LMFDB - Embedded newform 100.4.i.a.69.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [100,4,Mod(9,100)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(100, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 7]))

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

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

chi := DirichletCharacter("100.9");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 100 = 2^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	100.i (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.90019100057$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			69.1
Character	$\chi$	$=$	100.69
Dual form			100.4.i.a.29.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.78214 - 7.95843i) q^{3} +(10.1359 - 4.71846i) q^{5} -24.7439i q^{7} +(-21.5601 + 66.3550i) q^{9} +O(q^{10})$	\(q+(-5.78214 - 7.95843i) q^{3} +(10.1359 - 4.71846i) q^{5} -24.7439i q^{7} +(-21.5601 + 66.3550i) q^{9} +(1.97368 + 6.07436i) q^{11} +(-62.0111 - 20.1486i) q^{13} +(-96.1587 - 53.3829i) q^{15} +(-35.7939 + 49.2661i) q^{17} +(43.8361 + 31.8488i) q^{19} +(-196.923 + 143.073i) q^{21} +(7.45339 - 2.42175i) q^{23} +(80.4722 - 95.6516i) q^{25} +(400.141 - 130.014i) q^{27} +(105.212 - 76.4413i) q^{29} +(-231.860 - 168.456i) q^{31} +(36.9303 - 50.8302i) q^{33} +(-116.753 - 250.802i) q^{35} +(237.544 + 77.1828i) q^{37} +(198.205 + 610.013i) q^{39} +(18.4365 - 56.7416i) q^{41} +32.9665i q^{43} +(94.5635 + 774.297i) q^{45} +(-339.619 - 467.446i) q^{47} -269.262 q^{49} +599.046 q^{51} +(-0.813398 - 1.11955i) q^{53} +(48.6666 + 52.2563i) q^{55} -533.020i q^{57} +(-19.0425 + 58.6066i) q^{59} +(-185.588 - 571.180i) q^{61} +(1641.88 + 533.481i) q^{63} +(-723.607 + 88.3729i) q^{65} +(-357.055 + 491.444i) q^{67} +(-62.3699 - 45.3144i) q^{69} +(544.838 - 395.848i) q^{71} +(331.958 - 107.860i) q^{73} +(-1226.54 - 87.3619i) q^{75} +(150.304 - 48.8366i) q^{77} +(-7.93662 + 5.76629i) q^{79} +(-1824.37 - 1325.48i) q^{81} +(719.989 - 990.980i) q^{83} +(-130.343 + 668.247i) q^{85} +(-1216.71 - 395.332i) q^{87} +(-248.495 - 764.789i) q^{89} +(-498.556 + 1534.40i) q^{91} +2819.27i q^{93} +(594.594 + 115.976i) q^{95} +(528.015 + 726.751i) q^{97} -445.617 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 6 q^{5} + 122 q^{9}+O(q^{10}) $ 32 * q + 6 * q^5 + 122 * q^9	$ 32 q + 6 q^{5} + 122 q^{9} + 20 q^{11} + 68 q^{15} - 160 q^{17} + 2 q^{19} - 108 q^{21} + 290 q^{23} + 654 q^{25} + 600 q^{27} + 62 q^{29} - 378 q^{31} - 1280 q^{33} - 278 q^{35} + 680 q^{37} + 592 q^{39} - 528 q^{41} - 1044 q^{45} - 1810 q^{47} - 2796 q^{49} + 1664 q^{51} - 510 q^{53} - 1350 q^{55} + 144 q^{59} - 1346 q^{61} + 1660 q^{63} + 1142 q^{65} + 1890 q^{67} + 956 q^{69} + 786 q^{71} + 3720 q^{73} - 78 q^{75} + 2160 q^{77} + 896 q^{79} + 348 q^{81} + 570 q^{83} + 224 q^{85} + 3240 q^{87} - 2512 q^{89} - 2212 q^{91} + 1536 q^{95} - 2250 q^{97} - 2540 q^{99}+O(q^{100}) $ 32 * q + 6 * q^5 + 122 * q^9 + 20 * q^11 + 68 * q^15 - 160 * q^17 + 2 * q^19 - 108 * q^21 + 290 * q^23 + 654 * q^25 + 600 * q^27 + 62 * q^29 - 378 * q^31 - 1280 * q^33 - 278 * q^35 + 680 * q^37 + 592 * q^39 - 528 * q^41 - 1044 * q^45 - 1810 * q^47 - 2796 * q^49 + 1664 * q^51 - 510 * q^53 - 1350 * q^55 + 144 * q^59 - 1346 * q^61 + 1660 * q^63 + 1142 * q^65 + 1890 * q^67 + 956 * q^69 + 786 * q^71 + 3720 * q^73 - 78 * q^75 + 2160 * q^77 + 896 * q^79 + 348 * q^81 + 570 * q^83 + 224 * q^85 + 3240 * q^87 - 2512 * q^89 - 2212 * q^91 + 1536 * q^95 - 2250 * q^97 - 2540 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/100\mathbb{Z}\right)^\times$.

$n$	$51$	$77$
$\chi(n)$	$1$	$e\left(\frac{9}{10}\right)$

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
$3$	−5.78214	−	7.95843i	−1.11277	−	1.53160i	−0.817266	−	0.576261i	$-0.804511\pi$
$3$	−5.78214	−	7.95843i	−1.11277	−	1.53160i	−0.295507	−	0.955340i	$-0.595489\pi$
$4$		0			0
$5$	10.1359	−	4.71846i	0.906581	−	0.422032i
$5$	10.1359	−	4.71846i	0.906581	−	0.422032i
$6$		0			0
$7$		−	24.7439i		−	1.33605i	−0.744140	−	0.668024i	$-0.767141\pi$
$7$		−	24.7439i		−	1.33605i	0.744140	−	0.668024i	$-0.232859\pi$
$8$		0			0
$9$	−21.5601	+	66.3550i	−0.798520	+	2.45759i
$10$		0			0
$11$	1.97368	+	6.07436i	0.0540988	+	0.166499i	0.974455	−	0.224581i	$-0.0721015\pi$
$11$	1.97368	+	6.07436i	0.0540988	+	0.166499i	−0.920357	+	0.391080i	$0.872101\pi$
$12$		0			0
$13$	−62.0111	−	20.1486i	−1.32298	−	0.429863i	−0.439464	−	0.898260i	$-0.644832\pi$
$13$	−62.0111	−	20.1486i	−1.32298	−	0.429863i	−0.883518	+	0.468397i	$0.844832\pi$
$14$		0			0
$15$	−96.1587	−	53.3829i	−1.65520	−	0.918894i
$16$		0			0
$17$	−35.7939	+	49.2661i	−0.510664	+	0.702869i	−0.984031	−	0.177996i	$-0.943038\pi$
$17$	−35.7939	+	49.2661i	−0.510664	+	0.702869i	0.473367	+	0.880865i	$0.343038\pi$
$18$		0			0
$19$	43.8361	+	31.8488i	0.529299	+	0.384558i	0.820096	−	0.572227i	$-0.193920\pi$
$19$	43.8361	+	31.8488i	0.529299	+	0.384558i	−0.290796	+	0.956785i	$0.593920\pi$
$20$		0			0
$21$	−196.923	+	143.073i	−2.04629	+	1.48672i
$22$		0			0
$23$	7.45339	−	2.42175i	0.0675712	−	0.0219552i	−0.275036	−	0.961434i	$-0.588690\pi$
$23$	7.45339	−	2.42175i	0.0675712	−	0.0219552i	0.342608	+	0.939479i	$0.388690\pi$
$24$		0			0
$25$	80.4722	−	95.6516i	0.643778	−	0.765213i
$26$		0			0
$27$	400.141	−	130.014i	2.85212	−	0.926710i
$28$		0			0
$29$	105.212	−	76.4413i	0.673706	−	0.489476i	−0.197558	−	0.980291i	$-0.563301\pi$
$29$	105.212	−	76.4413i	0.673706	−	0.489476i	0.871264	+	0.490815i	$0.163301\pi$
$30$		0			0
$31$	−231.860	−	168.456i	−1.34333	−	0.975986i	−0.999314	−	0.0370221i	$-0.988213\pi$
$31$	−231.860	−	168.456i	−1.34333	−	0.975986i	−0.344015	−	0.938964i	$-0.611787\pi$
$32$		0			0
$33$	36.9303	−	50.8302i	0.194810	−	0.268133i
$34$		0			0
$35$	−116.753	−	250.802i	−0.563855	−	1.21123i
$36$		0			0
$37$	237.544	+	77.1828i	1.05546	+	0.342940i	0.784809	−	0.619738i	$-0.212761\pi$
$37$	237.544	+	77.1828i	1.05546	+	0.342940i	0.270651	+	0.962678i	$0.412761\pi$
$38$		0			0
$39$	198.205	+	610.013i	0.813801	+	2.50462i
$40$		0			0
$41$	18.4365	−	56.7416i	0.0702267	−	0.216135i	−0.909783	−	0.415083i	$-0.863752\pi$
$41$	18.4365	−	56.7416i	0.0702267	−	0.216135i	0.980010	+	0.198948i	$0.0637524\pi$
$42$		0			0
$43$			32.9665i			0.116915i	0.998290	+	0.0584575i	$0.0186182\pi$
$43$			32.9665i			0.116915i	−0.998290	+	0.0584575i	$0.981382\pi$
$44$		0			0
$45$	94.5635	+	774.297i	0.313260	+	2.56501i
$46$		0			0
$47$	−339.619	−	467.446i	−1.05401	−	1.45072i	−0.885278	−	0.465062i	$-0.846032\pi$
$47$	−339.619	−	467.446i	−1.05401	−	1.45072i	−0.168734	−	0.985662i	$-0.553968\pi$
$48$		0			0
$49$	−269.262			−0.785022
$50$		0			0
$51$	599.046			1.64477
$52$		0			0
$53$	−0.813398	−	1.11955i	−0.00210809	−	0.00290154i	0.807962	−	0.589235i	$-0.200571\pi$
$53$	−0.813398	−	1.11955i	−0.00210809	−	0.00290154i	−0.810070	+	0.586334i	$0.800571\pi$
$54$		0			0
$55$	48.6666	+	52.2563i	0.119313	+	0.128113i
$56$		0			0
$57$		−	533.020i		−	1.23860i
$58$		0			0
