LMFDB - Embedded newform 770.2.n.h.71.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,2,Mod(71,770)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("770.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.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:	$6.14848095564$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + 7 x^{10} - 9 x^{9} + 55 x^{8} - 32 x^{7} + 287 x^{6} - 302 x^{5} + 1175 x^{4} + \cdots + 361 $ x^12 - 3x^11 + 7x^10 - 9x^9 + 55x^8 - 32x^7 + 287x^6 - 302x^5 + 1175x^4 - 1639x^3 + 1692x^2 - 988*x + 361
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			71.1
Root			$2.55917 - 1.85934i$ of defining polynomial
Character	$\chi$	$=$	770.71
Dual form			770.2.n.h.141.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 + 0.951057i) q^{2} +(-1.75015 - 1.27156i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-0.309017 + 0.951057i) q^{5} +(0.668497 - 2.05742i) q^{6} +(-0.809017 + 0.587785i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(0.519111 + 1.59766i) q^{9} +O(q^{10})$	\(q+(0.309017 + 0.951057i) q^{2} +(-1.75015 - 1.27156i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-0.309017 + 0.951057i) q^{5} +(0.668497 - 2.05742i) q^{6} +(-0.809017 + 0.587785i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(0.519111 + 1.59766i) q^{9} -1.00000 q^{10} +(2.65784 - 1.98390i) q^{11} +2.16330 q^{12} +(-1.21150 - 3.72860i) q^{13} +(-0.809017 - 0.587785i) q^{14} +(1.75015 - 1.27156i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-1.87268 + 5.76352i) q^{17} +(-1.35905 + 0.987408i) q^{18} +(4.66837 + 3.39177i) q^{19} +(-0.309017 - 0.951057i) q^{20} +2.16330 q^{21} +(2.70812 + 1.91470i) q^{22} +1.51437 q^{23} +(0.668497 + 2.05742i) q^{24} +(-0.809017 - 0.587785i) q^{25} +(3.17174 - 2.30440i) q^{26} +(-0.882497 + 2.71605i) q^{27} +(0.309017 - 0.951057i) q^{28} +(3.33657 - 2.42416i) q^{29} +(1.75015 + 1.27156i) q^{30} +(1.78375 + 5.48982i) q^{31} +1.00000 q^{32} +(-7.17427 + 0.0925250i) q^{33} -6.06013 q^{34} +(-0.309017 - 0.951057i) q^{35} +(-1.35905 - 0.987408i) q^{36} +(3.68791 - 2.67942i) q^{37} +(-1.78316 + 5.48799i) q^{38} +(-2.62083 + 8.06610i) q^{39} +(0.809017 - 0.587785i) q^{40} +(4.48370 + 3.25760i) q^{41} +(0.668497 + 2.05742i) q^{42} +6.51122 q^{43} +(-0.984131 + 3.16725i) q^{44} -1.67988 q^{45} +(0.467965 + 1.44025i) q^{46} +(8.83643 + 6.42004i) q^{47} +(-1.75015 + 1.27156i) q^{48} +(0.309017 - 0.951057i) q^{49} +(0.309017 - 0.951057i) q^{50} +(10.6061 - 7.70580i) q^{51} +(3.17174 + 2.30440i) q^{52} +(1.15609 + 3.55809i) q^{53} -2.85582 q^{54} +(1.06549 + 3.14082i) q^{55} +1.00000 q^{56} +(-3.85751 - 11.8722i) q^{57} +(3.33657 + 2.42416i) q^{58} +(3.05324 - 2.21831i) q^{59} +(-0.668497 + 2.05742i) q^{60} +(-0.164673 + 0.506812i) q^{61} +(-4.66992 + 3.39290i) q^{62} +(-1.35905 - 0.987408i) q^{63} +(0.309017 + 0.951057i) q^{64} +3.92049 q^{65} +(-2.30497 - 6.79454i) q^{66} -1.15993 q^{67} +(-1.87268 - 5.76352i) q^{68} +(-2.65037 - 1.92560i) q^{69} +(0.809017 - 0.587785i) q^{70} +(0.192823 - 0.593448i) q^{71} +(0.519111 - 1.59766i) q^{72} +(-2.51213 + 1.82517i) q^{73} +(3.68791 + 2.67942i) q^{74} +(0.668497 + 2.05742i) q^{75} -5.77042 q^{76} +(-0.984131 + 3.16725i) q^{77} -8.48120 q^{78} +(1.16415 + 3.58288i) q^{79} +(0.809017 + 0.587785i) q^{80} +(9.07526 - 6.59357i) q^{81} +(-1.71262 + 5.27091i) q^{82} +(-3.82374 + 11.7683i) q^{83} +(-1.75015 + 1.27156i) q^{84} +(-4.90275 - 3.56205i) q^{85} +(2.01208 + 6.19254i) q^{86} -8.92194 q^{87} +(-3.31635 + 0.0427703i) q^{88} +3.59309 q^{89} +(-0.519111 - 1.59766i) q^{90} +(3.17174 + 2.30440i) q^{91} +(-1.22515 + 0.890122i) q^{92} +(3.85879 - 11.8761i) q^{93} +(-3.37522 + 10.3879i) q^{94} +(-4.66837 + 3.39177i) q^{95} +(-1.75015 - 1.27156i) q^{96} +(-4.83375 - 14.8768i) q^{97} +1.00000 q^{98} +(4.54932 + 3.21646i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{2} - 3 q^{4} + 3 q^{5} + 5 q^{6} - 3 q^{7} - 3 q^{8} - 3 q^{9}+O(q^{10}) $ 12 * q - 3 * q^2 - 3 * q^4 + 3 * q^5 + 5 * q^6 - 3 * q^7 - 3 * q^8 - 3 * q^9	$ 12 q - 3 q^{2} - 3 q^{4} + 3 q^{5} + 5 q^{6} - 3 q^{7} - 3 q^{8} - 3 q^{9} - 12 q^{10} - q^{11} - 10 q^{12} - 3 q^{14} - 3 q^{16} - 8 q^{18} - q^{19} + 3 q^{20} - 10 q^{21} - q^{22} - 4 q^{23} + 5 q^{24} - 3 q^{25} + 3 q^{27} - 3 q^{28} + 22 q^{29} + 6 q^{31} + 12 q^{32} - 29 q^{33} - 30 q^{34} + 3 q^{35} - 8 q^{36} - 10 q^{37} + 14 q^{38} + 20 q^{39} + 3 q^{40} + 16 q^{41} + 5 q^{42} + 30 q^{43} + 14 q^{44} - 22 q^{45} - 4 q^{46} + 34 q^{47} - 3 q^{49} - 3 q^{50} + 37 q^{51} - 26 q^{53} - 52 q^{54} + 11 q^{55} + 12 q^{56} - 19 q^{57} + 22 q^{58} + q^{59} - 5 q^{60} + 40 q^{61} - 4 q^{62} - 8 q^{63} - 3 q^{64} + 16 q^{66} - 58 q^{67} + 14 q^{69} + 3 q^{70} - 14 q^{71} - 3 q^{72} + 32 q^{73} - 10 q^{74} + 5 q^{75} - 26 q^{76} + 14 q^{77} - 60 q^{78} + 16 q^{79} + 3 q^{80} - 46 q^{81} + q^{82} + 35 q^{83} - 15 q^{85} + 5 q^{86} - q^{88} - 58 q^{89} + 3 q^{90} + 6 q^{92} + 46 q^{93} - 16 q^{94} + q^{95} + 57 q^{97} + 12 q^{98} + 69 q^{99}+O(q^{100}) $ 12 * q - 3 * q^2 - 3 * q^4 + 3 * q^5 + 5 * q^6 - 3 * q^7 - 3 * q^8 - 3 * q^9 - 12 * q^10 - q^11 - 10 * q^12 - 3 * q^14 - 3 * q^16 - 8 * q^18 - q^19 + 3 * q^20 - 10 * q^21 - q^22 - 4 * q^23 + 5 * q^24 - 3 * q^25 + 3 * q^27 - 3 * q^28 + 22 * q^29 + 6 * q^31 + 12 * q^32 - 29 * q^33 - 30 * q^34 + 3 * q^35 - 8 * q^36 - 10 * q^37 + 14 * q^38 + 20 * q^39 + 3 * q^40 + 16 * q^41 + 5 * q^42 + 30 * q^43 + 14 * q^44 - 22 * q^45 - 4 * q^46 + 34 * q^47 - 3 * q^49 - 3 * q^50 + 37 * q^51 - 26 * q^53 - 52 * q^54 + 11 * q^55 + 12 * q^56 - 19 * q^57 + 22 * q^58 + q^59 - 5 * q^60 + 40 * q^61 - 4 * q^62 - 8 * q^63 - 3 * q^64 + 16 * q^66 - 58 * q^67 + 14 * q^69 + 3 * q^70 - 14 * q^71 - 3 * q^72 + 32 * q^73 - 10 * q^74 + 5 * q^75 - 26 * q^76 + 14 * q^77 - 60 * q^78 + 16 * q^79 + 3 * q^80 - 46 * q^81 + q^82 + 35 * q^83 - 15 * q^85 + 5 * q^86 - q^88 - 58 * q^89 + 3 * q^90 + 6 * q^92 + 46 * q^93 - 16 * q^94 + q^95 + 57 * q^97 + 12 * q^98 + 69 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

$n$	$211$	$617$	$661$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$1$	$1$

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 $

$2$	0.309017	+	0.951057i	0.218508	+	0.672499i
$2$	0.309017	+	0.951057i	0.218508	+	0.672499i
$3$	−1.75015	−	1.27156i	−1.01045	−	0.734134i	−0.0461457	−	0.998935i	$-0.514694\pi$
$3$	−1.75015	−	1.27156i	−1.01045	−	0.734134i	−0.964303	+	0.264801i	$0.914694\pi$
$4$	−0.809017	+	0.587785i	−0.404508	+	0.293893i
$5$	−0.309017	+	0.951057i	−0.138197	+	0.425325i
$5$	−0.309017	+	0.951057i	−0.138197	+	0.425325i
$6$	0.668497	−	2.05742i	0.272913	−	0.839940i
$7$	−0.809017	+	0.587785i	−0.305780	+	0.222162i
$7$	−0.809017	+	0.587785i	−0.305780	+	0.222162i
$8$	−0.809017	−	0.587785i	−0.286031	−	0.207813i
$9$	0.519111	+	1.59766i	0.173037	+	0.532553i
$10$	−1.00000			−0.316228
$11$	2.65784	−	1.98390i	0.801370	−	0.598169i
$11$	2.65784	−	1.98390i	0.801370	−	0.598169i
$12$	2.16330			0.624492
$13$	−1.21150	−	3.72860i	−0.336009	−	1.03413i	−0.966223	−	0.257707i	$-0.917033\pi$
$13$	−1.21150	−	3.72860i	−0.336009	−	1.03413i	0.630214	−	0.776421i	$-0.282967\pi$
$14$	−0.809017	−	0.587785i	−0.216219	−	0.157092i
$15$	1.75015	−	1.27156i	0.451886	−	0.328315i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	−1.87268	+	5.76352i	−0.454192	+	1.39786i	0.417889	+	0.908498i	$0.362770\pi$
$17$	−1.87268	+	5.76352i	−0.454192	+	1.39786i	−0.872081	+	0.489361i	$0.837230\pi$
$18$	−1.35905	+	0.987408i	−0.320331	+	0.232734i
$19$	4.66837	+	3.39177i	1.07100	+	0.778124i	0.976091	−	0.217362i	$-0.0697451\pi$
$19$	4.66837	+	3.39177i	1.07100	+	0.778124i	0.0949054	+	0.995486i	$0.469745\pi$
$20$	−0.309017	−	0.951057i	−0.0690983	−	0.212663i
$21$	2.16330			0.472071
$22$	2.70812	+	1.91470i	0.577374	+	0.408215i
$23$	1.51437			0.315767			0.157884	−	0.987458i	$-0.449533\pi$
$23$	1.51437			0.315767			0.157884	+	0.987458i	$0.449533\pi$
$24$	0.668497	+	2.05742i	0.136456	+	0.419970i
$25$	−0.809017	−	0.587785i	−0.161803	−	0.117557i
$26$	3.17174	−	2.30440i	0.622029	−	0.451931i
$27$	−0.882497	+	2.71605i	−0.169837	+	0.522704i
$28$	0.309017	−	0.951057i	0.0583987	−	0.179733i
$29$	3.33657	−	2.42416i	0.619585	−	0.450155i	−0.233192	−	0.972431i	$-0.574917\pi$
$29$	3.33657	−	2.42416i	0.619585	−	0.450155i	0.852776	+	0.522276i	$0.174917\pi$
$30$	1.75015	+	1.27156i	0.319532	+	0.232154i
$31$	1.78375	+	5.48982i	0.320371	+	0.986001i	0.973487	+	0.228743i	$0.0734615\pi$
$31$	1.78375	+	5.48982i	0.320371	+	0.986001i	−0.653116	+	0.757258i	$0.726539\pi$
$32$	1.00000			0.176777
$33$	−7.17427	+	0.0925250i	−1.24888	+	0.0161065i
$34$	−6.06013			−1.03930
$35$	−0.309017	−	0.951057i	−0.0522334	−	0.160758i
$36$	−1.35905	−	0.987408i	−0.226508	−	0.164568i
