LMFDB - Embedded newform 56.4.i.b.25.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [56,4,Mod(9,56)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(56, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("56.9");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 56 = 2^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	56.i (of order $3$, degree $2$, 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:	$3.30410696032$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.11163123.4
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 14x^{4} + 49x^{2} + 27 $ x^6 + 14x^4 + 49x^2 + 27
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6}\cdot 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			25.1
Root			$0.821510i$ of defining polynomial
Character	$\chi$	$=$	56.25
Dual form			56.4.i.b.9.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40222 + 2.42872i) q^{3} +(3.34580 + 5.79509i) q^{5} +(-8.65024 + 16.3760i) q^{7} +(9.56754 + 16.5715i) q^{9} +O(q^{10})$	\(q+(-1.40222 + 2.42872i) q^{3} +(3.34580 + 5.79509i) q^{5} +(-8.65024 + 16.3760i) q^{7} +(9.56754 + 16.5715i) q^{9} +(-15.7441 + 27.2695i) q^{11} +18.6837 q^{13} -18.7662 q^{15} +(43.9769 - 76.1703i) q^{17} +(-6.54850 - 11.3423i) q^{19} +(-27.6432 - 43.9718i) q^{21} +(4.68840 + 8.12055i) q^{23} +(40.1113 - 69.4748i) q^{25} -129.383 q^{27} -5.11923 q^{29} +(128.706 - 222.925i) q^{31} +(-44.1533 - 76.4758i) q^{33} +(-123.842 + 4.66183i) q^{35} +(190.107 + 329.276i) q^{37} +(-26.1987 + 45.3774i) q^{39} -217.959 q^{41} +377.049 q^{43} +(-64.0221 + 110.889i) q^{45} +(178.855 + 309.786i) q^{47} +(-193.347 - 283.313i) q^{49} +(123.331 + 213.615i) q^{51} +(-382.195 + 661.981i) q^{53} -210.706 q^{55} +36.7298 q^{57} +(225.336 - 390.293i) q^{59} +(87.0388 + 150.756i) q^{61} +(-354.136 + 13.3308i) q^{63} +(62.5117 + 108.273i) q^{65} +(248.617 - 430.617i) q^{67} -26.2967 q^{69} +350.238 q^{71} +(531.343 - 920.312i) q^{73} +(112.490 + 194.838i) q^{75} +(-310.375 - 493.712i) q^{77} +(-280.224 - 485.363i) q^{79} +(-76.8993 + 133.194i) q^{81} -1105.27 q^{83} +588.551 q^{85} +(7.17830 - 12.4332i) q^{87} +(-603.357 - 1045.04i) q^{89} +(-161.618 + 305.964i) q^{91} +(360.948 + 625.181i) q^{93} +(43.8199 - 75.8983i) q^{95} +1442.99 q^{97} -602.528 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 7 q^{3} + 3 q^{5} - 4 q^{7} - 18 q^{9}+O(q^{10}) $ 6 * q + 7 * q^3 + 3 * q^5 - 4 * q^7 - 18 * q^9	$ 6 q + 7 q^{3} + 3 q^{5} - 4 q^{7} - 18 q^{9} + 3 q^{11} - 52 q^{13} + 254 q^{15} + 31 q^{17} + 89 q^{19} - 375 q^{21} + 201 q^{23} - 300 q^{25} - 938 q^{27} + 380 q^{29} + 339 q^{31} + 105 q^{33} - 473 q^{35} + 535 q^{37} + 134 q^{39} + 116 q^{41} + 536 q^{43} + 1410 q^{45} + 205 q^{47} - 1530 q^{49} + 965 q^{51} - 757 q^{53} - 3306 q^{55} + 522 q^{57} + 1799 q^{59} - 625 q^{61} - 1714 q^{63} + 1750 q^{65} + 495 q^{67} + 1946 q^{69} + 1280 q^{71} + 443 q^{73} + 1484 q^{75} - 1131 q^{77} - 79 q^{79} - 2523 q^{81} - 4744 q^{83} - 1954 q^{85} + 910 q^{87} - 821 q^{89} - 1352 q^{91} + 1321 q^{93} + 1327 q^{95} - 684 q^{97} + 4620 q^{99}+O(q^{100}) $ 6 * q + 7 * q^3 + 3 * q^5 - 4 * q^7 - 18 * q^9 + 3 * q^11 - 52 * q^13 + 254 * q^15 + 31 * q^17 + 89 * q^19 - 375 * q^21 + 201 * q^23 - 300 * q^25 - 938 * q^27 + 380 * q^29 + 339 * q^31 + 105 * q^33 - 473 * q^35 + 535 * q^37 + 134 * q^39 + 116 * q^41 + 536 * q^43 + 1410 * q^45 + 205 * q^47 - 1530 * q^49 + 965 * q^51 - 757 * q^53 - 3306 * q^55 + 522 * q^57 + 1799 * q^59 - 625 * q^61 - 1714 * q^63 + 1750 * q^65 + 495 * q^67 + 1946 * q^69 + 1280 * q^71 + 443 * q^73 + 1484 * q^75 - 1131 * q^77 - 79 * q^79 - 2523 * q^81 - 4744 * q^83 - 1954 * q^85 + 910 * q^87 - 821 * q^89 - 1352 * q^91 + 1321 * q^93 + 1327 * q^95 - 684 * q^97 + 4620 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/56\mathbb{Z}\right)^\times$.

$n$	$15$	$17$	$29$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.40222	+	2.42872i	−0.269858	+	0.467408i	−0.968825	−	0.247746i	$-0.920310\pi$
$3$	−1.40222	+	2.42872i	−0.269858	+	0.467408i	0.698967	+	0.715154i	$0.253643\pi$
$4$		0			0
$5$	3.34580	+	5.79509i	0.299257	+	0.518328i	0.975966	−	0.217922i	$-0.0699279\pi$
$5$	3.34580	+	5.79509i	0.299257	+	0.518328i	−0.676709	+	0.736250i	$0.736595\pi$
$6$		0			0
$7$	−8.65024	+	16.3760i	−0.467069	+	0.884221i
$7$	−8.65024	+	16.3760i	−0.467069	+	0.884221i
$8$		0			0
$9$	9.56754	+	16.5715i	0.354353	+	0.613758i
$10$		0			0
$11$	−15.7441	+	27.2695i	−0.431546	+	0.747460i	−0.997007	−	0.0773151i	$-0.975365\pi$
$11$	−15.7441	+	27.2695i	−0.431546	+	0.747460i	0.565460	+	0.824776i	$0.308699\pi$
$12$		0			0
$13$	18.6837			0.398609			0.199304	−	0.979938i	$-0.436132\pi$
$13$	18.6837			0.398609			0.199304	+	0.979938i	$0.436132\pi$
$14$		0			0
$15$	−18.7662			−0.323028
$16$		0			0
$17$	43.9769	−	76.1703i	0.627410	−	1.08671i	−0.360660	−	0.932698i	$-0.617448\pi$
$17$	43.9769	−	76.1703i	0.627410	−	1.08671i	0.988070	−	0.154008i	$-0.0492183\pi$
$18$		0			0
$19$	−6.54850	−	11.3423i	−0.0790700	−	0.136953i	0.823779	−	0.566911i	$-0.191862\pi$
$19$	−6.54850	−	11.3423i	−0.0790700	−	0.136953i	−0.902849	+	0.429958i	$0.858528\pi$
$20$		0			0
$21$	−27.6432	−	43.9718i	−0.287249	−	0.456926i
$22$		0			0
$23$	4.68840	+	8.12055i	0.0425043	+	0.0736197i	0.886495	−	0.462738i	$-0.153133\pi$
$23$	4.68840	+	8.12055i	0.0425043	+	0.0736197i	−0.843991	+	0.536358i	$0.819800\pi$
$24$		0			0
$25$	40.1113	−	69.4748i	0.320890	−	0.555799i
$26$		0			0
$27$	−129.383			−0.922216
$28$		0			0
$29$	−5.11923			−0.0327799			−0.0163900	−	0.999866i	$-0.505217\pi$
$29$	−5.11923			−0.0327799			−0.0163900	+	0.999866i	$0.505217\pi$
$30$		0			0
$31$	128.706	−	222.925i	0.745685	−	1.29156i	−0.204189	−	0.978932i	$-0.565456\pi$
$31$	128.706	−	222.925i	0.745685	−	1.29156i	0.949874	−	0.312633i	$-0.101211\pi$
$32$		0			0
$33$	−44.1533	−	76.4758i	−0.232912	−	0.403416i
$34$		0			0
$35$	−123.842	+	4.66183i	−0.598090	+	0.0225141i
$36$		0			0
$37$	190.107	+	329.276i	0.844688	+	1.46304i	0.885892	+	0.463892i	$0.153547\pi$
$37$	190.107	+	329.276i	0.844688	+	1.46304i	−0.0412040	+	0.999151i	$0.513119\pi$
$38$		0			0
$39$	−26.1987	+	45.3774i	−0.107568	+	0.186313i
$40$		0			0
$41$	−217.959			−0.830230			−0.415115	−	0.909769i	$-0.636259\pi$
$41$	−217.959			−0.830230			−0.415115	+	0.909769i	$0.636259\pi$
$42$		0			0
$43$	377.049			1.33720			0.668598	−	0.743624i	$-0.266895\pi$
$43$	377.049			1.33720			0.668598	+	0.743624i	$0.266895\pi$
$44$		0			0
$45$	−64.0221	+	110.889i	−0.212086	+	0.367343i
$46$		0			0
$47$	178.855	+	309.786i	0.555079	+	0.961425i	0.997897	+	0.0648137i	$0.0206453\pi$
$47$	178.855	+	309.786i	0.555079	+	0.961425i	−0.442818	+	0.896611i	$0.646021\pi$
$48$		0			0
$49$	−193.347	−	283.313i	−0.563693	−	0.825984i
$50$		0			0
$51$	123.331	+	213.615i	0.338623	+	0.586512i
$52$		0			0
$53$	−382.195	+	661.981i	−0.990538	+	1.71566i	−0.376415	+	0.926451i	$0.622843\pi$
