LMFDB - Embedded newform 804.2.ba.b.41.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(41,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([0, 33, 53]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("804.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.ba (of order $66$, degree $20$, 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:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$440$
Relative dimension:	$22$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			41.11
Character	$\chi$	$=$	804.41
Dual form			804.2.ba.b.353.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.313881 + 1.70337i) q^{3} +(0.391534 - 2.72318i) q^{5} +(0.116340 + 1.21837i) q^{7} +(-2.80296 - 1.06931i) q^{9} +O(q^{10})$	\(q+(-0.313881 + 1.70337i) q^{3} +(0.391534 - 2.72318i) q^{5} +(0.116340 + 1.21837i) q^{7} +(-2.80296 - 1.06931i) q^{9} +(1.23209 - 0.493254i) q^{11} +(-0.385910 - 0.404731i) q^{13} +(4.51569 + 1.52168i) q^{15} +(2.29296 - 0.793601i) q^{17} +(4.71345 + 0.450080i) q^{19} +(-2.11185 - 0.184253i) q^{21} +(5.02418 - 0.239331i) q^{23} +(-2.46494 - 0.723772i) q^{25} +(2.70124 - 4.43884i) q^{27} +(2.38566 - 1.37736i) q^{29} +(3.24107 - 3.39914i) q^{31} +(0.453466 + 2.25353i) q^{33} +(3.36339 + 0.160218i) q^{35} +(-3.40187 + 5.89222i) q^{37} +(0.810537 - 0.530311i) q^{39} +(-0.873683 - 0.168389i) q^{41} +(-0.960559 - 0.832329i) q^{43} +(-4.00939 + 7.21428i) q^{45} +(0.522344 - 1.01321i) q^{47} +(5.40261 - 1.04127i) q^{49} +(0.632081 + 4.15486i) q^{51} +(-1.34190 - 1.54863i) q^{53} +(-0.860814 - 3.54832i) q^{55} +(-2.24612 + 7.88750i) q^{57} +(0.531959 + 1.81168i) q^{59} +(2.74049 - 6.84541i) q^{61} +(0.976722 - 3.53944i) q^{63} +(-1.25325 + 0.892436i) q^{65} +(6.90314 + 4.39849i) q^{67} +(-1.16932 + 8.63317i) q^{69} +(1.94404 + 0.672840i) q^{71} +(4.71011 + 1.88564i) q^{73} +(2.00655 - 3.97154i) q^{75} +(0.744306 + 1.44375i) q^{77} +(7.34631 - 1.78219i) q^{79} +(6.71314 + 5.99448i) q^{81} +(-6.30692 + 8.01990i) q^{83} +(-1.26335 - 6.55486i) q^{85} +(1.59735 + 4.49599i) q^{87} +(-7.62896 + 11.8709i) q^{89} +(0.448214 - 0.517267i) q^{91} +(4.77269 + 6.58768i) q^{93} +(3.07113 - 12.6594i) q^{95} +(-16.2625 - 9.38917i) q^{97} +(-3.98094 + 0.0650804i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 440 q - 12 q^{7} + 4 q^{9}+O(q^{10}) $ 440 * q - 12 * q^7 + 4 * q^9	$ 440 q - 12 q^{7} + 4 q^{9} - 2 q^{15} - 10 q^{19} + 22 q^{21} - 68 q^{25} + 50 q^{31} + 11 q^{33} - 22 q^{37} - 45 q^{39} + 22 q^{43} + 22 q^{45} - 18 q^{49} - 6 q^{51} + 126 q^{55} - 183 q^{57} - 56 q^{61} - 141 q^{63} - 12 q^{67} + 33 q^{69} + 356 q^{73} + 165 q^{75} + 228 q^{79} + 24 q^{81} - 6 q^{85} + 75 q^{87} - 4 q^{91} - 75 q^{93} + 12 q^{97} + 88 q^{99}+O(q^{100}) $ 440 * q - 12 * q^7 + 4 * q^9 - 2 * q^15 - 10 * q^19 + 22 * q^21 - 68 * q^25 + 50 * q^31 + 11 * q^33 - 22 * q^37 - 45 * q^39 + 22 * q^43 + 22 * q^45 - 18 * q^49 - 6 * q^51 + 126 * q^55 - 183 * q^57 - 56 * q^61 - 141 * q^63 - 12 * q^67 + 33 * q^69 + 356 * q^73 + 165 * q^75 + 228 * q^79 + 24 * q^81 - 6 * q^85 + 75 * q^87 - 4 * q^91 - 75 * q^93 + 12 * q^97 + 88 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$-1$	$e\left(\frac{53}{66}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.313881	+	1.70337i	−0.181219	+	0.983443i
$3$	−0.313881	+	1.70337i	−0.181219	+	0.983443i
$4$		0			0
$5$	0.391534	−	2.72318i	0.175099	−	1.21784i	−0.692810	−	0.721120i	$-0.743628\pi$
$5$	0.391534	−	2.72318i	0.175099	−	1.21784i	0.867909	−	0.496723i	$-0.165463\pi$
$6$		0			0
$7$	0.116340	+	1.21837i	0.0439724	+	0.460500i	0.990464	+	0.137772i	$0.0439940\pi$
$7$	0.116340	+	1.21837i	0.0439724	+	0.460500i	−0.946492	+	0.322728i	$0.895400\pi$
$8$		0			0
$9$	−2.80296	−	1.06931i	−0.934319	−	0.356438i
$10$		0			0
$11$	1.23209	−	0.493254i	0.371489	−	0.148722i	−0.178403	−	0.983957i	$-0.557093\pi$
$11$	1.23209	−	0.493254i	0.371489	−	0.148722i	0.549892	+	0.835236i	$0.314669\pi$
$12$		0			0
$13$	−0.385910	−	0.404731i	−0.107032	−	0.112252i	0.668038	−	0.744127i	$-0.267134\pi$
$13$	−0.385910	−	0.404731i	−0.107032	−	0.112252i	−0.775071	+	0.631875i	$0.782286\pi$
$14$		0			0
$15$	4.51569	+	1.52168i	1.16595	+	0.392897i
$16$		0			0
$17$	2.29296	−	0.793601i	0.556124	−	0.192476i	−0.0345265	−	0.999404i	$-0.510992\pi$
$17$	2.29296	−	0.793601i	0.556124	−	0.192476i	0.590651	+	0.806927i	$0.298871\pi$
$18$		0			0
$19$	4.71345	+	0.450080i	1.08134	+	0.103255i	0.620484	−	0.784219i	$-0.286936\pi$
$19$	4.71345	+	0.450080i	1.08134	+	0.103255i	0.460856	+	0.887475i	$0.347542\pi$
$20$		0			0
$21$	−2.11185	−	0.184253i	−0.460844	−	0.0402072i
$22$		0			0
$23$	5.02418	−	0.239331i	1.04761	−	0.0499040i	0.483292	−	0.875459i	$-0.339441\pi$
$23$	5.02418	−	0.239331i	1.04761	−	0.0499040i	0.564321	+	0.825555i	$0.309138\pi$
$24$		0			0
$25$	−2.46494	−	0.723772i	−0.492988	−	0.144754i
$26$		0			0
$27$	2.70124	−	4.43884i	0.519853	−	0.854256i
$28$		0			0
$29$	2.38566	−	1.37736i	0.443006	−	0.255770i	−0.261866	−	0.965104i	$-0.584338\pi$
$29$	2.38566	−	1.37736i	0.443006	−	0.255770i	0.704872	+	0.709335i	$0.251005\pi$
$30$		0			0
$31$	3.24107	−	3.39914i	0.582114	−	0.610503i	−0.365154	−	0.930947i	$-0.618984\pi$
$31$	3.24107	−	3.39914i	0.582114	−	0.610503i	0.947267	+	0.320444i	$0.103832\pi$
$32$		0			0
$33$	0.453466	+	2.25353i	0.0789383	+	0.392289i
$34$		0			0
$35$	3.36339	+	0.160218i	0.568516	+	0.0270818i
$36$		0			0
$37$	−3.40187	+	5.89222i	−0.559264	+	0.968674i	0.438294	+	0.898832i	$0.355583\pi$
$37$	−3.40187	+	5.89222i	−0.559264	+	0.968674i	−0.997558	+	0.0698426i	$0.977750\pi$
$38$		0			0
$39$	0.810537	−	0.530311i	0.129790	−	0.0849177i
$40$		0			0
$41$	−0.873683	−	0.168389i	−0.136446	−	0.0262979i	0.120571	−	0.992705i	$-0.461528\pi$
$41$	−0.873683	−	0.168389i	−0.136446	−	0.0262979i	−0.257017	+	0.966407i	$0.582740\pi$
$42$		0			0
$43$	−0.960559	−	0.832329i	−0.146484	−	0.126929i	0.578536	−	0.815657i	$-0.303624\pi$
$43$	−0.960559	−	0.832329i	−0.146484	−	0.126929i	−0.725020	+	0.688728i	$0.758170\pi$
$44$		0			0
$45$	−4.00939	+	7.21428i	−0.597684	+	1.07544i
$46$		0			0
$47$	0.522344	−	1.01321i	0.0761917	−	0.147791i	−0.847663	−	0.530536i	$-0.821991\pi$
$47$	0.522344	−	1.01321i	0.0761917	−	0.147791i	0.923854	+	0.382745i	$0.125021\pi$
$48$		0			0
$49$	5.40261	−	1.04127i	0.771802	−	0.148753i
$50$		0			0
$51$	0.632081	+	4.15486i	0.0885091	+	0.581797i
$52$		0			0
$53$	−1.34190	−	1.54863i	−0.184324	−	0.212721i	0.656066	−	0.754704i	$-0.272219\pi$
$53$	−1.34190	−	1.54863i	−0.184324	−	0.212721i	−0.840390	+	0.541983i	$0.817674\pi$
$54$		0			0
$55$	−0.860814	−	3.54832i	−0.116072	−	0.478456i
$56$		0			0
$57$	−2.24612	+	7.88750i	−0.297506	+	1.04472i
$58$		0			0
$59$	0.531959	+	1.81168i	0.0692551	+	0.235861i	0.986846	−	0.161666i	$-0.0516867\pi$
$59$	0.531959	+	1.81168i	0.0692551	+	0.235861i	−0.917590	+	0.397527i	$0.869868\pi$
$60$		0			0
$61$	2.74049	−	6.84541i	0.350884	−	0.876465i	−0.642983	−	0.765881i	$-0.722303\pi$
$61$	2.74049	−	6.84541i	0.350884	−	0.876465i	0.993867	−	0.110585i	$-0.0352724\pi$
$62$		0			0
$63$	0.976722	−	3.53944i	0.123055	−	0.445927i
$64$		0			0
$65$	−1.25325	+	0.892436i	−0.155447	+	0.110693i