$37$	3.68791	−	2.67942i	0.606288	−	0.440494i	−0.241817	−	0.970322i	$-0.577743\pi$
$37$	3.68791	−	2.67942i	0.606288	−	0.440494i	0.848105	+	0.529828i	$0.177743\pi$
$38$	−1.78316	+	5.48799i	−0.289266	+	0.890270i
$39$	−2.62083	+	8.06610i	−0.419669	+	1.29161i
$40$	0.809017	−	0.587785i	0.127917	−	0.0929370i
$41$	4.48370	+	3.25760i	0.700237	+	0.508752i	0.880009	−	0.474957i	$-0.157536\pi$
$41$	4.48370	+	3.25760i	0.700237	+	0.508752i	−0.179773	+	0.983708i	$0.557536\pi$
$42$	0.668497	+	2.05742i	0.103151	+	0.317467i
$43$	6.51122			0.992951			0.496476	−	0.868051i	$-0.334627\pi$
$43$	6.51122			0.992951			0.496476	+	0.868051i	$0.334627\pi$
$44$	−0.984131	+	3.16725i	−0.148363	+	0.477481i
$45$	−1.67988			−0.250422
$46$	0.467965	+	1.44025i	0.0689977	+	0.212353i
$47$	8.83643	+	6.42004i	1.28893	+	0.936460i	0.999783	−	0.0208261i	$-0.00662964\pi$
$47$	8.83643	+	6.42004i	1.28893	+	0.936460i	0.289143	+	0.957286i	$0.406630\pi$
$48$	−1.75015	+	1.27156i	−0.252612	+	0.183534i
$49$	0.309017	−	0.951057i	0.0441453	−	0.135865i
$50$	0.309017	−	0.951057i	0.0437016	−	0.134500i
$51$	10.6061	−	7.70580i	1.48515	−	1.07903i
$52$	3.17174	+	2.30440i	0.439841	+	0.319563i
$53$	1.15609	+	3.55809i	0.158801	+	0.488741i	0.998526	−	0.0542716i	$-0.0172837\pi$
$53$	1.15609	+	3.55809i	0.158801	+	0.488741i	−0.839725	+	0.543012i	$0.817284\pi$
$54$	−2.85582			−0.388628
$55$	1.06549	+	3.14082i	0.143670	+	0.423508i
$56$	1.00000			0.133631
$57$	−3.85751	−	11.8722i	−0.510939	−	1.57251i
$58$	3.33657	+	2.42416i	0.438112	+	0.318307i
$59$	3.05324	−	2.21831i	0.397498	−	0.288800i	−0.371023	−	0.928624i	$-0.620993\pi$
$59$	3.05324	−	2.21831i	0.397498	−	0.288800i	0.768521	+	0.639824i	$0.220993\pi$
$60$	−0.668497	+	2.05742i	−0.0863026	+	0.265612i
$61$	−0.164673	+	0.506812i	−0.0210843	+	0.0648907i	−0.961045	−	0.276392i	$-0.910861\pi$
$61$	−0.164673	+	0.506812i	−0.0210843	+	0.0648907i	0.939961	+	0.341282i	$0.110861\pi$
$62$	−4.66992	+	3.39290i	−0.593080	+	0.430898i
$63$	−1.35905	−	0.987408i	−0.171224	−	0.124402i
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	3.92049			0.486276
$66$	−2.30497	−	6.79454i	−0.283722	−	0.836350i
$67$	−1.15993			−0.141708			−0.0708538	−	0.997487i	$-0.522572\pi$
$67$	−1.15993			−0.141708			−0.0708538	+	0.997487i	$0.522572\pi$
$68$	−1.87268	−	5.76352i	−0.227096	−	0.698930i
$69$	−2.65037	−	1.92560i	−0.319067	−	0.231815i
$70$	0.809017	−	0.587785i	0.0966960	−	0.0702538i
$71$	0.192823	−	0.593448i	0.0228839	−	0.0704293i	−0.938962	−	0.344020i	$-0.888211\pi$
$71$	0.192823	−	0.593448i	0.0228839	−	0.0704293i	0.961846	+	0.273590i	$0.0882113\pi$
$72$	0.519111	−	1.59766i	0.0611778	−	0.188286i
$73$	−2.51213	+	1.82517i	−0.294022	+	0.213620i	−0.725010	−	0.688738i	$-0.758165\pi$
$73$	−2.51213	+	1.82517i	−0.294022	+	0.213620i	0.430988	+	0.902358i	$0.358165\pi$
$74$	3.68791	+	2.67942i	0.428710	+	0.311476i
$75$	0.668497	+	2.05742i	0.0771914	+	0.237571i
$76$	−5.77042			−0.661912
$77$	−0.984131	+	3.16725i	−0.112152	+	0.360942i
$78$	−8.48120			−0.960307
$79$	1.16415	+	3.58288i	0.130977	+	0.403106i	0.994943	−	0.100445i	$-0.0320266\pi$
$79$	1.16415	+	3.58288i	0.130977	+	0.403106i	−0.863966	+	0.503551i	$0.832027\pi$
$80$	0.809017	+	0.587785i	0.0904508	+	0.0657164i
$81$	9.07526	−	6.59357i	1.00836	−	0.732618i
$82$	−1.71262	+	5.27091i	−0.189127	+	0.582074i
$83$	−3.82374	+	11.7683i	−0.419710	+	1.29174i	0.488259	+	0.872699i	$0.337632\pi$
$83$	−3.82374	+	11.7683i	−0.419710	+	1.29174i	−0.907969	+	0.419037i	$0.862368\pi$
$84$	−1.75015	+	1.27156i	−0.190957	+	0.138738i
$85$	−4.90275	−	3.56205i	−0.531777	−	0.386359i
$86$	2.01208	+	6.19254i	0.216968	+	0.667758i
$87$	−8.92194			−0.956532
$88$	−3.31635	+	0.0427703i	−0.353524	+	0.00455932i
$89$	3.59309			0.380866			0.190433	−	0.981700i	$-0.439011\pi$
$89$	3.59309			0.380866			0.190433	+	0.981700i	$0.439011\pi$
$90$	−0.519111	−	1.59766i	−0.0547191	−	0.168408i
$91$	3.17174	+	2.30440i	0.332489	+	0.241567i
$92$	−1.22515	+	0.890122i	−0.127731	+	0.0928017i
$93$	3.85879	−	11.8761i	0.400138	−	1.23150i
$94$	−3.37522	+	10.3879i	−0.348127	+	1.07142i
$95$	−4.66837	+	3.39177i	−0.478964	+	0.347988i
$96$	−1.75015	−	1.27156i	−0.178624	−	0.129778i
$97$	−4.83375	−	14.8768i	−0.490793	−	1.51051i	−0.823411	−	0.567445i	$-0.807932\pi$
$97$	−4.83375	−	14.8768i	−0.490793	−	1.51051i	0.332618	−	0.943062i	$-0.392068\pi$
$98$	1.00000			0.101015
$99$	4.54932	+	3.21646i	0.457224	+	0.323267i
$100$	1.00000			0.100000
$101$	−4.69449	−	14.4482i	−0.467119	−	1.43765i	−0.856297	−	0.516483i	$-0.827241\pi$
$101$	−4.69449	−	14.4482i	−0.467119	−	1.43765i	0.389178	−	0.921162i	$-0.372759\pi$
$102$	10.6061	+	7.70580i	1.05016	+	0.762988i
$103$	−4.48827	+	3.26092i	−0.442243	+	0.321308i	−0.786525	−	0.617558i	$-0.788122\pi$
$103$	−4.48827	+	3.26092i	−0.442243	+	0.321308i	0.344283	+	0.938866i	$0.388122\pi$
$104$	−1.21150	+	3.72860i	−0.118797	+	0.365620i
$105$	−0.668497	+	2.05742i	−0.0652387	+	0.200784i
$106$	−3.02669	+	2.19902i	−0.293978	+	0.213588i
$107$	−7.49103	−	5.44255i	−0.724186	−	0.526152i	0.163533	−	0.986538i	$-0.447711\pi$
$107$	−7.49103	−	5.44255i	−0.724186	−	0.526152i	−0.887719	+	0.460386i	$0.847711\pi$
$108$	−0.882497	−	2.71605i	−0.0849183	−	0.261352i
$109$	−0.167247			−0.0160193			−0.00800966	−	0.999968i	$-0.502550\pi$
$109$	−0.167247			−0.0160193			−0.00800966	+	0.999968i	$0.502550\pi$
$110$	−2.65784	+	1.98390i	−0.253415	+	0.189158i
$111$	−9.86142			−0.936005
$112$	0.309017	+	0.951057i	0.0291994	+	0.0898664i
$113$	−5.39100	−	3.91679i	−0.507142	−	0.368461i	0.304596	−	0.952482i	$-0.401479\pi$
$113$	−5.39100	−	3.91679i	−0.507142	−	0.368461i	−0.811739	+	0.584021i	$0.801479\pi$
$114$	10.0991	−	7.33742i	0.945866	−	0.687212i
$115$	−0.467965	+	1.44025i	−0.0436380	+	0.134304i
$116$	−1.27445	+	3.92237i	−0.118330	+	0.364183i
$117$	5.32814	−	3.87112i	0.492587	−	0.357885i
$118$	3.05324	+	2.21831i	0.281074	+	0.204212i
$119$	−1.87268	−	5.76352i	−0.171668	−	0.528341i
$120$	−2.16330			−0.197482
$121$	3.12826	−	10.5458i	0.284387	−	0.958710i
$122$	−0.532894			−0.0482459
$123$	−3.70492	−	11.4026i	−0.334061	−	1.02814i
$124$	−4.66992	−	3.39290i	−0.419371	−	0.304691i
$125$	0.809017	−	0.587785i	0.0723607	−	0.0525731i
$126$	0.519111	−	1.59766i	0.0462461	−	0.142331i
$127$	−0.638176	+	1.96410i	−0.0566290	+	0.174286i	−0.975370	−	0.220574i	$-0.929207\pi$
$127$	−0.638176	+	1.96410i	−0.0566290	+	0.174286i	0.918741	+	0.394860i	$0.129207\pi$
$128$	−0.809017	+	0.587785i	−0.0715077	+	0.0519534i
$129$	−11.3956	−	8.27939i	−1.00333	−	0.728959i
$130$	1.21150	+	3.72860i	0.106255	+	0.327020i
$131$	22.8396			1.99550			0.997751	−	0.0670258i	$-0.0213510\pi$
$131$	22.8396			1.99550			0.997751	+	0.0670258i	$0.0213510\pi$
$132$	5.74972	−	4.29178i	0.500449	−	0.373552i
$133$	−5.77042			−0.500359
$134$	−0.358437	−	1.10316i	−0.0309642	−	0.0952981i
$135$	−2.31041	−	1.67861i	−0.198848	−	0.144472i
$136$	4.90275	−	3.56205i	0.420407	−	0.305444i
$137$	1.73905	−	5.35225i	0.148577	−	0.457274i	−0.848876	−	0.528591i	$-0.822720\pi$
$137$	1.73905	−	5.35225i	0.148577	−	0.457274i	0.997454	+	0.0713176i	$0.0227204\pi$
$138$	1.01235	−	3.11569i	0.0861770	−	0.265225i
$139$	−6.91765	+	5.02597i	−0.586748	+	0.426297i	−0.841150	−	0.540801i	$-0.818121\pi$
$139$	−6.91765	+	5.02597i	−0.586748	+	0.426297i	0.254403	+	0.967098i	$0.418121\pi$
$140$	0.809017	+	0.587785i	0.0683744	+	0.0496769i
$141$	−7.30162	−	22.4721i	−0.614907	−	1.89249i
$142$	0.623988			0.0523639
$143$	−10.6172	−	7.50655i	−0.887851	−	0.627729i
$144$	1.67988			0.139990
$145$	1.27445	+	3.92237i	0.105838	+	0.325735i
$146$	−2.51213	−	1.82517i	−0.207905	−	0.151052i
$147$	−1.75015	+	1.27156i	−0.144350	+	0.104876i
$148$	−1.40865	+	4.33539i	−0.115791	+	0.356367i
$149$	−6.02223	+	18.5345i	−0.493361	+	1.51841i	0.326136	+	0.945323i	$0.394253\pi$
$149$	−6.02223	+	18.5345i	−0.493361	+	1.51841i	−0.819496	+	0.573085i	$0.805747\pi$
$150$	−1.75015	+	1.27156i	−0.142899	+	0.103822i
$151$	4.23751	+	3.07873i	0.344844	+	0.250544i	0.746703	−	0.665158i	$-0.231636\pi$
$151$	4.23751	+	3.07873i	0.344844	+	0.250544i	−0.401859	+	0.915702i	$0.631636\pi$
$152$	−1.78316	−	5.48799i	−0.144633	−	0.445135i
$153$	−10.1803			−0.823027
$154$	−3.31635	+	0.0427703i	−0.267239	+	0.00344653i
$155$	−5.77234			−0.463645
$156$	−2.62083	−	8.06610i	−0.209835	−	0.645805i
$157$	−12.7922	−	9.29411i	−1.02093	−	0.741751i	−0.0544583	−	0.998516i	$-0.517343\pi$
$157$	−12.7922	−	9.29411i	−1.02093	−	0.741751i	−0.966474	+	0.256766i	$0.917343\pi$
$158$	−3.04778	+	2.21434i	−0.242469	+	0.176164i
$159$	2.50098	−	7.69722i	0.198340	−	0.610429i
$160$	−0.309017	+	0.951057i	−0.0244299	+	0.0751876i
$161$	−1.22515	+	0.890122i	−0.0965552	+	0.0701515i
$162$	9.07526	+	6.59357i	0.713020	+	0.518039i
$163$	3.84570	+	11.8358i	0.301218	+	0.927054i	0.981061	+	0.193697i	$0.0620478\pi$
