LMFDB - Embedded newform 1183.2.e.i.508.7

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:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 11x^{14} + 85x^{12} + 334x^{10} + 952x^{8} + 1050x^{6} + 853x^{4} + 93x^{2} + 9 $ x^16 + 11x^14 + 85x^12 + 334x^10 + 952x^8 + 1050x^6 + 853x^4 + 93*x^2 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			508.7
Root			$1.06275 - 1.84073i$ of defining polynomial
Character	$\chi$	$=$	1183.508
Dual form			1183.2.e.i.170.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.06275 + 1.84073i) q^{2} +(0.0894272 - 0.154892i) q^{3} +(-1.25885 + 2.18040i) q^{4} +(-1.80301 - 3.12291i) q^{5} +0.380153 q^{6} +(-2.35320 - 1.20931i) q^{7} -1.10038 q^{8} +(1.48401 + 2.57037i) q^{9} +O(q^{10})$	\(q+(1.06275 + 1.84073i) q^{2} +(0.0894272 - 0.154892i) q^{3} +(-1.25885 + 2.18040i) q^{4} +(-1.80301 - 3.12291i) q^{5} +0.380153 q^{6} +(-2.35320 - 1.20931i) q^{7} -1.10038 q^{8} +(1.48401 + 2.57037i) q^{9} +(3.83229 - 6.63772i) q^{10} +(-1.99618 + 3.45748i) q^{11} +(0.225152 + 0.389974i) q^{12} +(-0.274848 - 5.61680i) q^{14} -0.644954 q^{15} +(1.34828 + 2.33529i) q^{16} +(-2.39458 + 4.14753i) q^{17} +(-3.15424 + 5.46330i) q^{18} +(1.57530 + 2.72850i) q^{19} +9.07892 q^{20} +(-0.397753 + 0.256349i) q^{21} -8.48572 q^{22} +(1.08943 + 1.88694i) q^{23} +(-0.0984042 + 0.170441i) q^{24} +(-4.00171 + 6.93117i) q^{25} +1.06740 q^{27} +(5.59912 - 3.60858i) q^{28} -6.57198 q^{29} +(-0.685421 - 1.18718i) q^{30} +(-0.743358 + 1.28753i) q^{31} +(-3.96614 + 6.86956i) q^{32} +(0.357025 + 0.618386i) q^{33} -10.1793 q^{34} +(0.466298 + 9.52925i) q^{35} -7.47259 q^{36} +(-2.48252 - 4.29984i) q^{37} +(-3.34828 + 5.79939i) q^{38} +(1.98401 + 3.43640i) q^{40} -2.11931 q^{41} +(-0.894578 - 0.459722i) q^{42} +1.43145 q^{43} +(-5.02580 - 8.70494i) q^{44} +(5.35136 - 9.26883i) q^{45} +(-2.31557 + 4.01068i) q^{46} +(-0.509464 - 0.882417i) q^{47} +0.482292 q^{48} +(4.07515 + 5.69150i) q^{49} -17.0112 q^{50} +(0.428281 + 0.741804i) q^{51} +(-3.01771 + 5.22682i) q^{53} +(1.13438 + 1.96480i) q^{54} +14.3966 q^{55} +(2.58943 + 1.33070i) q^{56} +0.563498 q^{57} +(-6.98434 - 12.0972i) q^{58} +(2.45161 - 4.24631i) q^{59} +(0.811902 - 1.40626i) q^{60} +(1.01771 + 1.76272i) q^{61} -3.16000 q^{62} +(-0.383795 - 7.84323i) q^{63} -11.4669 q^{64} +(-0.758854 + 1.31437i) q^{66} +(-1.95545 + 3.38694i) q^{67} +(-6.02885 - 10.4423i) q^{68} +0.389698 q^{69} +(-17.0452 + 10.9855i) q^{70} -8.80684 q^{71} +(-1.63297 - 2.82840i) q^{72} +(-1.54439 + 2.67497i) q^{73} +(5.27656 - 9.13927i) q^{74} +(0.715724 + 1.23967i) q^{75} -7.93228 q^{76} +(8.87858 - 5.72217i) q^{77} +(-0.984006 - 1.70435i) q^{79} +(4.86194 - 8.42112i) q^{80} +(-4.35656 + 7.54579i) q^{81} +(-2.25229 - 3.90108i) q^{82} +7.66020 q^{83} +(-0.0582290 - 1.18997i) q^{84} +17.2698 q^{85} +(1.52126 + 2.63491i) q^{86} +(-0.587714 + 1.01795i) q^{87} +(2.19656 - 3.80456i) q^{88} +(6.39960 + 11.0844i) q^{89} +22.7485 q^{90} -5.48572 q^{92} +(0.132953 + 0.230281i) q^{93} +(1.08286 - 1.87557i) q^{94} +(5.68057 - 9.83903i) q^{95} +(0.709362 + 1.22865i) q^{96} +1.35900 q^{97} +(-6.14567 + 13.5499i) q^{98} -11.8494 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{3} - 6 q^{4} - 12 q^{9}+O(q^{10}) $ 16 * q - 4 * q^3 - 6 * q^4 - 12 * q^9	$ 16 q - 4 q^{3} - 6 q^{4} - 12 q^{9} + 6 q^{10} - 18 q^{12} - 26 q^{14} + 2 q^{16} - 8 q^{17} - 36 q^{22} + 12 q^{23} + 32 q^{27} - 16 q^{29} - 38 q^{30} + 56 q^{36} - 34 q^{38} - 4 q^{40} + 16 q^{42} - 16 q^{43} + 36 q^{48} - 40 q^{49} - 16 q^{51} - 20 q^{53} + 24 q^{55} + 36 q^{56} - 12 q^{61} - 44 q^{62} - 88 q^{64} + 2 q^{66} - 2 q^{68} + 56 q^{69} + 42 q^{74} - 8 q^{75} + 76 q^{77} + 20 q^{79} - 24 q^{81} + 16 q^{82} - 68 q^{87} - 4 q^{88} + 216 q^{90} + 12 q^{92} - 26 q^{94} + 16 q^{95}+O(q^{100}) $ 16 * q - 4 * q^3 - 6 * q^4 - 12 * q^9 + 6 * q^10 - 18 * q^12 - 26 * q^14 + 2 * q^16 - 8 * q^17 - 36 * q^22 + 12 * q^23 + 32 * q^27 - 16 * q^29 - 38 * q^30 + 56 * q^36 - 34 * q^38 - 4 * q^40 + 16 * q^42 - 16 * q^43 + 36 * q^48 - 40 * q^49 - 16 * q^51 - 20 * q^53 + 24 * q^55 + 36 * q^56 - 12 * q^61 - 44 * q^62 - 88 * q^64 + 2 * q^66 - 2 * q^68 + 56 * q^69 + 42 * q^74 - 8 * q^75 + 76 * q^77 + 20 * q^79 - 24 * q^81 + 16 * q^82 - 68 * q^87 - 4 * q^88 + 216 * q^90 + 12 * q^92 - 26 * q^94 + 16 * q^95

Display 100 coefficients 10 coefficients

Character values

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

$n$	$339$	$1016$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	1.06275	+	1.84073i	0.751474	+	1.30159i	0.947108	+	0.320915i	$0.103990\pi$
$2$	1.06275	+	1.84073i	0.751474	+	1.30159i	−0.195634	+	0.980677i	$0.562676\pi$
$3$	0.0894272	−	0.154892i	0.0516308	−	0.0894272i	−0.839055	−	0.544047i	$-0.816891\pi$
$3$	0.0894272	−	0.154892i	0.0516308	−	0.0894272i	0.890686	+	0.454620i	$0.150225\pi$
$4$	−1.25885	+	2.18040i	−0.629427	+	1.09020i
$5$	−1.80301	−	3.12291i	−0.806332	−	1.39661i	−0.915388	−	0.402572i	$-0.868116\pi$
$5$	−1.80301	−	3.12291i	−0.806332	−	1.39661i	0.109056	−	0.994036i	$-0.465217\pi$
$6$	0.380153			0.155197
$7$	−2.35320	−	1.20931i	−0.889428	−	0.457076i
$7$	−2.35320	−	1.20931i	−0.889428	−	0.457076i
$8$	−1.10038			−0.389044
$9$	1.48401	+	2.57037i	0.494669	+	0.856791i
$10$	3.83229	−	6.63772i	1.21188	−	2.09903i
$11$	−1.99618	+	3.45748i	−0.601871	+	1.04247i	0.390667	+	0.920532i	$0.372244\pi$
$11$	−1.99618	+	3.45748i	−0.601871	+	1.04247i	−0.992538	+	0.121939i	$0.961089\pi$
$12$	0.225152	+	0.389974i	0.0649957	+	0.112576i
$13$		0			0
$13$		0			0
$14$	−0.274848	−	5.61680i	−0.0734563	−	1.50115i
$15$	−0.644954			−0.166526
$16$	1.34828	+	2.33529i	0.337070	+	0.583823i
$17$	−2.39458	+	4.14753i	−0.580771	+	1.00592i	0.414618	+	0.909996i	$0.363915\pi$
$17$	−2.39458	+	4.14753i	−0.580771	+	1.00592i	−0.995388	+	0.0959284i	$0.969418\pi$
$18$	−3.15424	+	5.46330i	−0.743461	+	1.28771i
$19$	1.57530	+	2.72850i	0.361398	+	0.625960i	0.988191	−	0.153226i	$-0.0489662\pi$
$19$	1.57530	+	2.72850i	0.361398	+	0.625960i	−0.626793	+	0.779186i	$0.715633\pi$
$20$	9.07892			2.03011
$21$	−0.397753	+	0.256349i	−0.0867969	+	0.0559398i
$22$	−8.48572			−1.80916
$23$	1.08943	+	1.88694i	0.227161	+	0.393455i	0.956966	−	0.290201i	$-0.0937222\pi$
$23$	1.08943	+	1.88694i	0.227161	+	0.393455i	−0.729804	+	0.683656i	$0.760389\pi$
$24$	−0.0984042	+	0.170441i	−0.0200867	+	0.0347911i
$25$	−4.00171	+	6.93117i	−0.800343	+	1.38623i
$26$		0			0
$27$	1.06740			0.205422
$28$	5.59912	−	3.60858i	1.05813	−	0.681958i
$29$	−6.57198			−1.22039			−0.610193	−	0.792253i	$-0.708908\pi$
$29$	−6.57198			−1.22039			−0.610193	+	0.792253i	$0.708908\pi$
$30$	−0.685421	−	1.18718i	−0.125140	−	0.216749i
$31$	−0.743358	+	1.28753i	−0.133511	+	0.231248i	−0.925028	−	0.379900i	$-0.875958\pi$
$31$	−0.743358	+	1.28753i	−0.133511	+	0.231248i	0.791517	+	0.611148i	$0.209292\pi$
$32$	−3.96614	+	6.86956i	−0.701121	+	1.21438i
$33$	0.357025	+	0.618386i	0.0621502	+	0.107647i
$34$	−10.1793			−1.74574
$35$	0.466298	+	9.52925i	0.0788187	+	1.61074i
$36$	−7.47259			−1.24543
$37$	−2.48252	−	4.29984i	−0.408123	−	0.706890i	0.586556	−	0.809908i	$-0.300483\pi$
$37$	−2.48252	−	4.29984i	−0.408123	−	0.706890i	−0.994679	+	0.103019i	$0.967150\pi$
$38$	−3.34828	+	5.79939i	−0.543163	+	0.940786i
$39$		0			0
$40$	1.98401	+	3.43640i	0.313699	+	0.543342i
$41$	−2.11931			−0.330981			−0.165490	−	0.986211i	$-0.552921\pi$
$41$	−2.11931			−0.330981			−0.165490	+	0.986211i	$0.552921\pi$
$42$	−0.894578	−	0.459722i	−0.138036	−	0.0709367i
$43$	1.43145			0.218294			0.109147	−	0.994026i	$-0.465188\pi$
$43$	1.43145			0.218294			0.109147	+	0.994026i	$0.465188\pi$
$44$	−5.02580	−	8.70494i	−0.757667	−	1.31232i
$45$	5.35136	−	9.26883i	0.797734	−	1.38172i
$46$	−2.31557	+	4.01068i	−0.341412	+	0.591342i
$47$	−0.509464	−	0.882417i	−0.0743129	−	0.128714i	0.826474	−	0.562974i	$-0.190343\pi$
$47$	−0.509464	−	0.882417i	−0.0743129	−	0.128714i	−0.900787	+	0.434261i	$0.857010\pi$
$48$	0.482292			0.0696129
$49$	4.07515	+	5.69150i	0.582164	+	0.813072i
$50$	−17.0112			−2.40575
$51$	0.428281	+	0.741804i	0.0599713	+	0.103873i
$52$		0			0
$53$	−3.01771	+	5.22682i	−0.414514	+	0.717959i	−0.995377	−	0.0960417i	$-0.969382\pi$
$53$	−3.01771	+	5.22682i	−0.414514	+	0.717959i	0.580863	+	0.814001i	$0.302715\pi$
$54$	1.13438	+	1.96480i	0.154369	+	0.267376i
$55$	14.3966			1.94123
$56$	2.58943	+	1.33070i	0.346027	+	0.177823i
$57$	0.563498			0.0746371
$58$	−6.98434	−	12.0972i	−0.917089	−	1.58844i
$59$	2.45161	−	4.24631i	0.319172	−	0.552823i	−0.661143	−	0.750260i	$-0.729928\pi$
$59$	2.45161	−	4.24631i	0.319172	−	0.552823i	0.980316	+	0.197437i	$0.0632618\pi$
$60$	0.811902	−	1.40626i	0.104816	−	0.181547i