$66$		0			0
$67$	6.90314	+	4.39849i	0.843352	+	0.537361i
$67$	6.90314	+	4.39849i	0.843352	+	0.537361i
$68$		0			0
$69$	−1.16932	+	8.63317i	−0.140770	+	1.03931i
$70$		0			0
$71$	1.94404	+	0.672840i	0.230716	+	0.0798515i	0.439980	−	0.898008i	$-0.354986\pi$
$71$	1.94404	+	0.672840i	0.230716	+	0.0798515i	−0.209264	+	0.977859i	$0.567107\pi$
$72$		0			0
$73$	4.71011	+	1.88564i	0.551276	+	0.220698i	0.630541	−	0.776156i	$-0.282833\pi$
$73$	4.71011	+	1.88564i	0.551276	+	0.220698i	−0.0792648	+	0.996854i	$0.525257\pi$
$74$		0			0
$75$	2.00655	−	3.97154i	0.231697	−	0.458593i
$76$		0			0
$77$	0.744306	+	1.44375i	0.0848216	+	0.164531i
$78$		0			0
$79$	7.34631	−	1.78219i	0.826524	−	0.200513i	0.199882	−	0.979820i	$-0.435944\pi$
$79$	7.34631	−	1.78219i	0.826524	−	0.200513i	0.626642	+	0.779307i	$0.284429\pi$
$80$		0			0
$81$	6.71314	+	5.99448i	0.745904	+	0.666053i
$82$		0			0
$83$	−6.30692	+	8.01990i	−0.692274	+	0.880298i	−0.997404	−	0.0720127i	$-0.977058\pi$
$83$	−6.30692	+	8.01990i	−0.692274	+	0.880298i	0.305130	+	0.952311i	$0.401300\pi$
$84$		0			0
$85$	−1.26335	−	6.55486i	−0.137029	−	0.710974i
$86$		0			0
$87$	1.59735	+	4.49599i	0.171253	+	0.482021i
$88$		0			0
$89$	−7.62896	+	11.8709i	−0.808668	+	1.25831i	0.154119	+	0.988052i	$0.450746\pi$
$89$	−7.62896	+	11.8709i	−0.808668	+	1.25831i	−0.962787	+	0.270260i	$0.912890\pi$
$90$		0			0
$91$	0.448214	−	0.517267i	0.0469856	−	0.0542243i
$92$		0			0
$93$	4.77269	+	6.58768i	0.494905	+	0.683111i
$94$		0			0
$95$	3.07113	−	12.6594i	0.315091	−	1.29882i
$96$		0			0
$97$	−16.2625	−	9.38917i	−1.65121	−	0.953326i	−0.976576	−	0.215172i	$-0.930969\pi$
$97$	−16.2625	−	9.38917i	−1.65121	−	0.953326i	−0.674632	−	0.738154i	$-0.735698\pi$
$98$		0			0
$99$	−3.98094	+	0.0650804i	−0.400099	+	0.00654083i
$100$		0			0
$101$	−0.376368	+	0.528535i	−0.0374500	+	0.0525912i	−0.832876	−	0.553459i	$-0.813308\pi$
$101$	−0.376368	+	0.528535i	−0.0374500	+	0.0525912i	0.795426	+	0.606050i	$0.207247\pi$
$102$		0			0
$103$	6.94853	+	6.62541i	0.684659	+	0.652821i	0.950331	−	0.311243i	$-0.100745\pi$
$103$	6.94853	+	6.62541i	0.684659	+	0.652821i	−0.265671	+	0.964064i	$0.585594\pi$
$104$		0			0
$105$	−1.32861	+	5.67881i	−0.129660	+	0.554195i
$106$		0			0
$107$	−16.4738	+	2.36858i	−1.59259	+	0.228979i	−0.880825	−	0.473443i	$-0.843011\pi$
$107$	−16.4738	+	2.36858i	−1.59259	+	0.228979i	−0.711761	+	0.702422i	$0.752102\pi$
$108$		0			0
$109$	1.09834	−	3.74061i	0.105202	−	0.358286i	−0.890020	−	0.455921i	$-0.849310\pi$
$109$	1.09834	−	3.74061i	0.105202	−	0.358286i	0.995222	+	0.0976356i	$0.0311280\pi$
$110$		0			0
$111$	−8.96886	−	7.64411i	−0.851286	−	0.725547i
$112$		0			0
$113$	5.10511	−	4.01470i	0.480248	−	0.377671i	−0.348486	−	0.937314i	$-0.613304\pi$
$113$	5.10511	−	4.01470i	0.480248	−	0.377671i	0.828734	+	0.559643i	$0.189062\pi$
$114$		0			0
$115$	1.31539	−	13.7754i	0.122661	−	1.28457i
$116$		0			0
$117$	0.648905	+	1.54710i	0.0599913	+	0.143030i
$118$		0			0
$119$	1.23366	+	2.70134i	0.113090	+	0.247632i
$120$		0			0
$121$	−6.68633	+	6.37540i	−0.607848	+	0.579582i
$122$		0			0
$123$	0.561061	−	1.43535i	0.0505892	−	0.129421i
$124$		0			0
$125$	2.77834	−	6.08372i	0.248502	−	0.544145i
$126$		0			0
$127$	−3.22444	+	0.307896i	−0.286122	+	0.0273214i	−0.237131	−	0.971478i	$-0.576207\pi$
$127$	−3.22444	+	0.307896i	−0.286122	+	0.0273214i	−0.0489919	+	0.998799i	$0.515601\pi$
$128$		0			0
$129$	1.71927	−	1.37494i	0.151373	−	0.121057i
$130$		0			0
$131$	−9.66705	−	15.0422i	−0.844614	−	1.31424i	−0.947567	−	0.319558i	$-0.896465\pi$
$131$	−9.66705	−	15.0422i	−0.844614	−	1.31424i	0.102953	−	0.994686i	$-0.467171\pi$
$132$		0			0
$133$			5.79509i			0.502498i
$134$		0			0
$135$	−11.0301	−	9.09391i	−0.949323	−	0.782679i
$136$		0			0
$137$	−3.60970	+	2.31981i	−0.308397	+	0.198195i	−0.685680	−	0.727903i	$-0.740495\pi$
$137$	−3.60970	+	2.31981i	−0.308397	+	0.198195i	0.377283	+	0.926098i	$0.376859\pi$
$138$		0			0
$139$	2.32375	+	0.334105i	0.197098	+	0.0283384i	0.240157	−	0.970734i	$-0.422801\pi$
$139$	2.32375	+	0.334105i	0.197098	+	0.0283384i	−0.0430588	+	0.999073i	$0.513710\pi$
$140$		0			0
$141$	1.56191	+	1.20777i	0.131537	+	0.101713i
$142$		0			0
$143$	−0.675110	−	0.308312i	−0.0564555	−	0.0257824i
$144$		0			0
$145$	−2.81673	−	7.03586i	−0.233917	−	0.584297i
$146$		0			0
$147$	0.0778891	+	9.52950i	0.00642418	+	0.785980i
$148$		0			0
$149$	−0.945908	+	0.431982i	−0.0774918	+	0.0353893i	−0.453784	−	0.891112i	$-0.649926\pi$
$149$	−0.945908	+	0.431982i	−0.0774918	+	0.0353893i	0.376292	+	0.926501i	$0.377199\pi$
$150$		0			0
$151$	−3.82320	−	11.0464i	−0.311128	−	0.898945i	−0.986829	−	0.161769i	$-0.948280\pi$
$151$	−3.82320	−	11.0464i	−0.311128	−	0.898945i	0.675701	−	0.737176i	$-0.263841\pi$
$152$		0			0
$153$	−7.27567	−	0.227463i	−0.588203	−	0.0183893i
$154$		0			0
$155$	−7.98747	−	10.1569i	−0.641569	−	0.815822i
$156$		0			0
$157$	−0.761451	−	15.9848i	−0.0607704	−	1.27573i	−0.799063	−	0.601247i	$-0.794671\pi$
$157$	−0.761451	−	15.9848i	−0.0607704	−	1.27573i	0.738293	−	0.674480i	$-0.235632\pi$
$158$		0			0
$159$	3.05910	−	1.79967i	0.242602	−	0.142723i
$160$		0			0
$161$	0.876106	+	6.09345i	0.0690469	+	0.480231i
$162$		0			0
$163$	−4.69557	−	8.13297i	−0.367786	−	0.637023i	0.621433	−	0.783467i	$-0.286551\pi$
$163$	−4.69557	−	8.13297i	−0.367786	−	0.637023i	−0.989219	+	0.146444i	$0.953217\pi$
$164$		0			0
$165$	6.31431	−	0.352535i	0.491569	−	0.0274448i
$166$		0			0
$167$	−1.98924	−	1.41653i	−0.153932	−	0.109615i	0.500496	−	0.865739i	$-0.333151\pi$
$167$	−1.98924	−	1.41653i	−0.153932	−	0.109615i	−0.654428	+	0.756124i	$0.727090\pi$
$168$		0			0
$169$	0.603684	−	12.6729i	0.0464373	−	0.974838i
$170$		0			0
$171$	−12.7303	−	6.30171i	−0.973513	−	0.481904i
$172$		0			0
$173$	5.71849	+	1.38729i	0.434769	+	0.105474i	0.447169	−	0.894449i	$-0.352432\pi$
$173$	5.71849	+	1.38729i	0.434769	+	0.105474i	−0.0124006	+	0.999923i	$0.503947\pi$
$174$		0			0
$175$	0.595050	−	3.08741i	0.0449815	−	0.233386i
$176$		0			0
$177$	−3.25295	+	0.337470i	−0.244506	+	0.0253658i
$178$		0			0
$179$	−5.21601	−	3.35213i	−0.389863	−	0.250550i	0.330995	−	0.943633i	$-0.392616\pi$
$179$	−5.21601	−	3.35213i	−0.389863	−	0.250550i	−0.720858	+	0.693083i	$0.756252\pi$
$180$		0			0
$181$	−14.7417	−	7.59988i	−1.09574	−	0.564895i	−0.187046	−	0.982351i	$-0.559891\pi$
$181$	−14.7417	−	7.59988i	−1.09574	−	0.564895i	−0.908697	+	0.417457i	$0.862922\pi$
$182$		0			0
$183$	10.8001	+	6.81672i	0.798367	+	0.503907i
$184$		0			0
$185$	14.7136	+	11.5709i	1.08177	+	0.850710i
$186$		0			0
$187$	2.43368	−	2.10880i	0.177968	−	0.154211i
$188$		0			0
$189$	5.72241	+	2.77468i	0.416244	+	0.201829i
$190$		0			0
$191$	−9.03973	+	4.66031i	−0.654092	+	0.337208i	−0.753126	−	0.657876i	$-0.771455\pi$
$191$	−9.03973	+	4.66031i	−0.654092	+	0.337208i	0.0990340	+	0.995084i	$0.468425\pi$
$192$		0			0
$193$	−13.2949	+	3.90374i	−0.956989	+	0.280997i	−0.722694	−	0.691168i	$-0.757096\pi$
$193$	−13.2949	+	3.90374i	−0.956989	+	0.280997i	−0.234295	+	0.972165i	$0.575278\pi$
$194$		0			0
$195$	−1.12678	−	2.41487i	−0.0806903	−	0.172933i
$196$		0			0
$197$	−1.26789	+	3.66332i	−0.0903332	+	0.261001i	−0.981113	−	0.193434i	$-0.938037\pi$
