LMFDB - Embedded newform 595.2.x.b.16.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [595,2,Mod(16,595)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("595.16"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(595, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 2, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 595 = 5 \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	595.x (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [92] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$4.75109892027$
Analytic rank:	$0$
Dimension:	$92$
Relative dimension:	$46$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			16.4
Character	$\chi$	$=$	595.16
Dual form			595.2.x.b.186.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.27624 + 2.21052i) q^{2} +(2.06818 - 1.19407i) q^{3} +(-2.25759 - 3.91027i) q^{4} +(0.866025 + 0.500000i) q^{5} +6.09567i q^{6} +(2.39657 - 1.12092i) q^{7} +6.41999 q^{8} +(1.35159 - 2.34102i) q^{9} +(-2.21052 + 1.27624i) q^{10} +(-3.62132 + 2.09077i) q^{11} +(-9.33824 - 5.39143i) q^{12} +4.01600 q^{13} +(-0.580801 + 6.72822i) q^{14} +2.38813 q^{15} +(-3.67828 + 6.37096i) q^{16} +(0.441388 - 4.09941i) q^{17} +(3.44991 + 5.97541i) q^{18} +(1.00501 - 1.74073i) q^{19} -4.51519i q^{20} +(3.61810 - 5.17992i) q^{21} -10.6733i q^{22} +(0.480161 + 0.277221i) q^{23} +(13.2777 - 7.66589i) q^{24} +(0.500000 + 0.866025i) q^{25} +(-5.12540 + 8.87745i) q^{26} +0.708861i q^{27} +(-9.79357 - 6.84066i) q^{28} -1.78257i q^{29} +(-3.04784 + 5.27901i) q^{30} +(5.36207 - 3.09579i) q^{31} +(-2.96876 - 5.14205i) q^{32} +(-4.99304 + 8.64820i) q^{33} +(8.49851 + 6.20754i) q^{34} +(2.63595 + 0.227543i) q^{35} -12.2053 q^{36} +(-1.18798 - 0.685881i) q^{37} +(2.56527 + 4.44318i) q^{38} +(8.30583 - 4.79537i) q^{39} +(5.55987 + 3.20999i) q^{40} +4.93364i q^{41} +(6.83274 + 14.6087i) q^{42} +11.3187 q^{43} +(16.3510 + 9.44023i) q^{44} +(2.34102 - 1.35159i) q^{45} +(-1.22560 + 0.707603i) q^{46} +(-4.97319 + 8.61381i) q^{47} +17.5684i q^{48} +(4.48709 - 5.37271i) q^{49} -2.55249 q^{50} +(-3.98210 - 9.00538i) q^{51} +(-9.06651 - 15.7037i) q^{52} +(-5.87953 - 10.1837i) q^{53} +(-1.56695 - 0.904679i) q^{54} -4.18154 q^{55} +(15.3859 - 7.19627i) q^{56} -4.80019i q^{57} +(3.94040 + 2.27499i) q^{58} +(4.72767 + 8.18856i) q^{59} +(-5.39143 - 9.33824i) q^{60} +(-1.03207 - 0.595865i) q^{61} +15.8039i q^{62} +(0.615088 - 7.12543i) q^{63} +0.442358 q^{64} +(3.47796 + 2.00800i) q^{65} +(-12.7447 - 22.0744i) q^{66} +(2.38498 + 4.13090i) q^{67} +(-17.0263 + 7.52887i) q^{68} +1.32408 q^{69} +(-3.86710 + 5.53641i) q^{70} -7.13069i q^{71} +(8.67717 - 15.0293i) q^{72} +(-14.1746 + 8.18373i) q^{73} +(3.03231 - 1.75070i) q^{74} +(2.06818 + 1.19407i) q^{75} -9.07561 q^{76} +(-6.33518 + 9.06988i) q^{77} +24.4803i q^{78} +(-7.84109 - 4.52706i) q^{79} +(-6.37096 + 3.67828i) q^{80} +(4.90119 + 8.48910i) q^{81} +(-10.9059 - 6.29653i) q^{82} -11.8416 q^{83} +(-28.4231 - 2.45357i) q^{84} +(2.43196 - 3.32950i) q^{85} +(-14.4454 + 25.0201i) q^{86} +(-2.12850 - 3.68668i) q^{87} +(-23.2488 + 13.4227i) q^{88} +(3.57568 - 6.19326i) q^{89} +6.89981i q^{90} +(9.62463 - 4.50160i) q^{91} -2.50341i q^{92} +(7.39317 - 12.8053i) q^{93} +(-12.6940 - 21.9866i) q^{94} +(1.74073 - 1.00501i) q^{95} +(-12.2799 - 7.08980i) q^{96} +3.47536i q^{97} +(6.14985 + 16.7757i) q^{98} +11.3034i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 92 q - 52 q^{4} + 40 q^{9} + 24 q^{13} - 4 q^{15} - 48 q^{16} + 12 q^{17} - 12 q^{18} - 8 q^{19} - 56 q^{21} + 46 q^{25} - 44 q^{26} - 20 q^{33} - 72 q^{34} + 6 q^{35} - 176 q^{36} + 8 q^{38} + 20 q^{42}+ \cdots - 152 q^{98}+O(q^{100}) $ 92 * q - 52 * q^4 + 40 * q^9 + 24 * q^13 - 4 * q^15 - 48 * q^16 + 12 * q^17 - 12 * q^18 - 8 * q^19 - 56 * q^21 + 46 * q^25 - 44 * q^26 - 20 * q^33 - 72 * q^34 + 6 * q^35 - 176 * q^36 + 8 * q^38 + 20 * q^42 - 16 * q^43 - 76 * q^47 + 6 * q^49 + 6 * q^51 + 8 * q^52 - 36 * q^53 + 24 * q^55 + 14 * q^59 - 28 * q^60 + 184 * q^64 + 4 * q^66 - 8 * q^67 + 44 * q^68 + 12 * q^69 - 4 * q^70 + 40 * q^72 - 136 * q^76 - 44 * q^77 + 10 * q^81 - 224 * q^83 + 124 * q^84 - 12 * q^85 + 12 * q^86 + 48 * q^87 - 6 * q^89 - 16 * q^93 - 140 * q^94 - 152 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/595\mathbb{Z}\right)^\times$.

$n$	$71$	$171$	$477$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	−1.27624	+	2.21052i	−0.902440	+	1.56307i	−0.0781236	+	0.996944i	$0.524893\pi$
$2$	−1.27624	+	2.21052i	−0.902440	+	1.56307i	−0.824317	+	0.566129i	$0.808440\pi$
$3$	2.06818	−	1.19407i	1.19407	−	0.689394i	0.234840	−	0.972034i	$-0.424543\pi$
$3$	2.06818	−	1.19407i	1.19407	−	0.689394i	0.959226	+	0.282640i	$0.0912101\pi$
$4$	−2.25759	−	3.91027i	−1.12880	−	1.95513i
$5$	0.866025	+	0.500000i	0.387298	+	0.223607i
$5$	0.866025	+	0.500000i	0.387298	+	0.223607i
$6$			6.09567i			2.48855i
$7$	2.39657	−	1.12092i	0.905818	−	0.423666i
$7$	2.39657	−	1.12092i	0.905818	−	0.423666i
$8$	6.41999			2.26981
$9$	1.35159	−	2.34102i	0.450529	−	0.780339i
$10$	−2.21052	+	1.27624i	−0.699027	+	0.403584i
$11$	−3.62132	+	2.09077i	−1.09187	+	0.630392i	−0.934074	−	0.357080i	$-0.883772\pi$
$11$	−3.62132	+	2.09077i	−1.09187	+	0.630392i	−0.157797	+	0.987472i	$0.550439\pi$
$12$	−9.33824	−	5.39143i	−2.69572	−	1.55637i
$13$	4.01600			1.11384			0.556920	−	0.830566i	$-0.311983\pi$
$13$	4.01600			1.11384			0.556920	+	0.830566i	$0.311983\pi$
$14$	−0.580801	+	6.72822i	−0.155225	+	1.79819i
$15$	2.38813			0.616613
$16$	−3.67828	+	6.37096i	−0.919569	+	1.59274i
$17$	0.441388	−	4.09941i	0.107052	−	0.994253i
$17$	0.441388	−	4.09941i	0.107052	−	0.994253i
$18$	3.44991	+	5.97541i	0.813151	+	1.40842i
$19$	1.00501	−	1.74073i	0.230565	−	0.399350i	−0.727410	−	0.686203i	$-0.759276\pi$
$19$	1.00501	−	1.74073i	0.230565	−	0.399350i	0.957974	+	0.286853i	$0.0926093\pi$
$20$		−	4.51519i		−	1.00963i
$21$	3.61810	−	5.17992i	0.789533	−	1.13035i
$22$		−	10.6733i		−	2.27556i
$23$	0.480161	+	0.277221i	0.100120	+	0.0578046i	0.549224	−	0.835675i	$-0.314923\pi$
$23$	0.480161	+	0.277221i	0.100120	+	0.0578046i	−0.449104	+	0.893480i	$0.648257\pi$
$24$	13.2777	−	7.66589i	2.71030	−	1.56479i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	−5.12540	+	8.87745i	−1.00517	+	1.74101i
$27$			0.708861i			0.136420i
$28$	−9.79357	−	6.84066i	−1.85081	−	1.29276i
$29$		−	1.78257i		−	0.331015i	−0.986209	−	0.165507i	$-0.947074\pi$
$29$		−	1.78257i		−	0.331015i	0.986209	−	0.165507i	$-0.0529261\pi$
$30$	−3.04784	+	5.27901i	−0.556456	+	0.963811i
$31$	5.36207	−	3.09579i	0.963057	−	0.556021i	0.0659444	−	0.997823i	$-0.478994\pi$
$31$	5.36207	−	3.09579i	0.963057	−	0.556021i	0.897113	+	0.441802i	$0.145661\pi$
$32$	−2.96876	−	5.14205i	−0.524808	−	0.908995i
$33$	−4.99304	+	8.64820i	−0.869177	+	1.50546i
$34$	8.49851	+	6.20754i	1.45748	+	1.06458i
$35$	2.63595	+	0.227543i	0.445557	+	0.0384618i
$36$	−12.2053			−2.03422
$37$	−1.18798	−	0.685881i	−0.195303	−	0.112758i	0.399160	−	0.916881i	$-0.369302\pi$
$37$	−1.18798	−	0.685881i	−0.195303	−	0.112758i	−0.594463	+	0.804123i	$0.702635\pi$
$38$	2.56527	+	4.44318i	0.416142	+	0.720779i
$39$	8.30583	−	4.79537i	1.33000	−	0.767874i
$40$	5.55987	+	3.20999i	0.879093	+	0.507544i
$41$			4.93364i			0.770506i	0.922811	+	0.385253i	$0.125886\pi$
$41$			4.93364i			0.770506i	−0.922811	+	0.385253i	$0.874114\pi$
$42$	6.83274	+	14.6087i	1.05431	+	2.25417i
$43$	11.3187			1.72608			0.863040	−	0.505135i	$-0.168557\pi$
$43$	11.3187			1.72608			0.863040	+	0.505135i	$0.168557\pi$
$44$	16.3510	+	9.44023i	2.46500	+	1.42317i
$45$	2.34102	−	1.35159i	0.348978	−	0.201483i
$46$	−1.22560	+	0.707603i	−0.180705	+	0.104330i
$47$	−4.97319	+	8.61381i	−0.725414	+	1.25645i	0.233390	+	0.972383i	$0.425018\pi$
$47$	−4.97319	+	8.61381i	−0.725414	+	1.25645i	−0.958804	+	0.284070i	$0.908315\pi$
$48$			17.5684i			2.53578i
$49$	4.48709	−	5.37271i	0.641013	−	0.767530i
$50$	−2.55249			−0.360976
$51$	−3.98210	−	9.00538i	−0.557605	−	1.26101i
$52$	−9.06651	−	15.7037i	−1.25730	−	2.17770i
$53$	−5.87953	−	10.1837i	−0.807616	−	1.39883i	−0.914511	−	0.404562i	$-0.867424\pi$
$53$	−5.87953	−	10.1837i	−0.807616	−	1.39883i	0.106895	−	0.994270i	$-0.465909\pi$
$54$	−1.56695	−	0.904679i	−0.213235	−	0.123111i
$55$	−4.18154			−0.563839
$56$	15.3859	−	7.19627i	2.05603	−	0.961641i
$57$		−	4.80019i		−	0.635800i
$58$	3.94040	+	2.27499i	0.517400	+	0.298721i
$59$	4.72767	+	8.18856i	0.615490	+	1.06606i	0.990298	+	0.138958i	$0.0443752\pi$
$59$	4.72767	+	8.18856i	0.615490	+	1.06606i	−0.374808	+	0.927102i	$0.622291\pi$
$60$	−5.39143	−	9.33824i	−0.696031	−	1.20556i
$61$	−1.03207	−	0.595865i	−0.132143	−	0.0762927i	0.432471	−	0.901648i	$-0.357642\pi$
$61$	−1.03207	−	0.595865i	−0.132143	−	0.0762927i	−0.564614	+	0.825355i	$0.690975\pi$