$163$	3.84570	+	11.8358i	0.301218	+	0.927054i	−0.679843	+	0.733358i	$0.737952\pi$
$164$	−5.54216			−0.432770
$165$	2.12897	−	6.85173i	0.165740	−	0.533406i
$166$	−12.3739			−0.960400
$167$	−5.52430	−	17.0020i	−0.427483	−	1.31566i	−0.900596	−	0.434656i	$-0.856870\pi$
$167$	−5.52430	−	17.0020i	−0.427483	−	1.31566i	0.473113	−	0.881002i	$-0.343130\pi$
$168$	−1.75015	−	1.27156i	−0.135027	−	0.0981028i
$169$	−1.91754	+	1.39318i	−0.147503	+	0.107167i
$170$	1.87268	−	5.76352i	0.143628	−	0.442042i
$171$	−2.99549	+	9.21917i	−0.229071	+	0.705007i
$172$	−5.26769	+	3.82720i	−0.401657	+	0.291821i
$173$	15.9198	+	11.5664i	1.21036	+	0.879378i	0.995263	−	0.0972144i	$-0.0309933\pi$
$173$	15.9198	+	11.5664i	1.21036	+	0.879378i	0.215097	+	0.976593i	$0.430993\pi$
$174$	−2.75703	−	8.48527i	−0.209010	−	0.643267i
$175$	1.00000			0.0755929
$176$	−1.06549	−	3.14082i	−0.0803140	−	0.236748i
$177$	−8.16434			−0.613669
$178$	1.11032	+	3.41723i	0.0832223	+	0.256132i
$179$	1.37428	+	0.998471i	0.102718	+	0.0746292i	0.637959	−	0.770071i	$-0.279779\pi$
$179$	1.37428	+	0.998471i	0.102718	+	0.0746292i	−0.535240	+	0.844700i	$0.679779\pi$
$180$	1.35905	−	0.987408i	0.101298	−	0.0735971i
$181$	−4.98146	+	15.3314i	−0.370269	+	1.13957i	0.576346	+	0.817205i	$0.304478\pi$
$181$	−4.98146	+	15.3314i	−0.370269	+	1.13957i	−0.946615	+	0.322365i	$0.895522\pi$
$182$	−1.21150	+	3.72860i	−0.0898021	+	0.276383i
$183$	0.932644	−	0.677605i	0.0689430	−	0.0500900i
$184$	−1.22515	−	0.890122i	−0.0903191	−	0.0656207i
$185$	1.40865	+	4.33539i	0.103566	+	0.318744i
$186$	12.4873			0.915614
$187$	6.45697	+	19.0338i	0.472181	+	1.39189i
$188$	−10.9224			−0.796600
$189$	−0.882497	−	2.71605i	−0.0641922	−	0.197563i
$190$	−4.66837	−	3.39177i	−0.338679	−	0.246065i
$191$	14.0476	−	10.2062i	1.01645	−	0.738493i	0.0508971	−	0.998704i	$-0.483792\pi$
$191$	14.0476	−	10.2062i	1.01645	−	0.738493i	0.965552	+	0.260210i	$0.0837919\pi$
$192$	0.668497	−	2.05742i	0.0482446	−	0.148482i
$193$	−1.64913	+	5.07551i	−0.118707	+	0.365343i	−0.992702	−	0.120592i	$-0.961521\pi$
$193$	−1.64913	+	5.07551i	−0.118707	+	0.365343i	0.873995	+	0.485935i	$0.161521\pi$
$194$	12.6549	−	9.19435i	0.908571	−	0.660116i
$195$	−6.86143	−	4.98512i	−0.491357	−	0.356992i
$196$	0.309017	+	0.951057i	0.0220726	+	0.0679326i
$197$	19.8667			1.41544			0.707722	−	0.706491i	$-0.249723\pi$
$197$	19.8667			1.41544			0.707722	+	0.706491i	$0.249723\pi$
$198$	−1.65322	+	5.32060i	−0.117489	+	0.378119i
$199$	2.93785			0.208259			0.104129	−	0.994564i	$-0.466794\pi$
$199$	2.93785			0.208259			0.104129	+	0.994564i	$0.466794\pi$
$200$	0.309017	+	0.951057i	0.0218508	+	0.0672499i
$201$	2.03004	+	1.47491i	0.143188	+	0.104032i
$202$	12.2903	−	8.92945i	0.864745	−	0.628274i
$203$	−1.27445	+	3.92237i	−0.0894492	+	0.275296i
$204$	−4.05118	+	12.4682i	−0.283639	+	0.872952i
$205$	−4.48370	+	3.25760i	−0.313155	+	0.227521i
$206$	−4.48827	−	3.26092i	−0.312713	−	0.227199i
$207$	0.786125	+	2.41944i	0.0546394	+	0.168163i
$208$	−3.92049			−0.271837
$209$	19.1367	−	0.246802i	1.32371	−	0.0170717i
$210$	−2.16330			−0.149282
$211$	5.55962	+	17.1107i	0.382740	+	1.17795i	0.938107	+	0.346346i	$0.112578\pi$
$211$	5.55962	+	17.1107i	0.382740	+	1.17795i	−0.555367	+	0.831605i	$0.687422\pi$
$212$	−3.02669	−	2.19902i	−0.207874	−	0.151029i
$213$	−1.09207	+	0.793437i	−0.0748276	+	0.0543654i
$214$	2.86132	−	8.80624i	0.195596	−	0.601982i
$215$	−2.01208	+	6.19254i	−0.137223	+	0.422327i
$216$	2.31041	−	1.67861i	0.157203	−	0.114215i
$217$	−4.66992	−	3.39290i	−0.317015	−	0.230325i
$218$	−0.0516820	−	0.159061i	−0.00350035	−	0.0107730i
$219$	6.71741			0.453920
$220$	−2.70812	−	1.91470i	−0.182582	−	0.129089i
$221$	23.7586			1.59818
$222$	−3.04735	−	9.37877i	−0.204525	−	0.629462i
$223$	−17.9963	−	13.0751i	−1.20512	−	0.875574i	−0.210345	−	0.977627i	$-0.567459\pi$
$223$	−17.9963	−	13.0751i	−1.20512	−	0.875574i	−0.994779	+	0.102053i	$0.967459\pi$
$224$	−0.809017	+	0.587785i	−0.0540547	+	0.0392731i
$225$	0.519111	−	1.59766i	0.0346074	−	0.106511i
$226$	2.05918	−	6.33750i	0.136975	−	0.421564i
$227$	21.2372	−	15.4297i	1.40956	−	1.02411i	0.416175	−	0.909285i	$-0.363371\pi$
$227$	21.2372	−	15.4297i	1.40956	−	1.02411i	0.993386	−	0.114821i	$-0.0366295\pi$
$228$	10.0991	+	7.33742i	0.668828	+	0.485932i
$229$	−2.81988	−	8.67871i	−0.186343	−	0.573505i	0.813626	−	0.581389i	$-0.197490\pi$
$229$	−2.81988	−	8.67871i	−0.186343	−	0.573505i	−0.999969	+	0.00788377i	$0.997490\pi$
$230$	−1.51437			−0.0998544
$231$	5.74972	−	4.29178i	0.378304	−	0.282379i
$232$	−4.12422			−0.270768
$233$	−0.117010	−	0.360121i	−0.00766561	−	0.0235923i	0.947151	−	0.320789i	$-0.103948\pi$
$233$	−0.117010	−	0.360121i	−0.00766561	−	0.0235923i	−0.954816	+	0.297197i	$0.903948\pi$
$234$	5.32814	+	3.87112i	0.348311	+	0.253063i
$235$	−8.83643	+	6.42004i	−0.576425	+	0.418798i
$236$	−1.16624	+	3.58930i	−0.0759155	+	0.233644i
$237$	2.51841	−	7.75086i	0.163588	−	0.503473i
$238$	4.90275	−	3.56205i	0.317798	−	0.230894i
$239$	0.140520	+	0.102093i	0.00908946	+	0.00660388i	0.592321	−	0.805702i	$-0.298212\pi$
$239$	0.140520	+	0.102093i	0.00908946	+	0.00660388i	−0.583231	+	0.812306i	$0.698212\pi$
$240$	−0.668497	−	2.05742i	−0.0431513	−	0.132806i
$241$	−27.9248			−1.79880			−0.899398	−	0.437131i	$-0.855995\pi$
$241$	−27.9248			−1.79880			−0.899398	+	0.437131i	$0.855995\pi$
$242$	10.9963	−	0.283682i	0.706872	−	0.0182358i
$243$	−15.6997			−1.00714
$244$	−0.164673	−	0.506812i	−0.0105421	−	0.0324453i
$245$	0.809017	+	0.587785i	0.0516862	+	0.0375522i
$246$	9.69961	−	7.04718i	0.618424	−	0.449312i
$247$	6.99084	−	21.5156i	0.444817	−	1.36900i
$248$	1.78375	−	5.48982i	0.113268	−	0.348604i
$249$	21.6562	−	15.7341i	1.37240	−	0.997109i
$250$	0.809017	+	0.587785i	0.0511667	+	0.0371748i
$251$	7.92391	+	24.3873i	0.500153	+	1.53931i	0.808769	+	0.588126i	$0.200134\pi$
$251$	7.92391	+	24.3873i	0.500153	+	1.53931i	−0.308616	+	0.951187i	$0.599866\pi$
$252$	1.67988			0.105822
$253$	4.02495	−	3.00436i	0.253046	−	0.188882i
$254$	−2.06518			−0.129581
$255$	4.05118	+	12.4682i	0.253695	+	0.780792i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	−25.4358	+	18.4802i	−1.58664	+	1.15276i	−0.678092	+	0.734977i	$0.737193\pi$
$257$	−25.4358	+	18.4802i	−1.58664	+	1.15276i	−0.908546	+	0.417784i	$0.862807\pi$
$258$	4.35273	−	13.3963i	0.270989	−	0.834019i
$259$	−1.40865	+	4.33539i	−0.0875296	+	0.269388i
$260$	−3.17174	+	2.30440i	−0.196703	+	0.142913i
$261$	5.60503	+	4.07229i	0.346942	+	0.252068i
$262$	7.05782	+	21.7217i	0.436033	+	1.34197i
$263$	24.0975			1.48592			0.742958	−	0.669338i	$-0.233422\pi$
$263$	24.0975			1.48592			0.742958	+	0.669338i	$0.233422\pi$
$264$	5.85849	+	4.14207i	0.360565	+	0.254927i
$265$	−3.74119			−0.229820
$266$	−1.78316	−	5.48799i	−0.109332	−	0.336490i
$267$	−6.28843	−	4.56881i	−0.384846	−	0.279607i
$268$	0.938400	−	0.681788i	0.0573219	−	0.0416468i
$269$	7.67821	−	23.6311i	0.468149	−	1.44081i	−0.386830	−	0.922151i	$-0.626430\pi$
$269$	7.67821	−	23.6311i	0.468149	−	1.44081i	0.854979	−	0.518663i	$-0.173570\pi$
$270$	0.882497	−	2.71605i	0.0537071	−	0.165293i
$271$	−0.243350	+	0.176804i	−0.0147825	+	0.0107401i	−0.595152	−	0.803613i	$-0.702908\pi$
$271$	−0.243350	+	0.176804i	−0.0147825	+	0.0107401i	0.580369	+	0.814353i	$0.302908\pi$
$272$	4.90275	+	3.56205i	0.297273	+	0.215981i
$273$	−2.62083	−	8.06610i	−0.158620	−	0.488183i
$274$	5.62769			0.339981
$275$	−3.31635	+	0.0427703i	−0.199983	+	0.00257914i
$276$	3.27603			0.197194
$277$	5.25647	+	16.1778i	0.315831	+	0.972027i	0.975411	+	0.220393i	$0.0707340\pi$
$277$	5.25647	+	16.1778i	0.315831	+	0.972027i	−0.659581	+	0.751634i	$0.729266\pi$
$278$	−6.91765	−	5.02597i	−0.414893	−	0.301438i
$279$	−7.84490	+	5.69965i	−0.469662	+	0.341229i
$280$	−0.309017	+	0.951057i	−0.0184673	+	0.0568365i
$281$	−6.81019	+	20.9596i	−0.406262	+	1.25034i	0.513576	+	0.858044i	$0.328321\pi$
$281$	−6.81019	+	20.9596i	−0.406262	+	1.25034i	−0.919837	+	0.392300i	$0.871679\pi$
$282$	19.1159	−	13.8885i	1.13833	−	0.827048i
$283$	−7.66264	−	5.56723i	−0.455497	−	0.330938i	0.336266	−	0.941767i	$-0.390836\pi$
$283$	−7.66264	−	5.56723i	−0.455497	−	0.330938i	−0.791762	+	0.610830i	$0.790836\pi$
$284$	0.192823	+	0.593448i	0.0114419	+	0.0352147i
$285$	12.4832			0.739439
$286$	3.85827	−	12.4172i	0.228144	−	0.734243i
$287$	−5.54216			−0.327143
$288$	0.519111	+	1.59766i	0.0305889	+	0.0941430i
$289$	−15.9580	−	11.5941i	−0.938704	−	0.682008i
$290$	−3.33657	+	2.42416i	−0.195930	+	0.142351i
$291$	−10.4569	+	32.1829i	−0.612993	+	1.88660i
$292$	0.959548	−	2.95318i	0.0561533	−	0.172822i
$293$	13.6254	−	9.89941i	0.796002	−	0.578329i	−0.113736	−	0.993511i	$-0.536282\pi$
$293$	13.6254	−	9.89941i	0.796002	−	0.578329i	0.909739	+	0.415181i	$0.136282\pi$
$294$	−1.75015	−	1.27156i	−0.102071	−	0.0741587i
