LMFDB - Embedded newform 825.2.d.b.824.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [825,2,Mod(824,825)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(825, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1]))

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

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

chi := DirichletCharacter("825.824");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	825.d (of order $2$, degree $1$, 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:	$6.58765816676$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.619810816.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{5} + 14x^{4} - 8x^{3} + 2x^{2} + 2x + 1 $ x^8 - 2x^5 + 14x^4 - 8x^3 + 2x^2 + 2*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 165)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			824.5
Root			$1.18254 - 1.18254i$ of defining polynomial
Character	$\chi$	$=$	825.824
Dual form			825.2.d.b.824.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.796815i q^{2} +(-0.759725 + 1.55654i) q^{3} +1.36509 q^{4} +(-1.24027 - 0.605361i) q^{6} +4.36509 q^{7} +2.68135i q^{8} +(-1.84564 - 2.36509i) q^{9} +O(q^{10})$	\(q+0.796815i q^{2} +(-0.759725 + 1.55654i) q^{3} +1.36509 q^{4} +(-1.24027 - 0.605361i) q^{6} +4.36509 q^{7} +2.68135i q^{8} +(-1.84564 - 2.36509i) q^{9} +(-3.31627 - 0.0488202i) q^{11} +(-1.03709 + 2.12481i) q^{12} -2.26745 q^{13} +3.47817i q^{14} +0.593630 q^{16} +5.57581i q^{17} +(1.88454 - 1.47063i) q^{18} +2.48055i q^{19} +(-3.31627 + 6.79443i) q^{21} +(0.0389007 - 2.64245i) q^{22} +6.80435 q^{23} +(-4.17363 - 2.03709i) q^{24} -1.80673i q^{26} +(5.08353 - 1.07599i) q^{27} +5.95872 q^{28} +1.21072 q^{29} +1.59363 q^{31} +5.83572i q^{32} +(2.59544 - 5.12481i) q^{33} -4.44289 q^{34} +(-2.51945 - 3.22854i) q^{36} +4.63253i q^{37} -1.97654 q^{38} +(1.72264 - 3.52937i) q^{39} +0.460711 q^{41} +(-5.41391 - 2.64245i) q^{42} -11.3214 q^{43} +(-4.52699 - 0.0666438i) q^{44} +5.42181i q^{46} +3.74561 q^{47} +(-0.450996 + 0.924009i) q^{48} +12.0540 q^{49} +(-8.67897 - 4.23608i) q^{51} -3.09526 q^{52} -9.36270 q^{53} +(0.857366 + 4.05063i) q^{54} +11.7043i q^{56} +(-3.86108 - 1.88454i) q^{57} +0.964721i q^{58} -7.51106i q^{59} -1.67143i q^{61} +1.26983i q^{62} +(-8.05636 - 10.3238i) q^{63} -3.46273 q^{64} +(4.08353 + 2.06809i) q^{66} +4.48055i q^{67} +7.61145i q^{68} +(-5.16944 + 10.5912i) q^{69} -6.63253i q^{71} +(6.34163 - 4.94880i) q^{72} +7.87615 q^{73} -3.69127 q^{74} +3.38616i q^{76} +(-14.4758 - 0.213104i) q^{77} +(2.81226 + 1.37262i) q^{78} +5.66781i q^{79} +(-2.18726 + 8.73017i) q^{81} +0.367101i q^{82} +1.56073i q^{83} +(-4.52699 + 9.27498i) q^{84} -9.02108i q^{86} +(-0.919815 + 1.88454i) q^{87} +(0.130904 - 8.89207i) q^{88} -8.80797i q^{89} -9.89759 q^{91} +9.28852 q^{92} +(-1.21072 + 2.48055i) q^{93} +2.98456i q^{94} +(-9.08353 - 4.43354i) q^{96} -12.0151i q^{97} +9.60479i q^{98} +(6.00515 + 7.93336i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{3} - 8 q^{4} - 14 q^{6} + 16 q^{7} - 4 q^{9}+O(q^{10}) $ 8 * q - 2 * q^3 - 8 * q^4 - 14 * q^6 + 16 * q^7 - 4 * q^9	$ 8 q - 2 q^{3} - 8 q^{4} - 14 q^{6} + 16 q^{7} - 4 q^{9} - 12 q^{11} - 6 q^{12} - 8 q^{13} - 8 q^{16} - 12 q^{18} - 12 q^{21} - 16 q^{22} + 12 q^{23} - 6 q^{24} - 14 q^{27} + 16 q^{28} - 20 q^{29} - 6 q^{33} + 16 q^{34} - 12 q^{36} - 20 q^{38} + 12 q^{39} - 12 q^{41} - 20 q^{42} + 8 q^{43} + 8 q^{44} - 20 q^{47} + 22 q^{48} + 8 q^{49} + 12 q^{51} + 32 q^{52} - 8 q^{53} - 6 q^{54} - 8 q^{57} - 24 q^{63} - 22 q^{66} + 20 q^{69} + 36 q^{72} - 32 q^{73} - 8 q^{74} - 28 q^{77} + 4 q^{78} + 8 q^{81} + 8 q^{84} + 8 q^{87} + 16 q^{88} + 8 q^{91} + 12 q^{92} + 20 q^{93} - 18 q^{96} - 36 q^{99}+O(q^{100}) $ 8 * q - 2 * q^3 - 8 * q^4 - 14 * q^6 + 16 * q^7 - 4 * q^9 - 12 * q^11 - 6 * q^12 - 8 * q^13 - 8 * q^16 - 12 * q^18 - 12 * q^21 - 16 * q^22 + 12 * q^23 - 6 * q^24 - 14 * q^27 + 16 * q^28 - 20 * q^29 - 6 * q^33 + 16 * q^34 - 12 * q^36 - 20 * q^38 + 12 * q^39 - 12 * q^41 - 20 * q^42 + 8 * q^43 + 8 * q^44 - 20 * q^47 + 22 * q^48 + 8 * q^49 + 12 * q^51 + 32 * q^52 - 8 * q^53 - 6 * q^54 - 8 * q^57 - 24 * q^63 - 22 * q^66 + 20 * q^69 + 36 * q^72 - 32 * q^73 - 8 * q^74 - 28 * q^77 + 4 * q^78 + 8 * q^81 + 8 * q^84 + 8 * q^87 + 16 * q^88 + 8 * q^91 + 12 * q^92 + 20 * q^93 - 18 * q^96 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/825\mathbb{Z}\right)^\times$.

$n$	$376$	$551$	$727$
$\chi(n)$	$-1$	$-1$	$-1$

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 $

$2$			0.796815i			0.563433i	0.959498	+	0.281717i	$0.0909038\pi$
$2$			0.796815i			0.563433i	−0.959498	+	0.281717i	$0.909096\pi$
$3$	−0.759725	+	1.55654i	−0.438628	+	0.898669i
$3$	−0.759725	+	1.55654i	−0.438628	+	0.898669i
$4$	1.36509			0.682543
$5$		0			0
$5$		0			0
$6$	−1.24027	−	0.605361i	−0.506340	−	0.247137i
$7$	4.36509			1.64985			0.824924	−	0.565244i	$-0.191218\pi$
$7$	4.36509			1.64985			0.824924	+	0.565244i	$0.191218\pi$
$8$			2.68135i			0.948001i
$9$	−1.84564	−	2.36509i	−0.615212	−	0.788362i
$10$		0			0
$11$	−3.31627	−	0.0488202i	−0.999892	−	0.0147198i
$11$	−3.31627	−	0.0488202i	−0.999892	−	0.0147198i
$12$	−1.03709	+	2.12481i	−0.299382	+	0.613380i
$13$	−2.26745			−0.628876			−0.314438	−	0.949278i	$-0.601816\pi$
$13$	−2.26745			−0.628876			−0.314438	+	0.949278i	$0.601816\pi$
$14$			3.47817i			0.929579i
$15$		0			0
$16$	0.593630			0.148408
$17$			5.57581i			1.35233i	0.736749	+	0.676166i	$0.236360\pi$
$17$			5.57581i			1.35233i	−0.736749	+	0.676166i	$0.763640\pi$
$18$	1.88454	−	1.47063i	0.444189	−	0.346631i
$19$			2.48055i			0.569077i	0.958665	+	0.284539i	$0.0918404\pi$
$19$			2.48055i			0.569077i	−0.958665	+	0.284539i	$0.908160\pi$
$20$		0			0
$21$	−3.31627	+	6.79443i	−0.723668	+	1.48267i
$22$	0.0389007	−	2.64245i	0.00829365	−	0.563372i
$23$	6.80435			1.41881			0.709403	−	0.704803i	$-0.248965\pi$
$23$	6.80435			1.41881			0.709403	+	0.704803i	$0.248965\pi$
$24$	−4.17363	−	2.03709i	−0.851939	−	0.415819i
$25$		0			0
$26$		−	1.80673i		−	0.354330i
$27$	5.08353	−	1.07599i	0.978325	−	0.207074i
$28$	5.95872			1.12609
$29$	1.21072			0.224825			0.112413	−	0.993662i	$-0.464142\pi$
$29$	1.21072			0.224825			0.112413	+	0.993662i	$0.464142\pi$
$30$		0			0
$31$	1.59363			0.286224			0.143112	−	0.989706i	$-0.454289\pi$
$31$	1.59363			0.286224			0.143112	+	0.989706i	$0.454289\pi$
$32$			5.83572i			1.03162i
$33$	2.59544	−	5.12481i	0.451808	−	0.892115i
$34$	−4.44289			−0.761949
$35$		0			0
$36$	−2.51945	−	3.22854i	−0.419908	−	0.538091i
$37$			4.63253i			0.761583i	0.924661	+	0.380792i	$0.124349\pi$
$37$			4.63253i			0.761583i	−0.924661	+	0.380792i	$0.875651\pi$
$38$	−1.97654			−0.320637
$39$	1.72264	−	3.52937i	0.275842	−	0.565151i
$40$		0			0
$41$	0.460711			0.0719509			0.0359755	−	0.999353i	$-0.488546\pi$
$41$	0.460711			0.0719509			0.0359755	+	0.999353i	$0.488546\pi$
$42$	−5.41391	−	2.64245i	−0.835384	−	0.407739i
$43$	−11.3214			−1.72650			−0.863250	−	0.504777i	$-0.831575\pi$
$43$	−11.3214			−1.72650			−0.863250	+	0.504777i	$0.831575\pi$
$44$	−4.52699	−	0.0666438i	−0.682469	−	0.0100469i
$45$		0			0
$46$			5.42181i			0.799402i
$47$	3.74561			0.546354			0.273177	−	0.961964i	$-0.411926\pi$
$47$	3.74561			0.546354			0.273177	+	0.961964i	$0.411926\pi$