$197$	−1.26789	+	3.66332i	−0.0903332	+	0.261001i	0.890780	+	0.454435i	$0.150159\pi$
$198$		0			0
$199$	0.123476	+	0.173398i	0.00875298	+	0.0122918i	0.818929	−	0.573894i	$-0.194568\pi$
$199$	0.123476	+	0.173398i	0.00875298	+	0.0122918i	−0.810176	+	0.586186i	$0.800629\pi$
$200$		0			0
$201$	−9.65903	+	10.3780i	−0.681296	+	0.732008i
$202$		0			0
$203$	1.95568	+	2.74637i	0.137262	+	0.192757i
$204$		0			0
$205$	−0.800629	+	2.31327i	−0.0559184	+	0.161565i
$206$		0			0
$207$	−14.3385	−	4.70158i	−0.996593	−	0.326783i
$208$		0			0
$209$	6.02940	−	1.77039i	0.417062	−	0.122460i
$210$		0			0
$211$	10.1272	−	5.22092i	0.697183	−	0.359423i	−0.0729238	−	0.997338i	$-0.523233\pi$
$211$	10.1272	−	5.22092i	0.697183	−	0.359423i	0.770107	+	0.637915i	$0.220203\pi$
$212$		0			0
$213$	−1.75630	+	3.10024i	−0.120339	+	0.212425i
$214$		0			0
$215$	−2.64267	+	2.28989i	−0.180229	+	0.156169i
$216$		0			0
$217$	4.51847	+	3.55336i	0.306734	+	0.241218i
$218$		0			0
$219$	−4.69037	+	7.43120i	−0.316946	+	0.502154i
$220$		0			0
$221$	−1.20607	−	0.621772i	−0.0811290	−	0.0418249i
$222$		0			0
$223$	11.9839	+	7.70158i	0.802501	+	0.515736i	0.876431	−	0.481528i	$-0.159918\pi$
$223$	11.9839	+	7.70158i	0.802501	+	0.515736i	−0.0739303	+	0.997263i	$0.523554\pi$
$224$		0			0
$225$	6.13519	+	4.66450i	0.409012	+	0.310967i
$226$		0			0
$227$	−5.18582	+	26.9066i	−0.344195	+	1.78585i	0.236397	+	0.971657i	$0.424033\pi$
$227$	−5.18582	+	26.9066i	−0.344195	+	1.78585i	−0.580592	+	0.814195i	$0.697179\pi$
$228$		0			0
$229$	−1.41830	−	0.344077i	−0.0937242	−	0.0227372i	0.188623	−	0.982050i	$-0.439598\pi$
$229$	−1.41830	−	0.344077i	−0.0937242	−	0.0227372i	−0.282347	+	0.959312i	$0.591113\pi$
$230$		0			0
$231$	−2.69287	+	0.814664i	−0.177178	+	0.0536010i
$232$		0			0
$233$	−1.05818	+	22.2139i	−0.0693235	+	1.45528i	0.649646	+	0.760237i	$0.274917\pi$
$233$	−1.05818	+	22.2139i	−0.0693235	+	1.45528i	−0.718969	+	0.695042i	$0.755386\pi$
$234$		0			0
$235$	−2.55463	−	1.81914i	−0.166645	−	0.118668i
$236$		0			0
$237$	0.729874	+	13.0729i	0.0474104	+	0.849176i
$238$		0			0
$239$	4.21922	+	7.30790i	0.272919	+	0.472709i	0.969608	−	0.244664i	$-0.0786777\pi$
$239$	4.21922	+	7.30790i	0.272919	+	0.472709i	−0.696689	+	0.717373i	$0.745344\pi$
$240$		0			0
$241$	−0.999176	−	6.94942i	−0.0643626	−	0.447651i	−0.996364	−	0.0851972i	$-0.972848\pi$
$241$	−0.999176	−	6.94942i	−0.0643626	−	0.447651i	0.932002	−	0.362454i	$-0.118061\pi$
$242$		0			0
$243$	−12.3180	+	9.55342i	−0.790198	+	0.612852i
$244$		0			0
$245$	−0.720253	−	15.1200i	−0.0460153	−	0.965980i
$246$		0			0
$247$	−1.63681	−	2.08137i	−0.104148	−	0.132434i
$248$		0			0
$249$	−11.6813	−	13.2603i	−0.740269	−	0.840339i
$250$		0			0
$251$	−1.04387	−	3.01606i	−0.0658885	−	0.190372i	0.907251	−	0.420591i	$-0.138177\pi$
$251$	−1.04387	−	3.01606i	−0.0658885	−	0.190372i	−0.973139	+	0.230218i	$0.926056\pi$
$252$		0			0
$253$	6.07218	−	2.77307i	0.381755	−	0.174342i
$254$		0			0
$255$	11.5619	−	0.0945009i	0.724035	−	0.00591788i
$256$		0			0
$257$	7.84302	+	19.5909i	0.489234	+	1.22205i	0.943557	+	0.331210i	$0.107457\pi$
$257$	7.84302	+	19.5909i	0.489234	+	1.22205i	−0.454323	+	0.890837i	$0.650119\pi$
$258$		0			0
$259$	−7.57467	−	3.45923i	−0.470667	−	0.214946i
$260$		0			0
$261$	−8.15973	+	1.30967i	−0.505075	+	0.0810663i
$262$		0			0
$263$	14.4057	+	2.07122i	0.888291	+	0.127717i	0.571329	−	0.820721i	$-0.306428\pi$
$263$	14.4057	+	2.07122i	0.888291	+	0.127717i	0.316962	+	0.948438i	$0.397337\pi$
$264$		0			0
$265$	−4.74260	+	3.04789i	−0.291336	+	0.187230i
$266$		0			0
$267$	−17.8260	−	16.7210i	−1.09093	−	1.02331i
$268$		0			0
$269$			2.11390i			0.128887i	0.997921	+	0.0644433i	$0.0205272\pi$
$269$			2.11390i			0.128887i	−0.997921	+	0.0644433i	$0.979473\pi$
$270$		0			0
$271$	14.4161	+	22.4319i	0.875715	+	1.36264i	0.931326	+	0.364186i	$0.118653\pi$
$271$	14.4161	+	22.4319i	0.875715	+	1.36264i	−0.0556111	+	0.998453i	$0.517711\pi$
$272$		0			0
$273$	0.740412	+	0.925836i	0.0448118	+	0.0560341i
$274$		0			0
$275$	−3.39403	+	0.324091i	−0.204668	+	0.0195434i
$276$		0			0
$277$	−7.66671	+	16.7878i	−0.460648	+	1.00868i	0.526691	+	0.850057i	$0.323432\pi$
$277$	−7.66671	+	16.7878i	−0.460648	+	1.00868i	−0.987339	+	0.158622i	$0.949295\pi$
$278$		0			0
$279$	−12.7193	+	6.06192i	−0.761486	+	0.362918i
$280$		0			0
$281$	−12.0772	+	11.5156i	−0.720465	+	0.686962i	−0.958756	−	0.284232i	$-0.908261\pi$
$281$	−12.0772	+	11.5156i	−0.720465	+	0.686962i	0.238291	+	0.971194i	$0.423413\pi$
$282$		0			0
$283$	8.00553	+	17.5297i	0.475879	+	1.04203i	0.983576	+	0.180494i	$0.0577697\pi$
$283$	8.00553	+	17.5297i	0.475879	+	1.04203i	−0.507697	+	0.861536i	$0.669503\pi$
$284$		0			0
$285$	20.5996	+	9.20481i	1.22022	+	0.545246i
$286$		0			0
$287$	0.103515	−	1.08406i	0.00611030	−	0.0639899i
$288$		0			0
$289$	−8.73504	+	6.86931i	−0.513826	+	0.404077i
$290$		0			0
$291$	21.0978	−	24.7540i	1.23677	−	1.45111i
$292$		0			0
$293$	7.87807	−	26.8302i	0.460242	−	1.56744i	−0.323423	−	0.946254i	$-0.604834\pi$
$293$	7.87807	−	26.8302i	0.460242	−	1.56744i	0.783665	−	0.621184i	$-0.213348\pi$
$294$		0			0
$295$	5.14182	−	0.739283i	0.299369	−	0.0430427i
$296$		0			0
$297$	1.13868	−	6.80144i	0.0660732	−	0.394660i
$298$		0			0
$299$	−2.03574	−	1.94108i	−0.117730	−	0.112255i
$300$		0			0
$301$	0.902332	−	1.26715i	0.0520096	−	0.0730372i
$302$		0			0
$303$	−0.782157	−	0.806992i	−0.0449338	−	0.0463605i
$304$		0			0
$305$	−17.5683	−	10.1431i	−1.00596	−	0.580790i
$306$		0			0
$307$	1.28221	−	5.28532i	0.0731793	−	0.301649i	−0.923447	−	0.383727i	$-0.874640\pi$
$307$	1.28221	−	5.28532i	0.0731793	−	0.301649i	0.996626	+	0.0820776i	$0.0261555\pi$
$308$		0			0
$309$	−13.4666	+	9.75635i	−0.766086	+	0.555019i
$310$		0			0
$311$	17.5738	−	20.2813i	0.996519	−	1.15004i	0.00784489	−	0.999969i	$-0.497503\pi$
$311$	17.5738	−	20.2813i	0.996519	−	1.15004i	0.988675	−	0.150075i	$-0.0479517\pi$
$312$		0			0
$313$	−6.64992	+	10.3475i	−0.375876	+	0.584874i	−0.976727	−	0.214487i	$-0.931192\pi$
$313$	−6.64992	+	10.3475i	−0.375876	+	0.584874i	0.600851	+	0.799361i	$0.294828\pi$
$314$		0			0
$315$	−9.25611	−	4.04560i	−0.521523	−	0.227944i
$316$		0			0
$317$	4.27531	+	22.1824i	0.240126	+	1.24589i	0.879091	+	0.476654i	$0.158151\pi$
$317$	4.27531	+	22.1824i	0.240126	+	1.24589i	−0.638965	+	0.769236i	$0.720637\pi$
$318$		0			0
$319$	2.25996	−	2.87377i	0.126533	−	0.160900i
$320$		0			0
$321$	1.13625	−	28.8045i	0.0634195	−	1.60771i
$322$		0			0
$323$	11.1649	−	2.70858i	0.621234	−	0.150710i
$324$		0			0
$325$	0.658312	+	1.27695i	0.0365166	+	0.0708323i
$326$		0			0
$327$	6.02691	+	3.04500i	0.333289	+	0.168389i
$328$		0			0
$329$	1.29523	+	0.518531i	0.0714082	+	0.0285875i
$330$		0			0
$331$	−14.2369	−	4.92743i	−0.782529	−	0.270836i	−0.0935477	−	0.995615i	$-0.529821\pi$
$331$	−14.2369	−	4.92743i	−0.782529	−	0.270836i	−0.688982	+	0.724779i	$0.741942\pi$
$332$		0			0
$333$	15.8359	−	12.8780i	0.867804	−	0.705708i
$334$		0			0
$335$	14.6807	−	17.0763i	0.802092	−	0.932979i
$336$		0			0
$337$	−0.383661	+	0.273204i	−0.0208993	+	0.0148824i	−0.590459	−	0.807068i	$-0.701053\pi$
