LMFDB - Embedded newform 880.2.bo.d.641.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [880,2,Mod(81,880)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(880, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("880.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 880 = 2^{4} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	880.bo (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:	$7.02683537787$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.13140625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 5x^{6} - 3x^{5} + 4x^{4} + 3x^{3} + 5x^{2} + 3x + 1 $ x^8 - 3x^7 + 5x^6 - 3x^5 + 4x^4 + 3x^3 + 5x^2 + 3*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 440)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			641.2
Root			$1.69513 - 1.23158i$ of defining polynomial
Character	$\chi$	$=$	880.641
Dual form			880.2.bo.d.81.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.400166 + 1.23158i) q^{3} +(-0.809017 - 0.587785i) q^{5} +(0.0703870 - 0.216629i) q^{7} +(1.07039 - 0.777682i) q^{9} +O(q^{10})$	\(q+(0.400166 + 1.23158i) q^{3} +(-0.809017 - 0.587785i) q^{5} +(0.0703870 - 0.216629i) q^{7} +(1.07039 - 0.777682i) q^{9} +(3.12020 + 1.12443i) q^{11} +(2.70598 - 1.96601i) q^{13} +(0.400166 - 1.23158i) q^{15} +(-4.89440 - 3.55599i) q^{17} +(0.686443 + 2.11265i) q^{19} +0.294963 q^{21} +3.47726 q^{23} +(0.309017 + 0.951057i) q^{25} +(4.52905 + 3.29055i) q^{27} +(0.00951362 - 0.0292799i) q^{29} +(1.79298 - 1.30268i) q^{31} +(-0.136234 + 4.29274i) q^{33} +(-0.184276 + 0.133884i) q^{35} +(2.70306 - 8.31916i) q^{37} +(3.50415 + 2.54591i) q^{39} +(3.16446 + 9.73920i) q^{41} +3.74411 q^{43} -1.32307 q^{45} +(1.64211 + 5.05390i) q^{47} +(5.62115 + 4.08400i) q^{49} +(2.42093 - 7.45085i) q^{51} +(8.25427 - 5.99708i) q^{53} +(-1.86337 - 2.74369i) q^{55} +(-2.32722 + 1.69082i) q^{57} +(-2.57843 + 7.93560i) q^{59} +(1.81667 + 1.31989i) q^{61} +(-0.0931270 - 0.286615i) q^{63} -3.34478 q^{65} -3.47330 q^{67} +(1.39148 + 4.28253i) q^{69} +(-12.1868 - 8.85423i) q^{71} +(-1.13220 + 3.48457i) q^{73} +(-1.04765 + 0.761160i) q^{75} +(0.463206 - 0.596780i) q^{77} +(-9.40175 + 6.83077i) q^{79} +(-1.01366 + 3.11972i) q^{81} +(1.23192 + 0.895044i) q^{83} +(1.86950 + 5.75372i) q^{85} +0.0398677 q^{87} -10.0058 q^{89} +(-0.235429 - 0.724575i) q^{91} +(2.32185 + 1.68692i) q^{93} +(0.686443 - 2.11265i) q^{95} +(6.74372 - 4.89960i) q^{97} +(4.21427 - 1.22295i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - q^{3} - 2 q^{5} - q^{7} + 7 q^{9}+O(q^{10}) $ 8 * q - q^3 - 2 * q^5 - q^7 + 7 * q^9	$ 8 q - q^{3} - 2 q^{5} - q^{7} + 7 q^{9} - 3 q^{11} - 4 q^{13} - q^{15} - 3 q^{17} - 9 q^{19} - 4 q^{21} + 22 q^{23} - 2 q^{25} + 8 q^{27} - 17 q^{29} + 4 q^{31} + 21 q^{33} - 6 q^{35} + 24 q^{37} + 13 q^{39} - 4 q^{41} + 14 q^{43} - 8 q^{45} + 12 q^{47} - 15 q^{49} + 17 q^{51} + 35 q^{53} - 3 q^{55} - q^{57} - 21 q^{59} - 22 q^{61} - 5 q^{63} + 6 q^{65} - 14 q^{67} + 3 q^{69} - 40 q^{71} + 9 q^{73} - q^{75} - 4 q^{77} - 41 q^{79} + 24 q^{81} + 7 q^{83} - 8 q^{85} + 46 q^{87} - 24 q^{89} + 18 q^{91} + 3 q^{93} - 9 q^{95} + 4 q^{97} - 22 q^{99}+O(q^{100}) $ 8 * q - q^3 - 2 * q^5 - q^7 + 7 * q^9 - 3 * q^11 - 4 * q^13 - q^15 - 3 * q^17 - 9 * q^19 - 4 * q^21 + 22 * q^23 - 2 * q^25 + 8 * q^27 - 17 * q^29 + 4 * q^31 + 21 * q^33 - 6 * q^35 + 24 * q^37 + 13 * q^39 - 4 * q^41 + 14 * q^43 - 8 * q^45 + 12 * q^47 - 15 * q^49 + 17 * q^51 + 35 * q^53 - 3 * q^55 - q^57 - 21 * q^59 - 22 * q^61 - 5 * q^63 + 6 * q^65 - 14 * q^67 + 3 * q^69 - 40 * q^71 + 9 * q^73 - q^75 - 4 * q^77 - 41 * q^79 + 24 * q^81 + 7 * q^83 - 8 * q^85 + 46 * q^87 - 24 * q^89 + 18 * q^91 + 3 * q^93 - 9 * q^95 + 4 * q^97 - 22 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/880\mathbb{Z}\right)^\times$.

$n$	$111$	$177$	$321$	$661$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{5}\right)$	$1$

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
$3$	0.400166	+	1.23158i	0.231036	+	0.711055i	0.997623	+	0.0689142i	$0.0219535\pi$
$3$	0.400166	+	1.23158i	0.231036	+	0.711055i	−0.766587	+	0.642141i	$0.778047\pi$
$4$		0			0
$5$	−0.809017	−	0.587785i	−0.361803	−	0.262866i
$5$	−0.809017	−	0.587785i	−0.361803	−	0.262866i
$6$		0			0
$7$	0.0703870	−	0.216629i	0.0266038	−	0.0818780i	−0.936873	−	0.349670i	$-0.886294\pi$
$7$	0.0703870	−	0.216629i	0.0266038	−	0.0818780i	0.963477	+	0.267792i	$0.0862939\pi$
$8$		0			0
$9$	1.07039	−	0.777682i	0.356796	−	0.259227i
$10$		0			0
$11$	3.12020	+	1.12443i	0.940776	+	0.339029i
$11$	3.12020	+	1.12443i	0.940776	+	0.339029i
$12$		0			0
$13$	2.70598	−	1.96601i	0.750504	−	0.545273i	−0.145479	−	0.989361i	$-0.546472\pi$
$13$	2.70598	−	1.96601i	0.750504	−	0.545273i	0.895983	+	0.444088i	$0.146472\pi$
$14$		0			0
$15$	0.400166	−	1.23158i	0.103322	−	0.317993i
$16$		0			0
$17$	−4.89440	−	3.55599i	−1.18707	−	0.862455i	−0.194116	−	0.980979i	$-0.562184\pi$
$17$	−4.89440	−	3.55599i	−1.18707	−	0.862455i	−0.992951	+	0.118524i	$0.962184\pi$
$18$		0			0
$19$	0.686443	+	2.11265i	0.157481	+	0.484676i	0.998404	−	0.0564789i	$-0.0179874\pi$
$19$	0.686443	+	2.11265i	0.157481	+	0.484676i	−0.840923	+	0.541155i	$0.817987\pi$
$20$		0			0
$21$	0.294963			0.0643662
$22$		0			0
$23$	3.47726			0.725059			0.362529	−	0.931972i	$-0.381913\pi$
$23$	3.47726			0.725059			0.362529	+	0.931972i	$0.381913\pi$
$24$		0			0
$25$	0.309017	+	0.951057i	0.0618034	+	0.190211i
$26$		0			0
$27$	4.52905	+	3.29055i	0.871617	+	0.633266i
$28$		0			0
$29$	0.00951362	−	0.0292799i	0.00176664	−	0.00543714i	−0.950169	−	0.311734i	$-0.899090\pi$
$29$	0.00951362	−	0.0292799i	0.00176664	−	0.00543714i	0.951936	+	0.306297i	$0.0990901\pi$
$30$		0			0
$31$	1.79298	−	1.30268i	0.322030	−	0.233968i	−0.415011	−	0.909816i	$-0.636222\pi$
$31$	1.79298	−	1.30268i	0.322030	−	0.233968i	0.737041	+	0.675848i	$0.236222\pi$
$32$		0			0
$33$	−0.136234	+	4.29274i	−0.0237152	+	0.747271i
$34$		0			0
$35$	−0.184276	+	0.133884i	−0.0311483	+	0.0226305i
$36$		0			0
$37$	2.70306	−	8.31916i	0.444380	−	1.36766i	−0.438782	−	0.898594i	$-0.644590\pi$
$37$	2.70306	−	8.31916i	0.444380	−	1.36766i	0.883162	−	0.469068i	$-0.155410\pi$
$38$		0			0
$39$	3.50415	+	2.54591i	0.561112	+	0.407672i
$40$		0			0
$41$	3.16446	+	9.73920i	0.494205	+	1.52101i	0.818191	+	0.574946i	$0.194977\pi$
$41$	3.16446	+	9.73920i	0.494205	+	1.52101i	−0.323986	+	0.946062i	$0.605023\pi$
$42$		0			0
$43$	3.74411			0.570972			0.285486	−	0.958383i	$-0.407845\pi$
$43$	3.74411			0.570972			0.285486	+	0.958383i	$0.407845\pi$
$44$		0			0
$45$	−1.32307			−0.197232
$46$		0			0
$47$	1.64211	+	5.05390i	0.239527	+	0.737188i	0.996489	+	0.0837286i	$0.0266829\pi$
$47$	1.64211	+	5.05390i	0.239527	+	0.737188i	−0.756962	+	0.653459i	$0.773317\pi$
$48$		0			0
$49$	5.62115	+	4.08400i	0.803021	+	0.583429i
$50$		0			0
$51$	2.42093	−	7.45085i	0.338998	−	1.04333i
$52$		0			0
$53$	8.25427	−	5.99708i	1.13381	−	0.823762i	0.147566	−	0.989052i	$-0.452856\pi$
$53$	8.25427	−	5.99708i	1.13381	−	0.823762i	0.986245	+	0.165290i	$0.0528561\pi$
