LMFDB - Embedded newform 176.4.m.b.81.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [176,4,Mod(49,176)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(176, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("176.49");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 176 = 2^{4} \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	176.m (of order $5$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$10.3843361610$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 71x^{6} - 141x^{5} + 2911x^{4} + 2710x^{3} + 75340x^{2} + 169400x + 5856400 $ x^8 - x^7 + 71x^6 - 141x^5 + 2911x^4 + 2710x^3 + 75340x^2 + 169400x + 5856400
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 22)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			81.2
Root			$-4.79501 - 3.48378i$ of defining polynomial
Character	$\chi$	$=$	176.81
Dual form			176.4.m.b.113.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.33153 - 4.09803i) q^{3} +(6.52241 - 4.73881i) q^{5} +(8.05890 + 24.8027i) q^{7} +(6.82261 + 4.95692i) q^{9} +O(q^{10})$	\(q+(1.33153 - 4.09803i) q^{3} +(6.52241 - 4.73881i) q^{5} +(8.05890 + 24.8027i) q^{7} +(6.82261 + 4.95692i) q^{9} +(33.3764 + 14.7314i) q^{11} +(2.64049 + 1.91843i) q^{13} +(-10.7350 - 33.0389i) q^{15} +(16.8855 - 12.2681i) q^{17} +(38.9268 - 119.804i) q^{19} +112.373 q^{21} -97.8394 q^{23} +(-18.5416 + 57.0651i) q^{25} +(123.520 - 89.7424i) q^{27} +(-81.5293 - 250.921i) q^{29} +(161.288 + 117.183i) q^{31} +(104.811 - 117.162i) q^{33} +(170.099 + 123.584i) q^{35} +(112.990 + 347.748i) q^{37} +(11.3776 - 8.26634i) q^{39} +(84.5880 - 260.335i) q^{41} -388.059 q^{43} +67.9898 q^{45} +(16.0238 - 49.3162i) q^{47} +(-272.737 + 198.155i) q^{49} +(-27.7912 - 85.5326i) q^{51} +(333.739 + 242.476i) q^{53} +(287.504 - 62.0801i) q^{55} +(-439.129 - 319.046i) q^{57} +(-8.12202 - 24.9970i) q^{59} +(-132.799 + 96.4844i) q^{61} +(-67.9624 + 209.167i) q^{63} +26.3134 q^{65} -276.961 q^{67} +(-130.276 + 400.948i) q^{69} +(-418.205 + 303.844i) q^{71} +(-74.6476 - 229.742i) q^{73} +(209.166 + 151.968i) q^{75} +(-96.4024 + 946.546i) q^{77} +(-220.959 - 160.536i) q^{79} +(-132.934 - 409.129i) q^{81} +(58.7298 - 42.6697i) q^{83} +(51.9984 - 160.035i) q^{85} -1136.84 q^{87} -1194.73 q^{89} +(-26.3028 + 80.9517i) q^{91} +(694.979 - 504.932i) q^{93} +(-313.833 - 965.880i) q^{95} +(-1184.10 - 860.299i) q^{97} +(154.692 + 265.951i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 3 q^{3} + 5 q^{5} + q^{7} - 21 q^{9}+O(q^{10}) $ 8 * q - 3 * q^3 + 5 * q^5 + q^7 - 21 * q^9	$ 8 q - 3 q^{3} + 5 q^{5} + q^{7} - 21 q^{9} + 155 q^{11} + 7 q^{13} - 211 q^{15} + 161 q^{17} + 272 q^{19} - 50 q^{21} - 628 q^{23} - 17 q^{25} + 528 q^{27} + 33 q^{29} - 323 q^{31} - 1144 q^{33} + 697 q^{35} + 49 q^{37} - 391 q^{39} + 361 q^{41} - 1442 q^{43} + 2652 q^{45} + 1069 q^{47} - 709 q^{49} + 1332 q^{51} - 281 q^{53} + 7 q^{55} - 438 q^{57} + 128 q^{59} - 617 q^{61} - 694 q^{63} - 138 q^{65} - 578 q^{67} - 310 q^{69} - 115 q^{71} - 1487 q^{73} + 1852 q^{75} + 553 q^{77} - 71 q^{79} + 1630 q^{81} - 1942 q^{83} - 329 q^{85} - 2122 q^{87} - 2202 q^{89} - 4523 q^{91} + 6019 q^{93} + 793 q^{95} - 5128 q^{97} + 2213 q^{99}+O(q^{100}) $ 8 * q - 3 * q^3 + 5 * q^5 + q^7 - 21 * q^9 + 155 * q^11 + 7 * q^13 - 211 * q^15 + 161 * q^17 + 272 * q^19 - 50 * q^21 - 628 * q^23 - 17 * q^25 + 528 * q^27 + 33 * q^29 - 323 * q^31 - 1144 * q^33 + 697 * q^35 + 49 * q^37 - 391 * q^39 + 361 * q^41 - 1442 * q^43 + 2652 * q^45 + 1069 * q^47 - 709 * q^49 + 1332 * q^51 - 281 * q^53 + 7 * q^55 - 438 * q^57 + 128 * q^59 - 617 * q^61 - 694 * q^63 - 138 * q^65 - 578 * q^67 - 310 * q^69 - 115 * q^71 - 1487 * q^73 + 1852 * q^75 + 553 * q^77 - 71 * q^79 + 1630 * q^81 - 1942 * q^83 - 329 * q^85 - 2122 * q^87 - 2202 * q^89 - 4523 * q^91 + 6019 * q^93 + 793 * q^95 - 5128 * q^97 + 2213 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/176\mathbb{Z}\right)^\times$.

$n$	$111$	$133$	$145$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{5}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.33153	−	4.09803i	0.256253	−	0.788665i	−0.737327	−	0.675536i	$-0.763912\pi$
$3$	1.33153	−	4.09803i	0.256253	−	0.788665i	0.993580	−	0.113130i	$-0.0360876\pi$
$4$		0			0
$5$	6.52241	−	4.73881i	0.583382	−	0.423852i	−0.256559	−	0.966528i	$-0.582589\pi$
$5$	6.52241	−	4.73881i	0.583382	−	0.423852i	0.839942	+	0.542676i	$0.182589\pi$
$6$		0			0
$7$	8.05890	+	24.8027i	0.435140	+	1.33922i	0.892943	+	0.450169i	$0.148636\pi$
$7$	8.05890	+	24.8027i	0.435140	+	1.33922i	−0.457804	+	0.889053i	$0.651364\pi$
$8$		0			0
$9$	6.82261	+	4.95692i	0.252689	+	0.183590i
$10$		0			0
$11$	33.3764	+	14.7314i	0.914852	+	0.403790i
$11$	33.3764	+	14.7314i	0.914852	+	0.403790i
$12$		0			0
$13$	2.64049	+	1.91843i	0.0563338	+	0.0409289i	0.615596	−	0.788062i	$-0.288915\pi$
$13$	2.64049	+	1.91843i	0.0563338	+	0.0409289i	−0.559262	+	0.828991i	$0.688915\pi$
$14$		0			0
$15$	−10.7350	−	33.0389i	−0.184784	−	0.568707i
$16$		0			0
$17$	16.8855	−	12.2681i	0.240902	−	0.175026i	−0.460783	−	0.887513i	$-0.652431\pi$
$17$	16.8855	−	12.2681i	0.240902	−	0.175026i	0.701685	+	0.712487i	$0.252431\pi$
$18$		0			0
$19$	38.9268	−	119.804i	0.470022	−	1.44658i	−0.382534	−	0.923942i	$-0.624948\pi$
$19$	38.9268	−	119.804i	0.470022	−	1.44658i	0.852555	−	0.522637i	$-0.175052\pi$
$20$		0			0
$21$	112.373			1.16770
$22$		0			0
$23$	−97.8394			−0.886997			−0.443498	−	0.896275i	$-0.646263\pi$
$23$	−97.8394			−0.886997			−0.443498	+	0.896275i	$0.646263\pi$
$24$		0			0
$25$	−18.5416	+	57.0651i	−0.148333	+	0.456521i
$26$		0			0
$27$	123.520	−	89.7424i	0.880422	−	0.639664i
$28$		0			0
$29$	−81.5293	−	250.921i	−0.522055	−	1.60672i	−0.770066	−	0.637964i	$-0.779777\pi$
$29$	−81.5293	−	250.921i	−0.522055	−	1.60672i	0.248011	−	0.968757i	$-0.420223\pi$
$30$		0			0
$31$	161.288	+	117.183i	0.934460	+	0.678925i	0.947081	−	0.320995i	$-0.104017\pi$
$31$	161.288	+	117.183i	0.934460	+	0.678925i	−0.0126205	+	0.999920i	$0.504017\pi$
$32$		0			0
$33$	104.811	−	117.162i	0.552889	−	0.618040i
$34$		0			0
$35$	170.099	+	123.584i	0.821485	+	0.596844i
$36$		0			0
$37$	112.990	+	347.748i	0.502039	+	1.54512i	0.805692	+	0.592335i	$0.201794\pi$
$37$	112.990	+	347.748i	0.502039	+	1.54512i	−0.303653	+	0.952783i	$0.598206\pi$
$38$		0			0
$39$	11.3776	−	8.26634i	0.0467149	−	0.0339404i
$40$		0			0
$41$	84.5880	−	260.335i	0.322205	−	0.991646i	−0.650481	−	0.759523i	$-0.725433\pi$
$41$	84.5880	−	260.335i	0.322205	−	0.991646i	0.972686	−	0.232124i	$-0.0745674\pi$
$42$		0			0
$43$	−388.059			−1.37624			−0.688121	−	0.725596i	$-0.741564\pi$
$43$	−388.059			−1.37624			−0.688121	+	0.725596i	$0.741564\pi$
$44$		0			0
$45$	67.9898			0.225229
$46$		0			0
$47$	16.0238	−	49.3162i	0.0497301	−	0.153053i	−0.923108	−	0.384542i	$-0.874359\pi$
$47$	16.0238	−	49.3162i	0.0497301	−	0.153053i	0.972838	+	0.231488i	$0.0743595\pi$
$48$		0			0
$49$	−272.737	+	198.155i	−0.795153	+	0.577712i
$50$		0			0
$51$	−27.7912	−	85.5326i	−0.0763049	−	0.234842i
$52$		0			0
$53$	333.739	+	242.476i	0.864955	+	0.628427i	0.929228	−	0.369506i	$-0.120473\pi$
