LMFDB - Embedded newform 315.2.l.b.151.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(121,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("315.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.l (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:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			151.6
Character	$\chi$	$=$	315.151
Dual form			315.2.l.b.121.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.308078 q^{2} +(-1.71752 - 0.223878i) q^{3} -1.90509 q^{4} +(0.500000 - 0.866025i) q^{5} +(0.529131 + 0.0689719i) q^{6} +(-2.36933 - 1.17741i) q^{7} +1.20307 q^{8} +(2.89976 + 0.769029i) q^{9} +O(q^{10})$	\(q-0.308078 q^{2} +(-1.71752 - 0.223878i) q^{3} -1.90509 q^{4} +(0.500000 - 0.866025i) q^{5} +(0.529131 + 0.0689719i) q^{6} +(-2.36933 - 1.17741i) q^{7} +1.20307 q^{8} +(2.89976 + 0.769029i) q^{9} +(-0.154039 + 0.266804i) q^{10} +(0.550395 + 0.953312i) q^{11} +(3.27203 + 0.426507i) q^{12} +(2.54250 + 4.40373i) q^{13} +(0.729938 + 0.362735i) q^{14} +(-1.05264 + 1.37548i) q^{15} +3.43953 q^{16} +(-3.17853 + 5.50538i) q^{17} +(-0.893353 - 0.236921i) q^{18} +(0.518175 + 0.897506i) q^{19} +(-0.952544 + 1.64985i) q^{20} +(3.80577 + 2.55267i) q^{21} +(-0.169565 - 0.293695i) q^{22} +(0.186013 - 0.322185i) q^{23} +(-2.06630 - 0.269341i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-0.783288 - 1.35669i) q^{26} +(-4.80823 - 1.97002i) q^{27} +(4.51377 + 2.24307i) q^{28} +(-1.91336 + 3.31404i) q^{29} +(0.324297 - 0.423755i) q^{30} +10.2333 q^{31} -3.46579 q^{32} +(-0.731889 - 1.76055i) q^{33} +(0.979237 - 1.69609i) q^{34} +(-2.20433 + 1.46319i) q^{35} +(-5.52429 - 1.46507i) q^{36} +(1.42002 + 2.45954i) q^{37} +(-0.159639 - 0.276502i) q^{38} +(-3.38089 - 8.13271i) q^{39} +(0.601537 - 1.04189i) q^{40} +(4.62313 + 8.00749i) q^{41} +(-1.17248 - 0.786422i) q^{42} +(2.67107 - 4.62643i) q^{43} +(-1.04855 - 1.81614i) q^{44} +(2.11588 - 2.12675i) q^{45} +(-0.0573067 + 0.0992582i) q^{46} -9.36949 q^{47} +(-5.90747 - 0.770035i) q^{48} +(4.22741 + 5.57934i) q^{49} +(0.154039 + 0.266804i) q^{50} +(6.69173 - 8.74400i) q^{51} +(-4.84368 - 8.38949i) q^{52} +(2.35612 - 4.08091i) q^{53} +(1.48131 + 0.606919i) q^{54} +1.10079 q^{55} +(-2.85047 - 1.41651i) q^{56} +(-0.689046 - 1.65749i) q^{57} +(0.589466 - 1.02099i) q^{58} -4.66171 q^{59} +(2.00538 - 2.62041i) q^{60} -8.30266 q^{61} -3.15266 q^{62} +(-5.96501 - 5.23629i) q^{63} -5.81133 q^{64} +5.08499 q^{65} +(0.225479 + 0.542389i) q^{66} +2.33934 q^{67} +(6.05538 - 10.4882i) q^{68} +(-0.391612 + 0.511715i) q^{69} +(0.679107 - 0.450777i) q^{70} -2.37665 q^{71} +(3.48862 + 0.925199i) q^{72} +(-5.94698 + 10.3005i) q^{73} +(-0.437477 - 0.757733i) q^{74} +(0.664877 + 1.59936i) q^{75} +(-0.987170 - 1.70983i) q^{76} +(-0.181625 - 2.90675i) q^{77} +(1.04158 + 2.50551i) q^{78} +10.5356 q^{79} +(1.71977 - 2.97872i) q^{80} +(7.81719 + 4.46000i) q^{81} +(-1.42429 - 2.46694i) q^{82} +(-7.01949 + 12.1581i) q^{83} +(-7.25033 - 4.86306i) q^{84} +(3.17853 + 5.50538i) q^{85} +(-0.822898 + 1.42530i) q^{86} +(4.02818 - 5.26358i) q^{87} +(0.662165 + 1.14690i) q^{88} +(-3.40723 - 5.90149i) q^{89} +(-0.651856 + 0.655205i) q^{90} +(-0.838997 - 13.4274i) q^{91} +(-0.354372 + 0.613790i) q^{92} +(-17.5759 - 2.29101i) q^{93} +2.88654 q^{94} +1.03635 q^{95} +(5.95257 + 0.775914i) q^{96} +(2.00631 - 3.47503i) q^{97} +(-1.30237 - 1.71887i) q^{98} +(0.862887 + 3.18764i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 2 q^{2} - 5 q^{3} + 14 q^{4} + 12 q^{5} + 3 q^{6} - 11 q^{7} + 12 q^{8} - 3 q^{9}+O(q^{10}) $ 24 * q + 2 * q^2 - 5 * q^3 + 14 * q^4 + 12 * q^5 + 3 * q^6 - 11 * q^7 + 12 * q^8 - 3 * q^9	\( 24 q + 2 q^{2} - 5 q^{3} + 14 q^{4} + 12 q^{5} + 3 q^{6} - 11 q^{7} + 12 q^{8} - 3 q^{9} + q^{10} + q^{11} - 7 q^{12} - 4 q^{13} + 8 q^{14} - q^{15} + 10 q^{16} - 7 q^{17} + 18 q^{18} - 2 q^{19} + 7 q^{20} - 17 q^{21} + 19 q^{22} + q^{23} + 18 q^{24} - 12 q^{25} + 11 q^{26} - 11 q^{27} - 28 q^{28} - 16 q^{31} - 34 q^{32} + 7 q^{33} + q^{34} - 7 q^{35} - 25 q^{36} + 17 q^{37} - 35 q^{38} - 17 q^{39} + 6 q^{40} + 20 q^{41} - 36 q^{42} + 31 q^{43} - 7 q^{44} + 6 q^{45} - 10 q^{46} + 62 q^{47} - 36 q^{48} - 11 q^{49} - q^{50} + 14 q^{51} - 4 q^{52} + 8 q^{53} - 51 q^{54} + 2 q^{55} + 5 q^{57} + 45 q^{58} + 42 q^{59} - 23 q^{60} - 10 q^{61} + 14 q^{62} + 18 q^{63} - 56 q^{64} - 8 q^{65} + 4 q^{66} - 86 q^{67} - 48 q^{68} + 26 q^{69} - 5 q^{70} + 24 q^{71} - 6 q^{72} - 18 q^{73} + 9 q^{74} + 4 q^{75} - 13 q^{76} + 35 q^{77} + 19 q^{78} - 80 q^{79} + 5 q^{80} + 21 q^{81} + 5 q^{82} - 60 q^{83} + 35 q^{84} + 7 q^{85} + 12 q^{86} + 68 q^{87} + 50 q^{88} - 4 q^{89} + 12 q^{90} - 33 q^{91} - 18 q^{92} + 7 q^{93} + 22 q^{94} - 4 q^{95} + 6 q^{97} - 15 q^{98} - q^{99}+O(q^{100}) \) 24 * q + 2 * q^2 - 5 * q^3 + 14 * q^4 + 12 * q^5 + 3 * q^6 - 11 * q^7 + 12 * q^8 - 3 * q^9 + q^10 + q^11 - 7 * q^12 - 4 * q^13 + 8 * q^14 - q^15 + 10 * q^16 - 7 * q^17 + 18 * q^18 - 2 * q^19 + 7 * q^20 - 17 * q^21 + 19 * q^22 + q^23 + 18 * q^24 - 12 * q^25 + 11 * q^26 - 11 * q^27 - 28 * q^28 - 16 * q^31 - 34 * q^32 + 7 * q^33 + q^34 - 7 * q^35 - 25 * q^36 + 17 * q^37 - 35 * q^38 - 17 * q^39 + 6 * q^40 + 20 * q^41 - 36 * q^42 + 31 * q^43 - 7 * q^44 + 6 * q^45 - 10 * q^46 + 62 * q^47 - 36 * q^48 - 11 * q^49 - q^50 + 14 * q^51 - 4 * q^52 + 8 * q^53 - 51 * q^54 + 2 * q^55 + 5 * q^57 + 45 * q^58 + 42 * q^59 - 23 * q^60 - 10 * q^61 + 14 * q^62 + 18 * q^63 - 56 * q^64 - 8 * q^65 + 4 * q^66 - 86 * q^67 - 48 * q^68 + 26 * q^69 - 5 * q^70 + 24 * q^71 - 6 * q^72 - 18 * q^73 + 9 * q^74 + 4 * q^75 - 13 * q^76 + 35 * q^77 + 19 * q^78 - 80 * q^79 + 5 * q^80 + 21 * q^81 + 5 * q^82 - 60 * q^83 + 35 * q^84 + 7 * q^85 + 12 * q^86 + 68 * q^87 + 50 * q^88 - 4 * q^89 + 12 * q^90 - 33 * q^91 - 18 * q^92 + 7 * q^93 + 22 * q^94 - 4 * q^95 + 6 * q^97 - 15 * q^98 - q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−0.308078			−0.217844			−0.108922	−	0.994050i	$-0.534740\pi$
$2$	−0.308078			−0.217844			−0.108922	+	0.994050i	$0.534740\pi$
$3$	−1.71752	−	0.223878i	−0.991611	−	0.129256i
$3$	−1.71752	−	0.223878i	−0.991611	−	0.129256i
$4$	−1.90509			−0.952544
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$	0.529131	+	0.0689719i	0.216017	+	0.0281577i
$7$	−2.36933	−	1.17741i	−0.895521	−	0.445020i
$7$	−2.36933	−	1.17741i	−0.895521	−	0.445020i
$8$	1.20307			0.425351
$9$	2.89976	+	0.769029i	0.966586	+	0.256343i
$10$	−0.154039	+	0.266804i	−0.0487115	+	0.0843707i
$11$	0.550395	+	0.953312i	0.165950	+	0.287434i	0.936992	−	0.349350i	$-0.113598\pi$
$11$	0.550395	+	0.953312i	0.165950	+	0.287434i	−0.771042	+	0.636784i	$0.780264\pi$
$12$	3.27203	+	0.426507i	0.944553	+	0.123122i
$13$	2.54250	+	4.40373i	0.705161	+	1.22138i	0.966633	+	0.256164i	$0.0824588\pi$
$13$	2.54250	+	4.40373i	0.705161	+	1.22138i	−0.261472	+	0.965211i	$0.584208\pi$
$14$	0.729938	+	0.362735i	0.195084	+	0.0969450i
$15$	−1.05264	+	1.37548i	−0.271792	+	0.355147i
$16$	3.43953			0.859884
$17$	−3.17853	+	5.50538i	−0.770907	+	1.33525i	0.166159	+	0.986099i	$0.446864\pi$
$17$	−3.17853	+	5.50538i	−0.770907	+	1.33525i	−0.937066	+	0.349152i	$0.886470\pi$
$18$	−0.893353	−	0.236921i	−0.210565	−	0.0558429i
$19$	0.518175	+	0.897506i	0.118878	+	0.205902i	0.919323	−	0.393503i	$-0.128737\pi$
$19$	0.518175	+	0.897506i	0.118878	+	0.205902i	−0.800446	+	0.599405i	$0.795404\pi$
$20$	−0.952544	+	1.64985i	−0.212995	+	0.368919i
$21$	3.80577	+	2.55267i	0.830487	+	0.557038i
$22$	−0.169565	−	0.293695i	−0.0361513	−	0.0626159i
$23$	0.186013	−	0.322185i	0.0387865	−	0.0671802i	−0.845980	−	0.533214i	$-0.820984\pi$
$23$	0.186013	−	0.322185i	0.0387865	−	0.0671802i	0.884767	+	0.466034i	$0.154317\pi$
$24$	−2.06630	−	0.269341i	−0.421782	−	0.0549791i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−0.783288	−	1.35669i	−0.153615	−	0.266070i
$27$	−4.80823	−	1.97002i	−0.925344	−	0.379130i
$28$	4.51377	+	2.24307i	0.853023	+	0.423901i
$29$	−1.91336	+	3.31404i	−0.355303	+	0.615402i	−0.987170	−	0.159674i	$-0.948956\pi$
$29$	−1.91336	+	3.31404i	−0.355303	+	0.615402i	0.631867	+	0.775077i	$0.282289\pi$
$30$	0.324297	−	0.423755i	0.0592083	−	0.0773667i
$31$	10.2333			1.83796			0.918978	−	0.394308i	$-0.129016\pi$
$31$	10.2333			1.83796			0.918978	+	0.394308i	$0.129016\pi$
$32$	−3.46579			−0.612671
$33$	−0.731889	−	1.76055i	−0.127406	−	0.306473i
$34$	0.979237	−	1.69609i	0.167938	−	0.290877i
$35$	−2.20433	+	1.46319i	−0.372600	+	0.247324i
$36$	−5.52429	−	1.46507i	−0.920715	−	0.244178i
$37$	1.42002	+	2.45954i	0.233450	+	0.404347i	0.958821	−	0.284011i	$-0.0916653\pi$
$37$	1.42002	+	2.45954i	0.233450	+	0.404347i	−0.725371	+	0.688358i	$0.758332\pi$
$38$	−0.159639	−	0.276502i	−0.0258968	−	0.0448546i
$39$	−3.38089	−	8.13271i	−0.541376	−	1.30228i
$40$	0.601537	−	1.04189i	0.0951113	−	0.164738i
$41$	4.62313	+	8.00749i	0.722011	+	1.25056i	0.960192	+	0.279340i	$0.0901155\pi$
$41$	4.62313	+	8.00749i	0.722011	+	1.25056i	−0.238181	+	0.971221i	$0.576551\pi$
$42$	−1.17248	−	0.786422i	−0.180917	−	0.121347i
$43$	2.67107	−	4.62643i	0.407334	−	0.705523i	−0.587256	−	0.809401i	$-0.699792\pi$
$43$	2.67107	−	4.62643i	0.407334	−	0.705523i	0.994590	+	0.103878i	$0.0331251\pi$
$44$	−1.04855	−	1.81614i	−0.158075	−	0.273794i
$45$	2.11588	−	2.12675i	0.315416	−	0.317037i
$46$	−0.0573067	+	0.0992582i	−0.00844942	+	0.0146348i
$47$	−9.36949			−1.36668			−0.683340	−	0.730100i	$-0.739473\pi$
$47$	−9.36949			−1.36668			−0.683340	+	0.730100i	$0.739473\pi$
