LMFDB - Embedded newform 633.2.d.a.632.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [633,2,Mod(632,633)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(633, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("633.632");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 633 = 3 \cdot 211 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	633.d (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.05453044795$
Analytic rank:	$0$
Dimension:	$68$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			632.15
Character	$\chi$	$=$	633.632
Dual form			633.2.d.a.632.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.76207 q^{2} +(1.49484 - 0.874902i) q^{3} +1.10489 q^{4} +0.0681843i q^{5} +(-2.63401 + 1.54164i) q^{6} +2.98322i q^{7} +1.57725 q^{8} +(1.46909 - 2.61568i) q^{9} +O(q^{10})$	\(q-1.76207 q^{2} +(1.49484 - 0.874902i) q^{3} +1.10489 q^{4} +0.0681843i q^{5} +(-2.63401 + 1.54164i) q^{6} +2.98322i q^{7} +1.57725 q^{8} +(1.46909 - 2.61568i) q^{9} -0.120145i q^{10} -5.70340i q^{11} +(1.65163 - 0.966668i) q^{12} -0.936356 q^{13} -5.25664i q^{14} +(0.0596545 + 0.101925i) q^{15} -4.98900 q^{16} -3.92728 q^{17} +(-2.58864 + 4.60900i) q^{18} +5.67663 q^{19} +0.0753359i q^{20} +(2.61003 + 4.45944i) q^{21} +10.0498i q^{22} +0.508814 q^{23} +(2.35774 - 1.37994i) q^{24} +4.99535 q^{25} +1.64992 q^{26} +(-0.0923992 - 5.19533i) q^{27} +3.29612i q^{28} +7.78957 q^{29} +(-0.105115 - 0.179598i) q^{30} +1.86001i q^{31} +5.63646 q^{32} +(-4.98991 - 8.52567i) q^{33} +6.92013 q^{34} -0.203409 q^{35} +(1.62318 - 2.89003i) q^{36} +0.722896 q^{37} -10.0026 q^{38} +(-1.39970 + 0.819220i) q^{39} +0.107544i q^{40} +5.45790 q^{41} +(-4.59905 - 7.85784i) q^{42} -6.07306 q^{43} -6.30161i q^{44} +(0.178348 + 0.100169i) q^{45} -0.896565 q^{46} -12.1362i q^{47} +(-7.45776 + 4.36488i) q^{48} -1.89961 q^{49} -8.80215 q^{50} +(-5.87065 + 3.43598i) q^{51} -1.03457 q^{52} -6.61940i q^{53} +(0.162814 + 9.15453i) q^{54} +0.388882 q^{55} +4.70529i q^{56} +(8.48565 - 4.96649i) q^{57} -13.7258 q^{58} -0.560202i q^{59} +(0.0659115 + 0.112615i) q^{60} -7.77561i q^{61} -3.27747i q^{62} +(7.80314 + 4.38263i) q^{63} +0.0461684 q^{64} -0.0638448i q^{65} +(8.79257 + 15.0228i) q^{66} -0.778412i q^{67} -4.33920 q^{68} +(0.760595 - 0.445162i) q^{69} +0.358420 q^{70} +7.65305i q^{71} +(2.31713 - 4.12558i) q^{72} -6.83316 q^{73} -1.27379 q^{74} +(7.46725 - 4.37044i) q^{75} +6.27203 q^{76} +17.0145 q^{77} +(2.46637 - 1.44352i) q^{78} +13.9019 q^{79} -0.340171i q^{80} +(-4.68353 - 7.68535i) q^{81} -9.61720 q^{82} -3.37653i q^{83} +(2.88378 + 4.92718i) q^{84} -0.267779i q^{85} +10.7012 q^{86} +(11.6442 - 6.81511i) q^{87} -8.99569i q^{88} -15.2595 q^{89} +(-0.314262 - 0.176505i) q^{90} -2.79336i q^{91} +0.562182 q^{92} +(1.62733 + 2.78042i) q^{93} +21.3848i q^{94} +0.387057i q^{95} +(8.42560 - 4.93135i) q^{96} -9.70320i q^{97} +3.34724 q^{98} +(-14.9182 - 8.37883i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q + 64 q^{4} - 14 q^{6} - 4 q^{9}+O(q^{10}) $ 68 * q + 64 * q^4 - 14 * q^6 - 4 * q^9	$ 68 q + 64 q^{4} - 14 q^{6} - 4 q^{9} - 16 q^{13} + 56 q^{16} + 4 q^{19} + 8 q^{21} - 38 q^{24} - 60 q^{25} - 14 q^{30} - 32 q^{34} - 18 q^{36} - 28 q^{37} + 40 q^{43} - 2 q^{45} - 8 q^{46} - 80 q^{49} + 16 q^{51} - 16 q^{52} + 52 q^{54} + 16 q^{55} - 40 q^{58} + 28 q^{64} + 18 q^{66} - 10 q^{69} + 80 q^{70} - 8 q^{76} + 32 q^{78} - 40 q^{79} - 28 q^{81} - 44 q^{82} + 84 q^{84} - 44 q^{87} - 10 q^{93} - 56 q^{96} + 68 q^{99}+O(q^{100}) $ 68 * q + 64 * q^4 - 14 * q^6 - 4 * q^9 - 16 * q^13 + 56 * q^16 + 4 * q^19 + 8 * q^21 - 38 * q^24 - 60 * q^25 - 14 * q^30 - 32 * q^34 - 18 * q^36 - 28 * q^37 + 40 * q^43 - 2 * q^45 - 8 * q^46 - 80 * q^49 + 16 * q^51 - 16 * q^52 + 52 * q^54 + 16 * q^55 - 40 * q^58 + 28 * q^64 + 18 * q^66 - 10 * q^69 + 80 * q^70 - 8 * q^76 + 32 * q^78 - 40 * q^79 - 28 * q^81 - 44 * q^82 + 84 * q^84 - 44 * q^87 - 10 * q^93 - 56 * q^96 + 68 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/633\mathbb{Z}\right)^\times$.

$n$	$212$	$424$
$\chi(n)$	$-1$	$-1$

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 $

$2$	−1.76207			−1.24597			−0.622985	−	0.782233i	$-0.714080\pi$
$2$	−1.76207			−1.24597			−0.622985	+	0.782233i	$0.714080\pi$
$3$	1.49484	−	0.874902i	0.863046	−	0.505125i
$3$	1.49484	−	0.874902i	0.863046	−	0.505125i
$4$	1.10489			0.552444
$5$			0.0681843i			0.0304929i	0.999884	+	0.0152465i	$0.00485329\pi$
$5$			0.0681843i			0.0304929i	−0.999884	+	0.0152465i	$0.995147\pi$
$6$	−2.63401	+	1.54164i	−1.07533	+	0.629371i
$7$			2.98322i			1.12755i	0.825928	+	0.563776i	$0.190652\pi$
$7$			2.98322i			1.12755i	−0.825928	+	0.563776i	$0.809348\pi$
$8$	1.57725			0.557642
$9$	1.46909	−	2.61568i	0.489698	−	0.871892i
$10$		−	0.120145i		−	0.0379933i
$11$		−	5.70340i		−	1.71964i	−0.510598	−	0.859820i	$-0.670576\pi$
$11$		−	5.70340i		−	1.71964i	0.510598	−	0.859820i	$-0.329424\pi$
$12$	1.65163	−	0.966668i	0.476784	−	0.279053i
$13$	−0.936356			−0.259698			−0.129849	−	0.991534i	$-0.541449\pi$
$13$	−0.936356			−0.259698			−0.129849	+	0.991534i	$0.541449\pi$
$14$		−	5.25664i		−	1.40490i
$15$	0.0596545	+	0.101925i	0.0154027	+	0.0263168i
$16$	−4.98900			−1.24725
$17$	−3.92728			−0.952504			−0.476252	−	0.879309i	$-0.658005\pi$
$17$	−3.92728			−0.952504			−0.476252	+	0.879309i	$0.658005\pi$
$18$	−2.58864	+	4.60900i	−0.610149	+	1.08635i
$19$	5.67663			1.30231			0.651154	−	0.758946i	$-0.274285\pi$
$19$	5.67663			1.30231			0.651154	+	0.758946i	$0.274285\pi$
$20$			0.0753359i			0.0168456i
$21$	2.61003	+	4.45944i	0.569554	+	0.973129i
$22$			10.0498i			2.14262i
$23$	0.508814			0.106095			0.0530475	−	0.998592i	$-0.483107\pi$
$23$	0.508814			0.106095			0.0530475	+	0.998592i	$0.483107\pi$
$24$	2.35774	−	1.37994i	0.481271	−	0.281679i
$25$	4.99535			0.999070
$26$	1.64992			0.323577
$27$	−0.0923992	−	5.19533i	−0.0177822	−	0.999842i
$28$			3.29612i			0.622909i
$29$	7.78957			1.44649			0.723244	−	0.690593i	$-0.242650\pi$
$29$	7.78957			1.44649			0.723244	+	0.690593i	$0.242650\pi$
$30$	−0.105115	−	0.179598i	−0.0191914	−	0.0327900i
$31$			1.86001i			0.334068i	0.985951	+	0.167034i	$0.0534190\pi$
$31$			1.86001i			0.334068i	−0.985951	+	0.167034i	$0.946581\pi$
$32$	5.63646			0.996395
$33$	−4.98991	−	8.52567i	−0.868632	−	1.48413i
$34$	6.92013			1.18679
$35$	−0.203409			−0.0343824
$36$	1.62318	−	2.89003i	0.270531	−	0.481671i
$37$	0.722896			0.118843			0.0594217	−	0.998233i	$-0.481074\pi$
$37$	0.722896			0.118843			0.0594217	+	0.998233i	$0.481074\pi$
$38$	−10.0026			−1.62264
$39$	−1.39970	+	0.819220i	−0.224132	+	0.131180i
$40$			0.107544i			0.0170042i
$41$	5.45790			0.852381			0.426190	−	0.904633i	$-0.359855\pi$
$41$	5.45790			0.852381			0.426190	+	0.904633i	$0.359855\pi$
$42$	−4.59905	−	7.85784i	−0.709648	−	1.21249i
$43$	−6.07306			−0.926133			−0.463066	−	0.886324i	$-0.653251\pi$
$43$	−6.07306			−0.926133			−0.463066	+	0.886324i	$0.653251\pi$
$44$		−	6.30161i		−	0.950004i
$45$	0.178348	+	0.100169i	0.0265866	+	0.0149323i
$46$	−0.896565			−0.132191
$47$		−	12.1362i		−	1.77024i	−0.465360	−	0.885122i	$-0.654075\pi$
$47$		−	12.1362i		−	1.77024i	0.465360	−	0.885122i	$-0.345925\pi$
$48$	−7.45776	+	4.36488i	−1.07643	+	0.630017i
$49$	−1.89961			−0.271373
$50$	−8.80215			−1.24481
$51$	−5.87065	+	3.43598i	−0.822055	+	0.481134i
$52$	−1.03457			−0.143469
$53$		−	6.61940i		−	0.909244i	−0.890684	−	0.454622i	$-0.849774\pi$
$53$		−	6.61940i		−	0.909244i	0.890684	−	0.454622i	$-0.150226\pi$
$54$	0.162814	+	9.15453i	0.0221561	+	1.24577i
$55$	0.388882			0.0524369
$56$			4.70529i			0.628771i