$295$	1.16624	+	3.58930i	0.0679008	+	0.208977i
$296$	−4.55850			−0.264958
$297$	3.04283	+	8.96962i	0.176563	+	0.520470i
$298$	−19.4884			−1.12893
$299$	−1.83465	−	5.64647i	−0.106101	−	0.326544i
$300$	−1.75015	−	1.27156i	−0.101045	−	0.0734134i
$301$	−5.26769	+	3.82720i	−0.303624	+	0.220596i
$302$	−1.61858	+	4.98149i	−0.0931391	+	0.286653i
$303$	−10.1556	+	31.2557i	−0.583424	+	1.79560i
$304$	4.66837	−	3.39177i	0.267749	−	0.194531i
$305$	−0.431120	−	0.313227i	−0.0246859	−	0.0179353i
$306$	−3.14588	−	9.68202i	−0.179838	−	0.553484i
$307$	−1.36644			−0.0779870			−0.0389935	−	0.999239i	$-0.512415\pi$
$307$	−1.36644			−0.0779870			−0.0389935	+	0.999239i	$0.512415\pi$
$308$	−1.06549	−	3.14082i	−0.0607116	−	0.178965i
$309$	12.0016			0.682747
$310$	−1.78375	−	5.48982i	−0.101310	−	0.311801i
$311$	−15.0107	−	10.9059i	−0.851180	−	0.618418i	0.0742912	−	0.997237i	$-0.476331\pi$
$311$	−15.0107	−	10.9059i	−0.851180	−	0.618418i	−0.925471	+	0.378818i	$0.876331\pi$
$312$	6.86143	−	4.98512i	0.388452	−	0.282227i
$313$	−4.28448	+	13.1863i	−0.242173	+	0.745332i	0.753916	+	0.656971i	$0.228163\pi$
$313$	−4.28448	+	13.1863i	−0.242173	+	0.745332i	−0.996089	+	0.0883605i	$0.971837\pi$
$314$	4.88620	−	15.0382i	0.275744	−	0.848654i
$315$	1.35905	−	0.987408i	0.0765738	−	0.0556342i
$316$	−3.04778	−	2.21434i	−0.171451	−	0.124567i
$317$	−7.26032	−	22.3450i	−0.407780	−	1.25502i	−0.918551	−	0.395302i	$-0.870640\pi$
$317$	−7.26032	−	22.3450i	−0.407780	−	1.25502i	0.510771	−	0.859717i	$-0.329360\pi$
$318$	8.09333			0.453852
$319$	4.05878	−	13.0624i	0.227248	−	0.731357i
$320$	−1.00000			−0.0559017
$321$	6.18990	+	19.0506i	0.345487	+	1.06330i
$322$	−1.22515	−	0.890122i	−0.0682748	−	0.0496046i
$323$	−28.2909	+	20.5545i	−1.57415	+	1.14368i
$324$	−3.46644	+	10.6686i	−0.192580	+	0.592701i
$325$	−1.21150	+	3.72860i	−0.0672018	+	0.206826i
$326$	−10.0682	+	7.31495i	−0.557624	+	0.405138i
$327$	0.292706	+	0.212664i	0.0161867	+	0.0117603i
$328$	−1.71262	−	5.27091i	−0.0945637	−	0.291037i
$329$	−10.9224			−0.602173
$330$	7.17427	−	0.0925250i	0.394930	−	0.00509333i
$331$	10.6438			0.585035			0.292518	−	0.956260i	$-0.405507\pi$
$331$	10.6438			0.585035			0.292518	+	0.956260i	$0.405507\pi$
$332$	−3.82374	−	11.7683i	−0.209855	−	0.645868i
$333$	6.19524	+	4.50110i	0.339497	+	0.246659i
$334$	14.4628	−	10.5078i	0.791369	−	0.574964i
$335$	0.358437	−	1.10316i	0.0195835	−	0.0602718i
$336$	0.668497	−	2.05742i	0.0364695	−	0.112242i
$337$	−10.8057	+	7.85082i	−0.588625	+	0.427661i	−0.841823	−	0.539753i	$-0.818518\pi$
$337$	−10.8057	+	7.85082i	−0.588625	+	0.427661i	0.253198	+	0.967414i	$0.418518\pi$
$338$	−1.91754	−	1.39318i	−0.104300	−	0.0757787i
$339$	4.45463	+	13.7099i	0.241942	+	0.744621i
$340$	6.06013			0.328656
$341$	15.6322	+	11.0523i	0.846531	+	0.598515i
$342$	−9.69360			−0.524170
$343$	0.309017	+	0.951057i	0.0166853	+	0.0513522i
$344$	−5.26769	−	3.82720i	−0.284015	−	0.206349i
$345$	2.65037	−	1.92560i	0.142691	−	0.103671i
$346$	−6.08082	+	18.7149i	−0.326907	+	1.00612i
$347$	4.48292	−	13.7970i	0.240656	−	0.740662i	−0.755665	−	0.654958i	$-0.772686\pi$
$347$	4.48292	−	13.7970i	0.240656	−	0.740662i	0.996321	−	0.0857039i	$-0.0273139\pi$
$348$	7.21800	−	5.24418i	0.386925	−	0.281118i
$349$	21.1195	+	15.3442i	1.13050	+	0.821355i	0.985767	−	0.168116i	$-0.0537682\pi$
$349$	21.1195	+	15.3442i	1.13050	+	0.821355i	0.144731	+	0.989471i	$0.453768\pi$
$350$	0.309017	+	0.951057i	0.0165177	+	0.0508361i
$351$	11.1962			0.597609
$352$	2.65784	−	1.98390i	0.141664	−	0.105742i
$353$	20.3692			1.08414			0.542072	−	0.840332i	$-0.317640\pi$
$353$	20.3692			1.08414			0.542072	+	0.840332i	$0.317640\pi$
$354$	−2.52292	−	7.76475i	−0.134092	−	0.412692i
$355$	0.504817	+	0.366771i	0.0267929	+	0.0194662i
$356$	−2.90687	+	2.11196i	−0.154064	+	0.111934i
$357$	−4.05118	+	12.4682i	−0.214411	+	0.659890i
$358$	−0.524927	+	1.61556i	−0.0277433	+	0.0853850i
$359$	−15.0439	+	10.9300i	−0.793987	+	0.576866i	−0.909144	−	0.416482i	$-0.863263\pi$
$359$	−15.0439	+	10.9300i	−0.793987	+	0.576866i	0.115157	+	0.993347i	$0.463263\pi$
$360$	1.35905	+	0.987408i	0.0716283	+	0.0520410i
$361$	4.41824	+	13.5979i	0.232539	+	0.715681i
$362$	−16.1203			−0.847266
$363$	−18.8845	+	14.4790i	−0.991180	+	0.759949i
$364$	−3.92049			−0.205489
$365$	−0.959548	−	2.95318i	−0.0502250	−	0.154577i
$366$	0.932644	+	0.677605i	0.0487501	+	0.0354190i
$367$	−7.63619	+	5.54801i	−0.398606	+	0.289604i	−0.768973	−	0.639281i	$-0.779232\pi$
$367$	−7.63619	+	5.54801i	−0.398606	+	0.289604i	0.370367	+	0.928885i	$0.379232\pi$
$368$	0.467965	−	1.44025i	0.0243944	−	0.0750781i
$369$	−2.87700	+	8.85449i	−0.149771	+	0.460946i
$370$	−3.68791	+	2.67942i	−0.191725	+	0.139296i
$371$	−3.02669	−	2.19902i	−0.157138	−	0.114167i
$372$	3.85879	+	11.8761i	0.200069	+	0.615749i
$373$	−17.1558			−0.888295			−0.444147	−	0.895954i	$-0.646493\pi$
$373$	−17.1558			−0.888295			−0.444147	+	0.895954i	$0.646493\pi$
$374$	−16.1069	+	12.0227i	−0.832866	+	0.621679i
$375$	−2.16330			−0.111712
$376$	−3.37522	−	10.3879i	−0.174064	−	0.535712i
$377$	−13.0810	−	9.50387i	−0.673704	−	0.489474i
$378$	2.31041	−	1.67861i	0.118835	−	0.0863384i
$379$	−2.50255	+	7.70205i	−0.128547	+	0.395628i	−0.994531	−	0.104445i	$-0.966693\pi$
$379$	−2.50255	+	7.70205i	−0.128547	+	0.395628i	0.865983	+	0.500073i	$0.166693\pi$
$380$	1.78316	−	5.48799i	0.0914740	−	0.281528i
$381$	3.61437	−	2.62600i	0.185170	−	0.134534i
$382$	14.0476	+	10.2062i	0.718738	+	0.522194i
$383$	7.20494	+	22.1745i	0.368155	+	1.13307i	0.947981	+	0.318326i	$0.103121\pi$
$383$	7.20494	+	22.1745i	0.368155	+	1.13307i	−0.579826	+	0.814740i	$0.696879\pi$
$384$	2.16330			0.110396
$385$	−2.70812	−	1.91470i	−0.138019	−	0.0975821i
$386$	−5.33671			−0.271631
$387$	3.38005	+	10.4027i	0.171817	+	0.528800i
$388$	12.6549	+	9.19435i	0.642457	+	0.466772i
$389$	−15.3327	+	11.1398i	−0.777397	+	0.564812i	−0.904197	−	0.427117i	$-0.859529\pi$
$389$	−15.3327	+	11.1398i	−0.777397	+	0.564812i	0.126800	+	0.991928i	$0.459529\pi$
$390$	2.62083	−	8.06610i	0.132711	−	0.408443i
$391$	−2.83593	+	8.72809i	−0.143419	+	0.441398i
$392$	−0.809017	+	0.587785i	−0.0408615	+	0.0296876i
$393$	−39.9726	−	29.0418i	−2.01635	−	1.46497i
$394$	6.13915	+	18.8944i	0.309286	+	0.951884i
$395$	−3.76727			−0.189552
$396$	−5.57107	+	0.0718489i	−0.279957	+	0.00361054i
$397$	6.76731			0.339641			0.169821	−	0.985475i	$-0.445681\pi$
$397$	6.76731			0.339641			0.169821	+	0.985475i	$0.445681\pi$
$398$	0.907846	+	2.79406i	0.0455062	+	0.140054i
$399$	10.0991	+	7.33742i	0.505587	+	0.367330i
$400$	−0.809017	+	0.587785i	−0.0404508	+	0.0293893i
$401$	−6.48457	+	19.9575i	−0.323824	+	0.996628i	0.648145	+	0.761517i	$0.275545\pi$
$401$	−6.48457	+	19.9575i	−0.323824	+	0.996628i	−0.971969	+	0.235110i	$0.924455\pi$
$402$	−0.775408	+	2.38646i	−0.0386738	+	0.119026i
$403$	18.3084	−	13.3018i	0.912004	−	0.662610i
$404$	12.2903	+	8.92945i	0.611467	+	0.444257i
$405$	3.46644	+	10.6686i	0.172249	+	0.530128i
$406$	−4.12422			−0.204682
$407$	4.48617	−	14.4379i	0.222371	−	0.715661i
$408$	−13.1099			−0.649036
$409$	−9.84833	−	30.3101i	−0.486969	−	1.49874i	−0.829109	−	0.559087i	$-0.811152\pi$
$409$	−9.84833	−	30.3101i	−0.486969	−	1.49874i	0.342140	−	0.939649i	$-0.388848\pi$
$410$	−4.48370	−	3.25760i	−0.221434	−	0.160881i
$411$	−9.84930	+	7.15593i	−0.485830	+	0.352976i
$412$	1.71437	−	5.27628i	0.0844608	−	0.259944i
$413$	−1.16624	+	3.58930i	−0.0573867	+	0.176618i
$414$	−2.05810	+	1.49530i	−0.101150	+	0.0734899i
$415$	−10.0107	−	7.27319i	−0.491405	−	0.357027i
$416$	−1.21150	−	3.72860i	−0.0593985	−	0.182810i
$417$	18.4977			0.905838
$418$	6.14829	+	18.1238i	0.300723	+	0.886466i
$419$	−13.6261			−0.665680			−0.332840	−	0.942983i	$-0.608007\pi$
$419$	−13.6261			−0.665680			−0.332840	+	0.942983i	$0.608007\pi$
$420$	−0.668497	−	2.05742i	−0.0326193	−	0.100392i
$421$	−13.4850	−	9.79741i	−0.657218	−	0.477497i	0.208505	−	0.978021i	$-0.433140\pi$
$421$	−13.4850	−	9.79741i	−0.657218	−	0.477497i	−0.865722	+	0.500525i	$0.833140\pi$
$422$	−14.5553	+	10.5750i	−0.708539	+	0.514784i
$423$	−5.66996	+	17.4503i	−0.275683	+	0.848464i
$424$	1.15609	−	3.55809i	0.0561448	−	0.172796i
$425$	4.90275	−	3.56205i	0.237818	−	0.172785i
$426$	−1.09207	−	0.793437i	−0.0529111	−	0.0384421i
$427$	−0.164673	−	0.506812i	−0.00796910	−	0.0245264i
$428$	9.25943			0.447571
$429$	9.03659	+	26.6379i	0.436291	+	1.28609i
$430$	−6.51122			−0.313999
$431$	−8.37640	−	25.7799i	−0.403477	−	1.24178i	−0.922160	−	0.386808i	$-0.873577\pi$
$431$	−8.37640	−	25.7799i	−0.403477	−	1.24178i	0.518683	−	0.854967i	$-0.326423\pi$
$432$	2.31041	+	1.67861i	0.111160	+	0.0807621i
$433$	15.4895	−	11.2538i	0.744378	−	0.540822i	−0.149701	−	0.988731i	$-0.547831\pi$
$433$	15.4895	−	11.2538i	0.744378	−	0.540822i	0.894079	+	0.447909i	$0.147831\pi$