$48$	−0.450996	+	0.924009i	−0.0650956	+	0.133369i
$49$	12.0540			1.72200
$50$		0			0
$51$	−8.67897	−	4.23608i	−1.21530	−	0.593170i
$52$	−3.09526			−0.429235
$53$	−9.36270			−1.28607			−0.643033	−	0.765838i	$-0.722324\pi$
$53$	−9.36270			−1.28607			−0.643033	+	0.765838i	$0.722324\pi$
$54$	0.857366	+	4.05063i	0.116673	+	0.551221i
$55$		0			0
$56$			11.7043i			1.56406i
$57$	−3.86108	−	1.88454i	−0.511412	−	0.249613i
$58$			0.964721i			0.126674i
$59$		−	7.51106i		−	0.977857i	−0.872324	−	0.488928i	$-0.837388\pi$
$59$		−	7.51106i		−	0.977857i	0.872324	−	0.488928i	$-0.162612\pi$
$60$		0			0
$61$		−	1.67143i		−	0.214005i	−0.994259	−	0.107002i	$-0.965875\pi$
$61$		−	1.67143i		−	0.214005i	0.994259	−	0.107002i	$-0.0341253\pi$
$62$			1.26983i			0.161268i
$63$	−8.05636	−	10.3238i	−1.01501	−	1.30068i
$64$	−3.46273			−0.432841
$65$		0			0
$66$	4.08353	+	2.06809i	0.502647	+	0.254564i
$67$			4.48055i			0.547386i	0.961817	+	0.273693i	$0.0882453\pi$
$67$			4.48055i			0.547386i	−0.961817	+	0.273693i	$0.911755\pi$
$68$			7.61145i			0.923024i
$69$	−5.16944	+	10.5912i	−0.622327	+	1.27504i
$70$		0			0
$71$		−	6.63253i		−	0.787137i	−0.919295	−	0.393568i	$-0.871240\pi$
$71$		−	6.63253i		−	0.787137i	0.919295	−	0.393568i	$-0.128760\pi$
$72$	6.34163	−	4.94880i	0.747368	−	0.583221i
$73$	7.87615			0.921833			0.460917	−	0.887443i	$-0.347521\pi$
$73$	7.87615			0.921833			0.460917	+	0.887443i	$0.347521\pi$
$74$	−3.69127			−0.429101
$75$		0			0
$76$			3.38616i			0.388420i
$77$	−14.4758	−	0.213104i	−1.64967	−	0.0242855i
$78$	2.81226	+	1.37262i	0.318425	+	0.155419i
$79$			5.66781i			0.637678i	0.947809	+	0.318839i	$0.103293\pi$
$79$			5.66781i			0.637678i	−0.947809	+	0.318839i	$0.896707\pi$
$80$		0			0
$81$	−2.18726	+	8.73017i	−0.243029	+	0.970019i
$82$			0.367101i			0.0405395i
$83$			1.56073i			0.171313i	0.996325	+	0.0856564i	$0.0272987\pi$
$83$			1.56073i			0.171313i	−0.996325	+	0.0856564i	$0.972701\pi$
$84$	−4.52699	+	9.27498i	−0.493935	+	1.01198i
$85$		0			0
$86$		−	9.02108i		−	0.972768i
$87$	−0.919815	+	1.88454i	−0.0986145	+	0.202043i
$88$	0.130904	−	8.89207i	0.0139544	−	0.947898i
$89$		−	8.80797i		−	0.933643i	−0.884351	−	0.466822i	$-0.845399\pi$
$89$		−	8.80797i		−	0.933643i	0.884351	−	0.466822i	$-0.154601\pi$
$90$		0			0
$91$	−9.89759			−1.03755
$92$	9.28852			0.968395
$93$	−1.21072	+	2.48055i	−0.125546	+	0.257221i
$94$			2.98456i			0.307834i
$95$		0			0
$96$	−9.08353	−	4.43354i	−0.927084	−	0.452496i
$97$		−	12.0151i		−	1.21995i	−0.792422	−	0.609973i	$-0.791180\pi$
$97$		−	12.0151i		−	1.21995i	0.792422	−	0.609973i	$-0.208820\pi$
$98$			9.60479i			0.970230i
$99$	6.00515	+	7.93336i	0.603541	+	0.797332i
$100$		0			0
$101$	12.4805			1.24186			0.620931	−	0.783866i	$-0.286755\pi$
$101$	12.4805			1.24186			0.620931	+	0.783866i	$0.286755\pi$
$102$	3.37537	−	6.91553i	0.334212	−	0.684740i
$103$		−	16.0187i		−	1.57837i	−0.614156	−	0.789184i	$-0.710504\pi$
$103$		−	16.0187i		−	1.57837i	0.614156	−	0.789184i	$-0.289496\pi$
$104$		−	6.07982i		−	0.596175i
$105$		0			0
$106$		−	7.46034i		−	0.724613i
$107$		−	8.51707i		−	0.823376i	−0.911325	−	0.411688i	$-0.864939\pi$
$107$		−	8.51707i		−	0.823376i	0.911325	−	0.411688i	$-0.135061\pi$
$108$	6.93945	−	1.46882i	0.667749	−	0.141337i
$109$		−	12.1754i		−	1.16620i	−0.812402	−	0.583098i	$-0.801840\pi$
$109$		−	12.1754i		−	1.16620i	0.812402	−	0.583098i	$-0.198160\pi$
$110$		0			0
$111$	−7.21072	−	3.51945i	−0.684411	−	0.334051i
$112$	2.59125			0.244850
$113$	−2.12852			−0.200234			−0.100117	−	0.994976i	$-0.531922\pi$
$113$	−2.12852			−0.200234			−0.100117	+	0.994976i	$0.531922\pi$
$114$	1.50163	−	3.07656i	0.140640	−	0.288147i
$115$		0			0
$116$	1.65274			0.153453
$117$	4.18488	+	5.36270i	0.386892	+	0.495782i
$118$	5.98493			0.550957
$119$			24.3389i			2.23114i
$120$		0			0
$121$	10.9952	+	0.323802i	0.999567	+	0.0294365i
$122$	1.33182			0.120577
$123$	−0.350013	+	0.717115i	−0.0315596	+	0.0646600i
$124$	2.17544			0.195360
$125$		0			0
$126$	8.22616	−	6.41943i	0.732845	−	0.571888i
$127$	−8.89998			−0.789745			−0.394873	−	0.918736i	$-0.629211\pi$
$127$	−8.89998			−0.789745			−0.394873	+	0.918736i	$0.629211\pi$
$128$			8.91228i			0.787742i
$129$	8.60117	−	17.6222i	0.757290	−	1.55155i
$130$		0			0
$131$	6.95633			0.607778			0.303889	−	0.952708i	$-0.401715\pi$
$131$	6.95633			0.607778			0.303889	+	0.952708i	$0.401715\pi$
$132$	3.54300	−	6.99581i	0.308379	−	0.608907i
$133$			10.8278i			0.938890i
$134$	−3.57017			−0.308416
$135$		0			0
$136$	−14.9507			−1.28201
$137$	9.38254			0.801605			0.400802	−	0.916165i	$-0.368731\pi$
$137$	9.38254			0.801605			0.400802	+	0.916165i	$0.368731\pi$
$138$	−8.43927	−	4.11909i	−0.718398	−	0.350640i
$139$		−	12.3003i		−	1.04330i	−0.853159	−	0.521651i	$-0.825316\pi$
$139$		−	12.3003i		−	1.04330i	0.853159	−	0.521651i	$-0.174684\pi$
$140$		0			0
$141$	−2.84564	+	5.83020i	−0.239646	+	0.490991i
$142$	5.28490			0.443499
$143$	7.51945	+	0.110697i	0.628808	+	0.00925696i
$144$	−1.09562	−	1.40399i	−0.0913021	−	0.116999i
$145$		0			0
$146$			6.27583i			0.519392i
$147$	−9.15771	+	18.7625i	−0.755315	+	1.54750i
$148$			6.32380i			0.519813i
$149$	7.26144			0.594880			0.297440	−	0.954740i	$-0.403867\pi$
$149$	7.26144			0.594880			0.297440	+	0.954740i	$0.403867\pi$
$150$		0			0
$151$			10.1869i			0.828998i	0.910050	+	0.414499i	$0.136043\pi$
$151$			10.1869i			0.828998i	−0.910050	+	0.414499i	$0.863957\pi$
$152$	−6.65122			−0.539486
$153$	13.1873	−	10.2909i	1.06613	−	0.831970i
$154$	0.169805	−	11.5345i	0.0136833	−	0.929478i
$155$		0			0
$156$	2.35154	−	4.81789i	0.188274	−	0.385740i
$157$			11.9127i			0.950734i	0.879788	+	0.475367i	$0.157685\pi$
$157$			11.9127i			0.950734i	−0.879788	+	0.475367i	$0.842315\pi$
$158$	−4.51620			−0.359289
$159$	7.11308	−	14.5734i	0.564104	−	1.15575i
$160$		0			0
$161$	29.7016			2.34081
$162$	−6.95633	−	1.74284i	−0.546541	−	0.136931i
$163$			11.8234i			0.926081i	0.886337	+	0.463041i	$0.153242\pi$
$163$			11.8234i			0.926081i	−0.886337	+	0.463041i	$0.846758\pi$
$164$	0.628909			0.0491096
$165$		0			0
$166$	−1.24362			−0.0965234
$167$			10.2909i			0.796334i	0.917313	+	0.398167i	$0.130354\pi$
$167$			10.2909i			0.796334i	−0.917313	+	0.398167i	$0.869646\pi$
$168$	−18.2183	−	8.89207i	−1.40557	−	0.686038i
$169$	−7.85869			−0.604515
$170$		0			0
$171$	5.86671	−	4.57819i	0.448639	−	0.350103i
$172$	−15.4547			−1.17841
$173$		−	3.58057i		−	0.272226i	−0.990693	−	0.136113i	$-0.956539\pi$
$173$		−	3.58057i		−	0.272226i	0.990693	−	0.136113i	$-0.0434610\pi$
$174$	−1.50163	−	0.732923i	−0.113838	−	0.0555627i
$175$		0			0
$176$	−1.96864	−	0.0289812i	−0.148391	−	0.00218454i
$177$	11.6913	+	5.70634i	0.878770	+	0.428915i
$178$	7.01833			0.526046
$179$		−	1.59363i		−	0.119114i	−0.998225	−	0.0595568i	$-0.981031\pi$
$179$		−	1.59363i		−	0.119114i	0.998225	−	0.0595568i	$-0.0189687\pi$
$180$		0			0
$181$	18.1238			1.34713			0.673564	−	0.739129i	$-0.264763\pi$
$181$	18.1238			1.34713			0.673564	+	0.739129i	$0.264763\pi$
$182$		−	7.88655i		−	0.584590i
$183$	2.60165	+	1.26983i	0.192320	+	0.0938684i
$184$			18.2449i			1.34503i
$185$		0			0
$186$	−1.97654	−	0.964721i	−0.144927	−	0.0707368i
$187$	0.272212	−	18.4909i	0.0199061	−	1.35219i
$188$	5.11308			0.372910
$189$	22.1900	−	4.69679i	1.61409	−	0.341641i
$190$		0			0