$53$	−382.195	+	661.981i	−0.990538	+	1.71566i	−0.614122	+	0.789211i	$0.710490\pi$
$54$		0			0
$55$	−210.706			−0.516573
$56$		0			0
$57$	36.7298			0.0853506
$58$		0			0
$59$	225.336	−	390.293i	0.497224	−	0.861216i	−0.502771	−	0.864419i	$-0.667686\pi$
$59$	225.336	−	390.293i	0.497224	−	0.861216i	0.999995	+	0.00320303i	$0.00101956\pi$
$60$		0			0
$61$	87.0388	+	150.756i	0.182691	+	0.316431i	0.942796	−	0.333370i	$-0.108186\pi$
$61$	87.0388	+	150.756i	0.182691	+	0.316431i	−0.760105	+	0.649801i	$0.774852\pi$
$62$		0			0
$63$	−354.136	+	13.3308i	−0.708205	+	0.0266592i
$64$		0			0
$65$	62.5117	+	108.273i	0.119287	+	0.206610i
$66$		0			0
$67$	248.617	−	430.617i	0.453334	−	0.785198i	−0.545256	−	0.838269i	$-0.683568\pi$
$67$	248.617	−	430.617i	0.453334	−	0.785198i	0.998591	+	0.0530711i	$0.0169010\pi$
$68$		0			0
$69$	−26.2967			−0.0458805
$70$		0			0
$71$	350.238			0.585432			0.292716	−	0.956199i	$-0.405441\pi$
$71$	350.238			0.585432			0.292716	+	0.956199i	$0.405441\pi$
$72$		0			0
$73$	531.343	−	920.312i	0.851903	−	1.47554i	−0.0275851	−	0.999619i	$-0.508782\pi$
$73$	531.343	−	920.312i	0.851903	−	1.47554i	0.879488	−	0.475920i	$-0.157885\pi$
$74$		0			0
$75$	112.490	+	194.838i	0.173190	+	0.299973i
$76$		0			0
$77$	−310.375	−	493.712i	−0.459358	−	0.730698i
$78$		0			0
$79$	−280.224	−	485.363i	−0.399085	−	0.691235i	0.594528	−	0.804075i	$-0.297339\pi$
$79$	−280.224	−	485.363i	−0.399085	−	0.691235i	−0.993613	+	0.112839i	$0.964005\pi$
$80$		0			0
$81$	−76.8993	+	133.194i	−0.105486	+	0.182707i
$82$		0			0
$83$	−1105.27			−1.46168			−0.730840	−	0.682549i	$-0.760871\pi$
$83$	−1105.27			−1.46168			−0.730840	+	0.682549i	$0.760871\pi$
$84$		0			0
$85$	588.551			0.751027
$86$		0			0
$87$	7.17830	−	12.4332i	0.00884592	−	0.0153216i
$88$		0			0
$89$	−603.357	−	1045.04i	−0.718604	−	1.24466i	−0.961553	−	0.274619i	$-0.911448\pi$
$89$	−603.357	−	1045.04i	−0.718604	−	1.24466i	0.242950	−	0.970039i	$-0.421885\pi$
$90$		0			0
$91$	−161.618	+	305.964i	−0.186178	+	0.352458i
$92$		0			0
$93$	360.948	+	625.181i	0.402458	+	0.697078i
$94$		0			0
$95$	43.8199	−	75.8983i	0.0473245	−	0.0819684i
$96$		0			0
$97$	1442.99			1.51045			0.755226	−	0.655465i	$-0.227527\pi$
$97$	1442.99			1.51045			0.755226	+	0.655465i	$0.227527\pi$
$98$		0			0
$99$	−602.528			−0.611680
$100$		0			0
$101$	−155.961	+	270.133i	−0.153651	+	0.266131i	−0.932567	−	0.360997i	$-0.882436\pi$
$101$	−155.961	+	270.133i	−0.153651	+	0.266131i	0.778916	+	0.627128i	$0.215770\pi$
$102$		0			0
$103$	290.816	+	503.708i	0.278203	+	0.481862i	0.970938	−	0.239330i	$-0.0769278\pi$
$103$	290.816	+	503.708i	0.278203	+	0.481862i	−0.692735	+	0.721192i	$0.743594\pi$
$104$		0			0
$105$	162.332	−	307.315i	0.150876	−	0.285628i
$106$		0			0
$107$	587.738	+	1017.99i	0.531016	+	0.919748i	0.999345	+	0.0361930i	$0.0115231\pi$
$107$	587.738	+	1017.99i	0.531016	+	0.919748i	−0.468328	+	0.883555i	$0.655144\pi$
$108$		0			0
$109$	−168.526	+	291.896i	−0.148091	+	0.256500i	−0.930522	−	0.366237i	$-0.880646\pi$
$109$	−168.526	+	291.896i	−0.148091	+	0.256500i	0.782431	+	0.622737i	$0.213979\pi$
$110$		0			0
$111$	−1066.29			−0.911783
$112$		0			0
$113$	−1168.16			−0.972487			−0.486243	−	0.873823i	$-0.661633\pi$
$113$	−1168.16			−0.972487			−0.486243	+	0.873823i	$0.661633\pi$
$114$		0			0
$115$	−31.3729	+	54.3394i	−0.0254394	+	0.0440624i
$116$		0			0
$117$	178.757	+	309.616i	0.141248	+	0.244649i
$118$		0			0
$119$	866.953	+	1379.06i	0.667844	+	1.06234i
$120$		0			0
$121$	169.749	+	294.015i	0.127535	+	0.220898i
$122$		0			0
$123$	305.627	−	529.361i	0.224044	−	0.388056i
$124$		0			0
$125$	1373.27			0.982629
$126$		0			0
$127$	23.4734			0.0164010			0.00820049	−	0.999966i	$-0.497390\pi$
$127$	23.4734			0.0164010			0.00820049	+	0.999966i	$0.497390\pi$
$128$		0			0
$129$	−528.707	+	915.747i	−0.360853	+	0.625016i
$130$		0			0
$131$	186.991	+	323.878i	0.124713	+	0.216010i	0.921621	−	0.388091i	$-0.126865\pi$
$131$	186.991	+	323.878i	0.124713	+	0.216010i	−0.796907	+	0.604101i	$0.793532\pi$
$132$		0			0
$133$	242.388	−	9.12429i	0.158028	−	0.00594870i
$134$		0			0
$135$	−432.890	−	749.788i	−0.275980	−	0.478011i
$136$		0			0
$137$	−569.069	+	985.656i	−0.354882	+	0.614674i	−0.987098	−	0.160119i	$-0.948812\pi$
$137$	−569.069	+	985.656i	−0.354882	+	0.614674i	0.632216	+	0.774792i	$0.282146\pi$
$138$		0			0
$139$	−1229.46			−0.750224			−0.375112	−	0.926979i	$-0.622396\pi$
$139$	−1229.46			−0.750224			−0.375112	+	0.926979i	$0.622396\pi$
$140$		0			0
$141$	−1003.18			−0.599170
$142$		0			0
$143$	−294.157	+	509.494i	−0.172018	+	0.297944i
$144$		0			0
$145$	−17.1279	−	29.6664i	−0.00980962	−	0.0169908i
$146$		0			0
$147$	959.203	−	72.3176i	0.538188	−	0.0405759i
$148$		0			0
$149$	−1481.38	−	2565.82i	−0.814492	−	1.41074i	−0.909692	−	0.415283i	$-0.863683\pi$
$149$	−1481.38	−	2565.82i	−0.814492	−	1.41074i	0.0952006	−	0.995458i	$-0.469651\pi$
$150$		0			0
$151$	1298.85	−	2249.68i	0.699993	−	1.21242i	−0.268475	−	0.963287i	$-0.586520\pi$
$151$	1298.85	−	2249.68i	0.699993	−	1.21242i	0.968468	−	0.249137i	$-0.0801471\pi$
$152$		0			0
$153$	1683.00			0.889299
$154$		0			0
$155$	1722.49			0.892606
$156$		0			0
$157$	−682.492	+	1182.11i	−0.346935	+	0.600909i	−0.985703	−	0.168490i	$-0.946111\pi$
$157$	−682.492	+	1182.11i	−0.346935	+	0.600909i	0.638768	+	0.769399i	$0.279444\pi$
$158$		0			0
$159$	−1071.84	−	1856.49i	−0.534609	−	0.925970i
$160$		0			0
$161$	−173.538	+	6.53254i	−0.0849485	+	0.00319774i
$162$		0			0
$163$	−1658.74	−	2873.02i	−0.797071	−	1.38057i	−0.921516	−	0.388341i	$-0.873048\pi$
$163$	−1658.74	−	2873.02i	−0.797071	−	1.38057i	0.124445	−	0.992227i	$-0.460285\pi$
$164$		0			0
$165$	295.456	−	511.745i	0.139401	−	0.241450i
$166$		0			0
$167$	3803.96			1.76263			0.881315	−	0.472530i	$-0.156659\pi$
$167$	3803.96			1.76263			0.881315	+	0.472530i	$0.156659\pi$
$168$		0			0
$169$	−1847.92			−0.841111
$170$		0			0
$171$	125.306	−	217.037i	0.0560374	−	0.0970597i
$172$		0			0
$173$	−1261.15	−	2184.37i	−0.554239	−	0.959970i	−0.997962	−	0.0638064i	$-0.979676\pi$
$173$	−1261.15	−	2184.37i	−0.554239	−	0.959970i	0.443723	−	0.896164i	$-0.353657\pi$
$174$		0			0
$175$	790.747	+	1257.84i	0.341571	+	0.543334i
$176$		0			0
$177$	631.941	+	1094.55i	0.268359	+	0.464812i
$178$		0			0
$179$	93.5182	−	161.978i	0.0390496	−	0.0676359i	−0.845840	−	0.533437i	$-0.820900\pi$
$179$	93.5182	−	161.978i	0.0390496	−	0.0676359i	0.884890	+	0.465801i	$0.154234\pi$
$180$		0			0
$181$	−457.654			−0.187940			−0.0939701	−	0.995575i	$-0.529956\pi$
$181$	−457.654			−0.187940			−0.0939701	+	0.995575i	$0.529956\pi$
$182$		0			0
$183$	−488.191			−0.197203
$184$		0			0
$185$	−1272.12	+	2203.38i	−0.505558	+	0.875652i
$186$		0			0
$187$	1384.75	+	2398.46i	0.541513	+	0.937928i
$188$		0			0
$189$	1119.20	−	2118.78i	0.430739	−	0.815443i
$190$		0			0
