LMFDB - Embedded newform 845.2.m.g.316.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [845,2,Mod(316,845)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(845, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("845.316");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.m (of order $6$, degree $2$, 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:	$6.74735897080$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.22581504.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 5x^{6} + 2x^{5} - 11x^{4} + 4x^{3} + 20x^{2} - 32x + 16 $ x^8 - 4x^7 + 5x^6 + 2x^5 - 11x^4 + 4x^3 + 20x^2 - 32*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			316.3
Root			$-1.27597 + 0.609843i$ of defining polynomial
Character	$\chi$	$=$	845.316
Dual form			845.2.m.g.361.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.190254 + 0.109843i) q^{2} +(0.800098 - 1.38581i) q^{3} +(-0.975869 - 1.69025i) q^{4} -1.00000i q^{5} +(0.304444 - 0.175771i) q^{6} +(0.287734 - 0.166123i) q^{7} -0.868145i q^{8} +(0.219687 + 0.380509i) q^{9} +O(q^{10})$	\(q+(0.190254 + 0.109843i) q^{2} +(0.800098 - 1.38581i) q^{3} +(-0.975869 - 1.69025i) q^{4} -1.00000i q^{5} +(0.304444 - 0.175771i) q^{6} +(0.287734 - 0.166123i) q^{7} -0.868145i q^{8} +(0.219687 + 0.380509i) q^{9} +(0.109843 - 0.190254i) q^{10} +(-4.65213 - 2.68591i) q^{11} -3.12316 q^{12} +0.0729902 q^{14} +(-1.38581 - 0.800098i) q^{15} +(-1.85638 + 3.21534i) q^{16} +(-2.53215 - 4.38581i) q^{17} +0.0965246i q^{18} +(1.96410 - 1.13397i) q^{19} +(-1.69025 + 0.975869i) q^{20} -0.531659i q^{21} +(-0.590059 - 1.02201i) q^{22} +(-1.41959 + 2.45880i) q^{23} +(-1.20308 - 0.694601i) q^{24} -1.00000 q^{25} +5.50367 q^{27} +(-0.561581 - 0.324229i) q^{28} +(1.45174 - 2.51448i) q^{29} +(-0.175771 - 0.304444i) q^{30} +5.46410i q^{31} +(-2.21004 + 1.27597i) q^{32} +(-7.44432 + 4.29798i) q^{33} -1.11256i q^{34} +(-0.166123 - 0.287734i) q^{35} +(0.428771 - 0.742653i) q^{36} +(5.17191 + 2.98601i) q^{37} +0.498239 q^{38} -0.868145 q^{40} +(-3.23205 - 1.86603i) q^{41} +(0.0583993 - 0.101151i) q^{42} +(-2.53215 - 4.38581i) q^{43} +10.4844i q^{44} +(0.380509 - 0.219687i) q^{45} +(-0.540166 + 0.311865i) q^{46} -8.34285i q^{47} +(2.97057 + 5.14517i) q^{48} +(-3.44481 + 5.96658i) q^{49} +(-0.190254 - 0.109843i) q^{50} -8.10387 q^{51} -1.56063 q^{53} +(1.04710 + 0.604542i) q^{54} +(-2.68591 + 4.65213i) q^{55} +(-0.144219 - 0.249795i) q^{56} -3.62916i q^{57} +(0.552399 - 0.318928i) q^{58} +(-2.34461 + 1.35366i) q^{59} +3.12316i q^{60} +(-7.05193 - 12.2143i) q^{61} +(-0.600196 + 1.03957i) q^{62} +(0.126423 + 0.0729902i) q^{63} +6.86488 q^{64} -1.88842 q^{66} +(-8.94799 - 5.16612i) q^{67} +(-4.94209 + 8.55995i) q^{68} +(2.27162 + 3.93456i) q^{69} -0.0729902i q^{70} +(11.0828 - 6.39866i) q^{71} +(0.330337 - 0.190720i) q^{72} +9.68922i q^{73} +(0.655986 + 1.13620i) q^{74} +(-0.800098 + 1.38581i) q^{75} +(-3.83341 - 2.21322i) q^{76} -1.78477 q^{77} +4.51851 q^{79} +(3.21534 + 1.85638i) q^{80} +(3.74441 - 6.48552i) q^{81} +(-0.409941 - 0.710039i) q^{82} -4.26371i q^{83} +(-0.898640 + 0.518830i) q^{84} +(-4.38581 + 2.53215i) q^{85} -1.11256i q^{86} +(-2.32306 - 4.02367i) q^{87} +(-2.33176 + 4.03872i) q^{88} +(2.79366 + 1.61292i) q^{89} +0.0965246 q^{90} +5.54133 q^{92} +(7.57221 + 4.37182i) q^{93} +(0.916407 - 1.58726i) q^{94} +(-1.13397 - 1.96410i) q^{95} +4.08359i q^{96} +(-2.17191 + 1.25396i) q^{97} +(-1.31078 + 0.756779i) q^{98} -2.36023i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{3} + 2 q^{4} + 18 q^{6} + 6 q^{7} - 4 q^{9}+O(q^{10}) $ 8 * q + 2 * q^3 + 2 * q^4 + 18 * q^6 + 6 * q^7 - 4 * q^9	$ 8 q + 2 q^{3} + 2 q^{4} + 18 q^{6} + 6 q^{7} - 4 q^{9} - 2 q^{10} + 20 q^{12} + 4 q^{14} + 6 q^{15} - 2 q^{16} - 2 q^{17} - 12 q^{19} - 12 q^{20} - 12 q^{22} - 10 q^{23} + 12 q^{24} - 8 q^{25} - 4 q^{27} + 18 q^{28} - 8 q^{29} + 4 q^{30} - 6 q^{32} - 42 q^{33} + 10 q^{35} + 20 q^{36} - 6 q^{37} - 16 q^{38} - 12 q^{40} - 12 q^{41} + 4 q^{42} - 2 q^{43} + 42 q^{46} + 28 q^{48} + 12 q^{49} - 8 q^{51} - 24 q^{53} - 18 q^{54} + 12 q^{56} - 36 q^{58} + 12 q^{59} - 28 q^{61} + 4 q^{62} + 24 q^{63} - 8 q^{64} + 12 q^{66} - 6 q^{67} - 14 q^{68} - 16 q^{69} + 48 q^{72} + 10 q^{74} - 2 q^{75} - 54 q^{76} - 36 q^{77} - 16 q^{79} + 8 q^{81} + 4 q^{82} + 30 q^{84} - 18 q^{85} + 22 q^{87} - 18 q^{88} - 24 q^{89} + 40 q^{90} + 44 q^{92} + 32 q^{94} - 16 q^{95} + 30 q^{97} - 72 q^{98}+O(q^{100}) $ 8 * q + 2 * q^3 + 2 * q^4 + 18 * q^6 + 6 * q^7 - 4 * q^9 - 2 * q^10 + 20 * q^12 + 4 * q^14 + 6 * q^15 - 2 * q^16 - 2 * q^17 - 12 * q^19 - 12 * q^20 - 12 * q^22 - 10 * q^23 + 12 * q^24 - 8 * q^25 - 4 * q^27 + 18 * q^28 - 8 * q^29 + 4 * q^30 - 6 * q^32 - 42 * q^33 + 10 * q^35 + 20 * q^36 - 6 * q^37 - 16 * q^38 - 12 * q^40 - 12 * q^41 + 4 * q^42 - 2 * q^43 + 42 * q^46 + 28 * q^48 + 12 * q^49 - 8 * q^51 - 24 * q^53 - 18 * q^54 + 12 * q^56 - 36 * q^58 + 12 * q^59 - 28 * q^61 + 4 * q^62 + 24 * q^63 - 8 * q^64 + 12 * q^66 - 6 * q^67 - 14 * q^68 - 16 * q^69 + 48 * q^72 + 10 * q^74 - 2 * q^75 - 54 * q^76 - 36 * q^77 - 16 * q^79 + 8 * q^81 + 4 * q^82 + 30 * q^84 - 18 * q^85 + 22 * q^87 - 18 * q^88 - 24 * q^89 + 40 * q^90 + 44 * q^92 + 32 * q^94 - 16 * q^95 + 30 * q^97 - 72 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/845\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$

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 $

$2$	0.190254	+	0.109843i	0.134530	+	0.0776710i	0.565755	−	0.824574i	$-0.308585\pi$
$2$	0.190254	+	0.109843i	0.134530	+	0.0776710i	−0.431224	+	0.902245i	$0.641918\pi$
$3$	0.800098	−	1.38581i	0.461937	−	0.800098i	−0.537121	−	0.843505i	$-0.680488\pi$
$3$	0.800098	−	1.38581i	0.461937	−	0.800098i	0.999057	+	0.0434075i	$0.0138214\pi$
$4$	−0.975869	−	1.69025i	−0.487934	−	0.845127i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	0.304444	−	0.175771i	0.124289	−	0.0717582i
$7$	0.287734	−	0.166123i	0.108753	−	0.0627887i	−0.444637	−	0.895711i	$-0.646667\pi$
$7$	0.287734	−	0.166123i	0.108753	−	0.0627887i	0.553390	+	0.832922i	$0.313334\pi$
$8$		−	0.868145i		−	0.306936i
$9$	0.219687	+	0.380509i	0.0732290	+	0.126836i
$10$	0.109843	−	0.190254i	0.0347355	−	0.0601637i
$11$	−4.65213	−	2.68591i	−1.40267	−	0.809832i	−0.408004	−	0.912980i	$-0.633775\pi$
$11$	−4.65213	−	2.68591i	−1.40267	−	0.809832i	−0.994666	+	0.103149i	$0.967108\pi$
$12$	−3.12316			−0.901579
$13$		0			0
$13$		0			0
$14$	0.0729902			0.0195074
$15$	−1.38581	−	0.800098i	−0.357815	−	0.206584i
$16$	−1.85638	+	3.21534i	−0.464094	+	0.803835i
$17$	−2.53215	−	4.38581i	−0.614136	−	1.06372i	−0.990535	−	0.137258i	$-0.956171\pi$
$17$	−2.53215	−	4.38581i	−0.614136	−	1.06372i	0.376399	−	0.926458i	$-0.377162\pi$
$18$			0.0965246i			0.0227511i
$19$	1.96410	−	1.13397i	0.450596	−	0.260152i	−0.257486	−	0.966282i	$-0.582894\pi$
$19$	1.96410	−	1.13397i	0.450596	−	0.260152i	0.708082	+	0.706130i	$0.249561\pi$
$20$	−1.69025	+	0.975869i	−0.377952	+	0.218211i
$21$		−	0.531659i		−	0.116018i
$22$	−0.590059	−	1.02201i	−0.125801	−	0.217894i
$23$	−1.41959	+	2.45880i	−0.296005	+	0.512695i	−0.975218	−	0.221246i	$-0.928988\pi$
$23$	−1.41959	+	2.45880i	−0.296005	+	0.512695i	0.679213	+	0.733941i	$0.262321\pi$
$24$	−1.20308	−	0.694601i	−0.245578	−	0.141785i
$25$	−1.00000			−0.200000
$26$		0			0
$27$	5.50367			1.05918
$28$	−0.561581	−	0.324229i	−0.106129	−	0.0612735i
$29$	1.45174	−	2.51448i	0.269581	−	0.466928i	−0.699173	−	0.714953i	$-0.746448\pi$
$29$	1.45174	−	2.51448i	0.269581	−	0.466928i	0.968754	+	0.248025i	$0.0797815\pi$
$30$	−0.175771	−	0.304444i	−0.0320912	−	0.0555837i
$31$			5.46410i			0.981382i	0.871334	+	0.490691i	$0.163256\pi$
$31$			5.46410i			0.981382i	−0.871334	+	0.490691i	$0.836744\pi$
$32$	−2.21004	+	1.27597i	−0.390683	+	0.225561i
$33$	−7.44432	+	4.29798i	−1.29589	+	0.748182i
$34$		−	1.11256i		−	0.190802i
$35$	−0.166123	−	0.287734i	−0.0280800	−	0.0486359i
$36$	0.428771	−	0.742653i	0.0714619	−	0.123776i
$37$	5.17191	+	2.98601i	0.850257	+	0.490896i	0.860738	−	0.509049i	$-0.170003\pi$
$37$	5.17191	+	2.98601i	0.850257	+	0.490896i	−0.0104803	+	0.999945i	$0.503336\pi$
$38$	0.498239			0.0808250
$39$		0			0
$40$	−0.868145			−0.137266
$41$	−3.23205	−	1.86603i	−0.504762	−	0.291424i	0.225916	−	0.974147i	$-0.427462\pi$
$41$	−3.23205	−	1.86603i	−0.504762	−	0.291424i	−0.730678	+	0.682723i	$0.760796\pi$
$42$	0.0583993	−	0.101151i	0.00901121	−	0.0156079i
$43$	−2.53215	−	4.38581i	−0.386149	−	0.668830i	0.605779	−	0.795633i	$-0.292862\pi$
$43$	−2.53215	−	4.38581i	−0.386149	−	0.668830i	−0.991928	+	0.126803i	$0.959528\pi$
$44$			10.4844i			1.58058i
$45$	0.380509	−	0.219687i	0.0567229	−	0.0327490i
$46$	−0.540166	+	0.311865i	−0.0796432	+	0.0459820i
$47$		−	8.34285i		−	1.21693i	−0.793581	−	0.608465i	$-0.791786\pi$
$47$		−	8.34285i		−	1.21693i	0.793581	−	0.608465i	$-0.208214\pi$
$48$	2.97057	+	5.14517i	0.428764	+	0.742642i
$49$	−3.44481	+	5.96658i	−0.492115	+	0.852368i
