LMFDB - Embedded newform 1183.2.e.k.170.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1183,2,Mod(170,1183)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1183, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1183.170");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1183 = 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1183.e (of order $3$, degree $2$, 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:	$9.44630255912$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			170.18
Character	$\chi$	$=$	1183.170
Dual form			1183.2.e.k.508.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.771913 - 1.33699i) q^{2} +(0.676597 + 1.17190i) q^{3} +(-0.191698 - 0.332031i) q^{4} +(0.170982 - 0.296150i) q^{5} +2.08910 q^{6} +(-2.12749 + 1.57282i) q^{7} +2.49575 q^{8} +(0.584432 - 1.01227i) q^{9} +O(q^{10})$	\(q+(0.771913 - 1.33699i) q^{2} +(0.676597 + 1.17190i) q^{3} +(-0.191698 - 0.332031i) q^{4} +(0.170982 - 0.296150i) q^{5} +2.08910 q^{6} +(-2.12749 + 1.57282i) q^{7} +2.49575 q^{8} +(0.584432 - 1.01227i) q^{9} +(-0.263967 - 0.457204i) q^{10} +(2.77782 + 4.81133i) q^{11} +(0.259405 - 0.449303i) q^{12} +(0.460616 + 4.05852i) q^{14} +0.462745 q^{15} +(2.30990 - 4.00086i) q^{16} +(-2.52228 - 4.36872i) q^{17} +(-0.902261 - 1.56276i) q^{18} +(-2.08225 + 3.60657i) q^{19} -0.131108 q^{20} +(-3.28265 - 1.42904i) q^{21} +8.57694 q^{22} +(0.621491 - 1.07645i) q^{23} +(1.68862 + 2.92478i) q^{24} +(2.44153 + 4.22885i) q^{25} +5.64128 q^{27} +(0.930063 + 0.404886i) q^{28} +0.715449 q^{29} +(0.357199 - 0.618687i) q^{30} +(4.55881 + 7.89609i) q^{31} +(-1.07033 - 1.85386i) q^{32} +(-3.75893 + 6.51066i) q^{33} -7.78792 q^{34} +(0.102029 + 0.898983i) q^{35} -0.448138 q^{36} +(-0.764519 + 1.32419i) q^{37} +(3.21464 + 5.56792i) q^{38} +(0.426730 - 0.739118i) q^{40} +3.73023 q^{41} +(-4.44454 + 3.28578i) q^{42} -6.37606 q^{43} +(1.06501 - 1.84464i) q^{44} +(-0.199855 - 0.346159i) q^{45} +(-0.959473 - 1.66186i) q^{46} +(0.189540 - 0.328293i) q^{47} +6.25149 q^{48} +(2.05245 - 6.69234i) q^{49} +7.53859 q^{50} +(3.41314 - 5.91173i) q^{51} +(-1.40635 - 2.43586i) q^{53} +(4.35458 - 7.54235i) q^{54} +1.89983 q^{55} +(-5.30970 + 3.92538i) q^{56} -5.63539 q^{57} +(0.552264 - 0.956549i) q^{58} +(-4.28354 - 7.41931i) q^{59} +(-0.0887074 - 0.153646i) q^{60} +(-1.66311 + 2.88060i) q^{61} +14.0760 q^{62} +(0.348742 + 3.07280i) q^{63} +5.93480 q^{64} +(5.80313 + 10.0513i) q^{66} +(3.96675 + 6.87061i) q^{67} +(-0.967033 + 1.67495i) q^{68} +1.68200 q^{69} +(1.28069 + 0.557525i) q^{70} +14.5113 q^{71} +(1.45860 - 2.52637i) q^{72} +(-3.72576 - 6.45321i) q^{73} +(1.18028 + 2.04431i) q^{74} +(-3.30387 + 5.72246i) q^{75} +1.59666 q^{76} +(-13.4772 - 5.86703i) q^{77} +(2.80770 - 4.86307i) q^{79} +(-0.789905 - 1.36816i) q^{80} +(2.06358 + 3.57423i) q^{81} +(2.87941 - 4.98728i) q^{82} -9.99425 q^{83} +(0.154792 + 1.36389i) q^{84} -1.72506 q^{85} +(-4.92176 + 8.52474i) q^{86} +(0.484071 + 0.838435i) q^{87} +(6.93275 + 12.0079i) q^{88} +(8.06158 - 13.9631i) q^{89} -0.617083 q^{90} -0.476555 q^{92} +(-6.16896 + 10.6849i) q^{93} +(-0.292617 - 0.506828i) q^{94} +(0.712058 + 1.23332i) q^{95} +(1.44836 - 2.50864i) q^{96} -12.1202 q^{97} +(-7.36330 - 7.91001i) q^{98} +6.49379 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - q^{2} - 23 q^{4} + 13 q^{5} - 28 q^{6} - 3 q^{7} - 26 q^{9}+O(q^{10}) $ 48 * q - q^2 - 23 * q^4 + 13 * q^5 - 28 * q^6 - 3 * q^7 - 26 * q^9	\( 48 q - q^{2} - 23 q^{4} + 13 q^{5} - 28 q^{6} - 3 q^{7} - 26 q^{9} - 5 q^{10} - q^{11} - 5 q^{12} - 2 q^{14} - 10 q^{15} - 17 q^{16} + 5 q^{17} + 24 q^{19} - 68 q^{20} + q^{21} - 28 q^{22} - 11 q^{23} + 32 q^{24} - 33 q^{25} - 42 q^{27} + 15 q^{28} + 8 q^{29} + 22 q^{30} + 40 q^{31} - 6 q^{32} + 24 q^{33} - 72 q^{34} + 44 q^{35} - 30 q^{36} - 4 q^{37} + 29 q^{38} + 4 q^{40} - 98 q^{41} - 9 q^{42} + 26 q^{43} + 10 q^{44} + 58 q^{45} - 10 q^{46} + 62 q^{47} + 178 q^{48} + 31 q^{49} + 46 q^{50} + 21 q^{51} + 18 q^{53} + 12 q^{54} - 28 q^{55} - 56 q^{56} + 26 q^{57} + 56 q^{58} + 79 q^{59} + 22 q^{60} - 13 q^{61} + 24 q^{62} - 22 q^{63} + 36 q^{64} + 38 q^{66} - 2 q^{67} + 12 q^{68} - 56 q^{69} - 85 q^{70} + 38 q^{71} + 81 q^{72} + 17 q^{73} - 17 q^{74} - 24 q^{75} - 116 q^{76} - 30 q^{77} + 9 q^{79} + 63 q^{80} - 16 q^{81} + 22 q^{82} - 162 q^{83} - 203 q^{84} + 68 q^{85} + 22 q^{86} - 70 q^{87} + 33 q^{88} + 72 q^{89} + 2 q^{90} - 8 q^{92} + 19 q^{93} + 30 q^{94} - 13 q^{95} + 11 q^{96} - 90 q^{97} - 81 q^{98} + 78 q^{99}+O(q^{100}) \) 48 * q - q^2 - 23 * q^4 + 13 * q^5 - 28 * q^6 - 3 * q^7 - 26 * q^9 - 5 * q^10 - q^11 - 5 * q^12 - 2 * q^14 - 10 * q^15 - 17 * q^16 + 5 * q^17 + 24 * q^19 - 68 * q^20 + q^21 - 28 * q^22 - 11 * q^23 + 32 * q^24 - 33 * q^25 - 42 * q^27 + 15 * q^28 + 8 * q^29 + 22 * q^30 + 40 * q^31 - 6 * q^32 + 24 * q^33 - 72 * q^34 + 44 * q^35 - 30 * q^36 - 4 * q^37 + 29 * q^38 + 4 * q^40 - 98 * q^41 - 9 * q^42 + 26 * q^43 + 10 * q^44 + 58 * q^45 - 10 * q^46 + 62 * q^47 + 178 * q^48 + 31 * q^49 + 46 * q^50 + 21 * q^51 + 18 * q^53 + 12 * q^54 - 28 * q^55 - 56 * q^56 + 26 * q^57 + 56 * q^58 + 79 * q^59 + 22 * q^60 - 13 * q^61 + 24 * q^62 - 22 * q^63 + 36 * q^64 + 38 * q^66 - 2 * q^67 + 12 * q^68 - 56 * q^69 - 85 * q^70 + 38 * q^71 + 81 * q^72 + 17 * q^73 - 17 * q^74 - 24 * q^75 - 116 * q^76 - 30 * q^77 + 9 * q^79 + 63 * q^80 - 16 * q^81 + 22 * q^82 - 162 * q^83 - 203 * q^84 + 68 * q^85 + 22 * q^86 - 70 * q^87 + 33 * q^88 + 72 * q^89 + 2 * q^90 - 8 * q^92 + 19 * q^93 + 30 * q^94 - 13 * q^95 + 11 * q^96 - 90 * q^97 - 81 * q^98 + 78 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times$.

$n$	$339$	$1016$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	0.771913	−	1.33699i	0.545825	−	0.945396i	−0.452730	−	0.891648i	$-0.649550\pi$
$2$	0.771913	−	1.33699i	0.545825	−	0.945396i	0.998555	−	0.0537483i	$-0.0171169\pi$
$3$	0.676597	+	1.17190i	0.390634	+	0.676597i	0.992533	−	0.121974i	$-0.0389226\pi$
$3$	0.676597	+	1.17190i	0.390634	+	0.676597i	−0.601900	+	0.798572i	$0.705589\pi$
$4$	−0.191698	−	0.332031i	−0.0958491	−	0.166015i
$5$	0.170982	−	0.296150i	0.0764657	−	0.132442i	−0.825257	−	0.564757i	$-0.808970\pi$
$5$	0.170982	−	0.296150i	0.0764657	−	0.132442i	0.901723	+	0.432315i	$0.142303\pi$
$6$	2.08910			0.852870
$7$	−2.12749	+	1.57282i	−0.804116	+	0.594472i
$7$	−2.12749	+	1.57282i	−0.804116	+	0.594472i
$8$	2.49575			0.882382
$9$	0.584432	−	1.01227i	0.194811	−	0.337422i
$10$	−0.263967	−	0.457204i	−0.0834737	−	0.144581i
$11$	2.77782	+	4.81133i	0.837544	+	1.45067i	0.891942	+	0.452150i	$0.149343\pi$
$11$	2.77782	+	4.81133i	0.837544	+	1.45067i	−0.0543976	+	0.998519i	$0.517324\pi$
$12$	0.259405	−	0.449303i	0.0748838	−	0.129702i
$13$		0			0
$13$		0			0
$14$	0.460616	+	4.05852i	0.123105	+	1.08469i
$15$	0.462745			0.119480
$16$	2.30990	−	4.00086i	0.577475	−	1.00022i
$17$	−2.52228	−	4.36872i	−0.611743	−	1.05957i	−0.990947	−	0.134257i	$-0.957135\pi$
$17$	−2.52228	−	4.36872i	−0.611743	−	1.05957i	0.379203	−	0.925313i	$-0.376198\pi$
$18$	−0.902261	−	1.56276i	−0.212665	−	0.368346i
$19$	−2.08225	+	3.60657i	−0.477702	+	0.827404i	−0.999673	−	0.0255589i	$-0.991863\pi$
$19$	−2.08225	+	3.60657i	−0.477702	+	0.827404i	0.521971	+	0.852963i	$0.325197\pi$
$20$	−0.131108			−0.0293167
$21$	−3.28265	−	1.42904i	−0.716333	−	0.311842i
$22$	8.57694			1.82861
$23$	0.621491	−	1.07645i	0.129590	−	0.224456i	−0.793928	−	0.608012i	$-0.791967\pi$
$23$	0.621491	−	1.07645i	0.129590	−	0.224456i	0.923518	+	0.383556i	$0.125301\pi$
$24$	1.68862	+	2.92478i	0.344688	+	0.597017i
$25$	2.44153	+	4.22885i	0.488306	+	0.845771i
$26$		0			0
$27$	5.64128			1.08567
$28$	0.930063	+	0.404886i	0.175765	+	0.0765162i
$29$	0.715449			0.132855			0.0664277	−	0.997791i	$-0.478840\pi$
$29$	0.715449			0.132855			0.0664277	+	0.997791i	$0.478840\pi$
$30$	0.357199	−	0.618687i	0.0652153	−	0.112956i
$31$	4.55881	+	7.89609i	0.818786	+	1.41818i	0.906577	+	0.422040i	$0.138686\pi$
$31$	4.55881	+	7.89609i	0.818786	+	1.41818i	−0.0877907	+	0.996139i	$0.527981\pi$
$32$	−1.07033	−	1.85386i	−0.189209	−	0.327720i
$33$	−3.75893	+	6.51066i	−0.654346	+	1.13336i
$34$	−7.78792			−1.33562
$35$	0.102029	+	0.898983i	0.0172460	+	0.151956i
$36$	−0.448138			−0.0746897
$37$	−0.764519	+	1.32419i	−0.125686	+	0.217695i	−0.922001	−	0.387188i	$-0.873447\pi$
$37$	−0.764519	+	1.32419i	−0.125686	+	0.217695i	0.796315	+	0.604882i	$0.206780\pi$
$38$	3.21464	+	5.56792i	0.521483	+	0.903235i
$39$		0			0
$40$	0.426730	−	0.739118i	0.0674719	−	0.116865i
$41$	3.73023			0.582564			0.291282	−	0.956637i	$-0.405918\pi$
$41$	3.73023			0.582564			0.291282	+	0.956637i	$0.405918\pi$
$42$	−4.44454	+	3.28578i	−0.685807	+	0.507007i
$43$	−6.37606			−0.972340			−0.486170	−	0.873864i	$-0.661606\pi$
$43$	−6.37606			−0.972340			−0.486170	+	0.873864i	$0.661606\pi$
$44$	1.06501	−	1.84464i	0.160556	−	0.278091i