$53$	333.739	+	242.476i	0.864955	+	0.628427i	−0.0642735	+	0.997932i	$0.520473\pi$
$54$		0			0
$55$	287.504	−	62.0801i	0.704856	−	0.152198i
$56$		0			0
$57$	−439.129	−	319.046i	−1.02042	−	0.741380i
$58$		0			0
$59$	−8.12202	−	24.9970i	−0.0179220	−	0.0551582i	0.941696	−	0.336466i	$-0.109232\pi$
$59$	−8.12202	−	24.9970i	−0.0179220	−	0.0551582i	−0.959618	+	0.281308i	$0.909232\pi$
$60$		0			0
$61$	−132.799	+	96.4844i	−0.278741	+	0.202517i	−0.718368	−	0.695663i	$-0.755111\pi$
$61$	−132.799	+	96.4844i	−0.278741	+	0.202517i	0.439627	+	0.898180i	$0.355111\pi$
$62$		0			0
$63$	−67.9624	+	209.167i	−0.135912	+	0.418294i
$64$		0			0
$65$	26.3134			0.0502119
$66$		0			0
$67$	−276.961			−0.505017			−0.252508	−	0.967595i	$-0.581256\pi$
$67$	−276.961			−0.505017			−0.252508	+	0.967595i	$0.581256\pi$
$68$		0			0
$69$	−130.276	+	400.948i	−0.227296	+	0.699544i
$70$		0			0
$71$	−418.205	+	303.844i	−0.699039	+	0.507882i	−0.879619	−	0.475679i	$-0.842203\pi$
$71$	−418.205	+	303.844i	−0.699039	+	0.507882i	0.180580	+	0.983560i	$0.442203\pi$
$72$		0			0
$73$	−74.6476	−	229.742i	−0.119683	−	0.368346i	0.873212	−	0.487340i	$-0.162033\pi$
$73$	−74.6476	−	229.742i	−0.119683	−	0.368346i	−0.992895	+	0.118995i	$0.962033\pi$
$74$		0			0
$75$	209.166	+	151.968i	0.322031	+	0.233969i
$76$		0			0
$77$	−96.4024	+	946.546i	−0.142676	+	1.40089i
$78$		0			0
$79$	−220.959	−	160.536i	−0.314681	−	0.228629i	0.419222	−	0.907884i	$-0.362303\pi$
$79$	−220.959	−	160.536i	−0.314681	−	0.228629i	−0.733902	+	0.679255i	$0.762303\pi$
$80$		0			0
$81$	−132.934	−	409.129i	−0.182351	−	0.561220i
$82$		0			0
$83$	58.7298	−	42.6697i	0.0776678	−	0.0564290i	−0.548274	−	0.836299i	$-0.684715\pi$
$83$	58.7298	−	42.6697i	0.0776678	−	0.0564290i	0.625942	+	0.779870i	$0.284715\pi$
$84$		0			0
$85$	51.9984	−	160.035i	0.0663532	−	0.204214i
$86$		0			0
$87$	−1136.84			−1.40094
$88$		0			0
$89$	−1194.73			−1.42294			−0.711470	−	0.702717i	$-0.751970\pi$
$89$	−1194.73			−1.42294			−0.711470	+	0.702717i	$0.751970\pi$
$90$		0			0
$91$	−26.3028	+	80.9517i	−0.0302998	+	0.0932532i
$92$		0			0
$93$	694.979	−	504.932i	0.774903	−	0.563000i
$94$		0			0
$95$	−313.833	−	965.880i	−0.338933	−	1.04313i
$96$		0			0
$97$	−1184.10	−	860.299i	−1.23946	−	0.900517i	−0.241893	−	0.970303i	$-0.577768\pi$
$97$	−1184.10	−	860.299i	−1.23946	−	0.900517i	−0.997562	+	0.0697858i	$0.977768\pi$
$98$		0			0
$99$	154.692	+	265.951i	0.157042	+	0.269991i
$100$		0			0
$101$	728.191	+	529.062i	0.717403	+	0.521224i	0.885553	−	0.464538i	$-0.153779\pi$
$101$	728.191	+	529.062i	0.717403	+	0.521224i	−0.168151	+	0.985761i	$0.553779\pi$
$102$		0			0
$103$	128.899	+	396.710i	0.123309	+	0.379505i	0.993589	−	0.113052i	$-0.0360625\pi$
$103$	128.899	+	396.710i	0.123309	+	0.379505i	−0.870281	+	0.492556i	$0.836063\pi$
$104$		0			0
$105$	732.943	−	532.514i	0.681218	−	0.494934i
$106$		0			0
$107$	−333.858	+	1027.51i	−0.301638	+	0.928346i	0.679273	+	0.733886i	$0.262295\pi$
$107$	−333.858	+	1027.51i	−0.301638	+	0.928346i	−0.980911	+	0.194460i	$0.937705\pi$
$108$		0			0
$109$	−1472.08			−1.29358			−0.646789	−	0.762669i	$-0.723888\pi$
$109$	−1472.08			−1.29358			−0.646789	+	0.762669i	$0.723888\pi$
$110$		0			0
$111$	1575.53			1.34723
$112$		0			0
$113$	−39.0846	+	120.290i	−0.0325378	+	0.100141i	−0.966006	−	0.258518i	$-0.916766\pi$
$113$	−39.0846	+	120.290i	−0.0325378	+	0.100141i	0.933469	+	0.358659i	$0.116766\pi$
$114$		0			0
$115$	−638.149	+	463.643i	−0.517458	+	0.375956i
$116$		0			0
$117$	8.50554	+	26.1774i	0.00672083	+	0.0206846i
$118$		0			0
$119$	440.360	+	319.940i	0.339225	+	0.246461i
$120$		0			0
$121$	896.971	+	983.364i	0.673907	+	0.738816i
$122$		0			0
$123$	−954.228	−	693.287i	−0.699511	−	0.508224i
$124$		0			0
$125$	460.902	+	1418.51i	0.329795	+	1.01500i
$126$		0			0
$127$	860.426	−	625.136i	0.601185	−	0.436786i	−0.245115	−	0.969494i	$-0.578826\pi$
$127$	860.426	−	625.136i	0.601185	−	0.436786i	0.846299	+	0.532708i	$0.178826\pi$
$128$		0			0
$129$	−516.712	+	1590.28i	−0.352666	+	1.08539i
$130$		0			0
$131$	1525.04			1.01713			0.508563	−	0.861025i	$-0.330177\pi$
$131$	1525.04			1.01713			0.508563	+	0.861025i	$0.330177\pi$
$132$		0			0
$133$	3285.18			2.14182
$134$		0			0
$135$	380.375	−	1170.67i	0.242500	−	0.746338i
$136$		0			0
$137$	1681.81	−	1221.91i	1.04881	−	0.762004i	0.0768227	−	0.997045i	$-0.475522\pi$
$137$	1681.81	−	1221.91i	1.04881	−	0.762004i	0.971985	+	0.235041i	$0.0755225\pi$
$138$		0			0
$139$	−465.826	−	1433.67i	−0.284251	−	0.874834i	−0.986622	−	0.163023i	$-0.947875\pi$
$139$	−465.826	−	1433.67i	−0.284251	−	0.874834i	0.702371	−	0.711811i	$-0.252125\pi$
$140$		0			0
$141$	−180.763	−	131.332i	−0.107964	−	0.0784408i
$142$		0			0
$143$	59.8688	+	102.928i	0.0350104	+	0.0601909i
$144$		0			0
$145$	−1720.84	−	1250.26i	−0.985570	−	0.716059i
$146$		0			0
$147$	448.888	+	1381.53i	0.251862	+	0.775150i
$148$		0			0
$149$	347.754	−	252.658i	0.191202	−	0.138916i	−0.488066	−	0.872807i	$-0.662297\pi$
$149$	347.754	−	252.658i	0.191202	−	0.138916i	0.679268	+	0.733890i	$0.262297\pi$
$150$		0			0
$151$	−275.545	+	848.040i	−0.148500	+	0.457036i	−0.997444	−	0.0714459i	$-0.977239\pi$
$151$	−275.545	+	848.040i	−0.148500	+	0.457036i	0.848944	+	0.528482i	$0.177239\pi$
$152$		0			0
$153$	176.015			0.0930064
$154$		0			0
$155$	1607.30			0.832912
$156$		0			0
$157$	167.188	−	514.551i	0.0849875	−	0.261565i	−0.899528	−	0.436864i	$-0.856089\pi$
$157$	167.188	−	514.551i	0.0849875	−	0.261565i	0.984515	+	0.175299i	$0.0560892\pi$
$158$		0			0
$159$	1438.06	−	1044.81i	0.717266	−	0.521124i
$160$		0			0
$161$	−788.478	−	2426.69i	−0.385968	−	1.18789i
$162$		0			0
$163$	−2368.47	−	1720.80i	−1.13812	−	0.826891i	−0.151261	−	0.988494i	$-0.548334\pi$
$163$	−2368.47	−	1720.80i	−1.13812	−	0.826891i	−0.986856	+	0.161603i	$0.948334\pi$
$164$		0			0
$165$	128.414	−	1260.86i	0.0605881	−	0.594897i
$166$		0			0
$167$	1407.88	+	1022.88i	0.652364	+	0.473970i	0.864076	−	0.503362i	$-0.167904\pi$
$167$	1407.88	+	1022.88i	0.652364	+	0.473970i	−0.211712	+	0.977332i	$0.567904\pi$
$168$		0			0
$169$	−675.619	−	2079.34i	−0.307519	−	0.946445i
$170$		0			0
$171$	859.443	−	624.422i	0.384346	−	0.279244i
$172$		0			0
$173$	−89.8625	+	276.568i	−0.0394920	+	0.121544i	−0.968859	−	0.247613i	$-0.920354\pi$
$173$	−89.8625	+	276.568i	−0.0394920	+	0.121544i	0.929367	+	0.369157i	$0.120354\pi$
$174$		0			0
$175$	−1564.80			−0.675928
$176$		0			0
$177$	−113.253			−0.0480939
$178$		0			0
$179$	−803.545	+	2473.06i	−0.335529	+	1.03265i	0.630932	+	0.775839i	$0.282673\pi$
$179$	−803.545	+	2473.06i	−0.335529	+	1.03265i	−0.966461	+	0.256814i	$0.917327\pi$
$180$		0			0
$181$	−1501.40	+	1090.83i	−0.616563	+	0.447959i	−0.851719	−	0.523998i	$-0.824440\pi$
$181$	−1501.40	+	1090.83i	−0.616563	+	0.447959i	0.235156	+	0.971958i	$0.424440\pi$
$182$		0			0
$183$	218.569	+	672.687i	0.0882902	+	0.271729i
$184$		0			0
$185$	2384.88	+	1732.72i	0.947782	+	0.688604i
$186$		0			0
$187$	744.304	−	160.716i	0.291064	−	0.0628487i
$188$		0			0
$189$	3221.29	+	2340.41i	1.23976	+	0.900738i
$190$		0			0