$57$	8.48565	−	4.96649i	1.12395	−	0.657828i
$58$	−13.7258			−1.80228
$59$		−	0.560202i		−	0.0729321i	−0.999335	−	0.0364661i	$-0.988390\pi$
$59$		−	0.560202i		−	0.0729321i	0.999335	−	0.0364661i	$-0.0116101\pi$
$60$	0.0659115	+	0.112615i	0.00850914	+	0.0145386i
$61$		−	7.77561i		−	0.995565i	−0.867302	−	0.497782i	$-0.834148\pi$
$61$		−	7.77561i		−	0.995565i	0.867302	−	0.497782i	$-0.165852\pi$
$62$		−	3.27747i		−	0.416239i
$63$	7.80314	+	4.38263i	0.983103	+	0.552160i
$64$	0.0461684			0.00577105
$65$		−	0.0638448i		−	0.00791897i
$66$	8.79257	+	15.0228i	1.08229	+	1.84918i
$67$		−	0.778412i		−	0.0950982i	−0.998869	−	0.0475491i	$-0.984859\pi$
$67$		−	0.778412i		−	0.0950982i	0.998869	−	0.0475491i	$-0.0151411\pi$
$68$	−4.33920			−0.526205
$69$	0.760595	−	0.445162i	0.0915649	−	0.0535912i
$70$	0.358420			0.0428394
$71$			7.65305i			0.908250i	0.890938	+	0.454125i	$0.150048\pi$
$71$			7.65305i			0.908250i	−0.890938	+	0.454125i	$0.849952\pi$
$72$	2.31713	−	4.12558i	0.273076	−	0.486204i
$73$	−6.83316			−0.799761			−0.399880	−	0.916567i	$-0.630948\pi$
$73$	−6.83316			−0.799761			−0.399880	+	0.916567i	$0.630948\pi$
$74$	−1.27379			−0.148075
$75$	7.46725	−	4.37044i	0.862244	−	0.504655i
$76$	6.27203			0.719451
$77$	17.0145			1.93898
$78$	2.46637	−	1.44352i	0.279262	−	0.163447i
$79$	13.9019			1.56409			0.782043	−	0.623225i	$-0.214178\pi$
$79$	13.9019			1.56409			0.782043	+	0.623225i	$0.214178\pi$
$80$		−	0.340171i		−	0.0380323i
$81$	−4.68353	−	7.68535i	−0.520392	−	0.853928i
$82$	−9.61720			−1.06204
$83$		−	3.37653i		−	0.370622i	−0.982680	−	0.185311i	$-0.940671\pi$
$83$		−	3.37653i		−	0.370622i	0.982680	−	0.185311i	$-0.0593292\pi$
$84$	2.88378	+	4.92718i	0.314647	+	0.537599i
$85$		−	0.267779i		−	0.0290447i
$86$	10.7012			1.15393
$87$	11.6442	−	6.81511i	1.24839	−	0.730657i
$88$		−	8.99569i		−	0.958944i
$89$	−15.2595			−1.61750			−0.808751	−	0.588151i	$-0.799856\pi$
$89$	−15.2595			−1.61750			−0.808751	+	0.588151i	$0.799856\pi$
$90$	−0.314262	−	0.176505i	−0.0331261	−	0.0186053i
$91$		−	2.79336i		−	0.292823i
$92$	0.562182			0.0586115
$93$	1.62733	+	2.78042i	0.168746	+	0.288316i
$94$			21.3848i			2.20567i
$95$			0.387057i			0.0397112i
$96$	8.42560	−	4.93135i	0.859935	−	0.503304i
$97$		−	9.70320i		−	0.985211i	−0.870253	−	0.492605i	$-0.836045\pi$
$97$		−	9.70320i		−	0.985211i	0.870253	−	0.492605i	$-0.163955\pi$
$98$	3.34724			0.338123
$99$	−14.9182	−	8.37883i	−1.49934	−	0.842104i
$100$	5.51930			0.551930
$101$		−	0.103513i		−	0.0102999i	−0.999987	−	0.00514997i	$-0.998361\pi$
$101$		−	0.103513i		−	0.0102999i	0.999987	−	0.00514997i	$-0.00163929\pi$
$102$	10.3445	−	6.05443i	1.02426	−	0.599478i
$103$	0.296539			0.0292189			0.0146094	−	0.999893i	$-0.495350\pi$
$103$	0.296539			0.0292189			0.0146094	+	0.999893i	$0.495350\pi$
$104$	−1.47687			−0.144819
$105$	−0.304064	+	0.177963i	−0.0296736	+	0.0173674i
$106$			11.6638i			1.13289i
$107$			16.1262i			1.55898i	0.626418	+	0.779488i	$0.284520\pi$
$107$			16.1262i			1.55898i	−0.626418	+	0.779488i	$0.715480\pi$
$108$	−0.102091	−	5.74025i	−0.00982368	−	0.552356i
$109$	14.7530			1.41308			0.706541	−	0.707672i	$-0.250254\pi$
$109$	14.7530			1.41308			0.706541	+	0.707672i	$0.250254\pi$
$110$	−0.685237			−0.0653348
$111$	1.08061	−	0.632463i	0.102567	−	0.0600308i
$112$		−	14.8833i		−	1.40634i
$113$			19.2120i			1.80732i	0.428253	+	0.903659i	$0.359129\pi$
$113$			19.2120i			1.80732i	−0.428253	+	0.903659i	$0.640871\pi$
$114$	−14.9523	+	8.75130i	−1.40041	+	0.819634i
$115$			0.0346931i			0.00323515i
$116$	8.60660			0.799103
$117$	−1.37560	+	2.44920i	−0.127174	+	0.226429i
$118$			0.987115i			0.0908713i
$119$		−	11.7159i		−	1.07400i
$120$	0.0940902	+	0.160761i	0.00858922	+	0.0146754i
$121$	−21.5287			−1.95716
$122$			13.7012i			1.24044i
$123$	8.15869	−	4.77513i	0.735644	−	0.430559i
$124$			2.05510i			0.184554i
$125$			0.681526i			0.0609575i
$126$	−13.7497	−	7.72250i	−1.22492	−	0.687975i
$127$			13.9403i			1.23701i	0.785783	+	0.618503i	$0.212260\pi$
$127$			13.9403i			1.23701i	−0.785783	+	0.618503i	$0.787740\pi$
$128$	−11.3543			−1.00359
$129$	−9.07825	+	5.31333i	−0.799296	+	0.467813i
$130$			0.112499i			0.00986681i
$131$	−6.97989			−0.609836			−0.304918	−	0.952379i	$-0.598629\pi$
$131$	−6.97989			−0.609836			−0.304918	+	0.952379i	$0.598629\pi$
$132$	−5.51329	−	9.41990i	−0.479870	−	0.819897i
$133$			16.9346i			1.46842i
$134$			1.37162i			0.118490i
$135$	0.354240	−	0.00630017i	0.0304881	−	0.000542232i
$136$	−6.19430			−0.531157
$137$			12.4613i			1.06464i	0.846544	+	0.532319i	$0.178679\pi$
$137$			12.4613i			1.06464i	−0.846544	+	0.532319i	$0.821321\pi$
$138$	−1.34022	+	0.784406i	−0.114087	+	0.0667731i
$139$	13.6421			1.15711			0.578555	−	0.815643i	$-0.303617\pi$
$139$	13.6421			1.15711			0.578555	+	0.815643i	$0.303617\pi$
$140$	−0.224744			−0.0189943
$141$	−10.6180	−	18.1416i	−0.894194	−	1.52780i
$142$		−	13.4852i		−	1.13165i
$143$			5.34041i			0.446588i
$144$	−7.32931	+	13.0496i	−0.610776	+	1.08747i
$145$			0.531126i			0.0441077i
$146$	12.0405			0.996479
$147$	−2.83961	+	1.66197i	−0.234207	+	0.137077i
$148$	0.798719			0.0656543
$149$	10.9824			0.899711			0.449856	−	0.893101i	$-0.351475\pi$
$149$	10.9824			0.899711			0.449856	+	0.893101i	$0.351475\pi$
$150$	−13.1578	+	7.70102i	−1.07433	+	0.628786i
$151$	8.91869			0.725793			0.362896	−	0.931830i	$-0.381788\pi$
$151$	8.91869			0.725793			0.362896	+	0.931830i	$0.381788\pi$
$152$	8.95346			0.726222
$153$	−5.76954	+	10.2725i	−0.466439	+	0.830481i
$154$	−29.9807			−2.41592
$155$	−0.126824			−0.0101867
$156$	−1.54651	+	0.905145i	−0.123820	+	0.0724696i
$157$		−	0.611324i		−	0.0487890i	−0.999702	−	0.0243945i	$-0.992234\pi$
$157$		−	0.611324i		−	0.0487890i	0.999702	−	0.0243945i	$-0.00776578\pi$
$158$	−24.4961			−1.94881
$159$	−5.79132	−	9.89494i	−0.459282	−	0.784720i
$160$			0.384318i			0.0303830i
$161$			1.51790i			0.119628i
$162$	8.25270	+	13.5421i	0.648393	+	1.06397i
$163$	−14.9038			−1.16735			−0.583676	−	0.811987i	$-0.698386\pi$
$163$	−14.9038			−1.16735			−0.583676	+	0.811987i	$0.698386\pi$
$164$	6.03036			0.470892
$165$	0.581317	−	0.340234i	0.0452554	−	0.0264872i
$166$			5.94967i			0.461784i
$167$	−14.4388			−1.11731			−0.558655	−	0.829400i	$-0.688682\pi$
$167$	−14.4388			−1.11731			−0.558655	+	0.829400i	$0.688682\pi$
$168$	4.11666	+	7.03365i	0.317608	+	0.542658i
$169$	−12.1232			−0.932557
$170$			0.471844i			0.0361888i
$171$	8.33950	−	14.8482i	0.637737	−	1.13547i
$172$	−6.71005			−0.511636
$173$			3.54632i			0.269622i	0.990871	+	0.134811i	$0.0430427\pi$
$173$			3.54632i			0.269622i	−0.990871	+	0.134811i	$0.956957\pi$
$174$	−20.5178	+	12.0087i	−1.55545	+	0.910377i
$175$			14.9022i			1.12650i
$176$			28.4542i			2.14482i
$177$	−0.490122	−	0.837413i	−0.0368398	−	0.0629438i
$178$	26.8883			2.01536
$179$		−	1.84255i		−	0.137719i	−0.997626	−	0.0688595i	$-0.978064\pi$
$179$		−	1.84255i		−	0.137719i	0.997626	−	0.0688595i	$-0.0219360\pi$
$180$	0.197054	+	0.110676i	0.0146876	+	0.00824927i
$181$			17.2251i			1.28033i	0.768236	+	0.640167i	$0.221135\pi$
$181$			17.2251i			1.28033i	−0.768236	+	0.640167i	$0.778865\pi$
$182$			4.92209i			0.364850i
$183$	−6.80289	−	11.6233i	−0.502884	−	0.859218i
$184$	0.802527			0.0591630
$185$			0.0492902i			0.00362389i
$186$	−2.86746	−	4.89929i	−0.210253	−	0.359234i
$187$			22.3988i			1.63796i
$188$		−	13.4091i		−	0.977960i
$189$	15.4988	−	0.275647i	1.12737	−	0.0200504i
$190$		−	0.682021i		−	0.0494790i
$191$	−14.4908			−1.04852			−0.524259	−	0.851559i	$-0.675658\pi$
$191$	−14.4908			−1.04852			−0.524259	+	0.851559i	$0.675658\pi$
$192$	0.0690144	−	0.0403928i	0.00498069	−	0.00291510i
