LMFDB - Embedded newform 385.2.n.c.36.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [385,2,Mod(36,385)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(385, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 8]))

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

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

chi := DirichletCharacter("385.36");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 385 = 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	385.n (of order $5$, degree $4$, 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:	$3.07424047782$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.13140625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 5x^{6} - 3x^{5} + 4x^{4} + 3x^{3} + 5x^{2} + 3x + 1 $ x^8 - 3x^7 + 5x^6 - 3x^5 + 4x^4 + 3x^3 + 5x^2 + 3*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			36.2
Root			$1.69513 - 1.23158i$ of defining polynomial
Character	$\chi$	$=$	385.36
Dual form			385.2.n.c.246.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.93376 - 1.40496i) q^{2} +(-0.456498 - 1.40496i) q^{3} +(1.14748 - 3.53158i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(-2.85666 - 2.07549i) q^{6} +(0.309017 - 0.951057i) q^{7} +(-1.26552 - 3.89486i) q^{8} +(0.661536 - 0.480634i) q^{9} +O(q^{10})$	\(q+(1.93376 - 1.40496i) q^{2} +(-0.456498 - 1.40496i) q^{3} +(1.14748 - 3.53158i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(-2.85666 - 2.07549i) q^{6} +(0.309017 - 0.951057i) q^{7} +(-1.26552 - 3.89486i) q^{8} +(0.661536 - 0.480634i) q^{9} -2.39026 q^{10} +(1.20381 + 3.09044i) q^{11} -5.48555 q^{12} +(-3.12889 + 2.27327i) q^{13} +(-0.738630 - 2.27327i) q^{14} +(-0.456498 + 1.40496i) q^{15} +(-1.91102 - 1.38844i) q^{16} +(1.23192 + 0.895044i) q^{17} +(0.603980 - 1.85886i) q^{18} +(-0.261370 - 0.804414i) q^{19} +(-3.00415 + 2.18264i) q^{20} -1.47726 q^{21} +(6.66983 + 4.28486i) q^{22} -0.986585 q^{23} +(-4.89440 + 3.55599i) q^{24} +(0.309017 + 0.951057i) q^{25} +(-2.85666 + 8.79191i) q^{26} +(-4.56265 - 3.31496i) q^{27} +(-3.00415 - 2.18264i) q^{28} +(2.01820 - 6.21138i) q^{29} +(1.09115 + 3.35821i) q^{30} +(6.88769 - 5.00420i) q^{31} +2.54445 q^{32} +(3.79240 - 3.10209i) q^{33} +3.63974 q^{34} +(-0.809017 + 0.587785i) q^{35} +(-0.938299 - 2.88779i) q^{36} +(-2.92705 + 9.00854i) q^{37} +(-1.63559 - 1.18833i) q^{38} +(4.62218 + 3.35821i) q^{39} +(-1.26552 + 3.89486i) q^{40} +(-1.02613 - 3.15810i) q^{41} +(-2.85666 + 2.07549i) q^{42} +3.28155 q^{43} +(12.2955 - 0.705148i) q^{44} -0.817703 q^{45} +(-1.90782 + 1.38611i) q^{46} +(4.13757 + 12.7341i) q^{47} +(-1.07832 + 3.31872i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(1.93376 + 1.40496i) q^{50} +(0.695128 - 2.13939i) q^{51} +(4.43790 + 13.6585i) q^{52} +(2.52368 - 1.83356i) q^{53} -13.4804 q^{54} +(0.842610 - 3.20780i) q^{55} -4.09529 q^{56} +(-1.01085 + 0.734428i) q^{57} +(-4.82402 - 14.8468i) q^{58} +(-1.96735 + 6.05488i) q^{59} +(4.43790 + 3.22433i) q^{60} +(0.372697 + 0.270780i) q^{61} +(6.28844 - 19.3538i) q^{62} +(-0.252684 - 0.777682i) q^{63} +(8.74238 - 6.35171i) q^{64} +3.86752 q^{65} +(2.97528 - 11.3269i) q^{66} -10.1146 q^{67} +(4.57453 - 3.32359i) q^{68} +(0.450375 + 1.38611i) q^{69} +(-0.738630 + 2.27327i) q^{70} +(4.65897 + 3.38494i) q^{71} +(-2.70918 - 1.96834i) q^{72} +(-1.66165 + 5.11404i) q^{73} +(6.99640 + 21.5327i) q^{74} +(1.19513 - 0.868312i) q^{75} -3.14077 q^{76} +(3.31118 - 0.189896i) q^{77} +13.6563 q^{78} +(4.63426 - 3.36698i) q^{79} +(0.729944 + 2.24654i) q^{80} +(-1.81648 + 5.59055i) q^{81} +(-6.42129 - 4.66534i) q^{82} +(-9.90175 - 7.19404i) q^{83} +(-1.69513 + 5.21707i) q^{84} +(-0.470553 - 1.44821i) q^{85} +(6.34572 - 4.61044i) q^{86} -9.64803 q^{87} +(10.5134 - 8.59969i) q^{88} -8.86318 q^{89} +(-1.58124 + 1.14884i) q^{90} +(1.19513 + 3.67823i) q^{91} +(-1.13209 + 3.48421i) q^{92} +(-10.1749 - 7.39251i) q^{93} +(25.8920 + 18.8116i) q^{94} +(-0.261370 + 0.804414i) q^{95} +(-1.16154 - 3.57484i) q^{96} +(-5.14077 + 3.73499i) q^{97} -2.39026 q^{98} +(2.28174 + 1.46584i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} + 4 q^{3} + 6 q^{4} - 2 q^{5} - 11 q^{6} - 2 q^{7} + 2 q^{8} + 4 q^{9}+O(q^{10}) $ 8 * q + 2 * q^2 + 4 * q^3 + 6 * q^4 - 2 * q^5 - 11 * q^6 - 2 * q^7 + 2 * q^8 + 4 * q^9	\( 8 q + 2 q^{2} + 4 q^{3} + 6 q^{4} - 2 q^{5} - 11 q^{6} - 2 q^{7} + 2 q^{8} + 4 q^{9} + 2 q^{10} + 3 q^{11} - 8 q^{12} - q^{13} - 3 q^{14} + 4 q^{15} + 4 q^{16} + 7 q^{17} - 6 q^{18} - 5 q^{19} - 9 q^{20} - 6 q^{21} + 22 q^{22} - 8 q^{23} - 3 q^{24} - 2 q^{25} - 11 q^{26} + q^{27} - 9 q^{28} + 3 q^{29} + 9 q^{30} + 19 q^{31} - 4 q^{32} + 9 q^{33} - 10 q^{34} - 2 q^{35} - 13 q^{36} - 10 q^{37} + 11 q^{38} + 13 q^{39} + 2 q^{40} - 8 q^{41} - 11 q^{42} + 20 q^{43} + 26 q^{44} - 6 q^{45} + 21 q^{46} + 13 q^{47} - 20 q^{48} - 2 q^{49} + 2 q^{50} - 5 q^{51} + 7 q^{52} - 6 q^{53} - 42 q^{54} - 7 q^{55} - 18 q^{56} + 7 q^{57} - 4 q^{58} + 7 q^{59} + 7 q^{60} - 3 q^{61} + 21 q^{62} - q^{63} + 18 q^{64} + 4 q^{65} + 14 q^{66} - 10 q^{67} + 20 q^{68} + 7 q^{69} - 3 q^{70} + 21 q^{71} - 13 q^{72} - q^{73} + 5 q^{74} - q^{75} - 22 q^{76} + 3 q^{77} + 10 q^{78} + 11 q^{79} - q^{80} - q^{81} - 6 q^{82} - 45 q^{83} - 3 q^{84} + 2 q^{85} - 14 q^{86} - 8 q^{87} + 7 q^{88} - 82 q^{89} + 4 q^{90} - q^{91} - 2 q^{92} - 3 q^{93} + 56 q^{94} - 5 q^{95} - 8 q^{96} - 38 q^{97} + 2 q^{98} - 11 q^{99}+O(q^{100}) \) 8 * q + 2 * q^2 + 4 * q^3 + 6 * q^4 - 2 * q^5 - 11 * q^6 - 2 * q^7 + 2 * q^8 + 4 * q^9 + 2 * q^10 + 3 * q^11 - 8 * q^12 - q^13 - 3 * q^14 + 4 * q^15 + 4 * q^16 + 7 * q^17 - 6 * q^18 - 5 * q^19 - 9 * q^20 - 6 * q^21 + 22 * q^22 - 8 * q^23 - 3 * q^24 - 2 * q^25 - 11 * q^26 + q^27 - 9 * q^28 + 3 * q^29 + 9 * q^30 + 19 * q^31 - 4 * q^32 + 9 * q^33 - 10 * q^34 - 2 * q^35 - 13 * q^36 - 10 * q^37 + 11 * q^38 + 13 * q^39 + 2 * q^40 - 8 * q^41 - 11 * q^42 + 20 * q^43 + 26 * q^44 - 6 * q^45 + 21 * q^46 + 13 * q^47 - 20 * q^48 - 2 * q^49 + 2 * q^50 - 5 * q^51 + 7 * q^52 - 6 * q^53 - 42 * q^54 - 7 * q^55 - 18 * q^56 + 7 * q^57 - 4 * q^58 + 7 * q^59 + 7 * q^60 - 3 * q^61 + 21 * q^62 - q^63 + 18 * q^64 + 4 * q^65 + 14 * q^66 - 10 * q^67 + 20 * q^68 + 7 * q^69 - 3 * q^70 + 21 * q^71 - 13 * q^72 - q^73 + 5 * q^74 - q^75 - 22 * q^76 + 3 * q^77 + 10 * q^78 + 11 * q^79 - q^80 - q^81 - 6 * q^82 - 45 * q^83 - 3 * q^84 + 2 * q^85 - 14 * q^86 - 8 * q^87 + 7 * q^88 - 82 * q^89 + 4 * q^90 - q^91 - 2 * q^92 - 3 * q^93 + 56 * q^94 - 5 * q^95 - 8 * q^96 - 38 * q^97 + 2 * q^98 - 11 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/385\mathbb{Z}\right)^\times$.

$n$	$211$	$232$	$276$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	1.93376	−	1.40496i	1.36737	−	0.993455i	0.369437	−	0.929256i	$-0.379551\pi$
$2$	1.93376	−	1.40496i	1.36737	−	0.993455i	0.997937	−	0.0641992i	$-0.0204493\pi$
$3$	−0.456498	−	1.40496i	−0.263559	−	0.811153i	−0.992022	−	0.126067i	$-0.959765\pi$
$3$	−0.456498	−	1.40496i	−0.263559	−	0.811153i	0.728462	−	0.685086i	$-0.240235\pi$
$4$	1.14748	−	3.53158i	0.573741	−	1.76579i
$5$	−0.809017	−	0.587785i	−0.361803	−	0.262866i
$5$	−0.809017	−	0.587785i	−0.361803	−	0.262866i
$6$	−2.85666	−	2.07549i	−1.16623	−	0.847314i
$7$	0.309017	−	0.951057i	0.116797	−	0.359466i
$7$	0.309017	−	0.951057i	0.116797	−	0.359466i
$8$	−1.26552	−	3.89486i	−0.447427	−	1.37704i
$9$	0.661536	−	0.480634i	0.220512	−	0.160211i
$10$	−2.39026			−0.755866
$11$	1.20381	+	3.09044i	0.362964	+	0.931803i
$11$	1.20381	+	3.09044i	0.362964	+	0.931803i
$12$	−5.48555			−1.58354
$13$	−3.12889	+	2.27327i	−0.867797	+	0.630491i	−0.929995	−	0.367572i	$-0.880189\pi$
$13$	−3.12889	+	2.27327i	−0.867797	+	0.630491i	0.0621978	+	0.998064i	$0.480189\pi$
$14$	−0.738630	−	2.27327i	−0.197407	−	0.607557i
$15$	−0.456498	+	1.40496i	−0.117867	+	0.362759i
$16$	−1.91102	−	1.38844i	−0.477755	−	0.347109i
$17$	1.23192	+	0.895044i	0.298785	+	0.217080i	0.727069	−	0.686564i	$-0.240882\pi$
$17$	1.23192	+	0.895044i	0.298785	+	0.217080i	−0.428284	+	0.903644i	$0.640882\pi$
$18$	0.603980	−	1.85886i	0.142359	−	0.438137i
$19$	−0.261370	−	0.804414i	−0.0599624	−	0.184545i	0.916589	−	0.399832i	$-0.130931\pi$
$19$	−0.261370	−	0.804414i	−0.0599624	−	0.184545i	−0.976551	+	0.215287i	$0.930931\pi$
$20$	−3.00415	+	2.18264i	−0.671747	+	0.488053i
$21$	−1.47726			−0.322365
$22$	6.66983	+	4.28486i	1.42201	+	0.913535i
$23$	−0.986585			−0.205717			−0.102859	−	0.994696i	$-0.532799\pi$
$23$	−0.986585			−0.205717			−0.102859	+	0.994696i	$0.532799\pi$
$24$	−4.89440	+	3.55599i	−0.999066	+	0.725864i
$25$	0.309017	+	0.951057i	0.0618034	+	0.190211i
$26$	−2.85666	+	8.79191i	−0.560238	+	1.72423i
$27$	−4.56265	−	3.31496i	−0.878082	−	0.637964i
$28$	−3.00415	−	2.18264i	−0.567730	−	0.412480i
$29$	2.01820	−	6.21138i	0.374770	−	1.15342i	−0.568863	−	0.822432i	$-0.692617\pi$
$29$	2.01820	−	6.21138i	0.374770	−	1.15342i	0.943634	−	0.330992i	$-0.107383\pi$
$30$	1.09115	+	3.35821i	0.199216	+	0.613122i
$31$	6.88769	−	5.00420i	1.23707	−	0.898781i	0.239667	−	0.970855i	$-0.422962\pi$
$31$	6.88769	−	5.00420i	1.23707	−	0.898781i	0.997399	+	0.0720737i	$0.0229617\pi$
$32$	2.54445			0.449799
$33$	3.79240	−	3.10209i	0.660172	−	0.540005i
$34$	3.63974			0.624210
$35$	−0.809017	+	0.587785i	−0.136749	+	0.0993538i
$36$	−0.938299	−	2.88779i	−0.156383	−	0.481298i
$37$	−2.92705	+	9.00854i	−0.481204	+	1.48099i	0.356200	+	0.934410i	$0.384072\pi$
$37$	−2.92705	+	9.00854i	−0.481204	+	1.48099i	−0.837404	+	0.546584i	$0.815928\pi$
$38$	−1.63559	−	1.18833i	−0.265328	−	0.192772i
$39$	4.62218	+	3.35821i	0.740141	+	0.537744i