$191$	−1445.80	−	2504.19i	−0.547719	−	0.948676i	−0.998430	−	0.0560069i	$-0.982163\pi$
$191$	−1445.80	−	2504.19i	−0.547719	−	0.948676i	0.450712	−	0.892670i	$-0.351170\pi$
$192$		0			0
$193$	−573.946	+	994.104i	−0.214060	+	0.370762i	−0.952981	−	0.303029i	$-0.902002\pi$
$193$	−573.946	+	994.104i	−0.214060	+	0.370762i	0.738922	+	0.673791i	$0.235335\pi$
$194$		0			0
$195$	−350.621			−0.128762
$196$		0			0
$197$	1638.22			0.592481			0.296240	−	0.955113i	$-0.404267\pi$
$197$	1638.22			0.592481			0.296240	+	0.955113i	$0.404267\pi$
$198$		0			0
$199$	−2655.64	+	4599.70i	−0.945996	+	1.63851i	−0.192251	+	0.981346i	$0.561579\pi$
$199$	−2655.64	+	4599.70i	−0.945996	+	1.63851i	−0.753745	+	0.657167i	$0.771755\pi$
$200$		0			0
$201$	697.233	+	1207.64i	0.244672	+	0.423784i
$202$		0			0
$203$	44.2826	−	83.8325i	0.0153105	−	0.0289847i
$204$		0			0
$205$	−729.245	−	1263.09i	−0.248452	−	0.430332i
$206$		0			0
$207$	−89.7130	+	155.387i	−0.0301231	+	0.0521748i
$208$		0			0
$209$	412.400			0.136489
$210$		0			0
$211$	−1505.74			−0.491277			−0.245639	−	0.969361i	$-0.578998\pi$
$211$	−1505.74			−0.491277			−0.245639	+	0.969361i	$0.578998\pi$
$212$		0			0
$213$	−491.112	+	850.632i	−0.157983	+	0.273635i
$214$		0			0
$215$	1261.53	+	2185.03i	0.400165	+	0.693107i
$216$		0			0
$217$	2537.28	+	4036.04i	0.793742	+	1.26260i
$218$		0			0
$219$	1490.12	+	2580.97i	0.459786	+	0.796372i
$220$		0			0
$221$	821.650	−	1423.14i	0.250091	−	0.433171i
$222$		0			0
$223$	−2520.23			−0.756802			−0.378401	−	0.925642i	$-0.623526\pi$
$223$	−2520.23			−0.756802			−0.378401	+	0.925642i	$0.623526\pi$
$224$		0			0
$225$	1535.07			0.454834
$226$		0			0
$227$	769.019	−	1331.98i	0.224853	−	0.389456i	−0.731423	−	0.681925i	$-0.761143\pi$
$227$	769.019	−	1331.98i	0.224853	−	0.389456i	0.956275	+	0.292468i	$0.0944766\pi$
$228$		0			0
$229$	−285.842	−	495.092i	−0.0824845	−	0.142867i	0.821832	−	0.569730i	$-0.192952\pi$
$229$	−285.842	−	495.092i	−0.0824845	−	0.142867i	−0.904317	+	0.426863i	$0.859619\pi$
$230$		0			0
$231$	1634.31	−	61.5207i	0.465495	−	0.0175228i
$232$		0			0
$233$	802.101	+	1389.28i	0.225525	+	0.390621i	0.956477	−	0.291808i	$-0.0942568\pi$
$233$	802.101	+	1389.28i	0.225525	+	0.390621i	−0.730952	+	0.682429i	$0.760923\pi$
$234$		0			0
$235$	−1196.83	+	2072.96i	−0.332223	+	0.575426i
$236$		0			0
$237$	1571.75			0.430785
$238$		0			0
$239$	−4699.38			−1.27187			−0.635936	−	0.771742i	$-0.719386\pi$
$239$	−4699.38			−1.27187			−0.635936	+	0.771742i	$0.719386\pi$
$240$		0			0
$241$	436.304	−	755.700i	0.116617	−	0.201987i	−0.801808	−	0.597582i	$-0.796128\pi$
$241$	436.304	−	755.700i	0.116617	−	0.201987i	0.918425	+	0.395595i	$0.129462\pi$
$242$		0			0
$243$	−1962.34	−	3398.86i	−0.518041	−	0.897273i
$244$		0			0
$245$	994.923	−	2068.37i	0.259442	−	0.539360i
$246$		0			0
$247$	−122.350	−	211.916i	−0.0315180	−	0.0545908i
$248$		0			0
$249$	1549.84	−	2684.40i	0.394446	−	0.683200i
$250$		0			0
$251$	3126.30			0.786176			0.393088	−	0.919501i	$-0.371407\pi$
$251$	3126.30			0.786176			0.393088	+	0.919501i	$0.371407\pi$
$252$		0			0
$253$	−295.258			−0.0733704
$254$		0			0
$255$	−825.280	+	1429.43i	−0.202671	+	0.351036i
$256$		0			0
$257$	−452.007	−	782.900i	−0.109710	−	0.190023i	0.805943	−	0.591993i	$-0.201659\pi$
$257$	−452.007	−	782.900i	−0.109710	−	0.190023i	−0.915653	+	0.401970i	$0.868326\pi$
$258$		0			0
$259$	−7036.69	+	264.884i	−1.68818	+	0.0635487i
$260$		0			0
$261$	−48.9785	−	84.8332i	−0.0116157	−	0.0201189i
$262$		0			0
$263$	46.3184	−	80.2258i	0.0108598	−	0.0188096i	−0.860544	−	0.509375i	$-0.829876\pi$
$263$	46.3184	−	80.2258i	0.0108598	−	0.0188096i	0.871404	+	0.490566i	$0.163210\pi$
$264$		0			0
$265$	−5114.98			−1.18570
$266$		0			0
$267$	3384.16			0.775683
$268$		0			0
$269$	2025.89	−	3508.94i	0.459184	−	0.795330i	−0.539734	−	0.841836i	$-0.681475\pi$
$269$	2025.89	−	3508.94i	0.459184	−	0.795330i	0.998918	+	0.0465054i	$0.0148085\pi$
$270$		0			0
$271$	−1395.65	−	2417.34i	−0.312840	−	0.541855i	0.666136	−	0.745830i	$-0.267947\pi$
$271$	−1395.65	−	2417.34i	−0.312840	−	0.541855i	−0.978976	+	0.203975i	$0.934614\pi$
$272$		0			0
$273$	−516.476	−	821.555i	−0.114500	−	0.182135i
$274$		0			0
$275$	1263.03	+	2187.63i	0.276958	+	0.479706i
$276$		0			0
$277$	1290.33	−	2234.92i	0.279886	−	0.484777i	−0.691470	−	0.722405i	$-0.743037\pi$
$277$	1290.33	−	2234.92i	0.279886	−	0.484777i	0.971356	+	0.237628i	$0.0763699\pi$
$278$		0			0
$279$	4925.59			1.05694
$280$		0			0
$281$	−919.487			−0.195203			−0.0976014	−	0.995226i	$-0.531117\pi$
$281$	−919.487			−0.195203			−0.0976014	+	0.995226i	$0.531117\pi$
$282$		0			0
$283$	4136.00	−	7163.77i	0.868762	−	1.50474i	0.00550035	−	0.999985i	$-0.498249\pi$
$283$	4136.00	−	7163.77i	0.868762	−	1.50474i	0.863262	−	0.504756i	$-0.168417\pi$
$284$		0			0
$285$	122.891	+	212.853i	0.0255418	+	0.0442396i
$286$		0			0
$287$	1885.39	−	3569.29i	0.387775	−	0.734107i
$288$		0			0
$289$	−1411.44	−	2444.68i	−0.287286	−	0.497595i
$290$		0			0
$291$	−2023.40	+	3504.63i	−0.407607	+	0.705997i
$292$		0			0
$293$	−2859.38			−0.570126			−0.285063	−	0.958509i	$-0.592014\pi$
$293$	−2859.38			−0.570126			−0.285063	+	0.958509i	$0.592014\pi$
$294$		0			0
$295$	3015.71			0.595191
$296$		0			0
$297$	2037.02	−	3528.22i	0.397979	−	0.689320i
$298$		0			0
$299$	87.5965	+	151.722i	0.0169426	+	0.0293455i
$300$		0			0
$301$	−3261.56	+	6174.55i	−0.624563	+	1.18238i
$302$		0			0
$303$	−437.385	−	757.573i	−0.0829277	−	0.143635i
$304$		0			0
$305$	−582.428	+	1008.79i	−0.109343	+	0.189388i
$306$		0			0
$307$	−3542.86			−0.658638			−0.329319	−	0.944219i	$-0.606819\pi$
$307$	−3542.86			−0.658638			−0.329319	+	0.944219i	$0.606819\pi$
$308$		0			0
$309$	−1631.15			−0.300301
$310$		0			0
$311$	311.274	−	539.143i	0.0567548	−	0.0983022i	−0.836252	−	0.548345i	$-0.815258\pi$
$311$	311.274	−	539.143i	0.0567548	−	0.0983022i	0.893007	+	0.450043i	$0.148591\pi$
$312$		0			0
$313$	3532.42	+	6118.34i	0.637905	+	1.10488i	0.985892	+	0.167385i	$0.0535322\pi$
$313$	3532.42	+	6118.34i	0.637905	+	1.10488i	−0.347986	+	0.937500i	$0.613134\pi$
$314$		0			0
$315$	−1262.12	−	2007.65i	−0.225754	−	0.359105i
$316$		0			0
$317$	3229.60	+	5593.84i	0.572217	+	0.991108i	0.996338	+	0.0855029i	$0.0272497\pi$
$317$	3229.60	+	5593.84i	0.572217	+	0.991108i	−0.424121	+	0.905605i	$0.639417\pi$
$318$		0			0
$319$	80.5975	−	139.599i	0.0141461	−	0.0245017i
$320$		0			0
$321$	−3296.56			−0.573196
$322$		0			0
$323$	−1151.93			−0.198437
$324$		0			0
$325$	749.426	−	1298.04i	0.127910	−	0.221546i
$326$		0			0
$327$	−472.622	−	818.606i	−0.0799268	−	0.138437i
$328$		0			0
$329$	−6620.20	+	249.206i	−1.10937	+	0.0417604i
$330$		0			0
$331$	4167.61	+	7218.51i	0.692062	+	1.19869i	0.971161	+	0.238424i	$0.0766308\pi$
$331$	4167.61	+	7218.51i	0.692062	+	1.19869i	−0.279099	+	0.960262i	$0.590036\pi$
$332$		0			0
$333$	−3637.72	+	6300.72i	−0.598636	+	1.03687i
$334$		0			0