$45$	−0.199855	−	0.346159i	−0.0297927	−	0.0516024i
$46$	−0.959473	−	1.66186i	−0.141467	−	0.245027i
$47$	0.189540	−	0.328293i	0.0276473	−	0.0478865i	−0.851871	−	0.523752i	$-0.824532\pi$
$47$	0.189540	−	0.328293i	0.0276473	−	0.0478865i	0.879518	+	0.475866i	$0.157865\pi$
$48$	6.25149			0.902325
$49$	2.05245	−	6.69234i	0.293206	−	0.956049i
$50$	7.53859			1.06612
$51$	3.41314	−	5.91173i	0.477935	−	0.827808i
$52$		0			0
$53$	−1.40635	−	2.43586i	−0.193176	−	0.334591i	0.753125	−	0.657878i	$-0.228546\pi$
$53$	−1.40635	−	2.43586i	−0.193176	−	0.334591i	−0.946301	+	0.323286i	$0.895212\pi$
$54$	4.35458	−	7.54235i	0.592583	−	1.02638i
$55$	1.89983			0.256174
$56$	−5.30970	+	3.92538i	−0.709538	+	0.524551i
$57$	−5.63539			−0.746426
$58$	0.552264	−	0.956549i	0.0725158	−	0.125601i
$59$	−4.28354	−	7.41931i	−0.557670	−	0.965912i	−0.997690	−	0.0679247i	$-0.978362\pi$
$59$	−4.28354	−	7.41931i	−0.557670	−	0.965912i	0.440021	−	0.897988i	$-0.354971\pi$
$60$	−0.0887074	−	0.153646i	−0.0114521	−	0.0198356i
$61$	−1.66311	+	2.88060i	−0.212940	+	0.368823i	−0.952633	−	0.304121i	$-0.901637\pi$
$61$	−1.66311	+	2.88060i	−0.212940	+	0.368823i	0.739693	+	0.672944i	$0.234970\pi$
$62$	14.0760			1.78765
$63$	0.348742	+	3.07280i	0.0439374	+	0.387136i
$64$	5.93480			0.741850
$65$		0			0
$66$	5.80313	+	10.0513i	0.714316	+	1.23723i
$67$	3.96675	+	6.87061i	0.484615	+	0.839378i	0.999844	−	0.0176746i	$-0.00562629\pi$
$67$	3.96675	+	6.87061i	0.484615	+	0.839378i	−0.515229	+	0.857053i	$0.672293\pi$
$68$	−0.967033	+	1.67495i	−0.117270	+	0.203118i
$69$	1.68200			0.202489
$70$	1.28069	+	0.557525i	0.153072	+	0.0666369i
$71$	14.5113			1.72218			0.861088	−	0.508455i	$-0.169783\pi$
$71$	14.5113			1.72218			0.861088	+	0.508455i	$0.169783\pi$
$72$	1.45860	−	2.52637i	0.171897	−	0.297735i
$73$	−3.72576	−	6.45321i	−0.436068	−	0.755291i	0.561315	−	0.827603i	$-0.310296\pi$
$73$	−3.72576	−	6.45321i	−0.436068	−	0.755291i	−0.997382	+	0.0723114i	$0.976962\pi$
$74$	1.18028	+	2.04431i	0.137205	+	0.237646i
$75$	−3.30387	+	5.72246i	−0.381498	+	0.660773i
$76$	1.59666			0.183149
$77$	−13.4772	−	5.86703i	−1.53587	−	0.668611i
$78$		0			0
$79$	2.80770	−	4.86307i	0.315890	−	0.547138i	−0.663736	−	0.747967i	$-0.731030\pi$
$79$	2.80770	−	4.86307i	0.315890	−	0.547138i	0.979626	+	0.200829i	$0.0643635\pi$
$80$	−0.789905	−	1.36816i	−0.0883140	−	0.152964i
$81$	2.06358	+	3.57423i	0.229287	+	0.397137i
$82$	2.87941	−	4.98728i	0.317978	−	0.550753i
$83$	−9.99425			−1.09701			−0.548506	−	0.836147i	$-0.684803\pi$
$83$	−9.99425			−1.09701			−0.548506	+	0.836147i	$0.684803\pi$
$84$	0.154792	+	1.36389i	0.0168892	+	0.148812i
$85$	−1.72506			−0.187109
$86$	−4.92176	+	8.52474i	−0.530727	+	0.919246i
$87$	0.484071	+	0.838435i	0.0518978	+	0.0898897i
$88$	6.93275	+	12.0079i	0.739034	+	1.28004i
$89$	8.06158	−	13.9631i	0.854526	−	1.48008i	−0.0225588	−	0.999746i	$-0.507181\pi$
$89$	8.06158	−	13.9631i	0.854526	−	1.48008i	0.877084	−	0.480336i	$-0.159485\pi$
$90$	−0.617083			−0.0650463
$91$		0			0
$92$	−0.476555			−0.0496843
$93$	−6.16896	+	10.6849i	−0.639691	+	1.10798i
$94$	−0.292617	−	0.506828i	−0.0301811	−	0.0522753i
$95$	0.712058	+	1.23332i	0.0730556	+	0.126536i
$96$	1.44836	−	2.50864i	0.147823	−	0.256037i
$97$	−12.1202			−1.23062			−0.615310	−	0.788285i	$-0.710969\pi$
$97$	−12.1202			−1.23062			−0.615310	+	0.788285i	$0.710969\pi$
$98$	−7.36330	−	7.91001i	−0.743806	−	0.799031i
$99$	6.49379			0.652650
$100$	0.936074	−	1.62133i	0.0936074	−	0.162133i
$101$	−6.58061	−	11.3980i	−0.654795	−	1.13414i	−0.981945	−	0.189166i	$-0.939422\pi$
$101$	−6.58061	−	11.3980i	−0.654795	−	1.13414i	0.327150	−	0.944972i	$-0.393912\pi$
$102$	−5.26929	−	9.12668i	−0.521737	−	0.903676i
$103$	−7.42938	+	12.8681i	−0.732039	+	1.26793i	0.223972	+	0.974596i	$0.428098\pi$
$103$	−7.42938	+	12.8681i	−0.732039	+	1.26793i	−0.956010	+	0.293333i	$0.905236\pi$
$104$		0			0
$105$	−0.984487	+	0.727817i	−0.0960761	+	0.0710277i
$106$	−4.34230			−0.421762
$107$	−2.46204	+	4.26438i	−0.238014	+	0.412253i	−0.960144	−	0.279504i	$-0.909830\pi$
$107$	−2.46204	+	4.26438i	−0.238014	+	0.412253i	0.722130	+	0.691757i	$0.243163\pi$
$108$	−1.08142	−	1.87308i	−0.104060	−	0.180237i
$109$	−6.50549	−	11.2678i	−0.623113	−	1.07926i	−0.988902	−	0.148566i	$-0.952534\pi$
$109$	−6.50549	−	11.2678i	−0.623113	−	1.07926i	0.365789	−	0.930698i	$-0.380799\pi$
$110$	1.46651	−	2.54006i	0.139826	−	0.242185i
$111$	−2.06909			−0.196389
$112$	1.37836	+	12.1449i	0.130243	+	1.14758i
$113$	6.96199			0.654929			0.327464	−	0.944864i	$-0.393806\pi$
$113$	6.96199			0.654929			0.327464	+	0.944864i	$0.393806\pi$
$114$	−4.35003	+	7.53447i	−0.407418	+	0.705668i
$115$	−0.212528	−	0.368109i	−0.0198183	−	0.0343264i
$116$	−0.137150	−	0.237551i	−0.0127341	−	0.0220561i
$117$		0			0
$118$	−13.2261			−1.21756
$119$	12.2374	+	5.32731i	1.12180	+	0.488354i
$120$	1.15490			0.105427
$121$	−9.93257	+	17.2037i	−0.902961	+	1.56397i
$122$	2.56756	+	4.44714i	0.232456	+	0.402625i
$123$	2.52386	+	4.37146i	0.227569	+	0.394161i
$124$	1.74783	−	3.02733i	0.156960	−	0.271862i
$125$	3.37966			0.302286
$126$	4.37750	+	1.90566i	0.389979	+	0.169770i
$127$	8.88200			0.788150			0.394075	−	0.919078i	$-0.371065\pi$
$127$	8.88200			0.788150			0.394075	+	0.919078i	$0.371065\pi$
$128$	6.72180	−	11.6425i	0.594129	−	1.02906i
$129$	−4.31403	−	7.47211i	−0.379829	−	0.657883i
$130$		0			0
$131$	11.0488	−	19.1370i	0.965335	−	1.67201i	0.256623	−	0.966512i	$-0.417390\pi$
$131$	11.0488	−	19.1370i	0.965335	−	1.67201i	0.708712	−	0.705498i	$-0.249277\pi$
$132$	2.88232			0.250874
$133$	−1.24252	−	10.9480i	−0.107740	−	0.949310i
$134$	12.2479			1.05806
$135$	0.964561	−	1.67067i	0.0830162	−	0.143788i
$136$	−6.29499	−	10.9032i	−0.539791	−	0.934946i
$137$	1.69885	+	2.94250i	0.145143	+	0.251395i	0.929426	−	0.369008i	$-0.120302\pi$
$137$	1.69885	+	2.94250i	0.145143	+	0.251395i	−0.784283	+	0.620403i	$0.786969\pi$
$138$	1.29835	−	2.24882i	0.110523	−	0.191432i
$139$	−4.71964			−0.400315			−0.200157	−	0.979764i	$-0.564145\pi$
$139$	−4.71964			−0.400315			−0.200157	+	0.979764i	$0.564145\pi$
$140$	0.278931	−	0.206210i	0.0235740	−	0.0174279i
$141$	0.512970			0.0431999
$142$	11.2015	−	19.4015i	0.940007	−	1.62814i
$143$		0			0
$144$	−2.69996	−	4.67646i	−0.224997	−	0.389705i
$145$	0.122329	−	0.211880i	0.0101589	−	0.0175957i
$146$	−11.5039			−0.952066
$147$	9.23144	−	2.12276i	0.761397	−	0.175082i
$148$	0.586228			0.0481876
$149$	−0.346531	+	0.600210i	−0.0283890	+	0.0491711i	−0.879871	−	0.475213i	$-0.842371\pi$
$149$	−0.346531	+	0.600210i	−0.0283890	+	0.0491711i	0.851482	+	0.524384i	$0.175704\pi$
$150$	5.10059	+	8.83448i	0.416462	+	0.721333i
$151$	−8.61973	−	14.9298i	−0.701463	−	1.21497i	−0.967953	−	0.251132i	$-0.919197\pi$
$151$	−8.61973	−	14.9298i	−0.701463	−	1.21497i	0.266489	−	0.963838i	$-0.414136\pi$
$152$	−5.19679	+	9.00111i	−0.421516	+	0.730087i
$153$	−5.89641			−0.476696
$154$	−18.2474	+	13.4900i	−1.47041	+	1.08706i
$155$	3.11791			0.250436
$156$		0			0
$157$	−0.772465	−	1.33795i	−0.0616494	−	0.106780i	0.833553	−	0.552439i	$-0.186303\pi$
$157$	−0.772465	−	1.33795i	−0.0616494	−	0.106780i	−0.895203	+	0.445659i	$0.852969\pi$
$158$	−4.33459	−	7.50773i	−0.344842	−	0.597283i
$159$	1.90306	−	3.29619i	0.150922	−	0.261405i
$160$	−0.732029			−0.0578720
$161$	0.370856	+	3.26764i	0.0292276	+	0.257526i
$162$	6.37162			0.500602
$163$	6.38319	−	11.0560i	0.499970	−	0.865973i	−0.500030	−	0.866008i	$-0.666678\pi$
$163$	6.38319	−	11.0560i	0.499970	−	0.865973i	1.00000		3.48695e-5i	$1.10993e-5\pi$
$164$	−0.715078	−	1.23855i	−0.0558382	−	0.0967146i
$165$	1.28542	+	2.22642i	0.100070	+	0.173326i
$166$	−7.71469	+	13.3622i	−0.598776	+	1.03711i
$167$	−23.6948			−1.83356			−0.916781	−	0.399391i	$-0.869222\pi$
$167$	−23.6948			−1.83356			−0.916781	+	0.399391i	$0.869222\pi$
$168$	−8.19269	−	3.56653i	−0.632080	−	0.275164i
$169$		0			0
$170$	−1.33160	+	2.30640i	−0.102129	+	0.176893i
$171$	2.43387	+	4.21559i	0.186123	+	0.322374i
$172$	1.22228	+	2.11705i	0.0931979	+	0.161423i
$173$	−1.17139	+	2.02891i	−0.0890593	+	0.154255i	−0.907114	−	0.420886i	$-0.861719\pi$
$173$	−1.17139	+	2.02891i	−0.0890593	+	0.154255i	0.818054	+	0.575141i	$0.195053\pi$
$174$	1.49464			0.113308
$175$	−11.8456	−	5.15675i	−0.895442	−	0.389814i
$176$	25.6659			1.93464
$177$	5.79647	−	10.0398i	0.435689	−	0.754636i
$178$	−12.4457	−	21.5565i	−0.932842	−	1.61573i
$179$	−0.0788659	−	0.136600i	−0.00589471	−	0.0102099i	0.863063	−	0.505096i	$-0.168543\pi$
$179$	−0.0788659	−	0.136600i	−0.00589471	−	0.0102099i	−0.868958	+	0.494886i	$0.835210\pi$
$180$	−0.0766237	+	0.132716i	−0.00571120	+	0.00989208i
$181$	13.9953			1.04026			0.520131	−	0.854086i	$-0.325883\pi$
$181$	13.9953			1.04026			0.520131	+	0.854086i	$0.325883\pi$
$182$		0			0
$183$	−4.50103			−0.332726
$184$	1.55109	−	2.68656i	0.114348	−	0.198056i
$185$	0.261439	+	0.452825i	0.0192214	+	0.0332924i
