LMFDB - Embedded newform 385.2.n.e.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:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			36.2
Character	$\chi$	$=$	385.36
Dual form			385.2.n.e.246.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.79013 + 1.30061i) q^{2} +(-0.342550 - 1.05426i) q^{3} +(0.894962 - 2.75441i) q^{4} +(0.809017 + 0.587785i) q^{5} +(1.98439 + 1.44174i) q^{6} +(0.309017 - 0.951057i) q^{7} +(0.612766 + 1.88590i) q^{8} +(1.43293 - 1.04108i) q^{9} +O(q^{10})$	\(q+(-1.79013 + 1.30061i) q^{2} +(-0.342550 - 1.05426i) q^{3} +(0.894962 - 2.75441i) q^{4} +(0.809017 + 0.587785i) q^{5} +(1.98439 + 1.44174i) q^{6} +(0.309017 - 0.951057i) q^{7} +(0.612766 + 1.88590i) q^{8} +(1.43293 - 1.04108i) q^{9} -2.21273 q^{10} +(-3.16228 + 0.999992i) q^{11} -3.21043 q^{12} +(0.640861 - 0.465613i) q^{13} +(0.683770 + 2.10443i) q^{14} +(0.342550 - 1.05426i) q^{15} +(1.13633 + 0.825594i) q^{16} +(-6.05022 - 4.39574i) q^{17} +(-1.21109 + 3.72736i) q^{18} +(0.190272 + 0.585597i) q^{19} +(2.34304 - 1.70232i) q^{20} -1.10851 q^{21} +(4.36031 - 5.90301i) q^{22} -1.76973 q^{23} +(1.77833 - 1.29203i) q^{24} +(0.309017 + 0.951057i) q^{25} +(-0.541647 + 1.66702i) q^{26} +(-4.27884 - 3.10876i) q^{27} +(-2.34304 - 1.70232i) q^{28} +(3.29833 - 10.1512i) q^{29} +(0.757969 + 2.33279i) q^{30} +(7.55952 - 5.49232i) q^{31} -7.07387 q^{32} +(2.13749 + 2.99132i) q^{33} +16.5478 q^{34} +(0.809017 - 0.587785i) q^{35} +(-1.58515 - 4.87860i) q^{36} +(2.26805 - 6.98035i) q^{37} +(-1.10224 - 0.800827i) q^{38} +(-0.710403 - 0.516138i) q^{39} +(-0.612766 + 1.88590i) q^{40} +(2.29908 + 7.07585i) q^{41} +(1.98439 - 1.44174i) q^{42} -3.59522 q^{43} +(-0.0757323 + 9.60517i) q^{44} +1.77120 q^{45} +(3.16806 - 2.30173i) q^{46} +(1.48081 + 4.55746i) q^{47} +(0.481140 - 1.48080i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(-1.79013 - 1.30061i) q^{50} +(-2.56175 + 7.88426i) q^{51} +(-0.708942 - 2.18190i) q^{52} +(8.52280 - 6.19218i) q^{53} +11.7030 q^{54} +(-3.14612 - 1.04973i) q^{55} +1.98295 q^{56} +(0.552193 - 0.401192i) q^{57} +(7.29830 + 22.4619i) q^{58} +(-0.517910 + 1.59396i) q^{59} +(-2.59729 - 1.88704i) q^{60} +(-7.83965 - 5.69584i) q^{61} +(-6.38921 + 19.6640i) q^{62} +(-0.547330 - 1.68451i) q^{63} +(10.3905 - 7.54914i) q^{64} +0.792148 q^{65} +(-7.71692 - 2.57482i) q^{66} +2.06539 q^{67} +(-17.5224 + 12.7308i) q^{68} +(0.606221 + 1.86576i) q^{69} +(-0.683770 + 2.10443i) q^{70} +(-7.90496 - 5.74329i) q^{71} +(2.84143 + 2.06442i) q^{72} +(4.31623 - 13.2840i) q^{73} +(5.01858 + 15.4456i) q^{74} +(0.896807 - 0.651568i) q^{75} +1.78326 q^{76} +(-0.0261492 + 3.31652i) q^{77} +1.94301 q^{78} +(-7.08093 + 5.14460i) q^{79} +(0.434040 + 1.33584i) q^{80} +(-0.169734 + 0.522387i) q^{81} +(-13.3186 - 9.67650i) q^{82} +(0.825326 + 0.599634i) q^{83} +(-0.992078 + 3.05330i) q^{84} +(-2.31098 - 7.11246i) q^{85} +(6.43592 - 4.67597i) q^{86} -11.8319 q^{87} +(-3.82362 - 5.35098i) q^{88} +3.53991 q^{89} +(-3.17068 + 2.30363i) q^{90} +(-0.244787 - 0.753377i) q^{91} +(-1.58384 + 4.87457i) q^{92} +(-8.37984 - 6.08831i) q^{93} +(-8.57832 - 6.23251i) q^{94} +(-0.190272 + 0.585597i) q^{95} +(2.42315 + 7.45769i) q^{96} +(-14.0998 + 10.2441i) q^{97} +2.21273 q^{98} +(-3.49025 + 4.72511i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 3 q^{2} - 3 q^{4} + 7 q^{5} + 7 q^{6} - 7 q^{7} - q^{8} - q^{9}+O(q^{10}) $ 28 * q + 3 * q^2 - 3 * q^4 + 7 * q^5 + 7 * q^6 - 7 * q^7 - q^8 - q^9	\( 28 q + 3 q^{2} - 3 q^{4} + 7 q^{5} + 7 q^{6} - 7 q^{7} - q^{8} - q^{9} + 2 q^{10} - 3 q^{11} + 30 q^{12} - 5 q^{13} - 2 q^{14} - 33 q^{16} + 7 q^{17} - 17 q^{18} - 13 q^{19} + 18 q^{20} + 10 q^{21} + 3 q^{22} + 16 q^{23} + 39 q^{24} - 7 q^{25} + 44 q^{26} - 18 q^{27} - 18 q^{28} + 7 q^{29} + 8 q^{30} + 7 q^{31} - 84 q^{32} + 4 q^{33} + 32 q^{34} + 7 q^{35} + 6 q^{36} - 24 q^{37} - 15 q^{38} - 18 q^{39} + q^{40} - 4 q^{41} + 7 q^{42} + q^{44} - 34 q^{45} + 3 q^{46} - 33 q^{47} + 83 q^{48} - 7 q^{49} + 3 q^{50} + 14 q^{51} + 24 q^{52} - 8 q^{53} - 114 q^{54} - 17 q^{55} - 6 q^{56} + 57 q^{57} - 16 q^{58} - 3 q^{59} + 15 q^{60} - 21 q^{61} - 19 q^{62} - 16 q^{63} - 19 q^{64} - 20 q^{65} - 126 q^{66} + 90 q^{67} - 7 q^{68} - 55 q^{69} + 2 q^{70} - 37 q^{71} + 117 q^{72} + 17 q^{73} + 49 q^{74} - 5 q^{75} - 10 q^{76} - 3 q^{77} + 104 q^{78} - 45 q^{79} - 2 q^{80} + 8 q^{81} - 48 q^{82} + q^{83} + 18 q^{85} + 134 q^{86} + 46 q^{87} + 74 q^{88} - 30 q^{89} - 38 q^{90} - 5 q^{91} + 18 q^{92} - 57 q^{93} + 43 q^{94} + 13 q^{95} - 119 q^{96} - 82 q^{97} - 2 q^{98} - 72 q^{99}+O(q^{100}) \) 28 * q + 3 * q^2 - 3 * q^4 + 7 * q^5 + 7 * q^6 - 7 * q^7 - q^8 - q^9 + 2 * q^10 - 3 * q^11 + 30 * q^12 - 5 * q^13 - 2 * q^14 - 33 * q^16 + 7 * q^17 - 17 * q^18 - 13 * q^19 + 18 * q^20 + 10 * q^21 + 3 * q^22 + 16 * q^23 + 39 * q^24 - 7 * q^25 + 44 * q^26 - 18 * q^27 - 18 * q^28 + 7 * q^29 + 8 * q^30 + 7 * q^31 - 84 * q^32 + 4 * q^33 + 32 * q^34 + 7 * q^35 + 6 * q^36 - 24 * q^37 - 15 * q^38 - 18 * q^39 + q^40 - 4 * q^41 + 7 * q^42 + q^44 - 34 * q^45 + 3 * q^46 - 33 * q^47 + 83 * q^48 - 7 * q^49 + 3 * q^50 + 14 * q^51 + 24 * q^52 - 8 * q^53 - 114 * q^54 - 17 * q^55 - 6 * q^56 + 57 * q^57 - 16 * q^58 - 3 * q^59 + 15 * q^60 - 21 * q^61 - 19 * q^62 - 16 * q^63 - 19 * q^64 - 20 * q^65 - 126 * q^66 + 90 * q^67 - 7 * q^68 - 55 * q^69 + 2 * q^70 - 37 * q^71 + 117 * q^72 + 17 * q^73 + 49 * q^74 - 5 * q^75 - 10 * q^76 - 3 * q^77 + 104 * q^78 - 45 * q^79 - 2 * q^80 + 8 * q^81 - 48 * q^82 + q^83 + 18 * q^85 + 134 * q^86 + 46 * q^87 + 74 * q^88 - 30 * q^89 - 38 * q^90 - 5 * q^91 + 18 * q^92 - 57 * q^93 + 43 * q^94 + 13 * q^95 - 119 * q^96 - 82 * q^97 - 2 * q^98 - 72 * 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 $

$2$	−1.79013	+	1.30061i	−1.26582	+	0.919669i	−0.999028	−	0.0440866i	$-0.985962\pi$
$2$	−1.79013	+	1.30061i	−1.26582	+	0.919669i	−0.266788	+	0.963755i	$0.585962\pi$
$3$	−0.342550	−	1.05426i	−0.197771	−	0.608677i	−0.999933	−	0.0115704i	$-0.996317\pi$
$3$	−0.342550	−	1.05426i	−0.197771	−	0.608677i	0.802162	−	0.597107i	$-0.203683\pi$
$4$	0.894962	−	2.75441i	0.447481	−	1.37721i
$5$	0.809017	+	0.587785i	0.361803	+	0.262866i
$5$	0.809017	+	0.587785i	0.361803	+	0.262866i
$6$	1.98439	+	1.44174i	0.810123	+	0.588589i
$7$	0.309017	−	0.951057i	0.116797	−	0.359466i
$7$	0.309017	−	0.951057i	0.116797	−	0.359466i
$8$	0.612766	+	1.88590i	0.216646	+	0.666766i
$9$	1.43293	−	1.04108i	0.477643	−	0.347028i
$10$	−2.21273			−0.699726
$11$	−3.16228	+	0.999992i	−0.953463	+	0.301509i
$11$	−3.16228	+	0.999992i	−0.953463	+	0.301509i
$12$	−3.21043			−0.926772
$13$	0.640861	−	0.465613i	0.177743	−	0.129138i	−0.495357	−	0.868690i	$-0.664963\pi$
$13$	0.640861	−	0.465613i	0.177743	−	0.129138i	0.673099	+	0.739552i	$0.264963\pi$
$14$	0.683770	+	2.10443i	0.182745	+	0.562432i
$15$	0.342550	−	1.05426i	0.0884459	−	0.272209i
$16$	1.13633	+	0.825594i	0.284083	+	0.206398i
$17$	−6.05022	−	4.39574i	−1.46739	−	1.06612i	−0.981359	−	0.192183i	$-0.938443\pi$
$17$	−6.05022	−	4.39574i	−1.46739	−	1.06612i	−0.486034	−	0.873940i	$-0.661557\pi$
$18$	−1.21109	+	3.72736i	−0.285457	+	0.878546i
$19$	0.190272	+	0.585597i	0.0436514	+	0.134345i	0.970507	−	0.241073i	$-0.0774992\pi$
$19$	0.190272	+	0.585597i	0.0436514	+	0.134345i	−0.926856	+	0.375418i	$0.877499\pi$
$20$	2.34304	−	1.70232i	0.523920	−	0.380650i
$21$	−1.10851			−0.241898
$22$	4.36031	−	5.90301i	0.929620	−	1.25853i
$23$	−1.76973			−0.369015			−0.184507	−	0.982831i	$-0.559069\pi$
$23$	−1.76973			−0.369015			−0.184507	+	0.982831i	$0.559069\pi$
$24$	1.77833	−	1.29203i	0.362999	−	0.263734i
$25$	0.309017	+	0.951057i	0.0618034	+	0.190211i
$26$	−0.541647	+	1.66702i	−0.106226	+	0.326929i
$27$	−4.27884	−	3.10876i	−0.823463	−	0.598281i
$28$	−2.34304	−	1.70232i	−0.442793	−	0.321708i
$29$	3.29833	−	10.1512i	0.612484	−	1.88503i	0.179075	−	0.983835i	$-0.442690\pi$
$29$	3.29833	−	10.1512i	0.612484	−	1.88503i	0.433409	−	0.901197i	$-0.357310\pi$
$30$	0.757969	+	2.33279i	0.138386	+	0.425907i
$31$	7.55952	−	5.49232i	1.35773	−	0.986449i	0.359145	−	0.933282i	$-0.383068\pi$
$31$	7.55952	−	5.49232i	1.35773	−	0.986449i	0.998586	−	0.0531671i	$-0.0169316\pi$
$32$	−7.07387			−1.25049
$33$	2.13749	+	2.99132i	0.372089	+	0.520721i
$34$	16.5478			2.83793
$35$	0.809017	−	0.587785i	0.136749	−	0.0993538i
$36$	−1.58515	−	4.87860i	−0.264192	−	0.813100i
$37$	2.26805	−	6.98035i	0.372866	−	1.14756i	−0.572042	−	0.820225i	$-0.693848\pi$
$37$	2.26805	−	6.98035i	0.372866	−	1.14756i	0.944907	−	0.327338i	$-0.106152\pi$
$38$	−1.10224	−	0.800827i	−0.178808	−	0.129911i
$39$	−0.710403	−	0.516138i	−0.113756	−	0.0826483i
$40$	−0.612766	+	1.88590i	−0.0968868	+	0.298187i
$41$	2.29908	+	7.07585i	0.359056	+	1.10506i	0.953620	+	0.301013i	$0.0973247\pi$
$41$	2.29908	+	7.07585i	0.359056	+	1.10506i	−0.594564	+	0.804048i	$0.702675\pi$
$42$	1.98439	−	1.44174i	0.306198	−	0.222466i
$43$	−3.59522			−0.548266			−0.274133	−	0.961692i	$-0.588391\pi$
$43$	−3.59522			−0.548266			−0.274133	+	0.961692i	$0.588391\pi$
$44$	−0.0757323	+	9.60517i	−0.0114171	+	1.44803i
$45$	1.77120			0.264034
$46$	3.16806	−	2.30173i	0.467104	−	0.339371i
$47$	1.48081	+	4.55746i	0.215998	+	0.664774i	0.999081	+	0.0428569i	$0.0136460\pi$
$47$	1.48081	+	4.55746i	0.215998	+	0.664774i	−0.783083	+	0.621917i	$0.786354\pi$
$48$	0.481140	−	1.48080i	0.0694466	−	0.213735i
$49$	−0.809017	−	0.587785i	−0.115574	−	0.0839693i
$50$	−1.79013	−	1.30061i	−0.253163	−	0.183934i