$62$			15.8039i			2.00710i
$63$	0.615088	−	7.12543i	0.0774938	−	0.897719i
$64$	0.442358			0.0552948
$65$	3.47796	+	2.00800i	0.431388	+	0.249062i
$66$	−12.7447	−	22.0744i	−1.56876	−	2.71717i
$67$	2.38498	+	4.13090i	0.291371	+	0.504670i	0.974134	−	0.225970i	$-0.0725552\pi$
$67$	2.38498	+	4.13090i	0.291371	+	0.504670i	−0.682763	+	0.730640i	$0.739222\pi$
$68$	−17.0263	+	7.52887i	−2.06474	+	0.913009i
$69$	1.32408			0.159401
$70$	−3.86710	+	5.53641i	−0.462207	+	0.661728i
$71$		−	7.13069i		−	0.846257i	−0.906070	−	0.423128i	$-0.860932\pi$
$71$		−	7.13069i		−	0.846257i	0.906070	−	0.423128i	$-0.139068\pi$
$72$	8.67717	−	15.0293i	1.02261	−	1.77122i
$73$	−14.1746	+	8.18373i	−1.65901	+	0.957833i	−0.685844	+	0.727748i	$0.740567\pi$
$73$	−14.1746	+	8.18373i	−1.65901	+	0.957833i	−0.973171	+	0.230084i	$0.926100\pi$
$74$	3.03231	−	1.75070i	0.352498	−	0.203515i
$75$	2.06818	+	1.19407i	0.238813	+	0.137879i
$76$	−9.07561			−1.04104
$77$	−6.33518	+	9.06988i	−0.721960	+	1.03361i
$78$			24.4803i			2.77184i
$79$	−7.84109	−	4.52706i	−0.882192	−	0.509334i	−0.0108111	−	0.999942i	$-0.503441\pi$
$79$	−7.84109	−	4.52706i	−0.882192	−	0.509334i	−0.871380	+	0.490608i	$0.836775\pi$
$80$	−6.37096	+	3.67828i	−0.712295	+	0.411244i
$81$	4.90119	+	8.48910i	0.544576	+	0.943234i
$82$	−10.9059	−	6.29653i	−1.20436	−	0.695336i
$83$	−11.8416			−1.29978			−0.649890	−	0.760028i	$-0.725185\pi$
$83$	−11.8416			−1.29978			−0.649890	+	0.760028i	$0.725185\pi$
$84$	−28.4231	−	2.45357i	−3.10121	−	0.267706i
$85$	2.43196	−	3.32950i	0.263783	−	0.361135i
$86$	−14.4454	+	25.0201i	−1.55768	+	2.69799i
$87$	−2.12850	−	3.68668i	−0.228200	−	0.395253i
$88$	−23.2488	+	13.4227i	−2.47834	+	1.43087i
$89$	3.57568	−	6.19326i	0.379021	−	0.656484i	−0.611899	−	0.790936i	$-0.709594\pi$
$89$	3.57568	−	6.19326i	0.379021	−	0.656484i	0.990920	+	0.134452i	$0.0429273\pi$
$90$			6.89981i			0.727304i
$91$	9.62463	−	4.50160i	1.00894	−	0.471896i
$92$		−	2.50341i		−	0.260999i
$93$	7.39317	−	12.8053i	0.766636	−	1.32785i
$94$	−12.6940	−	21.9866i	−1.30929	−	2.26775i
$95$	1.74073	−	1.00501i	0.178595	−	0.103112i
$96$	−12.2799	−	7.08980i	−1.25331	−	0.723600i
$97$			3.47536i			0.352869i	0.984312	+	0.176434i	$0.0564564\pi$
$97$			3.47536i			0.352869i	−0.984312	+	0.176434i	$0.943544\pi$
$98$	6.14985	+	16.7757i	0.621228	+	1.69460i
$99$			11.3034i			1.13604i
$100$	2.25759	−	3.91027i	0.225759	−	0.391027i
$101$	7.41280	+	12.8393i	0.737601	+	1.27756i	0.953573	+	0.301163i	$0.0973749\pi$
$101$	7.41280	+	12.8393i	0.737601	+	1.27756i	−0.215971	+	0.976400i	$0.569292\pi$
$102$	24.9887	+	2.69055i	2.47425	+	0.266405i
$103$	−0.403699	+	0.699228i	−0.0397777	+	0.0688970i	−0.885229	−	0.465156i	$-0.845998\pi$
$103$	−0.403699	+	0.699228i	−0.0397777	+	0.0688970i	0.845451	+	0.534053i	$0.179332\pi$
$104$	25.7827			2.52820
$105$	5.72332	−	2.67690i	0.558539	−	0.261238i
$106$	30.0149			2.91530
$107$	−11.5635	−	6.67622i	−1.11789	−	0.645414i	−0.177029	−	0.984206i	$-0.556648\pi$
$107$	−11.5635	−	6.67622i	−1.11789	−	0.645414i	−0.940861	+	0.338792i	$0.889982\pi$
$108$	2.77184	−	1.60032i	0.266720	−	0.153991i
$109$	−16.4050	+	9.47146i	−1.57132	+	0.907201i	−0.575311	+	0.817935i	$0.695119\pi$
$109$	−16.4050	+	9.47146i	−1.57132	+	0.907201i	−0.996008	+	0.0892662i	$0.971548\pi$
$110$	5.33667	−	9.24338i	0.508831	−	0.881322i
$111$	−3.27595			−0.310939
$112$	−1.67393	+	19.3915i	−0.158172	+	1.83232i
$113$			1.88312i			0.177149i	0.996070	+	0.0885745i	$0.0282311\pi$
$113$			1.88312i			0.177149i	−0.996070	+	0.0885745i	$0.971769\pi$
$114$	10.6109	+	6.12621i	0.993802	+	0.573772i
$115$	0.277221	+	0.480161i	0.0258510	+	0.0447752i
$116$	−6.97032	+	4.02432i	−0.647178	+	0.373648i
$117$	5.42798	−	9.40153i	0.501817	−	0.869172i
$118$	−24.1346			−2.22177
$119$	−3.53728	−	10.3193i	−0.324262	−	0.945967i
$120$	15.3318			1.39959
$121$	3.24266	−	5.61645i	0.294787	−	0.510586i
$122$	2.63434	−	1.52094i	0.238502	−	0.137699i
$123$	5.89110	+	10.2037i	0.531182	+	0.920035i
$124$	−24.2108	−	13.9781i	−2.17419	−	1.25527i
$125$			1.00000i			0.0894427i
$126$	14.9659	+	10.4534i	1.33327	+	0.931267i
$127$	2.73320			0.242533			0.121266	−	0.992620i	$-0.461304\pi$
$127$	2.73320			0.242533			0.121266	+	0.992620i	$0.461304\pi$
$128$	5.37297	−	9.30626i	0.474908	−	0.822565i
$129$	23.4091	−	13.5152i	2.06105	−	1.18995i
$130$	−8.87745	+	5.12540i	−0.778604	+	0.449527i
$131$	−0.675988	−	0.390282i	−0.0590613	−	0.0340991i	0.470179	−	0.882571i	$-0.344190\pi$
$131$	−0.675988	−	0.390282i	−0.0590613	−	0.0340991i	−0.529240	+	0.848472i	$0.677523\pi$
$132$	45.0890			3.92450
$133$	0.457365	−	5.29830i	0.0396586	−	0.459421i
$134$	−12.1752			−1.05178
$135$	−0.354431	+	0.613892i	−0.0305045	+	0.0528354i
$136$	2.83370	−	26.3182i	0.242988	−	2.25676i
$137$	4.43464	+	7.68103i	0.378877	+	0.656234i	0.990899	−	0.134606i	$-0.0429770\pi$
$137$	4.43464	+	7.68103i	0.378877	+	0.656234i	−0.612022	+	0.790841i	$0.709644\pi$
$138$	−1.68985	+	2.92690i	−0.143850	+	0.249155i
$139$		−	22.0264i		−	1.86825i	−0.356944	−	0.934126i	$-0.616181\pi$
$139$		−	22.0264i		−	1.86825i	0.356944	−	0.934126i	$-0.383819\pi$
$140$	−5.06115	−	10.8210i	−0.427745	−	0.914538i
$141$			23.7532i			2.00038i
$142$	15.7625	+	9.10049i	1.32276	+	0.763696i
$143$	−14.5433	+	8.39655i	−1.21617	+	0.702155i
$144$	9.94302	+	17.2218i	0.828585	+	1.43515i
$145$	0.891284	−	1.54375i	0.0740171	−	0.128201i
$146$		−	41.7777i		−	3.45755i
$147$	2.86476	−	16.4696i	0.236282	−	1.35839i
$148$			6.19377i			0.509125i
$149$	−2.37659	+	4.11638i	−0.194698	+	0.337227i	−0.946801	−	0.321818i	$-0.895706\pi$
$149$	−2.37659	+	4.11638i	−0.194698	+	0.337227i	0.752104	+	0.659045i	$0.229039\pi$
$150$	−5.27901	+	3.04784i	−0.431029	+	0.248855i
$151$	2.94374	+	5.09871i	0.239558	+	0.414927i	0.960588	−	0.277977i	$-0.0896640\pi$
$151$	2.94374	+	5.09871i	0.239558	+	0.414927i	−0.721029	+	0.692905i	$0.756331\pi$
$152$	6.45214	−	11.1754i	0.523338	−	0.906448i
$153$	−9.00022	−	6.57401i	−0.727625	−	0.531477i
$154$	−11.9639	−	25.5794i	−0.964080	−	2.06125i
$155$	6.19159			0.497320
$156$	−37.5024	−	21.6520i	−3.00259	−	1.73355i
$157$	−0.817105	−	1.41527i	−0.0652121	−	0.112951i	0.831576	−	0.555411i	$-0.187439\pi$
$157$	−0.817105	−	1.41527i	−0.0652121	−	0.112951i	−0.896788	+	0.442460i	$0.854106\pi$
$158$	20.0143	−	11.5552i	1.59225	−	0.919286i
$159$	−24.3199	−	14.0411i	−1.92869	−	1.11353i
$160$		−	5.93753i		−	0.469403i
$161$	1.46148	+	0.126159i	0.115181	+	0.00994275i
$162$	−25.0204			−1.96579
$163$	−6.26503	−	3.61712i	−0.490715	−	0.283314i	0.234156	−	0.972199i	$-0.424767\pi$
$163$	−6.26503	−	3.61712i	−0.490715	−	0.283314i	−0.724871	+	0.688885i	$0.758101\pi$
$164$	19.2919	−	11.1382i	1.50644	−	0.869745i
$165$	−8.64820	+	4.99304i	−0.673261	+	0.388708i
$166$	15.1127	−	26.1760i	1.17297	−	2.03165i
$167$		−	10.8682i		−	0.841005i	−0.907291	−	0.420502i	$-0.861854\pi$
$167$		−	10.8682i		−	0.841005i	0.907291	−	0.420502i	$-0.138146\pi$
$168$	23.2281	−	33.2550i	1.79209	−	2.56568i
$169$	3.12829			0.240638
$170$	4.25615	+	9.62514i	0.326432	+	0.738215i
$171$	−2.71671	−	4.70548i	−0.207752	−	0.359837i
$172$	−25.5530	−	44.2590i	−1.94839	−	3.37472i
$173$	7.50316	+	4.33195i	0.570455	+	0.329352i	0.757331	−	0.653031i	$-0.226503\pi$
$173$	7.50316	+	4.33195i	0.570455	+	0.329352i	−0.186876	+	0.982383i	$0.559836\pi$
$174$	10.8660			0.823746
$175$	2.16903	+	1.51503i	0.163963	+	0.114526i
$176$		−	30.7617i		−	2.31875i
$177$	19.5554	+	11.2903i	1.46987	+	0.848631i
$178$	9.12688	+	15.8082i	0.684088	+	1.18488i
$179$	−6.73669	−	11.6683i	−0.503524	−	0.872129i	−0.999992	−	0.00407376i	$-0.998703\pi$
$179$	−6.73669	−	11.6683i	−0.503524	−	0.872129i	0.496468	−	0.868055i	$-0.334630\pi$
$180$	−10.5701	−	6.10267i	−0.787851	−	0.454866i
$181$			7.33197i			0.544981i	0.962158	+	0.272491i	$0.0878473\pi$
$181$			7.33197i			0.544981i	−0.962158	+	0.272491i	$0.912153\pi$
$182$	−2.33250	+	27.0206i	−0.172896	+	2.00290i
$183$	−2.84601			−0.210383
$184$	3.08263	+	1.77975i	0.227254	+	0.131205i
$185$	−0.685881	−	1.18798i	−0.0504270	−	0.0873421i
$186$	18.8710	+	32.6855i	1.38369	+	2.39661i
$187$	6.97253	+	15.7681i	0.509882	+	1.15308i
$188$	44.9097			3.27538
$189$	0.794574	+	1.69884i	0.0577967	+	0.123572i
$190$			5.13054i			0.372209i
$191$	11.5621	−	20.0261i	0.836604	−	1.44904i	−0.0561145	−	0.998424i	$-0.517871\pi$
$191$	11.5621	−	20.0261i	0.836604	−	1.44904i	0.892718	−	0.450616i	$-0.148795\pi$
$192$	0.914878	−	0.528205i	0.0660256	−	0.0381199i
$193$	−12.3766	+	7.14566i	−0.890890	+	0.514356i	−0.874234	−	0.485505i	$-0.838636\pi$
$193$	−12.3766	+	7.14566i	−0.890890	+	0.514356i	−0.0166568	+	0.999861i	$0.505302\pi$
$194$	−7.68234	−	4.43540i	−0.551560	−	0.318443i
$195$	9.59075			0.686808
$196$	−31.1388	−	5.41634i	−2.22420	−	0.386882i
$197$			11.0259i			0.785561i	0.919632	+	0.392781i	$0.128487\pi$