$186$	9.52379	+	16.4957i	0.698318	+	1.20952i
$187$	14.0129	−	24.2710i	1.02472	−	1.77487i
$188$	−0.145338			−0.0105999
$189$	−12.0018	+	8.87275i	−0.873002	+	0.645398i
$190$	2.19859			0.159502
$191$	−7.94201	+	13.7560i	−0.574664	+	0.995346i	0.421415	+	0.906868i	$0.361534\pi$
$191$	−7.94201	+	13.7560i	−0.574664	+	0.995346i	−0.996078	+	0.0884784i	$0.971800\pi$
$192$	4.01547	+	6.95500i	0.289792	+	0.501934i
$193$	−8.36335	−	14.4857i	−0.602007	−	1.04271i	−0.992517	−	0.122108i	$-0.961035\pi$
$193$	−8.36335	−	14.4857i	−0.602007	−	1.04271i	0.390510	−	0.920599i	$-0.372299\pi$
$194$	−9.35574	+	16.2046i	−0.671703	+	1.16342i
$195$		0			0
$196$	−2.61552	+	0.601435i	−0.186823	+	0.0429596i
$197$	−18.2087			−1.29731			−0.648657	−	0.761081i	$-0.724669\pi$
$197$	−18.2087			−1.29731			−0.648657	+	0.761081i	$0.724669\pi$
$198$	5.01264	−	8.68214i	0.356232	−	0.617013i
$199$	−11.4928	−	19.9062i	−0.814706	−	1.41111i	−0.909539	−	0.415619i	$-0.863565\pi$
$199$	−11.4928	−	19.9062i	−0.814706	−	1.41111i	0.0948332	−	0.995493i	$-0.469768\pi$
$200$	6.09346	+	10.5542i	0.430872	+	0.746293i
$201$	−5.36778	+	9.29727i	−0.378614	+	0.655779i
$202$	−20.3186			−1.42961
$203$	−1.52211	+	1.12528i	−0.106831	+	0.0789788i
$204$	−2.61717			−0.183239
$205$	0.637804	−	1.10471i	0.0445461	−	0.0771562i
$206$	11.4697	+	19.8660i	0.799130	+	1.38413i
$207$	−0.726438	−	1.25823i	−0.0504909	−	0.0874529i
$208$		0			0
$209$	−23.1365			−1.60039
$210$	0.213148	+	1.87806i	0.0147086	+	0.129599i
$211$	10.3942			0.715565			0.357782	−	0.933805i	$-0.383533\pi$
$211$	10.3942			0.715565			0.357782	+	0.933805i	$0.383533\pi$
$212$	−0.539188	+	0.933900i	−0.0370316	+	0.0641405i
$213$	9.81832	+	17.0058i	0.672740	+	1.16522i
$214$	3.80096	+	6.58346i	0.259828	+	0.450036i
$215$	−1.09019	+	1.88827i	−0.0743506	+	0.128779i
$216$	14.0793			0.957972
$217$	−22.1180	−	9.62866i	−1.50147	−	0.653636i
$218$	−20.0867			−1.36044
$219$	5.04168	−	8.73245i	0.340685	−	0.590084i
$220$	−0.364195	−	0.630804i	−0.0245540	−	0.0425288i
$221$		0			0
$222$	−1.59715	+	2.76635i	−0.107194	+	0.185665i
$223$	−6.55154			−0.438724			−0.219362	−	0.975644i	$-0.570398\pi$
$223$	−6.55154			−0.438724			−0.219362	+	0.975644i	$0.570398\pi$
$224$	5.19292	+	2.26064i	0.346966	+	0.151045i
$225$	5.70763			0.380509
$226$	5.37404	−	9.30812i	0.357476	−	0.619167i
$227$	3.36925	+	5.83572i	0.223625	+	0.387330i	0.955906	−	0.293673i	$-0.0948775\pi$
$227$	3.36925	+	5.83572i	0.223625	+	0.387330i	−0.732281	+	0.681003i	$0.761544\pi$
$228$	1.08029	+	1.87112i	0.0715442	+	0.123918i
$229$	−2.36981	+	4.10462i	−0.156601	+	0.271241i	−0.933641	−	0.358210i	$-0.883387\pi$
$229$	−2.36981	+	4.10462i	−0.156601	+	0.271241i	0.777040	+	0.629452i	$0.216720\pi$
$230$	−0.656212			−0.0432694
$231$	−2.24303	−	19.7635i	−0.147581	−	1.30034i
$232$	1.78558			0.117229
$233$	−0.102491	+	0.177519i	−0.00671440	+	0.0116297i	−0.869363	−	0.494174i	$-0.835471\pi$
$233$	−0.102491	+	0.177519i	−0.00671440	+	0.0116297i	0.862649	+	0.505804i	$0.168804\pi$
$234$		0			0
$235$	−0.0648161	−	0.112265i	−0.00422814	−	0.00732335i
$236$	−1.64229	+	2.84454i	−0.106904	+	0.185164i
$237$	7.59872			0.493590
$238$	16.5687	−	12.2490i	1.07399	−	0.793987i
$239$	−19.7779			−1.27932			−0.639662	−	0.768656i	$-0.720926\pi$
$239$	−19.7779			−1.27932			−0.639662	+	0.768656i	$0.720926\pi$
$240$	1.06890	−	1.85138i	0.0689969	−	0.119506i
$241$	10.4605	+	18.1181i	0.673819	+	1.16709i	0.976812	+	0.214097i	$0.0686808\pi$
$241$	10.4605	+	18.1181i	0.673819	+	1.16709i	−0.302993	+	0.952993i	$0.597986\pi$
$242$	15.3342	+	26.5595i	0.985717	+	1.70731i
$243$	5.66950	−	9.81986i	0.363698	−	0.629944i
$244$	1.27526			0.0816403
$245$	−1.63101	−	1.75211i	−0.104201	−	0.111938i
$246$	7.79281			0.496851
$247$		0			0
$248$	11.3777	+	19.7067i	0.722482	+	1.25138i
$249$	−6.76208	−	11.7123i	−0.428530	−	0.742235i
$250$	2.60880	−	4.51858i	0.164995	−	0.285780i
$251$	11.7604			0.742311			0.371155	−	0.928571i	$-0.378962\pi$
$251$	11.7604			0.742311			0.371155	+	0.928571i	$0.378962\pi$
$252$	0.953410	−	0.704842i	0.0600592	−	0.0444009i
$253$	6.90556			0.434149
$254$	6.85613	−	11.8752i	0.430192	−	0.745114i
$255$	−1.16717	−	2.02160i	−0.0730913	−	0.126598i
$256$	−4.44249	−	7.69462i	−0.277656	−	0.480914i
$257$	0.598139	−	1.03601i	0.0373109	−	0.0646244i	−0.846767	−	0.531964i	$-0.821454\pi$
$257$	0.598139	−	1.03601i	0.0373109	−	0.0646244i	0.884078	+	0.467340i	$0.154787\pi$
$258$	−13.3202			−0.829280
$259$	−0.456204	−	4.01965i	−0.0283471	−	0.249769i
$260$		0			0
$261$	0.418131	−	0.724224i	0.0258817	−	0.0448283i
$262$	−17.0574	−	29.5442i	−1.05381	−	1.82525i
$263$	−1.20660	−	2.08990i	−0.0744022	−	0.128868i	0.826424	−	0.563048i	$-0.190372\pi$
$263$	−1.20660	−	2.08990i	−0.0744022	−	0.128868i	−0.900826	+	0.434180i	$0.857038\pi$
$264$	−9.38137	+	16.2490i	−0.577383	+	1.00006i
$265$	−0.961841			−0.0590854
$266$	−15.5965	−	6.78963i	−0.956281	−	0.416299i
$267$	21.8178			1.33523
$268$	1.52084	−	2.63417i	0.0928998	−	0.160907i
$269$	−10.1746	−	17.6229i	−0.620356	−	1.07449i	−0.989419	−	0.145084i	$-0.953655\pi$
$269$	−10.1746	−	17.6229i	−0.620356	−	1.07449i	0.369063	−	0.929404i	$-0.379679\pi$
$270$	−1.48911	−	2.57922i	−0.0906245	−	0.156966i
$271$	−14.2701	+	24.7166i	−0.866848	+	1.50143i	−0.00164822	+	0.999999i	$0.500525\pi$
$271$	−14.2701	+	24.7166i	−0.866848	+	1.50143i	−0.865200	+	0.501427i	$0.832809\pi$
$272$	−23.3049			−1.41307
$273$		0			0
$274$	5.24547			0.316890
$275$	−13.5643	+	23.4940i	−0.817956	+	1.41674i
$276$	−0.322436	−	0.558475i	−0.0194083	−	0.0336162i
$277$	−7.19409	−	12.4605i	−0.432251	−	0.748680i	0.564816	−	0.825217i	$-0.308947\pi$
$277$	−7.19409	−	12.4605i	−0.432251	−	0.748680i	−0.997067	+	0.0765367i	$0.975614\pi$
$278$	−3.64315	+	6.31012i	−0.218502	+	0.378456i
$279$	10.6573			0.638033
$280$	0.254638	+	2.24364i	0.0152176	+	0.134083i
$281$	15.2759			0.911286			0.455643	−	0.890163i	$-0.349409\pi$
$281$	15.2759			0.911286			0.455643	+	0.890163i	$0.349409\pi$
$282$	0.395968	−	0.685837i	0.0235795	−	0.0408410i
$283$	−15.2480	−	26.4104i	−0.906402	−	1.56994i	−0.819023	−	0.573760i	$-0.805484\pi$
$283$	−15.2480	−	26.4104i	−0.906402	−	1.56994i	−0.0873790	−	0.996175i	$-0.527849\pi$
$284$	−2.78179	−	4.81821i	−0.165069	−	0.285908i
$285$	−0.963553	+	1.66892i	−0.0570760	+	0.0988585i
$286$		0			0
$287$	−7.93603	+	5.86699i	−0.468449	+	0.346318i
$288$	−2.50214			−0.147440
$289$	−4.22381	+	7.31585i	−0.248459	+	0.430344i
$290$	−0.188855	−	0.327106i	−0.0110899	−	0.0192083i
$291$	−8.20050	−	14.2037i	−0.480722	−	0.832635i
$292$	−1.42844	+	2.47414i	−0.0835933	+	0.144788i
$293$	19.9508			1.16554			0.582770	−	0.812637i	$-0.301969\pi$
$293$	19.9508			1.16554			0.582770	+	0.812637i	$0.301969\pi$
$294$	4.28776	−	13.9810i	0.250067	−	0.815386i
$295$	−2.92964			−0.170570
$296$	−1.90805	+	3.30484i	−0.110903	+	0.192090i
$297$	15.6705	+	27.1421i	0.909293	+	1.57494i
$298$	0.534984	+	0.926619i	0.0309908	+	0.0536776i
$299$		0			0
$300$	2.53338			0.146265
$301$	13.5650	−	10.0284i	0.781875	−	0.578029i
$302$	−26.6147			−1.53150
$303$	8.90485	−	15.4236i	0.511570	−	0.886065i
$304$	9.61960	+	16.6616i	0.551722	+	0.955610i
$305$	0.568726	+	0.985063i	0.0325652	+	0.0564045i
$306$	−4.55151	+	7.88345i	−0.260193	+	0.450667i
$307$	3.98166			0.227245			0.113623	−	0.993524i	$-0.463755\pi$
$307$	3.98166			0.227245			0.113623	+	0.993524i	$0.463755\pi$
$308$	0.635511	+	5.59953i	0.0362116	+	0.319063i
$309$	−20.1068			−1.14384
$310$	2.40675	−	4.16861i	0.136694	−	0.236761i
$311$	10.6906	+	18.5167i	0.606210	+	1.04999i	0.991859	+	0.127341i	$0.0406441\pi$
$311$	10.6906	+	18.5167i	0.606210	+	1.04999i	−0.385649	+	0.922645i	$0.626023\pi$
$312$		0			0
$313$	−3.54293	+	6.13653i	−0.200258	+	0.346857i	−0.948612	−	0.316443i	$-0.897511\pi$
$313$	−3.54293	+	6.13653i	−0.200258	+	0.346857i	0.748353	+	0.663300i	$0.230845\pi$
$314$	−2.38510			−0.134599
$315$	0.969638	+	0.422114i	0.0546329	+	0.0237834i
$316$	−2.15292			−0.121111
$317$	−7.20748	+	12.4837i	−0.404813	+	0.701156i	−0.994300	−	0.106622i	$-0.965997\pi$
$317$	−7.20748	+	12.4837i	−0.404813	+	0.701156i	0.589487	+	0.807778i	$0.299330\pi$
$318$	−2.93799	−	5.08875i	−0.164754	−	0.285363i
$319$	1.98739	+	3.44226i	0.111272	+	0.192729i
$320$	1.01475	−	1.75759i	0.0567261	−	0.0982524i
$321$	−6.66324			−0.371906
$322$	4.65508	+	2.02650i	0.259418	+	0.112933i
$323$	21.0081			1.16892
$324$	0.791170	−	1.37035i	0.0439539	−	0.0761304i
$325$		0			0
$326$	−9.85453	−	17.0685i	−0.545792	−	0.945339i
$327$	8.80320	−	15.2476i	0.486818	−	0.843194i
$328$	9.30973			0.514044
$329$	0.113103	+	0.996555i	0.00623554	+	0.0549419i
$330$	3.96894			0.218483
$331$	9.27549	−	16.0656i	0.509827	−	0.883046i	−0.490108	−	0.871662i	$-0.663043\pi$
$331$	9.27549	−	16.0656i	0.509827	−	0.883046i	0.999935	−	0.0113848i	$-0.00362397\pi$
$332$	1.91588	+	3.31840i	0.105148	+	0.182121i
$333$	0.893619	+	1.54779i	0.0489700	+	0.0848186i