$191$			17.8976i			1.29502i	0.762055	+	0.647512i	$0.224191\pi$
$191$			17.8976i			1.29502i	−0.762055	+	0.647512i	$0.775809\pi$
$192$	2.63072	−	5.38987i	0.189856	−	0.388981i
$193$	1.50163			0.108089			0.0540447	−	0.998539i	$-0.482789\pi$
$193$	1.50163			0.108089			0.0540447	+	0.998539i	$0.482789\pi$
$194$	9.57379			0.687358
$195$		0			0
$196$	16.4547			1.17534
$197$		−	20.6147i		−	1.46874i	−0.678751	−	0.734369i	$-0.737478\pi$
$197$		−	20.6147i		−	1.46874i	0.678751	−	0.734369i	$-0.262522\pi$
$198$	−6.32142	+	4.78500i	−0.449244	+	0.340055i
$199$	−2.42144			−0.171651			−0.0858257	−	0.996310i	$-0.527353\pi$
$199$	−2.42144			−0.171651			−0.0858257	+	0.996310i	$0.527353\pi$
$200$		0			0
$201$	−6.97416	−	3.40399i	−0.491919	−	0.240099i
$202$			9.94469i			0.699706i
$203$	5.28490			0.370927
$204$	−11.8475	−	5.78261i	−0.829493	−	0.404864i
$205$		0			0
$206$	12.7639			0.889306
$207$	−12.5584	−	16.0929i	−0.872866	−	1.11853i
$208$	−1.34602			−0.0933300
$209$	0.121101	−	8.22616i	0.00837673	−	0.569015i
$210$		0			0
$211$		−	25.8734i		−	1.78120i	−0.454789	−	0.890599i	$-0.650285\pi$
$211$		−	25.8734i		−	1.78120i	0.454789	−	0.890599i	$-0.349715\pi$
$212$	−12.7809			−0.877795
$213$	10.3238	+	5.03890i	0.707375	+	0.345260i
$214$	6.78653			0.463917
$215$		0			0
$216$	2.88511	+	13.6307i	0.196307	+	0.927453i
$217$	6.95633			0.472227
$218$	9.70158			0.657074
$219$	−5.98371	+	12.2595i	−0.404341	+	0.828423i
$220$		0			0
$221$		−	12.6428i		−	0.850449i
$222$	2.80435	−	5.74561i	0.188216	−	0.385620i
$223$			7.45672i			0.499339i	0.968331	+	0.249669i	$0.0803220\pi$
$223$			7.45672i			0.499339i	−0.968331	+	0.249669i	$0.919678\pi$
$224$			25.4734i			1.70201i
$225$		0			0
$226$		−	1.69604i		−	0.112819i
$227$		−	13.0520i		−	0.866289i	−0.901325	−	0.433144i	$-0.857404\pi$
$227$		−	13.0520i		−	0.866289i	0.901325	−	0.433144i	$-0.142596\pi$
$228$	−5.27070	−	2.57255i	−0.349061	−	0.170371i
$229$	−6.87853			−0.454546			−0.227273	−	0.973831i	$-0.572981\pi$
$229$	−6.87853			−0.454546			−0.227273	+	0.973831i	$0.572981\pi$
$230$		0			0
$231$	11.3293	−	22.3702i	0.745415	−	1.47185i
$232$			3.24637i			0.213135i
$233$			21.1067i			1.38275i	0.722498	+	0.691373i	$0.242994\pi$
$233$			21.1067i			1.38275i	−0.722498	+	0.691373i	$0.757006\pi$
$234$	−4.27308	+	3.33457i	−0.279340	+	0.217988i
$235$		0			0
$236$		−	10.2532i		−	0.667429i
$237$	−8.82217	−	4.30598i	−0.573062	−	0.279703i
$238$	−19.3936			−1.25710
$239$	3.87148			0.250425			0.125213	−	0.992130i	$-0.460039\pi$
$239$	3.87148			0.250425			0.125213	+	0.992130i	$0.460039\pi$
$240$		0			0
$241$		−	27.4357i		−	1.76729i	−0.468156	−	0.883646i	$-0.655082\pi$
$241$		−	27.4357i		−	1.76729i	0.468156	−	0.883646i	$-0.344918\pi$
$242$	−0.258010	+	8.76117i	−0.0165855	+	0.563189i
$243$	−11.9271	−	10.0371i	−0.765127	−	0.643880i
$244$		−	2.28165i		−	0.146068i
$245$		0			0
$246$	−0.571408	−	0.278896i	−0.0364316	−	0.0177818i
$247$		−	5.62451i		−	0.357879i
$248$			4.27308i			0.271341i
$249$	−2.42935	−	1.18573i	−0.153954	−	0.0751425i
$250$		0			0
$251$		−	9.17219i		−	0.578943i	−0.957187	−	0.289472i	$-0.906520\pi$
$251$		−	9.17219i		−	0.578943i	0.957187	−	0.289472i	$-0.0934796\pi$
$252$	−10.9976	−	14.0929i	−0.692785	−	0.887768i
$253$	−22.5650	−	0.332190i	−1.41865	−	0.0208846i
$254$		−	7.09164i		−	0.444969i
$255$		0			0
$256$	−14.0269			−0.876681
$257$	17.0389			1.06286			0.531429	−	0.847103i	$-0.321655\pi$
$257$	17.0389			1.06286			0.531429	+	0.847103i	$0.321655\pi$
$258$	14.0417	+	6.85354i	0.874196	+	0.426683i
$259$			20.2214i			1.25650i
$260$		0			0
$261$	−2.23455	−	2.86346i	−0.138315	−	0.177244i
$262$			5.54291i			0.342442i
$263$		−	32.3519i		−	1.99491i	−0.0713303	−	0.997453i	$-0.522724\pi$
$263$		−	32.3519i		−	1.99491i	0.0713303	−	0.997453i	$-0.477276\pi$
$264$	13.7414	+	6.95929i	0.845726	+	0.428315i
$265$		0			0
$266$	−8.62776			−0.529002
$267$	13.7100	+	6.69164i	0.839036	+	0.409522i
$268$			6.11633i			0.373615i
$269$		−	6.41741i		−	0.391276i	−0.980676	−	0.195638i	$-0.937322\pi$
$269$		−	6.41741i		−	0.391276i	0.980676	−	0.195638i	$-0.0626778\pi$
$270$		0			0
$271$			16.8352i			1.02267i	0.859382	+	0.511334i	$0.170848\pi$
$271$			16.8352i			1.02267i	−0.859382	+	0.511334i	$0.829152\pi$
$272$			3.30997i			0.200696i
$273$	7.51945	−	15.4060i	0.455098	−	0.932414i
$274$			7.47615i			0.451651i
$275$		0			0
$276$	−7.05672	+	14.4580i	−0.424765	+	0.870267i
$277$	4.53328			0.272379			0.136189	−	0.990683i	$-0.456514\pi$
$277$	4.53328			0.272379			0.136189	+	0.990683i	$0.456514\pi$
$278$	9.80110			0.587831
$279$	−2.94126	−	3.76907i	−0.176089	−	0.225648i
$280$		0			0
$281$	2.72655			0.162652			0.0813262	−	0.996688i	$-0.474084\pi$
$281$	2.72655			0.162652			0.0813262	+	0.996688i	$0.474084\pi$
$282$	−4.64559	−	2.26745i	−0.276641	−	0.135024i
$283$	8.89998			0.529049			0.264524	−	0.964379i	$-0.414785\pi$
$283$	8.89998			0.529049			0.264524	+	0.964379i	$0.414785\pi$
$284$		−	9.05397i		−	0.537254i
$285$		0			0
$286$	−0.0882052	+	5.99161i	−0.00521568	+	0.354291i
$287$	2.01104			0.118708
$288$	13.8020	−	10.7706i	0.813289	−	0.634664i
$289$	−14.0896			−0.828801
$290$		0			0
$291$	18.7019	+	9.12815i	1.09633	+	0.535102i
$292$	10.7516			0.629191
$293$			11.8845i			0.694302i	0.937809	+	0.347151i	$0.112851\pi$
$293$			11.8845i			0.694302i	−0.937809	+	0.347151i	$0.887149\pi$
$294$	−14.9502	−	7.29700i	−0.871916	−	0.425570i
$295$		0			0
$296$	−12.4214			−0.721982
$297$	−16.9109	+	3.32009i	−0.981267	+	0.192651i
$298$			5.78603i			0.335175i
$299$	−15.4285			−0.892253
$300$		0			0
$301$	−49.4190			−2.84846
$302$	−8.11707			−0.467085
$303$	−9.48179	+	19.4265i	−0.544714	+	1.11602i
$304$			1.47253i			0.0844553i
$305$		0			0
$306$	8.19995	+	10.5078i	0.468760	+	0.600691i
$307$	−10.9818			−0.626765			−0.313382	−	0.949627i	$-0.601462\pi$
$307$	−10.9818			−0.626765			−0.313382	+	0.949627i	$0.601462\pi$
$308$	−19.7607	−	0.290906i	−1.12597	−	0.0165759i
$309$	24.9337	+	12.1698i	1.41843	+	0.692316i
$310$		0			0
$311$			21.8928i			1.24143i	0.784037	+	0.620714i	$0.213157\pi$
$311$			21.8928i			1.24143i	−0.784037	+	0.620714i	$0.786843\pi$
$312$	9.46348	+	4.61899i	0.535764	+	0.261499i
$313$		−	10.2111i		−	0.577165i	−0.957455	−	0.288582i	$-0.906816\pi$
$313$		−	10.2111i		−	0.577165i	0.957455	−	0.288582i	$-0.0931839\pi$
$314$	−9.49219			−0.535675
$315$		0			0
$316$			7.73705i			0.435243i
$317$	−2.51908			−0.141486			−0.0707429	−	0.997495i	$-0.522537\pi$
$317$	−2.51908			−0.141486			−0.0707429	+	0.997495i	$0.522537\pi$
$318$	11.6123	+	5.66781i	0.651187	+	0.317835i
$319$	−4.01507	−	0.0591077i	−0.224801	−	0.00330939i
$320$		0			0
$321$	13.2572	+	6.47063i	0.739942	+	0.361155i
$322$			23.6667i			1.31889i
$323$	−13.8311			−0.769581
$324$	−2.98580	+	11.9174i	−0.165878	+	0.662080i
$325$		0			0
$326$	−9.42107			−0.521785
$327$	18.9516	+	9.24999i	1.04802	+	0.511526i
$328$			1.23533i			0.0682095i
$329$	16.3499			0.901400
$330$		0			0
$331$	16.3587			0.899156			0.449578	−	0.893241i	$-0.351574\pi$
$331$	16.3587			0.899156			0.449578	+	0.893241i	$0.351574\pi$
$332$			2.13054i			0.116928i
$333$	10.9563	−	8.54996i	0.600403	−	0.468535i
$334$	−8.19995			−0.448681
$335$		0			0
$336$	−1.96864	+	4.03338i	−0.107398	+	0.220039i
$337$	10.9976			0.599078			0.299539	−	0.954084i	$-0.403167\pi$
