LMFDB - Embedded newform 1456.2.r.p.625.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1456,2,Mod(417,1456)]

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

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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			625.5
Root			$-0.606661 + 1.05077i$ of defining polynomial
Character	$\chi$	$=$	1456.625
Dual form			1456.2.r.p.417.5

$q$-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 $\left(\mathbb{Z}/1456\mathbb{Z}\right)^\times$.

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

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	0.963227	+	0.268690i	$0.0865908\pi$
$3$	1.23721	+	2.14292i	0.714306	+	1.23721i	−0.248921	+	0.968524i	$0.580076\pi$
$4$		0			0
$5$	1.06140	−	1.83839i	0.474671	−	0.822155i	−0.524908	−	0.851159i	$-0.675900\pi$
$5$	1.06140	−	1.83839i	0.474671	−	0.822155i	0.999579	+	0.0290040i	$0.00923354\pi$
$6$		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	0.960212	+	0.279272i	$0.0900930\pi$
$11$	2.39448	+	4.14736i	0.721962	+	1.25048i	−0.238250	+	0.971204i	$0.576574\pi$
$12$		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	0.998865	−	0.0476304i	$-0.0151670\pi$
$17$	1.88914	+	3.27208i	0.458183	+	0.793597i	−0.540682	+	0.841227i	$0.681834\pi$
$18$		0			0
$19$	−1.78362	+	3.08931i	−0.409190	+	0.708737i	−0.994799	−	0.101856i	$-0.967522\pi$
$19$	−1.78362	+	3.08931i	−0.409190	+	0.708737i	0.585609	+	0.810593i	$0.300855\pi$
$20$		0			0
$21$	−3.83967	−	5.30250i	−0.837886	−	1.15710i
$22$		0			0
$23$	2.23721	−	3.87497i	0.466491	−	0.807987i	−0.532776	−	0.846256i	$-0.678851\pi$
$23$	2.23721	−	3.87497i	0.466491	−	0.807987i	0.999267	+	0.0382695i	$0.0121845\pi$
$24$		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	0.645521	−	0.763743i	$-0.276640\pi$
$31$	−1.88558	−	3.26592i	−0.338660	−	0.586577i	−0.984181	+	0.177166i	$0.943307\pi$
$32$		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	−0.999081	−	0.0428524i	$-0.986355\pi$
$37$	−2.81285	+	4.87200i	−0.462429	+	0.800951i	0.536652	+	0.843804i	$0.319689\pi$
$38$		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	0.481311	+	0.876550i	$0.340161\pi$
$47$	−3.55438	+	6.15636i	−0.518459	+	0.897998i	−0.999770	+	0.0214479i	$0.993172\pi$
$48$		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	0.880968	+	0.473175i	$0.156892\pi$
$53$	6.19003	+	10.7214i	0.850266	+	1.47270i	−0.0307027	+	0.999529i	$0.509774\pi$
$54$		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	0.978738	−	0.205115i	$-0.0657567\pi$
$59$	2.39448	+	4.14736i	0.311734	+	0.539940i	−0.667003	+	0.745055i	$0.732423\pi$
$60$		0			0
$61$	−1.60348	+	2.77732i	−0.205305	+	0.355599i	−0.950230	−	0.311550i	$-0.899152\pi$
$61$	−1.60348	+	2.77732i	−0.205305	+	0.355599i	0.744925	+	0.667148i	$0.232485\pi$
$62$		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	0.763774	−	0.645484i	$-0.223344\pi$
$67$	−1.44978	−	2.51109i	−0.177118	−	0.306778i	−0.940892	+	0.338706i	$0.890011\pi$
$68$		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	0.547777	−	0.836625i	$-0.315474\pi$
$73$	−3.85035	−	6.66901i	−0.450650	−	0.780548i	−0.998426	+	0.0560762i	$0.982141\pi$
$74$		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	−0.974120	−	0.226029i	$-0.927425\pi$