$40$	−1.26552	+	3.89486i	−0.200096	+	0.615831i
$41$	−1.02613	−	3.15810i	−0.160255	−	0.493213i	0.838401	−	0.545054i	$-0.183491\pi$
$41$	−1.02613	−	3.15810i	−0.160255	−	0.493213i	−0.998655	+	0.0518415i	$0.983491\pi$
$42$	−2.85666	+	2.07549i	−0.440793	+	0.320255i
$43$	3.28155			0.500431			0.250216	−	0.968190i	$-0.419498\pi$
$43$	3.28155			0.500431			0.250216	+	0.968190i	$0.419498\pi$
$44$	12.2955	−	0.705148i	1.85362	−	0.106305i
$45$	−0.817703			−0.121896
$46$	−1.90782	+	1.38611i	−0.281292	+	0.204371i
$47$	4.13757	+	12.7341i	0.603527	+	1.85747i	0.506615	+	0.862172i	$0.330896\pi$
$47$	4.13757	+	12.7341i	0.603527	+	1.85747i	0.0969117	+	0.995293i	$0.469104\pi$
$48$	−1.07832	+	3.31872i	−0.155642	+	0.479016i
$49$	−0.809017	−	0.587785i	−0.115574	−	0.0839693i
$50$	1.93376	+	1.40496i	0.273475	+	0.198691i
$51$	0.695128	−	2.13939i	0.0973375	−	0.299574i
$52$	4.43790	+	13.6585i	0.615427	+	1.89409i
$53$	2.52368	−	1.83356i	0.346655	−	0.251859i	−0.400810	−	0.916161i	$-0.631271\pi$
$53$	2.52368	−	1.83356i	0.346655	−	0.251859i	0.747464	+	0.664302i	$0.231271\pi$
$54$	−13.4804			−1.83445
$55$	0.842610	−	3.20780i	0.113617	−	0.432540i
$56$	−4.09529			−0.547257
$57$	−1.01085	+	0.734428i	−0.133891	+	0.0972773i
$58$	−4.82402	−	14.8468i	−0.633424	−	1.94948i
$59$	−1.96735	+	6.05488i	−0.256127	+	0.788279i	0.737478	+	0.675371i	$0.236016\pi$
$59$	−1.96735	+	6.05488i	−0.256127	+	0.788279i	−0.993605	+	0.112908i	$0.963984\pi$
$60$	4.43790	+	3.22433i	0.572931	+	0.416259i
$61$	0.372697	+	0.270780i	0.0477189	+	0.0346698i	0.611389	−	0.791330i	$-0.290611\pi$
$61$	0.372697	+	0.270780i	0.0477189	+	0.0346698i	−0.563670	+	0.826000i	$0.690611\pi$
$62$	6.28844	−	19.3538i	0.798633	−	2.45794i
$63$	−0.252684	−	0.777682i	−0.0318352	−	0.0979787i
$64$	8.74238	−	6.35171i	1.09280	−	0.793964i
$65$	3.86752			0.479706
$66$	2.97528	−	11.3269i	0.366232	−	1.39424i
$67$	−10.1146			−1.23569			−0.617845	−	0.786300i	$-0.711994\pi$
$67$	−10.1146			−1.23569			−0.617845	+	0.786300i	$0.711994\pi$
$68$	4.57453	−	3.32359i	0.554744	−	0.403045i
$69$	0.450375	+	1.38611i	0.0542187	+	0.166868i
$70$	−0.738630	+	2.27327i	−0.0882832	+	0.271708i
$71$	4.65897	+	3.38494i	0.552918	+	0.401719i	0.828860	−	0.559456i	$-0.188990\pi$
$71$	4.65897	+	3.38494i	0.552918	+	0.401719i	−0.275942	+	0.961174i	$0.588990\pi$
$72$	−2.70918	−	1.96834i	−0.319280	−	0.231971i
$73$	−1.66165	+	5.11404i	−0.194482	+	0.598553i	0.805501	+	0.592595i	$0.201897\pi$
$73$	−1.66165	+	5.11404i	−0.194482	+	0.598553i	−0.999982	+	0.00595804i	$0.998103\pi$
$74$	6.99640	+	21.5327i	0.813315	+	2.50313i
$75$	1.19513	−	0.868312i	0.138002	−	0.100264i
$76$	−3.14077			−0.360271
$77$	3.31118	−	0.189896i	0.377344	−	0.0216407i
$78$	13.6563			1.54627
$79$	4.63426	−	3.36698i	0.521394	−	0.378815i	−0.295735	−	0.955270i	$-0.595564\pi$
$79$	4.63426	−	3.36698i	0.521394	−	0.378815i	0.817129	+	0.576455i	$0.195564\pi$
$80$	0.729944	+	2.24654i	0.0816102	+	0.251170i
$81$	−1.81648	+	5.59055i	−0.201831	+	0.621172i
$82$	−6.42129	−	4.66534i	−0.709113	−	0.515200i
$83$	−9.90175	−	7.19404i	−1.08686	−	0.789649i	−0.107992	−	0.994152i	$-0.534442\pi$
$83$	−9.90175	−	7.19404i	−1.08686	−	0.789649i	−0.978866	+	0.204503i	$0.934442\pi$
$84$	−1.69513	+	5.21707i	−0.184954	+	0.569229i
$85$	−0.470553	−	1.44821i	−0.0510386	−	0.157081i
$86$	6.34572	−	4.61044i	0.684277	−	0.497156i
$87$	−9.64803			−1.03438
$88$	10.5134	−	8.59969i	1.12073	−	0.916730i
$89$	−8.86318			−0.939496			−0.469748	−	0.882801i	$-0.655655\pi$
$89$	−8.86318			−0.939496			−0.469748	+	0.882801i	$0.655655\pi$
$90$	−1.58124	+	1.14884i	−0.166677	+	0.121098i
$91$	1.19513	+	3.67823i	0.125284	+	0.385583i
$92$	−1.13209	+	3.48421i	−0.118028	+	0.363254i
$93$	−10.1749	−	7.39251i	−1.05509	−	0.766568i
$94$	25.8920	+	18.8116i	2.67056	+	1.94027i
$95$	−0.261370	+	0.804414i	−0.0268160	+	0.0825312i
$96$	−1.16154	−	3.57484i	−0.118549	−	0.364855i
$97$	−5.14077	+	3.73499i	−0.521967	+	0.379231i	−0.817344	−	0.576150i	$-0.804555\pi$
$97$	−5.14077	+	3.73499i	−0.521967	+	0.379231i	0.295378	+	0.955381i	$0.404555\pi$
$98$	−2.39026			−0.241452
$99$	2.28174	+	1.46584i	0.229323	+	0.147323i
$100$	3.71333			0.371333
$101$	6.06813	−	4.40875i	0.603802	−	0.438687i	−0.243425	−	0.969920i	$-0.578271\pi$
$101$	6.06813	−	4.40875i	0.603802	−	0.438687i	0.847226	+	0.531232i	$0.178271\pi$
$102$	−1.66154	−	5.11368i	−0.164517	−	0.506330i
$103$	−1.97568	+	6.08051i	−0.194669	+	0.599130i	0.805311	+	0.592852i	$0.201998\pi$
$103$	−1.97568	+	6.08051i	−0.194669	+	0.599130i	−0.999980	+	0.00627773i	$0.998002\pi$
$104$	12.8137	+	9.30971i	1.25649	+	0.912892i
$105$	1.19513	+	0.868312i	0.116633	+	0.0847385i
$106$	2.30412	−	7.09134i	0.223796	−	0.688772i
$107$	4.41773	+	13.5964i	0.427078	+	1.31441i	0.900991	+	0.433838i	$0.142841\pi$
$107$	4.41773	+	13.5964i	0.427078	+	1.31441i	−0.473913	+	0.880572i	$0.657159\pi$
$108$	−16.9426	+	12.3095i	−1.63030	+	1.18448i
$109$	−15.6231			−1.49642			−0.748210	−	0.663462i	$-0.769087\pi$
$109$	−15.6231			−1.49642			−0.748210	+	0.663462i	$0.769087\pi$
$110$	−2.87743	−	7.38695i	−0.274352	−	0.704318i
$111$	13.9928			1.32814
$112$	−1.91102	+	1.38844i	−0.180574	+	0.131195i
$113$	−4.44486	−	13.6799i	−0.418137	−	1.28689i	−0.909415	−	0.415890i	$-0.863470\pi$
$113$	−4.44486	−	13.6799i	−0.418137	−	1.28689i	0.491278	−	0.871003i	$-0.336530\pi$
$114$	−0.922906	+	2.84041i	−0.0864380	+	0.266029i
$115$	0.798164	+	0.579900i	0.0744292	+	0.0540760i
$116$	−19.6202	−	14.2549i	−1.82169	−	1.32353i
$117$	−0.977260	+	3.00770i	−0.0903477	+	0.278062i
$118$	4.70248	+	14.4727i	0.432898	+	1.33232i
$119$	1.23192	−	0.895044i	0.112930	−	0.0820486i
$120$	6.04981			0.552270
$121$	−8.10166	+	7.44064i	−0.736515	+	0.676422i
$122$	1.10114			0.0996925
$123$	−3.96857	+	2.88334i	−0.357834	+	0.259982i
$124$	−9.76927	−	30.0667i	−0.877306	−	2.70007i
$125$	0.309017	−	0.951057i	0.0276393	−	0.0850651i
$126$	−1.58124	−	1.14884i	−0.140868	−	0.102347i
$127$	5.10556	+	3.70941i	0.453045	+	0.329157i	0.790797	−	0.612078i	$-0.209666\pi$
$127$	5.10556	+	3.70941i	0.453045	+	0.329157i	−0.337752	+	0.941235i	$0.609666\pi$
$128$	6.40921	−	19.7255i	0.566500	−	1.74351i
$129$	−1.49802	−	4.61044i	−0.131893	−	0.405926i
$130$	7.47884	−	5.43370i	0.655938	−	0.476567i
$131$	11.9054			1.04018			0.520091	−	0.854111i	$-0.325898\pi$
$131$	11.9054			1.04018			0.520091	+	0.854111i	$0.325898\pi$
$132$	−6.60358	−	16.9528i	−0.574768	−	1.47555i
$133$	−0.845811			−0.0733411
$134$	−19.5591	+	14.2105i	−1.68965	+	1.22760i
$135$	1.74278	+	5.36371i	0.149994	+	0.461635i
$136$	1.92705	−	5.93085i	0.165243	−	0.508566i
$137$	−17.5849	−	12.7762i	−1.50238	−	1.09154i	−0.969422	−	0.245401i	$-0.921080\pi$
$137$	−17.5849	−	12.7762i	−1.50238	−	1.09154i	−0.532958	−	0.846142i	$-0.678920\pi$
$138$	2.81834	+	2.04765i	0.239913	+	0.174307i
$139$	−2.30938	+	7.10753i	−0.195879	+	0.602853i	0.804086	+	0.594513i	$0.202655\pi$
$139$	−2.30938	+	7.10753i	−0.195879	+	0.602853i	−0.999965	+	0.00834062i	$0.997345\pi$
$140$	1.14748	+	3.53158i	0.0969799	+	0.298473i
$141$	16.0021	−	11.6262i	1.34762	−	0.979105i
$142$	13.7650			1.15514
$143$	−10.7920	−	6.93305i	−0.902473	−	0.579771i
$144$	−1.93154			−0.160961
$145$	−5.28371	+	3.83884i	−0.438789	+	0.318799i
$146$	3.97178	+	12.2239i	0.328706	+	1.01165i
$147$	−0.456498	+	1.40496i	−0.0376514	+	0.115879i
$148$	28.4557	+	20.6743i	2.33904	+	1.69941i
$149$	−7.71644	−	5.60632i	−0.632155	−	0.459288i	0.224991	−	0.974361i	$-0.427765\pi$
$149$	−7.71644	−	5.60632i	−0.632155	−	0.459288i	−0.857146	+	0.515073i	$0.827765\pi$
$150$	1.09115	−	3.35821i	0.0890919	−	0.274197i
$151$	3.36874	+	10.3679i	0.274144	+	0.843729i	0.989445	+	0.144912i	$0.0462899\pi$
$151$	3.36874	+	10.3679i	0.274144	+	0.843729i	−0.715300	+	0.698817i	$0.753710\pi$
$152$	−2.80231	+	2.03600i	−0.227297	+	0.165141i
$153$	1.24515			0.100664
$154$	6.13623	−	5.01929i	0.494472	−	0.404466i
$155$	−8.51366			−0.683834
$156$	17.1637	−	12.4701i	1.37419	−	0.998410i
$157$	0.0187111	+	0.0575868i	0.00149331	+	0.00459593i	0.951800	−	0.306718i	$-0.0992309\pi$
$157$	0.0187111	+	0.0575868i	0.00149331	+	0.00459593i	−0.950307	+	0.311314i	$0.899231\pi$
$158$	4.23106	−	13.0219i	0.336605	−	1.03596i
$159$	−3.72814	−	2.70865i	−0.295661	−	0.214810i
$160$	−2.05850	−	1.49559i	−0.162739	−	0.118237i
$161$	−0.304872	+	0.938298i	−0.0240272	+	0.0739483i
$162$	4.34185	+	13.3629i	0.341128	+	1.04988i
$163$	−10.3353	+	7.50905i	−0.809525	+	0.588154i	−0.913693	−	0.406406i	$-0.866782\pi$
$163$	−10.3353	+	7.50905i	−0.809525	+	0.588154i	0.104168	+	0.994560i	$0.466782\pi$
$164$	−12.3306			−0.962856
$165$	−4.89148	+	0.280526i	−0.380801	+	0.0218389i
$166$	−29.2549			−2.27062
$167$	16.2555	−	11.8103i	1.25788	−	0.913907i	0.259233	−	0.965815i	$-0.416530\pi$
$167$	16.2555	−	11.8103i	1.25788	−	0.913907i	0.998652	+	0.0519079i	$0.0165302\pi$
$168$	1.86950	+	5.75372i	0.144235	+	0.443909i
$169$	0.604958	−	1.86187i	0.0465353	−	0.143221i
$170$	−2.94461	−	2.13939i	−0.225841	−	0.164083i
$171$	−0.559534	−	0.406525i	−0.0427886	−	0.0310878i
$172$	3.76552	−	11.5891i	0.287118	−	0.883658i
$173$	2.27957	+	7.01579i	0.173312	+	0.533401i	0.999552	−	0.0299175i	$-0.00952445\pi$
$173$	2.27957	+	7.01579i	0.173312	+	0.533401i	−0.826240	+	0.563318i	$0.809524\pi$
$174$	−18.6570	+	13.5551i	−1.41438	+	1.02761i
$175$	1.00000			0.0755929
$176$	1.99037	−	7.57731i	0.150030	−	0.571161i
$177$	9.40495			0.706919
$178$	−17.1393	+	12.4524i	−1.28464	+	0.933347i
$179$	3.01247	+	9.27143i	0.225163	+	0.692979i	0.998275	+	0.0587103i	$0.0186988\pi$
$179$	3.01247	+	9.27143i	0.225163	+	0.692979i	−0.773112	+	0.634269i	$0.781301\pi$