$191$	−473.462	−	1457.17i	−0.179364	−	0.552026i	0.820442	−	0.571730i	$-0.193727\pi$
$191$	−473.462	−	1457.17i	−0.179364	−	0.552026i	−0.999806	+	0.0197044i	$0.993727\pi$
$192$		0			0
$193$	−850.742	+	618.100i	−0.317294	+	0.230528i	−0.735020	−	0.678045i	$-0.762827\pi$
$193$	−850.742	+	618.100i	−0.317294	+	0.230528i	0.417726	+	0.908573i	$0.362827\pi$
$194$		0			0
$195$	35.0371	−	107.833i	0.0128670	−	0.0396004i
$196$		0			0
$197$	−1577.77			−0.570616			−0.285308	−	0.958436i	$-0.592096\pi$
$197$	−1577.77			−0.570616			−0.285308	+	0.958436i	$0.592096\pi$
$198$		0			0
$199$	−3760.53			−1.33958			−0.669791	−	0.742550i	$-0.733616\pi$
$199$	−3760.53			−1.33958			−0.669791	+	0.742550i	$0.733616\pi$
$200$		0			0
$201$	−368.781	+	1134.99i	−0.129412	+	0.398289i
$202$		0			0
$203$	5566.50	−	4044.30i	1.92459	−	1.39830i
$204$		0			0
$205$	−681.961	−	2098.86i	−0.232342	−	0.715076i
$206$		0			0
$207$	−667.521	−	484.982i	−0.224135	−	0.162843i
$208$		0			0
$209$	3064.12	−	3425.19i	1.01411	−	1.13361i
$210$		0			0
$211$	1149.27	+	834.996i	0.374973	+	0.272434i	0.759270	−	0.650776i	$-0.225556\pi$
$211$	1149.27	+	834.996i	0.374973	+	0.272434i	−0.384297	+	0.923209i	$0.625556\pi$
$212$		0			0
$213$	688.307	+	2118.39i	0.221418	+	0.681454i
$214$		0			0
$215$	−2531.08	+	1838.94i	−0.802876	+	0.583323i
$216$		0			0
$217$	−1606.65	+	4944.76i	−0.502611	+	1.54688i
$218$		0			0
$219$	−1040.88			−0.321171
$220$		0			0
$221$	68.1213			0.0207346
$222$		0			0
$223$	−1624.34	+	4999.20i	−0.487774	+	1.50121i	0.340148	+	0.940372i	$0.389523\pi$
$223$	−1624.34	+	4999.20i	−0.487774	+	1.50121i	−0.827922	+	0.560843i	$0.810477\pi$
$224$		0			0
$225$	−409.369	+	297.424i	−0.121295	+	0.0881256i
$226$		0			0
$227$	−861.007	−	2649.91i	−0.251749	−	0.774804i	−0.994453	−	0.105184i	$-0.966457\pi$
$227$	−861.007	−	2649.91i	−0.251749	−	0.774804i	0.742704	−	0.669620i	$-0.233543\pi$
$228$		0			0
$229$	−3626.49	−	2634.80i	−1.04649	−	0.760316i	−0.0749442	−	0.997188i	$-0.523878\pi$
$229$	−3626.49	−	2634.80i	−1.04649	−	0.760316i	−0.971541	+	0.236872i	$0.923878\pi$
$230$		0			0
$231$	3750.61	+	1655.41i	1.06828	+	0.471507i
$232$		0			0
$233$	−255.337	−	185.513i	−0.0717925	−	0.0521603i	0.551310	−	0.834300i	$-0.314128\pi$
$233$	−255.337	−	185.513i	−0.0717925	−	0.0521603i	−0.623103	+	0.782140i	$0.714128\pi$
$234$		0			0
$235$	−129.186	−	397.595i	−0.0358604	−	0.110367i
$236$		0			0
$237$	−952.093	+	691.736i	−0.260950	+	0.189591i
$238$		0			0
$239$	−249.186	+	766.915i	−0.0674414	+	0.207563i	−0.979098	−	0.203390i	$-0.934804\pi$
$239$	−249.186	+	766.915i	−0.0674414	+	0.207563i	0.911656	+	0.410953i	$0.134804\pi$
$240$		0			0
$241$	−1009.91			−0.269935			−0.134967	−	0.990850i	$-0.543093\pi$
$241$	−1009.91			−0.269935			−0.134967	+	0.990850i	$0.543093\pi$
$242$		0			0
$243$	2268.70			0.598919
$244$		0			0
$245$	−839.886	+	2584.90i	−0.219014	+	0.674055i
$246$		0			0
$247$	332.621	−	241.663i	0.0856849	−	0.0622537i
$248$		0			0
$249$	−96.6610	−	297.492i	−0.0246010	−	0.0757140i
$250$		0			0
$251$	−2578.54	−	1873.42i	−0.648429	−	0.471111i	0.214307	−	0.976766i	$-0.431251\pi$
$251$	−2578.54	−	1873.42i	−0.648429	−	0.471111i	−0.862736	+	0.505655i	$0.831251\pi$
$252$		0			0
$253$	−3265.53	−	1441.31i	−0.811471	−	0.358160i
$254$		0			0
$255$	−586.589	−	426.182i	−0.144053	−	0.104661i
$256$		0			0
$257$	785.951	+	2418.91i	0.190764	+	0.587111i	1.00000		0.000372917i	$-0.000118703\pi$
$257$	785.951	+	2418.91i	0.190764	+	0.587111i	−0.809236	+	0.587484i	$0.800119\pi$
$258$		0			0
$259$	−7714.52	+	5604.93i	−1.85080	+	1.34468i
$260$		0			0
$261$	687.554	−	2116.07i	0.163059	−	0.501845i
$262$		0			0
$263$	−2992.29			−0.701568			−0.350784	−	0.936456i	$-0.614085\pi$
$263$	−2992.29			−0.701568			−0.350784	+	0.936456i	$0.614085\pi$
$264$		0			0
$265$	3325.83			0.770960
$266$		0			0
$267$	−1590.82	+	4896.05i	−0.364632	+	1.12222i
$268$		0			0
$269$	664.469	−	482.765i	0.150607	−	0.109423i	−0.509930	−	0.860216i	$-0.670329\pi$
$269$	664.469	−	482.765i	0.150607	−	0.109423i	0.660537	+	0.750793i	$0.270329\pi$
$270$		0			0
$271$	−1989.99	−	6124.55i	−0.446063	−	1.37284i	−0.881313	−	0.472532i	$-0.843340\pi$
$271$	−1989.99	−	6124.55i	−0.446063	−	1.37284i	0.435250	−	0.900310i	$-0.356660\pi$
$272$		0			0
$273$	296.719	+	215.579i	0.0657812	+	0.0477928i
$274$		0			0
$275$	−1459.50	+	1631.48i	−0.320041	+	0.357753i
$276$		0			0
$277$	−416.212	−	302.395i	−0.0902806	−	0.0655927i	0.541729	−	0.840553i	$-0.317770\pi$
$277$	−416.212	−	302.395i	−0.0902806	−	0.0655927i	−0.632010	+	0.774960i	$0.717770\pi$
$278$		0			0
$279$	519.543	+	1598.99i	0.111485	+	0.343114i
$280$		0			0
$281$	−6276.91	+	4560.44i	−1.33256	+	0.968160i	−0.332875	+	0.942971i	$0.608019\pi$
$281$	−6276.91	+	4560.44i	−1.33256	+	0.968160i	−0.999683	+	0.0251891i	$0.991981\pi$
$282$		0			0
$283$	1806.94	−	5561.18i	0.379545	−	1.16812i	−0.560816	−	0.827940i	$-0.689513\pi$
$283$	1806.94	−	5561.18i	0.379545	−	1.16812i	0.940361	−	0.340178i	$-0.110487\pi$
$284$		0			0
$285$	−4376.08			−0.909532
$286$		0			0
$287$	7138.71			1.46824
$288$		0			0
$289$	−1383.58	+	4258.24i	−0.281617	+	0.866728i
$290$		0			0
$291$	−5102.19	+	3706.96i	−1.02782	+	0.746755i
$292$		0			0
$293$	−2495.16	−	7679.30i	−0.497504	−	1.53116i	−0.813019	−	0.582238i	$-0.802177\pi$
$293$	−2495.16	−	7679.30i	−0.497504	−	1.53116i	0.315515	−	0.948921i	$-0.397823\pi$
$294$		0			0
$295$	−171.431	−	124.552i	−0.0338343	−	0.0245820i
$296$		0			0
$297$	5444.68	−	1175.66i	1.06375	−	0.229692i
$298$		0			0
$299$	−258.344	−	187.698i	−0.0499679	−	0.0363038i
$300$		0			0
$301$	−3127.33	−	9624.93i	−0.598858	−	1.84309i
$302$		0			0
$303$	3137.72	−	2279.68i	0.594908	−	0.432226i
$304$		0			0
$305$	−408.951	+	1258.62i	−0.0767753	+	0.236290i
$306$		0			0
$307$	4210.64			0.782781			0.391391	−	0.920225i	$-0.371994\pi$
$307$	4210.64			0.782781			0.391391	+	0.920225i	$0.371994\pi$
$308$		0			0
$309$	1797.36			0.330900
$310$		0			0
$311$	407.549	−	1254.31i	0.0743086	−	0.228698i	−0.907003	−	0.421124i	$-0.861636\pi$
$311$	407.549	−	1254.31i	0.0743086	−	0.228698i	0.981311	+	0.192426i	$0.0616356\pi$
$312$		0			0
$313$	3402.85	−	2472.31i	0.614505	−	0.446464i	−0.236493	−	0.971633i	$-0.575998\pi$
$313$	3402.85	−	2472.31i	0.614505	−	0.446464i	0.850998	+	0.525169i	$0.175998\pi$
$314$		0			0
$315$	547.923	+	1686.33i	0.0980063	+	0.301632i
$316$		0			0
$317$	1992.69	+	1447.77i	0.353062	+	0.256515i	0.750152	−	0.661265i	$-0.229980\pi$
$317$	1992.69	+	1447.77i	0.353062	+	0.256515i	−0.397090	+	0.917779i	$0.629980\pi$
$318$		0			0
$319$	975.271	−	9575.90i	0.171175	−	1.68071i
$320$		0			0
$321$	3766.21	+	2736.32i	0.654859	+	0.475783i
$322$		0			0
$323$	−812.466	−	2500.51i	−0.139959	−	0.430750i
$324$		0			0
$325$	−158.434	+	115.109i	−0.0270410	+	0.0196464i
$326$		0			0
$327$	−1960.12	+	6032.63i	−0.331483	+	1.02020i
$328$		0			0
$329$	1352.31			0.226612
$330$		0			0
$331$	3332.42			0.553373			0.276687	−	0.960960i	$-0.410764\pi$
$331$	3332.42			0.553373			0.276687	+	0.960960i	$0.410764\pi$
$332$		0			0
$333$	−952.869	+	2932.63i	−0.156808	+	0.482604i
$334$		0			0
$335$	−1806.45	+	1312.46i	−0.294618	+	0.214052i
