LMFDB - Embedded newform 1456.2.r.p.417.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1456,2,Mod(417,1456)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1456.417"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1456, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 4, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1456 = 2^{4} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1456.r (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [10,0,0,0,-2,0,-1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$11.6262185343$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + 8x^{8} + 7x^{7} + 41x^{6} + 18x^{5} + 58x^{4} + 28x^{3} + 64x^{2} + 16x + 4 $ x^10 - x^9 + 8x^8 + 7x^7 + 41x^6 + 18x^5 + 58x^4 + 28x^3 + 64x^2 + 16x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			417.5
Root			$-0.606661 - 1.05077i$ of defining polynomial
Character	$\chi$	$=$	1456.417
Dual form			1456.2.r.p.625.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.23721 - 2.14292i) q^{3} +(1.06140 + 1.83839i) q^{5} +(-2.63169 - 0.272389i) q^{7} +(-1.56140 - 2.70442i) q^{9} +(2.39448 - 4.14736i) q^{11} +1.00000 q^{13} +5.25271 q^{15} +(1.88914 - 3.27208i) q^{17} +(-1.78362 - 3.08931i) q^{19} +(-3.83967 + 5.30250i) q^{21} +(2.23721 + 3.87497i) q^{23} +(0.246870 - 0.427591i) q^{25} -0.303848 q^{27} -5.90107 q^{29} +(-1.88558 + 3.26592i) q^{31} +(-5.92496 - 10.2623i) q^{33} +(-2.29251 - 5.12720i) q^{35} +(-2.81285 - 4.87200i) q^{37} +(1.23721 - 2.14292i) q^{39} +10.3948 q^{41} -3.40733 q^{43} +(3.31453 - 5.74093i) q^{45} +(-3.55438 - 6.15636i) q^{47} +(6.85161 + 1.43369i) q^{49} +(-4.67454 - 8.09654i) q^{51} +(6.19003 - 10.7214i) q^{53} +10.1660 q^{55} -8.82686 q^{57} +(2.39448 - 4.14736i) q^{59} +(-1.60348 - 2.77732i) q^{61} +(3.37246 + 7.54251i) q^{63} +(1.06140 + 1.83839i) q^{65} +(-1.44978 + 2.51109i) q^{67} +11.0717 q^{69} +2.53876 q^{71} +(-3.85035 + 6.66901i) q^{73} +(-0.610862 - 1.05804i) q^{75} +(-7.43122 + 10.2623i) q^{77} +(-2.58925 - 4.48471i) q^{79} +(4.30827 - 7.46214i) q^{81} -3.46731 q^{83} +8.02051 q^{85} +(-7.30089 + 12.6455i) q^{87} +(-1.83216 - 3.17339i) q^{89} +(-2.63169 - 0.272389i) q^{91} +(4.66574 + 8.08129i) q^{93} +(3.78625 - 6.55798i) q^{95} -5.40733 q^{97} -14.9549 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 2 q^{5} - q^{7} - 3 q^{9} + 11 q^{11} + 10 q^{13} + 5 q^{17} + 9 q^{19} + 2 q^{21} + 10 q^{23} - 9 q^{25} - 6 q^{29} - 6 q^{31} - 8 q^{33} + 4 q^{35} - 4 q^{37} + 28 q^{41} - 4 q^{43} + 32 q^{45}+ \cdots - 22 q^{99}+O(q^{100}) $ 10 * q - 2 * q^5 - q^7 - 3 * q^9 + 11 * q^11 + 10 * q^13 + 5 * q^17 + 9 * q^19 + 2 * q^21 + 10 * q^23 - 9 * q^25 - 6 * q^29 - 6 * q^31 - 8 * q^33 + 4 * q^35 - 4 * q^37 + 28 * q^41 - 4 * q^43 + 32 * q^45 + q^47 - 11 * q^49 - 8 * q^51 - 17 * q^53 - 32 * q^57 + 11 * q^59 + 11 * q^61 - 5 * q^63 - 2 * q^65 + 13 * q^67 + 36 * q^69 - 30 * q^71 - 20 * q^75 - 46 * q^77 + 2 * q^79 + 19 * q^81 - 12 * q^83 - 44 * q^85 - 8 * q^87 + 4 * q^89 - q^91 - 18 * q^93 - 12 * q^95 - 24 * q^97 - 22 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1456\mathbb{Z}\right)^\times$.

$n$	$561$	$911$	$1093$	$1249$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.23721	−	2.14292i	0.714306	−	1.23721i	−0.248921	−	0.968524i	$-0.580076\pi$
$3$	1.23721	−	2.14292i	0.714306	−	1.23721i	0.963227	−	0.268690i	$-0.0865908\pi$
$4$		0			0
$5$	1.06140	+	1.83839i	0.474671	+	0.822155i	0.999579	−	0.0290040i	$-0.00923354\pi$
$5$	1.06140	+	1.83839i	0.474671	+	0.822155i	−0.524908	+	0.851159i	$0.675900\pi$
$6$		0			0
$7$	−2.63169	−	0.272389i	−0.994686	−	0.102953i
$7$	−2.63169	−	0.272389i	−0.994686	−	0.102953i
$8$		0			0
$9$	−1.56140	−	2.70442i	−0.520466	−	0.901473i
$10$		0			0
$11$	2.39448	−	4.14736i	0.721962	−	1.25048i	−0.238250	−	0.971204i	$-0.576574\pi$
$11$	2.39448	−	4.14736i	0.721962	−	1.25048i	0.960212	−	0.279272i	$-0.0900930\pi$
$12$		0			0
$13$	1.00000			0.277350
$13$	1.00000			0.277350
$14$		0			0
$15$	5.25271			1.35624
$16$		0			0
$17$	1.88914	−	3.27208i	0.458183	−	0.793597i	−0.540682	−	0.841227i	$-0.681834\pi$
$17$	1.88914	−	3.27208i	0.458183	−	0.793597i	0.998865	+	0.0476304i	$0.0151670\pi$
$18$		0			0
$19$	−1.78362	−	3.08931i	−0.409190	−	0.708737i	0.585609	−	0.810593i	$-0.300855\pi$
$19$	−1.78362	−	3.08931i	−0.409190	−	0.708737i	−0.994799	+	0.101856i	$0.967522\pi$
$20$		0			0
$21$	−3.83967	+	5.30250i	−0.837886	+	1.15710i
$22$		0			0
$23$	2.23721	+	3.87497i	0.466491	+	0.807987i	0.999267	−	0.0382695i	$-0.0121845\pi$
$23$	2.23721	+	3.87497i	0.466491	+	0.807987i	−0.532776	+	0.846256i	$0.678851\pi$
$24$		0			0
$25$	0.246870	−	0.427591i	0.0493740	−	0.0855182i
$26$		0			0
$27$	−0.303848			−0.0584757
$28$		0			0
$29$	−5.90107			−1.09580			−0.547901	−	0.836543i	$-0.684573\pi$
$29$	−5.90107			−1.09580			−0.547901	+	0.836543i	$0.684573\pi$
$30$		0			0
$31$	−1.88558	+	3.26592i	−0.338660	+	0.586577i	−0.984181	−	0.177166i	$-0.943307\pi$
$31$	−1.88558	+	3.26592i	−0.338660	+	0.586577i	0.645521	+	0.763743i	$0.276640\pi$
$32$		0			0
$33$	−5.92496	−	10.2623i	−1.03140	−	1.78644i
$34$		0			0
$35$	−2.29251	−	5.12720i	−0.387505	−	0.866655i
$36$		0			0
$37$	−2.81285	−	4.87200i	−0.462429	−	0.800951i	0.536652	−	0.843804i	$-0.319689\pi$
$37$	−2.81285	−	4.87200i	−0.462429	−	0.800951i	−0.999081	+	0.0428524i	$0.986355\pi$
$38$		0			0
$39$	1.23721	−	2.14292i	0.198113	−	0.343141i
$40$		0			0
$41$	10.3948			1.62340			0.811698	−	0.584077i	$-0.198543\pi$
$41$	10.3948			1.62340			0.811698	+	0.584077i	$0.198543\pi$
$42$		0			0
$43$	−3.40733			−0.519613			−0.259807	−	0.965661i	$-0.583659\pi$
$43$	−3.40733			−0.519613			−0.259807	+	0.965661i	$0.583659\pi$
$44$		0			0
$45$	3.31453	−	5.74093i	0.494101	−	0.855807i
$46$		0			0
$47$	−3.55438	−	6.15636i	−0.518459	−	0.897998i	−0.999770	−	0.0214479i	$-0.993172\pi$
$47$	−3.55438	−	6.15636i	−0.518459	−	0.897998i	0.481311	−	0.876550i	$-0.340161\pi$
$48$		0			0
$49$	6.85161	+	1.43369i	0.978801	+	0.204813i
$50$		0			0
$51$	−4.67454	−	8.09654i	−0.654566	−	1.13374i
$52$		0			0
$53$	6.19003	−	10.7214i	0.850266	−	1.47270i	−0.0307027	−	0.999529i	$-0.509774\pi$
$53$	6.19003	−	10.7214i	0.850266	−	1.47270i	0.880968	−	0.473175i	$-0.156892\pi$
$54$		0			0
$55$	10.1660			1.37078
$56$		0			0
$57$	−8.82686			−1.16915
$58$		0			0
$59$	2.39448	−	4.14736i	0.311734	−	0.539940i	−0.667003	−	0.745055i	$-0.732423\pi$
$59$	2.39448	−	4.14736i	0.311734	−	0.539940i	0.978738	+	0.205115i	$0.0657567\pi$
$60$		0			0
$61$	−1.60348	−	2.77732i	−0.205305	−	0.355599i	0.744925	−	0.667148i	$-0.232485\pi$
$61$	−1.60348	−	2.77732i	−0.205305	−	0.355599i	−0.950230	+	0.311550i	$0.899152\pi$
$62$		0			0