$180$	−0.938299	+	2.88779i	−0.0699367	+	0.215243i
$181$	4.27682	+	3.10729i	0.317893	+	0.230963i	0.735276	−	0.677768i	$-0.237053\pi$
$181$	4.27682	+	3.10729i	0.317893	+	0.230963i	−0.417383	+	0.908731i	$0.637053\pi$
$182$	7.47884	+	5.43370i	0.554369	+	0.402772i
$183$	0.210299	−	0.647233i	0.0155457	−	0.0478449i
$184$	1.24854	+	3.84261i	0.0920435	+	0.283281i
$185$	7.66312	−	5.56758i	0.563404	−	0.409337i
$186$	−30.0620			−2.20425
$187$	−1.28308	+	4.88465i	−0.0938278	+	0.357201i
$188$	49.7195			3.62617
$189$	−4.56265	+	3.31496i	−0.331884	+	0.241128i
$190$	0.624741	+	1.92276i	0.0453235	+	0.139491i
$191$	−3.75647	+	11.5612i	−0.271809	+	0.836541i	0.718238	+	0.695798i	$0.244949\pi$
$191$	−3.75647	+	11.5612i	−0.271809	+	0.836541i	−0.990046	+	0.140743i	$0.955051\pi$
$192$	−12.9148	−	9.38313i	−0.932043	−	0.677169i
$193$	−4.23741	−	3.07866i	−0.305015	−	0.221607i	0.424739	−	0.905316i	$-0.360366\pi$
$193$	−4.23741	−	3.07866i	−0.305015	−	0.221607i	−0.729755	+	0.683709i	$0.760366\pi$
$194$	−4.69351	+	14.4451i	−0.336974	+	1.03710i
$195$	−1.76552	−	5.43370i	−0.126431	−	0.389115i
$196$	−3.00415	+	2.18264i	−0.214582	+	0.155903i
$197$	−3.51610			−0.250512			−0.125256	−	0.992124i	$-0.539975\pi$
$197$	−3.51610			−0.250512			−0.125256	+	0.992124i	$0.539975\pi$
$198$	6.47178	−	0.371156i	0.459929	−	0.0263769i
$199$	7.63650			0.541337			0.270669	−	0.962673i	$-0.412755\pi$
$199$	7.63650			0.541337			0.270669	+	0.962673i	$0.412755\pi$
$200$	3.31316	−	2.40715i	0.234276	−	0.170211i
$201$	4.61728	+	14.2105i	0.325678	+	1.00233i
$202$	5.54018	−	17.0509i	0.389806	−	1.19970i
$203$	−5.28371	−	3.83884i	−0.370844	−	0.269434i
$204$	−6.75777	−	4.90981i	−0.473139	−	0.343755i
$205$	−1.02613	+	3.15810i	−0.0716680	+	0.220571i
$206$	4.72237	+	14.5340i	0.329023	+	1.01263i
$207$	−0.652661	+	0.474186i	−0.0453631	+	0.0329582i
$208$	9.13565			0.633443
$209$	2.17135	−	1.77611i	0.150196	−	0.122856i
$210$	3.53103			0.243664
$211$	−17.2971	+	12.5671i	−1.19078	+	0.865153i	−0.993347	−	0.115163i	$-0.963261\pi$
$211$	−17.2971	+	12.5671i	−1.19078	+	0.865153i	−0.197435	+	0.980316i	$0.563261\pi$
$212$	−3.57951	−	11.0166i	−0.245841	−	0.756622i
$213$	2.62889	−	8.09088i	0.180128	−	0.554378i
$214$	27.6451	+	20.0854i	1.88978	+	1.37301i
$215$	−2.65483	−	1.92885i	−0.181058	−	0.131546i
$216$	−7.13718	+	21.9660i	−0.485623	+	1.49460i
$217$	−2.63087	−	8.09697i	−0.178595	−	0.549658i
$218$	−30.2113	+	21.9498i	−2.04617	+	1.48663i
$219$	7.94355			0.536775
$220$	−10.3618	−	6.65664i	−0.698589	−	0.448791i
$221$	−5.88922			−0.396152
$222$	27.0587	−	19.6593i	1.81606	−	1.31945i
$223$	7.54759	+	23.2291i	0.505424	+	1.55554i	0.800056	+	0.599925i	$0.204803\pi$
$223$	7.54759	+	23.2291i	0.505424	+	1.55554i	−0.294632	+	0.955611i	$0.595197\pi$
$224$	0.786277	−	2.41991i	0.0525353	−	0.161687i
$225$	0.661536	+	0.480634i	0.0441024	+	0.0320422i
$226$	−27.8149	−	20.2087i	−1.85022	−	1.34426i
$227$	7.37202	−	22.6888i	0.489298	−	1.50591i	−0.336359	−	0.941734i	$-0.609196\pi$
$227$	7.37202	−	22.6888i	0.489298	−	1.50591i	0.825657	−	0.564172i	$-0.190804\pi$
$228$	1.43376	+	4.41265i	0.0949530	+	0.292235i
$229$	−0.776952	+	0.564489i	−0.0513424	+	0.0373025i	−0.613160	−	0.789958i	$-0.710102\pi$
$229$	−0.776952	+	0.564489i	−0.0513424	+	0.0373025i	0.561818	+	0.827261i	$0.310102\pi$
$230$	2.35819			0.155495
$231$	−1.77835	−	4.56539i	−0.117007	−	0.300380i
$232$	−26.7465			−1.75599
$233$	20.6239	−	14.9842i	1.35112	−	0.981644i	0.352163	−	0.935939i	$-0.385446\pi$
$233$	20.6239	−	14.9842i	1.35112	−	0.981644i	0.998955	−	0.0457057i	$-0.0145537\pi$
$234$	2.33590	+	7.18917i	0.152703	+	0.469971i
$235$	4.13757	−	12.7341i	0.269905	−	0.830684i
$236$	19.1258	+	13.8957i	1.24499	+	0.904535i
$237$	−6.84600	−	4.97391i	−0.444695	−	0.323090i
$238$	1.12474	−	3.46160i	0.0729062	−	0.224382i
$239$	−7.25580	−	22.3310i	−0.469338	−	1.44448i	−0.853443	−	0.521186i	$-0.825490\pi$
$239$	−7.25580	−	22.3310i	−0.469338	−	1.44448i	0.384105	−	0.923289i	$-0.374510\pi$
$240$	2.82307	−	2.05108i	0.182228	−	0.132397i
$241$	−13.0860			−0.842942			−0.421471	−	0.906842i	$-0.638486\pi$
$241$	−13.0860			−0.842942			−0.421471	+	0.906842i	$0.638486\pi$
$242$	−5.21288	+	25.7709i	−0.335096	+	1.65662i
$243$	−8.23551			−0.528308
$244$	1.38394	−	1.00549i	0.0885980	−	0.0643702i
$245$	0.309017	+	0.951057i	0.0197424	+	0.0607608i
$246$	−3.62330	+	11.1514i	−0.231013	+	0.710985i
$247$	2.64645	+	1.92276i	0.168389	+	0.122342i
$248$	−28.2071	−	20.4937i	−1.79115	−	1.30135i
$249$	−5.58719	+	17.1956i	−0.354074	+	1.08973i
$250$	−0.738630	−	2.27327i	−0.0467151	−	0.143774i
$251$	10.0246	−	7.28327i	0.632745	−	0.459716i	−0.224605	−	0.974450i	$-0.572109\pi$
$251$	10.0246	−	7.28327i	0.632745	−	0.459716i	0.857350	+	0.514734i	$0.172109\pi$
$252$	−3.03640			−0.191275
$253$	−1.18767	−	3.04898i	−0.0746679	−	0.191688i
$254$	15.0845			0.946485
$255$	−1.81987	+	1.32221i	−0.113965	+	0.0828002i
$256$	−8.64108	−	26.5945i	−0.540067	−	1.66216i
$257$	5.68644	−	17.5011i	0.354711	−	1.09169i	−0.601467	−	0.798898i	$-0.705417\pi$
$257$	5.68644	−	17.5011i	0.354711	−	1.09169i	0.956177	−	0.292789i	$-0.0945833\pi$
$258$	−9.37428	−	6.81081i	−0.583617	−	0.424023i
$259$	7.66312	+	5.56758i	0.476163	+	0.345953i
$260$	4.43790	−	13.6585i	0.275227	−	0.847062i
$261$	−1.65029	−	5.07906i	−0.102150	−	0.314386i
$262$	23.0222	−	16.7266i	1.42232	−	1.03337i
$263$	−9.82776			−0.606006			−0.303003	−	0.952990i	$-0.597989\pi$
$263$	−9.82776			−0.606006			−0.303003	+	0.952990i	$0.597989\pi$
$264$	−16.8815	−	10.8451i	−1.03899	−	0.667471i
$265$	−3.11945			−0.191626
$266$	−1.63559	+	1.18833i	−0.100285	+	0.0728611i
$267$	4.04603	+	12.4524i	0.247613	+	0.762074i
$268$	−11.6063	+	35.7204i	−0.708965	+	2.18197i
$269$	7.25368	+	5.27011i	0.442265	+	0.321324i	0.786534	−	0.617547i	$-0.211873\pi$
$269$	7.25368	+	5.27011i	0.442265	+	0.321324i	−0.344269	+	0.938871i	$0.611873\pi$
$270$	10.9059	+	7.92360i	0.663712	+	0.482215i
$271$	−2.38438	+	7.33836i	−0.144841	+	0.445774i	−0.996990	−	0.0775243i	$-0.975298\pi$
$271$	−2.38438	+	7.33836i	−0.144841	+	0.445774i	0.852150	+	0.523298i	$0.175298\pi$
$272$	−1.11152	−	3.42089i	−0.0673955	−	0.207422i
$273$	4.62218	−	3.35821i	0.279747	−	0.203248i
$274$	−51.9549			−3.13871
$275$	−2.56719	+	2.09989i	−0.154807	+	0.126628i
$276$	5.41196			0.325762
$277$	−2.36959	+	1.72160i	−0.142375	+	0.103441i	−0.656693	−	0.754158i	$-0.728045\pi$
$277$	−2.36959	+	1.72160i	−0.142375	+	0.103441i	0.514318	+	0.857600i	$0.328045\pi$
$278$	5.52001	+	16.9888i	0.331068	+	1.01892i
$279$	2.15127	−	6.62092i	0.128793	−	0.396384i
$280$	3.31316	+	2.40715i	0.197999	+	0.143855i
$281$	−23.2945	−	16.9245i	−1.38964	−	1.00963i	−0.995905	−	0.0904031i	$-0.971184\pi$
$281$	−23.2945	−	16.9245i	−1.38964	−	1.00963i	−0.393730	−	0.919226i	$-0.628816\pi$
$282$	14.6099	−	44.9646i	0.870007	−	2.67761i
$283$	−8.94098	−	27.5175i	−0.531486	−	1.63575i	−0.751122	−	0.660164i	$-0.770487\pi$
$283$	−8.94098	−	27.5175i	−0.531486	−	1.63575i	0.219636	−	0.975582i	$-0.429513\pi$
$284$	17.3003	−	12.5694i	1.02658	−	0.745857i
$285$	1.24948			0.0740130
$286$	−30.6098	+	1.75547i	−1.80999	+	0.103803i
$287$	−3.32063			−0.196010
$288$	1.68324	−	1.22295i	0.0991859	−	0.0720628i
$289$	−4.53676	−	13.9627i	−0.266868	−	0.821336i
$290$	−4.82402	+	14.8468i	−0.283276	+	0.871834i
$291$	7.59426	+	5.51755i	0.445183	+	0.323445i
$292$	16.1539	+	11.7365i	0.945338	+	0.686828i
$293$	5.98638	−	18.4242i	0.349728	−	1.07635i	−0.609276	−	0.792958i	$-0.708540\pi$
$293$	5.98638	−	18.4242i	0.349728	−	1.07635i	0.959004	−	0.283394i	$-0.0914603\pi$
$294$	1.09115	+	3.35821i	0.0636371	+	0.195855i
$295$	5.15059	−	3.74212i	0.299879	−	0.217875i
$296$	38.7912			2.25469
$297$	4.75210	−	18.0912i	0.275745	−	1.04976i
$298$	−22.7984			−1.32067
$299$	3.08691	−	2.24277i	0.178521	−	0.129703i
$300$	−1.69513	−	5.21707i	−0.0978683	−	0.301208i
$301$	1.01405	−	3.12094i	0.0584491	−	0.179888i
$302$	21.0808	+	15.3161i	1.21306	+	0.881343i
$303$	−8.96421	−	6.51288i	−0.514980	−	0.374155i
$304$	−0.617395	+	1.90015i	−0.0354100	+	0.108981i
$305$	−0.142357	−	0.438131i	−0.00815136	−	0.0250873i
$306$	2.40782	−	1.74938i	0.137646	−	0.100005i
$307$	−17.2849			−0.986504			−0.493252	−	0.869886i	$-0.664192\pi$
$307$	−17.2849			−0.986504			−0.493252	+	0.869886i	$0.664192\pi$
$308$	3.12889	−	11.9116i	0.178285	−	0.678728i
$309$	9.44475			0.537293
$310$	−16.4634	+	11.9613i	−0.935056	+	0.679358i
$311$	6.12194	+	18.8414i	0.347143	+	1.06840i	0.960426	+	0.278534i	$0.0898484\pi$
$311$	6.12194	+	18.8414i	0.347143	+	1.06840i	−0.613283	+	0.789863i	$0.710152\pi$
$312$	7.23030	−	22.2526i	0.409335	−	1.25980i
$313$	24.6269	+	17.8925i	1.39199	+	1.01134i	0.995643	+	0.0932427i	$0.0297233\pi$
$313$	24.6269	+	17.8925i	1.39199	+	1.01134i	0.396350	+	0.918100i	$0.370277\pi$
$314$	0.117090	+	0.0850707i	0.00660776	+	0.00480082i
$315$	−0.252684	+	0.777682i	−0.0142371	+	0.0438174i
$316$	−6.57307	−	20.2298i	−0.369764	−	1.13802i
$317$	3.52112	−	2.55825i	0.197766	−	0.143685i	−0.484495	−	0.874794i	$-0.660997\pi$
$317$	3.52112	−	2.55825i	0.197766	−	0.143685i	0.682261	+	0.731109i	$0.260997\pi$
$318$	−11.0149			−0.617683
$319$	21.6254	−	1.24022i	1.21079	−	0.0694390i
$320$	−10.8062			−0.604084
$321$	17.0856	−	12.4134i	0.953627	−	0.692850i
$322$	0.728721	+	2.24277i	0.0406101	+	0.124985i
$323$	0.397999	−	1.22491i	0.0221452	−	0.0681560i
$324$	17.6591	+	12.8301i	0.981063	+	0.712784i
$325$	−3.12889	−	2.27327i	−0.173559	−	0.126098i
$326$	−9.43611	+	29.0414i	−0.522618	+	1.60845i
$327$	7.13192	+	21.9498i	0.394396	+	1.21383i
$328$	−11.0018	+	7.99326i	−0.607471	+	0.441354i