$335$	3327.29			0.542654
$336$		0			0
$337$	5853.18			0.946122			0.473061	−	0.881030i	$-0.343149\pi$
$337$	5853.18			0.946122			0.473061	+	0.881030i	$0.343149\pi$
$338$		0			0
$339$	1638.02	−	2837.13i	0.262433	−	0.454548i
$340$		0			0
$341$	4052.70	+	7019.49i	0.643596	+	1.11474i
$342$		0			0
$343$	6312.02	−	715.521i	0.993636	−	0.112637i
$344$		0			0
$345$	−87.9835	−	152.392i	−0.0137301	−	0.0237812i
$346$		0			0
$347$	−3587.90	+	6214.43i	−0.555069	+	0.961407i	0.442830	+	0.896606i	$0.353975\pi$
$347$	−3587.90	+	6214.43i	−0.555069	+	0.961407i	−0.997898	+	0.0648013i	$0.979359\pi$
$348$		0			0
$349$	−10302.4			−1.58016			−0.790081	−	0.613003i	$-0.789961\pi$
$349$	−10302.4			−1.58016			−0.790081	+	0.613003i	$0.789961\pi$
$350$		0			0
$351$	−2417.35			−0.367604
$352$		0			0
$353$	−550.560	+	953.599i	−0.0830124	+	0.143782i	−0.904543	−	0.426383i	$-0.859787\pi$
$353$	−550.560	+	953.599i	−0.0830124	+	0.143782i	0.821530	+	0.570165i	$0.193121\pi$
$354$		0			0
$355$	1171.83	+	2029.66i	0.175195	+	0.303446i
$356$		0			0
$357$	−4565.01	+	171.842i	−0.676767	+	0.0254757i
$358$		0			0
$359$	2816.47	+	4878.26i	0.414060	+	0.717172i	0.995329	−	0.0965388i	$-0.0307772\pi$
$359$	2816.47	+	4878.26i	0.414060	+	0.717172i	−0.581270	+	0.813711i	$0.697444\pi$
$360$		0			0
$361$	3343.73	−	5791.52i	0.487496	−	0.844368i
$362$		0			0
$363$	−952.106			−0.137666
$364$		0			0
$365$	7111.05			1.01975
$366$		0			0
$367$	−1598.23	+	2768.22i	−0.227322	+	0.393733i	−0.957013	−	0.290044i	$-0.906330\pi$
$367$	−1598.23	+	2768.22i	−0.227322	+	0.393733i	0.729692	+	0.683776i	$0.239664\pi$
$368$		0			0
$369$	−2085.33	−	3611.90i	−0.294195	−	0.509560i
$370$		0			0
$371$	−7534.52	−	11985.1i	−1.05437	−	1.67719i
$372$		0			0
$373$	−457.697	−	792.755i	−0.0635353	−	0.110046i	0.832508	−	0.554013i	$-0.186904\pi$
$373$	−457.697	−	792.755i	−0.0635353	−	0.110046i	−0.896043	+	0.443967i	$0.853571\pi$
$374$		0			0
$375$	−1925.62	+	3335.28i	−0.265170	+	0.459288i
$376$		0			0
$377$	−95.6460			−0.0130664
$378$		0			0
$379$	11767.5			1.59487			0.797437	−	0.603402i	$-0.206188\pi$
$379$	11767.5			1.59487			0.797437	+	0.603402i	$0.206188\pi$
$380$		0			0
$381$	−32.9149	+	57.0103i	−0.00442594	+	0.00766595i
$382$		0			0
$383$	−4207.56	−	7287.71i	−0.561348	−	0.972283i	−0.997379	−	0.0723518i	$-0.976950\pi$
$383$	−4207.56	−	7287.71i	−0.561348	−	0.972283i	0.436031	−	0.899932i	$-0.356384\pi$
$384$		0			0
$385$	1822.65	−	3450.51i	0.241275	−	0.456765i
$386$		0			0
$387$	3607.43	+	6248.26i	0.473840	+	0.820715i
$388$		0			0
$389$	1681.19	−	2911.91i	0.219125	−	0.379536i	−0.735415	−	0.677616i	$-0.763013\pi$
$389$	1681.19	−	2911.91i	0.219125	−	0.379536i	0.954541	+	0.298080i	$0.0963463\pi$
$390$		0			0
$391$	824.726			0.106671
$392$		0			0
$393$	−1048.81			−0.134620
$394$		0			0
$395$	1875.15	−	3247.85i	0.238858	−	0.413714i
$396$		0			0
$397$	2431.72	+	4211.86i	0.307417	+	0.532462i	0.977797	−	0.209557i	$-0.0672020\pi$
$397$	2431.72	+	4211.86i	0.307417	+	0.532462i	−0.670380	+	0.742018i	$0.733869\pi$
$398$		0			0
$399$	−317.722	+	601.488i	−0.0398646	+	0.0754688i
$400$		0			0
$401$	−1869.43	−	3237.94i	−0.232805	−	0.403229i	0.725828	−	0.687876i	$-0.241457\pi$
$401$	−1869.43	−	3237.94i	−0.232805	−	0.403229i	−0.958632	+	0.284647i	$0.908124\pi$
$402$		0			0
$403$	2404.70	−	4165.06i	0.297237	−	0.514829i
$404$		0			0
$405$	−1029.16			−0.126270
$406$		0			0
$407$	−11972.2			−1.45809
$408$		0			0
$409$	7006.64	−	12135.9i	0.847081	−	1.46719i	−0.0367205	−	0.999326i	$-0.511691\pi$
$409$	7006.64	−	12135.9i	0.847081	−	1.46719i	0.883802	−	0.467862i	$-0.154976\pi$
$410$		0			0
$411$	−1595.92	−	2764.22i	−0.191535	−	0.331749i
$412$		0			0
$413$	4442.22	+	7066.22i	0.529268	+	0.841903i
$414$		0			0
$415$	−3698.01	−	6405.15i	−0.437418	−	0.757630i
$416$		0			0
$417$	1723.97	−	2986.01i	0.202454	−	0.350661i
$418$		0			0
$419$	−8043.46			−0.937826			−0.468913	−	0.883244i	$-0.655354\pi$
$419$	−8043.46			−0.937826			−0.468913	+	0.883244i	$0.655354\pi$
$420$		0			0
$421$	1832.27			0.212112			0.106056	−	0.994360i	$-0.466178\pi$
$421$	1832.27			0.212112			0.106056	+	0.994360i	$0.466178\pi$
$422$		0			0
$423$	−3422.41	+	5927.79i	−0.393388	+	0.681368i
$424$		0			0
$425$	−3527.94	−	6110.58i	−0.402660	−	0.697427i
$426$		0			0
$427$	−3221.68	+	121.275i	−0.365124	+	0.0137445i
$428$		0			0
$429$	−824.946	−	1428.85i	−0.0928410	−	0.160805i
$430$		0			0
$431$	−1431.63	+	2479.65i	−0.159998	+	0.277124i	−0.934868	−	0.354997i	$-0.884482\pi$
$431$	−1431.63	+	2479.65i	−0.159998	+	0.277124i	0.774870	+	0.632121i	$0.217815\pi$
$432$		0			0
$433$	−6856.23			−0.760946			−0.380473	−	0.924792i	$-0.624239\pi$
$433$	−6856.23			−0.760946			−0.380473	+	0.924792i	$0.624239\pi$
$434$		0			0
$435$	96.0685			0.0105888
$436$		0			0
$437$	61.4040	−	106.355i	0.00672163	−	0.0116422i
$438$		0			0
$439$	2037.21	+	3528.55i	0.221482	+	0.383618i	0.955258	−	0.295773i	$-0.0955772\pi$
$439$	2037.21	+	3528.55i	0.221482	+	0.383618i	−0.733776	+	0.679391i	$0.762244\pi$
$440$		0			0
$441$	2845.05	−	5914.64i	0.307208	−	0.638661i
$442$		0			0
$443$	1248.96	+	2163.27i	0.133950	+	0.232009i	0.925196	−	0.379490i	$-0.123900\pi$
$443$	1248.96	+	2163.27i	0.133950	+	0.232009i	−0.791246	+	0.611498i	$0.790567\pi$
$444$		0			0
$445$	4037.42	−	6993.01i	0.430094	−	0.744945i
$446$		0			0
$447$	8308.89			0.879188
$448$		0			0
$449$	9529.68			1.00163			0.500817	−	0.865553i	$-0.333033\pi$
$449$	9529.68			1.00163			0.500817	+	0.865553i	$0.333033\pi$
$450$		0			0
$451$	3431.55	−	5943.62i	0.358283	−	0.620564i
$452$		0			0
$453$	3642.56	+	6309.09i	0.377797	+	0.654364i
$454$		0			0
$455$	−2313.83	+	87.1001i	−0.238404	+	0.00897432i
$456$		0			0
$457$	−5275.95	−	9138.22i	−0.540041	−	0.935379i	−0.998901	−	0.0468699i	$-0.985075\pi$
$457$	−5275.95	−	9138.22i	−0.540041	−	0.935379i	0.458860	−	0.888509i	$-0.348258\pi$
$458$		0			0
$459$	−5689.88	+	9855.16i	−0.578608	+	1.00218i
$460$		0			0
$461$	13103.5			1.32384			0.661922	−	0.749573i	$-0.269741\pi$
$461$	13103.5			1.32384			0.661922	+	0.749573i	$0.269741\pi$
$462$		0			0
$463$	−816.035			−0.0819101			−0.0409550	−	0.999161i	$-0.513040\pi$
$463$	−816.035			−0.0819101			−0.0409550	+	0.999161i	$0.513040\pi$
$464$		0			0
$465$	−2415.32	+	4183.46i	−0.240877	+	0.417211i
$466$		0			0
$467$	2294.16	+	3973.61i	0.227326	+	0.393740i	0.957015	−	0.290039i	$-0.0936684\pi$
$467$	2294.16	+	3973.61i	0.227326	+	0.393740i	−0.729689	+	0.683779i	$0.760335\pi$
$468$		0			0
$469$	4901.19	+	7796.30i	0.482550	+	0.767590i
$470$		0			0
$471$	−1914.01	−	3315.17i	−0.187246	−	0.324320i
$472$		0			0
$473$	−5936.28	+	10281.9i	−0.577062	+	0.999501i
$474$		0			0
$475$	−1050.68			−0.101491
$476$		0			0
$477$	−14626.7			−1.40400
$478$		0			0
$479$	−8690.77	+	15052.9i	−0.829001	+	1.43587i	0.0698212	+	0.997560i	$0.477757\pi$
$479$	−8690.77	+	15052.9i	−0.829001	+	1.43587i	−0.898822	+	0.438313i	$0.855576\pi$
