			0
$767$	6.87221	+	4.99295i	0.248141	+	0.180285i
$768$		0			0
$769$	−53.7688			−1.93895			−0.969476	−	0.245185i	$-0.921151\pi$
$769$	−53.7688			−1.93895			−0.969476	+	0.245185i	$0.921151\pi$
$770$		0			0
$771$	−13.7730			−0.496024
$772$		0			0
$773$	7.87350	+	5.72044i	0.283190	+	0.205750i	0.720308	−	0.693655i	$-0.244001\pi$
$773$	7.87350	+	5.72044i	0.283190	+	0.205750i	−0.437117	+	0.899404i	$0.644001\pi$
$774$		0			0
$775$	−16.5654	+	50.9830i	−0.595046	+	1.83136i
$776$		0			0
$777$	−5.85558	+	4.25432i	−0.210068	+	0.152623i
$778$		0			0
$779$	−6.71998	−	20.6820i	−0.240768	−	0.741009i
$780$		0			0
$781$	−40.4803	+	13.5266i	−1.44850	+	0.484019i
$782$		0			0
$783$	4.02496	+	12.3875i	0.143840	+	0.442695i
$784$		0			0
$785$	63.1954	−	45.9141i	2.25554	−	1.63875i
$786$		0			0
$787$	11.8092	−	36.3451i	0.420954	−	1.29556i	−0.485862	−	0.874035i	$-0.661494\pi$
$787$	11.8092	−	36.3451i	0.420954	−	1.29556i	0.906816	−	0.421527i	$-0.138506\pi$
$788$		0			0
$789$	−6.66355	−	4.84135i	−0.237229	−	0.172357i
$790$		0			0
$791$	−34.6060			−1.23045
$792$		0			0
$793$	−14.3139			−0.508303
$794$		0			0
$795$	−0.946058	−	0.687351i	−0.0335532	−	0.0243778i
$796$		0			0
$797$	−6.72473	+	20.6966i	−0.238202	+	0.733110i	0.758478	+	0.651698i	$0.225943\pi$
$797$	−6.72473	+	20.6966i	−0.238202	+	0.733110i	−0.996681	+	0.0814124i	$0.974057\pi$
$798$		0			0
$799$	−4.83471	+	3.51263i	−0.171040	+	0.124268i
$800$		0			0
$801$	−1.61966	−	4.98480i	−0.0572278	−	0.176129i
$802$		0			0
$803$	−11.1370	−	3.51636i	−0.393015	−	0.124090i
$804$		0			0
$805$	8.04870	+	24.7713i	0.283679	+	0.873075i
$806$		0			0
$807$	−0.780757	+	0.567253i	−0.0274840	+	0.0199683i
$808$		0			0
$809$	−4.22367	+	12.9991i	−0.148496	+	0.457025i	−0.997444	−	0.0714523i	$-0.977237\pi$
$809$	−4.22367	+	12.9991i	−0.148496	+	0.457025i	0.848948	+	0.528477i	$0.177237\pi$
$810$		0			0
$811$	−28.7004	−	20.8520i	−1.00781	−	0.732214i	−0.0440580	−	0.999029i	$-0.514029\pi$
$811$	−28.7004	−	20.8520i	−1.00781	−	0.732214i	−0.963748	+	0.266815i	$0.914029\pi$
$812$		0			0
$813$	16.6963			0.585564
$814$		0			0
$815$	75.9553			2.66060
$816$		0			0
$817$	−0.832382	−	0.604761i	−0.0291214	−	0.0211579i
$818$		0			0
$819$	2.60359	−	8.01304i	0.0909769	−	0.279998i
$820$		0			0
$821$	−12.1076	+	8.79669i	−0.422558	+	0.307007i	−0.778666	−	0.627438i	$-0.784103\pi$
$821$	−12.1076	+	8.79669i	−0.422558	+	0.307007i	0.356108	+	0.934445i	$0.384103\pi$
$822$		0			0