$329$	13.3895			0.738185
$330$	−9.06481	+	7.41479i	−0.499001	+	0.408171i
$331$	7.44787			0.409372			0.204686	−	0.978828i	$-0.434383\pi$
$331$	7.44787			0.409372			0.204686	+	0.978828i	$0.434383\pi$
$332$	−36.7684	+	26.7138i	−2.01793	+	1.46611i
$333$	2.39346	+	7.36631i	0.131161	+	0.403671i
$334$	14.8412	−	45.6765i	0.812073	−	2.49930i
$335$	8.18285	+	5.94519i	0.447077	+	0.324820i
$336$	2.82307	+	2.05108i	0.154011	+	0.111896i
$337$	7.23174	−	22.2570i	0.393938	−	1.21242i	−0.535848	−	0.844315i	$-0.680008\pi$
$337$	7.23174	−	22.2570i	0.393938	−	1.21242i	0.929786	−	0.368101i	$-0.119992\pi$
$338$	−1.44601	−	4.45035i	−0.0786524	−	0.242067i
$339$	−17.1906	+	12.4897i	−0.933663	+	0.678346i
$340$	−5.65443			−0.306655
$341$	23.7567	+	15.2619i	1.28650	+	0.826478i
$342$	−1.65315			−0.0893924
$343$	−0.809017	+	0.587785i	−0.0436828	+	0.0317374i
$344$	−4.15285	−	12.7812i	−0.223907	−	0.689114i
$345$	0.450375	−	1.38611i	0.0242474	−	0.0746257i
$346$	14.2650	+	10.3642i	0.766893	+	0.557180i
$347$	18.9241	+	13.7492i	1.01590	+	0.738094i	0.965438	−	0.260633i	$-0.0839311\pi$
$347$	18.9241	+	13.7492i	1.01590	+	0.738094i	0.0504605	+	0.998726i	$0.483931\pi$
$348$	−11.0709	+	34.0728i	−0.593464	+	1.82650i
$349$	−0.633499	−	1.94971i	−0.0339104	−	0.104366i	0.932669	−	0.360734i	$-0.117474\pi$
$349$	−0.633499	−	1.94971i	−0.0339104	−	0.104366i	−0.966579	+	0.256369i	$0.917474\pi$
$350$	1.93376	−	1.40496i	0.103364	−	0.0750982i
$351$	21.8118			1.16423
$352$	3.06304	+	7.86346i	0.163261	+	0.419124i
$353$	−19.3842			−1.03172			−0.515858	−	0.856674i	$-0.672527\pi$
$353$	−19.3842			−1.03172			−0.515858	+	0.856674i	$0.672527\pi$
$354$	18.1869	−	13.2136i	0.966623	−	0.702293i
$355$	−1.77957	−	5.47695i	−0.0944497	−	0.290686i
$356$	−10.1703	+	31.3011i	−0.539027	+	1.65895i
$357$	−1.81987	−	1.32221i	−0.0963177	−	0.0699789i
$358$	18.8514	+	13.6963i	0.996325	+	0.723873i
$359$	2.67339	−	8.22784i	0.141096	−	0.434249i	−0.855392	−	0.517981i	$-0.826684\pi$
$359$	2.67339	−	8.22784i	0.141096	−	0.434249i	0.996488	+	0.0837318i	$0.0266839\pi$
$360$	1.03482	+	3.18484i	0.0545396	+	0.167856i
$361$	14.7926	−	10.7474i	0.778556	−	0.565654i
$362$	12.6359			0.664131
$363$	14.1522	+	7.98585i	0.742797	+	0.419149i
$364$	14.3614			0.752740
$365$	4.35026	−	3.16065i	0.227703	−	0.165436i
$366$	−0.502668	−	1.54705i	−0.0262749	−	0.0808658i
$367$	−3.37879	+	10.3988i	−0.176371	+	0.542815i	−0.999693	−	0.0247595i	$-0.992118\pi$
$367$	−3.37879	+	10.3988i	−0.176371	+	0.542815i	0.823322	+	0.567574i	$0.192118\pi$
$368$	1.88538	+	1.36981i	0.0982823	+	0.0714063i
$369$	−2.19671	−	1.59600i	−0.114356	−	0.0830847i
$370$	6.99640	−	21.5327i	0.363726	−	1.11943i
$371$	−0.963962	−	2.96677i	−0.0500464	−	0.154027i
$372$	−37.7828	+	27.4508i	−1.95895	+	1.42326i
$373$	−29.2848			−1.51631			−0.758154	−	0.652076i	$-0.773898\pi$
$373$	−29.2848			−1.51631			−0.758154	+	0.652076i	$0.773898\pi$
$374$	4.38157	+	11.2484i	0.226566	+	0.581641i
$375$	−1.47726			−0.0762854
$376$	44.3615	−	32.2305i	2.28777	−	1.66216i
$377$	7.80542	+	24.0226i	0.402000	+	1.23723i
$378$	−4.16568	+	12.8206i	−0.214260	+	0.659423i
$379$	−26.3901	−	19.1736i	−1.35557	−	0.984879i	−0.998713	−	0.0507203i	$-0.983848\pi$
$379$	−26.3901	−	19.1736i	−1.35557	−	0.984879i	−0.356857	−	0.934159i	$-0.616152\pi$
$380$	2.54094	+	1.84610i	0.130347	+	0.0947030i
$381$	2.88088	−	8.86644i	0.147592	−	0.454241i
$382$	8.97893	+	27.6343i	0.459402	+	1.41389i
$383$	15.3328	−	11.1400i	0.783471	−	0.569225i	−0.122548	−	0.992463i	$-0.539106\pi$
$383$	15.3328	−	11.1400i	0.783471	−	0.569225i	0.906019	+	0.423238i	$0.139106\pi$
$384$	−30.6393			−1.56356
$385$	−2.79042	−	1.79264i	−0.142213	−	0.0913612i
$386$	−12.5195			−0.637226
$387$	2.17086	−	1.57722i	0.110351	−	0.0801747i
$388$	7.29149	+	22.4409i	0.370170	+	1.13926i
$389$	−12.0031	+	36.9416i	−0.608580	+	1.87302i	−0.138574	+	0.990352i	$0.544252\pi$
$389$	−12.0031	+	36.9416i	−0.608580	+	1.87302i	−0.470006	+	0.882663i	$0.655748\pi$
$390$	−11.0482	−	8.02698i	−0.559447	−	0.406462i
$391$	−1.21540	−	0.883037i	−0.0614652	−	0.0446571i
$392$	−1.26552	+	3.89486i	−0.0639182	+	0.196720i
$393$	−5.43481	−	16.7266i	−0.274150	−	0.843746i
$394$	−6.79930	+	4.93998i	−0.342544	+	0.248873i
$395$	−5.72825			−0.288220
$396$	7.79500	−	6.37612i	0.391714	−	0.320412i
$397$	−7.29557			−0.366154			−0.183077	−	0.983099i	$-0.558606\pi$
$397$	−7.29557			−0.366154			−0.183077	+	0.983099i	$0.558606\pi$
$398$	14.7672	−	10.7290i	0.740211	−	0.537794i
$399$	0.386111	+	1.18833i	0.0193297	+	0.0594909i
$400$	0.729944	−	2.24654i	0.0364972	−	0.112327i
$401$	30.4424	+	22.1177i	1.52022	+	1.10451i	0.961377	+	0.275236i	$0.0887559\pi$
$401$	30.4424	+	22.1177i	1.52022	+	1.10451i	0.558847	+	0.829271i	$0.311244\pi$
$402$	28.8939	+	20.9926i	1.44110	+	1.04702i
$403$	−10.1749	+	31.3152i	−0.506849	+	1.55992i
$404$	−8.60682	−	26.4891i	−0.428205	−	1.31788i
$405$	4.75561	−	3.45515i	0.236308	−	0.171688i
$406$	−15.6108			−0.774753
$407$	−31.3640	+	1.79872i	−1.55466	+	0.0891595i
$408$	−9.21229			−0.456077
$409$	15.6164	−	11.3460i	0.772182	−	0.561023i	−0.130440	−	0.991456i	$-0.541639\pi$
$409$	15.6164	−	11.3460i	0.772182	−	0.561023i	0.902623	+	0.430433i	$0.141639\pi$
$410$	2.45271	+	7.54868i	0.121131	+	0.372803i
$411$	−9.92251	+	30.5383i	−0.489441	+	1.50635i
$412$	19.2068	+	13.9545i	0.946250	+	0.687491i
$413$	5.15059	+	3.74212i	0.253444	+	0.184138i
$414$	−0.595878	+	1.83392i	−0.0292858	+	0.0901324i
$415$	3.78213	+	11.6402i	0.185658	+	0.571395i
$416$	−7.96128	+	5.78421i	−0.390334	+	0.283594i
$417$	11.0400			0.540632
$418$	1.70351	−	6.48524i	0.0833214	−	0.317203i
$419$	18.1588			0.887114			0.443557	−	0.896246i	$-0.353716\pi$
$419$	18.1588			0.887114			0.443557	+	0.896246i	$0.353716\pi$
$420$	4.43790	−	3.22433i	0.216548	−	0.157331i
$421$	−6.04678	−	18.6101i	−0.294702	−	0.907000i	−0.983321	−	0.181877i	$-0.941783\pi$
$421$	−6.04678	−	18.6101i	−0.294702	−	0.907000i	0.688619	−	0.725123i	$-0.258217\pi$
$422$	−15.7922	+	48.6034i	−0.768752	+	2.36598i
$423$	8.85761	+	6.43543i	0.430672	+	0.312901i
$424$	−10.3352	−	7.50898i	−0.501923	−	0.364668i
$425$	−0.470553	+	1.44821i	−0.0228252	+	0.0702486i
$426$	−6.28371	−	19.3393i	−0.304447	−	0.936991i
$427$	0.372697	−	0.270780i	0.0180360	−	0.0131040i
$428$	53.0860			2.56601
$429$	−4.81411	+	18.3272i	−0.232427	+	0.884847i
$430$	−7.84374			−0.378259
$431$	24.5407	−	17.8299i	1.18209	−	0.858835i	0.189680	−	0.981846i	$-0.439255\pi$
$431$	24.5407	−	17.8299i	1.18209	−	0.858835i	0.992405	+	0.123011i	$0.0392550\pi$
$432$	4.11669	+	12.6699i	0.198065	+	0.609580i
$433$	−2.55622	+	7.86723i	−0.122844	+	0.378075i	−0.993502	−	0.113814i	$-0.963693\pi$
$433$	−2.55622	+	7.86723i	−0.122844	+	0.378075i	0.870658	+	0.491889i	$0.163693\pi$
$434$	−16.4634	−	11.9613i	−0.790267	−	0.574162i
$435$	7.80542	+	5.67097i	0.374241	+	0.271902i
$436$	−17.9272	+	55.1743i	−0.858557	+	2.64237i
$437$	0.257864	+	0.793623i	0.0123353	+	0.0379641i
$438$	15.3609	−	11.1604i	0.733973	−	0.533262i
$439$	−2.08907			−0.0997059			−0.0498530	−	0.998757i	$-0.515875\pi$
$439$	−2.08907			−0.0997059			−0.0498530	+	0.998757i	$0.515875\pi$
$440$	−13.5603	+	0.777682i	−0.646461	+	0.0370745i
$441$	−0.817703			−0.0389382
$442$	−11.3883	+	8.27411i	−0.541688	+	0.393559i
$443$	5.07973	+	15.6338i	0.241345	+	0.742784i	0.996216	+	0.0869107i	$0.0276995\pi$
$443$	5.07973	+	15.6338i	0.241345	+	0.742784i	−0.754871	+	0.655873i	$0.772301\pi$
$444$	16.0565	−	49.4168i	0.762007	−	2.34522i
$445$	7.17047	+	5.20965i	0.339913	+	0.246961i
$446$	47.2311	+	34.3154i	2.23646	+	1.62488i
$447$	−4.35410	+	13.4005i	−0.205942	+	0.633824i
$448$	−3.33929	−	10.2773i	−0.157767	−	0.485556i
$449$	7.20106	−	5.23188i	0.339839	−	0.246908i	−0.404755	−	0.914425i	$-0.632643\pi$
$449$	7.20106	−	5.23188i	0.339839	−	0.246908i	0.744594	+	0.667518i	$0.232643\pi$
$450$	1.95452			0.0921370
$451$	8.52466	−	6.97296i	0.401411	−	0.328344i
$452$	−53.4120			−2.51229
$453$	13.0287	−	9.46587i	0.612140	−	0.444746i
$454$	−17.6210	−	54.2319i	−0.826996	−	2.54523i
$455$	1.19513	−	3.67823i	0.0560285	−	0.172438i
$456$	4.13974	+	3.00770i	0.193861	+	0.140848i
$457$	−5.34400	−	3.88265i	−0.249982	−	0.181623i	0.455737	−	0.890115i	$-0.349376\pi$
$457$	−5.34400	−	3.88265i	−0.249982	−	0.181623i	−0.705719	+	0.708492i	$0.749376\pi$
$458$	−0.709355	+	2.18317i	−0.0331460	+	0.102013i
$459$	−2.65379	−	8.16754i	−0.123868	−	0.381228i
$460$	2.96385	−	2.15336i	0.138190	−	0.100401i
$461$	19.8327			0.923701			0.461851	−	0.886958i	$-0.347186\pi$
$461$	19.8327			0.923701			0.461851	+	0.886958i	$0.347186\pi$
$462$	−9.85307	−	6.32985i	−0.458406	−	0.294491i
$463$	10.7257			0.498465			0.249233	−	0.968444i	$-0.419822\pi$
$463$	10.7257			0.498465			0.249233	+	0.968444i	$0.419822\pi$
$464$	−12.4809	+	9.06792i	−0.579412	+	0.420968i
$465$	3.88647	+	11.9613i	0.180231	+	0.554693i
$466$	18.8296	−	57.9515i	0.872263	−	2.68455i
$467$	−15.5123	−	11.2703i	−0.717823	−	0.521529i	0.167865	−	0.985810i	$-0.446313\pi$
$467$	−15.5123	−	11.2703i	−0.717823	−	0.521529i	−0.885688	+	0.464281i	$0.846313\pi$
$468$	9.50055	+	6.90255i	0.439163	+	0.319071i
$469$	−3.12557	+	9.61951i	−0.144325	+	0.444188i
$470$	−9.88986	−	30.4379i	−0.456185	−	1.40399i
$471$	0.0723654	−	0.0525766i	0.00333442	−	0.00242260i
$472$	26.0726			1.20009
$473$	3.95037	+	10.1414i	0.181638	+	0.466304i
$474$	−20.2266			−0.929040
$475$	0.684276	−	0.497155i	0.0313967	−	0.0228110i
$476$	−1.74732	−	5.37769i	−0.0800881	−	0.246486i
$477$	0.788234	−	2.42594i	0.0360908	−	0.111076i
$478$	−45.4051	−	32.9888i	−2.07678	−	1.50887i
$479$	1.39074	+	1.01043i	0.0635446	+	0.0461679i	0.619104	−	0.785309i	$-0.287496\pi$