$63$	3.37246	+	7.54251i	0.424890	+	0.950267i
$64$		0			0
$65$	1.06140	+	1.83839i	0.131650	+	0.228025i
$66$		0			0
$67$	−1.44978	+	2.51109i	−0.177118	+	0.306778i	−0.940892	−	0.338706i	$-0.890011\pi$
$67$	−1.44978	+	2.51109i	−0.177118	+	0.306778i	0.763774	+	0.645484i	$0.223344\pi$
$68$		0			0
$69$	11.0717			1.33287
$70$		0			0
$71$	2.53876			0.301295			0.150648	−	0.988588i	$-0.451864\pi$
$71$	2.53876			0.301295			0.150648	+	0.988588i	$0.451864\pi$
$72$		0			0
$73$	−3.85035	+	6.66901i	−0.450650	+	0.780548i	−0.998426	−	0.0560762i	$-0.982141\pi$
$73$	−3.85035	+	6.66901i	−0.450650	+	0.780548i	0.547777	+	0.836625i	$0.315474\pi$
$74$		0			0
$75$	−0.610862	−	1.05804i	−0.0705362	−	0.122172i
$76$		0			0
$77$	−7.43122	+	10.2623i	−0.846867	+	1.16950i
$78$		0			0
$79$	−2.58925	−	4.48471i	−0.291313	−	0.504569i	0.682807	−	0.730598i	$-0.260759\pi$
$79$	−2.58925	−	4.48471i	−0.291313	−	0.504569i	−0.974120	+	0.226029i	$0.927425\pi$
$80$		0			0
$81$	4.30827	−	7.46214i	0.478696	−	0.829126i
$82$		0			0
$83$	−3.46731			−0.380587			−0.190294	−	0.981727i	$-0.560944\pi$
$83$	−3.46731			−0.380587			−0.190294	+	0.981727i	$0.560944\pi$
$84$		0			0
$85$	8.02051			0.869946
$86$		0			0
$87$	−7.30089	+	12.6455i	−0.782738	+	1.35574i
$88$		0			0
$89$	−1.83216	−	3.17339i	−0.194209	−	0.336379i	0.752432	−	0.658670i	$-0.228881\pi$
$89$	−1.83216	−	3.17339i	−0.194209	−	0.336379i	−0.946641	+	0.322291i	$0.895547\pi$
$90$		0			0
$91$	−2.63169	−	0.272389i	−0.275876	−	0.0285541i
$92$		0			0
$93$	4.66574	+	8.08129i	0.483814	+	0.837991i
$94$		0			0
$95$	3.78625	−	6.55798i	0.388461	−	0.672835i
$96$		0			0
$97$	−5.40733			−0.549031			−0.274516	−	0.961583i	$-0.588518\pi$
$97$	−5.40733			−0.549031			−0.274516	+	0.961583i	$0.588518\pi$
$98$		0			0
$99$	−14.9549			−1.50303
$100$		0			0
$101$	−4.65862	+	8.06897i	−0.463550	+	0.802892i	−0.999135	−	0.0415891i	$-0.986758\pi$
$101$	−4.65862	+	8.06897i	−0.463550	+	0.802892i	0.535585	+	0.844482i	$0.320091\pi$
$102$		0			0
$103$	3.65318	+	6.32749i	0.359958	+	0.623466i	0.987953	−	0.154751i	$-0.0494576\pi$
$103$	3.65318	+	6.32749i	0.359958	+	0.623466i	−0.627995	+	0.778217i	$0.716124\pi$
$104$		0			0
$105$	−13.8235	−	1.43078i	−1.34904	−	0.139630i
$106$		0			0
$107$	3.37365	+	5.84333i	0.326143	+	0.564896i	0.981743	−	0.190212i	$-0.0609176\pi$
$107$	3.37365	+	5.84333i	0.326143	+	0.564896i	−0.655600	+	0.755108i	$0.727584\pi$
$108$		0			0
$109$	−2.08822	+	3.61691i	−0.200016	+	0.346437i	−0.948533	−	0.316678i	$-0.897433\pi$
$109$	−2.08822	+	3.61691i	−0.200016	+	0.346437i	0.748518	+	0.663115i	$0.230766\pi$
$110$		0			0
$111$	−13.9204			−1.32126
$112$		0			0
$113$	5.90107			0.555126			0.277563	−	0.960707i	$-0.410473\pi$
$113$	5.90107			0.555126			0.277563	+	0.960707i	$0.410473\pi$
$114$		0			0
$115$	−4.74915	+	8.22577i	−0.442860	+	0.767057i
$116$		0			0
$117$	−1.56140	−	2.70442i	−0.144351	−	0.250024i
$118$		0			0
$119$	−5.86291	+	8.09654i	−0.537452	+	0.742208i
$120$		0			0
$121$	−5.96705	−	10.3352i	−0.542459	−	0.939567i
$122$		0			0
$123$	12.8606	−	22.2752i	1.15960	−	2.00849i
$124$		0			0
$125$	11.6621			1.04309
$126$		0			0
$127$	10.5268			0.934100			0.467050	−	0.884231i	$-0.345317\pi$
$127$	10.5268			0.934100			0.467050	+	0.884231i	$0.345317\pi$
$128$		0			0
$129$	−4.21560	+	7.30163i	−0.371163	+	0.642873i
$130$		0			0
$131$	2.71204	+	4.69740i	0.236952	+	0.410413i	0.959838	−	0.280554i	$-0.0905182\pi$
$131$	2.71204	+	4.69740i	0.236952	+	0.410413i	−0.722886	+	0.690967i	$0.757185\pi$
$132$		0			0
$133$	3.85243	+	8.61596i	0.334048	+	0.747099i
$134$		0			0
$135$	−0.322504	−	0.558593i	−0.0277567	−	0.0480761i
$136$		0			0
$137$	−11.1224	+	19.2645i	−0.950248	+	1.64588i	−0.205363	+	0.978686i	$0.565837\pi$
$137$	−11.1224	+	19.2645i	−0.950248	+	1.64588i	−0.744886	+	0.667192i	$0.767496\pi$
$138$		0			0
$139$	4.00000			0.339276			0.169638	−	0.985506i	$-0.445740\pi$
$139$	4.00000			0.339276			0.169638	+	0.985506i	$0.445740\pi$
$140$		0			0
$141$	−17.5901			−1.48135
$142$		0			0
$143$	2.39448	−	4.14736i	0.200236	−	0.346819i
$144$		0			0
$145$	−6.26338	−	10.8485i	−0.520146	−	0.900919i
$146$		0			0
$147$	11.5492	−	12.9087i	0.952561	−	1.06469i
$148$		0			0
$149$	−1.47736	−	2.55887i	−0.121030	−	0.209630i	0.799144	−	0.601140i	$-0.205286\pi$
$149$	−1.47736	−	2.55887i	−0.121030	−	0.209630i	−0.920174	+	0.391509i	$0.871953\pi$
$150$		0			0
$151$	−9.27736	+	16.0689i	−0.754981	+	1.30766i	0.190403	+	0.981706i	$0.439020\pi$
$151$	−9.27736	+	16.0689i	−0.754981	+	1.30766i	−0.945384	+	0.325959i	$0.894313\pi$
$152$		0			0
$153$	−11.7988			−0.953875
$154$		0			0
$155$	−8.00541			−0.643010
$156$		0			0
$157$	4.89982	−	8.48673i	0.391048	−	0.677315i	−0.601540	−	0.798843i	$-0.705446\pi$
$157$	4.89982	−	8.48673i	0.391048	−	0.677315i	0.992588	+	0.121528i	$0.0387793\pi$
$158$		0			0
$159$	−15.3168	−	26.5294i	−1.21470	−	2.10392i
$160$		0			0
$161$	−4.83216	−	10.8071i	−0.380828	−	0.851720i
$162$		0			0
$163$	6.91709	+	11.9808i	0.541788	+	0.938405i	0.998801	+	0.0489451i	$0.0155859\pi$
$163$	6.91709	+	11.9808i	0.541788	+	0.938405i	−0.457013	+	0.889460i	$0.651081\pi$
$164$		0			0
$165$	12.5775	−	21.7848i	0.979156	−	1.69595i
$166$		0			0
$167$	−17.3534			−1.34285			−0.671424	−	0.741073i	$-0.734317\pi$
$167$	−17.3534			−1.34285			−0.671424	+	0.741073i	$0.734317\pi$
$168$		0			0
$169$	1.00000			0.0769231
$170$		0			0
$171$	−5.56987	+	9.64730i	−0.425939	+	0.737747i
$172$		0			0
$173$	1.48069	+	2.56463i	0.112575	+	0.194985i	0.916808	−	0.399329i	$-0.130757\pi$
$173$	1.48069	+	2.56463i	0.112575	+	0.194985i	−0.804233	+	0.594314i	$0.797424\pi$
$174$		0			0
$175$	−0.766156	+	1.05804i	−0.0579160	+	0.0799806i
$176$		0			0
$177$	−5.92496	−	10.2623i	−0.445348	−	0.771365i
$178$		0			0
$179$	−2.83444	+	4.90939i	−0.211856	+	0.366945i	−0.952295	−	0.305178i	$-0.901284\pi$
$179$	−2.83444	+	4.90939i	−0.211856	+	0.366945i	0.740440	+	0.672123i	$0.234617\pi$
$180$		0			0
$181$	7.17645			0.533421			0.266711	−	0.963777i	$-0.414063\pi$
$181$	7.17645			0.533421			0.266711	+	0.963777i	$0.414063\pi$
$182$		0			0
$183$	−7.93541			−0.586603
$184$		0			0
$185$	5.97110	−	10.3423i	0.439004	−	0.760377i
$186$		0			0
$187$	−9.04700	−	15.6699i	−0.661582	−	1.14589i
$188$		0			0
$189$	0.799636	+	0.0827650i	0.0581649	+	0.00602027i
$190$		0			0
$191$	5.94088	+	10.2899i	0.429867	+	0.744552i	0.996861	−	0.0791703i	$-0.0252271\pi$
$191$	5.94088	+	10.2899i	0.429867	+	0.744552i	−0.566994	+	0.823722i	$0.691894\pi$
$192$		0			0
$193$	−11.4851	+	19.8927i	−0.826714	+	1.43191i	0.0738876	+	0.997267i	$0.476459\pi$
$193$	−11.4851	+	19.8927i	−0.826714	+	1.43191i	−0.900602	+	0.434645i	$0.856874\pi$
$194$		0			0
$195$	5.25271			0.376154
$196$		0			0