$336$		0			0
$337$	2572.10	+	7916.10i	0.415760	+	1.27958i	0.911569	+	0.411146i	$0.134871\pi$
$337$	2572.10	+	7916.10i	0.415760	+	1.27958i	−0.495810	+	0.868431i	$0.665129\pi$
$338$		0			0
$339$	440.910	+	320.340i	0.0706399	+	0.0513229i
$340$		0			0
$341$	3656.96	+	6287.16i	0.580749	+	0.998442i
$342$		0			0
$343$	124.015	+	90.1024i	0.0195224	+	0.0141839i
$344$		0			0
$345$	1050.30	+	3232.51i	0.163903	+	0.504441i
$346$		0			0
$347$	2930.66	−	2129.25i	0.453390	−	0.329407i	−0.337543	−	0.941310i	$-0.609596\pi$
$347$	2930.66	−	2129.25i	0.453390	−	0.329407i	0.790933	+	0.611903i	$0.209596\pi$
$348$		0			0
$349$	644.814	−	1984.53i	0.0988999	−	0.304383i	−0.889350	−	0.457226i	$-0.848843\pi$
$349$	644.814	−	1984.53i	0.0988999	−	0.304383i	0.988250	+	0.152843i	$0.0488430\pi$
$350$		0			0
$351$	498.316			0.0757782
$352$		0			0
$353$	7582.15			1.14322			0.571611	−	0.820525i	$-0.306319\pi$
$353$	7582.15			1.14322			0.571611	+	0.820525i	$0.306319\pi$
$354$		0			0
$355$	−1287.85	+	3963.59i	−0.192540	+	0.592579i
$356$		0			0
$357$	1897.48	−	1378.60i	0.281303	−	0.204378i
$358$		0			0
$359$	−1400.77	−	4311.13i	−0.205933	−	0.633796i	−0.999674	−	0.0255401i	$-0.991869\pi$
$359$	−1400.77	−	4311.13i	−0.205933	−	0.633796i	0.793741	−	0.608256i	$-0.208131\pi$
$360$		0			0
$361$	−7288.73	−	5295.57i	−1.06265	−	0.772061i
$362$		0			0
$363$	5224.19	−	2366.43i	0.755369	−	0.342164i
$364$		0			0
$365$	−1575.59	−	1144.73i	−0.225945	−	0.164159i
$366$		0			0
$367$	894.003	+	2751.46i	0.127157	+	0.391349i	0.994288	−	0.106732i	$-0.0340385\pi$
$367$	894.003	+	2751.46i	0.127157	+	0.391349i	−0.867131	+	0.498080i	$0.834039\pi$
$368$		0			0
$369$	1867.57	−	1356.87i	0.263474	−	0.191425i
$370$		0			0
$371$	−3324.49	+	10231.7i	−0.465227	+	1.43182i
$372$		0			0
$373$	−3389.46			−0.470508			−0.235254	−	0.971934i	$-0.575592\pi$
$373$	−3389.46			−0.470508			−0.235254	+	0.971934i	$0.575592\pi$
$374$		0			0
$375$	6426.80			0.885010
$376$		0			0
$377$	266.097	−	818.962i	0.0363520	−	0.111880i
$378$		0			0
$379$	6523.45	−	4739.57i	0.884135	−	0.642362i	−0.0502069	−	0.998739i	$-0.515988\pi$
$379$	6523.45	−	4739.57i	0.884135	−	0.642362i	0.934342	+	0.356377i	$0.115988\pi$
$380$		0			0
$381$	−1416.14	−	4358.43i	−0.190423	−	0.586061i
$382$		0			0
$383$	4250.99	+	3088.52i	0.567142	+	0.412053i	0.834066	−	0.551665i	$-0.186007\pi$
$383$	4250.99	+	3088.52i	0.567142	+	0.412053i	−0.266924	+	0.963718i	$0.586007\pi$
$384$		0			0
$385$	3856.73	+	6630.60i	0.510538	+	0.877731i
$386$		0			0
$387$	−2647.58	−	1923.58i	−0.347762	−	0.252664i
$388$		0			0
$389$	−3502.56	−	10779.8i	−0.456521	−	1.40503i	−0.869340	−	0.494214i	$-0.835456\pi$
$389$	−3502.56	−	10779.8i	−0.456521	−	1.40503i	0.412819	−	0.910813i	$-0.364544\pi$
$390$		0			0
$391$	−1652.07	+	1200.30i	−0.213680	+	0.155247i
$392$		0			0
$393$	2030.64	−	6249.67i	0.260642	−	0.802173i
$394$		0			0
$395$	−2201.93			−0.280484
$396$		0			0
$397$	9896.10			1.25106			0.625530	−	0.780200i	$-0.284883\pi$
$397$	9896.10			1.25106			0.625530	+	0.780200i	$0.284883\pi$
$398$		0			0
$399$	4374.32	−	13462.8i	0.548846	−	1.68918i
$400$		0			0
$401$	12016.9	−	8730.81i	1.49650	−	1.08727i	0.524752	−	0.851255i	$-0.324158\pi$
$401$	12016.9	−	8730.81i	1.49650	−	1.08727i	0.971749	−	0.236016i	$-0.0758418\pi$
$402$		0			0
$403$	201.073	+	618.840i	0.0248540	+	0.0764928i
$404$		0			0
$405$	−2805.84	−	2038.56i	−0.344255	−	0.250116i
$406$		0			0
$407$	−1351.61	+	13271.1i	−0.164612	+	1.61627i
$408$		0			0
$409$	−6748.88	−	4903.35i	−0.815919	−	0.592800i	0.0996219	−	0.995025i	$-0.468237\pi$
$409$	−6748.88	−	4903.35i	−0.815919	−	0.592800i	−0.915541	+	0.402226i	$0.868237\pi$
$410$		0			0
$411$	−2768.02	−	8519.10i	−0.332206	−	1.02242i
$412$		0			0
$413$	554.540	−	402.897i	0.0660705	−	0.0480030i
$414$		0			0
$415$	180.856	−	556.619i	0.0213925	−	0.0658394i
$416$		0			0
$417$	−6495.46			−0.762791
$418$		0			0
$419$	13082.4			1.52534			0.762670	−	0.646788i	$-0.223888\pi$
$419$	13082.4			1.52534			0.762670	+	0.646788i	$0.223888\pi$
$420$		0			0
$421$	−1716.75	+	5283.61i	−0.198739	+	0.611656i	0.801173	+	0.598432i	$0.204209\pi$
$421$	−1716.75	+	5283.61i	−0.198739	+	0.611656i	−0.999913	+	0.0132238i	$0.995791\pi$
$422$		0			0
$423$	353.781	−	257.037i	0.0406653	−	0.0295450i
$424$		0			0
$425$	386.993	+	1191.04i	0.0441693	+	0.135939i
$426$		0			0
$427$	−3463.29	−	2516.23i	−0.392507	−	0.285173i
$428$		0			0
$429$	501.520	−	108.292i	0.0564420	−	0.0121874i
$430$		0			0
$431$	−291.099	−	211.496i	−0.0325330	−	0.0236366i	0.571400	−	0.820672i	$-0.306401\pi$
$431$	−291.099	−	211.496i	−0.0325330	−	0.0236366i	−0.603933	+	0.797035i	$0.706401\pi$
$432$		0			0
$433$	4625.45	+	14235.7i	0.513360	+	1.57996i	0.786246	+	0.617913i	$0.212022\pi$
$433$	4625.45	+	14235.7i	0.513360	+	1.57996i	−0.272886	+	0.962046i	$0.587978\pi$
$434$		0			0
$435$	−7414.95	+	5387.27i	−0.817286	+	0.593793i
$436$		0			0
$437$	−3808.57	+	11721.6i	−0.416908	+	1.28311i
$438$		0			0
$439$	−15893.9			−1.72796			−0.863979	−	0.503527i	$-0.832035\pi$
$439$	−15893.9			−1.72796			−0.863979	+	0.503527i	$0.832035\pi$
$440$		0			0
$441$	−2843.02			−0.306989
$442$		0			0
$443$	812.238	−	2499.81i	0.0871119	−	0.268103i	−0.898006	−	0.439983i	$-0.854984\pi$
$443$	812.238	−	2499.81i	0.0871119	−	0.268103i	0.985118	+	0.171881i	$0.0549843\pi$
$444$		0			0
$445$	−7792.56	+	5661.62i	−0.830118	+	0.603116i
$446$		0			0
$447$	−572.355	−	1761.53i	−0.0605625	−	0.186392i
$448$		0			0
$449$	1049.68	+	762.635i	0.110328	+	0.0801580i	0.641581	−	0.767055i	$-0.278279\pi$
$449$	1049.68	+	762.635i	0.110328	+	0.0801580i	−0.531253	+	0.847213i	$0.678279\pi$
$450$		0			0
$451$	6658.35	−	7442.95i	0.695187	−	0.777106i
$452$		0			0
$453$	3108.39	+	2258.38i	0.322395	+	0.234234i
$454$		0			0
$455$	212.057	+	652.645i	0.0218492	+	0.0672449i
$456$		0			0
$457$	−1821.87	+	1323.67i	−0.186485	+	0.135489i	−0.677111	−	0.735881i	$-0.736768\pi$
$457$	−1821.87	+	1323.67i	−0.186485	+	0.135489i	0.490626	+	0.871370i	$0.336768\pi$
$458$		0			0
$459$	984.733	−	3030.70i	0.100138	−	0.308193i
$460$		0			0
$461$	16772.0			1.69447			0.847233	−	0.531222i	$-0.178267\pi$
$461$	16772.0			1.69447			0.847233	+	0.531222i	$0.178267\pi$
$462$		0			0
$463$	−7726.06			−0.775509			−0.387754	−	0.921763i	$-0.626749\pi$
$463$	−7726.06			−0.775509			−0.387754	+	0.921763i	$0.626749\pi$
$464$		0			0
$465$	2140.16	−	6586.75i	0.213436	−	0.656889i
$466$		0			0
$467$	−6112.55	+	4441.03i	−0.605685	+	0.440056i	−0.847892	−	0.530169i	$-0.822129\pi$
$467$	−6112.55	+	4441.03i	−0.605685	+	0.440056i	0.242207	+	0.970225i	$0.422129\pi$
$468$		0			0
$469$	−2232.00	−	6869.38i	−0.219753	−	0.676330i
$470$		0			0
$471$	−1886.03	−	1370.28i	−0.184509	−	0.134053i
$472$		0			0
$473$	−12952.0	−	5716.66i	−1.25906	−	0.555713i
$474$		0			0
$475$	6114.88	+	4442.72i	0.590673	+	0.429149i
$476$		0			0
$477$	1075.04	+	3308.64i	0.103192	+	0.317593i
$478$		0			0
$479$	10794.4	−	7842.59i	1.02966	−	0.748094i	0.0614218	−	0.998112i	$-0.480437\pi$
$479$	10794.4	−	7842.59i	1.02966	−	0.748094i	0.968241	+	0.250018i	$0.0804365\pi$
$480$		0			0