$479$	1.39074	+	1.01043i	0.0635446	+	0.0461679i	−0.555559	+	0.831477i	$0.687496\pi$
$480$	−1.16154	+	3.57484i	−0.0530166	+	0.163168i
$481$	−11.3204	−	34.8407i	−0.516167	−	1.58860i
$482$	−25.3051	+	18.3852i	−1.15262	+	0.837425i
$483$	1.45744			0.0663159
$484$	16.9807	+	37.1497i	0.771851	+	1.68862i
$485$	6.35435			0.288536
$486$	−15.9255	+	11.5705i	−0.722395	+	0.524851i
$487$	−4.98472	−	15.3414i	−0.225879	−	0.695185i	−0.998201	−	0.0599537i	$-0.980905\pi$
$487$	−4.98472	−	15.3414i	−0.225879	−	0.695185i	0.772322	−	0.635231i	$-0.219095\pi$
$488$	0.582995	−	1.79428i	0.0263910	−	0.0812230i
$489$	15.2680	+	11.0928i	0.690441	+	0.501635i
$490$	1.93376	+	1.40496i	0.0873583	+	0.0634695i
$491$	−5.57370	+	17.1541i	−0.251538	+	0.774154i	0.742954	+	0.669342i	$0.233424\pi$
$491$	−5.57370	+	17.1541i	−0.251538	+	0.774154i	−0.994492	+	0.104812i	$0.966576\pi$
$492$	5.62889	+	17.3239i	0.253770	+	0.781023i
$493$	8.04572	−	5.84556i	0.362361	−	0.263271i
$494$	7.81898			0.351793
$495$	−0.984362	−	2.52706i	−0.0442438	−	0.113583i
$496$	−20.1105			−0.902989
$497$	4.65897	−	3.38494i	0.208984	−	0.151835i
$498$	13.3548	+	41.1019i	0.598444	+	1.84182i
$499$	−2.27763	+	7.00981i	−0.101961	+	0.313802i	−0.989005	−	0.147882i	$-0.952755\pi$
$499$	−2.27763	+	7.00981i	−0.101961	+	0.313802i	0.887045	+	0.461684i	$0.152755\pi$
$500$	−3.00415	−	2.18264i	−0.134349	−	0.0976106i
$501$	−24.0135	−	17.4469i	−1.07285	−	0.779468i
$502$	9.15240	−	28.1682i	0.408492	−	1.25721i
$503$	−11.1260	−	34.2424i	−0.496086	−	1.52680i	−0.815258	−	0.579098i	$-0.803405\pi$
$503$	−11.1260	−	34.2424i	−0.496086	−	1.52680i	0.319172	−	0.947697i	$-0.396595\pi$
$504$	−2.70918	+	1.96834i	−0.120677	+	0.0876767i
$505$	−7.50062			−0.333773
$506$	−6.58035	−	4.22738i	−0.292532	−	0.187930i
$507$	−2.89201			−0.128439
$508$	18.9586	−	13.7743i	0.841153	−	0.611134i
$509$	−10.5385	−	32.4340i	−0.467109	−	1.43761i	−0.856311	−	0.516461i	$-0.827249\pi$
$509$	−10.5385	−	32.4340i	−0.467109	−	1.43761i	0.389202	−	0.921153i	$-0.372751\pi$
$510$	−1.66154	+	5.11368i	−0.0735740	+	0.226438i
$511$	4.35026	+	3.16065i	0.192444	+	0.139819i
$512$	−20.5148	−	14.9049i	−0.906637	−	0.658710i
$513$	−1.47406	+	4.53669i	−0.0650813	+	0.200300i
$514$	−13.5921	−	41.8321i	−0.599520	−	1.84513i
$515$	5.17239	−	3.75796i	0.227923	−	0.165596i
$516$	−18.0011			−0.792454
$517$	−34.3732	+	28.1165i	−1.51173	+	1.23656i
$518$	22.6408			0.994781
$519$	8.81627	−	6.40540i	0.386991	−	0.281166i
$520$	−4.89440	−	15.0634i	−0.214634	−	0.660575i
$521$	10.6919	−	32.9064i	0.468422	−	1.44165i	−0.386206	−	0.922413i	$-0.626215\pi$
$521$	10.6919	−	32.9064i	0.468422	−	1.44165i	0.854628	−	0.519242i	$-0.173785\pi$
$522$	−10.3271	−	7.50310i	−0.452006	−	0.328402i
$523$	34.5295	+	25.0871i	1.50987	+	1.09698i	0.966235	+	0.257661i	$0.0829517\pi$
$523$	34.5295	+	25.0871i	1.50987	+	1.09698i	0.543633	+	0.839323i	$0.317048\pi$
$524$	13.6613	−	42.0450i	0.596795	−	1.83675i
$525$	−0.456498	−	1.40496i	−0.0199232	−	0.0613174i
$526$	−19.0045	+	13.8076i	−0.828636	+	0.602039i
$527$	12.9641			0.564725
$528$	−11.5544	+	0.662645i	−0.502841	+	0.0288379i
$529$	−22.0266			−0.957680
$530$	−6.03225	+	4.38269i	−0.262024	+	0.190372i
$531$	1.60871	+	4.95110i	0.0698120	+	0.214859i
$532$	−0.970553	+	2.98705i	−0.0420788	+	0.129505i
$533$	10.3899	+	7.54868i	0.450035	+	0.326969i
$534$	25.3191	+	18.3954i	1.09567	+	0.796048i
$535$	4.41773	−	13.5964i	0.190995	−	0.587822i
$536$	12.8001	+	39.3947i	0.552881	+	1.70159i
$537$	11.6508	−	8.46479i	0.502768	−	0.365283i
$538$	21.4312			0.923963
$539$	0.842610	−	3.20780i	0.0362938	−	0.138170i
$540$	20.9422			0.901209
$541$	−11.4549	+	8.32250i	−0.492486	+	0.357812i	−0.806140	−	0.591725i	$-0.798447\pi$
$541$	−11.4549	+	8.32250i	−0.492486	+	0.357812i	0.313653	+	0.949538i	$0.398447\pi$
$542$	5.69927	+	17.5406i	0.244805	+	0.753432i
$543$	2.41325	−	7.42722i	0.103563	−	0.318733i
$544$	3.13456	+	2.27739i	0.134393	+	0.0976423i
$545$	12.6393	+	9.18302i	0.541410	+	0.393357i
$546$	4.22004	−	12.9879i	0.180601	−	0.555832i
$547$	−12.2499	−	37.7012i	−0.523767	−	1.61199i	−0.766741	−	0.641956i	$-0.778123\pi$
$547$	−12.2499	−	37.7012i	−0.523767	−	1.61199i	0.242974	−	0.970033i	$-0.421877\pi$
$548$	−65.2985	+	47.4421i	−2.78941	+	2.02663i
$549$	0.376698			0.0160771
$550$	−2.01405	+	7.66748i	−0.0858796	+	0.326942i
$551$	−5.52402			−0.235331
$552$	4.82874	−	3.50829i	0.205525	−	0.149323i
$553$	−1.77013	−	5.44789i	−0.0752735	−	0.231668i
$554$	−2.16342	+	6.65833i	−0.0919151	+	0.282886i
$555$	−11.3204	−	8.22477i	−0.480525	−	0.349122i
$556$	22.4509	+	16.3115i	0.952130	+	0.691763i
$557$	−6.76188	+	20.8109i	−0.286510	+	0.881787i	0.699432	+	0.714699i	$0.253436\pi$
$557$	−6.76188	+	20.8109i	−0.286510	+	0.881787i	−0.985942	+	0.167088i	$0.946564\pi$
$558$	−5.14208	−	15.8257i	−0.217682	−	0.669955i
$559$	−10.2676	+	7.45984i	−0.434273	+	0.315518i
$560$	2.36215			0.0998190
$561$	7.44845	−	0.427169i	0.314474	−	0.0180351i
$562$	−68.8242			−2.90317
$563$	−11.1289	+	8.08563i	−0.469028	+	0.340769i	−0.797062	−	0.603897i	$-0.793614\pi$
$563$	−11.1289	+	8.08563i	−0.469028	+	0.340769i	0.328034	+	0.944666i	$0.393614\pi$
$564$	−22.6969	−	69.8538i	−0.955710	−	2.94137i
$565$	−4.44486	+	13.6799i	−0.186996	+	0.575516i
$566$	−55.9506	−	40.6505i	−2.35178	−	1.70867i
$567$	4.75561	+	3.45515i	0.199717	+	0.145103i
$568$	7.28786	−	22.4297i	0.305792	−	0.941130i
$569$	−4.55812	−	14.0284i	−0.191086	−	0.588103i	−1.00000		0.000175504i	$-0.999944\pi$
$569$	−4.55812	−	14.0284i	−0.191086	−	0.588103i	0.808914	−	0.587927i	$-0.200056\pi$
$570$	2.41620	−	1.75547i	0.101203	−	0.0735286i
$571$	32.3734			1.35478			0.677392	−	0.735622i	$-0.263110\pi$
$571$	32.3734			1.35478			0.677392	+	0.735622i	$0.263110\pi$
$572$	−36.8683	+	30.1573i	−1.54154	+	1.26094i
$573$	17.9579			0.750200
$574$	−6.42129	+	4.66534i	−0.268019	+	0.194727i
$575$	−0.304872	−	0.938298i	−0.0127140	−	0.0391297i
$576$	2.73055	−	8.40377i	0.113773	−	0.350157i
$577$	−4.82741	−	3.50732i	−0.200968	−	0.146011i	0.482750	−	0.875758i	$-0.339638\pi$
$577$	−4.82741	−	3.50732i	−0.200968	−	0.146011i	−0.683718	+	0.729747i	$0.739638\pi$
$578$	−28.3900	−	20.6266i	−1.18087	−	0.857952i
$579$	−2.39101	+	7.35878i	−0.0993671	+	0.305820i
$580$	7.49424	+	23.0649i	0.311181	+	0.957717i
$581$	−9.90175	+	7.19404i	−0.410794	+	0.298459i
$582$	22.4374			0.930060
$583$	8.70457	+	5.59203i	0.360506	+	0.231598i
$584$	22.0213			0.911248
$585$	2.55850	−	1.85886i	0.105781	−	0.0768544i
$586$	−14.3090	−	44.0385i	−0.591099	−	1.81921i
$587$	−11.8278	+	36.4023i	−0.488186	+	1.50248i	0.339127	+	0.940741i	$0.389868\pi$
$587$	−11.8278	+	36.4023i	−0.488186	+	1.50248i	−0.827313	+	0.561741i	$0.810132\pi$
$588$	4.43790	+	3.22433i	0.183016	+	0.132969i
$589$	−5.82569	−	4.23261i	−0.240043	−	0.174402i
$590$	4.70248	−	14.4727i	0.193598	−	0.595833i
$591$	1.60510	+	4.93998i	0.0660248	+	0.203204i
$592$	18.1014	−	13.1515i	0.743964	−	0.540522i
$593$	−46.1732			−1.89611			−0.948053	−	0.318112i	$-0.896951\pi$
$593$	−46.1732			−1.89611			−0.948053	+	0.318112i	$0.896951\pi$
$594$	−16.2279	−	41.6605i	−0.665840	−	1.70935i
$595$	−1.52274			−0.0624263
$596$	−28.6537	+	20.8181i	−1.17370	+	0.852743i
$597$	−3.48605	−	10.7290i	−0.142675	−	0.439107i
$598$	2.81834	−	8.67397i	0.115251	−	0.354705i
$599$	−26.6274	−	19.3459i	−1.08797	−	0.790454i	−0.108911	−	0.994051i	$-0.534736\pi$
$599$	−26.6274	−	19.3459i	−1.08797	−	0.790454i	−0.979055	+	0.203598i	$0.934736\pi$
$600$	−4.89440	−	3.55599i	−0.199813	−	0.145173i
$601$	0.971287	−	2.98931i	0.0396196	−	0.121937i	−0.929290	−	0.369350i	$-0.879580\pi$
$601$	0.971287	−	2.98931i	0.0396196	−	0.121937i	0.968910	+	0.247413i	$0.0795805\pi$
$602$	−2.42385	−	7.45984i	−0.0987887	−	0.304040i
$603$	−6.69114	+	4.86140i	−0.272484	+	0.197971i
$604$	40.4807			1.64714
$605$	10.9279	−	1.25756i	0.444281	−	0.0511272i
$606$	−26.4849			−1.07588
$607$	−8.21766	+	5.97048i	−0.333545	+	0.242334i	−0.741933	−	0.670474i	$-0.766091\pi$
$607$	−8.21766	+	5.97048i	−0.333545	+	0.242334i	0.408389	+	0.912808i	$0.366091\pi$
$608$	−0.665042	−	2.04679i	−0.0269710	−	0.0830082i
$609$	−2.98141	+	9.17582i	−0.120813	+	0.371823i
$610$	−0.890840	−	0.647233i	−0.0360691	−	0.0262057i
$611$	−41.8941	−	30.4379i	−1.69485	−	1.23138i
$612$	1.42879	−	4.39735i	0.0577552	−	0.177752i
$613$	2.82963	+	8.70870i	0.114288	+	0.351741i	0.991798	−	0.127817i	$-0.0407970\pi$
$613$	2.82963	+	8.70870i	0.114288	+	0.351741i	−0.877510	+	0.479558i	$0.840797\pi$
$614$	−33.4249	+	24.2846i	−1.34892	+	0.980048i
$615$	4.90543			0.197806
$616$	−4.92997	−	12.6563i	−0.198634	−	0.509936i
$617$	37.1224			1.49449			0.747245	−	0.664548i	$-0.231376\pi$
$617$	37.1224			1.49449			0.747245	+	0.664548i	$0.231376\pi$
$618$	18.2639	−	13.2695i	0.734680	−	0.533777i
$619$	1.05262	+	3.23963i	0.0423084	+	0.130212i	0.969980	−	0.243186i	$-0.0781926\pi$
$619$	1.05262	+	3.23963i	0.0423084	+	0.130212i	−0.927671	+	0.373398i	$0.878193\pi$
$620$	−9.76927	+	30.0667i	−0.392343	+	1.20751i
$621$	4.50144	+	3.27049i	0.180636	+	0.131240i
$622$	38.3097	+	27.8336i	1.53608	+	1.11603i
$623$	−2.73887	+	8.42939i	−0.109731	+	0.337716i
$624$	−4.17041	−	12.8352i	−0.166950	−	0.513819i
$625$	−0.809017	+	0.587785i	−0.0323607	+	0.0235114i
$626$	72.7606			2.90810
$627$	−3.48659	−	2.23987i	−0.139241	−	0.0894517i
$628$	0.224843			0.00897222
$629$	−11.6689	+	8.47798i	−0.465271	+	0.338039i
$630$	0.603980	+	1.85886i	0.0240631	+	0.0740587i
$631$	−3.00580	+	9.25090i	−0.119659	+	0.368273i	−0.992890	−	0.119033i	$-0.962020\pi$
$631$	−3.00580	+	9.25090i	−0.119659	+	0.368273i	0.873231	+	0.487306i	$0.162020\pi$