$48$	−5.90747	−	0.770035i	−0.852670	−	0.111145i
$49$	4.22741	+	5.57934i	0.603915	+	0.797049i
$50$	0.154039	+	0.266804i	0.0217844	+	0.0377317i
$51$	6.69173	−	8.74400i	0.937029	−	1.22441i
$52$	−4.84368	−	8.38949i	−0.671697	−	1.16341i
$53$	2.35612	−	4.08091i	0.323637	−	0.560556i	−0.657598	−	0.753369i	$-0.728428\pi$
$53$	2.35612	−	4.08091i	0.323637	−	0.560556i	0.981236	+	0.192812i	$0.0617609\pi$
$54$	1.48131	+	0.606919i	0.201581	+	0.0825912i
$55$	1.10079			0.148430
$56$	−2.85047	−	1.41651i	−0.380910	−	0.189289i
$57$	−0.689046	−	1.65749i	−0.0912663	−	0.219540i
$58$	0.589466	−	1.02099i	0.0774007	−	0.134062i
$59$	−4.66171			−0.606903			−0.303452	−	0.952847i	$-0.598139\pi$
$59$	−4.66171			−0.606903			−0.303452	+	0.952847i	$0.598139\pi$
$60$	2.00538	−	2.62041i	0.258893	−	0.338293i
$61$	−8.30266			−1.06305			−0.531523	−	0.847044i	$-0.678380\pi$
$61$	−8.30266			−1.06305			−0.531523	+	0.847044i	$0.678380\pi$
$62$	−3.15266			−0.400388
$63$	−5.96501	−	5.23629i	−0.751520	−	0.659710i
$64$	−5.81133			−0.726417
$65$	5.08499			0.630715
$66$	0.225479	+	0.542389i	0.0277546	+	0.0667634i
$67$	2.33934			0.285795			0.142898	−	0.989737i	$-0.454358\pi$
$67$	2.33934			0.285795			0.142898	+	0.989737i	$0.454358\pi$
$68$	6.05538	−	10.4882i	0.734323	−	1.27188i
$69$	−0.391612	+	0.511715i	−0.0471445	+	0.0616032i
$70$	0.679107	−	0.450777i	0.0811688	−	0.0538782i
$71$	−2.37665			−0.282056			−0.141028	−	0.990006i	$-0.545041\pi$
$71$	−2.37665			−0.282056			−0.141028	+	0.990006i	$0.545041\pi$
$72$	3.48862	+	0.925199i	0.411138	+	0.109036i
$73$	−5.94698	+	10.3005i	−0.696041	+	1.20558i	0.273787	+	0.961790i	$0.411724\pi$
$73$	−5.94698	+	10.3005i	−0.696041	+	1.20558i	−0.969828	+	0.243788i	$0.921610\pi$
$74$	−0.437477	−	0.757733i	−0.0508557	−	0.0880846i
$75$	0.664877	+	1.59936i	0.0767734	+	0.184678i
$76$	−0.987170	−	1.70983i	−0.113236	−	0.196131i
$77$	−0.181625	−	2.90675i	−0.0206980	−	0.331255i
$78$	1.04158	+	2.50551i	0.117936	+	0.283693i
$79$	10.5356			1.18534			0.592671	−	0.805444i	$-0.298073\pi$
$79$	10.5356			1.18534			0.592671	+	0.805444i	$0.298073\pi$
$80$	1.71977	−	2.97872i	0.192276	−	0.333032i
$81$	7.81719	+	4.46000i	0.868576	+	0.495555i
$82$	−1.42429	−	2.46694i	−0.157286	−	0.272427i
$83$	−7.01949	+	12.1581i	−0.770489	+	1.33453i	0.166807	+	0.985990i	$0.446654\pi$
$83$	−7.01949	+	12.1581i	−0.770489	+	1.33453i	−0.937295	+	0.348536i	$0.886679\pi$
$84$	−7.25033	−	4.86306i	−0.791075	−	0.530603i
$85$	3.17853	+	5.50538i	0.344760	+	0.597142i
$86$	−0.822898	+	1.42530i	−0.0887354	+	0.153694i
$87$	4.02818	−	5.26358i	0.431867	−	0.564315i
$88$	0.662165	+	1.14690i	0.0705870	+	0.122260i
$89$	−3.40723	−	5.90149i	−0.361165	−	0.625556i	0.626988	−	0.779029i	$-0.284288\pi$
$89$	−3.40723	−	5.90149i	−0.361165	−	0.625556i	−0.988153	+	0.153473i	$0.950954\pi$
$90$	−0.651856	+	0.655205i	−0.0687117	+	0.0690647i
$91$	−0.838997	−	13.4274i	−0.0879508	−	1.40758i
$92$	−0.354372	+	0.613790i	−0.0369458	+	0.0639921i
$93$	−17.5759	−	2.29101i	−1.82254	−	0.237567i
$94$	2.88654			0.297724
$95$	1.03635			0.106327
$96$	5.95257	+	0.775914i	0.607532	+	0.0791914i
$97$	2.00631	−	3.47503i	0.203710	−	0.352836i	−0.746011	−	0.665934i	$-0.768033\pi$
$97$	2.00631	−	3.47503i	0.203710	−	0.352836i	0.949721	+	0.313098i	$0.101367\pi$
$98$	−1.30237	−	1.71887i	−0.131559	−	0.173632i
$99$	0.862887	+	3.18764i	0.0867234	+	0.320370i
$100$	0.952544	+	1.64985i	0.0952544	+	0.164985i
$101$	6.23745	+	10.8036i	0.620649	+	1.07500i	0.989365	+	0.145454i	$0.0464641\pi$
$101$	6.23745	+	10.8036i	0.620649	+	1.07500i	−0.368716	+	0.929542i	$0.620203\pi$
$102$	−2.06158	+	2.69384i	−0.204127	+	0.266730i
$103$	−4.82564	+	8.35826i	−0.475485	+	0.823563i	−0.999606	−	0.0280804i	$-0.991061\pi$
$103$	−4.82564	+	8.35826i	−0.475485	+	0.823563i	0.524121	+	0.851644i	$0.324394\pi$
$104$	3.05881	+	5.29801i	0.299941	+	0.519513i
$105$	4.11356	−	2.01956i	0.401442	−	0.197089i
$106$	−0.725868	+	1.25724i	−0.0705025	+	0.122114i
$107$	8.18116	+	14.1702i	0.790902	+	1.36988i	0.925409	+	0.378970i	$0.123722\pi$
$107$	8.18116	+	14.1702i	0.790902	+	1.36988i	−0.134506	+	0.990913i	$0.542945\pi$
$108$	9.16009	+	3.75305i	0.881430	+	0.361138i
$109$	−1.65472	+	2.86607i	−0.158494	+	0.274519i	−0.934326	−	0.356420i	$-0.883997\pi$
$109$	−1.65472	+	2.86607i	−0.158494	+	0.274519i	0.775832	+	0.630940i	$0.217330\pi$
$110$	−0.339129			−0.0323347
$111$	−1.88828	−	4.54223i	−0.179227	−	0.431129i
$112$	−8.14938	−	4.04975i	−0.770044	−	0.382665i
$113$	−5.14995	−	8.91997i	−0.484466	−	0.839120i	0.515375	−	0.856965i	$-0.327653\pi$
$113$	−5.14995	−	8.91997i	−0.484466	−	0.839120i	−0.999841	+	0.0178450i	$0.994319\pi$
$114$	0.212280	+	0.510638i	0.0198818	+	0.0478256i
$115$	−0.186013	−	0.322185i	−0.0173458	−	0.0300439i
$116$	3.64513	−	6.31354i	0.338441	−	0.586198i
$117$	3.98602	+	14.7250i	0.368508	+	1.36133i
$118$	1.43617			0.132210
$119$	14.0131	−	9.30160i	1.28458	−	0.852676i
$120$	−1.26641	+	1.65480i	−0.115607	+	0.151062i
$121$	4.89413	−	8.47688i	0.444921	−	0.770626i
$122$	2.55787			0.231579
$123$	−6.14762	−	14.7881i	−0.554312	−	1.33339i
$124$	−19.4953			−1.75073
$125$	−1.00000			−0.0894427
$126$	1.83769	+	1.61319i	0.163714	+	0.143714i
$127$	0.321507			0.0285291			0.0142646	−	0.999898i	$-0.495459\pi$
$127$	0.321507			0.0285291			0.0142646	+	0.999898i	$0.495459\pi$
$128$	8.72193			0.770917
$129$	−5.62337	+	7.34799i	−0.495110	+	0.646955i
$130$	−1.56658			−0.137398
$131$	−5.19404	+	8.99633i	−0.453805	+	0.786013i	−0.998619	−	0.0525439i	$-0.983267\pi$
$131$	−5.19404	+	8.99633i	−0.453805	+	0.786013i	0.544814	+	0.838557i	$0.316600\pi$
$132$	1.39431	+	3.35401i	0.121359	+	0.291929i
$133$	−0.170993	−	2.73659i	−0.0148269	−	0.237292i
$134$	−0.720699			−0.0622589
$135$	−4.11020	+	3.17904i	−0.353749	+	0.273608i
$136$	−3.82401	+	6.62337i	−0.327906	+	0.567950i
$137$	−7.06331	−	12.2340i	−0.603459	−	1.04522i	−0.992293	−	0.123914i	$-0.960455\pi$
$137$	−7.06331	−	12.2340i	−0.603459	−	1.04522i	0.388834	−	0.921308i	$-0.372878\pi$
$138$	0.120647	−	0.157648i	0.0102702	−	0.0134199i
$139$	−4.54342	−	7.86944i	−0.385368	−	0.667477i	0.606452	−	0.795120i	$-0.292592\pi$
$139$	−4.54342	−	7.86944i	−0.385368	−	0.667477i	−0.991820	+	0.127643i	$0.959259\pi$
$140$	4.19944	−	2.78751i	0.354918	−	0.235587i
$141$	16.0923	+	2.09762i	1.35522	+	0.176651i
$142$	0.732193			0.0614443
$143$	−2.79875	+	4.84758i	−0.234043	+	0.405375i
$144$	9.97382	+	2.64510i	0.831151	+	0.220425i
$145$	1.91336	+	3.31404i	0.158896	+	0.275216i
$146$	1.83214	−	3.17335i	0.151629	−	0.262628i
$147$	−6.01157	−	10.5291i	−0.495826	−	0.868422i
$148$	−2.70526	−	4.68565i	−0.222371	−	0.385158i
$149$	−1.12486	+	1.94832i	−0.0921522	+	0.159612i	−0.908417	−	0.418066i	$-0.862708\pi$
$149$	−1.12486	+	1.94832i	−0.0921522	+	0.159612i	0.816264	+	0.577679i	$0.196041\pi$
$150$	−0.204834	−	0.492727i	−0.0167246	−	0.0402310i
$151$	2.18691	+	3.78783i	0.177968	+	0.308249i	0.941184	−	0.337893i	$-0.109714\pi$
$151$	2.18691	+	3.78783i	0.177968	+	0.308249i	−0.763217	+	0.646143i	$0.776381\pi$
$152$	0.623403	+	1.07977i	0.0505647	+	0.0875806i
$153$	−13.4508	+	13.5199i	−1.08743	+	1.09302i
$154$	0.0559546	+	0.895506i	0.00450895	+	0.0721619i
$155$	5.11665	−	8.86230i	0.410980	−	0.711837i
$156$	6.44090	+	15.4935i	0.515684	+	1.24047i
$157$	16.5733			1.32269			0.661347	−	0.750080i	$-0.269985\pi$
$157$	16.5733			1.32269			0.661347	+	0.750080i	$0.269985\pi$
$158$	−3.24578			−0.258220
$159$	−4.96030	+	6.48157i	−0.393378	+	0.514022i
$160$	−1.73290	+	3.00146i	−0.136997	+	0.237287i
$161$	−0.820070	+	0.544346i	−0.0646306	+	0.0429005i
$162$	−2.40831	−	1.37403i	−0.189214	−	0.107954i
$163$	6.34528	+	10.9903i	0.497000	+	0.860830i	0.999994	−	0.00346026i	$-0.00110144\pi$
$163$	6.34528	+	10.9903i	0.497000	+	0.860830i	−0.502994	+	0.864290i	$0.667768\pi$
$164$	−8.80747	−	15.2550i	−0.687748	−	1.19121i
$165$	−1.89063	−	0.246442i	−0.147185	−	0.0191855i
$166$	2.16255	−	3.74565i	0.167847	−	0.290719i
$167$	1.92585	+	3.33567i	0.149027	+	0.258122i	0.930868	−	0.365356i	$-0.119053\pi$
$167$	1.92585	+	3.33567i	0.149027	+	0.258122i	−0.781841	+	0.623477i	$0.785719\pi$
$168$	4.57862	+	3.07105i	0.353248	+	0.236936i
$169$	−6.42856	+	11.1346i	−0.494505	+	0.856508i
$170$	−0.979237	−	1.69609i	−0.0751041	−	0.130084i
$171$	0.812374	+	3.00104i	0.0621238	+	0.229495i
$172$	−5.08862	+	8.81375i	−0.388004	+	0.672042i
$173$	25.2163			1.91716			0.958579	−	0.284826i	$-0.0919360\pi$
$173$	25.2163			1.91716			0.958579	+	0.284826i	$0.0919360\pi$
$174$	−1.24100	+	1.62160i	−0.0940797	+	0.122933i
$175$	0.164995	+	2.64060i	0.0124724	+	0.199611i
$176$	1.89310	+	3.27895i	0.142698	+	0.247160i
$177$	8.00659	+	1.04365i	0.601812	+	0.0784458i
$178$	1.04969	+	1.81812i	0.0786778	+	0.136274i
$179$	−5.17012	+	8.95491i	−0.386433	+	0.669321i	−0.991967	−	0.126498i	$-0.959626\pi$
$179$	−5.17012	+	8.95491i	−0.386433	+	0.669321i	0.605534	+	0.795819i	$0.292960\pi$
$180$	−4.03093	+	4.05164i	−0.300448	+	0.301992i
$181$	−9.02822			−0.671062			−0.335531	−	0.942029i	$-0.608916\pi$
$181$	−9.02822			−0.671062			−0.335531	+	0.942029i	$0.608916\pi$
$182$	0.258477	+	4.13670i	0.0191596	+	0.306633i
$183$	14.2600	+	1.85878i	1.05413	+	0.137405i
$184$	0.223788	−	0.387612i	0.0164979	−	0.0285751i
$185$	2.84004			0.208804
$186$	5.41476	+	0.705811i	0.397030	+	0.0517525i
$187$	−6.99779			−0.511729
$188$	17.8497			1.30182
$189$	9.07273	+	10.3289i	0.659944	+	0.751314i
$190$	−0.319277			−0.0231628
$191$	−21.8032			−1.57763			−0.788813	−	0.614634i	$-0.789304\pi$