$481$	−368.779	+	1134.99i	−0.0349582	+	0.107590i
$482$		0			0
$483$	−10994.5			−1.03575
$484$		0			0
$485$	−11800.0			−1.10476
$486$		0			0
$487$	−5815.72	+	17898.9i	−0.541141	+	1.66546i	0.188853	+	0.982005i	$0.439523\pi$
$487$	−5815.72	+	17898.9i	−0.541141	+	1.66546i	−0.729994	+	0.683454i	$0.760477\pi$
$488$		0			0
$489$	−10205.6	+	7414.77i	−0.943786	+	0.685701i
$490$		0			0
$491$	−970.055	−	2985.52i	−0.0891608	−	0.274409i	0.896527	−	0.442989i	$-0.146082\pi$
$491$	−970.055	−	2985.52i	−0.0891608	−	0.274409i	−0.985688	+	0.168580i	$0.946082\pi$
$492$		0			0
$493$	−4454.98	−	3236.73i	−0.406982	−	0.295690i
$494$		0			0
$495$	2269.26	+	1001.59i	0.206052	+	0.0909454i
$496$		0			0
$497$	−10906.4	−	7923.98i	−0.984346	−	0.715169i
$498$		0			0
$499$	1722.86	+	5302.43i	0.154561	+	0.475690i	0.998116	−	0.0613526i	$-0.0195414\pi$
$499$	1722.86	+	5302.43i	0.154561	+	0.475690i	−0.843555	+	0.537043i	$0.819541\pi$
$500$		0			0
$501$	6066.43	−	4407.52i	0.540974	−	0.393041i
$502$		0			0
$503$	−728.995	+	2243.62i	−0.0646209	+	0.198883i	−0.978154	−	0.207882i	$-0.933343\pi$
$503$	−728.995	+	2243.62i	−0.0646209	+	0.198883i	0.913533	+	0.406764i	$0.133343\pi$
$504$		0			0
$505$	7256.68			0.639442
$506$		0			0
$507$	−9420.79			−0.825231
$508$		0			0
$509$	−2355.68	+	7250.02i	−0.205135	+	0.631339i	0.794573	+	0.607168i	$0.207695\pi$
$509$	−2355.68	+	7250.02i	−0.205135	+	0.631339i	−0.999708	+	0.0241710i	$0.992305\pi$
$510$		0			0
$511$	5096.65	−	3702.93i	0.441218	−	0.320564i
$512$		0			0
$513$	−5943.30	−	18291.6i	−0.511507	−	1.57426i
$514$		0			0
$515$	2720.67	+	1976.68i	0.232790	+	0.169132i
$516$		0			0
$517$	1261.32	−	1409.95i	0.107297	−	0.119941i
$518$		0			0
$519$	1013.73	+	736.518i	0.0857376	+	0.0622920i
$520$		0			0
$521$	6472.30	+	19919.7i	0.544255	+	1.67504i	0.722755	+	0.691104i	$0.242875\pi$
$521$	6472.30	+	19919.7i	0.544255	+	1.67504i	−0.178500	+	0.983940i	$0.557125\pi$
$522$		0			0
$523$	−4837.79	+	3514.86i	−0.404477	+	0.293870i	−0.771362	−	0.636396i	$-0.780424\pi$
$523$	−4837.79	+	3514.86i	−0.404477	+	0.293870i	0.366885	+	0.930266i	$0.380424\pi$
$524$		0			0
$525$	−2083.57	+	6412.57i	−0.173209	+	0.533081i
$526$		0			0
$527$	4161.05			0.343943
$528$		0			0
$529$	−2594.45			−0.213237
$530$		0			0
$531$	68.4947	−	210.805i	0.00559777	−	0.0172282i
$532$		0			0
$533$	722.786	−	525.135i	0.0587380	−	0.0426757i
$534$		0			0
$535$	2691.61	+	8283.92i	0.217511	+	0.669430i
$536$		0			0
$537$	9064.70	+	6585.89i	0.728437	+	0.529241i
$538$		0			0
$539$	−12022.1	+	2595.91i	−0.960722	+	0.207446i
$540$		0			0
$541$	6838.05	+	4968.13i	0.543421	+	0.394818i	0.825354	−	0.564616i	$-0.190976\pi$
$541$	6838.05	+	4968.13i	0.543421	+	0.394818i	−0.281933	+	0.959434i	$0.590976\pi$
$542$		0			0
$543$	2471.09	+	7605.23i	0.195294	+	0.601053i
$544$		0			0
$545$	−9601.53	+	6975.92i	−0.754650	+	0.548285i
$546$		0			0
$547$	−375.960	+	1157.09i	−0.0293874	+	0.0904450i	−0.964674	−	0.263445i	$-0.915141\pi$
$547$	−375.960	+	1157.09i	−0.0293874	+	0.0904450i	0.935287	+	0.353890i	$0.115141\pi$
$548$		0			0
$549$	−1384.30			−0.107615
$550$		0			0
$551$	−33235.1			−2.56963
$552$		0			0
$553$	2201.05	−	6774.12i	0.169255	−	0.520913i
$554$		0			0
$555$	10276.2	−	7466.13i	0.785950	−	0.571026i
$556$		0			0
$557$	2045.70	+	6296.01i	0.155618	+	0.478942i	0.998223	−	0.0595897i	$-0.0189792\pi$
$557$	2045.70	+	6296.01i	0.155618	+	0.478942i	−0.842605	+	0.538532i	$0.818979\pi$
$558$		0			0
$559$	−1024.66	−	744.462i	−0.0775289	−	0.0563281i
$560$		0			0
$561$	332.445	−	3264.18i	0.0250193	−	0.245657i
$562$		0			0
$563$	785.836	+	570.943i	0.0588260	+	0.0427396i	0.616810	−	0.787112i	$-0.288425\pi$
$563$	785.836	+	570.943i	0.0588260	+	0.0427396i	−0.557984	+	0.829852i	$0.688425\pi$
$564$		0			0
$565$	315.106	+	969.797i	0.0234630	+	0.0722118i
$566$		0			0
$567$	9076.23	−	6594.27i	0.672250	−	0.488418i
$568$		0			0
$569$	1298.72	−	3997.04i	0.0956856	−	0.294490i	−0.891746	−	0.452536i	$-0.850519\pi$
$569$	1298.72	−	3997.04i	0.0956856	−	0.294490i	0.987432	+	0.158046i	$0.0505194\pi$
$570$		0			0
$571$	11418.5			0.836862			0.418431	−	0.908248i	$-0.362580\pi$
$571$	11418.5			0.836862			0.418431	+	0.908248i	$0.362580\pi$
$572$		0			0
$573$	−6601.93			−0.481326
$574$		0			0
$575$	1814.10	−	5583.21i	0.131570	−	0.404932i
$576$		0			0
$577$	1176.28	−	854.620i	0.0848688	−	0.0616608i	−0.544542	−	0.838734i	$-0.683296\pi$
$577$	1176.28	−	854.620i	0.0848688	−	0.0616608i	0.629411	+	0.777073i	$0.283296\pi$
$578$		0			0
$579$	1400.20	+	4309.38i	0.100502	+	0.309312i
$580$		0			0
$581$	1531.62	+	1112.79i	0.109367	+	0.0794600i
$582$		0			0
$583$	7567.01	+	13009.4i	0.537553	+	0.924177i
$584$		0			0
$585$	179.526	+	130.433i	0.0126880	+	0.00921839i
$586$		0			0
$587$	−3014.31	−	9277.09i	−0.211949	−	0.652311i	−0.999356	−	0.0358780i	$-0.988577\pi$
$587$	−3014.31	−	9277.09i	−0.211949	−	0.652311i	0.787408	−	0.616433i	$-0.211423\pi$
$588$		0			0
$589$	20317.5	−	14761.5i	1.42134	−	1.03266i
$590$		0			0
$591$	−2100.85	+	6465.74i	−0.146222	+	0.450025i
$592$		0			0
$593$	−22963.3			−1.59020			−0.795102	−	0.606476i	$-0.792583\pi$
$593$	−22963.3			−1.59020			−0.795102	+	0.606476i	$0.792583\pi$
$594$		0			0
$595$	4388.35			0.302361
$596$		0			0
$597$	−5007.25	+	15410.7i	−0.343272	+	1.05648i
$598$		0			0
$599$	8081.00	−	5871.19i	0.551220	−	0.400485i	−0.277015	−	0.960866i	$-0.589345\pi$
$599$	8081.00	−	5871.19i	0.551220	−	0.400485i	0.828235	+	0.560381i	$0.189345\pi$
$600$		0			0
$601$	−146.457	−	450.749i	−0.00994030	−	0.0305931i	0.945963	−	0.324274i	$-0.105120\pi$
$601$	−146.457	−	450.749i	−0.00994030	−	0.0305931i	−0.955904	+	0.293680i	$0.905120\pi$
$602$		0			0
$603$	−1889.60	−	1372.87i	−0.127612	−	0.0927158i
$604$		0			0
$605$	10510.4	+	2163.33i	0.706294	+	0.145375i
$606$		0			0
$607$	−3231.25	−	2347.64i	−0.216067	−	0.156982i	0.474488	−	0.880262i	$-0.342633\pi$
$607$	−3231.25	−	2347.64i	−0.216067	−	0.156982i	−0.690554	+	0.723281i	$0.742633\pi$
$608$		0			0
$609$	−9161.69	−	28196.8i	−0.609606	−	1.87618i
$610$		0			0
$611$	136.920	−	99.4783i	0.00906579	−	0.00658668i
$612$		0			0
$613$	3260.82	−	10035.8i	0.214850	−	0.661241i	−0.784314	−	0.620364i	$-0.786985\pi$
$613$	3260.82	−	10035.8i	0.214850	−	0.661241i	0.999164	−	0.0408768i	$-0.0130151\pi$
$614$		0			0
$615$	−9509.23			−0.623494
$616$		0			0
$617$	−14598.0			−0.952500			−0.476250	−	0.879310i	$-0.658004\pi$
$617$	−14598.0			−0.952500			−0.476250	+	0.879310i	$0.658004\pi$
$618$		0			0
$619$	4324.78	−	13310.3i	0.280820	−	0.864275i	−0.706801	−	0.707413i	$-0.749862\pi$
$619$	4324.78	−	13310.3i	0.280820	−	0.864275i	0.987621	−	0.156862i	$-0.0501378\pi$
$620$		0			0
$621$	−12085.1	+	8780.34i	−0.780932	+	0.567380i
$622$		0			0
$623$	−9628.25	−	29632.7i	−0.619178	−	1.90563i
$624$		0			0
$625$	3660.45	+	2659.47i	0.234269	+	0.170206i
$626$		0			0
$627$	−9956.55	−	17117.6i	−0.634173	−	1.09029i
$628$		0			0
$629$	6174.08	+	4485.73i	0.391378	+	0.284353i
$630$		0			0
$631$	2522.70	+	7764.08i	0.159156	+	0.489830i	0.998558	−	0.0536797i	$-0.0170950\pi$
$631$	2522.70	+	7764.08i	0.159156	+	0.489830i	−0.839403	+	0.543510i	$0.817095\pi$