$197$	16.9216			1.20561			0.602806	−	0.797888i	$-0.294049\pi$
$197$	16.9216			1.20561			0.602806	+	0.797888i	$0.294049\pi$
$198$		0			0
$199$	5.02953	−	8.71140i	0.356534	−	0.617535i	−0.630845	−	0.775909i	$-0.717292\pi$
$199$	5.02953	−	8.71140i	0.356534	−	0.617535i	0.987379	+	0.158374i	$0.0506251\pi$
$200$		0			0
$201$	3.58737	+	6.21351i	0.253034	+	0.438267i
$202$		0			0
$203$	15.5298	+	1.60739i	1.08998	+	0.112817i
$204$		0			0
$205$	11.0330	+	19.1098i	0.770580	+	1.33468i
$206$		0			0
$207$	6.98636	−	12.1007i	0.485586	−	0.841059i
$208$		0			0
$209$	−17.0833			−1.18168
$210$		0			0
$211$	24.4609			1.68396			0.841978	−	0.539512i	$-0.181391\pi$
$211$	24.4609			1.68396			0.841978	+	0.539512i	$0.181391\pi$
$212$		0			0
$213$	3.14099	−	5.44035i	0.215217	−	0.372767i
$214$		0			0
$215$	−3.61654	−	6.26402i	−0.246646	−	0.427203i
$216$		0			0
$217$	5.85187	−	8.08129i	0.397251	−	0.548594i
$218$		0			0
$219$	9.52742	+	16.5020i	0.643804	+	1.11510i
$220$		0			0
$221$	1.88914	−	3.27208i	0.127077	−	0.220104i
$222$		0			0
$223$	29.2625			1.95956			0.979780	−	0.200076i	$-0.0641188\pi$
$223$	29.2625			1.95956			0.979780	+	0.200076i	$0.0641188\pi$
$224$		0			0
$225$	−1.54185			−0.102790
$226$		0			0
$227$	−5.03685	+	8.72408i	−0.334307	+	0.579038i	−0.983352	−	0.181713i	$-0.941836\pi$
$227$	−5.03685	+	8.72408i	−0.334307	+	0.579038i	0.649044	+	0.760751i	$0.275169\pi$
$228$		0			0
$229$	5.56997	+	9.64748i	0.368074	+	0.637523i	0.989264	−	0.146137i	$-0.0466839\pi$
$229$	5.56997	+	9.64748i	0.368074	+	0.637523i	−0.621190	+	0.783660i	$0.713351\pi$
$230$		0			0
$231$	12.7973	+	28.6212i	0.842003	+	1.88314i
$232$		0			0
$233$	8.54166	+	14.7946i	0.559583	+	0.969226i	0.997531	+	0.0702257i	$0.0223720\pi$
$233$	8.54166	+	14.7946i	0.559583	+	0.969226i	−0.437948	+	0.899000i	$0.644295\pi$
$234$		0			0
$235$	7.54522	−	13.0687i	0.492196	−	0.852508i
$236$		0			0
$237$	−12.8138			−0.832347
$238$		0			0
$239$	−6.92142			−0.447710			−0.223855	−	0.974622i	$-0.571864\pi$
$239$	−6.92142			−0.447710			−0.223855	+	0.974622i	$0.571864\pi$
$240$		0			0
$241$	−3.24812	+	5.62592i	−0.209230	+	0.362397i	−0.951472	−	0.307735i	$-0.900429\pi$
$241$	−3.24812	+	5.62592i	−0.209230	+	0.362397i	0.742242	+	0.670132i	$0.233762\pi$
$242$		0			0
$243$	−11.1163	−	19.2539i	−0.713109	−	1.23514i
$244$		0			0
$245$	4.63660	+	14.1177i	0.296221	+	0.901945i
$246$		0			0
$247$	−1.78362	−	3.08931i	−0.113489	−	0.196568i
$248$		0			0
$249$	−4.28981	+	7.43017i	−0.271856	+	0.470868i
$250$		0			0
$251$	9.86804			0.622865			0.311433	−	0.950268i	$-0.399191\pi$
$251$	9.86804			0.622865			0.311433	+	0.950268i	$0.399191\pi$
$252$		0			0
$253$	21.4278			1.34716
$254$		0			0
$255$	9.92309	−	17.1873i	0.621408	−	1.07631i
$256$		0			0
$257$	−3.43234	−	5.94499i	−0.214104	−	0.370838i	0.738891	−	0.673825i	$-0.235350\pi$
$257$	−3.43234	−	5.94499i	−0.214104	−	0.370838i	−0.952995	+	0.302986i	$0.902016\pi$
$258$		0			0
$259$	6.07547	+	13.5878i	0.377511	+	0.844304i
$260$		0			0
$261$	9.21392	+	15.9590i	0.570327	+	0.987836i
$262$		0			0
$263$	−0.0632753	+	0.109596i	−0.00390172	+	0.00675798i	−0.867970	−	0.496617i	$-0.834575\pi$
$263$	−0.0632753	+	0.109596i	−0.00390172	+	0.00675798i	0.864068	+	0.503375i	$0.167909\pi$
$264$		0			0
$265$	26.2803			1.61439
$266$		0			0
$267$	−9.06710			−0.554897
$268$		0			0
$269$	2.12154	−	3.67462i	0.129353	−	0.224045i	−0.794073	−	0.607822i	$-0.792043\pi$
$269$	2.12154	−	3.67462i	0.129353	−	0.224045i	0.923426	+	0.383777i	$0.125377\pi$
$270$		0			0
$271$	0.783616	+	1.35726i	0.0476013	+	0.0824479i	0.888844	−	0.458209i	$-0.151509\pi$
$271$	0.783616	+	1.35726i	0.0476013	+	0.0824479i	−0.841243	+	0.540657i	$0.818176\pi$
$272$		0			0
$273$	−3.83967	+	5.30250i	−0.232388	+	0.320922i
$274$		0			0
$275$	−1.18225	−	2.04771i	−0.0712923	−	0.123482i
$276$		0			0
$277$	6.37260	−	11.0377i	0.382892	−	0.663189i	−0.608582	−	0.793491i	$-0.708261\pi$
$277$	6.37260	−	11.0377i	0.382892	−	0.663189i	0.991474	+	0.130302i	$0.0415947\pi$
$278$		0			0
$279$	11.7766			0.705045
$280$		0			0
$281$	4.62986			0.276194			0.138097	−	0.990419i	$-0.455901\pi$
$281$	4.62986			0.276194			0.138097	+	0.990419i	$0.455901\pi$
$282$		0			0
$283$	1.82416	−	3.15954i	0.108435	−	0.187815i	−0.806701	−	0.590959i	$-0.798749\pi$
$283$	1.82416	−	3.15954i	0.108435	−	0.187815i	0.915136	+	0.403144i	$0.132083\pi$
$284$		0			0
$285$	−9.36881	−	16.2273i	−0.554960	−	0.961220i
$286$		0			0
$287$	−27.3559	−	2.83143i	−1.61477	−	0.167134i
$288$		0			0
$289$	1.36231	+	2.35959i	0.0801360	+	0.138800i
$290$		0			0
$291$	−6.69003	+	11.5875i	−0.392176	+	0.679269i
$292$		0			0
$293$	−21.0415			−1.22926			−0.614630	−	0.788816i	$-0.710695\pi$
$293$	−21.0415			−1.22926			−0.614630	+	0.788816i	$0.710695\pi$
$294$		0			0
$295$	10.1660			0.591886
$296$		0			0
$297$	−0.727559	+	1.26017i	−0.0422172	+	0.0731224i
$298$		0			0
$299$	2.23721	+	3.87497i	0.129381	+	0.224095i
$300$		0			0
$301$	8.96705	+	0.928120i	0.516852	+	0.0534960i
$302$		0			0
$303$	11.5274	+	19.9661i	0.662233	+	1.14702i
$304$		0			0
$305$	3.40387	−	5.89567i	0.194905	−	0.337585i
$306$		0			0
$307$	4.95861			0.283003			0.141502	−	0.989938i	$-0.454807\pi$
$307$	4.95861			0.283003			0.141502	+	0.989938i	$0.454807\pi$
$308$		0			0
$309$	18.0791			1.02848
$310$		0			0
$311$	−1.21079	+	2.09715i	−0.0686575	+	0.118918i	−0.898311	−	0.439361i	$-0.855205\pi$
$311$	−1.21079	+	2.09715i	−0.0686575	+	0.118918i	0.829653	+	0.558279i	$0.188538\pi$
$312$		0			0
$313$	−6.98026	−	12.0902i	−0.394548	−	0.683377i	0.598496	−	0.801126i	$-0.295765\pi$
$313$	−6.98026	−	12.0902i	−0.394548	−	0.683377i	−0.993043	+	0.117749i	$0.962432\pi$
$314$		0			0
$315$	−10.2866	+	14.2055i	−0.579583	+	0.800390i
$316$		0			0
$317$	−1.53431	−	2.65750i	−0.0861753	−	0.149260i	0.819716	−	0.572770i	$-0.194131\pi$
$317$	−1.53431	−	2.65750i	−0.0861753	−	0.149260i	−0.905891	+	0.423510i	$0.860798\pi$
$318$		0			0
$319$	−14.1300	+	24.4739i	−0.791127	+	1.37027i
$320$		0			0
$321$	16.6957			0.931863
$322$		0			0
$323$	−13.4780			−0.749936
$324$		0			0
$325$	0.246870	−	0.427591i	0.0136939	−	0.0237185i
$326$		0			0
$327$	5.16716	+	8.94978i	0.285745	+	0.494924i
$328$		0			0
$329$	7.67710	+	17.1698i	0.423252	+	0.946603i
$330$		0			0
$331$	6.80261	+	11.7825i	0.373905	+	0.647623i	0.990162	−	0.139922i	$-0.0446853\pi$
$331$	6.80261	+	11.7825i	0.373905	+	0.647623i	−0.616257	+	0.787545i	$0.711352\pi$
$332$		0			0
$333$	−8.78395	+	15.2142i	−0.481358	+	0.833736i
$334$		0			0
$335$	−6.15516			−0.336292
$336$		0			0
$337$	−35.1646			−1.91554			−0.957769	−	0.287538i	$-0.907163\pi$
$337$	−35.1646			−1.91554			−0.957769	+	0.287538i	$0.907163\pi$
$338$		0			0