$79$	−2.58925	+	4.48471i	−0.291313	+	0.504569i	0.682807	+	0.730598i	$0.260759\pi$
$80$		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	−0.946641	−	0.322291i	$-0.895547\pi$
$89$	−1.83216	+	3.17339i	−0.194209	+	0.336379i	0.752432	+	0.658670i	$0.228881\pi$
$90$		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	0.535585	−	0.844482i	$-0.320091\pi$
$101$	−4.65862	−	8.06897i	−0.463550	−	0.802892i	−0.999135	+	0.0415891i	$0.986758\pi$
$102$		0			0
$103$	3.65318	−	6.32749i	0.359958	−	0.623466i	−0.627995	−	0.778217i	$-0.716124\pi$
$103$	3.65318	−	6.32749i	0.359958	−	0.623466i	0.987953	+	0.154751i	$0.0494576\pi$
$104$		0			0
$105$	−13.8235	+	1.43078i	−1.34904	+	0.139630i
$106$		0			0
$107$	3.37365	−	5.84333i	0.326143	−	0.564896i	−0.655600	−	0.755108i	$-0.727584\pi$
$107$	3.37365	−	5.84333i	0.326143	−	0.564896i	0.981743	+	0.190212i	$0.0609176\pi$
$108$		0			0
$109$	−2.08822	−	3.61691i	−0.200016	−	0.346437i	0.748518	−	0.663115i	$-0.230766\pi$
$109$	−2.08822	−	3.61691i	−0.200016	−	0.346437i	−0.948533	+	0.316678i	$0.897433\pi$
$110$		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	−0.722886	−	0.690967i	$-0.757185\pi$
$131$	2.71204	−	4.69740i	0.236952	−	0.410413i	0.959838	+	0.280554i	$0.0905182\pi$
$132$		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	−0.744886	−	0.667192i	$-0.767496\pi$
$137$	−11.1224	−	19.2645i	−0.950248	−	1.64588i	−0.205363	−	0.978686i	$-0.565837\pi$
$138$		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	−0.920174	−	0.391509i	$-0.871953\pi$
$149$	−1.47736	+	2.55887i	−0.121030	+	0.209630i	0.799144	+	0.601140i	$0.205286\pi$
$150$		0			0
$151$	−9.27736	−	16.0689i	−0.754981	−	1.30766i	−0.945384	−	0.325959i	$-0.894313\pi$
$151$	−9.27736	−	16.0689i	−0.754981	−	1.30766i	0.190403	−	0.981706i	$-0.439020\pi$
$152$		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	0.992588	−	0.121528i	$-0.0387793\pi$
$157$	4.89982	+	8.48673i	0.391048	+	0.677315i	−0.601540	+	0.798843i	$0.705446\pi$
$158$		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	−0.457013	−	0.889460i	$-0.651081\pi$
$163$	6.91709	−	11.9808i	0.541788	−	0.938405i	0.998801	−	0.0489451i	$-0.0155859\pi$
$164$		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	−0.804233	−	0.594314i	$-0.797424\pi$
$173$	1.48069	−	2.56463i	0.112575	−	0.194985i	0.916808	+	0.399329i	$0.130757\pi$
$174$		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	0.740440	−	0.672123i	$-0.234617\pi$
$179$	−2.83444	−	4.90939i	−0.211856	−	0.366945i	−0.952295	+	0.305178i	$0.901284\pi$
$180$		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	−0.566994	−	0.823722i	$-0.691894\pi$
$191$	5.94088	−	10.2899i	0.429867	−	0.744552i	0.996861	+	0.0791703i	$0.0252271\pi$
$192$		0			0
$193$	−11.4851	−	19.8927i	−0.826714	−	1.43191i	−0.900602	−	0.434645i	$-0.856874\pi$
$193$	−11.4851	−	19.8927i	−0.826714	−	1.43191i	0.0738876	−	0.997267i	$-0.476459\pi$
$194$		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	0.987379	−	0.158374i	$-0.0506251\pi$
$199$	5.02953	+	8.71140i	0.356534	+	0.617535i	−0.630845	+	0.775909i	$0.717292\pi$
$200$		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	0.649044	−	0.760751i	$-0.275169\pi$