$632$		0			0
$633$	4952.13	−	3597.93i	0.310947	−	0.225916i
$634$		0			0
$635$	2649.65	−	8154.79i	0.165588	−	0.509627i
$636$		0			0
$637$	−1100.31			−0.0684391
$638$		0			0
$639$	−4359.38			−0.269882
$640$		0			0
$641$	5457.36	−	16796.0i	0.336276	−	1.03495i	−0.629815	−	0.776745i	$-0.716869\pi$
$641$	5457.36	−	16796.0i	0.336276	−	1.03495i	0.966090	−	0.258204i	$-0.0831308\pi$
$642$		0			0
$643$	−14586.7	+	10597.8i	−0.894623	+	0.649981i	−0.937079	−	0.349117i	$-0.886482\pi$
$643$	−14586.7	+	10597.8i	−0.894623	+	0.649981i	0.0424565	+	0.999098i	$0.486482\pi$
$644$		0			0
$645$	4165.81	+	12821.0i	0.254308	+	0.782679i
$646$		0			0
$647$	7986.43	+	5802.48i	0.485285	+	0.352580i	0.803368	−	0.595483i	$-0.203039\pi$
$647$	7986.43	+	5802.48i	0.485285	+	0.352580i	−0.318083	+	0.948063i	$0.603039\pi$
$648$		0			0
$649$	97.1574	−	953.959i	0.00587636	−	0.0576983i
$650$		0			0
$651$	18124.5	+	13168.2i	1.09117	+	0.792784i
$652$		0			0
$653$	3078.59	+	9474.92i	0.184494	+	0.567813i	0.999939	−	0.0110205i	$-0.00350799\pi$
$653$	3078.59	+	9474.92i	0.184494	+	0.567813i	−0.815446	+	0.578834i	$0.803508\pi$
$654$		0			0
$655$	9946.96	−	7226.89i	0.593374	−	0.431111i
$656$		0			0
$657$	629.519	−	1937.46i	0.0373819	−	0.115050i
$658$		0			0
$659$	15778.5			0.932692			0.466346	−	0.884602i	$-0.345570\pi$
$659$	15778.5			0.932692			0.466346	+	0.884602i	$0.345570\pi$
$660$		0			0
$661$	9698.70			0.570704			0.285352	−	0.958423i	$-0.407889\pi$
$661$	9698.70			0.570704			0.285352	+	0.958423i	$0.407889\pi$
$662$		0			0
$663$	90.7056	−	279.163i	0.00531329	−	0.0163526i
$664$		0			0
$665$	21427.3	−	15567.9i	1.24950	−	0.907813i
$666$		0			0
$667$	7976.78	+	24550.0i	0.463062	+	1.42516i
$668$		0			0
$669$	18324.0	+	13313.1i	1.05896	+	0.769381i
$670$		0			0
$671$	−5853.72	+	1263.98i	−0.336781	+	0.0727204i
$672$		0			0
$673$	21866.7	+	15887.1i	1.25245	+	0.909960i	0.998362	−	0.0572204i	$-0.0182238\pi$
$673$	21866.7	+	15887.1i	1.25245	+	0.909960i	0.254091	+	0.967180i	$0.418224\pi$
$674$		0			0
$675$	2830.91	+	8712.63i	0.161425	+	0.496814i
$676$		0			0
$677$	−2811.85	+	2042.93i	−0.159628	+	0.115976i	−0.664732	−	0.747082i	$-0.731454\pi$
$677$	−2811.85	+	2042.93i	−0.159628	+	0.115976i	0.505104	+	0.863059i	$0.331454\pi$
$678$		0			0
$679$	11795.2	−	36302.0i	0.666656	−	2.05176i
$680$		0			0
$681$	−12005.8			−0.675572
$682$		0			0
$683$	2691.57			0.150790			0.0753952	−	0.997154i	$-0.475978\pi$
$683$	2691.57			0.150790			0.0753952	+	0.997154i	$0.475978\pi$
$684$		0			0
$685$	5179.08	−	15939.6i	0.288879	−	0.889079i
$686$		0			0
$687$	−15626.2	+	11353.1i	−0.867800	+	0.630493i
$688$		0			0
$689$	416.062	+	1280.51i	0.0230054	+	0.0708033i
$690$		0			0
$691$	5807.64	+	4219.50i	0.319730	+	0.232297i	0.736060	−	0.676916i	$-0.236684\pi$
$691$	5807.64	+	4219.50i	0.319730	+	0.232297i	−0.416331	+	0.909213i	$0.636684\pi$
$692$		0			0
$693$	−5349.67	+	5980.06i	−0.293243	+	0.327797i
$694$		0			0
$695$	−9832.18	−	7143.50i	−0.536627	−	0.389882i
$696$		0			0
$697$	−1765.49	−	5433.62i	−0.0959437	−	0.295284i
$698$		0			0
$699$	−1100.22	+	799.360i	−0.0595341	+	0.0432540i
$700$		0			0
$701$	1269.83	−	3908.15i	0.0684180	−	0.210569i	−0.911002	−	0.412402i	$-0.864690\pi$
$701$	1269.83	−	3908.15i	0.0684180	−	0.210569i	0.979420	+	0.201833i	$0.0646899\pi$
$702$		0			0
$703$	46060.0			2.47110
$704$		0			0
$705$	−1801.37			−0.0962319
$706$		0			0
$707$	−7253.76	+	22324.8i	−0.385864	+	1.18757i
$708$		0			0
$709$	12973.8	−	9426.03i	0.687224	−	0.499298i	−0.188522	−	0.982069i	$-0.560370\pi$
$709$	12973.8	−	9426.03i	0.687224	−	0.499298i	0.875746	+	0.482771i	$0.160370\pi$
$710$		0			0
$711$	−711.752	−	2190.55i	−0.0375426	−	0.115544i
$712$		0			0
$713$	−15780.4	−	11465.1i	−0.828863	−	0.602204i
$714$		0			0
$715$	878.247	+	387.634i	0.0459365	+	0.0202751i
$716$		0			0
$717$	2811.04	+	2042.34i	0.146416	+	0.106377i
$718$		0			0
$719$	11376.1	+	35011.9i	0.590064	+	1.81603i	0.577907	+	0.816103i	$0.303870\pi$
$719$	11376.1	+	35011.9i	0.590064	+	1.81603i	0.0121568	+	0.999926i	$0.496130\pi$
$720$		0			0
$721$	−8800.71	+	6394.09i	−0.454585	+	0.330275i
$722$		0			0
$723$	−1344.73	+	4138.65i	−0.0691716	+	0.212888i
$724$		0			0
$725$	15830.5			0.810939
$726$		0			0
$727$	21685.1			1.10627			0.553133	−	0.833093i	$-0.313432\pi$
$727$	21685.1			1.10627			0.553133	+	0.833093i	$0.313432\pi$
$728$		0			0
$729$	6610.06	−	20343.7i	0.335826	−	1.03357i
$730$		0			0
$731$	−6552.58	+	4760.73i	−0.331540	+	0.240878i
$732$		0			0
$733$	7456.99	+	22950.2i	0.375757	+	1.15646i	0.942966	+	0.332888i	$0.108023\pi$
$733$	7456.99	+	22950.2i	0.375757	+	1.15646i	−0.567209	+	0.823574i	$0.691977\pi$
$734$		0			0
$735$	9474.67	+	6883.75i	0.475481	+	0.345457i
$736$		0			0
$737$	−9243.95	−	4080.02i	−0.462015	−	0.203921i
$738$		0			0
$739$	−29175.8	−	21197.4i	−1.45230	−	1.05516i	−0.985287	−	0.170905i	$-0.945331\pi$
$739$	−29175.8	−	21197.4i	−1.45230	−	1.05516i	−0.467011	−	0.884252i	$-0.654669\pi$
$740$		0			0
$741$	−547.448	−	1684.87i	−0.0271404	−	0.0835294i
$742$		0			0
$743$	11375.4	−	8264.73i	0.561674	−	0.408080i	−0.270397	−	0.962749i	$-0.587155\pi$
$743$	11375.4	−	8264.73i	0.561674	−	0.408080i	0.832071	+	0.554669i	$0.187155\pi$
$744$		0			0
$745$	1070.90	−	3295.88i	0.0526639	−	0.162083i
$746$		0			0
$747$	612.201			0.0299856
$748$		0			0
$749$	−28175.6			−1.37452
$750$		0			0
$751$	8943.86	−	27526.4i	0.434575	−	1.33749i	−0.458946	−	0.888464i	$-0.651773\pi$
$751$	8943.86	−	27526.4i	0.434575	−	1.33749i	0.893521	−	0.449021i	$-0.148227\pi$
$752$		0			0
$753$	−11110.7	+	8072.40i	−0.537711	+	0.390670i
$754$		0			0
$755$	2221.48	+	6837.02i	0.107084	+	0.329569i
$756$		0			0
$757$	17493.1	+	12709.5i	0.839893	+	0.610218i	0.922341	−	0.386377i	$-0.126274\pi$
$757$	17493.1	+	12709.5i	0.839893	+	0.610218i	−0.0824476	+	0.996595i	$0.526274\pi$
$758$		0			0
$759$	−10254.7	+	11463.1i	−0.490410	+	0.548199i
$760$		0			0
$761$	−17469.7	−	12692.5i	−0.832163	−	0.604602i	0.0880073	−	0.996120i	$-0.471950\pi$
$761$	−17469.7	−	12692.5i	−0.832163	−	0.604602i	−0.920170	+	0.391518i	$0.871950\pi$
$762$		0			0
$763$	−11863.4	−	36511.7i	−0.562887	−	1.73239i
$764$		0			0
$765$	1148.04	−	834.103i	0.0542583	−	0.0394210i
$766$		0			0
$767$	26.5088	−	81.5857i	0.00124795	−	0.00384079i
$768$		0			0
$769$	30161.8			1.41439			0.707194	−	0.707020i	$-0.249961\pi$
$769$	30161.8			1.41439			0.707194	+	0.707020i	$0.249961\pi$
$770$		0			0
$771$	10959.3			0.511918
$772$		0			0
$773$	9582.84	−	29493.0i	0.445887	−	1.37230i	−0.435620	−	0.900131i	$-0.643471\pi$
$773$	9582.84	−	29493.0i	0.445887	−	1.37230i	0.881508	−	0.472170i	$-0.156529\pi$
$774$		0			0
$775$	−9677.60	+	7031.18i	−0.448554	+	0.325894i
$776$		0			0
$777$	12697.0	+	39077.4i	0.586233	+	1.80424i
$778$		0			0
$779$	−27896.5	−	20268.0i	−1.28305	−	0.932191i
$780$		0			0
$781$	−18434.2	+	3980.46i	−0.844595	+	0.182371i
$782$		0			0
$783$	−32588.8	−	23677.1i	−1.48739	−	1.08065i
$784$		0			0
$785$	−1347.89	−	4148.39i	−0.0612845	−	0.188614i
$786$		0			0
$787$	−15790.9	+	11472.8i	−0.715230	+	0.519645i	−0.884857	−	0.465864i	$-0.845744\pi$