$193$	−8.83792			−0.636168			−0.318084	−	0.948063i	$-0.603039\pi$
$193$	−8.83792			−0.636168			−0.318084	+	0.948063i	$0.603039\pi$
$194$			17.0977i			1.22754i
$195$	−0.0558579	−	0.0954377i	−0.00400007	−	0.00683444i
$196$	−2.09885			−0.149918
$197$	−10.2642			−0.731293			−0.365646	−	0.930754i	$-0.619152\pi$
$197$	−10.2642			−0.731293			−0.365646	+	0.930754i	$0.619152\pi$
$198$	26.2870	+	14.7641i	1.86813	+	1.04924i
$199$	11.3655			0.805681			0.402840	−	0.915270i	$-0.368023\pi$
$199$	11.3655			0.805681			0.402840	+	0.915270i	$0.368023\pi$
$200$	7.87892			0.557124
$201$	−0.681034	−	1.16360i	−0.0480365	−	0.0820742i
$202$			0.182397i			0.0128334i
$203$			23.2380i			1.63099i
$204$	−6.48641	+	3.79637i	−0.454139	+	0.265799i
$205$			0.372143i			0.0259916i
$206$	−0.522523			−0.0364059
$207$	0.747495	−	1.33089i	0.0519545	−	0.0925034i
$208$	4.67148			0.323909
$209$		−	32.3761i		−	2.23950i
$210$	0.535781	−	0.313583i	0.0369724	−	0.0216393i
$211$	−1.76082	−	14.4187i	−0.121220	−	0.992626i
$211$	−1.76082	−	14.4187i	−0.121220	−	0.992626i
$212$		−	7.31369i		−	0.502306i
$213$	6.69567	+	11.4401i	0.458780	+	0.783862i
$214$		−	28.4154i		−	1.94244i
$215$		−	0.414087i		−	0.0282405i
$216$	−0.145737	−	8.19434i	−0.00991612	−	0.557554i
$217$	−5.54883			−0.376679
$218$	−25.9958			−1.76066
$219$	−10.2145	+	5.97834i	−0.690231	+	0.403979i
$220$	0.429671			0.0289684
$221$	3.67733			0.247364
$222$	−1.90412	+	1.11444i	−0.127796	+	0.0747966i
$223$			7.47444i			0.500526i	0.968178	+	0.250263i	$0.0805170\pi$
$223$			7.47444i			0.500526i	−0.968178	+	0.250263i	$0.919483\pi$
$224$			16.8148i			1.12349i
$225$	7.33864	−	13.0662i	0.489243	−	0.871081i
$226$		−	33.8530i		−	2.25187i
$227$		−	20.4621i		−	1.35812i	−0.734083	−	0.679060i	$-0.762388\pi$
$227$		−	20.4621i		−	1.35812i	0.734083	−	0.679060i	$-0.237612\pi$
$228$	9.37569	−	5.48741i	0.620920	−	0.363413i
$229$			18.7263i			1.23747i	0.785601	+	0.618734i	$0.212354\pi$
$229$			18.7263i			1.23747i	−0.785601	+	0.618734i	$0.787646\pi$
$230$		−	0.0611316i		−	0.00403090i
$231$	25.4340	−	14.8860i	1.67343	−	0.979428i
$232$	12.2861			0.806623
$233$	−6.70431			−0.439214			−0.219607	−	0.975588i	$-0.570477\pi$
$233$	−6.70431			−0.439214			−0.219607	+	0.975588i	$0.570477\pi$
$234$	2.42389	−	4.31567i	0.158455	−	0.282124i
$235$	0.827497			0.0539799
$236$		−	0.618960i		−	0.0402909i
$237$	20.7811	−	12.1628i	1.34988	−	0.790058i
$238$			20.6443i			1.33817i
$239$	−19.2307			−1.24393			−0.621965	−	0.783045i	$-0.713666\pi$
$239$	−19.2307			−1.24393			−0.621965	+	0.783045i	$0.713666\pi$
$240$	−0.297616	−	0.508502i	−0.0192111	−	0.0328236i
$241$	1.62340			0.104572			0.0522861	−	0.998632i	$-0.483349\pi$
$241$	1.62340			0.104572			0.0522861	+	0.998632i	$0.483349\pi$
$242$	37.9351			2.43856
$243$	−13.7250	−	7.39074i	−0.880462	−	0.474116i
$244$		−	8.59117i		−	0.549993i
$245$		−	0.129524i		−	0.00827496i
$246$	−14.3762	+	8.41410i	−0.916591	+	0.536464i
$247$	−5.31535			−0.338207
$248$			2.93370i			0.186290i
$249$	−2.95413	−	5.04737i	−0.187210	−	0.319864i
$250$		−	1.20090i		−	0.0759513i
$251$	16.0239			1.01142			0.505711	−	0.862703i	$-0.331230\pi$
$251$	16.0239			1.01142			0.505711	+	0.862703i	$0.331230\pi$
$252$	8.62159	+	4.84231i	0.543109	+	0.305037i
$253$		−	2.90197i		−	0.182445i
$254$		−	24.5638i		−	1.54127i
$255$	−0.234280	−	0.400286i	−0.0146712	−	0.0250669i
$256$	19.9147			1.24467
$257$			1.96424i			0.122526i	0.998122	+	0.0612628i	$0.0195128\pi$
$257$			1.96424i			0.122526i	−0.998122	+	0.0612628i	$0.980487\pi$
$258$	15.9965	−	9.36245i	0.995899	−	0.582881i
$259$			2.15656i			0.134002i
$260$		−	0.0705413i		−	0.00437478i
$261$	11.4436	−	20.3750i	0.708342	−	1.26118i
$262$	12.2991			0.759838
$263$		−	8.86909i		−	0.546891i	−0.961887	−	0.273446i	$-0.911837\pi$
$263$		−	8.86909i		−	0.546891i	0.961887	−	0.273446i	$-0.0881634\pi$
$264$	−7.87034	−	13.4471i	−0.484386	−	0.827613i
$265$	0.451339			0.0277255
$266$		−	29.8400i		−	1.82961i
$267$	−22.8105	+	13.3506i	−1.39598	+	0.817041i
$268$		−	0.860058i		−	0.0525364i
$269$			24.1018i			1.46951i	0.678330	+	0.734757i	$0.262704\pi$
$269$			24.1018i			1.46951i	−0.678330	+	0.734757i	$0.737296\pi$
$270$	−0.624195	+	0.0111013i	−0.0379873	+	0.000675606i
$271$			11.8907i			0.722310i	0.932506	+	0.361155i	$0.117617\pi$
$271$			11.8907i			0.722310i	−0.932506	+	0.361155i	$0.882383\pi$
$272$	19.5932			1.18801
$273$	−2.44391	−	4.17562i	−0.147912	−	0.252720i
$274$		−	21.9576i		−	1.32651i
$275$		−	28.4905i		−	1.71804i
$276$	0.840372	−	0.491854i	0.0505844	−	0.0296061i
$277$	−9.64621			−0.579585			−0.289792	−	0.957090i	$-0.593586\pi$
$277$	−9.64621			−0.579585			−0.289792	+	0.957090i	$0.593586\pi$
$278$	−24.0384			−1.44173
$279$	4.86519	+	2.73253i	0.291271	+	0.163592i
$280$	−0.320827			−0.0191731
$281$			16.3783i			0.977049i	0.872550	+	0.488525i	$0.162465\pi$
$281$			16.3783i			0.977049i	−0.872550	+	0.488525i	$0.837535\pi$
$282$	18.7096	+	31.9668i	1.11414	+	1.90360i
$283$		−	7.81166i		−	0.464355i	−0.972673	−	0.232177i	$-0.925415\pi$
$283$		−	7.81166i		−	0.464355i	0.972673	−	0.232177i	$-0.0745850\pi$
$284$			8.45576i			0.501757i
$285$	0.338637	+	0.578588i	0.0200591	+	0.0342726i
$286$		−	9.41017i		−	0.556435i
$287$			16.2821i			0.961104i
$288$	8.28049	−	14.7432i	0.487932	−	0.868749i
$289$	−1.57650			−0.0927355
$290$		−	0.935881i		−	0.0549569i
$291$	−8.48934	−	14.5047i	−0.497654	−	0.850282i
$292$	−7.54987			−0.441823
$293$			30.4242i			1.77740i	0.458490	+	0.888700i	$0.348391\pi$
$293$			30.4242i			1.77740i	−0.458490	+	0.888700i	$0.651609\pi$
$294$	5.00359	−	2.92851i	0.291816	−	0.170794i
$295$	0.0381970			0.00222391
$296$	1.14019			0.0662721
$297$	−29.6310	+	0.526989i	−1.71937	+	0.0305790i
$298$	−19.3517			−1.12101
$299$	−0.476431			−0.0275527
$300$	8.25047	−	4.82884i	0.476341	−	0.278793i
$301$		−	18.1173i		−	1.04426i
$302$	−15.7153			−0.904317
$303$	−0.0905637	−	0.154735i	−0.00520275	−	0.00888932i
$304$	−28.3207			−1.62430
$305$	0.530174			0.0303577
$306$	10.1663	−	18.1008i	0.581170	−	1.03476i
$307$	25.4673			1.45350			0.726748	−	0.686904i	$-0.241031\pi$
$307$	25.4673			1.45350			0.726748	+	0.686904i	$0.241031\pi$
$308$	18.7991			1.07118
$309$	0.443279	−	0.259443i	0.0252172	−	0.0147592i
$310$	0.223472			0.0126923
$311$		−	23.4877i		−	1.33186i	−0.746012	−	0.665932i	$-0.768034\pi$
$311$		−	23.4877i		−	1.33186i	0.746012	−	0.665932i	$-0.231966\pi$
$312$	−2.20768	+	1.29211i	−0.124985	+	0.0731516i
$313$		−	3.36325i		−	0.190102i	−0.995472	−	0.0950511i	$-0.969699\pi$
$313$		−	3.36325i		−	0.190102i	0.995472	−	0.0950511i	$-0.0303015\pi$
$314$			1.07720i			0.0607896i
$315$	−0.298827	+	0.532052i	−0.0168370	+	0.0299777i
$316$	15.3600			0.864069
$317$	19.4272			1.09114			0.545571	−	0.838064i	$-0.316313\pi$
$317$	19.4272			1.09114			0.545571	+	0.838064i	$0.316313\pi$
$318$	10.2047	+	17.4356i	0.572252	+	0.977738i
$319$		−	44.4270i		−	2.48744i
$320$			0.00314796i			0.000175976i
$321$	14.1088	+	24.1060i	0.787477	+	1.34547i
$322$		−	2.67465i		−	0.149052i
$323$	−22.2937			−1.24045
$324$	−5.17477	−	8.49144i	−0.287487	−	0.471747i
$325$	−4.67743			−0.259457
$326$	26.2614			1.45449
$327$	22.0534	−	12.9074i	1.21956	−	0.713783i
$328$	8.60848			0.475324
$329$	36.2049			1.99604
$330$	−1.02432	+	0.599515i	−0.0563870	+	0.0330022i
$331$	−21.1771			−1.16400			−0.581999	−	0.813189i	$-0.697729\pi$
$331$	−21.1771			−1.16400			−0.581999	+	0.813189i	$0.697729\pi$
$332$		−	3.73068i		−	0.204748i
$333$	1.06200	−	1.89086i	0.0581974	−	0.103619i
$334$	25.4422			1.39214
$335$	0.0530755			0.00289982
$336$	−13.0214	−	22.2481i	−0.710376	−	1.21374i