$197$			11.0259i			0.785561i	−0.919632	+	0.392781i	$0.871513\pi$
$198$	−24.9865	−	14.4259i	−1.77571	−	1.02521i
$199$	−2.85324	+	1.64732i	−0.202261	+	0.116775i	−0.597710	−	0.801713i	$-0.703922\pi$
$199$	−2.85324	+	1.64732i	−0.202261	+	0.116775i	0.395449	+	0.918488i	$0.370589\pi$
$200$	3.20999	+	5.55987i	0.226981	+	0.393142i
$201$	9.86513	+	5.69564i	0.695833	+	0.401739i
$202$	−37.8422			−2.66256
$203$	−1.99811	−	4.27205i	−0.140240	−	0.299839i
$204$	−26.2235	+	35.9016i	−1.83601	+	2.51361i
$205$	−2.46682	+	4.27266i	−0.172290	+	0.298416i
$206$	−1.03044	−	1.78477i	−0.0717940	−	0.124351i
$207$	1.29796	−	0.749376i	0.0902143	−	0.0520853i
$208$	−14.7720	+	25.5858i	−1.02425	+	1.77406i
$209$			8.40498i			0.581385i
$210$	−1.38703	+	16.0679i	−0.0957140	+	1.10879i
$211$			19.3683i			1.33337i	0.745341	+	0.666684i	$0.232287\pi$
$211$			19.3683i			1.33337i	−0.745341	+	0.666684i	$0.767713\pi$
$212$	−26.5472	+	45.9811i	−1.82327	+	3.15800i
$213$	−8.51451	−	14.7476i	−0.583405	−	1.01049i
$214$	29.5158	−	17.0410i	2.01766	−	1.16490i
$215$	9.80225	+	5.65933i	0.668508	+	0.385963i
$216$			4.55088i			0.309648i
$217$	9.38046	−	13.4297i	0.636787	−	0.911669i
$218$		−	48.3515i		−	3.27478i
$219$	−19.5438	+	33.8509i	−1.32065	+	2.28743i
$220$	9.44023	+	16.3510i	0.636460	+	1.10238i
$221$	1.77261	−	16.4633i	0.119239	−	1.10744i
$222$	4.18091	−	7.24155i	0.280604	−	0.486021i
$223$	−9.89020			−0.662297			−0.331148	−	0.943579i	$-0.607436\pi$
$223$	−9.89020			−0.662297			−0.331148	+	0.943579i	$0.607436\pi$
$224$	−12.8787	−	8.99555i	−0.860491	−	0.601040i
$225$	2.70317			0.180212
$226$	−4.16267	−	2.40332i	−0.276897	−	0.159866i
$227$	1.99810	−	1.15360i	0.132619	−	0.0765674i	−0.432223	−	0.901767i	$-0.642271\pi$
$227$	1.99810	−	1.15360i	0.132619	−	0.0765674i	0.564842	+	0.825199i	$0.308937\pi$
$228$	−18.7700	+	10.8369i	−1.24307	+	0.717689i
$229$	−13.6129	+	23.5782i	−0.899565	+	1.55809i	−0.0715133	+	0.997440i	$0.522783\pi$
$229$	−13.6129	+	23.5782i	−0.899565	+	1.55809i	−0.828051	+	0.560652i	$0.810551\pi$
$230$	−1.41521			−0.0933159
$231$	−2.27226	+	26.3228i	−0.149504	+	1.73191i
$232$		−	11.4441i		−	0.751339i
$233$	−13.1573	−	7.59637i	−0.861963	−	0.497655i	0.00270593	−	0.999996i	$-0.499139\pi$
$233$	−13.1573	−	7.59637i	−0.861963	−	0.497655i	−0.864669	+	0.502342i	$0.832472\pi$
$234$	13.8548	+	23.9973i	0.905719	+	1.56875i
$235$	−8.61381	+	4.97319i	−0.561903	+	0.324415i
$236$	21.3463	−	36.9729i	1.38953	−	2.40673i
$237$	−21.6224			−1.40453
$238$	27.3254	+	5.35069i	1.77124	+	0.346834i
$239$	13.8180			0.893812			0.446906	−	0.894581i	$-0.352526\pi$
$239$	13.8180			0.893812			0.446906	+	0.894581i	$0.352526\pi$
$240$	−8.78421	+	15.2147i	−0.567018	+	0.982104i
$241$	−10.6681	+	6.15922i	−0.687192	+	0.396750i	−0.802559	−	0.596573i	$-0.796529\pi$
$241$	−10.6681	+	6.15922i	−0.687192	+	0.396750i	0.115368	+	0.993323i	$0.463195\pi$
$242$	8.27684	+	14.3359i	0.532056	+	0.921548i
$243$	18.4314	+	10.6414i	1.18238	+	0.682645i
$244$			5.38089i			0.344476i
$245$	6.57229	−	2.40935i	0.419888	−	0.153928i
$246$	−30.0739			−1.91744
$247$	4.03612	−	6.99076i	0.256812	−	0.444812i
$248$	34.4244	−	19.8750i	2.18595	−	1.26206i
$249$	−24.4905	+	14.1396i	−1.55202	+	0.896061i
$250$	−2.21052	−	1.27624i	−0.139805	−	0.0807167i
$251$	−6.23058			−0.393271			−0.196635	−	0.980477i	$-0.563002\pi$
$251$	−6.23058			−0.393271			−0.196635	+	0.980477i	$0.563002\pi$
$252$	−29.2509	+	13.6812i	−1.84264	+	0.861832i
$253$	−2.31842			−0.145758
$254$	−3.48823	+	6.04180i	−0.218871	+	0.379096i
$255$	1.05409	−	9.78994i	0.0660098	−	0.613070i
$256$	14.1568	+	24.5203i	0.884800	+	1.53252i
$257$	16.0287	−	27.7626i	0.999846	−	1.73178i	0.484705	−	0.874678i	$-0.338927\pi$
$257$	16.0287	−	27.7626i	0.999846	−	1.73178i	0.515140	−	0.857106i	$-0.327740\pi$
$258$			68.9949i			4.29543i
$259$	−3.61590	−	0.312135i	−0.224681	−	0.0193951i
$260$		−	18.1330i		−	1.12456i
$261$	−4.17302	−	2.40930i	−0.258304	−	0.149132i
$262$	1.72545	−	0.996189i	0.106599	−	0.0615448i
$263$	4.70760	+	8.15380i	0.290283	+	0.502785i	0.973877	−	0.227078i	$-0.0729172\pi$
$263$	4.70760	+	8.15380i	0.290283	+	0.502785i	−0.683594	+	0.729863i	$0.739584\pi$
$264$	−32.0552	+	55.5213i	−1.97286	+	3.41710i
$265$		−	11.7591i		−	0.722354i
$266$	11.1283	+	7.77294i	0.682319	+	0.476589i
$267$		−	17.0784i		−	1.04518i
$268$	10.7686	−	18.6518i	0.657798	−	1.13934i
$269$	2.28931	−	1.32173i	0.139582	−	0.0805874i	−0.428583	−	0.903502i	$-0.640987\pi$
$269$	2.28931	−	1.32173i	0.139582	−	0.0805874i	0.568165	+	0.822915i	$0.307654\pi$
$270$	−0.904679	−	1.56695i	−0.0550570	−	0.0953616i
$271$	13.7492	−	23.8143i	0.835205	−	1.44662i	−0.0586592	−	0.998278i	$-0.518683\pi$
$271$	13.7492	−	23.8143i	0.835205	−	1.44662i	0.893864	−	0.448339i	$-0.147984\pi$
$272$	24.4936	+	17.8908i	1.48515	+	1.08479i
$273$	14.5303	−	20.8026i	0.879413	−	1.25903i
$274$	−22.6387			−1.36766
$275$	−3.62132	−	2.09077i	−0.218374	−	0.126078i
$276$	−2.98924	−	5.17751i	−0.179931	−	0.311649i
$277$	−16.9891	+	9.80866i	−1.02078	+	0.589345i	−0.914329	−	0.404973i	$-0.867281\pi$
$277$	−16.9891	+	9.80866i	−1.02078	+	0.589345i	−0.106447	+	0.994318i	$0.533948\pi$
$278$	48.6897	+	28.1110i	2.92021	+	1.68599i
$279$		−	16.7369i		−	1.00201i
$280$	16.9228	+	1.46082i	1.01133	+	0.0873009i
$281$	−16.2136			−0.967225			−0.483612	−	0.875282i	$-0.660676\pi$
$281$	−16.2136			−0.967225			−0.483612	+	0.875282i	$0.660676\pi$
$282$	−52.5070	−	30.3149i	−3.12675	−	1.80523i
$283$	−5.06893	+	2.92655i	−0.301316	+	0.173965i	−0.643034	−	0.765838i	$-0.722325\pi$
$283$	−5.06893	+	2.92655i	−0.301316	+	0.173965i	0.341718	+	0.939803i	$0.388991\pi$
$284$	−27.8829	+	16.0982i	−1.65455	+	0.955252i
$285$	2.40009	−	4.15708i	0.142169	−	0.246244i
$286$		−	42.8642i		−	2.53461i
$287$	5.53020	+	11.8238i	0.326438	+	0.697938i
$288$	−16.0502			−0.945765
$289$	−16.6104	−	3.61886i	−0.977080	−	0.212874i
$290$	2.27499	+	3.94040i	0.133592	+	0.231388i
$291$	4.14980	+	7.18767i	0.243266	+	0.421349i
$292$	64.0011	+	36.9511i	3.74538	+	2.16240i
$293$	−28.9303			−1.69012			−0.845062	−	0.534668i	$-0.820437\pi$
$293$	−28.9303			−1.69012			−0.845062	+	0.534668i	$0.820437\pi$
$294$	32.7503	+	27.3519i	1.91004	+	1.59519i
$295$			9.45534i			0.550511i
$296$	−7.62682	−	4.40335i	−0.443300	−	0.255939i
$297$	−1.48207	−	2.56702i	−0.0859983	−	0.148953i
$298$	−6.06622	−	10.5070i	−0.351407	−	0.608654i
$299$	1.92833	+	1.11332i	0.111518	+	0.0643850i
$300$		−	10.7829i		−	0.622549i
$301$	27.1260	−	12.6873i	1.56351	−	0.731282i
$302$	−15.0277			−0.864749
$303$	30.6621	+	17.7027i	1.76149	+	1.01700i
$304$	7.39340	+	12.8057i	0.424040	+	0.734460i
$305$	−0.595865	−	1.03207i	−0.0341191	−	0.0590961i
$306$	26.0184	−	11.5051i	1.48737	−	0.657704i
$307$	−8.48579			−0.484309			−0.242155	−	0.970238i	$-0.577854\pi$
$307$	−8.48579			−0.484309			−0.242155	+	0.970238i	$0.577854\pi$
$308$	49.7679	+	4.29612i	2.83579	+	0.244794i
$309$			1.92817i			0.109690i
$310$	−7.90197	+	13.6866i	−0.448802	+	0.777348i
$311$	−14.4075	+	8.31815i	−0.816972	+	0.471679i	−0.849371	−	0.527796i	$-0.823019\pi$
$311$	−14.4075	+	8.31815i	−0.816972	+	0.471679i	0.0323991	+	0.999475i	$0.489685\pi$
$312$	53.3233	−	30.7862i	3.01884	−	1.74293i
$313$	−22.3342	−	12.8947i	−1.26240	−	0.728849i	−0.288865	−	0.957370i	$-0.593278\pi$
$313$	−22.3342	−	12.8947i	−1.26240	−	0.728849i	−0.973539	+	0.228521i	$0.926611\pi$
$314$	4.17130			0.235400
$315$	4.09539	−	5.86326i	0.230749	−	0.330357i
$316$			40.8810i			2.29974i
$317$	−3.52493	−	2.03512i	−0.197980	−	0.114304i	0.397733	−	0.917501i	$-0.369797\pi$
$317$	−3.52493	−	2.03512i	−0.197980	−	0.114304i	−0.595713	+	0.803197i	$0.703130\pi$
$318$	62.0762	−	35.8397i	3.48106	−	2.00979i
$319$	3.72694	+	6.45526i	0.208669	+	0.361425i
$320$	0.383093	+	0.221179i	0.0214156	+	0.0123643i
$321$	−31.8874			−1.77978
$322$	−2.14408	+	3.06962i	−0.119485	+	0.171063i
$323$	−6.69236	−	4.88828i	−0.372373	−	0.271991i
$324$	22.1298	−	38.3299i	1.22943	−	2.12944i
$325$	2.00800	+	3.47796i	0.111384	+	0.192923i
$326$	15.9914	−	9.23264i	0.885682	−	0.511349i
$327$	−22.6191	+	39.1774i	−1.25084	+	2.16652i
$328$			31.6739i			1.74890i
$329$	−2.26323	+	26.2181i	−0.124776	+	1.44545i
$330$		−	25.4893i		−	1.40314i
$331$	9.83344	−	17.0320i	0.540495	−	0.936164i	−0.458381	−	0.888756i	$-0.651570\pi$
$331$	9.83344	−	17.0320i	0.540495	−	0.936164i	0.998876	−	0.0474084i	$-0.0150962\pi$
$332$	26.7334	+	46.3037i	1.46719	+	2.54125i
$333$	−3.21132	+	1.85406i	−0.175979	+	0.101602i
$334$	24.0243	+	13.8704i	1.31455	+	0.758957i
$335$			4.76995i			0.260610i
$336$	19.6927	+	42.1039i	1.07433	+	2.29696i
$337$		−	6.34891i		−	0.345847i	−0.984935	−	0.172924i	$-0.944679\pi$
$337$		−	6.34891i		−	0.345847i	0.984935	−	0.172924i	$-0.0553214\pi$
$338$	−3.99246	+	6.91514i	−0.217161	+	0.376134i