$50$	−0.190254	−	0.109843i	−0.0269060	−	0.0155342i
$51$	−8.10387			−1.13477
$52$		0			0
$53$	−1.56063			−0.214369			−0.107184	−	0.994239i	$-0.534183\pi$
$53$	−1.56063			−0.214369			−0.107184	+	0.994239i	$0.534183\pi$
$54$	1.04710	+	0.604542i	0.142492	+	0.0822678i
$55$	−2.68591	+	4.65213i	−0.362168	+	0.627293i
$56$	−0.144219	−	0.249795i	−0.0192721	−	0.0333802i
$57$		−	3.62916i		−	0.480694i
$58$	0.552399	−	0.318928i	0.0725335	−	0.0418773i
$59$	−2.34461	+	1.35366i	−0.305242	+	0.176232i	−0.644795	−	0.764355i	$-0.723057\pi$
$59$	−2.34461	+	1.35366i	−0.305242	+	0.176232i	0.339553	+	0.940587i	$0.389724\pi$
$60$			3.12316i			0.403199i
$61$	−7.05193	−	12.2143i	−0.902908	−	1.56388i	−0.823702	−	0.567023i	$-0.808095\pi$
$61$	−7.05193	−	12.2143i	−0.902908	−	1.56388i	−0.0792059	−	0.996858i	$-0.525238\pi$
$62$	−0.600196	+	1.03957i	−0.0762249	+	0.132025i
$63$	0.126423	+	0.0729902i	0.0159278	+	0.00919590i
$64$	6.86488			0.858111
$65$		0			0
$66$	−1.88842			−0.232448
$67$	−8.94799	−	5.16612i	−1.09317	−	0.631142i	−0.158752	−	0.987319i	$-0.550747\pi$
$67$	−8.94799	−	5.16612i	−1.09317	−	0.631142i	−0.934419	+	0.356176i	$0.884080\pi$
$68$	−4.94209	+	8.55995i	−0.599316	+	1.03805i
$69$	2.27162	+	3.93456i	0.273471	+	0.473666i
$70$		−	0.0729902i		−	0.00872400i
$71$	11.0828	−	6.39866i	1.31529	−	0.759382i	0.332321	−	0.943166i	$-0.392168\pi$
$71$	11.0828	−	6.39866i	1.31529	−	0.759382i	0.982967	+	0.183785i	$0.0588349\pi$
$72$	0.330337	−	0.190720i	0.0389306	−	0.0224766i
$73$			9.68922i			1.13404i	0.823705	+	0.567019i	$0.191903\pi$
$73$			9.68922i			1.13404i	−0.823705	+	0.567019i	$0.808097\pi$
$74$	0.655986	+	1.13620i	0.0762569	+	0.132081i
$75$	−0.800098	+	1.38581i	−0.0923873	+	0.160020i
$76$	−3.83341	−	2.21322i	−0.439722	−	0.253874i
$77$	−1.78477			−0.203393
$78$		0			0
$79$	4.51851			0.508372			0.254186	−	0.967155i	$-0.418192\pi$
$79$	4.51851			0.508372			0.254186	+	0.967155i	$0.418192\pi$
$80$	3.21534	+	1.85638i	0.359486	+	0.207549i
$81$	3.74441	−	6.48552i	0.416046	−	0.720613i
$82$	−0.409941	−	0.710039i	−0.0452704	−	0.0784107i
$83$		−	4.26371i		−	0.468003i	−0.972236	−	0.234001i	$-0.924818\pi$
$83$		−	4.26371i		−	0.468003i	0.972236	−	0.234001i	$-0.0751821\pi$
$84$	−0.898640	+	0.518830i	−0.0980496	+	0.0566090i
$85$	−4.38581	+	2.53215i	−0.475708	+	0.274650i
$86$		−	1.11256i		−	0.119970i
$87$	−2.32306	−	4.02367i	−0.249059	−	0.431382i
$88$	−2.33176	+	4.03872i	−0.248566	+	0.430529i
$89$	2.79366	+	1.61292i	0.296127	+	0.170969i	0.640702	−	0.767790i	$-0.278644\pi$
$89$	2.79366	+	1.61292i	0.296127	+	0.170969i	−0.344575	+	0.938759i	$0.611977\pi$
$90$	0.0965246			0.0101746
$91$		0			0
$92$	5.54133			0.577724
$93$	7.57221	+	4.37182i	0.785201	+	0.453336i
$94$	0.916407	−	1.58726i	0.0945202	−	0.163714i
$95$	−1.13397	−	1.96410i	−0.116343	−	0.201513i
$96$			4.08359i			0.416780i
$97$	−2.17191	+	1.25396i	−0.220524	+	0.127320i	−0.606193	−	0.795318i	$-0.707304\pi$
$97$	−2.17191	+	1.25396i	−0.220524	+	0.127320i	0.385669	+	0.922637i	$0.373971\pi$
$98$	−1.31078	+	0.756779i	−0.132409	+	0.0764462i
$99$		−	2.36023i		−	0.237213i
$100$	0.975869	+	1.69025i	0.0975869	+	0.169025i
$101$	6.22336	−	10.7792i	0.619247	−	1.07257i	−0.370376	−	0.928882i	$-0.620771\pi$
$101$	6.22336	−	10.7792i	0.619247	−	1.07257i	0.989623	−	0.143686i	$-0.0458955\pi$
$102$	−1.54180	−	0.890157i	−0.152661	−	0.0881386i
$103$	15.0247			1.48043			0.740215	−	0.672370i	$-0.234724\pi$
$103$	15.0247			1.48043			0.740215	+	0.672370i	$0.234724\pi$
$104$		0			0
$105$	−0.531659			−0.0518846
$106$	−0.296916	−	0.171425i	−0.0288390	−	0.0166502i
$107$	6.53215	−	11.3140i	0.631487	−	1.09377i	−0.355761	−	0.934577i	$-0.615778\pi$
$107$	6.53215	−	11.3140i	0.631487	−	1.09377i	0.987248	−	0.159190i	$-0.0508883\pi$
$108$	−5.37086	−	9.30260i	−0.516811	−	0.895144i
$109$		−	11.2325i		−	1.07587i	−0.842985	−	0.537937i	$-0.819204\pi$
$109$		−	11.2325i		−	1.07587i	0.842985	−	0.537937i	$-0.180796\pi$
$110$	−1.02201	+	0.590059i	−0.0974450	+	0.0562599i
$111$	8.27607	−	4.77819i	0.785530	−	0.453526i
$112$			1.23355i			0.116560i
$113$	9.17191	+	15.8862i	0.862821	+	1.49445i	0.869195	+	0.494470i	$0.164638\pi$
$113$	9.17191	+	15.8862i	0.862821	+	1.49445i	−0.00637349	+	0.999980i	$0.502029\pi$
$114$	0.398640	−	0.690464i	0.0373360	−	0.0646679i
$115$	2.45880	+	1.41959i	0.229284	+	0.132377i
$116$	−5.66682			−0.526151
$117$		0			0
$118$	−0.594763			−0.0547524
$119$	−1.45717	−	0.841298i	−0.133579	−	0.0771216i
$120$	−0.694601	+	1.20308i	−0.0634081	+	0.109826i
$121$	8.92820	+	15.4641i	0.811655	+	1.40583i
$122$		−	3.09843i		−	0.280519i
$123$	−5.17191	+	2.98601i	−0.466336	+	0.269239i
$124$	9.23572	−	5.33225i	0.829392	−	0.478850i
$125$			1.00000i			0.0894427i
$126$	0.0160350	+	0.0277734i	0.00142851	+	0.00247425i
$127$	1.61998	−	2.80589i	0.143750	−	0.248982i	−0.785156	−	0.619298i	$-0.787417\pi$
$127$	1.61998	−	2.80589i	0.143750	−	0.248982i	0.928906	+	0.370316i	$0.120751\pi$
$128$	5.72615	+	3.30600i	0.506125	+	0.292212i
$129$	−8.10387			−0.713506
$130$		0			0
$131$	0.175664			0.0153478			0.00767390	−	0.999971i	$-0.497557\pi$
$131$	0.175664			0.0153478			0.00767390	+	0.999971i	$0.497557\pi$
$132$	14.5294	+	8.38853i	1.26462	+	0.730127i
$133$	0.376759	−	0.652566i	0.0326692	−	0.0565846i
$134$	−1.13493	−	1.96576i	−0.0980430	−	0.169815i
$135$		−	5.50367i		−	0.473681i
$136$	−3.80752	+	2.19827i	−0.326492	+	0.188500i
$137$	15.5736	−	8.99144i	1.33054	−	0.768190i	0.345162	−	0.938543i	$-0.387824\pi$
$137$	15.5736	−	8.99144i	1.33054	−	0.768190i	0.985383	+	0.170353i	$0.0544907\pi$
$138$			0.998090i			0.0849631i
$139$	−5.99307	−	10.3803i	−0.508325	−	0.880445i	−0.999954	−	0.00964021i	$-0.996931\pi$
$139$	−5.99307	−	10.3803i	−0.508325	−	0.880445i	0.491628	−	0.870805i	$-0.336402\pi$
$140$	−0.324229	+	0.561581i	−0.0274024	+	0.0474623i
$141$	−11.5616	−	6.67510i	−0.973663	−	0.562144i
$142$	2.81140			0.235928
$143$		0			0
$144$	−1.63129			−0.135941
$145$	−2.51448	−	1.45174i	−0.208816	−	0.120560i
$146$	−1.06430	+	1.84342i	−0.0880819	+	0.152562i
$147$	5.51236	+	9.54769i	0.454652	+	0.787481i
$148$		−	11.6558i		−	0.958101i
$149$	−2.95350	+	1.70520i	−0.241960	+	0.139696i	−0.616077	−	0.787686i	$-0.711279\pi$
$149$	−2.95350	+	1.70520i	−0.241960	+	0.139696i	0.374117	+	0.927381i	$0.377946\pi$
$150$	−0.304444	+	0.175771i	−0.0248578	+	0.0143516i
$151$		−	7.96141i		−	0.647890i	−0.946076	−	0.323945i	$-0.894991\pi$
$151$		−	7.96141i		−	0.647890i	0.946076	−	0.323945i	$-0.105009\pi$
$152$	−0.984454	−	1.70512i	−0.0798498	−	0.138304i
$153$	1.11256	−	1.92701i	0.0899451	−	0.155790i
$154$	−0.339560	−	0.196045i	−0.0273625	−	0.0157978i
$155$	5.46410			0.438887
$156$		0			0
$157$	−16.4329			−1.31148			−0.655742	−	0.754985i	$-0.727644\pi$
$157$	−16.4329			−1.31148			−0.655742	+	0.754985i	$0.727644\pi$
$158$	0.859667	+	0.496329i	0.0683914	+	0.0394858i
$159$	−1.24865	+	2.16273i	−0.0990247	+	0.171516i
$160$	1.27597	+	2.21004i	0.100874	+	0.174719i
$161$			0.943307i			0.0743430i
$162$	1.42478	−	0.822599i	0.111942	−	0.0646295i
$163$	−15.4215	+	8.90361i	−1.20791	+	0.697384i	−0.962301	−	0.271986i	$-0.912320\pi$
$163$	−15.4215	+	8.90361i	−1.20791	+	0.697384i	−0.245604	+	0.969370i	$0.578986\pi$
$164$			7.28398i			0.568784i
$165$	4.29798	+	7.44432i	0.334597	+	0.579539i
$166$	0.468341	−	0.811190i	0.0363503	−	0.0629605i
$167$	−5.45047	−	3.14683i	−0.421770	−	0.243509i	0.274064	−	0.961711i	$-0.411632\pi$
$167$	−5.45047	−	3.14683i	−0.421770	−	0.243509i	−0.695834	+	0.718202i	$0.744965\pi$
$168$	−0.461557			−0.0356099
$169$		0			0
$170$	−1.11256			−0.0853294
$171$	0.862975	+	0.498239i	0.0659933	+	0.0381013i
$172$	−4.94209	+	8.55995i	−0.376831	+	0.652690i
$173$	7.98756	+	13.8349i	0.607283	+	1.05184i	0.991686	+	0.128679i	$0.0410738\pi$
$173$	7.98756	+	13.8349i	0.607283	+	1.05184i	−0.384404	+	0.923165i	$0.625593\pi$
$174$		−	1.02069i		−	0.0773786i
$175$	−0.287734	+	0.166123i	−0.0217506	+	0.0125577i
$176$	17.2722	−	9.97212i	1.30194	−	0.751677i
$177$			4.33225i			0.325632i
$178$	0.354337	+	0.613729i	0.0265587	+	0.0460010i
$179$	11.8087	−	20.4533i	0.882625	−	1.52875i	0.0342123	−	0.999415i	$-0.489108\pi$
$179$	11.8087	−	20.4533i	0.882625	−	1.52875i	0.848412	−	0.529336i	$-0.177559\pi$
$180$	−0.742653	−	0.428771i	−0.0553541	−	0.0319587i
$181$	2.62590			0.195182			0.0975909	−	0.995227i	$-0.468886\pi$
$181$	2.62590			0.195182			0.0975909	+	0.995227i	$0.468886\pi$
$182$		0			0
$183$	−22.5689			−1.66834
$184$	2.13459	+	1.23241i	0.157364	+	0.0908544i
$185$	2.98601	−	5.17191i	0.219536	−	0.380247i
$186$	0.960431	+	1.66351i	0.0704222	+	0.121975i
$187$			27.2045i			1.98939i
$188$	−14.1015	+	8.14153i	−1.02846	+	0.593782i
$189$	1.58359	−	0.914288i	0.115189	−	0.0665046i
$190$		−	0.498239i		−	0.0361460i
$191$	1.00791	+	1.74575i	0.0729298	+	0.126318i	0.900184	−	0.435509i	$-0.143432\pi$
$191$	1.00791	+	1.74575i	0.0729298	+	0.126318i	−0.827254	+	0.561828i	$0.810098\pi$
$192$	5.49258	−	9.51343i	0.396393	−	0.686572i