$434$	1.78375	−	5.48982i	0.0856228	−	0.263520i
$435$	2.75703	−	8.48527i	0.132190	−	0.406838i
$436$	0.135305	−	0.0983050i	0.00647995	−	0.00470796i
$437$	7.06962	+	5.13638i	0.338186	+	0.245706i
$438$	2.07579	+	6.38863i	0.0991852	+	0.305261i
$439$	−17.6266			−0.841270			−0.420635	−	0.907230i	$-0.638193\pi$
$439$	−17.6266			−0.841270			−0.420635	+	0.907230i	$0.638193\pi$
$440$	0.984131	−	3.16725i	0.0469166	−	0.150993i
$441$	1.67988			0.0799943
$442$	7.34182	+	22.5958i	0.349215	+	1.07477i
$443$	24.0117	+	17.4456i	1.14083	+	0.828863i	0.987235	−	0.159270i	$-0.0509141\pi$
$443$	24.0117	+	17.4456i	1.14083	+	0.828863i	0.153598	+	0.988133i	$0.450914\pi$
$444$	7.97806	−	5.79640i	0.378622	−	0.275085i
$445$	−1.11032	+	3.41723i	−0.0526344	+	0.161992i
$446$	6.87399	−	21.1560i	0.325493	−	1.00176i
$447$	34.1075	−	24.7806i	1.61323	−	1.17208i
$448$	−0.809017	−	0.587785i	−0.0382225	−	0.0277702i
$449$	−7.01860	−	21.6010i	−0.331228	−	1.01942i	−0.968550	−	0.248818i	$-0.919958\pi$
$449$	−7.01860	−	21.6010i	−0.331228	−	1.01942i	0.637322	−	0.770598i	$-0.280042\pi$
$450$	1.67988			0.0791903
$451$	18.3797	−	0.237040i	0.865468	−	0.0111618i
$452$	6.66364			0.313431
$453$	−3.50149	−	10.7765i	−0.164514	−	0.506323i
$454$	21.2372	+	15.4297i	0.996710	+	0.724152i
$455$	−3.17174	+	2.30440i	−0.148693	+	0.108032i
$456$	−3.85751	+	11.8722i	−0.180644	+	0.555966i
$457$	0.338857	−	1.04290i	0.0158511	−	0.0487846i	−0.942818	−	0.333308i	$-0.891835\pi$
$457$	0.338857	−	1.04290i	0.0158511	−	0.0487846i	0.958669	+	0.284523i	$0.0918352\pi$
$458$	7.38255	−	5.36374i	0.344964	−	0.250631i
$459$	−14.0014	−	10.1726i	−0.653528	−	0.474816i
$460$	−0.467965	−	1.44025i	−0.0218190	−	0.0671519i
$461$	−2.22426			−0.103594			−0.0517971	−	0.998658i	$-0.516495\pi$
$461$	−2.22426			−0.103594			−0.0517971	+	0.998658i	$0.516495\pi$
$462$	5.85849	+	4.14207i	0.272562	+	0.192707i
$463$	−32.4265			−1.50699			−0.753495	−	0.657454i	$-0.771633\pi$
$463$	−32.4265			−1.50699			−0.753495	+	0.657454i	$0.771633\pi$
$464$	−1.27445	−	3.92237i	−0.0591651	−	0.182091i
$465$	10.1025	+	7.33986i	0.468490	+	0.340378i
$466$	0.306337	−	0.222567i	0.0141908	−	0.0103102i
$467$	−3.22381	+	9.92186i	−0.149180	+	0.459129i	−0.997525	−	0.0703152i	$-0.977599\pi$
$467$	−3.22381	+	9.92186i	−0.149180	+	0.459129i	0.848345	+	0.529444i	$0.177599\pi$
$468$	−2.03517	+	6.26360i	−0.0940757	+	0.289535i
$469$	0.938400	−	0.681788i	0.0433313	−	0.0314820i
$470$	−8.83643	−	6.42004i	−0.407594	−	0.296135i
$471$	10.5703	+	32.5321i	0.487055	+	1.49900i
$472$	−3.77402			−0.173713
$473$	17.3058	−	12.9176i	0.795721	−	0.593953i
$474$	8.14974			0.374330
$475$	−1.78316	−	5.48799i	−0.0818169	−	0.251806i
$476$	4.90275	+	3.56205i	0.224717	+	0.163266i
$477$	−5.08447	+	3.69409i	−0.232802	+	0.169141i
$478$	−0.0536737	+	0.165191i	−0.00245498	+	0.00755565i
$479$	9.12306	−	28.0779i	0.416843	−	1.28291i	−0.493749	−	0.869605i	$-0.664374\pi$
$479$	9.12306	−	28.0779i	0.416843	−	1.28291i	0.910592	−	0.413307i	$-0.135626\pi$
$480$	1.75015	−	1.27156i	0.0798830	−	0.0580384i
$481$	−14.4584	−	10.5046i	−0.659246	−	0.478970i
$482$	−8.62925	−	26.5581i	−0.393051	−	1.20969i
$483$	3.27603			0.149065
$484$	3.66785	+	10.3705i	0.166721	+	0.471385i
$485$	15.6424			0.710283
$486$	−4.85147	−	14.9313i	−0.220067	−	0.677298i
$487$	24.2730	+	17.6354i	1.09991	+	0.799135i	0.981046	−	0.193775i	$-0.0620732\pi$
$487$	24.2730	+	17.6354i	1.09991	+	0.799135i	0.118869	+	0.992910i	$0.462073\pi$
$488$	0.431120	−	0.313227i	0.0195159	−	0.0141791i
$489$	8.31941	−	25.6045i	0.376217	−	1.15788i
$490$	−0.309017	+	0.951057i	−0.0139600	+	0.0429644i
$491$	5.25266	−	3.81628i	0.237049	−	0.172227i	−0.462918	−	0.886401i	$-0.653198\pi$
$491$	5.25266	−	3.81628i	0.237049	−	0.172227i	0.699968	+	0.714174i	$0.253198\pi$
$492$	9.69961	+	7.04718i	0.437292	+	0.317711i
$493$	7.72336	+	23.7700i	0.347842	+	1.07055i
$494$	22.6228			1.01785
$495$	−4.46486	+	3.33272i	−0.200680	+	0.149795i
$496$	5.77234			0.259186
$497$	0.192823	+	0.593448i	0.00864929	+	0.0266198i
$498$	21.6562	+	15.7341i	0.970435	+	0.705063i
$499$	−35.7661	+	25.9856i	−1.60111	+	1.16327i	−0.715761	+	0.698346i	$0.753920\pi$
$499$	−35.7661	+	25.9856i	−1.60111	+	1.16327i	−0.885348	+	0.464928i	$0.846080\pi$
$500$	−0.309017	+	0.951057i	−0.0138197	+	0.0425325i
$501$	−11.9507	+	36.7806i	−0.533919	+	1.64323i
$502$	−20.7451	+	15.0722i	−0.925898	+	0.672704i
$503$	19.9772	+	14.5143i	0.890739	+	0.647160i	0.936071	−	0.351812i	$-0.114434\pi$
$503$	19.9772	+	14.5143i	0.890739	+	0.647160i	−0.0453314	+	0.998972i	$0.514434\pi$
$504$	0.519111	+	1.59766i	0.0231231	+	0.0711654i
$505$	15.1917			0.676021
$506$	4.10109	+	2.89956i	0.182316	+	0.128901i
$507$	5.12748			0.227720
$508$	−0.638176	−	1.96410i	−0.0283145	−	0.0871430i
$509$	−12.0826	−	8.77856i	−0.535554	−	0.389103i	0.286877	−	0.957967i	$-0.407383\pi$
$509$	−12.0826	−	8.77856i	−0.535554	−	0.389103i	−0.822431	+	0.568865i	$0.807383\pi$
$510$	−10.6061	+	7.70580i	−0.469647	+	0.341219i
$511$	0.959548	−	2.95318i	0.0424479	−	0.130641i
$512$	0.309017	−	0.951057i	0.0136568	−	0.0420312i
$513$	−13.3320	+	9.68628i	−0.588623	+	0.427660i
$514$	−25.4358	−	18.4802i	−1.12192	−	0.815125i
$515$	−1.71437	−	5.27628i	−0.0755441	−	0.232501i
$516$	14.0857			0.620090
$517$	36.2226	−	0.467155i	1.59307	−	0.0205455i
$518$	−4.55850			−0.200289
$519$	−13.1547	−	40.4859i	−0.577426	−	1.77713i
$520$	−3.17174	−	2.30440i	−0.139090	−	0.101055i
$521$	24.6557	−	17.9134i	1.08019	−	0.784801i	0.102470	−	0.994736i	$-0.467325\pi$
$521$	24.6557	−	17.9134i	1.08019	−	0.784801i	0.977715	+	0.209936i	$0.0673254\pi$
$522$	−2.14093	+	6.58910i	−0.0937060	+	0.288397i
$523$	7.80380	−	24.0176i	0.341236	−	1.05022i	−0.622332	−	0.782754i	$-0.713814\pi$
$523$	7.80380	−	24.0176i	0.341236	−	1.05022i	0.963568	−	0.267464i	$-0.0861855\pi$
$524$	−18.4776	+	13.4248i	−0.807198	+	0.586463i
$525$	−1.75015	−	1.27156i	−0.0763828	−	0.0554953i
$526$	7.44654	+	22.9181i	0.324685	+	0.999277i
$527$	−34.9811			−1.52380
$528$	−2.12897	+	6.85173i	−0.0926517	+	0.298183i
$529$	−20.7067			−0.900291
$530$	−1.15609	−	3.55809i	−0.0502174	−	0.154553i
$531$	5.12908	+	3.72650i	0.222583	+	0.161716i
$532$	4.66837	−	3.39177i	0.202399	−	0.147052i
$533$	6.71431	−	20.6645i	0.290829	−	0.895080i
$534$	2.40197	−	7.39250i	0.103943	−	0.319905i
$535$	7.49103	−	5.44255i	0.323866	−	0.235302i
$536$	0.938400	+	0.681788i	0.0405327	+	0.0294487i
$537$	−1.13558	−	3.49494i	−0.0490037	−	0.150818i
$538$	24.8472			1.07124
$539$	−1.06549	−	3.14082i	−0.0458937	−	0.135285i
$540$	2.85582			0.122895
$541$	2.75540	+	8.48025i	0.118464	+	0.364595i	0.992654	−	0.120990i	$-0.0386069\pi$
$541$	2.75540	+	8.48025i	0.118464	+	0.364595i	−0.874190	+	0.485584i	$0.838607\pi$
$542$	−0.243350	−	0.176804i	−0.0104528	−	0.00759440i
$543$	28.2130	−	20.4979i	1.21074	−	0.879651i
$544$	−1.87268	+	5.76352i	−0.0802906	+	0.247109i
$545$	0.0516820	−	0.159061i	0.00221381	−	0.00681342i
$546$	6.86143	−	4.98512i	0.293642	−	0.213344i
$547$	22.9299	+	16.6596i	0.980412	+	0.712311i	0.957801	−	0.287433i	$-0.0928019\pi$
$547$	22.9299	+	16.6596i	0.980412	+	0.712311i	0.0226115	+	0.999744i	$0.492802\pi$
$548$	1.73905	+	5.35225i	0.0742886	+	0.228637i
$549$	−0.895197			−0.0382061
$550$	−1.06549	−	3.14082i	−0.0454324	−	0.133925i
$551$	23.7985			1.01385
$552$	1.01235	+	3.11569i	0.0430885	+	0.132613i
$553$	−3.04778	−	2.21434i	−0.129605	−	0.0941635i
$554$	−13.7616	+	9.99840i	−0.584675	+	0.424791i
$555$	3.04735	−	9.37877i	0.129353	−	0.398107i
$556$	2.64231	−	8.13219i	0.112059	−	0.344882i
$557$	28.9320	−	21.0203i	1.22589	−	0.890659i	0.229312	−	0.973353i	$-0.426352\pi$
$557$	28.9320	−	21.0203i	1.22589	−	0.890659i	0.996575	+	0.0826935i	$0.0263522\pi$
$558$	−7.84490	−	5.69965i	−0.332101	−	0.241286i
$559$	−7.88832	−	24.2778i	−0.333640	−	1.02684i
$560$	−1.00000			−0.0422577
$561$	12.9019	−	41.5223i	0.544717	−	1.75307i
$562$	−22.0382			−0.929626
$563$	12.0245	+	37.0076i	0.506772	+	1.55968i	0.797771	+	0.602960i	$0.206012\pi$
$563$	12.0245	+	37.0076i	0.506772	+	1.55968i	−0.290999	+	0.956723i	$0.593988\pi$
$564$	19.1159	+	13.8885i	0.804924	+	0.584811i
$565$	5.39100	−	3.91679i	0.226801	−	0.164781i
$566$	2.92687	−	9.00797i	0.123025	−	0.378633i
$567$	−3.46644	+	10.6686i	−0.145577	+	0.448040i
$568$	−0.504817	+	0.366771i	−0.0211817	+	0.0153894i
$569$	31.1793	+	22.6531i	1.30710	+	0.949667i	0.999998	−	0.00200874i	$-0.000639403\pi$
$569$	31.1793	+	22.6531i	1.30710	+	0.949667i	0.307106	+	0.951675i	$0.400639\pi$
$570$	3.85751	+	11.8722i	0.161573	+	0.497271i
$571$	4.21906			0.176562			0.0882811	−	0.996096i	$-0.471863\pi$
$571$	4.21906			0.176562			0.0882811	+	0.996096i	$0.471863\pi$
$572$	13.0017	−	0.167680i	0.543628	−	0.00701106i
$573$	−37.5631			−1.56922
$574$	−1.71262	−	5.27091i	−0.0714834	−	0.220003i