$337$	10.9976			0.599078			0.299539	+	0.954084i	$0.403167\pi$
$338$		−	6.26192i		−	0.340604i
$339$	1.61709	−	3.31313i	0.0878283	−	0.179944i
$340$		0			0
$341$	−5.28490	−	0.0778014i	−0.286193	−	0.00421318i
$342$	3.64797	+	4.67469i	0.197260	+	0.252778i
$343$	22.0610			1.19118
$344$		−	30.3567i		−	1.63672i
$345$		0			0
$346$	2.85306			0.153381
$347$			16.6654i			0.894647i	0.894372	+	0.447323i	$0.147623\pi$
$347$			16.6654i			0.894647i	−0.894372	+	0.447323i	$0.852377\pi$
$348$	−1.25563	+	2.57255i	−0.0673086	+	0.137903i
$349$		−	8.36975i		−	0.448023i	−0.974587	−	0.224011i	$-0.928085\pi$
$349$		−	8.36975i		−	0.448023i	0.974587	−	0.224011i	$-0.0719153\pi$
$350$		0			0
$351$	−11.5266	+	2.43975i	−0.615245	+	0.130224i
$352$	0.284901	−	19.3528i	0.0151853	−	1.03151i
$353$	−13.9634			−0.743196			−0.371598	−	0.928394i	$-0.621190\pi$
$353$	−13.9634			−0.743196			−0.371598	+	0.928394i	$0.621190\pi$
$354$	−4.54690	+	9.31578i	−0.241665	+	0.495128i
$355$		0			0
$356$		−	12.0236i		−	0.637252i
$357$	−37.8844	−	18.4909i	−2.00506	−	0.978640i
$358$	1.26983			0.0671125
$359$	−25.4405			−1.34270			−0.671349	−	0.741141i	$-0.734285\pi$
$359$	−25.4405			−1.34270			−0.671349	+	0.741141i	$0.734285\pi$
$360$		0			0
$361$	12.8469			0.676151
$362$			14.4413i			0.759017i
$363$	−8.85737	+	16.8685i	−0.464891	+	0.885368i
$364$	−13.5111			−0.708172
$365$		0			0
$366$	−1.01182	+	2.07303i	−0.0528886	+	0.108359i
$367$			3.07340i			0.160430i	0.996778	+	0.0802152i	$0.0255607\pi$
$367$			3.07340i			0.160430i	−0.996778	+	0.0802152i	$0.974439\pi$
$368$	4.03927			0.210561
$369$	−0.850304	−	1.08962i	−0.0442650	−	0.0567234i
$370$		0			0
$371$	−40.8690			−2.12181
$372$	−1.65274	+	3.38616i	−0.0856905	+	0.175564i
$373$	9.98960			0.517242			0.258621	−	0.965979i	$-0.416732\pi$
$373$	9.98960			0.517242			0.258621	+	0.965979i	$0.416732\pi$
$374$	14.7338	+	0.216903i	0.761866	+	0.0112158i
$375$		0			0
$376$			10.0433i			0.517944i
$377$	−2.74524			−0.141387
$378$	3.74247	+	17.6814i	0.192492	+	0.909431i
$379$	17.8657			0.917702			0.458851	−	0.888513i	$-0.348261\pi$
$379$	17.8657			0.917702			0.458851	+	0.888513i	$0.348261\pi$
$380$		0			0
$381$	6.76154	−	13.8532i	0.346404	−	0.709719i
$382$	−14.2611			−0.729660
$383$	−26.8345			−1.37118			−0.685589	−	0.727989i	$-0.740455\pi$
$383$	−26.8345			−1.37118			−0.685589	+	0.727989i	$0.740455\pi$
$384$	−13.8723	−	6.77088i	−0.707919	−	0.345525i
$385$		0			0
$386$			1.19652i			0.0609012i
$387$	20.8952	+	26.7761i	1.06216	+	1.36111i
$388$		−	16.4016i		−	0.832665i
$389$			16.5650i			0.839881i	0.907552	+	0.419940i	$0.137949\pi$
$389$			16.5650i			0.839881i	−0.907552	+	0.419940i	$0.862051\pi$
$390$		0			0
$391$			37.9397i			1.91870i
$392$			32.3209i			1.63245i
$393$	−5.28490	+	10.8278i	−0.266588	+	0.546191i
$394$	16.4261			0.827535
$395$		0			0
$396$	8.19755	+	10.8297i	0.411942	+	0.544213i
$397$		−	12.1707i		−	0.610829i	−0.952220	−	0.305414i	$-0.901205\pi$
$397$		−	12.1707i		−	0.610829i	0.952220	−	0.305414i	$-0.0987950\pi$
$398$		−	1.92944i		−	0.0967142i
$399$	−16.8539	−	8.22616i	−0.843752	−	0.411823i
$400$		0			0
$401$			3.02689i			0.151156i	0.997140	+	0.0755779i	$0.0240801\pi$
$401$			3.02689i			0.151156i	−0.997140	+	0.0755779i	$0.975920\pi$
$402$	2.71235	−	5.55711i	0.135280	−	0.277164i
$403$	−3.61347			−0.180000
$404$	17.0370			0.847623
$405$		0			0
$406$			4.21109i			0.208993i
$407$	0.226161	−	15.3627i	0.0112104	−	0.761501i
$408$	11.3584	−	23.2714i	0.562326	−	1.15210i
$409$		−	6.29292i		−	0.311165i	−0.987823	−	0.155582i	$-0.950275\pi$
$409$		−	6.29292i		−	0.311165i	0.987823	−	0.155582i	$-0.0497254\pi$
$410$		0			0
$411$	−7.12815	+	14.6043i	−0.351606	+	0.720377i
$412$		−	21.8669i		−	1.07730i
$413$		−	32.7864i		−	1.61331i
$414$	12.8230	−	10.0067i	0.630218	−	0.491802i
$415$		0			0
$416$		−	13.2322i		−	0.648760i
$417$	19.1460	+	9.34488i	0.937582	+	0.457621i
$418$	6.55473	+	0.0964951i	0.320602	+	0.00471973i
$419$			23.0444i			1.12579i	0.826527	+	0.562897i	$0.190313\pi$
$419$			23.0444i			1.12579i	−0.826527	+	0.562897i	$0.809687\pi$
$420$		0			0
$421$	−1.24522			−0.0606884			−0.0303442	−	0.999540i	$-0.509660\pi$
$421$	−1.24522			−0.0606884			−0.0303442	+	0.999540i	$0.509660\pi$
$422$	20.6163			1.00359
$423$	−6.91303	−	8.85869i	−0.336123	−	0.430724i
$424$		−	25.1047i		−	1.21919i
$425$		0			0
$426$	−4.01507	+	8.22616i	−0.194531	+	0.398559i
$427$		−	7.29594i		−	0.353075i
$428$		−	11.6265i		−	0.561989i
$429$	−5.88502	+	11.6202i	−0.284131	+	0.561030i
$430$		0			0
$431$	−27.2801			−1.31404			−0.657019	−	0.753874i	$-0.728183\pi$
$431$	−27.2801			−1.31404			−0.657019	+	0.753874i	$0.728183\pi$
$432$	3.01774	−	0.638741i	0.145191	−	0.0307314i
$433$		−	21.1245i		−	1.01518i	−0.861599	−	0.507590i	$-0.830536\pi$
$433$		−	21.1245i		−	1.01518i	0.861599	−	0.507590i	$-0.169464\pi$
$434$			5.54291i			0.266068i
$435$		0			0
$436$		−	16.6205i		−	0.795979i
$437$			16.8785i			0.807410i
$438$	−9.76859	−	4.76791i	−0.466761	−	0.227819i
$439$		−	16.4090i		−	0.783160i	−0.920144	−	0.391580i	$-0.871929\pi$
$439$		−	16.4090i		−	0.783160i	0.920144	−	0.391580i	$-0.128071\pi$
$440$		0			0
$441$	−22.2472	−	28.5087i	−1.05939	−	1.35756i
$442$	10.0740			0.479171
$443$	28.6773			1.36250			0.681251	−	0.732050i	$-0.261436\pi$
$443$	28.6773			1.36250			0.681251	+	0.732050i	$0.261436\pi$
$444$	−9.84325	−	4.80435i	−0.467140	−	0.228004i
$445$		0			0
$446$	−5.94163			−0.281344
$447$	−5.51670	+	11.3027i	−0.260931	+	0.534601i
$448$	−15.1151			−0.714121
$449$		−	24.4047i		−	1.15173i	−0.817546	−	0.575864i	$-0.804666\pi$
$449$		−	24.4047i		−	1.15173i	0.817546	−	0.575864i	$-0.195334\pi$
$450$		0			0
$451$	−1.52784	−	0.0224920i	−0.0719431	−	0.00105911i
$452$	−2.90561			−0.136669
$453$	−15.8563	−	7.73924i	−0.744994	−	0.363621i
$454$	10.4000			0.488096
$455$		0			0
$456$	5.05310	−	10.3529i	0.236633	−	0.484819i
$457$	11.0634			0.517524			0.258762	−	0.965941i	$-0.416685\pi$
$457$	11.0634			0.517524			0.258762	+	0.965941i	$0.416685\pi$
$458$		−	5.48092i		−	0.256106i
$459$	5.99952	+	28.3448i	0.280033	+	1.32302i
$460$		0			0
$461$	2.55835			0.119154			0.0595771	−	0.998224i	$-0.481025\pi$
$461$	2.55835			0.119154			0.0595771	+	0.998224i	$0.481025\pi$
$462$	17.8249	+	9.02738i	0.829291	+	0.419992i
$463$			9.50438i			0.441706i	0.975307	+	0.220853i	$0.0708841\pi$
$463$			9.50438i			0.441706i	−0.975307	+	0.220853i	$0.929116\pi$
$464$	0.718721			0.0333658
$465$		0			0
$466$	−16.8181			−0.779085
$467$	−26.3822			−1.22082			−0.610411	−	0.792085i	$-0.708996\pi$
$467$	−26.3822			−1.22082			−0.610411	+	0.792085i	$0.708996\pi$
$468$	5.71272	+	7.32055i	0.264070	+	0.338392i
$469$			19.5580i			0.903104i
$470$		0			0
$471$	−18.5425	−	9.05035i	−0.854395	−	0.417018i
$472$	20.1398			0.927009
$473$	37.5448	+	0.552714i	1.72631	+	0.0254138i
$474$	3.43107	−	7.02964i	0.157594	−	0.322882i
$475$		0			0
$476$			33.2246i			1.52285i
$477$	17.2801	+	22.1436i	0.791203	+	1.01389i
$478$			3.08485i			0.141098i
$479$	11.6594			0.532733			0.266366	−	0.963872i	$-0.414177\pi$
$479$	11.6594			0.532733			0.266366	+	0.963872i	$0.414177\pi$
$480$		0			0
$481$		−	10.5040i		−	0.478942i
$482$	21.8612			0.995751
$483$	−22.5650	+	46.2317i	−1.02674	+	2.10362i
$484$	15.0094	+	0.442017i	0.682247	+	0.0200917i
$485$		0			0
$486$	7.99770	−	9.50373i	0.362783	−	0.431098i