$339$	2.24857	+	3.89463i	0.122125	+	0.211527i
$340$	−18.5096	−	1.99295i	−1.00382	−	0.108083i
$341$	−12.9452	+	22.4218i	−0.701022	+	1.21421i
$342$	13.8687			0.749936
$343$	4.73128	−	17.9057i	0.255465	−	0.966818i
$344$	72.6657			3.91787
$345$	1.14669	+	0.662040i	0.0617356	+	0.0356430i
$346$	−19.1517	+	11.0573i	−1.02960	+	0.594442i
$347$	0.423418	−	0.244460i	0.0227303	−	0.0131233i	−0.488592	−	0.872512i	$-0.662489\pi$
$347$	0.423418	−	0.244460i	0.0227303	−	0.0131233i	0.511322	+	0.859389i	$0.329156\pi$
$348$	−9.61059	+	16.6460i	−0.515182	+	0.892321i
$349$	31.9879			1.71227			0.856136	−	0.516750i	$-0.172858\pi$
$349$	31.9879			1.71227			0.856136	+	0.516750i	$0.172858\pi$
$350$	−6.11721	+	2.86112i	−0.326979	+	0.152933i
$351$			2.84679i			0.151950i
$352$	21.5017	+	12.4140i	1.14605	+	0.661669i
$353$	−1.75630	−	3.04201i	−0.0934787	−	0.161910i	0.815494	−	0.578766i	$-0.196465\pi$
$353$	−1.75630	−	3.04201i	−0.0934787	−	0.161910i	−0.908973	+	0.416856i	$0.863132\pi$
$354$	−49.9148	+	28.8183i	−2.65294	+	1.53168i
$355$	3.56534	−	6.17536i	0.189229	−	0.327754i
$356$	−32.2897			−1.71135
$357$	−19.6376	−	17.1184i	−1.03933	−	0.906003i
$358$	34.3906			1.81760
$359$	−1.34185	+	2.32415i	−0.0708201	+	0.122664i	−0.899261	−	0.437413i	$-0.855895\pi$
$359$	−1.34185	+	2.32415i	−0.0708201	+	0.122664i	0.828441	+	0.560077i	$0.189228\pi$
$360$	15.0293	−	8.67717i	0.792113	−	0.457327i
$361$	7.47991	+	12.9556i	0.393680	+	0.681873i
$362$	−16.2075	−	9.35738i	−0.851845	−	0.491813i
$363$		−	15.4878i		−	0.812898i
$364$	−39.3310	−	27.4721i	−2.06150	−	1.43993i
$365$	−16.3675			−0.856712
$366$	3.63220	−	6.29116i	0.189858	−	0.328844i
$367$	−2.69746	+	1.55738i	−0.140806	+	0.0812944i	−0.568748	−	0.822512i	$-0.692572\pi$
$367$	−2.69746	+	1.55738i	−0.140806	+	0.0812944i	0.427942	+	0.903806i	$0.359239\pi$
$368$	−3.53233	+	2.03939i	−0.184135	+	0.106311i
$369$	11.5497	+	6.66825i	0.601256	+	0.347135i
$370$	3.50141			0.182029
$371$	−25.5057	−	17.8154i	−1.32419	−	0.924928i
$372$	−66.7631			−3.46150
$373$	−17.0555	+	29.5409i	−0.883098	+	1.52957i	−0.0352196	+	0.999380i	$0.511213\pi$
$373$	−17.0555	+	29.5409i	−0.883098	+	1.52957i	−0.847878	+	0.530191i	$0.822120\pi$
$374$	−43.7544	−	4.71108i	−2.26249	−	0.243604i
$375$	1.19407	+	2.06818i	0.0616613	+	0.106800i
$376$	−31.9278	+	55.3005i	−1.64655	+	2.85191i
$377$		−	7.15880i		−	0.368697i
$378$	−4.76938	−	0.411707i	−0.245310	−	0.0211759i
$379$		−	8.45974i		−	0.434548i	−0.976111	−	0.217274i	$-0.930284\pi$
$379$		−	8.45974i		−	0.434548i	0.976111	−	0.217274i	$-0.0697165\pi$
$380$	−7.85971	−	4.53780i	−0.403194	−	0.232784i
$381$	5.65277	−	3.26363i	0.289600	−	0.167201i
$382$	29.5121	+	51.1164i	1.50997	+	2.61534i
$383$	−9.47529	+	16.4117i	−0.484165	+	0.838598i	−0.999835	−	0.0181897i	$-0.994210\pi$
$383$	−9.47529	+	16.4117i	−0.484165	+	0.838598i	0.515670	+	0.856787i	$0.327543\pi$
$384$		−	25.6627i		−	1.30960i
$385$	−10.0214	+	4.68716i	−0.510736	+	0.238880i
$386$		−	36.4784i		−	1.85670i
$387$	15.2982	−	26.4972i	0.777649	−	1.34693i
$388$	13.5896	−	7.84594i	0.689906	−	0.398317i
$389$	4.19278	+	7.26210i	0.212582	+	0.368203i	0.952522	−	0.304470i	$-0.0984793\pi$
$389$	4.19278	+	7.26210i	0.212582	+	0.368203i	−0.739940	+	0.672673i	$0.765146\pi$
$390$	−12.2401	+	21.2005i	−0.619803	+	1.07353i
$391$	1.34838	−	1.84602i	0.0681905	−	0.0933570i
$392$	28.8071	−	34.4927i	1.45498	−	1.74214i
$393$	−1.86409			−0.0940308
$394$	−24.3729	−	14.0717i	−1.22789	−	0.708922i
$395$	−4.52706	−	7.84109i	−0.227781	−	0.394528i
$396$	44.1995	−	25.5186i	2.22111	−	1.28236i
$397$	−12.7241	−	7.34629i	−0.638607	−	0.368700i	0.145471	−	0.989363i	$-0.453530\pi$
$397$	−12.7241	−	7.34629i	−0.638607	−	0.368700i	−0.784078	+	0.620663i	$0.786864\pi$
$398$		−	8.40951i		−	0.421531i
$399$	−5.38061	−	11.5040i	−0.269367	−	0.575919i
$400$	−7.35655			−0.367828
$401$	31.5604	+	18.2214i	1.57605	+	0.909932i	0.995403	+	0.0957758i	$0.0305332\pi$
$401$	31.5604	+	18.2214i	1.57605	+	0.909932i	0.580646	+	0.814156i	$0.302800\pi$
$402$	−25.1806	+	14.5380i	−1.25589	+	0.725091i
$403$	21.5341	−	12.4327i	1.07269	−	0.619318i
$404$	33.4702	−	57.9721i	1.66520	−	2.88422i
$405$			9.80237i			0.487084i
$406$	11.9935	+	1.03532i	0.595228	+	0.0513819i
$407$	5.73609			0.284327
$408$	−25.5650	−	57.8144i	−1.26566	−	2.86224i
$409$	1.08107	+	1.87246i	0.0534554	+	0.0925874i	0.891515	−	0.452991i	$-0.149643\pi$
$409$	1.08107	+	1.87246i	0.0534554	+	0.0925874i	−0.838060	+	0.545579i	$0.816310\pi$
$410$	−6.29653	−	10.9059i	−0.310964	−	0.538605i
$411$	18.3433	+	10.5905i	0.904809	+	0.522391i
$412$	3.64556			0.179604
$413$	20.5089	+	14.3251i	1.00918	+	0.704894i
$414$			3.82555i			0.188015i
$415$	−10.2551	−	5.92078i	−0.503403	−	0.290640i
$416$	−11.9226	−	20.6505i	−0.584552	−	1.01247i
$417$	−26.3009	−	45.5545i	−1.28796	−	2.23082i
$418$	−18.5794	−	10.7268i	−0.908746	−	0.524665i
$419$			29.8548i			1.45850i	0.684246	+	0.729251i	$0.260131\pi$
$419$			29.8548i			1.45850i	−0.684246	+	0.729251i	$0.739869\pi$
$420$	−23.3883	−	16.3364i	−1.14123	−	0.797134i
$421$	14.9505			0.728641			0.364320	−	0.931274i	$-0.381301\pi$
$421$	14.9505			0.728641			0.364320	+	0.931274i	$0.381301\pi$
$422$	−42.8139	−	24.7186i	−2.08415	−	1.20328i
$423$	13.4434	+	23.2846i	0.653640	+	1.13214i
$424$	−37.7465	−	65.3789i	−1.83313	−	3.17508i
$425$	3.77089	−	1.66745i	0.182915	−	0.0808834i
$426$	43.4663			2.10595
$427$	−3.14134	−	0.271170i	−0.152020	−	0.0131228i
$428$			60.2887i			2.91417i
$429$	−20.0521	+	34.7312i	−0.968123	+	1.67684i
$430$	−25.0201	+	14.4454i	−1.20658	+	0.696618i
$431$	−8.06117	+	4.65412i	−0.388293	+	0.224181i	−0.681420	−	0.731892i	$-0.738637\pi$
$431$	−8.06117	+	4.65412i	−0.388293	+	0.224181i	0.293127	+	0.956073i	$0.405304\pi$
$432$	−4.51613	−	2.60739i	−0.217282	−	0.125448i
$433$	18.1897			0.874142			0.437071	−	0.899427i	$-0.356016\pi$
$433$	18.1897			0.874142			0.437071	+	0.899427i	$0.356016\pi$
$434$	17.7149	+	37.8753i	0.850343	+	1.81807i
$435$		−	4.25701i		−	0.204108i
$436$	74.0719	+	42.7654i	3.54740	+	2.04809i
$437$	0.965132	−	0.557219i	0.0461685	−	0.0266554i
$438$	−49.8853	−	86.4039i	−2.38361	−	4.12854i
$439$	7.99031	+	4.61321i	0.381357	+	0.220176i	0.678408	−	0.734685i	$-0.262670\pi$
$439$	7.99031	+	4.61321i	0.381357	+	0.220176i	−0.297052	+	0.954861i	$0.596003\pi$
$440$	−26.8455			−1.27981
$441$	−6.51290	−	17.7660i	−0.310138	−	0.846002i
$442$	34.1300	+	24.9295i	1.62340	+	1.18578i
$443$	−1.22568	+	2.12293i	−0.0582336	+	0.100864i	−0.893673	−	0.448720i	$-0.851880\pi$
$443$	−1.22568	+	2.12293i	−0.0582336	+	0.100864i	0.835439	+	0.549583i	$0.185213\pi$
$444$	7.39577	+	12.8098i	0.350988	+	0.607928i
$445$	6.19326	−	3.57568i	0.293589	−	0.169504i
$446$	12.6223	−	21.8625i	0.597683	−	1.03522i
$447$			11.3512i			0.536895i
$448$	1.06014	−	0.495847i	0.0500870	−	0.0234265i
$449$		−	41.3217i		−	1.95009i	−0.222006	−	0.975045i	$-0.571260\pi$
$449$		−	41.3217i		−	1.95009i	0.222006	−	0.975045i	$-0.428740\pi$
$450$	−3.44991	+	5.97541i	−0.162630	+	0.281684i
$451$	−10.3151	−	17.8663i	−0.485720	−	0.841292i
$452$	7.36350	−	4.25132i	0.346350	−	0.199965i
$453$	12.1764	+	7.03005i	0.572097	+	0.330300i
$454$			5.88912i			0.276390i
$455$	10.5860	+	0.913814i	0.496278	+	0.0428402i
$456$		−	30.8171i		−	1.44314i
$457$	−1.78255	+	3.08746i	−0.0833840	+	0.144425i	−0.904701	−	0.426046i	$-0.859906\pi$
$457$	−1.78255	+	3.08746i	−0.0833840	+	0.144425i	0.821317	+	0.570471i	$0.193239\pi$
$458$	−34.7467	−	60.1831i	−1.62361	−	2.81217i
$459$	2.90591	+	0.312882i	0.135636	+	0.0146041i
$460$	1.25171	−	2.16802i	0.0583611	−	0.101084i
$461$	32.7219			1.52401			0.762004	−	0.647572i	$-0.224215\pi$
$461$	32.7219			1.52401			0.762004	+	0.647572i	$0.224215\pi$
$462$	−55.2871	−	38.6172i	−2.57219	−	1.79663i
$463$	28.8179			1.33928			0.669642	−	0.742684i	$-0.266448\pi$
$463$	28.8179			1.33928			0.669642	+	0.742684i	$0.266448\pi$
$464$	11.3567	+	6.55678i	0.527220	+	0.304391i
$465$	12.8053	−	7.39317i	0.593833	−	0.342850i
$466$	33.5838	−	19.3896i	1.55574	−	0.898207i
$467$	10.2062	−	17.6777i	0.472288	−	0.818026i	−0.527209	−	0.849735i	$-0.676762\pi$
$467$	10.2062	−	17.6777i	0.472288	−	0.818026i	0.999497	+	0.0317090i	$0.0100950\pi$
$468$	−49.0167			−2.26580
$469$	10.3462	+	7.22663i	0.477741	+	0.333695i
$470$		−	25.3880i		−	1.17106i
$471$	−3.37985	−	1.95136i	−0.155735	−	0.0899137i
$472$	30.3516	+	52.5704i	1.39704	+	2.41975i
$473$	−40.9886	+	23.6648i	−1.88466	+	1.08811i
$474$	27.5955	−	47.7967i	1.26750	−	2.19538i
$475$	2.01002			0.0922259
$476$	−32.3654	+	37.1285i	−1.48347	+	1.70178i
$477$	−31.7868			−1.45542
$478$	−17.6351	+	30.5449i	−0.806612	+	1.39709i
$479$	25.9797	−	14.9994i	1.18704	−	0.685338i	0.229408	−	0.973330i	$-0.426321\pi$
$479$	25.9797	−	14.9994i	1.18704	−	0.685338i	0.957633	+	0.287992i	$0.0929876\pi$