$339$	7.30089	−	12.6455i	0.396530	−	0.686810i
$340$		0			0
$341$	9.02997	+	15.6404i	0.489000	+	0.846973i
$342$		0			0
$343$	−17.6408	−	5.63933i	−0.952514	−	0.304495i
$344$		0			0
$345$	11.7514	+	20.3541i	0.632676	+	1.09583i
$346$		0			0
$347$	−2.73551	+	4.73804i	−0.146850	+	0.254351i	−0.930062	−	0.367404i	$-0.880247\pi$
$347$	−2.73551	+	4.73804i	−0.146850	+	0.254351i	0.783212	+	0.621755i	$0.213580\pi$
$348$		0			0
$349$	4.34196			0.232420			0.116210	−	0.993225i	$-0.462925\pi$
$349$	4.34196			0.232420			0.116210	+	0.993225i	$0.462925\pi$
$350$		0			0
$351$	−0.303848			−0.0162182
$352$		0			0
$353$	−13.7996	+	23.9016i	−0.734479	+	1.27216i	0.220472	+	0.975393i	$0.429240\pi$
$353$	−13.7996	+	23.9016i	−0.734479	+	1.27216i	−0.954951	+	0.296762i	$0.904093\pi$
$354$		0			0
$355$	2.69463	+	4.66724i	0.143016	+	0.247712i
$356$		0			0
$357$	10.0965	+	22.5809i	0.534365	+	1.19511i
$358$		0			0
$359$	3.31427	+	5.74049i	0.174921	+	0.302971i	0.940134	−	0.340806i	$-0.110700\pi$
$359$	3.31427	+	5.74049i	0.174921	+	0.302971i	−0.765213	+	0.643777i	$0.777366\pi$
$360$		0			0
$361$	3.13742	−	5.43418i	0.165128	−	0.286009i
$362$		0			0
$363$	−29.5301			−1.54993
$364$		0			0
$365$	−16.3470			−0.855643
$366$		0			0
$367$	15.6037	−	27.0264i	0.814506	−	1.41077i	−0.0951768	−	0.995460i	$-0.530342\pi$
$367$	15.6037	−	27.0264i	0.814506	−	1.41077i	0.909682	−	0.415305i	$-0.136325\pi$
$368$		0			0
$369$	−16.2304	−	28.1119i	−0.844923	−	1.46345i
$370$		0			0
$371$	−19.2107	+	26.5294i	−0.997368	+	1.37734i
$372$		0			0
$373$	7.88730	+	13.6612i	0.408389	+	0.707350i	0.994709	−	0.102729i	$-0.0327574\pi$
$373$	7.88730	+	13.6612i	0.408389	+	0.707350i	−0.586321	+	0.810079i	$0.699424\pi$
$374$		0			0
$375$	14.4285	−	24.9909i	0.745084	−	1.29052i
$376$		0			0
$377$	−5.90107			−0.303921
$378$		0			0
$379$	−31.6512			−1.62581			−0.812907	−	0.582393i	$-0.802116\pi$
$379$	−31.6512			−1.62581			−0.812907	+	0.582393i	$0.802116\pi$
$380$		0			0
$381$	13.0239	−	22.5580i	0.667233	−	1.15568i
$382$		0			0
$383$	6.19675	+	10.7331i	0.316639	+	0.548435i	0.979785	−	0.200055i	$-0.0641122\pi$
$383$	6.19675	+	10.7331i	0.316639	+	0.548435i	−0.663145	+	0.748491i	$0.730779\pi$
$384$		0			0
$385$	−26.7537	−	2.76910i	−1.36350	−	0.141126i
$386$		0			0
$387$	5.32020	+	9.21486i	0.270441	+	0.468418i
$388$		0			0
$389$	7.03705	−	12.1885i	0.356792	−	0.617983i	−0.630631	−	0.776083i	$-0.717204\pi$
$389$	7.03705	−	12.1885i	0.356792	−	0.617983i	0.987423	+	0.158100i	$0.0505370\pi$
$390$		0			0
$391$	16.9056			0.854954
$392$		0			0
$393$	13.4215			0.677026
$394$		0			0
$395$	5.49644	−	9.52012i	0.276556	−	0.479009i
$396$		0			0
$397$	3.48652	+	6.03884i	0.174984	+	0.303081i	0.940156	−	0.340745i	$-0.110679\pi$
$397$	3.48652	+	6.03884i	0.174984	+	0.303081i	−0.765172	+	0.643826i	$0.777346\pi$
$398$		0			0
$399$	23.2296	+	2.40434i	1.16293	+	0.120368i
$400$		0			0
$401$	−1.36841	−	2.37016i	−0.0683352	−	0.118360i	0.829833	−	0.558011i	$-0.188435\pi$
$401$	−1.36841	−	2.37016i	−0.0683352	−	0.118360i	−0.898169	+	0.439651i	$0.855102\pi$
$402$		0			0
$403$	−1.88558	+	3.26592i	−0.0939275	+	0.162687i
$404$		0			0
$405$	18.2911			0.908894
$406$		0			0
$407$	−26.9412			−1.33543
$408$		0			0
$409$	12.2577	−	21.2309i	0.606104	−	1.04980i	−0.385772	−	0.922594i	$-0.626065\pi$
$409$	12.2577	−	21.2309i	0.606104	−	1.04980i	0.991876	−	0.127208i	$-0.0406017\pi$
$410$		0			0
$411$	27.5215	+	47.6686i	1.35754	+	2.35132i
$412$		0			0
$413$	−7.43122	+	10.2623i	−0.365667	+	0.504977i
$414$		0			0
$415$	−3.68020	−	6.37429i	−0.180654	−	0.312902i
$416$		0			0
$417$	4.94886	−	8.57167i	0.242347	−	0.419757i
$418$		0			0
$419$	3.01252			0.147171			0.0735856	−	0.997289i	$-0.476556\pi$
$419$	3.01252			0.147171			0.0735856	+	0.997289i	$0.476556\pi$
$420$		0			0
$421$	−10.0000			−0.487370			−0.243685	−	0.969854i	$-0.578356\pi$
$421$	−10.0000			−0.487370			−0.243685	+	0.969854i	$0.578356\pi$
$422$		0			0
$423$	−11.0996	+	19.2251i	−0.539681	+	0.934755i
$424$		0			0
$425$	−0.932742	−	1.61556i	−0.0452447	−	0.0783660i
$426$		0			0
$427$	3.46337	+	7.74581i	0.167604	+	0.374846i
$428$		0			0
$429$	−5.92496	−	10.2623i	−0.286060	−	0.495470i
$430$		0			0
$431$	−9.39711	+	16.2763i	−0.452643	+	0.784001i	−0.998549	−	0.0538455i	$-0.982852\pi$
$431$	−9.39711	+	16.2763i	−0.452643	+	0.784001i	0.545906	+	0.837846i	$0.316185\pi$
$432$		0			0
$433$	−7.76911			−0.373360			−0.186680	−	0.982421i	$-0.559773\pi$
$433$	−7.76911			−0.373360			−0.186680	+	0.982421i	$0.559773\pi$
$434$		0			0
$435$	−30.9966			−1.48617
$436$		0			0
$437$	7.98066	−	13.8229i	0.381767	−	0.661240i
$438$		0			0
$439$	−18.9841	−	32.8814i	−0.906060	−	1.56934i	−0.819488	−	0.573096i	$-0.805742\pi$
$439$	−18.9841	−	32.8814i	−0.906060	−	1.56934i	−0.0865713	−	0.996246i	$-0.527591\pi$
$440$		0			0
$441$	−6.82079	−	20.7682i	−0.324799	−	0.988961i
$442$		0			0
$443$	17.8135	+	30.8539i	0.846344	+	1.46591i	0.884449	+	0.466637i	$0.154535\pi$
$443$	17.8135	+	30.8539i	0.846344	+	1.46591i	−0.0381050	+	0.999274i	$0.512132\pi$
$444$		0			0
$445$	3.88930	−	6.73647i	0.184371	−	0.319339i
$446$		0			0
$447$	−7.31125			−0.345810
$448$		0			0
$449$	−8.05285			−0.380038			−0.190019	−	0.981780i	$-0.560855\pi$
$449$	−8.05285			−0.380038			−0.190019	+	0.981780i	$0.560855\pi$
$450$		0			0
$451$	24.8901	−	43.1110i	1.17203	−	2.03002i
$452$		0			0
$453$	22.9562	+	39.7612i	1.07857	+	1.86815i
$454$		0			0
$455$	−2.29251	−	5.12720i	−0.107475	−	0.240367i
$456$		0			0
$457$	−7.79881	−	13.5079i	−0.364813	−	0.631875i	0.623933	−	0.781478i	$-0.285534\pi$
$457$	−7.79881	−	13.5079i	−0.364813	−	0.631875i	−0.988746	+	0.149603i	$0.952200\pi$
$458$		0			0
$459$	−0.574012	+	0.994218i	−0.0267926	+	0.0464061i
$460$		0			0
$461$	−25.6991			−1.19692			−0.598462	−	0.801151i	$-0.704221\pi$
$461$	−25.6991			−1.19692			−0.598462	+	0.801151i	$0.704221\pi$
$462$		0			0
$463$	20.5209			0.953685			0.476842	−	0.878989i	$-0.341781\pi$
$463$	20.5209			0.953685			0.476842	+	0.878989i	$0.341781\pi$
$464$		0			0
$465$	−9.90440	+	17.1549i	−0.459306	+	0.795541i
$466$		0			0
$467$	5.91241	+	10.2406i	0.273594	+	0.473878i	0.969779	−	0.243984i	$-0.0784543\pi$
$467$	5.91241	+	10.2406i	0.273594	+	0.473878i	−0.696186	+	0.717862i	$0.745121\pi$
$468$		0			0
$469$	4.49936	−	6.21351i	0.207761	−	0.286913i
$470$		0			0
$471$	−12.1242	−	20.9998i	−0.558656	−	0.967620i
$472$		0			0
$473$	−8.15878	+	14.1314i	−0.375141	+	0.649764i
$474$		0			0
$475$	−1.76128			−0.0808133
$476$		0			0
$477$	−38.6604			−1.77014
$478$		0			0
$479$	11.3276	−	19.6200i	0.517571	−	0.896459i	−0.482221	−	0.876050i	$-0.660170\pi$
$479$	11.3276	−	19.6200i	0.517571	−	0.896459i	0.999792	−	0.0204092i	$-0.00649690\pi$
$480$		0			0