$487$			33.3139i			1.50960i	0.655957	+	0.754798i	$0.272265\pi$
$487$			33.3139i			1.50960i	−0.655957	+	0.754798i	$0.727735\pi$
$488$	4.48170			0.202877
$489$	−18.4036	−	8.98254i	−0.832240	−	0.406205i
$490$		0			0
$491$	−38.0055			−1.71517			−0.857583	−	0.514346i	$-0.828035\pi$
$491$	−38.0055			−1.71517			−0.857583	+	0.514346i	$0.828035\pi$
$492$	−0.477798	+	0.978923i	−0.0215408	+	0.0441333i
$493$			6.75075i			0.304038i
$494$	4.48170			0.201641
$495$		0			0
$496$	0.946027			0.0424779
$497$		−	28.9516i		−	1.29866i
$498$	0.944807	−	1.93574i	0.0423378	−	0.0867426i
$499$	−26.7723			−1.19849			−0.599247	−	0.800564i	$-0.704533\pi$
$499$	−26.7723			−1.19849			−0.599247	+	0.800564i	$0.704533\pi$
$500$		0			0
$501$	−16.0182	−	7.81826i	−0.715641	−	0.349294i
$502$	7.30854			0.326196
$503$		−	21.9377i		−	0.978155i	−0.872240	−	0.489078i	$-0.837334\pi$
$503$		−	21.9377i		−	0.978155i	0.872240	−	0.489078i	$-0.162666\pi$
$504$	27.6817	−	21.6019i	1.23304	−	0.962226i
$505$		0			0
$506$	0.264694	−	17.9802i	0.0117671	−	0.799316i
$507$	5.97045	−	12.2324i	0.265157	−	0.543259i
$508$	−12.1492			−0.539035
$509$			26.7254i			1.18458i	0.805724	+	0.592291i	$0.201777\pi$
$509$			26.7254i			1.18458i	−0.805724	+	0.592291i	$0.798223\pi$
$510$		0			0
$511$	34.3801			1.52088
$512$			6.64772i			0.293790i
$513$	2.66905	+	12.6099i	0.117841	+	0.556742i
$514$			13.5769i			0.598849i
$515$		0			0
$516$	11.7413	−	24.0559i	0.516883	−	1.05900i
$517$	−12.4214	−	0.182862i	−0.546294	−	0.00804224i
$518$	−16.1127			−0.707952
$519$	5.57331	+	2.72025i	0.244641	+	0.119406i
$520$		0			0
$521$			3.34763i			0.146662i	0.997308	+	0.0733312i	$0.0233630\pi$
$521$			3.34763i			0.146662i	−0.997308	+	0.0733312i	$0.976637\pi$
$522$	2.28165	−	1.78052i	0.0998650	−	0.0779314i
$523$	−7.12614			−0.311604			−0.155802	−	0.987788i	$-0.549796\pi$
$523$	−7.12614			−0.311604			−0.155802	+	0.987788i	$0.549796\pi$
$524$	9.49599			0.414834
$525$		0			0
$526$	25.7785			1.12400
$527$			8.88577i			0.387070i
$528$	1.54073	−	3.04224i	0.0670518	−	0.132397i
$529$	23.2992			1.01301
$530$		0			0
$531$	−17.7643	+	13.8627i	−0.770905	+	0.601589i
$532$			14.7809i			0.640833i
$533$	−1.04464			−0.0452482
$534$	−5.33200	+	10.9243i	−0.230738	+	0.472741i
$535$		0			0
$536$	−12.0139			−0.518923
$537$	2.48055	+	1.21072i	0.107044	+	0.0522465i
$538$	5.11349			0.220458
$539$	−39.9742	−	0.588478i	−1.72181	−	0.0253475i
$540$		0			0
$541$			27.6697i			1.18961i	0.803868	+	0.594807i	$0.202772\pi$
$541$			27.6697i			1.18961i	−0.803868	+	0.594807i	$0.797228\pi$
$542$	−13.4146			−0.576205
$543$	−13.7691	+	28.2104i	−0.590887	+	1.21062i
$544$	−32.5388			−1.39509
$545$		0			0
$546$	12.2757	+	5.99161i	0.525353	+	0.256417i
$547$	3.25966			0.139373			0.0696864	−	0.997569i	$-0.477800\pi$
$547$	3.25966			0.139373			0.0696864	+	0.997569i	$0.477800\pi$
$548$	12.8080			0.547129
$549$	−3.95308	+	3.08485i	−0.168713	+	0.131658i
$550$		0			0
$551$			3.00325i			0.127943i
$552$	−28.3989	−	13.8611i	−1.20874	−	0.589967i
$553$			24.7405i			1.05207i
$554$			3.61219i			0.153467i
$555$		0			0
$556$		−	16.7910i		−	0.712098i
$557$		−	37.5590i		−	1.59143i	−0.605673	−	0.795714i	$-0.707096\pi$
$557$		−	37.5590i		−	1.59143i	0.605673	−	0.795714i	$-0.292904\pi$
$558$	3.00325	−	2.34364i	0.127138	−	0.0992142i
$559$	25.6707			1.08575
$560$		0			0
$561$	28.5750	+	14.4717i	1.20644	+	0.610995i
$562$			2.17256i			0.0916437i
$563$		−	7.52985i		−	0.317346i	−0.987331	−	0.158673i	$-0.949279\pi$
$563$		−	7.52985i		−	0.317346i	0.987331	−	0.158673i	$-0.0507215\pi$
$564$	−3.88454	+	7.95872i	−0.163568	+	0.335122i
$565$		0			0
$566$			7.09164i			0.298084i
$567$	−9.54758	+	38.1079i	−0.400961	+	1.60038i
$568$	17.7841			0.746206
$569$	−41.2115			−1.72768			−0.863838	−	0.503770i	$-0.831946\pi$
$569$	−41.2115			−1.72768			−0.863838	+	0.503770i	$0.831946\pi$
$570$		0			0
$571$			45.6844i			1.91183i	0.293640	+	0.955916i	$0.405133\pi$
$571$			45.6844i			1.91183i	−0.293640	+	0.955916i	$0.594867\pi$
$572$	10.2647	+	0.151111i	0.429188	+	0.00631827i
$573$	−27.8583	−	13.5973i	−1.16380	−	0.568033i
$574$			1.60243i			0.0668841i
$575$		0			0
$576$	6.39093	+	8.18964i	0.266289	+	0.341235i
$577$		−	25.2643i		−	1.05177i	−0.850556	−	0.525884i	$-0.823735\pi$
$577$		−	25.2643i		−	1.05177i	0.850556	−	0.525884i	$-0.176265\pi$
$578$		−	11.2268i		−	0.466974i
$579$	−1.14082	+	2.33734i	−0.0474110	+	0.0971366i
$580$		0			0
$581$			6.81274i			0.282640i
$582$	−7.27345	+	14.9020i	−0.301494	+	0.617707i
$583$	31.0492	+	0.457089i	1.28593	+	0.0189307i
$584$			21.1187i			0.873899i
$585$		0			0
$586$	−9.46978			−0.391193
$587$	−39.6472			−1.63642			−0.818208	−	0.574922i	$-0.805032\pi$
$587$	−39.6472			−1.63642			−0.818208	+	0.574922i	$0.805032\pi$
$588$	−12.5011	+	25.6124i	−0.515535	+	1.05624i
$589$			3.95308i			0.162884i
$590$		0			0
$591$	32.0876	+	15.6615i	1.31991	+	0.644229i
$592$			2.75001i			0.113025i
$593$			10.3529i			0.425143i	0.977146	+	0.212571i	$0.0681838\pi$
$593$			10.3529i			0.425143i	−0.977146	+	0.212571i	$0.931816\pi$
$594$	−2.64550	−	13.4748i	−0.108546	−	0.552879i
$595$		0			0
$596$	9.91249			0.406031
$597$	1.83963	−	3.76907i	0.0752911	−	0.154258i
$598$		−	12.2937i		−	0.502725i
$599$		−	18.8700i		−	0.771006i	−0.922707	−	0.385503i	$-0.874028\pi$
$599$		−	18.8700i		−	0.771006i	0.922707	−	0.385503i	$-0.125972\pi$
$600$		0			0
$601$		−	0.663411i		−	0.0270611i	−0.999908	−	0.0135306i	$-0.995693\pi$
$601$		−	0.663411i		−	0.0270611i	0.999908	−	0.0135306i	$-0.00430704\pi$
$602$		−	39.3778i		−	1.60492i
$603$	10.5969	−	8.26946i	0.431538	−	0.336758i
$604$			13.9060i			0.565826i
$605$		0			0
$606$	−15.4793	−	7.55523i	−0.628804	−	0.306910i
$607$	−43.6651			−1.77231			−0.886155	−	0.463389i	$-0.846633\pi$
$607$	−43.6651			−1.77231			−0.886155	+	0.463389i	$0.846633\pi$
$608$	−14.4758			−0.587071
$609$	−4.01507	+	8.22616i	−0.162699	+	0.333341i
$610$		0			0
$611$	−8.49297			−0.343589
$612$	18.0017	−	14.0480i	0.727677	−	0.567855i
$613$	−7.72376			−0.311960			−0.155980	−	0.987760i	$-0.549853\pi$
$613$	−7.72376			−0.311960			−0.155980	+	0.987760i	$0.549853\pi$
$614$		−	8.75047i		−	0.353140i
$615$		0			0
$616$	0.571408	−	38.8147i	0.0230227	−	1.56389i
$617$	15.3150			0.616561			0.308280	−	0.951296i	$-0.400247\pi$
$617$	15.3150			0.616561			0.308280	+	0.951296i	$0.400247\pi$
$618$	−9.69708	+	19.8676i	−0.390074	+	0.799191i
$619$	0.867490			0.0348674			0.0174337	−	0.999848i	$-0.494450\pi$
$619$	0.867490			0.0348674			0.0174337	+	0.999848i	$0.494450\pi$
$620$		0			0
$621$	34.5901	−	7.32142i	1.38805	−	0.293798i
$622$	−17.4445			−0.699462
$623$		−	38.4476i		−	1.54037i
$624$	1.02261	−	2.09514i	0.0409371	−	0.0838728i
$625$		0			0
$626$	8.13635			0.325194
$627$	12.7123	+	6.43812i	0.507682	+	0.257114i
$628$			16.2618i			0.648917i
$629$	−25.8301			−1.02991
$630$		0			0
$631$	−37.4905			−1.49247			−0.746236	−	0.665681i	$-0.768141\pi$
$631$	−37.4905			−1.49247			−0.746236	+	0.665681i	$0.768141\pi$
$632$	−15.1974			−0.604520
$633$	40.2730	+	19.6567i	1.60071	+	0.781283i
$634$		−	2.00724i		−	0.0797178i
$635$		0			0
$636$	9.70996	−	19.8940i	0.385025	−	0.788847i
$637$	−27.3317			−1.08292
$638$	0.0470979	−	3.19927i	0.00186462	−	0.126660i
$639$	−15.6865	+	12.2412i	−0.620549	+	0.484256i
$640$		0			0