$227$	−5.03685	−	8.72408i	−0.334307	−	0.579038i	−0.983352	+	0.181713i	$0.941836\pi$
$228$		0			0
$229$	5.56997	−	9.64748i	0.368074	−	0.637523i	−0.621190	−	0.783660i	$-0.713351\pi$
$229$	5.56997	−	9.64748i	0.368074	−	0.637523i	0.989264	+	0.146137i	$0.0466839\pi$
$230$		0			0
$231$	12.7973	−	28.6212i	0.842003	−	1.88314i
$232$		0			0
$233$	8.54166	−	14.7946i	0.559583	−	0.969226i	−0.437948	−	0.899000i	$-0.644295\pi$
$233$	8.54166	−	14.7946i	0.559583	−	0.969226i	0.997531	−	0.0702257i	$-0.0223720\pi$
$234$		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	0.742242	−	0.670132i	$-0.233762\pi$
$241$	−3.24812	−	5.62592i	−0.209230	−	0.362397i	−0.951472	+	0.307735i	$0.900429\pi$
$242$		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	−0.952995	−	0.302986i	$-0.902016\pi$
$257$	−3.43234	+	5.94499i	−0.214104	+	0.370838i	0.738891	+	0.673825i	$0.235350\pi$
$258$		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	0.864068	−	0.503375i	$-0.167909\pi$
$263$	−0.0632753	−	0.109596i	−0.00390172	−	0.00675798i	−0.867970	+	0.496617i	$0.834575\pi$
$264$		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	0.923426	−	0.383777i	$-0.125377\pi$
$269$	2.12154	+	3.67462i	0.129353	+	0.224045i	−0.794073	+	0.607822i	$0.792043\pi$
$270$		0			0
$271$	0.783616	−	1.35726i	0.0476013	−	0.0824479i	−0.841243	−	0.540657i	$-0.818176\pi$
$271$	0.783616	−	1.35726i	0.0476013	−	0.0824479i	0.888844	+	0.458209i	$0.151509\pi$
$272$		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	0.991474	−	0.130302i	$-0.0415947\pi$
$277$	6.37260	+	11.0377i	0.382892	+	0.663189i	−0.608582	+	0.793491i	$0.708261\pi$
$278$		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	0.915136	−	0.403144i	$-0.132083\pi$
$283$	1.82416	+	3.15954i	0.108435	+	0.187815i	−0.806701	+	0.590959i	$0.798749\pi$
$284$		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	0.829653	−	0.558279i	$-0.188538\pi$
$311$	−1.21079	−	2.09715i	−0.0686575	−	0.118918i	−0.898311	+	0.439361i	$0.855205\pi$
$312$		0			0
$313$	−6.98026	+	12.0902i	−0.394548	+	0.683377i	−0.993043	−	0.117749i	$-0.962432\pi$
$313$	−6.98026	+	12.0902i	−0.394548	+	0.683377i	0.598496	+	0.801126i	$0.295765\pi$
$314$		0			0
$315$	−10.2866	−	14.2055i	−0.579583	−	0.800390i
$316$		0			0
$317$	−1.53431	+	2.65750i	−0.0861753	+	0.149260i	−0.905891	−	0.423510i	$-0.860798\pi$
$317$	−1.53431	+	2.65750i	−0.0861753	+	0.149260i	0.819716	+	0.572770i	$0.194131\pi$
$318$		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	−0.616257	−	0.787545i	$-0.711352\pi$
$331$	6.80261	−	11.7825i	0.373905	−	0.647623i	0.990162	+	0.139922i	$0.0446853\pi$
$332$		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	0.783212	−	0.621755i	$-0.213580\pi$
$347$	−2.73551	−	4.73804i	−0.146850	−	0.254351i	−0.930062	+	0.367404i	$0.880247\pi$
$348$		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	−0.954951	−	0.296762i	$-0.904093\pi$
$353$	−13.7996	−	23.9016i	−0.734479	−	1.27216i	0.220472	−	0.975393i	$-0.429240\pi$
$354$		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	−0.765213	−	0.643777i	$-0.777366\pi$
$359$	3.31427	−	5.74049i	0.174921	−	0.302971i	0.940134	+	0.340806i	$0.110700\pi$
$360$		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	0.909682	+	0.415305i	$0.136325\pi$