$481$	−2.81285	−	4.87200i	−0.128255	−	0.222144i
$482$		0			0
$483$	−29.1372	−	3.01580i	−1.32579	−	0.137224i
$484$		0			0
$485$	−5.73933	−	9.94081i	−0.260610	−	0.451389i
$486$		0			0
$487$	−16.3584	+	28.3335i	−0.741268	+	1.28391i	0.210650	+	0.977562i	$0.432442\pi$
$487$	−16.3584	+	28.3335i	−0.741268	+	1.28391i	−0.951918	+	0.306353i	$0.900891\pi$
$488$		0			0
$489$	34.2317			1.54801
$490$		0			0
$491$	−6.17281			−0.278575			−0.139288	−	0.990252i	$-0.544481\pi$
$491$	−6.17281			−0.278575			−0.139288	+	0.990252i	$0.544481\pi$
$492$		0			0
$493$	−11.1479	+	19.3088i	−0.502078	+	0.869625i
$494$		0			0
$495$	−15.8731	−	27.4931i	−0.713444	−	1.23572i
$496$		0			0
$497$	−6.68123	−	0.691531i	−0.299694	−	0.0310194i
$498$		0			0
$499$	−7.31934	−	12.6775i	−0.327659	−	0.567521i	0.654388	−	0.756159i	$-0.272926\pi$
$499$	−7.31934	−	12.6775i	−0.327659	−	0.567521i	−0.982047	+	0.188637i	$0.939593\pi$
$500$		0			0
$501$	−21.4699	+	37.1870i	−0.959205	+	1.66139i
$502$		0			0
$503$	−12.7787			−0.569774			−0.284887	−	0.958561i	$-0.591956\pi$
$503$	−12.7787			−0.569774			−0.284887	+	0.958561i	$0.591956\pi$
$504$		0			0
$505$	−19.7786			−0.880136
$506$		0			0
$507$	1.23721	−	2.14292i	0.0549466	−	0.0951703i
$508$		0			0
$509$	−5.84263	−	10.1197i	−0.258970	−	0.448549i	0.706996	−	0.707217i	$-0.250050\pi$
$509$	−5.84263	−	10.1197i	−0.258970	−	0.448549i	−0.965966	+	0.258668i	$0.916716\pi$
$510$		0			0
$511$	11.9495	−	16.5020i	0.528615	−	0.730005i
$512$		0			0
$513$	0.541949	+	0.938683i	0.0239276	+	0.0414439i
$514$		0			0
$515$	−7.75495	+	13.4320i	−0.341724	+	0.591883i
$516$		0			0
$517$	−34.0435			−1.49723
$518$		0			0
$519$	7.32772			0.321651
$520$		0			0
$521$	−4.23838	+	7.34108i	−0.185687	+	0.321619i	−0.943808	−	0.330495i	$-0.892784\pi$
$521$	−4.23838	+	7.34108i	−0.185687	+	0.321619i	0.758121	+	0.652114i	$0.226118\pi$
$522$		0			0
$523$	16.3554	+	28.3284i	0.715172	+	1.23871i	0.962893	+	0.269883i	$0.0869849\pi$
$523$	16.3554	+	28.3284i	0.715172	+	1.23871i	−0.247721	+	0.968831i	$0.579682\pi$
$524$		0			0
$525$	1.31940	+	2.95084i	0.0575833	+	0.128785i
$526$		0			0
$527$	7.12425	+	12.3396i	0.310337	+	0.537520i
$528$		0			0
$529$	1.48975	−	2.58032i	0.0647716	−	0.112188i
$530$		0			0
$531$	−14.9549			−0.648989
$532$		0			0
$533$	10.3948			0.450249
$534$		0			0
$535$	−7.16156	+	12.4042i	−0.309621	+	0.536280i
$536$		0			0
$537$	7.01361	+	12.1479i	0.302660	+	0.524222i
$538$		0			0
$539$	22.3520	−	24.9831i	0.962771	−	1.07610i
$540$		0			0
$541$	14.0853	+	24.3964i	0.605573	+	1.04888i	0.991961	+	0.126547i	$0.0403893\pi$
$541$	14.0853	+	24.3964i	0.605573	+	1.04888i	−0.386388	+	0.922336i	$0.626277\pi$
$542$		0			0
$543$	8.87880	−	15.3785i	0.381026	−	0.659956i
$544$		0			0
$545$	−8.86574			−0.379767
$546$		0			0
$547$	18.5377			0.792615			0.396307	−	0.918118i	$-0.370291\pi$
$547$	18.5377			0.792615			0.396307	+	0.918118i	$0.370291\pi$
$548$		0			0
$549$	−5.00735	+	8.67299i	−0.213709	+	0.370154i
$550$		0			0
$551$	10.5252	+	18.2303i	0.448391	+	0.776635i
$552$		0			0
$553$	5.59252	+	12.5077i	0.237818	+	0.531880i
$554$		0			0
$555$	−14.7751	−	25.5912i	−0.627167	−	1.08628i
$556$		0			0
$557$	−2.00142	+	3.46655i	−0.0848027	+	0.146883i	−0.905307	−	0.424758i	$-0.860359\pi$
$557$	−2.00142	+	3.46655i	−0.0848027	+	0.146883i	0.820504	+	0.571640i	$0.193693\pi$
$558$		0			0
$559$	−3.40733			−0.144115
$560$		0			0
$561$	−44.7723			−1.89029
$562$		0			0
$563$	−8.93100	+	15.4689i	−0.376397	+	0.651938i	−0.990535	−	0.137260i	$-0.956170\pi$
$563$	−8.93100	+	15.4689i	−0.376397	+	0.651938i	0.614138	+	0.789199i	$0.289504\pi$
$564$		0			0
$565$	6.26338	+	10.8485i	0.263503	+	0.456400i
$566$		0			0
$567$	−13.3706	+	18.4645i	−0.561514	+	0.775437i
$568$		0			0
$569$	18.7336	+	32.4475i	0.785353	+	1.36027i	0.928788	+	0.370612i	$0.120852\pi$
$569$	18.7336	+	32.4475i	0.785353	+	1.36027i	−0.143434	+	0.989660i	$0.545815\pi$
$570$		0			0
$571$	8.78514	−	15.2163i	0.367646	−	0.636782i	−0.621551	−	0.783374i	$-0.713497\pi$
$571$	8.78514	−	15.2163i	0.367646	−	0.636782i	0.989197	+	0.146592i	$0.0468303\pi$
$572$		0			0
$573$	29.4006			1.22823
$574$		0			0
$575$	2.20920			0.0921301
$576$		0			0
$577$	17.1247	−	29.6608i	0.712910	−	1.23480i	−0.250850	−	0.968026i	$-0.580710\pi$
$577$	17.1247	−	29.6608i	0.712910	−	1.23480i	0.963760	−	0.266770i	$-0.0859565\pi$
$578$		0			0
$579$	28.4190	+	49.2232i	1.18105	+	2.04565i
$580$		0			0
$581$	9.12490	+	0.944459i	0.378565	+	0.0391828i
$582$		0			0
$583$	−29.6438	−	51.3445i	−1.22772	−	2.12647i
$584$		0			0
$585$	3.31453	−	5.74093i	0.137039	−	0.237358i
$586$		0			0
$587$	29.4494			1.21551			0.607754	−	0.794126i	$-0.292071\pi$
$587$	29.4494			1.21551			0.607754	+	0.794126i	$0.292071\pi$
$588$		0			0
$589$	13.4526			0.554305
$590$		0			0
$591$	20.9356	−	36.2616i	0.861176	−	1.49160i
$592$		0			0
$593$	17.0001	+	29.4450i	0.698109	+	1.20916i	0.969121	+	0.246584i	$0.0793081\pi$
$593$	17.0001	+	29.4450i	0.698109	+	1.20916i	−0.271013	+	0.962576i	$0.587359\pi$
$594$		0			0
$595$	−21.1075	−	2.18470i	−0.865324	−	0.0895640i
$596$		0			0
$597$	−12.4452	−	21.5557i	−0.509349	−	0.882218i
$598$		0			0
$599$	10.7209	−	18.5691i	0.438043	−	0.758713i	−0.559495	−	0.828834i	$-0.689005\pi$
$599$	10.7209	−	18.5691i	0.438043	−	0.758713i	0.997539	+	0.0701203i	$0.0223383\pi$
$600$		0			0
$601$	40.4039			1.64811			0.824054	−	0.566511i	$-0.191707\pi$
$601$	40.4039			1.64811			0.824054	+	0.566511i	$0.191707\pi$
$602$		0			0
$603$	9.05472			0.368737
$604$		0			0
$605$	12.6668	−	21.9396i	0.514980	−	0.891971i
$606$		0			0
$607$	−21.9456	−	38.0110i	−0.890746	−	1.54282i	−0.838983	−	0.544158i	$-0.816849\pi$
$607$	−21.9456	−	38.0110i	−0.890746	−	1.54282i	−0.0517636	−	0.998659i	$-0.516484\pi$
$608$		0			0
$609$	22.6582	−	31.2904i	0.918156	−	1.26795i
$610$		0			0
$611$	−3.55438	−	6.15636i	−0.143795	−	0.249060i
$612$		0			0
$613$	7.15777	−	12.3976i	0.289100	−	0.500735i	−0.684496	−	0.729017i	$-0.739977\pi$
$613$	7.15777	−	12.3976i	0.289100	−	0.500735i	0.973595	+	0.228282i	$0.0733108\pi$
$614$		0			0
$615$	54.6009			2.20172
$616$		0			0
$617$	−36.9097			−1.48593			−0.742965	−	0.669330i	$-0.766581\pi$
$617$	−36.9097			−1.48593			−0.742965	+	0.669330i	$0.766581\pi$
$618$		0			0
$619$	7.14646	−	12.3780i	0.287240	−	0.497515i	−0.685910	−	0.727687i	$-0.740595\pi$
$619$	7.14646	−	12.3780i	0.287240	−	0.497515i	0.973150	+	0.230172i	$0.0739288\pi$
$620$		0			0
$621$	−0.679774	−	1.17740i	−0.0272784	−	0.0472476i
$622$		0			0
$623$	3.95728	+	8.85046i	0.158545	+	0.354586i
$624$		0			0
$625$	11.1438	+	19.3016i	0.445750	+	0.772062i
$626$		0			0
$627$	−21.1357	+	36.6082i	−0.844080	+	1.46199i
$628$		0			0