$337$	8.06339			0.439241			0.219620	−	0.975585i	$-0.429518\pi$
$337$	8.06339			0.439241			0.219620	+	0.975585i	$0.429518\pi$
$338$	21.3620			1.16194
$339$	16.8087	+	28.7189i	0.912921	+	1.55980i
$340$		−	0.295865i		−	0.0160455i
$341$	10.6084			0.574476
$342$	−14.6948	+	26.1636i	−0.794602	+	1.41476i
$343$			15.2156i			0.821565i
$344$	−9.57874			−0.516451
$345$	0.0303530	+	0.0518606i	0.00163415	+	0.00279208i
$346$		−	6.24887i		−	0.335941i
$347$			33.4884i			1.79775i	0.438205	+	0.898875i	$0.355614\pi$
$347$			33.4884i			1.79775i	−0.438205	+	0.898875i	$0.644386\pi$
$348$	12.8655	−	7.52993i	0.689663	−	0.403647i
$349$			19.9219i			1.06639i	0.845992	+	0.533196i	$0.179009\pi$
$349$			19.9219i			1.06639i	−0.845992	+	0.533196i	$0.820991\pi$
$350$		−	26.2588i		−	1.40359i
$351$	0.0865185	+	4.86468i	0.00461802	+	0.259657i
$352$		−	32.1470i		−	1.71344i
$353$	17.1402			0.912280			0.456140	−	0.889908i	$-0.349232\pi$
$353$	17.1402			0.912280			0.456140	+	0.889908i	$0.349232\pi$
$354$	0.863629	+	1.47558i	0.0459013	+	0.0784261i
$355$	−0.521818			−0.0276952
$356$	−16.8600			−0.893579
$357$	−10.2503	−	17.5134i	−0.542503	−	0.926910i
$358$			3.24671i			0.171594i
$359$			4.86474i			0.256751i	0.991726	+	0.128376i	$0.0409763\pi$
$359$			4.86474i			0.256751i	−0.991726	+	0.128376i	$0.959024\pi$
$360$	0.281300	+	0.157992i	0.0148258	+	0.00832690i
$361$	13.2241			0.696005
$362$		−	30.3519i		−	1.59526i
$363$	−32.1820	+	18.8355i	−1.68912	+	0.988609i
$364$		−	3.08635i		−	0.161768i
$365$		−	0.465914i		−	0.0243871i
$366$	11.9872	+	20.4810i	0.626579	+	1.07056i
$367$		−	31.4108i		−	1.63963i	−0.572629	−	0.819815i	$-0.694076\pi$
$367$		−	31.4108i		−	1.63963i	0.572629	−	0.819815i	$-0.305924\pi$
$368$	−2.53847			−0.132327
$369$	8.01817	−	14.2761i	0.417409	−	0.743184i
$370$		−	0.0868527i		−	0.00451526i
$371$	19.7471			1.02522
$372$	1.79801	+	3.07205i	0.0932226	+	0.159278i
$373$			16.0021i			0.828557i	0.910150	+	0.414278i	$0.135966\pi$
$373$			16.0021i			0.828557i	−0.910150	+	0.414278i	$0.864034\pi$
$374$		−	39.4683i		−	2.04086i
$375$	0.596268	+	1.01877i	0.0307912	+	0.0526092i
$376$		−	19.1418i		−	0.987163i
$377$	−7.29382			−0.375651
$378$	−27.3100	+	0.485709i	−1.40467	+	0.0249822i
$379$			19.2363i			0.988103i	0.869433	+	0.494052i	$0.164485\pi$
$379$			19.2363i			0.988103i	−0.869433	+	0.494052i	$0.835515\pi$
$380$			0.427654i			0.0219382i
$381$	12.1964	+	20.8386i	0.624842	+	1.06759i
$382$	25.5338			1.30642
$383$		−	11.6279i		−	0.594158i	−0.954853	−	0.297079i	$-0.903988\pi$
$383$		−	11.6279i		−	0.594158i	0.954853	−	0.297079i	$-0.0960124\pi$
$384$	−16.9728	+	9.93387i	−0.866140	+	0.506936i
$385$			1.16012i			0.0591253i
$386$	15.5730			0.792646
$387$	−8.92190	+	15.8852i	−0.453525	+	0.807488i
$388$		−	10.7209i		−	0.544273i
$389$		−	12.5242i		−	0.635004i	−0.948258	−	0.317502i	$-0.897156\pi$
$389$		−	12.5242i		−	0.635004i	0.948258	−	0.317502i	$-0.102844\pi$
$390$	0.0984255	+	0.168168i	0.00498397	+	0.00851551i
$391$	−1.99825			−0.101056
$392$	−2.99616			−0.151329
$393$	−10.4338	+	6.10672i	−0.526317	+	0.308043i
$394$	18.0862			0.911169
$395$			0.947891i			0.0476936i
$396$	−16.4830	−	9.25766i	−0.828301	−	0.465215i
$397$		−	21.2456i		−	1.06629i	−0.846024	−	0.533144i	$-0.821010\pi$
$397$		−	21.2456i		−	1.06629i	0.846024	−	0.533144i	$-0.178990\pi$
$398$	−20.0268			−1.00385
$399$	14.8161	+	25.3146i	0.741735	+	1.26731i
$400$	−24.9218			−1.24609
$401$	−38.0241			−1.89884			−0.949418	−	0.314016i	$-0.898325\pi$
$401$	−38.0241			−1.89884			−0.949418	+	0.314016i	$0.898325\pi$
$402$	1.20003	+	2.05035i	0.0598520	+	0.102262i
$403$		−	1.74163i		−	0.0867569i
$404$		−	0.114370i		−	0.00569013i
$405$	0.524020	−	0.319343i	0.0260388	−	0.0158683i
$406$		−	40.9470i		−	2.03217i
$407$		−	4.12297i		−	0.204368i
$408$	−9.25949	+	5.41940i	−0.458413	+	0.268300i
$409$			35.0789i			1.73454i	0.497837	+	0.867271i	$0.334128\pi$
$409$			35.0789i			1.73454i	−0.497837	+	0.867271i	$0.665872\pi$
$410$		−	0.655742i		−	0.0323848i
$411$	10.9024	+	18.6276i	0.537775	+	0.918833i
$412$	0.327642			0.0161418
$413$	1.67121			0.0822347
$414$	−1.31714	+	2.34512i	−0.0647338	+	0.115256i
$415$	0.230226			0.0113013
$416$	−5.27773			−0.258762
$417$	20.3928	−	11.9355i	0.998640	−	0.584485i
$418$			57.0489i			2.79035i
$419$		−	3.54303i		−	0.173089i	−0.996248	−	0.0865443i	$-0.972418\pi$
$419$		−	3.54303i		−	0.173089i	0.996248	−	0.0865443i	$-0.0275824\pi$
$420$	−0.335956	+	0.196629i	−0.0163930	+	0.00959450i
$421$			18.2834i			0.891077i	0.895263	+	0.445538i	$0.146988\pi$
$421$			18.2834i			0.891077i	−0.895263	+	0.445538i	$0.853012\pi$
$422$	3.10268	+	25.4068i	0.151036	+	1.23678i
$423$	−31.7443	−	17.8292i	−1.54346	−	0.866885i
$424$		−	10.4404i		−	0.507033i
$425$	−19.6181			−0.951619
$426$	−11.7982	−	20.1582i	−0.571626	−	0.976669i
$427$	23.1964			1.12255
$428$			17.8176i			0.861246i
$429$	4.67234	+	7.98306i	0.225582	+	0.385426i
$430$			0.729650i			0.0351869i
$431$		−	33.0558i		−	1.59224i	−0.605138	−	0.796120i	$-0.706882\pi$
$431$		−	33.0558i		−	1.59224i	0.605138	−	0.796120i	$-0.293118\pi$
$432$	0.460979	+	25.9195i	0.0221789	+	1.24705i
$433$	12.9382			0.621770			0.310885	−	0.950447i	$-0.399375\pi$
$433$	12.9382			0.621770			0.310885	+	0.950447i	$0.399375\pi$
$434$	9.77742			0.469331
$435$	0.464683	+	0.793949i	0.0222799	+	0.0380669i
$436$	16.3004			0.780648
$437$	2.88835			0.138168
$438$	17.9986	−	10.5343i	0.860007	−	0.503346i
$439$		−	35.0696i		−	1.67378i	−0.547372	−	0.836890i	$-0.684372\pi$
$439$		−	35.0696i		−	1.67378i	0.547372	−	0.836890i	$-0.315628\pi$
$440$	0.613365			0.0292410
$441$	−2.79071	+	4.96877i	−0.132891	+	0.236608i
$442$	−6.47971			−0.308208
$443$		−	3.92303i		−	0.186389i	−0.995648	−	0.0931945i	$-0.970292\pi$
$443$		−	3.92303i		−	0.186389i	0.995648	−	0.0931945i	$-0.0297078\pi$
$444$	1.19396	−	0.698801i	0.0566627	−	0.0331636i
$445$		−	1.04046i		−	0.0493224i
$446$		−	13.1705i		−	0.623640i
$447$	16.4169	−	9.60850i	0.776493	−	0.454467i
$448$			0.137731i			0.00650716i
$449$	−37.6765			−1.77806			−0.889031	−	0.457847i	$-0.848621\pi$
$449$	−37.6765			−1.77806			−0.889031	+	0.457847i	$0.848621\pi$
$450$	−12.9312	+	23.0236i	−0.609582	+	1.08534i
$451$		−	31.1286i		−	1.46579i
$452$			21.2271i			0.998441i
$453$	13.3320	−	7.80298i	0.626393	−	0.366616i
$454$			36.0557i			1.69218i
$455$	0.190463			0.00892905
$456$	13.3840	−	7.83340i	0.626763	−	0.366833i
$457$		−	8.28329i		−	0.387476i	−0.981053	−	0.193738i	$-0.937939\pi$
$457$		−	8.28329i		−	0.387476i	0.981053	−	0.193738i	$-0.0620612\pi$
$458$		−	32.9970i		−	1.54185i
$459$	0.362877	+	20.4035i	0.0169377	+	0.952354i
$460$			0.0383319i			0.00178724i
$461$	−13.4523			−0.626535			−0.313268	−	0.949665i	$-0.601424\pi$
$461$	−13.4523			−0.626535			−0.313268	+	0.949665i	$0.601424\pi$
$462$	−44.8164	+	26.2302i	−2.08505	+	1.22034i
$463$			38.5939i			1.79361i	0.442428	+	0.896804i	$0.354117\pi$
$463$			38.5939i			1.79361i	−0.442428	+	0.896804i	$0.645883\pi$
$464$	−38.8622			−1.80413
$465$	−0.189581	+	0.110958i	−0.00879161	+	0.00514556i
$466$	11.8135			0.547248
$467$			10.5338i			0.487445i	0.969845	+	0.243722i	$0.0783686\pi$
$467$			10.5338i			0.487445i	−0.969845	+	0.243722i	$0.921631\pi$
$468$	−1.51988	+	2.70609i	−0.0702564	+	0.125089i
$469$	2.32218			0.107228
$470$	−1.45811			−0.0672574
$471$	−0.534849	−	0.913832i	−0.0246445	−	0.0421071i
$472$		−	0.883579i		−	0.0406700i
$473$			34.6371i			1.59261i
$474$	−36.6178	+	21.4317i	−1.68191	+	0.984390i
$475$	28.3567			1.30110
$476$		−	12.9448i		−	0.593323i
$477$	−17.3142	−	9.72452i	−0.792763	−	0.445255i
$478$	33.8858			1.54990
$479$	14.5323			0.663998			0.331999	−	0.943280i	$-0.392277\pi$