$59$	−19.0425	+	58.6066i	−0.0420189	+	0.129321i	−0.969865	−	0.243642i	$-0.921658\pi$
$59$	−19.0425	+	58.6066i	−0.0420189	+	0.129321i	0.927846	+	0.372962i	$0.121658\pi$
$60$		0			0
$61$	−185.588	−	571.180i	−0.389542	−	1.19889i	−0.933131	−	0.359536i	$-0.882935\pi$
$61$	−185.588	−	571.180i	−0.389542	−	1.19889i	0.543589	−	0.839352i	$-0.317065\pi$
$62$		0			0
$63$	1641.88	+	533.481i	3.28346	+	1.06686i
$64$		0			0
$65$	−723.607	+	88.3729i	−1.38081	+	0.168636i
$66$		0			0
$67$	−357.055	+	491.444i	−0.651063	+	0.896111i	−0.999145	−	0.0413530i	$-0.986833\pi$
$67$	−357.055	+	491.444i	−0.651063	+	0.896111i	0.348082	+	0.937464i	$0.386833\pi$
$68$		0			0
$69$	−62.3699	−	45.3144i	−0.108818	−	0.0790610i
$70$		0			0
$71$	544.838	−	395.848i	0.910709	−	0.661669i	−0.0304848	−	0.999535i	$-0.509705\pi$
$71$	544.838	−	395.848i	0.910709	−	0.661669i	0.941194	+	0.337866i	$0.109705\pi$
$72$		0			0
$73$	331.958	−	107.860i	0.532230	−	0.172932i	−0.0305584	−	0.999533i	$-0.509729\pi$
$73$	331.958	−	107.860i	0.532230	−	0.172932i	0.562788	+	0.826601i	$0.309729\pi$
$74$		0			0
$75$	−1226.54	−	87.3619i	−1.88838	−	0.134503i
$76$		0			0
$77$	150.304	−	48.8366i	0.222450	−	0.0722785i
$78$		0			0
$79$	−7.93662	+	5.76629i	−0.0113030	+	0.00821213i	−0.593422	−	0.804891i	$-0.702224\pi$
$79$	−7.93662	+	5.76629i	−0.0113030	+	0.00821213i	0.582119	+	0.813103i	$0.302224\pi$
$80$		0			0
$81$	−1824.37	−	1325.48i	−2.50256	−	1.81822i
$82$		0			0
$83$	719.989	−	990.980i	0.952157	−	1.31053i	0.00159463	−	0.999999i	$-0.499492\pi$
$83$	719.989	−	990.980i	0.952157	−	1.31053i	0.950563	−	0.310533i	$-0.100508\pi$
$84$		0			0
$85$	−130.343	+	668.247i	−0.166325	+	0.852724i
$86$		0			0
$87$	−1216.71	−	395.332i	−1.49936	−	0.487173i
$88$		0			0
$89$	−248.495	−	764.789i	−0.295960	−	0.910870i	−0.982897	−	0.184154i	$-0.941045\pi$
$89$	−248.495	−	764.789i	−0.295960	−	0.910870i	0.686938	−	0.726716i	$-0.258955\pi$
$90$		0			0
$91$	−498.556	+	1534.40i	−0.574317	+	1.76757i
$92$		0			0
$93$			2819.27i			3.14350i
$94$		0			0
$95$	594.594	+	115.976i	0.642148	+	0.125252i
$96$		0			0
$97$	528.015	+	726.751i	0.552699	+	0.760725i	0.990375	−	0.138408i	$-0.0441984\pi$
$97$	528.015	+	726.751i	0.552699	+	0.760725i	−0.437676	+	0.899133i	$0.644198\pi$
$98$		0			0
$99$	−445.617			−0.452386
$100$		0			0
$101$	841.011			0.828551			0.414276	−	0.910151i	$-0.364035\pi$
$101$	841.011			0.828551			0.414276	+	0.910151i	$0.364035\pi$
$102$		0			0
$103$	−738.149	−	1015.97i	−0.706135	−	0.971912i	−0.999872	−	0.0160254i	$-0.994899\pi$
$103$	−738.149	−	1015.97i	−0.706135	−	0.971912i	0.293736	−	0.955886i	$-0.405101\pi$
$104$		0			0
$105$	−1320.90	+	2379.34i	−1.22769	+	2.21143i
$106$		0			0
$107$		−	512.379i		−	0.462931i	−0.972843	−	0.231465i	$-0.925648\pi$
$107$		−	512.379i		−	0.462931i	0.972843	−	0.231465i	$-0.0743520\pi$
$108$		0			0
$109$	−479.719	+	1476.42i	−0.421548	+	1.29739i	0.484713	+	0.874673i	$0.338924\pi$
$109$	−479.719	+	1476.42i	−0.421548	+	1.29739i	−0.906261	+	0.422718i	$0.861076\pi$
$110$		0			0
$111$	−759.260	−	2336.76i	−0.649241	−	1.99816i
$112$		0			0
$113$	−586.952	−	190.712i	−0.488635	−	0.158767i	0.0543289	−	0.998523i	$-0.482698\pi$
$113$	−586.952	−	190.712i	−0.488635	−	0.158767i	−0.542964	+	0.839756i	$0.682698\pi$
$114$		0			0
$115$	64.1197	−	59.7151i	0.0519930	−	0.0484214i
$116$		0			0
$117$	2673.92	−	3680.34i	2.11286	−	2.90810i
$118$		0			0
$119$	1219.04	+	885.682i	0.939066	+	0.682271i
$120$		0			0
$121$	1043.80	−	758.364i	0.784222	−	0.569770i
$122$		0			0
$123$	−558.177	+	181.363i	−0.409180	+	0.132951i
$124$		0			0
$125$	364.328	−	1349.22i	0.260692	−	0.965422i
$126$		0			0
$127$	−1564.89	+	508.462i	−1.09339	+	0.355266i	−0.799557	−	0.600590i	$-0.794932\pi$
$127$	−1564.89	+	508.462i	−1.09339	+	0.355266i	−0.293838	+	0.955855i	$0.594932\pi$
$128$		0			0
$129$	262.362	−	190.617i	0.179067	−	0.130100i
$130$		0			0
$131$	488.802	+	355.135i	0.326006	+	0.236857i	0.738734	−	0.673997i	$-0.235424\pi$
$131$	488.802	+	355.135i	0.326006	+	0.236857i	−0.412728	+	0.910854i	$0.635424\pi$
$132$		0			0
$133$	788.064	−	1084.68i	0.513788	−	0.707168i
$134$		0			0
$135$	3442.32	−	3205.86i	2.19458	−	2.04382i
$136$		0			0
$137$	1931.66	+	627.636i	1.20462	+	0.391405i	0.841459	−	0.540321i	$-0.181697\pi$
$137$	1931.66	+	627.636i	1.20462	+	0.391405i	0.363162	+	0.931726i	$0.381697\pi$
$138$		0			0
$139$	656.265	+	2019.78i	0.400458	+	1.23248i	0.924629	+	0.380870i	$0.124375\pi$
$139$	656.265	+	2019.78i	0.400458	+	1.23248i	−0.524171	+	0.851613i	$0.675625\pi$
$140$		0			0
$141$	−1756.41	+	5405.68i	−1.04905	+	3.22865i
$142$		0			0
$143$		−	416.444i		−	0.243530i
$144$		0			0
$145$	705.735	−	1271.24i	0.404194	−	0.728075i
$146$		0			0
$147$	1556.91	+	2142.91i	0.873551	+	1.20234i
$148$		0			0
$149$	1358.75			0.747067			0.373533	−	0.927617i	$-0.378146\pi$
$149$	1358.75			0.747067			0.373533	+	0.927617i	$0.378146\pi$
$150$		0			0
$151$	759.274			0.409198			0.204599	−	0.978846i	$-0.434411\pi$
$151$	759.274			0.409198			0.204599	+	0.978846i	$0.434411\pi$
$152$		0			0
$153$	−2497.33	−	3437.28i	−1.31959	−	1.81626i
$154$		0			0
$155$	−3144.95	−	613.428i	−1.62973	−	0.317882i
$156$		0			0
$157$			1919.05i			0.975524i	0.872977	+	0.487762i	$0.162187\pi$
$157$			1919.05i			0.975524i	−0.872977	+	0.487762i	$0.837813\pi$
$158$		0			0
$159$	−4.20665	+	12.9467i	−0.00209817	+	0.00645751i
$160$		0			0
$161$	−59.9237	−	184.426i	−0.0293332	−	0.0902783i
$162$		0			0
$163$	2648.85	+	860.665i	1.27285	+	0.413574i	0.866056	−	0.499947i	$-0.166647\pi$
$163$	2648.85	+	860.665i	1.27285	+	0.413574i	0.406793	+	0.913521i	$0.366647\pi$
$164$		0			0
$165$	134.481	−	689.463i	0.0634504	−	0.325301i
$166$		0			0
$167$	−925.093	+	1273.28i	−0.428658	+	0.589997i	−0.967645	−	0.252317i	$-0.918807\pi$
$167$	−925.093	+	1273.28i	−0.428658	+	0.589997i	0.538987	+	0.842314i	$0.318807\pi$
$168$		0			0
$169$	1661.99	+	1207.51i	0.756484	+	0.549617i
$170$		0			0
$171$	−3058.43	+	2222.08i	−1.36774	+	0.993724i
$172$		0			0
$173$	17.3478	−	5.63663i	0.00762385	−	0.00247714i	−0.305203	−	0.952287i	$-0.598724\pi$
$173$	17.3478	−	5.63663i	0.00762385	−	0.00247714i	0.312826	+	0.949810i	$0.398724\pi$
$174$		0			0
$175$	−2366.80	−	1991.20i	−1.02236	−	0.860117i
$176$		0			0
$177$	576.523	−	187.324i	0.244826	−	0.0795487i
$178$		0			0
$179$	−1178.51	+	856.235i	−0.492099	+	0.357531i	−0.805991	−	0.591928i	$-0.798367\pi$
$179$	−1178.51	+	856.235i	−0.492099	+	0.357531i	0.313892	+	0.949459i	$0.398367\pi$
$180$		0			0
$181$	124.538	+	90.4824i	0.0511429	+	0.0371575i	0.613063	−	0.790034i	$-0.289937\pi$
$181$	124.538	+	90.4824i	0.0511429	+	0.0371575i	−0.561920	+	0.827192i	$0.689937\pi$
$182$		0			0
$183$	−3472.61	+	4779.63i	−1.40275	+	1.93071i
$184$		0			0
$185$	2771.90	−	338.528i	1.10159	−	0.134535i
$186$		0			0
$187$	−369.905	−	120.190i	−0.144653	−	0.0470007i
$188$		0			0
$189$	−3217.05	−	9901.07i	−1.23813	−	3.81057i
$190$		0			0
$191$	727.031	−	2237.57i	0.275425	−	0.847670i	−0.713682	−	0.700470i	$-0.752974\pi$
$191$	727.031	−	2237.57i	0.275425	−	0.847670i	0.989107	−	0.147200i	$-0.0470261\pi$