$61$	1.01771	+	1.76272i	0.130304	+	0.225693i	0.923794	−	0.382890i	$-0.125071\pi$
$61$	1.01771	+	1.76272i	0.130304	+	0.225693i	−0.793490	+	0.608584i	$0.791738\pi$
$62$	−3.16000			−0.401320
$63$	−0.383795	−	7.84323i	−0.0483537	−	0.988155i
$64$	−11.4669			−1.43336
$65$		0			0
$66$	−0.758854	+	1.31437i	−0.0934085	+	0.161788i
$67$	−1.95545	+	3.38694i	−0.238896	+	0.413781i	−0.960398	−	0.278632i	$-0.910119\pi$
$67$	−1.95545	+	3.38694i	−0.238896	+	0.413781i	0.721501	+	0.692413i	$0.243452\pi$
$68$	−6.02885	−	10.4423i	−0.731105	−	1.26631i
$69$	0.389698			0.0469141
$70$	−17.0452	+	10.9855i	−2.03729	+	1.31302i
$71$	−8.80684			−1.04518			−0.522590	−	0.852584i	$-0.675034\pi$
$71$	−8.80684			−1.04518			−0.522590	+	0.852584i	$0.675034\pi$
$72$	−1.63297	−	2.82840i	−0.192448	−	0.333330i
$73$	−1.54439	+	2.67497i	−0.180757	+	0.313081i	−0.942139	−	0.335223i	$-0.891188\pi$
$73$	−1.54439	+	2.67497i	−0.180757	+	0.313081i	0.761381	+	0.648304i	$0.224522\pi$
$74$	5.27656	−	9.13927i	0.613388	−	1.06242i
$75$	0.715724	+	1.23967i	0.0826447	+	0.143145i
$76$	−7.93228			−0.909895
$77$	8.87858	−	5.72217i	1.01181	−	0.652102i
$78$		0			0
$79$	−0.984006	−	1.70435i	−0.110709	−	0.191754i	0.805347	−	0.592803i	$-0.201979\pi$
$79$	−0.984006	−	1.70435i	−0.110709	−	0.191754i	−0.916056	+	0.401049i	$0.868646\pi$
$80$	4.86194	−	8.42112i	0.543581	−	0.941510i
$81$	−4.35656	+	7.54579i	−0.484062	+	0.838421i
$82$	−2.25229	−	3.90108i	−0.248724	−	0.430802i
$83$	7.66020			0.840816			0.420408	−	0.907335i	$-0.361887\pi$
$83$	7.66020			0.840816			0.420408	+	0.907335i	$0.361887\pi$
$84$	−0.0582290	−	1.18997i	−0.00635330	−	0.129836i
$85$	17.2698			1.87318
$86$	1.52126	+	2.63491i	0.164042	+	0.284129i
$87$	−0.587714	+	1.01795i	−0.0630095	+	0.109136i
$88$	2.19656	−	3.80456i	0.234154	−	0.405567i
$89$	6.39960	+	11.0844i	0.678356	+	1.17495i	0.975476	+	0.220107i	$0.0706406\pi$
$89$	6.39960	+	11.0844i	0.678356	+	1.17495i	−0.297120	+	0.954840i	$0.596026\pi$
$90$	22.7485			2.39791
$91$		0			0
$92$	−5.48572			−0.571926
$93$	0.132953	+	0.230281i	0.0137866	+	0.0238790i
$94$	1.08286	−	1.87557i	0.111689	−	0.193450i
$95$	5.68057	−	9.83903i	0.582814	−	1.00946i
$96$	0.709362	+	1.22865i	0.0723989	+	0.125399i
$97$	1.35900			0.137986			0.0689930	−	0.997617i	$-0.478021\pi$
$97$	1.35900			0.137986			0.0689930	+	0.997617i	$0.478021\pi$
$98$	−6.14567	+	13.5499i	−0.620806	+	1.36874i
$99$	−11.8494			−1.19091
$100$	−10.0751	−	17.4507i	−1.00751	−	1.74507i
$101$	−2.14400	+	3.71353i	−0.213336	+	0.369510i	−0.952757	−	0.303735i	$-0.901766\pi$
$101$	−2.14400	+	3.71353i	−0.213336	+	0.369510i	0.739420	+	0.673244i	$0.235100\pi$
$102$	−0.910307	+	1.57670i	−0.0901338	+	0.156116i
$103$	−7.21744	−	12.5010i	−0.711155	−	1.23176i	−0.964424	−	0.264361i	$-0.914839\pi$
$103$	−7.21744	−	12.5010i	−0.711155	−	1.23176i	0.253269	−	0.967396i	$-0.418494\pi$
$104$		0			0
$105$	1.51771	+	0.779948i	0.148113	+	0.0761151i
$106$	−12.8282			−1.24599
$107$	4.85942	+	8.41677i	0.469778	+	0.813680i	0.999403	−	0.0345525i	$-0.0110006\pi$
$107$	4.85942	+	8.41677i	0.469778	+	0.813680i	−0.529625	+	0.848232i	$0.677667\pi$
$108$	−1.34371	+	2.32737i	−0.129298	+	0.223951i
$109$	3.32428	−	5.75782i	0.318408	−	0.551499i	−0.661748	−	0.749726i	$-0.730185\pi$
$109$	3.32428	−	5.75782i	0.318408	−	0.551499i	0.980156	+	0.198227i	$0.0635185\pi$
$110$	15.2999	+	26.5001i	1.45878	+	2.52669i
$111$	−0.888018			−0.0842869
$112$	−0.348694	−	7.12591i	−0.0329485	−	0.673335i
$113$	17.5434			1.65035			0.825173	−	0.564880i	$-0.191078\pi$
$113$	17.5434			1.65035			0.825173	+	0.564880i	$0.191078\pi$
$114$	0.598855	+	1.03725i	0.0560879	+	0.0971471i
$115$	3.92850	−	6.80437i	0.366335	−	0.634511i
$116$	8.27316	−	14.3295i	0.768144	−	1.33046i
$117$		0			0
$118$	10.4217			0.959399
$119$	10.6506	−	6.86421i	0.976337	−	0.629241i
$120$	0.709696			0.0647861
$121$	−2.46946	−	4.27724i	−0.224497	−	0.388840i
$122$	−2.16313	+	3.74665i	−0.195840	+	0.339206i
$123$	−0.189524	+	0.328265i	−0.0170888	+	0.0295987i
$124$	−1.87156	−	3.24163i	−0.168071	−	0.291107i
$125$	10.8304			0.968704
$126$	14.0294	−	9.04182i	1.24984	−	0.805510i
$127$	19.5143			1.73162			0.865809	−	0.500375i	$-0.166805\pi$
$127$	19.5143			1.73162			0.865809	+	0.500375i	$0.166805\pi$
$128$	−4.25407	−	7.36826i	−0.376010	−	0.651269i
$129$	0.128010	−	0.221720i	0.0112707	−	0.0195214i
$130$		0			0
$131$	−9.53713	−	16.5188i	−0.833263	−	1.44325i	−0.895437	−	0.445188i	$-0.853137\pi$
$131$	−9.53713	−	16.5188i	−0.833263	−	1.44325i	0.0621741	−	0.998065i	$-0.480197\pi$
$132$	−1.79777			−0.156476
$133$	−0.407406	−	8.32573i	−0.0353266	−	0.721933i
$134$	−8.31259			−0.718098
$135$	−1.92455	−	3.33341i	−0.165638	−	0.286894i
$136$	2.63495	−	4.56387i	0.225945	−	0.391349i
$137$	3.21445	−	5.56759i	0.274629	−	0.475672i	−0.695412	−	0.718611i	$-0.744778\pi$
$137$	3.21445	−	5.56759i	0.274629	−	0.475672i	0.970042	+	0.242939i	$0.0781116\pi$
$138$	0.414149	+	0.717328i	0.0352547	+	0.0610630i
$139$	−2.42854			−0.205986			−0.102993	−	0.994682i	$-0.532842\pi$
$139$	−2.42854			−0.205986			−0.102993	+	0.994682i	$0.532842\pi$
$140$	−21.3646	−	10.9792i	−1.80564	−	0.927913i
$141$	−0.182240			−0.0153473
$142$	−9.35942	−	16.2110i	−0.785425	−	1.36040i
$143$		0			0
$144$	−4.00171	+	6.93117i	−0.333476	+	0.577598i
$145$	11.8494	+	20.5237i	0.984036	+	1.70440i
$146$	−6.56518			−0.543338
$147$	1.24600	−	0.122234i	0.102768	−	0.0100817i
$148$	12.5005			1.02753
$149$	0.0576764	+	0.0998984i	0.00472503	+	0.00818400i	0.868378	−	0.495902i	$-0.165163\pi$
$149$	0.0576764	+	0.0998984i	0.00472503	+	0.00818400i	−0.863653	+	0.504086i	$0.831829\pi$
$150$	−1.52126	+	2.63491i	−0.124211	+	0.215139i
$151$	−5.90155	+	10.2218i	−0.480262	+	0.831838i	−0.999744	−	0.0226438i	$-0.992792\pi$
$151$	−5.90155	+	10.2218i	−0.480262	+	0.831838i	0.519482	+	0.854481i	$0.326125\pi$
$152$	−1.73343	−	3.00239i	−0.140600	−	0.243526i
$153$	−14.2143			−1.14916
$154$	19.9686	+	10.2619i	1.60912	+	0.826924i
$155$	5.36114			0.430617
$156$		0			0
$157$	6.57343	−	11.3855i	0.524617	−	0.908663i	−0.474972	−	0.880001i	$-0.657542\pi$
$157$	6.57343	−	11.3855i	0.524617	−	0.908663i	0.999589	−	0.0286625i	$-0.00912481\pi$
$158$	2.09149	−	3.62257i	0.166390	−	0.288197i
$159$	0.539730	+	0.934840i	0.0428034	+	0.0741377i
$160$	28.6040			2.26135
$161$	−0.281749	−	5.75782i	−0.0222049	−	0.453780i
$162$	−18.5197			−1.45504
$163$	−9.32424	−	16.1501i	−0.730331	−	1.26497i	−0.956742	−	0.290938i	$-0.906033\pi$
$163$	−9.32424	−	16.1501i	−0.730331	−	1.26497i	0.226411	−	0.974032i	$-0.427301\pi$
$164$	2.66790	−	4.62094i	0.208328	−	0.360835i
$165$	1.28744	−	2.22992i	0.100227	−	0.173599i
$166$	8.14084	+	14.1003i	0.631852	+	1.09440i
$167$	0.972672			0.0752676			0.0376338	−	0.999292i	$-0.488018\pi$
$167$	0.972672			0.0752676			0.0376338	+	0.999292i	$0.488018\pi$
$168$	0.437681	−	0.282082i	0.0337678	−	0.0217631i
$169$		0			0
$170$	18.3534	+	31.7891i	1.40764	+	2.43811i
$171$	−4.67550	+	8.09821i	−0.357545	+	0.619286i
$172$	−1.80198	+	3.12113i	−0.137400	+	0.237984i
$173$	−1.22855	−	2.12791i	−0.0934050	−	0.161782i	0.815537	−	0.578705i	$-0.196442\pi$
$173$	−1.22855	−	2.12791i	−0.0934050	−	0.161782i	−0.908942	+	0.416923i	$0.863108\pi$
$174$	−2.49836			−0.189400
$175$	17.7988	−	11.4712i	1.34546	−	0.867138i
$176$	−10.7656			−0.811491
$177$	−0.438481	−	0.759471i	−0.0329583	−	0.0570854i
$178$	−13.6023	+	23.5598i	−1.01953	+	1.76588i
$179$	−7.23629	+	12.5336i	−0.540866	+	0.936807i	0.457989	+	0.888958i	$0.348570\pi$
$179$	−7.23629	+	12.5336i	−0.540866	+	0.936807i	−0.998855	+	0.0478492i	$0.984763\pi$
$180$	13.4732	+	23.3362i	1.00423	+	1.73938i
$181$	9.17885			0.682259			0.341129	−	0.940016i	$-0.389191\pi$
$181$	9.17885			0.682259			0.341129	+	0.940016i	$0.389191\pi$
$182$		0			0
$183$	0.364043			0.0269108
$184$	−1.19879	−	2.07636i	−0.0883758	−	0.153071i
$185$	−8.95202	+	15.5053i	−0.658165	+	1.13998i
$186$	−0.282590	+	0.489460i	−0.0207205	+	0.0358889i
$187$	−9.56002	−	16.5584i	−0.699098	−	1.21087i
$188$	2.56536			0.187098
$189$	−2.51182	−	1.29082i	−0.182708	−	0.0938935i
$190$	24.1480			1.75188
$191$	−8.79202	−	15.2282i	−0.636168	−	1.10188i	−0.986266	−	0.165162i	$-0.947185\pi$
$191$	−8.79202	−	15.2282i	−0.636168	−	1.10188i	0.350098	−	0.936713i	$-0.386148\pi$
$192$	−1.02545	+	1.77613i	−0.0740054	+	0.128181i
$193$	−9.87791	+	17.1090i	−0.711028	+	1.23154i	0.253444	+	0.967350i	$0.418437\pi$
$193$	−9.87791	+	17.1090i	−0.711028	+	1.23154i	−0.964472	+	0.264186i	$0.914897\pi$
$194$	1.44428	+	2.50156i	0.103693	+	0.179601i
$195$		0			0
$196$	−17.5398	+	1.72068i	−1.25284	+	0.122905i
$197$	−7.66020			−0.545767			−0.272883	−	0.962047i	$-0.587977\pi$
$197$	−7.66020			−0.545767			−0.272883	+	0.962047i	$0.587977\pi$