$823$	−3.77471	−	11.6174i	−0.131578	−	0.404955i	0.863464	−	0.504410i	$-0.168290\pi$
$823$	−3.77471	−	11.6174i	−0.131578	−	0.404955i	−0.995042	+	0.0994549i	$0.968290\pi$
$824$		0			0
$825$	−19.8294	+	27.7764i	−0.690371	+	0.967048i
$826$		0			0
$827$	4.29641	+	13.2230i	0.149401	+	0.459809i	0.997551	−	0.0699477i	$-0.0222833\pi$
$827$	4.29641	+	13.2230i	0.149401	+	0.459809i	−0.848150	+	0.529757i	$0.822283\pi$
$828$		0			0
$829$	−9.98862	+	7.25716i	−0.346919	+	0.252051i	−0.747575	−	0.664177i	$-0.768782\pi$
$829$	−9.98862	+	7.25716i	−0.346919	+	0.252051i	0.400656	+	0.916228i	$0.368782\pi$
$830$		0			0
$831$	5.66435	−	17.4331i	0.196494	−	0.604747i
$832$		0			0
$833$	5.24528	+	3.81092i	0.181738	+	0.132041i
$834$		0			0
$835$	71.4895			2.47400
$836$		0			0
$837$	−22.6883			−0.784223
$838$		0			0
$839$	16.4757	+	11.9703i	0.568804	+	0.413260i	0.834671	−	0.550749i	$-0.185658\pi$
$839$	16.4757	+	11.9703i	0.568804	+	0.413260i	−0.265866	+	0.964010i	$0.585658\pi$
$840$		0			0
$841$	−6.62645	+	20.3941i	−0.228498	+	0.703245i
$842$		0			0
$843$	−15.6208	+	11.3492i	−0.538009	+	0.390887i
$844$		0			0
$845$	−14.7957	−	45.5365i	−0.508987	−	1.56650i
$846$		0			0
$847$	−13.3030	−	38.7351i	−0.457096	−	1.33095i
$848$		0			0
$849$	−1.85935	−	5.72251i	−0.0638129	−	0.196396i
$850$		0			0
$851$	2.97437	−	2.16101i	0.101960	−	0.0740783i
$852$		0			0
$853$	16.1419	−	49.6795i	0.552687	−	1.70100i	−0.149288	−	0.988794i	$-0.547698\pi$
$853$	16.1419	−	49.6795i	0.552687	−	1.70100i	0.701975	−	0.712201i	$-0.252302\pi$
$854$		0			0
$855$	16.7138	+	12.1433i	0.571601	+	0.415293i
$856$		0			0
$857$	−38.4691			−1.31408			−0.657041	−	0.753855i	$-0.728192\pi$
$857$	−38.4691			−1.31408			−0.657041	+	0.753855i	$0.728192\pi$
$858$		0			0
$859$	33.3955			1.13944			0.569720	−	0.821839i	$-0.307052\pi$
$859$	33.3955			1.13944			0.569720	+	0.821839i	$0.307052\pi$
$860$		0			0
$861$	−25.2760	−	18.3641i	−0.861402	−	0.625846i
$862$		0			0
$863$	4.67070	−	14.3750i	0.158993	−	0.489329i	−0.839551	−	0.543281i	$-0.817182\pi$
$863$	4.67070	−	14.3750i	0.158993	−	0.489329i	0.998544	+	0.0539520i	$0.0171818\pi$
$864$		0			0
$865$	−20.6922	+	15.0337i	−0.703555	+	0.511163i
$866$		0			0
$867$	4.57494	+	14.0802i	0.155373	+	0.478190i
$868$		0			0
$869$	17.0293	−	23.8541i	0.577680	−	0.809194i
$870$		0			0
$871$	−1.84352	−	5.67377i	−0.0624653	−	0.192248i
$872$		0			0
$873$	2.58387	−	1.87729i	0.0874509	−	0.0635368i
$874$		0			0
$875$	28.6859	−	88.2863i	0.969762	−	2.98462i
$876$		0			0