$192$		0			0
$193$			392.086i			0.146233i	0.997323	+	0.0731165i	$0.0232945\pi$
$193$			392.086i			0.146233i	−0.997323	+	0.0731165i	$0.976706\pi$
$194$		0			0
$195$	4887.31	+	5247.80i	1.79481	+	1.92719i
$196$		0			0
$197$	−2995.29	−	4122.66i	−1.08328	−	1.49100i	−0.855863	−	0.517202i	$-0.826973\pi$
$197$	−2995.29	−	4122.66i	−1.08328	−	1.49100i	−0.227412	−	0.973799i	$-0.573027\pi$
$198$		0			0
$199$	509.909			0.181641			0.0908204	−	0.995867i	$-0.471051\pi$
$199$	509.909			0.181641			0.0908204	+	0.995867i	$0.471051\pi$
$200$		0			0
$201$	5975.67			2.09697
$202$		0			0
$203$	−1891.46	−	2603.37i	−0.653963	−	0.900102i
$204$		0			0
$205$	−80.8634	−	662.118i	−0.0275500	−	0.225582i
$206$		0			0
$207$			546.783i			0.183594i
$208$		0			0
$209$	−106.943	+	329.135i	−0.0353941	+	0.108932i
$210$		0			0
$211$	289.914	+	892.262i	0.0945899	+	0.291118i	0.987147	−	0.159817i	$-0.0510905\pi$
$211$	289.914	+	892.262i	0.0945899	+	0.291118i	−0.892557	+	0.450935i	$0.851091\pi$
$212$		0			0
$213$	−6300.66	−	2047.21i	−2.02683	−	0.658556i
$214$		0			0
$215$	155.551	+	334.145i	0.0493419	+	0.105993i
$216$		0			0
$217$	−4168.26	+	5737.12i	−1.30396	+	1.79475i
$218$		0			0
$219$	−2777.83	−	2018.21i	−0.857114	−	0.622730i
$220$		0			0
$221$	3212.26	−	2333.84i	0.977737	−	0.710368i
$222$		0			0
$223$	−365.685	+	118.818i	−0.109812	+	0.0356801i	−0.363408	−	0.931630i	$-0.618387\pi$
$223$	−365.685	+	118.818i	−0.109812	+	0.0356801i	0.253596	+	0.967310i	$0.418387\pi$
$224$		0			0
$225$	4611.98	+	7401.99i	1.36651	+	2.19318i
$226$		0			0
$227$	−2641.61	+	858.310i	−0.772377	+	0.250961i	−0.668582	−	0.743638i	$-0.733099\pi$
$227$	−2641.61	+	858.310i	−0.772377	+	0.250961i	−0.103795	+	0.994599i	$0.533099\pi$
$228$		0			0
$229$	1417.34	−	1029.75i	0.408996	−	0.297153i	−0.364199	−	0.931321i	$-0.618657\pi$
$229$	1417.34	−	1029.75i	0.408996	−	0.297153i	0.773195	+	0.634168i	$0.218657\pi$
$230$		0			0
$231$	−1257.74	−	913.801i	−0.358239	−	0.260276i
$232$		0			0
$233$	2441.24	−	3360.08i	0.686399	−	0.944747i	−0.313589	−	0.949559i	$-0.601532\pi$
$233$	2441.24	−	3360.08i	0.686399	−	0.944747i	0.999988	+	0.00481156i	$0.00153157\pi$
$234$		0			0
$235$	−5647.97	−	3135.50i	−1.56780	−	0.870371i
$236$		0			0
$237$	91.7813	+	29.8215i	0.0251554	+	0.00817349i
$238$		0			0
$239$	−379.265	−	1167.26i	−0.102647	−	0.315915i	0.886524	−	0.462682i	$-0.153113\pi$
$239$	−379.265	−	1167.26i	−0.102647	−	0.315915i	−0.989171	+	0.146768i	$0.953113\pi$
$240$		0			0
$241$	363.719	−	1119.41i	0.0972165	−	0.299202i	−0.890608	−	0.454771i	$-0.849721\pi$
$241$	363.719	−	1119.41i	0.0972165	−	0.299202i	0.987825	+	0.155569i	$0.0497212\pi$
$242$		0			0
$243$			10823.4i			2.85729i
$244$		0			0
$245$	−2729.21	+	1270.50i	−0.711686	+	0.331304i
$246$		0			0
$247$	−2076.61	−	2858.21i	−0.534946	−	0.736290i
$248$		0			0
$249$	−12049.7			−3.06675
$250$		0			0
$251$	−211.416			−0.0531651			−0.0265825	−	0.999647i	$-0.508462\pi$
$251$	−211.416			−0.0531651			−0.0265825	+	0.999647i	$0.508462\pi$
$252$		0			0
$253$	29.4212	+	40.4948i	0.00731105	+	0.0100628i
$254$		0			0
$255$	6071.86	−	2826.58i	1.49112	−	0.694145i
$256$		0			0
$257$			5863.61i			1.42320i	0.702586	+	0.711599i	$0.252029\pi$
$257$			5863.61i			1.42320i	−0.702586	+	0.711599i	$0.747971\pi$
$258$		0			0
$259$	1909.81	−	5877.78i	0.458184	−	1.41014i
$260$		0			0
$261$	2803.88	+	8629.45i	0.664965	+	2.04655i
$262$		0			0
$263$	1645.01	+	534.495i	0.385686	+	0.125317i	0.495441	−	0.868642i	$-0.335007\pi$
$263$	1645.01	+	534.495i	0.385686	+	0.125317i	−0.109755	+	0.993959i	$0.535007\pi$
$264$		0			0
$265$	−13.5270	−	7.50960i	−0.00313570	−	0.00174080i
$266$		0			0
$267$	−4649.69	+	6399.75i	−1.06575	+	1.46688i
$268$		0			0
$269$	2319.97	+	1685.55i	0.525840	+	0.382045i	0.818799	−	0.574080i	$-0.194640\pi$
$269$	2319.97	+	1685.55i	0.525840	+	0.382045i	−0.292960	+	0.956125i	$0.594640\pi$
$270$		0			0
$271$	300.862	−	218.589i	0.0674393	−	0.0489976i	−0.553555	−	0.832813i	$-0.686729\pi$
$271$	300.862	−	218.589i	0.0674393	−	0.0489976i	0.620994	+	0.783815i	$0.286729\pi$
$272$		0			0
$273$	15094.1	−	4904.38i	3.34629	−	1.08728i
$274$		0			0
$275$	739.849	+	300.032i	0.162235	+	0.0657913i
$276$		0			0
$277$	214.142	−	69.5790i	0.0464496	−	0.0150924i	−0.285700	−	0.958319i	$-0.592226\pi$
$277$	214.142	−	69.5790i	0.0464496	−	0.0150924i	0.332150	+	0.943227i	$0.392226\pi$
$278$		0			0
$279$	16176.8	−	11753.1i	3.47125	−	2.52201i
$280$		0			0
$281$	4188.35	+	3043.02i	0.889168	+	0.646018i	0.935661	−	0.352901i	$-0.114805\pi$
$281$	4188.35	+	3043.02i	0.889168	+	0.646018i	−0.0464933	+	0.998919i	$0.514805\pi$
$282$		0			0
$283$	−2533.43	+	3486.96i	−0.532143	+	0.732433i	−0.987455	−	0.157899i	$-0.949528\pi$
$283$	−2533.43	+	3486.96i	−0.532143	+	0.732433i	0.455312	+	0.890332i	$0.349528\pi$
$284$		0			0
$285$	−2515.04	−	5402.63i	−0.522730	−	1.12289i
$286$		0			0
$287$	−1404.01	−	456.191i	−0.288767	−	0.0938261i
$288$		0			0
$289$	372.259	+	1145.69i	0.0757701	+	0.233196i
$290$		0			0
$291$	2730.74	−	8404.35i	0.550099	−	1.69303i
$292$		0			0
$293$		−	5577.44i		−	1.11207i	−0.831158	−	0.556037i	$-0.812321\pi$
$293$		−	5577.44i		−	1.11207i	0.831158	−	0.556037i	$-0.187679\pi$
$294$		0			0
$295$	83.5212	+	683.881i	0.0164840	+	0.134973i
$296$		0			0
$297$	1579.50	+	2174.00i	0.308592	+	0.424741i
$298$		0			0
$299$	−510.987			−0.0988333
$300$		0			0
$301$	815.722			0.156204
$302$		0			0
$303$	−4862.84	−	6693.13i	−0.921990	−	1.26901i
$304$		0			0
$305$	−4576.19	−	4913.73i	−0.859121	−	0.922489i
$306$		0			0
$307$		−	3853.10i		−	0.716313i	−0.933662	−	0.358156i	$-0.883405\pi$
$307$		−	3853.10i		−	0.716313i	0.933662	−	0.358156i	$-0.116595\pi$
$308$		0			0
$309$	−3817.49	+	11749.0i	−0.702813	+	2.16304i
$310$		0			0
$311$	1513.01	+	4656.57i	0.275868	+	0.849035i	0.988988	+	0.147993i	$0.0472813\pi$
$311$	1513.01	+	4656.57i	0.275868	+	0.849035i	−0.713120	+	0.701042i	$0.752719\pi$
$312$		0			0
$313$	−2660.46	−	864.437i	−0.480442	−	0.156105i	0.0587763	−	0.998271i	$-0.481280\pi$
$313$	−2660.46	−	864.437i	−0.480442	−	0.156105i	−0.539218	+	0.842166i	$0.681280\pi$
$314$		0			0
$315$	19159.2	−	2339.87i	3.42697	−	0.418530i
$316$		0			0
$317$	4877.46	−	6713.25i	0.864181	−	1.18944i	−0.116375	−	0.993205i	$-0.537128\pi$
$317$	4877.46	−	6713.25i	0.864181	−	1.18944i	0.980556	−	0.196238i	$-0.0628725\pi$
$318$		0			0
$319$	671.988	+	488.228i	0.117944	+	0.0856912i
$320$		0			0
$321$	−4077.74	+	2962.65i	−0.709025	+	0.515137i
$322$		0			0
$323$	−3138.13	+	1019.64i	−0.540588	+	0.175648i
$324$		0			0
$325$	−6917.41	+	4310.05i	−1.18064	+	0.735627i
$326$		0			0
$327$	14523.8	−	4719.07i	2.45617	−	0.798059i
$328$		0			0
$329$	−11566.5	+	8403.52i	−1.93823	+	1.40821i
$330$		0			0
$331$	−901.021	−	654.630i	−0.149621	−	0.108706i	0.510456	−	0.859904i	$-0.329477\pi$
$331$	−901.021	−	654.630i	−0.149621	−	0.108706i	−0.660077	+	0.751198i	$0.729477\pi$
$332$		0			0
$333$	−10242.9	+	14098.2i	−1.68561	+	2.32005i
$334$		0			0
$335$	−1300.21	+	6665.97i	−0.212053	+	1.08717i