$198$	−12.5929	−	21.8115i	−0.894935	−	1.55007i
$199$	3.27171	−	5.66677i	0.231925	−	0.401706i	−0.726449	−	0.687220i	$-0.758831\pi$
$199$	3.27171	−	5.66677i	0.231925	−	0.401706i	0.958375	+	0.285514i	$0.0921642\pi$
$200$	4.40342	−	7.62694i	0.311369	−	0.539306i
$201$	0.349741	+	0.605769i	0.0246688	+	0.0427277i
$202$	−9.11412			−0.641267
$203$	15.4652	+	7.94755i	1.08545	+	0.557809i
$204$	−2.15657			−0.150990
$205$	3.82115	+	6.61842i	0.266880	+	0.462250i
$206$	15.3406	−	26.5707i	1.06883	−	1.85127i
$207$	−3.23343	+	5.60047i	−0.224739	+	0.389259i
$208$		0			0
$209$	−12.5783			−0.870060
$210$	0.177265	+	3.62257i	0.0122324	+	0.249981i
$211$	20.0452			1.37997			0.689983	−	0.723825i	$-0.257618\pi$
$211$	20.0452			1.37997			0.689983	+	0.723825i	$0.257618\pi$
$212$	−7.59771	−	13.1596i	−0.521813	−	0.903806i
$213$	−0.787571	+	1.36411i	−0.0539635	+	0.0934674i
$214$	−10.3287	+	17.8898i	−0.706052	+	1.22292i
$215$	−2.58092	−	4.47028i	−0.176017	−	0.304871i
$216$	−1.17455			−0.0799183
$217$	3.30630	−	2.13088i	0.224446	−	0.144654i
$218$	14.1314			0.957102
$219$	0.276221	+	0.478429i	0.0186653	+	0.0323293i
$220$	−18.1232	+	31.3902i	−1.22186	+	2.11633i
$221$		0			0
$222$	−0.943736	−	1.63460i	−0.0633394	−	0.109707i
$223$	−27.7139			−1.85586			−0.927931	−	0.372752i	$-0.878414\pi$
$223$	−27.7139			−1.85586			−0.927931	+	0.372752i	$0.878414\pi$
$224$	17.6406	−	11.3692i	1.17866	−	0.759636i
$225$	−23.7543			−1.58362
$226$	18.6442	+	32.2927i	1.24019	+	2.14808i
$227$	5.68555	−	9.84766i	0.377363	−	0.653612i	−0.613315	−	0.789839i	$-0.710164\pi$
$227$	5.68555	−	9.84766i	0.377363	−	0.653612i	0.990678	+	0.136227i	$0.0434976\pi$
$228$	−0.709362	+	1.22865i	−0.0469786	+	0.0813694i
$229$	−4.35556	−	7.54406i	−0.287824	−	0.498525i	0.685466	−	0.728104i	$-0.259598\pi$
$229$	−4.35556	−	7.54406i	−0.287824	−	0.498525i	−0.973290	+	0.229579i	$0.926265\pi$
$230$	16.7000			1.10116
$231$	−0.0923344	−	1.88694i	−0.00607516	−	0.124152i
$232$	7.23170			0.474784
$233$	1.68228	+	2.91380i	0.110210	+	0.190889i	0.915855	−	0.401510i	$-0.131514\pi$
$233$	1.68228	+	2.91380i	0.110210	+	0.190889i	−0.805645	+	0.592399i	$0.798181\pi$
$234$		0			0
$235$	−1.83714	+	3.18202i	−0.119842	+	0.207572i
$236$	6.17244	+	10.6910i	0.401791	+	0.695923i
$237$	−0.351987			−0.0228640
$238$	23.9540	+	12.3099i	1.55271	+	0.797934i
$239$	19.8798			1.28592			0.642958	−	0.765902i	$-0.277707\pi$
$239$	19.8798			1.28592			0.642958	+	0.765902i	$0.277707\pi$
$240$	−0.869579	−	1.50615i	−0.0561311	−	0.0972219i
$241$	−9.43595	+	16.3435i	−0.607823	+	1.05278i	0.383776	+	0.923426i	$0.374624\pi$
$241$	−9.43595	+	16.3435i	−0.607823	+	1.05278i	−0.991599	+	0.129354i	$0.958710\pi$
$242$	5.24882	−	9.09123i	0.337407	−	0.584406i
$243$	2.38030	+	4.12280i	0.152696	+	0.264477i
$244$	−5.12458			−0.328068
$245$	10.4265	−	22.9882i	0.666125	−	1.46866i
$246$	−0.805663			−0.0513672
$247$		0			0
$248$	0.817978	−	1.41678i	0.0519417	−	0.0899656i
$249$	0.685030	−	1.18651i	0.0434120	−	0.0751918i
$250$	11.5100	+	19.9359i	0.727956	+	1.26086i
$251$	−9.79601			−0.618319			−0.309159	−	0.951010i	$-0.600048\pi$
$251$	−9.79601			−0.618319			−0.309159	+	0.951010i	$0.600048\pi$
$252$	17.5845	+	9.03666i	1.10772	+	0.569256i
$253$	−8.69877			−0.546887
$254$	20.7388	+	35.9206i	1.30127	+	2.25386i
$255$	1.54439	−	2.67497i	0.0967136	−	0.167513i
$256$	−2.42488	+	4.20002i	−0.151555	+	0.262501i
$257$	−10.4697	−	18.1341i	−0.653083	−	1.13117i	−0.982371	−	0.186944i	$-0.940142\pi$
$257$	−10.4697	−	18.1341i	−0.653083	−	1.13117i	0.329287	−	0.944230i	$-0.393192\pi$
$258$	0.544170			0.0338785
$259$	0.642031	+	13.1205i	0.0398939	+	0.815271i
$260$		0			0
$261$	−9.75285	−	16.8924i	−0.603686	−	1.04562i
$262$	20.2711	−	35.1105i	1.25235	−	2.16914i
$263$	3.69340	−	6.39715i	0.227745	−	0.394465i	−0.729395	−	0.684093i	$-0.760198\pi$
$263$	3.69340	−	6.39715i	0.227745	−	0.394465i	0.957139	+	0.289628i	$0.0935316\pi$
$264$	−0.392865	−	0.680462i	−0.0241792	−	0.0418795i
$265$	21.7639			1.33694
$266$	14.8924	−	9.59806i	0.913114	−	0.588495i
$267$	2.28919			0.140096
$268$	−4.92326	−	8.52733i	−0.300736	−	0.520890i
$269$	−11.3946	+	19.7360i	−0.694740	+	1.20332i	0.275529	+	0.961293i	$0.411147\pi$
$269$	−11.3946	+	19.7360i	−0.694740	+	1.20332i	−0.970268	+	0.242032i	$0.922186\pi$
$270$	4.09060	−	7.08513i	0.248946	−	0.431187i
$271$	−2.08316	−	3.60814i	−0.126543	−	0.219179i	0.795792	−	0.605570i	$-0.207055\pi$
$271$	−2.08316	−	3.60814i	−0.126543	−	0.219179i	−0.922335	+	0.386391i	$0.873722\pi$
$272$	−12.9143			−0.783042
$273$		0			0
$274$	13.6646			0.825507
$275$	−15.9763	−	27.6717i	−0.963406	−	1.66867i
$276$	−0.490572	+	0.849696i	−0.0295290	+	0.0511457i
$277$	−0.388551	+	0.672989i	−0.0233457	+	0.0404360i	−0.877462	−	0.479646i	$-0.840765\pi$
$277$	−0.388551	+	0.672989i	−0.0233457	+	0.0404360i	0.854116	+	0.520082i	$0.174099\pi$
$278$	−2.58092	−	4.47028i	−0.154793	−	0.268110i
$279$	−4.41259			−0.264175
$280$	−0.513106	−	10.4858i	−0.0306639	−	0.626648i
$281$	−11.8988			−0.709824			−0.354912	−	0.934900i	$-0.615489\pi$
$281$	−11.8988			−0.709824			−0.354912	+	0.934900i	$0.615489\pi$
$282$	−0.193674	−	0.335454i	−0.0115331	−	0.0199760i
$283$	7.95202	−	13.7733i	0.472698	−	0.818738i	−0.526813	−	0.849981i	$-0.676613\pi$
$283$	7.95202	−	13.7733i	0.472698	−	0.818738i	0.999512	+	0.0312434i	$0.00994670\pi$
$284$	11.0865	−	19.2024i	0.657864	−	1.13945i
$285$	−1.01599	−	1.75975i	−0.0601823	−	0.104239i
$286$		0			0
$287$	4.98717	+	2.56290i	0.294383	+	0.151283i
$288$	−23.5431			−1.38729
$289$	−2.96801	−	5.14075i	−0.174589	−	0.302397i
$290$	−25.1857	+	43.6229i	−1.47896	+	2.56163i
$291$	0.121532	−	0.210500i	0.00712433	−	0.0123397i
$292$	−3.88833	−	6.73478i	−0.227547	−	0.394123i
$293$	−6.73698			−0.393579			−0.196789	−	0.980446i	$-0.563051\pi$
$293$	−6.73698			−0.393579			−0.196789	+	0.980446i	$0.563051\pi$
$294$	1.54918	+	2.16364i	0.0903500	+	0.126186i
$295$	−17.6811			−1.02944
$296$	2.73172	+	4.73148i	0.158778	+	0.275011i
$297$	−2.13073	+	3.69054i	−0.123638	+	0.214147i
$298$	−0.122591	+	0.212333i	−0.00710148	+	0.0123001i
$299$		0			0
$300$	−3.60397			−0.208075
$301$	−3.36849	−	1.73106i	−0.194157	−	0.0997768i
$302$	−25.0874			−1.44362
$303$	0.383465	+	0.664180i	0.0220295	+	0.0381562i
$304$	−4.24789	+	7.35756i	−0.243633	+	0.421985i
$305$	3.66988	−	6.35642i	0.210137	−	0.363968i
$306$	−15.1061	−	26.1646i	−0.863561	−	1.49573i
$307$	14.7179			0.839996			0.419998	−	0.907525i	$-0.362031\pi$
$307$	14.7179			0.839996			0.419998	+	0.907525i	$0.362031\pi$
$308$	1.29978	+	26.5622i	0.0740617	+	1.51352i
$309$	−2.58174			−0.146870
$310$	5.69752	+	9.86840i	0.323597	+	0.560487i
$311$	−14.3289	+	24.8184i	−0.812517	+	1.40732i	0.0985808	+	0.995129i	$0.468570\pi$
$311$	−14.3289	+	24.8184i	−0.812517	+	1.40732i	−0.911097	+	0.412191i	$0.864764\pi$
$312$		0			0
$313$	16.4125	+	28.4274i	0.927692	+	1.60681i	0.787174	+	0.616732i	$0.211544\pi$
$313$	16.4125	+	28.4274i	0.927692	+	1.60681i	0.140518	+	0.990078i	$0.455123\pi$
$314$	27.9435			1.57694
$315$	−23.8017	+	15.3400i	−1.34108	+	0.864312i
$316$	4.95488			0.278734
$317$	5.20605	+	9.01715i	0.292401	+	0.506453i	0.974377	−	0.224921i	$-0.0722125\pi$
$317$	5.20605	+	9.01715i	0.292401	+	0.506453i	−0.681976	+	0.731375i	$0.738879\pi$
$318$	−1.14719	+	1.98699i	−0.0643313	+	0.111425i
$319$	13.1188	−	22.7225i	0.734515	−	1.27222i
$320$	20.6749	+	35.8100i	1.15576	+	2.00184i
$321$	1.73826			0.0970201
$322$	10.2992	−	6.63772i	0.573949	−	0.369905i
$323$	−15.0887			−0.839558
$324$	−10.9686	−	18.9981i	−0.609364	−	1.05545i
$325$		0			0
$326$	19.8186	−	34.3268i	1.09765	−	1.90118i
$327$	−0.594562	−	1.02981i	−0.0328793	−	0.0569487i
$328$	2.33205			0.128766
$329$	0.131758	+	2.69261i	0.00726406	+	0.148448i
$330$	5.47290			0.301273
$331$	−2.23007	−	3.86260i	−0.122576	−	0.212308i	0.798207	−	0.602383i	$-0.205782\pi$
$331$	−2.23007	−	3.86260i	−0.122576	−	0.212308i	−0.920783	+	0.390076i	$0.872449\pi$
$332$	−9.64307	+	16.7023i	−0.529232	+	0.916657i
$333$	7.36813	−	12.7620i	0.403771	−	0.699352i
$334$	1.03370	+	1.79043i	0.0565617	+	0.0979677i
$335$	14.1028			0.770519
$336$	−1.13493	−	0.583240i	−0.0619156	−	0.0318183i
$337$	−10.7949			−0.588034			−0.294017	−	0.955800i	$-0.594992\pi$
$337$	−10.7949			−0.588034			−0.294017	+	0.955800i	$0.594992\pi$
$338$		0			0
$339$	1.56886	−	2.71734i	0.0852087	−	0.147586i
$340$	−21.7402	+	37.6551i	−1.17903	+	2.04214i
$341$	−2.96775	−	5.14030i	−0.160713	−	0.278363i
$342$	−19.8755			−1.07474
$343$	−2.70687	−	18.3214i	−0.146157	−	0.989261i
$344$	−1.57514			−0.0849259
$345$	−0.702630	−	1.21699i	−0.0378283	−	0.0655206i
$346$	2.61127	−	4.52286i	0.140383	−	0.243150i
$347$	2.03516	−	3.52499i	0.109253	−	0.189232i	−0.806215	−	0.591623i	$-0.798487\pi$