$480$	−7.08980	−	12.2799i	−0.323604	−	0.560498i
$481$	−4.77094	−	2.75450i	−0.217536	−	0.125594i
$482$		−	31.4427i		−	1.43217i
$483$	3.17325	−	1.48418i	0.144388	−	0.0675327i
$484$	−29.2824			−1.33102
$485$	−1.73768	+	3.00975i	−0.0789039	+	0.136666i
$486$	−47.0460	+	27.1620i	−2.13405	+	1.23209i
$487$	15.6303	−	9.02414i	0.708275	−	0.408923i	−0.102147	−	0.994769i	$-0.532571\pi$
$487$	15.6303	−	9.02414i	0.708275	−	0.408923i	0.810422	+	0.585847i	$0.199238\pi$
$488$	−6.62587	−	3.82545i	−0.299939	−	0.173170i
$489$	−17.2763			−0.781261
$490$	−3.06192	+	17.6031i	−0.138323	+	0.795227i
$491$	23.2793			1.05058			0.525291	−	0.850923i	$-0.323957\pi$
$491$	23.2793			1.05058			0.525291	+	0.850923i	$0.323957\pi$
$492$	26.5994	−	46.0715i	1.19919	−	2.07707i
$493$	−7.30748	−	0.786803i	−0.329112	−	0.0354358i
$494$	10.3021	+	17.8438i	0.463515	+	0.802832i
$495$	−5.65172	+	9.78907i	−0.254026	+	0.439986i
$496$			45.5487i			2.04520i
$497$	−7.99290	−	17.0892i	−0.358531	−	0.766555i
$498$		−	72.1823i		−	3.23457i
$499$	13.7129	+	7.91713i	0.613872	+	0.354419i	0.774479	−	0.632599i	$-0.218012\pi$
$499$	13.7129	+	7.91713i	0.613872	+	0.354419i	−0.160607	+	0.987018i	$0.551345\pi$
$500$	3.91027	−	2.25759i	0.174873	−	0.100963i
$501$	−12.9773	−	22.4774i	−0.579784	−	1.00422i
$502$	7.95174	−	13.7728i	0.354904	−	0.614711i
$503$			20.3691i			0.908214i	0.890947	+	0.454107i	$0.150042\pi$
$503$			20.3691i			0.908214i	−0.890947	+	0.454107i	$0.849958\pi$
$504$	3.94886	−	45.7451i	0.175896	−	2.03765i
$505$			14.8256i			0.659731i
$506$	2.95887	−	5.12492i	0.131538	−	0.227830i
$507$	6.46987	−	3.73538i	0.287337	−	0.165894i
$508$	−6.17047	−	10.6876i	−0.273770	−	0.474184i
$509$	9.59228	−	16.6143i	0.425170	−	0.736417i	−0.571266	−	0.820765i	$-0.693547\pi$
$509$	9.59228	−	16.6143i	0.425170	−	0.736417i	0.996436	+	0.0843483i	$0.0268808\pi$
$510$	20.2956	+	14.8244i	0.898702	+	0.656437i
$511$	−24.7972	+	35.5014i	−1.09696	+	1.57049i
$512$	−50.7782			−2.24410
$513$	1.23393	+	0.712412i	0.0544795	+	0.0314537i
$514$	40.9132	+	70.8637i	1.80460	+	3.12566i
$515$	−0.699228	+	0.403699i	−0.0308117	+	0.0177891i
$516$	−105.696	−	61.0238i	−4.65302	−	2.68642i
$517$		−	41.5912i		−	1.82918i
$518$	5.30474	−	7.59464i	0.233077	−	0.333689i
$519$	20.6905			0.908214
$520$	22.3285	+	12.8913i	0.979168	+	0.565323i
$521$	−10.9942	+	6.34748i	−0.481663	+	0.278088i	−0.721109	−	0.692821i	$-0.756367\pi$
$521$	−10.9942	+	6.34748i	−0.481663	+	0.278088i	0.239446	+	0.970910i	$0.423034\pi$
$522$	10.6516	−	6.14969i	0.466207	−	0.269165i
$523$	6.02068	−	10.4281i	0.263266	−	0.455990i	−0.703842	−	0.710357i	$-0.748534\pi$
$523$	6.02068	−	10.4281i	0.263266	−	0.455990i	0.967108	+	0.254366i	$0.0818669\pi$
$524$			3.52439i			0.153964i
$525$	6.29499	+	0.543403i	0.274736	+	0.0237160i
$526$	−24.0322			−1.04785
$527$	−10.3242	−	23.3478i	−0.449729	−	1.01705i
$528$	−36.7316	−	63.6209i	−1.59854	−	2.76875i
$529$	−11.3463	−	19.6524i	−0.493317	−	0.854451i
$530$	25.9936	+	15.0074i	1.12909	+	0.651881i
$531$	25.5594			1.10918
$532$	−21.7503	+	10.1730i	−0.942996	+	0.441055i
$533$			19.8135i			0.858220i
$534$	37.7521	+	21.7962i	1.63369	+	0.943213i
$535$	−6.67622	−	11.5635i	−0.288638	−	0.499936i
$536$	15.3115	+	26.5203i	0.661356	+	1.14550i
$537$	−27.8654	−	16.0881i	−1.20248	−	0.694253i
$538$			6.74741i			0.290901i
$539$	−5.01611	+	28.8378i	−0.216059	+	1.24213i
$540$	3.20064			0.137734
$541$	39.0061	+	22.5202i	1.67700	+	0.968219i	0.963554	+	0.267513i	$0.0862018\pi$
$541$	39.0061	+	22.5202i	1.67700	+	0.968219i	0.713450	+	0.700706i	$0.247132\pi$
$542$	35.0947	+	60.7857i	1.50744	+	2.61097i
$543$	8.75486	+	15.1639i	0.375707	+	0.650743i
$544$	−22.3898	+	9.90055i	−0.959953	+	0.424482i
$545$	−18.9429			−0.811425
$546$	27.4403	+	58.6686i	1.17434	+	2.51079i
$547$		−	2.62660i		−	0.112305i	−0.998422	−	0.0561527i	$-0.982117\pi$
$547$		−	2.62660i		−	0.112305i	0.998422	−	0.0561527i	$-0.0178834\pi$
$548$	20.0233	−	34.6813i	0.855351	−	1.48151i
$549$	−2.78986	+	1.61073i	−0.119068	+	0.0687442i
$550$	9.24338	−	5.33667i	0.394139	−	0.227556i
$551$	−3.10296	−	1.79150i	−0.132191	−	0.0763203i
$552$	8.50058			0.361809
$553$	−23.8662	−	2.06020i	−1.01489	−	0.0876086i
$554$		−	50.0729i		−	2.12740i
$555$	−2.83706	−	1.63797i	−0.120426	−	0.0695282i
$556$	−86.1290	+	49.7266i	−3.65268	+	2.10888i
$557$	7.90051	+	13.6841i	0.334755	+	0.579813i	0.983438	−	0.181246i	$-0.0580130\pi$
$557$	7.90051	+	13.6841i	0.334755	+	0.579813i	−0.648683	+	0.761059i	$0.724680\pi$
$558$	36.9973	+	21.3604i	1.56622	+	0.904258i
$559$	45.4558			1.92258
$560$	−11.1454	+	15.9566i	−0.470980	+	0.674288i
$561$	33.2487	+	24.2857i	1.40376	+	1.02534i
$562$	20.6925	−	35.8405i	0.872863	−	1.51184i
$563$	11.0417	+	19.1247i	0.465350	+	0.806010i	0.999217	−	0.0395581i	$-0.0125950\pi$
$563$	11.0417	+	19.1247i	0.465350	+	0.806010i	−0.533867	+	0.845569i	$0.679262\pi$
$564$	92.8816	−	53.6252i	3.91102	−	2.25803i
$565$	−0.941559	+	1.63083i	−0.0396117	+	0.0686095i
$566$		−	14.9399i		−	0.627973i
$567$	21.2616	+	14.8509i	0.892904	+	0.623680i
$568$		−	45.7789i		−	1.92084i
$569$	−22.0578	+	38.2053i	−0.924713	+	1.60165i	−0.132691	+	0.991157i	$0.542362\pi$
$569$	−22.0578	+	38.2053i	−0.924713	+	1.60165i	−0.792022	+	0.610492i	$0.790972\pi$
$570$	6.12621	+	10.6109i	0.256599	+	0.444442i
$571$	18.7173	−	10.8064i	0.783293	−	0.452235i	−0.0543029	−	0.998525i	$-0.517294\pi$
$571$	18.7173	−	10.8064i	0.783293	−	0.452235i	0.837596	+	0.546290i	$0.183960\pi$
$572$	65.6655	+	37.9120i	2.74561	+	1.58518i
$573$		−	55.2236i		−	2.30700i
$574$	−33.1947	−	2.86546i	−1.38552	−	0.119602i
$575$			0.554442i			0.0231218i
$576$	0.597886	−	1.03557i	0.0249119	−	0.0431487i
$577$	−3.98565	−	6.90334i	−0.165925	−	0.287390i	0.771059	−	0.636764i	$-0.219728\pi$
$577$	−3.98565	−	6.90334i	−0.165925	−	0.287390i	−0.936983	+	0.349374i	$0.886394\pi$
$578$	29.1984	−	32.0989i	1.21449	−	1.33514i
$579$	−17.0648	+	29.5571i	−0.709188	+	1.22835i
$580$	−8.04863			−0.334201
$581$	−28.3791	+	13.2734i	−1.17737	+	0.550674i
$582$	−21.1846			−0.878132
$583$	42.5834	+	24.5855i	1.76362	+	1.01823i
$584$	−91.0009	+	52.5394i	−3.76564	+	2.17410i
$585$	9.40153	−	5.42798i	0.388706	−	0.224419i
$586$	36.9221	−	63.9509i	1.52524	−	2.64179i
$587$	19.7698			0.815985			0.407993	−	0.912985i	$-0.366229\pi$
$587$	19.7698			0.815985			0.407993	+	0.912985i	$0.366229\pi$
$588$	−70.8681	+	25.9797i	−2.92255	+	1.07139i
$589$		−	12.4452i		−	0.512796i
$590$	−20.9012	−	12.0673i	−0.860489	−	0.496803i
$591$	13.1656	+	22.8035i	0.541561	+	0.938012i
$592$	8.73944	−	5.04572i	0.359189	−	0.207378i
$593$	0.111179	−	0.192567i	0.00456556	−	0.00790779i	−0.863734	−	0.503949i	$-0.831880\pi$
$593$	0.111179	−	0.192567i	0.00456556	−	0.00790779i	0.868299	+	0.496041i	$0.165213\pi$
$594$	7.56591			0.310433
$595$	2.09627	−	10.7054i	0.0859386	−	0.438879i
$596$	21.4615			0.879098
$597$	−3.93401	+	6.81391i	−0.161008	+	0.278875i
$598$	−4.92203	+	2.84174i	−0.201277	+	0.116207i
$599$	4.05509	+	7.02362i	0.165686	+	0.286977i	0.936899	−	0.349601i	$-0.113683\pi$
$599$	4.05509	+	7.02362i	0.165686	+	0.286977i	−0.771212	+	0.636578i	$0.780349\pi$
$600$	13.2777	+	7.66589i	0.542060	+	0.312958i
$601$		−	5.32198i		−	0.217088i	−0.994092	−	0.108544i	$-0.965381\pi$
$601$		−	5.32198i		−	0.217088i	0.994092	−	0.108544i	$-0.0346188\pi$
$602$	−6.57389	+	76.1545i	−0.267932	+	3.10383i
$603$	12.8940			0.525084
$604$	13.2916	−	23.0216i	0.540826	−	0.936738i
$605$	5.61645	−	3.24266i	0.228341	−	0.131833i
$606$	−78.2645	+	45.1860i	−3.17928	+	1.83556i
$607$	16.1740	+	9.33805i	0.656482	+	0.379020i	0.790935	−	0.611900i	$-0.209595\pi$
$607$	16.1740	+	9.33805i	0.656482	+	0.379020i	−0.134454	+	0.990920i	$0.542928\pi$
$608$	−11.9345			−0.484009
$609$	−9.23356	−	6.44950i	−0.374163	−	0.261347i
$610$	3.04188			0.123162
$611$	−19.9723	+	34.5931i	−0.807994	+	1.39949i
$612$	−5.38728	+	50.0347i	−0.217768	+	2.02253i
$613$	−10.4750	−	18.1432i	−0.423080	−	0.732796i	0.573159	−	0.819444i	$-0.305718\pi$
$613$	−10.4750	−	18.1432i	−0.423080	−	0.732796i	−0.996239	+	0.0866482i	$0.972384\pi$
$614$	10.8299	−	18.7580i	0.437060	−	0.757011i
$615$			11.7822i			0.475104i
$616$	−40.6717	+	58.2285i	−1.63871	+	2.34609i
$617$			24.9898i			1.00605i	0.864271	+	0.503026i	$0.167780\pi$
$617$			24.9898i			1.00605i	−0.864271	+	0.503026i	$0.832220\pi$
$618$	−4.26227	−	2.46082i	−0.171453	−	0.0989887i
$619$	25.9385	−	14.9756i	1.04256	−	0.601921i	0.122001	−	0.992530i	$-0.461069\pi$
$619$	25.9385	−	14.9756i	1.04256	−	0.601921i	0.920557	+	0.390609i	$0.127736\pi$
$620$	−13.9781	−	24.2108i	−0.561374	−	0.972328i
$621$	−0.196511	+	0.340367i	−0.00788572	+	0.0136585i
$622$		−	42.4639i		−	1.70265i
$623$	1.62724	−	18.8506i	0.0651941	−	0.755234i
$624$			70.5548i			2.82445i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	57.0078	−	32.9134i	2.27849	−	1.31549i