$337$	−0.383661	+	0.273204i	−0.0208993	+	0.0148824i	0.569560	+	0.821950i	$0.307114\pi$
$338$		0			0
$339$	5.23613	+	9.95604i	0.284388	+	0.540738i
$340$		0			0
$341$	2.31665	−	5.78671i	0.125454	−	0.313368i
$342$		0			0
$343$	4.31090	+	14.6816i	0.232767	+	0.792730i
$344$		0			0
$345$	23.0518	+	6.56446i	1.24107	+	0.353419i
$346$		0			0
$347$	−6.14122	−	25.3145i	−0.329678	−	1.35895i	−0.859627	−	0.510922i	$-0.829304\pi$
$347$	−6.14122	−	25.3145i	−0.329678	−	1.35895i	0.529949	−	0.848029i	$-0.322211\pi$
$348$		0			0
$349$	−6.63358	−	7.65556i	−0.355088	−	0.409793i	0.549900	−	0.835230i	$-0.314666\pi$
$349$	−6.63358	−	7.65556i	−0.355088	−	0.409793i	−0.904988	+	0.425437i	$0.860120\pi$
$350$		0			0
$351$	−2.83897	+	0.619721i	−0.151533	+	0.0330782i
$352$		0			0
$353$	18.5420	−	3.57367i	0.986889	−	0.190207i	0.329825	−	0.944042i	$-0.393010\pi$
$353$	18.5420	−	3.57367i	0.986889	−	0.190207i	0.657064	+	0.753835i	$0.271798\pi$
$354$		0			0
$355$	2.59342	−	5.03054i	0.137645	−	0.266993i
$356$		0			0
$357$	−4.98861	+	1.25348i	−0.264025	+	0.0663414i
$358$		0			0
$359$	23.8703	+	20.6837i	1.25983	+	1.09165i	0.991742	+	0.128250i	$0.0409361\pi$
$359$	23.8703	+	20.6837i	1.25983	+	1.09165i	0.268085	+	0.963395i	$0.413609\pi$
$360$		0			0
$361$	3.35742	+	0.647090i	0.176706	+	0.0340574i
$362$		0			0
$363$	−8.76097	−	13.3904i	−0.459832	−	0.702815i
$364$		0			0
$365$	6.97911	−	12.0882i	0.365303	−	0.632724i
$366$		0			0
$367$	5.04928	+	0.240527i	0.263570	+	0.0125554i	0.178951	−	0.983858i	$-0.442730\pi$
$367$	5.04928	+	0.240527i	0.263570	+	0.0125554i	0.0846192	+	0.996413i	$0.473033\pi$
$368$		0			0
$369$	2.26884	+	1.40623i	0.118111	+	0.0732053i
$370$		0			0
$371$	1.73069	−	1.81509i	0.0898529	−	0.0942350i
$372$		0			0
$373$	10.8855	−	6.28474i	0.563630	−	0.325412i	−0.190971	−	0.981596i	$-0.561164\pi$
$373$	10.8855	−	6.28474i	0.563630	−	0.325412i	0.754601	+	0.656184i	$0.227830\pi$
$374$		0			0
$375$	9.49077	+	6.64212i	0.490101	+	0.342998i
$376$		0			0
$377$	−1.47811	−	0.434012i	−0.0761265	−	0.0223528i
$378$		0			0
$379$	22.0364	−	1.04972i	1.13194	−	0.0539207i	0.526761	−	0.850014i	$-0.323406\pi$
$379$	22.0364	−	1.04972i	1.13194	−	0.0539207i	0.605174	+	0.796093i	$0.293103\pi$
$380$		0			0
$381$	0.487628	−	5.58906i	0.0249819	−	0.286336i
$382$		0			0
$383$	−14.1261	−	1.34888i	−0.721811	−	0.0689246i	−0.272317	−	0.962208i	$-0.587790\pi$
$383$	−14.1261	−	1.34888i	−0.721811	−	0.0689246i	−0.449495	+	0.893283i	$0.648396\pi$
$384$		0			0
$385$	4.22302	−	1.46160i	0.215225	−	0.0744901i
$386$		0			0
$387$	1.80239	+	3.36012i	0.0916204	+	0.170805i
$388$		0			0
$389$	−24.8341	−	26.0452i	−1.25914	−	1.32055i	−0.925931	−	0.377692i	$-0.876718\pi$
$389$	−24.8341	−	26.0452i	−1.25914	−	1.32055i	−0.333206	−	0.942854i	$-0.608131\pi$
$390$		0			0
$391$	11.3303	−	4.53597i	0.572998	−	0.229394i
$392$		0			0
$393$	28.6568	−	11.7451i	1.44554	−	0.592463i
$394$		0			0
$395$	−1.97691	−	20.7031i	−0.0994689	−	1.04169i
$396$		0			0
$397$	0.691067	−	4.80647i	0.0346836	−	0.241230i	−0.965103	−	0.261869i	$-0.915661\pi$
$397$	0.691067	−	4.80647i	0.0346836	−	0.241230i	0.999787	+	0.0206393i	$0.00657015\pi$
$398$		0			0
$399$	−9.87119	−	1.81897i	−0.494178	−	0.0910623i
$400$		0			0
$401$	−12.6244			−0.630431			−0.315215	−	0.949020i	$-0.602077\pi$
$401$	−12.6244			−0.630431			−0.315215	+	0.949020i	$0.602077\pi$
$402$		0			0
$403$	−2.62650			−0.130835
$404$		0			0
$405$	18.9525	−	15.9340i	0.941756	−	0.791768i
$406$		0			0
$407$	−1.28505	+	8.93772i	−0.0636976	+	0.443026i
$408$		0			0
$409$	2.55467	+	26.7538i	0.126321	+	1.32289i	0.807106	+	0.590406i	$0.201032\pi$
$409$	2.55467	+	26.7538i	0.126321	+	1.32289i	−0.680786	+	0.732482i	$0.738362\pi$
$410$		0			0
$411$	−2.81849	−	6.87680i	−0.139026	−	0.339208i
$412$		0			0
$413$	−2.14541	+	0.858893i	−0.105569	+	0.0422634i
$414$		0			0
$415$	19.3702	+	20.3149i	0.950848	+	0.997221i
$416$		0			0
$417$	−1.29849	+	3.85334i	−0.0635872	+	0.188699i
$418$		0			0
$419$	−2.18948	+	0.757785i	−0.106963	+	0.0370202i	−0.380025	−	0.924976i	$-0.624085\pi$
$419$	−2.18948	+	0.757785i	−0.106963	+	0.0370202i	0.273062	+	0.961996i	$0.411963\pi$
$420$		0			0
$421$	−17.5179	−	1.67276i	−0.853771	−	0.0815253i	−0.341013	−	0.940059i	$-0.610770\pi$
$421$	−17.5179	−	1.67276i	−0.853771	−	0.0815253i	−0.512758	+	0.858533i	$0.671376\pi$
$422$		0			0
$423$	−2.54754	+	2.28142i	−0.123866	+	0.110927i
$424$		0			0
$425$	−6.22640	+	0.296600i	−0.302025	+	0.0143872i
$426$		0			0
$427$	8.65907	+	2.54253i	0.419042	+	0.123042i
$428$		0			0
$429$	0.737075	−	1.05319i	0.0355863	−	0.0508485i
$430$		0			0
$431$	5.42894	−	3.13440i	0.261503	−	0.150979i	−0.363517	−	0.931588i	$-0.618424\pi$
$431$	5.42894	−	3.13440i	0.261503	−	0.150979i	0.625020	+	0.780609i	$0.285091\pi$
$432$		0			0
$433$	−27.1057	+	28.4277i	−1.30262	+	1.36615i	−0.412140	+	0.911121i	$0.635218\pi$
$433$	−27.1057	+	28.4277i	−1.30262	+	1.36615i	−0.890478	+	0.455026i	$0.849630\pi$
$434$		0			0
$435$	12.8688	−	2.58952i	0.617012	−	0.124158i
$436$		0			0
$437$	23.7889	+	1.13321i	1.13798	+	0.0542086i
$438$		0			0
$439$	−19.9893	+	34.6225i	−0.954037	+	1.65244i	−0.217480	+	0.976065i	$0.569784\pi$
$439$	−19.9893	+	34.6225i	−0.954037	+	1.65244i	−0.736557	+	0.676376i	$0.763549\pi$
$440$		0			0
$441$	−16.2567	−	2.85846i	−0.774130	−	0.136117i
$442$		0			0
$443$	−18.8957	−	3.64184i	−0.897760	−	0.173029i	−0.280561	−	0.959836i	$-0.590521\pi$
$443$	−18.8957	−	3.64184i	−0.897760	−	0.173029i	−0.617199	+	0.786807i	$0.711733\pi$
$444$		0			0
$445$	29.3396	+	25.4229i	1.39083	+	1.20516i
$446$		0			0
$447$	−0.438923	−	1.74682i	−0.0207603	−	0.0826220i
$448$		0			0
$449$	13.2613	−	25.7233i	0.625839	−	1.21396i	−0.336391	−	0.941722i	$-0.609206\pi$
$449$	13.2613	−	25.7233i	0.625839	−	1.21396i	0.962230	−	0.272236i	$-0.0877632\pi$
$450$		0			0
$451$	−1.15951	+	0.223478i	−0.0545994	+	0.0105232i
$452$		0			0
$453$	20.0162	−	3.04508i	0.940444	−	0.143070i
$454$		0			0
$455$	−1.23312	−	1.42310i	−0.0578095	−	0.0667157i
$456$		0			0
$457$	−4.23176	−	17.4436i	−0.197954	−	0.815975i	−0.980999	−	0.194011i	$-0.937850\pi$
$457$	−4.23176	−	17.4436i	−0.197954	−	0.815975i	0.783046	−	0.621964i	$-0.213665\pi$
$458$		0			0
$459$	2.67115	−	12.3218i	0.124679	−	0.575132i
$460$		0			0
$461$	−7.60647	−	25.9052i	−0.354268	−	1.20653i	−0.923257	−	0.384182i	$-0.874483\pi$
$461$	−7.60647	−	25.9052i	−0.354268	−	1.20653i	0.568989	−	0.822345i	$-0.307335\pi$
$462$		0			0
$463$	−15.6598	+	39.1164i	−0.727774	+	1.81789i	−0.174985	+	0.984571i	$0.555988\pi$
$463$	−15.6598	+	39.1164i	−0.727774	+	1.81789i	−0.552789	+	0.833321i	$0.686436\pi$
$464$		0			0
$465$	19.8081	−	10.4176i	0.918579	−	0.483104i
$466$		0			0
$467$	0.478506	−	0.340743i	0.0221426	−	0.0157677i	−0.568932	−	0.822385i	$-0.692643\pi$
$467$	0.478506	−	0.340743i	0.0221426	−	0.0157677i	0.591075	+	0.806617i	$0.298704\pi$
$468$		0			0
$469$	−4.55587	+	8.92228i	−0.210370	+	0.411993i
$470$		0			0
$471$	27.4671	+	3.72030i	1.26562	+	0.171422i
$472$		0			0
$473$	−1.59404	−	0.551704i	−0.0732942	−	0.0253674i
$474$		0			0
$475$	−11.2926	−	4.52089i	−0.518141	−	0.207433i
$476$		0			0
$477$	2.10531	+	5.77566i	0.0963955	+	0.264449i