$575$	−1.22515	−	0.890122i	−0.0510922	−	0.0371207i
$576$	−1.35905	+	0.987408i	−0.0566271	+	0.0411420i
$577$	−11.6835	+	35.9583i	−0.486392	+	1.49696i	0.343562	+	0.939130i	$0.388367\pi$
$577$	−11.6835	+	35.9583i	−0.486392	+	1.49696i	−0.829954	+	0.557832i	$0.811633\pi$
$578$	6.09540	−	18.7597i	0.253535	−	0.780301i
$579$	9.34003	−	6.78593i	0.388158	−	0.282014i
$580$	−3.33657	−	2.42416i	−0.138543	−	0.100658i
$581$	−3.82374	−	11.7683i	−0.158636	−	0.488230i
$582$	−33.8392			−1.40268
$583$	10.1316	+	7.16326i	0.419608	+	0.296672i
$584$	3.10516			0.128493
$585$	2.03517	+	6.26360i	0.0841439	+	0.258968i
$586$	13.6254	+	9.89941i	0.562859	+	0.408941i
$587$	−12.2061	+	8.86824i	−0.503799	+	0.366031i	−0.810466	−	0.585785i	$-0.800786\pi$
$587$	−12.2061	+	8.86824i	−0.503799	+	0.366031i	0.306667	+	0.951817i	$0.400786\pi$
$588$	0.668497	−	2.05742i	0.0275684	−	0.0848467i
$589$	−10.2930	+	31.6786i	−0.424115	+	1.30529i
$590$	−3.05324	+	2.21831i	−0.125700	+	0.0913264i
$591$	−34.7697	−	25.2617i	−1.43023	−	1.03913i
$592$	−1.40865	−	4.33539i	−0.0578954	−	0.178184i
$593$	38.3246			1.57380			0.786902	−	0.617079i	$-0.211684\pi$
$593$	38.3246			1.57380			0.786902	+	0.617079i	$0.211684\pi$
$594$	−7.59032	+	5.66567i	−0.311435	+	0.232465i
$595$	6.06013			0.248441
$596$	−6.02223	−	18.5345i	−0.246680	−	0.759204i
$597$	−5.14168	−	3.73565i	−0.210435	−	0.152890i
$598$	4.80318	−	3.48971i	0.196416	−	0.142705i
$599$	8.42669	−	25.9347i	0.344305	−	1.05966i	−0.617650	−	0.786453i	$-0.711915\pi$
$599$	8.42669	−	25.9347i	0.344305	−	1.05966i	0.961955	−	0.273209i	$-0.0880849\pi$
$600$	0.668497	−	2.05742i	0.0272913	−	0.0839940i
$601$	−26.8525	+	19.5095i	−1.09534	+	0.795808i	−0.980292	−	0.197552i	$-0.936701\pi$
$601$	−26.8525	+	19.5095i	−1.09534	+	0.795808i	−0.115043	+	0.993360i	$0.536701\pi$
$602$	−5.26769	−	3.82720i	−0.214695	−	0.155985i
$603$	−0.602131	−	1.85317i	−0.0245207	−	0.0754668i
$604$	−5.23785			−0.213125
$605$	9.06297	+	6.23398i	0.368462	+	0.253447i
$606$	−32.8642			−1.33502
$607$	6.04911	+	18.6172i	0.245526	+	0.755651i	0.995550	+	0.0942397i	$0.0300420\pi$
$607$	6.04911	+	18.6172i	0.245526	+	0.755651i	−0.750024	+	0.661411i	$0.769958\pi$
$608$	4.66837	+	3.39177i	0.189327	+	0.137554i
$609$	7.21800	−	5.24418i	0.292488	−	0.212505i
$610$	0.164673	−	0.506812i	0.00666743	−	0.0205202i
$611$	13.2325	−	40.7254i	0.535329	−	1.64757i
$612$	8.23602	−	5.98382i	0.332921	−	0.241882i
$613$	−13.9141	−	10.1092i	−0.561985	−	0.408306i	0.270200	−	0.962804i	$-0.412910\pi$
$613$	−13.9141	−	10.1092i	−0.561985	−	0.408306i	−0.832185	+	0.554498i	$0.812910\pi$
$614$	−0.422254	−	1.29956i	−0.0170408	−	0.0524462i
$615$	11.9894			0.483458
$616$	2.65784	−	1.98390i	0.107088	−	0.0799337i
$617$	−40.4745			−1.62944			−0.814722	−	0.579852i	$-0.803110\pi$
$617$	−40.4745			−1.62944			−0.814722	+	0.579852i	$0.803110\pi$
$618$	3.70870	+	11.4142i	0.149186	+	0.459146i
$619$	−19.6871	−	14.3035i	−0.791290	−	0.574906i	0.117056	−	0.993125i	$-0.462654\pi$
$619$	−19.6871	−	14.3035i	−0.791290	−	0.574906i	−0.908346	+	0.418220i	$0.862654\pi$
$620$	4.66992	−	3.39290i	0.187548	−	0.136262i
$621$	−1.33642	+	4.11309i	−0.0536289	+	0.165053i
$622$	5.73358	−	17.6462i	0.229896	−	0.707547i
$623$	−2.90687	+	2.11196i	−0.116461	+	0.0846140i
$624$	6.86143	+	4.98512i	0.274677	+	0.199565i
$625$	0.309017	+	0.951057i	0.0123607	+	0.0380423i
$626$	−13.8649			−0.554151
$627$	−33.8059	−	23.9015i	−1.35008	−	0.954534i
$628$	15.8121			0.630971
$629$	8.53663	+	26.2730i	0.340378	+	1.04757i
$630$	1.35905	+	0.987408i	0.0541459	+	0.0393393i
$631$	32.7867	−	23.8209i	1.30522	−	0.948296i	0.305226	−	0.952280i	$-0.401268\pi$
$631$	32.7867	−	23.8209i	1.30522	−	0.948296i	0.999992	+	0.00398374i	$0.00126807\pi$
$632$	1.16415	−	3.58288i	0.0463074	−	0.142520i
$633$	12.0271	−	37.0157i	0.478036	−	1.47124i
$634$	19.0078	−	13.8099i	0.754895	−	0.548463i
$635$	−1.67077	−	1.21388i	−0.0663024	−	0.0481715i
$636$	2.50098	+	7.69722i	0.0991702	+	0.305215i
$637$	−3.92049			−0.155335
$638$	13.6774	−	0.176394i	0.541492	−	0.00698351i
$639$	1.04822			0.0414671
$640$	−0.309017	−	0.951057i	−0.0122150	−	0.0375938i
$641$	12.0212	+	8.73389i	0.474808	+	0.344968i	0.799312	−	0.600916i	$-0.205197\pi$
$641$	12.0212	+	8.73389i	0.474808	+	0.344968i	−0.324504	+	0.945884i	$0.605197\pi$
$642$	−16.2054	+	11.7739i	−0.639575	+	0.464679i
$643$	−3.19616	+	9.83678i	−0.126044	+	0.387925i	−0.994090	−	0.108560i	$-0.965376\pi$
$643$	−3.19616	+	9.83678i	−0.126044	+	0.387925i	0.868045	+	0.496485i	$0.165376\pi$
$644$	0.467965	−	1.44025i	0.0184404	−	0.0567537i
$645$	11.3956	−	8.27939i	0.448701	−	0.326001i
$646$	−28.2909	−	20.5545i	−1.11309	−	0.808707i
$647$	−2.14656	−	6.60644i	−0.0843901	−	0.259726i	0.899954	−	0.435986i	$-0.143600\pi$
$647$	−2.14656	−	6.60644i	−0.0843901	−	0.259726i	−0.984344	+	0.176260i	$0.943600\pi$
$648$	−11.2176			−0.440671
$649$	3.71413	−	11.9533i	0.145792	−	0.469207i
$650$	−3.92049			−0.153774
$651$	3.85879	+	11.8761i	0.151238	+	0.465463i
$652$	−10.0682	−	7.31495i	−0.394300	−	0.286476i
$653$	20.4888	−	14.8860i	0.801788	−	0.582533i	−0.109650	−	0.993970i	$-0.534973\pi$
$653$	20.4888	−	14.8860i	0.801788	−	0.582533i	0.911438	+	0.411437i	$0.134973\pi$
$654$	−0.111804	+	0.344097i	−0.00437188	+	0.0134553i
$655$	−7.05782	+	21.7217i	−0.275772	+	0.848738i
$656$	4.48370	−	3.25760i	0.175059	−	0.127188i
$657$	−4.22007	−	3.06606i	−0.164641	−	0.119618i
$658$	−3.37522	−	10.3879i	−0.131580	−	0.404961i
$659$	2.24029			0.0872694			0.0436347	−	0.999048i	$-0.486106\pi$
$659$	2.24029			0.0872694			0.0436347	+	0.999048i	$0.486106\pi$
$660$	2.30497	+	6.79454i	0.0897207	+	0.264477i
$661$	0.565825			0.0220081			0.0110040	−	0.999939i	$-0.496497\pi$
$661$	0.565825			0.0220081			0.0110040	+	0.999939i	$0.496497\pi$
$662$	3.28911	+	10.1228i	0.127835	+	0.393435i
$663$	−41.5812	−	30.2105i	−1.61488	−	1.17328i
$664$	10.0107	−	7.27319i	0.388490	−	0.282255i
$665$	1.78316	−	5.48799i	0.0691479	−	0.212815i
$666$	−2.36637	+	7.28294i	−0.0916950	+	0.282208i
$667$	5.05278	−	3.67106i	0.195645	−	0.142144i
$668$	14.4628	+	10.5078i	0.559583	+	0.406561i
$669$	14.8705	+	45.7668i	0.574928	+	1.76945i
$670$	1.15993			0.0448119
$671$	0.567791	+	1.67372i	0.0219193	+	0.0646134i
$672$	2.16330			0.0834512
$673$	9.27411	+	28.5428i	0.357491	+	1.10024i	0.954551	+	0.298047i	$0.0963352\pi$
$673$	9.27411	+	28.5428i	0.357491	+	1.10024i	−0.597060	+	0.802196i	$0.703665\pi$
$674$	−10.8057	−	7.85082i	−0.416221	−	0.302402i
$675$	2.31041	−	1.67861i	0.0889276	−	0.0646097i
$676$	0.732436	−	2.25420i	0.0281706	−	0.0867002i
$677$	2.49879	−	7.69050i	0.0960364	−	0.295570i	−0.891486	−	0.453048i	$-0.850337\pi$
$677$	2.49879	−	7.69050i	0.0960364	−	0.295570i	0.987522	+	0.157479i	$0.0503365\pi$
$678$	−11.6624	+	8.47320i	−0.447890	+	0.325411i
$679$	12.6549	+	9.19435i	0.485652	+	0.352847i
$680$	1.87268	+	5.76352i	0.0718141	+	0.221021i
$681$	−56.7880			−2.17612
$682$	−5.68074	+	18.2825i	−0.217527	+	0.700071i
$683$	−47.9737			−1.83566			−0.917831	−	0.396972i	$-0.870061\pi$
$683$	−47.9737			−1.83566			−0.917831	+	0.396972i	$0.870061\pi$
$684$	−2.99549	−	9.21917i	−0.114535	−	0.352504i
$685$	4.55290	+	3.30787i	0.173957	+	0.126387i
$686$	−0.809017	+	0.587785i	−0.0308884	+	0.0224417i
$687$	−6.10026	+	18.7747i	−0.232739	+	0.716298i
$688$	2.01208	−	6.19254i	0.0767097	−	0.236088i
$689$	11.8661	−	8.62122i	0.452062	−	0.328442i
$690$	2.65037	+	1.92560i	0.100898	+	0.0733065i
$691$	−2.09759	−	6.45571i	−0.0797960	−	0.245587i	0.903198	−	0.429224i	$-0.141213\pi$
$691$	−2.09759	−	6.45571i	−0.0797960	−	0.245587i	−0.982994	+	0.183637i	$0.941213\pi$
$692$	−19.6780			−0.748044
$693$	−5.57107	+	0.0718489i	−0.211627	+	0.00272931i
$694$	14.5070			0.550680
$695$	−2.64231	−	8.13219i	−0.100228	−	0.308472i
$696$	7.21800	+	5.24418i	0.273598	+	0.198780i
$697$	−27.1718	+	19.7415i	−1.02921	+	0.747761i
$698$	−8.06691	+	24.8274i	−0.305337	+	0.939731i
$699$	−0.253129	+	0.779051i	−0.00957422	+	0.0294664i
$700$	−0.809017	+	0.587785i	−0.0305780	+	0.0222162i
$701$	−23.5216	−	17.0894i	−0.888398	−	0.645459i	0.0470620	−	0.998892i	$-0.485014\pi$
$701$	−23.5216	−	17.0894i	−0.888398	−	0.645459i	−0.935460	+	0.353433i	$0.885014\pi$
$702$	3.45982	+	10.6482i	0.130582	+	0.401891i
$703$	26.3045			0.992092
$704$	2.70812	+	1.91470i	0.102066	+	0.0721629i
$705$	23.6285			0.889902
$706$	6.29443	+	19.3723i	0.236894	+	0.729085i
$707$	12.2903	+	8.92945i	0.462226	+	0.335827i
$708$	6.60509	−	4.79888i	0.248235	−	0.180353i
$709$	2.57905	−	7.93751i	0.0968583	−	0.298099i	−0.890875	−	0.454248i	$-0.849908\pi$
$709$	2.57905	−	7.93751i	0.0968583	−	0.298099i	0.987734	+	0.156149i	$0.0499079\pi$
$710$	−0.192823	+	0.593448i	−0.00723652	+	0.0222717i
$711$	−5.11991	+	3.71983i	−0.192012	+	0.139505i
$712$	−2.90687	−	2.11196i	−0.108939	−	0.0791491i
$713$	2.70125	+	8.31360i	0.101163	+	0.311347i