$336$		0			0
$337$	−168.554	−	54.7665i	−0.0272455	−	0.00885259i	0.295363	−	0.955385i	$-0.404560\pi$
$337$	−168.554	−	54.7665i	−0.0272455	−	0.00885259i	−0.322608	+	0.946533i	$0.604560\pi$
$338$		0			0
$339$	1876.07	+	5773.94i	0.300572	+	0.925066i
$340$		0			0
$341$	565.645	−	1740.88i	0.0898282	−	0.276463i
$342$		0			0
$343$		−	1824.56i		−	0.287221i
$344$		0			0
$345$	−845.988	−	165.011i	−0.132019	−	0.0257504i
$346$		0			0
$347$	7347.74	+	10113.3i	1.13674	+	1.56458i	0.774593	+	0.632460i	$0.217955\pi$
$347$	7347.74	+	10113.3i	1.13674	+	1.56458i	0.362142	+	0.932123i	$0.382045\pi$
$348$		0			0
$349$	7795.77			1.19570			0.597848	−	0.801609i	$-0.296023\pi$
$349$	7795.77			1.19570			0.597848	+	0.801609i	$0.296023\pi$
$350$		0			0
$351$	−27432.8			−4.17166
$352$		0			0
$353$	−4245.54	−	5843.48i	−0.640133	−	0.881068i	0.358489	−	0.933534i	$-0.383292\pi$
$353$	−4245.54	−	5843.48i	−0.640133	−	0.881068i	−0.998623	+	0.0524657i	$0.983292\pi$
$354$		0			0
$355$	3654.62	−	6583.07i	0.546386	−	0.984205i
$356$		0			0
$357$		−	14822.8i		−	2.19749i
$358$		0			0
$359$	−2580.84	+	7943.01i	−0.379419	+	1.16773i	0.561029	+	0.827796i	$0.310406\pi$
$359$	−2580.84	+	7943.01i	−0.379419	+	1.16773i	−0.940448	+	0.339937i	$0.889594\pi$
$360$		0			0
$361$	−1212.29	−	3731.05i	−0.176745	−	0.543964i
$362$		0			0
$363$	−12070.8	−	3922.04i	−1.74532	−	0.567090i
$364$		0			0
$365$	2855.76	−	2659.59i	0.409527	−	0.381395i
$366$		0			0
$367$	1307.75	−	1799.97i	0.186006	−	0.256015i	−0.705823	−	0.708388i	$-0.749423\pi$
$367$	1307.75	−	1799.97i	0.186006	−	0.256015i	0.891829	+	0.452373i	$0.149423\pi$
$368$		0			0
$369$	3367.60	+	2446.70i	0.475096	+	0.345177i
$370$		0			0
$371$	−27.7020	+	20.1267i	−0.00387659	+	0.00281651i
$372$		0			0
$373$	9930.63	−	3226.66i	1.37852	−	0.447909i	0.476339	−	0.879262i	$-0.341964\pi$
$373$	9930.63	−	3226.66i	1.37852	−	0.447909i	0.902183	+	0.431353i	$0.141964\pi$
$374$		0			0
$375$	−12844.3	+	4901.88i	−1.76873	+	0.675019i
$376$		0			0
$377$	−8064.52	+	2620.32i	−1.10171	+	0.357967i
$378$		0			0
$379$	8348.88	−	6065.81i	1.13154	−	0.822111i	0.145620	−	0.989341i	$-0.453482\pi$
$379$	8348.88	−	6065.81i	1.13154	−	0.822111i	0.985918	+	0.167230i	$0.0534822\pi$
$380$		0			0
$381$	13094.9	+	9514.04i	1.76083	+	1.27931i
$382$		0			0
$383$	−1889.75	+	2601.01i	−0.252119	+	0.347012i	−0.916252	−	0.400603i	$-0.868801\pi$
$383$	−1889.75	+	2601.01i	−0.252119	+	0.347012i	0.664133	+	0.747614i	$0.268801\pi$
$384$		0			0
$385$	1293.03	−	1204.20i	0.171165	−	0.159408i
$386$		0			0
$387$	−2187.49	−	710.760i	−0.287330	−	0.0933591i
$388$		0			0
$389$	−88.6585	−	272.863i	−0.0115557	−	0.0355648i	0.945112	−	0.326745i	$-0.105952\pi$
$389$	−88.6585	−	272.863i	−0.0115557	−	0.0355648i	−0.956668	+	0.291181i	$0.905952\pi$
$390$		0			0
$391$	−147.475	+	453.883i	−0.0190746	+	0.0587055i
$392$		0			0
$393$		−	5943.53i		−	0.762880i
$394$		0			0
$395$	−53.2366	+	95.8951i	−0.00678133	+	0.0122152i
$396$		0			0
$397$	4072.02	+	5604.65i	0.514783	+	0.708538i	0.984717	−	0.174164i	$-0.0557222\pi$
$397$	4072.02	+	5604.65i	0.514783	+	0.708538i	−0.469934	+	0.882702i	$0.655722\pi$
$398$		0			0
$399$	−13189.0			−1.65483
$400$		0			0
$401$	−16018.6			−1.99484			−0.997421	−	0.0717782i	$-0.977133\pi$
$401$	−16018.6			−1.99484			−0.997421	+	0.0717782i	$0.977133\pi$
$402$		0			0
$403$	10983.7	+	15117.8i	1.35766	+	1.86866i
$404$		0			0
$405$	−24745.8	−	4826.70i	−3.03612	−	0.592199i
$406$		0			0
$407$			1595.26i			0.194286i
$408$		0			0
$409$	2119.64	−	6523.57i	0.256257	−	0.788679i	−0.737322	−	0.675541i	$-0.763910\pi$
$409$	2119.64	−	6523.57i	0.256257	−	0.788679i	0.993579	−	0.113137i	$-0.0360901\pi$
$410$		0			0
$411$	−6174.15	−	19002.1i	−0.740994	−	2.28054i
$412$		0			0
$413$	1450.16	+	471.185i	0.172779	+	0.0561393i
$414$		0			0
$415$	2621.82	−	13441.7i	0.310121	−	1.58994i
$416$		0			0
$417$	12279.6	−	16901.5i	1.44205	−	1.98482i
$418$		0			0
$419$	9867.17	+	7168.92i	1.15046	+	0.835859i	0.988542	−	0.150946i	$-0.0482318\pi$
$419$	9867.17	+	7168.92i	1.15046	+	0.835859i	0.161918	+	0.986804i	$0.448232\pi$
$420$		0			0
$421$	−6177.03	+	4487.88i	−0.715084	+	0.519539i	−0.884810	−	0.465953i	$-0.845712\pi$
$421$	−6177.03	+	4487.88i	−0.715084	+	0.519539i	0.169726	+	0.985491i	$0.445712\pi$
$422$		0			0
$423$	38339.6	−	12457.3i	4.40694	−	1.43190i
$424$		0			0
$425$	1831.96	+	7388.29i	0.209090	+	0.843258i
$426$		0			0
$427$	−14133.3	+	4592.17i	−1.60177	+	0.520447i
$428$		0			0
$429$	−3314.25	+	2407.94i	−0.372991	+	0.270994i
$430$		0			0
$431$	9273.88	+	6737.87i	1.03644	+	0.753020i	0.969588	−	0.244743i	$-0.0787034\pi$
$431$	9273.88	+	6737.87i	1.03644	+	0.753020i	0.0668552	+	0.997763i	$0.478703\pi$
$432$		0			0
$433$	472.206	−	649.936i	0.0524083	−	0.0721338i	−0.782009	−	0.623268i	$-0.785805\pi$
$433$	472.206	−	649.936i	0.0524083	−	0.0721338i	0.834417	+	0.551134i	$0.185805\pi$
$434$		0			0
$435$	−14197.7	+	1733.95i	−1.56490	+	0.191118i
$436$		0			0
$437$	403.857	+	131.221i	0.0442085	+	0.0143642i
$438$		0			0
$439$	−118.941	−	366.064i	−0.0129311	−	0.0397979i	0.944383	−	0.328848i	$-0.106660\pi$
$439$	−118.941	−	366.064i	−0.0129311	−	0.0397979i	−0.957314	+	0.289050i	$0.906660\pi$
$440$		0			0
$441$	5805.31	−	17866.9i	0.626856	−	1.92926i
$442$		0			0
$443$			16787.2i			1.80041i	0.435462	+	0.900207i	$0.356585\pi$
$443$			16787.2i			1.80041i	−0.435462	+	0.900207i	$0.643415\pi$
$444$		0			0
$445$	−6127.34	−	6579.30i	−0.652728	−	0.700873i
$446$		0			0
$447$	−7856.47	−	10813.5i	−0.831316	−	1.14421i
$448$		0			0
$449$	−7286.13			−0.765821			−0.382910	−	0.923785i	$-0.625078\pi$
$449$	−7286.13			−0.765821			−0.382910	+	0.923785i	$0.625078\pi$
$450$		0			0
$451$	381.057			0.0397855
$452$		0			0
$453$	−4390.23	−	6042.63i	−0.455344	−	0.626728i
$454$		0			0
$455$	2186.69	+	17904.9i	0.225305	+	1.84482i
$456$		0			0
$457$			18506.7i			1.89433i	0.320751	+	0.947164i	$0.396065\pi$
$457$			18506.7i			1.89433i	−0.320751	+	0.947164i	$0.603935\pi$
$458$		0			0
$459$	−7917.34	+	24367.1i	−0.805120	+	2.47790i
$460$		0			0
$461$	5204.42	+	16017.6i	0.525801	+	1.61825i	0.762727	+	0.646720i	$0.223860\pi$
$461$	5204.42	+	16017.6i	0.525801	+	1.61825i	−0.236927	+	0.971528i	$0.576140\pi$
$462$		0			0
$463$	−537.427	−	174.620i	−0.0539446	−	0.0175277i	0.281920	−	0.959438i	$-0.409029\pi$
$463$	−537.427	−	174.620i	−0.0539446	−	0.0175277i	−0.335865	+	0.941910i	$0.609029\pi$
$464$		0			0
$465$	13302.6	+	28575.8i	1.32666	+	2.84983i
$466$		0			0
$467$	3211.94	−	4420.86i	0.318268	−	0.438058i	−0.619670	−	0.784863i	$-0.712733\pi$
$467$	3211.94	−	4420.86i	0.318268	−	0.438058i	0.937937	+	0.346805i	$0.112733\pi$
$468$		0			0
$469$	12160.3	+	8834.95i	1.19725	+	0.869851i
$470$		0			0
$471$	15272.7	−	11096.2i	1.49411	−	1.08554i
$472$		0			0
$473$	−200.251	+	65.0654i	−0.0194662	+	0.00632496i
$474$		0			0
$475$	6573.97	−	1630.05i	0.635020	−	0.157456i
$476$		0			0
$477$	91.8244	−	29.8356i	0.00881416	−	0.00286389i
$478$		0			0
$479$	5789.46	−	4206.29i	0.552249	−	0.401232i	−0.276365	−	0.961053i	$-0.589130\pi$