$479$	14.5323			0.663998			0.331999	+	0.943280i	$0.392277\pi$
$480$	0.336240	+	0.574494i	0.0153472	+	0.0262219i
$481$	−0.676889			−0.0308635
$482$	−2.86054			−0.130294
$483$	1.32802	+	2.26902i	0.0604268	+	0.103244i
$484$	−23.7868			−1.08122
$485$	0.661606			0.0300420
$486$	24.1845	+	13.0230i	1.09703	+	0.590735i
$487$	−13.3894			−0.606734			−0.303367	−	0.952874i	$-0.598111\pi$
$487$	−13.3894			−0.606734			−0.303367	+	0.952874i	$0.598111\pi$
$488$		−	12.2641i		−	0.555169i
$489$	−22.2787	+	13.0393i	−1.00748	+	0.589658i
$490$			0.228229i			0.0103104i
$491$		−	29.1187i		−	1.31411i	−0.753842	−	0.657055i	$-0.771802\pi$
$491$		−	29.1187i		−	1.31411i	0.753842	−	0.657055i	$-0.228198\pi$
$492$	9.01443	−	5.27598i	0.406402	−	0.237859i
$493$	−30.5918			−1.37779
$494$	9.36601			0.421397
$495$	0.571304	−	1.01719i	0.0256782	−	0.0457193i
$496$		−	9.27960i		−	0.416666i
$497$	−22.8308			−1.02410
$498$	5.20538	+	8.89381i	0.233259	+	0.398541i
$499$			16.4853i			0.737983i	0.929433	+	0.368992i	$0.120297\pi$
$499$			16.4853i			0.737983i	−0.929433	+	0.368992i	$0.879703\pi$
$500$			0.753009i			0.0336756i
$501$	−21.5837	+	12.6326i	−0.964290	+	0.564381i
$502$	−28.2353			−1.26020
$503$		−	16.5629i		−	0.738503i	−0.929329	−	0.369252i	$-0.879614\pi$
$503$		−	16.5629i		−	0.738503i	0.929329	−	0.369252i	$-0.120386\pi$
$504$	12.3075	+	6.91251i	0.548220	+	0.307908i
$505$	0.00705796			0.000314075
$506$			5.11346i			0.227321i
$507$	−18.1223	+	10.6066i	−0.804840	+	0.471057i
$508$			15.4025i			0.683375i
$509$			12.5881i			0.557956i	0.960297	+	0.278978i	$0.0899957\pi$
$509$			12.5881i			0.557956i	−0.960297	+	0.278978i	$0.910004\pi$
$510$	0.412817	+	0.705332i	0.0182799	+	0.0312326i
$511$		−	20.3848i		−	0.901772i
$512$	−12.3825			−0.547234
$513$	−0.524516	−	29.4920i	−0.0231579	−	1.30210i
$514$		−	3.46112i		−	0.152663i
$515$			0.0202193i			0.000890969i
$516$	−10.0304	+	5.87063i	−0.441566	+	0.258440i
$517$	−69.2174			−3.04418
$518$		−	3.80001i		−	0.166963i
$519$	3.10269	+	5.30119i	0.136193	+	0.232696i
$520$		−	0.100699i		−	0.00441595i
$521$			2.84884i			0.124810i	0.998051	+	0.0624050i	$0.0198770\pi$
$521$			2.84884i			0.124810i	−0.998051	+	0.0624050i	$0.980123\pi$
$522$	−20.1644	+	35.9022i	−0.882574	+	1.57139i
$523$	1.45188			0.0634864			0.0317432	−	0.999496i	$-0.489894\pi$
$523$	1.45188			0.0634864			0.0317432	+	0.999496i	$0.489894\pi$
$524$	−7.71200			−0.336900
$525$	13.0380	+	22.2765i	0.569025	+	0.972225i
$526$			15.6279i			0.681411i
$527$		−	7.30478i		−	0.318201i
$528$	24.8947	+	42.5345i	1.08340	+	1.85108i
$529$	−22.7411			−0.988744
$530$	−0.795290			−0.0345452
$531$	−1.46531	−	0.822990i	−0.0635889	−	0.0357147i
$532$			18.7109i			0.811219i
$533$	−5.11054			−0.221362
$534$	40.1937	−	23.5246i	1.73935	−	1.01801i
$535$	−1.09955			−0.0475377
$536$		−	1.22775i		−	0.0530308i
$537$	−1.61205	−	2.75432i	−0.0695653	−	0.118858i
$538$		−	42.4691i		−	1.83097i
$539$			10.8342i			0.466663i
$540$	0.391395	−	0.00696098i	0.0168430	−	0.000299553i
$541$	0.503223			0.0216352			0.0108176	−	0.999941i	$-0.496557\pi$
$541$	0.503223			0.0216352			0.0108176	+	0.999941i	$0.496557\pi$
$542$		−	20.9523i		−	0.899977i
$543$	15.0703	+	25.7488i	0.646728	+	1.10499i
$544$	−22.1359			−0.949070
$545$			1.00592i			0.0430890i
$546$	4.30634	+	7.35774i	0.184295	+	0.314882i
$547$	−31.7990			−1.35963			−0.679814	−	0.733384i	$-0.737940\pi$
$547$	−31.7990			−1.35963			−0.679814	+	0.733384i	$0.737940\pi$
$548$			13.7683i			0.588153i
$549$	−20.3385	−	11.4231i	−0.868025	−	0.487526i
$550$			50.2022i			2.14063i
$551$	44.2185			1.88377
$552$	1.19965	−	0.702132i	0.0510604	−	0.0298847i
$553$			41.4724i			1.76359i
$554$	16.9973			0.722146
$555$	0.0431241	+	0.0736809i	0.00183051	+	0.00312758i
$556$	15.0730			0.639238
$557$	−3.94970			−0.167354			−0.0836770	−	0.996493i	$-0.526666\pi$
$557$	−3.94970			−0.167354			−0.0836770	+	0.996493i	$0.526666\pi$
$558$	−8.57280	−	4.81491i	−0.362915	−	0.203831i
$559$	5.68655			0.240515
$560$	1.01481			0.0428834
$561$	19.5968	+	33.4827i	0.827376	+	1.41364i
$562$		−	28.8598i		−	1.21738i
$563$	19.6862			0.829677			0.414838	−	0.909895i	$-0.363838\pi$
$563$	19.6862			0.829677			0.414838	+	0.909895i	$0.363838\pi$
$564$	−11.7317	−	20.0445i	−0.493992	−	0.844024i
$565$	−1.30996			−0.0551104
$566$			13.7647i			0.578573i
$567$	22.9271	−	13.9720i	0.962848	−	0.586769i
$568$			12.0708i			0.506479i
$569$	26.4959			1.11077			0.555384	−	0.831594i	$-0.312571\pi$
$569$	26.4959			1.11077			0.555384	+	0.831594i	$0.312571\pi$
$570$	−0.596701	−	1.01951i	−0.0249931	−	0.0427027i
$571$		−	32.8206i		−	1.37350i	−0.726895	−	0.686749i	$-0.759037\pi$
$571$		−	32.8206i		−	1.37350i	0.726895	−	0.686749i	$-0.240963\pi$
$572$			5.90055i			0.246714i
$573$	−21.6614	+	12.6780i	−0.904920	+	0.529632i
$574$		−	28.6902i		−	1.19751i
$575$	2.54170			0.105996
$576$	0.0678258	−	0.120762i	0.00282607	−	0.00503174i
$577$		−	21.4580i		−	0.893309i	−0.894707	−	0.446655i	$-0.852615\pi$
$577$		−	21.4580i		−	0.893309i	0.894707	−	0.446655i	$-0.147385\pi$
$578$	2.77791			0.115546
$579$	−13.2113	+	7.73232i	−0.549042	+	0.321344i
$580$			0.586835i			0.0243670i
$581$	10.0729			0.417895
$582$	14.9588	+	25.5583i	0.620063	+	1.05943i
$583$	−37.7531			−1.56357
$584$	−10.7776			−0.445981
$585$	−0.166997	−	0.0937940i	−0.00690449	−	0.00387790i
$586$		−	53.6095i		−	2.21459i
$587$	−8.64366			−0.356762			−0.178381	−	0.983962i	$-0.557086\pi$
$587$	−8.64366			−0.356762			−0.178381	+	0.983962i	$0.557086\pi$
$588$	−3.13745	+	1.83629i	−0.129386	+	0.0757274i
$589$			10.5586i			0.435059i
$590$	−0.0673057			−0.00277093
$591$	−15.3433	+	8.98015i	−0.631139	+	0.369394i
$592$	−3.60653			−0.148227
$593$			17.1338i			0.703603i	0.936075	+	0.351801i	$0.114431\pi$
$593$			17.1338i			0.703603i	−0.936075	+	0.351801i	$0.885569\pi$
$594$	52.2119	−	0.928592i	2.14228	−	0.0381006i
$595$	0.798843			0.0327494
$596$	12.1343			0.497040
$597$	16.9896	−	9.94372i	0.695340	−	0.406969i
$598$	0.839504			0.0343299
$599$	28.1840			1.15157			0.575783	−	0.817602i	$-0.304697\pi$
$599$	28.1840			1.15157			0.575783	+	0.817602i	$0.304697\pi$
$600$	11.7777	−	6.89328i	0.480824	−	0.281417i
$601$	41.2918			1.68433			0.842164	−	0.539222i	$-0.181281\pi$
$601$	41.2918			1.68433			0.842164	+	0.539222i	$0.181281\pi$
$602$			31.9239i			1.30112i
$603$	−2.03608	−	1.14356i	−0.0829154	−	0.0465694i
$604$	9.85415			0.400960
$605$		−	1.46792i		−	0.0596795i
$606$	0.159580	+	0.272654i	0.00648247	+	0.0110758i
$607$	34.9103			1.41696			0.708482	−	0.705729i	$-0.249380\pi$
$607$	34.9103			1.41696			0.708482	+	0.705729i	$0.249380\pi$
$608$	31.9961			1.29761
$609$	20.3310	+	34.7371i	0.823853	+	1.40762i
$610$	−0.934204			−0.0378248
$611$			11.3638i			0.459730i
$612$	−6.37469	+	11.3499i	−0.257681	+	0.458794i
$613$		−	42.5189i		−	1.71732i	−0.512542	−	0.858662i	$-0.671296\pi$
$613$		−	42.5189i		−	1.71732i	0.512542	−	0.858662i	$-0.328704\pi$
$614$	−44.8752			−1.81101
$615$	0.325589	+	0.556294i	0.0131290	+	0.0224320i
$616$	26.8361			1.08126
$617$	−20.4344			−0.822658			−0.411329	−	0.911487i	$-0.634935\pi$
$617$	−20.4344			−0.822658			−0.411329	+	0.911487i	$0.634935\pi$
$618$	−0.781088	+	0.457156i	−0.0314200	+	0.0183895i
$619$		−	40.7303i		−	1.63709i	−0.574444	−	0.818544i	$-0.694782\pi$
$619$		−	40.7303i		−	1.63709i	0.574444	−	0.818544i	$-0.305218\pi$
$620$	−0.140126			−0.00562758
$621$	−0.0470140	−	2.64345i	−0.00188661	−	0.106078i
$622$			41.3869i			1.65946i
$623$		−	45.5224i		−	1.82382i
$624$	6.98312	−	4.08709i	0.279548	−	0.163614i
$625$	24.9303			0.997211
$626$			5.92628i			0.236862i
$627$	−28.3259	−	48.3970i	−1.13123	−	1.93279i