$478$		0			0
$479$	9.48141	+	18.3914i	0.433217	+	0.840323i	0.999866	+	0.0163640i	$0.00520905\pi$
$479$	9.48141	+	18.3914i	0.433217	+	0.840323i	−0.566650	+	0.823959i	$0.691761\pi$
$480$		0			0
$481$	3.69758	−	0.897022i	0.168595	−	0.0409007i
$482$		0			0
$483$	−10.6544	−	0.420285i	−0.484793	−	0.0191236i
$484$		0			0
$485$	−31.9357	+	40.6096i	−1.45013	+	1.84399i
$486$		0			0
$487$	2.22781	+	11.5590i	0.100952	+	0.523787i	0.996835	+	0.0794976i	$0.0253316\pi$
$487$	2.22781	+	11.5590i	0.100952	+	0.523787i	−0.895883	+	0.444289i	$0.853456\pi$
$488$		0			0
$489$	15.3273	−	5.44552i	0.693126	−	0.246255i
$490$		0			0
$491$	−14.6960	+	22.8674i	−0.663222	+	1.03199i	0.332810	+	0.942994i	$0.392003\pi$
$491$	−14.6960	+	22.8674i	−0.663222	+	1.03199i	−0.996032	+	0.0889991i	$0.971633\pi$
$492$		0			0
$493$	4.37714	−	5.05149i	0.197137	−	0.227508i
$494$		0			0
$495$	−1.38145	+	10.8663i	−0.0620914	+	0.488403i
$496$		0			0
$497$	−0.593597	+	2.44684i	−0.0266265	+	0.109756i
$498$		0			0
$499$	−10.1839	−	5.87965i	−0.455892	−	0.263209i	0.254423	−	0.967093i	$-0.418114\pi$
$499$	−10.1839	−	5.87965i	−0.455892	−	0.263209i	−0.710315	+	0.703884i	$0.751448\pi$
$500$		0			0
$501$	3.03727	−	2.94380i	0.135695	−	0.131519i
$502$		0			0
$503$	0.482854	−	0.678074i	0.0215294	−	0.0302338i	−0.803671	−	0.595074i	$-0.797123\pi$
$503$	0.482854	−	0.678074i	0.0215294	−	0.0302338i	0.825200	+	0.564840i	$0.191062\pi$
$504$		0			0
$505$	1.29193	+	1.23186i	0.0574903	+	0.0548169i
$506$		0			0
$507$	21.3972	+	5.00608i	0.950282	+	0.222328i
$508$		0			0
$509$	−21.3596	+	3.07105i	−0.946749	+	0.136122i	−0.598359	−	0.801228i	$-0.704180\pi$
$509$	−21.3596	+	3.07105i	−0.946749	+	0.136122i	−0.348390	+	0.937350i	$0.613271\pi$
$510$		0			0
$511$	−1.74943	+	5.95802i	−0.0773904	+	0.263567i
$512$		0			0
$513$	14.7300	−	19.7065i	0.650345	−	0.870064i
$514$		0			0
$515$	20.7628	−	16.3280i	0.914917	−	0.719499i
$516$		0			0
$517$	0.143806	−	1.50601i	0.00632460	−	0.0662342i
$518$		0			0
$519$	−4.15800	+	9.30527i	−0.182516	+	0.408456i
$520$		0			0
$521$	11.9834	+	26.2401i	0.525004	+	1.14960i	0.967510	+	0.252833i	$0.0813624\pi$
$521$	11.9834	+	26.2401i	0.525004	+	1.14960i	−0.442506	+	0.896766i	$0.645910\pi$
$522$		0			0
$523$	18.3875	−	17.5325i	0.804031	−	0.766642i	−0.171808	−	0.985130i	$-0.554961\pi$
$523$	18.3875	−	17.5325i	0.804031	−	0.766642i	0.975840	+	0.218488i	$0.0701125\pi$
$524$		0			0
$525$	5.07224	+	1.98267i	0.221371	+	0.0865309i
$526$		0			0
$527$	4.73409	−	10.3662i	0.206220	−	0.451559i
$528$		0			0
$529$	2.28921	−	0.218593i	0.0995309	−	0.00950405i
$530$		0			0
$531$	0.446202	−	5.64691i	0.0193635	−	0.245055i
$532$		0			0
$533$	0.269011	+	0.418589i	0.0116522	+	0.0181311i
$534$		0			0
$535$			45.7886i			1.97961i
$536$		0			0
$537$	7.34713	−	7.83264i	0.317052	−	0.338004i
$538$		0			0
$539$	6.14289	−	3.94780i	0.264593	−	0.170044i
$540$		0			0
$541$	21.6401	+	3.11138i	0.930382	+	0.133769i	0.590809	−	0.806811i	$-0.298809\pi$
$541$	21.6401	+	3.11138i	0.930382	+	0.133769i	0.339572	+	0.940580i	$0.389718\pi$
$542$		0			0
$543$	17.5726	−	22.7252i	0.754111	−	0.975230i
$544$		0			0
$545$	−9.75632	−	4.45556i	−0.417915	−	0.190855i
$546$		0			0
$547$	−10.0117	−	25.0080i	−0.428070	−	1.06927i	−0.973004	−	0.230788i	$-0.925870\pi$
$547$	−10.0117	−	25.0080i	−0.428070	−	1.06927i	0.544934	−	0.838479i	$-0.316555\pi$
$548$		0			0
$549$	−15.0014	+	16.2570i	−0.640243	+	0.693830i
$550$		0			0
$551$	11.8646	−	5.41839i	0.505450	−	0.230831i
$552$		0			0
$553$	3.02604	+	8.74317i	0.128680	+	0.371797i
$554$		0			0
$555$	−24.3279	+	21.4309i	−1.03266	+	0.909690i
$556$		0			0
$557$	0.432284	+	0.549693i	0.0183164	+	0.0232913i	0.795125	−	0.606446i	$-0.207405\pi$
$557$	0.432284	+	0.549693i	0.0183164	+	0.0232913i	−0.776809	+	0.629737i	$0.783163\pi$
$558$		0			0
$559$	0.0338201	+	0.709972i	0.00143044	+	0.0300286i
$560$		0			0
$561$	2.82818	+	4.80738i	0.119406	+	0.202968i
$562$		0			0
$563$	2.63758	+	18.3448i	0.111161	+	0.773141i	0.966794	+	0.255558i	$0.0822590\pi$
$563$	2.63758	+	18.3448i	0.111161	+	0.773141i	−0.855633	+	0.517583i	$0.826832\pi$
$564$		0			0
$565$	−8.93392	−	15.4740i	−0.375853	−	0.650996i
$566$		0			0
$567$	−6.52248	+	8.87647i	−0.273918	+	0.372777i
$568$		0			0
$569$	−13.6750	−	9.73792i	−0.573285	−	0.408235i	0.256314	−	0.966594i	$-0.417492\pi$
$569$	−13.6750	−	9.73792i	−0.573285	−	0.408235i	−0.829600	+	0.558359i	$0.811431\pi$
$570$		0			0
$571$	−0.974025	+	20.4473i	−0.0407617	+	0.855693i	0.882217	+	0.470842i	$0.156050\pi$
$571$	−0.974025	+	20.4473i	−0.0407617	+	0.855693i	−0.922979	+	0.384850i	$0.874253\pi$
$572$		0			0
$573$	−5.10084	−	16.8608i	−0.213091	−	0.704371i
$574$		0			0
$575$	−12.5575	−	3.04642i	−0.523685	−	0.127045i
$576$		0			0
$577$	0.506839	−	2.62973i	0.0211000	−	0.109477i	−0.969852	−	0.243696i	$-0.921640\pi$
$577$	0.506839	−	2.62973i	0.0211000	−	0.109477i	0.990952	+	0.134218i	$0.0428524\pi$
$578$		0			0
$579$	−2.47650	−	23.8715i	−0.102920	−	0.992066i
$580$		0			0
$581$	−10.5049	−	6.75111i	−0.435818	−	0.280083i
$582$		0			0
$583$	−2.41721	−	1.24616i	−0.100110	−	0.0516105i
$584$		0			0
$585$	4.46710	−	1.16134i	0.184692	−	0.0480156i
$586$		0			0
$587$	32.5963	+	25.6340i	1.34539	+	1.05803i	0.992484	+	0.122371i	$0.0390496\pi$
$587$	32.5963	+	25.6340i	1.34539	+	1.05803i	0.352908	+	0.935658i	$0.385193\pi$
$588$		0			0
$589$	16.8065	−	14.5629i	0.692501	−	0.600055i
$590$		0			0
$591$	−5.84203	−	3.30953i	−0.240309	−	0.136136i
$592$		0			0
$593$	36.1310	−	18.6268i	1.48372	−	0.764912i	0.489474	−	0.872018i	$-0.337189\pi$
$593$	36.1310	−	18.6268i	1.48372	−	0.764912i	0.994248	+	0.107106i	$0.0341584\pi$
$594$		0			0
$595$	7.83926	−	2.30181i	0.321378	−	0.0943652i
$596$		0			0
$597$	−0.334118	+	0.155899i	−0.0136745	+	0.00638054i
$598$		0			0
$599$	−5.35408	+	15.4696i	−0.218762	+	0.632071i	0.781208	+	0.624271i	$0.214604\pi$
$599$	−5.35408	+	15.4696i	−0.218762	+	0.632071i	−0.999970	+	0.00779958i	$0.997517\pi$
$600$		0			0
$601$	−16.4721	−	23.1319i	−0.671912	−	0.943569i	0.328087	−	0.944647i	$-0.393596\pi$
$601$	−16.4721	−	23.1319i	−0.671912	−	0.943569i	−0.999999	+	0.00107875i	$0.999657\pi$
$602$		0			0
$603$	−14.6458	−	19.7104i	−0.596424	−	0.802669i
$604$		0			0
$605$	14.7434	+	20.7043i	0.599406	+	0.841748i
$606$		0			0
$607$	−3.91860	+	11.3220i	−0.159051	+	0.459548i	−0.996166	−	0.0874786i	$-0.972119\pi$
$607$	−3.91860	+	11.3220i	−0.159051	+	0.459548i	0.837115	+	0.547026i	$0.184240\pi$
$608$		0			0
$609$	−5.29194	+	2.46922i	−0.214440	+	0.100058i
$610$		0			0
$611$	−0.611653	+	0.179598i	−0.0247448	+	0.00726574i
$612$		0			0
$613$	10.0645	−	5.18862i	0.406502	−	0.209566i	−0.242834	−	0.970068i	$-0.578077\pi$
$613$	10.0645	−	5.18862i	0.406502	−	0.209566i	0.649336	+	0.760501i	$0.275047\pi$
$614$		0			0
$615$	−3.68905	−	2.08986i	−0.148757	−	0.0842713i
$616$		0			0
$617$	−9.49940	+	8.23127i	−0.382431	+	0.331379i	−0.824769	−	0.565470i	$-0.808695\pi$
$617$	−9.49940	+	8.23127i	−0.382431	+	0.331379i	0.442338	+	0.896849i	$0.354149\pi$
$618$		0			0
$619$	−27.4773	−	21.6084i	−1.10441	−	0.868515i	−0.112270	−	0.993678i	$-0.535812\pi$