$193$	19.7636	+	11.4105i	1.42262	+	0.821348i	0.996522	−	0.0833298i	$-0.0265555\pi$
$193$	19.7636	+	11.4105i	1.42262	+	0.821348i	0.426095	+	0.904678i	$0.359889\pi$
$194$	−0.550955			−0.0395563
$195$		0			0
$196$	13.4467			0.960480
$197$	0.556877	+	0.321513i	0.0396758	+	0.0229068i	0.519707	−	0.854345i	$-0.326041\pi$
$197$	0.556877	+	0.321513i	0.0396758	+	0.0229068i	−0.480031	+	0.877252i	$0.659375\pi$
$198$	0.259256	−	0.449045i	0.0184245	−	0.0319122i
$199$	1.53342	+	2.65596i	0.108701	+	0.188276i	0.915244	−	0.402899i	$-0.131997\pi$
$199$	1.53342	+	2.65596i	0.108701	+	0.188276i	−0.806543	+	0.591175i	$0.798664\pi$
$200$			0.868145i			0.0613871i
$201$	−14.3185	+	8.26681i	−1.00995	+	0.583096i
$202$	2.36804	−	1.36719i	0.166615	−	0.0961952i
$203$		−	0.964670i		−	0.0677065i
$204$	7.90831	+	13.6976i	0.553693	+	0.959024i
$205$	−1.86603	+	3.23205i	−0.130329	+	0.225736i
$206$	2.85852	+	1.65037i	0.199163	+	0.114987i
$207$	−1.24746			−0.0867045
$208$		0			0
$209$	−12.1830			−0.842716
$210$	−0.101151	−	0.0583993i	−0.00698005	−	0.00402993i
$211$	4.10020	−	7.10175i	0.282269	−	0.488904i	−0.689674	−	0.724120i	$-0.742246\pi$
$211$	4.10020	−	7.10175i	0.282269	−	0.488904i	0.971943	+	0.235215i	$0.0755796\pi$
$212$	1.52297	+	2.63786i	0.104598	+	0.181169i
$213$		−	20.4782i		−	1.40314i
$214$	2.48554	−	1.43503i	0.169908	−	0.0980964i
$215$	−4.38581	+	2.53215i	−0.299110	+	0.172691i
$216$		−	4.77798i		−	0.325101i
$217$	0.907714	+	1.57221i	0.0616197	+	0.106728i
$218$	1.23381	−	2.13703i	0.0835643	−	0.144738i
$219$	13.4274	+	7.75232i	0.907341	+	0.523854i
$220$	10.4844			0.706856
$221$		0			0
$222$	2.09941			0.140903
$223$	−8.87174	−	5.12210i	−0.594095	−	0.343001i	0.172620	−	0.984989i	$-0.444777\pi$
$223$	−8.87174	−	5.12210i	−0.594095	−	0.343001i	−0.766715	+	0.641987i	$0.778110\pi$
$224$	−0.423935	+	0.734278i	−0.0283254	+	0.0490610i
$225$	−0.219687	−	0.380509i	−0.0146458	−	0.0253673i
$226$			4.02990i			0.268065i
$227$	6.10012	−	3.52190i	0.404879	−	0.233757i	−0.283708	−	0.958911i	$-0.591565\pi$
$227$	6.10012	−	3.52190i	0.404879	−	0.233757i	0.688587	+	0.725154i	$0.258231\pi$
$228$	−6.13421	+	3.54159i	−0.406248	+	0.234547i
$229$		−	1.32899i		−	0.0878219i	−0.999035	−	0.0439109i	$-0.986018\pi$
$229$		−	1.32899i		−	0.0878219i	0.999035	−	0.0439109i	$-0.0139818\pi$
$230$	0.311865	+	0.540166i	0.0205638	+	0.0356175i
$231$	−1.42799	+	2.47335i	−0.0939547	+	0.162734i
$232$	−2.18294	−	1.26032i	−0.143317	−	0.0827440i
$233$	1.24746			0.0817238			0.0408619	−	0.999165i	$-0.486990\pi$
$233$	1.24746			0.0817238			0.0408619	+	0.999165i	$0.486990\pi$
$234$		0			0
$235$	−8.34285			−0.544227
$236$	4.57606	+	2.64199i	0.297876	+	0.171979i
$237$	3.61525	−	6.26180i	0.234836	−	0.406748i
$238$	−0.184822	−	0.320121i	−0.0119802	−	0.0207504i
$239$		−	9.94207i		−	0.643099i	−0.946893	−	0.321549i	$-0.895796\pi$
$239$		−	9.94207i		−	0.643099i	0.946893	−	0.321549i	$-0.104204\pi$
$240$	5.14517	−	2.97057i	0.332120	−	0.191749i
$241$	19.5608	−	11.2934i	1.26002	−	0.727475i	0.286944	−	0.957947i	$-0.407360\pi$
$241$	19.5608	−	11.2934i	1.26002	−	0.727475i	0.973079	+	0.230472i	$0.0740272\pi$
$242$			3.92282i			0.252168i
$243$	2.26371	+	3.92086i	0.145217	+	0.251523i
$244$	−13.7635	+	23.8391i	−0.881119	+	1.52614i
$245$	5.96658	+	3.44481i	0.381191	+	0.220081i
$246$	−1.31197			−0.0836483
$247$		0			0
$248$	4.74363			0.301221
$249$	−5.90869	−	3.41139i	−0.374448	−	0.216188i
$250$	−0.109843	+	0.190254i	−0.00694711	+	0.0120327i
$251$	−3.38418	−	5.86157i	−0.213608	−	0.369979i	0.739233	−	0.673449i	$-0.235188\pi$
$251$	−3.38418	−	5.86157i	−0.213608	−	0.369979i	−0.952841	+	0.303470i	$0.901855\pi$
$252$		−	0.284915i		−	0.0179480i
$253$	13.2082	−	7.62577i	0.830394	−	0.479428i
$254$	0.616417	−	0.355888i	0.0386774	−	0.0223304i
$255$			8.10387i			0.507484i
$256$	−6.13860	−	10.6324i	−0.383663	−	0.664523i
$257$	−5.12691	+	8.88007i	−0.319808	+	0.553924i	−0.980448	−	0.196779i	$-0.936952\pi$
$257$	−5.12691	+	8.88007i	−0.319808	+	0.553924i	0.660640	+	0.750703i	$0.270285\pi$
$258$	−1.54180	−	0.890157i	−0.0959881	−	0.0554187i
$259$	1.98418			0.123291
$260$		0			0
$261$	1.27571			0.0789645
$262$	0.0334208	+	0.0192955i	0.00206474	+	0.00119208i
$263$	−9.32850	+	16.1574i	−0.575220	+	0.996310i	0.420798	+	0.907154i	$0.361750\pi$
$263$	−9.32850	+	16.1574i	−0.575220	+	0.996310i	−0.996018	+	0.0891555i	$0.971583\pi$
$264$	3.73127	+	6.46275i	0.229644	+	0.397754i
$265$			1.56063i			0.0958685i
$266$	0.143360	−	0.0827690i	0.00878998	−	0.00507489i
$267$	4.47040	−	2.58098i	0.273584	−	0.157954i
$268$			20.1658i			1.23182i
$269$	−8.97894	−	15.5520i	−0.547456	−	0.948221i	−0.998448	−	0.0556934i	$-0.982263\pi$
$269$	−8.97894	−	15.5520i	−0.547456	−	0.948221i	0.450992	−	0.892528i	$-0.351070\pi$
$270$	0.604542	−	1.04710i	0.0367913	−	0.0637243i
$271$	26.7582	+	15.4488i	1.62544	+	0.938450i	0.985429	+	0.170086i	$0.0544047\pi$
$271$	26.7582	+	15.4488i	1.62544	+	0.938450i	0.640014	+	0.768363i	$0.278929\pi$
$272$	18.8025			1.14007
$273$		0			0
$274$	3.95060			0.238665
$275$	4.65213	+	2.68591i	0.280534	+	0.161966i
$276$	4.43361	−	7.67923i	0.266872	−	0.462235i
$277$	13.2522	+	22.9536i	0.796250	+	1.37915i	0.922042	+	0.387089i	$0.126519\pi$
$277$	13.2522	+	22.9536i	0.796250	+	1.37915i	−0.125792	+	0.992057i	$0.540147\pi$
$278$		−	2.63320i		−	0.157929i
$279$	−2.07914	+	1.20039i	−0.124475	+	0.0718656i
$280$	−0.249795	+	0.144219i	−0.0149281	+	0.00861874i
$281$		−	4.97766i		−	0.296942i	−0.988917	−	0.148471i	$-0.952565\pi$
$281$		−	4.97766i		−	0.296942i	0.988917	−	0.148471i	$-0.0474352\pi$
$282$	−1.46643	−	2.53993i	−0.0873247	−	0.151251i
$283$	−6.29317	+	10.9001i	−0.374090	+	0.647943i	−0.990190	−	0.139725i	$-0.955378\pi$
$283$	−6.29317	+	10.9001i	−0.374090	+	0.647943i	0.616100	+	0.787668i	$0.288712\pi$
$284$	−21.6307	−	12.4885i	−1.28355	−	0.741057i
$285$	−3.62916			−0.214973
$286$		0			0
$287$	−1.23996			−0.0731926
$288$	−0.971033	−	0.560626i	−0.0572187	−	0.0330352i
$289$	−4.32355	+	7.48861i	−0.254327	+	0.440507i
$290$	−0.318928	−	0.552399i	−0.0187281	−	0.0324380i
$291$			4.01315i			0.235255i
$292$	16.3772	−	9.45541i	0.958406	−	0.553336i
$293$	−14.6511	+	8.45880i	−0.855925	+	0.494168i	−0.862645	−	0.505809i	$-0.831194\pi$
$293$	−14.6511	+	8.45880i	−0.855925	+	0.494168i	0.00672072	+	0.999977i	$0.497861\pi$
$294$			2.42199i			0.141253i
$295$	1.35366	+	2.34461i	0.0788132	+	0.136508i
$296$	2.59229	−	4.48997i	0.150674	−	0.260974i
$297$	−25.6038	−	14.7824i	−1.48568	−	0.857759i
$298$	−0.749222			−0.0434012
$299$		0			0
$300$	3.12316			0.180316
$301$	−1.45717	−	0.841298i	−0.0839899	−	0.0484916i
$302$	0.874509	−	1.51469i	0.0503223	−	0.0871608i
$303$	−9.95859	−	17.2488i	−0.572106	−	0.990917i
$304$			8.42034i			0.482940i
$305$	−12.2143	+	7.05193i	−0.699389	+	0.403793i
$306$	0.423339	−	0.244415i	0.0242007	−	0.0139723i
$307$			4.30426i			0.245657i	0.992428	+	0.122828i	$0.0391965\pi$
$307$			4.30426i			0.245657i	−0.992428	+	0.122828i	$0.960803\pi$
$308$	1.74170	+	3.01671i	0.0992425	+	0.171893i
$309$	12.0213	−	20.8214i	0.683865	−	1.18449i
$310$	1.03957	+	0.600196i	0.0590436	+	0.0340888i
$311$	2.22512			0.126175			0.0630875	−	0.998008i	$-0.479905\pi$
$311$	2.22512			0.126175			0.0630875	+	0.998008i	$0.479905\pi$
$312$		0			0
$313$	7.20887			0.407469			0.203735	−	0.979026i	$-0.434692\pi$
$313$	7.20887			0.407469			0.203735	+	0.979026i	$0.434692\pi$
$314$	−3.12642	−	1.80504i	−0.176434	−	0.101864i
$315$	0.0729902	−	0.126423i	0.00411253	−	0.00712311i
$316$	−4.40948	−	7.63744i	−0.248052	−	0.429639i
$317$		−	0.321644i		−	0.0180653i	−0.999959	−	0.00903266i	$-0.997125\pi$
$317$		−	0.321644i		−	0.0180653i	0.999959	−	0.00903266i	$-0.00287522\pi$
$318$	−0.475124	+	0.274313i	−0.0266436	+	0.0153827i
$319$	−13.5073	+	7.79847i	−0.756266	+	0.436630i
$320$		−	6.86488i		−	0.383759i
$321$	−10.4527	−	18.1046i	−0.583414	−	1.01050i
$322$	−0.103616	+	0.179468i	−0.00577430	+	0.0100014i
$323$	−9.94679	−	5.74278i	−0.553454	−	0.319537i
$324$	−14.6162			−0.812013
$325$		0			0
$326$	−3.91201			−0.216666
$327$	−15.5661	−	8.98707i	−0.860805	−	0.496986i
$328$	−1.61998	+	2.80589i	−0.0894485	+	0.154929i
$329$	−1.38594	−	2.40052i	−0.0764094	−	0.132345i
$330$			1.88842i			0.103954i
$331$	14.4037	−	8.31600i	0.791701	−	0.457089i	−0.0488600	−	0.998806i	$-0.515559\pi$
$331$	14.4037	−	8.31600i	0.791701	−	0.457089i	0.840561	+	0.541717i	$0.182225\pi$
$332$	−7.20676	+	4.16082i	−0.395522	+	0.228355i
$333$			2.62395i			0.143791i
$334$	−0.691317	−	1.19740i	−0.0378272	−	0.0655186i
$335$	−5.16612	+	8.94799i	−0.282255	+	0.488881i
$336$	1.70947	+	0.986961i	0.0932590	+	0.0538431i
$337$	−24.2186			−1.31927			−0.659636	−	0.751586i	$-0.729289\pi$
$337$	−24.2186			−1.31927			−0.659636	+	0.751586i	$0.729289\pi$
$338$		0			0
$339$	29.3537			1.59427
$340$	8.55995	+	4.94209i	0.464229	+	0.268022i
$341$	14.6761	−	25.4197i	0.794754	−	1.37655i
$342$	0.109456	+	0.189584i	0.00591873	+	0.0102515i