$191$	−21.8032			−1.57763			−0.788813	+	0.614634i	$0.789304\pi$
$192$	9.98109	+	1.30103i	0.720323	+	0.0938936i
$193$	1.46412			0.105390			0.0526949	−	0.998611i	$-0.483219\pi$
$193$	1.46412			0.105390			0.0526949	+	0.998611i	$0.483219\pi$
$194$	−0.618101	+	1.07058i	−0.0443771	+	0.0768634i
$195$	−8.73358	−	1.13842i	−0.625425	−	0.0815237i
$196$	−8.05358	−	10.6291i	−0.575256	−	0.759224i
$197$	16.2333			1.15658			0.578289	−	0.815832i	$-0.303721\pi$
$197$	16.2333			1.15658			0.578289	+	0.815832i	$0.303721\pi$
$198$	−0.265837	−	0.982044i	−0.0188922	−	0.0697908i
$199$	−2.83862	+	4.91664i	−0.201225	+	0.348531i	−0.948923	−	0.315507i	$-0.897825\pi$
$199$	−2.83862	+	4.91664i	−0.201225	+	0.348531i	0.747699	+	0.664038i	$0.231159\pi$
$200$	−0.601537	−	1.04189i	−0.0425351	−	0.0736729i
$201$	−4.01786	−	0.523725i	−0.283398	−	0.0369407i
$202$	−1.92162	−	3.32835i	−0.135205	−	0.234182i
$203$	8.43537	−	5.59923i	0.592047	−	0.392989i
$204$	−12.7483	+	16.6581i	−0.892562	+	1.16630i
$205$	9.24626			0.645787
$206$	1.48668	−	2.57500i	0.103582	−	0.179409i
$207$	0.787163	−	0.791208i	0.0547116	−	0.0549927i
$208$	8.74500	+	15.1468i	0.606357	+	1.05024i
$209$	−0.570402	+	0.987965i	−0.0394555	+	0.0683390i
$210$	−1.26730	+	0.622183i	−0.0874519	+	0.0429347i
$211$	−5.46167	−	9.45989i	−0.375997	−	0.651245i	0.614479	−	0.788933i	$-0.289366\pi$
$211$	−5.46167	−	9.45989i	−0.375997	−	0.651245i	−0.990476	+	0.137688i	$0.956033\pi$
$212$	−4.48861	+	7.77449i	−0.308279	+	0.533954i
$213$	4.08194	+	0.532078i	0.279690	+	0.0364574i
$214$	−2.52044	−	4.36553i	−0.172294	−	0.298421i
$215$	−2.67107	−	4.62643i	−0.182165	−	0.315520i
$216$	−5.78465	−	2.37007i	−0.393595	−	0.161263i
$217$	−24.2460	−	12.0488i	−1.64593	−	0.817926i
$218$	0.509785	−	0.882973i	0.0345270	−	0.0598025i
$219$	12.5201	−	16.3599i	0.846030	−	1.10550i
$220$	−2.09710			−0.141386
$221$	−32.3256			−2.17446
$222$	0.581737	+	1.39936i	0.0390436	+	0.0939191i
$223$	6.00289	−	10.3973i	0.401983	−	0.696255i	−0.591982	−	0.805951i	$-0.701654\pi$
$223$	6.00289	−	10.3973i	0.401983	−	0.696255i	0.993965	+	0.109696i	$0.0349878\pi$
$224$	8.21159	+	4.08066i	0.548660	+	0.272651i
$225$	−0.783880	−	2.89578i	−0.0522586	−	0.193052i
$226$	1.58659	+	2.74805i	0.105538	+	0.182798i
$227$	−3.19990	−	5.54239i	−0.212385	−	0.367861i	0.740076	−	0.672524i	$-0.234790\pi$
$227$	−3.19990	−	5.54239i	−0.212385	−	0.367861i	−0.952460	+	0.304662i	$0.901456\pi$
$228$	1.31269	+	3.15767i	0.0869352	+	0.209122i
$229$	10.2397	−	17.7356i	0.676656	−	1.17200i	−0.299326	−	0.954151i	$-0.596762\pi$
$229$	10.2397	−	17.7356i	0.676656	−	1.17200i	0.975982	−	0.217852i	$-0.0699049\pi$
$230$	0.0573067	+	0.0992582i	0.00377869	+	0.00654489i
$231$	−0.338812	+	5.03306i	−0.0222922	+	0.331151i
$232$	−2.30192	+	3.98704i	−0.151128	+	0.261762i
$233$	−7.56021	−	13.0947i	−0.495286	−	0.857860i	0.504700	−	0.863295i	$-0.331603\pi$
$233$	−7.56021	−	13.0947i	−0.495286	−	0.857860i	−0.999985	+	0.00543518i	$0.998270\pi$
$234$	−1.22801	−	4.53646i	−0.0802773	−	0.296557i
$235$	−4.68474	+	8.11422i	−0.305599	+	0.529313i
$236$	8.88097			0.578102
$237$	−18.0950	−	2.35868i	−1.17540	−	0.153212i
$238$	−4.31712	+	2.86562i	−0.279838	+	0.185751i
$239$	−2.25196	−	3.90050i	−0.145667	−	0.252302i	0.783955	−	0.620818i	$-0.213199\pi$
$239$	−2.25196	−	3.90050i	−0.145667	−	0.252302i	−0.929622	+	0.368516i	$0.879866\pi$
$240$	−3.62061	+	4.73100i	−0.233709	+	0.305385i
$241$	−2.49037	−	4.31344i	−0.160419	−	0.277853i	0.774600	−	0.632451i	$-0.217951\pi$
$241$	−2.49037	−	4.31344i	−0.160419	−	0.277853i	−0.935019	+	0.354598i	$0.884618\pi$
$242$	−1.50778	+	2.61154i	−0.0969235	+	0.167876i
$243$	−12.4277	−	9.41023i	−0.797237	−	0.603667i
$244$	15.8173			1.01260
$245$	6.94555	−	0.871372i	0.443735	−	0.0556699i
$246$	1.89395	+	4.55588i	0.120754	+	0.290472i
$247$	−2.63492	+	4.56381i	−0.167656	+	0.290388i
$248$	12.3114			0.781776
$249$	14.7780	−	19.3103i	0.936521	−	1.22374i
$250$	0.308078			0.0194846
$251$	18.5933			1.17360			0.586799	−	0.809733i	$-0.300388\pi$
$251$	18.5933			1.17360			0.586799	+	0.809733i	$0.300388\pi$
$252$	11.3639	+	9.97559i	0.715856	+	0.628403i
$253$	0.409523			0.0257465
$254$	−0.0990494			−0.00621491
$255$	−4.22666	−	10.1672i	−0.264684	−	0.636695i
$256$	8.93563			0.558477
$257$	10.4461	−	18.0931i	0.651607	−	1.12862i	−0.331125	−	0.943587i	$-0.607428\pi$
$257$	10.4461	−	18.0931i	0.651607	−	1.12862i	0.982733	−	0.185030i	$-0.0592384\pi$
$258$	1.73244	−	2.26376i	0.107857	−	0.140935i
$259$	−0.468592	−	7.49941i	−0.0291169	−	0.465991i
$260$	−9.68735			−0.600784
$261$	−8.09689	+	8.13849i	−0.501185	+	0.503760i
$262$	1.60017	−	2.77158i	0.0988588	−	0.171229i
$263$	−8.66011	−	14.9998i	−0.534005	−	0.924924i	−0.999211	−	0.0397217i	$-0.987353\pi$
$263$	−8.66011	−	14.9998i	−0.534005	−	0.924924i	0.465205	−	0.885203i	$-0.345980\pi$
$264$	−0.880516	−	2.11808i	−0.0541920	−	0.130359i
$265$	−2.35612	−	4.08091i	−0.144735	−	0.250688i
$266$	0.0526791	+	0.843084i	0.00322996	+	0.0516928i
$267$	4.53077	+	10.8987i	0.277279	+	0.666991i
$268$	−4.45664			−0.272233
$269$	−12.3514	+	21.3933i	−0.753080	+	1.30437i	0.193243	+	0.981151i	$0.438099\pi$
$269$	−12.3514	+	21.3933i	−0.753080	+	1.30437i	−0.946323	+	0.323222i	$0.895234\pi$
$270$	1.26626	−	0.979393i	0.0770623	−	0.0596040i
$271$	−9.83132	−	17.0283i	−0.597210	−	1.03440i	−0.993231	−	0.116157i	$-0.962943\pi$
$271$	−9.83132	−	17.0283i	−0.597210	−	1.03440i	0.396021	−	0.918241i	$-0.370391\pi$
$272$	−10.9327	+	18.9359i	−0.662891	+	1.14816i
$273$	−1.56511	+	23.2497i	−0.0947246	+	1.40714i
$274$	2.17605	+	3.76903i	0.131460	+	0.227696i
$275$	0.550395	−	0.953312i	0.0331901	−	0.0574869i
$276$	0.746055	−	0.974862i	0.0449072	−	0.0586798i
$277$	16.1553	+	27.9818i	0.970679	+	1.68127i	0.693514	+	0.720443i	$0.256062\pi$
$277$	16.1553	+	27.9818i	0.970679	+	1.68127i	0.277165	+	0.960822i	$0.410605\pi$
$278$	1.39973	+	2.42440i	0.0839502	+	0.145406i
$279$	29.6741	+	7.86971i	1.77654	+	0.471148i
$280$	−2.65197	+	1.76033i	−0.158486	+	0.105200i
$281$	1.05955	−	1.83519i	0.0632073	−	0.109478i	−0.832690	−	0.553739i	$-0.813200\pi$
$281$	1.05955	−	1.83519i	0.0632073	−	0.109478i	0.895897	+	0.444261i	$0.146534\pi$
$282$	−4.95769	−	0.646231i	−0.295226	−	0.0384825i
$283$	−5.67542			−0.337369			−0.168684	−	0.985670i	$-0.553952\pi$
$283$	−5.67542			−0.337369			−0.168684	+	0.985670i	$0.553952\pi$
$284$	4.52772			0.268671
$285$	−1.77995	−	0.232016i	−0.105435	−	0.0137434i
$286$	0.862235	−	1.49343i	0.0509850	−	0.0883087i
$287$	−1.52559	−	24.4157i	−0.0900524	−	1.44121i
$288$	−10.0500	−	2.66530i	−0.592199	−	0.157054i
$289$	−11.7061	−	20.2756i	−0.688596	−	1.19268i
$290$	−0.589466	−	1.02099i	−0.0346146	−	0.0599543i
$291$	−4.22387	+	5.51928i	−0.247607	+	0.323546i
$292$	11.3295	−	19.6233i	0.663010	−	1.14837i
$293$	−9.65153	−	16.7169i	−0.563849	−	0.976615i	−0.997156	−	0.0753682i	$-0.975987\pi$
$293$	−9.65153	−	16.7169i	−0.563849	−	0.976615i	0.433307	−	0.901246i	$-0.357347\pi$
$294$	1.85203	+	3.24377i	0.108013	+	0.189181i
$295$	−2.33086	+	4.03716i	−0.135708	+	0.235053i
$296$	1.70839	+	2.95901i	0.0992979	+	0.171989i
$297$	−0.768384	−	5.66802i	−0.0445861	−	0.328892i
$298$	0.346545	−	0.600234i	0.0200748	−	0.0347706i
$299$	1.89175			0.109403
$300$	−1.26665	−	3.04691i	−0.0731300	−	0.175914i
$301$	−11.7758	+	7.81656i	−0.678748	+	0.450539i
$302$	−0.673738	−	1.16695i	−0.0387693	−	0.0671504i
$303$	−8.29426	−	19.9518i	−0.476493	−	1.14620i
$304$	1.78228	+	3.08700i	0.102221	+	0.177052i
$305$	−4.15133	+	7.19031i	−0.237704	+	0.411716i
$306$	4.14389	−	4.16518i	0.236891	−	0.238108i
$307$	2.52185			0.143930			0.0719648	−	0.997407i	$-0.477073\pi$
$307$	2.52185			0.143930			0.0719648	+	0.997407i	$0.477073\pi$
$308$	0.346011	+	5.53761i	0.0197158	+	0.315534i
$309$	10.1594	−	13.2751i	0.577946	−	0.755196i
$310$	−1.57633	+	2.73028i	−0.0895296	+	0.155070i
$311$	−27.2383			−1.54454			−0.772271	−	0.635294i	$-0.780879\pi$
$311$	−27.2383			−1.54454			−0.772271	+	0.635294i	$0.780879\pi$
$312$	−4.06746	−	9.78424i	−0.230275	−	0.553924i
$313$	−12.5956			−0.711945			−0.355972	−	0.934497i	$-0.615850\pi$
$313$	−12.5956			−0.711945			−0.355972	+	0.934497i	$0.615850\pi$
$314$	−5.10587			−0.288141
$315$	−7.51726	+	2.54770i	−0.423550	+	0.143547i
$316$	−20.0712			−1.12909
$317$	10.9552			0.615303			0.307652	−	0.951499i	$-0.400457\pi$
$317$	10.9552			0.615303			0.307652	+	0.951499i	$0.400457\pi$
$318$	1.52816	−	1.99683i	0.0856951	−	0.111977i
$319$	−4.21242			−0.235850
$320$	−2.90567	+	5.03276i	−0.162432	+	0.281340i
$321$	−10.8789	−	26.1692i	−0.607202	−	1.46062i
$322$	0.252646	−	0.167701i	0.0140794	−	0.00934563i
$323$	−6.58815			−0.366574
$324$	−14.8924	−	8.49669i	−0.827357	−	0.472038i
$325$	2.54250	−	4.40373i	0.141032	−	0.244275i
$326$	−1.95484	−	3.38589i	−0.108269	−	0.187527i
$327$	3.48367	−	4.55208i	0.192648	−	0.251730i
$328$	5.56196	+	9.63360i	0.307108	+	0.531927i
$329$	22.1994	+	11.0317i	1.22389	+	0.608200i
$330$	0.582462	+	0.0759235i	0.0320635	+	0.00417945i
$331$	2.59638			0.142710			0.0713550	−	0.997451i	$-0.477268\pi$
$331$	2.59638			0.142710			0.0713550	+	0.997451i	$0.477268\pi$
$332$	13.3727	−	23.1623i	0.733924	−	1.27119i
$333$	2.22625	+	8.22412i	0.121998	+	0.450679i
$334$	−0.593312	−	1.02765i	−0.0324646	−	0.0562303i
$335$	1.16967	−	2.02592i	0.0639058	−	0.110688i
$336$	13.0901	+	8.77999i	0.714122	+	0.478988i
$337$	6.92188	+	11.9890i	0.377059	+	0.653085i	0.990633	−	0.136552i	$-0.0436022\pi$
$337$	6.92188	+	11.9890i	0.377059	+	0.653085i	−0.613574	+	0.789637i	$0.710269\pi$