$334$	−18.2903	+	31.6798i	−1.00080	+	1.73344i
$335$	2.71298			0.148226
$336$	−13.3000	+	9.83250i	−0.725574	+	0.536407i
$337$	30.1297			1.64127			0.820635	−	0.571452i	$-0.193620\pi$
$337$	30.1297			1.64127			0.820635	+	0.571452i	$0.193620\pi$
$338$		0			0
$339$	4.71046	+	8.15876i	0.255837	+	0.443123i
$340$	0.330692	+	0.572775i	0.0179343	+	0.0310631i
$341$	−25.3271	+	43.8678i	−1.37154	+	2.37558i
$342$	7.51495			0.406362
$343$	6.15932	+	17.4660i	0.332572	+	0.943078i
$344$	−15.9131			−0.857976
$345$	0.287592	−	0.498124i	0.0154834	−	0.0268181i
$346$	1.80842	+	3.13228i	0.0972215	+	0.168393i
$347$	11.8550	+	20.5334i	0.636409	+	1.10229i	0.986215	+	0.165470i	$0.0529141\pi$
$347$	11.8550	+	20.5334i	0.636409	+	1.10229i	−0.349806	+	0.936822i	$0.613753\pi$
$348$	0.185591	−	0.321453i	0.00994872	−	0.0172317i
$349$	−18.4712			−0.988739			−0.494369	−	0.869252i	$-0.664601\pi$
$349$	−18.4712			−0.988739			−0.494369	+	0.869252i	$0.664601\pi$
$350$	−16.0383	+	11.8569i	−0.857283	+	0.633777i
$351$		0			0
$352$	5.94636	−	10.2994i	0.316942	−	0.548960i
$353$	3.91006	+	6.77243i	0.208112	+	0.360460i	0.951120	−	0.308822i	$-0.0999349\pi$
$353$	3.91006	+	6.77243i	0.208112	+	0.360460i	−0.743008	+	0.669283i	$0.766602\pi$
$354$	−8.94873	−	15.4997i	−0.475620	−	0.823798i
$355$	2.48118	−	4.29753i	0.131687	−	0.228089i
$356$	−6.18156			−0.327622
$357$	2.03669	+	17.9454i	0.107793	+	0.949773i
$358$	−0.243510			−0.0128699
$359$	−9.21982	+	15.9692i	−0.486603	+	0.842822i	−0.999881	−	0.0154006i	$-0.995098\pi$
$359$	−9.21982	+	15.9692i	−0.486603	+	0.842822i	0.513278	+	0.858222i	$0.328431\pi$
$360$	−0.498789	−	0.863928i	−0.0262885	−	0.0455330i
$361$	0.828430	+	1.43488i	0.0436016	+	0.0755202i
$362$	10.8032	−	18.7116i	0.567801	−	0.983460i
$363$	−26.8814			−1.41091
$364$		0			0
$365$	−2.54816			−0.133377
$366$	−3.47440	+	6.01784i	−0.181610	+	0.314558i
$367$	0.903722	+	1.56529i	0.0471739	+	0.0817076i	0.888648	−	0.458590i	$-0.151645\pi$
$367$	0.903722	+	1.56529i	0.0471739	+	0.0817076i	−0.841474	+	0.540297i	$0.818312\pi$
$368$	−2.87116	−	4.97300i	−0.149670	−	0.259236i
$369$	2.18006	−	3.77598i	0.113490	−	0.196570i
$370$	0.807232			0.0419660
$371$	6.82317	+	2.97034i	0.354241	+	0.154212i
$372$	4.73031			0.245255
$373$	5.27830	−	9.14229i	0.273300	−	0.473370i	−0.696405	−	0.717649i	$-0.745218\pi$
$373$	5.27830	−	9.14229i	0.273300	−	0.473370i	0.969705	+	0.244279i	$0.0785514\pi$
$374$	−21.6335	−	37.4702i	−1.11864	−	1.93754i
$375$	2.28667	+	3.96063i	0.118083	+	0.204526i
$376$	0.473046	−	0.819339i	0.0243955	−	0.0422542i
$377$		0			0
$378$	2.59846	+	22.8953i	0.133651	+	1.17761i
$379$	−11.9486			−0.613760			−0.306880	−	0.951748i	$-0.599285\pi$
$379$	−11.9486			−0.613760			−0.306880	+	0.951748i	$0.599285\pi$
$380$	0.273000	−	0.472851i	0.0140046	−	0.0242567i
$381$	6.00954	+	10.4088i	0.307878	+	0.533261i
$382$	12.2611	+	21.2368i	0.627331	+	1.08657i
$383$	−2.84299	+	4.92421i	−0.145270	+	0.251615i	−0.929474	−	0.368888i	$-0.879738\pi$
$383$	−2.84299	+	4.92421i	−0.145270	+	0.251615i	0.784204	+	0.620504i	$0.213072\pi$
$384$	18.1918			0.928347
$385$	−4.04188	+	2.98811i	−0.205993	+	0.152288i
$386$	−25.8231			−1.31436
$387$	−3.72637	+	6.45427i	−0.189422	+	0.328089i
$388$	2.32342	+	4.02428i	0.117954	+	0.204302i
$389$	−2.10381	−	3.64390i	−0.106667	−	0.184753i	0.807751	−	0.589524i	$-0.200685\pi$
$389$	−2.10381	−	3.64390i	−0.106667	−	0.184753i	−0.914418	+	0.404771i	$0.867351\pi$
$390$		0			0
$391$	−6.27030			−0.317103
$392$	5.12240	−	16.7024i	0.258720	−	0.843601i
$393$	29.9023			1.50837
$394$	−14.0555	+	24.3449i	−0.708106	+	1.22648i
$395$	−0.960133	−	1.66300i	−0.0483095	−	0.0836746i
$396$	−1.24485	−	2.15614i	−0.0625559	−	0.108350i
$397$	−0.379805	+	0.657841i	−0.0190618	+	0.0330161i	−0.875399	−	0.483401i	$-0.839401\pi$
$397$	−0.379805	+	0.657841i	−0.0190618	+	0.0330161i	0.856337	+	0.516417i	$0.172735\pi$
$398$	−35.4859			−1.77875
$399$	11.9893	−	8.86348i	0.600213	−	0.443729i
$400$	22.5588			1.12794
$401$	8.71097	−	15.0878i	0.435005	−	0.753451i	−0.562291	−	0.826939i	$-0.690080\pi$
$401$	8.71097	−	15.0878i	0.435005	−	0.753451i	0.997296	+	0.0734888i	$0.0234133\pi$
$402$	8.28692	+	14.3534i	0.413314	+	0.715881i
$403$		0			0
$404$	−2.52298	+	4.36993i	−0.125523	+	0.217412i
$405$	1.41135			0.0701304
$406$	0.329547	+	2.90366i	0.0163551	+	0.144106i
$407$	−8.49479			−0.421071
$408$	8.51835	−	14.7542i	0.421721	−	0.730443i
$409$	9.84205	+	17.0469i	0.486658	+	0.842916i	0.999882	−	0.0153383i	$-0.00488251\pi$
$409$	9.84205	+	17.0469i	0.486658	+	0.842916i	−0.513224	+	0.858254i	$0.671549\pi$
$410$	−0.984657	−	1.70548i	−0.0486288	−	0.0842275i
$411$	−2.29888	+	3.98178i	−0.113395	+	0.196407i
$412$	5.69679			0.280661
$413$	20.7825	+	9.04727i	1.02264	+	0.445187i
$414$	−2.24299			−0.110237
$415$	−1.70884	+	2.95980i	−0.0838837	+	0.145291i
$416$		0			0
$417$	−3.19330	−	5.53095i	−0.156376	−	0.270852i
$418$	−17.8594	+	30.9333i	−0.873530	+	1.51300i
$419$	−9.57664			−0.467849			−0.233925	−	0.972255i	$-0.575157\pi$
$419$	−9.57664			−0.467849			−0.233925	+	0.972255i	$0.575157\pi$
$420$	0.430382	+	0.187359i	0.0210005	+	0.00914218i
$421$	21.0440			1.02562			0.512811	−	0.858501i	$-0.328604\pi$
$421$	21.0440			1.02562			0.512811	+	0.858501i	$0.328604\pi$
$422$	8.02340	−	13.8969i	0.390573	−	0.676492i
$423$	−0.221547	−	0.383730i	−0.0107720	−	0.0186576i
$424$	−3.50989	−	6.07931i	−0.170455	−	0.295237i
$425$	12.3165	−	21.3327i	0.597436	−	1.03479i
$426$	30.3155			1.46879
$427$	−0.992413	−	8.74423i	−0.0480262	−	0.423163i
$428$	1.88787			0.0912539
$429$		0			0
$430$	1.68307	+	2.91516i	0.0811648	+	0.140582i
$431$	5.64500	+	9.77743i	0.271910	+	0.470962i	0.969351	−	0.245680i	$-0.0790113\pi$
$431$	5.64500	+	9.77743i	0.271910	+	0.470962i	−0.697441	+	0.716642i	$0.745678\pi$
$432$	13.0308	−	22.5700i	0.626945	−	1.08590i
$433$	14.8922			0.715674			0.357837	−	0.933784i	$-0.383514\pi$
$433$	14.8922			0.715674			0.357837	+	0.933784i	$0.383514\pi$
$434$	−29.9466	+	22.1391i	−1.43748	+	1.06271i
$435$	0.331070			0.0158736
$436$	−2.49418	+	4.32005i	−0.119450	+	0.206893i
$437$	2.58820	+	4.48290i	0.123811	+	0.214446i
$438$	−7.78348	−	13.4814i	−0.371909	−	0.644165i
$439$	−8.33921	+	14.4439i	−0.398009	+	0.689372i	−0.993480	−	0.114005i	$-0.963632\pi$
$439$	−8.33921	+	14.4439i	−0.398009	+	0.689372i	0.595471	+	0.803377i	$0.296965\pi$
$440$	4.74152			0.226043
$441$	−5.57492	−	5.98884i	−0.265472	−	0.285183i
$442$		0			0
$443$	7.93238	−	13.7393i	0.376879	−	0.652773i	−0.613727	−	0.789518i	$-0.710331\pi$
$443$	7.93238	−	13.7393i	0.376879	−	0.652773i	0.990606	+	0.136745i	$0.0436640\pi$
$444$	0.396640	+	0.687001i	0.0188237	+	0.0326036i
$445$	−2.75678	−	4.77488i	−0.130684	−	0.226351i
$446$	−5.05722	+	8.75936i	−0.239466	+	0.414768i
$447$	−0.937849			−0.0443587
$448$	−12.6262	+	9.33440i	−0.596534	+	0.441009i
$449$	−22.4560			−1.05976			−0.529882	−	0.848072i	$-0.677764\pi$
$449$	−22.4560			−1.05976			−0.529882	+	0.848072i	$0.677764\pi$
$450$	4.40579	−	7.63106i	0.207691	−	0.359731i
$451$	10.3619	+	17.9473i	0.487923	+	0.845107i
$452$	−1.33460	−	2.31159i	−0.0627743	−	0.108728i
$453$	11.6642	−	20.2029i	0.548030	−	0.949217i
$454$	10.4031			0.488240
$455$		0			0
$456$	−14.0646			−0.658633
$457$	1.89740	−	3.28639i	0.0887566	−	0.153731i	−0.818229	−	0.574892i	$-0.805044\pi$
$457$	1.89740	−	3.28639i	0.0887566	−	0.153731i	0.906986	+	0.421161i	$0.138377\pi$
$458$	3.65857	+	6.33682i	0.170954	+	0.296100i
$459$	−14.2289	−	24.6452i	−0.664149	−	1.15034i
$460$	−0.0814825	+	0.141132i	−0.00379914	+	0.00658030i
$461$	4.70212			0.219000			0.109500	−	0.993987i	$-0.465075\pi$
$461$	4.70212			0.219000			0.109500	+	0.993987i	$0.465075\pi$
$462$	−28.1551	−	12.2568i	−1.30989	−	0.570238i
$463$	−34.0179			−1.58094			−0.790472	−	0.612498i	$-0.790165\pi$
$463$	−34.0179			−1.58094			−0.790472	+	0.612498i	$0.790165\pi$
$464$	1.65261	−	2.86241i	0.0767207	−	0.132884i
$465$	2.10957	+	3.65388i	0.0978288	+	0.169444i
$466$	0.158228	+	0.274059i	0.00732977	+	0.0126955i
$467$	7.68279	−	13.3070i	0.355517	−	0.615774i	−0.631689	−	0.775222i	$-0.717638\pi$
$467$	7.68279	−	13.3070i	0.355517	−	0.615774i	0.987206	+	0.159448i	$0.0509714\pi$
$468$		0			0
$469$	−19.2455	−	8.37816i	−0.888674	−	0.386868i
$470$	−0.200130			−0.00923129
$471$	1.04530	−	1.81051i	0.0481647	−	0.0834237i
$472$	−10.6907	−	18.5168i	−0.492078	−	0.852304i
$473$	−17.7116	−	30.6773i	−0.814378	−	1.41054i
$474$	5.86555	−	10.1594i	0.269413	−	0.466638i
$475$	−20.3355			−0.933059
$476$	−0.577048	−	5.08442i	−0.0264490	−	0.233044i
$477$	−3.28765			−0.150531
$478$	−15.2668	+	26.4428i	−0.698287	+	1.20947i
$479$	6.57241	+	11.3838i	0.300301	+	0.520137i	0.976204	−	0.216854i	$-0.0695794\pi$
$479$	6.57241	+	11.3838i	0.300301	+	0.520137i	−0.675903	+	0.736991i	$0.736246\pi$
$480$	−0.495289	−	0.857866i	−0.0226068	−	0.0391560i
$481$		0			0
$482$	32.2983			1.47115