$51$	−2.56175	+	7.88426i	−0.358717	+	1.10402i
$52$	−0.708942	−	2.18190i	−0.0983126	−	0.302575i
$53$	8.52280	−	6.19218i	1.17070	−	0.850561i	0.179604	−	0.983739i	$-0.442518\pi$
$53$	8.52280	−	6.19218i	1.17070	−	0.850561i	0.991092	+	0.133178i	$0.0425183\pi$
$54$	11.7030			1.59257
$55$	−3.14612	−	1.04973i	−0.424223	−	0.141546i
$56$	1.98295			0.264983
$57$	0.552193	−	0.401192i	0.0731398	−	0.0531392i
$58$	7.29830	+	22.4619i	0.958314	+	2.94939i
$59$	−0.517910	+	1.59396i	−0.0674261	+	0.207516i	−0.979093	−	0.203414i	$-0.934796\pi$
$59$	−0.517910	+	1.59396i	−0.0674261	+	0.207516i	0.911667	+	0.410931i	$0.134796\pi$
$60$	−2.59729	−	1.88704i	−0.335309	−	0.243616i
$61$	−7.83965	−	5.69584i	−1.00376	−	0.729277i	−0.0408719	−	0.999164i	$-0.513014\pi$
$61$	−7.83965	−	5.69584i	−1.00376	−	0.729277i	−0.962892	+	0.269887i	$0.913014\pi$
$62$	−6.38921	+	19.6640i	−0.811430	+	2.49732i
$63$	−0.547330	−	1.68451i	−0.0689571	−	0.212228i
$64$	10.3905	−	7.54914i	1.29881	−	0.943642i
$65$	0.792148			0.0982539
$66$	−7.71692	−	2.57482i	−0.949887	−	0.316938i
$67$	2.06539			0.252327			0.126164	−	0.992009i	$-0.459734\pi$
$67$	2.06539			0.252327			0.126164	+	0.992009i	$0.459734\pi$
$68$	−17.5224	+	12.7308i	−2.12490	+	1.54383i
$69$	0.606221	+	1.86576i	0.0729804	+	0.224611i
$70$	−0.683770	+	2.10443i	−0.0817262	+	0.251527i
$71$	−7.90496	−	5.74329i	−0.938146	−	0.681603i	0.00982789	−	0.999952i	$-0.496872\pi$
$71$	−7.90496	−	5.74329i	−0.938146	−	0.681603i	−0.947974	+	0.318349i	$0.896872\pi$
$72$	2.84143	+	2.06442i	0.334866	+	0.243294i
$73$	4.31623	−	13.2840i	0.505176	−	1.55477i	−0.295297	−	0.955405i	$-0.595419\pi$
$73$	4.31623	−	13.2840i	0.505176	−	1.55477i	0.800474	−	0.599368i	$-0.204581\pi$
$74$	5.01858	+	15.4456i	0.583398	+	1.79552i
$75$	0.896807	−	0.651568i	0.103554	−	0.0752366i
$76$	1.78326			0.204554
$77$	−0.0261492	+	3.31652i	−0.00297998	+	0.377953i
$78$	1.94301			0.220003
$79$	−7.08093	+	5.14460i	−0.796667	+	0.578812i	−0.909934	−	0.414752i	$-0.863868\pi$
$79$	−7.08093	+	5.14460i	−0.796667	+	0.578812i	0.113267	+	0.993565i	$0.463868\pi$
$80$	0.434040	+	1.33584i	0.0485272	+	0.149351i
$81$	−0.169734	+	0.522387i	−0.0188593	+	0.0580430i
$82$	−13.3186	−	9.67650i	−1.47079	−	1.06859i
$83$	0.825326	+	0.599634i	0.0905912	+	0.0658184i	0.632159	−	0.774839i	$-0.282169\pi$
$83$	0.825326	+	0.599634i	0.0905912	+	0.0658184i	−0.541568	+	0.840657i	$0.682169\pi$
$84$	−0.992078	+	3.05330i	−0.108245	+	0.333143i
$85$	−2.31098	−	7.11246i	−0.250661	−	0.771454i
$86$	6.43592	−	4.67597i	0.694003	−	0.504223i
$87$	−11.8319			−1.26851
$88$	−3.82362	−	5.35098i	−0.407600	−	0.570417i
$89$	3.53991			0.375230			0.187615	−	0.982243i	$-0.439924\pi$
$89$	3.53991			0.375230			0.187615	+	0.982243i	$0.439924\pi$
$90$	−3.17068	+	2.30363i	−0.334219	+	0.242824i
$91$	−0.244787	−	0.753377i	−0.0256607	−	0.0789754i
$92$	−1.58384	+	4.87457i	−0.165127	+	0.508209i
$93$	−8.37984	−	6.08831i	−0.868949	−	0.631328i
$94$	−8.57832	−	6.23251i	−0.884786	−	0.642834i
$95$	−0.190272	+	0.585597i	−0.0195215	+	0.0600810i
$96$	2.42315	+	7.45769i	0.247312	+	0.761147i
$97$	−14.0998	+	10.2441i	−1.43162	+	1.04013i	−0.441903	+	0.897063i	$0.645697\pi$
$97$	−14.0998	+	10.2441i	−1.43162	+	1.04013i	−0.989713	+	0.143067i	$0.954303\pi$
$98$	2.21273			0.223519
$99$	−3.49025	+	4.72511i	−0.350783	+	0.474892i
$100$	2.89616			0.289616
$101$	−8.60999	+	6.25552i	−0.856726	+	0.622448i	−0.926992	−	0.375080i	$-0.877615\pi$
$101$	−8.60999	+	6.25552i	−0.856726	+	0.622448i	0.0702663	+	0.997528i	$0.477615\pi$
$102$	−5.66845	−	17.4457i	−0.561260	−	1.72738i
$103$	−2.92132	+	8.99089i	−0.287846	+	0.885899i	0.697685	+	0.716404i	$0.254213\pi$
$103$	−2.92132	+	8.99089i	−0.287846	+	0.885899i	−0.985531	+	0.169494i	$0.945787\pi$
$104$	1.27080	+	0.923288i	0.124612	+	0.0905359i
$105$	−0.896807	−	0.651568i	−0.0875194	−	0.0635865i
$106$	−7.20335	+	22.1696i	−0.699651	+	2.15331i
$107$	3.80371	+	11.7066i	0.367718	+	1.13172i	0.948261	+	0.317491i	$0.102840\pi$
$107$	3.80371	+	11.7066i	0.367718	+	1.13172i	−0.580543	+	0.814230i	$0.697160\pi$
$108$	−12.3922	+	9.00346i	−1.19244	+	0.866358i
$109$	5.28033			0.505764			0.252882	−	0.967497i	$-0.418622\pi$
$109$	5.28033			0.505764			0.252882	+	0.967497i	$0.418622\pi$
$110$	6.99726	−	2.21271i	0.667163	−	0.210974i
$111$	−8.13602			−0.772237
$112$	1.13633	−	0.825594i	0.107373	−	0.0780113i
$113$	−2.35579	−	7.25037i	−0.221614	−	0.682057i	−0.998618	−	0.0525613i	$-0.983262\pi$
$113$	−2.35579	−	7.25037i	−0.221614	−	0.682057i	0.777004	−	0.629496i	$-0.216738\pi$
$114$	−0.466706	+	1.43637i	−0.0437110	+	0.134529i
$115$	−1.43174	−	1.04022i	−0.133511	−	0.0970012i
$116$	−25.0087	−	18.1699i	−2.32200	−	1.68703i
$117$	0.433566	−	1.33438i	0.0400832	−	0.123363i
$118$	−1.14599	−	3.52700i	−0.105497	−	0.324687i
$119$	−6.05022	+	4.39574i	−0.554622	+	0.402957i
$120$	2.19813			0.200661
$121$	9.00003	−	6.32451i	0.818185	−	0.574956i
$122$	21.4421			1.94127
$123$	6.67223	−	4.84766i	0.601614	−	0.437098i
$124$	−8.36260	−	25.7374i	−0.750984	−	2.31129i
$125$	−0.309017	+	0.951057i	−0.0276393	+	0.0850651i
$126$	3.17068	+	2.30363i	0.282466	+	0.205224i
$127$	18.1140	+	13.1606i	1.60736	+	1.16782i	0.871080	+	0.491142i	$0.163420\pi$
$127$	18.1140	+	13.1606i	1.60736	+	1.16782i	0.736282	+	0.676675i	$0.236580\pi$
$128$	−4.41002	+	13.5726i	−0.389794	+	1.19966i
$129$	1.23154	+	3.79029i	0.108431	+	0.333717i
$130$	−1.41805	+	1.03027i	−0.124371	+	0.0903610i
$131$	0.600588			0.0524736			0.0262368	−	0.999656i	$-0.491648\pi$
$131$	0.600588			0.0524736			0.0262368	+	0.999656i	$0.491648\pi$
$132$	10.1523	−	3.21041i	0.883643	−	0.279430i
$133$	0.615733			0.0533908
$134$	−3.69732	+	2.68626i	−0.319400	+	0.232057i
$135$	−1.63437	−	5.03008i	−0.140664	−	0.432920i
$136$	4.58256	−	14.1037i	0.392951	−	1.20938i
$137$	8.38170	+	6.08966i	0.716097	+	0.520275i	0.885135	−	0.465335i	$-0.154066\pi$
$137$	8.38170	+	6.08966i	0.716097	+	0.520275i	−0.169038	+	0.985610i	$0.554066\pi$
$138$	−3.51183	−	2.55150i	−0.298947	−	0.217198i
$139$	2.78731	−	8.57846i	0.236417	−	0.727615i	−0.760514	−	0.649322i	$-0.775053\pi$
$139$	2.78731	−	8.57846i	0.236417	−	0.727615i	0.996930	−	0.0782936i	$-0.0249472\pi$
$140$	−0.894962	−	2.75441i	−0.0756381	−	0.232790i
$141$	4.29750	−	3.12231i	0.361914	−	0.262946i
$142$	21.6207			1.81437
$143$	−1.56097	+	2.11325i	−0.130535	+	0.176719i
$144$	2.48780			0.207316
$145$	8.63514	−	6.27379i	0.717109	−	0.521010i
$146$	9.55063	+	29.3938i	0.790416	+	2.43265i
$147$	−0.342550	+	1.05426i	−0.0282530	+	0.0869538i
$148$	−17.1969	−	12.4943i	−1.41358	−	1.02703i
$149$	11.5843	+	8.41651i	0.949026	+	0.689508i	0.950576	−	0.310491i	$-0.100493\pi$
$149$	11.5843	+	8.41651i	0.949026	+	0.689508i	−0.00155032	+	0.999999i	$0.500493\pi$
$150$	−0.757969	+	2.33279i	−0.0618879	+	0.190471i
$151$	0.212045	+	0.652608i	0.0172560	+	0.0531085i	0.959314	−	0.282342i	$-0.0911114\pi$
$151$	0.212045	+	0.652608i	0.0172560	+	0.0531085i	−0.942058	+	0.335451i	$0.891111\pi$
$152$	−0.987785	+	0.717668i	−0.0801199	+	0.0582105i
$153$	−13.2459			−1.07086
$154$	−4.26668	−	5.97103i	−0.343819	−	0.481159i
$155$	9.34408			0.750535
$156$	−2.05744	+	1.49482i	−0.164727	+	0.119681i
$157$	0.709085	+	2.18234i	0.0565911	+	0.174170i	0.975357	−	0.220634i	$-0.0708126\pi$
$157$	0.709085	+	2.18234i	0.0565911	+	0.174170i	−0.918766	+	0.394804i	$0.870813\pi$
$158$	5.98471	−	18.4190i	0.476118	−	1.46534i
$159$	−9.44764	−	6.86411i	−0.749247	−	0.544360i
$160$	−5.72288	−	4.15791i	−0.452433	−	0.328712i
$161$	−0.546877	+	1.68311i	−0.0431000	+	0.132648i
$162$	−0.375575	−	1.15590i	−0.0295079	−	0.0908161i
$163$	15.8970	−	11.5499i	1.24515	−	0.904656i	0.247222	−	0.968959i	$-0.420482\pi$
$163$	15.8970	−	11.5499i	1.24515	−	0.904656i	0.997930	+	0.0643031i	$0.0204824\pi$
$164$	21.5474			1.68257
$165$	−0.0289868	+	3.67641i	−0.00225662	+	0.286208i
$166$	−2.25733			−0.175203
$167$	−13.2100	+	9.59764i	−1.02222	+	0.742688i	−0.966737	−	0.255772i	$-0.917670\pi$
$167$	−13.2100	+	9.59764i	−1.02222	+	0.742688i	−0.0554849	+	0.998460i	$0.517670\pi$
$168$	−0.679260	−	2.09055i	−0.0524060	−	0.161289i
$169$	−3.82331	+	11.7669i	−0.294101	+	0.905150i
$170$	13.3875	+	9.72657i	1.02677	+	0.745994i
$171$	0.882301	+	0.641029i	0.0674713	+	0.0490207i
$172$	−3.21758	+	9.90271i	−0.245338	+	0.755074i
$173$	1.97155	+	6.06781i	0.149894	+	0.461327i	0.997608	−	0.0691272i	$-0.0220214\pi$
$173$	1.97155	+	6.06781i	0.149894	+	0.461327i	−0.847714	+	0.530454i	$0.822021\pi$
$174$	21.1806	−	15.3886i	1.60570	−	1.16661i
$175$	1.00000			0.0755929
$176$	−4.41899	−	1.47444i	−0.333094	−	0.111140i
$177$	1.85786			0.139645
$178$	−6.33692	+	4.60404i	−0.474972	+	0.345087i
$179$	−1.87610	−	5.77406i	−0.140227	−	0.431573i	0.856140	−	0.516744i	$-0.172856\pi$
$179$	−1.87610	−	5.77406i	−0.140227	−	0.431573i	−0.996366	+	0.0851712i	$0.972856\pi$
$180$	1.58515	−	4.87860i	0.118150	−	0.363630i
$181$	−0.629501	−	0.457359i	−0.0467904	−	0.0339952i	0.564144	−	0.825676i	$-0.309206\pi$
$181$	−0.629501	−	0.457359i	−0.0467904	−	0.0339952i	−0.610935	+	0.791681i	$0.709206\pi$
$182$	1.41805	+	1.03027i	0.105113	+	0.0763690i
$183$	−3.31942	+	10.2161i	−0.245379	+	0.755198i
$184$	−1.08443	−	3.33754i	−0.0799454	−	0.246047i
$185$	5.93784	−	4.31409i	0.436559	−	0.317179i
$186$	22.9195			1.68054
$187$	23.5282	+	7.85039i	1.72055	+	0.574077i
$188$	13.8784			1.01219
$189$	−4.27884	+	3.10876i	−0.311240	+	0.226129i
$190$	−0.421020	−	1.29577i	−0.0305440	−	0.0940047i
$191$	1.60695	−	4.94569i	0.116275	−	0.357857i	−0.875936	−	0.482427i	$-0.839755\pi$