$479$	5789.46	−	4206.29i	0.552249	−	0.401232i	0.828614	+	0.559820i	$0.189130\pi$
$480$		0			0
$481$	−13175.2	−	9572.37i	−1.24894	−	0.907407i
$482$		0			0
$483$	−1121.26	+	1543.28i	−0.105629	+	0.145386i
$484$		0			0
$485$	8781.05	+	4874.84i	0.822117	+	0.456402i
$486$		0			0
$487$	−4598.62	−	1494.18i	−0.427892	−	0.139030i	0.0871506	−	0.996195i	$-0.472224\pi$
$487$	−4598.62	−	1494.18i	−0.427892	−	0.139030i	−0.515042	+	0.857165i	$0.672224\pi$
$488$		0			0
$489$	−8466.50	−	26057.2i	−0.782962	−	2.40971i
$490$		0			0
$491$	5054.15	−	15555.1i	0.464543	−	1.42972i	−0.395014	−	0.918675i	$-0.629260\pi$
$491$	5054.15	−	15555.1i	0.464543	−	1.42972i	0.859557	−	0.511040i	$-0.170740\pi$
$492$		0			0
$493$			7919.53i			0.723484i
$494$		0			0
$495$	−4516.72	+	2102.63i	−0.410124	+	0.190921i
$496$		0			0
$497$	−9794.84	−	13481.4i	−0.884021	−	1.21675i
$498$		0			0
$499$	−10342.3			−0.927827			−0.463914	−	0.885880i	$-0.653555\pi$
$499$	−10342.3			−0.927827			−0.463914	+	0.885880i	$0.653555\pi$
$500$		0			0
$501$	15482.3			1.38064
$502$		0			0
$503$	1244.86	+	1713.41i	0.110349	+	0.151883i	0.860619	−	0.509249i	$-0.170077\pi$
$503$	1244.86	+	1713.41i	0.110349	+	0.151883i	−0.750270	+	0.661131i	$0.770077\pi$
$504$		0			0
$505$	8524.38	−	3968.28i	0.751149	−	0.349675i
$506$		0			0
$507$		−	20208.9i		−	1.77023i
$508$		0			0
$509$	3680.95	−	11328.8i	0.320540	−	0.986522i	−0.652873	−	0.757467i	$-0.726437\pi$
$509$	3680.95	−	11328.8i	0.320540	−	0.986522i	0.973414	−	0.229055i	$-0.0735634\pi$
$510$		0			0
$511$	−2668.88	−	8213.96i	−0.231045	−	0.711084i
$512$		0			0
$513$	21681.4	+	7044.71i	1.86600	+	0.606300i
$514$		0			0
$515$	−12275.6	−	6814.87i	−1.05035	−	0.583105i
$516$		0			0
$517$	2169.14	−	2985.56i	0.184523	−	0.253974i
$518$		0			0
$519$	−145.166	−	105.469i	−0.0122776	−	0.00892020i
$520$		0			0
$521$	3308.23	−	2403.57i	0.278189	−	0.202116i	−0.439938	−	0.898028i	$-0.645000\pi$
$521$	3308.23	−	2403.57i	0.278189	−	0.202116i	0.718127	+	0.695912i	$0.245000\pi$
$522$		0			0
$523$	13364.9	−	4342.53i	1.11741	−	0.363070i	0.308634	−	0.951181i	$-0.400128\pi$
$523$	13364.9	−	4342.53i	1.11741	−	0.363070i	0.808780	+	0.588111i	$0.200128\pi$
$524$		0			0
$525$	−2161.68	+	30349.4i	−0.179702	+	2.52296i
$526$		0			0
$527$	16598.3	−	5393.12i	1.37198	−	0.445784i
$528$		0			0
$529$	−9793.62	+	7115.48i	−0.804933	+	0.584818i
$530$		0			0
$531$	−3478.29	−	2527.12i	−0.284265	−	0.206531i
$532$		0			0
$533$	−2286.53	+	3147.14i	−0.185817	+	0.255756i
$534$		0			0
$535$	−2417.64	−	5193.42i	−0.195372	−	0.419684i
$536$		0			0
$537$	13628.6	+	4428.20i	1.09519	+	0.355849i
$538$		0			0
$539$	−531.438	−	1635.60i	−0.0424687	−	0.130705i
$540$		0			0
$541$	1135.65	−	3495.17i	0.0902502	−	0.277762i	−0.895737	−	0.444585i	$-0.853351\pi$
$541$	1135.65	−	3495.17i	0.0902502	−	0.277762i	0.985987	+	0.166824i	$0.0533511\pi$
$542$		0			0
$543$		−	1514.31i		−	0.119678i
$544$		0			0
$545$	2104.07	+	17228.4i	0.165373	+	1.35410i
$546$		0			0
$547$	2808.03	+	3864.93i	0.219493	+	0.302107i	0.904537	−	0.426396i	$-0.140217\pi$
$547$	2808.03	+	3864.93i	0.219493	+	0.302107i	−0.685044	+	0.728502i	$0.740217\pi$
$548$		0			0
$549$	41902.0			3.25744
$550$		0			0
$551$	7046.66			0.544824
$552$		0			0
$553$	142.681	+	196.383i	0.0109718	+	0.0151014i
$554$		0			0
$555$	−18721.7	−	20102.6i	−1.43188	−	1.53749i
$556$		0			0
$557$			3100.94i			0.235891i	0.993020	+	0.117945i	$0.0376308\pi$
$557$			3100.94i			0.235891i	−0.993020	+	0.117945i	$0.962369\pi$
$558$		0			0
$559$	664.230	−	2044.29i	0.0502575	−	0.154677i
$560$		0			0
$561$	1182.32	+	3638.82i	0.0889800	+	0.273852i
$562$		0			0
$563$	−3024.78	−	982.810i	−0.226428	−	0.0735710i	0.193606	−	0.981079i	$-0.437982\pi$
$563$	−3024.78	−	982.810i	−0.226428	−	0.0735710i	−0.420034	+	0.907508i	$0.637982\pi$
$564$		0			0
$565$	−6849.14	+	836.474i	−0.509992	+	0.0622845i
$566$		0			0
$567$	−32797.6	+	45142.0i	−2.42922	+	3.34354i
$568$		0			0
$569$	−14804.6	−	10756.2i	−1.09076	−	0.792483i	−0.111233	−	0.993794i	$-0.535480\pi$
$569$	−14804.6	−	10756.2i	−1.09076	−	0.792483i	−0.979527	+	0.201311i	$0.935480\pi$
$570$		0			0
$571$	−20696.9	+	15037.2i	−1.51688	+	1.10208i	−0.553873	+	0.832601i	$0.686851\pi$
$571$	−20696.9	+	15037.2i	−1.51688	+	1.10208i	−0.963007	+	0.269477i	$0.913149\pi$
$572$		0			0
$573$	−22011.3	+	7151.92i	−1.60478	+	0.521424i
$574$		0			0
$575$	368.146	−	907.812i	0.0267004	−	0.0658406i
$576$		0			0
$577$	1513.97	−	491.918i	0.109233	−	0.0354919i	−0.253891	−	0.967233i	$-0.581710\pi$
$577$	1513.97	−	491.918i	0.109233	−	0.0354919i	0.363123	+	0.931741i	$0.381710\pi$
$578$		0			0
$579$	3120.39	−	2267.10i	0.223971	−	0.162724i
$580$		0			0
$581$	−24520.7	−	17815.4i	−1.75093	−	1.27213i
$582$		0			0
$583$	5.19514	−	7.15050i	0.000369058	−	0.000507965i
$584$		0			0
$585$	9737.02	−	49920.3i	0.688165	−	3.52812i
$586$		0			0
$587$	3220.30	+	1046.34i	0.226433	+	0.0735725i	0.420036	−	0.907507i	$-0.362017\pi$
$587$	3220.30	+	1046.34i	0.226433	+	0.0735725i	−0.193603	+	0.981080i	$0.562017\pi$
$588$		0			0
$589$	−4798.70	−	14768.9i	−0.335700	−	1.03318i
$590$		0			0
$591$	−15490.7	+	47675.6i	−1.07818	+	3.31829i
$592$		0			0
$593$			5216.87i			0.361267i	0.983550	+	0.180633i	$0.0578148\pi$
$593$			5216.87i			0.361267i	−0.983550	+	0.180633i	$0.942185\pi$
$594$		0			0
$595$	16535.1	+	3225.19i	1.13928	+	0.222218i
$596$		0			0
$597$	−2948.37	−	4058.08i	−0.202125	−	0.278201i
$598$		0			0
$599$	−14010.0			−0.955649			−0.477825	−	0.878455i	$-0.658575\pi$
$599$	−14010.0			−0.955649			−0.477825	+	0.878455i	$0.658575\pi$
$600$		0			0
$601$	−20125.4			−1.36595			−0.682973	−	0.730444i	$-0.739313\pi$
$601$	−20125.4			−1.36595			−0.682973	+	0.730444i	$0.739313\pi$
$602$		0			0
$603$	−24911.7	−	34288.0i	−1.68239	−	2.31561i
$604$		0			0
$605$	7001.51	−	12611.8i	0.470499	−	0.847510i
$606$		0			0
$607$			8609.46i			0.575696i	0.957676	+	0.287848i	$0.0929398\pi$
$607$			8609.46i			0.575696i	−0.957676	+	0.287848i	$0.907060\pi$
$608$		0			0
$609$	−9782.06	+	30106.1i	−0.650885	+	2.00322i
$610$		0			0
$611$	11641.8	+	35829.7i	0.770827	+	2.37236i
$612$		0			0
$613$	5638.16	+	1831.95i	0.371490	+	0.120704i	0.488811	−	0.872390i	$-0.337431\pi$
$613$	5638.16	+	1831.95i	0.371490	+	0.120704i	−0.117321	+	0.993094i	$0.537431\pi$
$614$		0			0
$615$	−4801.86	+	4472.01i	−0.314845	+	0.293217i
$616$		0			0
$617$	10511.2	−	14467.4i	0.685841	−	0.943978i	−0.314145	−	0.949375i	$-0.601718\pi$
$617$	10511.2	−	14467.4i	0.685841	−	0.943978i	0.999985	+	0.00539657i	$0.00171779\pi$
$618$		0			0
$619$	6546.91	+	4756.61i	0.425109	+	0.308860i	0.779690	−	0.626165i	$-0.215377\pi$
$619$	6546.91	+	4756.61i	0.425109	+	0.308860i	−0.354581	+	0.935025i	$0.615377\pi$
$620$		0			0
$621$	2667.55	−	1938.09i	0.172375	−	0.125238i
$622$		0			0
$623$	−18923.9	+	6148.74i	−1.21697	+	0.395416i
$624$		0			0
$625$	−2673.45	−	15394.6i	−0.171101	−	0.985254i
$626$		0			0
$627$	3237.76	−	1052.01i	0.206226	−	0.0670068i
$628$		0			0
$629$	−12305.1	+	8940.19i	−0.780027	+	0.566723i