$347$	2.03516	−	3.52499i	0.109253	−	0.189232i	0.915468	+	0.402391i	$0.131821\pi$
$348$	−1.47969	−	2.56290i	−0.0793198	−	0.137386i
$349$	23.8727			1.27788			0.638938	−	0.769258i	$-0.279374\pi$
$349$	23.8727			1.27788			0.638938	+	0.769258i	$0.279374\pi$
$350$	40.0309	+	20.5718i	2.13974	+	1.09961i
$351$		0			0
$352$	−15.8343	−	27.4257i	−0.843969	−	1.46180i
$353$	−13.0420	+	22.5894i	−0.694154	+	1.20231i	0.276311	+	0.961068i	$0.410888\pi$
$353$	−13.0420	+	22.5894i	−0.694154	+	1.20231i	−0.970465	+	0.241242i	$0.922445\pi$
$354$	0.931987	−	1.61425i	0.0495346	−	0.0857964i
$355$	15.8788	+	27.5030i	0.842762	+	1.45971i
$356$	−32.2246			−1.70790
$357$	−0.110763	−	2.26354i	−0.00586217	−	0.119799i
$358$	−30.7613			−1.62579
$359$	11.4472	+	19.8271i	0.604160	+	1.04644i	0.992184	+	0.124786i	$0.0398244\pi$
$359$	11.4472	+	19.8271i	0.604160	+	1.04644i	−0.388024	+	0.921649i	$0.626842\pi$
$360$	−5.88855	+	10.1993i	−0.310354	+	0.537549i
$361$	4.53687	−	7.85809i	0.238783	−	0.413584i
$362$	9.75478	+	16.8958i	0.512700	+	0.888022i
$363$	−0.883349			−0.0463638
$364$		0			0
$365$	11.1382			0.583002
$366$	0.386885	+	0.670104i	0.0202228	+	0.0350269i
$367$	9.08003	−	15.7271i	0.473974	−	0.820946i	−0.525582	−	0.850743i	$-0.676153\pi$
$367$	9.08003	−	15.7271i	0.473974	−	0.820946i	0.999556	+	0.0297964i	$0.00948589\pi$
$368$	−2.93771	+	5.08826i	−0.153139	+	0.265244i
$369$	−3.14507	−	5.44742i	−0.163726	−	0.283581i
$370$	−38.0548			−1.97838
$371$	13.4221	−	8.65045i	0.696842	−	0.449109i
$372$	−0.669473			−0.0347105
$373$	7.93457	+	13.7431i	0.410836	+	0.711590i	0.994981	−	0.100060i	$-0.0319034\pi$
$373$	7.93457	+	13.7431i	0.410836	+	0.711590i	−0.584145	+	0.811649i	$0.698570\pi$
$374$	20.3197	−	35.1948i	1.05071	−	1.81988i
$375$	0.968536	−	1.67755i	0.0500150	−	0.0866285i
$376$	0.560605	+	0.970997i	0.0289110	+	0.0500754i
$377$		0			0
$378$	−0.293375	−	5.99540i	−0.0150896	−	0.308370i
$379$	27.7634			1.42611			0.713055	−	0.701108i	$-0.247311\pi$
$379$	27.7634			1.42611			0.713055	+	0.701108i	$0.247311\pi$
$380$	14.3020	+	24.7718i	0.733678	+	1.27077i
$381$	1.74511	−	3.02262i	0.0894048	−	0.154854i
$382$	18.6873	−	32.3674i	0.956128	−	1.65606i
$383$	13.1234	+	22.7304i	0.670576	+	1.16147i	0.977741	+	0.209815i	$0.0672863\pi$
$383$	13.1234	+	22.7304i	0.670576	+	1.16147i	−0.307165	+	0.951656i	$0.599380\pi$
$384$	−1.52172			−0.0776548
$385$	−33.8780	−	17.4099i	−1.72658	−	0.887289i
$386$	−41.9908			−2.13728
$387$	2.12428	+	3.67936i	0.107983	+	0.187032i
$388$	−1.71079	+	2.96317i	−0.0868521	+	0.150432i
$389$	12.6277	−	21.8718i	0.640250	−	1.10895i	−0.345127	−	0.938556i	$-0.612164\pi$
$389$	12.6277	−	21.8718i	0.640250	−	1.10895i	0.985377	−	0.170389i	$-0.0545026\pi$
$390$		0			0
$391$	−10.4349			−0.527714
$392$	−4.48422	−	6.26283i	−0.226487	−	0.316321i
$393$	−3.41151			−0.172088
$394$	−8.14084	−	14.1003i	−0.410129	−	0.710365i
$395$	−3.54835	+	6.14592i	−0.178537	+	0.309235i
$396$	14.9166	−	25.8363i	0.749588	−	1.29833i
$397$	7.48827	+	12.9701i	0.375826	+	0.650949i	0.990450	−	0.137871i	$-0.0440258\pi$
$397$	7.48827	+	12.9701i	0.375826	+	0.650949i	−0.614625	+	0.788820i	$0.710692\pi$
$398$	13.9080			0.697143
$399$	−1.32603	−	0.681443i	−0.0663843	−	0.0341148i
$400$	−21.5817			−1.07909
$401$	2.67204	+	4.62811i	0.133435	+	0.231117i	0.924999	−	0.379970i	$-0.124066\pi$
$401$	2.67204	+	4.62811i	0.133435	+	0.231117i	−0.791563	+	0.611087i	$0.790733\pi$
$402$	−0.743371	+	1.28756i	−0.0370760	+	0.0642175i
$403$		0			0
$404$	−5.39798	−	9.34957i	−0.268559	−	0.465159i
$405$	31.4198			1.56126
$406$	1.80630	+	36.9135i	0.0896451	+	1.83199i
$407$	19.8222			0.982549
$408$	−0.471273	−	0.816269i	−0.0233315	−	0.0404113i
$409$	1.68259	−	2.91433i	0.0831985	−	0.144104i	−0.821424	−	0.570319i	$-0.806820\pi$
$409$	1.68259	−	2.91433i	0.0831985	−	0.144104i	0.904622	+	0.426214i	$0.140153\pi$
$410$	−8.12181	+	14.0674i	−0.401107	+	0.694739i
$411$	−0.574919	−	0.995789i	−0.0283587	−	0.0491186i
$412$	36.3428			1.79048
$413$	−10.9042	+	7.02769i	−0.536562	+	0.345810i
$414$	−13.7453			−0.675542
$415$	−13.8114	−	23.9221i	−0.677977	−	1.17429i
$416$		0			0
$417$	−0.217178	+	0.376163i	−0.0106352	+	0.0184208i
$418$	−13.3675	−	23.1533i	−0.653828	−	1.13246i
$419$	−28.8639			−1.41010			−0.705048	−	0.709160i	$-0.749074\pi$
$419$	−28.8639			−1.41010			−0.705048	+	0.709160i	$0.749074\pi$
$420$	−3.61117	+	2.32737i	−0.176207	+	0.113564i
$421$	−16.6125			−0.809644			−0.404822	−	0.914395i	$-0.632667\pi$
$421$	−16.6125			−0.809644			−0.404822	+	0.914395i	$0.632667\pi$
$422$	21.3029	+	36.8977i	1.03701	+	1.79615i
$423$	1.51209	−	2.61902i	0.0735205	−	0.127341i
$424$	3.32064	−	5.75151i	0.161264	−	0.279318i
$425$	−19.1648	−	33.1945i	−0.929631	−	1.61017i
$426$	−3.34795			−0.162209
$427$	−0.263201	−	5.37877i	−0.0127372	−	0.260297i
$428$	−24.4692			−1.18276
$429$		0			0
$430$	5.48572	−	9.50154i	0.264545	−	0.458205i
$431$	−10.2777	+	17.8015i	−0.495060	+	0.857469i	−0.999984	−	0.00569505i	$-0.998187\pi$
$431$	−10.2777	+	17.8015i	−0.495060	+	0.857469i	0.504924	+	0.863164i	$0.331521\pi$
$432$	1.43916	+	2.49270i	0.0692417	+	0.119930i
$433$	19.4092			0.932748			0.466374	−	0.884588i	$-0.345560\pi$
$433$	19.4092			0.932748			0.466374	+	0.884588i	$0.345560\pi$
$434$	7.43613	+	3.82141i	0.356945	+	0.183434i
$435$	4.23862			0.203226
$436$	8.36956	+	14.4965i	0.400829	+	0.694257i
$437$	−3.43235	+	5.94500i	−0.164191	+	0.284388i
$438$	−0.587106	+	1.01690i	−0.0280530	+	0.0485892i
$439$	−6.71256	−	11.6265i	−0.320373	−	0.554902i	0.660192	−	0.751097i	$-0.270475\pi$
$439$	−6.71256	−	11.6265i	−0.320373	−	0.554902i	−0.980565	+	0.196195i	$0.937142\pi$
$440$	−15.8417			−0.755225
$441$	−8.58174	+	18.9209i	−0.408654	+	0.900994i
$442$		0			0
$443$	16.7766	+	29.0579i	0.797080	+	1.38058i	0.921510	+	0.388354i	$0.126956\pi$
$443$	16.7766	+	29.0579i	0.797080	+	1.38058i	−0.124430	+	0.992228i	$0.539710\pi$
$444$	1.11788	−	1.93623i	0.0530524	−	0.0918895i
$445$	23.0771	−	39.9707i	1.09396	−	1.89479i
$446$	−29.4528	−	51.0138i	−1.39463	−	2.41557i
$447$	0.0206313			0.000975829
$448$	26.9839	+	13.8670i	1.27487	+	0.655153i
$449$	34.4284			1.62478			0.812388	−	0.583117i	$-0.198167\pi$
$449$	34.4284			1.62478			0.812388	+	0.583117i	$0.198167\pi$
$450$	−25.2447	−	43.7251i	−1.19005	−	2.06122i
$451$	4.23052	−	7.32748i	0.199208	−	0.345038i
$452$	−22.0846	+	38.2517i	−1.03877	+	1.79921i
$453$	1.05552	+	1.82821i	0.0495926	+	0.0858969i
$454$	24.1691			1.13431
$455$		0			0
$456$	−0.620064			−0.0290371
$457$	6.73967	+	11.6735i	0.315269	+	0.546061i	0.979495	−	0.201471i	$-0.0645720\pi$
$457$	6.73967	+	11.6735i	0.315269	+	0.546061i	−0.664226	+	0.747532i	$0.731239\pi$
$458$	9.25771	−	16.0348i	0.432584	−	0.749258i
$459$	−2.55598	+	4.42710i	−0.119303	+	0.206639i
$460$	9.89082	+	17.1314i	0.461162	+	0.798756i
$461$	−1.35900			−0.0632951			−0.0316476	−	0.999499i	$-0.510075\pi$
$461$	−1.35900			−0.0632951			−0.0316476	+	0.999499i	$0.510075\pi$
$462$	3.37522	−	2.17530i	0.157030	−	0.101204i
$463$	2.49836			0.116109			0.0580543	−	0.998313i	$-0.481510\pi$
$463$	2.49836			0.116109			0.0580543	+	0.998313i	$0.481510\pi$
$464$	−8.86088	−	15.3475i	−0.411356	−	0.712489i
$465$	0.479431	−	0.830399i	0.0222331	−	0.0385088i
$466$	−3.57567	+	6.19325i	−0.165640	+	0.286897i
$467$	13.1091	+	22.7056i	0.606617	+	1.05069i	0.991794	+	0.127849i	$0.0408072\pi$
$467$	13.1091	+	22.7056i	0.606617	+	1.05069i	−0.385176	+	0.922843i	$0.625859\pi$
$468$		0			0
$469$	8.69744	−	5.60542i	0.401610	−	0.258834i
$470$	−7.80965			−0.360232
$471$	−1.17569	−	2.03635i	−0.0541728	−	0.0938301i
$472$	−2.69771	+	4.67257i	−0.124172	+	0.215072i
$473$	−2.85743	+	4.94921i	−0.131385	+	0.227565i
$474$	−0.374073	−	0.647913i	−0.0171817	−	0.0297596i
$475$	−25.2156			−1.15697
$476$	1.55919	+	31.8635i	0.0714653	+	1.46046i
$477$	−17.9132			−0.820188
$478$	21.1271	+	36.5933i	0.966332	+	1.67374i
$479$	−11.9230	+	20.6513i	−0.544778	+	0.943583i	0.453843	+	0.891082i	$0.350053\pi$
$479$	−11.9230	+	20.6513i	−0.544778	+	0.943583i	−0.998621	+	0.0525011i	$0.983281\pi$
$480$	2.55798	−	4.43055i	0.116755	−	0.202226i
$481$		0			0
$482$	−40.1120			−1.82705
$483$	−0.917038	−	0.471265i	−0.0417267	−	0.0214433i
$484$	12.4348			0.565217
$485$	−2.45030	−	4.24405i	−0.111263	−	0.192712i
$486$	−5.05930	+	8.76296i	−0.229494	+	0.397496i
$487$	−5.29733	+	9.17524i	−0.240045	+	0.415770i	−0.960727	−	0.277496i	$-0.910496\pi$
$487$	−5.29733	+	9.17524i	−0.240045	+	0.415770i	0.720682	+	0.693266i	$0.243829\pi$
$488$	−1.11987	−	1.93967i	−0.0506941	−	0.0878047i
$489$	−3.33536			−0.150830
$490$	53.3957	−	5.23820i	2.41217	−	0.236638i
$491$	−19.7704			−0.892224			−0.446112	−	0.894977i	$-0.647192\pi$