$343$			4.61478i			0.249174i
$344$	−3.80752	+	2.19827i	−0.205288	+	0.118523i
$345$	3.93456	−	2.27162i	0.211830	−	0.122300i
$346$			3.50952i			0.188673i
$347$	3.13680	+	5.43309i	0.168392	+	0.291664i	0.937855	−	0.347028i	$-0.112809\pi$
$347$	3.13680	+	5.43309i	0.168392	+	0.291664i	−0.769463	+	0.638692i	$0.779476\pi$
$348$	−4.53401	+	7.85314i	−0.243049	+	0.420972i
$349$	6.12275	+	3.53497i	0.327743	+	0.189223i	0.654839	−	0.755769i	$-0.272737\pi$
$349$	6.12275	+	3.53497i	0.327743	+	0.189223i	−0.327095	+	0.944991i	$0.606070\pi$
$350$	−0.0729902			−0.00390149
$351$		0			0
$352$	13.7085			0.730666
$353$	18.8705	+	10.8949i	1.00438	+	0.579878i	0.909541	−	0.415615i	$-0.136434\pi$
$353$	18.8705	+	10.8949i	1.00438	+	0.579878i	0.0948371	+	0.995493i	$0.469767\pi$
$354$	−0.475869	+	0.824229i	−0.0252921	+	0.0438073i
$355$	−6.39866	−	11.0828i	−0.339606	−	0.588214i
$356$		−	6.29598i		−	0.333687i
$357$	−2.33176	+	1.34624i	−0.123410	+	0.0712506i
$358$	4.49332	−	2.59422i	0.237479	−	0.137109i
$359$		−	23.9737i		−	1.26528i	−0.774444	−	0.632642i	$-0.781971\pi$
$359$		−	23.9737i		−	1.26528i	0.774444	−	0.632642i	$-0.218029\pi$
$360$	−0.190720	−	0.330337i	−0.0100518	−	0.0174103i
$361$	−6.92820	+	12.0000i	−0.364642	+	0.631579i
$362$	0.499589	+	0.288438i	0.0262578	+	0.0151600i
$363$	28.5737			1.49973
$364$		0			0
$365$	9.68922			0.507157
$366$	−4.29384	−	2.47905i	−0.224443	−	0.129582i
$367$	−3.19566	+	5.53505i	−0.166812	+	0.288927i	−0.937297	−	0.348531i	$-0.886681\pi$
$367$	−3.19566	+	5.53505i	−0.166812	+	0.288927i	0.770485	+	0.637458i	$0.220014\pi$
$368$	−5.27059	−	9.12892i	−0.274748	−	0.475878i
$369$		−	1.63977i		−	0.0853628i
$370$	1.13620	−	0.655986i	0.0590683	−	0.0341031i
$371$	−0.449045	+	0.259256i	−0.0233133	+	0.0134599i
$372$		−	17.0653i		−	0.884793i
$373$	10.0401	+	17.3899i	0.519855	+	0.900414i	0.999734	+	0.0230798i	$0.00734719\pi$
$373$	10.0401	+	17.3899i	0.519855	+	0.900414i	−0.479879	+	0.877335i	$0.659319\pi$
$374$	−2.98823	+	5.17577i	−0.154518	+	0.267633i
$375$	1.38581	+	0.800098i	0.0715629	+	0.0413169i
$376$	−7.24280			−0.373519
$377$		0			0
$378$	0.401714			0.0206619
$379$	4.73007	+	2.73091i	0.242968	+	0.140277i	0.616540	−	0.787324i	$-0.288534\pi$
$379$	4.73007	+	2.73091i	0.242968	+	0.140277i	−0.373572	+	0.927601i	$0.621867\pi$
$380$	−2.21322	+	3.83341i	−0.113536	+	0.196650i
$381$	−2.59229	−	4.48997i	−0.132807	−	0.230028i
$382$			0.442849i			0.0226581i
$383$	−4.90842	+	2.83388i	−0.250808	+	0.144804i	−0.620134	−	0.784496i	$-0.712922\pi$
$383$	−4.90842	+	2.83388i	−0.250808	+	0.144804i	0.369326	+	0.929300i	$0.379589\pi$
$384$	9.16297	−	5.29024i	0.467596	−	0.269966i
$385$			1.78477i			0.0909602i
$386$	2.50675	+	4.34181i	0.127590	+	0.220992i
$387$	1.11256	−	1.92701i	0.0565546	−	0.0979554i
$388$	4.23901	+	2.44739i	0.215203	+	0.124247i
$389$	−10.6174			−0.538325			−0.269162	−	0.963095i	$-0.586747\pi$
$389$	−10.6174			−0.538325			−0.269162	+	0.963095i	$0.586747\pi$
$390$		0			0
$391$	14.3784			0.727149
$392$	5.17986	+	2.99059i	0.261622	+	0.151048i
$393$	0.140548	−	0.243436i	0.00708971	−	0.0122797i
$394$	0.0706321	+	0.122338i	0.00355840	+	0.00616332i
$395$		−	4.51851i		−	0.227351i
$396$	−3.98940	+	2.30328i	−0.200475	+	0.115744i
$397$	−24.2780	+	14.0169i	−1.21848	+	0.703487i	−0.964592	−	0.263748i	$-0.915041\pi$
$397$	−24.2780	+	14.0169i	−1.21848	+	0.703487i	−0.253884	+	0.967235i	$0.581708\pi$
$398$			0.673745i			0.0337718i
$399$	−0.602888	−	1.04423i	−0.0301822	−	0.0522770i
$400$	1.85638	−	3.21534i	0.0928189	−	0.160767i
$401$	−19.4979	−	11.2571i	−0.973680	−	0.562155i	−0.0733241	−	0.997308i	$-0.523361\pi$
$401$	−19.4979	−	11.2571i	−0.973680	−	0.562155i	−0.900356	+	0.435154i	$0.856694\pi$
$402$	−3.63222			−0.181159
$403$		0			0
$404$	−24.2927			−1.20861
$405$	−6.48552	−	3.74441i	−0.322268	−	0.186061i
$406$	0.105963	−	0.183533i	0.00525884	−	0.00910857i
$407$	−16.0403	−	27.7826i	−0.795087	−	1.37713i
$408$			7.03533i			0.348301i
$409$	3.71328	−	2.14386i	0.183610	−	0.106007i	−0.405378	−	0.914149i	$-0.632860\pi$
$409$	3.71328	−	2.14386i	0.183610	−	0.106007i	0.588988	+	0.808142i	$0.299527\pi$
$410$	−0.710039	+	0.409941i	−0.0350663	+	0.0202456i
$411$		−	28.7761i		−	1.41942i
$412$	−14.6622	−	25.3956i	−0.722353	−	1.25115i
$413$	−0.449749	+	0.778989i	−0.0221307	+	0.0383315i
$414$	−0.237335	−	0.137025i	−0.0116644	−	0.00673443i
$415$	−4.26371			−0.209297
$416$		0			0
$417$	−19.1802			−0.939257
$418$	−2.31787	−	1.33822i	−0.113371	−	0.0654546i
$419$	−8.85578	+	15.3387i	−0.432633	+	0.749343i	−0.997099	−	0.0761137i	$-0.975749\pi$
$419$	−8.85578	+	15.3387i	−0.432633	+	0.749343i	0.564466	+	0.825456i	$0.309082\pi$
$420$	0.518830	+	0.898640i	0.0253163	+	0.0438491i
$421$			12.8787i			0.627672i	0.949477	+	0.313836i	$0.101614\pi$
$421$			12.8787i			0.627672i	−0.949477	+	0.313836i	$0.898386\pi$
$422$	1.56016	−	0.900759i	0.0759474	−	0.0438483i
$423$	3.17453	−	1.83281i	0.154351	−	0.0891145i
$424$			1.35485i			0.0657973i
$425$	2.53215	+	4.38581i	0.122827	+	0.212743i
$426$	2.24940	−	3.89607i	0.108984	−	0.188765i
$427$	−4.05816	−	2.34298i	−0.196388	−	0.113385i
$428$	−25.4981			−1.23250
$429$		0			0
$430$	−1.11256			−0.0536524
$431$	−8.22590	−	4.74923i	−0.396228	−	0.228762i	0.288627	−	0.957442i	$-0.406801\pi$
$431$	−8.22590	−	4.74923i	−0.396228	−	0.228762i	−0.684855	+	0.728679i	$0.740134\pi$
$432$	−10.2169	+	17.6962i	−0.491560	+	0.851408i
$433$	−0.698141	−	1.20922i	−0.0335505	−	0.0581112i	0.848763	−	0.528774i	$-0.177348\pi$
$433$	−0.698141	−	1.20922i	−0.0335505	−	0.0581112i	−0.882313	+	0.470663i	$0.844015\pi$
$434$			0.398826i			0.0191443i
$435$	−4.02367	+	2.32306i	−0.192920	+	0.111382i
$436$	−18.9857	+	10.9614i	−0.909251	+	0.524956i
$437$			6.43911i			0.308024i
$438$	1.70308	+	2.94983i	0.0813765	+	0.140948i
$439$	2.08090	−	3.60422i	0.0993159	−	0.172020i	−0.812086	−	0.583538i	$-0.801668\pi$
$439$	2.08090	−	3.60422i	0.0993159	−	0.172020i	0.911402	+	0.411518i	$0.135001\pi$
$440$	4.03872	+	2.33176i	0.192539	+	0.111162i
$441$	−3.02711			−0.144148
$442$		0			0
$443$	9.54563			0.453526			0.226763	−	0.973950i	$-0.427186\pi$
$443$	9.54563			0.453526			0.226763	+	0.973950i	$0.427186\pi$
$444$	−16.1527	−	9.32578i	−0.766574	−	0.442582i
$445$	1.61292	−	2.79366i	0.0764596	−	0.132432i
$446$	−1.12526	−	1.94900i	−0.0532825	−	0.0922880i
$447$			5.45732i			0.258122i
$448$	1.97526	−	1.14042i	0.0933223	−	0.0538796i
$449$	−18.8075	+	10.8585i	−0.887582	+	0.512446i	−0.873151	−	0.487450i	$-0.837927\pi$
$449$	−18.8075	+	10.8585i	−0.887582	+	0.512446i	−0.0144310	+	0.999896i	$0.504594\pi$
$450$		−	0.0965246i		−	0.00455022i
$451$	10.0239	+	17.3620i	0.472009	+	0.817544i
$452$	17.9012	−	31.0057i	0.842000	−	1.45839i
$453$	−11.0330	−	6.36991i	−0.518376	−	0.299284i
$454$	1.54743			0.0726246
$455$		0			0
$456$	−3.15064			−0.147542
$457$	−4.08989	−	2.36130i	−0.191317	−	0.110457i	0.401282	−	0.915955i	$-0.368565\pi$
$457$	−4.08989	−	2.36130i	−0.191317	−	0.110457i	−0.592599	+	0.805498i	$0.701898\pi$
$458$	0.145980	−	0.252845i	0.00682122	−	0.0118147i
$459$	−13.9361	−	24.1381i	−0.650482	−	1.12667i
$460$		−	5.54133i		−	0.258366i
$461$	−1.54283	+	0.890753i	−0.0718568	+	0.0414865i	−0.535498	−	0.844537i	$-0.679876\pi$
$461$	−1.54283	+	0.890753i	−0.0718568	+	0.0414865i	0.463641	+	0.886023i	$0.346543\pi$
$462$	−0.543362	+	0.313710i	−0.0252795	+	0.0145951i
$463$		−	6.80200i		−	0.316116i	−0.987430	−	0.158058i	$-0.949477\pi$
$463$		−	6.80200i		−	0.316116i	0.987430	−	0.158058i	$-0.0505232\pi$
$464$	5.38995	+	9.33566i	0.250222	+	0.433397i
$465$	4.37182	−	7.57221i	0.202738	−	0.351153i
$466$	0.237335	+	0.137025i	0.0109943	+	0.00634758i
$467$	−18.2374			−0.843927			−0.421963	−	0.906613i	$-0.638659\pi$
$467$	−18.2374			−0.843927			−0.421963	+	0.906613i	$0.638659\pi$
$468$		0			0
$469$	−3.43285			−0.158514
$470$	−1.58726	−	0.916407i	−0.0732150	−	0.0422707i
$471$	−13.1479	+	22.7728i	−0.605823	+	1.04932i
$472$	1.17517	+	2.03546i	0.0540918	+	0.0936897i
$473$			27.2045i			1.25086i
$474$	1.37564	−	0.794223i	0.0631850	−	0.0364799i
$475$	−1.96410	+	1.13397i	−0.0901192	+	0.0520303i
$476$			3.28398i			0.150521i
$477$	−0.342849	−	0.593832i	−0.0156980	−	0.0271897i
$478$	1.09207	−	1.89152i	0.0499502	−	0.0865162i
$479$	−30.4674	−	17.5904i	−1.39209	−	0.803724i	−0.398544	−	0.917149i	$-0.630485\pi$
$479$	−30.4674	−	17.5904i	−1.39209	−	0.803724i	−0.993547	+	0.113425i	$0.963818\pi$
$480$	4.08359			0.186390
$481$		0			0
$482$	4.96204			0.226015
$483$	1.30724	+	0.754738i	0.0594817	+	0.0343418i
$484$	17.4255	−	30.1819i	0.792069	−	1.37190i
$485$	1.25396	+	2.17191i	0.0569392	+	0.0986215i
$486$			0.994615i			0.0451166i
$487$	−8.92352	+	5.15200i	−0.404363	+	0.233459i	−0.688365	−	0.725364i	$-0.741671\pi$
$487$	−8.92352	+	5.15200i	−0.404363	+	0.233459i	0.284002	+	0.958824i	$0.408338\pi$
$488$	−10.6038	+	6.12210i	−0.480011	+	0.277134i
$489$			28.4950i			1.28859i
$490$	0.756779	+	1.31078i	0.0341878	+	0.0592150i