$630$		0			0
$631$	−7102.88	−	5160.54i	−0.448116	−	0.325575i	0.340736	−	0.940159i	$-0.389324\pi$
$631$	−7102.88	−	5160.54i	−0.448116	−	0.325575i	−0.788851	+	0.614584i	$0.789324\pi$
$632$		0			0
$633$	5424.69	−	7466.44i	0.340619	−	0.468822i
$634$		0			0
$635$	−13462.3	+	12537.6i	−0.841317	+	0.783525i
$636$		0			0
$637$	16697.2	+	5425.26i	1.03857	+	0.337452i
$638$		0			0
$639$	14519.8	+	44687.2i	0.898893	+	2.76651i
$640$		0			0
$641$	1191.85	−	3668.13i	0.0734402	−	0.226026i	−0.907598	−	0.419840i	$-0.862086\pi$
$641$	1191.85	−	3668.13i	0.0734402	−	0.226026i	0.981038	+	0.193815i	$0.0620860\pi$
$642$		0			0
$643$		−	879.229i		−	0.0539244i	−0.999636	−	0.0269622i	$-0.991417\pi$
$643$		−	879.229i		−	0.0539244i	0.999636	−	0.0269622i	$-0.00858338\pi$
$644$		0			0
$645$	1759.85	−	3170.02i	0.107433	−	0.193518i
$646$		0			0
$647$	−15445.1	−	21258.3i	−0.938498	−	1.29173i	−0.956451	−	0.291893i	$-0.905715\pi$
$647$	−15445.1	−	21258.3i	−0.938498	−	1.29173i	0.0179534	−	0.999839i	$-0.494285\pi$
$648$		0			0
$649$	−393.582			−0.0238050
$650$		0			0
$651$	69760.0			4.19986
$652$		0			0
$653$	−16730.4	−	23027.4i	−1.00262	−	1.37999i	−0.923705	−	0.383104i	$-0.874855\pi$
$653$	−16730.4	−	23027.4i	−1.00262	−	1.37999i	−0.0789131	−	0.996881i	$-0.525145\pi$
$654$		0			0
$655$	6630.13	+	1293.22i	0.395512	+	0.0771452i
$656$		0			0
$657$			24352.6i			1.44609i
$658$		0			0
$659$	7059.47	−	21726.8i	0.417296	−	1.28431i	−0.492885	−	0.870094i	$-0.664058\pi$
$659$	7059.47	−	21726.8i	0.417296	−	1.28431i	0.910181	−	0.414211i	$-0.135942\pi$
$660$		0			0
$661$	−9523.72	−	29311.0i	−0.560408	−	1.72476i	−0.681215	−	0.732083i	$-0.738548\pi$
$661$	−9523.72	−	29311.0i	−0.560408	−	1.72476i	0.120807	−	0.992676i	$-0.461452\pi$
$662$		0			0
$663$	−37147.5	−	12069.9i	−2.17600	−	0.707025i
$664$		0			0
$665$	2869.71	−	14712.6i	0.167342	−	0.857940i
$666$		0			0
$667$	599.067	−	824.545i	0.0347766	−	0.0478658i
$668$		0			0
$669$	3060.05	+	2223.26i	0.176844	+	0.128484i
$670$		0			0
$671$	3103.26	−	2254.65i	0.178540	−	0.129717i
$672$		0			0
$673$	−15369.0	+	4993.68i	−0.880283	+	0.286021i	−0.714075	−	0.700070i	$-0.753152\pi$
$673$	−15369.0	+	4993.68i	−0.880283	+	0.286021i	−0.166208	+	0.986091i	$0.553152\pi$
$674$		0			0
$675$	19764.2	−	48736.6i	1.12700	−	2.77907i
$676$		0			0
$677$	19045.5	−	6188.26i	1.08121	−	0.351306i	0.286366	−	0.958120i	$-0.407553\pi$
$677$	19045.5	−	6188.26i	1.08121	−	0.351306i	0.794844	+	0.606814i	$0.207553\pi$
$678$		0			0
$679$	17982.7	−	13065.2i	1.01636	−	0.738432i
$680$		0			0
$681$	22105.0	+	16060.2i	1.24385	+	0.903712i
$682$		0			0
$683$	7574.67	−	10425.6i	0.424358	−	0.584079i	−0.542289	−	0.840192i	$-0.682442\pi$
$683$	7574.67	−	10425.6i	0.424358	−	0.584079i	0.966647	+	0.256113i	$0.0824420\pi$
$684$		0			0
$685$	22540.6	−	2752.84i	1.25727	−	0.153549i
$686$		0			0
$687$	−16390.5	−	5325.59i	−0.910241	−	0.295755i
$688$		0			0
$689$	27.8824	+	85.8131i	0.00154170	+	0.00474488i
$690$		0			0
$691$	−7882.69	+	24260.4i	−0.433968	+	1.33562i	0.460173	+	0.887829i	$0.347787\pi$
$691$	−7882.69	+	24260.4i	−0.433968	+	1.33562i	−0.894141	+	0.447786i	$0.852213\pi$
$692$		0			0
$693$			11026.3i			0.604409i
$694$		0			0
$695$	16182.1	+	17375.6i	0.883195	+	0.948339i
$696$		0			0
$697$	2135.52	+	2939.30i	0.116053	+	0.159733i
$698$		0			0
$699$	−40856.6			−2.21078
$700$		0			0
$701$	10490.7			0.565233			0.282617	−	0.959233i	$-0.408798\pi$
$701$	10490.7			0.565233			0.282617	+	0.959233i	$0.408798\pi$
$702$		0			0
$703$	7954.82	+	10948.9i	0.426774	+	0.587404i
$704$		0			0
$705$	7703.71	+	63078.8i	0.411544	+	3.36977i
$706$		0			0
$707$		−	20809.9i		−	1.10698i
$708$		0			0
$709$	10963.4	−	33741.8i	0.580732	−	1.78731i	−0.0350430	−	0.999386i	$-0.511157\pi$
$709$	10963.4	−	33741.8i	0.580732	−	1.78731i	0.615775	−	0.787922i	$-0.288843\pi$
$710$		0			0
$711$	−211.508	−	650.956i	−0.0111564	−	0.0343358i
$712$		0			0
$713$	−2136.10	−	694.060i	−0.112198	−	0.0364555i
$714$		0			0
$715$	−1964.98	−	4221.03i	−0.102778	−	0.220780i
$716$		0			0
$717$	−7096.57	+	9767.60i	−0.369632	+	0.508755i
$718$		0			0
$719$	2003.15	+	1455.37i	0.103901	+	0.0754885i	0.638523	−	0.769603i	$-0.279546\pi$
$719$	2003.15	+	1455.37i	0.103901	+	0.0754885i	−0.534622	+	0.845092i	$0.679546\pi$
$720$		0			0
$721$	−25139.2	+	18264.7i	−1.29852	+	0.943430i
$722$		0			0
$723$	−11011.8	+	3577.96i	−0.566437	+	0.184047i
$724$		0			0
$725$	1154.95	−	16215.1i	0.0591636	−	0.830641i
$726$		0			0
$727$	−16170.6	+	5254.15i	−0.824944	+	0.268041i	−0.690914	−	0.722937i	$-0.742792\pi$
$727$	−16170.6	+	5254.15i	−0.824944	+	0.268041i	−0.134030	+	0.990977i	$0.542792\pi$
$728$		0			0
$729$	36879.4	−	26794.4i	1.87367	−	1.36130i
$730$		0			0
$731$	−1624.13	−	1180.00i	−0.0821760	−	0.0597043i
$732$		0			0
$733$	−14404.7	+	19826.3i	−0.725851	+	0.999049i	0.273458	+	0.961884i	$0.411833\pi$
$733$	−14404.7	+	19826.3i	−0.725851	+	0.999049i	−0.999309	+	0.0371647i	$0.988167\pi$
$734$		0			0
$735$	25891.9	+	14374.0i	1.29937	+	0.721352i
$736$		0			0
$737$	−3689.92	−	1198.93i	−0.184423	−	0.0599228i
$738$		0			0
$739$	−10240.7	−	31517.7i	−0.509759	−	1.56888i	−0.792621	−	0.609715i	$-0.791284\pi$
$739$	−10240.7	−	31517.7i	−0.509759	−	1.56888i	0.282862	−	0.959161i	$-0.408716\pi$
$740$		0			0
$741$	−10739.6	+	33053.2i	−0.532429	+	1.63865i
$742$		0			0
$743$			7311.98i			0.361037i	0.983572	+	0.180519i	$0.0577776\pi$
$743$			7311.98i			0.361037i	−0.983572	+	0.180519i	$0.942222\pi$
$744$		0			0
$745$	13772.1	−	6411.20i	0.677276	−	0.315286i
$746$		0			0
$747$	50233.5	+	69140.4i	2.46044	+	3.38650i
$748$		0			0
$749$	−12678.3			−0.618497
$750$		0			0
$751$	−17898.0			−0.869649			−0.434824	−	0.900515i	$-0.643190\pi$
$751$	−17898.0			−0.869649			−0.434824	+	0.900515i	$0.643190\pi$
$752$		0			0
$753$	1222.43	+	1682.54i	0.0591607	+	0.0814277i
$754$		0			0
$755$	7695.91	−	3582.61i	0.370971	−	0.172695i
$756$		0			0
$757$			15640.0i			0.750918i	0.926839	+	0.375459i	$0.122515\pi$
$757$			15640.0i			0.750918i	−0.926839	+	0.375459i	$0.877485\pi$
$758$		0			0
$759$	152.158	−	468.293i	0.00727664	−	0.0223952i
$760$		0			0
$761$	−10318.7	−	31757.8i	−0.491529	−	1.51277i	−0.822297	−	0.569058i	$-0.807308\pi$
$761$	−10318.7	−	31757.8i	−0.491529	−	1.51277i	0.330769	−	0.943712i	$-0.392692\pi$
$762$		0			0
$763$	36532.5	+	11870.1i	1.73338	+	0.563208i
$764$		0			0
$765$	−41531.3	−	23056.3i	−1.96284	−	1.08968i
$766$		0			0
$767$	2361.69	−	3250.58i	0.111181	−	0.153027i
$768$		0			0
$769$	8298.58	+	6029.27i	0.389148	+	0.282732i	0.765106	−	0.643904i	$-0.222686\pi$
$769$	8298.58	+	6029.27i	0.389148	+	0.282732i	−0.375958	+	0.926637i	$0.622686\pi$
$770$		0			0
$771$	46665.2	−	33904.2i	2.17977	−	1.58370i
$772$		0			0
$773$	10793.7	−	3507.07i	0.502227	−	0.163183i	−0.0469376	−	0.998898i	$-0.514946\pi$
$773$	10793.7	−	3507.07i	0.502227	−	0.163183i	0.549164	+	0.835715i	$0.314946\pi$
$774$		0			0
$775$	−34771.3	+	8621.72i	−1.61164	+	0.399615i
$776$		0			0
$777$	−57820.7	+	18787.1i	−2.66963	+	0.867416i
$778$		0			0