$714$	−13.1099			−0.490625
$715$	10.4200	−	7.77786i	0.389687	−	0.290876i
$716$	−1.69870			−0.0634834
$717$	−0.116113	−	0.357358i	−0.00433630	−	0.0133458i
$718$	−15.0439	−	10.9300i	−0.561434	−	0.407906i
$719$	−30.0326	+	21.8200i	−1.12003	+	0.813747i	−0.984213	−	0.176988i	$-0.943365\pi$
$719$	−30.0326	+	21.8200i	−1.12003	+	0.813747i	−0.135813	+	0.990734i	$0.543365\pi$
$720$	−0.519111	+	1.59766i	−0.0193461	+	0.0595413i
$721$	1.71437	−	5.27628i	0.0638464	−	0.196499i
$722$	−11.5671	+	8.40398i	−0.430483	+	0.312764i
$723$	48.8726	+	35.5080i	1.81759	+	1.32056i
$724$	−4.98146	−	15.3314i	−0.185134	−	0.569785i
$725$	−4.12422			−0.153170
$726$	−19.6060	−	13.4860i	−0.727645	−	0.500512i
$727$	−4.58789			−0.170155			−0.0850777	−	0.996374i	$-0.527114\pi$
$727$	−4.58789			−0.170155			−0.0850777	+	0.996374i	$0.527114\pi$
$728$	−1.21150	−	3.72860i	−0.0449011	−	0.138191i
$729$	0.251014	+	0.182372i	0.00929682	+	0.00675454i
$730$	2.51213	−	1.82517i	0.0929781	−	0.0675525i
$731$	−12.1934	+	37.5275i	−0.450991	+	1.38801i
$732$	−0.356238	+	1.09639i	−0.0131669	+	0.0405237i
$733$	22.9974	−	16.7086i	0.849428	−	0.617145i	−0.0755605	−	0.997141i	$-0.524075\pi$
$733$	22.9974	−	16.7086i	0.849428	−	0.617145i	0.924988	+	0.379996i	$0.124075\pi$
$734$	−7.63619	−	5.54801i	−0.281857	−	0.204781i
$735$	−0.668497	−	2.05742i	−0.0246579	−	0.0758892i
$736$	1.51437			0.0558203
$737$	−3.08290	+	2.30118i	−0.113560	+	0.0847651i
$738$	−9.31016			−0.342712
$739$	−13.5807	−	41.7970i	−0.499573	−	1.53753i	−0.809706	−	0.586835i	$-0.800374\pi$
$739$	−13.5807	−	41.7970i	−0.499573	−	1.53753i	0.310133	−	0.950693i	$-0.399626\pi$
$740$	−3.68791	−	2.67942i	−0.135570	−	0.0984975i
$741$	−39.5933	+	28.7662i	−1.45450	+	1.05675i
$742$	1.15609	−	3.55809i	0.0424415	−	0.130621i
$743$	11.7256	−	36.0878i	0.430172	−	1.32393i	−0.467781	−	0.883844i	$-0.654947\pi$
$743$	11.7256	−	36.0878i	0.430172	−	1.32393i	0.897954	−	0.440090i	$-0.145053\pi$
$744$	−10.1025	+	7.33986i	−0.370374	+	0.269092i
$745$	−15.7664	−	11.4550i	−0.577637	−	0.419678i
$746$	−5.30144	−	16.3162i	−0.194100	−	0.597377i
$747$	−20.7866			−0.760544
$748$	−16.4116	−	11.6033i	−0.600066	−	0.424259i
$749$	9.25943			0.338332
$750$	−0.668497	−	2.05742i	−0.0244101	−	0.0751265i
$751$	−38.4110	−	27.9072i	−1.40164	−	1.01835i	−0.994473	−	0.104994i	$-0.966518\pi$
$751$	−38.4110	−	27.9072i	−1.40164	−	1.01835i	−0.407164	−	0.913355i	$-0.633482\pi$
$752$	8.83643	−	6.42004i	0.322232	−	0.234115i
$753$	17.1418	−	52.7571i	0.624683	−	1.92258i
$754$	4.99648	−	15.3776i	0.181961	−	0.560019i
$755$	−4.23751	+	3.07873i	−0.154219	+	0.112047i
$756$	2.31041	+	1.67861i	0.0840287	+	0.0610504i
$757$	−2.81672	−	8.66897i	−0.102375	−	0.315079i	0.886730	−	0.462288i	$-0.152971\pi$
$757$	−2.81672	−	8.66897i	−0.102375	−	0.315079i	−0.989106	+	0.147208i	$0.952971\pi$
$758$	−8.09841			−0.294148
$759$	−10.8645	+	0.140117i	−0.394355	+	0.00508592i
$760$	5.77042			0.209315
$761$	−14.7424	−	45.3723i	−0.534410	−	1.64474i	−0.744921	−	0.667153i	$-0.767513\pi$
$761$	−14.7424	−	45.3723i	−0.534410	−	1.64474i	0.210511	−	0.977591i	$-0.432487\pi$
$762$	3.61437	+	2.62600i	0.130935	+	0.0951298i
$763$	0.135305	−	0.0983050i	0.00489838	−	0.00355888i
$764$	−5.36571	+	16.5139i	−0.194124	+	0.597454i
$765$	3.14588	−	9.68202i	0.113740	−	0.350054i
$766$	−18.8628	+	13.7046i	−0.681540	+	0.495168i
$767$	−11.9702	−	8.69686i	−0.432219	−	0.314025i
$768$	0.668497	+	2.05742i	0.0241223	+	0.0742409i
$769$	21.7046			0.782689			0.391345	−	0.920244i	$-0.372010\pi$
$769$	21.7046			0.782689			0.391345	+	0.920244i	$0.372010\pi$
$770$	0.984131	−	3.16725i	0.0354656	−	0.114140i
$771$	68.0149			2.44950
$772$	−1.64913	−	5.07551i	−0.0593536	−	0.182672i
$773$	−36.4258	−	26.4649i	−1.31015	−	0.951877i	−0.999999	−	0.00118818i	$-0.999622\pi$
$773$	−36.4258	−	26.4649i	−1.31015	−	0.951877i	−0.310147	−	0.950689i	$-0.600378\pi$
$774$	−8.84908	+	6.42923i	−0.318073	+	0.231094i
$775$	1.78375	−	5.48982i	0.0640742	−	0.197200i
$776$	−4.83375	+	14.8768i	−0.173522	+	0.534045i
$777$	7.97806	−	5.79640i	0.286211	−	0.207945i
$778$	−15.3327	−	11.1398i	−0.549702	−	0.399382i
$779$	9.88254	+	30.4153i	0.354079	+	1.08974i
$780$	8.48120			0.303676
$781$	−0.664850	−	1.95983i	−0.0237902	−	0.0701284i
$782$	−9.17725			−0.328178
$783$	3.63961	+	11.2016i	0.130069	+	0.400312i
$784$	−0.809017	−	0.587785i	−0.0288935	−	0.0209923i
$785$	12.7922	−	9.29411i	0.456575	−	0.331721i
$786$	15.2682	−	46.9907i	0.544598	−	1.67610i
$787$	14.9657	−	46.0597i	0.533470	−	1.64185i	−0.213463	−	0.976951i	$-0.568474\pi$
$787$	14.9657	−	46.0597i	0.533470	−	1.64185i	0.746933	−	0.664900i	$-0.231526\pi$
$788$	−16.0725	+	11.6774i	−0.572559	+	0.415989i
$789$	−42.1742	−	30.6414i	−1.50144	−	1.09086i
$790$	−1.16415	−	3.58288i	−0.0414186	−	0.127473i
$791$	6.66364			0.236932
$792$	−1.78989	−	5.27620i	−0.0636008	−	0.187481i
$793$	2.08920			0.0741898
$794$	2.09121	+	6.43609i	0.0742144	+	0.228408i
$795$	6.54764	+	4.75714i	0.232221	+	0.168718i
$796$	−2.37677	+	1.72683i	−0.0842424	+	0.0612057i
$797$	5.12364	−	15.7690i	0.181489	−	0.558565i	−0.818381	−	0.574675i	$-0.805128\pi$
$797$	5.12364	−	15.7690i	0.181489	−	0.558565i	0.999870	+	0.0161103i	$0.00512830\pi$
$798$	−3.85751	+	11.8722i	−0.136554	+	0.420271i
$799$	−53.5499	+	38.9063i	−1.89446	+	1.37641i
$800$	−0.809017	−	0.587785i	−0.0286031	−	0.0207813i
$801$	1.86521	+	5.74053i	0.0659040	+	0.202832i
$802$	−20.9845			−0.740989
$803$	−3.05589	+	9.83483i	−0.107840	+	0.347064i
$804$	−2.50927			−0.0884952
$805$	−0.467965	−	1.44025i	−0.0164936	−	0.0507621i
$806$	18.3084	+	13.3018i	0.644884	+	0.468536i
$807$	−43.4863	+	31.5947i	−1.53079	+	1.11218i
$808$	−4.69449	+	14.4482i	−0.165152	+	0.508284i
$809$	−13.6720	+	42.0782i	−0.480683	+	1.47939i	0.357454	+	0.933931i	$0.383645\pi$
$809$	−13.6720	+	42.0782i	−0.480683	+	1.47939i	−0.838137	+	0.545459i	$0.816355\pi$
$810$	−9.07526	+	6.59357i	−0.318872	+	0.231674i
$811$	−24.9972	−	18.1615i	−0.877771	−	0.637738i	0.0548898	−	0.998492i	$-0.482519\pi$
$811$	−24.9972	−	18.1615i	−0.877771	−	0.637738i	−0.932661	+	0.360754i	$0.882519\pi$
$812$	−1.27445	−	3.92237i	−0.0447246	−	0.137648i
$813$	0.650716			0.0228216
$814$	15.1176	−	0.194968i	0.529871	−	0.00683364i
$815$	−12.4449			−0.435927
$816$	−4.05118	−	12.4682i	−0.141820	−	0.436476i
$817$	30.3967	+	22.0845i	1.06345	+	0.772640i
$818$	25.7833	−	18.7326i	0.901491	−	0.654972i
$819$	−2.03517	+	6.26360i	−0.0711145	+	0.218868i
$820$	1.71262	−	5.27091i	0.0598073	−	0.184068i
$821$	−3.52481	+	2.56093i	−0.123017	+	0.0893770i	−0.647592	−	0.761987i	$-0.724224\pi$
$821$	−3.52481	+	2.56093i	−0.123017	+	0.0893770i	0.524576	+	0.851364i	$0.324224\pi$
$822$	−9.84930	−	7.15593i	−0.343534	−	0.249592i
$823$	−11.9384	−	36.7427i	−0.416147	−	1.28077i	−0.911221	−	0.411918i	$-0.864859\pi$
$823$	−11.9384	−	36.7427i	−0.416147	−	1.28077i	0.495074	−	0.868851i	$-0.335141\pi$
$824$	5.54781			0.193267
$825$	5.85849	+	4.14207i	0.203966	+	0.144209i
$826$	−3.77402			−0.131315
$827$	−3.95455	−	12.1709i	−0.137513	−	0.423222i	0.858459	−	0.512882i	$-0.171422\pi$
$827$	−3.95455	−	12.1709i	−0.137513	−	0.423222i	−0.995972	+	0.0896596i	$0.971422\pi$
$828$	−2.05810	−	1.49530i	−0.0715240	−	0.0519652i
$829$	6.32219	−	4.59334i	0.219579	−	0.159533i	−0.472558	−	0.881299i	$-0.656669\pi$
$829$	6.32219	−	4.59334i	0.219579	−	0.159533i	0.692137	+	0.721766i	$0.256669\pi$
$830$	3.82374	−	11.7683i	0.132724	−	0.408483i
$831$	11.3713	−	34.9974i	0.394467	−	1.21405i
$832$	3.17174	−	2.30440i	0.109960	−	0.0798908i
$833$	4.90275	+	3.56205i	0.169870	+	0.123418i
$834$	5.71611	+	17.5924i	0.197933	+	0.609175i
$835$	17.8770			0.618659
$836$	−15.3369	+	11.4479i	−0.530436	+	0.395936i
$837$	−16.4848			−0.569797
$838$	−4.21070	−	12.9592i	−0.145456	−	0.447669i
$839$	−19.2768	−	14.0054i	−0.665508	−	0.483520i	0.203011	−	0.979177i	$-0.434927\pi$
$839$	−19.2768	−	14.0054i	−0.665508	−	0.483520i	−0.868519	+	0.495657i	$0.834927\pi$
$840$	1.75015	−	1.27156i	0.0603859	−	0.0438729i
$841$	−3.70536	+	11.4039i	−0.127771	+	0.393239i
$842$	5.15080	−	15.8525i	0.177508	−	0.546315i
$843$	38.5702	−	28.0229i	1.32843	−	0.965159i
$844$	−14.5553	−	10.5750i	−0.501013	−	0.364007i
$845$	−0.732436	−	2.25420i	−0.0251965	−	0.0775470i
$846$	−18.3484			−0.630830
$847$	3.66785	+	10.3705i	0.126029	+	0.356334i
$848$	3.74119			0.128473
$849$	6.33170	+	19.4870i	0.217303	+	0.668791i
$850$	4.90275	+	3.56205i	0.168163	+	0.122177i
$851$	5.58484	−	4.05762i	0.191446	−	0.139094i
$852$	0.417134	−	1.28381i	0.0142908	−	0.0439825i
$853$	3.39033	−	10.4344i	0.116083	−	0.357265i	−0.876089	−	0.482150i	$-0.839856\pi$
$853$	3.39033	−	10.4344i	0.116083	−	0.357265i	0.992171	+	0.124885i	$0.0398560\pi$
$854$	0.431120	−	0.313227i	0.0147526	−	0.0107184i
$855$	−7.84229	−	5.69776i	−0.268201	−	0.194859i