$191$	1.60695	−	4.94569i	0.116275	−	0.357857i	0.992211	+	0.124570i	$0.0397552\pi$
$192$	−11.5180	−	8.36833i	−0.831241	−	0.603932i
$193$	3.59427	+	2.61139i	0.258721	+	0.187972i	0.709583	−	0.704622i	$-0.248883\pi$
$193$	3.59427	+	2.61139i	0.258721	+	0.187972i	−0.450862	+	0.892594i	$0.648883\pi$
$194$	11.9169	−	36.6766i	0.855587	−	2.63323i
$195$	−0.271350	−	0.835129i	−0.0194318	−	0.0598049i
$196$	−2.34304	+	1.70232i	−0.167360	+	0.121594i
$197$	9.25786			0.659595			0.329798	−	0.944052i	$-0.393019\pi$
$197$	9.25786			0.659595			0.329798	+	0.944052i	$0.393019\pi$
$198$	0.102483	−	12.9980i	0.00728317	−	0.923730i
$199$	−10.4019			−0.737369			−0.368684	−	0.929555i	$-0.620192\pi$
$199$	−10.4019			−0.737369			−0.368684	+	0.929555i	$0.620192\pi$
$200$	−1.60424	+	1.16555i	−0.113437	+	0.0824169i
$201$	−0.707498	−	2.17745i	−0.0499030	−	0.153586i
$202$	7.27705	−	22.3964i	0.512011	−	1.57581i
$203$	−8.63514	−	6.27379i	−0.606068	−	0.440334i
$204$	19.4238	+	14.1122i	1.35994	+	0.988053i
$205$	−2.29908	+	7.07585i	−0.160575	+	0.494198i
$206$	−6.46408	−	19.8944i	−0.450374	−	1.38611i
$207$	−2.53590	+	1.84244i	−0.176257	+	0.128058i
$208$	1.11264			0.0771476
$209$	−1.18729	−	1.66155i	−0.0821262	−	0.114932i
$210$	2.45284			0.169262
$211$	−9.27550	+	6.73905i	−0.638552	+	0.463935i	−0.859352	−	0.511384i	$-0.829133\pi$
$211$	−9.27550	+	6.73905i	−0.638552	+	0.463935i	0.220800	+	0.975319i	$0.429133\pi$
$212$	−9.42821	−	29.0170i	−0.647532	−	1.99290i
$213$	−3.34707	+	10.3012i	−0.229338	+	0.705829i
$214$	−22.0349	−	16.0093i	−1.50627	−	1.09437i
$215$	−2.90859	−	2.11322i	−0.198364	−	0.144120i
$216$	3.24088	−	9.97441i	0.220514	−	0.678673i
$217$	−2.88748	−	8.88675i	−0.196015	−	0.603272i
$218$	−9.45250	+	6.86764i	−0.640204	+	0.465136i
$219$	−15.4833			−1.04626
$220$	−5.70705	+	7.72623i	−0.384769	+	0.520902i
$221$	−5.92406			−0.398495
$222$	14.5646	−	10.5818i	0.977510	−	0.710202i
$223$	5.54012	+	17.0507i	0.370994	+	1.14180i	0.946142	+	0.323752i	$0.104945\pi$
$223$	5.54012	+	17.0507i	0.370994	+	1.14180i	−0.575148	+	0.818049i	$0.695055\pi$
$224$	−2.18594	+	6.72765i	−0.146055	+	0.449510i
$225$	1.43293	+	1.04108i	0.0955286	+	0.0694056i
$226$	13.6471	+	9.91517i	0.907789	+	0.659547i
$227$	2.05228	−	6.31627i	0.136215	−	0.419225i	−0.859562	−	0.511031i	$-0.829264\pi$
$227$	2.05228	−	6.31627i	0.136215	−	0.419225i	0.995777	+	0.0918055i	$0.0292638\pi$
$228$	−0.610855	−	1.88002i	−0.0404549	−	0.124507i
$229$	−0.758167	+	0.550841i	−0.0501011	+	0.0364006i	−0.612554	−	0.790429i	$-0.709858\pi$
$229$	−0.758167	+	0.550841i	−0.0501011	+	0.0364006i	0.562453	+	0.826829i	$0.309858\pi$
$230$	3.91593			0.258209
$231$	3.50543	−	1.10851i	0.230640	−	0.0729343i
$232$	21.1653			1.38957
$233$	9.24991	−	6.72045i	0.605982	−	0.440272i	−0.242015	−	0.970272i	$-0.577808\pi$
$233$	9.24991	−	6.72045i	0.605982	−	0.440272i	0.847997	+	0.530001i	$0.177808\pi$
$234$	0.959364	+	2.95262i	0.0627156	+	0.193019i
$235$	−1.48081	+	4.55746i	−0.0965973	+	0.297296i
$236$	3.92692	+	2.85307i	0.255621	+	0.185719i
$237$	7.84931	+	5.70286i	0.509868	+	0.370440i
$238$	5.11356	−	15.7379i	0.331463	−	1.02014i
$239$	−1.86704	−	5.74615i	−0.120769	−	0.371688i	0.872338	−	0.488904i	$-0.162603\pi$
$239$	−1.86704	−	5.74615i	−0.120769	−	0.371688i	−0.993106	+	0.117216i	$0.962603\pi$
$240$	1.25964	−	0.915182i	0.0813094	−	0.0590748i
$241$	6.08268			0.391820			0.195910	−	0.980622i	$-0.437234\pi$
$241$	6.08268			0.391820			0.195910	+	0.980622i	$0.437234\pi$
$242$	−7.88555	+	23.0272i	−0.506902	+	1.48025i
$243$	−15.2579			−0.978797
$244$	−22.7049	+	16.4960i	−1.45353	+	1.05605i
$245$	−0.309017	−	0.951057i	−0.0197424	−	0.0607608i
$246$	−5.63927	+	17.3559i	−0.359547	+	1.10657i
$247$	0.394599	+	0.286693i	0.0251077	+	0.0182418i
$248$	14.9902	+	10.8910i	0.951877	+	0.691579i
$249$	0.349455	−	1.07551i	0.0221458	−	0.0681578i
$250$	−0.683770	−	2.10443i	−0.0432454	−	0.133096i
$251$	3.72989	−	2.70993i	0.235429	−	0.171049i	−0.463816	−	0.885932i	$-0.653520\pi$
$251$	3.72989	−	2.70993i	0.235429	−	0.171049i	0.699244	+	0.714883i	$0.253520\pi$
$252$	−5.12967			−0.323139
$253$	5.59639	−	1.76972i	0.351842	−	0.111261i
$254$	−49.5434			−3.10863
$255$	−6.70675	+	4.87274i	−0.419993	+	0.305143i
$256$	−1.82053	−	5.60300i	−0.113783	−	0.350188i
$257$	−3.62186	+	11.1470i	−0.225926	+	0.695328i	0.772271	+	0.635294i	$0.219121\pi$
$257$	−3.62186	+	11.1470i	−0.225926	+	0.695328i	−0.998196	+	0.0600340i	$0.980879\pi$
$258$	−7.13431	−	5.18338i	−0.444163	−	0.322703i
$259$	−5.93784	−	4.31409i	−0.368960	−	0.268065i
$260$	0.708942	−	2.18190i	0.0439667	−	0.135316i
$261$	−5.84199	−	17.9798i	−0.361610	−	1.11292i
$262$	−1.07513	+	0.781130i	−0.0664219	+	0.0482583i
$263$	18.9004			1.16545			0.582724	−	0.812670i	$-0.301987\pi$
$263$	18.9004			1.16545			0.582724	+	0.812670i	$0.301987\pi$
$264$	−4.33154	+	5.86407i	−0.266588	+	0.360908i
$265$	10.5348			0.647145
$266$	−1.10224	+	0.800827i	−0.0675829	+	0.0491019i
$267$	−1.21260	−	3.73199i	−0.0742097	−	0.228394i
$268$	1.84844	−	5.68892i	0.112912	−	0.347506i
$269$	−0.282324	−	0.205120i	−0.0172136	−	0.0125064i	0.579145	−	0.815224i	$-0.303386\pi$
$269$	−0.282324	−	0.205120i	−0.0172136	−	0.0125064i	−0.596359	+	0.802718i	$0.703386\pi$
$270$	9.46790	+	6.87883i	0.576198	+	0.418633i
$271$	−3.77596	+	11.6212i	−0.229373	+	0.705937i	0.768445	+	0.639916i	$0.221031\pi$
$271$	−3.77596	+	11.6212i	−0.229373	+	0.705937i	−0.997818	+	0.0660218i	$0.978969\pi$
$272$	−3.24596	−	9.99004i	−0.196815	−	0.605735i
$273$	−0.710403	+	0.516138i	−0.0429956	+	0.0312381i
$274$	−22.9246			−1.38493
$275$	−1.92825	−	2.69849i	−0.116278	−	0.162725i
$276$	5.68160			0.341992
$277$	13.4234	−	9.75264i	0.806531	−	0.585979i	−0.106292	−	0.994335i	$-0.533898\pi$
$277$	13.4234	−	9.75264i	0.806531	−	0.585979i	0.912823	+	0.408356i	$0.133898\pi$
$278$	6.16756	+	18.9818i	0.369905	+	1.13845i
$279$	5.11430	−	15.7402i	0.306185	−	0.942340i
$280$	1.60424	+	1.16555i	0.0958718	+	0.0696550i
$281$	1.67648	+	1.21804i	0.100011	+	0.0726619i	0.636667	−	0.771139i	$-0.280313\pi$
$281$	1.67648	+	1.21804i	0.100011	+	0.0726619i	−0.536656	+	0.843801i	$0.680313\pi$
$282$	−3.63218	+	11.1787i	−0.216293	+	0.665683i
$283$	−1.85680	−	5.71463i	−0.110375	−	0.339699i	0.880579	−	0.473899i	$-0.157154\pi$
$283$	−1.85680	−	5.71463i	−0.110375	−	0.339699i	−0.990954	+	0.134199i	$0.957154\pi$
$284$	−22.8940	+	16.6335i	−1.35851	+	0.987015i
$285$	0.682548			0.0404307
$286$	0.0458345	−	5.81322i	0.00271025	−	0.343743i
$287$	7.43998			0.439168
$288$	−10.1363	+	7.36449i	−0.597290	+	0.433956i
$289$	12.0293	+	37.0224i	0.707606	+	2.17779i
$290$	−7.29830	+	22.4619i	−0.428571	+	1.31901i
$291$	15.6298	+	11.3557i	0.916236	+	0.665684i
$292$	−32.7267	−	23.7773i	−1.91518	−	1.39146i
$293$	7.72007	−	23.7599i	0.451011	−	1.38807i	−0.424743	−	0.905314i	$-0.639636\pi$
$293$	7.72007	−	23.7599i	0.451011	−	1.38807i	0.875755	−	0.482757i	$-0.160364\pi$
$294$	−0.757969	−	2.33279i	−0.0442056	−	0.136051i
$295$	−1.35591	+	0.985123i	−0.0789439	+	0.0573561i
$296$	14.5540			0.845936
$297$	16.6396	+	5.55196i	0.965529	+	0.322158i
$298$	−31.6841			−1.83541
$299$	−1.13415	+	0.824010i	−0.0655897	+	0.0476537i
$300$	−0.992078	−	3.05330i	−0.0572776	−	0.176282i
$301$	−1.11098	+	3.41926i	−0.0640360	+	0.197083i
$302$	−1.22838	−	0.892467i	−0.0706851	−	0.0513557i
$303$	9.54429	+	6.93433i	0.548305	+	0.398367i
$304$	−0.267253	+	0.822520i	−0.0153280	+	0.0471748i
$305$	−2.99448	−	9.21606i	−0.171463	−	0.527710i
$306$	23.7118	−	17.2277i	1.35552	−	0.984840i
$307$	−28.5978			−1.63216			−0.816081	−	0.577938i	$-0.803858\pi$
$307$	−28.5978			−1.63216			−0.816081	+	0.577938i	$0.803858\pi$
$308$	9.11166	+	3.04019i	0.519185	+	0.173231i
$309$	10.4794			0.596154
$310$	−16.7272	+	12.1530i	−0.950039	+	0.690243i
$311$	−3.97946	−	12.2475i	−0.225654	−	0.694493i	−0.998225	−	0.0595635i	$-0.981029\pi$
$311$	−3.97946	−	12.2475i	−0.225654	−	0.694493i	0.772570	−	0.634929i	$-0.218971\pi$
$312$	0.538074	−	1.65602i	0.0304625	−	0.0937538i
$313$	−9.41630	−	6.84134i	−0.532241	−	0.386696i	0.288954	−	0.957343i	$-0.406692\pi$
$313$	−9.41630	−	6.84134i	−0.532241	−	0.386696i	−0.821195	+	0.570647i	$0.806692\pi$
$314$	−4.10772	−	2.98444i	−0.231812	−	0.168421i
$315$	0.547330	−	1.68451i	0.0308385	−	0.0949113i
$316$	7.83317	+	24.1080i	0.440650	+	1.35618i
$317$	−9.37349	+	6.81024i	−0.526468	+	0.382501i	−0.819035	−	0.573744i	$-0.805490\pi$
$317$	−9.37349	+	6.81024i	−0.526468	+	0.382501i	0.292567	+	0.956245i	$0.405490\pi$
$318$	25.8401			1.44904
$319$	−0.279107	+	35.3993i	−0.0156270	+	1.98198i
$320$	12.8434			0.717966
$321$	11.0388	−	8.02019i	0.616128	−	0.447643i
$322$	−1.21009	−	3.72427i	−0.0674357	−	0.207546i
$323$	1.42294	−	4.37937i	0.0791747	−	0.243675i
$324$	1.28696	+	0.935034i	0.0714980	+	0.0519463i
$325$	0.640861	+	0.465613i	0.0355486	+	0.0258276i
$326$	−13.4360	+	41.3516i	−0.744149	+	2.29025i
$327$	−1.80878	−	5.56684i	−0.100026	−	0.307847i
$328$	−11.9355	+	8.67168i	−0.659030	+	0.478813i
$329$	4.79200			0.264191
$330$	−4.72968	−	6.61896i	−0.260360	−	0.364362i
$331$	−20.8658			−1.14689			−0.573445	−	0.819244i	$-0.694393\pi$
$331$	−20.8658			−1.14689			−0.573445	+	0.819244i	$0.694393\pi$
$332$	2.39027	−	1.73664i	0.131183	−	0.0953102i
$333$	−4.01717	−	12.3636i	−0.220140	−	0.677520i
$334$	11.1649	−	34.3621i	0.610918	−	1.88021i
$335$	1.67093	+	1.21400i	0.0912929	+	0.0663281i
$336$	−1.25964	−	0.915182i	−0.0687190	−	0.0499273i
$337$	−8.13563	+	25.0389i	−0.443176	+	1.36396i	0.441296	+	0.897362i	$0.354519\pi$