$779$	2615.33	−	1900.15i	0.120288	−	0.0873940i
$780$		0			0
$781$	3479.86	+	2528.27i	0.159436	+	0.115837i
$782$		0			0
$783$	32161.4	−	44266.4i	1.46789	−	2.02037i
$784$		0			0
$785$	9054.99	+	19451.3i	0.411702	+	0.884391i
$786$		0			0
$787$	10842.3	+	3522.89i	0.491090	+	0.159565i	0.544085	−	0.839030i	$-0.316877\pi$
$787$	10842.3	+	3522.89i	0.491090	+	0.159565i	−0.0529953	+	0.998595i	$0.516877\pi$
$788$		0			0
$789$	−5257.92	−	16182.2i	−0.237246	−	0.730167i
$790$		0			0
$791$	−4718.97	+	14523.5i	−0.212120	+	0.652840i
$792$		0			0
$793$			39158.8i			1.75356i
$794$		0			0
$795$	18.4506	+	151.076i	0.000823114	+	0.00673975i
$796$		0			0
$797$	13269.3	+	18263.6i	0.589739	+	0.811706i	0.994721	−	0.102619i	$-0.0327221\pi$
$797$	13269.3	+	18263.6i	0.589739	+	0.811706i	−0.404982	+	0.914325i	$0.632722\pi$
$798$		0			0
$799$	35185.5			1.55791
$800$		0			0
$801$	56105.1			2.47488
$802$		0			0
$803$	1310.36	+	1803.55i	0.0575860	+	0.0792604i
$804$		0			0
$805$	−1477.59	−	1586.57i	−0.0646933	−	0.0694651i
$806$		0			0
$807$		−	28209.4i		−	1.23051i
$808$		0			0
$809$	2207.49	−	6793.94i	0.0959346	−	0.295256i	−0.891562	−	0.452900i	$-0.850390\pi$
$809$	2207.49	−	6793.94i	0.0959346	−	0.295256i	0.987496	+	0.157643i	$0.0503896\pi$
$810$		0			0
$811$	−5545.60	−	17067.6i	−0.240114	−	0.738994i	−0.996402	−	0.0847555i	$-0.972989\pi$
$811$	−5545.60	−	17067.6i	−0.240114	−	0.738994i	0.756288	−	0.654239i	$-0.227011\pi$
$812$		0			0
$813$	−3479.25	−	1130.48i	−0.150089	−	0.0487670i
$814$		0			0
$815$	30909.5	−	3774.92i	1.32848	−	0.162245i
$816$		0			0
$817$	−1049.94	+	1445.12i	−0.0449607	+	0.0618830i
$818$		0			0
$819$	−91066.1	−	66163.4i	−3.88536	−	2.82288i
$820$		0			0
$821$	8112.04	−	5893.74i	0.344838	−	0.250539i	−0.401862	−	0.915700i	$-0.631637\pi$
$821$	8112.04	−	5893.74i	0.344838	−	0.250539i	0.746700	+	0.665161i	$0.231637\pi$
$822$		0			0
$823$	−16948.1	+	5506.76i	−0.717828	+	0.233237i	−0.645081	−	0.764114i	$-0.723177\pi$
$823$	−16948.1	+	5506.76i	−0.717828	+	0.233237i	−0.0727470	+	0.997350i	$0.523177\pi$
$824$		0			0
$825$	−1890.13	−	7622.86i	−0.0797645	−	0.321690i
$826$		0			0
$827$	10830.3	−	3518.98i	0.455389	−	0.147965i	−0.0723359	−	0.997380i	$-0.523045\pi$
$827$	10830.3	−	3518.98i	0.455389	−	0.147965i	0.527724	+	0.849416i	$0.323045\pi$
$828$		0			0
$829$	−21500.4	+	15620.9i	−0.900770	+	0.654448i	−0.938664	−	0.344834i	$-0.887935\pi$
$829$	−21500.4	+	15620.9i	−0.900770	+	0.654448i	0.0378936	+	0.999282i	$0.487935\pi$
$830$		0			0
$831$	−1791.94	−	1301.92i	−0.0748034	−	0.0543479i
$832$		0			0
$833$	9637.95	−	13265.5i	0.400882	−	0.551767i
$834$		0			0
$835$	−3368.70	+	17270.9i	−0.139615	+	0.715787i
$836$		0			0
$837$	−114678.	−	37261.2i	−4.73579	−	1.53875i
$838$		0			0
$839$	5479.22	+	16863.3i	0.225463	+	0.693905i	0.998244	+	0.0592318i	$0.0188651\pi$
$839$	5479.22	+	16863.3i	0.225463	+	0.693905i	−0.772781	+	0.634673i	$0.781135\pi$
$840$		0			0
$841$	−2310.23	+	7110.16i	−0.0947243	+	0.291532i
$842$		0			0
$843$		−	50927.8i		−	2.08072i
$844$		0			0
$845$	22543.4	+	4397.12i	0.917770	+	0.179012i
$846$		0			0
$847$	−18764.9	−	25827.7i	−0.761240	−	1.04776i
$848$		0			0
$849$	42399.4			1.71395
$850$		0			0
$851$	1957.43			0.0788481
$852$		0			0
$853$	22628.8	+	31145.9i	0.908319	+	1.25019i	0.967738	+	0.251960i	$0.0810753\pi$
$853$	22628.8	+	31145.9i	0.908319	+	1.25019i	−0.0594187	+	0.998233i	$0.518925\pi$
$854$		0			0
$855$	−20515.1	+	36953.9i	−0.820587	+	1.47812i
$856$		0			0
$857$			8456.15i			0.337056i	0.985697	+	0.168528i	$0.0539013\pi$
$857$			8456.15i			0.337056i	−0.985697	+	0.168528i	$0.946099\pi$
$858$		0			0
$859$	8746.12	−	26917.8i	0.347397	−	1.06918i	−0.612891	−	0.790167i	$-0.709994\pi$
$859$	8746.12	−	26917.8i	0.347397	−	1.06918i	0.960288	−	0.279010i	$-0.0900063\pi$
$860$		0			0
$861$	4487.62	+	13811.5i	0.177628	+	0.546683i
$862$		0			0
$863$	34741.8	+	11288.3i	1.37037	+	0.445259i	0.899490	−	0.436941i	$-0.143938\pi$
$863$	34741.8	+	11288.3i	1.37037	+	0.445259i	0.470875	+	0.882200i	$0.343938\pi$
$864$		0			0
$865$	149.239	−	138.987i	0.00586620	−	0.00546323i
$866$		0			0
$867$	6965.48	−	9587.16i	0.272849	−	0.375544i
$868$		0			0
$869$	−50.6909	−	36.8291i	−0.00197879	−	0.00143768i
$870$		0			0
$871$	32043.3	−	23280.8i	1.24655	−	0.905672i
$872$		0			0
$873$	−59607.6	+	19367.7i	−2.31089	+	0.750855i
$874$		0			0
$875$	−33385.0	−	9014.92i	−1.28985	−	0.348297i
$876$		0			0
$877$	−43085.1	+	13999.2i	−1.65893	+	0.539018i	−0.980647	−	0.195785i	$-0.937275\pi$
$877$	−43085.1	+	13999.2i	−1.65893	+	0.539018i	−0.678281	+	0.734803i	$0.737275\pi$
$878$		0			0
$879$	−44387.7	+	32249.6i	−1.70325	+	1.23749i
$880$		0			0
$881$	7595.24	+	5518.26i	0.290454	+	0.211027i	0.723464	−	0.690362i	$-0.242549\pi$
$881$	7595.24	+	5518.26i	0.290454	+	0.211027i	−0.433010	+	0.901389i	$0.642549\pi$
$882$		0			0
$883$	−26440.0	+	36391.6i	−1.00768	+	1.38695i	−0.0871801	+	0.996193i	$0.527786\pi$
$883$	−26440.0	+	36391.6i	−1.00768	+	1.38695i	−0.920495	+	0.390754i	$0.872214\pi$
$884$		0			0
$885$	4959.69	−	4618.99i	0.188382	−	0.175442i
$886$		0			0
$887$	13876.0	+	4508.59i	0.525266	+	0.170669i	0.559634	−	0.828740i	$-0.310942\pi$
$887$	13876.0	+	4508.59i	0.525266	+	0.170669i	−0.0343676	+	0.999409i	$0.510942\pi$
$888$		0			0
$889$	12581.4	+	38721.4i	0.474651	+	1.46083i
$890$		0			0
$891$	4450.73	−	13697.9i	0.167346	−	0.515037i
$892$		0			0
$893$		−	31307.4i		−	1.17320i
$894$		0			0
$895$	−7905.09	+	14239.4i	−0.295238	+	0.531812i
$896$		0			0
$897$	2954.60	+	4066.66i	0.109979	+	0.151373i
$898$		0			0
$899$	−37271.5			−1.38273
$900$		0			0
$901$	84.2703			0.00311593
$902$		0			0
$903$	−4716.62	−	6491.86i	−0.173820	−	0.239242i
$904$		0			0
$905$	1689.24	+	329.489i	0.0620468	+	0.0121023i
$906$		0			0
$907$			9662.49i			0.353735i	0.984235	+	0.176867i	$0.0565964\pi$
$907$			9662.49i			0.353735i	−0.984235	+	0.176867i	$0.943404\pi$
$908$		0			0
$909$	−18132.2	+	55805.3i	−0.661615	+	2.03624i
$910$		0			0
$911$	−10908.0	−	33571.3i	−0.396704	−	1.22093i	−0.927627	−	0.373509i	$-0.878155\pi$
$911$	−10908.0	−	33571.3i	−0.396704	−	1.22093i	0.530923	−	0.847420i	$-0.321845\pi$
$912$		0			0
$913$	7440.60	+	2417.60i	0.269713	+	0.0876350i
$914$		0			0
$915$	−12645.4	+	64831.1i	−0.456879	+	2.34235i
$916$		0			0
$917$	8787.44	−	12094.9i	0.316452	−	0.435559i
$918$		0			0
$919$	26718.4	+	19412.0i	0.959040	+	0.696783i	0.952928	−	0.303198i	$-0.0980543\pi$
$919$	26718.4	+	19412.0i	0.959040	+	0.696783i	0.00611251	+	0.999981i	$0.498054\pi$
$920$		0			0
$921$	−30664.6	+	22279.2i	−1.09711	+	0.797094i
$922$		0			0
$923$	−41761.8	+	13569.2i	−1.48928	+	0.483896i
$924$		0			0
$925$	26498.4	−	16510.4i	0.941903	−	0.586874i
$926$		0			0
$927$	83329.5	−	27075.4i	2.95243	−	0.959302i
$928$		0			0
$929$	8376.35	−	6085.77i	0.295823	−	0.214928i	−0.429967	−	0.902845i	$-0.641475\pi$
$929$	8376.35	−	6085.77i	0.295823	−	0.214928i	0.725789	+	0.687917i	$0.241475\pi$
$930$		0			0
$931$	−11803.4	−	8575.68i	−0.415511	−	0.301887i
$932$		0			0
$933$	28310.5	−	38966.1i	0.993404	−	1.36730i