$628$		−	0.675444i		−	0.0269532i
$629$	−2.83901			−0.113199
$630$	0.526553	−	0.937512i	0.0209784	−	0.0373514i
$631$	−18.8382			−0.749937			−0.374969	−	0.927037i	$-0.622347\pi$
$631$	−18.8382			−0.749937			−0.374969	+	0.927037i	$0.622347\pi$
$632$	21.9268			0.872200
$633$	−15.2471	−	20.0131i	−0.606018	−	0.795451i
$634$	−34.2321			−1.35953
$635$	−0.950512			−0.0377199
$636$	−6.39876	−	10.9328i	−0.253727	−	0.433513i
$637$	1.77871			0.0704751
$638$			78.2835i			3.09927i
$639$	20.0179	+	11.2431i	0.791896	+	0.444768i
$640$		−	0.774183i		−	0.0306023i
$641$	−27.6670			−1.09278			−0.546391	−	0.837530i	$-0.683999\pi$
$641$	−27.6670			−1.09278			−0.546391	+	0.837530i	$0.683999\pi$
$642$	−24.8607	−	42.4765i	−0.981173	−	1.67641i
$643$		−	20.6133i		−	0.812908i	−0.913671	−	0.406454i	$-0.866765\pi$
$643$		−	20.6133i		−	0.812908i	0.913671	−	0.406454i	$-0.133235\pi$
$644$			1.67711i			0.0660875i
$645$	−0.362286	−	0.618994i	−0.0142650	−	0.0243729i
$646$	39.2830			1.54557
$647$			11.7848i			0.463307i	0.972798	+	0.231654i	$0.0744136\pi$
$647$			11.7848i			0.463307i	−0.972798	+	0.231654i	$0.925586\pi$
$648$	−7.38709	−	12.1217i	−0.290192	−	0.476186i
$649$	−3.19506			−0.125417
$650$	8.24195			0.323276
$651$	−8.29461	+	4.85468i	−0.325091	+	0.190270i
$652$	−16.4670			−0.644896
$653$			32.5651i			1.27437i	0.770711	+	0.637185i	$0.219901\pi$
$653$			32.5651i			1.27437i	−0.770711	+	0.637185i	$0.780099\pi$
$654$	−38.8596	+	22.7438i	−1.51953	+	0.889353i
$655$		−	0.475919i		−	0.0185957i
$656$	−27.2295			−1.06313
$657$	−10.0386	+	17.8733i	−0.391641	+	0.697305i
$658$	−63.7955			−2.48701
$659$	32.7080			1.27412			0.637062	−	0.770813i	$-0.280150\pi$
$659$	32.7080			1.27412			0.637062	+	0.770813i	$0.280150\pi$
$660$	0.642289	−	0.375920i	0.0250011	−	0.0146327i
$661$			34.1983i			1.33016i	0.746773	+	0.665080i	$0.231602\pi$
$661$			34.1983i			1.33016i	−0.746773	+	0.665080i	$0.768398\pi$
$662$	37.3155			1.45031
$663$	5.49702	−	3.21730i	0.213487	−	0.124950i
$664$		−	5.32563i		−	0.206674i
$665$	−1.15468			−0.0447764
$666$	−1.87132	+	3.33183i	−0.0725123	+	0.129106i
$667$	3.96344			0.153465
$668$	−15.9533			−0.617251
$669$	6.53940	+	11.1731i	0.252828	+	0.431977i
$670$	−0.0935227			−0.00361310
$671$	−44.3474			−1.71201
$672$	14.7113	+	25.1354i	0.567501	+	0.969621i
$673$			10.9552i			0.422293i	0.977454	+	0.211146i	$0.0677197\pi$
$673$			10.9552i			0.422293i	−0.977454	+	0.211146i	$0.932280\pi$
$674$	−14.2082			−0.547281
$675$	−0.461566	−	25.9525i	−0.0177657	−	0.998912i
$676$	−13.3948			−0.515185
$677$		−	3.93419i		−	0.151203i	−0.997138	−	0.0756017i	$-0.975912\pi$
$677$		−	3.93419i		−	0.151203i	0.997138	−	0.0756017i	$-0.0240877\pi$
$678$	−29.6180	−	50.6048i	−1.13747	−	1.94346i
$679$	28.9468			1.11088
$680$		−	0.422354i		−	0.0161965i
$681$	−17.9024	−	30.5876i	−0.686020	−	1.17212i
$682$	−18.6927			−0.715781
$683$	49.5719			1.89682			0.948409	−	0.317051i	$-0.102693\pi$
$683$	49.5719			1.89682			0.948409	+	0.317051i	$0.102693\pi$
$684$	9.21421	−	16.4056i	0.352314	−	0.627284i
$685$	−0.849663			−0.0324640
$686$		−	26.8109i		−	1.02365i
$687$	16.3837	+	27.9928i	0.625076	+	1.06799i
$688$	30.2985			1.15512
$689$			6.19811i			0.236129i
$690$	−0.0534842	−	0.0913820i	−0.00203611	−	0.00347885i
$691$	42.2515			1.60732			0.803662	−	0.595086i	$-0.202882\pi$
$691$	42.2515			1.60732			0.803662	+	0.595086i	$0.202882\pi$
$692$			3.91829i			0.148951i
$693$	24.9959	−	44.5044i	0.949516	−	1.69058i
$694$		−	59.0088i		−	2.23994i
$695$			0.930179i			0.0352837i
$696$	18.3658	−	10.7491i	0.696153	−	0.407445i
$697$	−21.4347			−0.811896
$698$		−	35.1037i		−	1.32869i
$699$	−10.0219	+	5.86561i	−0.379062	+	0.221858i
$700$			16.4653i			0.622329i
$701$	23.4442			0.885475			0.442738	−	0.896651i	$-0.354007\pi$
$701$	23.4442			0.885475			0.442738	+	0.896651i	$0.354007\pi$
$702$	−0.152452	−	8.57190i	−0.00575392	−	0.323526i
$703$	4.10361			0.154771
$704$		−	0.263317i		−	0.00992413i
$705$	1.23698	−	0.723978i	0.0465872	−	0.0272666i
$706$	−30.2022			−1.13667
$707$	0.308802			0.0116137
$708$	−0.541529	−	0.925247i	−0.0203519	−	0.0347729i
$709$	−12.0034			−0.450796			−0.225398	−	0.974267i	$-0.572368\pi$
$709$	−12.0034			−0.450796			−0.225398	+	0.974267i	$0.572368\pi$
$710$	0.919479			0.0345074
$711$	20.4232	−	36.3629i	0.765930	−	1.36371i
$712$	−24.0680			−0.901988
$713$			0.946399i			0.0354429i
$714$	18.0617	+	30.8599i	0.675943	+	1.15490i
$715$	−0.364132			−0.0136178
$716$		−	2.03581i		−	0.0760820i
$717$	−28.7468	+	16.8250i	−1.07357	+	0.628340i
$718$		−	8.57201i		−	0.319904i
$719$	14.8866			0.555176			0.277588	−	0.960700i	$-0.410465\pi$
$719$	14.8866			0.555176			0.277588	+	0.960700i	$0.410465\pi$
$720$	−0.889778	−	0.499744i	−0.0331601	−	0.0186243i
$721$			0.884642i			0.0329458i
$722$	−23.3018			−0.867202
$723$	2.42672	−	1.42031i	0.0902506	−	0.0528220i
$724$			19.0318i			0.707312i
$725$	38.9117			1.44514
$726$	56.7070	−	33.1895i	2.10459	−	1.23178i
$727$			25.2546i			0.936640i	0.883559	+	0.468320i	$0.155141\pi$
$727$			25.2546i			0.936640i	−0.883559	+	0.468320i	$0.844859\pi$
$728$		−	4.40583i		−	0.163291i
$729$	−26.9829	+	0.960089i	−0.999368	+	0.0355588i
$730$			0.820973i			0.0303856i
$731$	23.8506			0.882146
$732$	−7.51643	−	12.8424i	−0.277815	−	0.474670i
$733$	37.8454			1.39785			0.698926	−	0.715194i	$-0.253662\pi$
$733$	37.8454			1.39785			0.698926	+	0.715194i	$0.253662\pi$
$734$			55.3480i			2.04293i
$735$	−0.113320	−	0.193617i	−0.00417989	−	0.00714167i
$736$	2.86791			0.105712
$737$	−4.43960			−0.163535
$738$	−14.1286	+	25.1555i	−0.520080	+	0.925986i
$739$		−	28.9390i		−	1.06454i	−0.846575	−	0.532270i	$-0.821339\pi$
$739$		−	28.9390i		−	1.06454i	0.846575	−	0.532270i	$-0.178661\pi$
$740$			0.0544601i			0.00200199i
$741$	−7.94559	+	4.65040i	−0.291889	+	0.170837i
$742$	−34.7958			−1.27739
$743$	25.4303			0.932946			0.466473	−	0.884535i	$-0.345525\pi$
$743$	25.4303			0.932946			0.466473	+	0.884535i	$0.345525\pi$
$744$	2.56670	+	4.38542i	0.0940999	+	0.160777i
$745$			0.748826i			0.0274348i
$746$		−	28.1968i		−	1.03236i
$747$	−8.83190	−	4.96043i	−0.323142	−	0.181493i
$748$			24.7482i			0.904883i
$749$	−48.1079			−1.75783
$750$	−1.05067	−	1.79515i	−0.0383649	−	0.0655495i
$751$			16.9394i			0.618128i	0.951041	+	0.309064i	$0.100016\pi$
$751$			16.9394i			0.618128i	−0.951041	+	0.309064i	$0.899984\pi$
$752$			60.5474i			2.20794i
$753$	23.9532	−	14.0194i	0.872904	−	0.510894i
$754$	12.8522			0.468050
$755$			0.608115i			0.0221316i
$756$	17.1244	−	0.304559i	0.622810	−	0.0110767i
$757$		−	22.4882i		−	0.817348i	−0.912680	−	0.408674i	$-0.865991\pi$
$757$		−	22.4882i		−	0.817348i	0.912680	−	0.408674i	$-0.134009\pi$
$758$		−	33.8957i		−	1.23115i
$759$	−2.53894	−	4.33798i	−0.0921575	−	0.157459i
$760$			0.610486i			0.0221446i
$761$	−19.7349			−0.715391			−0.357696	−	0.933838i	$-0.616437\pi$
$761$	−19.7349			−0.715391			−0.357696	+	0.933838i	$0.616437\pi$
$762$	−21.4909	−	36.7190i	−0.778535	−	1.33019i
$763$			44.0115i			1.59332i
$764$	−16.0107			−0.579247
$765$	−0.700422	−	0.393392i	−0.0253238	−	0.0142231i
$766$			20.4891i			0.740303i
$767$			0.524549i			0.0189404i
$768$	29.7692	−	17.4234i	1.07421	−	0.628712i
$769$	−13.6716			−0.493010			−0.246505	−	0.969142i	$-0.579282\pi$
$769$	−13.6716			−0.493010			−0.246505	+	0.969142i	$0.579282\pi$
$770$		−	2.04421i		−	0.0736684i
$771$	1.71851	+	2.93622i	0.0618907	+	0.105745i
$772$	−9.76491			−0.351447
$773$	−17.5135			−0.629915			−0.314958	−	0.949106i	$-0.601990\pi$
$773$	−17.5135			−0.629915			−0.314958	+	0.949106i	$0.601990\pi$
$774$	15.7210	−	27.9907i	0.565079	−	1.00611i
$775$			9.29141i			0.333757i