$54$		0			0
$55$	−1.86337	−	2.74369i	−0.251257	−	0.369959i
$56$		0			0
$57$	−2.32722	+	1.69082i	−0.308247	+	0.223955i
$58$		0			0
$59$	−2.57843	+	7.93560i	−0.335683	+	1.03313i	0.630701	+	0.776026i	$0.282767\pi$
$59$	−2.57843	+	7.93560i	−0.335683	+	1.03313i	−0.966384	+	0.257102i	$0.917233\pi$
$60$		0			0
$61$	1.81667	+	1.31989i	0.232601	+	0.168994i	0.697980	−	0.716117i	$-0.254082\pi$
$61$	1.81667	+	1.31989i	0.232601	+	0.168994i	−0.465380	+	0.885111i	$0.654082\pi$
$62$		0			0
$63$	−0.0931270	−	0.286615i	−0.0117329	−	0.0361102i
$64$		0			0
$65$	−3.34478			−0.414869
$66$		0			0
$67$	−3.47330			−0.424332			−0.212166	−	0.977234i	$-0.568052\pi$
$67$	−3.47330			−0.424332			−0.212166	+	0.977234i	$0.568052\pi$
$68$		0			0
$69$	1.39148	+	4.28253i	0.167514	+	0.515557i
$70$		0			0
$71$	−12.1868	−	8.85423i	−1.44631	−	1.05080i	−0.986677	−	0.162694i	$-0.947982\pi$
$71$	−12.1868	−	8.85423i	−1.44631	−	1.05080i	−0.459631	−	0.888110i	$-0.652018\pi$
$72$		0			0
$73$	−1.13220	+	3.48457i	−0.132515	+	0.407838i	−0.995195	−	0.0979113i	$-0.968784\pi$
$73$	−1.13220	+	3.48457i	−0.132515	+	0.407838i	0.862681	+	0.505749i	$0.168784\pi$
$74$		0			0
$75$	−1.04765	+	0.761160i	−0.120972	+	0.0878912i
$76$		0			0
$77$	0.463206	−	0.596780i	0.0527872	−	0.0680094i
$78$		0			0
$79$	−9.40175	+	6.83077i	−1.05778	+	0.768522i	−0.973676	−	0.227935i	$-0.926803\pi$
$79$	−9.40175	+	6.83077i	−1.05778	+	0.768522i	−0.0841031	+	0.996457i	$0.526803\pi$
$80$		0			0
$81$	−1.01366	+	3.11972i	−0.112629	+	0.346636i
$82$		0			0
$83$	1.23192	+	0.895044i	0.135221	+	0.0982439i	0.653340	−	0.757065i	$-0.273367\pi$
$83$	1.23192	+	0.895044i	0.135221	+	0.0982439i	−0.518119	+	0.855309i	$0.673367\pi$
$84$		0			0
$85$	1.86950	+	5.75372i	0.202775	+	0.624078i
$86$		0			0
$87$	0.0398677			0.00427426
$88$		0			0
$89$	−10.0058			−1.06062			−0.530309	−	0.847805i	$-0.677924\pi$
$89$	−10.0058			−1.06062			−0.530309	+	0.847805i	$0.677924\pi$
$90$		0			0
$91$	−0.235429	−	0.724575i	−0.0246796	−	0.0759561i
$92$		0			0
$93$	2.32185	+	1.68692i	0.240764	+	0.174926i
$94$		0			0
$95$	0.686443	−	2.11265i	0.0704275	−	0.216754i
$96$		0			0
$97$	6.74372	−	4.89960i	0.684721	−	0.497479i	−0.190200	−	0.981745i	$-0.560913\pi$
$97$	6.74372	−	4.89960i	0.684721	−	0.497479i	0.874921	+	0.484267i	$0.160913\pi$
$98$		0			0
$99$	4.21427	−	1.22295i	0.423550	−	0.122911i
$100$		0			0
$101$	−1.39376	+	1.01263i	−0.138685	+	0.100760i	−0.654964	−	0.755660i	$-0.727316\pi$
$101$	−1.39376	+	1.01263i	−0.138685	+	0.100760i	0.516280	+	0.856420i	$0.327316\pi$
$102$		0			0
$103$	0.603980	−	1.85886i	0.0595119	−	0.183159i	−0.916881	−	0.399160i	$-0.869302\pi$
$103$	0.603980	−	1.85886i	0.0595119	−	0.183159i	0.976393	+	0.216002i	$0.0693016\pi$
$104$		0			0
$105$	−0.238630	−	0.173375i	−0.0232879	−	0.0169197i
$106$		0			0
$107$	−4.14096	−	12.7446i	−0.400322	−	1.23206i	−0.924739	−	0.380603i	$-0.875717\pi$
$107$	−4.14096	−	12.7446i	−0.400322	−	1.23206i	0.524417	−	0.851462i	$-0.324283\pi$
$108$		0			0
$109$	7.46306			0.714831			0.357416	−	0.933945i	$-0.383658\pi$
$109$	7.46306			0.714831			0.357416	+	0.933945i	$0.383658\pi$
$110$		0			0
$111$	11.3274			1.07515
$112$		0			0
$113$	1.63548	+	5.03348i	0.153853	+	0.473510i	0.998043	−	0.0625337i	$-0.0199181\pi$
$113$	1.63548	+	5.03348i	0.153853	+	0.473510i	−0.844190	+	0.536044i	$0.819918\pi$
$114$		0			0
$115$	−2.81316	−	2.04388i	−0.262329	−	0.190593i
$116$		0			0
$117$	1.36752	−	4.20878i	0.126427	−	0.389102i
$118$		0			0
$119$	−1.11483	+	0.809973i	−0.102197	+	0.0742501i
$120$		0			0
$121$	8.47131	+	7.01690i	0.770119	+	0.637900i
$122$		0			0
$123$	−10.7283	+	7.79459i	−0.967341	+	0.702814i
$124$		0			0
$125$	0.309017	−	0.951057i	0.0276393	−	0.0850651i
$126$		0			0
$127$	−9.86456	−	7.16702i	−0.875338	−	0.635970i	0.0566759	−	0.998393i	$-0.481950\pi$
$127$	−9.86456	−	7.16702i	−0.875338	−	0.635970i	−0.932014	+	0.362422i	$0.881950\pi$
$128$		0			0
$129$	1.49827	+	4.61119i	0.131915	+	0.405992i
$130$		0			0
$131$	2.06530			0.180446			0.0902229	−	0.995922i	$-0.471242\pi$
$131$	2.06530			0.180446			0.0902229	+	0.995922i	$0.471242\pi$
$132$		0			0
$133$	0.505978			0.0438739
$134$		0			0
$135$	−1.72994	−	5.32422i	−0.148890	−	0.458236i
$136$		0			0
$137$	−11.6851	−	8.48974i	−0.998328	−	0.725328i	−0.0365990	−	0.999330i	$-0.511652\pi$
$137$	−11.6851	−	8.48974i	−0.998328	−	0.725328i	−0.961729	+	0.274002i	$0.911652\pi$
$138$		0			0
$139$	5.04999	−	15.5423i	0.428334	−	1.31828i	−0.471431	−	0.881903i	$-0.656262\pi$
$139$	5.04999	−	15.5423i	0.428334	−	1.31828i	0.899765	−	0.436374i	$-0.143738\pi$
$140$		0			0
$141$	−5.56719	+	4.04480i	−0.468842	+	0.340633i
$142$		0			0
$143$	10.6538	−	3.09166i	0.890920	−	0.258537i
$144$		0			0
$145$	−0.0249070	+	0.0180960i	−0.00206841	+	0.00150279i
$146$		0			0
$147$	−2.78040	+	8.55718i	−0.229323	+	0.705785i
$148$		0			0
$149$	−12.1204	−	8.80602i	−0.992946	−	0.721417i	−0.0323814	−	0.999476i	$-0.510309\pi$
$149$	−12.1204	−	8.80602i	−0.992946	−	0.721417i	−0.960564	+	0.278058i	$0.910309\pi$
$150$		0			0
$151$	−3.80960	−	11.7247i	−0.310021	−	0.954146i	−0.977756	−	0.209747i	$-0.932736\pi$
$151$	−3.80960	−	11.7247i	−0.310021	−	0.954146i	0.667735	−	0.744399i	$-0.267264\pi$
$152$		0			0
$153$	−8.00433			−0.647112
$154$		0			0
$155$	−2.21625			−0.178014
$156$		0			0
$157$	−6.44122	−	19.8240i	−0.514065	−	1.58213i	−0.784976	−	0.619526i	$-0.787325\pi$
$157$	−6.44122	−	19.8240i	−0.514065	−	1.58213i	0.270911	−	0.962605i	$-0.412675\pi$
$158$		0			0
$159$	10.6890	+	7.76599i	0.847690	+	0.615883i
$160$		0			0
$161$	0.244754	−	0.753275i	0.0192893	−	0.0593664i
$162$		0			0
$163$	0.457082	−	0.332090i	0.0358014	−	0.0260113i	−0.569741	−	0.821825i	$-0.692956\pi$
$163$	0.457082	−	0.332090i	0.0358014	−	0.0260113i	0.605542	+	0.795813i	$0.292956\pi$
$164$		0			0
$165$	2.63343	−	3.39283i	0.205012	−	0.264131i
$166$		0			0
$167$	−18.1506	+	13.1872i	−1.40454	+	1.02046i	−0.410451	+	0.911883i	$0.634629\pi$
$167$	−18.1506	+	13.1872i	−1.40454	+	1.02046i	−0.994088	+	0.108575i	$0.965371\pi$
$168$		0			0
$169$	−0.560083	+	1.72376i	−0.0430833	+	0.132597i
$170$		0			0
$171$	2.37773	+	1.72752i	0.181830	+	0.132107i
$172$		0			0
$173$	0.669243	+	2.05972i	0.0508816	+	0.156597i	0.973269	−	0.229669i	$-0.0737644\pi$
$173$	0.669243	+	2.05972i	0.0508816	+	0.156597i	−0.922387	+	0.386267i	$0.873764\pi$
$174$		0			0
$175$	0.227777			0.0172183
$176$		0			0
$177$	−10.8052			−0.812165
$178$		0			0
$179$	6.84683	+	21.0724i	0.511756	+	1.57502i	0.789108	+	0.614254i	$0.210543\pi$
$179$	6.84683	+	21.0724i	0.511756	+	1.57502i	−0.277352	+	0.960768i	$0.589457\pi$
$180$		0			0
$181$	7.23000	+	5.25290i	0.537402	+	0.390445i	0.823119	−	0.567869i	$-0.192232\pi$
$181$	7.23000	+	5.25290i	0.537402	+	0.390445i	−0.285717	+	0.958314i	$0.592232\pi$
$182$		0			0
$183$	−0.898582	+	2.76555i	−0.0664251	+	0.204435i
$184$		0			0
$185$	−7.07670	+	5.14152i	−0.520289	+	0.378012i
$186$		0			0
$187$	−11.2731	−	16.5988i	−0.824367	−	1.21383i
$188$		0			0
$189$	1.03161	−	0.749512i	0.0750389	−	0.0545190i