$483$	−3.57843	+	2.64549i	−0.162824	+	0.120374i
$484$	7.61622			0.346192
$485$	−2.07234	+	3.58940i	−0.0941003	+	0.162986i
$486$	−8.75271	−	15.1601i	−0.397031	−	0.687678i
$487$	−13.4890	−	23.3637i	−0.611245	−	1.05871i	−0.991031	−	0.133633i	$-0.957336\pi$
$487$	−13.4890	−	23.3637i	−0.611245	−	1.05871i	0.379785	−	0.925075i	$-0.375998\pi$
$488$	−4.15072	+	7.18926i	−0.187894	+	0.325442i
$489$	17.2754			0.781220
$490$	−3.60155	+	0.828171i	−0.162701	+	0.0374130i
$491$	27.0835			1.22226			0.611131	−	0.791530i	$-0.290715\pi$
$491$	27.0835			1.22226			0.611131	+	0.791530i	$0.290715\pi$
$492$	0.967640	−	1.67600i	0.0436246	−	0.0755600i
$493$	−1.80456	−	3.12560i	−0.0812734	−	0.140770i
$494$		0			0
$495$	1.11032	−	1.92314i	0.0499053	−	0.0864386i
$496$	42.1216			1.89131
$497$	−30.8727	+	22.8238i	−1.38483	+	1.02379i
$498$	−20.8790			−0.935608
$499$	17.1065	−	29.6293i	0.765792	−	1.32639i	−0.174036	−	0.984739i	$-0.555681\pi$
$499$	17.1065	−	29.6293i	0.765792	−	1.32639i	0.939827	−	0.341650i	$-0.110986\pi$
$500$	−0.647875	−	1.12215i	−0.0289738	−	0.0501841i
$501$	−16.0319	−	27.7680i	−0.716251	−	1.24058i
$502$	9.07801	−	15.7236i	0.405172	−	0.701778i
$503$	−4.68225			−0.208771			−0.104386	−	0.994537i	$-0.533288\pi$
$503$	−4.68225			−0.208771			−0.104386	+	0.994537i	$0.533288\pi$
$504$	0.870375	+	7.66894i	0.0387696	+	0.341602i
$505$	−4.50068			−0.200277
$506$	5.33049	−	9.23268i	0.236969	−	0.410443i
$507$		0			0
$508$	−1.70266	−	2.94910i	−0.0755435	−	0.130845i
$509$	10.9941	−	19.0423i	0.487303	−	0.844034i	−0.512590	−	0.858633i	$-0.671314\pi$
$509$	10.9941	−	19.0423i	0.487303	−	0.844034i	0.999893	+	0.0145995i	$0.00464733\pi$
$510$	−3.60382			−0.159580
$511$	18.0763	+	7.86918i	0.799648	+	0.348112i
$512$	13.1704			0.582053
$513$	−11.7466	+	20.3457i	−0.518625	+	0.898284i
$514$	−0.923423	−	1.59941i	−0.0407304	−	0.0705472i
$515$	2.54059	+	4.40043i	0.111952	+	0.193906i
$516$	−1.65398	+	2.86478i	−0.0728125	+	0.126115i
$517$	2.10604			0.0926233
$518$	−5.72639	−	2.49288i	−0.251603	−	0.109531i
$519$	−3.17024			−0.139158
$520$		0			0
$521$	7.64007	+	13.2330i	0.334718	+	0.579748i	0.983431	−	0.181285i	$-0.0580257\pi$
$521$	7.64007	+	13.2330i	0.334718	+	0.579748i	−0.648713	+	0.761033i	$0.724692\pi$
$522$	−0.645521	−	1.11808i	−0.0282537	−	0.0489368i
$523$	13.9941	−	24.2385i	0.611918	−	1.05987i	−0.378998	−	0.925397i	$-0.623731\pi$
$523$	13.9941	−	24.2385i	0.611918	−	1.05987i	0.990917	−	0.134477i	$-0.0429353\pi$
$524$	−8.47211			−0.370106
$525$	−1.97148	−	17.3709i	−0.0860426	−	0.758128i
$526$	−3.72556			−0.162442
$527$	22.9972	−	39.8323i	1.00177	−	1.73512i
$528$	17.3655	+	30.0780i	0.755737	+	1.30897i
$529$	10.7275	+	18.5806i	0.466413	+	0.807851i
$530$	−0.742458	+	1.28597i	−0.0322503	+	0.0558591i
$531$	−10.0138			−0.434560
$532$	−3.39688	+	2.51126i	−0.147273	+	0.108877i
$533$		0			0
$534$	16.8414	−	29.1702i	0.728799	−	1.26232i
$535$	0.841932	+	1.45827i	0.0363999	+	0.0630464i
$536$	9.90002	+	17.1473i	0.427616	+	0.740652i
$537$	0.106721	−	0.184846i	0.00460535	−	0.00797669i
$538$	−31.4156			−1.35442
$539$	37.9004	−	8.71515i	1.63248	−	0.375388i
$540$	−0.739618			−0.0318281
$541$	20.4614	−	35.4403i	0.879706	−	1.52370i	0.0280422	−	0.999607i	$-0.491073\pi$
$541$	20.4614	−	35.4403i	0.879706	−	1.52370i	0.851664	−	0.524089i	$-0.175594\pi$
$542$	22.0306	+	38.1581i	0.946294	+	1.63903i
$543$	9.46919	+	16.4011i	0.406362	+	0.703839i
$544$	−5.39934	+	9.35193i	−0.231495	+	0.400961i
$545$	−4.44930			−0.190587
$546$		0			0
$547$	35.7420			1.52822			0.764108	−	0.645088i	$-0.223179\pi$
$547$	35.7420			1.52822			0.764108	+	0.645088i	$0.223179\pi$
$548$	0.651334	−	1.12814i	0.0278236	−	0.0481919i
$549$	1.94395	+	3.36702i	0.0829659	+	0.143701i
$550$	20.9409	+	36.2706i	0.892921	+	1.54658i
$551$	−1.48975	+	2.58032i	−0.0634653	+	0.109925i
$552$	4.19785			0.178672
$553$	1.67541	+	14.7622i	0.0712456	+	0.627751i
$554$	−22.2128			−0.943732
$555$	−0.353778	+	0.612761i	−0.0150170	+	0.0260103i
$556$	0.904746	+	1.56707i	0.0383698	+	0.0664584i
$557$	−10.8495	−	18.7919i	−0.459709	−	0.796240i	0.539236	−	0.842155i	$-0.318713\pi$
$557$	−10.8495	−	18.7919i	−0.459709	−	0.796240i	−0.998945	+	0.0459146i	$0.985380\pi$
$558$	8.22647	−	14.2487i	0.348254	−	0.603194i
$559$		0			0
$560$	3.83238	+	1.66836i	0.161948	+	0.0705010i
$561$	37.9243			1.60117
$562$	11.7917	−	20.4238i	0.497402	−	0.861526i
$563$	9.71238	+	16.8223i	0.409328	+	0.708977i	0.994815	−	0.101705i	$-0.0324299\pi$
$563$	9.71238	+	16.8223i	0.409328	+	0.708977i	−0.585487	+	0.810682i	$0.699097\pi$
$564$	−0.0983354	−	0.170322i	−0.00414067	−	0.00717184i
$565$	1.19038	−	2.06179i	0.0500796	−	0.0867403i
$566$	−47.0806			−1.97895
$567$	−10.0119	−	4.35849i	−0.420460	−	0.183040i
$568$	36.2167			1.51962
$569$	−2.43643	+	4.22003i	−0.102141	+	0.176913i	−0.912566	−	0.408929i	$-0.865903\pi$
$569$	−2.43643	+	4.22003i	−0.102141	+	0.176913i	0.810426	+	0.585841i	$0.199236\pi$
$570$	1.48756	+	2.57653i	0.0623069	+	0.107919i
$571$	−6.54584	−	11.3377i	−0.273935	−	0.474469i	0.695931	−	0.718109i	$-0.254992\pi$
$571$	−6.54584	−	11.3377i	−0.273935	−	0.474469i	−0.969866	+	0.243640i	$0.921659\pi$
$572$		0			0
$573$	−21.4942			−0.897932
$574$	1.71820	+	15.1392i	0.0717164	+	0.631899i
$575$	6.06956			0.253118
$576$	3.46849	−	6.00759i	0.144520	−	0.250316i
$577$	1.52148	+	2.63528i	0.0633401	+	0.109708i	0.895956	−	0.444142i	$-0.146491\pi$
$577$	1.52148	+	2.63528i	0.0633401	+	0.109708i	−0.832616	+	0.553850i	$0.813158\pi$
$578$	6.52083	+	11.2944i	0.271231	+	0.469785i
$579$	11.3172	−	19.6020i	0.470329	−	0.814633i
$580$	−0.0938011			−0.00389488
$581$	21.2627	−	15.7192i	0.882125	−	0.652142i
$582$	−25.3203			−1.04956
$583$	7.81315	−	13.5328i	0.323588	−	0.560470i
$584$	−9.29859	−	16.1056i	−0.384778	−	0.666455i
$585$		0			0
$586$	15.4003	−	26.6741i	0.636180	−	1.10190i
$587$	−8.39535			−0.346513			−0.173257	−	0.984877i	$-0.555429\pi$
$587$	−8.39535			−0.346513			−0.173257	+	0.984877i	$0.555429\pi$
$588$	−2.47447	−	2.65820i	−0.102046	−	0.109622i
$589$	−37.9704			−1.56454
$590$	−2.26143	+	3.91691i	−0.0931015	+	0.161257i
$591$	−12.3199	−	21.3388i	−0.506775	−	0.877760i
$592$	3.53193	+	6.11748i	0.145161	+	0.251427i
$593$	−11.4526	+	19.8364i	−0.470301	+	0.814585i	−0.999423	−	0.0339605i	$-0.989188\pi$
$593$	−11.4526	+	19.8364i	−0.470301	+	0.814585i	0.529122	+	0.848546i	$0.322521\pi$
$594$	48.3850			1.98526
$595$	3.67006	−	2.71322i	0.150458	−	0.111231i
$596$	0.265718			0.0108842
$597$	15.5521	−	26.9369i	0.636503	−	1.10246i
$598$		0			0
$599$	9.33663	+	16.1715i	0.381484	+	0.660750i	0.991275	−	0.131812i	$-0.0420796\pi$
$599$	9.33663	+	16.1715i	0.381484	+	0.660750i	−0.609790	+	0.792563i	$0.708746\pi$
$600$	−8.24563	+	14.2819i	−0.336627	+	0.583054i
$601$	−13.7395			−0.560444			−0.280222	−	0.959935i	$-0.590408\pi$
$601$	−13.7395			−0.560444			−0.280222	+	0.959935i	$0.590408\pi$
$602$	−2.93691	−	25.8774i	−0.119700	−	1.05468i
$603$	9.27317			0.377633
$604$	−3.30477	+	5.72403i	−0.134469	+	0.232908i
$605$	3.39659	+	5.88307i	0.138091	+	0.239181i
$606$	−13.7475	−	23.8114i	−0.558455	−	0.967273i
$607$	19.7372	−	34.1859i	0.801109	−	1.38756i	−0.117778	−	0.993040i	$-0.537577\pi$
$607$	19.7372	−	34.1859i	0.801109	−	1.38756i	0.918887	−	0.394521i	$-0.129090\pi$
$608$	8.91478			0.361542
$609$	−2.34857	−	1.02241i	−0.0951688	−	0.0414300i
$610$	1.75603			0.0710995
$611$		0			0
$612$	1.13033	+	1.95779i	0.0456909	+	0.0791390i
$613$	16.0394	+	27.7811i	0.647826	+	1.12207i	0.983641	+	0.180139i	$0.0576548\pi$
$613$	16.0394	+	27.7811i	0.647826	+	1.12207i	−0.335815	+	0.941928i	$0.609012\pi$
$614$	3.07349	−	5.32344i	0.124036	−	0.214837i
$615$	1.72614			0.0696049
$616$	−33.6357	−	14.6427i	−1.35522	−	0.589970i
$617$	−12.2636			−0.493713			−0.246857	−	0.969052i	$-0.579398\pi$
$617$	−12.2636			−0.493713			−0.246857	+	0.969052i	$0.579398\pi$
$618$	−15.5207	+	26.8826i	−0.624334	+	1.08138i
$619$	1.69129	+	2.92940i	0.0679786	+	0.117742i	0.898011	−	0.439972i	$-0.145012\pi$
$619$	1.69129	+	2.92940i	0.0679786	+	0.117742i	−0.830033	+	0.557715i	$0.811678\pi$
$620$	−0.597697	−	1.03524i	−0.0240041	−	0.0415763i
$621$	3.50601	−	6.07258i	0.140691	−	0.243684i
$622$	33.0089			1.32354
$623$	4.81051	+	42.3858i	0.192729	+	1.69815i
$624$		0			0
$625$	−11.6298	+	20.1434i	−0.465191	+	0.805735i
$626$	5.46966	+	9.47373i	0.218612	+	0.378647i
$627$	−15.6541	−	27.1137i	−0.625165	−	1.08282i
$628$	−0.296160	+	0.512965i	−0.0118181	+	0.0204695i
$629$	7.71333			0.307551
$630$	1.31284	−	0.970563i	0.0523048	−	0.0386682i
$631$	−17.4166			−0.693346			−0.346673	−	0.937986i	$-0.612689\pi$
$631$	−17.4166			−0.693346			−0.346673	+	0.937986i	$0.612689\pi$
$632$	7.00732	−	12.1370i	0.278736	−	0.482785i
$633$	7.03267	+	12.1809i	0.279524	+	0.484149i
$634$	11.1271	+	19.2727i	0.441913	+	0.765417i
$635$	1.51867	−	2.63041i	0.0602665	−	0.104385i
$636$	−1.45925			−0.0578631
$637$		0			0
$638$	6.13636			0.242941