$480$		0			0
$481$	3551.90	+	6152.07i	0.336700	+	0.583182i
$482$		0			0
$483$	227.473	−	430.635i	0.0214294	−	0.0405685i
$484$		0			0
$485$	4827.96	+	8362.28i	0.452013	+	0.782910i
$486$		0			0
$487$	8176.24	−	14161.7i	0.760781	−	1.31771i	−0.181667	−	0.983360i	$-0.558149\pi$
$487$	8176.24	−	14161.7i	0.760781	−	1.31771i	0.942448	−	0.334352i	$-0.108517\pi$
$488$		0			0
$489$	9303.70			0.860384
$490$		0			0
$491$	−13094.7			−1.20358			−0.601789	−	0.798655i	$-0.705545\pi$
$491$	−13094.7			−1.20358			−0.601789	+	0.798655i	$0.705545\pi$
$492$		0			0
$493$	−225.128	+	389.933i	−0.0205664	+	0.0356221i
$494$		0			0
$495$	−2015.93	−	3491.70i	−0.183050	−	0.317051i
$496$		0			0
$497$	−3029.65	+	5735.50i	−0.273437	+	0.517651i
$498$		0			0
$499$	4880.53	+	8453.32i	0.437840	+	0.758362i	0.997523	−	0.0703455i	$-0.0224102\pi$
$499$	4880.53	+	8453.32i	0.437840	+	0.758362i	−0.559682	+	0.828707i	$0.689077\pi$
$500$		0			0
$501$	−5334.00	+	9238.75i	−0.475660	+	0.823866i
$502$		0			0
$503$	14229.0			1.26131			0.630657	−	0.776061i	$-0.282785\pi$
$503$	14229.0			1.26131			0.630657	+	0.776061i	$0.282785\pi$
$504$		0			0
$505$	−2087.26			−0.183924
$506$		0			0
$507$	2591.20	−	4488.08i	0.226980	−	0.393142i
$508$		0			0
$509$	−10160.2	−	17597.9i	−0.884757	−	1.53244i	−0.845992	−	0.533196i	$-0.820991\pi$
$509$	−10160.2	−	17597.9i	−0.884757	−	1.53244i	−0.0387650	−	0.999248i	$-0.512342\pi$
$510$		0			0
$511$	10474.8	+	16662.2i	0.906805	+	1.44245i
$512$		0			0
$513$	847.267	+	1467.51i	0.0729196	+	0.126300i
$514$		0			0
$515$	−1946.02	+	3370.61i	−0.166509	+	0.288401i
$516$		0			0
$517$	−11263.6			−0.958170
$518$		0			0
$519$	7073.65			0.598263
$520$		0			0
$521$	−10092.7	+	17481.0i	−0.848692	+	1.46998i	0.0336847	+	0.999433i	$0.489276\pi$
$521$	−10092.7	+	17481.0i	−0.848692	+	1.46998i	−0.882376	+	0.470544i	$0.844058\pi$
$522$		0			0
$523$	1355.34	+	2347.51i	0.113317	+	0.196271i	0.917106	−	0.398644i	$-0.130519\pi$
$523$	1355.34	+	2347.51i	0.113317	+	0.196271i	−0.803789	+	0.594915i	$0.797186\pi$
$524$		0			0
$525$	−4163.74	+	156.737i	−0.346134	+	0.0130296i
$526$		0			0
$527$	−11320.2	−	19607.1i	−0.935701	−	1.62068i
$528$		0			0
$529$	6039.54	−	10460.8i	0.496387	−	0.859767i
$530$		0			0
$531$	8623.63			0.704771
$532$		0			0
$533$	−4072.27			−0.330937
$534$		0			0
$535$	−3932.90	+	6811.99i	−0.317821	+	0.550482i
$536$		0			0
$537$	262.267	+	454.259i	0.0210757	+	0.0365042i
$538$		0			0
$539$	10769.9	−	811.977i	0.860650	−	0.0648874i
$540$		0			0
$541$	−1828.34	−	3166.77i	−0.145298	−	0.251664i	0.784186	−	0.620526i	$-0.213081\pi$
$541$	−1828.34	−	3166.77i	−0.145298	−	0.251664i	−0.929484	+	0.368862i	$0.879747\pi$
$542$		0			0
$543$	641.733	−	1111.51i	0.0507171	−	0.0878447i
$544$		0			0
$545$	−2255.42			−0.177269
$546$		0			0
$547$	787.130			0.0615269			0.0307635	−	0.999527i	$-0.490206\pi$
$547$	787.130			0.0615269			0.0307635	+	0.999527i	$0.490206\pi$
$548$		0			0
$549$	−1665.49	+	2884.72i	−0.129475	+	0.224257i
$550$		0			0
$551$	33.5233	+	58.0640i	0.00259191	+	0.00448931i
$552$		0			0
$553$	10372.3	−	390.448i	0.797605	−	0.0300245i
$554$		0			0
$555$	−3567.59	−	6179.25i	−0.272857	−	0.472603i
$556$		0			0
$557$	6228.68	−	10788.4i	0.473820	−	0.820680i	−0.525731	−	0.850651i	$-0.676208\pi$
$557$	6228.68	−	10788.4i	0.473820	−	0.820680i	0.999551	+	0.0299707i	$0.00954140\pi$
$558$		0			0
$559$	7044.66			0.533018
$560$		0			0
$561$	−7766.91			−0.584526
$562$		0			0
$563$	7959.35	−	13786.0i	0.595820	−	1.03199i	−0.397611	−	0.917554i	$-0.630161\pi$
$563$	7959.35	−	13786.0i	0.595820	−	1.03199i	0.993431	−	0.114436i	$-0.0365061\pi$
$564$		0			0
$565$	−3908.42	−	6769.57i	−0.291023	−	0.504067i
$566$		0			0
$567$	−1515.98	−	2411.46i	−0.112284	−	0.178610i
$568$		0			0
$569$	3908.25	+	6769.28i	0.287948	+	0.498740i	0.973320	−	0.229453i	$-0.0736937\pi$
$569$	3908.25	+	6769.28i	0.287948	+	0.498740i	−0.685372	+	0.728193i	$0.740360\pi$
$570$		0			0
$571$	10918.9	−	18912.1i	0.800248	−	1.38607i	−0.119206	−	0.992870i	$-0.538035\pi$
$571$	10918.9	−	18912.1i	0.800248	−	1.38607i	0.919453	−	0.393200i	$-0.128632\pi$
$572$		0			0
$573$	8109.32			0.591225
$574$		0			0
$575$	752.232			0.0545569
$576$		0			0
$577$	−7592.30	+	13150.3i	−0.547785	+	0.948791i	0.450641	+	0.892705i	$0.351195\pi$
$577$	−7592.30	+	13150.3i	−0.547785	+	0.948791i	−0.998426	+	0.0560856i	$0.982138\pi$
$578$		0			0
$579$	−1609.60	−	2787.91i	−0.115531	−	0.200106i
$580$		0			0
$581$	9560.87	−	18099.9i	0.682705	−	1.29245i
$582$		0			0
$583$	−12034.6	−	20844.5i	−0.854926	−	1.48078i
$584$		0			0
$585$	−1196.17	+	2071.82i	−0.0845392	+	0.146426i
$586$		0			0
$587$	−21861.6			−1.53718			−0.768591	−	0.639740i	$-0.779042\pi$
$587$	−21861.6			−1.53718			−0.768591	+	0.639740i	$0.779042\pi$
$588$		0			0
$589$	−3371.32			−0.235845
$590$		0			0
$591$	−2297.16	+	3978.79i	−0.159886	+	0.276930i
$592$		0			0
$593$	136.751	+	236.860i	0.00946997	+	0.0164025i	0.870722	−	0.491776i	$-0.163652\pi$
$593$	136.751	+	236.860i	0.00946997	+	0.0164025i	−0.861252	+	0.508179i	$0.830319\pi$
$594$		0			0
$595$	−5091.11	+	9638.11i	−0.350782	+	0.664074i
$596$		0			0
$597$	−7447.59	−	12899.6i	−0.510569	−	0.884331i
$598$		0			0
$599$	1221.81	−	2116.24i	0.0833421	−	0.144353i	−0.821341	−	0.570437i	$-0.806774\pi$
$599$	1221.81	−	2116.24i	0.0833421	−	0.144353i	0.904684	+	0.426084i	$0.140107\pi$
$600$		0			0
$601$	−1107.14			−0.0751431			−0.0375716	−	0.999294i	$-0.511962\pi$
$601$	−1107.14			−0.0751431			−0.0375716	+	0.999294i	$0.511962\pi$
$602$		0			0
$603$	9514.62			0.642562
$604$		0			0
$605$	−1135.89	+	1967.43i	−0.0763317	+	0.132210i
$606$		0			0
$607$	709.429	+	1228.77i	0.0474379	+	0.0821649i	0.888769	−	0.458355i	$-0.151561\pi$
$607$	709.429	+	1228.77i	0.0474379	+	0.0821649i	−0.841331	+	0.540520i	$0.818228\pi$
$608$		0			0
$609$	141.512	+	225.102i	0.00941600	+	0.0149780i
$610$		0			0
$611$	3341.67	+	5787.94i	0.221259	+	0.383233i
$612$		0			0
$613$	−4701.49	+	8143.22i	−0.309774	+	0.536544i	−0.978313	−	0.207133i	$-0.933587\pi$
$613$	−4701.49	+	8143.22i	−0.309774	+	0.536544i	0.668539	+	0.743677i	$0.266920\pi$
$614$		0			0
$615$	4090.26			0.268187
$616$		0			0
$617$	−11223.0			−0.732284			−0.366142	−	0.930559i	$-0.619322\pi$
$617$	−11223.0			−0.732284			−0.366142	+	0.930559i	$0.619322\pi$
$618$		0			0
$619$	−7939.57	+	13751.7i	−0.515538	+	0.892938i	0.484299	+	0.874903i	$0.339075\pi$
$619$	−7939.57	+	13751.7i	−0.515538	+	0.892938i	−0.999837	+	0.0180360i	$0.994259\pi$
$620$		0			0
$621$	−606.601	−	1050.66i	−0.0391982	−	0.0678932i
$622$		0			0
$623$	22332.8	−	840.682i	1.43619	−	0.0540629i
$624$		0			0
$625$	−419.247	−	726.156i	−0.0268318	−	0.0464740i
$626$		0			0
$627$	−578.277	+	1001.60i	−0.0368328	+	0.0637962i
$628$		0			0
$629$	33441.3			2.11986
$630$		0			0
$631$	−9079.04			−0.572791			−0.286395	−	0.958112i	$-0.592457\pi$