$632$	−18.9786	−	13.7888i	−0.754930	−	0.548488i
$633$	25.5523	+	18.5648i	1.01561	+	0.737886i
$634$	3.21477	−	9.89406i	0.127675	−	0.392943i
$635$	−1.95015	−	6.00195i	−0.0773894	−	0.238180i
$636$	−13.8438	+	10.0581i	−0.548942	+	0.398830i
$637$	3.86752			0.153237
$638$	40.0759	−	32.7811i	1.58662	−	1.29782i
$639$	4.70899			0.186285
$640$	−16.7795	+	12.1910i	−0.663269	+	0.481893i
$641$	−5.44029	−	16.7435i	−0.214879	−	0.661329i	−0.999162	−	0.0409260i	$-0.986969\pi$
$641$	−5.44029	−	16.7435i	−0.214879	−	0.661329i	0.784283	−	0.620403i	$-0.213031\pi$
$642$	15.5991	−	48.0092i	0.615648	−	1.89477i
$643$	−30.8947	−	22.4463i	−1.21837	−	0.885196i	−0.222405	−	0.974954i	$-0.571391\pi$
$643$	−30.8947	−	22.4463i	−1.21837	−	0.885196i	−0.995964	+	0.0897579i	$0.971391\pi$
$644$	2.96385	+	2.15336i	0.116792	+	0.0848543i
$645$	−1.49802	+	4.61044i	−0.0589845	+	0.181536i
$646$	−0.951319	−	2.92786i	−0.0374291	−	0.115195i
$647$	15.2665	−	11.0917i	0.600186	−	0.436061i	−0.245759	−	0.969331i	$-0.579037\pi$
$647$	15.2665	−	11.0917i	0.600186	−	0.436061i	0.845945	+	0.533270i	$0.179037\pi$
$648$	24.0732			0.945684
$649$	−21.0806	+	1.20897i	−0.827486	+	0.0474563i
$650$	−9.24436			−0.362594
$651$	−10.1749	+	7.39251i	−0.398786	+	0.289735i
$652$	14.6593	+	45.1165i	0.574101	+	1.76690i
$653$	5.05751	−	15.5654i	0.197916	−	0.609122i	−0.802014	−	0.597305i	$-0.796238\pi$
$653$	5.05751	−	15.5654i	0.197916	−	0.609122i	0.999930	−	0.0118173i	$-0.00376165\pi$
$654$	44.6299	+	32.4255i	1.74517	+	1.26794i
$655$	−9.63169	−	6.99783i	−0.376341	−	0.273428i
$656$	−2.42387	+	7.45991i	−0.0946363	+	0.291260i
$657$	1.35874	+	4.18176i	0.0530094	+	0.163146i
$658$	25.8920	−	18.8116i	1.00938	−	0.733354i
$659$	−5.42317			−0.211257			−0.105628	−	0.994406i	$-0.533685\pi$
$659$	−5.42317			−0.211257			−0.105628	+	0.994406i	$0.533685\pi$
$660$	−4.62218	+	17.5966i	−0.179918	+	0.684946i
$661$	−17.4333			−0.678077			−0.339039	−	0.940772i	$-0.610102\pi$
$661$	−17.4333			−0.678077			−0.339039	+	0.940772i	$0.610102\pi$
$662$	14.4024	−	10.4639i	0.559765	−	0.406693i
$663$	2.68842	+	8.27411i	0.104410	+	0.321340i
$664$	−15.4889	+	47.6701i	−0.601087	+	1.84996i
$665$	0.684276	+	0.497155i	0.0265351	+	0.0192789i
$666$	14.9777	+	10.8819i	0.580375	+	0.421667i
$667$	−1.99113	+	6.12805i	−0.0770967	+	0.237279i
$668$	−23.0562	−	70.9596i	−0.892070	−	2.74551i
$669$	29.1904	−	21.2081i	1.12857	−	0.819952i
$670$	24.1764			0.934015
$671$	−0.388172	+	1.47777i	−0.0149852	+	0.0570485i
$672$	−3.75881			−0.144999
$673$	1.98747	−	1.44398i	0.0766115	−	0.0556615i	−0.548820	−	0.835940i	$-0.684923\pi$
$673$	1.98747	−	1.44398i	0.0766115	−	0.0556615i	0.625432	+	0.780279i	$0.284923\pi$
$674$	−17.2857	−	53.1999i	−0.665821	−	2.04919i
$675$	1.74278	−	5.36371i	0.0670795	−	0.206449i
$676$	−5.88118	−	4.27292i	−0.226199	−	0.164343i
$677$	−17.8596	−	12.9758i	−0.686401	−	0.498700i	0.189074	−	0.981963i	$-0.439451\pi$
$677$	−17.8596	−	12.9758i	−0.686401	−	0.498700i	−0.875475	+	0.483263i	$0.839451\pi$
$678$	−15.6949	+	48.3040i	−0.602760	+	1.85510i
$679$	1.96360	+	6.04334i	0.0753561	+	0.231922i
$680$	−5.04508	+	3.66547i	−0.193470	+	0.140564i
$681$	−35.2421			−1.35048
$682$	67.3820	−	3.86436i	2.58019	−	0.147974i
$683$	0.861150			0.0329510			0.0164755	−	0.999864i	$-0.494755\pi$
$683$	0.861150			0.0329510			0.0164755	+	0.999864i	$0.494755\pi$
$684$	−2.07773	+	1.50956i	−0.0794441	+	0.0577195i
$685$	6.71683	+	20.6723i	0.256637	+	0.789848i
$686$	−0.738630	+	2.27327i	−0.0282010	+	0.0867938i
$687$	1.14776	+	0.833896i	0.0437898	+	0.0318151i
$688$	−6.27110	−	4.55622i	−0.239083	−	0.173704i
$689$	−3.72814	+	11.4740i	−0.142031	+	0.437126i
$690$	−1.07651	−	3.31316i	−0.0409821	−	0.126130i
$691$	−19.4307	+	14.1172i	−0.739179	+	0.537045i	−0.892454	−	0.451139i	$-0.851018\pi$
$691$	−19.4307	+	14.1172i	−0.739179	+	0.537045i	0.153275	+	0.988184i	$0.451018\pi$
$692$	27.3926			1.04131
$693$	2.09920	−	1.71709i	0.0797418	−	0.0652269i
$694$	55.9116			2.12238
$695$	6.04603	−	4.39270i	0.229339	−	0.166625i
$696$	12.2097	+	37.5777i	0.462809	+	1.42438i
$697$	1.56253	−	4.80897i	0.0591850	−	0.182153i
$698$	−3.96430	−	2.88023i	−0.150051	−	0.109018i
$699$	−30.4669	−	22.1355i	−1.15236	−	0.837241i
$700$	1.14748	−	3.53158i	0.0433707	−	0.133481i
$701$	3.50582	+	10.7898i	0.132413	+	0.407526i	0.995179	−	0.0980786i	$-0.0312697\pi$
$701$	3.50582	+	10.7898i	0.132413	+	0.407526i	−0.862766	+	0.505604i	$0.831270\pi$
$702$	42.1787	−	30.6446i	1.59193	−	1.15661i
$703$	8.01164			0.302165
$704$	30.1538	+	19.3715i	1.13646	+	0.730092i
$705$	−19.7797			−0.744947
$706$	−37.4844	+	27.2340i	−1.41074	+	1.02496i
$707$	−2.31782	−	7.13351i	−0.0871706	−	0.268283i
$708$	10.7920	−	33.2144i	0.405588	−	1.24827i
$709$	35.5355	+	25.8181i	1.33457	+	0.969618i	0.999625	+	0.0273790i	$0.00871609\pi$
$709$	35.5355	+	25.8181i	1.33457	+	0.969618i	0.334940	+	0.942239i	$0.391284\pi$
$710$	−11.1361	−	8.09088i	−0.417932	−	0.303645i
$711$	1.44744	−	4.45476i	0.0542832	−	0.167066i
$712$	11.2165	+	34.5208i	0.420356	+	1.29372i
$713$	−6.79530	+	4.93707i	−0.254486	+	0.184895i
$714$	−5.37684			−0.201223
$715$	4.65577	+	11.9523i	0.174116	+	0.446992i
$716$	36.1996			1.35284
$717$	−28.0619	+	20.3882i	−1.04799	+	0.761410i
$718$	−6.39008	−	19.6667i	−0.238476	−	0.733953i
$719$	−3.02238	+	9.30193i	−0.112716	+	0.346903i	−0.991464	−	0.130383i	$-0.958379\pi$
$719$	−3.02238	+	9.30193i	−0.112716	+	0.346903i	0.878748	+	0.477286i	$0.158379\pi$
$720$	1.56265	+	1.13533i	0.0582364	+	0.0423112i
$721$	5.17239	+	3.75796i	0.192630	+	0.139954i
$722$	13.5056	−	41.5658i	0.502625	−	1.54692i
$723$	5.97373	+	18.3852i	0.222165	+	0.683755i
$724$	15.8812	−	11.5384i	0.590221	−	0.428821i
$725$	6.53103			0.242556
$726$	38.5867	−	4.44050i	1.43209	−	0.164802i
$727$	1.08785			0.0403460			0.0201730	−	0.999797i	$-0.493578\pi$
$727$	1.08785			0.0403460			0.0201730	+	0.999797i	$0.493578\pi$
$728$	12.8137	−	9.30971i	0.474908	−	0.345041i
$729$	9.20894	+	28.3422i	0.341072	+	1.04971i
$730$	3.97178	−	12.2239i	0.147002	−	0.452426i
$731$	4.04261	+	2.93713i	0.149521	+	0.108634i
$732$	−2.04445	−	1.48538i	−0.0755649	−	0.0549011i
$733$	−2.60001	+	8.00200i	−0.0960334	+	0.295561i	−0.987522	−	0.157483i	$-0.949662\pi$
$733$	−2.60001	+	8.00200i	−0.0960334	+	0.295561i	0.891488	+	0.453044i	$0.149662\pi$
$734$	8.07617	+	24.8559i	0.298097	+	0.917447i
$735$	1.19513	−	0.868312i	0.0440830	−	0.0320282i
$736$	−2.51031			−0.0925313
$737$	−12.1760	−	31.2584i	−0.448510	−	1.15142i
$738$	−6.49023			−0.238909
$739$	2.15958	−	1.56903i	0.0794416	−	0.0577177i	−0.547356	−	0.836900i	$-0.684365\pi$
$739$	2.15958	−	1.56903i	0.0794416	−	0.0577177i	0.626797	+	0.779182i	$0.284365\pi$
$740$	−10.8691	−	33.4517i	−0.399556	−	1.22971i
$741$	1.49329	−	4.59588i	0.0548575	−	0.168834i
$742$	−6.03225	−	4.38269i	−0.221451	−	0.160894i
$743$	−14.0794	−	10.2293i	−0.516524	−	0.375277i	0.298769	−	0.954326i	$-0.403424\pi$
$743$	−14.0794	−	10.2293i	−0.516524	−	0.375277i	−0.815293	+	0.579049i	$0.803424\pi$
$744$	−15.9162	+	48.9852i	−0.583518	+	1.79588i
$745$	2.94742	+	9.07122i	0.107985	+	0.332344i
$746$	−56.6297	+	41.1439i	−2.07336	+	1.50638i
$747$	−10.0081			−0.366176
$748$	15.7783	+	10.1363i	0.576910	+	0.370621i
$749$	14.2961			0.522367
$750$	−2.85666	+	2.07549i	−0.104311	+	0.0757861i
$751$	7.20446	+	22.1731i	0.262895	+	0.809106i	0.992171	+	0.124887i	$0.0398569\pi$
$751$	7.20446	+	22.1731i	0.262895	+	0.809106i	−0.729276	+	0.684219i	$0.760143\pi$
$752$	9.77356	−	30.0799i	0.356405	−	1.09690i
$753$	−14.8089	−	10.7593i	−0.539666	−	0.392090i
$754$	48.8446	+	35.4876i	1.77881	+	1.29238i
$755$	3.36874	−	10.3679i	0.122601	−	0.377327i
$756$	6.47150	+	19.9172i	0.235366	+	0.724382i
$757$	−10.5266	+	7.64801i	−0.382595	+	0.277972i	−0.762415	−	0.647089i	$-0.775986\pi$
$757$	−10.5266	+	7.64801i	−0.382595	+	0.277972i	0.379819	+	0.925061i	$0.375986\pi$
$758$	−77.9702			−2.83200
$759$	−3.74153	+	3.06048i	−0.135809	+	0.111088i
$760$	3.46385			0.125647
$761$	−11.1301	+	8.08650i	−0.403466	+	0.293135i	−0.770951	−	0.636894i	$-0.780219\pi$
$761$	−11.1301	+	8.08650i	−0.403466	+	0.293135i	0.367485	+	0.930029i	$0.380219\pi$
$762$	−6.88605	−	21.1931i	−0.249455	−	0.767744i
$763$	−4.82780	+	14.8584i	−0.174778	+	0.537912i
$764$	36.5190	+	26.5326i	1.32121	+	0.959915i
$765$	−1.00735	−	0.731880i	−0.0364207	−	0.0264612i
$766$	13.9988	−	43.0840i	0.505798	−	1.55669i
$767$	−7.60876	−	23.4174i	−0.274737	−	0.845552i
$768$	−33.4195	+	24.2807i	−1.20592	+	0.876154i
$769$	−32.1927			−1.16090			−0.580450	−	0.814296i	$-0.697123\pi$
$769$	−32.1927			−1.16090			−0.580450	+	0.814296i	$0.697123\pi$
$770$	−7.91458	+	0.453901i	−0.285222	+	0.0163575i
$771$	−27.1841			−0.979012
$772$	−15.7349	+	11.4321i	−0.566311	+	0.411449i
$773$	2.92829	+	9.01237i	0.105323	+	0.324152i	0.989806	−	0.142421i	$-0.0454886\pi$
$773$	2.92829	+	9.01237i	0.105323	+	0.324152i	−0.884483	+	0.466573i	$0.845489\pi$
$774$	1.98199	−	6.09993i	0.0712411	−	0.219258i
$775$	6.88769	+	5.00420i	0.247413	+	0.179756i
$776$	21.0530	+	15.2959i	0.755758	+	0.549090i
$777$	4.32402	−	13.3080i	0.155123	−	0.477420i
$778$	28.6904	+	88.3000i	1.02860	+	3.16571i
$779$	−2.27222	+	1.65087i	−0.0814108	+	0.0591484i
$780$	−21.2155			−0.759635
$781$	−4.85243	+	18.4731i	−0.173634	+	0.661021i
$782$	−3.59091			−0.128411
$783$	−29.7988	+	21.6501i	−1.06492	+	0.773711i
$784$	0.729944	+	2.24654i	0.0260694	+	0.0802335i
$785$	0.0187111	−	0.0575868i	0.000667827	−	0.00205536i
$786$	−34.0098	−	24.7096i	−1.21309	−	0.881361i
$787$	−29.3084	−	21.2938i	−1.04473	−	0.759042i	−0.0735280	−	0.997293i	$-0.523426\pi$