$367$	15.6037	+	27.0264i	0.814506	+	1.41077i	−0.0951768	+	0.995460i	$0.530342\pi$
$368$		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	−0.586321	−	0.810079i	$-0.699424\pi$
$373$	7.88730	−	13.6612i	0.408389	−	0.707350i	0.994709	+	0.102729i	$0.0327574\pi$
$374$		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	−0.663145	−	0.748491i	$-0.730779\pi$
$383$	6.19675	−	10.7331i	0.316639	−	0.548435i	0.979785	+	0.200055i	$0.0641122\pi$
$384$		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	0.987423	−	0.158100i	$-0.0505370\pi$
$389$	7.03705	+	12.1885i	0.356792	+	0.617983i	−0.630631	+	0.776083i	$0.717204\pi$
$390$		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	−0.765172	−	0.643826i	$-0.777346\pi$
$397$	3.48652	−	6.03884i	0.174984	−	0.303081i	0.940156	+	0.340745i	$0.110679\pi$
$398$		0			0
$399$	23.2296	−	2.40434i	1.16293	−	0.120368i
$400$		0			0
$401$	−1.36841	+	2.37016i	−0.0683352	+	0.118360i	−0.898169	−	0.439651i	$-0.855102\pi$
$401$	−1.36841	+	2.37016i	−0.0683352	+	0.118360i	0.829833	+	0.558011i	$0.188435\pi$
$402$		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	0.991876	+	0.127208i	$0.0406017\pi$
$409$	12.2577	+	21.2309i	0.606104	+	1.04980i	−0.385772	+	0.922594i	$0.626065\pi$
$410$		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	0.545906	−	0.837846i	$-0.316185\pi$
$431$	−9.39711	−	16.2763i	−0.452643	−	0.784001i	−0.998549	+	0.0538455i	$0.982852\pi$
$432$		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	−0.0865713	+	0.996246i	$0.527591\pi$
$439$	−18.9841	+	32.8814i	−0.906060	+	1.56934i	−0.819488	+	0.573096i	$0.805742\pi$
$440$		0			0
$441$	−6.82079	+	20.7682i	−0.324799	+	0.988961i
$442$		0			0
$443$	17.8135	−	30.8539i	0.846344	−	1.46591i	−0.0381050	−	0.999274i	$-0.512132\pi$
$443$	17.8135	−	30.8539i	0.846344	−	1.46591i	0.884449	−	0.466637i	$-0.154535\pi$
$444$		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	−0.988746	−	0.149603i	$-0.952200\pi$
$457$	−7.79881	+	13.5079i	−0.364813	+	0.631875i	0.623933	+	0.781478i	$0.285534\pi$
$458$		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	−0.696186	−	0.717862i	$-0.745121\pi$
$467$	5.91241	−	10.2406i	0.273594	−	0.473878i	0.969779	+	0.243984i	$0.0784543\pi$
$468$		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	0.999792	+	0.0204092i	$0.00649690\pi$
$479$	11.3276	+	19.6200i	0.517571	+	0.896459i	−0.482221	+	0.876050i	$0.660170\pi$
$480$		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	−0.951918	−	0.306353i	$-0.900891\pi$
$487$	−16.3584	−	28.3335i	−0.741268	−	1.28391i	0.210650	−	0.977562i	$-0.432442\pi$
$488$		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	−0.982047	−	0.188637i	$-0.939593\pi$
$499$	−7.31934	+	12.6775i	−0.327659	+	0.567521i	0.654388	+	0.756159i	$0.272926\pi$
$500$		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	−0.965966	−	0.258668i	$-0.916716\pi$
$509$	−5.84263	+	10.1197i	−0.258970	+	0.448549i	0.706996	+	0.707217i	$0.250050\pi$
$510$		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	0.758121	−	0.652114i	$-0.226118\pi$
$521$	−4.23838	−	7.34108i	−0.185687	−	0.321619i	−0.943808	+	0.330495i	$0.892784\pi$
$522$		0			0
$523$	16.3554	−	28.3284i	0.715172	−	1.23871i	−0.247721	−	0.968831i	$-0.579682\pi$