$631$	−9079.04			−0.572791			−0.286395	+	0.958112i	$0.592457\pi$
$632$		0			0
$633$	2111.38	−	3657.03i	0.132575	−	0.229627i
$634$		0			0
$635$	78.5371	+	136.030i	0.00490811	+	0.00850110i
$636$		0			0
$637$	−3612.42	−	5293.32i	−0.224693	−	0.329245i
$638$		0			0
$639$	3350.92	+	5803.97i	0.207450	+	0.359314i
$640$		0			0
$641$	−4967.58	+	8604.10i	−0.306096	+	0.530174i	−0.977505	−	0.210913i	$-0.932356\pi$
$641$	−4967.58	+	8604.10i	−0.306096	+	0.530174i	0.671409	+	0.741087i	$0.265689\pi$
$642$		0			0
$643$	−21282.8			−1.30531			−0.652653	−	0.757657i	$-0.726344\pi$
$643$	−21282.8			−1.30531			−0.652653	+	0.757657i	$0.726344\pi$
$644$		0			0
$645$	−7075.78			−0.431951
$646$		0			0
$647$	−3438.07	+	5954.91i	−0.208910	+	0.361842i	−0.951371	−	0.308046i	$-0.900325\pi$
$647$	−3438.07	+	5954.91i	−0.208910	+	0.361842i	0.742462	+	0.669888i	$0.233658\pi$
$648$		0			0
$649$	7095.39	+	12289.6i	0.429150	+	0.743310i
$650$		0			0
$651$	−13360.3	+	502.924i	−0.804347	+	0.0302783i
$652$		0			0
$653$	701.120	+	1214.38i	0.0420168	+	0.0727752i	0.886269	−	0.463171i	$-0.153288\pi$
$653$	701.120	+	1214.38i	0.0420168	+	0.0727752i	−0.844252	+	0.535946i	$0.819955\pi$
$654$		0			0
$655$	−1251.27	+	2167.26i	−0.0746428	+	0.129285i
$656$		0			0
$657$	20334.6			1.20750
$658$		0			0
$659$	19975.7			1.18079			0.590395	−	0.807114i	$-0.298972\pi$
$659$	19975.7			1.18079			0.590395	+	0.807114i	$0.298972\pi$
$660$		0			0
$661$	−328.416	+	568.832i	−0.0193251	+	0.0334720i	−0.875526	−	0.483171i	$-0.839485\pi$
$661$	−328.416	+	568.832i	−0.0193251	+	0.0334720i	0.856201	+	0.516643i	$0.172818\pi$
$662$		0			0
$663$	2304.27	+	3991.12i	0.134978	+	0.233789i
$664$		0			0
$665$	863.857	+	1374.13i	0.0503744	+	0.0801302i
$666$		0			0
$667$	−24.0010	−	41.5710i	−0.00139329	−	0.00241325i
$668$		0			0
$669$	3533.92	−	6120.93i	0.204229	−	0.353735i
$670$		0			0
$671$	−5481.37			−0.315359
$672$		0			0
$673$	14668.1			0.840140			0.420070	−	0.907492i	$-0.362006\pi$
$673$	14668.1			0.840140			0.420070	+	0.907492i	$0.362006\pi$
$674$		0			0
$675$	−5189.73	+	8988.88i	−0.295930	+	0.512566i
$676$		0			0
$677$	−9605.04	−	16636.4i	−0.545276	−	0.944446i	−0.998589	−	0.0530944i	$-0.983092\pi$
$677$	−9605.04	−	16636.4i	−0.545276	−	0.944446i	0.453314	−	0.891351i	$-0.350242\pi$
$678$		0			0
$679$	−12482.2	+	23630.5i	−0.705485	+	1.33557i
$680$		0			0
$681$	2156.67	+	3735.46i	0.121357	+	0.210196i
$682$		0			0
$683$	−9223.01	+	15974.7i	−0.516704	+	0.894957i	0.483108	+	0.875561i	$0.339508\pi$
$683$	−9223.01	+	15974.7i	−0.516704	+	0.894957i	−0.999812	+	0.0193965i	$0.993826\pi$
$684$		0			0
$685$	−7615.95			−0.424804
$686$		0			0
$687$	1603.25			0.0890364
$688$		0			0
$689$	−7140.80	+	12368.2i	−0.394837	+	0.683878i
$690$		0			0
$691$	12451.0	+	21565.7i	0.685467	+	1.18726i	0.973290	+	0.229581i	$0.0737355\pi$
$691$	12451.0	+	21565.7i	0.685467	+	1.18726i	−0.287822	+	0.957684i	$0.592931\pi$
$692$		0			0
$693$	5212.01	−	9866.99i	0.285697	−	0.540860i
$694$		0			0
$695$	−4113.51	−	7124.81i	−0.224510	−	0.388863i
$696$		0			0
$697$	−9585.15	+	16602.0i	−0.520894	+	0.902216i
$698$		0			0
$699$	−4498.90			−0.243439
$700$		0			0
$701$	22637.7			1.21970			0.609852	−	0.792515i	$-0.291229\pi$
$701$	22637.7			1.21970			0.609852	+	0.792515i	$0.291229\pi$
$702$		0			0
$703$	2489.84	−	4312.52i	0.133579	−	0.231365i
$704$		0			0
$705$	−3356.43	−	5813.51i	−0.179306	−	0.310567i
$706$		0			0
$707$	−3074.59	−	4890.73i	−0.163553	−	0.260163i
$708$		0			0
$709$	−3.49494	−	6.05341i	−0.000185127	−	0.000320650i	0.865933	−	0.500160i	$-0.166726\pi$
$709$	−3.49494	−	6.05341i	−0.000185127	−	0.000320650i	−0.866118	+	0.499840i	$0.833392\pi$
$710$		0			0
$711$	5362.12	−	9287.46i	0.282834	−	0.489883i
$712$		0			0
$713$	2413.70			0.126779
$714$		0			0
$715$	−3936.75			−0.205911
$716$		0			0
$717$	6589.57	−	11413.5i	0.343225	−	0.594483i
$718$		0			0
$719$	9509.80	+	16471.5i	0.493262	+	0.854355i	0.999970	−	0.00776257i	$-0.00247093\pi$
$719$	9509.80	+	16471.5i	0.493262	+	0.854355i	−0.506708	+	0.862118i	$0.669138\pi$
$720$		0			0
$721$	−10764.3	+	405.206i	−0.556013	+	0.0209302i
$722$		0			0
$723$	1223.59	+	2119.32i	0.0629402	+	0.109016i
$724$		0			0
$725$	−205.339	+	355.658i	−0.0105188	+	0.0182190i
$726$		0			0
$727$	−33880.6			−1.72842			−0.864210	−	0.503130i	$-0.832182\pi$
$727$	−33880.6			−1.72842			−0.864210	+	0.503130i	$0.832182\pi$
$728$		0			0
$729$	6853.96			0.348217
$730$		0			0
$731$	16581.5	−	28719.9i	0.838970	−	1.45314i
$732$		0			0
$733$	5222.71	+	9045.99i	0.263172	+	0.455827i	0.967083	−	0.254461i	$-0.0818980\pi$
$733$	5222.71	+	9045.99i	0.263172	+	0.455827i	−0.703911	+	0.710288i	$0.748565\pi$
$734$		0			0
$735$	3628.38	+	5316.70i	0.182088	+	0.266816i
$736$		0			0
$737$	7828.48	+	13559.3i	0.391270	+	0.677699i
$738$		0			0
$739$	12837.3	−	22234.8i	0.639007	−	1.10679i	−0.346644	−	0.937997i	$-0.612679\pi$
$739$	12837.3	−	22234.8i	0.639007	−	1.10679i	0.985651	−	0.168796i	$-0.0539880\pi$
$740$		0			0
$741$	686.248			0.0340215
$742$		0			0
$743$	−30646.2			−1.51319			−0.756596	−	0.653883i	$-0.773139\pi$
$743$	−30646.2			−1.51319			−0.756596	+	0.653883i	$0.773139\pi$
$744$		0			0
$745$	9912.78	−	17169.4i	0.487485	−	0.844348i
$746$		0			0
$747$	−10574.7	−	18316.0i	−0.517951	−	0.897118i
$748$		0			0
$749$	−21754.7	+	818.919i	−1.06128	+	0.0399501i
$750$		0			0
$751$	4355.95	+	7544.73i	0.211652	+	0.366593i	0.952232	−	0.305376i	$-0.0987822\pi$
$751$	4355.95	+	7544.73i	0.211652	+	0.366593i	−0.740579	+	0.671969i	$0.765449\pi$
$752$		0			0
$753$	−4383.77	+	7592.91i	−0.212156	+	0.367465i
$754$		0			0
$755$	17382.8			0.837912
$756$		0			0
$757$	−18830.7			−0.904114			−0.452057	−	0.891989i	$-0.649310\pi$
$757$	−18830.7			−0.904114			−0.452057	+	0.891989i	$0.649310\pi$
$758$		0			0
$759$	414.017	−	717.099i	0.0197996	−	0.0342939i
$760$		0			0
$761$	−10900.3	−	18879.9i	−0.519232	−	0.899336i	−0.999750	−	0.0223513i	$-0.992885\pi$
$761$	−10900.3	−	18879.9i	−0.519232	−	0.899336i	0.480518	−	0.876985i	$-0.340449\pi$
$762$		0			0
$763$	−3322.29	−	5284.75i	−0.157634	−	0.250748i
$764$		0			0
$765$	5630.99	+	9753.16i	0.266129	+	0.460949i
$766$		0			0
$767$	4210.09	−	7292.10i	0.198198	−	0.343289i
$768$		0			0
$769$	4412.21			0.206903			0.103452	−	0.994634i	$-0.467011\pi$
$769$	4412.21			0.206903			0.103452	+	0.994634i	$0.467011\pi$
$770$		0			0
$771$	2535.26			0.118424
$772$		0			0
$773$	15223.4	−	26367.7i	0.708342	−	1.22688i	−0.257130	−	0.966377i	$-0.582777\pi$
$773$	15223.4	−	26367.7i	0.708342	−	1.22688i	0.965472	−	0.260507i	$-0.0838897\pi$
$774$		0			0
$775$	−10325.1	−	17883.6i	−0.478567	−	0.828902i
$776$		0			0
$777$	9223.68	−	17461.6i	0.425866	−	0.806217i
$778$		0			0
$779$	1427.30	+	2472.16i	0.0656462	+	0.113703i
$780$		0			0
$781$	−5514.17	+	9550.83i	−0.252641	+	0.437587i
$782$		0			0
$783$	662.343			0.0302302
$784$		0			0
$785$	−9133.92			−0.415291
$786$		0			0