$641$		−	26.6381i		−	1.05214i	−0.850441	−	0.526070i	$-0.823665\pi$
$641$		−	26.6381i		−	1.05214i	0.850441	−	0.526070i	$-0.176335\pi$
$642$	−5.15590	+	10.5635i	−0.203487	+	0.416908i
$643$		−	30.4234i		−	1.19978i	−0.800082	−	0.599890i	$-0.795211\pi$
$643$		−	30.4234i		−	1.19978i	0.800082	−	0.599890i	$-0.204789\pi$
$644$	40.5452			1.59770
$645$		0			0
$646$		−	11.0208i		−	0.433608i
$647$	20.3661			0.800675			0.400338	−	0.916368i	$-0.368893\pi$
$647$	20.3661			0.800675			0.400338	+	0.916368i	$0.368893\pi$
$648$	−23.4087	−	5.86481i	−0.919579	−	0.230392i
$649$	−0.366692	+	24.9087i	−0.0143939	+	0.977751i
$650$		0			0
$651$	−5.28490	+	10.8278i	−0.207132	+	0.424375i
$652$			16.1400i			0.632090i
$653$	−8.53966			−0.334183			−0.167091	−	0.985941i	$-0.553437\pi$
$653$	−8.53966			−0.334183			−0.167091	+	0.985941i	$0.553437\pi$
$654$	−7.37053	+	15.1009i	−0.288211	+	0.590492i
$655$		0			0
$656$	0.273492			0.0106781
$657$	−14.5365	−	18.6278i	−0.567123	−	0.726738i
$658$			13.0279i			0.507879i
$659$	−6.85315			−0.266961			−0.133480	−	0.991051i	$-0.542615\pi$
$659$	−6.85315			−0.266961			−0.133480	+	0.991051i	$0.542615\pi$
$660$		0			0
$661$	25.7691			1.00230			0.501150	−	0.865360i	$-0.332910\pi$
$661$	25.7691			1.00230			0.501150	+	0.865360i	$0.332910\pi$
$662$			13.0349i			0.506615i
$663$	19.6791	+	9.60508i	0.764272	+	0.373030i
$664$	−4.18488			−0.162405
$665$		0			0
$666$	6.81274	+	8.73017i	0.263988	+	0.338287i
$667$	8.23817			0.318983
$668$			14.0480i			0.543532i
$669$	−11.6067	−	5.66506i	−0.448740	−	0.219024i
$670$		0			0
$671$	−0.0815996	+	5.54291i	−0.00315012	+	0.213982i
$672$	−39.6504	−	19.3528i	−1.52955	−	0.746550i
$673$	−37.4753			−1.44457			−0.722284	−	0.691597i	$-0.756907\pi$
$673$	−37.4753			−1.44457			−0.722284	+	0.691597i	$0.756907\pi$
$674$			8.76307i			0.337541i
$675$		0			0
$676$	−10.7278			−0.412607
$677$		−	41.0575i		−	1.57797i	−0.614414	−	0.788984i	$-0.710607\pi$
$677$		−	41.0575i		−	1.57797i	0.614414	−	0.788984i	$-0.289393\pi$
$678$	2.63995	+	1.28852i	0.101387	+	0.0494854i
$679$		−	52.4468i		−	2.01272i
$680$		0			0
$681$	20.3159	+	9.91590i	0.778507	+	0.379978i
$682$	0.0619933	−	4.21109i	0.00237385	−	0.161251i
$683$	13.6583			0.522619			0.261310	−	0.965255i	$-0.415846\pi$
$683$	13.6583			0.522619			0.261310	+	0.965255i	$0.415846\pi$
$684$	8.00857	−	6.24962i	0.306215	−	0.238960i
$685$		0			0
$686$			17.5786i			0.671152i
$687$	5.22579	−	10.7067i	0.199376	−	0.408486i
$688$	−6.72074			−0.256226
$689$	21.2294			0.808776
$690$		0			0
$691$	10.9920			0.418155			0.209077	−	0.977899i	$-0.432954\pi$
$691$	10.9920			0.418155			0.209077	+	0.977899i	$0.432954\pi$
$692$		−	4.88779i		−	0.185806i
$693$	26.2130	+	34.6298i	0.995750	+	1.31548i
$694$	−13.2793			−0.504074
$695$		0			0
$696$	−5.05310	−	2.46635i	−0.191537	−	0.0934867i
$697$			2.56883i			0.0973015i
$698$	6.66915			0.252431
$699$	−32.8534	−	16.0353i	−1.24263	−	0.606511i
$700$		0			0
$701$	37.1552			1.40333			0.701667	−	0.712505i	$-0.252439\pi$
$701$	37.1552			1.40333			0.701667	+	0.712505i	$0.252439\pi$
$702$	−1.94403	−	9.18458i	−0.0733727	−	0.346650i
$703$	−11.4912			−0.433400
$704$	11.4833	+	0.169051i	0.432794	+	0.00637135i
$705$		0			0
$706$		−	11.1262i		−	0.418741i
$707$	54.4787			2.04888
$708$	15.9596	+	7.78965i	0.599798	+	0.292753i
$709$	17.3467			0.651468			0.325734	−	0.945462i	$-0.394389\pi$
$709$	17.3467			0.651468			0.325734	+	0.945462i	$0.394389\pi$
$710$		0			0
$711$	13.4049	−	10.4607i	0.502721	−	0.392307i
$712$	23.6173			0.885095
$713$	10.8436			0.406097
$714$	14.7338	−	30.1869i	0.551398	−	1.12972i
$715$		0			0
$716$		−	2.17544i		−	0.0813001i
$717$	−2.94126	+	6.02611i	−0.109843	+	0.225049i
$718$		−	20.2714i		−	0.756521i
$719$		−	23.9285i		−	0.892381i	−0.894938	−	0.446191i	$-0.852780\pi$
$719$		−	23.9285i		−	0.892381i	0.894938	−	0.446191i	$-0.147220\pi$
$720$		0			0
$721$		−	69.9230i		−	2.60407i
$722$			10.2366i			0.380966i
$723$	42.7048	+	20.8436i	1.58821	+	0.775183i
$724$	24.7405			0.919473
$725$		0			0
$726$	−13.4411	−	7.05768i	−0.498846	−	0.261935i
$727$			12.3854i			0.459349i	0.973268	+	0.229674i	$0.0737661\pi$
$727$			12.3854i			0.459349i	−0.973268	+	0.229674i	$0.926234\pi$
$728$		−	26.5389i		−	0.983598i
$729$	24.6845	−	10.9397i	0.914240	−	0.405172i
$730$		0			0
$731$		−	63.1260i		−	2.33480i
$732$	3.55148	+	1.73342i	0.131266	+	0.0640692i
$733$	19.8460			0.733029			0.366514	−	0.930412i	$-0.380551\pi$
$733$	19.8460			0.733029			0.366514	+	0.930412i	$0.380551\pi$
$734$	−2.44893			−0.0903918
$735$		0			0
$736$			39.7083i			1.46367i
$737$	0.218741	−	14.8587i	0.00805744	−	0.547327i
$738$	0.868226	−	0.677535i	0.0319598	−	0.0249404i
$739$			2.09096i			0.0769171i	0.999260	+	0.0384585i	$0.0122448\pi$
$739$			2.09096i			0.0769171i	−0.999260	+	0.0384585i	$0.987755\pi$
$740$		0			0
$741$	8.75478	+	4.27308i	0.321615	+	0.156976i
$742$		−	32.5650i		−	1.19550i
$743$			11.9465i			0.438276i	0.975694	+	0.219138i	$0.0703244\pi$
$743$			11.9465i			0.438276i	−0.975694	+	0.219138i	$0.929676\pi$
$744$	−6.65122	−	3.24637i	−0.243846	−	0.119018i
$745$		0			0
$746$			7.95986i			0.291431i
$747$	3.69127	−	2.88055i	0.135057	−	0.105394i
$748$	0.371593	−	25.2416i	0.0135868	−	0.922924i
$749$		−	37.1777i		−	1.35844i
$750$		0			0
$751$	−14.1792			−0.517408			−0.258704	−	0.965957i	$-0.583295\pi$
$751$	−14.1792			−0.517408			−0.258704	+	0.965957i	$0.583295\pi$
$752$	2.22351			0.0810830
$753$	14.2769	+	6.96834i	0.520278	+	0.253941i
$754$		−	2.18745i		−	0.0796623i
$755$		0			0
$756$	30.2913	−	6.41152i	1.10168	−	0.233185i
$757$			47.4436i			1.72437i	0.506597	+	0.862183i	$0.330903\pi$
$757$			47.4436i			1.72437i	−0.506597	+	0.862183i	$0.669097\pi$
$758$			14.2357i			0.517064i
$759$	17.6603	−	34.8710i	0.641028	−	1.26574i
$760$		0			0
$761$	26.0328			0.943688			0.471844	−	0.881682i	$-0.343589\pi$
$761$	26.0328			0.943688			0.471844	+	0.881682i	$0.343589\pi$
$762$	11.0384	+	5.38769i	0.399880	+	0.195176i
$763$		−	53.1468i		−	1.92405i
$764$			24.4317i			0.883910i
$765$		0			0
$766$		−	21.3821i		−	0.772568i
$767$			17.0309i			0.614951i
$768$	10.6566	−	21.8334i	0.384536	−	0.787846i
$769$			33.7287i			1.21629i	0.793827	+	0.608143i	$0.208085\pi$
$769$			33.7287i			1.21629i	−0.793827	+	0.608143i	$0.791915\pi$
$770$		0			0
$771$	−12.9449	+	26.5217i	−0.466199	+	0.955157i
$772$	2.04985			0.0737757
$773$	−33.6396			−1.20993			−0.604966	−	0.796251i	$-0.706813\pi$
$773$	−33.6396			−1.20993			−0.604966	+	0.796251i	$0.706813\pi$
$774$	−21.3356	+	16.6496i	−0.766893	+	0.598458i
$775$		0			0
$776$	32.2166			1.15651
$777$	−31.4754	−	15.3627i	−1.12917	−	0.551134i
$778$	−13.1993			−0.473217
$779$			1.14282i			0.0409456i
$780$		0			0
$781$	−0.323802	+	21.9952i	−0.0115865	+	0.787051i
$782$	−30.2310			−1.08106
$783$	6.15473	−	1.30272i	0.219952	−	0.0465556i
$784$	7.15560			0.255557
$785$		0			0
$786$	−8.62776	−	4.21109i	−0.307742	−	0.150205i
$787$	43.5468			1.55228			0.776139	−	0.630562i	$-0.217176\pi$
$787$	43.5468			1.55228			0.776139	+	0.630562i	$0.217176\pi$
$788$		−	28.1408i		−	1.00248i
$789$	50.3571	+	24.5786i	1.79276	+	0.875020i
$790$		0			0
$791$	−9.29118			−0.330356
$792$	−21.2721	+	16.1019i	−0.755872	+	0.572157i
$793$			3.78988i			0.134583i
$794$	9.69778			0.344161
$795$		0			0
$796$	−3.30548			−0.117159