$627$	10.0361	+	17.3830i	0.400803	+	0.694211i
$628$	−3.68939	+	6.39020i	−0.147222	+	0.254997i
$629$	−3.33607	+	4.56729i	−0.133018	+	0.182110i
$630$	7.73411	+	16.5359i	0.308134	+	0.658805i
$631$	−32.0099			−1.27429			−0.637147	−	0.770743i	$-0.719885\pi$
$631$	−32.0099			−1.27429			−0.637147	+	0.770743i	$0.719885\pi$
$632$	−50.3397	−	29.0636i	−2.00241	−	1.15609i
$633$	23.1270	+	40.0571i	0.919216	+	1.59213i
$634$	8.99734	−	5.19462i	0.357330	−	0.206305i
$635$	2.36702	+	1.36660i	0.0939325	+	0.0542320i
$636$			126.796i			5.02781i
$637$	18.0202	−	21.5768i	0.713986	−	0.854905i
$638$	−19.0260			−0.753245
$639$	−16.6931	−	9.63774i	−0.660367	−	0.381263i
$640$	9.30626	−	5.37297i	0.367862	−	0.212385i
$641$	19.8696	−	11.4717i	0.784800	−	0.453105i	−0.0533284	−	0.998577i	$-0.516983\pi$
$641$	19.8696	−	11.4717i	0.784800	−	0.453105i	0.838129	+	0.545472i	$0.183650\pi$
$642$	40.6960	−	70.4876i	1.60614	−	2.78192i
$643$		−	19.9546i		−	0.786933i	−0.919339	−	0.393466i	$-0.871276\pi$
$643$		−	19.9546i		−	0.786933i	0.919339	−	0.393466i	$-0.128724\pi$
$644$	−2.80611	−	5.99960i	−0.110576	−	0.236417i
$645$	27.0305			1.06432
$646$	19.3467	−	8.55494i	0.761186	−	0.336590i
$647$	−0.0956873	−	0.165735i	−0.00376185	−	0.00651572i	0.864138	−	0.503254i	$-0.167864\pi$
$647$	−0.0956873	−	0.165735i	−0.00376185	−	0.00651572i	−0.867900	+	0.496739i	$0.834531\pi$
$648$	31.4655	+	54.4999i	1.23608	+	2.14096i
$649$	−34.2408	−	19.7690i	−1.34407	−	0.776000i
$650$	−10.2508			−0.402069
$651$	3.36453	−	38.9760i	0.131866	−	1.52759i
$652$			32.6639i			1.27922i
$653$	−16.2203	−	9.36481i	−0.634750	−	0.366473i	0.147839	−	0.989011i	$-0.452768\pi$
$653$	−16.2203	−	9.36481i	−0.634750	−	0.366473i	−0.782589	+	0.622538i	$0.786102\pi$
$654$	−57.7349	−	99.9998i	−2.25761	−	3.91030i
$655$	−0.390282	−	0.675988i	−0.0152496	−	0.0264130i
$656$	−31.4321	−	18.1473i	−1.22722	−	0.708533i
$657$			44.2441i			1.72613i
$658$	−55.0672	−	38.4636i	−2.14674	−	1.49947i
$659$	−23.1762			−0.902815			−0.451408	−	0.892318i	$-0.649078\pi$
$659$	−23.1762			−0.902815			−0.451408	+	0.892318i	$0.649078\pi$
$660$	39.0483	+	22.5445i	1.51995	+	0.877544i
$661$	20.0053	+	34.6503i	0.778118	+	1.34774i	0.933025	+	0.359810i	$0.117159\pi$
$661$	20.0053	+	34.6503i	0.778118	+	1.34774i	−0.154908	+	0.987929i	$0.549508\pi$
$662$	25.0997	+	43.4740i	0.975528	+	1.68966i
$663$	−15.9921	−	36.1656i	−0.621082	−	1.40456i
$664$	−76.0227			−2.95025
$665$	3.04524	−	4.35978i	0.118089	−	0.169065i
$666$		−	9.46491i		−	0.366758i
$667$	0.494165	−	0.855919i	0.0191342	−	0.0331413i
$668$	−42.4975	+	24.5359i	−1.64428	+	0.949324i
$669$	−20.4547	+	11.8095i	−0.790826	+	0.456584i
$670$	−10.5441	−	6.08762i	−0.407353	−	0.235185i
$671$	4.98328			0.192377
$672$	−37.3767	−	3.22647i	−1.44184	−	0.124464i
$673$			31.3048i			1.20671i	0.797472	+	0.603356i	$0.206170\pi$
$673$			31.3048i			1.20671i	−0.797472	+	0.603356i	$0.793830\pi$
$674$	14.0344	+	8.10276i	0.540584	+	0.312107i
$675$	−0.613892	+	0.354431i	−0.0236287	+	0.0136420i
$676$	−7.06240	−	12.2324i	−0.271631	−	0.470479i
$677$	29.6058	+	17.0929i	1.13785	+	0.656935i	0.945896	−	0.324470i	$-0.105186\pi$
$677$	29.6058	+	17.0929i	1.13785	+	0.656935i	0.191949	+	0.981405i	$0.438519\pi$
$678$	−11.4789			−0.440844
$679$	3.89558	+	8.32893i	0.149499	+	0.319635i
$680$	15.6131	−	21.3753i	0.598737	−	0.819707i
$681$	2.75496	−	4.77173i	0.105570	−	0.182853i
$682$	−33.0425	−	57.2312i	−1.26526	−	2.19150i
$683$	−9.09878	+	5.25319i	−0.348155	+	0.201008i	−0.663873	−	0.747846i	$-0.731088\pi$
$683$	−9.09878	+	5.25319i	−0.348155	+	0.201008i	0.315717	+	0.948853i	$0.397755\pi$
$684$	−12.2665	+	21.2462i	−0.469020	+	0.812367i
$685$			8.86929i			0.338878i
$686$	33.5427	+	33.3106i	1.28067	+	1.27181i
$687$			65.0187i			2.48062i
$688$	−41.6332	+	72.1108i	−1.58725	+	2.74920i
$689$	−23.6122	−	40.8976i	−0.899554	−	1.55807i
$690$	−2.92690	+	1.68985i	−0.111425	+	0.0643315i
$691$	−35.9175	−	20.7370i	−1.36637	−	0.788872i	−0.375904	−	0.926659i	$-0.622668\pi$
$691$	−35.9175	−	20.7370i	−1.36637	−	0.788872i	−0.990462	+	0.137787i	$0.956001\pi$
$692$		−	39.1192i		−	1.48709i
$693$	12.6702	+	27.0895i	0.481301	+	1.02904i
$694$			1.24796i			0.0473721i
$695$	11.0132	−	19.0754i	0.417754	−	0.723571i
$696$	−13.6650	−	23.6684i	−0.517969	−	0.897149i
$697$	20.2250	+	2.17765i	0.766078	+	0.0824844i
$698$	−40.8243	+	70.7098i	−1.54522	+	2.67641i
$699$	−36.2823			−1.37232
$700$	1.02740	−	11.9018i	0.0388321	−	0.449846i
$701$	−50.0455			−1.89019			−0.945097	−	0.326791i	$-0.894033\pi$
$701$	−50.0455			−1.89019			−0.945097	+	0.326791i	$0.894033\pi$
$702$	−6.29288	−	3.63320i	−0.237509	−	0.137126i
$703$	−2.38786	+	1.37863i	−0.0900600	+	0.0519961i
$704$	−1.60192	+	0.924870i	−0.0603747	+	0.0348574i
$705$	−11.8766	+	20.5709i	−0.447299	+	0.774745i
$706$	8.96589			0.337436
$707$	32.1571	+	22.4613i	1.20939	+	0.844743i
$708$		−	101.956i		−	3.83173i
$709$	−0.631206	−	0.364427i	−0.0237054	−	0.0136863i	0.488100	−	0.872787i	$-0.337690\pi$
$709$	−0.631206	−	0.364427i	−0.0237054	−	0.0136863i	−0.511806	+	0.859101i	$0.671023\pi$
$710$	9.10049	+	15.7625i	0.341535	+	0.591557i
$711$	−21.1958	+	12.2374i	−0.794906	+	0.458939i
$712$	22.9558	−	39.7606i	0.860306	−	1.49009i
$713$	3.43288			0.128562
$714$	62.9030	−	21.5621i	2.35409	−	0.806942i
$715$	−16.7931			−0.628026
$716$	−30.4174	+	52.6845i	−1.13675	+	1.96891i
$717$	28.5781	−	16.4996i	1.06727	−	0.616189i
$718$	−3.42505	−	5.93236i	−0.127822	−	0.221394i
$719$	−18.5728	−	10.7230i	−0.692649	−	0.399901i	0.111955	−	0.993713i	$-0.464289\pi$
$719$	−18.5728	−	10.7230i	−0.692649	−	0.399901i	−0.804604	+	0.593812i	$0.797622\pi$
$720$			19.8860i			0.741109i
$721$	−0.183718	+	2.12826i	−0.00684201	+	0.0792606i
$722$	−38.1848			−1.42109
$723$	−14.7090	+	25.4768i	−0.547035	+	0.947492i
$724$	28.6700	−	16.5526i	1.06551	−	0.615173i
$725$	1.54375	−	0.891284i	0.0573334	−	0.0331015i
$726$	34.2361	+	19.7662i	1.27062	+	0.733592i
$727$	3.60775			0.133804			0.0669019	−	0.997760i	$-0.478689\pi$
$727$	3.60775			0.133804			0.0669019	+	0.997760i	$0.478689\pi$
$728$	61.7900	−	28.9002i	2.29009	−	1.07111i
$729$	21.4190			0.793295
$730$	20.8889	−	36.1806i	0.773131	−	1.33910i
$731$	4.99592	−	46.3999i	0.184781	−	1.71616i
$732$	6.42514	+	11.1287i	0.237480	+	0.411327i
$733$	2.10346	−	3.64330i	0.0776930	−	0.134568i	−0.824561	−	0.565773i	$-0.808578\pi$
$733$	2.10346	−	3.64330i	0.0776930	−	0.134568i	0.902254	+	0.431205i	$0.141911\pi$
$734$		−	7.95037i		−	0.293453i
$735$	10.7158	−	12.8307i	0.395257	−	0.473269i
$736$		−	3.29201i		−	0.121345i
$737$	−17.2735	−	9.97288i	−0.636279	−	0.367356i
$738$	−29.4806	+	17.0206i	−1.08519	+	0.626538i
$739$	6.13241	+	10.6216i	0.225584	+	0.390723i	0.956495	−	0.291750i	$-0.0942376\pi$
$739$	6.13241	+	10.6216i	0.225584	+	0.390723i	−0.730910	+	0.682474i	$0.760904\pi$
$740$	−3.09688	+	5.36396i	−0.113844	+	0.197183i
$741$		−	19.2776i		−	0.708179i
$742$	71.9327	−	33.6441i	2.64073	−	1.23512i
$743$			34.5668i			1.26813i	0.773279	+	0.634066i	$0.218615\pi$
$743$			34.5668i			1.26813i	−0.773279	+	0.634066i	$0.781385\pi$
$744$	47.4640	−	82.2101i	1.74012	−	3.01397i
$745$	−4.11638	+	2.37659i	−0.150812	+	0.0870716i
$746$	−43.5338	−	75.4028i	−1.59389	−	2.76069i
$747$	−16.0049	+	27.7213i	−0.585589	+	1.01427i
$748$	45.9165	−	62.8625i	1.67887	−	2.29848i
$749$	−35.1963	−	3.03825i	−1.28605	−	0.111015i
$750$	−6.09567			−0.222583
$751$	−8.87008	−	5.12114i	−0.323674	−	0.186873i	0.329355	−	0.944206i	$-0.393169\pi$
$751$	−8.87008	−	5.12114i	−0.323674	−	0.186873i	−0.653029	+	0.757333i	$0.726502\pi$
$752$	−36.5855	−	63.3679i	−1.33414	−	2.31079i
$753$	−12.8860	+	7.43973i	−0.469591	+	0.271119i
$754$	15.8247	+	9.13637i	0.576300	+	0.332727i
$755$			5.88749i			0.214268i
$756$	4.84908	−	6.94228i	0.176359	−	0.252488i
$757$	11.1825			0.406434			0.203217	−	0.979134i	$-0.434860\pi$
$757$	11.1825			0.406434			0.203217	+	0.979134i	$0.434860\pi$
$758$	18.7004	+	10.7967i	0.679230	+	0.392153i
$759$	−4.79492	+	2.76835i	−0.174045	+	0.100485i
$760$	11.1754	−	6.45214i	0.405376	−	0.234044i
$761$	12.1257	−	21.0023i	0.439555	−	0.761332i	−0.558100	−	0.829774i	$-0.688469\pi$
$761$	12.1257	−	21.0023i	0.439555	−	0.761332i	0.997655	+	0.0684418i	$0.0218028\pi$
$762$			16.6607i			0.603554i
$763$	−28.6991	+	41.0877i	−1.03898	+	1.48747i
$764$	−104.410			−3.77742
$765$	−4.50741	−	10.1934i	−0.162966	−	0.368542i
$766$	−24.1855	−	41.8906i	−0.873859	−	1.51357i
$767$	18.9863	+	32.8853i	0.685557	+	1.18742i
$768$	58.5577	+	33.8083i	2.11302	+	1.21995i
$769$	−21.4970			−0.775202			−0.387601	−	0.921827i	$-0.626696\pi$
$769$	−21.4970			−0.775202			−0.387601	+	0.921827i	$0.626696\pi$
$770$	2.42864	−	28.1344i	0.0875222	−	1.01389i
$771$		−	76.5575i		−	2.75715i
$772$	55.8829	+	32.2640i	2.01127	+	1.16121i