$787$	5606.01	−	9709.90i	0.253917	−	0.439797i	−0.710684	−	0.703512i	$-0.751614\pi$
$787$	5606.01	−	9709.90i	0.253917	−	0.439797i	0.964601	+	0.263714i	$0.0849476\pi$
$788$		0			0
$789$	129.897	+	224.989i	0.00586118	+	0.0101519i
$790$		0			0
$791$	10104.8	−	19129.7i	0.454219	−	0.859893i
$792$		0			0
$793$	1626.20	+	2816.67i	0.0728224	+	0.126132i
$794$		0			0
$795$	7172.35	−	12422.9i	0.319971	−	0.554206i
$796$		0			0
$797$	−11809.3			−0.524852			−0.262426	−	0.964952i	$-0.584523\pi$
$797$	−11809.3			−0.524852			−0.262426	+	0.964952i	$0.584523\pi$
$798$		0			0
$799$	31462.0			1.39305
$800$		0			0
$801$	11545.3	−	19997.0i	0.509279	−	0.882097i
$802$		0			0
$803$	16731.0	+	28978.9i	0.735272	+	1.27353i
$804$		0			0
$805$	−618.479	−	983.811i	−0.0270789	−	0.0430743i
$806$		0			0
$807$	5681.49	+	9840.63i	0.247829	+	0.429252i
$808$		0			0
$809$	−7163.83	+	12408.1i	−0.311331	+	0.539241i	−0.978651	−	0.205530i	$-0.934108\pi$
$809$	−7163.83	+	12408.1i	−0.311331	+	0.539241i	0.667320	+	0.744771i	$0.267441\pi$
$810$		0			0
$811$	−32413.9			−1.40346			−0.701730	−	0.712443i	$-0.747589\pi$
$811$	−32413.9			−1.40346			−0.701730	+	0.712443i	$0.747589\pi$
$812$		0			0
$813$	7828.05			0.337690
$814$		0			0
$815$	11099.6	−	19225.1i	0.477058	−	0.826289i
$816$		0			0
$817$	−2469.11	−	4276.62i	−0.105732	−	0.183133i
$818$		0			0
$819$	−6616.56	+	249.069i	−0.282297	+	0.0106266i
$820$		0			0
$821$	−1203.08	−	2083.80i	−0.0511423	−	0.0885810i	0.839321	−	0.543636i	$-0.182953\pi$
$821$	−1203.08	−	2083.80i	−0.0511423	−	0.0885810i	−0.890463	+	0.455055i	$0.849620\pi$
$822$		0			0
$823$	980.182	−	1697.72i	0.0415152	−	0.0719064i	−0.844521	−	0.535522i	$-0.820115\pi$
$823$	980.182	−	1697.72i	0.0415152	−	0.0719064i	0.886036	+	0.463616i	$0.153448\pi$
$824$		0			0
$825$	−7084.19			−0.298958
$826$		0			0
$827$	17517.2			0.736557			0.368278	−	0.929716i	$-0.379947\pi$
$827$	17517.2			0.736557			0.368278	+	0.929716i	$0.379947\pi$
$828$		0			0
$829$	−16749.4	+	29010.8i	−0.701724	+	1.21542i	0.266136	+	0.963935i	$0.414253\pi$
$829$	−16749.4	+	29010.8i	−0.701724	+	1.21542i	−0.967861	+	0.251487i	$0.919080\pi$
$830$		0			0
$831$	3618.67	+	6267.71i	0.151059	+	0.261642i
$832$		0			0
$833$	−30082.8	+	2268.05i	−1.25127	+	0.0943375i
$834$		0			0
$835$	12727.3	+	22044.3i	0.527479	+	0.913621i
$836$		0			0
$837$	−16652.4	+	28842.8i	−0.687683	+	1.19110i
$838$		0			0
$839$	−1609.45			−0.0662268			−0.0331134	−	0.999452i	$-0.510542\pi$
$839$	−1609.45			−0.0662268			−0.0331134	+	0.999452i	$0.510542\pi$
$840$		0			0
$841$	−24362.8			−0.998925
$842$		0			0
$843$	1289.33	−	2233.18i	0.0526770	−	0.0912393i
$844$		0			0
$845$	−6182.76	−	10708.9i	−0.251708	−	0.435972i
$846$		0			0
$847$	−6283.16	+	236.519i	−0.254890	+	0.00959490i
$848$		0			0
$849$	11599.2	+	20090.4i	0.468885	+	0.812132i
$850$		0			0
$851$	−1782.60	+	3087.55i	−0.0718058	+	0.124371i
$852$		0			0
$853$	−20446.9			−0.820739			−0.410369	−	0.911919i	$-0.634600\pi$
$853$	−20446.9			−0.820739			−0.410369	+	0.911919i	$0.634600\pi$
$854$		0			0
$855$	1676.99			0.0670784
$856$		0			0
$857$	2892.11	−	5009.28i	0.115277	−	0.199666i	−0.802613	−	0.596500i	$-0.796558\pi$
$857$	2892.11	−	5009.28i	0.115277	−	0.199666i	0.917891	+	0.396834i	$0.129891\pi$
$858$		0			0
$859$	−16180.7	−	28025.7i	−0.642697	−	1.11318i	−0.984828	−	0.173532i	$-0.944482\pi$
$859$	−16180.7	−	28025.7i	−0.642697	−	1.11318i	0.342131	−	0.939652i	$-0.388851\pi$
$860$		0			0
$861$	6025.07	+	9584.04i	0.238483	+	0.379353i
$862$		0			0
$863$	14415.6	+	24968.6i	0.568614	+	0.984868i	0.996703	+	0.0811320i	$0.0258535\pi$
$863$	14415.6	+	24968.6i	0.568614	+	0.984868i	−0.428089	+	0.903736i	$0.640813\pi$
$864$		0			0
$865$	8439.09	−	14616.9i	0.331720	−	0.574556i
$866$		0			0
$867$	7916.60			0.310106
$868$		0			0
$869$	17647.5			0.688895
$870$		0			0
$871$	4645.08	−	8045.51i	0.180703	−	0.312987i
$872$		0			0
$873$	13805.9	+	23912.5i	0.535234	+	0.927052i
$874$		0			0
$875$	−11879.1	+	22488.6i	−0.458956	+	0.868861i
$876$		0			0
$877$	6552.70	+	11349.6i	0.252302	+	0.437000i	0.964159	−	0.265324i	$-0.0854790\pi$
$877$	6552.70	+	11349.6i	0.252302	+	0.437000i	−0.711857	+	0.702324i	$0.752146\pi$
$878$		0			0
$879$	4009.49	−	6944.64i	0.153853	−	0.266481i
$880$		0			0
$881$	−3089.10			−0.118132			−0.0590661	−	0.998254i	$-0.518812\pi$
$881$	−3089.10			−0.118132			−0.0590661	+	0.998254i	$0.518812\pi$
$882$		0			0
$883$	1601.96			0.0610536			0.0305268	−	0.999534i	$-0.490282\pi$
$883$	1601.96			0.0610536			0.0305268	+	0.999534i	$0.490282\pi$
$884$		0			0
$885$	−4228.69	+	7324.31i	−0.160617	+	0.278197i
$886$		0			0
$887$	11285.2	+	19546.6i	0.427194	+	0.739921i	0.996622	−	0.0821197i	$-0.0261690\pi$
$887$	11285.2	+	19546.6i	0.427194	+	0.739921i	−0.569429	+	0.822041i	$0.692836\pi$
$888$		0			0
$889$	−203.050	+	384.400i	−0.00766039	+	0.0145021i
$890$		0			0
$891$	−2421.42	−	4194.01i	−0.0910443	−	0.157693i
$892$		0			0
$893$	2342.47	−	4057.27i	0.0877801	−	0.152040i
$894$		0			0
$895$	1251.57			0.0467435
$896$		0			0
$897$	−491.320			−0.0182884
$898$		0			0
$899$	−658.875	+	1141.20i	−0.0244435	+	0.0423374i
$900$		0			0
$901$	33615.5	+	58223.8i	1.24295	+	2.15285i
$902$		0			0
$903$	−10422.8	−	16579.5i	−0.384109	−	0.610999i
$904$		0			0
$905$	−1531.22	−	2652.15i	−0.0562424	−	0.0974147i
$906$		0			0
$907$	−24172.1	+	41867.4i	−0.884920	+	1.53273i	−0.0391146	+	0.999235i	$0.512454\pi$
$907$	−24172.1	+	41867.4i	−0.884920	+	1.53273i	−0.845805	+	0.533492i	$0.820880\pi$
$908$		0			0
$909$	−5968.66			−0.217787
$910$		0			0
$911$	14697.9			0.534539			0.267269	−	0.963622i	$-0.413879\pi$
$911$	14697.9			0.534539			0.267269	+	0.963622i	$0.413879\pi$
$912$		0			0
$913$	17401.5	−	30140.2i	0.630783	−	1.09255i
$914$		0			0
$915$	−1633.39	−	2829.11i	−0.0590143	−	0.102216i
$916$		0			0
$917$	−6921.34	+	260.542i	−0.249250	+	0.00938261i
$918$		0			0
$919$	−7665.28	−	13276.7i	−0.275141	−	0.476558i	0.695030	−	0.718981i	$-0.255391\pi$
$919$	−7665.28	−	13276.7i	−0.275141	−	0.476558i	−0.970171	+	0.242423i	$0.922058\pi$
$920$		0			0
$921$	4967.88	−	8604.63i	0.177739	−	0.307852i
$922$		0			0
$923$	6543.74			0.233358
$924$		0			0
$925$	30501.8			1.08421
$926$		0			0
$927$	−5564.79	+	9638.49i	−0.197165	+	0.341499i
$928$		0			0
$929$	−27955.2	−	48419.7i	−0.987275	−	1.71001i	−0.631353	−	0.775495i	$-0.717500\pi$
$929$	−27955.2	−	48419.7i	−0.987275	−	1.71001i	−0.355922	−	0.934516i	$-0.615833\pi$
$930$		0			0
$931$	−1947.30	+	4048.28i	−0.0685500	+	0.142510i
$932$		0			0
$933$	872.952	+	1512.00i	0.0306315	+	0.0530553i
$934$		0			0
$935$	−9266.18	+	16049.5i	−0.324103	+	0.561363i
$936$		0			0
$937$	18627.7			0.649457			0.324728	−	0.945807i	$-0.394727\pi$
$937$	18627.7			0.649457			0.324728	+	0.945807i	$0.394727\pi$
$938$		0			0
$939$	−19813.0			−0.688575
$940$		0			0
$941$	−20282.3	+	35130.0i	−0.702641	+	1.21701i	0.264896	+	0.964277i	$0.414663\pi$