$629$	−21.2554			−0.847510
$630$		0			0
$631$	0.0431064			0.00171604			0.000858019	−	1.00000i	$-0.499727\pi$
$631$	0.0431064			0.00171604			0.000858019		1.00000i	$0.499727\pi$
$632$		0			0
$633$	30.2633	−	52.4176i	1.20286	−	2.08341i
$634$		0			0
$635$	11.1731	+	19.3524i	0.443390	+	0.767975i
$636$		0			0
$637$	6.85161	+	1.43369i	0.271471	+	0.0568048i
$638$		0			0
$639$	−3.96401	−	6.86587i	−0.156814	−	0.271610i
$640$		0			0
$641$	−21.3328	+	36.9494i	−0.842594	+	1.45942i	0.0451008	+	0.998982i	$0.485639\pi$
$641$	−21.3328	+	36.9494i	−0.842594	+	1.45942i	−0.887695	+	0.460433i	$0.847694\pi$
$642$		0			0
$643$	5.49737			0.216795			0.108398	−	0.994108i	$-0.465428\pi$
$643$	5.49737			0.216795			0.108398	+	0.994108i	$0.465428\pi$
$644$		0			0
$645$	−17.8977			−0.704722
$646$		0			0
$647$	−19.0933	+	33.0706i	−0.750637	+	1.30014i	0.196877	+	0.980428i	$0.436920\pi$
$647$	−19.0933	+	33.0706i	−0.750637	+	1.30014i	−0.947514	+	0.319713i	$0.896413\pi$
$648$		0			0
$649$	−11.4671	−	19.8615i	−0.450121	−	0.779633i
$650$		0			0
$651$	−10.0775	−	22.5384i	−0.394969	−	0.883348i
$652$		0			0
$653$	−19.2510	−	33.3437i	−0.753349	−	1.30484i	−0.946191	−	0.323608i	$-0.895104\pi$
$653$	−19.2510	−	33.3437i	−0.753349	−	1.30484i	0.192843	−	0.981230i	$-0.438229\pi$
$654$		0			0
$655$	−5.75711	+	9.97161i	−0.224949	+	0.389623i
$656$		0			0
$657$	24.0477			0.938192
$658$		0			0
$659$	−19.4843			−0.759002			−0.379501	−	0.925191i	$-0.623904\pi$
$659$	−19.4843			−0.759002			−0.379501	+	0.925191i	$0.623904\pi$
$660$		0			0
$661$	20.8334	−	36.0844i	0.810324	−	1.40352i	−0.102314	−	0.994752i	$-0.532625\pi$
$661$	20.8334	−	36.0844i	0.810324	−	1.40352i	0.912638	−	0.408770i	$-0.134042\pi$
$662$		0			0
$663$	−4.67454	−	8.09654i	−0.181544	−	0.314443i
$664$		0			0
$665$	−11.7506	+	16.2273i	−0.455668	+	0.629266i
$666$		0			0
$667$	−13.2020	−	22.8665i	−0.511182	−	0.885393i
$668$		0			0
$669$	36.2040	−	62.7071i	1.39973	−	2.42440i
$670$		0			0
$671$	−15.3580			−0.592890
$672$		0			0
$673$	−14.3157			−0.551830			−0.275915	−	0.961182i	$-0.588981\pi$
$673$	−14.3157			−0.551830			−0.275915	+	0.961182i	$0.588981\pi$
$674$		0			0
$675$	−0.0750110	+	0.129923i	−0.00288718	+	0.00500073i
$676$		0			0
$677$	14.7641	+	25.5721i	0.567429	+	0.982815i	0.996819	+	0.0796963i	$0.0253950\pi$
$677$	14.7641	+	25.5721i	0.567429	+	0.982815i	−0.429391	+	0.903119i	$0.641272\pi$
$678$		0			0
$679$	14.2304	+	1.47290i	0.546114	+	0.0565247i
$680$		0			0
$681$	12.4633	+	21.5871i	0.477596	+	0.827220i
$682$		0			0
$683$	23.5349	−	40.7637i	0.900539	−	1.55978i	0.0737441	−	0.997277i	$-0.476505\pi$
$683$	23.5349	−	40.7637i	0.900539	−	1.55978i	0.826795	−	0.562503i	$-0.190161\pi$
$684$		0			0
$685$	−47.2210			−1.80422
$686$		0			0
$687$	27.5650			1.05167
$688$		0			0
$689$	6.19003	−	10.7214i	0.235821	−	0.408454i
$690$		0			0
$691$	−15.4334	−	26.7314i	−0.587113	−	1.01691i	−0.994608	−	0.103703i	$-0.966931\pi$
$691$	−15.4334	−	26.7314i	−0.587113	−	1.01691i	0.407495	−	0.913207i	$-0.366402\pi$
$692$		0			0
$693$	39.3568	+	4.07356i	1.49504	+	0.154742i
$694$		0			0
$695$	4.24559	+	7.35358i	0.161044	+	0.278937i
$696$		0			0
$697$	19.6372	−	34.0127i	0.743813	−	1.28832i
$698$		0			0
$699$	42.2715			1.59885
$700$		0			0
$701$	6.48958			0.245108			0.122554	−	0.992462i	$-0.460892\pi$
$701$	6.48958			0.245108			0.122554	+	0.992462i	$0.460892\pi$
$702$		0			0
$703$	−10.0341	+	17.3795i	−0.378443	+	0.655482i
$704$		0			0
$705$	−18.6701	−	32.3376i	−0.703157	−	1.21790i
$706$		0			0
$707$	14.4580	−	19.9661i	0.543747	−	0.750902i
$708$		0			0
$709$	6.68689	+	11.5820i	0.251131	+	0.434972i	0.963838	−	0.266490i	$-0.0858641\pi$
$709$	6.68689	+	11.5820i	0.251131	+	0.434972i	−0.712706	+	0.701463i	$0.752531\pi$
$710$		0			0
$711$	−8.08569	+	14.0048i	−0.303237	+	0.525222i
$712$		0			0
$713$	−16.8738			−0.631929
$714$		0			0
$715$	10.1660			0.380186
$716$		0			0
$717$	−8.56328	+	14.8320i	−0.319802	+	0.553913i
$718$		0			0
$719$	−8.37048	−	14.4981i	−0.312166	−	0.540688i	0.666665	−	0.745358i	$-0.267721\pi$
$719$	−8.37048	−	14.4981i	−0.312166	−	0.540688i	−0.978831	+	0.204670i	$0.934388\pi$
$720$		0			0
$721$	−7.89050	−	17.6471i	−0.293858	−	0.657212i
$722$		0			0
$723$	8.03725	+	13.9209i	0.298909	+	0.517725i
$724$		0			0
$725$	−1.45680	+	2.52325i	−0.0541041	+	0.0937110i
$726$		0			0
$727$	−38.8138			−1.43952			−0.719761	−	0.694221i	$-0.755749\pi$
$727$	−38.8138			−1.43952			−0.719761	+	0.694221i	$0.755749\pi$
$728$		0			0
$729$	−29.1632			−1.08012
$730$		0			0
$731$	−6.43692	+	11.1491i	−0.238078	+	0.412364i
$732$		0			0
$733$	−18.8639	−	32.6733i	−0.696756	−	1.20682i	−0.969585	−	0.244754i	$-0.921293\pi$
$733$	−18.8639	−	32.6733i	−0.696756	−	1.20682i	0.272830	−	0.962062i	$-0.412040\pi$
$734$		0			0
$735$	35.9895	+	7.53074i	1.32749	+	0.277776i
$736$		0			0
$737$	6.94292	+	12.0255i	0.255746	+	0.442965i
$738$		0			0
$739$	−4.61476	+	7.99300i	−0.169757	+	0.294027i	−0.938334	−	0.345729i	$-0.887632\pi$
$739$	−4.61476	+	7.99300i	−0.169757	+	0.294027i	0.768578	+	0.639757i	$0.220965\pi$
$740$		0			0
$741$	−8.82686			−0.324263
$742$		0			0
$743$	3.56327			0.130724			0.0653619	−	0.997862i	$-0.479180\pi$
$743$	3.56327			0.130724			0.0653619	+	0.997862i	$0.479180\pi$
$744$		0			0
$745$	3.13614	−	5.43195i	0.114899	−	0.199011i
$746$		0			0
$747$	5.41386	+	9.37707i	0.198083	+	0.343089i
$748$		0			0
$749$	−7.28674	−	16.2968i	−0.266252	−	0.595472i
$750$		0			0
$751$	25.6053	+	44.3496i	0.934350	+	1.61834i	0.775789	+	0.630992i	$0.217352\pi$
$751$	25.6053	+	44.3496i	0.934350	+	1.61834i	0.158561	+	0.987349i	$0.449315\pi$
$752$		0			0
$753$	12.2089	−	21.1464i	0.444916	−	0.770618i
$754$		0			0
$755$	−39.3879			−1.43347
$756$		0			0
$757$	25.2305			0.917019			0.458509	−	0.888690i	$-0.348384\pi$
$757$	25.2305			0.917019			0.458509	+	0.888690i	$0.348384\pi$
$758$		0			0
$759$	26.5108	−	45.9181i	0.962282	−	1.66672i
$760$		0			0
$761$	−1.82372	−	3.15878i	−0.0661099	−	0.114506i	0.831076	−	0.556159i	$-0.187725\pi$
$761$	−1.82372	−	3.15878i	−0.0661099	−	0.114506i	−0.897186	+	0.441653i	$0.854392\pi$
$762$		0			0
$763$	6.48077	−	8.94978i	0.234620	−	0.324004i
$764$		0			0
$765$	−12.5232	−	21.6908i	−0.452777	−	0.784233i
$766$		0			0
$767$	2.39448	−	4.14736i	0.0864596	−	0.149752i
$768$		0			0
$769$	21.9882			0.792914			0.396457	−	0.918053i	$-0.370240\pi$
$769$	21.9882			0.792914			0.396457	+	0.918053i	$0.370240\pi$
$770$		0			0
$771$	−16.9862			−0.611742
$772$		0			0
$773$	−10.9295	+	18.9305i	−0.393108	+	0.680882i	−0.992858	−	0.119305i	$-0.961933\pi$
$773$	−10.9295	+	18.9305i	−0.393108	+	0.680882i	0.599750	+	0.800187i	$0.295267\pi$
$774$		0			0
$775$	0.930986	+	1.61252i	0.0334420	+	0.0579233i