$877$	12.9419	+	9.40283i	0.437016	+	0.317511i	0.784448	−	0.620194i	$-0.212946\pi$
$877$	12.9419	+	9.40283i	0.437016	+	0.317511i	−0.347432	+	0.937705i	$0.612946\pi$
$878$		0			0
$879$	−14.7274			−0.496741
$880$		0			0
$881$	−43.0908			−1.45177			−0.725883	−	0.687818i	$-0.758569\pi$
$881$	−43.0908			−1.45177			−0.725883	+	0.687818i	$0.758569\pi$
$882$		0			0
$883$	36.3842	+	26.4347i	1.22443	+	0.889598i	0.996460	−	0.0840715i	$-0.0267924\pi$
$883$	36.3842	+	26.4347i	1.22443	+	0.889598i	0.227966	+	0.973669i	$0.426792\pi$
$884$		0			0
$885$	−9.24726	+	28.4601i	−0.310843	+	0.956677i
$886$		0			0
$887$	−36.6560	+	26.6322i	−1.23079	+	0.894221i	−0.996949	−	0.0780543i	$-0.975129\pi$
$887$	−36.6560	+	26.6322i	−1.23079	+	0.894221i	−0.233840	+	0.972275i	$0.575129\pi$
$888$		0			0
$889$	−9.15384	−	28.1726i	−0.307010	−	0.944880i
$890$		0			0
$891$	6.67486	+	2.10750i	0.223616	+	0.0706040i
$892$		0			0
$893$	−4.65596	−	14.3296i	−0.155806	−	0.479521i
$894$		0			0
$895$	4.58281	−	3.32960i	0.153186	−	0.111296i
$896$		0			0
$897$	0.518401	−	1.59547i	0.0173089	−	0.0532713i
$898$		0			0
$899$	10.6486	+	7.73668i	0.355152	+	0.258033i
$900$		0			0
$901$	0.298682			0.00995054
$902$		0			0
$903$	−1.47819			−0.0491910
$904$		0			0
$905$	56.4576	+	41.0188i	1.87671	+	1.36351i
$906$		0			0
$907$	−6.55486	+	20.1738i	−0.217651	+	0.669860i	0.781304	+	0.624150i	$0.214555\pi$
$907$	−6.55486	+	20.1738i	−0.217651	+	0.669860i	−0.998955	+	0.0457093i	$0.985445\pi$
$908$		0			0
$909$	7.58084	−	5.50780i	0.251441	−	0.182682i
$910$		0			0
$911$	5.91191	+	18.1950i	0.195870	+	0.602827i	0.999965	+	0.00832598i	$0.00265027\pi$
$911$	5.91191	+	18.1950i	0.195870	+	0.602827i	−0.804095	+	0.594501i	$0.797350\pi$
$912$		0			0
$913$	−46.1365	+	15.4166i	−1.52689	+	0.510214i
$914$		0			0
$915$	−15.5824	−	47.9576i	−0.515138	−	1.58543i
$916$		0			0
$917$	−36.9502	+	26.8459i	−1.22020	+	0.886530i
$918$		0			0
$919$	−12.7027	+	39.0949i	−0.419023	+	1.28962i	0.489580	+	0.871959i	$0.337150\pi$
$919$	−12.7027	+	39.0949i	−0.419023	+	1.28962i	−0.908603	+	0.417662i	$0.862850\pi$
$920$		0			0
$921$	8.03196	+	5.83556i	0.264662	+	0.192288i
$922$		0			0
$923$	−13.5118			−0.444748
$924$		0			0
$925$	−23.6783			−0.778539
$926$		0			0
$927$	−19.3354	−	14.0480i	−0.635056	−	0.461395i
$928$		0			0
$929$	−14.6696	+	45.1485i	−0.481295	+	1.48128i	0.355980	+	0.934494i	$0.384147\pi$
$929$	−14.6696	+	45.1485i	−0.481295	+	1.48128i	−0.837275	+	0.546781i	$0.815853\pi$
$930$		0			0