$190$		0			0
$191$	3.55618	−	10.9448i	0.257316	−	0.791938i	−0.736048	−	0.676929i	$-0.763310\pi$
$191$	3.55618	−	10.9448i	0.257316	−	0.791938i	0.993364	−	0.115009i	$-0.0366897\pi$
$192$		0			0
$193$	−6.72449	−	4.88563i	−0.484039	−	0.351675i	0.318848	−	0.947806i	$-0.396704\pi$
$193$	−6.72449	−	4.88563i	−0.484039	−	0.351675i	−0.802887	+	0.596131i	$0.796704\pi$
$194$		0			0
$195$	−1.33846	−	4.11937i	−0.0958494	−	0.294994i
$196$		0			0
$197$	3.64765			0.259885			0.129942	−	0.991522i	$-0.458521\pi$
$197$	3.64765			0.259885			0.129942	+	0.991522i	$0.458521\pi$
$198$		0			0
$199$	6.34757			0.449967			0.224984	−	0.974363i	$-0.427767\pi$
$199$	6.34757			0.449967			0.224984	+	0.974363i	$0.427767\pi$
$200$		0			0
$201$	−1.38990	−	4.27766i	−0.0980357	−	0.301723i
$202$		0			0
$203$	−0.00567324	−	0.00412185i	−0.000398184	−	0.000289297i
$204$		0			0
$205$	3.16446	−	9.73920i	0.221015	−	0.680215i
$206$		0			0
$207$	3.72201	−	2.70420i	0.258698	−	0.187955i
$208$		0			0
$209$	−0.233694	+	7.36376i	−0.0161650	+	0.509362i
$210$		0			0
$211$	−15.5771	+	11.3174i	−1.07237	+	0.779122i	−0.976337	−	0.216256i	$-0.930615\pi$
$211$	−15.5771	+	11.3174i	−1.07237	+	0.779122i	−0.0960325	+	0.995378i	$0.530615\pi$
$212$		0			0
$213$	6.02798	−	18.5522i	0.413030	−	1.27118i
$214$		0			0
$215$	−3.02905	−	2.20074i	−0.206580	−	0.150089i
$216$		0			0
$217$	−0.155995	−	0.480104i	−0.0105896	−	0.0325916i
$218$		0			0
$219$	−4.74460			−0.320611
$220$		0			0
$221$	−20.2353			−1.36117
$222$		0			0
$223$	6.71498	+	20.6666i	0.449669	+	1.38394i	0.877282	+	0.479976i	$0.159355\pi$
$223$	6.71498	+	20.6666i	0.449669	+	1.38394i	−0.427613	+	0.903962i	$0.640645\pi$
$224$		0			0
$225$	1.07039	+	0.777682i	0.0713591	+	0.0518454i
$226$		0			0
$227$	1.85557	−	5.71085i	0.123158	−	0.379043i	−0.870403	−	0.492341i	$-0.836141\pi$
$227$	1.85557	−	5.71085i	0.123158	−	0.379043i	0.993561	+	0.113298i	$0.0361415\pi$
$228$		0			0
$229$	18.7756	−	13.6413i	1.24073	−	0.901440i	0.243079	−	0.970007i	$-0.421843\pi$
$229$	18.7756	−	13.6413i	1.24073	−	0.901440i	0.997647	+	0.0685670i	$0.0218427\pi$
$230$		0			0
$231$	0.920344	+	0.331666i	0.0605542	+	0.0218220i
$232$		0			0
$233$	−19.5930	+	14.2351i	−1.28358	+	0.932576i	−0.999655	−	0.0262707i	$-0.991637\pi$
$233$	−19.5930	+	14.2351i	−1.28358	+	0.932576i	−0.283925	+	0.958846i	$0.591637\pi$
$234$		0			0
$235$	1.64211	−	5.05390i	0.107120	−	0.329680i
$236$		0			0
$237$	−12.1749	−	8.84559i	−0.790846	−	0.574583i
$238$		0			0
$239$	5.68197	+	17.4873i	0.367536	+	1.13116i	0.948378	+	0.317144i	$0.102724\pi$
$239$	5.68197	+	17.4873i	0.367536	+	1.13116i	−0.580841	+	0.814017i	$0.697276\pi$
$240$		0			0
$241$	−12.3990			−0.798692			−0.399346	−	0.916800i	$-0.630763\pi$
$241$	−12.3990			−0.798692			−0.399346	+	0.916800i	$0.630763\pi$
$242$		0			0
$243$	12.5468			0.804879
$244$		0			0
$245$	−2.14709	−	6.60805i	−0.137172	−	0.422173i
$246$		0			0
$247$	6.01100	+	4.36725i	0.382471	+	0.277881i
$248$		0			0
$249$	−0.609348	+	1.87538i	−0.0386159	+	0.118847i
$250$		0			0
$251$	−17.6317	+	12.8101i	−1.11290	+	0.808569i	−0.983118	−	0.182973i	$-0.941428\pi$
$251$	−17.6317	+	12.8101i	−1.11290	+	0.808569i	−0.129782	+	0.991542i	$0.541428\pi$
$252$		0			0
$253$	10.8498	+	3.90994i	0.682118	+	0.245816i
$254$		0			0
$255$	−6.33807	+	4.60488i	−0.396905	+	0.288369i
$256$		0			0
$257$	4.54531	−	13.9890i	0.283529	−	0.872611i	−0.703307	−	0.710886i	$-0.748294\pi$
$257$	4.54531	−	13.9890i	0.283529	−	0.872611i	0.986836	−	0.161725i	$-0.0517058\pi$
$258$		0			0
$259$	−1.61191	−	1.17112i	−0.100159	−	0.0727699i
$260$		0			0
$261$	−0.0125872	−	0.0387394i	−0.000779128	−	0.00239791i
$262$		0			0
$263$	−27.4694			−1.69384			−0.846918	−	0.531724i	$-0.821544\pi$
$263$	−27.4694			−1.69384			−0.846918	+	0.531724i	$0.821544\pi$
$264$		0			0
$265$	−10.2028			−0.626755
$266$		0			0
$267$	−4.00399	−	12.3230i	−0.245040	−	0.754157i
$268$		0			0
$269$	1.14812	+	0.834158i	0.0700022	+	0.0508595i	0.622236	−	0.782830i	$-0.286224\pi$
$269$	1.14812	+	0.834158i	0.0700022	+	0.0508595i	−0.552234	+	0.833689i	$0.686224\pi$
$270$		0			0
$271$	−3.19827	+	9.84328i	−0.194281	+	0.597936i	0.805703	+	0.592320i	$0.201788\pi$
$271$	−3.19827	+	9.84328i	−0.194281	+	0.597936i	−0.999984	+	0.00561654i	$0.998212\pi$
$272$		0			0
$273$	0.798164	−	0.579900i	0.0483071	−	0.0350972i
$274$		0			0
$275$	−0.105203	+	3.31496i	−0.00634396	+	0.199899i
$276$		0			0
$277$	−14.4052	+	10.4660i	−0.865524	+	0.628840i	−0.929382	−	0.369119i	$-0.879660\pi$
$277$	−14.4052	+	10.4660i	−0.865524	+	0.628840i	0.0638580	+	0.997959i	$0.479660\pi$
$278$		0			0
$279$	0.906117	−	2.78874i	0.0542478	−	0.166958i
$280$		0			0
$281$	−13.8660	−	10.0742i	−0.827176	−	0.600978i	0.0915833	−	0.995797i	$-0.470807\pi$
$281$	−13.8660	−	10.0742i	−0.827176	−	0.600978i	−0.918759	+	0.394819i	$0.870807\pi$
$282$		0			0
$283$	−3.06707	−	9.43947i	−0.182318	−	0.561118i	0.817574	−	0.575824i	$-0.195319\pi$
$283$	−3.06707	−	9.43947i	−0.182318	−	0.561118i	−0.999892	+	0.0147061i	$0.995319\pi$
$284$		0			0
$285$	2.87660			0.170395
$286$		0			0
$287$	2.33253			0.137685
$288$		0			0
$289$	6.05681	+	18.6409i	0.356283	+	1.09653i
$290$		0			0
$291$	8.73287	+	6.34480i	0.511930	+	0.371939i
$292$		0			0
$293$	−5.59429	+	17.2175i	−0.326822	+	1.00586i	0.643789	+	0.765203i	$0.277361\pi$
$293$	−5.59429	+	17.2175i	−0.326822	+	1.00586i	−0.970611	+	0.240652i	$0.922639\pi$
$294$		0			0
$295$	6.75043	−	4.90447i	0.393025	−	0.285549i
$296$		0			0
$297$	10.4316	+	15.3598i	0.605300	+	0.891265i
$298$		0			0
$299$	9.40940	−	6.83633i	0.544160	−	0.395355i
$300$		0			0
$301$	0.263537	−	0.811083i	0.0151900	−	0.0467501i
$302$		0			0
$303$	−1.80487	−	1.31132i	−0.103687	−	0.0753331i
$304$		0			0
$305$	−0.693906	−	2.13562i	−0.0397329	−	0.122285i
$306$		0			0
$307$	6.00433			0.342685			0.171343	−	0.985211i	$-0.445189\pi$
$307$	6.00433			0.342685			0.171343	+	0.985211i	$0.445189\pi$
$308$		0			0
$309$	2.53103			0.143985
$310$		0			0
$311$	4.59712	+	14.1485i	0.260679	+	0.802287i	0.992657	+	0.120959i	$0.0385971\pi$
$311$	4.59712	+	14.1485i	0.260679	+	0.802287i	−0.731979	+	0.681328i	$0.761403\pi$
$312$		0			0
$313$	1.95733	+	1.42208i	0.110635	+	0.0803808i	0.641727	−	0.766933i	$-0.278218\pi$
$313$	1.95733	+	1.42208i	0.110635	+	0.0803808i	−0.531092	+	0.847314i	$0.678218\pi$
$314$		0			0
$315$	−0.0931270	+	0.286615i	−0.00524711	+	0.0161490i
$316$		0			0
$317$	−15.5635	+	11.3075i	−0.874133	+	0.635095i	−0.931693	−	0.363247i	$-0.881668\pi$
$317$	−15.5635	+	11.3075i	−0.874133	+	0.635095i	0.0575596	+	0.998342i	$0.481668\pi$
$318$		0			0
$319$	0.0626077	−	0.0806618i	0.00350536	−	0.00451620i
$320$		0			0
$321$	14.0389	−	10.1999i	0.783576	−	0.569302i
$322$		0			0
$323$	4.15285	−	12.7812i	0.231071	−	0.711163i
$324$		0			0
$325$	2.70598	+	1.96601i	0.150101	+	0.109055i
$326$		0			0
$327$	2.98646	+	9.19137i	0.165151	+	0.508284i
$328$		0			0
$329$	1.21041			0.0667318
$330$		0			0
$331$	13.8876			0.763330			0.381665	−	0.924301i	$-0.375351\pi$
$331$	13.8876			0.763330			0.381665	+	0.924301i	$0.375351\pi$