$523$	16.3554	−	28.3284i	0.715172	−	1.23871i	0.962893	−	0.269883i	$-0.0869849\pi$
$524$		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	−0.386388	−	0.922336i	$-0.626277\pi$
$541$	14.0853	−	24.3964i	0.605573	−	1.04888i	0.991961	−	0.126547i	$-0.0403893\pi$
$542$		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	0.820504	−	0.571640i	$-0.193693\pi$
$557$	−2.00142	−	3.46655i	−0.0848027	−	0.146883i	−0.905307	+	0.424758i	$0.860359\pi$
$558$		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	0.614138	−	0.789199i	$-0.289504\pi$
$563$	−8.93100	−	15.4689i	−0.376397	−	0.651938i	−0.990535	+	0.137260i	$0.956170\pi$
$564$		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	−0.143434	−	0.989660i	$-0.545815\pi$
$569$	18.7336	−	32.4475i	0.785353	−	1.36027i	0.928788	−	0.370612i	$-0.120852\pi$
$570$		0			0
$571$	8.78514	+	15.2163i	0.367646	+	0.636782i	0.989197	−	0.146592i	$-0.0468303\pi$
$571$	8.78514	+	15.2163i	0.367646	+	0.636782i	−0.621551	+	0.783374i	$0.713497\pi$
$572$		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	0.963760	+	0.266770i	$0.0859565\pi$
$577$	17.1247	+	29.6608i	0.712910	+	1.23480i	−0.250850	+	0.968026i	$0.580710\pi$
$578$		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	−0.271013	−	0.962576i	$-0.587359\pi$
$593$	17.0001	−	29.4450i	0.698109	−	1.20916i	0.969121	−	0.246584i	$-0.0793081\pi$
$594$		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	0.997539	−	0.0701203i	$-0.0223383\pi$
$599$	10.7209	+	18.5691i	0.438043	+	0.758713i	−0.559495	+	0.828834i	$0.689005\pi$
$600$		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	−0.0517636	+	0.998659i	$0.516484\pi$
$607$	−21.9456	+	38.0110i	−0.890746	+	1.54282i	−0.838983	+	0.544158i	$0.816849\pi$
$608$		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	0.973595	−	0.228282i	$-0.0733108\pi$
$613$	7.15777	+	12.3976i	0.289100	+	0.500735i	−0.684496	+	0.729017i	$0.739977\pi$
$614$		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	0.973150	−	0.230172i	$-0.0739288\pi$
$619$	7.14646	+	12.3780i	0.287240	+	0.497515i	−0.685910	+	0.727687i	$0.740595\pi$
$620$		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	−0.887695	−	0.460433i	$-0.847694\pi$
$641$	−21.3328	−	36.9494i	−0.842594	−	1.45942i	0.0451008	−	0.998982i	$-0.485639\pi$
$642$		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	−0.947514	−	0.319713i	$-0.896413\pi$
$647$	−19.0933	−	33.0706i	−0.750637	−	1.30014i	0.196877	−	0.980428i	$-0.436920\pi$
$648$		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	0.192843	+	0.981230i	$0.438229\pi$
$653$	−19.2510	+	33.3437i	−0.753349	+	1.30484i	−0.946191	+	0.323608i	$0.895104\pi$
$654$		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	0.912638	+	0.408770i	$0.134042\pi$
$661$	20.8334	+	36.0844i	0.810324	+	1.40352i	−0.102314	+	0.994752i	$0.532625\pi$
$662$		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	−0.429391	−	0.903119i	$-0.641272\pi$
$677$	14.7641	−	25.5721i	0.567429	−	0.982815i	0.996819	−	0.0796963i	$-0.0253950\pi$
$678$		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	0.826795	+	0.562503i	$0.190161\pi$
$683$	23.5349	+	40.7637i	0.900539	+	1.55978i	0.0737441	+	0.997277i	$0.476505\pi$
$684$		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	0.407495	+	0.913207i	$0.366402\pi$