$776$		0			0
$777$	36.6342	+	3.79176i	1.31424	+	0.136029i
$778$		0			0
$779$	−18.5404	−	32.1128i	−0.664277	−	1.15056i
$780$		0			0
$781$	6.07900	−	10.5291i	0.217524	−	0.376762i
$782$		0			0
$783$	1.79303			0.0640777
$784$		0			0
$785$	20.8026			0.742477
$786$		0			0
$787$	19.9336	−	34.5261i	0.710557	−	1.23072i	−0.254091	−	0.967180i	$-0.581776\pi$
$787$	19.9336	−	34.5261i	0.710557	−	1.23072i	0.964648	−	0.263541i	$-0.0848905\pi$
$788$		0			0
$789$	0.156570	+	0.271188i	0.00557405	+	0.00965454i
$790$		0			0
$791$	−15.5298	−	1.60739i	−0.552176	−	0.0571521i
$792$		0			0
$793$	−1.60348	−	2.77732i	−0.0569414	−	0.0986254i
$794$		0			0
$795$	32.5144	−	56.3166i	1.15317	−	1.99734i
$796$		0			0
$797$	−40.1971			−1.42385			−0.711927	−	0.702253i	$-0.752178\pi$
$797$	−40.1971			−1.42385			−0.711927	+	0.702253i	$0.752178\pi$
$798$		0			0
$799$	−26.8589			−0.950198
$800$		0			0
$801$	−5.72146	+	9.90986i	−0.202158	+	0.350148i
$802$		0			0
$803$	18.4392	+	31.9376i	0.650704	+	1.12705i
$804$		0			0
$805$	14.7389	−	20.3541i	0.519478	−	0.717387i
$806$		0			0
$807$	−5.24960	−	9.09258i	−0.184795	−	0.320074i
$808$		0			0
$809$	−1.26924	+	2.19840i	−0.0446243	+	0.0772915i	−0.887475	−	0.460856i	$-0.847542\pi$
$809$	−1.26924	+	2.19840i	−0.0446243	+	0.0772915i	0.842851	+	0.538148i	$0.180876\pi$
$810$		0			0
$811$	41.7062			1.46450			0.732251	−	0.681035i	$-0.238470\pi$
$811$	41.7062			1.46450			0.732251	+	0.681035i	$0.238470\pi$
$812$		0			0
$813$	3.87801			0.136008
$814$		0			0
$815$	−14.6836	+	25.4327i	−0.514343	+	0.890868i
$816$		0			0
$817$	6.07737	+	10.5263i	0.212620	+	0.368269i
$818$		0			0
$819$	3.37246	+	7.54251i	0.117843	+	0.263557i
$820$		0			0
$821$	−15.9652	−	27.6525i	−0.557189	−	0.965079i	−0.997730	−	0.0673467i	$-0.978547\pi$
$821$	−15.9652	−	27.6525i	−0.557189	−	0.965079i	0.440541	−	0.897733i	$-0.354787\pi$
$822$		0			0
$823$	−17.1266	+	29.6641i	−0.596995	+	1.03402i	0.396267	+	0.918135i	$0.370305\pi$
$823$	−17.1266	+	29.6641i	−0.596995	+	1.03402i	−0.993262	+	0.115890i	$0.963028\pi$
$824$		0			0
$825$	−5.85078			−0.203698
$826$		0			0
$827$	−36.9755			−1.28576			−0.642882	−	0.765965i	$-0.722261\pi$
$827$	−36.9755			−1.28576			−0.642882	+	0.765965i	$0.722261\pi$
$828$		0			0
$829$	9.99473	−	17.3114i	0.347131	−	0.601249i	−0.638607	−	0.769533i	$-0.720489\pi$
$829$	9.99473	−	17.3114i	0.347131	−	0.601249i	0.985739	+	0.168284i	$0.0538225\pi$
$830$		0			0
$831$	−15.7685	−	27.3119i	−0.547005	−	0.947440i
$832$		0			0
$833$	17.6348	−	19.7106i	0.611009	−	0.682932i
$834$		0			0
$835$	−18.4189	−	31.9024i	−0.637412	−	1.10403i
$836$		0			0
$837$	0.572931	−	0.992346i	0.0198034	−	0.0343005i
$838$		0			0
$839$	−12.8147			−0.442411			−0.221206	−	0.975227i	$-0.570999\pi$
$839$	−12.8147			−0.442411			−0.221206	+	0.975227i	$0.570999\pi$
$840$		0			0
$841$	5.82265			0.200781
$842$		0			0
$843$	5.72812	−	9.92140i	0.197287	−	0.341711i
$844$		0			0
$845$	1.06140	+	1.83839i	0.0365132	+	0.0632427i
$846$		0			0
$847$	12.8882	+	28.8245i	0.442845	+	0.990422i
$848$		0			0
$849$	−4.51375	−	7.81805i	−0.154912	−	0.268315i
$850$		0			0
$851$	12.5859	−	21.7994i	0.431439	−	0.747274i
$852$		0			0
$853$	−30.1839			−1.03348			−0.516739	−	0.856143i	$-0.672854\pi$
$853$	−30.1839			−1.03348			−0.516739	+	0.856143i	$0.672854\pi$
$854$		0			0
$855$	−23.6474			−0.808724
$856$		0			0
$857$	26.6164	−	46.1009i	0.909197	−	1.57478i	0.0940154	−	0.995571i	$-0.470030\pi$
$857$	26.6164	−	46.1009i	0.909197	−	1.57478i	0.815182	−	0.579205i	$-0.196637\pi$
$858$		0			0
$859$	−6.13597	−	10.6278i	−0.209357	−	0.362616i	0.742155	−	0.670228i	$-0.233804\pi$
$859$	−6.13597	−	10.6278i	−0.209357	−	0.362616i	−0.951512	+	0.307611i	$0.900470\pi$
$860$		0			0
$861$	−39.9127	+	55.1185i	−1.36022	+	1.87843i
$862$		0			0
$863$	12.2226	+	21.1702i	0.416064	+	0.720643i	0.995539	−	0.0943460i	$-0.0300760\pi$
$863$	12.2226	+	21.1702i	0.416064	+	0.720643i	−0.579476	+	0.814989i	$0.696743\pi$
$864$		0			0
$865$	−3.14320	+	5.44418i	−0.106872	+	0.185108i
$866$		0			0
$867$	6.74189			0.228967
$868$		0			0
$869$	−24.7996			−0.841268
$870$		0			0
$871$	−1.44978	+	2.51109i	−0.0491238	+	0.0850850i
$872$		0			0
$873$	8.44300	+	14.6237i	0.285752	+	0.494937i
$874$		0			0
$875$	−30.6910	−	3.17663i	−1.03755	−	0.107390i
$876$		0			0
$877$	26.4376	+	45.7913i	0.892736	+	1.54626i	0.836582	+	0.547842i	$0.184550\pi$
$877$	26.4376	+	45.7913i	0.892736	+	1.54626i	0.0561539	+	0.998422i	$0.482116\pi$
$878$		0			0
$879$	−26.0329	+	45.0903i	−0.878068	+	1.52086i
$880$		0			0
$881$	55.0118			1.85339			0.926697	−	0.375809i	$-0.122635\pi$
$881$	55.0118			1.85339			0.926697	+	0.375809i	$0.122635\pi$
$882$		0			0
$883$	−44.1730			−1.48654			−0.743269	−	0.668992i	$-0.766726\pi$
$883$	−44.1730			−1.48654			−0.743269	+	0.668992i	$0.766726\pi$
$884$		0			0
$885$	12.5775	−	21.7848i	0.422788	−	0.732290i
$886$		0			0
$887$	−2.54330	−	4.40512i	−0.0853955	−	0.147909i	0.820164	−	0.572128i	$-0.193882\pi$
$887$	−2.54330	−	4.40512i	−0.0853955	−	0.147909i	−0.905560	+	0.424219i	$0.860549\pi$
$888$		0			0
$889$	−27.7032	−	2.86738i	−0.929136	−	0.0961688i
$890$		0			0
$891$	−20.6321	−	35.7359i	−0.691202	−	1.19720i
$892$		0			0
$893$	−12.6793	+	21.9612i	−0.424296	+	0.734903i
$894$		0			0
$895$	−12.0339			−0.402248
$896$		0			0
$897$	11.0717			0.369672
$898$		0			0
$899$	11.1270	−	19.2724i	0.371105	−	0.642772i
$900$		0			0
$901$	−23.3876	−	40.5086i	−0.779155	−	1.34954i
$902$		0			0
$903$	13.0830	−	18.0674i	0.435377	−	0.601244i
$904$		0			0
$905$	7.61706	+	13.1931i	0.253200	+	0.438555i
$906$		0			0
$907$	−9.06264	+	15.6969i	−0.300920	+	0.521209i	−0.976345	−	0.216220i	$-0.930627\pi$
$907$	−9.06264	+	15.6969i	−0.300920	+	0.521209i	0.675425	+	0.737429i	$0.263960\pi$
$908$		0			0
$909$	29.0958			0.965048
$910$		0			0
$911$	9.65804			0.319985			0.159993	−	0.987118i	$-0.448853\pi$
$911$	9.65804			0.319985			0.159993	+	0.987118i	$0.448853\pi$
$912$		0			0
$913$	−8.30241	+	14.3802i	−0.274770	+	0.475915i
$914$		0			0
$915$	−8.42263	−	14.5884i	−0.278444	−	0.482278i
$916$		0			0
$917$	−5.85774	−	13.1008i	−0.193440	−	0.432628i
$918$		0			0
$919$	23.8801	+	41.3616i	0.787733	+	1.36439i	0.927353	+	0.374188i	$0.122078\pi$
$919$	23.8801	+	41.3616i	0.787733	+	1.36439i	−0.139620	+	0.990205i	$0.544588\pi$
$920$		0			0
$921$	6.13487	−	10.6259i	0.202151	−	0.350135i
$922$		0			0
$923$	2.53876			0.0835643
$924$		0			0
$925$	−2.77763			−0.0913279
$926$		0			0
$927$	11.4081	−	19.7595i	0.374692	−	0.648986i
$928$		0			0
$929$	−16.9905	−	29.4285i	−0.557442	−	0.965517i	−0.997709	−	0.0676505i	$-0.978450\pi$
$929$	−16.9905	−	29.4285i	−0.557442	−	0.965517i	0.440267	−	0.897867i	$-0.354884\pi$