$337$	−8.13563	+	25.0389i	−0.443176	+	1.36396i	−0.884472	+	0.466594i	$0.845481\pi$
$338$	−8.45995	−	26.0370i	−0.460160	−	1.41623i
$339$	−6.83679	+	4.96722i	−0.371324	+	0.269782i
$340$	−21.6589			−1.17462
$341$	−18.4131	+	24.9277i	−0.997123	+	1.34991i
$342$	−2.41316			−0.130489
$343$	−0.809017	+	0.587785i	−0.0436828	+	0.0317374i
$344$	−2.20303	−	6.78022i	−0.118779	−	0.365565i
$345$	−0.606221	+	1.86576i	−0.0326378	+	0.100449i
$346$	−11.4212	−	8.29797i	−0.614006	−	0.446102i
$347$	−4.73441	−	3.43975i	−0.254156	−	0.184655i	0.453410	−	0.891302i	$-0.350207\pi$
$347$	−4.73441	−	3.43975i	−0.254156	−	0.184655i	−0.707567	+	0.706646i	$0.750207\pi$
$348$	−10.5891	+	32.5898i	−0.567633	+	1.74699i
$349$	−2.34156	−	7.20657i	−0.125341	−	0.385759i	0.868622	−	0.495475i	$-0.165006\pi$
$349$	−2.34156	−	7.20657i	−0.125341	−	0.385759i	−0.993963	+	0.109716i	$0.965006\pi$
$350$	−1.79013	+	1.30061i	−0.0956866	+	0.0695204i
$351$	−4.18962			−0.223625
$352$	22.3695	−	7.07381i	1.19230	−	0.377035i
$353$	32.4394			1.72658			0.863289	−	0.504710i	$-0.168401\pi$
$353$	32.4394			1.72658			0.863289	+	0.504710i	$0.168401\pi$
$354$	−3.32582	+	2.41635i	−0.176765	+	0.128427i
$355$	−3.01942	−	9.29283i	−0.160254	−	0.493212i
$356$	3.16809	−	9.75038i	0.167908	−	0.516769i
$357$	6.70675	+	4.87274i	0.354959	+	0.257893i
$358$	10.8683	+	7.89625i	0.574405	+	0.417330i
$359$	2.41500	−	7.43261i	0.127459	−	0.392278i	−0.866882	−	0.498513i	$-0.833880\pi$
$359$	2.41500	−	7.43261i	0.127459	−	0.392278i	0.994341	+	0.106235i	$0.0338795\pi$
$360$	1.08533	+	3.34030i	0.0572019	+	0.176049i
$361$	15.0646	−	10.9451i	0.792874	−	0.576057i
$362$	1.72174			0.0904924
$363$	−9.75063	−	7.32191i	−0.511775	−	0.384301i
$364$	−2.29419			−0.120248
$365$	11.3000	−	8.20996i	0.591471	−	0.429729i
$366$	−7.34497	−	22.6055i	−0.383928	−	1.18161i
$367$	0.196587	−	0.605034i	0.0102618	−	0.0315825i	−0.945795	−	0.324766i	$-0.894715\pi$
$367$	0.196587	−	0.605034i	0.0102618	−	0.0315825i	0.956056	+	0.293183i	$0.0947146\pi$
$368$	−2.01100	−	1.46108i	−0.104831	−	0.0761641i
$369$	10.6610	+	7.74564i	0.554988	+	0.403222i
$370$	−5.01858	+	15.4456i	−0.260904	+	0.802979i
$371$	−3.25542	−	10.0192i	−0.169013	−	0.520168i
$372$	−24.2693	+	17.6327i	−1.25831	+	0.914213i
$373$	6.77575			0.350835			0.175417	−	0.984494i	$-0.443872\pi$
$373$	6.77575			0.350835			0.175417	+	0.984494i	$0.443872\pi$
$374$	−52.3289	+	16.5477i	−2.70586	+	0.855661i
$375$	1.10851			0.0572434
$376$	−7.68753	+	5.58532i	−0.396454	+	0.288041i
$377$	−2.61276	−	8.04126i	−0.134564	−	0.414146i
$378$	3.61642	−	11.1302i	0.186008	−	0.572475i
$379$	−7.96278	−	5.78530i	−0.409021	−	0.297171i	0.364185	−	0.931327i	$-0.381348\pi$
$379$	−7.96278	−	5.78530i	−0.409021	−	0.297171i	−0.773205	+	0.634156i	$0.781348\pi$
$380$	1.44269	+	1.04817i	0.0740083	+	0.0537702i
$381$	7.66975	−	23.6051i	0.392933	−	1.20932i
$382$	3.55574	+	10.9434i	0.181928	+	0.559916i
$383$	−15.2626	+	11.0889i	−0.779883	+	0.566618i	−0.904944	−	0.425531i	$-0.860087\pi$
$383$	−15.2626	+	11.0889i	−0.779883	+	0.566618i	0.125061	+	0.992149i	$0.460087\pi$
$384$	15.8197			0.807297
$385$	−1.97056	+	2.66775i	−0.100429	+	0.135961i
$386$	−9.83062			−0.500365
$387$	−5.15169	+	3.74292i	−0.261875	+	0.190263i
$388$	15.5977	+	48.0047i	0.791851	+	2.43707i
$389$	−1.54112	+	4.74309i	−0.0781381	+	0.240484i	−0.982494	−	0.186295i	$-0.940352\pi$
$389$	−1.54112	+	4.74309i	−0.0781381	+	0.240484i	0.904356	+	0.426779i	$0.140352\pi$
$390$	1.57193	+	1.14207i	0.0795977	+	0.0578311i
$391$	10.7073	+	7.77928i	0.541489	+	0.393415i
$392$	0.612766	−	1.88590i	0.0309494	−	0.0952523i
$393$	−0.205731	−	0.633176i	−0.0103778	−	0.0319395i
$394$	−16.5728	+	12.0408i	−0.834926	+	0.606609i
$395$	−8.75251			−0.440387
$396$	9.89127	+	13.8424i	0.497055	+	0.695605i
$397$	9.47965			0.475770			0.237885	−	0.971293i	$-0.423546\pi$
$397$	9.47965			0.475770			0.237885	+	0.971293i	$0.423546\pi$
$398$	18.6207	−	13.5288i	0.933373	−	0.678135i
$399$	−0.210919	−	0.649142i	−0.0105592	−	0.0324978i
$400$	−0.434040	+	1.33584i	−0.0217020	+	0.0667920i
$401$	−14.4398	−	10.4911i	−0.721088	−	0.523901i	0.165644	−	0.986186i	$-0.447030\pi$
$401$	−14.4398	−	10.4911i	−0.721088	−	0.523901i	−0.886732	+	0.462285i	$0.847030\pi$
$402$	4.09853	+	2.97776i	0.204416	+	0.148517i
$403$	2.28731	−	7.03962i	0.113939	−	0.350669i
$404$	9.52466	+	29.3139i	0.473870	+	1.45842i
$405$	−0.444369	+	0.322853i	−0.0220809	+	0.0160427i
$406$	23.6178			1.17213
$407$	−0.191924	+	24.3419i	−0.00951333	+	1.20658i
$408$	−16.4387			−0.813836
$409$	15.3768	−	11.1719i	0.760332	−	0.552413i	−0.138680	−	0.990337i	$-0.544286\pi$
$409$	15.3768	−	11.1719i	0.760332	−	0.552413i	0.899012	+	0.437924i	$0.144286\pi$
$410$	−5.08724	−	15.6569i	−0.251241	−	0.773240i
$411$	3.54893	−	10.9225i	0.175056	−	0.538767i
$412$	22.1501	+	16.0930i	1.09126	+	0.792846i
$413$	1.35591	+	0.985123i	0.0667198	+	0.0484747i
$414$	2.14331	−	6.59642i	0.105338	−	0.324196i
$415$	0.315246	+	0.970228i	0.0154748	+	0.0476266i
$416$	−4.53337	+	3.29368i	−0.222267	+	0.161486i
$417$	−9.99871			−0.489639
$418$	4.28642	+	1.43020i	0.209656	+	0.0699536i
$419$	1.91623			0.0936141			0.0468071	−	0.998904i	$-0.485095\pi$
$419$	1.91623			0.0936141			0.0468071	+	0.998904i	$0.485095\pi$
$420$	−2.59729	+	1.88704i	−0.126735	+	0.0920783i
$421$	11.3413	+	34.9050i	0.552742	+	1.70117i	0.701832	+	0.712342i	$0.252366\pi$
$421$	11.3413	+	34.9050i	0.552742	+	1.70117i	−0.149090	+	0.988824i	$0.547634\pi$
$422$	7.83953	−	24.1276i	0.381622	−	1.17451i
$423$	6.86659	+	4.98887i	0.333865	+	0.242567i
$424$	16.9003	+	12.2788i	0.820751	+	0.596311i
$425$	2.31098	−	7.11246i	0.112099	−	0.345005i
$426$	−7.40616	−	22.7938i	−0.358830	−	1.10436i
$427$	−7.83965	+	5.69584i	−0.379387	+	0.275641i
$428$	35.6490			1.72316
$429$	2.76263	+	0.921776i	0.133381	+	0.0445038i
$430$	7.95523			0.383635
$431$	27.9915	−	20.3370i	1.34830	−	0.979601i	0.349210	−	0.937044i	$-0.386450\pi$
$431$	27.9915	−	20.3370i	1.34830	−	0.979601i	0.999094	−	0.0425562i	$-0.0135501\pi$
$432$	−2.29561	−	7.06517i	−0.110448	−	0.339923i
$433$	−1.96636	+	6.05182i	−0.0944971	+	0.290832i	−0.987122	−	0.159967i	$-0.948861\pi$
$433$	−1.96636	+	6.05182i	−0.0944971	+	0.290832i	0.892625	+	0.450800i	$0.148861\pi$
$434$	16.7272	+	12.1530i	0.802929	+	0.583362i
$435$	−9.57217	−	6.95459i	−0.458950	−	0.333447i
$436$	4.72570	−	14.5442i	0.226320	−	0.696541i
$437$	−0.336730	−	1.03635i	−0.0161080	−	0.0495753i
$438$	27.7172	−	20.1377i	1.32438	−	0.962216i
$439$	5.84756			0.279089			0.139544	−	0.990216i	$-0.455436\pi$
$439$	5.84756			0.279089			0.139544	+	0.990216i	$0.455436\pi$
$440$	0.0518526	−	6.57651i	0.00247198	−	0.313523i
$441$	−1.77120			−0.0843427
$442$	10.6049	−	7.70488i	0.504422	−	0.366484i
$443$	4.33513	+	13.3422i	0.205968	+	0.633905i	0.999672	+	0.0256011i	$0.00814997\pi$
$443$	4.33513	+	13.3422i	0.205968	+	0.633905i	−0.793704	+	0.608304i	$0.791850\pi$
$444$	−7.28143	+	22.4099i	−0.345561	+	1.06353i
$445$	2.86385	+	2.08071i	0.135760	+	0.0986351i
$446$	−32.0939	−	23.3176i	−1.51969	−	1.10412i
$447$	4.90498	−	15.0960i	0.231998	−	0.714015i
$448$	−3.96882	−	12.2148i	−0.187509	−	0.577093i
$449$	30.5011	−	22.1603i	1.43944	−	1.04581i	0.451276	−	0.892384i	$-0.350969\pi$
$449$	30.5011	−	22.1603i	1.43944	−	1.04581i	0.988160	−	0.153427i	$-0.0490310\pi$
$450$	−3.91917			−0.184752
$451$	−14.3461	−	20.0767i	−0.675533	−	0.945377i
$452$	−22.0788			−1.03850
$453$	0.615382	−	0.447101i	0.0289132	−	0.0210066i
$454$	4.54113	+	13.9762i	0.213126	+	0.655934i
$455$	0.244787	−	0.753377i	0.0114758	−	0.0353189i
$456$	1.09497	+	0.795545i	0.0512768	+	0.0372548i
$457$	9.65844	+	7.01726i	0.451803	+	0.328254i	0.790307	−	0.612711i	$-0.209921\pi$
$457$	9.65844	+	7.01726i	0.451803	+	0.328254i	−0.338505	+	0.940965i	$0.609921\pi$
$458$	0.640792	−	1.97216i	0.0299423	−	0.0921528i
$459$	12.2226	+	37.6173i	0.570503	+	1.75583i
$460$	−4.14655	+	3.01265i	−0.193334	+	0.140465i
$461$	−32.5597			−1.51646			−0.758229	−	0.651989i	$-0.773935\pi$
$461$	−32.5597			−1.51646			−0.758229	+	0.651989i	$0.773935\pi$
$462$	−4.83346	+	6.54356i	−0.224873	+	0.304434i
$463$	11.1073			0.516198			0.258099	−	0.966118i	$-0.416904\pi$
$463$	11.1073			0.516198			0.258099	+	0.966118i	$0.416904\pi$
$464$	12.1288	−	8.81207i	0.563064	−	0.409090i
$465$	−3.20081	−	9.85109i	−0.148434	−	0.456833i
$466$	−7.81790	+	24.0610i	−0.362157	+	1.11461i
$467$	11.9362	+	8.67214i	0.552340	+	0.401299i	0.828648	−	0.559771i	$-0.189111\pi$
$467$	11.9362	+	8.67214i	0.552340	+	0.401299i	−0.276307	+	0.961069i	$0.589111\pi$
$468$	−3.28740	−	2.38844i	−0.151960	−	0.110406i
$469$	0.638240	−	1.96430i	0.0294712	−	0.0907030i
$470$	−3.27663	−	10.0844i	−0.151139	−	0.465159i
$471$	2.05785	−	1.49512i	0.0948209	−	0.0688914i
$472$	−3.32341			−0.152972
$473$	11.3691	−	3.59519i	0.522751	−	0.165307i
$474$	−21.4685			−0.986081
$475$	−0.498138	+	0.361919i	−0.0228562	+	0.0166060i
$476$	6.69295	+	20.5988i	0.306771	+	0.944144i
$477$	5.76599	−	17.7459i	0.264006	−	0.812528i
$478$	10.8157	+	7.85809i	0.494700	+	0.359421i
$479$	26.8578	+	19.5134i	1.22717	+	0.891588i	0.996674	−	0.0814864i	$-0.0259667\pi$
$479$	26.8578	+	19.5134i	1.22717	+	0.891588i	0.230491	+	0.973074i	$0.425967\pi$
$480$	−2.42315	+	7.45769i	−0.110601	+	0.340395i
$481$	−1.79663	−	5.52947i	−0.0819195	−	0.252122i
$482$	−10.8888	+	7.91118i	−0.495972	+	0.360345i
$483$	1.96177			0.0892637
$484$	−9.36561	−	30.4500i	−0.425710	−	1.38409i
$485$	−17.4283			−0.791378