$639$	8.48088	−	14.6893i	0.335498	−	0.581100i
$640$	−2.29862	−	3.98133i	−0.0908610	−	0.157376i
$641$	18.7203	+	32.4245i	0.739407	+	1.28069i	0.952763	+	0.303716i	$0.0982274\pi$
$641$	18.7203	+	32.4245i	0.739407	+	1.28069i	−0.213356	+	0.976975i	$0.568439\pi$
$642$	−5.14344	+	8.90870i	−0.202995	+	0.351598i
$643$	−13.8498			−0.546183			−0.273092	−	0.961988i	$-0.588046\pi$
$643$	−13.8498			−0.546183			−0.273092	+	0.961988i	$0.588046\pi$
$644$	1.01387	−	0.749537i	0.0399519	−	0.0295359i
$645$	−2.95049			−0.116175
$646$	16.2164	−	28.0877i	0.638027	−	1.10510i
$647$	12.7593	+	22.0998i	0.501622	+	0.868834i	0.999998	+	0.00187362i	$0.000596393\pi$
$647$	12.7593	+	22.0998i	0.501622	+	0.868834i	−0.498377	+	0.866961i	$0.666070\pi$
$648$	5.15020	+	8.92040i	0.202319	+	0.350426i
$649$	23.7978	−	41.2190i	0.934146	−	1.61799i
$650$		0			0
$651$	−3.68114	−	32.4348i	−0.144275	−	1.27122i
$652$	−4.89458			−0.191687
$653$	11.5767	−	20.0515i	0.453033	−	0.784676i	−0.545540	−	0.838085i	$-0.683675\pi$
$653$	11.5767	−	20.0515i	0.453033	−	0.784676i	0.998573	+	0.0534086i	$0.0170086\pi$
$654$	−13.5906	−	23.5396i	−0.531435	−	0.920472i
$655$	−3.77829	−	6.54419i	−0.147630	−	0.255703i
$656$	8.61645	−	14.9241i	0.336416	−	0.582690i
$657$	−8.70982			−0.339802
$658$	1.41969	+	0.618036i	0.0553453	+	0.0240936i
$659$	−7.95017			−0.309695			−0.154847	−	0.987938i	$-0.549489\pi$
$659$	−7.95017			−0.309695			−0.154847	+	0.987938i	$0.549489\pi$
$660$	0.492826	−	0.853600i	0.0191832	−	0.0332263i
$661$	5.40752	+	9.36609i	0.210328	+	0.364299i	0.951817	−	0.306666i	$-0.0992135\pi$
$661$	5.40752	+	9.36609i	0.210328	+	0.364299i	−0.741489	+	0.670965i	$0.765880\pi$
$662$	−14.3197	−	24.8025i	−0.556552	−	0.963977i
$663$		0			0
$664$	−24.9432			−0.967983
$665$	−3.45470	−	1.50394i	−0.133967	−	0.0583202i
$666$	2.75918			0.106916
$667$	0.444645	−	0.770148i	0.0172167	−	0.0298202i
$668$	4.54226	+	7.86742i	0.175745	+	0.304400i
$669$	−4.43276	−	7.67776i	−0.171380	−	0.296839i
$670$	2.09418	−	3.62723i	0.0809053	−	0.140132i
$671$	−18.4793			−0.713386
$672$	0.864267	+	7.61513i	0.0333398	+	0.293760i
$673$	−9.53857			−0.367685			−0.183842	−	0.982956i	$-0.558854\pi$
$673$	−9.53857			−0.367685			−0.183842	+	0.982956i	$0.558854\pi$
$674$	23.2575	−	40.2832i	0.895846	−	1.55165i
$675$	13.7734	+	23.8562i	0.530137	+	0.918224i
$676$		0			0
$677$	−12.7570	+	22.0958i	−0.490291	+	0.849209i	−0.999938	−	0.0111749i	$-0.996443\pi$
$677$	−12.7570	+	22.0958i	−0.490291	+	0.849209i	0.509647	+	0.860384i	$0.329776\pi$
$678$	14.5443			0.558569
$679$	25.7856	−	19.0630i	0.989562	−	0.731569i
$680$	−4.30533			−0.165102
$681$	−4.55925	+	7.89686i	−0.174711	+	0.302608i
$682$	39.1006	+	67.7243i	1.49724	+	2.59330i
$683$	−4.64395	−	8.04356i	−0.177696	−	0.307778i	0.763395	−	0.645932i	$-0.223531\pi$
$683$	−4.64395	−	8.04356i	−0.177696	−	0.307778i	−0.941091	+	0.338154i	$0.890198\pi$
$684$	0.933137	−	1.61624i	0.0356794	−	0.0617985i
$685$	1.16190			0.0443938
$686$	28.1064	+	5.24730i	1.07311	+	0.200343i
$687$	−6.41362			−0.244695
$688$	−14.7281	+	25.5098i	−0.561502	+	0.972550i
$689$		0			0
$690$	−0.443992	−	0.769016i	−0.0169025	−	0.0292759i
$691$	−0.613250	+	1.06218i	−0.0233291	+	0.0404072i	−0.877454	−	0.479660i	$-0.840760\pi$
$691$	−0.613250	+	1.06218i	−0.0233291	+	0.0404072i	0.854125	+	0.520068i	$0.174093\pi$
$692$	0.898215			0.0341450
$693$	−13.8155	+	10.2136i	−0.524807	+	0.387982i
$694$	36.6040			1.38947
$695$	−0.806975	+	1.39772i	−0.0306103	+	0.0530186i
$696$	1.20812	+	2.09253i	0.0457937	+	0.0793170i
$697$	−9.40869	−	16.2963i	−0.356379	−	0.617267i
$698$	−14.2581	+	24.6958i	−0.539678	+	0.934749i
$699$	−0.277380			−0.0104915
$700$	0.558574	+	4.92164i	0.0211121	+	0.186020i
$701$	−14.4024			−0.543973			−0.271986	−	0.962301i	$-0.587681\pi$
$701$	−14.4024			−0.543973			−0.271986	+	0.962301i	$0.587681\pi$
$702$		0			0
$703$	−3.18385	−	5.51459i	−0.120081	−	0.207987i
$704$	16.4858	+	28.5543i	0.621332	+	1.07618i
$705$	0.0877089	−	0.151916i	0.00330331	−	0.00572149i
$706$	12.0729			0.454370
$707$	31.9272	+	13.8989i	1.20074	+	0.522722i
$708$	−4.44469			−0.167042
$709$	−17.6166	+	30.5129i	−0.661607	+	1.14594i	0.318586	+	0.947894i	$0.396792\pi$
$709$	−17.6166	+	30.5129i	−0.661607	+	1.14594i	−0.980193	+	0.198043i	$0.936541\pi$
$710$	−3.83051	−	6.63464i	−0.143756	−	0.248994i
$711$	−3.28181	−	5.68427i	−0.123078	−	0.213177i
$712$	20.1197	−	34.8484i	0.754018	−	1.30600i
$713$	11.3330			0.424425
$714$	25.5650	+	11.1293i	0.956747	+	0.416502i
$715$		0			0
$716$	−0.0302369	+	0.0523718i	−0.00113001	+	0.00195723i
$717$	−13.3817	−	23.1777i	−0.499747	−	0.865587i
$718$	14.2338	+	24.6536i	0.531200	+	0.920066i
$719$	12.0874	−	20.9360i	0.450784	−	0.780781i	−0.547651	−	0.836707i	$-0.684478\pi$
$719$	12.0874	−	20.9360i	0.450784	−	0.780781i	0.998435	+	0.0559262i	$0.0178112\pi$
$720$	−1.84658			−0.0688180
$721$	−4.43326	−	39.0618i	−0.165103	−	1.45474i
$722$	2.55790			0.0951953
$723$	−14.1551	+	24.5173i	−0.526433	+	0.911809i
$724$	−2.68287	−	4.64687i	−0.0997082	−	0.172700i
$725$	1.74679	+	3.02553i	0.0648741	+	0.112365i
$726$	−20.7501	+	35.9402i	−0.770108	+	1.33387i
$727$	−24.4973			−0.908556			−0.454278	−	0.890860i	$-0.650103\pi$
$727$	−24.4973			−0.908556			−0.454278	+	0.890860i	$0.650103\pi$
$728$		0			0
$729$	27.7254			1.02687
$730$	−1.96696	+	3.40687i	−0.0728003	+	0.126094i
$731$	16.0822	+	27.8552i	0.594822	+	1.03026i
$732$	0.862840	+	1.49448i	0.0318915	+	0.0552376i
$733$	−1.81657	+	3.14640i	−0.0670967	+	0.116215i	−0.897622	−	0.440766i	$-0.854707\pi$
$733$	−1.81657	+	3.14640i	−0.0670967	+	0.116215i	0.830525	+	0.556981i	$0.188040\pi$
$734$	2.79038			0.102995
$735$	0.949759	−	3.09685i	0.0350324	−	0.114229i
$736$	−2.66080			−0.0980783
$737$	−22.0378	+	38.1706i	−0.811774	+	1.40603i
$738$	−3.36564	−	5.82946i	−0.123891	−	0.214585i
$739$	13.9473	+	24.1574i	0.513059	+	0.888644i	0.999885	+	0.0151450i	$0.00482099\pi$
$739$	13.9473	+	24.1574i	0.513059	+	0.888644i	−0.486827	+	0.873499i	$0.661846\pi$
$740$	0.100235	−	0.173612i	0.00368470	−	0.00638209i
$741$		0			0
$742$	9.23821	−	6.82968i	0.339145	−	0.250725i
$743$	−6.29101			−0.230795			−0.115397	−	0.993319i	$-0.536814\pi$
$743$	−6.29101			−0.230795			−0.115397	+	0.993319i	$0.536814\pi$
$744$	−15.3962	+	26.6670i	−0.564452	+	0.977659i
$745$	0.118502	+	0.205251i	0.00434156	+	0.00751981i
$746$	−8.14878	−	14.1141i	−0.298348	−	0.516754i
$747$	−5.84096	+	10.1168i	−0.213709	+	0.370156i
$748$	−10.7450			−0.392875
$749$	−1.46915	−	12.9448i	−0.0536816	−	0.472992i
$750$	7.06043			0.257811
$751$	−16.4460	+	28.4853i	−0.600124	+	1.03944i	0.392678	+	0.919676i	$0.371549\pi$
$751$	−16.4460	+	28.4853i	−0.600124	+	1.03944i	−0.992802	+	0.119769i	$0.961785\pi$
$752$	−0.875638	−	1.51665i	−0.0319312	−	0.0553065i
$753$	7.95707	+	13.7820i	0.289972	+	0.502246i
$754$		0			0
$755$	−5.89529			−0.214552
$756$	5.24675	+	2.28408i	0.190822	+	0.0830710i
$757$	−40.5203			−1.47273			−0.736367	−	0.676582i	$-0.763460\pi$
$757$	−40.5203			−1.47273			−0.736367	+	0.676582i	$0.763460\pi$
$758$	−9.22330	+	15.9752i	−0.335005	+	0.580246i
$759$	4.67228	+	8.09263i	0.169593	+	0.293744i
$760$	1.77712	+	3.07806i	0.0644630	+	0.111653i
$761$	19.0327	−	32.9656i	0.689935	−	1.19500i	−0.281924	−	0.959437i	$-0.590973\pi$
$761$	19.0327	−	32.9656i	0.689935	−	1.19500i	0.971859	−	0.235565i	$-0.0756941\pi$
$762$	18.5554			0.672190
$763$	31.5627	+	13.7403i	1.14265	+	0.497430i
$764$	6.08987			0.220324
$765$	−1.00818	+	1.74622i	−0.0364509	+	0.0631348i
$766$	4.38908	+	7.60211i	0.158584	+	0.274675i
$767$		0			0
$768$	6.01155	−	10.4123i	0.216923	−	0.375722i
$769$	8.24161			0.297200			0.148600	−	0.988897i	$-0.452523\pi$
$769$	8.24161			0.297200			0.148600	+	0.988897i	$0.452523\pi$
$770$	0.875094	+	7.71052i	0.0315362	+	0.277868i
$771$	1.61880			0.0582996
$772$	−3.20648	+	5.55378i	−0.115404	+	0.199885i
$773$	9.55303	+	16.5463i	0.343599	+	0.595131i	0.985098	−	0.171993i	$-0.0550206\pi$
$773$	9.55303	+	16.5463i	0.343599	+	0.595131i	−0.641499	+	0.767124i	$0.721687\pi$
$774$	5.75287	+	9.96426i	0.206783	+	0.358158i
$775$	−22.2609	+	38.5571i	−0.799636	+	1.38501i
$776$	−30.2491			−1.08588
$777$	4.40197	−	3.25431i	0.157920	−	0.116748i
$778$	−6.49582			−0.232887
$779$	−7.76728	+	13.4533i	−0.278292	+	0.482016i
$780$		0			0
$781$	40.3098	+	69.8187i	1.44240	+	2.49831i
$782$	−4.84012	+	8.38334i	−0.173083	+	0.299788i
$783$	4.03605			0.144237
$784$	−22.0342	−	23.6702i	−0.786936	−	0.845364i
$785$	−0.528312			−0.0188563
$786$	23.0819	−	39.9791i	0.823305	−	1.42601i
$787$	−0.0303444	−	0.0525580i	−0.00108166	−	0.00187349i	0.865484	−	0.500936i	$-0.167011\pi$
$787$	−0.0303444	−	0.0525580i	−0.00108166	−	0.00187349i	−0.866566	+	0.499063i	$0.833678\pi$
$788$	3.49057	+	6.04584i	0.124346	+	0.215374i
$789$	1.63277	−	2.82804i	0.0581280	−	0.100681i
$790$	−2.96456			−0.105474
$791$	−14.8116	+	10.9500i	−0.526639	+	0.389337i