$491$	4.66599	−	8.08174i	0.210573	−	0.364724i	−0.741321	−	0.671151i	$-0.765800\pi$
$491$	4.66599	−	8.08174i	0.210573	−	0.364724i	0.951894	+	0.306427i	$0.0991336\pi$
$492$	10.0942	+	5.82790i	0.455083	+	0.262742i
$493$	−14.7041			−0.662238
$494$		0			0
$495$	−2.36023			−0.106085
$496$	−17.5689	−	10.1434i	−0.788869	−	0.455454i
$497$	2.12593	−	3.68222i	0.0953611	−	0.165170i
$498$	−0.749437	−	1.29806i	−0.0335831	−	0.0581676i
$499$			23.9421i			1.07179i	0.844283	+	0.535897i	$0.180026\pi$
$499$			23.9421i			1.07179i	−0.844283	+	0.535897i	$0.819974\pi$
$500$	1.69025	−	0.975869i	0.0755905	−	0.0436422i
$501$	−8.72181	+	5.03554i	−0.389662	+	0.224971i
$502$		−	1.48692i		−	0.0663645i
$503$	−21.0721	−	36.4980i	−0.939560	−	1.62737i	−0.766294	−	0.642490i	$-0.777901\pi$
$503$	−21.0721	−	36.4980i	−0.939560	−	1.62737i	−0.173266	−	0.984875i	$-0.555432\pi$
$504$	0.0633661	−	0.109753i	0.00282255	−	0.00488880i
$505$	−10.7792	−	6.22336i	−0.479667	−	0.276936i
$506$	3.35056			0.148951
$507$		0			0
$508$	−6.32355			−0.280562
$509$	29.0640	+	16.7801i	1.28824	+	0.743765i	0.978340	−	0.207005i	$-0.0663715\pi$
$509$	29.0640	+	16.7801i	1.28824	+	0.743765i	0.309899	+	0.950770i	$0.399705\pi$
$510$	−0.890157	+	1.54180i	−0.0394168	+	0.0682719i
$511$	1.60960	+	2.78792i	0.0712047	+	0.123330i
$512$		−	15.9211i		−	0.703621i
$513$	10.8098	−	6.24102i	0.477263	−	0.275548i
$514$	−1.95084	+	1.12632i	−0.0860477	+	0.0496796i
$515$		−	15.0247i		−	0.662069i
$516$	7.90831	+	13.6976i	0.348144	+	0.603003i
$517$	−22.4081	+	38.8120i	−0.985508	+	1.70695i
$518$	0.377499	+	0.217949i	0.0165864	+	0.00957614i
$519$	25.5633			1.12210
$520$		0			0
$521$	12.4649			0.546098			0.273049	−	0.962000i	$-0.411968\pi$
$521$	12.4649			0.546098			0.273049	+	0.962000i	$0.411968\pi$
$522$	0.242710	+	0.140128i	0.0106231	+	0.00613326i
$523$	2.82978	−	4.90132i	0.123738	−	0.214320i	−0.797501	−	0.603317i	$-0.793845\pi$
$523$	2.82978	−	4.90132i	0.123738	−	0.214320i	0.921239	+	0.388998i	$0.127179\pi$
$524$	−0.171425	−	0.296916i	−0.00748872	−	0.0129708i
$525$			0.531659i			0.0232035i
$526$	−3.54958	+	2.04935i	−0.154769	+	0.0893558i
$527$	23.9645	−	13.8359i	1.04391	−	0.602702i
$528$		−	31.9147i		−	1.38891i
$529$	7.46953	+	12.9376i	0.324762	+	0.562505i
$530$	−0.171425	+	0.296916i	−0.00744621	+	0.0128972i
$531$	−1.03016	−	0.594763i	−0.0447051	−	0.0258105i
$532$	−1.47067			−0.0637616
$533$		0			0
$534$	1.13402			0.0490737
$535$	−11.3140	−	6.53215i	−0.489147	−	0.282409i
$536$	−4.48494	+	7.76815i	−0.193720	+	0.335533i
$537$	−18.8963	−	32.7293i	−0.815433	−	1.41237i
$538$		−	3.94511i		−	0.170086i
$539$	32.0514	−	18.5049i	1.38055	−	0.797061i
$540$	−9.30260	+	5.37086i	−0.400320	+	0.231125i
$541$			15.4750i			0.665321i	0.943047	+	0.332660i	$0.107946\pi$
$541$			15.4750i			0.665321i	−0.943047	+	0.332660i	$0.892054\pi$
$542$	3.39391	+	5.87842i	0.145781	+	0.252500i
$543$	2.10098	−	3.63900i	0.0901616	−	0.156165i
$544$	11.1923	+	6.46187i	0.479866	+	0.277051i
$545$	−11.2325			−0.481146
$546$		0			0
$547$	25.1765			1.07647			0.538234	−	0.842795i	$-0.319092\pi$
$547$	25.1765			1.07647			0.538234	+	0.842795i	$0.319092\pi$
$548$	−30.3956	−	17.5489i	−1.29844	−	0.749653i
$549$	3.09843	−	5.36665i	0.132238	−	0.229043i
$550$	0.590059	+	1.02201i	0.0251602	+	0.0435787i
$551$		−	6.58493i		−	0.280528i
$552$	3.41577	−	1.97210i	0.145385	−	0.0839380i
$553$	1.30013	−	0.750630i	0.0552871	−	0.0319200i
$554$			5.82269i			0.247382i
$555$	−4.77819	−	8.27607i	−0.202823	−	0.351300i
$556$	−11.6969	+	20.2596i	−0.496059	+	0.859199i
$557$	36.6752	+	21.1744i	1.55398	+	0.897190i	0.997812	+	0.0661194i	$0.0210618\pi$
$557$	36.6752	+	21.1744i	1.55398	+	0.897190i	0.556167	+	0.831071i	$0.312272\pi$
$558$	−0.527420			−0.0223275
$559$		0			0
$560$	1.23355			0.0521270
$561$	37.7002	+	21.7662i	1.59171	+	0.918971i
$562$	0.546763	−	0.947022i	0.0230638	−	0.0399477i
$563$	11.8953	+	20.6032i	0.501326	+	0.868322i	0.999999	+	0.00153173i	$0.000487565\pi$
$563$	11.8953	+	20.6032i	0.501326	+	0.868322i	−0.498673	+	0.866790i	$0.666179\pi$
$564$			26.0561i			1.09716i
$565$	15.8862	−	9.17191i	0.668338	−	0.385865i
$566$	−2.39461	+	1.38253i	−0.100653	+	0.0581119i
$567$		−	2.48814i		−	0.104492i
$568$	−5.55497	−	9.62148i	−0.233081	−	0.403709i
$569$	−13.3710	+	23.1593i	−0.560543	+	0.970889i	0.436906	+	0.899507i	$0.356074\pi$
$569$	−13.3710	+	23.1593i	−0.560543	+	0.970889i	−0.997449	+	0.0713817i	$0.977259\pi$
$570$	−0.690464	−	0.398640i	−0.0289204	−	0.0166972i
$571$	16.7159			0.699539			0.349769	−	0.936836i	$-0.386260\pi$
$571$	16.7159			0.699539			0.349769	+	0.936836i	$0.386260\pi$
$572$		0			0
$573$	3.22571			0.134756
$574$	−0.235908	−	0.136202i	−0.00984661	−	0.00568494i
$575$	1.41959	−	2.45880i	0.0592010	−	0.102539i
$576$	1.50812	+	2.61215i	0.0628385	+	0.108840i
$577$		−	20.6768i		−	0.860786i	−0.902642	−	0.430393i	$-0.858375\pi$
$577$		−	20.6768i		−	0.860786i	0.902642	−	0.430393i	$-0.141625\pi$
$578$	−1.64515	+	0.949828i	−0.0684292	+	0.0395076i
$579$	31.6257	−	18.2591i	1.31432	−	0.758822i
$580$			5.66682i			0.235302i
$581$	−0.708301	−	1.22681i	−0.0293853	−	0.0508968i
$582$	−0.440818	+	0.763519i	−0.0182725	+	0.0316489i
$583$	7.26023	+	4.19170i	0.300688	+	0.173602i
$584$	8.41165			0.348076
$585$		0			0
$586$	−3.71657			−0.153530
$587$	−18.0109	−	10.3986i	−0.743388	−	0.429196i	0.0799116	−	0.996802i	$-0.474536\pi$
$587$	−18.0109	−	10.3986i	−0.743388	−	0.429196i	−0.823300	+	0.567606i	$0.807870\pi$
$588$	10.7587	−	18.6346i	0.443681	−	0.768478i
$589$	6.19615	+	10.7321i	0.255308	+	0.442206i
$590$			0.594763i			0.0244860i
$591$	0.891111	−	0.514483i	0.0366554	−	0.0211630i
$592$	−19.2021	+	11.0863i	−0.789199	+	0.455644i
$593$			21.8475i			0.897169i	0.893740	+	0.448585i	$0.148072\pi$
$593$			21.8475i			0.897169i	−0.893740	+	0.448585i	$0.851928\pi$
$594$	−3.24749	−	5.62482i	−0.133246	−	0.230789i
$595$	−0.841298	+	1.45717i	−0.0344898	+	0.0597381i
$596$	5.76446	+	3.32811i	0.236121	+	0.136325i
$597$	4.90755			0.200853
$598$		0			0
$599$	−3.58040			−0.146291			−0.0731456	−	0.997321i	$-0.523304\pi$
$599$	−3.58040			−0.146291			−0.0731456	+	0.997321i	$0.523304\pi$
$600$	1.20308	+	0.694601i	0.0491157	+	0.0283570i
$601$	−10.6743	+	18.4885i	−0.435414	+	0.754160i	−0.997329	−	0.0730352i	$-0.976731\pi$
$601$	−10.6743	+	18.4885i	−0.435414	+	0.754160i	0.561915	+	0.827195i	$0.310065\pi$
$602$	−0.184822	−	0.320121i	−0.00753278	−	0.0130472i
$603$		−	4.53972i		−	0.184872i
$604$	−13.4568	+	7.76929i	−0.547550	+	0.316128i
$605$	15.4641	−	8.92820i	0.628705	−	0.362983i
$606$		−	4.37554i		−	0.177744i
$607$	1.64988	+	2.85767i	0.0669665	+	0.115989i	0.897565	−	0.440883i	$-0.145335\pi$
$607$	1.64988	+	2.85767i	0.0669665	+	0.115989i	−0.830598	+	0.556872i	$0.812001\pi$
$608$	−2.89383	+	5.01226i	−0.117360	+	0.203274i
$609$	−1.33685	−	0.771830i	−0.0541718	−	0.0312761i
$610$	−3.09843			−0.125452
$611$		0			0
$612$	−4.34285			−0.175549
$613$	−8.56183	−	4.94318i	−0.345809	−	0.199653i	0.317029	−	0.948416i	$-0.397315\pi$
$613$	−8.56183	−	4.94318i	−0.345809	−	0.199653i	−0.662838	+	0.748763i	$0.730648\pi$
$614$	−0.472795	+	0.818904i	−0.0190804	+	0.0330483i
$615$	2.98601	+	5.17191i	0.120407	+	0.208552i
$616$			1.54944i			0.0624286i
$617$	−39.5920	+	22.8584i	−1.59391	+	0.920246i	−0.601287	+	0.799033i	$0.705345\pi$
$617$	−39.5920	+	22.8584i	−1.59391	+	0.920246i	−0.992626	+	0.121213i	$0.961321\pi$
$618$	4.57419	−	2.64091i	0.184001	−	0.106233i
$619$		−	19.9143i		−	0.800425i	−0.916422	−	0.400212i	$-0.868936\pi$
$619$		−	19.9143i		−	0.800425i	0.916422	−	0.400212i	$-0.131064\pi$
$620$	−5.33225	−	9.23572i	−0.214148	−	0.370916i
$621$	−7.81295	+	13.5324i	−0.313523	+	0.543038i
$622$	0.423339	+	0.244415i	0.0169743	+	0.00980014i
$623$	1.07177			0.0429397
$624$		0			0
$625$	1.00000			0.0400000
$626$	1.37152	+	0.791847i	0.0548169	+	0.0316486i
$627$	−9.74760	+	16.8833i	−0.389282	+	0.674255i
$628$	16.0363	+	27.7757i	0.639918	+	1.10837i
$629$		−	30.2440i		−	1.20591i
$630$	0.0277734	−	0.0160350i	0.00110652	−	0.000638849i
$631$	−12.6403	+	7.29790i	−0.503204	+	0.290525i	−0.730036	−	0.683409i	$-0.760497\pi$
$631$	−12.6403	+	7.29790i	−0.503204	+	0.290525i	0.226832	+	0.973934i	$0.427163\pi$
$632$		−	3.92272i		−	0.156038i
$633$	−6.56112	−	11.3642i	−0.260781	−	0.451686i
$634$	0.0353305	−	0.0611942i	0.00140315	−	0.00243033i
$635$	−2.80589	−	1.61998i	−0.111348	−	0.0642870i
$636$	4.87409			0.193270
$637$		0			0
$638$	−3.42644			−0.135654
$639$	4.86950	+	2.81140i	0.192634	+	0.111217i
$640$	3.30600	−	5.72615i	0.130681	−	0.226346i
$641$	−7.08183	−	12.2661i	−0.279716	−	0.484482i	0.691598	−	0.722282i	$-0.256907\pi$
$641$	−7.08183	−	12.2661i	−0.279716	−	0.484482i	−0.971314	+	0.237801i	$0.923573\pi$
$642$		−	4.59265i		−	0.181257i
$643$	14.5246	−	8.38581i	0.572796	−	0.330704i	−0.185469	−	0.982650i	$-0.559380\pi$
$643$	14.5246	−	8.38581i	0.572796	−	0.330704i	0.758265	+	0.651946i	$0.226047\pi$
$644$	1.59443	−	0.920544i	0.0628293	−	0.0362745i