$491$	−19.7704			−0.892224			−0.446112	+	0.894977i	$0.647192\pi$
$492$	−0.477166	−	0.826476i	−0.0215123	−	0.0372604i
$493$	15.7371	−	27.2575i	0.708764	−	1.22762i
$494$		0			0
$495$	21.3646	+	37.0045i	0.960266	+	1.66323i
$496$	−4.00902			−0.180010
$497$	20.7243	+	10.6502i	0.929612	+	0.477726i
$498$	2.91205			0.130492
$499$	6.59530	+	11.4234i	0.295246	+	0.511381i	0.975042	−	0.222020i	$-0.0712650\pi$
$499$	6.59530	+	11.4234i	0.295246	+	0.511381i	−0.679796	+	0.733401i	$0.737932\pi$
$500$	−13.6339	+	23.6147i	−0.609728	+	1.05608i
$501$	0.0869833	−	0.150660i	0.00388613	−	0.00673097i
$502$	−10.4107	−	18.0318i	−0.464651	−	0.804798i
$503$	37.9046			1.69008			0.845040	−	0.534703i	$-0.179576\pi$
$503$	37.9046			1.69008			0.845040	+	0.534703i	$0.179576\pi$
$504$	0.422322	+	8.63056i	0.0188117	+	0.384436i
$505$	15.4627			0.688080
$506$	−9.24457	−	16.0121i	−0.410971	−	0.711823i
$507$		0			0
$508$	−24.5657	+	42.5490i	−1.08993	+	1.88781i
$509$	13.8313	+	23.9565i	0.613062	+	1.06185i	0.990721	+	0.135909i	$0.0433956\pi$
$509$	13.8313	+	23.9565i	0.613062	+	1.06185i	−0.377660	+	0.925944i	$0.623271\pi$
$510$	6.56518			0.290711
$511$	6.86913	−	4.42710i	0.303872	−	0.195843i
$512$	−27.3244			−1.20758
$513$	1.68148	+	2.91241i	0.0742392	+	0.128586i
$514$	22.2533	−	38.5438i	0.981551	−	1.70010i
$515$	−26.0263	+	45.0788i	−1.14685	+	1.98641i
$516$	0.322293	+	0.558227i	0.0141881	+	0.0245746i
$517$	4.06792			0.178907
$518$	−23.4690	+	15.1256i	−1.03117	+	0.664580i
$519$	−0.439464			−0.0192903
$520$		0			0
$521$	−7.78339	+	13.4812i	−0.340996	+	0.590623i	−0.984618	−	0.174721i	$-0.944098\pi$
$521$	−7.78339	+	13.4812i	−0.340996	+	0.590623i	0.643622	+	0.765344i	$0.277431\pi$
$522$	20.7296	−	35.9047i	0.907310	−	1.57151i
$523$	−13.6169	−	23.5852i	−0.595425	−	1.03131i	−0.993487	−	0.113948i	$-0.963650\pi$
$523$	−13.6169	−	23.5852i	−0.595425	−	1.03131i	0.398061	−	0.917359i	$-0.369683\pi$
$524$	48.0234			2.09791
$525$	−0.185101	−	3.78273i	−0.00807849	−	0.165092i
$526$	15.7005			0.684577
$527$	−3.56006	−	6.16620i	−0.155079	−	0.268604i
$528$	−0.962741	+	1.66752i	−0.0418979	+	0.0725694i
$529$	9.12630	−	15.8072i	0.396796	−	0.687270i
$530$	23.1294	+	40.0614i	1.00468	+	1.74015i
$531$	14.5528			0.631538
$532$	18.6663	+	9.59258i	0.809286	+	0.415891i
$533$		0			0
$534$	2.43283	+	4.21378i	0.105279	+	0.182348i
$535$	17.5232	−	30.3511i	0.757594	−	1.31219i
$536$	2.15175	−	3.72693i	0.0929413	−	0.160979i
$537$	1.29424	+	2.24169i	0.0558507	+	0.0967362i
$538$	−48.4381			−2.08832
$539$	−27.8130	+	2.72850i	−1.19799	+	0.117525i
$540$	9.69089			0.417029
$541$	12.1027	+	20.9626i	0.520338	+	0.901251i	0.999720	+	0.0236453i	$0.00752724\pi$
$541$	12.1027	+	20.9626i	0.520338	+	0.901251i	−0.479383	+	0.877606i	$0.659139\pi$
$542$	4.42774	−	7.66907i	0.190188	−	0.329415i
$543$	0.820839	−	1.42174i	0.0352256	−	0.0610125i
$544$	−18.9945	−	32.8994i	−0.814381	−	1.41055i
$545$	−23.9749			−1.02697
$546$		0			0
$547$	−22.2177			−0.949960			−0.474980	−	0.879997i	$-0.657545\pi$
$547$	−22.2177			−0.949960			−0.474980	+	0.879997i	$0.657545\pi$
$548$	8.09305	+	14.0176i	0.345718	+	0.598801i
$549$	−3.02057	+	5.23178i	−0.128915	+	0.223287i
$550$	33.9574	−	58.8160i	1.44795	−	2.50792i
$551$	−10.3528	−	17.9316i	−0.441045	−	0.763913i
$552$	−0.428817			−0.0182517
$553$	0.254485	+	5.20065i	0.0108218	+	0.221154i
$554$	−1.65172			−0.0701749
$555$	1.60111	+	2.77320i	0.0679632	+	0.117716i
$556$	3.05718	−	5.29519i	0.129653	−	0.224566i
$557$	−11.1602	+	19.3300i	−0.472873	+	0.819040i	−0.999518	−	0.0310455i	$-0.990116\pi$
$557$	−11.1602	+	19.3300i	−0.472873	+	0.819040i	0.526645	+	0.850085i	$0.323450\pi$
$558$	−4.68946	−	8.12238i	−0.198521	−	0.343848i
$559$		0			0
$560$	−21.6249	+	13.9370i	−0.913818	+	0.588948i
$561$	−3.41970			−0.144380
$562$	−12.6454	−	21.9025i	−0.533415	−	0.923901i
$563$	−13.3519	+	23.1262i	−0.562717	+	0.974655i	0.434541	+	0.900652i	$0.356911\pi$
$563$	−13.3519	+	23.1262i	−0.562717	+	0.974655i	−0.997258	+	0.0740027i	$0.976423\pi$
$564$	0.229413	−	0.397355i	0.00966004	−	0.0167317i
$565$	−31.6310	−	54.7865i	−1.33073	−	2.30489i
$566$	33.8039			1.42088
$567$	19.3771	−	12.4884i	0.813760	−	0.524462i
$568$	9.69090			0.406621
$569$	−3.30510	−	5.72461i	−0.138557	−	0.239988i	0.788393	−	0.615171i	$-0.210913\pi$
$569$	−3.30510	−	5.72461i	−0.138557	−	0.239988i	−0.926951	+	0.375183i	$0.877580\pi$
$570$	2.15949	−	3.74034i	0.0904509	−	0.156666i
$571$	21.0643	−	36.4844i	0.881513	−	1.52683i	0.0318546	−	0.999493i	$-0.489859\pi$
$571$	21.0643	−	36.4844i	0.881513	−	1.52683i	0.849659	−	0.527333i	$-0.176808\pi$
$572$		0			0
$573$	−3.14498			−0.131383
$574$	0.582489	+	11.9037i	0.0243126	+	0.496853i
$575$	−17.4383			−0.727227
$576$	−17.0169	−	29.4741i	−0.709037	−	1.22809i
$577$	7.94195	−	13.7559i	0.330628	−	0.572664i	−0.652007	−	0.758213i	$-0.726073\pi$
$577$	7.94195	−	13.7559i	0.330628	−	0.572664i	0.982635	+	0.185549i	$0.0594063\pi$
$578$	6.30848	−	10.9266i	0.262398	−	0.454487i
$579$	1.76671	+	3.06003i	0.0734219	+	0.127170i
$580$	−59.6665			−2.47752
$581$	−18.0260	−	9.26354i	−0.747845	−	0.384316i
$582$	0.516630			0.0214150
$583$	−12.0478	−	20.8674i	−0.498968	−	0.864238i
$584$	1.69942	−	2.94349i	0.0703226	−	0.121802i
$585$		0			0
$586$	−7.15969	−	12.4010i	−0.295764	−	0.512279i
$587$	−18.5676			−0.766366			−0.383183	−	0.923672i	$-0.625172\pi$
$587$	−18.5676			−0.766366			−0.383183	+	0.923672i	$0.625172\pi$
$588$	−1.30201	+	2.87065i	−0.0536940	+	0.118384i
$589$	−4.68404			−0.193003
$590$	−18.7905	−	32.5462i	−0.773594	−	1.33990i
$591$	−0.685030	+	1.18651i	−0.0281784	+	0.0488064i
$592$	6.69426	−	11.5948i	0.275132	−	0.476543i
$593$	−10.3050	−	17.8487i	−0.423175	−	0.732960i	0.573073	−	0.819504i	$-0.305751\pi$
$593$	−10.3050	−	17.8487i	−0.423175	−	0.732960i	−0.996248	+	0.0865442i	$0.972418\pi$
$594$	−9.05770			−0.371642
$595$	−40.6394	−	20.8845i	−1.66605	−	0.856183i
$596$	−0.290425			−0.0118963
$597$	−0.585159	−	1.01353i	−0.0239490	−	0.0414809i
$598$		0			0
$599$	6.80224	−	11.7818i	0.277932	−	0.481393i	−0.692939	−	0.720997i	$-0.743684\pi$
$599$	6.80224	−	11.7818i	0.277932	−	0.481393i	0.970871	+	0.239604i	$0.0770176\pi$
$600$	−0.787571	−	1.36411i	−0.0321524	−	0.0556897i
$601$	−12.1503			−0.495621			−0.247810	−	0.968809i	$-0.579711\pi$
$601$	−12.1503			−0.495621			−0.247810	+	0.968809i	$0.579711\pi$
$602$	−0.393431	−	8.04015i	−0.0160351	−	0.327692i
$603$	−11.6076			−0.472698
$604$	−14.8584	−	25.7355i	−0.604579	−	1.04716i
$605$	−8.90496	+	15.4238i	−0.362038	+	0.627068i
$606$	−0.815050	+	1.41171i	−0.0331092	+	0.0573467i
$607$	−17.6166	−	30.5128i	−0.715035	−	1.23848i	−0.962946	−	0.269695i	$-0.913077\pi$
$607$	−17.6166	−	30.5128i	−0.715035	−	1.23848i	0.247911	−	0.968783i	$-0.420256\pi$
$608$	−24.9914			−1.01354
$609$	2.61403	−	1.68472i	0.105926	−	0.0682682i
$610$	15.6006			0.631650
$611$		0			0
$612$	17.8937	−	30.9928i	0.723310	−	1.25281i
$613$	15.0310	−	26.0345i	0.607097	−	1.05152i	−0.384619	−	0.923075i	$-0.625667\pi$
$613$	15.0310	−	26.0345i	0.607097	−	1.05152i	0.991716	−	0.128448i	$-0.0409996\pi$
$614$	15.6414	+	27.0917i	0.631236	+	1.09333i
$615$	1.36686			0.0551170
$616$	−9.76984	+	6.29658i	−0.393638	+	0.253697i
$617$	7.01712			0.282499			0.141249	−	0.989974i	$-0.454888\pi$
$617$	7.01712			0.282499			0.141249	+	0.989974i	$0.454888\pi$
$618$	−2.74373	−	4.75228i	−0.110369	−	0.191165i
$619$	21.9241	−	37.9736i	0.881203	−	1.52629i	0.0311993	−	0.999513i	$-0.490067\pi$
$619$	21.9241	−	37.9736i	0.881203	−	1.52629i	0.850004	−	0.526776i	$-0.176599\pi$
$620$	−6.74889	+	11.6894i	−0.271042	+	0.469458i
$621$	1.16286	+	2.01413i	0.0466640	+	0.0808244i
$622$	−60.9118			−2.44234
$623$	−1.65507	−	33.8230i	−0.0663091	−	1.35509i
$624$		0			0
$625$	0.481145	+	0.833367i	0.0192458	+	0.0333347i
$626$	−34.8847	+	60.4221i	−1.39427	+	2.41495i
$627$	−1.12484	+	1.94829i	−0.0449219	+	0.0778070i
$628$	16.5500	+	28.6654i	0.660416	+	1.14387i
$629$	23.7783			0.948103
$630$	−53.5320	−	27.5100i	−2.13276	−	1.09602i
$631$	−23.4936			−0.935267			−0.467634	−	0.883922i	$-0.654893\pi$
$631$	−23.4936			−0.935267			−0.467634	+	0.883922i	$0.654893\pi$
$632$	1.08278	+	1.87544i	0.0430708	+	0.0746008i
$633$	1.79258	−	3.10485i	0.0712488	−	0.123407i
$634$	−11.0654	+	19.1659i	−0.439464	+	0.761173i
$635$	−35.1846	−	60.9415i	−1.39626	−	2.41839i
$636$	−2.71777			−0.107766
$637$		0			0
$638$	55.7680			2.20788
$639$	−13.0694	−	22.6369i	−0.517017	−	0.895500i
$640$	−15.3403	+	26.5702i	−0.606378	+	1.05028i
$641$	−3.70233	+	6.41262i	−0.146233	+	0.253283i	−0.929832	−	0.367983i	$-0.880048\pi$
$641$	−3.70233	+	6.41262i	−0.146233	+	0.253283i	0.783599	+	0.621267i	$0.213382\pi$