$792$	16.2069			0.575887
$793$		0			0
$794$	0.586352	+	1.01559i	0.0208088	+	0.0360420i
$795$	−0.650779	−	1.12718i	−0.0230808	−	0.0399771i
$796$	−4.40631	+	7.63196i	−0.156178	+	0.270508i
$797$	−49.1593			−1.74131			−0.870656	−	0.491893i	$-0.836305\pi$
$797$	−49.1593			−1.74131			−0.870656	+	0.491893i	$0.836305\pi$
$798$	−2.59575	−	22.8714i	−0.0918886	−	0.809638i
$799$	−1.91230			−0.0676522
$800$	5.22648	−	9.05252i	0.184784	−	0.320055i
$801$	−9.42289	−	16.3209i	−0.332941	−	0.576671i
$802$	−13.4482	−	23.2930i	−0.474873	−	0.822504i
$803$	20.6990	−	35.8517i	0.730452	−	1.26518i
$804$	4.11597			0.145159
$805$	1.03112	+	0.448881i	0.0363423	+	0.0158210i
$806$		0			0
$807$	13.7682	−	23.8473i	0.484664	−	0.839463i
$808$	−16.4236	−	28.4465i	−0.577780	−	1.00074i
$809$	11.3094	+	19.5885i	0.397617	+	0.688693i	0.993431	−	0.114429i	$-0.0365038\pi$
$809$	11.3094	+	19.5885i	0.397617	+	0.688693i	−0.595814	+	0.803122i	$0.703171\pi$
$810$	1.08944	−	1.88696i	0.0382789	−	0.0663010i
$811$	−20.3325			−0.713972			−0.356986	−	0.934110i	$-0.616196\pi$
$811$	−20.3325			−0.713972			−0.356986	+	0.934110i	$0.616196\pi$
$812$	0.665412	+	0.289675i	0.0233514	+	0.0101656i
$813$	−38.6205			−1.35448
$814$	−6.55724	+	11.3575i	−0.229831	+	0.398079i
$815$	−2.18283	−	3.78077i	−0.0764611	−	0.132434i
$816$	−15.7680	−	27.3110i	−0.551991	−	0.956077i
$817$	13.2766	−	22.9957i	0.464489	−	0.804518i
$818$	30.3888			1.06252
$819$		0			0
$820$	−0.489063			−0.0170788
$821$	18.6872	−	32.3672i	0.652187	−	1.12962i	−0.330404	−	0.943840i	$-0.607185\pi$
$821$	18.6872	−	32.3672i	0.652187	−	1.12962i	0.982591	−	0.185782i	$-0.0594818\pi$
$822$	3.54907	+	6.14717i	0.123788	+	0.214407i
$823$	−13.9417	−	24.1478i	−0.485979	−	0.841740i	0.513891	−	0.857855i	$-0.328203\pi$
$823$	−13.9417	−	24.1478i	−0.485979	−	0.841740i	−0.999870	+	0.0161154i	$0.994870\pi$
$824$	−18.5419	+	32.1155i	−0.645938	+	1.11880i
$825$	−36.7102			−1.27808
$826$	28.1384	−	20.8023i	0.979060	−	0.723805i
$827$	−3.32489			−0.115618			−0.0578089	−	0.998328i	$-0.518411\pi$
$827$	−3.32489			−0.115618			−0.0578089	+	0.998328i	$0.518411\pi$
$828$	−0.278514	+	0.482400i	−0.00967902	+	0.0167646i
$829$	−5.81954	−	10.0797i	−0.202121	−	0.350084i	0.747091	−	0.664722i	$-0.231450\pi$
$829$	−5.81954	−	10.0797i	−0.202121	−	0.350084i	−0.949212	+	0.314638i	$0.898117\pi$
$830$	2.63815	+	4.56941i	0.0915716	+	0.158607i
$831$	9.73500	−	16.8615i	0.337703	−	0.584919i
$832$		0			0
$833$	−34.4138	+	7.91342i	−1.19237	+	0.274184i
$834$	−9.85978			−0.341416
$835$	−4.05140	+	7.01723i	−0.140205	+	0.242841i
$836$	4.43523	+	7.68204i	0.153396	+	0.265689i
$837$	25.7175	+	44.5441i	0.888928	+	1.53967i
$838$	−7.39233	+	12.8039i	−0.255364	+	0.442303i
$839$	23.5833			0.814186			0.407093	−	0.913387i	$-0.366542\pi$
$839$	23.5833			0.814186			0.407093	+	0.913387i	$0.366542\pi$
$840$	−2.45704	+	1.81645i	−0.0847758	+	0.0626735i
$841$	−28.4881			−0.982349
$842$	16.2441	−	28.1357i	0.559810	−	0.969619i
$843$	10.3357	+	17.9019i	0.355979	+	0.616574i
$844$	−1.99254	−	3.45119i	−0.0685862	−	0.118795i
$845$		0			0
$846$	−0.684059			−0.0235184
$847$	−5.92697	−	52.2230i	−0.203653	−	1.79440i
$848$	−12.9941			−0.446218
$849$	20.6336	−	35.7384i	0.708143	−	1.22654i
$850$	−19.0145	−	32.9340i	−0.652190	−	1.12963i
$851$	0.950284	+	1.64594i	0.0325753	+	0.0564221i
$852$	3.76431	−	6.51997i	0.128963	−	0.223371i
$853$	48.5012			1.66065			0.830325	−	0.557279i	$-0.188155\pi$
$853$	48.5012			1.66065			0.830325	+	0.557279i	$0.188155\pi$
$854$	−12.4570	−	5.42293i	−0.426271	−	0.185569i
$855$	1.66460			0.0569280
$856$	−6.14465	+	10.6428i	−0.210020	+	0.363765i
$857$	19.0242	+	32.9509i	0.649855	+	1.12558i	0.983157	+	0.182762i	$0.0585037\pi$
$857$	19.0242	+	32.9509i	0.649855	+	1.12558i	−0.333302	+	0.942820i	$0.608163\pi$
$858$		0			0
$859$	−9.96344	+	17.2572i	−0.339948	+	0.588808i	−0.984423	−	0.175818i	$-0.943743\pi$
$859$	−9.96344	+	17.2572i	−0.339948	+	0.588808i	0.644474	+	0.764626i	$0.277076\pi$
$860$	0.835953			0.0285058
$861$	−12.2450	−	5.33065i	−0.417310	−	0.181668i
$862$	17.4298			0.593661
$863$	−8.46769	+	14.6665i	−0.288244	+	0.499252i	−0.973391	−	0.229152i	$-0.926405\pi$
$863$	−8.46769	+	14.6665i	−0.288244	+	0.499252i	0.685147	+	0.728405i	$0.259738\pi$
$864$	−6.03803	−	10.4582i	−0.205418	−	0.355794i
$865$	0.400575	+	0.693816i	0.0136200	+	0.0235905i
$866$	11.4955	−	19.9108i	0.390632	−	0.676595i
$867$	−11.4313			−0.388227
$868$	1.04297	+	9.18965i	0.0354006	+	0.311917i
$869$	31.1971			1.05829
$870$	0.255557	−	0.442638i	0.00866421	−	0.0150068i
$871$		0			0
$872$	−16.2361	−	28.1218i	−0.549824	−	0.952323i
$873$	−7.08344	+	12.2689i	−0.239738	+	0.415238i
$874$	7.99147			0.270316
$875$	−7.19020	+	5.31561i	−0.243073	+	0.179700i
$876$	−3.86593			−0.130618
$877$	−3.63251	+	6.29169i	−0.122661	+	0.212455i	−0.920816	−	0.389997i	$-0.872476\pi$
$877$	−3.63251	+	6.29169i	−0.122661	+	0.212455i	0.798155	+	0.602452i	$0.205809\pi$
$878$	12.8743	+	22.2989i	0.434486	+	0.752552i
$879$	13.4987	+	23.3804i	0.455299	+	0.788601i
$880$	4.38843	−	7.60098i	0.147934	−	0.256229i
$881$	−22.7537			−0.766593			−0.383297	−	0.923625i	$-0.625211\pi$
$881$	−22.7537			−0.766593			−0.383297	+	0.923625i	$0.625211\pi$
$882$	−12.3104	+	2.83076i	−0.414512	+	0.0953165i
$883$	−56.6808			−1.90746			−0.953731	−	0.300661i	$-0.902793\pi$
$883$	−56.6808			−1.90746			−0.953731	+	0.300661i	$0.902793\pi$
$884$		0			0
$885$	−1.98219	−	3.43325i	−0.0666305	−	0.115407i
$886$	−12.2462	−	21.2111i	−0.411420	−	0.712600i
$887$	6.52672	−	11.3046i	0.219146	−	0.379572i	−0.735401	−	0.677632i	$-0.763006\pi$
$887$	6.52672	−	11.3046i	0.219146	−	0.379572i	0.954547	+	0.298060i	$0.0963396\pi$
$888$	−5.16393			−0.173290
$889$	−18.8964	+	13.9698i	−0.633765	+	0.468533i
$890$	−8.51196			−0.285322
$891$	−11.4645	+	19.8571i	−0.384076	+	0.665239i
$892$	1.25592	+	2.17531i	0.0420513	+	0.0728349i
$893$	0.789342	+	1.36718i	0.0264143	+	0.0457510i
$894$	−0.723938	+	1.25390i	−0.0242121	+	0.0419366i
$895$	−0.0539387			−0.00180297
$896$	4.01104	+	35.3416i	0.133999	+	1.18068i
$897$		0			0
$898$	−17.3341	+	30.0235i	−0.578445	+	1.00190i
$899$	3.26159	+	5.64925i	0.108780	+	0.188413i
$900$	−1.09414	−	1.89511i	−0.0364714	−	0.0631703i
$901$	−7.09440	+	12.2879i	−0.236349	+	0.409368i
$902$	31.9939			1.06528
$903$	20.9304	+	9.11165i	0.696519	+	0.303217i
$904$	17.3754			0.577897
$905$	2.39295	−	4.14471i	0.0795444	−	0.137775i
$906$	−18.0074	−	31.1898i	−0.598257	−	1.03621i
$907$	−15.1268	−	26.2004i	−0.502278	−	0.869971i	−0.999997	−	0.00263256i	$-0.999162\pi$
$907$	−15.1268	−	26.2004i	−0.502278	−	0.869971i	0.497718	−	0.867339i	$-0.334171\pi$
$908$	1.29176	−	2.23739i	0.0428685	−	0.0742505i
$909$	−15.3837			−0.510244
$910$		0			0
$911$	26.8529			0.889677			0.444839	−	0.895611i	$-0.353261\pi$
$911$	26.8529			0.889677			0.444839	+	0.895611i	$0.353261\pi$
$912$	−13.0172	+	22.5464i	−0.431042	+	0.746587i
$913$	−27.7622	−	48.0856i	−0.918796	−	1.59140i
$914$	−2.92925	−	5.07361i	−0.0968910	−	0.167820i
$915$	−0.769598	+	1.33298i	−0.0254421	+	0.0440670i
$916$	1.81715			0.0600403
$917$	6.59302	+	58.0916i	0.217721	+	1.91835i
$918$	−43.9339			−1.45003
$919$	−1.43927	+	2.49290i	−0.0474773	+	0.0822330i	−0.888787	−	0.458320i	$-0.848451\pi$
$919$	−1.43927	+	2.49290i	−0.0474773	+	0.0822330i	0.841310	+	0.540553i	$0.181785\pi$
$920$	−0.530418	−	0.918711i	−0.0174874	−	0.0302890i
$921$	2.69398	+	4.66611i	0.0887696	+	0.153753i
$922$	3.62963	−	6.28670i	0.119535	−	0.207041i
$923$		0			0
$924$	−6.13212	+	4.53339i	−0.201732	+	0.149137i
$925$	−7.46639			−0.245493
$926$	−26.2588	+	45.4816i	−0.862918	+	1.49462i
$927$	8.68393	+	15.0410i	0.285218	+	0.494012i
$928$	−0.765765	−	1.32634i	−0.0251375	−	0.0435394i
$929$	15.3744	−	26.6292i	0.504417	−	0.873676i	−0.495570	−	0.868568i	$-0.665041\pi$
$929$	15.3744	−	26.6292i	0.504417	−	0.873676i	0.999987	−	0.00510770i	$-0.00162584\pi$
$930$	6.51360			0.213590
$931$	19.8627	+	21.3375i	0.650974	+	0.699307i
$932$	0.0785893			0.00257428
$933$	−14.4665	+	25.0567i	−0.473612	+	0.820320i
$934$	−11.8609	−	20.5437i	−0.388100	−	0.672209i
$935$	−4.79192	−	8.29984i	−0.156712	−	0.271434i
$936$		0			0
$937$	60.5164			1.97699			0.988493	−	0.151269i	$-0.0483360\pi$
$937$	60.5164			1.97699			0.988493	+	0.151269i	$0.0483360\pi$
$938$	−26.0574	+	19.2638i	−0.850803	+	0.628987i
$939$	−9.58855			−0.312910
$940$	−0.0248503	+	0.0430419i	−0.000810526	+	0.00140387i
$941$	−8.33919	−	14.4439i	−0.271850	−	0.470857i	0.697486	−	0.716599i	$-0.254302\pi$
$941$	−8.33919	−	14.4439i	−0.271850	−	0.470857i	−0.969335	+	0.245741i	$0.920969\pi$
$942$	−1.61375	−	2.79510i	−0.0525790	−	0.0910694i
$943$	2.31830	−	4.01542i	0.0754943	−	0.130760i
$944$	−39.5782			−1.28816
$945$	0.575573	+	5.07142i	0.0187234	+	0.164973i
$946$	−54.6871			−1.77803
$947$	−15.7963	+	27.3600i	−0.513311	+	0.889081i	0.486569	+	0.873642i	$0.338248\pi$