$645$			8.10387i			0.319089i
$646$	−1.26161	−	2.18518i	−0.0496376	−	0.0859748i
$647$	−1.49584	+	2.59087i	−0.0588075	+	0.101858i	−0.893930	−	0.448206i	$-0.852063\pi$
$647$	−1.49584	+	2.59087i	−0.0588075	+	0.101858i	0.835123	+	0.550063i	$0.185396\pi$
$648$	−5.63037	−	3.25069i	−0.221182	−	0.127699i
$649$	14.5432			0.570872
$650$		0			0
$651$	2.90504			0.113858
$652$	30.0987	+	17.3775i	1.17876	+	0.680556i
$653$	5.83217	−	10.1016i	0.228230	−	0.395307i	−0.729053	−	0.684457i	$-0.760039\pi$
$653$	5.83217	−	10.1016i	0.228230	−	0.395307i	0.957284	+	0.289150i	$0.0933727\pi$
$654$	−1.97434	−	3.41966i	−0.0772028	−	0.133719i
$655$		−	0.175664i		−	0.00686374i
$656$	11.9998	−	6.92810i	0.468514	−	0.270497i
$657$	−3.68683	+	2.12859i	−0.143837	+	0.0830444i
$658$		−	0.608946i		−	0.0237392i
$659$	0.905237	+	1.56792i	0.0352630	+	0.0610773i	0.883118	−	0.469150i	$-0.155440\pi$
$659$	0.905237	+	1.56792i	0.0352630	+	0.0610773i	−0.847855	+	0.530228i	$0.822106\pi$
$660$	8.38853	−	14.5294i	0.326523	−	0.565554i
$661$	−10.6872	−	6.17028i	−0.415686	−	0.239996i	0.277544	−	0.960713i	$-0.410480\pi$
$661$	−10.6872	−	6.17028i	−0.415686	−	0.239996i	−0.693230	+	0.720717i	$0.743813\pi$
$662$	3.65383			0.142010
$663$		0			0
$664$	−3.70152			−0.143647
$665$	−0.652566	−	0.376759i	−0.0253054	−	0.0146101i
$666$	−0.288223	+	0.499217i	−0.0111684	+	0.0193443i
$667$	4.12174	+	7.13907i	0.159594	+	0.276426i
$668$			12.2836i			0.475265i
$669$	−14.1965	+	8.19636i	−0.548869	+	0.316890i
$670$	−1.96576	+	1.13493i	−0.0759438	+	0.0438461i
$671$			75.7634i			2.92481i
$672$	0.678380	+	1.17499i	0.0261691	+	0.0453262i
$673$	4.63313	−	8.02481i	0.178594	−	0.309334i	−0.762805	−	0.646628i	$-0.776178\pi$
$673$	4.63313	−	8.02481i	0.178594	−	0.309334i	0.941399	+	0.337295i	$0.109512\pi$
$674$	−4.60770	−	2.66025i	−0.177482	−	0.102469i
$675$	−5.50367			−0.211836
$676$		0			0
$677$	13.8984			0.534158			0.267079	−	0.963675i	$-0.413941\pi$
$677$	13.8984			0.534158			0.267079	+	0.963675i	$0.413941\pi$
$678$	5.58467	+	3.22431i	0.214478	+	0.123829i
$679$	−0.416622	+	0.721611i	−0.0159885	+	0.0276929i
$680$	2.19827	+	3.80752i	0.0842999	+	0.146012i
$681$		−	11.2715i		−	0.431924i
$682$	5.58438	−	3.22414i	0.213837	−	0.123459i
$683$	32.6935	−	18.8756i	1.25098	−	0.722255i	0.279678	−	0.960094i	$-0.409772\pi$
$683$	32.6935	−	18.8756i	1.25098	−	0.722255i	0.971305	+	0.237838i	$0.0764388\pi$
$684$		−	1.94486i		−	0.0743637i
$685$	−8.99144	−	15.5736i	−0.343545	−	0.595038i
$686$	−0.506903	+	0.877981i	−0.0193536	+	0.0335215i
$687$	−1.84172	−	1.06332i	−0.0702661	−	0.0405681i
$688$	18.8025			0.716838
$689$		0			0
$690$	0.998090			0.0379966
$691$	1.43146	+	0.826456i	0.0544554	+	0.0314399i	0.526981	−	0.849877i	$-0.323324\pi$
$691$	1.43146	+	0.826456i	0.0544554	+	0.0314399i	−0.472525	+	0.881317i	$0.656657\pi$
$692$	15.5896	−	27.0020i	0.592628	−	1.02646i
$693$	−0.392090	−	0.679120i	−0.0148943	−	0.0257976i
$694$			1.37823i			0.0523168i
$695$	−10.3803	+	5.99307i	−0.393747	+	0.227330i
$696$	−3.49312	+	2.01676i	−0.132407	+	0.0764450i
$697$			18.9002i			0.715897i
$698$	0.776587	+	1.34509i	0.0293943	+	0.0509123i
$699$	0.998090	−	1.72874i	0.0377512	−	0.0653871i
$700$	0.561581	+	0.324229i	0.0212258	+	0.0122547i
$701$	−20.4819			−0.773590			−0.386795	−	0.922166i	$-0.626418\pi$
$701$	−20.4819			−0.773590			−0.386795	+	0.922166i	$0.626418\pi$
$702$		0			0
$703$	13.5442			0.510830
$704$	−31.9363	−	18.4384i	−1.20365	−	0.694925i
$705$	−6.67510	+	11.5616i	−0.251399	+	0.435435i
$706$	2.39347	+	4.14561i	0.0900794	+	0.156022i
$707$		−	4.13538i		−	0.155527i
$708$	7.32260	−	4.22770i	0.275200	−	0.158887i
$709$	−19.0021	+	10.9709i	−0.713639	+	0.412020i	−0.812407	−	0.583091i	$-0.801843\pi$
$709$	−19.0021	+	10.9709i	−0.713639	+	0.412020i	0.0987679	+	0.995110i	$0.468510\pi$
$710$		−	2.81140i		−	0.105510i
$711$	0.992658	+	1.71933i	0.0372276	+	0.0644801i
$712$	1.40025	−	2.42530i	0.0524764	−	0.0908919i
$713$	−13.4351	−	7.75678i	−0.503150	−	0.290494i
$714$	−0.591503			−0.0221364
$715$		0			0
$716$	−46.0950			−1.72265
$717$	−13.7778	−	7.95463i	−0.514542	−	0.297071i
$718$	2.63335	−	4.56110i	0.0982759	−	0.170219i
$719$	19.4237	+	33.6429i	0.724384	+	1.25467i	0.959227	+	0.282636i	$0.0912089\pi$
$719$	19.4237	+	33.6429i	0.724384	+	1.25467i	−0.234844	+	0.972033i	$0.575458\pi$
$720$			1.63129i			0.0607945i
$721$	4.32312	−	2.49596i	0.161002	−	0.0929543i
$722$	−2.63624	+	1.52204i	−0.0981108	+	0.0566443i
$723$		−	36.1434i		−	1.34419i
$724$	−2.56254	−	4.43844i	−0.0952359	−	0.164953i
$725$	−1.45174	+	2.51448i	−0.0539162	+	0.0933856i
$726$	5.43628	+	3.13864i	0.201759	+	0.116486i
$727$	30.6598			1.13711			0.568555	−	0.822645i	$-0.307503\pi$
$727$	30.6598			1.13711			0.568555	+	0.822645i	$0.307503\pi$
$728$		0			0
$729$	29.7112			1.10042
$730$	1.84342	+	1.06430i	0.0682279	+	0.0393914i
$731$	−12.8236	+	22.2110i	−0.474296	+	0.821505i
$732$	22.0243	+	38.1473i	0.814043	+	1.40996i
$733$			24.3858i			0.900709i	0.892850	+	0.450355i	$0.148702\pi$
$733$			24.3858i			0.900709i	−0.892850	+	0.450355i	$0.851298\pi$
$734$	−1.21598	+	0.702045i	−0.0448826	+	0.0259130i
$735$	9.54769	−	5.51236i	0.352172	−	0.203327i
$736$		−	7.24539i		−	0.267069i
$737$	27.7515	+	48.0669i	1.02224	+	1.77057i
$738$	0.180117	−	0.311973i	0.00663021	−	0.0114839i
$739$	33.1504	+	19.1394i	1.21946	+	0.704054i	0.964802	−	0.262977i	$-0.0847044\pi$
$739$	33.1504	+	19.1394i	1.21946	+	0.704054i	0.254656	+	0.967032i	$0.418038\pi$
$740$	−11.6558			−0.428476
$741$		0			0
$742$	−0.113910			−0.00418178
$743$	34.6479	+	20.0040i	1.27111	+	0.733874i	0.975196	−	0.221342i	$-0.0710437\pi$
$743$	34.6479	+	20.0040i	1.27111	+	0.733874i	0.295910	+	0.955216i	$0.404377\pi$
$744$	3.79537	−	6.57377i	0.139145	−	0.241006i
$745$	1.70520	+	2.95350i	0.0624738	+	0.108208i
$746$			4.41134i			0.161511i
$747$	1.62238	−	0.936681i	0.0593598	−	0.0342714i
$748$	45.9825	−	26.5480i	1.68129	−	0.970691i
$749$		−	4.34057i		−	0.158601i
$750$	0.175771	+	0.304444i	0.00641825	+	0.0111167i
$751$	12.8010	−	22.1720i	0.467115	−	0.809067i	−0.532179	−	0.846632i	$-0.678627\pi$
$751$	12.8010	−	22.1720i	0.467115	−	0.809067i	0.999294	+	0.0375648i	$0.0119601\pi$
$752$	26.8251	+	15.4875i	0.978211	+	0.564770i
$753$	−10.8307			−0.394693
$754$		0			0
$755$	−7.96141			−0.289745
$756$	−3.09076	−	1.78445i	−0.112410	−	0.0648998i
$757$	0.924239	−	1.60083i	0.0335920	−	0.0581831i	−0.848741	−	0.528809i	$-0.822639\pi$
$757$	0.924239	−	1.60083i	0.0335920	−	0.0581831i	0.882333	+	0.470626i	$0.155972\pi$
$758$	0.599945	+	1.03914i	0.0217910	+	0.0377431i
$759$		−	24.4055i		−	0.885862i
$760$	−1.70512	+	0.984454i	−0.0618514	+	0.0357099i
$761$	−22.7006	+	13.1062i	−0.822896	+	0.475099i	−0.851414	−	0.524494i	$-0.824255\pi$
$761$	−22.7006	+	13.1062i	−0.822896	+	0.475099i	0.0285179	+	0.999593i	$0.490921\pi$
$762$		−	1.13898i		−	0.0412610i
$763$	−1.86597	−	3.23196i	−0.0675528	−	0.117005i
$764$	1.96718	−	3.40725i	0.0711699	−	0.123270i
$765$	−1.92701	−	1.11256i	−0.0696712	−	0.0402247i
$766$	−1.24513			−0.0449884
$767$		0			0
$768$	−19.6459			−0.708911
$769$	38.4078	+	22.1747i	1.38502	+	0.799641i	0.992749	−	0.120208i	$-0.0383562\pi$
$769$	38.4078	+	22.1747i	1.38502	+	0.799641i	0.392271	+	0.919850i	$0.371690\pi$
$770$	−0.196045	+	0.339560i	−0.00706497	+	0.0122369i
$771$	8.20406	+	14.2099i	0.295462	+	0.511755i
$772$		−	44.5408i		−	1.60306i
$773$	−20.1471	+	11.6319i	−0.724640	+	0.418371i	−0.816458	−	0.577405i	$-0.804065\pi$
$773$	−20.1471	+	11.6319i	−0.724640	+	0.418371i	0.0918181	+	0.995776i	$0.470732\pi$
$774$	0.423339	−	0.244415i	0.0152166	−	0.00878531i
$775$		−	5.46410i		−	0.196276i
$776$	1.08861	+	1.88554i	0.0390790	+	0.0676868i
$777$	1.58754	−	2.74970i	0.0569526	−	0.0986448i
$778$	−2.02001	−	1.16625i	−0.0724209	−	0.0418122i
$779$	−8.46410			−0.303258
$780$		0			0
$781$	−68.7449			−2.45989
$782$	2.73556	+	1.57938i	0.0978235	+	0.0564784i
$783$	7.98989	−	13.8389i	0.285535	−	0.494562i
$784$	−12.7897	−	22.1524i	−0.456776	−	0.791159i
$785$			16.4329i			0.586514i
$786$	0.0534798	−	0.0308766i	0.00190756	−	0.00110133i
$787$	41.4942	−	23.9567i	1.47911	−	0.853963i	0.479387	−	0.877604i	$-0.340859\pi$
$787$	41.4942	−	23.9567i	1.47911	−	0.853963i	0.999721	+	0.0236408i	$0.00752582\pi$
$788$		−	1.25502i		−	0.0447081i
$789$	14.9274	+	25.8551i	0.531430	+	0.920464i
$790$	0.496329	−	0.859667i	0.0176586	−	0.0305856i
$791$	5.27814	+	3.04734i	0.187669	+	0.108351i
$792$	−2.04903			−0.0728090
$793$		0			0
$794$	−6.15865			−0.218562
$795$	2.16273	+	1.24865i	0.0767042	+	0.0442852i
$796$	2.99284	−	5.18374i	0.106078	−	0.183733i
$797$	−10.3476	−	17.9225i	−0.366530	−	0.634849i	0.622490	−	0.782627i	$-0.286121\pi$
$797$	−10.3476	−	17.9225i	−0.366530	−	0.634849i	−0.989020	+	0.147779i	$0.952788\pi$
$798$		−	0.264893i		−	0.00937712i
$799$	−36.5902	+	21.1253i	−1.29447	+	0.747361i
$800$	2.21004	−	1.27597i	0.0781367	−	0.0451122i
$801$			1.41735i			0.0500795i