$787$	−15790.9	+	11472.8i	−0.715230	+	0.519645i	0.169627	+	0.985508i	$0.445744\pi$
$788$		0			0
$789$	−3984.32	+	12262.5i	−0.179779	+	0.553303i
$790$		0			0
$791$	−3298.51			−0.148270
$792$		0			0
$793$	−535.753			−0.0239913
$794$		0			0
$795$	4428.44	−	13629.3i	0.197561	−	0.608029i
$796$		0			0
$797$	−17707.6	+	12865.3i	−0.786997	+	0.571787i	−0.907071	−	0.420978i	$-0.861687\pi$
$797$	−17707.6	+	12865.3i	−0.786997	+	0.571787i	0.120074	+	0.992765i	$0.461687\pi$
$798$		0			0
$799$	−334.444	−	1029.31i	−0.0148082	−	0.0455750i
$800$		0			0
$801$	−8151.21	−	5922.20i	−0.359562	−	0.261237i
$802$		0			0
$803$	892.952	−	8767.62i	0.0392423	−	0.385308i
$804$		0			0
$805$	−16642.4	−	12091.4i	−0.728655	−	0.529399i
$806$		0			0
$807$	−1093.62	−	3365.83i	−0.0477043	−	0.146819i
$808$		0			0
$809$	30067.6	−	21845.4i	1.30670	−	0.949372i	0.306702	−	0.951806i	$-0.400775\pi$
$809$	30067.6	−	21845.4i	1.30670	−	0.949372i	0.999997	+	0.00243364i	$0.000774654\pi$
$810$		0			0
$811$	−8825.17	+	27161.1i	−0.382113	+	1.17602i	0.556440	+	0.830888i	$0.312167\pi$
$811$	−8825.17	+	27161.1i	−0.382113	+	1.17602i	−0.938553	+	0.345135i	$0.887833\pi$
$812$		0			0
$813$	−27748.3			−1.19702
$814$		0			0
$815$	−23602.7			−1.01444
$816$		0			0
$817$	−15105.9	+	46491.1i	−0.646864	+	1.99084i
$818$		0			0
$819$	−580.725	+	421.921i	−0.0247768	+	0.0180014i
$820$		0			0
$821$	1944.69	+	5985.14i	0.0826677	+	0.254425i	0.983844	−	0.179028i	$-0.0572951\pi$
$821$	1944.69	+	5985.14i	0.0826677	+	0.254425i	−0.901176	+	0.433453i	$0.857295\pi$
$822$		0			0
$823$	12085.9	+	8780.90i	0.511892	+	0.371911i	0.813541	−	0.581508i	$-0.197537\pi$
$823$	12085.9	+	8780.90i	0.511892	+	0.371911i	−0.301649	+	0.953419i	$0.597537\pi$
$824$		0			0
$825$	4742.50	+	8153.44i	0.200136	+	0.344080i
$826$		0			0
$827$	28039.7	+	20372.1i	1.17900	+	0.856597i	0.992059	−	0.125773i	$-0.0401411\pi$
$827$	28039.7	+	20372.1i	1.17900	+	0.856597i	0.186946	+	0.982370i	$0.440141\pi$
$828$		0			0
$829$	−9061.51	−	27888.5i	−0.379637	−	1.16840i	−0.940296	−	0.340357i	$-0.889452\pi$
$829$	−9061.51	−	27888.5i	−0.379637	−	1.16840i	0.560659	−	0.828047i	$-0.310548\pi$
$830$		0			0
$831$	−1793.42	+	1303.00i	−0.0748654	+	0.0543929i
$832$		0			0
$833$	−2174.34	+	6691.92i	−0.0904397	+	0.278345i
$834$		0			0
$835$	14030.0			0.581471
$836$		0			0
$837$	30438.6			1.25700
$838$		0			0
$839$	−1819.80	+	5600.75i	−0.0748824	+	0.230464i	−0.981491	−	0.191508i	$-0.938662\pi$
$839$	−1819.80	+	5600.75i	−0.0748824	+	0.230464i	0.906609	+	0.421973i	$0.138662\pi$
$840$		0			0
$841$	−36583.4	+	26579.4i	−1.49999	+	1.08981i
$842$		0			0
$843$	10330.9	+	31795.3i	0.422082	+	1.29904i
$844$		0			0
$845$	−14260.3	−	10360.7i	−0.580554	−	0.421797i
$846$		0			0
$847$	−17161.5	+	30172.2i	−0.696195	+	1.22400i
$848$		0			0
$849$	−20383.9	−	14809.7i	−0.823996	−	0.598668i
$850$		0			0
$851$	−11054.9	−	34023.4i	−0.445307	−	1.37051i
$852$		0			0
$853$	−30854.3	+	22416.9i	−1.23849	+	0.899814i	−0.997497	−	0.0707136i	$-0.977472\pi$
$853$	−30854.3	+	22416.9i	−1.23849	+	0.899814i	−0.240991	+	0.970527i	$0.577472\pi$
$854$		0			0
$855$	2646.62	−	8145.47i	0.105863	−	0.325812i
$856$		0			0
$857$	12704.1			0.506377			0.253188	−	0.967417i	$-0.418521\pi$
$857$	12704.1			0.506377			0.253188	+	0.967417i	$0.418521\pi$
$858$		0			0
$859$	11123.7			0.441833			0.220916	−	0.975293i	$-0.429095\pi$
$859$	11123.7			0.441833			0.220916	+	0.975293i	$0.429095\pi$
$860$		0			0
$861$	9505.40	−	29254.6i	0.376241	−	1.15795i
$862$		0			0
$863$	−11067.7	+	8041.19i	−0.436559	+	0.317179i	−0.784266	−	0.620424i	$-0.786960\pi$
$863$	−11067.7	+	8041.19i	−0.436559	+	0.317179i	0.347707	+	0.937603i	$0.386960\pi$
$864$		0			0
$865$	724.485	+	2229.74i	0.0284777	+	0.0876454i
$866$		0			0
$867$	15608.1	+	11339.9i	0.611393	+	0.444203i
$868$		0			0
$869$	−5009.89	−	8613.14i	−0.195568	−	0.336227i
$870$		0			0
$871$	−731.311	−	531.328i	−0.0284495	−	0.0206698i
$872$		0			0
$873$	−3814.23	−	11739.0i	−0.147872	−	0.455102i
$874$		0			0
$875$	−31468.6	+	22863.3i	−1.21581	+	0.883338i
$876$		0			0
$877$	14031.6	−	43184.7i	0.540264	−	1.66276i	−0.191726	−	0.981448i	$-0.561409\pi$
$877$	14031.6	−	43184.7i	0.540264	−	1.66276i	0.731991	−	0.681315i	$-0.238591\pi$
$878$		0			0
$879$	−34792.3			−1.33506
$880$		0			0
$881$	13620.9			0.520884			0.260442	−	0.965490i	$-0.416132\pi$
$881$	13620.9			0.520884			0.260442	+	0.965490i	$0.416132\pi$
$882$		0			0
$883$	2455.36	−	7556.84i	0.0935783	−	0.288004i	−0.893302	−	0.449456i	$-0.851618\pi$
$883$	2455.36	−	7556.84i	0.0935783	−	0.288004i	0.986881	+	0.161452i	$0.0516177\pi$
$884$		0			0
$885$	−738.683	+	536.685i	−0.0280571	+	0.0203847i
$886$		0			0
$887$	12836.9	+	39507.9i	0.485931	+	1.49554i	0.830627	+	0.556829i	$0.187982\pi$
$887$	12836.9	+	39507.9i	0.485931	+	1.49554i	−0.344696	+	0.938714i	$0.612018\pi$
$888$		0			0
$889$	22439.2	+	16303.0i	0.846553	+	0.615057i
$890$		0			0
$891$	1590.19	−	15613.6i	0.0597905	−	0.587065i
$892$		0			0
$893$	−5284.54	−	3839.44i	−0.198030	−	0.143877i
$894$		0			0
$895$	6478.29	+	19938.1i	0.241950	+	0.744646i
$896$		0			0
$897$	−1113.18	+	808.774i	−0.0414360	+	0.0301050i
$898$		0			0
$899$	16254.0	−	50024.6i	0.603003	−	1.85585i
$900$		0			0
$901$	8610.07			0.318361
$902$		0			0
$903$	−43607.3			−1.60704
$904$		0			0
$905$	−4623.50	+	14229.7i	−0.169824	+	0.522663i
$906$		0			0
$907$	34974.7	−	25410.6i	1.28039	−	0.930259i	0.280827	−	0.959758i	$-0.409391\pi$
$907$	34974.7	−	25410.6i	1.28039	−	0.930259i	0.999565	+	0.0294988i	$0.00939112\pi$
$908$		0			0
$909$	2345.65	+	7219.17i	0.0855889	+	0.263415i
$910$		0			0
$911$	−27102.7	−	19691.3i	−0.985679	−	0.716138i	−0.0267083	−	0.999643i	$-0.508503\pi$
$911$	−27102.7	−	19691.3i	−0.985679	−	0.716138i	−0.958971	+	0.283506i	$0.908503\pi$
$912$		0			0
$913$	2588.77	−	558.988i	0.0938400	−	0.0202627i
$914$		0			0
$915$	4613.33	+	3351.78i	0.166680	+	0.121100i
$916$		0			0
$917$	12290.2	+	37825.3i	0.442592	+	1.36216i
$918$		0			0
$919$	15290.8	−	11109.4i	0.548854	−	0.398766i	−0.278509	−	0.960434i	$-0.589840\pi$
$919$	15290.8	−	11109.4i	0.548854	−	0.398766i	0.827363	+	0.561668i	$0.189840\pi$
$920$		0			0
$921$	5606.59	−	17255.3i	0.200590	−	0.617353i
$922$		0			0
$923$	−1687.17			−0.0601665
$924$		0			0
$925$	−21939.3			−0.779847
$926$		0			0
$927$	−1087.03	+	3345.54i	−0.0385144	+	0.118535i
$928$		0			0
$929$	−23582.2	+	17133.5i	−0.832838	+	0.605092i	−0.920361	−	0.391070i	$-0.872105\pi$
$929$	−23582.2	+	17133.5i	−0.832838	+	0.605092i	0.0875229	+	0.996163i	$0.472105\pi$
$930$		0			0
$931$	13123.1	+	40388.7i	0.461967	+	1.42179i
$932$		0			0
$933$	−4597.51	−	3340.29i	−0.161325	−	0.117209i
$934$		0			0
$935$	4093.06	−	4575.37i	0.143163	−	0.160033i
$936$		0			0
$937$	26044.7	+	18922.6i	0.908049	+	0.659736i	0.940521	−	0.339737i	$-0.110338\pi$
$937$	26044.7	+	18922.6i	0.908049	+	0.659736i	−0.0324717	+	0.999473i	$0.510338\pi$
$938$		0			0
$939$	−5600.61	−	17236.9i	−0.194642	−	0.599047i
$940$		0			0
$941$	−30253.9	+	21980.7i	−1.04809	+	0.761479i	−0.971847	−	0.235611i	$-0.924291\pi$