$787$	−29.3084	−	21.2938i	−1.04473	−	0.759042i	−0.971204	+	0.238251i	$0.923426\pi$
$788$	−4.03466	+	12.4174i	−0.143729	+	0.442352i
$789$	4.48636	+	13.8076i	0.159719	+	0.491563i
$790$	−11.0771	+	8.04796i	−0.394104	+	0.286333i
$791$	−14.3839			−0.511431
$792$	2.82168	−	10.7421i	0.100264	−	0.381703i
$793$	−1.78168			−0.0632693
$794$	−14.1079	+	10.2500i	−0.500670	+	0.363758i
$795$	1.42402	+	4.38269i	0.0505049	+	0.155438i
$796$	8.76275	−	26.9690i	0.310587	−	0.955890i
$797$	−8.04935	−	5.84819i	−0.285122	−	0.207154i	0.436026	−	0.899934i	$-0.356386\pi$
$797$	−8.04935	−	5.84819i	−0.285122	−	0.207154i	−0.721149	+	0.692780i	$0.756386\pi$
$798$	2.41620	+	1.75547i	0.0855325	+	0.0621430i
$799$	−6.30045	+	19.3908i	−0.222894	+	0.685997i
$800$	0.786277	+	2.41991i	0.0277991	+	0.0855568i
$801$	−5.86331	+	4.25994i	−0.207170	+	0.150518i
$802$	89.9428			3.17599
$803$	−17.8050	+	1.02111i	−0.628323	+	0.0360344i
$804$	55.4839			1.95677
$805$	0.798164	−	0.579900i	0.0281316	−	0.0204388i
$806$	24.3207	+	74.8513i	0.856659	+	2.63652i
$807$	4.09299	−	12.5969i	0.144080	−	0.443432i
$808$	−24.8508	−	18.0551i	−0.874247	−	0.635178i
$809$	−10.5350	−	7.65414i	−0.370392	−	0.269105i	0.386982	−	0.922087i	$-0.373518\pi$
$809$	−10.5350	−	7.65414i	−0.370392	−	0.269105i	−0.757373	+	0.652982i	$0.773518\pi$
$810$	4.34185	−	13.3629i	0.152557	−	0.469523i
$811$	−9.69373	−	29.8342i	−0.340393	−	1.04762i	−0.964004	−	0.265887i	$-0.914335\pi$
$811$	−9.69373	−	29.8342i	−0.340393	−	1.04762i	0.623611	−	0.781735i	$-0.285665\pi$
$812$	−19.6202	+	14.2549i	−0.688533	+	0.500248i
$813$	11.3985			0.399765
$814$	−58.1232	+	47.5434i	−2.03722	+	1.66639i
$815$	12.7752			0.447494
$816$	−4.29880	+	3.12326i	−0.150488	+	0.109336i
$817$	−0.857698	−	2.63972i	−0.0300071	−	0.0923522i
$818$	14.2577	−	43.8808i	0.498510	−	1.53426i
$819$	2.55850	+	1.85886i	0.0894012	+	0.0649538i
$820$	9.97564	+	7.24773i	0.348365	+	0.253102i
$821$	3.32495	−	10.2331i	0.116042	−	0.357139i	−0.876121	−	0.482091i	$-0.839878\pi$
$821$	3.32495	−	10.2331i	0.116042	−	0.357139i	0.992163	+	0.124952i	$0.0398776\pi$
$822$	23.7173	+	72.9945i	0.827238	+	2.54598i
$823$	38.3465	−	27.8604i	1.33668	−	0.971152i	0.337117	−	0.941463i	$-0.390548\pi$
$823$	38.3465	−	27.8604i	1.33668	−	0.971152i	0.999559	−	0.0296896i	$-0.00945187\pi$
$824$	26.1829			0.912126
$825$	4.12218	+	2.64819i	0.143516	+	0.0921981i
$826$	15.2175			0.529486
$827$	37.1648	−	27.0018i	1.29235	−	0.938945i	0.292498	−	0.956266i	$-0.405514\pi$
$827$	37.1648	−	27.0018i	1.29235	−	0.938945i	0.999850	+	0.0173209i	$0.00551368\pi$
$828$	0.925712	+	2.84905i	0.0321707	+	0.0990113i
$829$	−16.2560	+	50.0307i	−0.564593	+	1.73764i	0.104564	+	0.994518i	$0.466655\pi$
$829$	−16.2560	+	50.0307i	−0.564593	+	1.73764i	−0.669157	+	0.743121i	$0.733345\pi$
$830$	23.6677	+	17.1956i	0.821519	+	0.596868i
$831$	3.50049	+	2.54326i	0.121431	+	0.0882246i
$832$	−12.9148	+	39.7476i	−0.447739	+	1.37800i
$833$	−0.470553	−	1.44821i	−0.0163037	−	0.0501776i
$834$	21.3487	−	15.5107i	0.739246	−	0.537093i
$835$	−20.0928			−0.695342
$836$	−3.78091	−	9.70638i	−0.130765	−	0.335702i
$837$	−48.0148			−1.65964
$838$	35.1147	−	25.5123i	1.21302	−	0.881308i
$839$	−9.22859	−	28.4027i	−0.318606	−	0.980570i	−0.974244	−	0.225494i	$-0.927600\pi$
$839$	−9.22859	−	28.4027i	−0.318606	−	0.980570i	0.655638	−	0.755075i	$-0.272400\pi$
$840$	1.86950	−	5.75372i	0.0645037	−	0.198522i
$841$	−11.0466	−	8.02583i	−0.380918	−	0.276753i
$842$	−37.8394	−	27.4919i	−1.30403	−	0.947435i
$843$	−13.1442	+	40.4538i	−0.452712	+	1.39330i
$844$	24.5336	+	75.5066i	0.844481	+	2.59905i
$845$	−1.58380	+	1.15070i	−0.0544844	+	0.0395853i
$846$	26.1700			0.899742
$847$	4.57291	+	10.0044i	0.157127	+	0.343756i
$848$	−7.36859			−0.253039
$849$	−34.5794	+	25.1234i	−1.18676	+	0.862233i
$850$	1.12474	+	3.46160i	0.0385783	+	0.118732i
$851$	2.88778	−	8.88769i	0.0989920	−	0.304666i
$852$	−25.5570	−	18.5683i	−0.875570	−	0.636139i
$853$	42.6200	+	30.9652i	1.45928	+	1.06023i	0.983550	+	0.180638i	$0.0578163\pi$
$853$	42.6200	+	30.9652i	1.45928	+	1.06023i	0.475731	+	0.879591i	$0.342184\pi$
$854$	0.340271	−	1.04725i	0.0116438	−	0.0358360i
$855$	0.213723	+	0.657772i	0.00730917	+	0.0224953i
$856$	47.3652	−	34.4128i	1.61891	−	1.17621i
$857$	−0.0751683			−0.00256770			−0.00128385	−	0.999999i	$-0.500409\pi$
$857$	−0.0751683			−0.00256770			−0.00128385	+	0.999999i	$0.500409\pi$
$858$	16.4397	+	42.2041i	0.561241	+	1.44082i
$859$	32.9785			1.12521			0.562606	−	0.826725i	$-0.309799\pi$
$859$	32.9785			1.12521			0.562606	+	0.826725i	$0.309799\pi$
$860$	−9.85825	+	7.16244i	−0.336163	+	0.244237i
$861$	1.51586	+	4.66534i	0.0516604	+	0.158994i
$862$	22.4056	−	68.9574i	0.763138	−	2.34870i
$863$	41.3308	+	30.0285i	1.40692	+	1.02218i	0.993762	+	0.111522i	$0.0355726\pi$
$863$	41.3308	+	30.0285i	1.40692	+	1.02218i	0.413153	+	0.910662i	$0.364427\pi$
$864$	−11.6094	−	8.43473i	−0.394960	−	0.286955i
$865$	2.27957	−	7.01579i	0.0775077	−	0.238544i
$866$	6.11001	+	18.8047i	0.207627	+	0.639009i
$867$	−17.5460	+	12.7479i	−0.595893	+	0.432942i
$868$	−31.6140			−1.07305
$869$	15.9842	+	10.2687i	0.542229	+	0.348341i
$870$	23.0613			0.781850
$871$	31.6473	−	22.9931i	1.07233	−	0.779092i
$872$	19.7713	+	60.8497i	0.669539	+	2.06063i
$873$	−1.60564	+	4.94166i	−0.0543428	+	0.167250i
$874$	1.61365	+	1.17239i	0.0545826	+	0.0396566i
$875$	−0.809017	−	0.587785i	−0.0273498	−	0.0198708i
$876$	9.11508	−	28.0533i	0.307970	−	0.947834i
$877$	6.68017	+	20.5594i	0.225573	+	0.694243i	0.998233	+	0.0594226i	$0.0189259\pi$
$877$	6.68017	+	20.5594i	0.225573	+	0.694243i	−0.772660	+	0.634820i	$0.781074\pi$
$878$	−4.03976	+	2.93506i	−0.136335	+	0.0990534i
$879$	−28.6180			−0.965260
$880$	−6.06407	+	4.96026i	−0.204420	+	0.167210i
$881$	12.2075			0.411280			0.205640	−	0.978628i	$-0.434072\pi$
$881$	12.2075			0.411280			0.205640	+	0.978628i	$0.434072\pi$
$882$	−1.58124	+	1.14884i	−0.0532431	+	0.0386834i
$883$	0.732936	+	2.25574i	0.0246652	+	0.0759118i	0.962631	−	0.270815i	$-0.0872931\pi$
$883$	0.732936	+	2.25574i	0.0246652	+	0.0759118i	−0.937966	+	0.346727i	$0.887293\pi$
$884$	−6.75777	+	20.7983i	−0.227289	+	0.699522i
$885$	−7.60876	−	5.52809i	−0.255766	−	0.185825i
$886$	31.7878	+	23.0952i	1.06793	+	0.775898i
$887$	−3.14139	+	9.66819i	−0.105477	+	0.324626i	−0.989842	−	0.142170i	$-0.954592\pi$
$887$	−3.14139	+	9.66819i	−0.105477	+	0.324626i	0.884365	+	0.466796i	$0.154592\pi$
$888$	−17.7081	−	54.5000i	−0.594245	−	1.82890i
$889$	5.10556	−	3.70941i	0.171235	−	0.124410i
$890$	21.1853			0.710132
$891$	−19.4640	+	1.11626i	−0.652068	+	0.0373961i
$892$	90.6962			3.03674
$893$	9.16208	−	6.65664i	0.306597	−	0.222756i
$894$	10.4074	+	32.0308i	0.348076	+	1.07127i
$895$	3.01247	−	9.27143i	0.100696	−	0.309910i
$896$	−16.7795	−	12.1910i	−0.560565	−	0.407274i
$897$	−4.56017	−	3.31316i	−0.152260	−	0.110623i
$898$	6.57455	−	20.2344i	0.219396	−	0.675230i
$899$	−17.1823	−	52.8816i	−0.573061	−	1.76370i
$900$	2.45650	−	1.78475i	0.0818833	−	0.0594917i
$901$	4.75010			0.158249
$902$	6.68792	−	25.4608i	0.222683	−	0.847753i
$903$	−4.84770			−0.161321
$904$	−47.6560	+	34.6241i	−1.58502	+	1.15158i
$905$	−1.63360	−	5.02770i	−0.0543027	−	0.167126i
$906$	11.8951	−	36.6094i	0.395189	−	1.21627i
$907$	27.2434	+	19.7935i	0.904601	+	0.657231i	0.939644	−	0.342155i	$-0.111157\pi$
$907$	27.2434	+	19.7935i	0.904601	+	0.657231i	−0.0350426	+	0.999386i	$0.511157\pi$
$908$	−71.6680	−	52.0698i	−2.37839	−	1.72800i
$909$	1.89529	−	5.83310i	0.0628627	−	0.193472i
$910$	−2.85666	−	8.79191i	−0.0946975	−	0.291449i
$911$	−37.8360	+	27.4894i	−1.25356	+	0.910766i	−0.998423	−	0.0561389i	$-0.982121\pi$
$911$	−37.8360	+	27.4894i	−1.25356	+	0.910766i	−0.255138	+	0.966905i	$0.582121\pi$
$912$	2.95146			0.0977328
$913$	10.3129	−	39.2611i	0.341307	−	1.29935i
$914$	−15.7890			−0.522253
$915$	−0.550570	+	0.400012i	−0.0182013	+	0.0132240i
$916$	1.10200	+	3.39161i	0.0364112	+	0.112062i
$917$	3.67898	−	11.3227i	0.121491	−	0.373910i
$918$	−16.6068	−	12.0656i	−0.548107	−	0.398223i
$919$	4.46730	+	3.24568i	0.147362	+	0.107065i	0.659024	−	0.752122i	$-0.270970\pi$
$919$	4.46730	+	3.24568i	0.147362	+	0.107065i	−0.511661	+	0.859187i	$0.670970\pi$
$920$	1.24854	−	3.84261i	0.0411631	−	0.126687i
$921$	7.89055	+	24.2846i	0.260003	+	0.800205i
$922$	38.3517	−	27.8641i	1.26304	−	0.917656i
$923$	−22.2723			−0.733101
$924$	−18.1637	+	1.04169i	−0.597541	+	0.0342690i
$925$	−9.47214			−0.311442
$926$	20.7409	−	15.0692i	0.681589	−	0.495203i
$927$	1.61552	+	4.97205i	0.0530605	+	0.163303i
$928$	5.13520	−	15.8045i	0.168571	−	0.518809i
$929$	3.73103	+	2.71075i	0.122411	+	0.0889370i	0.647306	−	0.762230i	$-0.275895\pi$
$929$	3.73103	+	2.71075i	0.122411	+	0.0889370i	−0.524895	+	0.851167i	$0.675895\pi$
$930$	24.3207	+	17.6700i	0.797506	+	0.579422i
$931$	−0.261370	+	0.804414i	−0.00856606	+	0.0263636i
$932$	−29.2522	−	90.0291i	−0.958189	−	2.94900i
$933$	23.6767	−	17.2021i	0.775140	−	0.563172i
$934$	−45.8314			−1.49965
$935$	3.90916	−	3.19759i	0.127843	−	0.104572i
$936$	12.9513			0.423326
$937$	0.647948	−	0.470762i	0.0211676	−	0.0153791i	−0.577151	−	0.816637i	$-0.695836\pi$
$937$	0.647948	−	0.470762i	0.0211676	−	0.0153791i	0.598319	+	0.801258i	$0.295836\pi$
$938$	7.47091	+	22.9931i	0.243934	+	0.750752i
$939$	13.8960	−	42.7676i	0.453480	−	1.39567i
$940$	−40.2239	−	29.2244i	−1.31196	−	0.953194i
$941$	−0.455276	−	0.330777i	−0.0148416	−	0.0107830i	0.580340	−	0.814374i	$-0.302920\pi$
$941$	−0.455276	−	0.330777i	−0.0148416	−	0.0107830i	−0.595181	+	0.803591i	$0.702920\pi$