$934$		0			0
$935$	−4316.43	+	527.158i	−0.150976	+	0.0184384i
$936$		0			0
$937$	24117.9	+	7836.38i	0.840873	+	0.273216i	0.697618	−	0.716470i	$-0.254243\pi$
$937$	24117.9	+	7836.38i	0.840873	+	0.273216i	0.143255	+	0.989686i	$0.454243\pi$
$938$		0			0
$939$	8503.61	+	26171.4i	0.295532	+	0.909555i
$940$		0			0
$941$	−2352.02	+	7238.77i	−0.0814810	+	0.250773i	−0.983495	−	0.180933i	$-0.942088\pi$
$941$	−2352.02	+	7238.77i	−0.0814810	+	0.250773i	0.902014	+	0.431706i	$0.142088\pi$
$942$		0			0
$943$		−	467.566i		−	0.0161464i
$944$		0			0
$945$	−79325.5	−	85176.5i	−2.73064	−	2.93206i
$946$		0			0
$947$	−17827.2	−	24537.1i	−0.611729	−	0.841973i	0.384989	−	0.922921i	$-0.374205\pi$
$947$	−17827.2	−	24537.1i	−0.611729	−	0.841973i	−0.996718	+	0.0809482i	$0.974205\pi$
$948$		0			0
$949$	−22758.3			−0.778468
$950$		0			0
$951$	−81629.1			−2.78339
$952$		0			0
$953$	540.675	+	744.175i	0.0183779	+	0.0252951i	0.818107	−	0.575066i	$-0.195024\pi$
$953$	540.675	+	744.175i	0.0183779	+	0.0252951i	−0.799729	+	0.600361i	$0.795024\pi$
$954$		0			0
$955$	−3188.80	−	26110.2i	−0.108049	−	0.884719i
$956$		0			0
$957$		−	8170.97i		−	0.275998i
$958$		0			0
$959$	15530.2	−	47797.0i	0.522936	−	1.60943i
$960$		0			0
$961$	16175.6	+	49783.3i	0.542969	+	1.67109i
$962$		0			0
$963$	33998.9	+	11046.9i	1.13770	+	0.369660i
$964$		0			0
$965$	1850.04	+	3974.14i	0.0617150	+	0.132572i
$966$		0			0
$967$	−2766.67	+	3808.00i	−0.0920063	+	0.126636i	−0.852539	−	0.522664i	$-0.824938\pi$
$967$	−2766.67	+	3808.00i	−0.0920063	+	0.126636i	0.760532	+	0.649300i	$0.224938\pi$
$968$		0			0
$969$	26259.8	+	19078.9i	0.870574	+	0.632509i
$970$		0			0
$971$	−18343.7	+	13327.5i	−0.606259	+	0.440473i	−0.848095	−	0.529844i	$-0.822250\pi$
$971$	−18343.7	+	13327.5i	−0.606259	+	0.440473i	0.241836	+	0.970317i	$0.422250\pi$
$972$		0			0
$973$	49977.2	−	16238.6i	1.64666	−	0.535031i
$974$		0			0
$975$	74298.7	+	30130.5i	2.44047	+	0.989689i
$976$		0			0
$977$	−3761.32	+	1222.13i	−0.123168	+	0.0400197i	−0.369952	−	0.929051i	$-0.620626\pi$
$977$	−3761.32	+	1222.13i	−0.123168	+	0.0400197i	0.246784	+	0.969070i	$0.420626\pi$
$978$		0			0
$979$	4155.15	−	3018.90i	0.135648	−	0.0985540i
$980$		0			0
$981$	−87625.3	−	63663.5i	−2.85184	−	2.07199i
$982$		0			0
$983$	−8003.68	+	11016.1i	−0.259692	+	0.357436i	−0.918876	−	0.394546i	$-0.870902\pi$
$983$	−8003.68	+	11016.1i	−0.259692	+	0.357436i	0.659184	+	0.751982i	$0.270902\pi$
$984$		0			0
$985$	−49812.5	−	27653.6i	−1.61133	−	0.894536i
$986$		0			0
$987$	133758.	+	43460.5i	4.31363	+	1.40158i
$988$		0			0
$989$	79.8367	+	245.712i	0.00256690	+	0.00790009i
$990$		0			0
$991$	−14756.5	+	45415.8i	−0.473013	+	1.45578i	0.375607	+	0.926779i	$0.377434\pi$
$991$	−14756.5	+	45415.8i	−0.473013	+	1.45578i	−0.848619	+	0.529004i	$0.822566\pi$
$992$		0			0
$993$			10955.9i			0.350125i
$994$		0			0
$995$	5168.38	−	2405.99i	0.164672	−	0.0766582i
$996$		0			0
$997$	2736.79	+	3766.86i	0.0869357	+	0.119657i	0.850270	−	0.526347i	$-0.176439\pi$
$997$	2736.79	+	3766.86i	0.0869357	+	0.119657i	−0.763334	+	0.646004i	$0.776439\pi$
$998$		0			0
$999$	105086.			3.32810

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	100.4.i.a.69.1	yes	32
5.2	odd	4		500.4.g.b.401.1		64
5.3	odd	4		500.4.g.b.401.16		64
5.4	even	2		500.4.i.a.349.8		32
25.2	odd	20		2500.4.a.g.1.32		32
25.3	odd	20		500.4.g.b.101.16		64
25.4	even	10	inner	100.4.i.a.29.1	✓	32
25.21	even	5		500.4.i.a.149.8		32
25.22	odd	20		500.4.g.b.101.1		64
25.23	odd	20		2500.4.a.g.1.1		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
100.4.i.a.29.1	✓	32	25.4	even	10	inner
100.4.i.a.69.1	yes	32	1.1	even	1	trivial
500.4.g.b.101.1		64	25.22	odd	20
500.4.g.b.101.16		64	25.3	odd	20
500.4.g.b.401.1		64	5.2	odd	4
500.4.g.b.401.16		64	5.3	odd	4
500.4.i.a.149.8		32	25.21	even	5
500.4.i.a.349.8		32	5.4	even	2
2500.4.a.g.1.1		32	25.23	odd	20
2500.4.a.g.1.32		32	25.2	odd	20

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:	\( N \)	\(=\)	\( 100 = 2^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	100.i (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-5.78214 - 7.95843i) q^{3} +(10.1359 - 4.71846i) q^{5} -24.7439i q^{7} +(-21.5601 + 66.3550i) q^{9} +O(q^{10})\)	\(q+(-5.78214 - 7.95843i) q^{3} +(10.1359 - 4.71846i) q^{5} -24.7439i q^{7} +(-21.5601 + 66.3550i) q^{9} +(1.97368 + 6.07436i) q^{11} +(-62.0111 - 20.1486i) q^{13} +(-96.1587 - 53.3829i) q^{15} +(-35.7939 + 49.2661i) q^{17} +(43.8361 + 31.8488i) q^{19} +(-196.923 + 143.073i) q^{21} +(7.45339 - 2.42175i) q^{23} +(80.4722 - 95.6516i) q^{25} +(400.141 - 130.014i) q^{27} +(105.212 - 76.4413i) q^{29} +(-231.860 - 168.456i) q^{31} +(36.9303 - 50.8302i) q^{33} +(-116.753 - 250.802i) q^{35} +(237.544 + 77.1828i) q^{37} +(198.205 + 610.013i) q^{39} +(18.4365 - 56.7416i) q^{41} +32.9665i q^{43} +(94.5635 + 774.297i) q^{45} +(-339.619 - 467.446i) q^{47} -269.262 q^{49} +599.046 q^{51} +(-0.813398 - 1.11955i) q^{53} +(48.6666 + 52.2563i) q^{55} -533.020i q^{57} +(-19.0425 + 58.6066i) q^{59} +(-185.588 - 571.180i) q^{61} +(1641.88 + 533.481i) q^{63} +(-723.607 + 88.3729i) q^{65} +(-357.055 + 491.444i) q^{67} +(-62.3699 - 45.3144i) q^{69} +(544.838 - 395.848i) q^{71} +(331.958 - 107.860i) q^{73} +(-1226.54 - 87.3619i) q^{75} +(150.304 - 48.8366i) q^{77} +(-7.93662 + 5.76629i) q^{79} +(-1824.37 - 1325.48i) q^{81} +(719.989 - 990.980i) q^{83} +(-130.343 + 668.247i) q^{85} +(-1216.71 - 395.332i) q^{87} +(-248.495 - 764.789i) q^{89} +(-498.556 + 1534.40i) q^{91} +2819.27i q^{93} +(594.594 + 115.976i) q^{95} +(528.015 + 726.751i) q^{97} -445.617 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 6 q^{5} + 122 q^{9}+O(q^{10}) \) 32 * q + 6 * q^5 + 122 * q^9	\( 32 q + 6 q^{5} + 122 q^{9} + 20 q^{11} + 68 q^{15} - 160 q^{17} + 2 q^{19} - 108 q^{21} + 290 q^{23} + 654 q^{25} + 600 q^{27} + 62 q^{29} - 378 q^{31} - 1280 q^{33} - 278 q^{35} + 680 q^{37} + 592 q^{39} - 528 q^{41} - 1044 q^{45} - 1810 q^{47} - 2796 q^{49} + 1664 q^{51} - 510 q^{53} - 1350 q^{55} + 144 q^{59} - 1346 q^{61} + 1660 q^{63} + 1142 q^{65} + 1890 q^{67} + 956 q^{69} + 786 q^{71} + 3720 q^{73} - 78 q^{75} + 2160 q^{77} + 896 q^{79} + 348 q^{81} + 570 q^{83} + 224 q^{85} + 3240 q^{87} - 2512 q^{89} - 2212 q^{91} + 1536 q^{95} - 2250 q^{97} - 2540 q^{99}+O(q^{100}) \) 32 * q + 6 * q^5 + 122 * q^9 + 20 * q^11 + 68 * q^15 - 160 * q^17 + 2 * q^19 - 108 * q^21 + 290 * q^23 + 654 * q^25 + 600 * q^27 + 62 * q^29 - 378 * q^31 - 1280 * q^33 - 278 * q^35 + 680 * q^37 + 592 * q^39 - 528 * q^41 - 1044 * q^45 - 1810 * q^47 - 2796 * q^49 + 1664 * q^51 - 510 * q^53 - 1350 * q^55 + 144 * q^59 - 1346 * q^61 + 1660 * q^63 + 1142 * q^65 + 1890 * q^67 + 956 * q^69 + 786 * q^71 + 3720 * q^73 - 78 * q^75 + 2160 * q^77 + 896 * q^79 + 348 * q^81 + 570 * q^83 + 224 * q^85 + 3240 * q^87 - 2512 * q^89 - 2212 * q^91 + 1536 * q^95 - 2250 * q^97 - 2540 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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