$941$	−30253.9	+	21980.7i	−1.04809	+	0.761479i	−0.0762380	+	0.997090i	$0.524291\pi$
$942$		0			0
$943$	−8276.04	+	25471.0i	−0.285795	+	0.879587i
$944$		0			0
$945$	32101.3			1.10503
$946$		0			0
$947$	−3065.34			−0.105185			−0.0525925	−	0.998616i	$-0.516748\pi$
$947$	−3065.34			−0.105185			−0.0525925	+	0.998616i	$0.516748\pi$
$948$		0			0
$949$	243.636	−	749.836i	0.00833380	−	0.0256488i
$950$		0			0
$951$	8586.34	−	6238.34i	0.292777	−	0.212715i
$952$		0			0
$953$	5063.37	+	15583.5i	0.172108	+	0.529693i	0.999490	−	0.0319466i	$-0.0101706\pi$
$953$	5063.37	+	15583.5i	0.172108	+	0.529693i	−0.827382	+	0.561640i	$0.810171\pi$
$954$		0			0
$955$	−9993.35	−	7260.60i	−0.338615	−	0.246018i
$956$		0			0
$957$	−37943.7	−	16747.3i	−1.28166	−	0.565687i
$958$		0			0
$959$	43860.2	+	31866.3i	1.47687	+	1.07301i
$960$		0			0
$961$	3076.21	+	9467.60i	0.103260	+	0.317801i
$962$		0			0
$963$	−7371.06	+	5355.39i	−0.246655	+	0.179206i
$964$		0			0
$965$	−2619.83	+	8063.01i	−0.0873942	+	0.268972i
$966$		0			0
$967$	−16183.5			−0.538187			−0.269094	−	0.963114i	$-0.586724\pi$
$967$	−16183.5			−0.538187			−0.269094	+	0.963114i	$0.586724\pi$
$968$		0			0
$969$	−11329.0			−0.375583
$970$		0			0
$971$	−1450.54	+	4464.30i	−0.0479403	+	0.147545i	−0.972161	−	0.234313i	$-0.924716\pi$
$971$	−1450.54	+	4464.30i	−0.0479403	+	0.147545i	0.924221	+	0.381858i	$0.124716\pi$
$972$		0			0
$973$	31804.8	−	23107.5i	1.04791	−	0.761350i
$974$		0			0
$975$	260.760	+	802.537i	0.00856513	+	0.0263608i
$976$		0			0
$977$	6199.97	+	4504.54i	0.203024	+	0.147506i	0.684652	−	0.728870i	$-0.259954\pi$
$977$	6199.97	+	4504.54i	0.203024	+	0.147506i	−0.481628	+	0.876376i	$0.659954\pi$
$978$		0			0
$979$	−39876.0	−	17600.1i	−1.30178	−	0.574569i
$980$		0			0
$981$	−10043.4	−	7296.99i	−0.326873	−	0.237487i
$982$		0			0
$983$	−11556.4	−	35566.9i	−0.374966	−	1.15403i	−0.943501	−	0.331368i	$-0.892490\pi$
$983$	−11556.4	−	35566.9i	−0.374966	−	1.15403i	0.568535	−	0.822659i	$-0.307510\pi$
$984$		0			0
$985$	−10290.9	+	7476.75i	−0.332887	+	0.241857i
$986$		0			0
$987$	1800.64	−	5541.81i	0.0580700	−	0.178721i
$988$		0			0
$989$	37967.5			1.22072
$990$		0			0
$991$	−15536.1			−0.498002			−0.249001	−	0.968503i	$-0.580102\pi$
$991$	−15536.1			−0.498002			−0.249001	+	0.968503i	$0.580102\pi$
$992$		0			0
$993$	4437.22	−	13656.4i	0.141804	−	0.436426i
$994$		0			0
$995$	−24527.7	+	17820.4i	−0.781488	+	0.567785i
$996$		0			0
$997$	−12721.6	−	39152.9i	−0.404108	−	1.24372i	−0.921638	−	0.388051i	$-0.873148\pi$
$997$	−12721.6	−	39152.9i	−0.404108	−	1.24372i	0.517530	−	0.855665i	$-0.326852\pi$
$998$		0			0
$999$	45164.2	+	32813.7i	1.43036	+	1.03922i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	176.4.m.b.81.2		8
4.3	odd	2		22.4.c.b.15.1	yes	8
11.3	even	5	inner	176.4.m.b.113.2		8
11.5	even	5		1936.4.a.bn.1.3		4
11.6	odd	10		1936.4.a.bm.1.3		4
12.11	even	2		198.4.f.d.37.1		8
44.3	odd	10		22.4.c.b.3.1	✓	8
44.7	even	10		242.4.c.n.9.2		8
44.15	odd	10		242.4.c.r.9.2		8
44.19	even	10		242.4.c.q.3.1		8
44.27	odd	10		242.4.a.n.1.2		4
44.31	odd	10		242.4.c.r.27.2		8
44.35	even	10		242.4.c.n.27.2		8
44.39	even	10		242.4.a.o.1.2		4
44.43	even	2		242.4.c.q.81.1		8
132.47	even	10		198.4.f.d.91.1		8
132.71	even	10		2178.4.a.by.1.4		4
132.83	odd	10		2178.4.a.bt.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
22.4.c.b.3.1	✓	8	44.3	odd	10
22.4.c.b.15.1	yes	8	4.3	odd	2
176.4.m.b.81.2		8	1.1	even	1	trivial
176.4.m.b.113.2		8	11.3	even	5	inner
198.4.f.d.37.1		8	12.11	even	2
198.4.f.d.91.1		8	132.47	even	10
242.4.a.n.1.2		4	44.27	odd	10
242.4.a.o.1.2		4	44.39	even	10
242.4.c.n.9.2		8	44.7	even	10
242.4.c.n.27.2		8	44.35	even	10
242.4.c.q.3.1		8	44.19	even	10
242.4.c.q.81.1		8	44.43	even	2
242.4.c.r.9.2		8	44.15	odd	10
242.4.c.r.27.2		8	44.31	odd	10
1936.4.a.bm.1.3		4	11.6	odd	10
1936.4.a.bn.1.3		4	11.5	even	5
2178.4.a.bt.1.4		4	132.83	odd	10
2178.4.a.by.1.4		4	132.71	even	10

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:	\( N \)	\(=\)	\( 176 = 2^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	176.m (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.33153 - 4.09803i) q^{3} +(6.52241 - 4.73881i) q^{5} +(8.05890 + 24.8027i) q^{7} +(6.82261 + 4.95692i) q^{9} +O(q^{10})\)	\(q+(1.33153 - 4.09803i) q^{3} +(6.52241 - 4.73881i) q^{5} +(8.05890 + 24.8027i) q^{7} +(6.82261 + 4.95692i) q^{9} +(33.3764 + 14.7314i) q^{11} +(2.64049 + 1.91843i) q^{13} +(-10.7350 - 33.0389i) q^{15} +(16.8855 - 12.2681i) q^{17} +(38.9268 - 119.804i) q^{19} +112.373 q^{21} -97.8394 q^{23} +(-18.5416 + 57.0651i) q^{25} +(123.520 - 89.7424i) q^{27} +(-81.5293 - 250.921i) q^{29} +(161.288 + 117.183i) q^{31} +(104.811 - 117.162i) q^{33} +(170.099 + 123.584i) q^{35} +(112.990 + 347.748i) q^{37} +(11.3776 - 8.26634i) q^{39} +(84.5880 - 260.335i) q^{41} -388.059 q^{43} +67.9898 q^{45} +(16.0238 - 49.3162i) q^{47} +(-272.737 + 198.155i) q^{49} +(-27.7912 - 85.5326i) q^{51} +(333.739 + 242.476i) q^{53} +(287.504 - 62.0801i) q^{55} +(-439.129 - 319.046i) q^{57} +(-8.12202 - 24.9970i) q^{59} +(-132.799 + 96.4844i) q^{61} +(-67.9624 + 209.167i) q^{63} +26.3134 q^{65} -276.961 q^{67} +(-130.276 + 400.948i) q^{69} +(-418.205 + 303.844i) q^{71} +(-74.6476 - 229.742i) q^{73} +(209.166 + 151.968i) q^{75} +(-96.4024 + 946.546i) q^{77} +(-220.959 - 160.536i) q^{79} +(-132.934 - 409.129i) q^{81} +(58.7298 - 42.6697i) q^{83} +(51.9984 - 160.035i) q^{85} -1136.84 q^{87} -1194.73 q^{89} +(-26.3028 + 80.9517i) q^{91} +(694.979 - 504.932i) q^{93} +(-313.833 - 965.880i) q^{95} +(-1184.10 - 860.299i) q^{97} +(154.692 + 265.951i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 3 q^{3} + 5 q^{5} + q^{7} - 21 q^{9}+O(q^{10}) \) 8 * q - 3 * q^3 + 5 * q^5 + q^7 - 21 * q^9	\( 8 q - 3 q^{3} + 5 q^{5} + q^{7} - 21 q^{9} + 155 q^{11} + 7 q^{13} - 211 q^{15} + 161 q^{17} + 272 q^{19} - 50 q^{21} - 628 q^{23} - 17 q^{25} + 528 q^{27} + 33 q^{29} - 323 q^{31} - 1144 q^{33} + 697 q^{35} + 49 q^{37} - 391 q^{39} + 361 q^{41} - 1442 q^{43} + 2652 q^{45} + 1069 q^{47} - 709 q^{49} + 1332 q^{51} - 281 q^{53} + 7 q^{55} - 438 q^{57} + 128 q^{59} - 617 q^{61} - 694 q^{63} - 138 q^{65} - 578 q^{67} - 310 q^{69} - 115 q^{71} - 1487 q^{73} + 1852 q^{75} + 553 q^{77} - 71 q^{79} + 1630 q^{81} - 1942 q^{83} - 329 q^{85} - 2122 q^{87} - 2202 q^{89} - 4523 q^{91} + 6019 q^{93} + 793 q^{95} - 5128 q^{97} + 2213 q^{99}+O(q^{100}) \) 8 * q - 3 * q^3 + 5 * q^5 + q^7 - 21 * q^9 + 155 * q^11 + 7 * q^13 - 211 * q^15 + 161 * q^17 + 272 * q^19 - 50 * q^21 - 628 * q^23 - 17 * q^25 + 528 * q^27 + 33 * q^29 - 323 * q^31 - 1144 * q^33 + 697 * q^35 + 49 * q^37 - 391 * q^39 + 361 * q^41 - 1442 * q^43 + 2652 * q^45 + 1069 * q^47 - 709 * q^49 + 1332 * q^51 - 281 * q^53 + 7 * q^55 - 438 * q^57 + 128 * q^59 - 617 * q^61 - 694 * q^63 - 138 * q^65 - 578 * q^67 - 310 * q^69 - 115 * q^71 - 1487 * q^73 + 1852 * q^75 + 553 * q^77 - 71 * q^79 + 1630 * q^81 - 1942 * q^83 - 329 * q^85 - 2122 * q^87 - 2202 * q^89 - 4523 * q^91 + 6019 * q^93 + 793 * q^95 - 5128 * q^97 + 2213 * q^99

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