$931$	−13.2246	+	9.60824i	−0.433419	+	0.314897i
$932$		0			0
$933$	0.905858	+	2.78794i	0.0296565	+	0.0912732i
$934$		0			0
$935$	−0.105010	−	12.6095i	−0.00343420	−	0.412376i
$936$		0			0
$937$	−8.48605	−	26.1174i	−0.277227	−	0.853218i	−0.988621	−	0.150425i	$-0.951936\pi$
$937$	−8.48605	−	26.1174i	−0.277227	−	0.853218i	0.711394	−	0.702793i	$-0.248064\pi$
$938$		0			0
$939$	11.1950	−	8.13362i	0.365334	−	0.265430i
$940$		0			0
$941$	4.99497	−	15.3729i	0.162831	−	0.501144i	−0.836038	−	0.548671i	$-0.815134\pi$
$941$	4.99497	−	15.3729i	0.162831	−	0.501144i	0.998870	+	0.0475271i	$0.0151340\pi$
$942$		0			0
$943$	12.8391	+	9.32812i	0.418097	+	0.303765i
$944$		0			0
$945$	70.9971			2.30954
$946$		0			0
$947$	−28.3252			−0.920445			−0.460223	−	0.887804i	$-0.652230\pi$
$947$	−28.3252			−0.920445			−0.460223	+	0.887804i	$0.652230\pi$
$948$		0			0
$949$	−2.99119	−	2.17323i	−0.0970983	−	0.0705460i
$950$		0			0
$951$	3.76333	−	11.5823i	0.122034	−	0.375583i
$952$		0			0
$953$	43.1890	−	31.3787i	1.39903	−	1.01645i	0.404224	−	0.914660i	$-0.367542\pi$
$953$	43.1890	−	31.3787i	1.39903	−	1.01645i	0.994805	−	0.101794i	$-0.0324584\pi$
$954$		0			0
$955$	8.69199	+	26.7512i	0.281266	+	0.865648i
$956$		0			0
$957$	4.98177	+	6.73809i	0.161038	+	0.217812i
$958$		0			0
$959$	−2.89717	−	8.91656i	−0.0935544	−	0.287931i
$960$		0			0
$961$	6.53068	−	4.74481i	0.210667	−	0.153059i
$962$		0			0
$963$	−6.36223	+	19.5809i	−0.205020	+	0.630987i
$964$		0			0
$965$	−75.9870	−	55.2078i	−2.44611	−	1.77720i
$966$		0			0
$967$	45.0985			1.45027			0.725136	−	0.688606i	$-0.241777\pi$
$967$	45.0985			1.45027			0.725136	+	0.688606i	$0.241777\pi$
$968$		0			0
$969$	2.06840			0.0664466
$970$		0			0
$971$	38.4582	+	27.9415i	1.23418	+	0.896686i	0.997197	−	0.0748274i	$-0.0238406\pi$
$971$	38.4582	+	27.9415i	1.23418	+	0.896686i	0.236986	+	0.971513i	$0.423841\pi$
$972$		0			0
$973$	16.2175	−	49.9122i	0.519908	−	1.60011i
$974$		0			0
$975$	−8.74088	+	6.35062i	−0.279932	+	0.203383i
$976$		0			0
$977$	−1.64262	−	5.05545i	−0.0525519	−	0.161738i	0.921336	−	0.388767i	$-0.127099\pi$
$977$	−1.64262	−	5.05545i	−0.0525519	−	0.161738i	−0.973888	+	0.227029i	$0.927099\pi$
$978$		0			0
$979$	−4.79517	−	6.48570i	−0.153254	−	0.207284i
$980$		0			0
$981$	2.76298	+	8.50357i	0.0882151	+	0.271498i
$982$		0			0
$983$	2.87735	−	2.09052i	0.0917731	−	0.0666771i	−0.540952	−	0.841053i	$-0.681936\pi$
$983$	2.87735	−	2.09052i	0.0917731	−	0.0666771i	0.632726	+	0.774376i	$0.281936\pi$