$486$	27.3137	−	19.8446i	1.23898	−	0.900169i
$487$	0.145074	+	0.446492i	0.00657394	+	0.0202325i	0.954290	−	0.298883i	$-0.0966141\pi$
$487$	0.145074	+	0.446492i	0.00657394	+	0.0202325i	−0.947716	+	0.319116i	$0.896614\pi$
$488$	5.93791	−	18.2750i	0.268797	−	0.827271i
$489$	−17.6221	−	12.8032i	−0.796898	−	0.578980i
$490$	1.79013	+	1.30061i	0.0808700	+	0.0587555i
$491$	9.31088	−	28.6559i	0.420194	−	1.29322i	−0.487328	−	0.873219i	$-0.662028\pi$
$491$	9.31088	−	28.6559i	0.420194	−	1.29322i	0.907522	−	0.420005i	$-0.137972\pi$
$492$	−7.38104	−	22.7165i	−0.332763	−	1.02414i
$493$	−64.5777	+	46.9184i	−2.90843	+	2.11310i
$494$	−1.07926			−0.0485582
$495$	−5.60102	+	1.77118i	−0.251747	+	0.0796088i
$496$	13.1246			0.589310
$497$	−7.90496	+	5.74329i	−0.354586	+	0.257622i
$498$	0.773248	+	2.37981i	0.0346501	+	0.106642i
$499$	12.5771	−	38.7082i	0.563027	−	1.73282i	−0.110716	−	0.993852i	$-0.535314\pi$
$499$	12.5771	−	38.7082i	0.563027	−	1.73282i	0.673743	−	0.738966i	$-0.264686\pi$
$500$	2.34304	+	1.70232i	0.104784	+	0.0761300i
$501$	14.6435	+	10.6391i	0.654223	+	0.475321i
$502$	−3.15246	+	9.70226i	−0.140701	+	0.433033i
$503$	2.39554	+	7.37272i	0.106812	+	0.328733i	0.990151	−	0.140000i	$-0.0447104\pi$
$503$	2.39554	+	7.37272i	0.106812	+	0.328733i	−0.883339	+	0.468734i	$0.844710\pi$
$504$	2.84143	−	2.06442i	0.126567	−	0.0919565i
$505$	−10.6425			−0.473586
$506$	−7.71657	+	10.4467i	−0.343043	+	0.464414i
$507$	13.7151			0.609109
$508$	52.4611	−	38.1152i	2.32759	−	1.69109i
$509$	−6.68102	−	20.5621i	−0.296131	−	0.911397i	−0.982839	−	0.184464i	$-0.940945\pi$
$509$	−6.68102	−	20.5621i	−0.296131	−	0.911397i	0.686708	−	0.726933i	$-0.259055\pi$
$510$	5.66845	−	17.4457i	0.251003	−	0.772509i
$511$	−11.3000	−	8.20996i	−0.499884	−	0.363187i
$512$	−12.5449	−	9.11437i	−0.554409	−	0.402802i
$513$	1.00634	−	3.09718i	0.0444308	−	0.136744i
$514$	−8.01419	−	24.6652i	−0.353491	−	1.08793i
$515$	−7.64811	+	5.55668i	−0.337016	+	0.244856i
$516$	11.5422			0.508117
$517$	−9.24016	−	12.9312i	−0.406382	−	0.568712i
$518$	16.2405			0.713565
$519$	5.72169	−	4.15705i	0.251154	−	0.182474i
$520$	0.485401	+	1.49391i	0.0212863	+	0.0655124i
$521$	−10.3856	+	31.9637i	−0.455003	+	1.40035i	0.416130	+	0.909305i	$0.363386\pi$
$521$	−10.3856	+	31.9637i	−0.455003	+	1.40035i	−0.871132	+	0.491049i	$0.836614\pi$
$522$	33.8426	+	24.5881i	1.48125	+	1.07619i
$523$	−4.50858	−	3.27567i	−0.197146	−	0.143235i	0.484833	−	0.874607i	$-0.338880\pi$
$523$	−4.50858	−	3.27567i	−0.197146	−	0.143235i	−0.681979	+	0.731372i	$0.738880\pi$
$524$	0.537504	−	1.65427i	0.0234810	−	0.0722669i
$525$	−0.342550	−	1.05426i	−0.0149501	−	0.0460117i
$526$	−33.8342	+	24.5820i	−1.47524	+	1.07183i
$527$	−69.8795			−3.04400
$528$	−0.0407144	+	5.16383i	−0.00177186	+	0.224727i
$529$	−19.8680			−0.863828
$530$	−18.8586	+	13.7016i	−0.819166	+	0.595159i
$531$	0.917320	+	2.82322i	0.0398083	+	0.122517i
$532$	0.551058	−	1.69598i	0.0238914	−	0.0735301i
$533$	4.76800	+	3.46415i	0.206525	+	0.150049i
$534$	7.02456	+	5.10364i	0.303983	+	0.220856i
$535$	−3.80371	+	11.7066i	−0.164449	+	0.506121i
$536$	1.26560	+	3.89511i	0.0546656	+	0.168243i
$537$	−5.44469	+	3.95580i	−0.234956	+	0.170705i
$538$	0.772179			0.0332910
$539$	3.14612	+	1.04973i	0.135513	+	0.0452151i
$540$	−15.3176			−0.659165
$541$	22.3327	−	16.2257i	0.960158	−	0.697596i	0.00697051	−	0.999976i	$-0.497781\pi$
$541$	22.3327	−	16.2257i	0.960158	−	0.697596i	0.953187	+	0.302380i	$0.0977812\pi$
$542$	−8.35516	−	25.7145i	−0.358885	−	1.10453i
$543$	−0.266540	+	0.820325i	−0.0114383	+	0.0352035i
$544$	42.7984	+	31.0949i	1.83497	+	1.33318i
$545$	4.27188	+	3.10370i	0.182987	+	0.132948i
$546$	0.600423	−	1.84791i	0.0256957	−	0.0790834i
$547$	−8.25384	−	25.4027i	−0.352909	−	1.08614i	−0.957212	−	0.289387i	$-0.906548\pi$
$547$	−8.25384	−	25.4027i	−0.352909	−	1.08614i	0.604303	−	0.796754i	$-0.293452\pi$
$548$	24.2747	−	17.6366i	1.03696	−	0.753399i
$549$	−17.1635			−0.732520
$550$	6.96150	+	2.32277i	0.296839	+	0.0990431i
$551$	6.57210			0.279981
$552$	−3.14716	+	2.28654i	−0.133952	+	0.0973218i
$553$	2.70468	+	8.32413i	0.115014	+	0.353978i
$554$	−11.3452	+	34.9170i	−0.482013	+	1.48348i
$555$	−6.58218	−	4.78223i	−0.279398	−	0.202995i
$556$	−21.1341	−	15.3548i	−0.896284	−	0.651188i
$557$	−5.70102	+	17.5459i	−0.241560	+	0.743445i	0.754623	+	0.656158i	$0.227820\pi$
$557$	−5.70102	+	17.5459i	−0.241560	+	0.743445i	−0.996183	+	0.0872868i	$0.972180\pi$
$558$	11.3165	+	34.8287i	0.479067	+	1.47442i
$559$	−2.30404	+	1.67398i	−0.0974503	+	0.0708018i
$560$	1.40458			0.0593545
$561$	0.216777	−	27.4940i	0.00915233	−	1.16080i
$562$	−4.58532			−0.193420
$563$	28.0180	−	20.3563i	1.18082	−	0.857914i	0.188554	−	0.982063i	$-0.439620\pi$
$563$	28.0180	−	20.3563i	1.18082	−	0.857914i	0.992264	+	0.124149i	$0.0396200\pi$
$564$	−4.75404	−	14.6314i	−0.200181	−	0.616094i
$565$	2.35579	−	7.25037i	0.0991087	−	0.305025i
$566$	10.7564	+	7.81498i	0.452125	+	0.328488i
$567$	0.444369	+	0.322853i	0.0186618	+	0.0135586i
$568$	5.98738	−	18.4272i	0.251225	−	0.773190i
$569$	4.28194	+	13.1785i	0.179508	+	0.552469i	0.999811	−	0.0194606i	$-0.00619489\pi$
$569$	4.28194	+	13.1785i	0.179508	+	0.552469i	−0.820302	+	0.571930i	$0.806195\pi$
$570$	−1.22185	+	0.887728i	−0.0511778	+	0.0371828i
$571$	0.401219			0.0167905			0.00839524	−	0.999965i	$-0.497328\pi$
$571$	0.401219			0.0167905			0.00839524	+	0.999965i	$0.497328\pi$
$572$	4.42376	+	6.19084i	0.184967	+	0.258852i
$573$	−5.76450			−0.240815
$574$	−13.3186	+	9.67650i	−0.555906	+	0.403889i
$575$	−0.546877	−	1.68311i	−0.0228064	−	0.0701907i
$576$	7.02956	−	21.6348i	0.292898	−	0.901448i
$577$	−12.0406	−	8.74803i	−0.501258	−	0.364185i	0.308239	−	0.951309i	$-0.400260\pi$
$577$	−12.0406	−	8.74803i	−0.501258	−	0.364185i	−0.809497	+	0.587124i	$0.800260\pi$
$578$	−69.6857	−	50.6296i	−2.89854	−	2.10591i
$579$	1.52187	−	4.68383i	0.0632466	−	0.194653i
$580$	−9.55248	−	29.3995i	−0.396645	−	1.22075i
$581$	0.825326	−	0.599634i	0.0342403	−	0.0248770i
$582$	−42.7488			−1.77199
$583$	−20.7593	+	28.1041i	−0.859764	+	1.16395i
$584$	27.6971			1.14611
$585$	1.13509	−	0.824692i	0.0469302	−	0.0340968i
$586$	17.0824	+	52.5742i	0.705668	+	2.17182i
$587$	3.44200	−	10.5934i	0.142067	−	0.437236i	−0.854556	−	0.519360i	$-0.826170\pi$
$587$	3.44200	−	10.5934i	0.142067	−	0.437236i	0.996622	+	0.0821241i	$0.0261704\pi$
$588$	2.59729	+	1.88704i	0.107111	+	0.0778204i
$589$	4.65465	+	3.38180i	0.191791	+	0.139345i
$590$	1.14599	−	3.52700i	0.0471798	−	0.145204i
$591$	−3.17128	−	9.76019i	−0.130449	−	0.401480i
$592$	8.34020	−	6.05951i	0.342780	−	0.249044i
$593$	14.0923			0.578700			0.289350	−	0.957223i	$-0.406561\pi$
$593$	14.0923			0.578700			0.289350	+	0.957223i	$0.406561\pi$
$594$	−37.0081	+	11.7029i	−1.51846	+	0.480175i
$595$	−7.47848			−0.306588
$596$	33.5501	−	24.3756i	1.37426	−	0.998462i
$597$	3.56316	+	10.9663i	0.145830	+	0.448819i
$598$	0.958570	−	2.95017i	0.0391988	−	0.120642i
$599$	−16.0541	−	11.6640i	−0.655952	−	0.476577i	0.209341	−	0.977843i	$-0.432868\pi$
$599$	−16.0541	−	11.6640i	−0.655952	−	0.476577i	−0.865294	+	0.501265i	$0.832868\pi$
$600$	1.77833	+	1.29203i	0.0725998	+	0.0527469i
$601$	−11.4861	+	35.3506i	−0.468527	+	1.44198i	0.385964	+	0.922514i	$0.373869\pi$
$601$	−11.4861	+	35.3506i	−0.468527	+	1.44198i	−0.854492	+	0.519465i	$0.826131\pi$
$602$	−2.45830	−	7.56588i	−0.100193	−	0.308362i
$603$	2.95955	−	2.15024i	0.120522	−	0.0875646i
$604$	1.98732			0.0808630
$605$	10.9986	+	0.173449i	0.447158	+	0.00705170i
$606$	−26.1044			−1.06042
$607$	−15.5828	+	11.3216i	−0.632488	+	0.459530i	−0.857261	−	0.514881i	$-0.827836\pi$
$607$	−15.5828	+	11.3216i	−0.632488	+	0.459530i	0.224773	+	0.974411i	$0.427836\pi$
$608$	−1.34596	−	4.14243i	−0.0545858	−	0.167998i
$609$	−3.65624	+	11.2528i	−0.148158	+	0.455985i
$610$	17.3470	+	12.6033i	0.702359	+	0.510294i
$611$	3.07101	+	2.23122i	0.124240	+	0.0902653i
$612$	−11.8545	+	36.4845i	−0.479191	+	1.47480i
$613$	−6.92688	−	21.3187i	−0.279774	−	0.861056i	−0.987917	−	0.154987i	$-0.950467\pi$
$613$	−6.92688	−	21.3187i	−0.279774	−	0.861056i	0.708143	−	0.706070i	$-0.249533\pi$
$614$	51.1938	−	37.1945i	2.06601	−	1.50105i
$615$	8.24733			0.332564
$616$	−6.27065	+	1.98294i	−0.252652	+	0.0798948i
$617$	19.4081			0.781342			0.390671	−	0.920530i	$-0.372243\pi$
$617$	19.4081			0.781342			0.390671	+	0.920530i	$0.372243\pi$
$618$	−18.7596	+	13.6296i	−0.754621	+	0.548264i
$619$	5.35542	+	16.4823i	0.215252	+	0.662479i	0.999136	+	0.0415703i	$0.0132361\pi$
$619$	5.35542	+	16.4823i	0.215252	+	0.662479i	−0.783883	+	0.620908i	$0.786764\pi$
$620$	8.36260	−	25.7374i	0.335850	−	1.03364i
$621$	7.57240	+	5.50167i	0.303870	+	0.220774i
$622$	23.0530	+	16.7490i	0.924340	+	0.671573i
$623$	1.09389	−	3.36666i	0.0438259	−	0.134882i
$624$	−0.381134	−	1.17301i	−0.0152576	−	0.0469580i
$625$	−0.809017	+	0.587785i	−0.0323607	+	0.0235114i
$626$	25.7543			1.02935
$627$	−1.34500	+	1.82087i	−0.0537142	+	0.0727185i
$628$	6.64566			0.265191
$629$	−44.4060	+	32.2629i	−1.77058	+	1.28640i
$630$	1.21109	+	3.72736i	0.0482510	+	0.148501i
$631$	6.76291	−	20.8141i	0.269227	−	0.828596i	−0.721462	−	0.692454i	$-0.756530\pi$
$631$	6.76291	−	20.8141i	0.269227	−	0.828596i	0.990689	−	0.136142i	$-0.0434704\pi$
$632$	−14.0412	−	10.2015i	−0.558527	−	0.405794i
$633$	10.2820	+	7.47033i	0.408674	+	0.296919i
$634$	7.92235	−	24.3825i	0.314637	−	0.968352i
$635$	6.91895	+	21.2943i	0.274570	+	0.845040i
$636$	−27.3619	+	19.8796i	−1.08497	+	0.788276i