$338$	1.98050	−	3.43033i	0.107725	−	0.186585i
$339$	6.84816	+	16.4732i	0.371941	+	0.894701i
$340$	−6.05538	−	10.4882i	−0.328399	−	0.568804i
$341$	5.63236	+	9.75553i	0.305009	+	0.528292i
$342$	−0.250275	−	0.924556i	−0.0135333	−	0.0499943i
$343$	−3.44693	−	18.1967i	−0.186117	−	0.982528i
$344$	3.21349	−	5.56593i	0.173260	−	0.300095i
$345$	0.247352	+	0.595003i	0.0133170	+	0.0320339i
$346$	−7.76859			−0.417642
$347$	0.777351			0.0417304			0.0208652	−	0.999782i	$-0.493358\pi$
$347$	0.777351			0.0417304			0.0208652	+	0.999782i	$0.493358\pi$
$348$	−7.67404	+	10.0276i	−0.411372	+	0.537535i
$349$	13.5162	−	23.4108i	0.723508	−	1.25315i	−0.236077	−	0.971734i	$-0.575862\pi$
$349$	13.5162	−	23.4108i	0.723508	−	1.25315i	0.959585	−	0.281419i	$-0.0908049\pi$
$350$	−0.0508314	−	0.813512i	−0.00271705	−	0.0434841i
$351$	−3.54947	−	26.1829i	−0.189457	−	1.39754i
$352$	−1.90755	−	3.30398i	−0.101673	−	0.176103i
$353$	8.40881	+	14.5645i	0.447556	+	0.775189i	0.998226	−	0.0595333i	$-0.0189612\pi$
$353$	8.40881	+	14.5645i	0.447556	+	0.775189i	−0.550670	+	0.834723i	$0.685628\pi$
$354$	−2.46666	−	0.321527i	−0.131101	−	0.0170890i
$355$	−1.18832	+	2.05824i	−0.0630696	+	0.109240i
$356$	6.49106	+	11.2429i	0.344026	+	0.595870i
$357$	−26.1502	+	12.8385i	−1.38401	+	0.679484i
$358$	1.59280	−	2.75881i	0.0841822	−	0.145808i
$359$	−6.04397	−	10.4685i	−0.318989	−	0.552504i	0.661289	−	0.750131i	$-0.270010\pi$
$359$	−6.04397	−	10.4685i	−0.318989	−	0.552504i	−0.980277	+	0.197627i	$0.936676\pi$
$360$	2.54556	−	2.55863i	0.134163	−	0.134852i
$361$	8.96299	−	15.5244i	0.471736	−	0.817071i
$362$	2.78140			0.146187
$363$	−10.3036	+	13.4635i	−0.540797	+	0.706653i
$364$	1.59836	+	25.5804i	0.0837770	+	1.34078i
$365$	5.94698	+	10.3005i	0.311279	+	0.539151i
$366$	−4.39319	−	0.572650i	−0.229636	−	0.0299329i
$367$	−4.58803	−	7.94670i	−0.239493	−	0.414814i	0.721076	−	0.692856i	$-0.243648\pi$
$367$	−4.58803	−	7.94670i	−0.239493	−	0.414814i	−0.960569	+	0.278042i	$0.910315\pi$
$368$	0.639800	−	1.10817i	0.0333519	−	0.0577671i
$369$	7.24795	+	26.7751i	0.377313	+	1.39386i
$370$	−0.874954			−0.0454867
$371$	−10.3873	+	6.89489i	−0.539282	+	0.357965i
$372$	33.4837	+	4.36457i	1.73605	+	0.226293i
$373$	−5.71799	+	9.90385i	−0.296066	+	0.512802i	−0.975232	−	0.221183i	$-0.929008\pi$
$373$	−5.71799	+	9.90385i	−0.296066	+	0.512802i	0.679166	+	0.733985i	$0.262342\pi$
$374$	2.15587			0.111477
$375$	1.71752	+	0.223878i	0.0886924	+	0.0115610i
$376$	−11.2722			−0.581318
$377$	−19.4589			−1.00218
$378$	−2.79511	−	3.18210i	−0.143765	−	0.163670i
$379$	6.79206			0.348885			0.174442	−	0.984667i	$-0.444188\pi$
$379$	6.79206			0.348885			0.174442	+	0.984667i	$0.444188\pi$
$380$	−1.97434			−0.101281
$381$	−0.552195	−	0.0719783i	−0.0282898	−	0.00368756i
$382$	6.71710			0.343677
$383$	4.44194	−	7.69367i	0.226973	−	0.393128i	−0.729937	−	0.683515i	$-0.760451\pi$
$383$	4.44194	−	7.69367i	0.226973	−	0.393128i	0.956909	+	0.290387i	$0.0937839\pi$
$384$	−14.9801	−	1.95265i	−0.764450	−	0.0996456i
$385$	−2.60813	−	1.29608i	−0.132923	−	0.0660544i
$386$	−0.451064			−0.0229586
$387$	11.3033	−	11.3614i	0.574579	−	0.577532i
$388$	−3.82220	+	6.62024i	−0.194043	+	0.336092i
$389$	2.32374	+	4.02483i	0.117818	+	0.204067i	0.918903	−	0.394484i	$-0.129077\pi$
$389$	2.32374	+	4.02483i	0.117818	+	0.204067i	−0.801085	+	0.598551i	$0.795743\pi$
$390$	2.69063	+	0.350721i	0.136245	+	0.0177595i
$391$	1.18250	+	2.04815i	0.0598016	+	0.103579i
$392$	5.08588	+	6.71235i	0.256876	+	0.339025i
$393$	10.9349	−	14.2886i	0.551595	−	0.720763i
$394$	−5.00114			−0.251954
$395$	5.26778	−	9.12406i	0.265051	−	0.459081i
$396$	−1.64387	−	6.07274i	−0.0826078	−	0.305167i
$397$	11.2841	+	19.5447i	0.566333	+	0.980918i	0.996924	+	0.0783708i	$0.0249718\pi$
$397$	11.2841	+	19.5447i	0.566333	+	0.980918i	−0.430591	+	0.902547i	$0.641695\pi$
$398$	0.874518	−	1.51471i	0.0438356	−	0.0759255i
$399$	−0.318978	+	4.73843i	−0.0159689	+	0.237218i
$400$	−1.71977	−	2.97872i	−0.0859884	−	0.148936i
$401$	9.10247	−	15.7659i	0.454556	−	0.787314i	−0.544107	−	0.839016i	$-0.683131\pi$
$401$	9.10247	−	15.7659i	0.454556	−	0.787314i	0.998663	+	0.0517023i	$0.0164647\pi$
$402$	1.23782	+	0.161348i	0.0617366	+	0.00804733i
$403$	26.0181	+	45.0647i	1.29606	+	2.24483i
$404$	−11.8829	−	20.5818i	−0.591195	−	1.02398i
$405$	7.77107	−	4.53988i	0.386147	−	0.225589i
$406$	−2.59876	+	1.72500i	−0.128974	+	0.0856104i
$407$	−1.56314	+	2.70744i	−0.0774821	+	0.134203i
$408$	8.05064	−	10.5197i	0.398566	−	0.520802i
$409$	−26.5633			−1.31347			−0.656735	−	0.754122i	$-0.728063\pi$
$409$	−26.5633			−1.31347			−0.656735	+	0.754122i	$0.728063\pi$
$410$	−2.84857			−0.140681
$411$	9.39246	+	22.5935i	0.463296	+	1.11445i
$412$	9.19327	−	15.9232i	0.452920	−	0.784480i
$413$	11.0451	+	5.48875i	0.543494	+	0.270084i
$414$	−0.242508	+	0.243754i	−0.0119186	+	0.0119799i
$415$	7.01949	+	12.1581i	0.344573	+	0.596818i
$416$	−8.81176	−	15.2624i	−0.432032	−	0.748302i
$417$	6.04163	+	14.5331i	0.295860	+	0.711689i
$418$	0.175729	−	0.304371i	0.00859516	−	0.0148873i
$419$	17.9849	+	31.1507i	0.878618	+	1.52181i	0.852858	+	0.522142i	$0.174867\pi$
$419$	17.9849	+	31.1507i	0.878618	+	1.52181i	0.0257595	+	0.999668i	$0.491800\pi$
$420$	−7.83669	+	3.84744i	−0.382391	+	0.187736i
$421$	2.04505	−	3.54212i	0.0996694	−	0.172632i	−0.811878	−	0.583827i	$-0.801555\pi$
$421$	2.04505	−	3.54212i	0.0996694	−	0.172632i	0.911548	+	0.411194i	$0.134888\pi$
$422$	1.68262	+	2.91439i	0.0819087	+	0.141870i
$423$	−27.1692	−	7.20541i	−1.32101	−	0.350339i
$424$	2.83458	−	4.90963i	0.137659	−	0.238433i
$425$	6.35707			0.308363
$426$	−1.25756	−	0.163922i	−0.0609289	−	0.00794204i
$427$	19.6717	+	9.77564i	0.951980	+	0.473076i
$428$	−15.5858	−	26.9954i	−0.753369	−	1.30487i
$429$	5.89218	−	7.69924i	0.284477	−	0.371723i
$430$	0.822898	+	1.42530i	0.0396837	+	0.0687342i
$431$	−13.7180	+	23.7603i	−0.660774	+	1.14449i	0.319638	+	0.947540i	$0.396439\pi$
$431$	−13.7180	+	23.7603i	−0.660774	+	1.14449i	−0.980412	+	0.196955i	$0.936895\pi$
$432$	−16.5381	−	6.77594i	−0.795688	−	0.326007i
$433$	19.9809			0.960223			0.480111	−	0.877208i	$-0.340596\pi$
$433$	19.9809			0.960223			0.480111	+	0.877208i	$0.340596\pi$
$434$	7.46968	+	3.71198i	0.358556	+	0.178181i
$435$	−2.54430	−	6.12030i	−0.121990	−	0.293446i
$436$	3.15240	−	5.46011i	0.150972	−	0.261492i
$437$	0.385550			0.0184434
$438$	−3.85717	+	5.04012i	−0.184303	+	0.240826i
$439$	31.0671			1.48275			0.741377	−	0.671089i	$-0.234173\pi$
$439$	31.0671			1.48275			0.741377	+	0.671089i	$0.234173\pi$
$440$	1.32433			0.0631350
$441$	7.96778	+	19.4297i	0.379418	+	0.925225i
$442$	9.95882			0.473693
$443$	−23.7766			−1.12966			−0.564830	−	0.825207i	$-0.691058\pi$
$443$	−23.7766			−1.12966			−0.564830	+	0.825207i	$0.691058\pi$
$444$	3.59733	+	8.65335i	0.170722	+	0.410670i
$445$	−6.81445			−0.323036
$446$	−1.84936	+	3.20318i	−0.0875697	+	0.151675i
$447$	2.36816	−	3.09444i	0.112010	−	0.146362i
$448$	13.7689	+	6.84233i	0.650521	+	0.323270i
$449$	−16.0596			−0.757897			−0.378949	−	0.925418i	$-0.623714\pi$
$449$	−16.0596			−0.757897			−0.378949	+	0.925418i	$0.623714\pi$
$450$	0.241496	+	0.892127i	0.0113842	+	0.0420553i
$451$	−5.08909	+	8.81457i	−0.239636	+	0.415062i
$452$	9.81110	+	16.9933i	0.461475	+	0.799299i
$453$	−2.90805	−	6.99528i	−0.136632	−	0.328667i
$454$	0.985820	+	1.70749i	0.0462668	+	0.0801365i
$455$	−12.0480	−	5.98712i	−0.564819	−	0.280681i
$456$	−0.828972	−	1.99409i	−0.0388202	−	0.0933816i
$457$	−18.7197			−0.875671			−0.437836	−	0.899055i	$-0.644255\pi$
$457$	−18.7197			−0.875671			−0.437836	+	0.899055i	$0.644255\pi$
$458$	−3.15462	+	5.46396i	−0.147406	+	0.255314i
$459$	26.1288	−	20.2094i	1.21959	−	0.943292i
$460$	0.354372	+	0.613790i	0.0165227	+	0.0286181i
$461$	−9.79966	+	16.9735i	−0.456416	+	0.790535i	−0.998768	−	0.0496156i	$-0.984200\pi$
$461$	−9.79966	+	16.9735i	−0.456416	+	0.790535i	0.542353	+	0.840151i	$0.317534\pi$
$462$	0.104381	−	1.55058i	0.00485622	−	0.0721394i
$463$	11.2918	+	19.5580i	0.524776	+	0.908939i	0.999584	+	0.0288493i	$0.00918430\pi$
$463$	11.2918	+	19.5580i	0.524776	+	0.908939i	−0.474808	+	0.880090i	$0.657482\pi$
$464$	−6.58108	+	11.3988i	−0.305519	+	0.529174i
$465$	−10.7720	+	14.0757i	−0.499541	+	0.652744i
$466$	2.32914	+	4.03418i	0.107895	+	0.186880i
$467$	15.1957	+	26.3197i	0.703173	+	1.21793i	0.967347	+	0.253456i	$0.0815672\pi$
$467$	15.1957	+	26.3197i	0.703173	+	1.21793i	−0.264174	+	0.964475i	$0.585099\pi$
$468$	−7.59372	−	28.0524i	−0.351020	−	1.29672i
$469$	−5.54265	−	2.75436i	−0.255936	−	0.127185i
$470$	1.44327	−	2.49981i	0.0665730	−	0.115308i
$471$	−28.4650	−	3.71039i	−1.31160	−	0.170966i
$472$	−5.60838			−0.258147
$473$	5.88057			0.270389
$474$	5.57469	+	0.726657i	0.256054	+	0.0333765i
$475$	0.518175	−	0.897506i	0.0237755	−	0.0411804i
$476$	−26.6961	+	17.7204i	−1.22362	+	0.812211i
$477$	9.97050	−	10.0217i	0.456518	−	0.458864i
$478$	0.693779	+	1.20166i	0.0317327	+	0.0549627i
$479$	3.79361	+	6.57072i	0.173334	+	0.300224i	0.939584	−	0.342320i	$-0.111213\pi$
$479$	3.79361	+	6.57072i	0.173334	+	0.300224i	−0.766249	+	0.642543i	$0.777879\pi$
$480$	3.64825	−	4.76712i	0.166519	−	0.217588i
$481$	−7.22078	+	12.5068i	−0.329239	+	0.570259i
$482$	0.767228	+	1.32888i	0.0349463	+	0.0605287i
$483$	1.53036	−	0.751331i	0.0696336	−	0.0341867i
$484$	−9.32375	+	16.1492i	−0.423807	+	0.734055i
$485$	−2.00631	−	3.47503i	−0.0911019	−	0.157793i
$486$	3.82870	+	2.89909i	0.173673	+	0.131505i