$642$	1.84732	+	3.19966i	0.0729081	+	0.126281i
$643$	39.9607			1.57590			0.787948	−	0.615742i	$-0.211144\pi$
$643$	39.9607			1.57590			0.787948	+	0.615742i	$0.211144\pi$
$644$	12.9090	+	6.63393i	0.508687	+	0.261413i
$645$	−0.923218			−0.0363517
$646$	−16.0354	−	27.7742i	−0.630906	−	1.09276i
$647$	−13.6234	+	23.5964i	−0.535591	+	0.927670i	0.463544	+	0.886074i	$0.346578\pi$
$647$	−13.6234	+	23.5964i	−0.535591	+	0.927670i	−0.999134	+	0.0415963i	$0.986756\pi$
$648$	4.79389	−	8.30326i	0.188322	−	0.326183i
$649$	9.78770	+	16.9528i	0.384201	+	0.665456i
$650$		0			0
$651$	−0.0343844	−	0.702679i	−0.00134763	−	0.0275402i
$652$	46.9514			1.83876
$653$	−9.57255	−	16.5801i	−0.374603	−	0.648831i	0.615665	−	0.788008i	$-0.288888\pi$
$653$	−9.57255	−	16.5801i	−0.374603	−	0.648831i	−0.990267	+	0.139177i	$0.955554\pi$
$654$	1.26373	−	2.18885i	0.0494159	−	0.0855909i
$655$	−34.3911	+	59.5672i	−1.34377	+	2.32748i
$656$	−2.85743	−	4.94921i	−0.111564	−	0.193234i
$657$	−9.16755			−0.357660
$658$	−4.81633	+	3.10409i	−0.187760	+	0.121010i
$659$	41.5725			1.61943			0.809717	−	0.586820i	$-0.199620\pi$
$659$	41.5725			1.61943			0.809717	+	0.586820i	$0.199620\pi$
$660$	3.24141	+	5.61428i	0.126172	+	0.218536i
$661$	−17.1023	+	29.6221i	−0.665203	+	1.15217i	0.314027	+	0.949414i	$0.398322\pi$
$661$	−17.1023	+	29.6221i	−0.665203	+	1.15217i	−0.979230	+	0.202752i	$0.935012\pi$
$662$	4.74000	−	8.20992i	0.184225	−	0.319088i
$663$		0			0
$664$	−8.42915			−0.327115
$665$	−25.2660	+	16.2837i	−0.979772	+	0.631455i
$666$	31.3218			1.21369
$667$	−7.15969	−	12.4010i	−0.277224	−	0.480167i
$668$	−1.22445	+	2.12081i	−0.0473755	+	0.0820567i
$669$	−2.47838	+	4.29268i	−0.0958197	+	0.165965i
$670$	14.9877	+	25.9595i	0.579025	+	1.00290i
$671$	−8.12611			−0.313705
$672$	−0.183456	−	3.74910i	−0.00707697	−	0.144625i
$673$	21.4308			0.826098			0.413049	−	0.910709i	$-0.364464\pi$
$673$	21.4308			0.826098			0.413049	+	0.910709i	$0.364464\pi$
$674$	−11.4722	−	19.8704i	−0.441893	−	0.765381i
$675$	−4.27145	+	7.39837i	−0.164408	+	0.284763i
$676$		0			0
$677$	−4.89083	−	8.47117i	−0.187970	−	0.325573i	0.756603	−	0.653874i	$-0.226857\pi$
$677$	−4.89083	−	8.47117i	−0.187970	−	0.325573i	−0.944573	+	0.328301i	$0.893524\pi$
$678$	6.66919			0.256129
$679$	−3.19802	−	1.64346i	−0.122729	−	0.0630700i
$680$	−19.0034			−0.728748
$681$	−1.01688	−	1.76130i	−0.0389671	−	0.0674930i
$682$	6.30793	−	10.9256i	0.241543	−	0.418365i
$683$	−7.63818	+	13.2297i	−0.292267	+	0.506221i	−0.974345	−	0.225058i	$-0.927743\pi$
$683$	−7.63818	+	13.2297i	−0.292267	+	0.506221i	0.682079	+	0.731279i	$0.261076\pi$
$684$	−11.7716	−	20.3889i	−0.450097	−	0.779590i
$685$	−23.1828			−0.885769
$686$	30.8480	−	24.4536i	1.17778	−	0.933642i
$687$	−1.55802			−0.0594423
$688$	1.92999	+	3.34285i	0.0735803	+	0.127445i
$689$		0			0
$690$	1.49343	−	2.58670i	0.0568540	−	0.0984741i
$691$	−21.2286	−	36.7690i	−0.807573	−	1.39876i	−0.914540	−	0.404496i	$-0.867447\pi$
$691$	−21.2286	−	36.7690i	−0.807573	−	1.39876i	0.106967	−	0.994263i	$-0.465886\pi$
$692$	6.18627			0.235167
$693$	27.8840	+	14.3295i	1.05922	+	0.544334i
$694$	8.65141			0.328403
$695$	4.37869	+	7.58412i	0.166093	+	0.287682i
$696$	0.646710	−	1.12013i	0.0245135	−	0.0424586i
$697$	5.07486	−	8.78991i	0.192224	−	0.332942i
$698$	25.3706	+	43.9432i	0.960291	+	1.66327i
$699$	0.601767			0.0227609
$700$	2.60565	+	53.2489i	0.0984842	+	2.01262i
$701$	−2.79985			−0.105749			−0.0528744	−	0.998601i	$-0.516838\pi$
$701$	−2.79985			−0.105749			−0.0528744	+	0.998601i	$0.516838\pi$
$702$		0			0
$703$	7.82141	−	13.5471i	0.294990	−	0.510937i
$704$	22.8899	−	39.6465i	0.862696	−	1.49423i
$705$	0.328581	+	0.569118i	0.0123751	+	0.0214342i
$706$	−55.4412			−2.08656
$707$	9.53608	−	6.14592i	0.358641	−	0.231141i
$708$	2.20793			0.0829793
$709$	7.28319	+	12.6149i	0.273526	+	0.473761i	0.969762	−	0.244052i	$-0.0784767\pi$
$709$	7.28319	+	12.6149i	0.273526	+	0.473761i	−0.696236	+	0.717813i	$0.745143\pi$
$710$	−33.7503	+	58.4573i	−1.26663	+	2.19386i
$711$	2.92054	−	5.05852i	0.109529	−	0.189709i
$712$	−7.04201	−	12.1971i	−0.263910	−	0.457106i
$713$	−3.23934			−0.121314
$714$	4.04885	−	2.60945i	0.151524	−	0.0976562i
$715$		0			0
$716$	−18.2189	−	31.5560i	−0.680871	−	1.17930i
$717$	1.77779	−	3.07923i	0.0663928	−	0.114996i
$718$	−24.3309	+	42.1423i	−0.908021	+	1.57274i
$719$	−17.2529	−	29.8828i	−0.643423	−	1.11444i	−0.984663	−	0.174465i	$-0.944180\pi$
$719$	−17.2529	−	29.8828i	−0.643423	−	1.11444i	0.341240	−	0.939976i	$-0.389153\pi$
$720$	28.8606			1.07557
$721$	1.86658	+	38.1454i	0.0695152	+	1.42061i
$722$	19.2861			0.717756
$723$	1.68766	+	2.92311i	0.0627648	+	0.108712i
$724$	−11.5548	+	20.0136i	−0.429432	+	0.743798i
$725$	26.2992	−	45.5515i	0.976727	−	1.69174i
$726$	−0.938775	−	1.62601i	−0.0348412	−	0.0603467i
$727$	35.7571			1.32616			0.663078	−	0.748550i	$-0.269250\pi$
$727$	35.7571			1.32616			0.663078	+	0.748550i	$0.269250\pi$
$728$		0			0
$729$	−25.2879			−0.936590
$730$	11.8371	+	20.5025i	0.438111	+	0.758830i
$731$	−3.42771	+	5.93698i	−0.126779	+	0.219587i
$732$	−0.458277	+	0.793759i	−0.0169384	+	0.0293382i
$733$	20.5250	+	35.5504i	0.758108	+	1.31308i	0.943814	+	0.330477i	$0.107210\pi$
$733$	20.5250	+	35.5504i	0.758108	+	1.31308i	−0.185706	+	0.982605i	$0.559457\pi$
$734$	38.5990			1.42472
$735$	−2.62828	−	3.67075i	−0.0969456	−	0.135398i
$736$	−17.2833			−0.637071
$737$	−7.80686	−	13.5219i	−0.287570	−	0.498085i
$738$	6.68481	−	11.5784i	0.246071	−	0.426208i
$739$	0.363205	−	0.629089i	0.0133607	−	0.0231414i	−0.859268	−	0.511526i	$-0.829080\pi$
$739$	0.363205	−	0.629089i	0.0133607	−	0.0231414i	0.872628	+	0.488385i	$0.162414\pi$
$740$	−22.5386	−	39.0379i	−0.828534	−	1.43506i
$741$		0			0
$742$	30.1874	+	15.5133i	1.10822	+	0.569510i
$743$	16.4547			0.603664			0.301832	−	0.953361i	$-0.402402\pi$
$743$	16.4547			0.603664			0.301832	+	0.953361i	$0.402402\pi$
$744$	−0.146299	−	0.253397i	−0.00536358	−	0.00929000i
$745$	0.207983	−	0.360236i	0.00761989	−	0.0131980i
$746$	−16.8648	+	29.2108i	−0.617466	+	1.06948i
$747$	11.3678	+	19.6896i	0.415925	+	0.720404i
$748$	48.1387			1.76012
$749$	−1.25675	−	25.6829i	−0.0459206	−	0.938433i
$750$	4.11723			0.150340
$751$	−12.5854	−	21.7985i	−0.459247	−	0.795439i	0.539675	−	0.841874i	$-0.318547\pi$
$751$	−12.5854	−	21.7985i	−0.459247	−	0.795439i	−0.998921	+	0.0464350i	$0.985214\pi$
$752$	1.37380	−	2.37949i	0.0500974	−	0.0867712i
$753$	−0.876030	+	1.51733i	−0.0319243	+	0.0552945i
$754$		0			0
$755$	42.5623			1.54900
$756$	5.97652	−	3.85182i	0.217364	−	0.140089i
$757$	44.0743			1.60191			0.800953	−	0.598727i	$-0.204327\pi$
$757$	44.0743			1.60191			0.800953	+	0.598727i	$0.204327\pi$
$758$	29.5054	+	51.1049i	1.07168	+	1.85621i
$759$	−0.777906	+	1.34737i	−0.0282362	+	0.0489066i
$760$	−6.25080	+	10.8267i	−0.226740	+	0.392726i
$761$	19.3511	+	33.5171i	0.701477	+	1.21499i	0.967948	+	0.251151i	$0.0808090\pi$
$761$	19.3511	+	33.5171i	0.701477	+	1.21499i	−0.266471	+	0.963843i	$0.585858\pi$
$762$	7.41844			0.268742
$763$	−14.7857	+	9.52925i	−0.535278	+	0.344982i
$764$	44.2715			1.60169
$765$	25.6285	+	44.3899i	0.926601	+	1.60492i
$766$	−27.8937	+	48.3133i	−1.00784	+	1.74563i
$767$		0			0
$768$	0.433701	+	0.751191i	0.0156498	+	0.0271063i
$769$	−36.1506			−1.30362			−0.651811	−	0.758381i	$-0.725991\pi$
$769$	−36.1506			−1.30362			−0.651811	+	0.758381i	$0.725991\pi$
$770$	−3.95687	−	80.8625i	−0.142596	−	2.91408i
$771$	−3.74511			−0.134877
$772$	−24.8697	−	43.0756i	−0.895080	−	1.55032i
$773$	−15.0366	+	26.0441i	−0.540827	+	0.936740i	0.458030	+	0.888937i	$0.348555\pi$
$773$	−15.0366	+	26.0441i	−0.540827	+	0.936740i	−0.998857	+	0.0478033i	$0.984778\pi$
$774$	−4.51513	+	7.82043i	−0.162293	+	0.281100i
$775$	−5.94941	−	10.3047i	−0.213709	−	0.370155i
$776$	−1.49543			−0.0536827
$777$	2.08969	+	1.07389i	0.0749671	+	0.0385255i
$778$	53.6801			1.92453
$779$	−3.33855	−	5.78253i	−0.119616	−	0.207181i
$780$		0			0
$781$	17.5800	−	30.4495i	0.629063	−	1.08957i
$782$	−11.0896	−	19.2078i	−0.396564	−	0.686868i
$783$	−7.01496			−0.250694
$784$	−7.79687	+	17.1904i	−0.278460	+	0.613943i
$785$	−47.4079			−1.69206
$786$	−3.62557	−	6.27967i	−0.129320	−	0.223988i
$787$	18.4236	−	31.9106i	0.656730	−	1.13749i	−0.324727	−	0.945808i	$-0.605272\pi$
$787$	18.4236	−	31.9106i	0.656730	−	1.13749i	0.981457	−	0.191682i	$-0.0613943\pi$
$788$	9.64307	−	16.7023i	0.343520	−	0.594994i
$789$	−0.660580	−	1.14416i	−0.0235173	−	0.0407331i
$790$	−15.0840			−0.536663
$791$	−41.2833	−	21.2154i	−1.46786	−	0.754333i
$792$	13.0388			0.463315
$793$		0			0
$794$	−15.9163	+	27.5678i	−0.564847	+	0.978343i
$795$	1.94628	−	3.37106i	0.0690275	−	0.119559i
$796$	8.23721	+	14.2673i	0.291960	+	0.505690i