$332$		0			0
$333$	−3.57634	−	11.0068i	−0.195982	−	0.603171i
$334$		0			0
$335$	2.80996	+	2.04156i	0.153525	+	0.111542i
$336$		0			0
$337$	−0.953253	+	2.93381i	−0.0519270	+	0.159815i	−0.973657	−	0.228017i	$-0.926776\pi$
$337$	−0.953253	+	2.93381i	−0.0519270	+	0.159815i	0.921730	+	0.387832i	$0.126776\pi$
$338$		0			0
$339$	−5.54469	+	4.02845i	−0.301146	+	0.218796i
$340$		0			0
$341$	7.05925	−	2.04853i	0.382280	−	0.110934i
$342$		0			0
$343$	2.57030	−	1.86743i	0.138783	−	0.100832i
$344$		0			0
$345$	1.39148	−	4.28253i	0.0749147	−	0.230564i
$346$		0			0
$347$	−23.1556	−	16.8235i	−1.24306	−	0.903134i	−0.245259	−	0.969458i	$-0.578873\pi$
$347$	−23.1556	−	16.8235i	−1.24306	−	0.903134i	−0.997798	+	0.0663235i	$0.978873\pi$
$348$		0			0
$349$	5.19773	+	15.9970i	0.278228	+	0.856298i	0.988347	+	0.152216i	$0.0486410\pi$
$349$	5.19773	+	15.9970i	0.278228	+	0.856298i	−0.710119	+	0.704081i	$0.751359\pi$
$350$		0			0
$351$	18.7248			0.999455
$352$		0			0
$353$	−14.6656			−0.780573			−0.390287	−	0.920693i	$-0.627624\pi$
$353$	−14.6656			−0.780573			−0.390287	+	0.920693i	$0.627624\pi$
$354$		0			0
$355$	4.65494	+	14.3264i	0.247059	+	0.760369i
$356$		0			0
$357$	−1.44367	−	1.04889i	−0.0764070	−	0.0555129i
$358$		0			0
$359$	9.54113	−	29.3646i	0.503561	−	1.54980i	−0.299614	−	0.954060i	$-0.596858\pi$
$359$	9.54113	−	29.3646i	0.503561	−	1.54980i	0.803176	−	0.595742i	$-0.203142\pi$
$360$		0			0
$361$	11.3792	−	8.26749i	0.598907	−	0.435131i
$362$		0			0
$363$	−5.25197	+	13.2410i	−0.275657	+	0.694974i
$364$		0			0
$365$	2.96415	−	2.15358i	0.155151	−	0.112724i
$366$		0			0
$367$	1.12218	−	3.45371i	0.0585773	−	0.180282i	−0.917486	−	0.397767i	$-0.869785\pi$
$367$	1.12218	−	3.45371i	0.0585773	−	0.180282i	0.976064	+	0.217485i	$0.0697852\pi$
$368$		0			0
$369$	10.9612	+	7.96377i	0.570617	+	0.414577i
$370$		0			0
$371$	−0.718147	−	2.21023i	−0.0372843	−	0.114749i
$372$		0			0
$373$	29.2244			1.51318			0.756590	−	0.653890i	$-0.226864\pi$
$373$	29.2244			1.51318			0.756590	+	0.653890i	$0.226864\pi$
$374$		0			0
$375$	1.29496			0.0668716
$376$		0			0
$377$	−0.0318209	−	0.0979348i	−0.00163886	−	0.00504390i
$378$		0			0
$379$	2.95555	+	2.14734i	0.151817	+	0.110301i	0.661101	−	0.750297i	$-0.270090\pi$
$379$	2.95555	+	2.14734i	0.151817	+	0.110301i	−0.509284	+	0.860599i	$0.670090\pi$
$380$		0			0
$381$	4.87933	−	15.0170i	0.249975	−	0.769345i
$382$		0			0
$383$	−11.5255	+	8.37373i	−0.588923	+	0.427878i	−0.841930	−	0.539587i	$-0.818581\pi$
$383$	−11.5255	+	8.37373i	−0.588923	+	0.427878i	0.253007	+	0.967465i	$0.418581\pi$
$384$		0			0
$385$	−0.725520	+	0.210540i	−0.0369759	+	0.0107301i
$386$		0			0
$387$	4.00765	−	2.91173i	0.203720	−	0.148012i
$388$		0			0
$389$	−2.54825	+	7.84271i	−0.129201	+	0.397641i	−0.994643	−	0.103368i	$-0.967038\pi$
$389$	−2.54825	+	7.84271i	−0.129201	+	0.397641i	0.865442	+	0.501010i	$0.167038\pi$
$390$		0			0
$391$	−17.0191	−	12.3651i	−0.860693	−	0.625330i
$392$		0			0
$393$	0.826461	+	2.54358i	0.0416894	+	0.128307i
$394$		0			0
$395$	11.6212			0.584726
$396$		0			0
$397$	−2.57097			−0.129033			−0.0645167	−	0.997917i	$-0.520551\pi$
$397$	−2.57097			−0.129033			−0.0645167	+	0.997917i	$0.520551\pi$
$398$		0			0
$399$	0.202475	+	0.623154i	0.0101364	+	0.0311967i
$400$		0			0
$401$	31.5282	+	22.9066i	1.57444	+	1.14390i	0.922737	+	0.385431i	$0.125947\pi$
$401$	31.5282	+	22.9066i	1.57444	+	1.14390i	0.651708	+	0.758470i	$0.274053\pi$
$402$		0			0
$403$	2.29070	−	7.05005i	0.114108	−	0.351188i
$404$		0			0
$405$	2.65379	−	1.92809i	0.131868	−	0.0958078i
$406$		0			0
$407$	17.7884	−	22.9180i	0.881739	−	1.13601i
$408$		0			0
$409$	2.76891	−	2.01173i	0.136914	−	0.0994735i	−0.517220	−	0.855852i	$-0.673033\pi$
$409$	2.76891	−	2.01173i	0.136914	−	0.0994735i	0.654134	+	0.756379i	$0.273033\pi$
$410$		0			0
$411$	5.77984	−	17.7885i	0.285098	−	0.877442i
$412$		0			0
$413$	1.53759	+	1.11713i	0.0756600	+	0.0549702i
$414$		0			0
$415$	−0.470553	−	1.44821i	−0.0230985	−	0.0710899i
$416$		0			0
$417$	21.1624			1.03633
$418$		0			0
$419$	−10.5914			−0.517426			−0.258713	−	0.965954i	$-0.583298\pi$
$419$	−10.5914			−0.517426			−0.258713	+	0.965954i	$0.583298\pi$
$420$		0			0
$421$	0.732540	+	2.25453i	0.0357018	+	0.109879i	0.967319	−	0.253561i	$-0.0816020\pi$
$421$	0.732540	+	2.25453i	0.0357018	+	0.109879i	−0.931617	+	0.363440i	$0.881602\pi$
$422$		0			0
$423$	5.68803	+	4.13259i	0.276561	+	0.200934i
$424$		0			0
$425$	1.86950	−	5.75372i	0.0906838	−	0.279096i
$426$		0			0
$427$	0.413796	−	0.300640i	0.0200250	−	0.0145490i
$428$		0			0
$429$	8.07094	+	11.8839i	0.389668	+	0.573761i
$430$		0			0
$431$	−21.2254	+	15.4211i	−1.02239	+	0.742810i	−0.966771	−	0.255642i	$-0.917713\pi$
$431$	−21.2254	+	15.4211i	−1.02239	+	0.742810i	−0.0556186	+	0.998452i	$0.517713\pi$
$432$		0			0
$433$	−6.19078	+	19.0533i	−0.297510	+	0.915641i	0.684857	+	0.728677i	$0.259865\pi$
$433$	−6.19078	+	19.0533i	−0.297510	+	0.915641i	−0.982367	+	0.186963i	$0.940135\pi$
$434$		0			0
$435$	−0.0322536	−	0.0234336i	−0.00154644	−	0.00112356i
$436$		0			0
$437$	2.38694	+	7.34624i	0.114183	+	0.351418i
$438$		0			0
$439$	−21.9546			−1.04783			−0.523917	−	0.851769i	$-0.675530\pi$
$439$	−21.9546			−1.04783			−0.523917	+	0.851769i	$0.675530\pi$
$440$		0			0
$441$	9.19285			0.437755
$442$		0			0
$443$	−5.04993	−	15.5421i	−0.239929	−	0.738427i	−0.996429	−	0.0844329i	$-0.973092\pi$
$443$	−5.04993	−	15.5421i	−0.239929	−	0.738427i	0.756500	−	0.653994i	$-0.226908\pi$
$444$		0			0
$445$	8.09490	+	5.88129i	0.383735	+	0.278800i
$446$		0			0
$447$	5.99516	−	18.4512i	0.283561	−	0.872712i
$448$		0			0
$449$	30.7811	−	22.3638i	1.45265	−	1.05541i	0.467448	−	0.884021i	$-0.345174\pi$
$449$	30.7811	−	22.3638i	1.45265	−	1.05541i	0.985203	−	0.171392i	$-0.0548264\pi$
$450$		0			0
$451$	−1.07732	+	33.9465i	−0.0507289	+	1.59848i
$452$		0			0
$453$	12.9155	−	9.38368i	0.606824	−	0.440884i
$454$		0			0
$455$	−0.235429	+	0.724575i	−0.0110371	+	0.0339686i
$456$		0			0
$457$	23.7055	+	17.2231i	1.10890	+	0.805660i	0.982489	−	0.186318i	$-0.0596555\pi$
$457$	23.7055	+	17.2231i	1.10890	+	0.805660i	0.126407	+	0.991978i	$0.459656\pi$
$458$		0			0
$459$	−10.4658	−	32.2105i	−0.488504	−	1.50346i
$460$		0			0
$461$	−12.1136			−0.564188			−0.282094	−	0.959387i	$-0.591029\pi$
$461$	−12.1136			−0.564188			−0.282094	+	0.959387i	$0.591029\pi$
$462$		0			0
$463$	3.92452			0.182388			0.0911940	−	0.995833i	$-0.470932\pi$
$463$	3.92452			0.182388			0.0911940	+	0.995833i	$0.470932\pi$
$464$		0			0
$465$	−0.886867	−	2.72950i	−0.0411275	−	0.126577i
$466$		0			0
$467$	28.4609	+	20.6780i	1.31701	+	0.956865i	0.999964	+	0.00845484i	$0.00269129\pi$
$467$	28.4609	+	20.6780i	1.31701	+	0.956865i	0.317047	+	0.948410i	$0.397309\pi$
$468$		0			0
$469$	−0.244475	+	0.752418i	−0.0112888	+	0.0347434i
$470$		0			0
$471$	21.8374	−	15.8658i	1.00621	−	0.731057i
$472$		0			0
$473$	11.6824	+	4.21000i	0.537157	+	0.193576i
$474$		0			0
$475$	−1.79713	+	1.30569i	−0.0824580	+	0.0599092i
$476$		0			0