$637$	−0.792148			−0.0313860
$638$	−45.5409	−	63.7324i	−1.80298	−	2.52319i
$639$	−17.3065			−0.684634
$640$	−11.5456	+	8.38835i	−0.456379	+	0.331579i
$641$	−8.52864	−	26.2485i	−0.336861	−	1.03675i	−0.965798	−	0.259296i	$-0.916510\pi$
$641$	−8.52864	−	26.2485i	−0.336861	−	1.03675i	0.628937	−	0.777456i	$-0.283490\pi$
$642$	−9.32988	+	28.7144i	−0.368221	+	1.13327i
$643$	16.7301	+	12.1552i	0.659772	+	0.479353i	0.866586	−	0.499028i	$-0.166309\pi$
$643$	16.7301	+	12.1552i	0.659772	+	0.479353i	−0.206814	+	0.978380i	$0.566309\pi$
$644$	4.14655	+	3.01265i	0.163397	+	0.118715i
$645$	−1.23154	+	3.79029i	−0.0484919	+	0.149243i
$646$	3.14859	+	9.69035i	0.123879	+	0.381262i
$647$	15.6270	−	11.3537i	0.614362	−	0.446360i	−0.236586	−	0.971611i	$-0.576028\pi$
$647$	15.6270	−	11.3537i	0.614362	−	0.446360i	0.850948	+	0.525251i	$0.176028\pi$
$648$	−1.08918			−0.0427869
$649$	0.0438259	−	5.55846i	0.00172032	−	0.218189i
$650$	−1.75281			−0.0687507
$651$	−8.37984	+	6.08831i	−0.328432	+	0.238620i
$652$	−17.5858	−	54.1237i	−0.688715	−	2.11965i
$653$	1.46678	−	4.51427i	0.0573994	−	0.176657i	−0.918246	−	0.396010i	$-0.870395\pi$
$653$	1.46678	−	4.51427i	0.0573994	−	0.176657i	0.975646	+	0.219353i	$0.0703946\pi$
$654$	10.4782	+	7.61288i	0.409731	+	0.297687i
$655$	0.485886	+	0.353017i	0.0189851	+	0.0137935i
$656$	−3.22925	+	9.93862i	−0.126081	+	0.388038i
$657$	−7.64489	−	23.5286i	−0.298256	−	0.917936i
$658$	−8.57832	+	6.23251i	−0.334418	+	0.242969i
$659$	−6.55284			−0.255262			−0.127631	−	0.991822i	$-0.540737\pi$
$659$	−6.55284			−0.255262			−0.127631	+	0.991822i	$0.540737\pi$
$660$	10.1004	+	3.37009i	0.393158	+	0.131181i
$661$	−3.35159			−0.130362			−0.0651809	−	0.997873i	$-0.520762\pi$
$661$	−3.35159			−0.130362			−0.0651809	+	0.997873i	$0.520762\pi$
$662$	37.3526	−	27.1383i	1.45175	−	1.05476i
$663$	2.02928	+	6.24550i	0.0788109	+	0.242555i
$664$	−0.625118	+	1.92392i	−0.0242593	+	0.0746625i
$665$	0.498138	+	0.361919i	0.0193170	+	0.0140346i
$666$	23.2714	+	16.9077i	0.901750	+	0.655160i
$667$	−5.83716	+	17.9649i	−0.226016	+	0.695604i
$668$	14.6134	+	44.9753i	0.565408	+	1.74015i
$669$	16.0781	−	11.6814i	0.621617	−	0.451631i
$670$	−4.57014			−0.176560
$671$	30.4869	+	10.1722i	1.17694	+	0.392695i
$672$	7.84148			0.302492
$673$	−0.0802241	+	0.0582862i	−0.00309241	+	0.00224677i	−0.589330	−	0.807892i	$-0.700608\pi$
$673$	−0.0802241	+	0.0582862i	−0.00309241	+	0.00224677i	0.586238	+	0.810139i	$0.300608\pi$
$674$	−18.0019	−	55.4042i	−0.693408	−	2.13409i
$675$	1.63437	−	5.03008i	0.0629070	−	0.193608i
$676$	28.9893	+	21.0619i	1.11497	+	0.810075i
$677$	−0.921422	−	0.669452i	−0.0354131	−	0.0257291i	0.569938	−	0.821688i	$-0.306967\pi$
$677$	−0.921422	−	0.669452i	−0.0354131	−	0.0257291i	−0.605351	+	0.795959i	$0.706967\pi$
$678$	5.77836	−	17.7840i	0.221917	−	0.682989i
$679$	5.38564	+	16.5753i	0.206682	+	0.636101i
$680$	11.9973	−	8.71654i	0.460075	−	0.334264i
$681$	−7.36199			−0.282112
$682$	0.540659	−	68.5721i	0.0207029	−	2.62576i
$683$	4.89316			0.187232			0.0936158	−	0.995608i	$-0.470157\pi$
$683$	4.89316			0.187232			0.0936158	+	0.995608i	$0.470157\pi$
$684$	2.55528	−	1.85652i	0.0977037	−	0.0709859i
$685$	3.20152	+	9.85328i	0.122324	+	0.376474i
$686$	0.683770	−	2.10443i	0.0261065	−	0.0803474i
$687$	0.840439	+	0.610614i	0.0320647	+	0.0232964i
$688$	−4.08536	−	2.96819i	−0.155753	−	0.113161i
$689$	2.57877	−	7.93665i	0.0982434	−	0.302362i
$690$	−1.34140	−	4.12841i	−0.0510663	−	0.157166i
$691$	14.0027	−	10.1735i	0.532686	−	0.387019i	−0.288675	−	0.957427i	$-0.593215\pi$
$691$	14.0027	−	10.1735i	0.532686	−	0.387019i	0.821362	+	0.570408i	$0.193215\pi$
$692$	18.4777			0.702417
$693$	3.41531	+	4.77956i	0.129737	+	0.181561i
$694$	12.9490			0.491537
$695$	7.29727	−	5.30178i	0.276801	−	0.201108i
$696$	−7.25016	−	22.3137i	−0.274816	−	0.845798i
$697$	17.1936	−	52.9166i	0.651255	−	2.00436i
$698$	13.5646	+	9.85527i	0.513428	+	0.373028i
$699$	−10.2537	−	7.44972i	−0.387829	−	0.281774i
$700$	0.894962	−	2.75441i	0.0338264	−	0.104107i
$701$	2.26813	+	6.98057i	0.0856659	+	0.263653i	0.984709	−	0.174208i	$-0.0557364\pi$
$701$	2.26813	+	6.98057i	0.0856659	+	0.263653i	−0.899043	+	0.437860i	$0.855736\pi$
$702$	7.49998	−	5.44905i	0.283069	−	0.205661i
$703$	4.51922			0.170446
$704$	−25.3086	+	34.2629i	−0.953853	+	1.29133i
$705$	5.31200			0.200061
$706$	−58.0709	+	42.1910i	−2.18553	+	1.58788i
$707$	3.28872	+	10.1216i	0.123685	+	0.380664i
$708$	1.66271	−	5.11731i	0.0624886	−	0.192320i
$709$	32.4001	+	23.5401i	1.21681	+	0.884066i	0.995831	−	0.0912123i	$-0.0290742\pi$
$709$	32.4001	+	23.5401i	1.21681	+	0.884066i	0.220981	+	0.975278i	$0.429074\pi$
$710$	17.4915	+	12.7083i	0.656444	+	0.476935i
$711$	−4.79051	+	14.7437i	−0.179658	+	0.552931i
$712$	2.16914	+	6.67592i	0.0812919	+	0.250191i
$713$	−13.3783	+	9.71992i	−0.501022	+	0.364014i
$714$	−18.3435			−0.686488
$715$	−2.50499	+	0.792142i	−0.0936814	+	0.0296244i
$716$	−17.5832			−0.657114
$717$	−5.41838	+	3.93668i	−0.202353	+	0.147018i
$718$	5.34374	+	16.4463i	0.199427	+	0.613772i
$719$	−10.8688	+	33.4507i	−0.405338	+	1.24750i	0.515275	+	0.857025i	$0.327690\pi$
$719$	−10.8688	+	33.4507i	−0.405338	+	1.24750i	−0.920613	+	0.390477i	$0.872310\pi$
$720$	2.01267	+	1.46229i	0.0750077	+	0.0544963i
$721$	7.64811	+	5.55668i	0.284830	+	0.206941i
$722$	−12.7324	+	39.1863i	−0.473851	+	1.45836i
$723$	−2.08362	−	6.41272i	−0.0774907	−	0.238492i
$724$	−1.82313	+	1.32458i	−0.0677562	+	0.0492278i
$725$	10.6736			0.396408
$726$	26.9779	+	0.425442i	1.00124	+	0.0157896i
$727$	28.6567			1.06282			0.531408	−	0.847116i	$-0.321663\pi$
$727$	28.6567			1.06282			0.531408	+	0.847116i	$0.321663\pi$
$728$	1.27080	−	0.923288i	0.0470989	−	0.0342193i
$729$	5.73580	+	17.6530i	0.212437	+	0.653814i
$730$	−9.55063	+	29.3938i	−0.353485	+	1.08791i
$731$	21.7518	+	15.8036i	0.804521	+	0.584519i
$732$	25.1686	+	18.2861i	0.930260	+	0.675873i
$733$	13.4257	−	41.3201i	0.495890	−	1.52619i	−0.319675	−	0.947527i	$-0.603574\pi$
$733$	13.4257	−	41.3201i	0.495890	−	1.52619i	0.815565	−	0.578665i	$-0.196426\pi$
$734$	0.434994	+	1.33877i	0.0160559	+	0.0494151i
$735$	−0.896807	+	0.651568i	−0.0330792	+	0.0240335i
$736$	12.5188			0.461451
$737$	−6.53133	+	2.06537i	−0.240585	+	0.0760789i
$738$	−29.1586			−1.07334
$739$	−4.66034	+	3.38593i	−0.171433	+	0.124554i	−0.670193	−	0.742186i	$-0.733789\pi$
$739$	−4.66034	+	3.38593i	−0.171433	+	0.124554i	0.498760	+	0.866740i	$0.333789\pi$
$740$	−6.56864	−	20.2162i	−0.241468	−	0.743162i
$741$	0.167079	−	0.514217i	0.00613780	−	0.0188902i
$742$	18.8586	+	13.7016i	0.692322	+	0.503001i
$743$	−23.6460	−	17.1798i	−0.867488	−	0.630267i	0.0624239	−	0.998050i	$-0.480117\pi$
$743$	−23.6460	−	17.1798i	−0.867488	−	0.630267i	−0.929912	+	0.367783i	$0.880117\pi$
$744$	6.34706	−	19.5342i	0.232695	−	0.716160i
$745$	4.42482	+	13.6182i	0.162113	+	0.498932i
$746$	−12.1295	+	8.81259i	−0.444092	+	0.322652i
$747$	1.80690			0.0661111
$748$	42.6800	−	57.7805i	1.56054	−	2.11266i
$749$	12.3091			0.449763
$750$	−1.98439	+	1.44174i	−0.0724596	+	0.0526450i
$751$	0.302130	+	0.929861i	0.0110249	+	0.0339311i	0.956418	−	0.292002i	$-0.0943215\pi$
$751$	0.302130	+	0.929861i	0.0110249	+	0.0339311i	−0.945393	+	0.325933i	$0.894321\pi$
$752$	−2.07992	+	6.40134i	−0.0758469	+	0.233433i
$753$	−4.13464	−	3.00399i	−0.150675	−	0.109472i
$754$	15.1357	+	10.9967i	0.551211	+	0.400478i
$755$	−0.212045	+	0.652608i	−0.00771711	+	0.0237508i
$756$	4.73340	+	14.5679i	0.172152	+	0.529830i
$757$	−21.7740	+	15.8198i	−0.791390	+	0.574979i	−0.908376	−	0.418155i	$-0.862677\pi$
$757$	−21.7740	+	15.8198i	−0.791390	+	0.574979i	0.116985	+	0.993134i	$0.462677\pi$
$758$	21.7788			0.791043
$759$	−3.78278	−	5.29383i	−0.137306	−	0.192154i
$760$	−1.22097			−0.0442892
$761$	31.8032	−	23.1063i	1.15286	−	0.837604i	0.164004	−	0.986460i	$-0.447559\pi$
$761$	31.8032	−	23.1063i	1.15286	−	0.837604i	0.988859	+	0.148855i	$0.0475588\pi$
$762$	16.9711	+	52.2316i	0.614797	+	1.89215i
$763$	1.63171	−	5.02190i	0.0590720	−	0.181805i
$764$	−12.1843	−	8.85240i	−0.440812	−	0.320269i
$765$	−10.7161	−	7.78572i	−0.387442	−	0.281493i
$766$	12.8997	−	39.7013i	0.466087	−	1.43447i
$767$	0.410261	+	1.26265i	0.0148137	+	0.0455918i
$768$	−5.28340	+	3.83861i	−0.190648	+	0.138514i
$769$	43.0211			1.55138			0.775691	−	0.631113i	$-0.217402\pi$
$769$	43.0211			1.55138			0.775691	+	0.631113i	$0.217402\pi$
$770$	0.0578611	−	7.33856i	0.00208517	−	0.264463i
$771$	12.9924			0.467911
$772$	10.4096	−	7.56300i	0.374649	−	0.272198i
$773$	0.447820	+	1.37825i	0.0161070	+	0.0495722i	0.958787	−	0.284126i	$-0.0917034\pi$
$773$	0.447820	+	1.37825i	0.0161070	+	0.0495722i	−0.942680	+	0.333698i	$0.891703\pi$
$774$	4.35414	−	13.4007i	0.156506	−	0.481677i
$775$	7.55952	+	5.49232i	0.271546	+	0.197290i
$776$	−27.9592	−	20.3136i	−1.00368	−	0.729214i
$777$	−2.51417	+	7.73782i	−0.0901953	+	0.277593i
$778$	−3.41009	−	10.4952i	−0.122258	−	0.376270i
$779$	−3.70614	+	2.69267i	−0.132786	+	0.0964749i
$780$	−2.54314			−0.0910589
$781$	30.7409	+	10.2570i	1.10000	+	0.367024i
$782$	−29.2852			−1.04724
$783$	−45.6707	+	33.1817i	−1.63214	+	1.18582i
$784$	−0.434040	−	1.33584i	−0.0155014	−	0.0477085i
$785$	−0.709085	+	2.18234i	−0.0253083	+	0.0778910i
$786$	1.19180	+	0.865893i	0.0425101	+	0.0308854i
$787$	−34.8231	−	25.3005i	−1.24131	−	0.901864i	−0.243625	−	0.969870i	$-0.578337\pi$
$787$	−34.8231	−	25.3005i	−1.24131	−	0.901864i	−0.997685	+	0.0680051i	$0.978337\pi$