$776$		−	15.3044i		−	0.549395i
$777$	1.88678	+	3.22371i	0.0676878	+	0.115650i
$778$			22.0686i			0.791196i
$779$	30.9825			1.11006
$780$	−0.0617167	−	0.105448i	−0.00220981	−	0.00377564i
$781$	43.6484			1.56186
$782$	3.52106			0.125913
$783$	−0.719750	−	40.4694i	−0.0257218	−	1.44626i
$784$	9.47715			0.338470
$785$	0.0416827			0.00148772
$786$	18.3851	−	10.7605i	0.655776	−	0.383813i
$787$	4.27238			0.152294			0.0761469	−	0.997097i	$-0.475738\pi$
$787$	4.27238			0.152294			0.0761469	+	0.997097i	$0.475738\pi$
$788$	−11.3408			−0.403998
$789$	−7.75958	−	13.2579i	−0.276248	−	0.471992i
$790$		−	1.67025i		−	0.0594248i
$791$	−57.3138			−2.03784
$792$	−23.5298	−	13.2155i	−0.836095	−	0.469593i
$793$			7.28074i			0.258547i
$794$			37.4363i			1.32856i
$795$	0.674680	−	0.394877i	0.0239284	−	0.0140049i
$796$	12.5576			0.445093
$797$	−8.78524			−0.311189			−0.155595	−	0.987821i	$-0.549729\pi$
$797$	−8.78524			−0.311189			−0.155595	+	0.987821i	$0.549729\pi$
$798$	−26.1071	−	44.6060i	−0.924180	−	1.57904i
$799$			47.6621i			1.68616i
$800$	28.1561			0.995468
$801$	−22.4176	+	39.9139i	−0.792088	+	1.41029i
$802$	67.0012			2.36589
$803$			38.9722i			1.37530i
$804$	−0.752466	−	1.28565i	−0.0265374	−	0.0453413i
$805$	−0.103497			−0.00364780
$806$			3.06888i			0.108097i
$807$	21.0867	+	36.0284i	0.742288	+	1.26826i
$808$		−	0.163266i		−	0.00574368i
$809$		−	29.3247i		−	1.03100i	−0.856889	−	0.515501i	$-0.827606\pi$
$809$		−	29.3247i		−	1.03100i	0.856889	−	0.515501i	$-0.172394\pi$
$810$	−0.923359	+	0.562704i	−0.0324435	+	0.0197714i
$811$	−32.6502			−1.14650			−0.573252	−	0.819379i	$-0.694318\pi$
$811$	−32.6502			−1.14650			−0.573252	+	0.819379i	$0.694318\pi$
$812$			25.6754i			0.901030i
$813$	10.4032	+	17.7747i	0.364857	+	0.623387i
$814$			7.26495i			0.254636i
$815$		−	1.01620i		−	0.0355960i
$816$	29.2887	−	17.1421i	1.02531	−	0.600094i
$817$	−34.4745			−1.20611
$818$		−	61.8115i		−	2.16119i
$819$	−7.30652	−	4.10371i	−0.255310	−	0.143395i
$820$			0.411176i			0.0143589i
$821$			16.8235i			0.587143i	0.955937	+	0.293572i	$0.0948439\pi$
$821$			16.8235i			0.587143i	−0.955937	+	0.293572i	$0.905156\pi$
$822$	−19.2108	−	32.8231i	−0.670053	−	1.14484i
$823$			27.1486i			0.946340i	0.880971	+	0.473170i	$0.156890\pi$
$823$			27.1486i			0.946340i	−0.880971	+	0.473170i	$0.843110\pi$
$824$	0.467717			0.0162937
$825$	−24.9264	−	42.5887i	−0.867825	−	1.48275i
$826$	−2.94478			−0.102462
$827$			22.1425i			0.769969i	0.922923	+	0.384985i	$0.125793\pi$
$827$			22.1425i			0.769969i	−0.922923	+	0.384985i	$0.874207\pi$
$828$	0.825898	−	1.47049i	0.0287019	−	0.0511029i
$829$	−13.0220			−0.452274			−0.226137	−	0.974096i	$-0.572610\pi$
$829$	−13.0220			−0.452274			−0.226137	+	0.974096i	$0.572610\pi$
$830$	−0.405674			−0.0140812
$831$	−14.4195	+	8.43949i	−0.500208	+	0.292763i
$832$	−0.0432301			−0.00149873
$833$	7.46029			0.258484
$834$	−35.9335	+	21.0312i	−1.24428	+	0.728251i
$835$		−	0.984501i		−	0.0340701i
$836$		−	35.7719i		−	1.23720i
$837$	9.66338	−	0.171864i	0.334015	−	0.00594047i
$838$			6.24307i			0.215663i
$839$	−2.29822			−0.0793434			−0.0396717	−	0.999213i	$-0.512631\pi$
$839$	−2.29822			−0.0793434			−0.0396717	+	0.999213i	$0.512631\pi$
$840$	−0.479585	+	0.280692i	−0.0165472	+	0.00968479i
$841$	31.6775			1.09233
$842$		−	32.2165i		−	1.11026i
$843$	14.3294	+	24.4830i	0.493532	+	0.843239i
$844$	−1.94550	−	15.9311i	−0.0669670	−	0.548370i
$845$		−	0.826614i		−	0.0284364i
$846$	55.9357	+	31.4163i	1.92311	+	1.08011i
$847$		−	64.2250i		−	2.20680i
$848$			33.0242i			1.13405i
$849$	−6.83443	−	11.6772i	−0.234557	−	0.400760i
$850$	34.5685			1.18569
$851$	0.367820			0.0126087
$852$	7.39796	+	12.6400i	0.253450	+	0.433040i
$853$	−31.9185			−1.09287			−0.546434	−	0.837502i	$-0.684015\pi$
$853$	−31.9185			−1.09287			−0.546434	+	0.837502i	$0.684015\pi$
$854$	−40.8736			−1.39867
$855$	1.01242	+	0.568623i	0.0346239	+	0.0194465i
$856$			25.4350i			0.869351i
$857$		−	31.6016i		−	1.07949i	−0.841829	−	0.539745i	$-0.818521\pi$
$857$		−	31.6016i		−	1.07949i	0.841829	−	0.539745i	$-0.181479\pi$
$858$	−8.23298	−	14.0667i	−0.281069	−	0.480229i
$859$			3.13059i			0.106814i	0.998573	+	0.0534071i	$0.0170081\pi$
$859$			3.13059i			0.106814i	−0.998573	+	0.0534071i	$0.982992\pi$
$860$		−	0.457520i		−	0.0156013i
$861$	14.2453	+	24.3392i	0.485477	+	0.829477i
$862$			58.2466i			1.98389i
$863$			31.2516i			1.06382i	0.846802	+	0.531908i	$0.178525\pi$
$863$			31.2516i			1.06382i	−0.846802	+	0.531908i	$0.821475\pi$
$864$	−0.520804	−	29.2833i	−0.0177181	−	0.996237i
$865$	−0.241804			−0.00822157
$866$	−22.7980			−0.774708
$867$	−2.35662	+	1.37929i	−0.0800350	+	0.0468430i
$868$	−6.13083			−0.208094
$869$		−	79.2881i		−	2.68966i
$870$	−0.818804	−	1.39899i	−0.0277601	−	0.0474303i
$871$			0.728871i			0.0246969i
$872$	23.2692			0.787995
$873$	−25.3804	−	14.2549i	−0.858997	−	0.482456i
$874$	−5.08946			−0.172154
$875$	−2.03314			−0.0687328
$876$	−11.2858	+	6.60539i	−0.381314	+	0.223176i
$877$		−	4.12539i		−	0.139305i	−0.997571	−	0.0696523i	$-0.977811\pi$
$877$		−	4.12539i		−	0.139305i	0.997571	−	0.0696523i	$-0.0221890\pi$
$878$			61.7950i			2.08548i
$879$	26.6182	+	45.4793i	0.897808	+	1.53398i
$880$	−1.94013			−0.0654018
$881$			41.9475i			1.41325i	0.707589	+	0.706624i	$0.249783\pi$
$881$			41.9475i			1.41325i	−0.707589	+	0.706624i	$0.750217\pi$
$882$	4.91742	−	8.75531i	0.165578	−	0.294807i
$883$		−	7.64257i		−	0.257193i	−0.991697	−	0.128597i	$-0.958953\pi$
$883$		−	7.64257i		−	0.257193i	0.991697	−	0.128597i	$-0.0410472\pi$
$884$	4.06303			0.136655
$885$	0.0570984	−	0.0334186i	0.00191934	−	0.00112335i
$886$			6.91266i			0.232235i
$887$		−	9.47872i		−	0.318264i	−0.987257	−	0.159132i	$-0.949130\pi$
$887$		−	9.47872i		−	0.318264i	0.987257	−	0.159132i	$-0.0508696\pi$
$888$	1.70440	−	0.997553i	0.0571959	−	0.0334757i
$889$	−41.5871			−1.39479
$890$			1.83336i			0.0614543i
$891$	−43.8326	+	26.7120i	−1.46845	+	0.894886i
$892$			8.25841i			0.276512i
$893$		−	68.8926i		−	2.30540i
$894$	−28.9277	+	16.9308i	−0.967487	+	0.566252i
$895$	0.125633			0.00419946
$896$		−	33.8723i		−	1.13159i
$897$	−0.712188	+	0.416830i	−0.0237793	+	0.0139176i
$898$	66.3885			2.21541
$899$			14.4887i			0.483225i
$900$	8.10837	−	14.4367i	0.270279	−	0.481223i
$901$			25.9962i			0.866059i
$902$			54.8507i			1.82633i
$903$	−15.8508	−	27.0824i	−0.527483	−	0.901247i
$904$			30.3022i			1.00784i
$905$	−1.17448			−0.0390411
$906$	−23.4919	+	13.7494i	−0.780467	+	0.456793i
$907$		−	12.2634i		−	0.407201i	−0.979054	−	0.203600i	$-0.934736\pi$
$907$		−	12.2634i		−	0.407201i	0.979054	−	0.203600i	$-0.0652644\pi$
$908$		−	22.6083i		−	0.750284i
$909$	−0.270757	−	0.152070i	−0.00898043	−	0.00504386i
$910$	−0.335609			−0.0111253
$911$	5.62288			0.186294			0.0931472	−	0.995652i	$-0.470307\pi$
$911$	5.62288			0.186294			0.0931472	+	0.995652i	$0.470307\pi$
$912$	−42.3349	+	24.7778i	−1.40185	+	0.820476i
$913$	−19.2577			−0.637336
$914$			14.5957i			0.482784i
$915$	0.792526	−	0.463850i	0.0262001	−	0.0153344i
$916$			20.6904i			0.683631i
$917$		−	20.8226i		−	0.687622i
$918$	−0.639414	−	35.9524i	−0.0211038	−	1.18661i
$919$		−	40.1151i		−	1.32327i	−0.749824	−	0.661637i	$-0.769862\pi$
$919$		−	40.1151i		−	1.32327i	0.749824	−	0.661637i	$-0.230138\pi$
$920$			0.0547197i			0.00180405i
$921$	38.0696	−	22.2814i	1.25443	−	0.734197i
$922$	23.7039			0.780645
$923$		−	7.16598i		−	0.235871i
$924$	28.1016	−	16.4474i	0.924476	−	0.541079i
$925$	3.61112			0.118733
$926$		−	68.0050i		−	2.23478i
$927$	0.435644	−	0.775651i	0.0143084	−	0.0254757i
$928$	43.9056			1.44127