$477$	4.17144	−	12.8384i	0.190997	−	0.587829i
$478$		0			0
$479$	28.2934	+	20.5564i	1.29276	+	0.939244i	0.999857	−	0.0168983i	$-0.00537914\pi$
$479$	28.2934	+	20.5564i	1.29276	+	0.939244i	0.292902	+	0.956143i	$0.405379\pi$
$480$		0			0
$481$	−9.04113	−	27.8257i	−0.412240	−	1.26874i
$482$		0			0
$483$	1.02566			0.0466693
$484$		0			0
$485$	−8.33570			−0.378504
$486$		0			0
$487$	−3.28735	−	10.1174i	−0.148964	−	0.458464i	0.848535	−	0.529139i	$-0.177485\pi$
$487$	−3.28735	−	10.1174i	−0.148964	−	0.458464i	−0.997499	+	0.0706745i	$0.977485\pi$
$488$		0			0
$489$	0.591904	+	0.430044i	0.0267668	+	0.0194472i
$490$		0			0
$491$	−8.99192	+	27.6743i	−0.405800	+	1.24892i	0.514426	+	0.857535i	$0.328005\pi$
$491$	−8.99192	+	27.6743i	−0.405800	+	1.24892i	−0.920226	+	0.391388i	$0.871995\pi$
$492$		0			0
$493$	−0.150683	+	0.109477i	−0.00678641	+	0.00493061i
$494$		0			0
$495$	−4.12825	−	1.48770i	−0.185551	−	0.0668673i
$496$		0			0
$497$	−2.77587	+	2.01679i	−0.124515	+	0.0904654i
$498$		0			0
$499$	7.15335	−	22.0158i	0.320228	−	0.985561i	−0.653321	−	0.757081i	$-0.726625\pi$
$499$	7.15335	−	22.0158i	0.320228	−	0.985561i	0.973549	−	0.228479i	$-0.0733754\pi$
$500$		0			0
$501$	−23.5044	−	17.0770i	−1.05010	−	0.762942i
$502$		0			0
$503$	−3.91243	−	12.0412i	−0.174447	−	0.536891i	0.825161	−	0.564897i	$-0.191084\pi$
$503$	−3.91243	−	12.0412i	−0.174447	−	0.536891i	−0.999608	+	0.0280059i	$0.991084\pi$
$504$		0			0
$505$	1.72279			0.0766630
$506$		0			0
$507$	−2.34708			−0.104237
$508$		0			0
$509$	3.04711	+	9.37803i	0.135061	+	0.415674i	0.995599	−	0.0937109i	$-0.0298729\pi$
$509$	3.04711	+	9.37803i	0.135061	+	0.415674i	−0.860539	+	0.509385i	$0.829873\pi$
$510$		0			0
$511$	0.675166	+	0.490536i	0.0298676	+	0.0217001i
$512$		0			0
$513$	−3.84285	+	11.8271i	−0.169666	+	0.522179i
$514$		0			0
$515$	−1.58124	+	1.14884i	−0.0696778	+	0.0506239i
$516$		0			0
$517$	−0.559046	+	17.6156i	−0.0245868	+	0.774735i
$518$		0			0
$519$	−2.26891	+	1.64846i	−0.0995939	+	0.0723592i
$520$		0			0
$521$	−0.779230	+	2.39822i	−0.0341387	+	0.105068i	−0.966674	−	0.256011i	$-0.917592\pi$
$521$	−0.779230	+	2.39822i	−0.0341387	+	0.105068i	0.932535	+	0.361079i	$0.117592\pi$
$522$		0			0
$523$	16.7639	+	12.1797i	0.733033	+	0.532580i	0.890522	−	0.454941i	$-0.150340\pi$
$523$	16.7639	+	12.1797i	0.733033	+	0.532580i	−0.157488	+	0.987521i	$0.550340\pi$
$524$		0			0
$525$	0.0911485	+	0.280526i	0.00397805	+	0.0122432i
$526$		0			0
$527$	−13.4079			−0.584057
$528$		0			0
$529$	−10.9087			−0.474290
$530$		0			0
$531$	3.41145	+	10.4994i	0.148044	+	0.455634i
$532$		0			0
$533$	27.7103	+	20.1327i	1.20027	+	0.872046i
$534$		0			0
$535$	−4.14096	+	12.7446i	−0.179029	+	0.550996i
$536$		0			0
$537$	−23.2125	+	16.8649i	−1.00169	+	0.727773i
$538$		0			0
$539$	12.9469	+	19.0635i	0.557663	+	0.821123i
$540$		0			0
$541$	−21.6636	+	15.7395i	−0.931390	+	0.676694i	−0.946333	−	0.323194i	$-0.895243\pi$
$541$	−21.6636	+	15.7395i	−0.931390	+	0.676694i	0.0149428	+	0.999888i	$0.495243\pi$
$542$		0			0
$543$	−3.57619	+	11.0064i	−0.153469	+	0.472329i
$544$		0			0
$545$	−6.03774	−	4.38667i	−0.258628	−	0.187904i
$546$		0			0
$547$	1.41231	+	4.34665i	0.0603862	+	0.185849i	0.976699	−	0.214614i	$-0.0688492\pi$
$547$	1.41231	+	4.34665i	0.0603862	+	0.185849i	−0.916313	+	0.400463i	$0.868849\pi$
$548$		0			0
$549$	2.97099			0.126799
$550$		0			0
$551$	0.0683889			0.00291346
$552$		0			0
$553$	0.817981	+	2.51749i	0.0347841	+	0.107054i
$554$		0			0
$555$	−9.16406	−	6.65808i	−0.388993	−	0.282620i
$556$		0			0
$557$	−9.82160	+	30.2278i	−0.416155	+	1.28079i	0.495059	+	0.868859i	$0.335146\pi$
$557$	−9.82160	+	30.2278i	−0.416155	+	1.28079i	−0.911214	+	0.411933i	$0.864854\pi$
$558$		0			0
$559$	10.1315	−	7.36097i	0.428517	−	0.311336i
$560$		0			0
$561$	15.9317	−	20.5260i	0.672639	−	0.866607i
$562$		0			0
$563$	−7.52271	+	5.46557i	−0.317044	+	0.230346i	−0.734913	−	0.678161i	$-0.762777\pi$
$563$	−7.52271	+	5.46557i	−0.317044	+	0.230346i	0.417869	+	0.908507i	$0.362777\pi$
$564$		0			0
$565$	1.63548	−	5.03348i	0.0688051	−	0.211760i
$566$		0			0
$567$	0.604473	+	0.439176i	0.0253855	+	0.0184436i
$568$		0			0
$569$	−14.5753	−	44.8582i	−0.611029	−	1.88055i	−0.448305	−	0.893881i	$-0.647972\pi$
$569$	−14.5753	−	44.8582i	−0.611029	−	1.88055i	−0.162724	−	0.986672i	$-0.552028\pi$
$570$		0			0
$571$	4.32635			0.181052			0.0905260	−	0.995894i	$-0.471145\pi$
$571$	4.32635			0.181052			0.0905260	+	0.995894i	$0.471145\pi$
$572$		0			0
$573$	14.9025			0.622561
$574$		0			0
$575$	1.07453	+	3.30707i	0.0448111	+	0.137914i
$576$		0			0
$577$	−7.10111	−	5.15926i	−0.295623	−	0.214783i	0.430080	−	0.902791i	$-0.358485\pi$
$577$	−7.10111	−	5.15926i	−0.295623	−	0.214783i	−0.725703	+	0.688008i	$0.758485\pi$
$578$		0			0
$579$	3.32614	−	10.2368i	0.138230	−	0.425428i
$580$		0			0
$581$	0.280604	−	0.203871i	0.0116414	−	0.00845798i
$582$		0			0
$583$	32.4983	−	9.43073i	1.34594	−	0.390581i
$584$		0			0
$585$	−3.58021	+	2.60117i	−0.148023	+	0.107545i
$586$		0			0
$587$	6.39416	−	19.6792i	0.263915	−	0.812247i	−0.728026	−	0.685549i	$-0.759562\pi$
$587$	6.39416	−	19.6792i	0.263915	−	0.812247i	0.991941	−	0.126698i	$-0.0404379\pi$
$588$		0			0
$589$	3.98289	+	2.89374i	0.164112	+	0.119234i
$590$		0			0
$591$	1.45967	+	4.49239i	0.0600426	+	0.184792i
$592$		0			0
$593$	−46.8273			−1.92296			−0.961482	−	0.274866i	$-0.911366\pi$
$593$	−46.8273			−1.92296			−0.961482	+	0.274866i	$0.911366\pi$
$594$		0			0
$595$	1.37801			0.0564929
$596$		0			0
$597$	2.54008	+	7.81755i	0.103958	+	0.319951i
$598$		0			0
$599$	−25.0840	−	18.2246i	−1.02490	−	0.744635i	−0.0576205	−	0.998339i	$-0.518351\pi$
$599$	−25.0840	−	18.2246i	−1.02490	−	0.744635i	−0.967282	+	0.253703i	$0.918351\pi$
$600$		0			0
$601$	12.9877	−	39.9719i	0.529778	−	1.63049i	−0.224891	−	0.974384i	$-0.572203\pi$
$601$	12.9877	−	39.9719i	0.529778	−	1.63049i	0.754669	−	0.656105i	$-0.227797\pi$
$602$		0			0
$603$	−3.71778	+	2.70112i	−0.151400	+	0.109998i
$604$		0			0
$605$	−2.72900	−	10.6561i	−0.110950	−	0.433232i
$606$		0			0
$607$	8.78543	−	6.38299i	0.356590	−	0.259078i	−0.395039	−	0.918665i	$-0.629269\pi$
$607$	8.78543	−	6.38299i	0.356590	−	0.259078i	0.751628	+	0.659587i	$0.229269\pi$
$608$		0			0
$609$	0.00280617	−	0.00863649i	0.000113712	−	0.000349968i
$610$		0			0
$611$	14.3796	+	10.4474i	0.581735	+	0.422655i
$612$		0			0
$613$	−11.4399	−	35.2084i	−0.462054	−	1.42205i	−0.862651	−	0.505800i	$-0.831197\pi$
$613$	−11.4399	−	35.2084i	−0.462054	−	1.42205i	0.400597	−	0.916254i	$-0.368803\pi$
$614$		0			0
$615$	13.2609			0.534733
$616$		0			0
$617$	37.3620			1.50414			0.752068	−	0.659085i	$-0.229056\pi$
$617$	37.3620			1.50414			0.752068	+	0.659085i	$0.229056\pi$
$618$		0			0
$619$	12.2758	+	37.7811i	0.493407	+	1.51855i	0.819424	+	0.573187i	$0.194293\pi$
$619$	12.2758	+	37.7811i	0.493407	+	1.51855i	−0.326017	+	0.945364i	$0.605707\pi$
$620$		0			0
$621$	15.7487	+	11.4421i	0.631973	+	0.459155i
$622$		0			0
$623$	−0.704281	+	2.16756i	−0.0282164	+	0.0868413i