$773$	12.4804	+	21.6166i	0.448887	+	0.777495i	0.998314	−	0.0580466i	$-0.0184872\pi$
$773$	12.4804	+	21.6166i	0.448887	+	0.777495i	−0.549427	+	0.835542i	$0.685154\pi$
$774$	39.0483	+	67.6337i	1.40356	+	2.43104i
$775$	5.36207	+	3.09579i	0.192611	+	0.111204i
$776$			22.3117i			0.800945i
$777$	−7.85104	+	3.67207i	−0.281655	+	0.131735i
$778$	−21.4040			−0.767371
$779$	8.58812	+	4.95836i	0.307701	+	0.177652i
$780$	−21.6520	−	37.5024i	−0.775267	−	1.34280i
$781$	14.9086	+	25.8225i	0.533473	+	0.924003i
$782$	2.35979	+	5.33658i	0.0843859	+	0.190836i
$783$	1.26359			0.0451571
$784$	17.7245	+	48.3494i	0.633019	+	1.72676i
$785$		−	1.63421i		−	0.0583275i
$786$	2.37903	−	4.12060i	0.0848572	−	0.146977i
$787$	17.5185	−	10.1143i	0.624469	−	0.360537i	−0.154138	−	0.988049i	$-0.549260\pi$
$787$	17.5185	−	10.1143i	0.624469	−	0.360537i	0.778607	+	0.627512i	$0.215927\pi$
$788$	43.1141	−	24.8920i	1.53588	−	0.886739i
$789$	19.4723	+	11.2424i	0.693234	+	0.400239i
$790$	23.1105			0.822235
$791$	2.11082	+	4.51303i	0.0750521	+	0.160465i
$792$			72.5679i			2.57859i
$793$	−4.14479	−	2.39300i	−0.147186	−	0.0849778i
$794$	32.4782	−	18.7513i	1.15261	−	0.665459i
$795$	−14.0411	−	24.3199i	−0.497987	−	0.862538i
$796$	12.8829	+	7.43795i	0.456623	+	0.263631i
$797$	14.3783			0.509304			0.254652	−	0.967033i	$-0.418039\pi$
$797$	14.3783			0.509304			0.254652	+	0.967033i	$0.418039\pi$
$798$	32.2967	+	2.78795i	1.14329	+	0.0986924i
$799$	33.1165	+	24.1892i	1.17158	+	0.855751i
$800$	2.96876	−	5.14205i	0.104962	−	0.181799i
$801$	−9.66569	−	16.7415i	−0.341520	−	0.591530i
$802$	−80.5574	+	46.5098i	−2.84458	+	1.64232i
$803$	34.2206	−	59.2719i	1.20762	−	2.09166i
$804$		−	51.4337i		−	1.81393i
$805$	1.20260	+	0.839997i	0.0423861	+	0.0296060i
$806$			63.4687i			2.23559i
$807$	3.15647	−	5.46717i	0.111113	−	0.192453i
$808$	47.5901	+	82.4284i	1.67421	+	2.89982i
$809$	−11.8158	+	6.82188i	−0.415423	+	0.239844i	−0.693117	−	0.720825i	$-0.743763\pi$
$809$	−11.8158	+	6.82188i	−0.415423	+	0.239844i	0.277694	+	0.960669i	$0.410430\pi$
$810$	−21.6683	−	12.5102i	−0.761347	−	0.439564i
$811$			49.3640i			1.73340i	0.498826	+	0.866702i	$0.333765\pi$
$811$			49.3640i			1.73340i	−0.498826	+	0.866702i	$0.666235\pi$
$812$	−12.1939	+	17.4577i	−0.427923	+	0.612645i
$813$		−	65.6698i		−	2.30314i
$814$	−7.32064	+	12.6797i	−0.256588	+	0.444424i
$815$	−3.61712	−	6.26503i	−0.126702	−	0.219454i
$816$	72.0202	+	7.75448i	2.52121	+	0.271461i
$817$	11.3754	−	19.7027i	0.397973	−	0.689310i
$818$	−5.51882			−0.192961
$819$	2.47020	−	28.6157i	0.0863157	−	0.999915i
$820$	22.2763			0.777923
$821$	−36.5761	−	21.1172i	−1.27652	−	0.736997i	−0.300310	−	0.953842i	$-0.597090\pi$
$821$	−36.5761	−	21.1172i	−1.27652	−	0.736997i	−0.976206	+	0.216845i	$0.930423\pi$
$822$	−46.8210	+	27.0321i	−1.63307	+	0.942854i
$823$	−20.9035	+	12.0687i	−0.728651	+	0.420687i	−0.817928	−	0.575320i	$-0.804878\pi$
$823$	−20.9035	+	12.0687i	−0.728651	+	0.420687i	0.0892776	+	0.996007i	$0.471544\pi$
$824$	−2.59174	+	4.48903i	−0.0902877	+	0.156383i
$825$	−9.98608			−0.347671
$826$	−57.8403	+	27.0529i	−2.01252	+	0.941290i
$827$		−	27.9977i		−	0.973574i	−0.873521	−	0.486787i	$-0.838169\pi$
$827$		−	27.9977i		−	0.973574i	0.873521	−	0.486787i	$-0.161831\pi$
$828$	−5.86053	−	3.38358i	−0.203667	−	0.117587i
$829$	−8.28747	−	14.3543i	−0.287836	−	0.498546i	0.685457	−	0.728113i	$-0.259602\pi$
$829$	−8.28747	−	14.3543i	−0.287836	−	0.498546i	−0.973293	+	0.229567i	$0.926269\pi$
$830$	26.1760	−	15.1127i	0.908582	−	0.524570i
$831$	−23.4244	+	40.5722i	−0.812582	+	1.40743i
$832$	1.77651			0.0615895
$833$	−20.0444	−	20.7659i	−0.694497	−	0.719495i
$834$	134.266			4.64923
$835$	5.43409	−	9.41212i	0.188054	−	0.325720i
$836$	32.8657	−	18.9750i	1.13668	−	0.656265i
$837$	2.19449	+	3.80097i	0.0758526	+	0.131381i
$838$	−65.9946	−	38.1020i	−2.27975	−	1.31621i
$839$		−	18.7238i		−	0.646417i	−0.946328	−	0.323209i	$-0.895238\pi$
$839$		−	18.7238i		−	0.646417i	0.946328	−	0.323209i	$-0.104762\pi$
$840$	36.7437	−	17.1856i	1.26778	−	0.592961i
$841$	25.8225			0.890429
$842$	−19.0804	+	33.0483i	−0.657555	+	1.13892i
$843$	−33.5328	+	19.3602i	−1.15493	+	0.666799i
$844$	75.7352	−	43.7257i	2.60691	−	1.50510i
$845$	2.70918	+	1.56414i	0.0931985	+	0.0538082i
$846$	−68.6281			−2.35948
$847$	1.47569	−	17.0950i	0.0507053	−	0.587390i
$848$	86.5062			2.97063
$849$	−6.98898	+	12.1053i	−0.239861	+	0.415452i
$850$	−1.12664	+	10.4637i	−0.0386433	+	0.358902i
$851$	−0.380281	−	0.658667i	−0.0130359	−	0.0225788i
$852$	−38.4446	+	66.5880i	−1.31709	+	2.28127i
$853$		−	20.5922i		−	0.705062i	−0.935800	−	0.352531i	$-0.885321\pi$
$853$		−	20.5922i		−	0.705062i	0.935800	−	0.352531i	$-0.114679\pi$
$854$	4.60854	−	6.59791i	0.157701	−	0.225776i
$855$		−	5.43343i		−	0.185819i
$856$	−74.2378	−	42.8612i	−2.53740	−	1.46497i
$857$	−30.0770	+	17.3650i	−1.02741	+	0.593177i	−0.916242	−	0.400625i	$-0.868793\pi$
$857$	−30.0770	+	17.3650i	−1.02741	+	0.593177i	−0.111170	+	0.993801i	$0.535460\pi$
$858$	−51.1826	−	88.6509i	−1.74735	−	3.02649i
$859$	7.69235	−	13.3235i	0.262459	−	0.454593i	−0.704435	−	0.709768i	$-0.748800\pi$
$859$	7.69235	−	13.3235i	0.262459	−	0.454593i	0.966895	+	0.255175i	$0.0821331\pi$
$860$		−	51.1059i		−	1.74270i
$861$	25.5559	+	17.8504i	0.870943	+	0.608340i
$862$		−	23.7591i		−	0.809240i
$863$	13.1720	−	22.8145i	0.448379	−	0.776616i	−0.549902	−	0.835230i	$-0.685335\pi$
$863$	13.1720	−	22.8145i	0.448379	−	0.776616i	0.998281	+	0.0586139i	$0.0186681\pi$
$864$	3.64500	−	2.10444i	0.124005	−	0.0715945i
$865$	4.33195	+	7.50316i	0.147291	+	0.255115i
$866$	−23.2145	+	40.2087i	−0.788861	+	1.36635i
$867$	−38.6744	+	12.3494i	−1.31345	+	0.419407i
$868$	−73.6911	−	6.36124i	−2.50124	−	0.215914i
$869$	37.8602			1.28432
$870$	9.41019	+	5.43298i	0.319035	+	0.184195i
$871$	9.57807	+	16.5897i	0.324541	+	0.562121i
$872$	−105.320	+	60.8066i	−3.56659	+	2.05917i
$873$	8.13587	+	4.69724i	0.275357	+	0.158978i
$874$			2.84459i			0.0962196i
$875$	1.12092	+	2.39657i	0.0378939	+	0.0810188i
$876$	176.488			5.96298
$877$	4.34632	+	2.50935i	0.146765	+	0.0847348i	0.571584	−	0.820543i	$-0.306329\pi$
$877$	4.34632	+	2.50935i	0.146765	+	0.0847348i	−0.424819	+	0.905278i	$0.639662\pi$
$878$	−20.3952	+	11.7752i	−0.688303	+	0.397392i
$879$	−59.8331	+	34.5446i	−2.01812	+	1.16516i
$880$	15.3809	−	26.6405i	0.518489	−	0.898050i
$881$		−	27.6859i		−	0.932762i	−0.884584	−	0.466381i	$-0.845558\pi$
$881$		−	27.6859i		−	0.932762i	0.884584	−	0.466381i	$-0.154442\pi$
$882$	47.5842	+	8.27690i	1.60224	+	0.278698i
$883$	14.2981			0.481168			0.240584	−	0.970628i	$-0.422661\pi$
$883$	14.2981			0.481168			0.240584	+	0.970628i	$0.422661\pi$
$884$	−68.3776	+	30.2360i	−2.29979	+	1.01695i
$885$	11.2903	+	19.5554i	0.379519	+	0.657346i
$886$	−3.12852	−	5.41876i	−0.105105	−	0.182047i
$887$	−30.7439	−	17.7500i	−1.03228	−	0.595986i	−0.114641	−	0.993407i	$-0.536572\pi$
$887$	−30.7439	−	17.7500i	−1.03228	−	0.595986i	−0.917636	+	0.397421i	$0.869905\pi$
$888$	−21.0316			−0.705773
$889$	6.55031	−	3.06369i	0.219691	−	0.102753i
$890$			18.2538i			0.611867i
$891$	−35.4976	−	20.4945i	−1.18921	−	0.686593i
$892$	22.3281	+	38.6733i	0.747599	+	1.29488i
$893$	9.99619	+	17.3139i	0.334510	+	0.579388i
$894$	−25.0921	−	14.4869i	−0.839205	−	0.484515i
$895$		−	13.4734i		−	0.450365i
$896$	2.44516	−	28.3257i	0.0816872	−	0.946297i
$897$	5.31751			0.177547
$898$	91.3423	+	52.7365i	3.04813	+	1.75984i
$899$	−5.51846	−	9.55826i	−0.184051	−	0.318786i
$900$	−6.10267	−	10.5701i	−0.203422	−	0.352338i
$901$	−44.3421	+	19.6077i	−1.47725	+	0.653227i
$902$	52.6585			1.75333
$903$	40.9520	−	58.6298i	1.36280	−	1.95108i
$904$			12.0896i			0.402094i
$905$	−3.66599	+	6.34967i	−0.121861	+	0.211070i
$906$	−31.0801	+	17.9441i	−1.03257	+	0.596153i
$907$	43.7064	−	25.2339i	1.45125	−	0.837878i	0.452695	−	0.891665i	$-0.350463\pi$
$907$	43.7064	−	25.2339i	1.45125	−	0.837878i	0.998552	+	0.0537873i	$0.0171293\pi$
$908$	−9.02181	−	5.20874i	−0.299399	−	0.172858i
$909$	40.0762			1.32924
$910$	−15.5303	+	22.2343i	−0.514824	+	0.737058i
$911$		−	10.0962i		−	0.334501i	−0.985914	−	0.167250i	$-0.946511\pi$
$911$		−	10.0962i		−	0.334501i	0.985914	−	0.167250i	$-0.0534888\pi$
$912$	30.5818	+	17.6564i	1.01266	+	0.584662i
$913$	42.8821	−	24.7580i	1.41919	−	0.819371i
$914$	−4.54993	−	7.88071i	−0.150498	−	0.260671i
$915$	−2.46472	−	1.42300i	−0.0814810	−	0.0470431i
$916$	122.929			4.06170
$917$	−2.05752	−	0.177612i	−0.0679455	−	0.00586526i
$918$	−4.40029	+	6.02426i	−0.145231	+	0.198830i
$919$	17.6287	−	30.5339i	0.581518	−	1.00722i	−0.413782	−	0.910376i	$-0.635792\pi$
$919$	17.6287	−	30.5339i	0.581518	−	1.00722i	0.995300	−	0.0968427i	$-0.0308744\pi$
$920$	1.77975	+	3.08263i	0.0586768	+	0.101631i
$921$	−17.5502	+	10.1326i	−0.578297	+	0.333880i