$487$	3.96052	−	6.85981i	0.179468	−	0.310848i	−0.762230	−	0.647306i	$-0.775896\pi$
$487$	3.96052	−	6.85981i	0.179468	−	0.310848i	0.941698	+	0.336458i	$0.109229\pi$
$488$	−9.98870			−0.452167
$489$	−8.43765	−	20.2967i	−0.381564	−	0.917849i
$490$	−2.13977	+	0.268451i	−0.0966652	+	0.0121274i
$491$	1.52520	+	2.64172i	0.0688313	+	0.119219i	0.898387	−	0.439204i	$-0.144740\pi$
$491$	1.52520	+	2.64172i	0.0688313	+	0.119219i	−0.829556	+	0.558424i	$0.811406\pi$
$492$	11.7118	+	28.1725i	0.528007	+	1.27012i
$493$	−12.1634	−	21.0676i	−0.547811	−	0.948836i
$494$	0.811761	−	1.40601i	0.0365229	−	0.0632594i
$495$	3.19202	+	0.846540i	0.143471	+	0.0380491i
$496$	35.1978			1.58043
$497$	5.63105	+	2.79829i	0.252587	+	0.125520i
$498$	−4.55280	+	5.94909i	−0.204016	+	0.266585i
$499$	−1.26250	+	2.18671i	−0.0565172	+	0.0978907i	−0.892900	−	0.450255i	$-0.851333\pi$
$499$	−1.26250	+	2.18671i	−0.0565172	+	0.0978907i	0.836383	+	0.548146i	$0.184666\pi$
$500$	1.90509			0.0851981
$501$	−2.56090	−	6.16023i	−0.114413	−	0.275219i
$502$	−5.72819			−0.255662
$503$	32.5749			1.45245			0.726223	−	0.687460i	$-0.241274\pi$
$503$	32.5749			1.45245			0.726223	+	0.687460i	$0.241274\pi$
$504$	−7.17634	−	6.29964i	−0.319659	−	0.280608i
$505$	12.4749			0.555125
$506$	−0.126165			−0.00560873
$507$	13.5340	−	17.6847i	0.601065	−	0.785405i
$508$	−0.612499			−0.0271753
$509$	−5.38988	+	9.33554i	−0.238902	+	0.413791i	−0.960400	−	0.278627i	$-0.910121\pi$
$509$	−5.38988	+	9.33554i	−0.238902	+	0.413791i	0.721497	+	0.692417i	$0.243454\pi$
$510$	1.30214	+	3.13230i	0.0576599	+	0.138700i
$511$	26.2182	−	17.4031i	1.15983	−	0.769869i
$512$	−20.1967			−0.892578
$513$	−0.723404	−	5.33623i	−0.0319391	−	0.235600i
$514$	−3.21821	+	5.57410i	−0.141949	+	0.245863i
$515$	4.82564	+	8.35826i	0.212643	+	0.368309i
$516$	10.7130	−	13.9986i	0.471614	−	0.616253i
$517$	−5.15692	−	8.93204i	−0.226801	−	0.392831i
$518$	0.144363	+	2.31041i	0.00634295	+	0.101513i
$519$	−43.3095	−	5.64536i	−1.90108	−	0.247804i
$520$	6.11762			0.268275
$521$	17.3610	−	30.0701i	0.760598	−	1.31739i	−0.181945	−	0.983309i	$-0.558239\pi$
$521$	17.3610	−	30.0701i	0.760598	−	1.31739i	0.942543	−	0.334085i	$-0.108427\pi$
$522$	2.49448	−	2.50729i	0.109180	−	0.109741i
$523$	−1.09943	−	1.90427i	−0.0480748	−	0.0832680i	0.840987	−	0.541056i	$-0.181975\pi$
$523$	−1.09943	−	1.90427i	−0.0480748	−	0.0832680i	−0.889061	+	0.457788i	$0.848642\pi$
$524$	9.89509	−	17.1388i	0.432269	−	0.748712i
$525$	0.307790	−	4.57223i	0.0134330	−	0.199548i
$526$	2.66799	+	4.62110i	0.116330	+	0.201490i
$527$	−32.5269	+	56.3382i	−1.41689	+	2.45413i
$528$	−2.51736	−	6.05549i	−0.109554	−	0.263531i
$529$	11.4308	+	19.7987i	0.496991	+	0.860814i
$530$	0.725868	+	1.25724i	0.0315297	+	0.0546110i
$531$	−13.5178	−	3.58499i	−0.586624	−	0.155575i
$532$	0.325756	+	5.21344i	0.0141233	+	0.226031i
$533$	−23.5086	+	40.7180i	−1.01827	+	1.76369i
$534$	−1.39583	−	3.35766i	−0.0604036	−	0.145300i
$535$	16.3623			0.707405
$536$	2.81439			0.121563
$537$	10.8846	−	14.2228i	0.469705	−	0.613758i
$538$	3.80521	−	6.59082i	0.164054	−	0.284150i
$539$	−2.99211	+	7.10088i	−0.128879	+	0.305856i
$540$	7.83028	−	6.05635i	0.336962	−	0.260624i
$541$	9.96222	+	17.2551i	0.428309	+	0.741853i	0.996723	−	0.0808895i	$-0.0257761\pi$
$541$	9.96222	+	17.2551i	0.428309	+	0.741853i	−0.568414	+	0.822743i	$0.692443\pi$
$542$	3.02882	+	5.24606i	0.130099	+	0.225338i
$543$	15.5062	+	2.02122i	0.665433	+	0.0867387i
$544$	11.0161	−	19.0805i	0.472313	−	0.818070i
$545$	1.65472	+	2.86607i	0.0708806	+	0.122769i
$546$	0.482176	−	7.16274i	0.0206352	−	0.306537i
$547$	15.6823	−	27.1625i	0.670527	−	1.16139i	−0.307228	−	0.951636i	$-0.599401\pi$
$547$	15.6823	−	27.1625i	0.670527	−	1.16139i	0.977755	−	0.209751i	$-0.0672652\pi$
$548$	13.4562	+	23.3069i	0.574821	+	0.995620i
$549$	−24.0757	−	6.38499i	−1.02753	−	0.272505i
$550$	−0.169565	+	0.293695i	−0.00723026	+	0.0125232i
$551$	−3.96583			−0.168950
$552$	−0.471138	+	0.615630i	−0.0200530	+	0.0262030i
$553$	−24.9622	−	12.4047i	−1.06150	−	0.527501i
$554$	−4.97710	−	8.62060i	−0.211457	−	0.366254i
$555$	−4.87782	−	0.635821i	−0.207052	−	0.0269891i
$556$	8.65562	+	14.9920i	0.367080	+	0.635801i
$557$	1.62778	−	2.81940i	0.0689714	−	0.119462i	−0.829477	−	0.558540i	$-0.811362\pi$
$557$	1.62778	−	2.81940i	0.0689714	−	0.119462i	0.898449	+	0.439078i	$0.144695\pi$
$558$	−9.14195	−	2.42449i	−0.387010	−	0.102637i
$559$	27.1647			1.14895
$560$	−7.58187	+	5.03269i	−0.320393	+	0.212670i
$561$	12.0189	+	1.56665i	0.507436	+	0.0661440i
$562$	−0.326424	+	0.565383i	−0.0137694	+	0.0238492i
$563$	−15.2153			−0.641249			−0.320624	−	0.947206i	$-0.603893\pi$
$563$	−15.2153			−0.641249			−0.320624	+	0.947206i	$0.603893\pi$
$564$	−30.6572	−	3.99615i	−1.29090	−	0.168268i
$565$	−10.2999			−0.433320
$566$	1.74847			0.0734939
$567$	−13.2702	−	19.7712i	−0.557296	−	0.830314i
$568$	−2.85928			−0.119973
$569$	−25.2226			−1.05738			−0.528692	−	0.848814i	$-0.677317\pi$
$569$	−25.2226			−1.05738			−0.528692	+	0.848814i	$0.677317\pi$
$570$	0.548365	+	0.0714791i	0.0229685	+	0.00299393i
$571$	−30.4970			−1.27626			−0.638130	−	0.769929i	$-0.720292\pi$
$571$	−30.4970			−1.27626			−0.638130	+	0.769929i	$0.720292\pi$
$572$	5.33187	−	9.23507i	0.222937	−	0.386138i
$573$	37.4475	+	4.88125i	1.56439	+	0.203917i
$574$	0.470000	+	7.52194i	0.0196174	+	0.313960i
$575$	−0.372027			−0.0155146
$576$	−16.8515	−	4.46909i	−0.702144	−	0.186212i
$577$	22.6240	−	39.1860i	0.941850	−	1.63133i	0.179912	−	0.983683i	$-0.442419\pi$
$577$	22.6240	−	39.1860i	0.941850	−	1.63133i	0.761938	−	0.647650i	$-0.224248\pi$
$578$	3.60641	+	6.24648i	0.150007	+	0.259819i
$579$	−2.51466	−	0.327784i	−0.104506	−	0.0136223i
$580$	−3.64513	−	6.31354i	−0.151356	−	0.262156i
$581$	30.9465	−	20.5417i	1.28388	−	0.852213i
$582$	1.30128	−	1.70037i	0.0539399	−	0.0704826i
$583$	5.18717			0.214831
$584$	−7.15465	+	12.3922i	−0.296062	+	0.512794i
$585$	14.7452	+	3.91051i	0.609641	+	0.161680i
$586$	2.97343	+	5.15013i	0.122831	+	0.212750i
$587$	9.03121	−	15.6425i	0.372758	−	0.645635i	−0.617231	−	0.786782i	$-0.711746\pi$
$587$	9.03121	−	15.6425i	0.372758	−	0.645635i	0.989989	+	0.141147i	$0.0450789\pi$
$588$	11.4526	+	20.0588i	0.472296	+	0.827210i
$589$	5.30265	+	9.18446i	0.218492	+	0.378439i
$590$	0.718086	−	1.24376i	0.0295631	−	0.0512049i
$591$	−27.8811	−	3.63428i	−1.14688	−	0.149494i
$592$	4.88420	+	8.45969i	0.200740	+	0.347691i
$593$	−12.2672	−	21.2475i	−0.503755	−	0.872530i	−0.999991	−	0.00434177i	$-0.998618\pi$
$593$	−12.2672	−	21.2475i	−0.503755	−	0.872530i	0.496235	−	0.868188i	$-0.334715\pi$
$594$	0.236722	+	1.74620i	0.00971284	+	0.0716473i
$595$	−1.04888	−	16.7865i	−0.0430000	−	0.688178i
$596$	2.14296	−	3.71171i	0.0877790	−	0.152038i
$597$	5.97612	−	7.80893i	0.244586	−	0.319598i
$598$	−0.582808			−0.0238328
$599$	14.7842			0.604065			0.302032	−	0.953298i	$-0.402335\pi$
$599$	14.7842			0.604065			0.302032	+	0.953298i	$0.402335\pi$
$600$	0.799895	+	1.92414i	0.0326556	+	0.0785528i
$601$	−20.4846	+	35.4804i	−0.835584	+	1.44727i	0.0579702	+	0.998318i	$0.481537\pi$
$601$	−20.4846	+	35.4804i	−0.835584	+	1.44727i	−0.893554	+	0.448955i	$0.851796\pi$
$602$	3.62788	−	2.40811i	0.147861	−	0.0981474i
$603$	6.78351	+	1.79902i	0.276246	+	0.0732617i
$604$	−4.16625	−	7.21615i	−0.169522	−	0.293621i
$605$	−4.89413	−	8.47688i	−0.198975	−	0.344634i
$606$	2.55528	+	6.14671i	0.103801	+	0.249693i
$607$	−16.0263	+	27.7584i	−0.650488	+	1.12668i	0.332516	+	0.943098i	$0.392102\pi$
$607$	−16.0263	+	27.7584i	−0.650488	+	1.12668i	−0.983004	+	0.183581i	$0.941231\pi$
$608$	−1.79589	−	3.11057i	−0.0728329	−	0.126150i
$609$	−15.7415	+	7.72831i	−0.637877	+	0.313167i
$610$	1.27893	−	2.21518i	0.0517825	−	0.0896900i
$611$	−23.8219	−	41.2607i	−0.963730	−	1.66923i
$612$	25.6249	−	25.7566i	1.03583	−	1.04115i
$613$	10.2678	−	17.7844i	0.414714	−	0.718306i	−0.580684	−	0.814129i	$-0.697215\pi$
$613$	10.2678	−	17.7844i	0.414714	−	0.718306i	0.995398	+	0.0958231i	$0.0305483\pi$
$614$	−0.776928			−0.0313542
$615$	−15.8806	−	2.07003i	−0.640369	−	0.0834717i
$616$	−0.218508	−	3.49703i	−0.00880393	−	0.140899i
$617$	−4.14649	−	7.18193i	−0.166931	−	0.289133i	0.770408	−	0.637551i	$-0.220052\pi$
$617$	−4.14649	−	7.18193i	−0.166931	−	0.289133i	−0.937339	+	0.348418i	$0.886719\pi$
$618$	−3.12988	+	4.08978i	−0.125902	+	0.164515i
$619$	9.71591	+	16.8284i	0.390515	+	0.676392i	0.992518	−	0.122102i	$-0.0389635\pi$
$619$	9.71591	+	16.8284i	0.390515	+	0.676392i	−0.602002	+	0.798494i	$0.705630\pi$
$620$	−9.74767	+	16.8835i	−0.391476	+	0.678056i
$621$	−1.52910	+	1.18269i	−0.0613608	+	0.0474596i
$622$	8.39153			0.336470
$623$	1.12435	+	17.9942i	0.0450461	+	0.720924i
$624$	−11.6287	−	27.9727i	−0.465520	−	1.11981i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	3.88043			0.155093
$627$	1.20086	−	1.56915i	0.0479578	−	0.0626659i
$628$	−31.5736			−1.25992
$629$	−18.0543			−0.719872
$630$	2.31591	−	0.784892i	0.0922679	−	0.0312709i
$631$	−9.92160			−0.394973			−0.197486	−	0.980306i	$-0.563278\pi$
$631$	−9.92160			−0.394973			−0.197486	+	0.980306i	$0.563278\pi$
$632$	12.6750			0.504186
$633$	7.26267	+	17.4703i	0.288665	+	0.694382i
$634$	−3.37505			−0.134040
$635$	0.160754	−	0.278433i	0.00637931	−	0.0110493i
$636$	9.44981	−	12.3480i	0.374709	−	0.489628i
$637$	−13.8218	+	32.8018i	−0.547638	+	1.29965i
$638$	1.29776			0.0513787
$639$	−6.89170	−	1.82771i	−0.272631	−	0.0723031i
$640$	4.36097	−	7.55341i	0.172382	−	0.298575i