$624$		0			0
$625$	−0.809017	+	0.587785i	−0.0323607	+	0.0235114i
$626$		0			0
$627$	−9.16260	+	2.65891i	−0.365919	+	0.106187i
$628$		0			0
$629$	−42.8127	+	31.1053i	−1.70705	+	1.24025i
$630$		0			0
$631$	−2.29915	+	7.07604i	−0.0915276	+	0.281693i	−0.986333	−	0.164763i	$-0.947314\pi$
$631$	−2.29915	+	7.07604i	−0.0915276	+	0.281693i	0.894806	+	0.446456i	$0.147314\pi$
$632$		0			0
$633$	−20.1717	−	14.6556i	−0.801754	−	0.582508i
$634$		0			0
$635$	3.76793	+	11.5965i	0.149526	+	0.460192i
$636$		0			0
$637$	23.2399			0.920798
$638$		0			0
$639$	−19.9304			−0.788433
$640$		0			0
$641$	−0.576593	−	1.77457i	−0.0227741	−	0.0700913i	0.939024	−	0.343853i	$-0.111732\pi$
$641$	−0.576593	−	1.77457i	−0.0227741	−	0.0700913i	−0.961798	+	0.273761i	$0.911732\pi$
$642$		0			0
$643$	36.9990	+	26.8813i	1.45910	+	1.06010i	0.983597	+	0.180382i	$0.0577333\pi$
$643$	36.9990	+	26.8813i	1.45910	+	1.06010i	0.475501	+	0.879715i	$0.342267\pi$
$644$		0			0
$645$	1.49827	−	4.61119i	0.0589942	−	0.181565i
$646$		0			0
$647$	−27.5385	+	20.0079i	−1.08265	+	0.786591i	−0.978143	−	0.207933i	$-0.933327\pi$
$647$	−27.5385	+	20.0079i	−1.08265	+	0.786591i	−0.104507	+	0.994524i	$0.533327\pi$
$648$		0			0
$649$	−16.9683	+	21.8614i	−0.666063	+	0.858135i
$650$		0			0
$651$	0.528864	−	0.384242i	0.0207278	−	0.0150596i
$652$		0			0
$653$	0.960362	−	2.95569i	0.0375819	−	0.115665i	−0.930506	−	0.366278i	$-0.880632\pi$
$653$	0.960362	−	2.95569i	0.0375819	−	0.115665i	0.968087	+	0.250613i	$0.0806320\pi$
$654$		0			0
$655$	−1.67086	−	1.21395i	−0.0652859	−	0.0474330i
$656$		0			0
$657$	1.49799	+	4.61033i	0.0584420	+	0.179866i
$658$		0			0
$659$	10.1518			0.395459			0.197729	−	0.980257i	$-0.436643\pi$
$659$	10.1518			0.395459			0.197729	+	0.980257i	$0.436643\pi$
$660$		0			0
$661$	−44.7642			−1.74113			−0.870564	−	0.492056i	$-0.836246\pi$
$661$	−44.7642			−1.74113			−0.870564	+	0.492056i	$0.836246\pi$
$662$		0			0
$663$	−8.09746	−	24.9214i	−0.314479	−	0.967868i
$664$		0			0
$665$	−0.409345	−	0.297407i	−0.0158737	−	0.0115329i
$666$		0			0
$667$	0.0330813	−	0.101814i	0.00128091	−	0.00394225i
$668$		0			0
$669$	−22.7655	+	16.5401i	−0.880166	+	0.639478i
$670$		0			0
$671$	4.18425	+	6.16103i	0.161531	+	0.237844i
$672$		0			0
$673$	4.34015	−	3.15330i	0.167300	−	0.121551i	−0.500985	−	0.865456i	$-0.667029\pi$
$673$	4.34015	−	3.15330i	0.167300	−	0.121551i	0.668285	+	0.743905i	$0.267029\pi$
$674$		0			0
$675$	−1.72994	+	5.32422i	−0.0665856	+	0.204929i
$676$		0			0
$677$	9.15379	+	6.65062i	0.351809	+	0.255604i	0.749627	−	0.661860i	$-0.230233\pi$
$677$	9.15379	+	6.65062i	0.351809	+	0.255604i	−0.397819	+	0.917464i	$0.630233\pi$
$678$		0			0
$679$	−0.586725	−	1.80575i	−0.0225164	−	0.0692984i
$680$		0			0
$681$	7.77592			0.297974
$682$		0			0
$683$	−31.0817			−1.18931			−0.594655	−	0.803981i	$-0.702711\pi$
$683$	−31.0817			−1.18931			−0.594655	+	0.803981i	$0.702711\pi$
$684$		0			0
$685$	4.46332	+	13.7367i	0.170535	+	0.524852i
$686$		0			0
$687$	24.3137	+	17.6649i	0.927625	+	0.673959i
$688$		0			0
$689$	10.5456	−	32.4560i	0.401755	−	1.23647i
$690$		0			0
$691$	3.20162	−	2.32611i	0.121795	−	0.0884895i	−0.525220	−	0.850967i	$-0.676017\pi$
$691$	3.20162	−	2.32611i	0.121795	−	0.0884895i	0.647015	+	0.762477i	$0.276017\pi$
$692$		0			0
$693$	0.0317044	−	0.999013i	0.00120435	−	0.0379494i
$694$		0			0
$695$	−13.2210	+	9.60564i	−0.501502	+	0.364363i
$696$		0			0
$697$	19.1444	−	58.9204i	0.725145	−	2.23177i
$698$		0			0
$699$	−25.3722	−	18.4340i	−0.959665	−	0.697238i
$700$		0			0
$701$	7.08605	+	21.8086i	0.267636	+	0.823700i	0.991074	+	0.133311i	$0.0425608\pi$
$701$	7.08605	+	21.8086i	0.267636	+	0.823700i	−0.723438	+	0.690389i	$0.757439\pi$
$702$		0			0
$703$	19.4310			0.732854
$704$		0			0
$705$	6.88142			0.259169
$706$		0			0
$707$	0.121262	+	0.373205i	0.00456052	+	0.0140358i
$708$		0			0
$709$	−26.2985	−	19.1070i	−0.987660	−	0.717577i	−0.0282525	−	0.999601i	$-0.508994\pi$
$709$	−26.2985	−	19.1070i	−0.987660	−	0.717577i	−0.959407	+	0.282024i	$0.908994\pi$
$710$		0			0
$711$	−4.75134	+	14.6231i	−0.178189	+	0.548410i
$712$		0			0
$713$	6.23467	−	4.52976i	0.233490	−	0.169641i
$714$		0			0
$715$	−10.4364	−	3.76097i	−0.390298	−	0.140652i
$716$		0			0
$717$	−19.2634	+	13.9956i	−0.719403	+	0.522677i
$718$		0			0
$719$	−9.40526	+	28.9464i	−0.350757	+	1.07952i	0.607672	+	0.794188i	$0.292103\pi$
$719$	−9.40526	+	28.9464i	−0.350757	+	1.07952i	−0.958429	+	0.285331i	$0.907897\pi$
$720$		0			0
$721$	−0.360170	−	0.261679i	−0.0134134	−	0.00974544i
$722$		0			0
$723$	−4.96167	−	15.2704i	−0.184526	−	0.567914i
$724$		0			0
$725$	0.0307867			0.00114339
$726$		0			0
$727$	−36.6338			−1.35867			−0.679337	−	0.733827i	$-0.737732\pi$
$727$	−36.6338			−1.35867			−0.679337	+	0.733827i	$0.737732\pi$
$728$		0			0
$729$	8.06178	+	24.8116i	0.298585	+	0.918949i
$730$		0			0
$731$	−18.3252	−	13.3140i	−0.677782	−	0.492438i
$732$		0			0
$733$	9.94139	−	30.5964i	0.367194	−	1.13011i	−0.581402	−	0.813616i	$-0.697496\pi$
$733$	9.94139	−	30.5964i	0.367194	−	1.13011i	0.948596	−	0.316489i	$-0.102504\pi$
$734$		0			0
$735$	7.27917	−	5.28863i	0.268496	−	0.195074i
$736$		0			0
$737$	−10.8374	−	3.90549i	−0.399201	−	0.143861i
$738$		0			0
$739$	16.8109	−	12.2138i	0.618398	−	0.449292i	−0.233964	−	0.972245i	$-0.575170\pi$
$739$	16.8109	−	12.2138i	0.618398	−	0.449292i	0.852362	+	0.522953i	$0.175170\pi$
$740$		0			0
$741$	−2.97323	+	9.15066i	−0.109224	+	0.336158i
$742$		0			0
$743$	−30.6146	−	22.2428i	−1.12314	−	0.816010i	−0.138459	−	0.990368i	$-0.544215\pi$
$743$	−30.6146	−	22.2428i	−1.12314	−	0.816010i	−0.984682	+	0.174358i	$0.944215\pi$
$744$		0			0
$745$	4.62960	+	14.2484i	0.169615	+	0.522022i
$746$		0			0
$747$	2.01469			0.0737138
$748$		0			0
$749$	−3.05231			−0.111529
$750$		0			0
$751$	4.03103	+	12.4062i	0.147094	+	0.452710i	0.997274	−	0.0737821i	$-0.0235069\pi$
$751$	4.03103	+	12.4062i	0.147094	+	0.452710i	−0.850180	+	0.526492i	$0.823507\pi$
$752$		0			0
$753$	−22.8323	−	16.5887i	−0.832057	−	0.604525i
$754$		0			0
$755$	−3.80960	+	11.7247i	−0.138646	+	0.426707i
$756$		0			0
$757$	−33.3075	+	24.1993i	−1.21058	+	0.879540i	−0.995284	−	0.0970086i	$-0.969073\pi$
$757$	−33.3075	+	24.1993i	−1.21058	+	0.879540i	−0.215299	+	0.976548i	$0.569073\pi$
$758$		0			0
$759$	−0.473719	+	14.9270i	−0.0171949	+	0.541815i
$760$		0			0
$761$	35.3819	−	25.7065i	1.28259	−	0.931858i	0.282965	−	0.959130i	$-0.408682\pi$
$761$	35.3819	−	25.7065i	1.28259	−	0.931858i	0.999628	+	0.0272718i	$0.00868196\pi$
$762$		0			0
$763$	0.525302	−	1.61671i	0.0190172	−	0.0585290i
$764$		0			0
$765$	6.47564	+	4.70483i	0.234127	+	0.170103i
$766$		0			0
$767$	8.62429	+	26.5428i	0.311405	+	0.958406i
$768$		0			0
$769$	−17.3914			−0.627151			−0.313575	−	0.949563i	$-0.601527\pi$
$769$	−17.3914			−0.627151			−0.313575	+	0.949563i	$0.601527\pi$
$770$		0			0
$771$	19.0475			0.685979
$772$		0			0
$773$	7.68850	+	23.6628i	0.276536	+	0.851091i	0.988809	+	0.149188i	$0.0476660\pi$
$773$	7.68850	+	23.6628i	0.276536	+	0.851091i	−0.712273	+	0.701903i	$0.752334\pi$