$942$	0.0660694	−	0.203341i	0.00215266	−	0.00662520i
$943$	1.01236	+	3.11574i	0.0329671	+	0.101462i
$944$	12.1665	−	8.83945i	0.395985	−	0.287700i
$945$	5.63974			0.183461
$946$	21.8874	+	14.0610i	0.711619	+	0.457162i
$947$	43.8097			1.42362			0.711812	−	0.702370i	$-0.247875\pi$
$947$	43.8097			1.42362			0.711812	+	0.702370i	$0.247875\pi$
$948$	−25.4214	+	18.4698i	−0.825650	+	0.599870i
$949$	−6.42647	−	19.7786i	−0.208612	−	0.642042i
$950$	0.624741	−	1.92276i	0.0202693	−	0.0623825i
$951$	−5.20161	−	3.77919i	−0.168674	−	0.122549i
$952$	−5.04508	−	3.66547i	−0.163512	−	0.118799i
$953$	−8.26625	+	25.4409i	−0.267770	+	0.824112i	0.723272	+	0.690563i	$0.242637\pi$
$953$	−8.26625	+	25.4409i	−0.267770	+	0.824112i	−0.991042	+	0.133549i	$0.957363\pi$
$954$	−1.88408	−	5.79861i	−0.0609994	−	0.187737i
$955$	9.83456	−	7.14523i	0.318239	−	0.231214i
$956$	−87.1899			−2.81992
$957$	−11.6144	−	29.8167i	−0.375441	−	0.963836i
$958$	4.10897			0.132755
$959$	−17.5849	+	12.7762i	−0.567846	+	0.412564i
$960$	4.93300	+	15.1822i	0.159212	+	0.490004i
$961$	12.8188	−	39.4521i	0.413509	−	1.27265i
$962$	−70.8406	−	51.4687i	−2.28399	−	1.65942i
$963$	9.45735	+	6.87117i	0.304759	+	0.221420i
$964$	−15.0159	+	46.2142i	−0.483630	+	1.48846i
$965$	1.61855	+	4.98137i	0.0521028	+	0.160356i
$966$	2.81834	−	2.04765i	0.0906787	−	0.0658819i
$967$	−10.8617			−0.349290			−0.174645	−	0.984631i	$-0.555878\pi$
$967$	−10.8617			−0.349290			−0.174645	+	0.984631i	$0.555878\pi$
$968$	39.2330	+	22.1386i	1.26100	+	0.711560i
$969$	−1.90264			−0.0611215
$970$	12.2878	−	8.92759i	0.394537	−	0.286648i
$971$	−16.3248	−	50.2425i	−0.523887	−	1.61236i	−0.766506	−	0.642237i	$-0.778007\pi$
$971$	−16.3248	−	50.2425i	−0.523887	−	1.61236i	0.242619	−	0.970122i	$-0.421993\pi$
$972$	−9.45010	+	29.0844i	−0.303112	+	0.932883i
$973$	6.04603	+	4.39270i	0.193827	+	0.140823i
$974$	−31.1933	−	22.6632i	−0.999497	−	0.726177i
$975$	−1.76552	+	5.43370i	−0.0565417	+	0.174018i
$976$	−0.336269	−	1.03493i	−0.0107637	−	0.0331273i
$977$	10.4529	−	7.59446i	0.334417	−	0.242968i	−0.407885	−	0.913033i	$-0.633734\pi$
$977$	10.4529	−	7.59446i	0.334417	−	0.242968i	0.742303	+	0.670065i	$0.233734\pi$
$978$	45.1095			1.44244
$979$	−10.6696	−	27.3912i	−0.341003	−	0.875425i
$980$	3.71333			0.118618
$981$	−10.3352	+	7.50898i	−0.329978	+	0.239743i
$982$	13.3226	+	41.0027i	0.425141	+	1.30845i
$983$	−10.3136	+	31.7421i	−0.328954	+	1.01242i	0.640670	+	0.767816i	$0.278657\pi$
$983$	−10.3136	+	31.7421i	−0.328954	+	1.01242i	−0.969624	+	0.244600i	$0.921343\pi$
$984$	16.2525	+	11.8081i	0.518110	+	0.376429i
$985$	2.84459	+	2.06671i	0.0906361	+	0.0658510i
$986$	7.34572	−	22.6078i	0.233935	−	0.719979i
$987$	−6.11227	−	18.8116i	−0.194556	−	0.598781i
$988$	9.82713	−	7.13983i	0.312643	−	0.227148i
$989$	−3.23753			−0.102947
$990$	−5.45394	−	3.50374i	−0.173337	−	0.111356i
$991$	21.2540			0.675157			0.337579	−	0.941297i	$-0.390392\pi$
$991$	21.2540			0.675157			0.337579	+	0.941297i	$0.390392\pi$
$992$	17.5254	−	12.7329i	0.556431	−	0.404271i
$993$	−3.39994	−	10.4639i	−0.107894	−	0.332063i
$994$	4.25363	−	13.0913i	0.134917	−	0.415232i
$995$	−6.17806	−	4.48862i	−0.195858	−	0.142299i
$996$	54.3165	+	39.4633i	1.72109	+	1.25044i
$997$	4.03120	−	12.4068i	0.127669	−	0.392926i	−0.866709	−	0.498815i	$-0.833769\pi$
$997$	4.03120	−	12.4068i	0.127669	−	0.392926i	0.994378	+	0.105889i	$0.0337687\pi$
$998$	5.44411	+	16.7552i	0.172330	+	0.530378i
$999$	43.2180	−	31.3997i	1.36736	−	0.993443i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	385.2.n.c.36.2	✓	8
11.2	odd	10		4235.2.a.t.1.4		4
11.4	even	5	inner	385.2.n.c.246.2	yes	8
11.9	even	5		4235.2.a.w.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
385.2.n.c.36.2	✓	8	1.1	even	1	trivial
385.2.n.c.246.2	yes	8	11.4	even	5	inner
4235.2.a.t.1.4		4	11.2	odd	10
4235.2.a.w.1.1		4	11.9	even	5

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:	\( N \)	\(=\)	\( 385 = 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	385.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.93376 - 1.40496i) q^{2} +(-0.456498 - 1.40496i) q^{3} +(1.14748 - 3.53158i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(-2.85666 - 2.07549i) q^{6} +(0.309017 - 0.951057i) q^{7} +(-1.26552 - 3.89486i) q^{8} +(0.661536 - 0.480634i) q^{9} +O(q^{10})\)	\(q+(1.93376 - 1.40496i) q^{2} +(-0.456498 - 1.40496i) q^{3} +(1.14748 - 3.53158i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(-2.85666 - 2.07549i) q^{6} +(0.309017 - 0.951057i) q^{7} +(-1.26552 - 3.89486i) q^{8} +(0.661536 - 0.480634i) q^{9} -2.39026 q^{10} +(1.20381 + 3.09044i) q^{11} -5.48555 q^{12} +(-3.12889 + 2.27327i) q^{13} +(-0.738630 - 2.27327i) q^{14} +(-0.456498 + 1.40496i) q^{15} +(-1.91102 - 1.38844i) q^{16} +(1.23192 + 0.895044i) q^{17} +(0.603980 - 1.85886i) q^{18} +(-0.261370 - 0.804414i) q^{19} +(-3.00415 + 2.18264i) q^{20} -1.47726 q^{21} +(6.66983 + 4.28486i) q^{22} -0.986585 q^{23} +(-4.89440 + 3.55599i) q^{24} +(0.309017 + 0.951057i) q^{25} +(-2.85666 + 8.79191i) q^{26} +(-4.56265 - 3.31496i) q^{27} +(-3.00415 - 2.18264i) q^{28} +(2.01820 - 6.21138i) q^{29} +(1.09115 + 3.35821i) q^{30} +(6.88769 - 5.00420i) q^{31} +2.54445 q^{32} +(3.79240 - 3.10209i) q^{33} +3.63974 q^{34} +(-0.809017 + 0.587785i) q^{35} +(-0.938299 - 2.88779i) q^{36} +(-2.92705 + 9.00854i) q^{37} +(-1.63559 - 1.18833i) q^{38} +(4.62218 + 3.35821i) q^{39} +(-1.26552 + 3.89486i) q^{40} +(-1.02613 - 3.15810i) q^{41} +(-2.85666 + 2.07549i) q^{42} +3.28155 q^{43} +(12.2955 - 0.705148i) q^{44} -0.817703 q^{45} +(-1.90782 + 1.38611i) q^{46} +(4.13757 + 12.7341i) q^{47} +(-1.07832 + 3.31872i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(1.93376 + 1.40496i) q^{50} +(0.695128 - 2.13939i) q^{51} +(4.43790 + 13.6585i) q^{52} +(2.52368 - 1.83356i) q^{53} -13.4804 q^{54} +(0.842610 - 3.20780i) q^{55} -4.09529 q^{56} +(-1.01085 + 0.734428i) q^{57} +(-4.82402 - 14.8468i) q^{58} +(-1.96735 + 6.05488i) q^{59} +(4.43790 + 3.22433i) q^{60} +(0.372697 + 0.270780i) q^{61} +(6.28844 - 19.3538i) q^{62} +(-0.252684 - 0.777682i) q^{63} +(8.74238 - 6.35171i) q^{64} +3.86752 q^{65} +(2.97528 - 11.3269i) q^{66} -10.1146 q^{67} +(4.57453 - 3.32359i) q^{68} +(0.450375 + 1.38611i) q^{69} +(-0.738630 + 2.27327i) q^{70} +(4.65897 + 3.38494i) q^{71} +(-2.70918 - 1.96834i) q^{72} +(-1.66165 + 5.11404i) q^{73} +(6.99640 + 21.5327i) q^{74} +(1.19513 - 0.868312i) q^{75} -3.14077 q^{76} +(3.31118 - 0.189896i) q^{77} +13.6563 q^{78} +(4.63426 - 3.36698i) q^{79} +(0.729944 + 2.24654i) q^{80} +(-1.81648 + 5.59055i) q^{81} +(-6.42129 - 4.66534i) q^{82} +(-9.90175 - 7.19404i) q^{83} +(-1.69513 + 5.21707i) q^{84} +(-0.470553 - 1.44821i) q^{85} +(6.34572 - 4.61044i) q^{86} -9.64803 q^{87} +(10.5134 - 8.59969i) q^{88} -8.86318 q^{89} +(-1.58124 + 1.14884i) q^{90} +(1.19513 + 3.67823i) q^{91} +(-1.13209 + 3.48421i) q^{92} +(-10.1749 - 7.39251i) q^{93} +(25.8920 + 18.8116i) q^{94} +(-0.261370 + 0.804414i) q^{95} +(-1.16154 - 3.57484i) q^{96} +(-5.14077 + 3.73499i) q^{97} -2.39026 q^{98} +(2.28174 + 1.46584i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} + 4 q^{3} + 6 q^{4} - 2 q^{5} - 11 q^{6} - 2 q^{7} + 2 q^{8} + 4 q^{9}+O(q^{10}) \) 8 * q + 2 * q^2 + 4 * q^3 + 6 * q^4 - 2 * q^5 - 11 * q^6 - 2 * q^7 + 2 * q^8 + 4 * q^9	\( 8 q + 2 q^{2} + 4 q^{3} + 6 q^{4} - 2 q^{5} - 11 q^{6} - 2 q^{7} + 2 q^{8} + 4 q^{9} + 2 q^{10} + 3 q^{11} - 8 q^{12} - q^{13} - 3 q^{14} + 4 q^{15} + 4 q^{16} + 7 q^{17} - 6 q^{18} - 5 q^{19} - 9 q^{20} - 6 q^{21} + 22 q^{22} - 8 q^{23} - 3 q^{24} - 2 q^{25} - 11 q^{26} + q^{27} - 9 q^{28} + 3 q^{29} + 9 q^{30} + 19 q^{31} - 4 q^{32} + 9 q^{33} - 10 q^{34} - 2 q^{35} - 13 q^{36} - 10 q^{37} + 11 q^{38} + 13 q^{39} + 2 q^{40} - 8 q^{41} - 11 q^{42} + 20 q^{43} + 26 q^{44} - 6 q^{45} + 21 q^{46} + 13 q^{47} - 20 q^{48} - 2 q^{49} + 2 q^{50} - 5 q^{51} + 7 q^{52} - 6 q^{53} - 42 q^{54} - 7 q^{55} - 18 q^{56} + 7 q^{57} - 4 q^{58} + 7 q^{59} + 7 q^{60} - 3 q^{61} + 21 q^{62} - q^{63} + 18 q^{64} + 4 q^{65} + 14 q^{66} - 10 q^{67} + 20 q^{68} + 7 q^{69} - 3 q^{70} + 21 q^{71} - 13 q^{72} - q^{73} + 5 q^{74} - q^{75} - 22 q^{76} + 3 q^{77} + 10 q^{78} + 11 q^{79} - q^{80} - q^{81} - 6 q^{82} - 45 q^{83} - 3 q^{84} + 2 q^{85} - 14 q^{86} - 8 q^{87} + 7 q^{88} - 82 q^{89} + 4 q^{90} - q^{91} - 2 q^{92} - 3 q^{93} + 56 q^{94} - 5 q^{95} - 8 q^{96} - 38 q^{97} + 2 q^{98} - 11 q^{99}+O(q^{100}) \) 8 * q + 2 * q^2 + 4 * q^3 + 6 * q^4 - 2 * q^5 - 11 * q^6 - 2 * q^7 + 2 * q^8 + 4 * q^9 + 2 * q^10 + 3 * q^11 - 8 * q^12 - q^13 - 3 * q^14 + 4 * q^15 + 4 * q^16 + 7 * q^17 - 6 * q^18 - 5 * q^19 - 9 * q^20 - 6 * q^21 + 22 * q^22 - 8 * q^23 - 3 * q^24 - 2 * q^25 - 11 * q^26 + q^27 - 9 * q^28 + 3 * q^29 + 9 * q^30 + 19 * q^31 - 4 * q^32 + 9 * q^33 - 10 * q^34 - 2 * q^35 - 13 * q^36 - 10 * q^37 + 11 * q^38 + 13 * q^39 + 2 * q^40 - 8 * q^41 - 11 * q^42 + 20 * q^43 + 26 * q^44 - 6 * q^45 + 21 * q^46 + 13 * q^47 - 20 * q^48 - 2 * q^49 + 2 * q^50 - 5 * q^51 + 7 * q^52 - 6 * q^53 - 42 * q^54 - 7 * q^55 - 18 * q^56 + 7 * q^57 - 4 * q^58 + 7 * q^59 + 7 * q^60 - 3 * q^61 + 21 * q^62 - q^63 + 18 * q^64 + 4 * q^65 + 14 * q^66 - 10 * q^67 + 20 * q^68 + 7 * q^69 - 3 * q^70 + 21 * q^71 - 13 * q^72 - q^73 + 5 * q^74 - q^75 - 22 * q^76 + 3 * q^77 + 10 * q^78 + 11 * q^79 - q^80 - q^81 - 6 * q^82 - 45 * q^83 - 3 * q^84 + 2 * q^85 - 14 * q^86 - 8 * q^87 + 7 * q^88 - 82 * q^89 + 4 * q^90 - q^91 - 2 * q^92 - 3 * q^93 + 56 * q^94 - 5 * q^95 - 8 * q^96 - 38 * q^97 + 2 * q^98 - 11 * q^99

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