$619$	−27.4773	−	21.6084i	−1.10441	−	0.868515i	−0.992136	+	0.125163i	$0.960055\pi$
$620$		0			0
$621$	12.5091	−	22.9480i	0.501974	−	0.920872i
$622$		0			0
$623$	−15.3507	−	7.91382i	−0.615012	−	0.317061i
$624$		0			0
$625$	−26.2852	−	16.8925i	−1.05141	−	0.675698i
$626$		0			0
$627$	1.12312	+	10.8260i	0.0448531	+	0.432349i
$628$		0			0
$629$	−3.12429	+	16.2103i	−0.124573	+	0.646349i
$630$		0			0
$631$	−11.0020	−	2.66905i	−0.437982	−	0.106253i	0.0107043	−	0.999943i	$-0.496593\pi$
$631$	−11.0020	−	2.66905i	−0.437982	−	0.106253i	−0.448686	+	0.893690i	$0.648108\pi$
$632$		0			0
$633$	5.71444	+	18.8891i	0.227129	+	0.750774i
$634$		0			0
$635$	−0.424020	+	8.90127i	−0.0168267	+	0.353236i
$636$		0			0
$637$	−2.50635	−	1.78477i	−0.0993054	−	0.0707151i
$638$		0			0
$639$	−4.72960	−	3.96474i	−0.187100	−	0.156843i
$640$		0			0
$641$	−4.78783	−	8.29276i	−0.189108	−	0.327544i	0.755845	−	0.654750i	$-0.227226\pi$
$641$	−4.78783	−	8.29276i	−0.189108	−	0.327544i	−0.944953	+	0.327206i	$0.893893\pi$
$642$		0			0
$643$	5.98513	+	41.6275i	0.236031	+	1.64163i	0.671197	+	0.741279i	$0.265780\pi$
$643$	5.98513	+	41.6275i	0.236031	+	1.64163i	−0.435167	+	0.900350i	$0.643311\pi$
$644$		0			0
$645$	−3.07105	−	5.22021i	−0.120922	−	0.205546i
$646$		0			0
$647$	−1.36358	−	28.6251i	−0.0536079	−	1.12537i	−0.852106	−	0.523370i	$-0.824675\pi$
$647$	−1.36358	−	28.6251i	−0.0536079	−	1.12537i	0.798498	−	0.601998i	$-0.205628\pi$
$648$		0			0
$649$	1.54904	+	1.96977i	0.0608052	+	0.0773201i
$650$		0			0
$651$	−7.47097	+	6.58130i	−0.292810	+	0.257942i
$652$		0			0
$653$	3.80338	+	10.9891i	0.148838	+	0.430038i	0.994633	−	0.103470i	$-0.0329946\pi$
$653$	3.80338	+	10.9891i	0.148838	+	0.430038i	−0.845795	+	0.533508i	$0.820873\pi$
$654$		0			0
$655$	−44.7476	+	20.4356i	−1.74843	+	0.798483i
$656$		0			0
$657$	−11.1859	−	10.3220i	−0.436403	−	0.402698i
$658$		0			0
$659$	11.3100	+	28.2510i	0.440575	+	1.10050i	0.968011	+	0.250908i	$0.0807291\pi$
$659$	11.3100	+	28.2510i	0.440575	+	1.10050i	−0.527436	+	0.849595i	$0.676847\pi$
$660$		0			0
$661$	−22.5536	−	10.2999i	−0.877234	−	0.400619i	−0.0746864	−	0.997207i	$-0.523796\pi$
$661$	−22.5536	−	10.2999i	−0.877234	−	0.400619i	−0.802548	+	0.596588i	$0.796523\pi$
$662$		0			0
$663$	1.43767	−	1.85922i	0.0558346	−	0.0722063i
$664$		0			0
$665$	15.7811	+	2.26897i	0.611963	+	0.0879870i
$666$		0			0
$667$	11.6563	−	7.49107i	0.451335	−	0.290055i
$668$		0			0
$669$	−16.8802	+	17.9957i	−0.652625	+	0.695752i
$670$		0			0
$671$		−	9.78592i		−	0.377781i
$672$		0			0
$673$	−7.02204	−	10.9265i	−0.270680	−	0.421186i	0.679128	−	0.734020i	$-0.262358\pi$
$673$	−7.02204	−	10.9265i	−0.270680	−	0.421186i	−0.949808	+	0.312834i	$0.898722\pi$
$674$		0			0
$675$	−9.87110	+	8.98641i	−0.379939	+	0.345887i
$676$		0			0
$677$	−31.8794	+	3.04411i	−1.22522	+	0.116995i	−0.687537	−	0.726149i	$-0.741308\pi$
$677$	−31.8794	+	3.04411i	−1.22522	+	0.116995i	−0.537688	+	0.843144i	$0.680702\pi$
$678$		0			0
$679$	9.54748	−	20.9061i	0.366399	−	0.802302i
$680$		0			0
$681$	−44.2042	−	17.2788i	−1.69391	−	0.662127i
$682$		0			0
$683$	8.13714	−	7.75874i	0.311359	−	0.296880i	−0.518245	−	0.855232i	$-0.673415\pi$
$683$	8.13714	−	7.75874i	0.311359	−	0.296880i	0.829604	+	0.558352i	$0.188566\pi$
$684$		0			0
$685$	4.90394	+	10.7381i	0.187370	+	0.410283i
$686$		0			0
$687$	1.03127	−	2.30790i	0.0393454	−	0.0880519i
$688$		0			0
$689$	−0.108927	+	1.14074i	−0.00414980	+	0.0434587i
$690$		0			0
$691$	−20.8296	+	16.3806i	−0.792395	+	0.623147i	−0.930092	−	0.367328i	$-0.880273\pi$
$691$	−20.8296	+	16.3806i	−0.792395	+	0.623147i	0.137696	+	0.990475i	$0.456030\pi$
$692$		0			0
$693$	−0.542434	−	4.84267i	−0.0206054	−	0.183958i
$694$		0			0
$695$	1.81965	−	6.19718i	0.0690234	−	0.235072i
$696$		0			0
$697$	−2.13695	+	0.307247i	−0.0809429	+	0.0116378i
$698$		0			0
$699$	−37.5064	−	8.77499i	−1.41862	−	0.331901i
$700$		0			0
$701$	−23.1230	−	22.0477i	−0.873344	−	0.832732i	0.113645	−	0.993521i	$-0.463747\pi$
$701$	−23.1230	−	22.0477i	−0.873344	−	0.832732i	−0.986989	+	0.160790i	$0.948596\pi$
$702$		0			0
$703$	−18.6865	+	26.2416i	−0.704776	+	0.989720i
$704$		0			0
$705$	3.90052	−	3.78049i	0.146902	−	0.142381i
$706$		0			0
$707$	−0.687737	−	0.397065i	−0.0258650	−	0.0149332i
$708$		0			0
$709$	9.35642	−	38.5677i	0.351388	−	1.44844i	−0.472321	−	0.881427i	$-0.656584\pi$
$709$	9.35642	−	38.5677i	0.351388	−	1.44844i	0.823709	−	0.567013i	$-0.191901\pi$
$710$		0			0
$711$	−22.4971	−	2.86009i	−0.843707	−	0.107262i
$712$		0			0
$713$	15.4702	−	17.8536i	0.579363	−	0.668621i
$714$		0			0
$715$	−1.10392	+	1.71773i	−0.0412842	+	0.0642395i
$716$		0			0
$717$	−13.7724	+	4.89309i	−0.514340	+	0.182736i
$718$		0			0
$719$	9.00803	+	46.7381i	0.335943	+	1.74304i	0.620343	+	0.784331i	$0.286993\pi$
$719$	9.00803	+	46.7381i	0.335943	+	1.74304i	−0.284400	+	0.958706i	$0.591795\pi$
$720$		0			0
$721$	−7.26380	+	9.23667i	−0.270518	+	0.343992i
$722$		0			0
$723$	12.1511	+	0.479324i	0.451903	+	0.0178263i
$724$		0			0
$725$	−6.87741	+	1.66844i	−0.255420	+	0.0619643i
$726$		0			0
$727$	−6.14806	−	11.9256i	−0.228019	−	0.442295i	0.746875	−	0.664964i	$-0.231553\pi$
$727$	−6.14806	−	11.9256i	−0.228019	−	0.442295i	−0.974894	+	0.222669i	$0.928523\pi$
$728$		0			0
$729$	−12.4067	−	23.9807i	−0.459506	−	0.888175i
$730$		0			0
$731$	−2.86306	−	1.14620i	−0.105894	−	0.0423936i
$732$		0			0
$733$	40.6330	+	14.0632i	1.50081	+	0.519437i	0.949203	−	0.314664i	$-0.101892\pi$
$733$	40.6330	+	14.0632i	1.50081	+	0.519437i	0.551612	+	0.834101i	$0.314013\pi$
$734$		0			0
$735$	25.9810	+	3.51902i	0.958325	+	0.129801i
$736$		0			0
$737$	10.6748	+	2.01433i	0.393213	+	0.0741988i
$738$		0			0
$739$	10.6843	−	7.60824i	0.393028	−	0.279874i	−0.366410	−	0.930453i	$-0.619413\pi$
$739$	10.6843	−	7.60824i	0.393028	−	0.279874i	0.759438	+	0.650580i	$0.225474\pi$
$740$		0			0
$741$	4.05911	−	2.13479i	0.149115	−	0.0784234i
$742$		0			0
$743$	7.58373	−	18.9432i	0.278220	−	0.694960i	−0.721776	−	0.692127i	$-0.756674\pi$
$743$	7.58373	−	18.9432i	0.278220	−	0.694960i	0.999996	−	0.00283325i	$-0.000901852\pi$
$744$		0			0
$745$	0.806008	+	2.74501i	0.0295299	+	0.100569i
$746$		0			0
$747$	26.2538	−	15.7354i	0.960576	−	0.575727i
$748$		0			0
$749$	−4.80237	−	19.7956i	−0.175475	−	0.723317i
$750$		0			0
$751$	−9.68114	−	11.1726i	−0.353270	−	0.407695i	0.551104	−	0.834437i	$-0.314207\pi$
$751$	−9.68114	−	11.1726i	−0.353270	−	0.407695i	−0.904374	+	0.426742i	$0.859661\pi$
$752$		0			0
$753$	5.46513	−	0.831413i	0.199160	−	0.0302984i
$754$		0			0
$755$	−31.5783	+	6.08622i	−1.14925	+	0.221500i
$756$		0			0
$757$	−4.18141	+	8.11081i	−0.151976	+	0.294792i	−0.952517	−	0.304486i	$-0.901515\pi$
$757$	−4.18141	+	8.11081i	−0.151976	+	0.294792i	0.800541	+	0.599278i	$0.204546\pi$
$758$		0			0
$759$	2.81763	+	11.2136i	0.102274	+	0.407028i
$760$		0			0
$761$	34.8272	+	30.1779i	1.26248	+	1.09395i	0.991328	+	0.131413i	$0.0419515\pi$
$761$	34.8272	+	30.1779i	1.26248	+	1.09395i	0.271156	+	0.962535i	$0.412594\pi$
$762$		0			0
$763$	4.68523	+	0.903004i	0.169617	+	0.0326909i
$764$		0			0
$765$	−3.46810	+	19.7239i	−0.125389	+	0.713119i
$766$		0			0
$767$	0.527956	−	0.914447i	0.0190634	−	0.0330188i