$797$	27.5910			0.977323			0.488661	−	0.872474i	$-0.337485\pi$
$797$	27.5910			0.977323			0.488661	+	0.872474i	$0.337485\pi$
$798$	−0.154877	−	3.16505i	−0.00548257	−	0.112042i
$799$	4.87980			0.172635
$800$	−31.7427	−	54.9800i	−1.12227	−	1.94384i
$801$	−18.9941	+	32.8987i	−0.671123	+	1.16242i
$802$	−5.67939	+	9.83700i	−0.200546	+	0.347356i
$803$	−6.16577	−	10.6794i	−0.217585	−	0.376869i
$804$	−1.76109			−0.0621089
$805$	−17.4732	+	11.2613i	−0.615848	+	0.396909i
$806$		0			0
$807$	2.03797	+	3.52987i	0.0717399	+	0.124257i
$808$	2.35923	−	4.08630i	0.0829973	−	0.143756i
$809$	−17.8551	+	30.9260i	−0.627752	+	1.08730i	0.360250	+	0.932856i	$0.382692\pi$
$809$	−17.8551	+	30.9260i	−0.627752	+	1.08730i	−0.988002	+	0.154443i	$0.950642\pi$
$810$	33.3912	+	57.8352i	1.17325	+	2.03212i
$811$	2.22418			0.0781015			0.0390508	−	0.999237i	$-0.487567\pi$
$811$	2.22418			0.0781015			0.0390508	+	0.999237i	$0.487567\pi$
$812$	−36.7973	+	23.7155i	−1.29133	+	0.832252i
$813$	−0.745166			−0.0261341
$814$	21.0659	+	36.4873i	0.738360	+	1.27888i
$815$	−33.6234	+	58.2375i	−1.17778	+	2.03997i
$816$	−1.15489	+	2.00032i	−0.0404291	+	0.0700252i
$817$	2.25496	+	3.90570i	0.0788910	+	0.136643i
$818$	7.15264			0.250086
$819$		0			0
$820$	−19.2411			−0.671927
$821$	26.6847	+	46.2192i	0.931302	+	1.61306i	0.781099	+	0.624407i	$0.214659\pi$
$821$	26.6847	+	46.2192i	0.931302	+	1.61306i	0.150203	+	0.988655i	$0.452007\pi$
$822$	1.22198	−	2.11654i	0.0426216	−	0.0738228i
$823$	−25.6043	+	44.3479i	−0.892509	+	1.54587i	−0.0556519	+	0.998450i	$0.517724\pi$
$823$	−25.6043	+	44.3479i	−0.892509	+	1.54587i	−0.836857	+	0.547421i	$0.815610\pi$
$824$	7.94195	+	13.7559i	0.276671	+	0.479208i
$825$	−5.71485			−0.198966
$826$	−24.5245	−	12.6031i	−0.853316	−	0.438518i
$827$	8.97196			0.311986			0.155993	−	0.987758i	$-0.450142\pi$
$827$	8.97196			0.311986			0.155993	+	0.987758i	$0.450142\pi$
$828$	−8.14084	−	14.1003i	−0.282914	−	0.490021i
$829$	−20.2858	+	35.1360i	−0.704554	+	1.22032i	0.262298	+	0.964987i	$0.415520\pi$
$829$	−20.2858	+	35.1360i	−0.704554	+	1.22032i	−0.966852	+	0.255337i	$0.917814\pi$
$830$	29.3561	−	50.8462i	1.01896	−	1.76490i
$831$	0.0694940	+	0.120367i	0.00241072	+	0.00417549i
$832$		0			0
$833$	−33.3639	+	3.27305i	−1.15599	+	0.113405i
$834$	−0.923218			−0.0319684
$835$	−1.75374	−	3.03757i	−0.0606907	−	0.105119i
$836$	15.8343	−	27.4257i	0.547639	−	0.948539i
$837$	−0.793464	+	1.37432i	−0.0274261	+	0.0475034i
$838$	−30.6750	−	53.1307i	−1.05965	−	1.83537i
$839$	−32.3005			−1.11514			−0.557568	−	0.830131i	$-0.688266\pi$
$839$	−32.3005			−1.11514			−0.557568	+	0.830131i	$0.688266\pi$
$840$	−1.67006	−	0.858242i	−0.0576226	−	0.0296121i
$841$	14.1909			0.489342
$842$	−17.6549	−	30.5791i	−0.608427	−	1.05383i
$843$	−1.06408	+	1.84304i	−0.0366488	+	0.0634776i
$844$	−25.2340	+	43.7065i	−0.868588	+	1.50444i
$845$		0			0
$846$	6.42788			0.220995
$847$	0.638656	+	13.0516i	0.0219445	+	0.448457i
$848$	−16.2749			−0.558882
$849$	−1.42225	−	2.46341i	−0.0488116	−	0.0845442i
$850$	40.7347	−	70.5545i	1.39719	−	2.42000i
$851$	5.40904	−	9.36873i	0.185419	−	0.321156i
$852$	−1.98287	−	3.43444i	−0.0679321	−	0.117662i
$853$	35.5887			1.21853			0.609267	−	0.792965i	$-0.291464\pi$
$853$	35.5887			1.21853			0.609267	+	0.792965i	$0.291464\pi$
$854$	9.62114	−	6.20074i	0.329229	−	0.212185i
$855$	33.7200			1.15320
$856$	−5.34723	−	9.26167i	−0.182764	−	0.316557i
$857$	−23.0114	+	39.8570i	−0.786055	+	1.36149i	0.142311	+	0.989822i	$0.454547\pi$
$857$	−23.0114	+	39.8570i	−0.786055	+	1.36149i	−0.928367	+	0.371666i	$0.878787\pi$
$858$		0			0
$859$	−12.6229	−	21.8635i	−0.430689	−	0.745975i	0.566244	−	0.824238i	$-0.308396\pi$
$859$	−12.6229	−	21.8635i	−0.430689	−	0.745975i	−0.996933	+	0.0782630i	$0.975063\pi$
$860$	12.9960			0.443160
$861$	0.842963	−	0.543282i	0.0287281	−	0.0185150i
$862$	−43.6903			−1.48810
$863$	−6.91684	−	11.9803i	−0.235452	−	0.407815i	0.723952	−	0.689850i	$-0.242324\pi$
$863$	−6.91684	−	11.9803i	−0.235452	−	0.407815i	−0.959404	+	0.282036i	$0.908990\pi$
$864$	−4.23348	+	7.33260i	−0.144026	+	0.249460i
$865$	−4.43019	+	7.67331i	−0.150631	+	0.260900i
$866$	20.6271	+	35.7271i	0.700936	+	1.21406i
$867$	−1.06168			−0.0360567
$868$	0.484025	+	9.89152i	0.0164289	+	0.335740i
$869$	7.85701			0.266531
$870$	4.50457	+	7.80215i	0.152719	+	0.264518i
$871$		0			0
$872$	−3.65798	+	6.33581i	−0.123875	+	0.214557i
$873$	2.01677	+	3.49315i	0.0682573	+	0.118225i
$874$	−14.5908			−0.493542
$875$	−25.4862	−	13.0973i	−0.861592	−	0.442771i
$876$	−1.39089			−0.0469938
$877$	1.82708	+	3.16459i	0.0616961	+	0.106861i	0.895224	−	0.445617i	$-0.147016\pi$
$877$	1.82708	+	3.16459i	0.0616961	+	0.106861i	−0.833528	+	0.552478i	$0.813682\pi$
$878$	14.2675	−	24.7120i	0.481504	−	0.833989i
$879$	−0.602469	+	1.04351i	−0.0203208	+	0.0351966i
$880$	19.4106	+	33.6201i	0.654331	+	1.13333i
$881$	36.6320			1.23416			0.617082	−	0.786899i	$-0.288315\pi$
$881$	36.6320			1.23416			0.617082	+	0.786899i	$0.288315\pi$
$882$	−43.9484	+	4.31140i	−1.47982	+	0.145172i
$883$	−7.11145			−0.239319			−0.119660	−	0.992815i	$-0.538180\pi$
$883$	−7.11145			−0.239319			−0.119660	+	0.992815i	$0.538180\pi$
$884$		0			0
$885$	−1.58117	+	2.73867i	−0.0531506	+	0.0920595i
$886$	−35.6585	+	61.7623i	−1.19797	+	2.07494i
$887$	3.36773	+	5.83308i	0.113077	+	0.195856i	0.917010	−	0.398865i	$-0.130596\pi$
$887$	3.36773	+	5.83308i	0.113077	+	0.195856i	−0.803932	+	0.594721i	$0.797263\pi$
$888$	0.977160			0.0327913
$889$	−45.9212	−	23.5989i	−1.54015	−	0.791480i
$890$	98.1004			3.28833
$891$	−17.3930	−	30.1255i	−0.582686	−	1.00924i
$892$	34.8878	−	60.4274i	1.16813	−	2.02326i
$893$	1.60512	−	2.78014i	0.0537131	−	0.0930339i
$894$	0.0219259	+	0.0379767i	0.000733311	+	0.00127013i
$895$	52.1885			1.74447
$896$	1.10019	+	22.4835i	0.0367549	+	0.751122i
$897$		0			0
$898$	36.5886	+	63.3733i	1.22098	+	2.11479i
$899$	4.88533	−	8.46164i	0.162935	−	0.282212i
$900$	29.9031	−	51.7938i	0.996772	−	1.72646i
$901$	−14.4523	−	25.0321i	−0.481475	−	0.833939i
$902$	17.9839			0.598798
$903$	−0.569363	+	0.366950i	−0.0189472	+	0.0122113i
$904$	−19.3045			−0.642058
$905$	−16.5496	−	28.6647i	−0.550127	−	0.952848i
$906$	−2.24350	+	3.88585i	−0.0745351	+	0.129099i
$907$	2.46630	−	4.27175i	0.0818921	−	0.141841i	−0.822171	−	0.569241i	$-0.807237\pi$
$907$	2.46630	−	4.27175i	0.0818921	−	0.141841i	0.904063	+	0.427400i	$0.140570\pi$
$908$	14.3145	+	24.7935i	0.475045	+	0.822802i
$909$	−12.7269			−0.422123
$910$		0			0
$911$	−26.6258			−0.882152			−0.441076	−	0.897470i	$-0.645403\pi$
$911$	−26.6258			−0.882152			−0.441076	+	0.897470i	$0.645403\pi$
$912$	0.759754	+	1.31593i	0.0251580	+	0.0435749i
$913$	−15.2911	+	26.4850i	−0.506063	+	0.876526i
$914$	−14.3251	+	24.8118i	−0.473833	+	0.820702i
$915$	−0.656374	−	1.13687i	−0.0216991	−	0.0375839i
$916$	21.9321			0.724656
$917$	2.46650	+	50.4054i	0.0814512	+	1.66453i
$918$	−10.8654			−0.358613
$919$	16.1918	+	28.0450i	0.534118	+	0.925119i	0.999205	+	0.0398544i	$0.0126894\pi$
$919$	16.1918	+	28.0450i	0.534118	+	0.925119i	−0.465088	+	0.885265i	$0.653977\pi$
$920$	−4.32286	+	7.48741i	−0.142520	+	0.246853i
$921$	1.31618	−	2.27970i	0.0433697	−	0.0751185i
$922$	−1.44428	−	2.50156i	−0.0475647	−	0.0823844i
$923$		0			0
$924$	4.23052	+	2.17406i	0.139174	+	0.0715213i
$925$	39.7373			1.30655
$926$	2.65512	+	4.59880i	0.0872526	+	0.151126i
$927$	21.4214	−	37.1030i	0.703572	−	1.21862i
$928$	26.0654	−	45.1466i	0.855639	−	1.48201i
$929$	−14.0135	−	24.2722i	−0.459769	−	0.796344i	0.539179	−	0.842191i	$-0.318735\pi$
$929$	−14.0135	−	24.2722i	−0.459769	−	0.796344i	−0.998948	+	0.0458472i	$0.985401\pi$
$930$	2.03805			0.0668304
$931$	−9.10967	+	20.0848i	−0.298557	+	0.658254i
$932$	−8.47099			−0.277476
$933$	2.56278	+	4.43887i	0.0839018	+	0.145322i
$934$	−27.8633	+	48.2606i	−0.911714	+	1.57914i
$935$	−34.4737	+	59.7102i	−1.12741	+	1.95273i
$936$		0			0
$937$	14.1324			0.461686			0.230843	−	0.972991i	$-0.425852\pi$
$937$	14.1324			0.461686			0.230843	+	0.972991i	$0.425852\pi$
$938$	19.5612	+	10.0525i	0.638696	+	0.328225i
$939$	5.87091			0.191590
$940$	−4.62538	−	8.01140i	−0.150863	−	0.261303i
$941$	−4.48647	+	7.77080i	−0.146255	+	0.253321i	−0.929840	−	0.367963i	$-0.880055\pi$
$941$	−4.48647	+	7.77080i	−0.146255	+	0.253321i	0.783586	+	0.621284i	$0.213389\pi$
$942$	2.49891	−	4.32824i	0.0814189	−	0.141022i
$943$	−2.30883	−	3.99902i	−0.0751860	−	0.130226i
$944$	13.2218			0.430334
$945$	0.497728	+	10.1716i	0.0161911	+	0.330881i
$946$	−12.1469			−0.394929
$947$	23.1479	+	40.0933i	0.752205	+	1.30286i	0.946752	+	0.321964i	$0.104343\pi$
$947$	23.1479	+	40.0933i	0.752205	+	1.30286i	−0.194546	+	0.980893i	$0.562324\pi$