$984$		0			0
$985$	13.4485	−	41.3901i	0.428504	−	1.31880i
$986$		0			0
$987$	−17.5125	−	12.7236i	−0.557430	−	0.404996i
$988$		0			0
$989$	0.750852			0.0238757
$990$		0			0
$991$	38.1592			1.21217			0.606083	−	0.795401i	$-0.292740\pi$
$991$	38.1592			1.21217			0.606083	+	0.795401i	$0.292740\pi$
$992$		0			0
$993$	−24.9505	−	18.1276i	−0.791780	−	0.575262i
$994$		0			0
$995$	−11.2848	+	34.7309i	−0.357751	+	1.10104i
$996$		0			0
$997$	23.5980	−	17.1450i	0.747357	−	0.542987i	−0.147649	−	0.989040i	$-0.547171\pi$
$997$	23.5980	−	17.1450i	0.747357	−	0.542987i	0.895007	+	0.446053i	$0.147171\pi$
$998$		0			0
$999$	−3.09683	−	9.53106i	−0.0979793	−	0.301549i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	704.2.m.i.577.2		8
4.3	odd	2		704.2.m.l.577.1		8
8.3	odd	2		88.2.i.b.49.2	yes	8
8.5	even	2		176.2.m.d.49.1		8
11.3	even	5		7744.2.a.dr.1.2		4
11.8	odd	10		7744.2.a.ds.1.2		4
11.9	even	5	inner	704.2.m.i.449.2		8
24.11	even	2		792.2.r.g.577.2		8
44.3	odd	10		7744.2.a.di.1.3		4
44.19	even	10		7744.2.a.dh.1.3		4
44.31	odd	10		704.2.m.l.449.1		8
88.3	odd	10		968.2.a.n.1.2		4
88.19	even	10		968.2.a.m.1.2		4
88.27	odd	10		968.2.i.s.81.1		8
88.35	even	10		968.2.i.p.9.2		8
88.43	even	2		968.2.i.p.753.2		8
88.51	even	10		968.2.i.t.729.1		8
88.53	even	10		176.2.m.d.97.1		8
88.59	odd	10		968.2.i.s.729.1		8
88.69	even	10		1936.2.a.bb.1.3		4
88.75	odd	10		88.2.i.b.9.2	✓	8
88.83	even	10		968.2.i.t.81.1		8
88.85	odd	10		1936.2.a.bc.1.3		4
264.107	odd	10		8712.2.a.cd.1.4		4
264.179	even	10		8712.2.a.ce.1.4		4
264.251	even	10		792.2.r.g.361.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
88.2.i.b.9.2	✓	8	88.75	odd	10
88.2.i.b.49.2	yes	8	8.3	odd	2
176.2.m.d.49.1		8	8.5	even	2
176.2.m.d.97.1		8	88.53	even	10
704.2.m.i.449.2		8	11.9	even	5	inner
704.2.m.i.577.2		8	1.1	even	1	trivial
704.2.m.l.449.1		8	44.31	odd	10
704.2.m.l.577.1		8	4.3	odd	2
792.2.r.g.361.2		8	264.251	even	10
792.2.r.g.577.2		8	24.11	even	2
968.2.a.m.1.2		4	88.19	even	10
968.2.a.n.1.2		4	88.3	odd	10
968.2.i.p.9.2		8	88.35	even	10
968.2.i.p.753.2		8	88.43	even	2
968.2.i.s.81.1		8	88.27	odd	10
968.2.i.s.729.1		8	88.59	odd	10
968.2.i.t.81.1		8	88.83	even	10
968.2.i.t.729.1		8	88.51	even	10
1936.2.a.bb.1.3		4	88.69	even	10
1936.2.a.bc.1.3		4	88.85	odd	10
7744.2.a.dh.1.3		4	44.19	even	10
7744.2.a.di.1.3		4	44.3	odd	10
7744.2.a.dr.1.2		4	11.3	even	5
7744.2.a.ds.1.2		4	11.8	odd	10
8712.2.a.cd.1.4		4	264.107	odd	10
8712.2.a.ce.1.4		4	264.179	even	10