$797$	−37.0397			−1.31201			−0.656006	−	0.754755i	$-0.727756\pi$
$797$	−37.0397			−1.31201			−0.656006	+	0.754755i	$0.727756\pi$
$798$	6.55473	−	13.4295i	0.232035	−	0.475398i
$799$			20.8848i			0.738851i
$800$		0			0
$801$	−20.8316	+	16.2563i	−0.736049	+	0.574388i
$802$	−2.41187			−0.0851662
$803$	−26.1194	−	0.384515i	−0.921733	−	0.0135692i
$804$	−9.52032	−	4.64673i	−0.335756	−	0.163878i
$805$		0			0
$806$		−	2.87927i		−	0.101418i
$807$	9.98896	+	4.87547i	0.351628	+	0.171625i
$808$			33.4647i			1.17729i
$809$	31.4575			1.10599			0.552993	−	0.833186i	$-0.313486\pi$
$809$	31.4575			1.10599			0.552993	+	0.833186i	$0.313486\pi$
$810$		0			0
$811$		−	33.1535i		−	1.16418i	−0.813125	−	0.582089i	$-0.802236\pi$
$811$		−	33.1535i		−	1.16418i	0.813125	−	0.582089i	$-0.197764\pi$
$812$	7.21434			0.253174
$813$	−26.2047	−	12.7901i	−0.919040	−	0.448570i
$814$	12.2412	+	0.180209i	0.429055	+	0.00631631i
$815$		0			0
$816$	−5.15210	−	2.51467i	−0.180359	−	0.0880309i
$817$		−	28.0833i		−	0.982512i
$818$	5.01429			0.175321
$819$	18.2673	+	23.4087i	0.638313	+	0.817965i
$820$		0			0
$821$	−15.7418			−0.549393			−0.274697	−	0.961531i	$-0.588577\pi$
$821$	−15.7418			−0.549393			−0.274697	+	0.961531i	$0.588577\pi$
$822$	−11.6369	−	5.67982i	−0.405885	−	0.198106i
$823$			47.6487i			1.66093i	0.557070	+	0.830465i	$0.311925\pi$
$823$			47.6487i			1.66093i	−0.557070	+	0.830465i	$0.688075\pi$
$824$	42.9517			1.49629
$825$		0			0
$826$	26.1247			0.908995
$827$		−	32.0439i		−	1.11428i	−0.830420	−	0.557138i	$-0.811899\pi$
$827$		−	32.0439i		−	1.11428i	0.830420	−	0.557138i	$-0.188101\pi$
$828$	−17.1432	−	21.9682i	−0.595768	−	0.763446i
$829$	15.9842			0.555154			0.277577	−	0.960703i	$-0.410469\pi$
$829$	15.9842			0.555154			0.277577	+	0.960703i	$0.410469\pi$
$830$		0			0
$831$	−3.44405	+	7.05624i	−0.119473	+	0.244778i
$832$	7.85154			0.272203
$833$			67.2106i			2.32871i
$834$	−7.44614	+	15.2558i	−0.257839	+	0.528265i
$835$		0			0
$836$	0.165313	−	11.2294i	0.00571748	−	0.388377i
$837$	8.10126	−	1.71473i	0.280021	−	0.0592698i
$838$	−18.3622			−0.634310
$839$		−	3.70634i		−	0.127957i	−0.997951	−	0.0639786i	$-0.979621\pi$
$839$		−	3.70634i		−	0.127957i	0.997951	−	0.0639786i	$-0.0203789\pi$
$840$		0			0
$841$	−27.5342			−0.949454
$842$		−	0.992212i		−	0.0341939i
$843$	−2.07143	+	4.24398i	−0.0713438	+	0.146171i
$844$		−	35.3194i		−	1.21574i
$845$		0			0
$846$	7.05874	−	5.50841i	0.242684	−	0.189383i
$847$	47.9951	+	1.41342i	1.64913	+	0.0485657i
$848$	−5.55798			−0.190862
$849$	−6.76154	+	13.8532i	−0.232055	+	0.475440i
$850$		0			0
$851$			31.5214i			1.08054i
$852$	14.0929	+	6.87853i	0.482814	+	0.235655i
$853$	0.223000			0.00763538			0.00381769	−	0.999993i	$-0.498785\pi$
$853$	0.223000			0.00763538			0.00381769	+	0.999993i	$0.498785\pi$
$854$	5.81352			0.198934
$855$		0			0
$856$	22.8372			0.780561
$857$		−	14.0846i		−	0.481120i	−0.970634	−	0.240560i	$-0.922669\pi$
$857$		−	14.0846i		−	0.481120i	0.970634	−	0.240560i	$-0.0773311\pi$
$858$	−9.25917	−	4.68927i	−0.316103	−	0.160089i
$859$	−15.9136			−0.542966			−0.271483	−	0.962443i	$-0.587514\pi$
$859$	−15.9136			−0.542966			−0.271483	+	0.962443i	$0.587514\pi$
$860$		0			0
$861$	−1.52784	+	3.13027i	−0.0520686	+	0.106679i
$862$		−	21.7372i		−	0.740373i
$863$	−39.2471			−1.33599			−0.667994	−	0.744167i	$-0.732847\pi$
$863$	−39.2471			−1.33599			−0.667994	+	0.744167i	$0.732847\pi$
$864$	6.27918	+	29.6660i	0.213622	+	1.00926i
$865$		0			0
$866$	16.8323			0.571986
$867$	10.7042	−	21.9311i	0.363535	−	0.744818i
$868$	9.49599			0.322315
$869$	0.276704	−	18.7960i	0.00938653	−	0.637609i
$870$		0			0
$871$		−	10.1594i		−	0.344238i
$872$	32.6466			1.10555
$873$	−28.4167	+	22.1754i	−0.961759	+	0.750525i
$874$	−13.4491			−0.454922
$875$		0			0
$876$	−8.16827	+	16.7353i	−0.275980	+	0.565434i
$877$	−28.5762			−0.964949			−0.482474	−	0.875910i	$-0.660262\pi$
$877$	−28.5762			−0.964949			−0.482474	+	0.875910i	$0.660262\pi$
$878$	13.0750			0.441258
$879$	−18.4988	−	9.02898i	−0.623948	−	0.304540i
$880$		0			0
$881$			28.2142i			0.950559i	0.879835	+	0.475279i	$0.157653\pi$
$881$			28.2142i			0.950559i	−0.879835	+	0.475279i	$0.842347\pi$
$882$	22.7161	−	17.7269i	0.764892	−	0.596897i
$883$			16.6203i			0.559319i	0.960099	+	0.279660i	$0.0902216\pi$
$883$			16.6203i			0.559319i	−0.960099	+	0.279660i	$0.909778\pi$
$884$		−	17.2586i		−	0.580468i
$885$		0			0
$886$			22.8505i			0.767679i
$887$			44.6464i			1.49908i	0.661960	+	0.749539i	$0.269725\pi$
$887$			44.6464i			1.49908i	−0.661960	+	0.749539i	$0.730275\pi$
$888$	9.43688	−	19.3345i	0.316681	−	0.648822i
$889$	−38.8492			−1.30296
$890$		0			0
$891$	7.67975	−	28.8448i	0.257281	−	0.966337i
$892$			10.1791i			0.340820i
$893$			9.29118i			0.310917i
$894$	−9.00618	−	4.39579i	−0.301212	−	0.147017i
$895$		0			0
$896$			38.9029i			1.29965i
$897$	11.7214	−	24.0151i	0.391367	−	0.801840i
$898$	19.4460			0.648922
$899$	1.92944			0.0643505
$900$		0			0
$901$		−	52.2046i		−	1.73919i
$902$	0.0179220	−	1.21740i	0.000596736	−	0.0405352i
$903$	37.5448	−	76.9226i	1.24941	−	2.55982i
$904$		−	5.70731i		−	0.189822i
$905$		0			0
$906$	6.16674	−	12.6345i	0.204876	−	0.419755i
$907$		−	3.12032i		−	0.103609i	−0.998657	−	0.0518043i	$-0.983503\pi$
$907$		−	3.12032i		−	0.103609i	0.998657	−	0.0518043i	$-0.0164972\pi$
$908$		−	17.8170i		−	0.591279i
$909$	−23.0345	−	29.5176i	−0.764008	−	0.979036i
$910$		0			0
$911$			13.4754i			0.446460i	0.974766	+	0.223230i	$0.0716602\pi$
$911$			13.4754i			0.446460i	−0.974766	+	0.223230i	$0.928340\pi$
$912$	−2.29205	−	1.11872i	−0.0758974	−	0.0370444i
$913$	0.0761954	−	5.17581i	0.00252170	−	0.171294i
$914$			8.81549i			0.291591i
$915$		0			0
$916$	−9.38978			−0.310247
$917$	30.3650			1.00274
$918$	−22.5855	+	4.78050i	−0.745434	+	0.157780i
$919$		−	31.2115i		−	1.02957i	−0.857319	−	0.514786i	$-0.827871\pi$
$919$		−	31.2115i		−	1.02957i	0.857319	−	0.514786i	$-0.172129\pi$
$920$		0			0
$921$	8.34316	−	17.0936i	0.274916	−	0.563254i
$922$			2.03853i			0.0671355i
$923$			15.0389i			0.495011i
$924$	15.4655	−	30.5373i	0.508777	−	1.00460i
$925$		0			0
$926$	−7.57323			−0.248872
$927$	−37.8856	+	29.5647i	−1.24433	+	0.971031i
$928$			7.06542i			0.231934i
$929$			50.2207i			1.64769i	0.566818	+	0.823843i	$0.308174\pi$
$929$			50.2207i			1.64769i	−0.566818	+	0.823843i	$0.691826\pi$
$930$		0			0
$931$			29.9005i			0.979949i
$932$			28.8125i			0.943784i
$933$	−34.0771	−	16.6325i	−1.11563	−	0.544525i
$934$		−	21.0217i		−	0.687852i
$935$		0			0
$936$	−14.3793	+	11.2211i	−0.470002	+	0.366774i
$937$	7.74456			0.253004			0.126502	−	0.991966i	$-0.459625\pi$
$937$	7.74456			0.253004			0.126502	+	0.991966i	$0.459625\pi$
$938$	−15.5841			−0.508839
$939$	15.8940	+	7.75762i	0.518680	+	0.253160i
$940$		0			0
$941$	33.2838			1.08502			0.542510	−	0.840050i	$-0.317474\pi$
$941$	33.2838			1.08502			0.542510	+	0.840050i	$0.317474\pi$
$942$	7.21146	−	14.7750i	0.234962	−	0.481395i
$943$	3.13484			0.102084
$944$		−	4.45879i		−	0.145121i
$945$		0			0
$946$	−0.440411	+	29.9163i	−0.0143190	+	0.972662i
$947$	−45.6884			−1.48467			−0.742337	−	0.670027i	$-0.766283\pi$
$947$	−45.6884			−1.48467			−0.742337	+	0.670027i	$0.766283\pi$
$948$	−12.0430	−	5.87803i	−0.391139	−	0.190910i
$949$	−17.8587			−0.579719
$950$		0			0