$802$	−2.47305	−	4.28344i	−0.0873263	−	0.151254i
$803$	26.0244	−	45.0755i	0.918380	−	1.59068i
$804$	27.9460	+	16.1346i	0.985580	+	0.569025i
$805$	0.943307			0.0332472
$806$		0			0
$807$	−28.7361			−1.01156
$808$	−9.35788	−	5.40278i	−0.329209	−	0.190069i
$809$	−7.94574	+	13.7624i	−0.279357	+	0.483861i	−0.971225	−	0.238163i	$-0.923455\pi$
$809$	−7.94574	+	13.7624i	−0.279357	+	0.483861i	0.691868	+	0.722024i	$0.256788\pi$
$810$	−0.822599	−	1.42478i	−0.0289032	−	0.0500618i
$811$		−	23.8796i		−	0.838525i	−0.907865	−	0.419263i	$-0.862289\pi$
$811$		−	23.8796i		−	0.838525i	0.907865	−	0.419263i	$-0.137711\pi$
$812$	−1.63054	+	0.941391i	−0.0572206	+	0.0330363i
$813$	42.8183	−	24.7212i	1.50170	−	0.867009i
$814$		−	7.04768i		−	0.247021i
$815$	8.90361	+	15.4215i	0.311880	+	0.540192i
$816$	15.0438	−	26.0567i	0.526640	−	0.912167i
$817$	−9.94679	−	5.74278i	−0.347994	−	0.200915i
$818$	0.941956			0.0329347
$819$		0			0
$820$	7.28398			0.254368
$821$	−13.7782	−	7.95484i	−0.480862	−	0.277626i	0.239914	−	0.970794i	$-0.422881\pi$
$821$	−13.7782	−	7.95484i	−0.480862	−	0.277626i	−0.720776	+	0.693169i	$0.756214\pi$
$822$	3.16087	−	5.47478i	0.110248	−	0.190955i
$823$	−7.40573	−	12.8271i	−0.258147	−	0.447124i	0.707598	−	0.706615i	$-0.249779\pi$
$823$	−7.40573	−	12.8271i	−0.258147	−	0.447124i	−0.965746	+	0.259491i	$0.916445\pi$
$824$		−	13.0436i		−	0.454397i
$825$	7.44432	−	4.29798i	0.259178	−	0.149636i
$826$	−0.171134	+	0.0988040i	−0.00595450	+	0.00343783i
$827$		−	33.9498i		−	1.18055i	−0.807202	−	0.590275i	$-0.799019\pi$
$827$		−	33.9498i		−	1.18055i	0.807202	−	0.590275i	$-0.200981\pi$
$828$	1.21736	+	2.10853i	0.0423061	+	0.0732763i
$829$	11.6573	−	20.1910i	0.404875	−	0.701264i	−0.589432	−	0.807818i	$-0.700648\pi$
$829$	11.6573	−	20.1910i	0.404875	−	0.701264i	0.994307	+	0.106554i	$0.0339818\pi$
$830$	−0.811190	−	0.468341i	−0.0281568	−	0.0162563i
$831$	42.4124			1.47127
$832$		0			0
$833$	34.8910			1.20890
$834$	−3.64911	−	2.10682i	−0.126358	−	0.0729530i
$835$	−3.14683	+	5.45047i	−0.108900	+	0.188621i
$836$	11.8890	+	20.5924i	0.411190	+	0.712202i
$837$			30.0726i			1.03946i
$838$	−3.36970	+	1.94550i	−0.116404	+	0.0672061i
$839$	12.8111	−	7.39649i	0.442288	−	0.255355i	−0.262280	−	0.964992i	$-0.584474\pi$
$839$	12.8111	−	7.39649i	0.442288	−	0.255355i	0.704568	+	0.709637i	$0.251141\pi$
$840$			0.461557i			0.0159252i
$841$	10.2849	+	17.8140i	0.354652	+	0.614276i
$842$	−1.41465	+	2.45024i	−0.0487519	+	0.0844408i
$843$	−6.89809	−	3.98261i	−0.237583	−	0.137169i
$844$	−16.0050			−0.550915
$845$		0			0
$846$	0.805291			0.0276865
$847$	5.13789	+	2.96636i	0.176540	+	0.101925i
$848$	2.89711	−	5.01794i	0.0994872	−	0.172317i
$849$	10.0703	+	17.4423i	0.345612	+	0.598617i
$850$			1.11256i			0.0381605i
$851$	−14.6840	+	8.47780i	−0.503360	+	0.290615i
$852$	−34.6134	+	19.9841i	−1.18584	+	0.684643i
$853$			16.3452i			0.559650i	0.960051	+	0.279825i	$0.0902765\pi$
$853$			16.3452i			0.559650i	−0.960051	+	0.279825i	$0.909724\pi$
$854$	−0.514722	−	0.891525i	−0.0176134	−	0.0305073i
$855$	0.498239	−	0.862975i	0.0170394	−	0.0295131i
$856$	−9.82220	−	5.67085i	−0.335716	−	0.193826i
$857$	34.1418			1.16626			0.583132	−	0.812378i	$-0.301827\pi$
$857$	34.1418			1.16626			0.583132	+	0.812378i	$0.301827\pi$
$858$		0			0
$859$	−45.1996			−1.54219			−0.771096	−	0.636719i	$-0.780291\pi$
$859$	−45.1996			−1.54219			−0.771096	+	0.636719i	$0.780291\pi$
$860$	8.55995	+	4.94209i	0.291892	+	0.168524i
$861$	−0.992090	+	1.71835i	−0.0338103	+	0.0585612i
$862$	−1.04334	−	1.80712i	−0.0355364	−	0.0615508i
$863$			4.75058i			0.161712i	0.996726	+	0.0808559i	$0.0257653\pi$
$863$			4.75058i			0.161712i	−0.996726	+	0.0808559i	$0.974235\pi$
$864$	−12.1633	+	7.02250i	−0.413805	+	0.238910i
$865$	13.8349	−	7.98756i	0.470399	−	0.271585i
$866$		−	0.306745i		−	0.0104236i
$867$	6.91853	+	11.9832i	0.234966	+	0.406972i
$868$	1.77162	−	3.06854i	0.0601327	−	0.104153i
$869$	−21.0207	−	12.1363i	−0.713079	−	0.411696i
$870$	−1.02069			−0.0346048
$871$		0			0
$872$	−9.75140			−0.330224
$873$	−0.954282	−	0.550955i	−0.0322975	−	0.0186470i
$874$	−0.707294	+	1.22507i	−0.0239246	+	0.0414386i
$875$	0.166123	+	0.287734i	0.00561599	+	0.00972718i
$876$		−	30.2610i		−	1.02242i
$877$	1.95294	−	1.12753i	0.0659462	−	0.0380741i	−0.466664	−	0.884434i	$-0.654544\pi$
$877$	1.95294	−	1.12753i	0.0659462	−	0.0380741i	0.532611	+	0.846360i	$0.321211\pi$
$878$	0.791801	−	0.457146i	0.0267220	−	0.0154279i
$879$			27.0715i			0.913098i
$880$	−9.97212	−	17.2722i	−0.336160	−	0.582246i
$881$	−1.49152	+	2.58339i	−0.0502507	+	0.0870367i	−0.890057	−	0.455850i	$-0.849335\pi$
$881$	−1.49152	+	2.58339i	−0.0502507	+	0.0870367i	0.839806	+	0.542887i	$0.182669\pi$
$882$	−0.575922	−	0.332509i	−0.0193923	−	0.0111961i
$883$	−28.2874			−0.951947			−0.475973	−	0.879460i	$-0.657904\pi$
$883$	−28.2874			−0.951947			−0.475973	+	0.879460i	$0.657904\pi$
$884$		0			0
$885$	4.33225			0.145627
$886$	1.81610	+	1.04852i	0.0610130	+	0.0352259i
$887$	13.9908	−	24.2328i	0.469766	−	0.813658i	−0.529637	−	0.848225i	$-0.677672\pi$
$887$	13.9908	−	24.2328i	0.469766	−	0.813658i	0.999402	+	0.0345665i	$0.0110051\pi$
$888$	−4.14816	−	7.18483i	−0.139203	−	0.241107i
$889$		−	1.07647i		−	0.0361035i
$890$	0.613729	−	0.354337i	0.0205723	−	0.0118774i
$891$	−34.8390	+	20.1143i	−1.16715	+	0.673855i
$892$			19.9940i			0.669448i
$893$	−9.46058	−	16.3862i	−0.316586	−	0.548343i
$894$	−0.599451	+	1.03828i	−0.0200486	+	0.0347252i
$895$	−20.4533	−	11.8087i	−0.683678	−	0.394722i
$896$	2.19681			0.0733903
$897$		0			0
$898$	−4.77095			−0.159209
$899$	13.7394	+	7.93244i	0.458234	+	0.264562i
$900$	−0.428771	+	0.742653i	−0.0142924	+	0.0247551i
$901$	3.95174	+	6.84461i	0.131651	+	0.228027i
$902$			4.40426i			0.146646i
$903$	−2.33176	+	1.34624i	−0.0775960	+	0.0448001i
$904$	13.7915	−	7.96255i	0.458700	−	0.264830i
$905$		−	2.62590i		−	0.0872879i
$906$	−1.39938	−	2.42381i	−0.0464914	−	0.0805255i
$907$	8.27600	−	14.3344i	0.274800	−	0.475967i	−0.695285	−	0.718734i	$-0.744722\pi$
$907$	8.27600	−	14.3344i	0.274800	−	0.475967i	0.970085	+	0.242767i	$0.0780550\pi$
$908$	−11.9058	−	6.87383i	−0.395109	−	0.228116i
$909$	5.46876			0.181387
$910$		0			0
$911$	7.04863			0.233532			0.116766	−	0.993159i	$-0.462747\pi$
$911$	7.04863			0.233532			0.116766	+	0.993159i	$0.462747\pi$
$912$	11.6690	+	6.73710i	0.386399	+	0.223088i
$913$	−11.4519	+	19.8353i	−0.379004	+	0.656454i
$914$	−0.518746	−	0.898494i	−0.0171586	−	0.0297196i
$915$			22.5689i			0.746106i
$916$	−2.24632	+	1.29692i	−0.0742206	+	0.0428513i
$917$	0.0505443	−	0.0291818i	0.00166912	−	0.000963668i
$918$		−	6.12316i		−	0.202094i
$919$	−8.27188	−	14.3273i	−0.272864	−	0.472615i	0.696730	−	0.717334i	$-0.254638\pi$
$919$	−8.27188	−	14.3273i	−0.272864	−	0.472615i	−0.969594	+	0.244719i	$0.921304\pi$
$920$	1.23241	−	2.13459i	0.0406313	−	0.0703755i
$921$	5.96488	+	3.44383i	0.196550	+	0.113478i
$922$	−0.391374			−0.0128892
$923$		0			0
$924$	5.57412			0.183375
$925$	−5.17191	−	2.98601i	−0.170051	−	0.0981793i
$926$	0.747155	−	1.29411i	0.0245530	−	0.0425271i
$927$	3.30074	+	5.71704i	0.108410	+	0.187772i
$928$			7.40948i			0.243228i
$929$	29.3035	−	16.9184i	0.961416	−	0.555074i	0.0648073	−	0.997898i	$-0.479357\pi$
$929$	29.3035	−	16.9184i	0.961416	−	0.555074i	0.896609	+	0.442824i	$0.146023\pi$
$930$	1.66351	−	0.960431i	0.0545488	−	0.0314938i
$931$			15.6253i			0.512098i
$932$	−1.21736	−	2.10853i	−0.0398759	−	0.0690670i
$933$	1.78031	−	3.08359i	0.0582848	−	0.100952i
$934$	−3.46975	−	2.00326i	−0.113534	−	0.0655487i
$935$	27.2045			0.889681
$936$		0			0
$937$	−30.4606			−0.995104			−0.497552	−	0.867434i	$-0.665768\pi$
$937$	−30.4606			−0.995104			−0.497552	+	0.867434i	$0.665768\pi$
$938$	−0.653115	−	0.377076i	−0.0213250	−	0.0123120i
$939$	5.76780	−	9.99012i	0.188225	−	0.326015i
$940$	8.14153	+	14.1015i	0.265547	+	0.459941i
$941$		−	38.2101i		−	1.24561i	−0.782375	−	0.622807i	$-0.785992\pi$
$941$		−	38.2101i		−	1.24561i	0.782375	−	0.622807i	$-0.214008\pi$
$942$	−5.00289	+	2.88842i	−0.163003	+	0.0941098i
$943$	9.17637	−	5.29798i	0.298824	−	0.172526i
$944$		−	10.0516i		−	0.327153i
$945$	−0.914288	−	1.58359i	−0.0297418	−	0.0515143i
$946$	−2.98823	+	5.17577i	−0.0971558	+	0.168279i
$947$	45.4215	+	26.2241i	1.47600	+	0.852169i	0.999633	−	0.0270773i	$-0.00862003\pi$
$947$	45.4215	+	26.2241i	1.47600	+	0.852169i	0.476367	+	0.879247i	$0.341953\pi$
$948$	−14.1120			−0.458338
$949$		0			0
$950$	−0.498239			−0.0161650
$951$	−0.445737	−	0.257347i	−0.0144540	−	0.00834504i
$952$	−0.730368	+	1.26503i	−0.0236714	+	0.0410000i
$953$	19.8750	+	34.4245i	0.643814	+	1.11512i	0.984574	+	0.174969i	$0.0559824\pi$
$953$	19.8750	+	34.4245i	0.643814	+	1.11512i	−0.340760	+	0.940150i	$0.610684\pi$
$954$		−	0.150639i		−	0.00487711i
$955$	1.74575	−	1.00791i	0.0564912	−	0.0326152i
$956$	−16.8046	+	9.70215i	−0.543500	+	0.313790i
$957$			24.9581i			0.806782i