$691$	−15.4334	+	26.7314i	−0.587113	+	1.01691i	−0.994608	+	0.103703i	$0.966931\pi$
$692$		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	−0.712706	−	0.701463i	$-0.752531\pi$
$709$	6.68689	−	11.5820i	0.251131	−	0.434972i	0.963838	+	0.266490i	$0.0858641\pi$
$710$		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	−0.978831	−	0.204670i	$-0.934388\pi$
$719$	−8.37048	+	14.4981i	−0.312166	+	0.540688i	0.666665	+	0.745358i	$0.267721\pi$
$720$		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	0.272830	+	0.962062i	$0.412040\pi$
$733$	−18.8639	+	32.6733i	−0.696756	+	1.20682i	−0.969585	+	0.244754i	$0.921293\pi$
$734$		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	0.768578	−	0.639757i	$-0.220965\pi$
$739$	−4.61476	−	7.99300i	−0.169757	−	0.294027i	−0.938334	+	0.345729i	$0.887632\pi$
$740$		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	0.158561	−	0.987349i	$-0.449315\pi$
$751$	25.6053	−	44.3496i	0.934350	−	1.61834i	0.775789	−	0.630992i	$-0.217352\pi$
$752$		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	−0.897186	−	0.441653i	$-0.854392\pi$
$761$	−1.82372	+	3.15878i	−0.0661099	+	0.114506i	0.831076	+	0.556159i	$0.187725\pi$
$762$		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	0.599750	−	0.800187i	$-0.295267\pi$
$773$	−10.9295	−	18.9305i	−0.393108	−	0.680882i	−0.992858	+	0.119305i	$0.961933\pi$
$774$		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	0.964648	+	0.263541i	$0.0848905\pi$
$787$	19.9336	+	34.5261i	0.710557	+	1.23072i	−0.254091	+	0.967180i	$0.581776\pi$
$788$		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	0.842851	−	0.538148i	$-0.180876\pi$
$809$	−1.26924	−	2.19840i	−0.0446243	−	0.0772915i	−0.887475	+	0.460856i	$0.847542\pi$
$810$		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	0.440541	+	0.897733i	$0.354787\pi$
$821$	−15.9652	+	27.6525i	−0.557189	+	0.965079i	−0.997730	+	0.0673467i	$0.978547\pi$
$822$		0			0
$823$	−17.1266	−	29.6641i	−0.596995	−	1.03402i	−0.993262	−	0.115890i	$-0.963028\pi$
$823$	−17.1266	−	29.6641i	−0.596995	−	1.03402i	0.396267	−	0.918135i	$-0.370305\pi$
$824$		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	0.985739	−	0.168284i	$-0.0538225\pi$
$829$	9.99473	+	17.3114i	0.347131	+	0.601249i	−0.638607	+	0.769533i	$0.720489\pi$
$830$		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	0.815182	+	0.579205i	$0.196637\pi$
$857$	26.6164	+	46.1009i	0.909197	+	1.57478i	0.0940154	+	0.995571i	$0.470030\pi$
$858$		0			0
$859$	−6.13597	+	10.6278i	−0.209357	+	0.362616i	−0.951512	−	0.307611i	$-0.900470\pi$
$859$	−6.13597	+	10.6278i	−0.209357	+	0.362616i	0.742155	+	0.670228i	$0.233804\pi$
$860$		0			0
$861$	−39.9127	−	55.1185i	−1.36022	−	1.87843i
$862$		0			0
$863$	12.2226	−	21.1702i	0.416064	−	0.720643i	−0.579476	−	0.814989i	$-0.696743\pi$
$863$	12.2226	−	21.1702i	0.416064	−	0.720643i	0.995539	+	0.0943460i	$0.0300760\pi$
$864$		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	0.0561539	−	0.998422i	$-0.482116\pi$
$877$	26.4376	−	45.7913i	0.892736	−	1.54626i	0.836582	−	0.547842i	$-0.184550\pi$
$878$		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	−0.905560	−	0.424219i	$-0.860549\pi$