$788$	8.28543	−	25.4999i	0.295156	−	0.908398i
$789$	−6.47432	−	19.9259i	−0.230492	−	0.709381i
$790$	15.6682	−	11.3836i	0.557448	−	0.405010i
$791$	−7.62349			−0.271060
$792$	−11.0498	−	3.68686i	−0.392637	−	0.131007i
$793$	−7.67618			−0.272589
$794$	−16.9698	+	12.3293i	−0.602237	+	0.437551i
$795$	−3.60868	−	11.1064i	−0.127987	−	0.393902i
$796$	−9.30928	+	28.6510i	−0.329959	+	1.01551i
$797$	18.8906	+	13.7248i	0.669139	+	0.486158i	0.869737	−	0.493516i	$-0.164289\pi$
$797$	18.8906	+	13.7248i	0.669139	+	0.486158i	−0.200598	+	0.979674i	$0.564289\pi$
$798$	1.22185	+	0.887728i	0.0432531	+	0.0314252i
$799$	11.0742	−	34.0829i	0.391777	−	1.20577i
$800$	−2.18594	−	6.72765i	−0.0772848	−	0.237858i
$801$	5.07244	−	3.68535i	0.179226	−	0.130215i
$802$	39.4939			1.39458
$803$	−0.365242	+	46.3239i	−0.0128891	+	1.63473i
$804$	−6.63079			−0.233850
$805$	−1.43174	+	1.04022i	−0.0504623	+	0.0366630i
$806$	5.06120	+	15.5768i	0.178273	+	0.548668i
$807$	−0.119540	+	0.367907i	−0.00420801	+	0.0129509i
$808$	−17.0732	−	12.4044i	−0.600633	−	0.436386i
$809$	3.76170	+	2.73304i	0.132254	+	0.0960884i	0.651946	−	0.758266i	$-0.273953\pi$
$809$	3.76170	+	2.73304i	0.132254	+	0.0960884i	−0.519691	+	0.854354i	$0.673953\pi$
$810$	0.375575	−	1.15590i	0.0131964	−	0.0406142i
$811$	12.7838	+	39.3443i	0.448898	+	1.38157i	0.878152	+	0.478382i	$0.158777\pi$
$811$	12.7838	+	39.3443i	0.448898	+	1.38157i	−0.429253	+	0.903184i	$0.641223\pi$
$812$	−25.0087	+	18.1699i	−0.877634	+	0.637638i
$813$	13.5452			0.475051
$814$	−31.3157	−	43.8248i	−1.09761	−	1.53606i
$815$	19.6498			0.688303
$816$	−9.42019	+	6.84417i	−0.329773	+	0.239594i
$817$	−0.684069	−	2.10535i	−0.0239325	−	0.0736568i
$818$	−12.9962	+	39.9983i	−0.454402	+	1.39851i
$819$	−1.13509	−	0.824692i	−0.0396633	−	0.0288171i
$820$	17.4322	+	12.6652i	0.608758	+	0.442289i
$821$	8.76517	−	26.9764i	0.305906	−	0.941483i	−0.673431	−	0.739250i	$-0.735180\pi$
$821$	8.76517	−	26.9764i	0.305906	−	0.941483i	0.979337	−	0.202233i	$-0.0648199\pi$
$822$	7.85282	+	24.1685i	0.273899	+	0.842973i
$823$	−31.5869	+	22.9492i	−1.10105	+	0.799960i	−0.981231	−	0.192835i	$-0.938232\pi$
$823$	−31.5869	+	22.9492i	−1.10105	+	0.799960i	−0.119820	+	0.992796i	$0.538232\pi$
$824$	−18.7460			−0.653048
$825$	−2.18439	+	2.95724i	−0.0760507	+	0.102958i
$826$	−3.70851			−0.129036
$827$	23.7017	−	17.2203i	0.824188	−	0.598808i	−0.0937207	−	0.995599i	$-0.529876\pi$
$827$	23.7017	−	17.2203i	0.824188	−	0.598808i	0.917909	+	0.396791i	$0.129876\pi$
$828$	2.80530	+	8.63382i	0.0974908	+	0.300046i
$829$	0.937829	−	2.88634i	0.0325721	−	0.100247i	−0.933449	−	0.358711i	$-0.883216\pi$
$829$	0.937829	−	2.88634i	0.0325721	−	0.100247i	0.966021	+	0.258464i	$0.0832164\pi$
$830$	−1.82622	−	1.32683i	−0.0633890	−	0.0460548i
$831$	−14.8800	−	10.8109i	−0.516181	−	0.375027i
$832$	3.14389	−	9.67590i	0.108995	−	0.335451i
$833$	2.31098	+	7.11246i	0.0800706	+	0.246432i
$834$	17.8990	−	13.0044i	0.619793	−	0.450306i
$835$	−16.3285			−0.565070
$836$	−5.63917	+	1.78325i	−0.195035	+	0.0616748i
$837$	−49.4203			−1.70821
$838$	−3.43031	+	2.49227i	−0.118498	+	0.0860940i
$839$	−10.8558	−	33.4108i	−0.374784	−	1.15347i	−0.943624	−	0.331019i	$-0.892607\pi$
$839$	−10.8558	−	33.4108i	−0.374784	−	1.15347i	0.568839	−	0.822449i	$-0.307393\pi$
$840$	0.679260	−	2.09055i	0.0234367	−	0.0721307i
$841$	−68.7066	−	49.9183i	−2.36919	−	1.72132i
$842$	−65.7002	−	47.7340i	−2.26418	−	1.64502i
$843$	0.709847	−	2.18469i	0.0244484	−	0.0752446i
$844$	10.2609	+	31.5797i	0.353194	+	1.08702i
$845$	−10.0096	+	7.27237i	−0.344339	+	0.250177i
$846$	−18.7807			−0.645693
$847$	−3.23380	−	10.5139i	−0.111115	−	0.361263i
$848$	14.7970			0.508130
$849$	−5.38866	+	3.91509i	−0.184938	+	0.134365i
$850$	5.11356	+	15.7379i	0.175394	+	0.539806i
$851$	−4.01385	+	12.3533i	−0.137593	+	0.423467i
$852$	25.3783	+	18.4384i	0.869447	+	0.631690i
$853$	−33.0724	−	24.0285i	−1.13238	−	0.822720i	−0.146338	−	0.989235i	$-0.546749\pi$
$853$	−33.0724	−	24.0285i	−1.13238	−	0.822720i	−0.986039	+	0.166514i	$0.946749\pi$
$854$	6.62596	−	20.3926i	0.226736	−	0.697821i
$855$	0.337009	+	1.03721i	0.0115255	+	0.0354717i
$856$	−19.7467	+	14.3468i	−0.674929	+	0.490364i
$857$	4.02385			0.137452			0.0687260	−	0.997636i	$-0.478107\pi$
$857$	4.02385			0.137452			0.0687260	+	0.997636i	$0.478107\pi$
$858$	−6.14434	+	1.94300i	−0.209764	+	0.0663328i
$859$	−42.6505			−1.45522			−0.727608	−	0.685993i	$-0.759368\pi$
$859$	−42.6505			−1.45522			−0.727608	+	0.685993i	$0.759368\pi$
$860$	−8.42374	+	6.12021i	−0.287247	+	0.208697i
$861$	−2.54856	−	7.84367i	−0.0868548	−	0.267312i
$862$	−23.6581	+	72.8120i	−0.805797	+	2.47999i
$863$	15.6895	+	11.3991i	0.534077	+	0.388029i	0.821880	−	0.569660i	$-0.192925\pi$
$863$	15.6895	+	11.3991i	0.534077	+	0.388029i	−0.287804	+	0.957689i	$0.592925\pi$
$864$	30.2679	+	21.9910i	1.02974	+	0.748147i
$865$	−1.97155	+	6.06781i	−0.0670347	+	0.206312i
$866$	−4.35101	−	13.3910i	−0.147853	−	0.455046i
$867$	34.9106	−	25.3640i	1.18562	−	0.861407i
$868$	−27.0619			−0.918542
$869$	17.2473	−	23.3495i	0.585076	−	0.792079i
$870$	26.1806			0.887607
$871$	1.32363	−	0.961671i	0.0448494	−	0.0325850i
$872$	3.23561	+	9.95818i	0.109572	+	0.337227i
$873$	−9.53903	+	29.3581i	−0.322847	+	0.993621i
$874$	1.95068	+	1.41725i	0.0659826	+	0.0479392i
$875$	0.809017	+	0.587785i	0.0273498	+	0.0198708i
$876$	−13.8570	+	42.6473i	−0.468183	+	1.44092i
$877$	8.07142	+	24.8413i	0.272552	+	0.838830i	0.989857	+	0.142070i	$0.0453758\pi$
$877$	8.07142	+	24.8413i	0.272552	+	0.838830i	−0.717304	+	0.696760i	$0.754624\pi$
$878$	−10.4679	+	7.60538i	−0.353275	+	0.256669i
$879$	−27.6936			−0.934084
$880$	−2.70839	−	3.79026i	−0.0912997	−	0.127770i
$881$	−3.57429			−0.120421			−0.0602105	−	0.998186i	$-0.519177\pi$
$881$	−3.57429			−0.120421			−0.0602105	+	0.998186i	$0.519177\pi$
$882$	3.17068	−	2.30363i	0.106762	−	0.0775674i
$883$	−8.21032	−	25.2688i	−0.276299	−	0.850362i	−0.988873	−	0.148764i	$-0.952470\pi$
$883$	−8.21032	−	25.2688i	−0.276299	−	0.850362i	0.712573	−	0.701598i	$-0.247530\pi$
$884$	−5.30181	+	16.3173i	−0.178319	+	0.548810i
$885$	1.50304	+	1.09202i	0.0505241	+	0.0367079i
$886$	−25.1134	−	18.2459i	−0.843701	−	0.612985i
$887$	−2.87355	+	8.84387i	−0.0964843	+	0.296948i	−0.987638	−	0.156754i	$-0.949897\pi$
$887$	−2.87355	+	8.84387i	−0.0964843	+	0.296948i	0.891153	+	0.453702i	$0.149897\pi$
$888$	−4.98548	−	15.3437i	−0.167302	−	0.514902i
$889$	18.1140	−	13.1606i	0.607526	−	0.441393i
$890$	−7.83286			−0.262558
$891$	0.0143630	−	1.82167i	0.000481178	−	0.0610282i
$892$	51.9229			1.73851
$893$	−2.38708	+	1.73431i	−0.0798805	+	0.0580366i
$894$	10.8534	+	33.4033i	0.362991	+	1.11717i
$895$	1.87610	−	5.77406i	0.0627113	−	0.193005i
$896$	11.5456	+	8.38835i	0.385711	+	0.280235i
$897$	1.25722	+	0.913426i	0.0419775	+	0.0304984i
$898$	−25.7791	+	79.3399i	−0.860260	+	2.64761i
$899$	−30.8199	−	94.8538i	−1.02790	−	3.16355i
$900$	4.14999	−	3.01514i	0.138333	−	0.100505i
$901$	−78.7840			−2.62467
$902$	51.7935	+	17.2814i	1.72453	+	0.575406i
$903$	3.98535			0.132624
$904$	12.2299	−	8.88556i	0.406761	−	0.295529i
$905$	−0.240448	−	0.740023i	−0.00799276	−	0.0245992i
$906$	−0.520112	+	1.60074i	−0.0172796	+	0.0531811i
$907$	−7.11095	−	5.16641i	−0.236115	−	0.171548i	0.463436	−	0.886131i	$-0.346617\pi$
$907$	−7.11095	−	5.16641i	−0.236115	−	0.171548i	−0.699551	+	0.714583i	$0.746617\pi$
$908$	−15.5609	−	11.3056i	−0.516406	−	0.375191i
$909$	−5.82498	+	17.9274i	−0.193202	+	0.594615i
$910$	0.541647	+	1.66702i	0.0179554	+	0.0552611i
$911$	5.95304	−	4.32514i	0.197233	−	0.143298i	−0.484785	−	0.874633i	$-0.661102\pi$
$911$	5.95304	−	4.32514i	0.197233	−	0.143298i	0.682019	+	0.731335i	$0.261102\pi$
$912$	0.958697			0.0317456
$913$	−3.20954	−	1.07089i	−0.106220	−	0.0354413i
$914$	−26.4166			−0.873783
$915$	−8.69036	+	6.31391i	−0.287294	+	0.208732i
$916$	0.838710	+	2.58128i	0.0277118	+	0.0852880i
$917$	0.185592	−	0.571193i	0.00612878	−	0.0188625i
$918$	−70.8055	−	51.4432i	−2.33693	−	1.69788i
$919$	23.8168	+	17.3039i	0.785644	+	0.570804i	0.906667	−	0.421846i	$-0.138618\pi$
$919$	23.8168	+	17.3039i	0.785644	+	0.570804i	−0.121024	+	0.992650i	$0.538618\pi$
$920$	1.08443	−	3.33754i	0.0357526	−	0.110035i
$921$	9.79616	+	30.1495i	0.322794	+	0.993459i
$922$	58.2863	−	42.3474i	1.91956	−	1.39464i
$923$	−7.74013			−0.254769
$924$	0.0839503	−	10.6475i	0.00276176	−	0.350276i
$925$	7.33958			0.241324
$926$	−19.8835	+	14.4462i	−0.653411	+	0.474731i
$927$	5.17423	+	15.9246i	0.169944	+	0.523034i
$928$	−23.3319	+	71.8083i	−0.765908	+	2.35722i
$929$	−15.9549	−	11.5919i	−0.523464	−	0.380319i	0.294443	−	0.955669i	$-0.404866\pi$
$929$	−15.9549	−	11.5919i	−0.523464	−	0.380319i	−0.817907	+	0.575350i	$0.804866\pi$
$930$	18.5423	+	13.4718i	0.608025	+	0.441756i
$931$	0.190272	−	0.585597i	0.00623591	−	0.0191922i
$932$	−10.2326	−	31.4926i	−0.335179	−	1.03157i
$933$	−11.5489	+	8.39076i	−0.378094	+	0.274701i
$934$	−32.6464			−1.06822
$935$	14.4204	+	20.1806i	0.471596	+	0.659977i
$936$	2.78218			0.0909385
$937$	1.31599	−	0.956123i	0.0429916	−	0.0312352i	−0.566082	−	0.824349i	$-0.691541\pi$
$937$	1.31599	−	0.956123i	0.0429916	−	0.0312352i	0.609074	+	0.793114i	$0.291541\pi$
$938$	1.41225	+	4.34646i	0.0461116	+	0.141917i
$939$	−3.98700	+	12.2707i	−0.130111	+	0.400440i
$940$	11.2278	+	8.15751i	0.366212	+	0.266069i
$941$	31.5442	+	22.9182i	1.02831	+	0.747113i	0.967970	−	0.251065i	$-0.0807808\pi$
$941$	31.5442	+	22.9182i	1.02831	+	0.747113i	0.0603422	+	0.998178i	$0.480781\pi$