$958$	−3.86437	−	6.69329i	−0.124852	−	0.216250i
$959$	2.98737	−	5.17428i	0.0964673	−	0.167086i
$960$	−9.51343	−	5.49258i	−0.307045	−	0.177272i
$961$	1.14359			0.0368901
$962$		0			0
$963$	5.74011			0.184972
$964$	−38.1776	−	22.0418i	−1.22962	−	0.709920i
$965$	11.4105	−	19.7636i	0.367318	−	0.636214i
$966$	0.165806	+	0.287184i	0.00533472	+	0.00924001i
$967$			25.7857i			0.829214i	0.910001	+	0.414607i	$0.136081\pi$
$967$			25.7857i			0.829214i	−0.910001	+	0.414607i	$0.863919\pi$
$968$	13.4251	−	7.75097i	0.431498	−	0.249126i
$969$	−15.9168	+	9.18958i	−0.511322	+	0.295212i
$970$			0.550955i			0.0176901i
$971$	27.7626	+	48.0863i	0.890945	+	1.54316i	0.838744	+	0.544525i	$0.183290\pi$
$971$	27.7626	+	48.0863i	0.890945	+	1.54316i	0.0522005	+	0.998637i	$0.483377\pi$
$972$	4.41817	−	7.65249i	0.141713	−	0.245454i
$973$	−3.44882	−	1.99118i	−0.110564	−	0.0638342i
$974$	−2.26365			−0.0725321
$975$		0			0
$976$	52.3642			1.67614
$977$	35.0879	+	20.2580i	1.12256	+	0.648112i	0.942054	−	0.335461i	$-0.108892\pi$
$977$	35.0879	+	20.2580i	1.12256	+	0.648112i	0.180509	+	0.983573i	$0.442226\pi$
$978$	−3.12999	+	5.42130i	−0.100086	+	0.173354i
$979$	−8.66430	−	15.0070i	−0.276912	−	0.479626i
$980$		−	13.4467i		−	0.429540i
$981$	4.27405	−	2.46762i	0.136460	−	0.0787852i
$982$	1.77545	−	1.02506i	0.0566569	−	0.0327109i
$983$		−	34.8059i		−	1.11014i	−0.831805	−	0.555068i	$-0.812692\pi$
$983$		−	34.8059i		−	1.11014i	0.831805	−	0.555068i	$-0.187308\pi$
$984$	2.59229	+	4.48997i	0.0826390	+	0.143135i
$985$	0.321513	−	0.556877i	0.0102443	−	0.0177436i
$986$	−2.79751	−	1.61514i	−0.0890910	−	0.0514367i
$987$	−4.43555			−0.141185
$988$		0			0
$989$	14.3784			0.457208
$990$	−0.449045	−	0.259256i	−0.0142716	−	0.00823971i
$991$	−21.9427	+	38.0059i	−0.697034	+	1.20730i	0.272456	+	0.962168i	$0.412164\pi$
$991$	−21.9427	+	38.0059i	−0.697034	+	1.20730i	−0.969490	+	0.245130i	$0.921169\pi$
$992$	−6.97201	−	12.0759i	−0.221362	−	0.383410i
$993$		−	26.6145i		−	0.844584i
$994$	0.808936	−	0.467040i	0.0256579	−	0.0148136i
$995$	2.65596	−	1.53342i	0.0841997	−	0.0486127i
$996$			13.3163i			0.421942i
$997$	2.74569	+	4.75567i	0.0869568	+	0.150614i	0.906223	−	0.422799i	$-0.138952\pi$
$997$	2.74569	+	4.75567i	0.0869568	+	0.150614i	−0.819267	+	0.573413i	$0.805619\pi$
$998$	−2.62988	+	4.55508i	−0.0832474	+	0.144189i
$999$	28.4645	+	16.4340i	0.900577	+	0.519949i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.m.g.316.3		8
13.2	odd	12		845.2.e.m.146.3		8
13.3	even	3		65.2.m.a.36.2	✓	8
13.4	even	6		845.2.c.g.506.5		8
13.5	odd	4		845.2.e.m.191.3		8
13.6	odd	12		845.2.a.m.1.2		4
13.7	odd	12		845.2.a.l.1.3		4
13.8	odd	4		845.2.e.n.191.2		8
13.9	even	3		845.2.c.g.506.4		8
13.10	even	6	inner	845.2.m.g.361.3		8
13.11	odd	12		845.2.e.n.146.2		8
13.12	even	2		65.2.m.a.56.2	yes	8
39.20	even	12		7605.2.a.cj.1.2		4
39.29	odd	6		585.2.bu.c.361.3		8
39.32	even	12		7605.2.a.cf.1.3		4
39.38	odd	2		585.2.bu.c.316.3		8
52.3	odd	6		1040.2.da.b.881.2		8
52.51	odd	2		1040.2.da.b.641.2		8
65.3	odd	12		325.2.m.b.49.3		8
65.12	odd	4		325.2.m.b.199.3		8
65.19	odd	12		4225.2.a.bi.1.3		4
65.29	even	6		325.2.n.d.101.3		8
65.38	odd	4		325.2.m.c.199.2		8
65.42	odd	12		325.2.m.c.49.2		8
65.59	odd	12		4225.2.a.bl.1.2		4
65.64	even	2		325.2.n.d.251.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.m.a.36.2	✓	8	13.3	even	3
65.2.m.a.56.2	yes	8	13.12	even	2
325.2.m.b.49.3		8	65.3	odd	12
325.2.m.b.199.3		8	65.12	odd	4
325.2.m.c.49.2		8	65.42	odd	12
325.2.m.c.199.2		8	65.38	odd	4
325.2.n.d.101.3		8	65.29	even	6
325.2.n.d.251.3		8	65.64	even	2
585.2.bu.c.316.3		8	39.38	odd	2
585.2.bu.c.361.3		8	39.29	odd	6
845.2.a.l.1.3		4	13.7	odd	12
845.2.a.m.1.2		4	13.6	odd	12
845.2.c.g.506.4		8	13.9	even	3
845.2.c.g.506.5		8	13.4	even	6
845.2.e.m.146.3		8	13.2	odd	12
845.2.e.m.191.3		8	13.5	odd	4
845.2.e.n.146.2		8	13.11	odd	12
845.2.e.n.191.2		8	13.8	odd	4
845.2.m.g.316.3		8	1.1	even	1	trivial
845.2.m.g.361.3		8	13.10	even	6	inner
1040.2.da.b.641.2		8	52.51	odd	2
1040.2.da.b.881.2		8	52.3	odd	6
4225.2.a.bi.1.3		4	65.19	odd	12
4225.2.a.bl.1.2		4	65.59	odd	12
7605.2.a.cf.1.3		4	39.32	even	12
7605.2.a.cj.1.2		4	39.20	even	12

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:	\( N \)	\(=\)	\( 845 = 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	845.m (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.190254 + 0.109843i) q^{2} +(0.800098 - 1.38581i) q^{3} +(-0.975869 - 1.69025i) q^{4} -1.00000i q^{5} +(0.304444 - 0.175771i) q^{6} +(0.287734 - 0.166123i) q^{7} -0.868145i q^{8} +(0.219687 + 0.380509i) q^{9} +O(q^{10})\)	\(q+(0.190254 + 0.109843i) q^{2} +(0.800098 - 1.38581i) q^{3} +(-0.975869 - 1.69025i) q^{4} -1.00000i q^{5} +(0.304444 - 0.175771i) q^{6} +(0.287734 - 0.166123i) q^{7} -0.868145i q^{8} +(0.219687 + 0.380509i) q^{9} +(0.109843 - 0.190254i) q^{10} +(-4.65213 - 2.68591i) q^{11} -3.12316 q^{12} +0.0729902 q^{14} +(-1.38581 - 0.800098i) q^{15} +(-1.85638 + 3.21534i) q^{16} +(-2.53215 - 4.38581i) q^{17} +0.0965246i q^{18} +(1.96410 - 1.13397i) q^{19} +(-1.69025 + 0.975869i) q^{20} -0.531659i q^{21} +(-0.590059 - 1.02201i) q^{22} +(-1.41959 + 2.45880i) q^{23} +(-1.20308 - 0.694601i) q^{24} -1.00000 q^{25} +5.50367 q^{27} +(-0.561581 - 0.324229i) q^{28} +(1.45174 - 2.51448i) q^{29} +(-0.175771 - 0.304444i) q^{30} +5.46410i q^{31} +(-2.21004 + 1.27597i) q^{32} +(-7.44432 + 4.29798i) q^{33} -1.11256i q^{34} +(-0.166123 - 0.287734i) q^{35} +(0.428771 - 0.742653i) q^{36} +(5.17191 + 2.98601i) q^{37} +0.498239 q^{38} -0.868145 q^{40} +(-3.23205 - 1.86603i) q^{41} +(0.0583993 - 0.101151i) q^{42} +(-2.53215 - 4.38581i) q^{43} +10.4844i q^{44} +(0.380509 - 0.219687i) q^{45} +(-0.540166 + 0.311865i) q^{46} -8.34285i q^{47} +(2.97057 + 5.14517i) q^{48} +(-3.44481 + 5.96658i) q^{49} +(-0.190254 - 0.109843i) q^{50} -8.10387 q^{51} -1.56063 q^{53} +(1.04710 + 0.604542i) q^{54} +(-2.68591 + 4.65213i) q^{55} +(-0.144219 - 0.249795i) q^{56} -3.62916i q^{57} +(0.552399 - 0.318928i) q^{58} +(-2.34461 + 1.35366i) q^{59} +3.12316i q^{60} +(-7.05193 - 12.2143i) q^{61} +(-0.600196 + 1.03957i) q^{62} +(0.126423 + 0.0729902i) q^{63} +6.86488 q^{64} -1.88842 q^{66} +(-8.94799 - 5.16612i) q^{67} +(-4.94209 + 8.55995i) q^{68} +(2.27162 + 3.93456i) q^{69} -0.0729902i q^{70} +(11.0828 - 6.39866i) q^{71} +(0.330337 - 0.190720i) q^{72} +9.68922i q^{73} +(0.655986 + 1.13620i) q^{74} +(-0.800098 + 1.38581i) q^{75} +(-3.83341 - 2.21322i) q^{76} -1.78477 q^{77} +4.51851 q^{79} +(3.21534 + 1.85638i) q^{80} +(3.74441 - 6.48552i) q^{81} +(-0.409941 - 0.710039i) q^{82} -4.26371i q^{83} +(-0.898640 + 0.518830i) q^{84} +(-4.38581 + 2.53215i) q^{85} -1.11256i q^{86} +(-2.32306 - 4.02367i) q^{87} +(-2.33176 + 4.03872i) q^{88} +(2.79366 + 1.61292i) q^{89} +0.0965246 q^{90} +5.54133 q^{92} +(7.57221 + 4.37182i) q^{93} +(0.916407 - 1.58726i) q^{94} +(-1.13397 - 1.96410i) q^{95} +4.08359i q^{96} +(-2.17191 + 1.25396i) q^{97} +(-1.31078 + 0.756779i) q^{98} -2.36023i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{3} + 2 q^{4} + 18 q^{6} + 6 q^{7} - 4 q^{9}+O(q^{10}) \) 8 * q + 2 * q^3 + 2 * q^4 + 18 * q^6 + 6 * q^7 - 4 * q^9	\( 8 q + 2 q^{3} + 2 q^{4} + 18 q^{6} + 6 q^{7} - 4 q^{9} - 2 q^{10} + 20 q^{12} + 4 q^{14} + 6 q^{15} - 2 q^{16} - 2 q^{17} - 12 q^{19} - 12 q^{20} - 12 q^{22} - 10 q^{23} + 12 q^{24} - 8 q^{25} - 4 q^{27} + 18 q^{28} - 8 q^{29} + 4 q^{30} - 6 q^{32} - 42 q^{33} + 10 q^{35} + 20 q^{36} - 6 q^{37} - 16 q^{38} - 12 q^{40} - 12 q^{41} + 4 q^{42} - 2 q^{43} + 42 q^{46} + 28 q^{48} + 12 q^{49} - 8 q^{51} - 24 q^{53} - 18 q^{54} + 12 q^{56} - 36 q^{58} + 12 q^{59} - 28 q^{61} + 4 q^{62} + 24 q^{63} - 8 q^{64} + 12 q^{66} - 6 q^{67} - 14 q^{68} - 16 q^{69} + 48 q^{72} + 10 q^{74} - 2 q^{75} - 54 q^{76} - 36 q^{77} - 16 q^{79} + 8 q^{81} + 4 q^{82} + 30 q^{84} - 18 q^{85} + 22 q^{87} - 18 q^{88} - 24 q^{89} + 40 q^{90} + 44 q^{92} + 32 q^{94} - 16 q^{95} + 30 q^{97} - 72 q^{98}+O(q^{100}) \) 8 * q + 2 * q^3 + 2 * q^4 + 18 * q^6 + 6 * q^7 - 4 * q^9 - 2 * q^10 + 20 * q^12 + 4 * q^14 + 6 * q^15 - 2 * q^16 - 2 * q^17 - 12 * q^19 - 12 * q^20 - 12 * q^22 - 10 * q^23 + 12 * q^24 - 8 * q^25 - 4 * q^27 + 18 * q^28 - 8 * q^29 + 4 * q^30 - 6 * q^32 - 42 * q^33 + 10 * q^35 + 20 * q^36 - 6 * q^37 - 16 * q^38 - 12 * q^40 - 12 * q^41 + 4 * q^42 - 2 * q^43 + 42 * q^46 + 28 * q^48 + 12 * q^49 - 8 * q^51 - 24 * q^53 - 18 * q^54 + 12 * q^56 - 36 * q^58 + 12 * q^59 - 28 * q^61 + 4 * q^62 + 24 * q^63 - 8 * q^64 + 12 * q^66 - 6 * q^67 - 14 * q^68 - 16 * q^69 + 48 * q^72 + 10 * q^74 - 2 * q^75 - 54 * q^76 - 36 * q^77 - 16 * q^79 + 8 * q^81 + 4 * q^82 + 30 * q^84 - 18 * q^85 + 22 * q^87 - 18 * q^88 - 24 * q^89 + 40 * q^90 + 44 * q^92 + 32 * q^94 - 16 * q^95 + 30 * q^97 - 72 * q^98

Introduction

L-functions

Modular forms

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Database

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