$641$	−1.63580	−	2.83330i	−0.0646104	−	0.111908i	0.831911	−	0.554910i	$-0.187247\pi$
$641$	−1.63580	−	2.83330i	−0.0646104	−	0.111908i	−0.896521	+	0.443001i	$0.853914\pi$
$642$	3.35156	+	8.06215i	0.132276	+	0.318188i
$643$	−17.6824	−	30.6268i	−0.697326	−	1.20780i	−0.969390	−	0.245525i	$-0.921040\pi$
$643$	−17.6824	−	30.6268i	−0.697326	−	1.20780i	0.272064	−	0.962279i	$-0.412294\pi$
$644$	1.56231	−	1.03703i	0.0615635	−	0.0408646i
$645$	3.55186	+	8.54398i	0.139854	+	0.336419i
$646$	2.02967			0.0798562
$647$	2.85758	−	4.94947i	0.112343	−	0.194584i	−0.804371	−	0.594127i	$-0.797498\pi$
$647$	2.85758	−	4.94947i	0.112343	−	0.194584i	0.916715	+	0.399543i	$0.130831\pi$
$648$	9.40465	+	5.36570i	0.369449	+	0.210785i
$649$	−2.56578	−	4.44406i	−0.100716	−	0.174445i
$650$	−0.783288	+	1.35669i	−0.0307231	+	0.0532139i
$651$	38.9456	+	26.1222i	1.52640	+	1.02381i
$652$	−12.0883	−	20.9376i	−0.473415	−	0.819978i
$653$	5.17880	−	8.96994i	0.202662	−	0.351021i	−0.746723	−	0.665135i	$-0.768374\pi$
$653$	5.17880	−	8.96994i	0.202662	−	0.351021i	0.949385	+	0.314114i	$0.101707\pi$
$654$	−1.07324	+	1.40240i	−0.0419672	+	0.0548380i
$655$	5.19404	+	8.99633i	0.202948	+	0.351516i
$656$	15.9014	+	27.5421i	0.620846	+	1.07534i
$657$	−25.1662	+	25.2955i	−0.981825	+	0.986870i
$658$	−6.83915	−	3.39864i	−0.266618	−	0.132493i
$659$	19.4979	−	33.7713i	0.759529	−	1.31554i	−0.183562	−	0.983008i	$-0.558763\pi$
$659$	19.4979	−	33.7713i	0.759529	−	1.31554i	0.943091	−	0.332534i	$-0.107904\pi$
$660$	3.60181	+	0.469494i	0.140200	+	0.0182750i
$661$	27.9806			1.08832			0.544161	−	0.838981i	$-0.316848\pi$
$661$	27.9806			1.08832			0.544161	+	0.838981i	$0.316848\pi$
$662$	−0.799889			−0.0310885
$663$	55.5199	+	7.23699i	2.15622	+	0.281061i
$664$	−8.44496	+	14.6271i	−0.327728	+	0.567641i
$665$	−2.45545	−	1.22021i	−0.0952184	−	0.0473178i
$666$	−0.685859	−	2.53367i	−0.0265765	−	0.0981779i
$667$	0.711823	+	1.23291i	0.0275619	+	0.0477386i
$668$	−3.66891	−	6.35474i	−0.141954	−	0.245872i
$669$	−12.6378	+	16.5137i	−0.488606	+	0.638456i
$670$	−0.360350	+	0.624144i	−0.0139215	+	0.0241128i
$671$	−4.56974	−	7.91502i	−0.176413	−	0.305556i
$672$	−13.1900	−	8.84702i	−0.508816	−	0.341281i
$673$	−9.90276	+	17.1521i	−0.381723	+	0.661164i	−0.991309	−	0.131556i	$-0.958003\pi$
$673$	−9.90276	+	17.1521i	−0.381723	+	0.661164i	0.609586	+	0.792720i	$0.291336\pi$
$674$	−2.13248	−	3.69356i	−0.0821401	−	0.142271i
$675$	0.698030	+	5.14905i	0.0268672	+	0.198187i
$676$	12.2470	−	21.2124i	0.471038	−	0.815861i
$677$	6.14399			0.236133			0.118066	−	0.993006i	$-0.462330\pi$
$677$	6.14399			0.236133			0.118066	+	0.993006i	$0.462330\pi$
$678$	−2.10977	−	5.07503i	−0.0810252	−	0.194906i
$679$	−8.84515	+	5.87123i	−0.339446	+	0.225317i
$680$	3.82401	+	6.62337i	0.146644	+	0.253995i
$681$	4.25508	+	10.2356i	0.163055	+	0.392227i
$682$	−1.73521	−	3.00547i	−0.0664446	−	0.115085i
$683$	11.3132	−	19.5951i	0.432889	−	0.749785i	−0.564232	−	0.825616i	$-0.690828\pi$
$683$	11.3132	−	19.5951i	0.432889	−	0.749785i	0.997121	+	0.0758310i	$0.0241610\pi$
$684$	−1.54764	−	5.71725i	−0.0591757	−	0.218604i
$685$	−14.1266			−0.539750
$686$	1.06192	+	5.60600i	0.0405444	+	0.214038i
$687$	−21.5574	+	28.1689i	−0.822468	+	1.07471i
$688$	9.18723	−	15.9128i	0.350260	−	0.606668i
$689$	23.9616			0.912866
$690$	−0.0762038	−	0.183308i	−0.00290103	−	0.00697840i
$691$	0.194567			0.00740166			0.00370083	−	0.999993i	$-0.498822\pi$
$691$	0.194567			0.00740166			0.00370083	+	0.999993i	$0.498822\pi$
$692$	−48.0392			−1.82618
$693$	1.70871	−	8.56854i	0.0649084	−	0.325492i
$694$	−0.239485			−0.00909073
$695$	−9.08685			−0.344684
$696$	4.84620	−	6.33247i	0.183695	−	0.240032i
$697$	−58.7791			−2.22642
$698$	−4.16406	+	7.21237i	−0.157612	+	0.272992i
$699$	10.0532	+	24.1829i	0.380247	+	0.914682i
$700$	−0.314330	−	5.03058i	−0.0118805	−	0.190138i
$701$	36.4248			1.37575			0.687873	−	0.725831i	$-0.258545\pi$
$701$	36.4248			1.37575			0.687873	+	0.725831i	$0.258545\pi$
$702$	1.09352	+	8.06638i	0.0412721	+	0.304446i
$703$	−1.47164	+	2.54895i	−0.0555039	+	0.0961355i
$704$	−3.19853	−	5.54001i	−0.120549	−	0.208797i
$705$	9.86274	−	12.8875i	0.371452	−	0.485372i
$706$	−2.59057	−	4.48700i	−0.0974975	−	0.168871i
$707$	−2.05829	−	32.9412i	−0.0774101	−	1.23888i
$708$	−15.2533	−	1.98825i	−0.573252	−	0.0747231i
$709$	−43.7470			−1.64295			−0.821476	−	0.570243i	$-0.806849\pi$
$709$	−43.7470			−1.64295			−0.821476	+	0.570243i	$0.806849\pi$
$710$	0.366097	−	0.634098i	0.0137394	−	0.0237973i
$711$	30.5506	+	8.10215i	1.14574	+	0.303854i
$712$	−4.09914	−	7.09992i	−0.153622	−	0.266081i
$713$	1.90353	−	3.29702i	0.0712879	−	0.123474i
$714$	8.05630	−	3.95526i	0.301500	−	0.148022i
$715$	2.79875	+	4.84758i	0.104667	+	0.181289i
$716$	9.84953	−	17.0599i	0.368094	−	0.637558i
$717$	2.99455	+	7.20336i	0.111833	+	0.269014i
$718$	1.86202	+	3.22511i	0.0694898	+	0.120360i
$719$	−13.2417	−	22.9353i	−0.493833	−	0.855343i	0.506142	−	0.862450i	$-0.331071\pi$
$719$	−13.2417	−	22.9353i	−0.493833	−	0.855343i	−0.999975	+	0.00710678i	$0.997738\pi$
$720$	7.27763	−	7.31503i	0.271221	−	0.272615i
$721$	21.2746	−	14.1217i	0.792308	−	0.525918i
$722$	−2.76130	+	4.78272i	−0.102765	+	0.177994i
$723$	3.31157	+	7.96597i	0.123159	+	0.296257i
$724$	17.1995			0.639216
$725$	3.82673			0.142121
$726$	3.17430	−	4.14783i	0.117809	−	0.153940i
$727$	4.55349	−	7.88688i	0.168880	−	0.292508i	−0.769147	−	0.639072i	$-0.779318\pi$
$727$	4.55349	−	7.88688i	0.168880	−	0.292508i	0.938026	+	0.346564i	$0.112652\pi$
$728$	−1.00938	−	16.1542i	−0.0374099	−	0.598714i
$729$	19.2381	+	18.9446i	0.712521	+	0.701650i
$730$	−1.83214	−	3.17335i	−0.0678104	−	0.117451i
$731$	16.9802	+	29.4105i	0.628034	+	1.08779i
$732$	−27.1665	−	3.54114i	−1.00410	−	0.130884i
$733$	13.6256	−	23.6003i	0.503274	−	0.871697i	−0.496719	−	0.867912i	$-0.665462\pi$
$733$	13.6256	−	23.6003i	0.503274	−	0.871697i	0.999993	−	0.00378494i	$-0.00120479\pi$
$734$	1.41347	+	2.44821i	0.0521722	+	0.0903650i
$735$	−12.1242	−	0.0583557i	−0.447208	−	0.00215248i
$736$	−0.644684	+	1.11663i	−0.0237634	+	0.0411594i
$737$	1.28756	+	2.23012i	0.0474278	+	0.0821474i
$738$	−2.23294	−	8.24883i	−0.0821956	−	0.303644i
$739$	0.299946	−	0.519521i	0.0110337	−	0.0191109i	−0.860456	−	0.509525i	$-0.829821\pi$
$739$	0.299946	−	0.519521i	0.0110337	−	0.0191109i	0.871490	+	0.490414i	$0.163154\pi$
$740$	−5.41052			−0.198895
$741$	5.54726	−	7.24854i	0.203784	−	0.266282i
$742$	3.20011	−	2.12417i	0.117480	−	0.0779806i
$743$	17.4297	+	30.1891i	0.639432	+	1.10753i	0.985558	+	0.169341i	$0.0541639\pi$
$743$	17.4297	+	30.1891i	0.639432	+	1.10753i	−0.346125	+	0.938188i	$0.612503\pi$
$744$	−21.1451	−	2.75625i	−0.775218	−	0.101049i
$745$	1.12486	+	1.94832i	0.0412117	+	0.0713808i
$746$	1.76159	−	3.05116i	0.0644964	−	0.111711i
$747$	−29.7048	+	29.8574i	−1.08684	+	1.09242i
$748$	13.3314			0.487444
$749$	−2.69970	−	43.2064i	−0.0986448	−	1.57873i
$750$	−0.529131	−	0.0689719i	−0.0193211	−	0.00251850i
$751$	−4.04812	+	7.01156i	−0.147718	+	0.255855i	−0.930384	−	0.366587i	$-0.880526\pi$
$751$	−4.04812	+	7.01156i	−0.147718	+	0.255855i	0.782666	+	0.622442i	$0.213860\pi$
$752$	−32.2267			−1.17519
$753$	−31.9344	−	4.16262i	−1.16375	−	0.151694i
$754$	5.99486			0.218320
$755$	4.37381			0.159179
$756$	−17.2844	−	19.6774i	−0.628626	−	0.715660i
$757$	−10.2822			−0.373711			−0.186856	−	0.982387i	$-0.559830\pi$
$757$	−10.2822			−0.373711			−0.186856	+	0.982387i	$0.559830\pi$
$758$	−2.09249			−0.0760025
$759$	−0.703365	−	0.0916832i	−0.0255305	−	0.00332789i
$760$	1.24681			0.0452264
$761$	18.0068	−	31.1888i	0.652748	−	1.13059i	−0.329706	−	0.944084i	$-0.606949\pi$
$761$	18.0068	−	31.1888i	0.652748	−	1.13059i	0.982453	−	0.186508i	$-0.0597172\pi$
$762$	0.170119	+	0.0221750i	0.00616278	+	0.000803314i
$763$	7.29512	−	4.84236i	0.264101	−	0.175305i
$764$	41.5370			1.50276
$765$	4.98317	+	18.4087i	0.180167	+	0.665566i
$766$	−1.36847	+	2.37025i	−0.0494447	+	0.0856407i
$767$	−11.8524	−	20.5289i	−0.427965	−	0.741256i
$768$	−15.3471	−	2.00049i	−0.553792	−	0.0721864i
$769$	−13.1335	−	22.7478i	−0.473605	−	0.820308i	0.525939	−	0.850523i	$-0.323714\pi$
$769$	−13.1335	−	22.7478i	−0.473605	−	0.820308i	−0.999543	+	0.0302150i	$0.990381\pi$
$770$	0.803508	+	0.399295i	0.0289564	+	0.0143896i
$771$	−21.9920	+	28.7367i	−0.792022	+	1.03493i
$772$	−2.78928			−0.100388
$773$	−6.09814	+	10.5623i	−0.219335	+	0.379899i	−0.954605	−	0.297875i	$-0.903722\pi$
$773$	−6.09814	+	10.5623i	−0.219335	+	0.379899i	0.735270	+	0.677774i	$0.237055\pi$
$774$	−3.48231	+	3.50020i	−0.125169	+	0.125812i
$775$	−5.11665	−	8.86230i	−0.183796	−	0.318343i
$776$	2.41374	−	4.18072i	0.0866482	−	0.150079i
$777$	−0.874134	+	12.9853i	−0.0313594	+	0.465845i
$778$	−0.715894	−	1.23996i	−0.0256660	−	0.0444549i
$779$	−4.79118	+	8.29857i	−0.171662	+	0.297327i
$780$	16.6382	+	2.16878i	0.595744	+	0.0776549i
$781$	−1.30809	−	2.26568i	−0.0468073	−	0.0810726i
$782$	−0.364303	−	0.630991i	−0.0130274	−	0.0225642i
$783$	15.7286	−	12.1653i	0.562094	−	0.434753i
$784$	14.5403	+	19.1903i	0.519297	+	0.685369i
$785$	8.28665	−	14.3529i	0.295763	−	0.512277i
$786$	−3.36882	+	4.40200i	−0.120162	+	0.157014i
$787$	10.9639			0.390821			0.195410	−	0.980722i	$-0.437396\pi$
$787$	10.9639			0.390821			0.195410	+	0.980722i	$0.437396\pi$
$788$	−30.9259			−1.10169
$789$	11.5158	+	27.7012i	0.409974	+	0.986189i
$790$	−1.62289	+	2.81093i	−0.0577398	+	0.100008i
$791$	1.69943	+	27.1979i	0.0604248	+	0.967046i