$922$	−41.7611	+	72.3323i	−1.37533	+	2.38214i
$923$		−	28.6369i		−	0.942594i
$924$	108.059	−	50.5410i	3.55488	−	1.66268i
$925$		−	1.37176i		−	0.0451033i
$926$	−36.7787	+	63.7026i	−1.20862	+	2.09340i
$927$	1.09127	+	1.89013i	0.0358420	+	0.0620801i
$928$	−9.16605	+	5.29202i	−0.300890	+	0.173719i
$929$	11.9205	+	6.88229i	0.391098	+	0.225801i	0.682636	−	0.730759i	$-0.260834\pi$
$929$	11.9205	+	6.88229i	0.391098	+	0.225801i	−0.291538	+	0.956559i	$0.594167\pi$
$930$			37.7419i			1.23761i
$931$	−4.84284	−	13.2104i	−0.158718	−	0.432954i
$932$			68.5981i			2.24701i
$933$	−19.8648	+	34.4069i	−0.650346	+	1.12643i
$934$	26.0513	+	45.1221i	0.852423	+	1.47644i
$935$	−1.84568	+	17.1419i	−0.0603603	+	0.560599i
$936$	34.8475	−	60.3577i	1.13903	−	1.97285i
$937$	−17.5488			−0.573294			−0.286647	−	0.958036i	$-0.592541\pi$
$937$	−17.5488			−0.573294			−0.286647	+	0.958036i	$0.592541\pi$
$938$	−29.1788	+	13.6474i	−0.952722	+	0.445604i
$939$	−61.5883			−2.00986
$940$	38.8930	+	22.4549i	1.26855	+	0.732397i
$941$	4.45340	−	2.57117i	0.145177	−	0.0838178i	−0.425652	−	0.904887i	$-0.639955\pi$
$941$	4.45340	−	2.57117i	0.145177	−	0.0838178i	0.570829	+	0.821069i	$0.306622\pi$
$942$	8.62701	−	4.98081i	0.281083	−	0.162284i
$943$	−1.36771	+	2.36894i	−0.0445388	+	0.0771434i
$944$	−69.5587			−2.26394
$945$	−0.161296	+	1.86852i	−0.00524697	+	0.0607830i
$946$		−	120.808i		−	3.92780i
$947$	28.2056	+	16.2845i	0.916560	+	0.529176i	0.882536	−	0.470245i	$-0.155834\pi$
$947$	28.2056	+	16.2845i	0.916560	+	0.529176i	0.0340237	+	0.999421i	$0.489168\pi$
$948$	48.8146	+	84.5494i	1.58543	+	2.74604i
$949$	−56.9254	+	32.8659i	−1.84788	+	1.06687i
$950$	−2.56527	+	4.44318i	−0.0832284	+	0.144156i
$951$	−9.72027			−0.315201
$952$	−22.7093	−	66.2497i	−0.736012	−	2.14716i
$953$	−6.59131			−0.213514			−0.106757	−	0.994285i	$-0.534047\pi$
$953$	−6.59131			−0.213514			−0.106757	+	0.994285i	$0.534047\pi$
$954$	40.5677	−	70.2653i	1.31343	−	2.27492i
$955$	20.0261	−	11.5621i	0.648030	−	0.374140i
$956$	−31.1954	−	54.0321i	−1.00893	−	1.74752i
$957$	15.4160	+	8.90043i	0.498329	+	0.287710i
$958$			76.5714i			2.47391i
$959$	19.2377	+	13.4373i	0.621218	+	0.433912i
$960$	1.05641			0.0340955
$961$	3.66789	−	6.35297i	0.118319	−	0.204935i
$962$	12.1778	−	7.03083i	0.392627	−	0.226683i
$963$	−31.2583	+	18.0470i	−1.00728	+	0.581555i
$964$	48.1684	+	27.8100i	1.55140	+	0.895701i
$965$	−14.2913			−0.460054
$966$	−0.769027	+	8.90871i	−0.0247430	+	0.286633i
$967$	17.4534			0.561264			0.280632	−	0.959815i	$-0.409456\pi$
$967$	17.4534			0.561264			0.280632	+	0.959815i	$0.409456\pi$
$968$	20.8178	−	36.0575i	0.669110	−	1.15893i
$969$	−19.6779	−	2.11874i	−0.632147	−	0.0680638i
$970$	−4.43540	−	7.68234i	−0.142412	−	0.246665i
$971$	24.5594	−	42.5382i	0.788150	−	1.36512i	−0.138950	−	0.990299i	$-0.544373\pi$
$971$	24.5594	−	42.5382i	0.788150	−	1.36512i	0.927099	−	0.374816i	$-0.122294\pi$
$972$		−	96.0958i		−	3.08227i
$973$	−24.6897	−	52.7877i	−0.791515	−	1.69230i
$974$			46.0680i			1.47611i
$975$	8.30583	+	4.79537i	0.265999	+	0.153575i
$976$	7.59247	−	4.38351i	0.243029	−	0.140313i
$977$	−15.7047	−	27.2014i	−0.502438	−	0.870249i	−0.999996	−	0.00281801i	$-0.999103\pi$
$977$	−15.7047	−	27.2014i	−0.502438	−	0.870249i	0.497558	−	0.867431i	$-0.334230\pi$
$978$	22.0488	−	38.1896i	0.705042	−	1.22117i
$979$			29.9037i			0.955728i
$980$	−24.2588	−	20.2601i	−0.774919	−	0.647184i
$981$			51.2060i			1.63488i
$982$	−29.7101	+	51.4594i	−0.948087	+	1.64214i
$983$	−24.5225	+	14.1581i	−0.782147	+	0.451573i	−0.837191	−	0.546911i	$-0.815803\pi$
$983$	−24.5225	+	14.1581i	−0.782147	+	0.451573i	0.0550438	+	0.998484i	$0.482470\pi$
$984$	37.8208	+	65.5075i	1.20568	+	2.08830i
$985$	−5.51294	+	9.54869i	−0.175657	+	0.304247i
$986$	11.0654	−	15.1492i	0.352393	−	0.482448i
$987$	26.6254	+	56.9263i	0.847496	+	1.81198i
$988$	−36.4477			−1.15956
$989$	5.43478	+	3.13777i	0.172816	+	0.0997753i
$990$	−14.4259	−	24.9865i	−0.458487	−	0.794122i
$991$	33.8002	−	19.5145i	1.07370	−	0.619899i	0.144508	−	0.989504i	$-0.453840\pi$
$991$	33.8002	−	19.5145i	1.07370	−	0.619899i	0.929189	+	0.369604i	$0.120507\pi$
$992$	−31.8375	−	18.3814i	−1.01084	−	0.583609i
$993$		−	46.9671i		−	1.49046i
$994$	47.9769	+	4.14151i	1.52173	+	0.131361i
$995$	−3.29464			−0.104447
$996$	110.579	+	63.8430i	3.50384	+	2.02294i
$997$	0.115844	−	0.0668825i	0.00366881	−	0.00211819i	−0.498164	−	0.867083i	$-0.665992\pi$
$997$	0.115844	−	0.0668825i	0.00366881	−	0.00211819i	0.501833	+	0.864964i	$0.332659\pi$
$998$	−35.0019	+	20.2084i	−1.10797	+	0.639685i
$999$	0.486195	−	0.842114i	0.0153825	−	0.0266433i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	595.2.x.b.16.4	yes	92
7.4	even	3	inner	595.2.x.b.186.3	yes	92
17.16	even	2	inner	595.2.x.b.16.3	✓	92
119.67	even	6	inner	595.2.x.b.186.4	yes	92

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
595.2.x.b.16.3	✓	92	17.16	even	2	inner
595.2.x.b.16.4	yes	92	1.1	even	1	trivial
595.2.x.b.186.3	yes	92	7.4	even	3	inner
595.2.x.b.186.4	yes	92	119.67	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 595 = 5 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	595.x (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.27624 + 2.21052i) q^{2} +(2.06818 - 1.19407i) q^{3} +(-2.25759 - 3.91027i) q^{4} +(0.866025 + 0.500000i) q^{5} +6.09567i q^{6} +(2.39657 - 1.12092i) q^{7} +6.41999 q^{8} +(1.35159 - 2.34102i) q^{9} +(-2.21052 + 1.27624i) q^{10} +(-3.62132 + 2.09077i) q^{11} +(-9.33824 - 5.39143i) q^{12} +4.01600 q^{13} +(-0.580801 + 6.72822i) q^{14} +2.38813 q^{15} +(-3.67828 + 6.37096i) q^{16} +(0.441388 - 4.09941i) q^{17} +(3.44991 + 5.97541i) q^{18} +(1.00501 - 1.74073i) q^{19} -4.51519i q^{20} +(3.61810 - 5.17992i) q^{21} -10.6733i q^{22} +(0.480161 + 0.277221i) q^{23} +(13.2777 - 7.66589i) q^{24} +(0.500000 + 0.866025i) q^{25} +(-5.12540 + 8.87745i) q^{26} +0.708861i q^{27} +(-9.79357 - 6.84066i) q^{28} -1.78257i q^{29} +(-3.04784 + 5.27901i) q^{30} +(5.36207 - 3.09579i) q^{31} +(-2.96876 - 5.14205i) q^{32} +(-4.99304 + 8.64820i) q^{33} +(8.49851 + 6.20754i) q^{34} +(2.63595 + 0.227543i) q^{35} -12.2053 q^{36} +(-1.18798 - 0.685881i) q^{37} +(2.56527 + 4.44318i) q^{38} +(8.30583 - 4.79537i) q^{39} +(5.55987 + 3.20999i) q^{40} +4.93364i q^{41} +(6.83274 + 14.6087i) q^{42} +11.3187 q^{43} +(16.3510 + 9.44023i) q^{44} +(2.34102 - 1.35159i) q^{45} +(-1.22560 + 0.707603i) q^{46} +(-4.97319 + 8.61381i) q^{47} +17.5684i q^{48} +(4.48709 - 5.37271i) q^{49} -2.55249 q^{50} +(-3.98210 - 9.00538i) q^{51} +(-9.06651 - 15.7037i) q^{52} +(-5.87953 - 10.1837i) q^{53} +(-1.56695 - 0.904679i) q^{54} -4.18154 q^{55} +(15.3859 - 7.19627i) q^{56} -4.80019i q^{57} +(3.94040 + 2.27499i) q^{58} +(4.72767 + 8.18856i) q^{59} +(-5.39143 - 9.33824i) q^{60} +(-1.03207 - 0.595865i) q^{61} +15.8039i q^{62} +(0.615088 - 7.12543i) q^{63} +0.442358 q^{64} +(3.47796 + 2.00800i) q^{65} +(-12.7447 - 22.0744i) q^{66} +(2.38498 + 4.13090i) q^{67} +(-17.0263 + 7.52887i) q^{68} +1.32408 q^{69} +(-3.86710 + 5.53641i) q^{70} -7.13069i q^{71} +(8.67717 - 15.0293i) q^{72} +(-14.1746 + 8.18373i) q^{73} +(3.03231 - 1.75070i) q^{74} +(2.06818 + 1.19407i) q^{75} -9.07561 q^{76} +(-6.33518 + 9.06988i) q^{77} +24.4803i q^{78} +(-7.84109 - 4.52706i) q^{79} +(-6.37096 + 3.67828i) q^{80} +(4.90119 + 8.48910i) q^{81} +(-10.9059 - 6.29653i) q^{82} -11.8416 q^{83} +(-28.4231 - 2.45357i) q^{84} +(2.43196 - 3.32950i) q^{85} +(-14.4454 + 25.0201i) q^{86} +(-2.12850 - 3.68668i) q^{87} +(-23.2488 + 13.4227i) q^{88} +(3.57568 - 6.19326i) q^{89} +6.89981i q^{90} +(9.62463 - 4.50160i) q^{91} -2.50341i q^{92} +(7.39317 - 12.8053i) q^{93} +(-12.6940 - 21.9866i) q^{94} +(1.74073 - 1.00501i) q^{95} +(-12.2799 - 7.08980i) q^{96} +3.47536i q^{97} +(6.14985 + 16.7757i) q^{98} +11.3034i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 92 q - 52 q^{4} + 40 q^{9} + 24 q^{13} - 4 q^{15} - 48 q^{16} + 12 q^{17} - 12 q^{18} - 8 q^{19} - 56 q^{21} + 46 q^{25} - 44 q^{26} - 20 q^{33} - 72 q^{34} + 6 q^{35} - 176 q^{36} + 8 q^{38} + 20 q^{42}+ \cdots - 152 q^{98}+O(q^{100}) \) 92 * q - 52 * q^4 + 40 * q^9 + 24 * q^13 - 4 * q^15 - 48 * q^16 + 12 * q^17 - 12 * q^18 - 8 * q^19 - 56 * q^21 + 46 * q^25 - 44 * q^26 - 20 * q^33 - 72 * q^34 + 6 * q^35 - 176 * q^36 + 8 * q^38 + 20 * q^42 - 16 * q^43 - 76 * q^47 + 6 * q^49 + 6 * q^51 + 8 * q^52 - 36 * q^53 + 24 * q^55 + 14 * q^59 - 28 * q^60 + 184 * q^64 + 4 * q^66 - 8 * q^67 + 44 * q^68 + 12 * q^69 - 4 * q^70 + 40 * q^72 - 136 * q^76 - 44 * q^77 + 10 * q^81 - 224 * q^83 + 124 * q^84 - 12 * q^85 + 12 * q^86 + 48 * q^87 - 6 * q^89 - 16 * q^93 - 140 * q^94 - 152 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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