$930$		0			0
$931$	−7.79153	−	23.7239i	−0.255357	−	0.777520i
$932$		0			0
$933$	2.99601	+	5.18924i	0.0980850	+	0.169888i
$934$		0			0
$935$	19.2049	−	33.2639i	0.628068	−	1.08785i
$936$		0			0
$937$	−24.7948			−0.810012			−0.405006	−	0.914314i	$-0.632731\pi$
$937$	−24.7948			−0.810012			−0.405006	+	0.914314i	$0.632731\pi$
$938$		0			0
$939$	−34.5443			−1.12731
$940$		0			0
$941$	4.12098	−	7.13774i	0.134340	−	0.232684i	−0.791005	−	0.611810i	$-0.790442\pi$
$941$	4.12098	−	7.13774i	0.134340	−	0.232684i	0.925345	+	0.379126i	$0.123775\pi$
$942$		0			0
$943$	23.2554	+	40.2796i	0.757301	+	1.31168i
$944$		0			0
$945$	0.696577	+	1.55789i	0.0226596	+	0.0506783i
$946$		0			0
$947$	9.98643	+	17.2970i	0.324515	+	0.562077i	0.981414	−	0.191902i	$-0.0614655\pi$
$947$	9.98643	+	17.2970i	0.324515	+	0.562077i	−0.656899	+	0.753979i	$0.728132\pi$
$948$		0			0
$949$	−3.85035	+	6.66901i	−0.124988	+	0.216485i
$950$		0			0
$951$	−7.59307			−0.246222
$952$		0			0
$953$	−21.5341			−0.697557			−0.348778	−	0.937205i	$-0.613403\pi$
$953$	−21.5341			−0.697557			−0.348778	+	0.937205i	$0.613403\pi$
$954$		0			0
$955$	−12.6113	+	21.8434i	−0.408091	+	0.706835i
$956$		0			0
$957$	34.9636	+	60.5588i	1.13021	+	1.95759i
$958$		0			0
$959$	34.5181	−	47.6686i	1.11465	−	1.53930i
$960$		0			0
$961$	8.38917	+	14.5305i	0.270618	+	0.468725i
$962$		0			0
$963$	10.5352	−	18.2475i	0.339492	−	0.588018i
$964$		0			0
$965$	−48.7610			−1.56967
$966$		0			0
$967$	−43.2887			−1.39207			−0.696036	−	0.718007i	$-0.745055\pi$
$967$	−43.2887			−1.39207			−0.696036	+	0.718007i	$0.745055\pi$
$968$		0			0
$969$	−16.6752	+	28.8822i	−0.535683	+	0.927831i
$970$		0			0
$971$	−26.3356	−	45.6147i	−0.845151	−	1.46384i	−0.885490	−	0.464658i	$-0.846177\pi$
$971$	−26.3356	−	45.6147i	−0.845151	−	1.46384i	0.0403390	−	0.999186i	$-0.487156\pi$
$972$		0			0
$973$	−10.5268	−	1.08956i	−0.337473	−	0.0349296i
$974$		0			0
$975$	−0.610862	−	1.05804i	−0.0195632	−	0.0338845i
$976$		0			0
$977$	−7.70305	+	13.3421i	−0.246442	+	0.426851i	−0.962536	−	0.271153i	$-0.912595\pi$
$977$	−7.70305	+	13.3421i	−0.246442	+	0.426851i	0.716094	+	0.698004i	$0.245928\pi$
$978$		0			0
$979$	−17.5483			−0.560845
$980$		0			0
$981$	13.0422			0.416405
$982$		0			0
$983$	3.79073	−	6.56574i	0.120906	−	0.209415i	−0.799219	−	0.601039i	$-0.794754\pi$
$983$	3.79073	−	6.56574i	0.120906	−	0.209415i	0.920125	+	0.391625i	$0.128087\pi$
$984$		0			0
$985$	17.9605	+	31.1085i	0.572270	+	0.991201i
$986$		0			0
$987$	46.2918	+	4.79136i	1.47348	+	0.152511i
$988$		0			0
$989$	−7.62293	−	13.2033i	−0.242395	−	0.419841i
$990$		0			0
$991$	−9.50923	+	16.4705i	−0.302071	+	0.523202i	−0.976605	−	0.215042i	$-0.931011\pi$
$991$	−9.50923	+	16.4705i	−0.302071	+	0.523202i	0.674534	+	0.738244i	$0.264345\pi$
$992$		0			0
$993$	33.6651			1.06833
$994$		0			0
$995$	21.3533			0.676946
$996$		0			0
$997$	−23.0499	+	39.9236i	−0.729998	+	1.26439i	0.226885	+	0.973922i	$0.427146\pi$
$997$	−23.0499	+	39.9236i	−0.729998	+	1.26439i	−0.956883	+	0.290473i	$0.906187\pi$
$998$		0			0
$999$	0.854680	+	1.48035i	0.0270409	+	0.0468362i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1456.2.r.p.417.5		10
4.3	odd	2		91.2.e.c.53.2	✓	10
7.2	even	3	inner	1456.2.r.p.625.5		10
12.11	even	2		819.2.j.h.235.4		10
28.3	even	6		637.2.a.k.1.4		5
28.11	odd	6		637.2.a.l.1.4		5
28.19	even	6		637.2.e.m.79.2		10
28.23	odd	6		91.2.e.c.79.2	yes	10
28.27	even	2		637.2.e.m.508.2		10
52.51	odd	2		1183.2.e.f.508.4		10
84.11	even	6		5733.2.a.bl.1.2		5
84.23	even	6		819.2.j.h.352.4		10
84.59	odd	6		5733.2.a.bm.1.2		5
364.51	odd	6		1183.2.e.f.170.4		10
364.207	odd	6		8281.2.a.bw.1.2		5
364.311	even	6		8281.2.a.bx.1.2		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.e.c.53.2	✓	10	4.3	odd	2
91.2.e.c.79.2	yes	10	28.23	odd	6
637.2.a.k.1.4		5	28.3	even	6
637.2.a.l.1.4		5	28.11	odd	6
637.2.e.m.79.2		10	28.19	even	6
637.2.e.m.508.2		10	28.27	even	2
819.2.j.h.235.4		10	12.11	even	2
819.2.j.h.352.4		10	84.23	even	6
1183.2.e.f.170.4		10	364.51	odd	6
1183.2.e.f.508.4		10	52.51	odd	2
1456.2.r.p.417.5		10	1.1	even	1	trivial
1456.2.r.p.625.5		10	7.2	even	3	inner
5733.2.a.bl.1.2		5	84.11	even	6
5733.2.a.bm.1.2		5	84.59	odd	6
8281.2.a.bw.1.2		5	364.207	odd	6
8281.2.a.bx.1.2		5	364.311	even	6

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1456 = 2^{4} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1456.r (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.23721 - 2.14292i) q^{3} +(1.06140 + 1.83839i) q^{5} +(-2.63169 - 0.272389i) q^{7} +(-1.56140 - 2.70442i) q^{9} +(2.39448 - 4.14736i) q^{11} +1.00000 q^{13} +5.25271 q^{15} +(1.88914 - 3.27208i) q^{17} +(-1.78362 - 3.08931i) q^{19} +(-3.83967 + 5.30250i) q^{21} +(2.23721 + 3.87497i) q^{23} +(0.246870 - 0.427591i) q^{25} -0.303848 q^{27} -5.90107 q^{29} +(-1.88558 + 3.26592i) q^{31} +(-5.92496 - 10.2623i) q^{33} +(-2.29251 - 5.12720i) q^{35} +(-2.81285 - 4.87200i) q^{37} +(1.23721 - 2.14292i) q^{39} +10.3948 q^{41} -3.40733 q^{43} +(3.31453 - 5.74093i) q^{45} +(-3.55438 - 6.15636i) q^{47} +(6.85161 + 1.43369i) q^{49} +(-4.67454 - 8.09654i) q^{51} +(6.19003 - 10.7214i) q^{53} +10.1660 q^{55} -8.82686 q^{57} +(2.39448 - 4.14736i) q^{59} +(-1.60348 - 2.77732i) q^{61} +(3.37246 + 7.54251i) q^{63} +(1.06140 + 1.83839i) q^{65} +(-1.44978 + 2.51109i) q^{67} +11.0717 q^{69} +2.53876 q^{71} +(-3.85035 + 6.66901i) q^{73} +(-0.610862 - 1.05804i) q^{75} +(-7.43122 + 10.2623i) q^{77} +(-2.58925 - 4.48471i) q^{79} +(4.30827 - 7.46214i) q^{81} -3.46731 q^{83} +8.02051 q^{85} +(-7.30089 + 12.6455i) q^{87} +(-1.83216 - 3.17339i) q^{89} +(-2.63169 - 0.272389i) q^{91} +(4.66574 + 8.08129i) q^{93} +(3.78625 - 6.55798i) q^{95} -5.40733 q^{97} -14.9549 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 2 q^{5} - q^{7} - 3 q^{9} + 11 q^{11} + 10 q^{13} + 5 q^{17} + 9 q^{19} + 2 q^{21} + 10 q^{23} - 9 q^{25} - 6 q^{29} - 6 q^{31} - 8 q^{33} + 4 q^{35} - 4 q^{37} + 28 q^{41} - 4 q^{43} + 32 q^{45}+ \cdots - 22 q^{99}+O(q^{100}) \) 10 * q - 2 * q^5 - q^7 - 3 * q^9 + 11 * q^11 + 10 * q^13 + 5 * q^17 + 9 * q^19 + 2 * q^21 + 10 * q^23 - 9 * q^25 - 6 * q^29 - 6 * q^31 - 8 * q^33 + 4 * q^35 - 4 * q^37 + 28 * q^41 - 4 * q^43 + 32 * q^45 + q^47 - 11 * q^49 - 8 * q^51 - 17 * q^53 - 32 * q^57 + 11 * q^59 + 11 * q^61 - 5 * q^63 - 2 * q^65 + 13 * q^67 + 36 * q^69 - 30 * q^71 - 20 * q^75 - 46 * q^77 + 2 * q^79 + 19 * q^81 - 12 * q^83 - 44 * q^85 - 8 * q^87 + 4 * q^89 - q^91 - 18 * q^93 - 12 * q^95 - 24 * q^97 - 22 * q^99

Introduction

L-functions

Modular forms

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Database

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