$768$		0			0
$769$	44.5794	+	2.12358i	1.60758	+	0.0765783i	0.832036	−	0.554721i	$-0.187175\pi$
$769$	44.5794	+	2.12358i	1.60758	+	0.0765783i	0.775539	+	0.631299i	$0.217478\pi$
$770$		0			0
$771$	−35.8324	+	7.21036i	−1.29047	+	0.259675i
$772$		0			0
$773$	9.12213	−	9.56701i	0.328100	−	0.344102i	−0.538936	−	0.842347i	$-0.681174\pi$
$773$	9.12213	−	9.56701i	0.328100	−	0.344102i	0.867036	+	0.498245i	$0.166022\pi$
$774$		0			0
$775$	−10.4493	+	6.03288i	−0.375348	+	0.216707i
$776$		0			0
$777$	8.26991	−	11.8167i	0.296681	−	0.423921i
$778$		0			0
$779$	−4.04228	−	1.18692i	−0.144830	−	0.0425258i
$780$		0			0
$781$	2.72712	−	0.129909i	0.0975839	−	0.00464849i
$782$		0			0
$783$	0.330337	−	14.3101i	0.0118053	−	0.511403i
$784$		0			0
$785$	−43.8276	−	4.18503i	−1.56428	−	0.149370i
$786$		0			0
$787$	4.17136	−	1.44372i	0.148693	−	0.0514632i	−0.251708	−	0.967803i	$-0.580992\pi$
$787$	4.17136	−	1.44372i	0.148693	−	0.0514632i	0.400401	+	0.916340i	$0.368871\pi$
$788$		0			0
$789$	−8.04973	+	23.8881i	−0.286578	+	0.850439i
$790$		0			0
$791$	5.48531	+	5.75283i	0.195035	+	0.204547i
$792$		0			0
$793$	−3.82813	+	1.53255i	−0.135941	+	0.0544225i
$794$		0			0
$795$	−3.70307	−	9.03510i	−0.131334	−	0.320442i
$796$		0			0
$797$	4.15784	+	43.5429i	0.147278	+	1.54237i	0.703115	+	0.711077i	$0.251792\pi$
$797$	4.15784	+	43.5429i	0.147278	+	1.54237i	−0.555836	+	0.831292i	$0.687602\pi$
$798$		0			0
$799$	0.393632	−	2.73777i	0.0139257	−	0.0968554i
$800$		0			0
$801$	34.0774	−	25.1159i	1.20406	−	0.887425i
$802$		0			0
$803$	6.73337			0.237615
$804$		0			0
$805$	16.9366			0.596936
$806$		0			0
$807$	−3.60076	−	0.663513i	−0.126753	−	0.0233568i
$808$		0			0
$809$	4.66669	−	32.4575i	0.164072	−	1.14115i	−0.726786	−	0.686864i	$-0.758987\pi$
$809$	4.66669	−	32.4575i	0.164072	−	1.14115i	0.890858	−	0.454282i	$-0.150104\pi$
$810$		0			0
$811$	−3.82079	−	40.0131i	−0.134166	−	1.40505i	−0.772365	−	0.635179i	$-0.780926\pi$
$811$	−3.82079	−	40.0131i	−0.134166	−	1.40505i	0.638199	−	0.769871i	$-0.279680\pi$
$812$		0			0
$813$	−42.7348	+	17.5150i	−1.49877	+	0.614279i
$814$		0			0
$815$	−23.9860	+	9.60255i	−0.840193	+	0.336363i
$816$		0			0
$817$	−4.15294	−	4.35547i	−0.145293	−	0.152379i
$818$		0			0
$819$	−1.80945	+	0.970595i	−0.0632271	+	0.0339153i
$820$		0			0
$821$	−2.75413	+	0.953212i	−0.0961196	+	0.0332673i	−0.374705	−	0.927144i	$-0.622256\pi$
$821$	−2.75413	+	0.953212i	−0.0961196	+	0.0332673i	0.278585	+	0.960412i	$0.410135\pi$
$822$		0			0
$823$	32.0021	+	3.05583i	1.11552	+	0.106520i	0.636496	−	0.771280i	$-0.280383\pi$
$823$	32.0021	+	3.05583i	1.11552	+	0.106520i	0.479028	+	0.877800i	$0.340989\pi$
$824$		0			0
$825$	0.513275	−	5.88303i	0.0178700	−	0.204821i
$826$		0			0
$827$	1.39318	−	0.0663653i	0.0484456	−	0.00230775i	−0.0233451	−	0.999727i	$-0.507432\pi$
$827$	1.39318	−	0.0663653i	0.0484456	−	0.00230775i	0.0717907	+	0.997420i	$0.477129\pi$
$828$		0			0
$829$	3.07621	+	0.903258i	0.106841	+	0.0313714i	0.334716	−	0.942319i	$-0.391360\pi$
$829$	3.07621	+	0.903258i	0.106841	+	0.0313714i	−0.227875	+	0.973690i	$0.573178\pi$
$830$		0			0
$831$	−26.1894	−	18.3286i	−0.908499	−	0.635813i
$832$		0			0
$833$	11.5616	−	6.67511i	0.400586	−	0.231279i
$834$		0			0
$835$	−4.63633	+	4.86244i	−0.160447	+	0.168272i
$836$		0			0
$837$	−6.33335	−	23.5685i	−0.218912	−	0.814646i
$838$		0			0
$839$	24.8118	+	1.18193i	0.856598	+	0.0408048i	0.471285	−	0.881981i	$-0.343790\pi$
$839$	24.8118	+	1.18193i	0.856598	+	0.0408048i	0.385313	+	0.922786i	$0.374093\pi$
$840$		0			0
$841$	−10.7058	+	18.5429i	−0.369164	+	0.639411i
$842$		0			0
$843$	−15.8245	−	24.1865i	−0.545026	−	0.833027i
$844$		0			0
$845$	−34.2742	−	6.60581i	−1.17907	−	0.227247i
$846$		0			0
$847$	−8.54548	−	7.40470i	−0.293626	−	0.254429i
$848$		0			0
$849$	−32.3723	+	8.13417i	−1.11102	+	0.279164i
$850$		0			0
$851$	−15.6814	+	30.4177i	−0.537552	+	1.04271i
$852$		0			0
$853$	−37.5445	+	7.23611i	−1.28550	+	0.247760i	−0.785822	−	0.618452i	$-0.787760\pi$
$853$	−37.5445	+	7.23611i	−1.28550	+	0.247760i	−0.499677	+	0.866212i	$0.666548\pi$
$854$		0			0
$855$	−22.1451	+	32.1996i	−0.757345	+	1.10120i
$856$		0			0
$857$	−32.6402	−	37.6689i	−1.11497	−	1.28674i	−0.954007	−	0.299783i	$-0.903086\pi$
$857$	−32.6402	−	37.6689i	−1.11497	−	1.28674i	−0.160962	−	0.986961i	$-0.551460\pi$
$858$		0			0
$859$	−7.19609	−	29.6627i	−0.245527	−	1.01208i	−0.952428	−	0.304765i	$-0.901422\pi$
$859$	−7.19609	−	29.6627i	−0.245527	−	1.01208i	0.706900	−	0.707313i	$-0.250093\pi$
$860$		0			0
$861$	1.81406	+	0.516590i	0.0618231	+	0.0176053i
$862$		0			0
$863$	10.0709	+	34.2985i	0.342819	+	1.16753i	0.932884	+	0.360178i	$0.117284\pi$
$863$	10.0709	+	34.2985i	0.342819	+	1.16753i	−0.590065	+	0.807356i	$0.700898\pi$
$864$		0			0
$865$	6.01682	−	15.0293i	0.204578	−	0.511011i
$866$		0			0
$867$	−8.95924	−	17.0352i	−0.304272	−	0.578545i
$868$		0			0
$869$	8.17223	−	5.81942i	0.277224	−	0.197410i
$870$		0			0
$871$	−0.883785	−	4.49133i	−0.0299459	−	0.152183i
$872$		0			0
$873$	35.5432	+	43.7072i	1.20295	+	1.47926i
$874$		0			0
$875$	7.73545	+	2.67726i	0.261506	+	0.0905080i
$876$		0			0
$877$	−15.2821	−	6.11803i	−0.516040	−	0.206591i	0.0989998	−	0.995087i	$-0.468436\pi$
$877$	−15.2821	−	6.11803i	−0.516040	−	0.206591i	−0.615039	+	0.788496i	$0.710860\pi$
$878$		0			0
$879$	43.2291	+	21.8408i	1.45808	+	0.736671i
$880$		0			0
$881$	−17.1491	−	33.2646i	−0.577768	−	1.12071i	−0.978832	−	0.204664i	$-0.934390\pi$
$881$	−17.1491	−	33.2646i	−0.577768	−	1.12071i	0.401064	−	0.916050i	$-0.368641\pi$
$882$		0			0
$883$	−5.80677	+	1.40871i	−0.195413	+	0.0474068i	−0.332271	−	0.943184i	$-0.607815\pi$
$883$	−5.80677	+	1.40871i	−0.195413	+	0.0474068i	0.136858	+	0.990591i	$0.456300\pi$
$884$		0			0
$885$	−0.354648	+	8.99049i	−0.0119214	+	0.302212i
$886$		0			0
$887$	−28.7384	+	36.5439i	−0.964942	+	1.22702i	0.00893817	+	0.999960i	$0.497155\pi$
$887$	−28.7384	+	36.5439i	−0.964942	+	1.22702i	−0.973880	+	0.227063i	$0.927088\pi$
$888$		0			0
$889$	−0.750262	−	3.89273i	−0.0251630	−	0.130558i
$890$		0			0
$891$	11.2280	+	4.07445i	0.376152	+	0.136499i
$892$		0			0
$893$	2.91807	−	4.54060i	0.0976494	−	0.151945i
$894$		0			0
$895$	−11.1707	+	12.8917i	−0.373395	+	0.430921i
$896$		0			0
$897$	3.94536	−	2.85836i	0.131732	−	0.0954379i
$898$		0			0
$899$	3.05025	−	12.5733i	0.101732	−	0.419343i
$900$		0			0
$901$	−4.30591	−	2.48602i	−0.143451	−	0.0828213i
$902$		0			0
$903$	1.87520	+	1.93474i	0.0624028	+	0.0643842i
$904$		0			0
$905$	−26.4677	+	37.1687i	−0.879817	+	1.23553i
$906$		0			0
$907$	−14.9122	−	14.2188i	−0.495152	−	0.472127i	0.400871	−	0.916135i	$-0.368708\pi$
$907$	−14.9122	−	14.2188i	−0.495152	−	0.472127i	−0.896023	+	0.444008i	$0.853556\pi$
$908$		0			0
$909$	1.62011	−	1.07901i	0.0537358	−	0.0357884i
$910$		0			0
$911$	−27.6435	+	3.97453i	−0.915869	+	0.131682i	−0.584103	−	0.811680i	$-0.698554\pi$
$911$	−27.6435	+	3.97453i	−0.915869	+	0.131682i	−0.331766	+	0.943362i	$0.607644\pi$
$912$		0			0
$913$	−3.81484	+	12.9921i	−0.126253	+	0.429977i
$914$		0			0
$915$	22.7918	−	26.7416i	0.753473	−	0.884051i
$916$		0			0
$917$	17.2023	−	13.5280i	0.568070	−	0.446735i