$951$	1.91381	−	3.92105i	0.0620596	−	0.127149i
$952$	−65.2611			−2.11512
$953$		−	1.89333i		−	0.0613311i	−0.999530	−	0.0306655i	$-0.990237\pi$
$953$		−	1.89333i		−	0.0613311i	0.999530	−	0.0306655i	$-0.00976268\pi$
$954$	−17.6443	+	13.7691i	−0.571257	+	0.445790i
$955$		0			0
$956$	5.28490			0.170926
$957$	3.14235	−	6.20472i	0.101578	−	0.200570i
$958$			9.29040i			0.300159i
$959$	40.9556			1.32253
$960$		0			0
$961$	−28.4603			−0.918076
$962$	8.36975			0.269852
$963$	−20.1436	+	15.7194i	−0.649118	+	0.506551i
$964$		−	37.4521i		−	1.20625i
$965$		0			0
$966$	−36.8381	−	17.9802i	−1.18525	−	0.578502i
$967$	3.87309			0.124550			0.0622750	−	0.998059i	$-0.480164\pi$
$967$	3.87309			0.124550			0.0622750	+	0.998059i	$0.480164\pi$
$968$	−0.868226	+	29.4821i	−0.0279058	+	0.947590i
$969$	10.5078	−	21.5286i	0.337559	−	0.691599i
$970$		0			0
$971$		−	48.1278i		−	1.54449i	−0.635322	−	0.772247i	$-0.719133\pi$
$971$		−	48.1278i		−	1.54449i	0.635322	−	0.772247i	$-0.280867\pi$
$972$	−16.2816	−	13.7015i	−0.522232	−	0.439475i
$973$		−	53.6920i		−	1.72129i
$974$	−26.5450			−0.850557
$975$		0			0
$976$		−	0.992212i		−	0.0317599i
$977$	−51.3570			−1.64305			−0.821527	−	0.570169i	$-0.806878\pi$
$977$	−51.3570			−1.64305			−0.821527	+	0.570169i	$0.806878\pi$
$978$	7.15743	−	14.6643i	0.228869	−	0.468912i
$979$	−0.430007	+	29.2096i	−0.0137431	+	0.933542i
$980$		0			0
$981$	−28.7960	+	22.4714i	−0.919384	+	0.717457i
$982$		−	30.2834i		−	0.966382i
$983$	57.9519			1.84838			0.924190	−	0.381933i	$-0.124742\pi$
$983$	57.9519			1.84838			0.924190	+	0.381933i	$0.124742\pi$
$984$	−1.92284	−	0.938509i	−0.0612978	−	0.0299186i
$985$		0			0
$986$	−5.37910			−0.171305
$987$	−12.4214	+	25.4493i	−0.395379	+	0.810060i
$988$		−	7.67794i		−	0.244268i
$989$	−77.0349			−2.44957
$990$		0			0
$991$	28.4842			0.904830			0.452415	−	0.891808i	$-0.350563\pi$
$991$	28.4842			0.904830			0.452415	+	0.891808i	$0.350563\pi$
$992$			9.29997i			0.295274i
$993$	−12.4281	+	25.4630i	−0.394395	+	0.808044i
$994$	23.0690			0.731706
$995$		0			0
$996$	−3.31627	−	1.61862i	−0.105080	−	0.0512880i
$997$	−33.2142			−1.05191			−0.525953	−	0.850514i	$-0.676291\pi$
$997$	−33.2142			−1.05191			−0.525953	+	0.850514i	$0.676291\pi$
$998$		−	21.3326i		−	0.675271i
$999$	4.98456	+	23.5496i	0.157704	+	0.745076i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.2.d.b.824.5		8
3.2	odd	2		825.2.d.e.824.4		8
5.2	odd	4		825.2.f.c.626.4		8
5.3	odd	4		165.2.f.a.131.5	✓	8
5.4	even	2		825.2.d.d.824.4		8
11.10	odd	2		825.2.d.c.824.4		8
15.2	even	4		825.2.f.d.626.5		8
15.8	even	4		165.2.f.b.131.4	yes	8
15.14	odd	2		825.2.d.c.824.5		8
20.3	even	4		2640.2.f.d.1121.8		8
33.32	even	2		825.2.d.d.824.5		8
55.32	even	4		825.2.f.d.626.6		8
55.43	even	4		165.2.f.b.131.3	yes	8
55.54	odd	2		825.2.d.e.824.5		8
60.23	odd	4		2640.2.f.c.1121.7		8
165.32	odd	4		825.2.f.c.626.3		8
165.98	odd	4		165.2.f.a.131.6	yes	8
165.164	even	2	inner	825.2.d.b.824.4		8
220.43	odd	4		2640.2.f.c.1121.8		8
660.263	even	4		2640.2.f.d.1121.7		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.f.a.131.5	✓	8	5.3	odd	4
165.2.f.a.131.6	yes	8	165.98	odd	4
165.2.f.b.131.3	yes	8	55.43	even	4
165.2.f.b.131.4	yes	8	15.8	even	4
825.2.d.b.824.4		8	165.164	even	2	inner
825.2.d.b.824.5		8	1.1	even	1	trivial
825.2.d.c.824.4		8	11.10	odd	2
825.2.d.c.824.5		8	15.14	odd	2
825.2.d.d.824.4		8	5.4	even	2
825.2.d.d.824.5		8	33.32	even	2
825.2.d.e.824.4		8	3.2	odd	2
825.2.d.e.824.5		8	55.54	odd	2
825.2.f.c.626.3		8	165.32	odd	4
825.2.f.c.626.4		8	5.2	odd	4
825.2.f.d.626.5		8	15.2	even	4
825.2.f.d.626.6		8	55.32	even	4
2640.2.f.c.1121.7		8	60.23	odd	4
2640.2.f.c.1121.8		8	220.43	odd	4
2640.2.f.d.1121.7		8	660.263	even	4
2640.2.f.d.1121.8		8	20.3	even	4

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:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	825.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+0.796815i q^{2} +(-0.759725 + 1.55654i) q^{3} +1.36509 q^{4} +(-1.24027 - 0.605361i) q^{6} +4.36509 q^{7} +2.68135i q^{8} +(-1.84564 - 2.36509i) q^{9} +O(q^{10})\)	\(q+0.796815i q^{2} +(-0.759725 + 1.55654i) q^{3} +1.36509 q^{4} +(-1.24027 - 0.605361i) q^{6} +4.36509 q^{7} +2.68135i q^{8} +(-1.84564 - 2.36509i) q^{9} +(-3.31627 - 0.0488202i) q^{11} +(-1.03709 + 2.12481i) q^{12} -2.26745 q^{13} +3.47817i q^{14} +0.593630 q^{16} +5.57581i q^{17} +(1.88454 - 1.47063i) q^{18} +2.48055i q^{19} +(-3.31627 + 6.79443i) q^{21} +(0.0389007 - 2.64245i) q^{22} +6.80435 q^{23} +(-4.17363 - 2.03709i) q^{24} -1.80673i q^{26} +(5.08353 - 1.07599i) q^{27} +5.95872 q^{28} +1.21072 q^{29} +1.59363 q^{31} +5.83572i q^{32} +(2.59544 - 5.12481i) q^{33} -4.44289 q^{34} +(-2.51945 - 3.22854i) q^{36} +4.63253i q^{37} -1.97654 q^{38} +(1.72264 - 3.52937i) q^{39} +0.460711 q^{41} +(-5.41391 - 2.64245i) q^{42} -11.3214 q^{43} +(-4.52699 - 0.0666438i) q^{44} +5.42181i q^{46} +3.74561 q^{47} +(-0.450996 + 0.924009i) q^{48} +12.0540 q^{49} +(-8.67897 - 4.23608i) q^{51} -3.09526 q^{52} -9.36270 q^{53} +(0.857366 + 4.05063i) q^{54} +11.7043i q^{56} +(-3.86108 - 1.88454i) q^{57} +0.964721i q^{58} -7.51106i q^{59} -1.67143i q^{61} +1.26983i q^{62} +(-8.05636 - 10.3238i) q^{63} -3.46273 q^{64} +(4.08353 + 2.06809i) q^{66} +4.48055i q^{67} +7.61145i q^{68} +(-5.16944 + 10.5912i) q^{69} -6.63253i q^{71} +(6.34163 - 4.94880i) q^{72} +7.87615 q^{73} -3.69127 q^{74} +3.38616i q^{76} +(-14.4758 - 0.213104i) q^{77} +(2.81226 + 1.37262i) q^{78} +5.66781i q^{79} +(-2.18726 + 8.73017i) q^{81} +0.367101i q^{82} +1.56073i q^{83} +(-4.52699 + 9.27498i) q^{84} -9.02108i q^{86} +(-0.919815 + 1.88454i) q^{87} +(0.130904 - 8.89207i) q^{88} -8.80797i q^{89} -9.89759 q^{91} +9.28852 q^{92} +(-1.21072 + 2.48055i) q^{93} +2.98456i q^{94} +(-9.08353 - 4.43354i) q^{96} -12.0151i q^{97} +9.60479i q^{98} +(6.00515 + 7.93336i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{3} - 8 q^{4} - 14 q^{6} + 16 q^{7} - 4 q^{9}+O(q^{10}) \) 8 * q - 2 * q^3 - 8 * q^4 - 14 * q^6 + 16 * q^7 - 4 * q^9	\( 8 q - 2 q^{3} - 8 q^{4} - 14 q^{6} + 16 q^{7} - 4 q^{9} - 12 q^{11} - 6 q^{12} - 8 q^{13} - 8 q^{16} - 12 q^{18} - 12 q^{21} - 16 q^{22} + 12 q^{23} - 6 q^{24} - 14 q^{27} + 16 q^{28} - 20 q^{29} - 6 q^{33} + 16 q^{34} - 12 q^{36} - 20 q^{38} + 12 q^{39} - 12 q^{41} - 20 q^{42} + 8 q^{43} + 8 q^{44} - 20 q^{47} + 22 q^{48} + 8 q^{49} + 12 q^{51} + 32 q^{52} - 8 q^{53} - 6 q^{54} - 8 q^{57} - 24 q^{63} - 22 q^{66} + 20 q^{69} + 36 q^{72} - 32 q^{73} - 8 q^{74} - 28 q^{77} + 4 q^{78} + 8 q^{81} + 8 q^{84} + 8 q^{87} + 16 q^{88} + 8 q^{91} + 12 q^{92} + 20 q^{93} - 18 q^{96} - 36 q^{99}+O(q^{100}) \) 8 * q - 2 * q^3 - 8 * q^4 - 14 * q^6 + 16 * q^7 - 4 * q^9 - 12 * q^11 - 6 * q^12 - 8 * q^13 - 8 * q^16 - 12 * q^18 - 12 * q^21 - 16 * q^22 + 12 * q^23 - 6 * q^24 - 14 * q^27 + 16 * q^28 - 20 * q^29 - 6 * q^33 + 16 * q^34 - 12 * q^36 - 20 * q^38 + 12 * q^39 - 12 * q^41 - 20 * q^42 + 8 * q^43 + 8 * q^44 - 20 * q^47 + 22 * q^48 + 8 * q^49 + 12 * q^51 + 32 * q^52 - 8 * q^53 - 6 * q^54 - 8 * q^57 - 24 * q^63 - 22 * q^66 + 20 * q^69 + 36 * q^72 - 32 * q^73 - 8 * q^74 - 28 * q^77 + 4 * q^78 + 8 * q^81 + 8 * q^84 + 8 * q^87 + 16 * q^88 + 8 * q^91 + 12 * q^92 + 20 * q^93 - 18 * q^96 - 36 * q^99

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