$929$	−16.2731			−0.533904			−0.266952	−	0.963710i	$-0.586017\pi$
$929$	−16.2731			−0.533904			−0.266952	+	0.963710i	$0.586017\pi$
$930$	0.334055	−	0.195516i	0.0109541	−	0.00641122i
$931$	−10.7834			−0.353411
$932$	−7.40751			−0.242641
$933$	−20.5494	−	35.1103i	−0.672757	−	1.14946i
$934$		−	18.5612i		−	0.607342i
$935$	−1.52725			−0.0499463
$936$	−2.16966	+	3.86301i	−0.0709175	+	0.126266i
$937$	40.2527			1.31500			0.657500	−	0.753455i	$-0.271614\pi$
$937$	40.2527			1.31500			0.657500	+	0.753455i	$0.271614\pi$
$938$	−4.09184			−0.133603
$939$	−2.94252	−	5.02752i	−0.0960254	−	0.164067i
$940$	0.914290			0.0298209
$941$	−22.6063			−0.736943			−0.368472	−	0.929639i	$-0.620119\pi$
$941$	−22.6063			−0.736943			−0.368472	+	0.929639i	$0.620119\pi$
$942$	0.942440	+	1.61023i	0.0307064	+	0.0524643i
$943$	2.77705			0.0904333
$944$			2.79485i			0.0909646i
$945$	0.0187948	+	1.05678i	0.000611395	+	0.0343769i
$946$		−	61.0329i		−	1.98435i
$947$		−	4.84359i		−	0.157396i	−0.996899	−	0.0786978i	$-0.974924\pi$
$947$		−	4.84359i		−	0.157396i	0.996899	−	0.0786978i	$-0.0250762\pi$
$948$	22.9608	−	13.4385i	0.745732	−	0.436463i
$949$	6.39827			0.207697
$950$	−49.9665			−1.62113
$951$	29.0406	−	16.9969i	0.941707	−	0.551163i
$952$		−	18.4790i		−	0.598907i
$953$			10.7085i			0.346882i	0.984844	+	0.173441i	$0.0554886\pi$
$953$			10.7085i			0.346882i	−0.984844	+	0.173441i	$0.944511\pi$
$954$	30.5088	+	17.1353i	0.987760	+	0.554775i
$955$		−	0.988045i		−	0.0319724i
$956$	−21.2478			−0.687202
$957$	−38.8693	−	66.4113i	−1.25647	−	2.14677i
$958$	−25.6069			−0.827322
$959$	−37.1748			−1.20044
$960$	0.00275416	+	0.00470570i	8.88900e−5	+	0.000151876i
$961$	27.5404			0.888399
$962$	1.19272			0.0384550
$963$	42.1808	+	23.6909i	1.35926	+	0.763427i
$964$	1.79367			0.0577702
$965$		−	0.602608i		−	0.0193986i
$966$	−2.34006	−	3.99818i	−0.0752901	−	0.128639i
$967$	−34.0553			−1.09514			−0.547572	−	0.836758i	$-0.684448\pi$
$967$	−34.0553			−1.09514			−0.547572	+	0.836758i	$0.684448\pi$
$968$	−33.9562			−1.09139
$969$	−33.3255	+	19.5048i	−1.07057	+	0.626584i
$970$	−1.16579			−0.0374314
$971$	19.4784			0.625092			0.312546	−	0.949903i	$-0.398818\pi$
$971$	19.4784			0.625092			0.312546	+	0.949903i	$0.398818\pi$
$972$	−15.1646	−	8.16594i	−0.486406	−	0.261923i
$973$			40.6975i			1.30470i
$974$	23.5931			0.755972
$975$	−6.99201	+	4.09229i	−0.223923	+	0.131058i
$976$			38.7925i			1.24172i
$977$	−18.8313			−0.602466			−0.301233	−	0.953551i	$-0.597398\pi$
$977$	−18.8313			−0.602466			−0.301233	+	0.953551i	$0.597398\pi$
$978$	39.2567	−	22.9762i	1.25529	−	0.734697i
$979$			87.0309i			2.78152i
$980$		−	0.143109i		−	0.00457145i
$981$	21.6736	−	38.5891i	0.691984	−	1.23206i
$982$			51.3092i			1.63734i
$983$			39.3262i			1.25431i	0.778893	+	0.627156i	$0.215781\pi$
$983$			39.3262i			1.25431i	−0.778893	+	0.627156i	$0.784219\pi$
$984$	12.8683	−	7.53157i	0.410226	−	0.240098i
$985$		−	0.699856i		−	0.0222993i
$986$	53.9049			1.71668
$987$	54.1205	−	31.6757i	1.72268	−	1.00825i
$988$	−5.87286			−0.186840
$989$	−3.09006			−0.0982580
$990$	−1.00668	+	1.79236i	−0.0319943	+	0.0569649i
$991$		−	19.3951i		−	0.616104i	−0.951369	−	0.308052i	$-0.900323\pi$
$991$		−	19.3951i		−	0.616104i	0.951369	−	0.308052i	$-0.0996771\pi$
$992$			10.4839i			0.332863i
$993$	−31.6564	+	18.5279i	−1.00458	+	0.587964i
$994$	40.2294			1.27600
$995$			0.774950i			0.0245676i
$996$	−3.26398	−	5.57677i	−0.103423	−	0.176707i
$997$			61.2338i			1.93929i	0.244507	+	0.969647i	$0.421374\pi$
$997$			61.2338i			1.93929i	−0.244507	+	0.969647i	$0.578626\pi$
$998$		−	29.0482i		−	0.919506i
$999$	−0.0667950	−	3.75569i	−0.00211330	−	0.118825i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	633.2.d.a.632.15	✓	68
3.2	odd	2	inner	633.2.d.a.632.53	yes	68
211.210	odd	2	inner	633.2.d.a.632.54	yes	68
633.632	even	2	inner	633.2.d.a.632.16	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
633.2.d.a.632.15	✓	68	1.1	even	1	trivial
633.2.d.a.632.16	yes	68	633.632	even	2	inner
633.2.d.a.632.53	yes	68	3.2	odd	2	inner
633.2.d.a.632.54	yes	68	211.210	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 633 = 3 \cdot 211 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	633.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.76207 q^{2} +(1.49484 - 0.874902i) q^{3} +1.10489 q^{4} +0.0681843i q^{5} +(-2.63401 + 1.54164i) q^{6} +2.98322i q^{7} +1.57725 q^{8} +(1.46909 - 2.61568i) q^{9} +O(q^{10})\)	\(q-1.76207 q^{2} +(1.49484 - 0.874902i) q^{3} +1.10489 q^{4} +0.0681843i q^{5} +(-2.63401 + 1.54164i) q^{6} +2.98322i q^{7} +1.57725 q^{8} +(1.46909 - 2.61568i) q^{9} -0.120145i q^{10} -5.70340i q^{11} +(1.65163 - 0.966668i) q^{12} -0.936356 q^{13} -5.25664i q^{14} +(0.0596545 + 0.101925i) q^{15} -4.98900 q^{16} -3.92728 q^{17} +(-2.58864 + 4.60900i) q^{18} +5.67663 q^{19} +0.0753359i q^{20} +(2.61003 + 4.45944i) q^{21} +10.0498i q^{22} +0.508814 q^{23} +(2.35774 - 1.37994i) q^{24} +4.99535 q^{25} +1.64992 q^{26} +(-0.0923992 - 5.19533i) q^{27} +3.29612i q^{28} +7.78957 q^{29} +(-0.105115 - 0.179598i) q^{30} +1.86001i q^{31} +5.63646 q^{32} +(-4.98991 - 8.52567i) q^{33} +6.92013 q^{34} -0.203409 q^{35} +(1.62318 - 2.89003i) q^{36} +0.722896 q^{37} -10.0026 q^{38} +(-1.39970 + 0.819220i) q^{39} +0.107544i q^{40} +5.45790 q^{41} +(-4.59905 - 7.85784i) q^{42} -6.07306 q^{43} -6.30161i q^{44} +(0.178348 + 0.100169i) q^{45} -0.896565 q^{46} -12.1362i q^{47} +(-7.45776 + 4.36488i) q^{48} -1.89961 q^{49} -8.80215 q^{50} +(-5.87065 + 3.43598i) q^{51} -1.03457 q^{52} -6.61940i q^{53} +(0.162814 + 9.15453i) q^{54} +0.388882 q^{55} +4.70529i q^{56} +(8.48565 - 4.96649i) q^{57} -13.7258 q^{58} -0.560202i q^{59} +(0.0659115 + 0.112615i) q^{60} -7.77561i q^{61} -3.27747i q^{62} +(7.80314 + 4.38263i) q^{63} +0.0461684 q^{64} -0.0638448i q^{65} +(8.79257 + 15.0228i) q^{66} -0.778412i q^{67} -4.33920 q^{68} +(0.760595 - 0.445162i) q^{69} +0.358420 q^{70} +7.65305i q^{71} +(2.31713 - 4.12558i) q^{72} -6.83316 q^{73} -1.27379 q^{74} +(7.46725 - 4.37044i) q^{75} +6.27203 q^{76} +17.0145 q^{77} +(2.46637 - 1.44352i) q^{78} +13.9019 q^{79} -0.340171i q^{80} +(-4.68353 - 7.68535i) q^{81} -9.61720 q^{82} -3.37653i q^{83} +(2.88378 + 4.92718i) q^{84} -0.267779i q^{85} +10.7012 q^{86} +(11.6442 - 6.81511i) q^{87} -8.99569i q^{88} -15.2595 q^{89} +(-0.314262 - 0.176505i) q^{90} -2.79336i q^{91} +0.562182 q^{92} +(1.62733 + 2.78042i) q^{93} +21.3848i q^{94} +0.387057i q^{95} +(8.42560 - 4.93135i) q^{96} -9.70320i q^{97} +3.34724 q^{98} +(-14.9182 - 8.37883i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 64 q^{4} - 14 q^{6} - 4 q^{9}+O(q^{10}) \) 68 * q + 64 * q^4 - 14 * q^6 - 4 * q^9	\( 68 q + 64 q^{4} - 14 q^{6} - 4 q^{9} - 16 q^{13} + 56 q^{16} + 4 q^{19} + 8 q^{21} - 38 q^{24} - 60 q^{25} - 14 q^{30} - 32 q^{34} - 18 q^{36} - 28 q^{37} + 40 q^{43} - 2 q^{45} - 8 q^{46} - 80 q^{49} + 16 q^{51} - 16 q^{52} + 52 q^{54} + 16 q^{55} - 40 q^{58} + 28 q^{64} + 18 q^{66} - 10 q^{69} + 80 q^{70} - 8 q^{76} + 32 q^{78} - 40 q^{79} - 28 q^{81} - 44 q^{82} + 84 q^{84} - 44 q^{87} - 10 q^{93} - 56 q^{96} + 68 q^{99}+O(q^{100}) \) 68 * q + 64 * q^4 - 14 * q^6 - 4 * q^9 - 16 * q^13 + 56 * q^16 + 4 * q^19 + 8 * q^21 - 38 * q^24 - 60 * q^25 - 14 * q^30 - 32 * q^34 - 18 * q^36 - 28 * q^37 + 40 * q^43 - 2 * q^45 - 8 * q^46 - 80 * q^49 + 16 * q^51 - 16 * q^52 + 52 * q^54 + 16 * q^55 - 40 * q^58 + 28 * q^64 + 18 * q^66 - 10 * q^69 + 80 * q^70 - 8 * q^76 + 32 * q^78 - 40 * q^79 - 28 * q^81 - 44 * q^82 + 84 * q^84 - 44 * q^87 - 10 * q^93 - 56 * q^96 + 68 * q^99

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