$941$	−20282.3	+	35130.0i	−0.702641	+	1.21701i	−0.967536	+	0.252732i	$0.918671\pi$
$942$		0			0
$943$	−1021.88	−	1769.94i	−0.0352884	−	0.0611212i
$944$		0			0
$945$	16023.1	−	603.164i	0.551569	−	0.0207629i
$946$		0			0
$947$	−13345.1	−	23114.3i	−0.457926	−	0.793151i	0.540925	−	0.841071i	$-0.318074\pi$
$947$	−13345.1	−	23114.3i	−0.457926	−	0.793151i	−0.998851	+	0.0479196i	$0.984741\pi$
$948$		0			0
$949$	9927.43	−	17194.8i	0.339576	−	0.588163i
$950$		0			0
$951$	−18114.5			−0.617669
$952$		0			0
$953$	−7182.06			−0.244123			−0.122062	−	0.992523i	$-0.538951\pi$
$953$	−7182.06			−0.244123			−0.122062	+	0.992523i	$0.538951\pi$
$954$		0			0
$955$	9674.69	−	16757.0i	0.327817	−	0.567796i
$956$		0			0
$957$	226.031	+	391.498i	0.00763485	+	0.0132239i
$958$		0			0
$959$	−11218.5	−	17845.2i	−0.377753	−	0.600889i
$960$		0			0
$961$	−18234.9	−	31583.7i	−0.612093	−	1.06018i
$962$		0			0
$963$	−11246.4	+	19479.4i	−0.376335	+	0.651831i
$964$		0			0
$965$	−7681.22			−0.256236
$966$		0			0
$967$	18129.4			0.602898			0.301449	−	0.953482i	$-0.402530\pi$
$967$	18129.4			0.602898			0.301449	+	0.953482i	$0.402530\pi$
$968$		0			0
$969$	1615.26	−	2797.72i	0.0535498	−	0.0927510i
$970$		0			0
$971$	10488.0	+	18165.8i	0.346629	+	0.600378i	0.985648	−	0.168812i	$-0.0539931\pi$
$971$	10488.0	+	18165.8i	0.346629	+	0.600378i	−0.639020	+	0.769190i	$0.720660\pi$
$972$		0			0
$973$	10635.1	−	20133.6i	0.350407	−	0.663364i
$974$		0			0
$975$	2101.73	+	3640.29i	0.0690349	+	0.119572i
$976$		0			0
$977$	22347.4	−	38706.8i	0.731786	−	1.26749i	−0.224333	−	0.974513i	$-0.572020\pi$
$977$	22347.4	−	38706.8i	0.731786	−	1.26749i	0.956119	−	0.292979i	$-0.0946465\pi$
$978$		0			0
$979$	37997.1			1.24044
$980$		0			0
$981$	−6449.52			−0.209906
$982$		0			0
$983$	−7713.11	+	13359.5i	−0.250265	+	0.433471i	−0.963599	−	0.267353i	$-0.913851\pi$
$983$	−7713.11	+	13359.5i	−0.250265	+	0.433471i	0.713334	+	0.700824i	$0.247184\pi$
$984$		0			0
$985$	5481.17	+	9493.66i	0.177304	+	0.307100i
$986$		0			0
$987$	8677.74	−	16428.1i	0.279854	−	0.529798i
$988$		0			0
$989$	1767.76	+	3061.85i	0.0568366	+	0.0984439i
$990$		0			0
$991$	−14124.0	+	24463.5i	−0.452739	+	0.784167i	−0.998555	−	0.0537377i	$-0.982887\pi$
$991$	−14124.0	+	24463.5i	−0.452739	+	0.784167i	0.545816	+	0.837905i	$0.316220\pi$
$992$		0			0
$993$	−23375.7			−0.747034
$994$		0			0
$995$	−35540.9			−1.13238
$996$		0			0
$997$	18560.8	−	32148.2i	0.589594	−	1.02121i	−0.404691	−	0.914453i	$-0.632621\pi$
$997$	18560.8	−	32148.2i	0.589594	−	1.02121i	0.994285	−	0.106754i	$-0.0340457\pi$
$998$		0			0
$999$	−24596.7	−	42602.8i	−0.778985	−	1.34924i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	56.4.i.b.25.1	yes	6
3.2	odd	2		504.4.s.h.361.2		6
4.3	odd	2		112.4.i.e.81.3		6
7.2	even	3	inner	56.4.i.b.9.1	✓	6
7.3	odd	6		392.4.a.l.1.1		3
7.4	even	3		392.4.a.i.1.3		3
7.5	odd	6		392.4.i.m.177.3		6
7.6	odd	2		392.4.i.m.361.3		6
8.3	odd	2		448.4.i.m.193.1		6
8.5	even	2		448.4.i.j.193.3		6
21.2	odd	6		504.4.s.h.289.2		6
28.3	even	6		784.4.a.bb.1.3		3
28.11	odd	6		784.4.a.be.1.1		3
28.23	odd	6		112.4.i.e.65.3		6
56.37	even	6		448.4.i.j.65.3		6
56.51	odd	6		448.4.i.m.65.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.4.i.b.9.1	✓	6	7.2	even	3	inner
56.4.i.b.25.1	yes	6	1.1	even	1	trivial
112.4.i.e.65.3		6	28.23	odd	6
112.4.i.e.81.3		6	4.3	odd	2
392.4.a.i.1.3		3	7.4	even	3
392.4.a.l.1.1		3	7.3	odd	6
392.4.i.m.177.3		6	7.5	odd	6
392.4.i.m.361.3		6	7.6	odd	2
448.4.i.j.65.3		6	56.37	even	6
448.4.i.j.193.3		6	8.5	even	2
448.4.i.m.65.1		6	56.51	odd	6
448.4.i.m.193.1		6	8.3	odd	2
504.4.s.h.289.2		6	21.2	odd	6
504.4.s.h.361.2		6	3.2	odd	2
784.4.a.bb.1.3		3	28.3	even	6
784.4.a.be.1.1		3	28.11	odd	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:	\( N \)	\(=\)	\( 56 = 2^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	56.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40222 + 2.42872i) q^{3} +(3.34580 + 5.79509i) q^{5} +(-8.65024 + 16.3760i) q^{7} +(9.56754 + 16.5715i) q^{9} +O(q^{10})\)	\(q+(-1.40222 + 2.42872i) q^{3} +(3.34580 + 5.79509i) q^{5} +(-8.65024 + 16.3760i) q^{7} +(9.56754 + 16.5715i) q^{9} +(-15.7441 + 27.2695i) q^{11} +18.6837 q^{13} -18.7662 q^{15} +(43.9769 - 76.1703i) q^{17} +(-6.54850 - 11.3423i) q^{19} +(-27.6432 - 43.9718i) q^{21} +(4.68840 + 8.12055i) q^{23} +(40.1113 - 69.4748i) q^{25} -129.383 q^{27} -5.11923 q^{29} +(128.706 - 222.925i) q^{31} +(-44.1533 - 76.4758i) q^{33} +(-123.842 + 4.66183i) q^{35} +(190.107 + 329.276i) q^{37} +(-26.1987 + 45.3774i) q^{39} -217.959 q^{41} +377.049 q^{43} +(-64.0221 + 110.889i) q^{45} +(178.855 + 309.786i) q^{47} +(-193.347 - 283.313i) q^{49} +(123.331 + 213.615i) q^{51} +(-382.195 + 661.981i) q^{53} -210.706 q^{55} +36.7298 q^{57} +(225.336 - 390.293i) q^{59} +(87.0388 + 150.756i) q^{61} +(-354.136 + 13.3308i) q^{63} +(62.5117 + 108.273i) q^{65} +(248.617 - 430.617i) q^{67} -26.2967 q^{69} +350.238 q^{71} +(531.343 - 920.312i) q^{73} +(112.490 + 194.838i) q^{75} +(-310.375 - 493.712i) q^{77} +(-280.224 - 485.363i) q^{79} +(-76.8993 + 133.194i) q^{81} -1105.27 q^{83} +588.551 q^{85} +(7.17830 - 12.4332i) q^{87} +(-603.357 - 1045.04i) q^{89} +(-161.618 + 305.964i) q^{91} +(360.948 + 625.181i) q^{93} +(43.8199 - 75.8983i) q^{95} +1442.99 q^{97} -602.528 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 7 q^{3} + 3 q^{5} - 4 q^{7} - 18 q^{9}+O(q^{10}) \) 6 * q + 7 * q^3 + 3 * q^5 - 4 * q^7 - 18 * q^9	\( 6 q + 7 q^{3} + 3 q^{5} - 4 q^{7} - 18 q^{9} + 3 q^{11} - 52 q^{13} + 254 q^{15} + 31 q^{17} + 89 q^{19} - 375 q^{21} + 201 q^{23} - 300 q^{25} - 938 q^{27} + 380 q^{29} + 339 q^{31} + 105 q^{33} - 473 q^{35} + 535 q^{37} + 134 q^{39} + 116 q^{41} + 536 q^{43} + 1410 q^{45} + 205 q^{47} - 1530 q^{49} + 965 q^{51} - 757 q^{53} - 3306 q^{55} + 522 q^{57} + 1799 q^{59} - 625 q^{61} - 1714 q^{63} + 1750 q^{65} + 495 q^{67} + 1946 q^{69} + 1280 q^{71} + 443 q^{73} + 1484 q^{75} - 1131 q^{77} - 79 q^{79} - 2523 q^{81} - 4744 q^{83} - 1954 q^{85} + 910 q^{87} - 821 q^{89} - 1352 q^{91} + 1321 q^{93} + 1327 q^{95} - 684 q^{97} + 4620 q^{99}+O(q^{100}) \) 6 * q + 7 * q^3 + 3 * q^5 - 4 * q^7 - 18 * q^9 + 3 * q^11 - 52 * q^13 + 254 * q^15 + 31 * q^17 + 89 * q^19 - 375 * q^21 + 201 * q^23 - 300 * q^25 - 938 * q^27 + 380 * q^29 + 339 * q^31 + 105 * q^33 - 473 * q^35 + 535 * q^37 + 134 * q^39 + 116 * q^41 + 536 * q^43 + 1410 * q^45 + 205 * q^47 - 1530 * q^49 + 965 * q^51 - 757 * q^53 - 3306 * q^55 + 522 * q^57 + 1799 * q^59 - 625 * q^61 - 1714 * q^63 + 1750 * q^65 + 495 * q^67 + 1946 * q^69 + 1280 * q^71 + 443 * q^73 + 1484 * q^75 - 1131 * q^77 - 79 * q^79 - 2523 * q^81 - 4744 * q^83 - 1954 * q^85 + 910 * q^87 - 821 * q^89 - 1352 * q^91 + 1321 * q^93 + 1327 * q^95 - 684 * q^97 + 4620 * q^99

Introduction

L-functions

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