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:	\( N \)	\(=\)	\( 704 = 2^{6} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	704.m (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.743592 + 0.540251i) q^{3} +(1.24359 - 3.82738i) q^{5} +(-3.01217 + 2.18847i) q^{7} +(-0.665993 - 2.04972i) q^{9} +(-1.97174 - 2.66688i) q^{11} +(-0.324462 - 0.998590i) q^{13} +(2.99248 - 2.17416i) q^{15} +(-0.291947 + 0.898521i) q^{17} +(-1.92705 - 1.40008i) q^{19} -3.42216 q^{21} +1.73830 q^{23} +(-9.05726 - 6.58048i) q^{25} +(1.46422 - 4.50639i) q^{27} +(-2.22389 + 1.61575i) q^{29} +(-1.47966 - 4.55393i) q^{31} +(-0.0253858 - 3.04831i) q^{33} +(4.63021 + 14.2503i) q^{35} +(1.71108 - 1.24317i) q^{37} +(0.298223 - 0.917835i) q^{39} +(7.38598 + 5.36623i) q^{41} +0.431946 q^{43} -8.67327 q^{45} +(5.11739 + 3.71800i) q^{47} +(2.12066 - 6.52673i) q^{49} +(-0.702517 + 0.510409i) q^{51} +(-0.0976943 - 0.300672i) q^{53} +(-12.6592 + 4.23010i) q^{55} +(-0.676543 - 2.08218i) q^{57} +(-6.54508 + 4.75528i) q^{59} +(4.21270 - 12.9654i) q^{61} +(6.49184 + 4.71659i) q^{63} -4.22549 q^{65} +5.68178 q^{67} +(1.29259 + 0.939120i) q^{69} +(3.97664 - 12.2388i) q^{71} +(2.84881 - 2.06978i) q^{73} +(-3.17979 - 9.78640i) q^{75} +(11.7756 + 3.71800i) q^{77} +(2.73078 + 8.40447i) q^{79} +(-1.70741 + 1.24051i) q^{81} +(4.53227 - 13.9489i) q^{83} +(3.07592 + 2.23479i) q^{85} -2.52658 q^{87} +2.43195 q^{89} +(3.16272 + 2.29785i) q^{91} +(1.36000 - 4.18565i) q^{93} +(-7.75513 + 5.63443i) q^{95} +(0.457940 + 1.40940i) q^{97} +(-4.15318 + 5.81763i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - q^{3} + 3 q^{5} - 7 q^{7} - 13 q^{9} + 7 q^{11} - 7 q^{13} + 13 q^{15} + q^{17} - 2 q^{19} + 2 q^{21} + 4 q^{23} - 33 q^{25} - 22 q^{27} - 17 q^{29} + 13 q^{31} + 16 q^{33} + 11 q^{35} - q^{37}+ \cdots - 27 q^{99}+O(q^{100}) \) 8 * q - q^3 + 3 * q^5 - 7 * q^7 - 13 * q^9 + 7 * q^11 - 7 * q^13 + 13 * q^15 + q^17 - 2 * q^19 + 2 * q^21 + 4 * q^23 - 33 * q^25 - 22 * q^27 - 17 * q^29 + 13 * q^31 + 16 * q^33 + 11 * q^35 - q^37 - 39 * q^39 + 9 * q^41 + 6 * q^43 - 44 * q^45 + q^47 + 3 * q^49 + 38 * q^51 + 33 * q^53 - 13 * q^55 - 6 * q^57 - 30 * q^59 + 9 * q^61 + 10 * q^63 - 10 * q^65 - 10 * q^67 + 38 * q^69 + 25 * q^71 - 7 * q^73 - 6 * q^75 + 7 * q^77 + q^79 + 14 * q^81 - 39 * q^85 + 6 * q^87 + 22 * q^89 + 7 * q^91 + 5 * q^93 - 7 * q^95 + 8 * q^97 - 27 * q^99

Introduction

L-functions

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