$774$		0			0
$775$	1.79298	+	1.30268i	0.0644059	+	0.0467936i
$776$		0			0
$777$	0.797302	−	2.45384i	0.0286031	−	0.0880311i
$778$		0			0
$779$	−18.4033	+	13.3708i	−0.659368	+	0.479059i
$780$		0			0
$781$	−28.0693	−	41.3302i	−1.00440	−	1.47891i
$782$		0			0
$783$	0.139435	−	0.101305i	0.00498299	−	0.00362035i
$784$		0			0
$785$	−6.44122	+	19.8240i	−0.229897	+	0.707550i
$786$		0			0
$787$	21.8953	+	15.9079i	0.780484	+	0.567055i	0.905124	−	0.425147i	$-0.139778\pi$
$787$	21.8953	+	15.9079i	0.780484	+	0.567055i	−0.124641	+	0.992202i	$0.539778\pi$
$788$		0			0
$789$	−10.9923	−	33.8308i	−0.391336	−	1.20441i
$790$		0			0
$791$	1.20551			0.0428632
$792$		0			0
$793$	7.51078			0.266716
$794$		0			0
$795$	−4.08282	−	12.5656i	−0.144803	−	0.445657i
$796$		0			0
$797$	9.73988	+	7.07644i	0.345004	+	0.250660i	0.746770	−	0.665082i	$-0.231603\pi$
$797$	9.73988	+	7.07644i	0.345004	+	0.250660i	−0.401766	+	0.915742i	$0.631603\pi$
$798$		0			0
$799$	9.93448	−	30.5752i	0.351457	−	1.08167i
$800$		0			0
$801$	−10.7101	+	7.78136i	−0.378424	+	0.274941i
$802$		0			0
$803$	−7.45086	+	9.59946i	−0.262935	+	0.338758i
$804$		0			0
$805$	−0.640774	+	0.465550i	−0.0225843	+	0.0164085i
$806$		0			0
$807$	−0.567897	+	1.74781i	−0.0199909	+	0.0615257i
$808$		0			0
$809$	−22.1601	−	16.1003i	−0.779109	−	0.566056i	0.125603	−	0.992081i	$-0.459914\pi$
$809$	−22.1601	−	16.1003i	−0.779109	−	0.566056i	−0.904711	+	0.426025i	$0.859914\pi$
$810$		0			0
$811$	−16.7926	−	51.6823i	−0.589668	−	1.81481i	−0.579657	−	0.814860i	$-0.696814\pi$
$811$	−16.7926	−	51.6823i	−0.589668	−	1.81481i	−0.0100101	−	0.999950i	$-0.503186\pi$
$812$		0			0
$813$	−13.4026			−0.470051
$814$		0			0
$815$	−0.564984			−0.0197905
$816$		0			0
$817$	2.57012	+	7.91001i	0.0899171	+	0.276736i
$818$		0			0
$819$	−0.815489	−	0.592487i	−0.0284955	−	0.0207032i
$820$		0			0
$821$	−12.2988	+	37.8517i	−0.429230	+	1.32103i	0.469655	+	0.882850i	$0.344378\pi$
$821$	−12.2988	+	37.8517i	−0.429230	+	1.32103i	−0.898885	+	0.438185i	$0.855622\pi$
$822$		0			0
$823$	19.3221	−	14.0384i	0.673528	−	0.489347i	−0.197676	−	0.980267i	$-0.563340\pi$
$823$	19.3221	−	14.0384i	0.673528	−	0.489347i	0.871204	+	0.490921i	$0.163340\pi$
$824$		0			0
$825$	−4.12474	+	1.19697i	−0.143605	+	0.0416730i
$826$		0			0
$827$	6.33938	−	4.60583i	0.220442	−	0.160160i	−0.472084	−	0.881554i	$-0.656498\pi$
$827$	6.33938	−	4.60583i	0.220442	−	0.160160i	0.692526	+	0.721393i	$0.256498\pi$
$828$		0			0
$829$	11.1578	−	34.3400i	0.387525	−	1.19268i	−0.547107	−	0.837063i	$-0.684271\pi$
$829$	11.1578	−	34.3400i	0.387525	−	1.19268i	0.934632	−	0.355616i	$-0.115729\pi$
$830$		0			0
$831$	−18.6542	−	13.5531i	−0.647107	−	0.470151i
$832$		0			0
$833$	−12.9895	−	39.9775i	−0.450059	−	1.38514i
$834$		0			0
$835$	22.4354			0.776410
$836$		0			0
$837$	12.4071			0.428850
$838$		0			0
$839$	−7.84756	−	24.1523i	−0.270928	−	0.833830i	−0.990268	−	0.139172i	$-0.955556\pi$
$839$	−7.84756	−	24.1523i	−0.270928	−	0.833830i	0.719340	−	0.694658i	$-0.244444\pi$
$840$		0			0
$841$	23.4607	+	17.0452i	0.808991	+	0.587766i
$842$		0			0
$843$	6.85856	−	21.1085i	0.236221	−	0.727015i
$844$		0			0
$845$	1.46632	−	1.06534i	0.0504428	−	0.0366489i
$846$		0			0
$847$	2.11633	−	1.34123i	0.0727181	−	0.0460853i
$848$		0			0
$849$	10.3982	−	7.55470i	0.356864	−	0.259277i
$850$		0			0
$851$	9.39924	−	28.9279i	0.322202	−	0.991635i
$852$		0			0
$853$	13.8067	+	10.0312i	0.472732	+	0.343460i	0.798505	−	0.601988i	$-0.205624\pi$
$853$	13.8067	+	10.0312i	0.472732	+	0.343460i	−0.325773	+	0.945448i	$0.605624\pi$
$854$		0			0
$855$	−0.908212	−	2.79519i	−0.0310602	−	0.0955935i
$856$		0			0
$857$	31.2827			1.06860			0.534298	−	0.845296i	$-0.320576\pi$
$857$	31.2827			1.06860			0.534298	+	0.845296i	$0.320576\pi$
$858$		0			0
$859$	−50.6101			−1.72679			−0.863396	−	0.504526i	$-0.831667\pi$
$859$	−50.6101			−1.72679			−0.863396	+	0.504526i	$0.831667\pi$
$860$		0			0
$861$	0.933398	+	2.87270i	0.0318101	+	0.0979015i
$862$		0			0
$863$	−24.2231	−	17.5991i	−0.824564	−	0.599081i	0.0934519	−	0.995624i	$-0.470210\pi$
$863$	−24.2231	−	17.5991i	−0.824564	−	0.599081i	−0.918016	+	0.396543i	$0.870210\pi$
$864$		0			0
$865$	0.669243	−	2.05972i	0.0227549	−	0.0700325i
$866$		0			0
$867$	−20.5341	+	14.9189i	−0.697376	+	0.506673i
$868$		0			0
$869$	−37.0161	+	10.7418i	−1.25568	+	0.364389i
$870$		0			0
$871$	−9.39869	+	6.82855i	−0.318463	+	0.231377i
$872$		0			0
$873$	3.40806	−	10.4889i	0.115345	−	0.354997i
$874$		0			0
$875$	−0.184276	−	0.133884i	−0.00622965	−	0.00452611i
$876$		0			0
$877$	7.35371	+	22.6324i	0.248317	+	0.764241i	0.995073	+	0.0991433i	$0.0316102\pi$
$877$	7.35371	+	22.6324i	0.248317	+	0.764241i	−0.746756	+	0.665098i	$0.768390\pi$
$878$		0			0
$879$	−23.4434			−0.790726
$880$		0			0
$881$	34.7141			1.16955			0.584773	−	0.811197i	$-0.301184\pi$
$881$	34.7141			1.16955			0.584773	+	0.811197i	$0.301184\pi$
$882$		0			0
$883$	2.24074	+	6.89628i	0.0754068	+	0.232078i	0.981654	−	0.190669i	$-0.0610657\pi$
$883$	2.24074	+	6.89628i	0.0754068	+	0.232078i	−0.906248	+	0.422747i	$0.861066\pi$
$884$		0			0
$885$	8.74155	+	6.35111i	0.293844	+	0.213490i
$886$		0			0
$887$	4.42222	−	13.6102i	0.148483	−	0.456985i	−0.848959	−	0.528459i	$-0.822770\pi$
$887$	4.42222	−	13.6102i	0.148483	−	0.456985i	0.997442	+	0.0714735i	$0.0227702\pi$
$888$		0			0
$889$	−2.24692	+	1.63248i	−0.0753593	+	0.0547517i
$890$		0			0
$891$	−6.67073	+	8.59437i	−0.223478	+	0.287922i
$892$		0			0
$893$	−9.54993	+	6.93843i	−0.319576	+	0.232186i
$894$		0			0
$895$	6.84683	−	21.0724i	0.228864	−	0.704372i
$896$		0			0
$897$	12.1848	+	8.85279i	0.406839	+	0.295586i
$898$		0			0
$899$	−0.0210846	−	0.0648916i	−0.000703210	−	0.00216426i
$900$		0			0
$901$	−61.7253			−2.05637
$902$		0			0
$903$	1.10437			0.0367513
$904$		0			0
$905$	−2.76161	−	8.49937i	−0.0917992	−	0.282529i
$906$		0			0
$907$	45.1350	+	32.7925i	1.49868	+	1.08886i	0.970902	+	0.239477i	$0.0769760\pi$
$907$	45.1350	+	32.7925i	1.49868	+	1.08886i	0.527782	+	0.849380i	$0.323024\pi$
$908$		0			0
$909$	−0.704364	+	2.16781i	−0.0233623	+	0.0719017i
$910$		0			0
$911$	31.4629	−	22.8591i	1.04241	−	0.757356i	0.0716567	−	0.997429i	$-0.477171\pi$
$911$	31.4629	−	22.8591i	1.04241	−	0.757356i	0.970755	+	0.240073i	$0.0771714\pi$
$912$		0			0
$913$	2.83743	+	4.17793i	0.0939052	+	0.138269i
$914$		0			0
$915$	2.35252	−	1.70920i	0.0777719	−	0.0565046i
$916$		0			0
$917$	0.145370	−	0.447403i	0.00480054	−	0.0147746i
$918$		0			0
$919$	−30.2058	−	21.9458i	−0.996398	−	0.723926i	−0.0350852	−	0.999384i	$-0.511170\pi$
$919$	−30.2058	−	21.9458i	−0.996398	−	0.723926i	−0.961313	+	0.275459i	$0.911170\pi$
$920$		0			0
$921$	2.40273	+	7.39484i	0.0791726	+	0.243668i
$922$		0			0
$923$	−50.3848			−1.65844
$924$		0			0
$925$	8.74728			0.287609
$926$		0			0
$927$	−0.799108	−	2.45940i	−0.0262462	−	0.0807774i
$928$		0			0
$929$	−37.9302	−	27.5579i	−1.24445	−	0.904145i	−0.246563	−	0.969127i	$-0.579301\pi$
$929$	−37.9302	−	27.5579i	−1.24445	−	0.904145i	−0.997886	+	0.0649818i	$0.979301\pi$