$942$	−1.73927	+	5.35292i	−0.0566685	+	0.174408i
$943$	−4.06876	−	12.5223i	−0.132497	−	0.407784i
$944$	−1.90448	+	1.38369i	−0.0619857	+	0.0450352i
$945$	−5.28894			−0.172049
$946$	−15.6762	+	21.2226i	−0.509679	+	0.690006i
$947$	49.9675			1.62373			0.811863	−	0.583849i	$-0.198454\pi$
$947$	49.9675			1.62373			0.811863	+	0.583849i	$0.198454\pi$
$948$	22.7328	−	16.5164i	0.738329	−	0.536427i
$949$	−3.41909	−	10.5229i	−0.110988	−	0.341587i
$950$	0.421020	−	1.29577i	0.0136597	−	0.0420402i
$951$	10.3906	+	7.54924i	0.336940	+	0.244801i
$952$	−11.9973	−	8.71654i	−0.388834	−	0.282505i
$953$	−9.69170	+	29.8280i	−0.313945	+	0.966223i	0.662242	+	0.749290i	$0.269605\pi$
$953$	−9.69170	+	29.8280i	−0.313945	+	0.966223i	−0.976187	+	0.216933i	$0.930395\pi$
$954$	12.7586	+	39.2668i	0.413073	+	1.27131i
$955$	4.20705	−	3.05660i	0.136137	−	0.0989093i
$956$	−17.4982			−0.565932
$957$	37.4156	−	11.8318i	1.20948	−	0.382466i
$958$	−73.4583			−2.37333
$959$	8.38170	−	6.08966i	0.270659	−	0.196645i
$960$	−4.39949	−	13.5402i	−0.141993	−	0.437009i
$961$	17.4013	−	53.5558i	0.561334	−	1.72761i
$962$	10.4079	+	7.56177i	0.335564	+	0.243801i
$963$	17.6380	+	12.8148i	0.568377	+	0.412950i
$964$	5.44377	−	16.7542i	0.175332	−	0.539616i
$965$	1.37289	+	4.22532i	0.0441949	+	0.136018i
$966$	−3.51183	+	2.55150i	−0.112991	+	0.0820931i
$967$	36.5295			1.17471			0.587354	−	0.809330i	$-0.300170\pi$
$967$	36.5295			1.17471			0.587354	+	0.809330i	$0.300170\pi$
$968$	17.4423	+	13.0977i	0.560617	+	0.420976i
$969$	−5.10442			−0.163978
$970$	31.1990	−	22.6674i	1.00174	−	0.727806i
$971$	−14.5536	−	44.7913i	−0.467046	−	1.43742i	−0.856391	−	0.516329i	$-0.827298\pi$
$971$	−14.5536	−	44.7913i	−0.467046	−	1.43742i	0.389344	−	0.921092i	$-0.372702\pi$
$972$	−13.6553	+	42.0266i	−0.437993	+	1.34800i
$973$	−7.29727	−	5.30178i	−0.233940	−	0.169967i
$974$	−0.840413	−	0.610596i	−0.0269286	−	0.0195648i
$975$	0.271350	−	0.835129i	0.00869015	−	0.0267455i
$976$	−4.20600	−	12.9447i	−0.134631	−	0.414351i
$977$	−22.0952	+	16.0531i	−0.706887	+	0.513583i	−0.882168	−	0.470935i	$-0.843917\pi$
$977$	−22.0952	+	16.0531i	−0.706887	+	0.513583i	0.175281	+	0.984518i	$0.443917\pi$
$978$	48.1978			1.54120
$979$	−11.1942	+	3.53989i	−0.357768	+	0.113135i
$980$	−2.89616			−0.0925144
$981$	7.56634	−	5.49727i	0.241575	−	0.175514i
$982$	20.6024	+	63.4077i	0.657450	+	2.02342i
$983$	−14.7991	+	45.5470i	−0.472019	+	1.45272i	0.377917	+	0.925839i	$0.376640\pi$
$983$	−14.7991	+	45.5470i	−0.472019	+	1.45272i	−0.849936	+	0.526886i	$0.823360\pi$
$984$	13.2307	+	9.61267i	0.421780	+	0.306441i
$985$	7.48977	+	5.44163i	0.238644	+	0.173385i
$986$	54.5802	−	167.980i	1.73819	−	5.34959i
$987$	−1.64150	−	5.05201i	−0.0522494	−	0.160807i
$988$	1.14282	−	0.830309i	0.0363580	−	0.0264156i
$989$	6.36257			0.202318
$990$	7.72296	−	10.4554i	0.245452	−	0.332294i
$991$	−40.5949			−1.28954			−0.644770	−	0.764377i	$-0.723047\pi$
$991$	−40.5949			−1.28954			−0.644770	+	0.764377i	$0.723047\pi$
$992$	−53.4751	+	38.8519i	−1.69783	+	1.23355i
$993$	7.14758	+	21.9980i	0.226822	+	0.698085i
$994$	6.68116	−	20.5625i	0.211914	−	0.652203i
$995$	−8.41529	−	6.11406i	−0.266783	−	0.193829i
$996$	−2.64965	−	1.92508i	−0.0839574	−	0.0609986i
$997$	5.60273	−	17.2434i	0.177440	−	0.546105i	−0.822296	−	0.569060i	$-0.807307\pi$
$997$	5.60273	−	17.2434i	0.177440	−	0.546105i	0.999737	+	0.0229548i	$0.00730739\pi$
$998$	27.8296	+	85.6507i	0.880931	+	2.71123i
$999$	−31.4049	+	22.8170i	−0.993606	+	0.721897i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	385.2.n.e.36.2	✓	28
11.2	odd	10		4235.2.a.bn.1.3		14
11.4	even	5	inner	385.2.n.e.246.2	yes	28
11.9	even	5		4235.2.a.bm.1.12		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
385.2.n.e.36.2	✓	28	1.1	even	1	trivial
385.2.n.e.246.2	yes	28	11.4	even	5	inner
4235.2.a.bm.1.12		14	11.9	even	5
4235.2.a.bn.1.3		14	11.2	odd	10

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)

\(f(q)\)	\(=\)	\(q+(-1.79013 + 1.30061i) q^{2} +(-0.342550 - 1.05426i) q^{3} +(0.894962 - 2.75441i) q^{4} +(0.809017 + 0.587785i) q^{5} +(1.98439 + 1.44174i) q^{6} +(0.309017 - 0.951057i) q^{7} +(0.612766 + 1.88590i) q^{8} +(1.43293 - 1.04108i) q^{9} +O(q^{10})\)	\(q+(-1.79013 + 1.30061i) q^{2} +(-0.342550 - 1.05426i) q^{3} +(0.894962 - 2.75441i) q^{4} +(0.809017 + 0.587785i) q^{5} +(1.98439 + 1.44174i) q^{6} +(0.309017 - 0.951057i) q^{7} +(0.612766 + 1.88590i) q^{8} +(1.43293 - 1.04108i) q^{9} -2.21273 q^{10} +(-3.16228 + 0.999992i) q^{11} -3.21043 q^{12} +(0.640861 - 0.465613i) q^{13} +(0.683770 + 2.10443i) q^{14} +(0.342550 - 1.05426i) q^{15} +(1.13633 + 0.825594i) q^{16} +(-6.05022 - 4.39574i) q^{17} +(-1.21109 + 3.72736i) q^{18} +(0.190272 + 0.585597i) q^{19} +(2.34304 - 1.70232i) q^{20} -1.10851 q^{21} +(4.36031 - 5.90301i) q^{22} -1.76973 q^{23} +(1.77833 - 1.29203i) q^{24} +(0.309017 + 0.951057i) q^{25} +(-0.541647 + 1.66702i) q^{26} +(-4.27884 - 3.10876i) q^{27} +(-2.34304 - 1.70232i) q^{28} +(3.29833 - 10.1512i) q^{29} +(0.757969 + 2.33279i) q^{30} +(7.55952 - 5.49232i) q^{31} -7.07387 q^{32} +(2.13749 + 2.99132i) q^{33} +16.5478 q^{34} +(0.809017 - 0.587785i) q^{35} +(-1.58515 - 4.87860i) q^{36} +(2.26805 - 6.98035i) q^{37} +(-1.10224 - 0.800827i) q^{38} +(-0.710403 - 0.516138i) q^{39} +(-0.612766 + 1.88590i) q^{40} +(2.29908 + 7.07585i) q^{41} +(1.98439 - 1.44174i) q^{42} -3.59522 q^{43} +(-0.0757323 + 9.60517i) q^{44} +1.77120 q^{45} +(3.16806 - 2.30173i) q^{46} +(1.48081 + 4.55746i) q^{47} +(0.481140 - 1.48080i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(-1.79013 - 1.30061i) q^{50} +(-2.56175 + 7.88426i) q^{51} +(-0.708942 - 2.18190i) q^{52} +(8.52280 - 6.19218i) q^{53} +11.7030 q^{54} +(-3.14612 - 1.04973i) q^{55} +1.98295 q^{56} +(0.552193 - 0.401192i) q^{57} +(7.29830 + 22.4619i) q^{58} +(-0.517910 + 1.59396i) q^{59} +(-2.59729 - 1.88704i) q^{60} +(-7.83965 - 5.69584i) q^{61} +(-6.38921 + 19.6640i) q^{62} +(-0.547330 - 1.68451i) q^{63} +(10.3905 - 7.54914i) q^{64} +0.792148 q^{65} +(-7.71692 - 2.57482i) q^{66} +2.06539 q^{67} +(-17.5224 + 12.7308i) q^{68} +(0.606221 + 1.86576i) q^{69} +(-0.683770 + 2.10443i) q^{70} +(-7.90496 - 5.74329i) q^{71} +(2.84143 + 2.06442i) q^{72} +(4.31623 - 13.2840i) q^{73} +(5.01858 + 15.4456i) q^{74} +(0.896807 - 0.651568i) q^{75} +1.78326 q^{76} +(-0.0261492 + 3.31652i) q^{77} +1.94301 q^{78} +(-7.08093 + 5.14460i) q^{79} +(0.434040 + 1.33584i) q^{80} +(-0.169734 + 0.522387i) q^{81} +(-13.3186 - 9.67650i) q^{82} +(0.825326 + 0.599634i) q^{83} +(-0.992078 + 3.05330i) q^{84} +(-2.31098 - 7.11246i) q^{85} +(6.43592 - 4.67597i) q^{86} -11.8319 q^{87} +(-3.82362 - 5.35098i) q^{88} +3.53991 q^{89} +(-3.17068 + 2.30363i) q^{90} +(-0.244787 - 0.753377i) q^{91} +(-1.58384 + 4.87457i) q^{92} +(-8.37984 - 6.08831i) q^{93} +(-8.57832 - 6.23251i) q^{94} +(-0.190272 + 0.585597i) q^{95} +(2.42315 + 7.45769i) q^{96} +(-14.0998 + 10.2441i) q^{97} +2.21273 q^{98} +(-3.49025 + 4.72511i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 3 q^{2} - 3 q^{4} + 7 q^{5} + 7 q^{6} - 7 q^{7} - q^{8} - q^{9}+O(q^{10}) \) 28 * q + 3 * q^2 - 3 * q^4 + 7 * q^5 + 7 * q^6 - 7 * q^7 - q^8 - q^9	\( 28 q + 3 q^{2} - 3 q^{4} + 7 q^{5} + 7 q^{6} - 7 q^{7} - q^{8} - q^{9} + 2 q^{10} - 3 q^{11} + 30 q^{12} - 5 q^{13} - 2 q^{14} - 33 q^{16} + 7 q^{17} - 17 q^{18} - 13 q^{19} + 18 q^{20} + 10 q^{21} + 3 q^{22} + 16 q^{23} + 39 q^{24} - 7 q^{25} + 44 q^{26} - 18 q^{27} - 18 q^{28} + 7 q^{29} + 8 q^{30} + 7 q^{31} - 84 q^{32} + 4 q^{33} + 32 q^{34} + 7 q^{35} + 6 q^{36} - 24 q^{37} - 15 q^{38} - 18 q^{39} + q^{40} - 4 q^{41} + 7 q^{42} + q^{44} - 34 q^{45} + 3 q^{46} - 33 q^{47} + 83 q^{48} - 7 q^{49} + 3 q^{50} + 14 q^{51} + 24 q^{52} - 8 q^{53} - 114 q^{54} - 17 q^{55} - 6 q^{56} + 57 q^{57} - 16 q^{58} - 3 q^{59} + 15 q^{60} - 21 q^{61} - 19 q^{62} - 16 q^{63} - 19 q^{64} - 20 q^{65} - 126 q^{66} + 90 q^{67} - 7 q^{68} - 55 q^{69} + 2 q^{70} - 37 q^{71} + 117 q^{72} + 17 q^{73} + 49 q^{74} - 5 q^{75} - 10 q^{76} - 3 q^{77} + 104 q^{78} - 45 q^{79} - 2 q^{80} + 8 q^{81} - 48 q^{82} + q^{83} + 18 q^{85} + 134 q^{86} + 46 q^{87} + 74 q^{88} - 30 q^{89} - 38 q^{90} - 5 q^{91} + 18 q^{92} - 57 q^{93} + 43 q^{94} + 13 q^{95} - 119 q^{96} - 82 q^{97} - 2 q^{98} - 72 q^{99}+O(q^{100}) \) 28 * q + 3 * q^2 - 3 * q^4 + 7 * q^5 + 7 * q^6 - 7 * q^7 - q^8 - q^9 + 2 * q^10 - 3 * q^11 + 30 * q^12 - 5 * q^13 - 2 * q^14 - 33 * q^16 + 7 * q^17 - 17 * q^18 - 13 * q^19 + 18 * q^20 + 10 * q^21 + 3 * q^22 + 16 * q^23 + 39 * q^24 - 7 * q^25 + 44 * q^26 - 18 * q^27 - 18 * q^28 + 7 * q^29 + 8 * q^30 + 7 * q^31 - 84 * q^32 + 4 * q^33 + 32 * q^34 + 7 * q^35 + 6 * q^36 - 24 * q^37 - 15 * q^38 - 18 * q^39 + q^40 - 4 * q^41 + 7 * q^42 + q^44 - 34 * q^45 + 3 * q^46 - 33 * q^47 + 83 * q^48 - 7 * q^49 + 3 * q^50 + 14 * q^51 + 24 * q^52 - 8 * q^53 - 114 * q^54 - 17 * q^55 - 6 * q^56 + 57 * q^57 - 16 * q^58 - 3 * q^59 + 15 * q^60 - 21 * q^61 - 19 * q^62 - 16 * q^63 - 19 * q^64 - 20 * q^65 - 126 * q^66 + 90 * q^67 - 7 * q^68 - 55 * q^69 + 2 * q^70 - 37 * q^71 + 117 * q^72 + 17 * q^73 + 49 * q^74 - 5 * q^75 - 10 * q^76 - 3 * q^77 + 104 * q^78 - 45 * q^79 - 2 * q^80 + 8 * q^81 - 48 * q^82 + q^83 + 18 * q^85 + 134 * q^86 + 46 * q^87 + 74 * q^88 - 30 * q^89 - 38 * q^90 - 5 * q^91 + 18 * q^92 - 57 * q^93 + 43 * q^94 + 13 * q^95 - 119 * q^96 - 82 * q^97 - 2 * q^98 - 72 * q^99

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