$947$	−15.7963	+	27.3600i	−0.513311	+	0.889081i	−0.999881	+	0.0154395i	$0.995085\pi$
$948$	−1.45666	−	2.52301i	−0.0473101	−	0.0819435i
$949$		0			0
$950$	−15.6973	+	27.1885i	−0.509287	+	0.882110i
$951$	−19.5063			−0.632534
$952$	30.5414	+	13.2957i	0.989854	+	0.430915i
$953$	8.57339			0.277719			0.138860	−	0.990312i	$-0.455656\pi$
$953$	8.57339			0.277719			0.138860	+	0.990312i	$0.455656\pi$
$954$	−2.53778	+	4.39556i	−0.0821637	+	0.142312i
$955$	2.71589	+	4.70406i	0.0878841	+	0.152220i
$956$	3.79138	+	6.56686i	0.122622	+	0.212388i
$957$	−2.68932	+	4.65804i	−0.0869335	+	0.150573i
$958$	20.2933			0.655647
$959$	−8.24234	−	3.58815i	−0.266159	−	0.115867i
$960$	2.74630			0.0886365
$961$	−26.0655	+	45.1467i	−0.840822	+	1.45635i
$962$		0			0
$963$	2.87779	+	4.98448i	0.0927355	+	0.160623i
$964$	4.01051	−	6.94641i	0.129170	−	0.223729i
$965$	−5.71994			−0.184132
$966$	0.774754	+	6.82642i	0.0249273	+	0.219637i
$967$	−2.85867			−0.0919287			−0.0459644	−	0.998943i	$-0.514636\pi$
$967$	−2.85867			−0.0919287			−0.0459644	+	0.998943i	$0.514636\pi$
$968$	−24.7892	+	42.9362i	−0.796757	+	1.38002i
$969$	14.2140	+	24.6195i	0.456621	+	0.790891i
$970$	3.19934	+	5.54141i	0.102724	+	0.177924i
$971$	12.1360	−	21.0202i	0.389463	−	0.674570i	−0.602914	−	0.797806i	$-0.705994\pi$
$971$	12.1360	−	21.0202i	0.389463	−	0.674570i	0.992377	+	0.123236i	$0.0393273\pi$
$972$	−4.34733			−0.139441
$973$	10.0410	−	7.42316i	0.321900	−	0.237976i
$974$	−41.6493			−1.33453
$975$		0			0
$976$	7.68325	+	13.3078i	0.245935	+	0.425972i
$977$	−9.68491	−	16.7747i	−0.309848	−	0.536672i	0.668481	−	0.743729i	$-0.266945\pi$
$977$	−9.68491	−	16.7747i	−0.309848	−	0.536672i	−0.978329	+	0.207057i	$0.933611\pi$
$978$	13.3351	−	23.0971i	0.426409	−	0.738562i
$979$	89.5745			2.86281
$980$	−0.269092	+	0.877420i	−0.00859583	+	0.0280282i
$981$	−15.2081			−0.485556
$982$	20.9061	−	36.2104i	0.667141	−	1.15552i
$983$	13.9809	+	24.2156i	0.445921	+	0.772358i	0.998116	−	0.0613574i	$-0.0195429\pi$
$983$	13.9809	+	24.2156i	0.445921	+	0.772358i	−0.552195	+	0.833715i	$0.686210\pi$
$984$	6.29894	+	10.9101i	0.200803	+	0.347801i
$985$	−3.11336	+	5.39251i	−0.0992000	+	0.171819i
$986$	−5.57186			−0.177444
$987$	−1.09134	+	0.806812i	−0.0347377	+	0.0256811i
$988$		0			0
$989$	−3.96266	+	6.86354i	−0.126005	+	0.218248i
$990$	−1.71415	−	2.96899i	−0.0544791	−	0.0943606i
$991$	12.3944	+	21.4678i	0.393722	+	0.681946i	0.992937	−	0.118642i	$-0.0378541\pi$
$991$	12.3944	+	21.4678i	0.393722	+	0.681946i	−0.599215	+	0.800588i	$0.704521\pi$
$992$	9.75884	−	16.9028i	0.309844	−	0.536665i
$993$	25.1031			0.796623
$994$	6.68414	+	58.8945i	0.212008	+	1.86802i
$995$	−7.86030			−0.249188
$996$	−2.59256	+	4.49044i	−0.0821483	+	0.142285i
$997$	30.5347	+	52.8876i	0.967042	+	1.67497i	0.704025	+	0.710175i	$0.251384\pi$
$997$	30.5347	+	52.8876i	0.967042	+	1.67497i	0.263017	+	0.964791i	$0.415283\pi$
$998$	−26.4094	−	45.7425i	−0.835976	−	1.44795i
$999$	−4.31287	+	7.47011i	−0.136453	+	0.236344i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1183.2.e.k.170.18	✓	48
7.2	even	3		8281.2.a.cv.1.7		24
7.4	even	3	inner	1183.2.e.k.508.18	yes	48
7.5	odd	6		8281.2.a.cw.1.7		24
13.12	even	2		1183.2.e.l.170.7	yes	48
91.12	odd	6		8281.2.a.ct.1.18		24
91.25	even	6		1183.2.e.l.508.7	yes	48
91.51	even	6		8281.2.a.cu.1.18		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1183.2.e.k.170.18	✓	48	1.1	even	1	trivial
1183.2.e.k.508.18	yes	48	7.4	even	3	inner
1183.2.e.l.170.7	yes	48	13.12	even	2
1183.2.e.l.508.7	yes	48	91.25	even	6
8281.2.a.ct.1.18		24	91.12	odd	6
8281.2.a.cu.1.18		24	91.51	even	6
8281.2.a.cv.1.7		24	7.2	even	3
8281.2.a.cw.1.7		24	7.5	odd	6

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:	\( N \)	\(=\)	\( 1183 = 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1183.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.771913 - 1.33699i) q^{2} +(0.676597 + 1.17190i) q^{3} +(-0.191698 - 0.332031i) q^{4} +(0.170982 - 0.296150i) q^{5} +2.08910 q^{6} +(-2.12749 + 1.57282i) q^{7} +2.49575 q^{8} +(0.584432 - 1.01227i) q^{9} +O(q^{10})\)	\(q+(0.771913 - 1.33699i) q^{2} +(0.676597 + 1.17190i) q^{3} +(-0.191698 - 0.332031i) q^{4} +(0.170982 - 0.296150i) q^{5} +2.08910 q^{6} +(-2.12749 + 1.57282i) q^{7} +2.49575 q^{8} +(0.584432 - 1.01227i) q^{9} +(-0.263967 - 0.457204i) q^{10} +(2.77782 + 4.81133i) q^{11} +(0.259405 - 0.449303i) q^{12} +(0.460616 + 4.05852i) q^{14} +0.462745 q^{15} +(2.30990 - 4.00086i) q^{16} +(-2.52228 - 4.36872i) q^{17} +(-0.902261 - 1.56276i) q^{18} +(-2.08225 + 3.60657i) q^{19} -0.131108 q^{20} +(-3.28265 - 1.42904i) q^{21} +8.57694 q^{22} +(0.621491 - 1.07645i) q^{23} +(1.68862 + 2.92478i) q^{24} +(2.44153 + 4.22885i) q^{25} +5.64128 q^{27} +(0.930063 + 0.404886i) q^{28} +0.715449 q^{29} +(0.357199 - 0.618687i) q^{30} +(4.55881 + 7.89609i) q^{31} +(-1.07033 - 1.85386i) q^{32} +(-3.75893 + 6.51066i) q^{33} -7.78792 q^{34} +(0.102029 + 0.898983i) q^{35} -0.448138 q^{36} +(-0.764519 + 1.32419i) q^{37} +(3.21464 + 5.56792i) q^{38} +(0.426730 - 0.739118i) q^{40} +3.73023 q^{41} +(-4.44454 + 3.28578i) q^{42} -6.37606 q^{43} +(1.06501 - 1.84464i) q^{44} +(-0.199855 - 0.346159i) q^{45} +(-0.959473 - 1.66186i) q^{46} +(0.189540 - 0.328293i) q^{47} +6.25149 q^{48} +(2.05245 - 6.69234i) q^{49} +7.53859 q^{50} +(3.41314 - 5.91173i) q^{51} +(-1.40635 - 2.43586i) q^{53} +(4.35458 - 7.54235i) q^{54} +1.89983 q^{55} +(-5.30970 + 3.92538i) q^{56} -5.63539 q^{57} +(0.552264 - 0.956549i) q^{58} +(-4.28354 - 7.41931i) q^{59} +(-0.0887074 - 0.153646i) q^{60} +(-1.66311 + 2.88060i) q^{61} +14.0760 q^{62} +(0.348742 + 3.07280i) q^{63} +5.93480 q^{64} +(5.80313 + 10.0513i) q^{66} +(3.96675 + 6.87061i) q^{67} +(-0.967033 + 1.67495i) q^{68} +1.68200 q^{69} +(1.28069 + 0.557525i) q^{70} +14.5113 q^{71} +(1.45860 - 2.52637i) q^{72} +(-3.72576 - 6.45321i) q^{73} +(1.18028 + 2.04431i) q^{74} +(-3.30387 + 5.72246i) q^{75} +1.59666 q^{76} +(-13.4772 - 5.86703i) q^{77} +(2.80770 - 4.86307i) q^{79} +(-0.789905 - 1.36816i) q^{80} +(2.06358 + 3.57423i) q^{81} +(2.87941 - 4.98728i) q^{82} -9.99425 q^{83} +(0.154792 + 1.36389i) q^{84} -1.72506 q^{85} +(-4.92176 + 8.52474i) q^{86} +(0.484071 + 0.838435i) q^{87} +(6.93275 + 12.0079i) q^{88} +(8.06158 - 13.9631i) q^{89} -0.617083 q^{90} -0.476555 q^{92} +(-6.16896 + 10.6849i) q^{93} +(-0.292617 - 0.506828i) q^{94} +(0.712058 + 1.23332i) q^{95} +(1.44836 - 2.50864i) q^{96} -12.1202 q^{97} +(-7.36330 - 7.91001i) q^{98} +6.49379 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - q^{2} - 23 q^{4} + 13 q^{5} - 28 q^{6} - 3 q^{7} - 26 q^{9}+O(q^{10}) \) 48 * q - q^2 - 23 * q^4 + 13 * q^5 - 28 * q^6 - 3 * q^7 - 26 * q^9	\( 48 q - q^{2} - 23 q^{4} + 13 q^{5} - 28 q^{6} - 3 q^{7} - 26 q^{9} - 5 q^{10} - q^{11} - 5 q^{12} - 2 q^{14} - 10 q^{15} - 17 q^{16} + 5 q^{17} + 24 q^{19} - 68 q^{20} + q^{21} - 28 q^{22} - 11 q^{23} + 32 q^{24} - 33 q^{25} - 42 q^{27} + 15 q^{28} + 8 q^{29} + 22 q^{30} + 40 q^{31} - 6 q^{32} + 24 q^{33} - 72 q^{34} + 44 q^{35} - 30 q^{36} - 4 q^{37} + 29 q^{38} + 4 q^{40} - 98 q^{41} - 9 q^{42} + 26 q^{43} + 10 q^{44} + 58 q^{45} - 10 q^{46} + 62 q^{47} + 178 q^{48} + 31 q^{49} + 46 q^{50} + 21 q^{51} + 18 q^{53} + 12 q^{54} - 28 q^{55} - 56 q^{56} + 26 q^{57} + 56 q^{58} + 79 q^{59} + 22 q^{60} - 13 q^{61} + 24 q^{62} - 22 q^{63} + 36 q^{64} + 38 q^{66} - 2 q^{67} + 12 q^{68} - 56 q^{69} - 85 q^{70} + 38 q^{71} + 81 q^{72} + 17 q^{73} - 17 q^{74} - 24 q^{75} - 116 q^{76} - 30 q^{77} + 9 q^{79} + 63 q^{80} - 16 q^{81} + 22 q^{82} - 162 q^{83} - 203 q^{84} + 68 q^{85} + 22 q^{86} - 70 q^{87} + 33 q^{88} + 72 q^{89} + 2 q^{90} - 8 q^{92} + 19 q^{93} + 30 q^{94} - 13 q^{95} + 11 q^{96} - 90 q^{97} - 81 q^{98} + 78 q^{99}+O(q^{100}) \) 48 * q - q^2 - 23 * q^4 + 13 * q^5 - 28 * q^6 - 3 * q^7 - 26 * q^9 - 5 * q^10 - q^11 - 5 * q^12 - 2 * q^14 - 10 * q^15 - 17 * q^16 + 5 * q^17 + 24 * q^19 - 68 * q^20 + q^21 - 28 * q^22 - 11 * q^23 + 32 * q^24 - 33 * q^25 - 42 * q^27 + 15 * q^28 + 8 * q^29 + 22 * q^30 + 40 * q^31 - 6 * q^32 + 24 * q^33 - 72 * q^34 + 44 * q^35 - 30 * q^36 - 4 * q^37 + 29 * q^38 + 4 * q^40 - 98 * q^41 - 9 * q^42 + 26 * q^43 + 10 * q^44 + 58 * q^45 - 10 * q^46 + 62 * q^47 + 178 * q^48 + 31 * q^49 + 46 * q^50 + 21 * q^51 + 18 * q^53 + 12 * q^54 - 28 * q^55 - 56 * q^56 + 26 * q^57 + 56 * q^58 + 79 * q^59 + 22 * q^60 - 13 * q^61 + 24 * q^62 - 22 * q^63 + 36 * q^64 + 38 * q^66 - 2 * q^67 + 12 * q^68 - 56 * q^69 - 85 * q^70 + 38 * q^71 + 81 * q^72 + 17 * q^73 - 17 * q^74 - 24 * q^75 - 116 * q^76 - 30 * q^77 + 9 * q^79 + 63 * q^80 - 16 * q^81 + 22 * q^82 - 162 * q^83 - 203 * q^84 + 68 * q^85 + 22 * q^86 - 70 * q^87 + 33 * q^88 + 72 * q^89 + 2 * q^90 - 8 * q^92 + 19 * q^93 + 30 * q^94 - 13 * q^95 + 11 * q^96 - 90 * q^97 - 81 * q^98 + 78 * q^99

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