$930$		0			0
$931$	−4.76948	+	14.6790i	−0.156314	+	0.481084i
$932$		0			0
$933$	−15.5854	+	11.3235i	−0.510244	+	0.370714i
$934$		0			0
$935$	−0.636456	+	20.0549i	−0.0208144	+	0.655864i
$936$		0			0
$937$	−43.0614	+	31.2859i	−1.40675	+	1.02207i	−0.412971	+	0.910744i	$0.635509\pi$
$937$	−43.0614	+	31.2859i	−1.40675	+	1.02207i	−0.993784	+	0.111323i	$0.964491\pi$
$938$		0			0
$939$	−0.968156	+	2.97968i	−0.0315946	+	0.0972381i
$940$		0			0
$941$	21.1858	+	15.3924i	0.690638	+	0.501778i	0.876870	−	0.480728i	$-0.159628\pi$
$941$	21.1858	+	15.3924i	0.690638	+	0.501778i	−0.186232	+	0.982506i	$0.559628\pi$
$942$		0			0
$943$	11.0036	+	33.8657i	0.358328	+	1.10282i
$944$		0			0
$945$	−1.27515			−0.0414805
$946$		0			0
$947$	−27.9451			−0.908095			−0.454047	−	0.890977i	$-0.650020\pi$
$947$	−27.9451			−0.908095			−0.454047	+	0.890977i	$0.650020\pi$
$948$		0			0
$949$	3.78697	+	11.6551i	0.122930	+	0.378341i
$950$		0			0
$951$	−20.1542	−	14.6429i	−0.653543	−	0.474827i
$952$		0			0
$953$	−2.26135	+	6.95972i	−0.0732523	+	0.225447i	−0.980979	−	0.194115i	$-0.937816\pi$
$953$	−2.26135	+	6.95972i	−0.0732523	+	0.225447i	0.907726	+	0.419562i	$0.137816\pi$
$954$		0			0
$955$	−9.31021	+	6.76426i	−0.301271	+	0.218886i
$956$		0			0
$957$	0.124395	+	0.0448285i	0.00402112	+	0.00144910i
$958$		0			0
$959$	−2.66161	+	1.93377i	−0.0859477	+	0.0624447i
$960$		0			0
$961$	−8.06171	+	24.8114i	−0.260055	+	0.800367i
$962$		0			0
$963$	−14.3437	−	10.4213i	−0.462218	−	0.335821i
$964$		0			0
$965$	2.56853	+	7.90511i	0.0826837	+	0.254474i
$966$		0			0
$967$	39.7018			1.27673			0.638363	−	0.769736i	$-0.279612\pi$
$967$	39.7018			1.27673			0.638363	+	0.769736i	$0.279612\pi$
$968$		0			0
$969$	17.4029			0.559061
$970$		0			0
$971$	−18.2605	−	56.2000i	−0.586007	−	1.80354i	−0.595190	−	0.803585i	$-0.702923\pi$
$971$	−18.2605	−	56.2000i	−0.586007	−	1.80354i	0.00918293	−	0.999958i	$-0.497077\pi$
$972$		0			0
$973$	−3.01145	−	2.18795i	−0.0965426	−	0.0701423i
$974$		0			0
$975$	−1.33846	+	4.11937i	−0.0428652	+	0.131925i
$976$		0			0
$977$	41.2873	−	29.9969i	1.32090	−	0.959687i	0.320976	−	0.947087i	$-0.395989\pi$
$977$	41.2873	−	29.9969i	1.32090	−	0.959687i	0.999921	−	0.0125998i	$-0.00401074\pi$
$978$		0			0
$979$	−31.2202	−	11.2509i	−0.997803	−	0.359580i
$980$		0			0
$981$	7.98836	−	5.80388i	0.255049	−	0.185304i
$982$		0			0
$983$	6.67179	−	20.5337i	0.212797	−	0.654922i	−0.786505	−	0.617583i	$-0.788112\pi$
$983$	6.67179	−	20.5337i	0.212797	−	0.654922i	0.999303	−	0.0373391i	$-0.0118882\pi$
$984$		0			0
$985$	−2.95101	−	2.14404i	−0.0940271	−	0.0683147i
$986$		0			0
$987$	0.484362	+	1.49071i	0.0154174	+	0.0474500i
$988$		0			0
$989$	13.0193			0.413988
$990$		0			0
$991$	−33.7197			−1.07114			−0.535570	−	0.844491i	$-0.679903\pi$
$991$	−33.7197			−1.07114			−0.535570	+	0.844491i	$0.679903\pi$
$992$		0			0
$993$	5.55733	+	17.1037i	0.176356	+	0.542769i
$994$		0			0
$995$	−5.13529	−	3.73101i	−0.162800	−	0.118281i
$996$		0			0
$997$	4.48212	−	13.7945i	0.141950	−	0.436877i	−0.854656	−	0.519194i	$-0.826232\pi$
$997$	4.48212	−	13.7945i	0.141950	−	0.436877i	0.996606	+	0.0823171i	$0.0262320\pi$
$998$		0			0
$999$	39.6169	−	28.7834i	1.25342	−	0.910665i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	880.2.bo.d.641.2		8
4.3	odd	2		440.2.y.a.201.1	yes	8
11.2	odd	10		9680.2.a.ct.1.3		4
11.4	even	5	inner	880.2.bo.d.81.2		8
11.9	even	5		9680.2.a.cu.1.3		4
44.15	odd	10		440.2.y.a.81.1	✓	8
44.31	odd	10		4840.2.a.y.1.2		4
44.35	even	10		4840.2.a.z.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
440.2.y.a.81.1	✓	8	44.15	odd	10
440.2.y.a.201.1	yes	8	4.3	odd	2
880.2.bo.d.81.2		8	11.4	even	5	inner
880.2.bo.d.641.2		8	1.1	even	1	trivial
4840.2.a.y.1.2		4	44.31	odd	10
4840.2.a.z.1.2		4	44.35	even	10
9680.2.a.ct.1.3		4	11.2	odd	10
9680.2.a.cu.1.3		4	11.9	even	5

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:	\( N \)	\(=\)	\( 880 = 2^{4} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	880.bo (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.400166 + 1.23158i) q^{3} +(-0.809017 - 0.587785i) q^{5} +(0.0703870 - 0.216629i) q^{7} +(1.07039 - 0.777682i) q^{9} +O(q^{10})\)	\(q+(0.400166 + 1.23158i) q^{3} +(-0.809017 - 0.587785i) q^{5} +(0.0703870 - 0.216629i) q^{7} +(1.07039 - 0.777682i) q^{9} +(3.12020 + 1.12443i) q^{11} +(2.70598 - 1.96601i) q^{13} +(0.400166 - 1.23158i) q^{15} +(-4.89440 - 3.55599i) q^{17} +(0.686443 + 2.11265i) q^{19} +0.294963 q^{21} +3.47726 q^{23} +(0.309017 + 0.951057i) q^{25} +(4.52905 + 3.29055i) q^{27} +(0.00951362 - 0.0292799i) q^{29} +(1.79298 - 1.30268i) q^{31} +(-0.136234 + 4.29274i) q^{33} +(-0.184276 + 0.133884i) q^{35} +(2.70306 - 8.31916i) q^{37} +(3.50415 + 2.54591i) q^{39} +(3.16446 + 9.73920i) q^{41} +3.74411 q^{43} -1.32307 q^{45} +(1.64211 + 5.05390i) q^{47} +(5.62115 + 4.08400i) q^{49} +(2.42093 - 7.45085i) q^{51} +(8.25427 - 5.99708i) q^{53} +(-1.86337 - 2.74369i) q^{55} +(-2.32722 + 1.69082i) q^{57} +(-2.57843 + 7.93560i) q^{59} +(1.81667 + 1.31989i) q^{61} +(-0.0931270 - 0.286615i) q^{63} -3.34478 q^{65} -3.47330 q^{67} +(1.39148 + 4.28253i) q^{69} +(-12.1868 - 8.85423i) q^{71} +(-1.13220 + 3.48457i) q^{73} +(-1.04765 + 0.761160i) q^{75} +(0.463206 - 0.596780i) q^{77} +(-9.40175 + 6.83077i) q^{79} +(-1.01366 + 3.11972i) q^{81} +(1.23192 + 0.895044i) q^{83} +(1.86950 + 5.75372i) q^{85} +0.0398677 q^{87} -10.0058 q^{89} +(-0.235429 - 0.724575i) q^{91} +(2.32185 + 1.68692i) q^{93} +(0.686443 - 2.11265i) q^{95} +(6.74372 - 4.89960i) q^{97} +(4.21427 - 1.22295i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - q^{3} - 2 q^{5} - q^{7} + 7 q^{9}+O(q^{10}) \) 8 * q - q^3 - 2 * q^5 - q^7 + 7 * q^9	\( 8 q - q^{3} - 2 q^{5} - q^{7} + 7 q^{9} - 3 q^{11} - 4 q^{13} - q^{15} - 3 q^{17} - 9 q^{19} - 4 q^{21} + 22 q^{23} - 2 q^{25} + 8 q^{27} - 17 q^{29} + 4 q^{31} + 21 q^{33} - 6 q^{35} + 24 q^{37} + 13 q^{39} - 4 q^{41} + 14 q^{43} - 8 q^{45} + 12 q^{47} - 15 q^{49} + 17 q^{51} + 35 q^{53} - 3 q^{55} - q^{57} - 21 q^{59} - 22 q^{61} - 5 q^{63} + 6 q^{65} - 14 q^{67} + 3 q^{69} - 40 q^{71} + 9 q^{73} - q^{75} - 4 q^{77} - 41 q^{79} + 24 q^{81} + 7 q^{83} - 8 q^{85} + 46 q^{87} - 24 q^{89} + 18 q^{91} + 3 q^{93} - 9 q^{95} + 4 q^{97} - 22 q^{99}+O(q^{100}) \) 8 * q - q^3 - 2 * q^5 - q^7 + 7 * q^9 - 3 * q^11 - 4 * q^13 - q^15 - 3 * q^17 - 9 * q^19 - 4 * q^21 + 22 * q^23 - 2 * q^25 + 8 * q^27 - 17 * q^29 + 4 * q^31 + 21 * q^33 - 6 * q^35 + 24 * q^37 + 13 * q^39 - 4 * q^41 + 14 * q^43 - 8 * q^45 + 12 * q^47 - 15 * q^49 + 17 * q^51 + 35 * q^53 - 3 * q^55 - q^57 - 21 * q^59 - 22 * q^61 - 5 * q^63 + 6 * q^65 - 14 * q^67 + 3 * q^69 - 40 * q^71 + 9 * q^73 - q^75 - 4 * q^77 - 41 * q^79 + 24 * q^81 + 7 * q^83 - 8 * q^85 + 46 * q^87 - 24 * q^89 + 18 * q^91 + 3 * q^93 - 9 * q^95 + 4 * q^97 - 22 * q^99

Introduction

L-functions

Modular forms

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Database

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