$948$	0.443101	−	0.767473i	0.0143912	−	0.0249264i
$949$		0			0
$950$	−26.7977	−	46.4150i	−0.869433	−	1.50590i
$951$	1.86225			0.0603876
$952$	−11.7197	+	7.55326i	−0.379838	+	0.244803i
$953$	19.1097			0.619023			0.309512	−	0.950896i	$-0.399834\pi$
$953$	19.1097			0.619023			0.309512	+	0.950896i	$0.399834\pi$
$954$	−19.0371	−	32.9733i	−0.616350	−	1.06755i
$955$	−31.7042	+	54.9134i	−1.02593	+	1.77695i
$956$	−25.0257	+	43.3458i	−0.809390	+	1.40190i
$957$	−2.34636	−	4.06402i	−0.0758472	−	0.131371i
$958$	−50.6846			−1.63755
$959$	−14.2972	+	9.21443i	−0.461681	+	0.297549i
$960$	7.39560			0.238692
$961$	14.3948	+	24.9326i	0.464350	+	0.804277i
$962$		0			0
$963$	−14.4228	+	24.9811i	−0.464769	+	0.805003i
$964$	−23.7570	−	41.1483i	−0.765160	−	1.32530i
$965$	71.2400			2.29330
$966$	−0.107108	−	2.18885i	−0.00344614	−	0.0704252i
$967$	22.5432			0.724942			0.362471	−	0.931995i	$-0.381933\pi$
$967$	22.5432			0.724942			0.362471	+	0.931995i	$0.381933\pi$
$968$	2.71736	+	4.70660i	0.0873392	+	0.151276i
$969$	−1.34934	+	2.33713i	−0.0433471	+	0.0750793i
$970$	5.20809	−	9.02068i	0.167222	−	0.289637i
$971$	−13.6429	−	23.6301i	−0.437820	−	0.758327i	0.559701	−	0.828695i	$-0.310916\pi$
$971$	−13.6429	−	23.6301i	−0.437820	−	0.758327i	−0.997521	+	0.0703679i	$0.977583\pi$
$972$	−11.9858			−0.384444
$973$	5.71485	+	2.93685i	0.183210	+	0.0941512i
$974$	−22.5188			−0.721550
$975$		0			0
$976$	−2.74431	+	4.75329i	−0.0878433	+	0.152149i
$977$	28.0920	−	48.6568i	0.898744	−	1.55667i	0.0696427	−	0.997572i	$-0.477814\pi$
$977$	28.0920	−	48.6568i	0.898744	−	1.55667i	0.829101	−	0.559098i	$-0.188853\pi$
$978$	−3.54464	−	6.13949i	−0.113345	−	0.196319i
$979$	−51.0990			−1.63313
$980$	36.9979	+	51.6727i	1.18186	+	1.65062i
$981$	19.7330			0.630026
$982$	−21.0108	−	36.3919i	−0.670483	−	1.16131i
$983$	−13.2445	+	22.9402i	−0.422435	+	0.731678i	−0.996177	−	0.0873577i	$-0.972158\pi$
$983$	−13.2445	+	22.9402i	−0.422435	+	0.731678i	0.573742	+	0.819036i	$0.305491\pi$
$984$	0.208549	−	0.361218i	0.00664830	−	0.0115152i
$985$	13.8114	+	23.9221i	0.440069	+	0.762222i
$986$	66.8982			2.13047
$987$	0.428847	+	0.220384i	0.0136504	+	0.00701490i
$988$		0			0
$989$	1.55946	+	2.70106i	0.0495879	+	0.0858887i
$990$	−45.4102	+	78.6527i	−1.44323	+	2.49975i
$991$	−2.55629	+	4.42763i	−0.0812033	+	0.140648i	−0.903767	−	0.428025i	$-0.859210\pi$
$991$	−2.55629	+	4.42763i	−0.0812033	+	0.140648i	0.822564	+	0.568673i	$0.192543\pi$
$992$	−5.89652	−	10.2131i	−0.187215	−	0.324266i
$993$	−0.797717			−0.0253148
$994$	2.42055	+	49.4662i	0.0767750	+	1.56897i
$995$	−23.5957			−0.748035
$996$	1.72471	+	2.98728i	0.0546494	+	0.0946555i
$997$	−1.01771	+	1.76272i	−0.0322311	+	0.0558260i	−0.881691	−	0.471827i	$-0.843595\pi$
$997$	−1.01771	+	1.76272i	−0.0322311	+	0.0558260i	0.849460	+	0.527653i	$0.176928\pi$
$998$	−14.0182	+	24.2803i	−0.443740	+	0.768580i
$999$	−2.64985	−	4.58967i	−0.0838375	−	0.145211i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1183.2.e.i.508.7		16
7.2	even	3	inner	1183.2.e.i.170.7		16
7.3	odd	6		8281.2.a.cj.1.2		8
7.4	even	3		8281.2.a.ck.1.2		8
13.5	odd	4		91.2.r.a.25.7	yes	16
13.8	odd	4		91.2.r.a.25.2	✓	16
13.12	even	2	inner	1183.2.e.i.508.2		16
39.5	even	4		819.2.dl.e.298.2		16
39.8	even	4		819.2.dl.e.298.7		16
91.5	even	12		637.2.r.f.324.2		16
91.18	odd	12		637.2.c.f.246.7		8
91.25	even	6		8281.2.a.ck.1.7		8
91.31	even	12		637.2.c.e.246.7		8
91.34	even	4		637.2.r.f.116.2		16
91.38	odd	6		8281.2.a.cj.1.7		8
91.44	odd	12		91.2.r.a.51.2	yes	16
91.47	even	12		637.2.r.f.324.7		16
91.51	even	6	inner	1183.2.e.i.170.2		16
91.60	odd	12		637.2.c.f.246.2		8
91.73	even	12		637.2.c.e.246.2		8
91.83	even	4		637.2.r.f.116.7		16
91.86	odd	12		91.2.r.a.51.7	yes	16
273.44	even	12		819.2.dl.e.415.7		16
273.86	even	12		819.2.dl.e.415.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.r.a.25.2	✓	16	13.8	odd	4
91.2.r.a.25.7	yes	16	13.5	odd	4
91.2.r.a.51.2	yes	16	91.44	odd	12
91.2.r.a.51.7	yes	16	91.86	odd	12
637.2.c.e.246.2		8	91.73	even	12
637.2.c.e.246.7		8	91.31	even	12
637.2.c.f.246.2		8	91.60	odd	12
637.2.c.f.246.7		8	91.18	odd	12
637.2.r.f.116.2		16	91.34	even	4
637.2.r.f.116.7		16	91.83	even	4
637.2.r.f.324.2		16	91.5	even	12
637.2.r.f.324.7		16	91.47	even	12
819.2.dl.e.298.2		16	39.5	even	4
819.2.dl.e.298.7		16	39.8	even	4
819.2.dl.e.415.2		16	273.86	even	12
819.2.dl.e.415.7		16	273.44	even	12
1183.2.e.i.170.2		16	91.51	even	6	inner
1183.2.e.i.170.7		16	7.2	even	3	inner
1183.2.e.i.508.2		16	13.12	even	2	inner
1183.2.e.i.508.7		16	1.1	even	1	trivial
8281.2.a.cj.1.2		8	7.3	odd	6
8281.2.a.cj.1.7		8	91.38	odd	6
8281.2.a.ck.1.2		8	7.4	even	3
8281.2.a.ck.1.7		8	91.25	even	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)

\(f(q)\)	\(=\)	\(q+(1.06275 + 1.84073i) q^{2} +(0.0894272 - 0.154892i) q^{3} +(-1.25885 + 2.18040i) q^{4} +(-1.80301 - 3.12291i) q^{5} +0.380153 q^{6} +(-2.35320 - 1.20931i) q^{7} -1.10038 q^{8} +(1.48401 + 2.57037i) q^{9} +O(q^{10})\)	\(q+(1.06275 + 1.84073i) q^{2} +(0.0894272 - 0.154892i) q^{3} +(-1.25885 + 2.18040i) q^{4} +(-1.80301 - 3.12291i) q^{5} +0.380153 q^{6} +(-2.35320 - 1.20931i) q^{7} -1.10038 q^{8} +(1.48401 + 2.57037i) q^{9} +(3.83229 - 6.63772i) q^{10} +(-1.99618 + 3.45748i) q^{11} +(0.225152 + 0.389974i) q^{12} +(-0.274848 - 5.61680i) q^{14} -0.644954 q^{15} +(1.34828 + 2.33529i) q^{16} +(-2.39458 + 4.14753i) q^{17} +(-3.15424 + 5.46330i) q^{18} +(1.57530 + 2.72850i) q^{19} +9.07892 q^{20} +(-0.397753 + 0.256349i) q^{21} -8.48572 q^{22} +(1.08943 + 1.88694i) q^{23} +(-0.0984042 + 0.170441i) q^{24} +(-4.00171 + 6.93117i) q^{25} +1.06740 q^{27} +(5.59912 - 3.60858i) q^{28} -6.57198 q^{29} +(-0.685421 - 1.18718i) q^{30} +(-0.743358 + 1.28753i) q^{31} +(-3.96614 + 6.86956i) q^{32} +(0.357025 + 0.618386i) q^{33} -10.1793 q^{34} +(0.466298 + 9.52925i) q^{35} -7.47259 q^{36} +(-2.48252 - 4.29984i) q^{37} +(-3.34828 + 5.79939i) q^{38} +(1.98401 + 3.43640i) q^{40} -2.11931 q^{41} +(-0.894578 - 0.459722i) q^{42} +1.43145 q^{43} +(-5.02580 - 8.70494i) q^{44} +(5.35136 - 9.26883i) q^{45} +(-2.31557 + 4.01068i) q^{46} +(-0.509464 - 0.882417i) q^{47} +0.482292 q^{48} +(4.07515 + 5.69150i) q^{49} -17.0112 q^{50} +(0.428281 + 0.741804i) q^{51} +(-3.01771 + 5.22682i) q^{53} +(1.13438 + 1.96480i) q^{54} +14.3966 q^{55} +(2.58943 + 1.33070i) q^{56} +0.563498 q^{57} +(-6.98434 - 12.0972i) q^{58} +(2.45161 - 4.24631i) q^{59} +(0.811902 - 1.40626i) q^{60} +(1.01771 + 1.76272i) q^{61} -3.16000 q^{62} +(-0.383795 - 7.84323i) q^{63} -11.4669 q^{64} +(-0.758854 + 1.31437i) q^{66} +(-1.95545 + 3.38694i) q^{67} +(-6.02885 - 10.4423i) q^{68} +0.389698 q^{69} +(-17.0452 + 10.9855i) q^{70} -8.80684 q^{71} +(-1.63297 - 2.82840i) q^{72} +(-1.54439 + 2.67497i) q^{73} +(5.27656 - 9.13927i) q^{74} +(0.715724 + 1.23967i) q^{75} -7.93228 q^{76} +(8.87858 - 5.72217i) q^{77} +(-0.984006 - 1.70435i) q^{79} +(4.86194 - 8.42112i) q^{80} +(-4.35656 + 7.54579i) q^{81} +(-2.25229 - 3.90108i) q^{82} +7.66020 q^{83} +(-0.0582290 - 1.18997i) q^{84} +17.2698 q^{85} +(1.52126 + 2.63491i) q^{86} +(-0.587714 + 1.01795i) q^{87} +(2.19656 - 3.80456i) q^{88} +(6.39960 + 11.0844i) q^{89} +22.7485 q^{90} -5.48572 q^{92} +(0.132953 + 0.230281i) q^{93} +(1.08286 - 1.87557i) q^{94} +(5.68057 - 9.83903i) q^{95} +(0.709362 + 1.22865i) q^{96} +1.35900 q^{97} +(-6.14567 + 13.5499i) q^{98} -11.8494 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{3} - 6 q^{4} - 12 q^{9}+O(q^{10}) \) 16 * q - 4 * q^3 - 6 * q^4 - 12 * q^9	\( 16 q - 4 q^{3} - 6 q^{4} - 12 q^{9} + 6 q^{10} - 18 q^{12} - 26 q^{14} + 2 q^{16} - 8 q^{17} - 36 q^{22} + 12 q^{23} + 32 q^{27} - 16 q^{29} - 38 q^{30} + 56 q^{36} - 34 q^{38} - 4 q^{40} + 16 q^{42} - 16 q^{43} + 36 q^{48} - 40 q^{49} - 16 q^{51} - 20 q^{53} + 24 q^{55} + 36 q^{56} - 12 q^{61} - 44 q^{62} - 88 q^{64} + 2 q^{66} - 2 q^{68} + 56 q^{69} + 42 q^{74} - 8 q^{75} + 76 q^{77} + 20 q^{79} - 24 q^{81} + 16 q^{82} - 68 q^{87} - 4 q^{88} + 216 q^{90} + 12 q^{92} - 26 q^{94} + 16 q^{95}+O(q^{100}) \) 16 * q - 4 * q^3 - 6 * q^4 - 12 * q^9 + 6 * q^10 - 18 * q^12 - 26 * q^14 + 2 * q^16 - 8 * q^17 - 36 * q^22 + 12 * q^23 + 32 * q^27 - 16 * q^29 - 38 * q^30 + 56 * q^36 - 34 * q^38 - 4 * q^40 + 16 * q^42 - 16 * q^43 + 36 * q^48 - 40 * q^49 - 16 * q^51 - 20 * q^53 + 24 * q^55 + 36 * q^56 - 12 * q^61 - 44 * q^62 - 88 * q^64 + 2 * q^66 - 2 * q^68 + 56 * q^69 + 42 * q^74 - 8 * q^75 + 76 * q^77 + 20 * q^79 - 24 * q^81 + 16 * q^82 - 68 * q^87 - 4 * q^88 + 216 * q^90 + 12 * q^92 - 26 * q^94 + 16 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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