$887$	−2.54330	+	4.40512i	−0.0853955	+	0.147909i	0.820164	+	0.572128i	$0.193882\pi$
$888$		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	0.675425	−	0.737429i	$-0.263960\pi$
$907$	−9.06264	−	15.6969i	−0.300920	−	0.521209i	−0.976345	+	0.216220i	$0.930627\pi$
$908$		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	−0.139620	−	0.990205i	$-0.544588\pi$
$919$	23.8801	−	41.3616i	0.787733	−	1.36439i	0.927353	−	0.374188i	$-0.122078\pi$
$920$		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	0.440267	+	0.897867i	$0.354884\pi$
$929$	−16.9905	+	29.4285i	−0.557442	+	0.965517i	−0.997709	+	0.0676505i	$0.978450\pi$
$930$		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	0.925345	−	0.379126i	$-0.123775\pi$
$941$	4.12098	+	7.13774i	0.134340	+	0.232684i	−0.791005	+	0.611810i	$0.790442\pi$
$942$		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	−0.656899	−	0.753979i	$-0.728132\pi$
$947$	9.98643	−	17.2970i	0.324515	−	0.562077i	0.981414	+	0.191902i	$0.0614655\pi$
$948$		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	0.0403390	+	0.999186i	$0.487156\pi$
$971$	−26.3356	+	45.6147i	−0.845151	+	1.46384i	−0.885490	+	0.464658i	$0.846177\pi$
$972$		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	0.716094	−	0.698004i	$-0.245928\pi$
$977$	−7.70305	−	13.3421i	−0.246442	−	0.426851i	−0.962536	+	0.271153i	$0.912595\pi$
$978$		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	0.920125	−	0.391625i	$-0.128087\pi$
$983$	3.79073	+	6.56574i	0.120906	+	0.209415i	−0.799219	+	0.601039i	$0.794754\pi$
$984$		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	0.674534	−	0.738244i	$-0.264345\pi$
$991$	−9.50923	−	16.4705i	−0.302071	−	0.523202i	−0.976605	+	0.215042i	$0.931011\pi$
$992$		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	−0.956883	−	0.290473i	$-0.906187\pi$
$997$	−23.0499	−	39.9236i	−0.729998	−	1.26439i	0.226885	−	0.973922i	$-0.427146\pi$
$998$		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.625.5		10
4.3	odd	2		91.2.e.c.79.2	yes	10
7.4	even	3	inner	1456.2.r.p.417.5		10
12.11	even	2		819.2.j.h.352.4		10
28.3	even	6		637.2.e.m.508.2		10
28.11	odd	6		91.2.e.c.53.2	✓	10
28.19	even	6		637.2.a.k.1.4		5
28.23	odd	6		637.2.a.l.1.4		5
28.27	even	2		637.2.e.m.79.2		10
52.51	odd	2		1183.2.e.f.170.4		10
84.11	even	6		819.2.j.h.235.4		10
84.23	even	6		5733.2.a.bl.1.2		5
84.47	odd	6		5733.2.a.bm.1.2		5
364.51	odd	6		8281.2.a.bw.1.2		5
364.103	even	6		8281.2.a.bx.1.2		5
364.207	odd	6		1183.2.e.f.508.4		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.e.c.53.2	✓	10	28.11	odd	6
91.2.e.c.79.2	yes	10	4.3	odd	2
637.2.a.k.1.4		5	28.19	even	6
637.2.a.l.1.4		5	28.23	odd	6
637.2.e.m.79.2		10	28.27	even	2
637.2.e.m.508.2		10	28.3	even	6
819.2.j.h.235.4		10	84.11	even	6
819.2.j.h.352.4		10	12.11	even	2
1183.2.e.f.170.4		10	52.51	odd	2
1183.2.e.f.508.4		10	364.207	odd	6
1456.2.r.p.417.5		10	7.4	even	3	inner
1456.2.r.p.625.5		10	1.1	even	1	trivial
5733.2.a.bl.1.2		5	84.23	even	6
5733.2.a.bm.1.2		5	84.47	odd	6
8281.2.a.bw.1.2		5	364.51	odd	6
8281.2.a.bx.1.2		5	364.103	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 $\F_{q}$

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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