$792$	1.03812	+	3.83497i	0.0368878	+	0.136270i
$793$	−21.1095	−	36.5627i	−0.749619	−	1.29838i
$794$	−3.47639	−	6.02128i	−0.123372	−	0.213687i
$795$	3.13305	+	7.53653i	0.111118	+	0.267293i
$796$	5.40782	−	9.36663i	0.191675	−	0.331991i
$797$	−14.1648	−	24.5342i	−0.501744	−	0.869046i	−0.999998	−	0.00201494i	$-0.999359\pi$
$797$	−14.1648	−	24.5342i	−0.501744	−	0.869046i	0.498254	−	0.867031i	$-0.333975\pi$
$798$	0.0982703	−	1.45981i	0.00347873	−	0.0516767i
$799$	29.7812	−	51.5826i	1.05358	−	1.82486i
$800$	1.73290	+	3.00146i	0.0612671	+	0.106118i
$801$	−5.34171	−	19.7331i	−0.188740	−	0.697236i
$802$	−2.80428	+	4.85715i	−0.0990224	+	0.171512i
$803$	−13.0927			−0.462033
$804$	7.65438	+	0.997743i	0.269949	+	0.0351877i
$805$	0.0613825	+	0.982375i	0.00216345	+	0.0346242i
$806$	−8.01563	−	13.8835i	−0.282338	−	0.489024i
$807$	26.0033	−	33.9783i	0.915361	−	1.19609i
$808$	7.50410	+	12.9975i	0.263993	+	0.457250i
$809$	10.0749	−	17.4502i	0.354215	−	0.613518i	−0.632769	−	0.774341i	$-0.718082\pi$
$809$	10.0749	−	17.4502i	0.354215	−	0.613518i	0.986983	+	0.160823i	$0.0514149\pi$
$810$	−2.39410	+	1.39864i	−0.0841200	+	0.0491432i
$811$	−37.4364			−1.31457			−0.657285	−	0.753642i	$-0.728295\pi$
$811$	−37.4364			−1.31457			−0.657285	+	0.753642i	$0.728295\pi$
$812$	−16.0701	+	10.6670i	−0.563951	+	0.374339i
$813$	13.0732	+	31.4475i	0.458498	+	1.10291i
$814$	0.481570	−	0.834104i	0.0168790	−	0.0292353i
$815$	12.6906			0.444531
$816$	23.0164	−	30.0753i	0.805736	−	1.05285i
$817$	5.53633			0.193692
$818$	8.18357			0.286132
$819$	7.89320	−	39.5815i	0.275811	−	1.38309i
$820$	−17.6149			−0.615140
$821$	10.6897			0.373072			0.186536	−	0.982448i	$-0.440274\pi$
$821$	10.6897			0.373072			0.186536	+	0.982448i	$0.440274\pi$
$822$	−2.89361	−	6.96057i	−0.100926	−	0.242778i
$823$	−11.7647			−0.410092			−0.205046	−	0.978752i	$-0.565734\pi$
$823$	−11.7647			−0.410092			−0.205046	+	0.978752i	$0.565734\pi$
$824$	−5.80560	+	10.0556i	−0.202248	+	0.350303i
$825$	−1.15874	+	1.51411i	−0.0403421	+	0.0527146i
$826$	−3.40276	−	1.69097i	−0.118397	−	0.0588362i
$827$	6.23898			0.216951			0.108475	−	0.994099i	$-0.465403\pi$
$827$	6.23898			0.216951			0.108475	+	0.994099i	$0.465403\pi$
$828$	−1.49962	+	1.50732i	−0.0521152	+	0.0523830i
$829$	−4.29825	+	7.44479i	−0.149284	+	0.258568i	−0.930963	−	0.365113i	$-0.881030\pi$
$829$	−4.29825	+	7.44479i	−0.149284	+	0.258568i	0.781679	+	0.623681i	$0.214364\pi$
$830$	−2.16255	−	3.74565i	−0.0750633	−	0.130013i
$831$	−21.4826	−	51.6762i	−0.745223	−	1.79263i
$832$	−14.7753	−	25.5915i	−0.512241	−	0.887227i
$833$	−44.1533	+	5.53937i	−1.52982	+	0.191928i
$834$	−1.86130	−	4.47733i	−0.0644514	−	0.155037i
$835$	3.85170			0.133293
$836$	1.08667	−	1.88216i	0.0375831	−	0.0650959i
$837$	−49.2041	−	20.1598i	−1.70074	−	0.696824i
$838$	−5.54075	−	9.59685i	−0.191402	−	0.331518i
$839$	−5.10011	+	8.83366i	−0.176076	+	0.304972i	−0.940533	−	0.339702i	$-0.889674\pi$
$839$	−5.10011	+	8.83366i	−0.176076	+	0.304972i	0.764457	+	0.644674i	$0.223007\pi$
$840$	4.94891	−	2.42968i	0.170754	−	0.0838319i
$841$	7.17808	+	12.4328i	0.247520	+	0.428717i
$842$	−0.630034	+	1.09125i	−0.0217124	+	0.0376070i
$843$	−2.23065	+	2.91477i	−0.0768278	+	0.100390i
$844$	10.4050	+	18.0219i	0.358153	+	0.620340i
$845$	6.42856	+	11.1346i	0.221149	+	0.383042i
$846$	8.37026	+	2.21983i	0.287775	+	0.0763194i
$847$	−21.5766	+	14.3221i	−0.741380	+	0.492113i
$848$	8.10394	−	14.0364i	0.278290	−	0.482013i
$849$	9.74765	+	1.27060i	0.334539	+	0.0436069i
$850$	−1.95847			−0.0671751
$851$	1.05657			0.0362188
$852$	−7.77645	−	1.01366i	−0.266417	−	0.0347273i
$853$	−3.92667	+	6.80119i	−0.134447	+	0.232868i	−0.925386	−	0.379026i	$-0.876259\pi$
$853$	−3.92667	+	6.80119i	−0.134447	+	0.232868i	0.790939	+	0.611895i	$0.209592\pi$
$854$	−6.06042	−	3.01166i	−0.207383	−	0.103057i
$855$	3.00517	+	0.796984i	0.102775	+	0.0272563i
$856$	9.84253	+	17.0478i	0.336411	+	0.582681i
$857$	−4.00345	−	6.93418i	−0.136755	−	0.236867i	0.789511	−	0.613736i	$-0.210334\pi$
$857$	−4.00345	−	6.93418i	−0.136755	−	0.236867i	−0.926267	+	0.376869i	$0.877001\pi$
$858$	−1.81525	+	2.37197i	−0.0619717	+	0.0809777i
$859$	−11.1653	+	19.3389i	−0.380956	+	0.659835i	−0.991199	−	0.132379i	$-0.957738\pi$
$859$	−11.1653	+	19.3389i	−0.380956	+	0.659835i	0.610243	+	0.792214i	$0.291072\pi$
$860$	5.08862	+	8.81375i	0.173520	+	0.300546i
$861$	−2.84590	+	42.2760i	−0.0969881	+	1.44076i
$862$	4.22623	−	7.32004i	0.143946	−	0.249322i
$863$	28.1563	+	48.7682i	0.958452	+	1.66009i	0.726263	+	0.687416i	$0.241255\pi$
$863$	28.1563	+	48.7682i	0.958452	+	1.66009i	0.232188	+	0.972671i	$0.425411\pi$
$864$	16.6643	+	6.82766i	0.566931	+	0.232282i
$865$	12.6081	−	21.8379i	0.428690	−	0.742512i
$866$	−6.15570			−0.209179
$867$	15.5663	+	37.4446i	0.528659	+	1.27168i
$868$	46.1908	+	22.9540i	1.56782	+	0.779111i
$869$	5.79871	+	10.0437i	0.196708	+	0.340708i
$870$	0.783844	+	1.88553i	0.0265748	+	0.0639255i
$871$	5.94775	+	10.3018i	0.201532	+	0.349063i
$872$	−1.99075	+	3.44809i	−0.0674155	+	0.116767i
$873$	8.49022	−	8.53384i	0.287350	−	0.288827i
$874$	−0.118780			−0.00401778
$875$	2.36933	+	1.17741i	0.0800978	+	0.0398038i
$876$	−23.8519	+	31.1670i	−0.805881	+	1.05304i
$877$	−22.2746	+	38.5808i	−0.752161	+	1.30278i	0.194613	+	0.980880i	$0.437655\pi$
$877$	−22.2746	+	38.5808i	−0.752161	+	1.30278i	−0.946774	+	0.321900i	$0.895678\pi$
$878$	−9.57112			−0.323010
$879$	12.8342	+	30.8725i	0.432886	+	1.04130i
$880$	3.78620			0.127633
$881$	51.4571			1.73363			0.866817	−	0.498626i	$-0.166162\pi$
$881$	51.4571			1.73363			0.866817	+	0.498626i	$0.166162\pi$
$882$	−2.45470	−	5.98588i	−0.0826540	−	0.201555i
$883$	−57.6295			−1.93939			−0.969693	−	0.244327i	$-0.921433\pi$
$883$	−57.6295			−1.93939			−0.969693	+	0.244327i	$0.921433\pi$
$884$	61.5831			2.07126
$885$	4.90712	−	6.41208i	0.164951	−	0.215540i
$886$	7.32505			0.246090
$887$	9.80957	−	16.9907i	0.329373	−	0.570491i	−0.653014	−	0.757345i	$-0.726496\pi$
$887$	9.80957	−	16.9907i	0.329373	−	0.570491i	0.982388	+	0.186854i	$0.0598293\pi$
$888$	−2.27173	−	5.46464i	−0.0762344	−	0.183381i
$889$	−0.761755	−	0.378546i	−0.0255484	−	0.0126960i
$890$	2.09938			0.0703715
$891$	0.0507709	+	9.90698i	0.00170089	+	0.331896i
$892$	−11.4360	+	19.8078i	−0.382906	+	0.663213i
$893$	−4.85504	−	8.40917i	−0.162468	−	0.281402i
$894$	−0.729578	+	0.953331i	−0.0244007	+	0.0318842i
$895$	5.17012	+	8.95491i	0.172818	+	0.299330i
$896$	−20.6651	−	10.2693i	−0.690372	−	0.343073i
$897$	−3.24913	−	0.423521i	−0.108485	−	0.0141410i
$898$	4.94760			0.165104
$899$	−19.5800	+	33.9136i	−0.653031	+	1.13108i
$900$	1.49336	+	5.51671i	0.0497787	+	0.183890i
$901$	14.9780	+	25.9426i	0.498989	+	0.864274i
$902$	1.56784	−	2.71558i	0.0522033	−	0.0904188i
$903$	21.9752	−	10.7888i	0.731289	−	0.359028i
$904$	−6.19576	−	10.7314i	−0.206068	−	0.356920i
$905$	−4.51411	+	7.81867i	−0.150054	+	0.259901i
$906$	0.895906	+	2.15509i	0.0297645	+	0.0715982i
$907$	10.2376	+	17.7321i	0.339934	+	0.588783i	0.984420	−	0.175833i	$-0.0562618\pi$
$907$	10.2376	+	17.7321i	0.339934	+	0.588783i	−0.644486	+	0.764616i	$0.722929\pi$
$908$	6.09609	+	10.5587i	0.202306	+	0.350404i
$909$	9.77881	+	36.1245i	0.324343	+	1.19817i
$910$	3.71173	+	1.84450i	0.123043	+	0.0611447i
$911$	−16.1511	+	27.9746i	−0.535111	+	0.926839i	0.464047	+	0.885811i	$0.346397\pi$
$911$	−16.1511	+	27.9746i	−0.535111	+	0.926839i	−0.999158	+	0.0410287i	$0.986937\pi$
$912$	−2.37000	−	5.70101i	−0.0784784	−	0.188779i
$913$	−15.4540			−0.511451
$914$	5.76714			0.190760
$915$	8.73974	−	11.4201i	0.288927	−	0.377538i
$916$	−19.5075	+	33.7879i	−0.644544	+	1.11638i
$917$	22.8987	−	15.1997i	0.756183	−	0.501939i
$918$	−8.04971	+	6.22607i	−0.265680	+	0.205491i
$919$	1.57549	+	2.72883i	0.0519706	+	0.0900158i	0.890840	−	0.454316i	$-0.150116\pi$
$919$	1.57549	+	2.72883i	0.0519706	+	0.0900158i	−0.838870	+	0.544332i	$0.816783\pi$
$920$	−0.223788	−	0.387612i	−0.00737806	−	0.0127792i
$921$	−4.33133	−	0.564586i	−0.142722	−	0.0186037i
$922$	3.01906	−	5.22917i	0.0994276	−	0.172214i
$923$	−6.04261	−	10.4661i	−0.198895	−	0.344496i
$924$	0.645466	−	9.58842i	0.0212343	−	0.315436i
$925$	1.42002	−	2.45954i	0.0466899	−	0.0808693i
$926$	−3.47877	−	6.02541i	−0.114319	−	0.198007i
$927$	−20.4209	+	20.5259i	−0.670711	+	0.674157i
$928$	6.63132	−	11.4858i	0.217684	−	0.377039i
$929$	13.0972			0.429706			0.214853	−	0.976646i	$-0.431073\pi$
$929$	13.0972			0.429706			0.214853	+	0.976646i	$0.431073\pi$
$930$	3.31863	−	4.33642i	0.108822	−	0.142197i
$931$	−2.81695	+	6.68520i	−0.0923219	+	0.219099i
$932$	14.4029	+	24.9465i	0.471781	+	0.817149i
$933$	46.7823	+	6.09805i	1.53158	+	0.199641i
$934$	−4.68146	−	8.10853i	−0.153182	−	0.265319i
$935$	−3.49890	+	6.06026i	−0.114426	+	0.198192i
$936$	4.79547	+	17.7153i	0.156745	+	0.579041i
$937$	−20.3207			−0.663849			−0.331924	−	0.943306i	$-0.607698\pi$
$937$	−20.3207			−0.663849			−0.331924	+	0.943306i	$0.607698\pi$
$938$	1.70757	+	0.848559i	0.0557542	+	0.0277064i
$939$	21.6332	+	2.81987i	0.705972	+	0.0920230i
$940$	8.92485	−	15.4583i	0.291096	−	0.504194i
$941$	43.3099			1.41186			0.705931	−	0.708280i	$-0.250529\pi$
$941$	43.3099			1.41186			0.705931	+	0.708280i	$0.250529\pi$
$942$	8.76945	+	1.14309i	0.285724	+	0.0372439i
$943$	3.43986			0.112017
$944$	−16.0341			−0.521866
$945$	13.4814	−	2.69279i	0.438551	−	0.0875963i
$946$	−1.81168			−0.0589027
$947$	41.8946			1.36139			0.680695	−	0.732567i	$-0.261678\pi$
$947$	41.8946			1.36139			0.680695	+	0.732567i	$0.261678\pi$