$918$		0			0
$919$	2.83597	−	29.6997i	0.0935501	−	0.979701i	−0.819834	−	0.572602i	$-0.805934\pi$
$919$	2.83597	−	29.6997i	0.0935501	−	0.979701i	0.913384	−	0.407100i	$-0.133460\pi$
$920$		0			0
$921$	8.60041	+	3.84304i	0.283393	+	0.126632i
$922$		0			0
$923$	−0.477907	−	1.04647i	−0.0157305	−	0.0344450i
$924$		0			0
$925$	12.6500	−	12.0618i	0.415931	−	0.396589i
$926$		0			0
$927$	−12.3918	−	26.0009i	−0.407000	−	0.853982i
$928$		0			0
$929$	19.0656	−	41.7479i	0.625522	−	1.36970i	−0.285912	−	0.958256i	$-0.592296\pi$
$929$	19.0656	−	41.7479i	0.625522	−	1.36970i	0.911434	−	0.411447i	$-0.134976\pi$
$930$		0			0
$931$	25.9336	−	2.47636i	0.849940	−	0.0811594i
$932$		0			0
$933$	29.0305	+	36.3007i	0.950414	+	1.18843i
$934$		0			0
$935$	−4.78977	−	7.45302i	−0.156642	−	0.243740i
$936$		0			0
$937$		−	24.8575i		−	0.812061i	−0.913860	−	0.406030i	$-0.866913\pi$
$937$		−	24.8575i		−	0.812061i	0.913860	−	0.406030i	$-0.133087\pi$
$938$		0			0
$939$	−15.5383	−	14.5752i	−0.507074	−	0.475643i
$940$		0			0
$941$	11.9807	−	7.69951i	0.390559	−	0.250997i	−0.330594	−	0.943773i	$-0.607249\pi$
$941$	11.9807	−	7.69951i	0.390559	−	0.250997i	0.721153	+	0.692776i	$0.243613\pi$
$942$		0			0
$943$	−4.42984	−	0.636915i	−0.144255	−	0.0207408i
$944$		0			0
$945$	9.79648	−	14.4968i	0.318680	−	0.471580i
$946$		0			0
$947$	−1.57095	−	0.717428i	−0.0510489	−	0.0233133i	0.389727	−	0.920930i	$-0.372569\pi$
$947$	−1.57095	−	0.717428i	−0.0510489	−	0.0233133i	−0.440776	+	0.897617i	$0.645297\pi$
$948$		0			0
$949$	−1.05450	−	2.63401i	−0.0342305	−	0.0855036i
$950$		0			0
$951$	−39.1269	+	0.319802i	−1.26878	+	0.0103703i
$952$		0			0
$953$	29.4645	−	13.4560i	0.954448	−	0.435882i	0.123570	−	0.992336i	$-0.460566\pi$
$953$	29.4645	−	13.4560i	0.954448	−	0.435882i	0.830878	+	0.556454i	$0.187838\pi$
$954$		0			0
$955$	9.15149	+	26.4415i	0.296135	+	0.855626i
$956$		0			0
$957$	4.18574	+	4.75157i	0.135306	+	0.153596i
$958$		0			0
$959$	−3.24634	−	4.12805i	−0.104830	−	0.133302i
$960$		0			0
$961$	0.425445	+	8.93118i	0.0137240	+	0.288103i
$962$		0			0
$963$	48.7082	+	10.9767i	1.56960	+	0.353718i
$964$		0			0
$965$	5.42517	+	37.7329i	0.174642	+	1.21467i
$966$		0			0
$967$	−2.55920	−	4.43266i	−0.0822983	−	0.142545i	0.821938	−	0.569576i	$-0.192893\pi$
$967$	−2.55920	−	4.43266i	−0.0822983	−	0.142545i	−0.904237	+	0.427031i	$0.859559\pi$
$968$		0			0
$969$	1.10926	+	19.8682i	0.0356347	+	0.638259i
$970$		0			0
$971$	−24.2429	−	17.2633i	−0.777991	−	0.554005i	0.120647	−	0.992695i	$-0.461503\pi$
$971$	−24.2429	−	17.2633i	−0.777991	−	0.554005i	−0.898638	+	0.438691i	$0.855442\pi$
$972$		0			0
$973$	−0.136718	+	2.87005i	−0.00438296	+	0.0920097i
$974$		0			0
$975$	−2.38175	+	0.720541i	−0.0762771	+	0.0230758i
$976$		0			0
$977$	−16.3666	−	3.97049i	−0.523613	−	0.127027i	−0.0347642	−	0.999396i	$-0.511068\pi$
$977$	−16.3666	−	3.97049i	−0.523613	−	0.127027i	−0.488849	+	0.872368i	$0.662583\pi$
$978$		0			0
$979$	−3.54419	+	18.3890i	−0.113273	+	0.587715i
$980$		0			0
$981$	−7.07850	+	9.31031i	−0.225999	+	0.297255i
$982$		0			0
$983$	51.2611	+	32.9435i	1.63498	+	1.05073i	0.945087	+	0.326819i	$0.105977\pi$
$983$	51.2611	+	32.9435i	1.63498	+	1.05073i	0.689888	+	0.723916i	$0.257660\pi$
$984$		0			0
$985$	9.47945	+	4.88700i	0.302040	+	0.155713i
$986$		0			0
$987$	−1.28980	+	2.04350i	−0.0410548	+	0.0650453i
$988$		0			0
$989$	−5.02522	−	3.95188i	−0.159793	−	0.125662i
$990$		0			0
$991$	20.7676	−	17.9953i	0.659706	−	0.571638i	−0.259342	−	0.965786i	$-0.583506\pi$
$991$	20.7676	−	17.9953i	0.659706	−	0.571638i	0.919047	+	0.394148i	$0.128960\pi$
$992$		0			0
$993$	12.8619	−	22.7041i	0.408161	−	0.720492i
$994$		0			0
$995$	0.520538	−	0.268356i	0.0165022	−	0.00850746i
$996$		0			0
$997$	6.40925	−	1.88193i	0.202983	−	0.0596012i	−0.178661	−	0.983911i	$-0.557176\pi$
$997$	6.40925	−	1.88193i	0.202983	−	0.0596012i	0.381644	+	0.924310i	$0.375358\pi$
$998$		0			0
$999$	16.9654	+	31.0166i	0.536760	+	0.981323i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.ba.b.41.11	✓	440
3.2	odd	2	inner	804.2.ba.b.41.21	yes	440
67.18	odd	66	inner	804.2.ba.b.353.21	yes	440
201.152	even	66	inner	804.2.ba.b.353.11	yes	440

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.ba.b.41.11	✓	440	1.1	even	1	trivial
804.2.ba.b.41.21	yes	440	3.2	odd	2	inner
804.2.ba.b.353.11	yes	440	201.152	even	66	inner
804.2.ba.b.353.21	yes	440	67.18	odd	66	inner

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:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.ba (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.313881 + 1.70337i) q^{3} +(0.391534 - 2.72318i) q^{5} +(0.116340 + 1.21837i) q^{7} +(-2.80296 - 1.06931i) q^{9} +O(q^{10})\)	\(q+(-0.313881 + 1.70337i) q^{3} +(0.391534 - 2.72318i) q^{5} +(0.116340 + 1.21837i) q^{7} +(-2.80296 - 1.06931i) q^{9} +(1.23209 - 0.493254i) q^{11} +(-0.385910 - 0.404731i) q^{13} +(4.51569 + 1.52168i) q^{15} +(2.29296 - 0.793601i) q^{17} +(4.71345 + 0.450080i) q^{19} +(-2.11185 - 0.184253i) q^{21} +(5.02418 - 0.239331i) q^{23} +(-2.46494 - 0.723772i) q^{25} +(2.70124 - 4.43884i) q^{27} +(2.38566 - 1.37736i) q^{29} +(3.24107 - 3.39914i) q^{31} +(0.453466 + 2.25353i) q^{33} +(3.36339 + 0.160218i) q^{35} +(-3.40187 + 5.89222i) q^{37} +(0.810537 - 0.530311i) q^{39} +(-0.873683 - 0.168389i) q^{41} +(-0.960559 - 0.832329i) q^{43} +(-4.00939 + 7.21428i) q^{45} +(0.522344 - 1.01321i) q^{47} +(5.40261 - 1.04127i) q^{49} +(0.632081 + 4.15486i) q^{51} +(-1.34190 - 1.54863i) q^{53} +(-0.860814 - 3.54832i) q^{55} +(-2.24612 + 7.88750i) q^{57} +(0.531959 + 1.81168i) q^{59} +(2.74049 - 6.84541i) q^{61} +(0.976722 - 3.53944i) q^{63} +(-1.25325 + 0.892436i) q^{65} +(6.90314 + 4.39849i) q^{67} +(-1.16932 + 8.63317i) q^{69} +(1.94404 + 0.672840i) q^{71} +(4.71011 + 1.88564i) q^{73} +(2.00655 - 3.97154i) q^{75} +(0.744306 + 1.44375i) q^{77} +(7.34631 - 1.78219i) q^{79} +(6.71314 + 5.99448i) q^{81} +(-6.30692 + 8.01990i) q^{83} +(-1.26335 - 6.55486i) q^{85} +(1.59735 + 4.49599i) q^{87} +(-7.62896 + 11.8709i) q^{89} +(0.448214 - 0.517267i) q^{91} +(4.77269 + 6.58768i) q^{93} +(3.07113 - 12.6594i) q^{95} +(-16.2625 - 9.38917i) q^{97} +(-3.98094 + 0.0650804i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 440 q - 12 q^{7} + 4 q^{9}+O(q^{10}) \) 440 * q - 12 * q^7 + 4 * q^9	\( 440 q - 12 q^{7} + 4 q^{9} - 2 q^{15} - 10 q^{19} + 22 q^{21} - 68 q^{25} + 50 q^{31} + 11 q^{33} - 22 q^{37} - 45 q^{39} + 22 q^{43} + 22 q^{45} - 18 q^{49} - 6 q^{51} + 126 q^{55} - 183 q^{57} - 56 q^{61} - 141 q^{63} - 12 q^{67} + 33 q^{69} + 356 q^{73} + 165 q^{75} + 228 q^{79} + 24 q^{81} - 6 q^{85} + 75 q^{87} - 4 q^{91} - 75 q^{93} + 12 q^{97} + 88 q^{99}+O(q^{100}) \) 440 * q - 12 * q^7 + 4 * q^9 - 2 * q^15 - 10 * q^19 + 22 * q^21 - 68 * q^25 + 50 * q^31 + 11 * q^33 - 22 * q^37 - 45 * q^39 + 22 * q^43 + 22 * q^45 - 18 * q^49 - 6 * q^51 + 126 * q^55 - 183 * q^57 - 56 * q^61 - 141 * q^63 - 12 * q^67 + 33 * q^69 + 356 * q^73 + 165 * q^75 + 228 * q^79 + 24 * q^81 - 6 * q^85 + 75 * q^87 - 4 * q^91 - 75 * q^93 + 12 * q^97 + 88 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more