$948$	34.4726	+	4.49348i	1.11962	+	0.145942i
$949$	−60.4807			−1.96329
$950$	−0.159639	+	0.276502i	−0.00517936	+	0.00897092i
$951$	−18.8157	−	2.45262i	−0.610142	−	0.0795316i
$952$	16.8588	−	11.1905i	0.546395	−	0.362686i
$953$	12.2216			0.395898			0.197949	−	0.980212i	$-0.436572\pi$
$953$	12.2216			0.395898			0.197949	+	0.980212i	$0.436572\pi$
$954$	−3.07170	+	3.08748i	−0.0994498	+	0.0999608i
$955$	−10.9016	+	18.8821i	−0.352768	+	0.611012i
$956$	4.29017	+	7.43080i	0.138754	+	0.240329i
$957$	7.23492	+	0.943067i	0.233872	+	0.0304850i
$958$	−1.16873	−	2.02430i	−0.0377599	−	0.0654021i
$959$	2.33082	+	37.3028i	0.0752661	+	1.20457i
$960$	6.11727	−	7.99336i	0.197434	−	0.257985i
$961$	73.7206			2.37808
$962$	2.22457	−	3.85306i	0.0717229	−	0.124228i
$963$	12.8261	+	47.3816i	0.413315	+	1.52685i
$964$	4.74437	+	8.21749i	0.152806	+	0.264667i
$965$	0.732061	−	1.26797i	0.0235659	−	0.0408173i
$966$	−0.471469	+	0.231469i	−0.0151693	+	0.00744739i
$967$	13.2130	+	22.8856i	0.424902	+	0.735951i	0.996411	−	0.0846440i	$-0.0269753\pi$
$967$	13.2130	+	22.8856i	0.424902	+	0.735951i	−0.571509	+	0.820595i	$0.693642\pi$
$968$	5.88800	−	10.1983i	0.189247	−	0.327786i
$969$	11.3153	+	1.47494i	0.363499	+	0.0473819i
$970$	0.618101	+	1.07058i	0.0198460	+	0.0343743i
$971$	−5.81824	−	10.0775i	−0.186716	−	0.323402i	0.757437	−	0.652908i	$-0.226451\pi$
$971$	−5.81824	−	10.0775i	−0.186716	−	0.323402i	−0.944153	+	0.329506i	$0.893118\pi$
$972$	23.6758	+	17.9273i	0.759403	+	0.575019i
$973$	1.49928	+	23.9947i	0.0480648	+	0.769236i
$974$	−1.22015	+	2.11336i	−0.0390961	+	0.0677164i
$975$	−5.35269	+	6.99429i	−0.171423	+	0.223997i
$976$	−28.5573			−0.914096
$977$	38.7452			1.23957			0.619784	−	0.784772i	$-0.287220\pi$
$977$	38.7452			1.23957			0.619784	+	0.784772i	$0.287220\pi$
$978$	2.59946	+	6.25298i	0.0831215	+	0.199948i
$979$	3.75064	−	6.49630i	0.119871	−	0.207623i
$980$	−13.2319	+	1.66004i	−0.422677	+	0.0530280i
$981$	−7.00239	+	7.03837i	−0.223569	+	0.224718i
$982$	−0.469881	−	0.813858i	−0.0149945	−	0.0259713i
$983$	−18.8099	−	32.5796i	−0.599942	−	1.03913i	−0.992829	−	0.119543i	$-0.961857\pi$
$983$	−18.8099	−	32.5796i	−0.599942	−	1.03913i	0.392888	−	0.919587i	$-0.371476\pi$
$984$	−7.39604	−	17.7911i	−0.235777	−	0.567160i
$985$	8.11667	−	14.0585i	0.258619	−	0.447941i
$986$	3.74727	+	6.49047i	0.119338	+	0.206699i
$987$	−35.6581	−	23.9172i	−1.13501	−	0.761293i
$988$	5.01975	−	8.69446i	0.159699	−	0.276608i
$989$	−0.993709	−	1.72116i	−0.0315981	−	0.0547295i
$990$	−0.983393	−	0.260801i	−0.0312543	−	0.00828879i
$991$	3.39416	−	5.87886i	0.107819	−	0.186748i	−0.807067	−	0.590459i	$-0.798947\pi$
$991$	3.39416	−	5.87886i	0.107819	−	0.186748i	0.914886	+	0.403711i	$0.132280\pi$
$992$	−35.4665			−1.12606
$993$	−4.45934	−	0.581272i	−0.141513	−	0.0184461i
$994$	−1.73480	−	0.862093i	−0.0550247	−	0.0273439i
$995$	2.83862	+	4.91664i	0.0899904	+	0.155868i
$996$	−28.1535	+	36.7878i	−0.892077	+	1.16567i
$997$	−1.78648	−	3.09427i	−0.0565783	−	0.0979964i	0.836349	−	0.548197i	$-0.184686\pi$
$997$	−1.78648	−	3.09427i	−0.0565783	−	0.0979964i	−0.892927	+	0.450201i	$0.851352\pi$
$998$	0.388949	−	0.673679i	0.0123120	−	0.0213249i
$999$	−1.98243	−	14.6235i	−0.0627213	−	0.462667i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.l.b.151.6	yes	24
3.2	odd	2		945.2.l.b.46.7		24
7.2	even	3		315.2.k.b.16.7	✓	24
9.4	even	3		315.2.k.b.256.7	yes	24
9.5	odd	6		945.2.k.b.361.6		24
21.2	odd	6		945.2.k.b.856.6		24
63.23	odd	6		945.2.l.b.226.7		24
63.58	even	3	inner	315.2.l.b.121.6	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.k.b.16.7	✓	24	7.2	even	3
315.2.k.b.256.7	yes	24	9.4	even	3
315.2.l.b.121.6	yes	24	63.58	even	3	inner
315.2.l.b.151.6	yes	24	1.1	even	1	trivial
945.2.k.b.361.6		24	9.5	odd	6
945.2.k.b.856.6		24	21.2	odd	6
945.2.l.b.46.7		24	3.2	odd	2
945.2.l.b.226.7		24	63.23	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.l (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-0.308078 q^{2} +(-1.71752 - 0.223878i) q^{3} -1.90509 q^{4} +(0.500000 - 0.866025i) q^{5} +(0.529131 + 0.0689719i) q^{6} +(-2.36933 - 1.17741i) q^{7} +1.20307 q^{8} +(2.89976 + 0.769029i) q^{9} +O(q^{10})\)	\(q-0.308078 q^{2} +(-1.71752 - 0.223878i) q^{3} -1.90509 q^{4} +(0.500000 - 0.866025i) q^{5} +(0.529131 + 0.0689719i) q^{6} +(-2.36933 - 1.17741i) q^{7} +1.20307 q^{8} +(2.89976 + 0.769029i) q^{9} +(-0.154039 + 0.266804i) q^{10} +(0.550395 + 0.953312i) q^{11} +(3.27203 + 0.426507i) q^{12} +(2.54250 + 4.40373i) q^{13} +(0.729938 + 0.362735i) q^{14} +(-1.05264 + 1.37548i) q^{15} +3.43953 q^{16} +(-3.17853 + 5.50538i) q^{17} +(-0.893353 - 0.236921i) q^{18} +(0.518175 + 0.897506i) q^{19} +(-0.952544 + 1.64985i) q^{20} +(3.80577 + 2.55267i) q^{21} +(-0.169565 - 0.293695i) q^{22} +(0.186013 - 0.322185i) q^{23} +(-2.06630 - 0.269341i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-0.783288 - 1.35669i) q^{26} +(-4.80823 - 1.97002i) q^{27} +(4.51377 + 2.24307i) q^{28} +(-1.91336 + 3.31404i) q^{29} +(0.324297 - 0.423755i) q^{30} +10.2333 q^{31} -3.46579 q^{32} +(-0.731889 - 1.76055i) q^{33} +(0.979237 - 1.69609i) q^{34} +(-2.20433 + 1.46319i) q^{35} +(-5.52429 - 1.46507i) q^{36} +(1.42002 + 2.45954i) q^{37} +(-0.159639 - 0.276502i) q^{38} +(-3.38089 - 8.13271i) q^{39} +(0.601537 - 1.04189i) q^{40} +(4.62313 + 8.00749i) q^{41} +(-1.17248 - 0.786422i) q^{42} +(2.67107 - 4.62643i) q^{43} +(-1.04855 - 1.81614i) q^{44} +(2.11588 - 2.12675i) q^{45} +(-0.0573067 + 0.0992582i) q^{46} -9.36949 q^{47} +(-5.90747 - 0.770035i) q^{48} +(4.22741 + 5.57934i) q^{49} +(0.154039 + 0.266804i) q^{50} +(6.69173 - 8.74400i) q^{51} +(-4.84368 - 8.38949i) q^{52} +(2.35612 - 4.08091i) q^{53} +(1.48131 + 0.606919i) q^{54} +1.10079 q^{55} +(-2.85047 - 1.41651i) q^{56} +(-0.689046 - 1.65749i) q^{57} +(0.589466 - 1.02099i) q^{58} -4.66171 q^{59} +(2.00538 - 2.62041i) q^{60} -8.30266 q^{61} -3.15266 q^{62} +(-5.96501 - 5.23629i) q^{63} -5.81133 q^{64} +5.08499 q^{65} +(0.225479 + 0.542389i) q^{66} +2.33934 q^{67} +(6.05538 - 10.4882i) q^{68} +(-0.391612 + 0.511715i) q^{69} +(0.679107 - 0.450777i) q^{70} -2.37665 q^{71} +(3.48862 + 0.925199i) q^{72} +(-5.94698 + 10.3005i) q^{73} +(-0.437477 - 0.757733i) q^{74} +(0.664877 + 1.59936i) q^{75} +(-0.987170 - 1.70983i) q^{76} +(-0.181625 - 2.90675i) q^{77} +(1.04158 + 2.50551i) q^{78} +10.5356 q^{79} +(1.71977 - 2.97872i) q^{80} +(7.81719 + 4.46000i) q^{81} +(-1.42429 - 2.46694i) q^{82} +(-7.01949 + 12.1581i) q^{83} +(-7.25033 - 4.86306i) q^{84} +(3.17853 + 5.50538i) q^{85} +(-0.822898 + 1.42530i) q^{86} +(4.02818 - 5.26358i) q^{87} +(0.662165 + 1.14690i) q^{88} +(-3.40723 - 5.90149i) q^{89} +(-0.651856 + 0.655205i) q^{90} +(-0.838997 - 13.4274i) q^{91} +(-0.354372 + 0.613790i) q^{92} +(-17.5759 - 2.29101i) q^{93} +2.88654 q^{94} +1.03635 q^{95} +(5.95257 + 0.775914i) q^{96} +(2.00631 - 3.47503i) q^{97} +(-1.30237 - 1.71887i) q^{98} +(0.862887 + 3.18764i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 2 q^{2} - 5 q^{3} + 14 q^{4} + 12 q^{5} + 3 q^{6} - 11 q^{7} + 12 q^{8} - 3 q^{9}+O(q^{10}) \) 24 * q + 2 * q^2 - 5 * q^3 + 14 * q^4 + 12 * q^5 + 3 * q^6 - 11 * q^7 + 12 * q^8 - 3 * q^9	\( 24 q + 2 q^{2} - 5 q^{3} + 14 q^{4} + 12 q^{5} + 3 q^{6} - 11 q^{7} + 12 q^{8} - 3 q^{9} + q^{10} + q^{11} - 7 q^{12} - 4 q^{13} + 8 q^{14} - q^{15} + 10 q^{16} - 7 q^{17} + 18 q^{18} - 2 q^{19} + 7 q^{20} - 17 q^{21} + 19 q^{22} + q^{23} + 18 q^{24} - 12 q^{25} + 11 q^{26} - 11 q^{27} - 28 q^{28} - 16 q^{31} - 34 q^{32} + 7 q^{33} + q^{34} - 7 q^{35} - 25 q^{36} + 17 q^{37} - 35 q^{38} - 17 q^{39} + 6 q^{40} + 20 q^{41} - 36 q^{42} + 31 q^{43} - 7 q^{44} + 6 q^{45} - 10 q^{46} + 62 q^{47} - 36 q^{48} - 11 q^{49} - q^{50} + 14 q^{51} - 4 q^{52} + 8 q^{53} - 51 q^{54} + 2 q^{55} + 5 q^{57} + 45 q^{58} + 42 q^{59} - 23 q^{60} - 10 q^{61} + 14 q^{62} + 18 q^{63} - 56 q^{64} - 8 q^{65} + 4 q^{66} - 86 q^{67} - 48 q^{68} + 26 q^{69} - 5 q^{70} + 24 q^{71} - 6 q^{72} - 18 q^{73} + 9 q^{74} + 4 q^{75} - 13 q^{76} + 35 q^{77} + 19 q^{78} - 80 q^{79} + 5 q^{80} + 21 q^{81} + 5 q^{82} - 60 q^{83} + 35 q^{84} + 7 q^{85} + 12 q^{86} + 68 q^{87} + 50 q^{88} - 4 q^{89} + 12 q^{90} - 33 q^{91} - 18 q^{92} + 7 q^{93} + 22 q^{94} - 4 q^{95} + 6 q^{97} - 15 q^{98} - q^{99}+O(q^{100}) \) 24 * q + 2 * q^2 - 5 * q^3 + 14 * q^4 + 12 * q^5 + 3 * q^6 - 11 * q^7 + 12 * q^8 - 3 * q^9 + q^10 + q^11 - 7 * q^12 - 4 * q^13 + 8 * q^14 - q^15 + 10 * q^16 - 7 * q^17 + 18 * q^18 - 2 * q^19 + 7 * q^20 - 17 * q^21 + 19 * q^22 + q^23 + 18 * q^24 - 12 * q^25 + 11 * q^26 - 11 * q^27 - 28 * q^28 - 16 * q^31 - 34 * q^32 + 7 * q^33 + q^34 - 7 * q^35 - 25 * q^36 + 17 * q^37 - 35 * q^38 - 17 * q^39 + 6 * q^40 + 20 * q^41 - 36 * q^42 + 31 * q^43 - 7 * q^44 + 6 * q^45 - 10 * q^46 + 62 * q^47 - 36 * q^48 - 11 * q^49 - q^50 + 14 * q^51 - 4 * q^52 + 8 * q^53 - 51 * q^54 + 2 * q^55 + 5 * q^57 + 45 * q^58 + 42 * q^59 - 23 * q^60 - 10 * q^61 + 14 * q^62 + 18 * q^63 - 56 * q^64 - 8 * q^65 + 4 * q^66 - 86 * q^67 - 48 * q^68 + 26 * q^69 - 5 * q^70 + 24 * q^71 - 6 * q^72 - 18 * q^73 + 9 * q^74 + 4 * q^75 - 13 * q^76 + 35 * q^77 + 19 * q^78 - 80 * q^79 + 5 * q^80 + 21 * q^81 + 5 * q^82 - 60 * q^83 + 35 * q^84 + 7 * q^85 + 12 * q^86 + 68 * q^87 + 50 * q^88 - 4 * q^89 + 12 * q^90 - 33 * q^91 - 18 * q^92 + 7 * q^93 + 22 * q^94 - 4 * q^95 + 6 * q^97 - 15 * q^98 - q^99

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