$856$	2.86132	+	8.80624i	0.0977979	+	0.300991i
$857$	−46.9137			−1.60254			−0.801270	−	0.598302i	$-0.795842\pi$
$857$	−46.9137			−1.60254			−0.801270	+	0.598302i	$0.795842\pi$
$858$	−22.5417	+	16.8259i	−0.769561	+	0.574426i
$859$	−12.5547			−0.428362			−0.214181	−	0.976794i	$-0.568708\pi$
$859$	−12.5547			−0.428362			−0.214181	+	0.976794i	$0.568708\pi$
$860$	−2.01208	−	6.19254i	−0.0686113	−	0.211164i
$861$	9.69961	+	7.04718i	0.330562	+	0.240167i
$862$	21.9297	−	15.9329i	0.746929	−	0.542676i
$863$	14.5412	−	44.7532i	0.494989	−	1.52342i	−0.321986	−	0.946744i	$-0.604350\pi$
$863$	14.5412	−	44.7532i	0.494989	−	1.52342i	0.816975	−	0.576674i	$-0.195650\pi$
$864$	−0.882497	+	2.71605i	−0.0300232	+	0.0924018i
$865$	−15.9198	+	11.5664i	−0.541290	+	0.393270i
$866$	15.4895	+	11.2538i	0.526355	+	0.382419i
$867$	13.1862	+	40.5829i	0.447827	+	1.37827i
$868$	5.77234			0.195926
$869$	10.2022	+	7.21318i	0.346087	+	0.244691i
$870$	8.92194			0.302482
$871$	1.40525	+	4.32491i	0.0476150	+	0.146544i
$872$	0.135305	+	0.0983050i	0.00458202	+	0.00332903i
$873$	21.2588	−	15.4454i	0.719500	−	0.522747i
$874$	−2.70035	+	8.31083i	−0.0913408	+	0.281118i
$875$	−0.309017	+	0.951057i	−0.0104467	+	0.0321516i
$876$	−5.43450	+	3.94839i	−0.183615	+	0.133404i
$877$	−12.8208	−	9.31487i	−0.432928	−	0.314541i	0.349890	−	0.936791i	$-0.386219\pi$
$877$	−12.8208	−	9.31487i	−0.432928	−	0.314541i	−0.782819	+	0.622250i	$0.786219\pi$
$878$	−5.44691	−	16.7639i	−0.183824	−	0.565753i
$879$	−36.4341			−1.22889
$880$	3.31635	−	0.0427703i	0.111794	−	0.00144179i
$881$	−51.3201			−1.72902			−0.864509	−	0.502617i	$-0.832371\pi$
$881$	−51.3201			−1.72902			−0.864509	+	0.502617i	$0.832371\pi$
$882$	0.519111	+	1.59766i	0.0174794	+	0.0537960i
$883$	16.2140	+	11.7801i	0.545643	+	0.396433i	0.826177	−	0.563411i	$-0.190511\pi$
$883$	16.2140	+	11.7801i	0.545643	+	0.396433i	−0.280533	+	0.959844i	$0.590511\pi$
$884$	−19.2211	+	13.9650i	−0.646477	+	0.469693i
$885$	2.52292	−	7.76475i	0.0848070	−	0.261009i
$886$	−9.17167	+	28.2275i	−0.308128	+	0.948322i
$887$	16.6700	−	12.1114i	0.559723	−	0.406662i	−0.271635	−	0.962400i	$-0.587564\pi$
$887$	16.6700	−	12.1114i	0.559723	−	0.406662i	0.831357	+	0.555738i	$0.187564\pi$
$888$	7.97806	+	5.79640i	0.267726	+	0.194514i
$889$	−0.638176	−	1.96410i	−0.0214037	−	0.0658739i
$890$	−3.59309			−0.120440
$891$	11.0396	−	35.5291i	0.369842	−	1.19027i
$892$	22.2447			0.744808
$893$	19.4764	+	59.9422i	0.651753	+	2.00589i
$894$	34.1075	+	24.7806i	1.14073	+	0.828786i
$895$	−1.37428	+	0.998471i	−0.0459370	+	0.0333752i
$896$	0.309017	−	0.951057i	0.0103235	−	0.0317726i
$897$	−3.96890	+	12.2150i	−0.132518	+	0.407848i
$898$	18.3749	−	13.3502i	0.613180	−	0.445501i
$899$	19.2598	+	13.9931i	0.642350	+	0.466694i
$900$	0.519111	+	1.59766i	0.0173037	+	0.0532553i
$901$	−22.6721			−0.755317
$902$	5.90509	+	17.4069i	0.196618	+	0.579587i
$903$	14.0857			0.468744
$904$	2.05918	+	6.33750i	0.0684873	+	0.210782i
$905$	−13.0416	−	9.47530i	−0.433518	−	0.314970i
$906$	9.16702	−	6.66023i	0.304554	−	0.221271i
$907$	−6.07049	+	18.6831i	−0.201567	+	0.620361i	0.798270	+	0.602300i	$0.205749\pi$
$907$	−6.07049	+	18.6831i	−0.201567	+	0.620361i	−0.999837	+	0.0180602i	$0.994251\pi$
$908$	−8.11188	+	24.9658i	−0.269202	+	0.828519i
$909$	20.6463	−	15.0004i	0.684794	−	0.497532i
$910$	−3.17174	−	2.30440i	−0.105142	−	0.0763902i
$911$	4.19440	+	12.9090i	0.138967	+	0.427696i	0.996186	−	0.0872560i	$-0.0278098\pi$
$911$	4.19440	+	12.9090i	0.138967	+	0.427696i	−0.857219	+	0.514952i	$0.827810\pi$
$912$	−12.4832			−0.413359
$913$	13.1842	+	38.8641i	0.436333	+	1.28622i
$914$	1.09657			0.0362712
$915$	0.356238	+	1.09639i	0.0117769	+	0.0362455i
$916$	7.38255	+	5.36374i	0.243926	+	0.177223i
$917$	−18.4776	+	13.4248i	−0.610184	+	0.443325i
$918$	5.34804	−	16.4596i	0.176512	−	0.543247i
$919$	12.8761	−	39.6285i	0.424743	−	1.30722i	−0.478498	−	0.878089i	$-0.658818\pi$
$919$	12.8761	−	39.6285i	0.424743	−	1.30722i	0.903240	−	0.429135i	$-0.141182\pi$
$920$	1.22515	−	0.890122i	0.0403919	−	0.0293465i
$921$	2.39148	+	1.73751i	0.0788019	+	0.0572529i
$922$	−0.687335	−	2.11540i	−0.0226362	−	0.0696669i
$923$	−2.44634			−0.0805222
$924$	−2.12897	+	6.85173i	−0.0700381	+	0.225405i
$925$	−4.55850			−0.149883
$926$	−10.0204	−	30.8395i	−0.329289	−	1.01345i
$927$	−7.53976	−	5.47795i	−0.247638	−	0.179920i
$928$	3.33657	−	2.42416i	0.109528	−	0.0795768i
$929$	−12.6249	+	38.8555i	−0.414210	+	1.27481i	0.498745	+	0.866749i	$0.333794\pi$
$929$	−12.6249	+	38.8555i	−0.414210	+	1.27481i	−0.912955	+	0.408060i	$0.866206\pi$
$930$	−3.85879	+	11.8761i	−0.126535	+	0.389434i
$931$	4.66837	−	3.39177i	0.152999	−	0.111161i
$932$	0.306337	+	0.222567i	0.0100344	+	0.00729043i
$933$	12.4035	+	38.1740i	0.406072	+	1.24976i
$934$	−10.4325			−0.341361
$935$	−20.0975	+	0.259193i	−0.657258	+	0.00847652i
$936$	−6.58594			−0.215268
$937$	−10.8248	−	33.3154i	−0.353632	−	1.08837i	−0.956798	−	0.290752i	$-0.906095\pi$
$937$	−10.8248	−	33.3154i	−0.353632	−	1.08837i	0.603166	−	0.797615i	$-0.293905\pi$
$938$	0.938400	+	0.681788i	0.0306399	+	0.0222612i
$939$	24.2656	−	17.6300i	0.791877	−	0.575332i
$940$	3.37522	−	10.3879i	0.110087	−	0.338814i
$941$	10.3097	−	31.7301i	0.336087	−	1.03437i	−0.630097	−	0.776517i	$-0.716985\pi$
$941$	10.3097	−	31.7301i	0.336087	−	1.03437i	0.966184	−	0.257854i	$-0.0830153\pi$
$942$	−27.6735	+	20.1060i	−0.901651	+	0.655088i
$943$	6.78997	+	4.93320i	0.221112	+	0.160647i
$944$	−1.16624	−	3.58930i	−0.0379577	−	0.116822i
$945$	2.85582			0.0928999
$946$	17.6332	+	12.4670i	0.573304	+	0.405338i
$947$	40.2802			1.30893			0.654466	−	0.756091i	$-0.272893\pi$
$947$	40.2802			1.30893			0.654466	+	0.756091i	$0.272893\pi$
$948$	2.51841	+	7.75086i	0.0817941	+	0.251736i
$949$	9.84877	+	7.15555i	0.319704	+	0.232279i
$950$	4.66837	−	3.39177i	0.151462	−	0.110043i
$951$	−15.7063	+	48.3389i	−0.509311	+	1.56750i
$952$	−1.87268	+	5.76352i	−0.0606940	+	0.186797i
$953$	−4.28441	+	3.11280i	−0.138786	+	0.100834i	−0.655012	−	0.755619i	$-0.727336\pi$
$953$	−4.28441	+	3.11280i	−0.138786	+	0.100834i	0.516226	+	0.856452i	$0.327336\pi$
$954$	−5.08447	−	3.69409i	−0.164616	−	0.119600i
$955$	5.36571	+	16.5139i	0.173630	+	0.534379i
$956$	−0.173692			−0.00561760
$957$	−23.7131	+	17.7003i	−0.766536	+	0.572168i
$958$	29.5228			0.953840
$959$	1.73905	+	5.35225i	0.0561569	+	0.172833i
$960$	1.75015	+	1.27156i	0.0564858	+	0.0410393i
$961$	−1.87683	+	1.36360i	−0.0605429	+	0.0439870i
$962$	5.52261	−	16.9969i	0.178056	−	0.548000i
$963$	4.80667	−	14.7934i	0.154893	−	0.476711i
$964$	22.5917	−	16.4138i	0.727628	−	0.528653i
$965$	−4.31749	−	3.13684i	−0.138985	−	0.100978i
$966$	1.01235	+	3.11569i	0.0325718	+	0.100246i
$967$	36.5071			1.17399			0.586995	−	0.809590i	$-0.300311\pi$
$967$	36.5071			1.17399			0.586995	+	0.809590i	$0.300311\pi$
$968$	−8.72948	+	6.69299i	−0.280576	+	0.215121i
$969$	75.6495			2.43021
$970$	4.83375	+	14.8768i	0.155202	+	0.477664i
$971$	14.3564	+	10.4306i	0.460720	+	0.334732i	0.793814	−	0.608161i	$-0.208093\pi$
$971$	14.3564	+	10.4306i	0.460720	+	0.334732i	−0.333094	+	0.942894i	$0.608093\pi$
$972$	12.7013	−	9.22805i	0.407395	−	0.295990i
$973$	2.64231	−	8.13219i	0.0847085	−	0.260706i
$974$	−9.27146	+	28.5346i	−0.297077	+	0.914309i
$975$	6.86143	−	4.98512i	0.219742	−	0.159652i
$976$	0.431120	+	0.313227i	0.0137998	+	0.0100262i
$977$	−5.02985	−	15.4803i	−0.160919	−	0.495259i	0.837793	−	0.545988i	$-0.183845\pi$
$977$	−5.02985	−	15.4803i	−0.160919	−	0.495259i	−0.998712	+	0.0507291i	$0.983845\pi$
$978$	26.9222			0.860876
$979$	9.54986	−	7.12833i	0.305215	−	0.227822i
$980$	−1.00000			−0.0319438
$981$	−0.0868196	−	0.267203i	−0.00277194	−	0.00853114i
$982$	5.25266	+	3.81628i	0.167619	+	0.121783i
$983$	−13.7963	+	10.0236i	−0.440033	+	0.319703i	−0.785648	−	0.618673i	$-0.787670\pi$
$983$	−13.7963	+	10.0236i	−0.440033	+	0.319703i	0.345615	+	0.938376i	$0.387670\pi$
$984$	−3.70492	+	11.4026i	−0.118109	+	0.363501i
$985$	−6.13915	+	18.8944i	−0.195610	+	0.602024i
$986$	−20.2200	+	14.6907i	−0.643936	+	0.467847i
$987$	19.1159	+	13.8885i	0.608465	+	0.442076i
$988$	6.99084	+	21.5156i	0.222408	+	0.684502i
$989$	9.86037			0.313541
$990$	−4.54932	−	3.21646i	−0.144587	−	0.102226i
$991$	−16.9081			−0.537105			−0.268552	−	0.963265i	$-0.586545\pi$
$991$	−16.9081			−0.537105			−0.268552	+	0.963265i	$0.586545\pi$
$992$	1.78375	+	5.48982i	0.0566341	+	0.174302i
$993$	−18.6282	−	13.5342i	−0.591148	−	0.429494i
$994$	−0.504817	+	0.366771i	−0.0160118	+	0.0116333i
$995$	−0.907846	+	2.79406i	−0.0287806	+	0.0885777i
$996$	−8.27191	+	25.4583i	−0.262106	+	0.806678i
$997$	32.6339	−	23.7099i	1.03353	−	0.750900i	0.0645140	−	0.997917i	$-0.479450\pi$
$997$	32.6339	−	23.7099i	1.03353	−	0.750900i	0.969011	+	0.247017i	$0.0794503\pi$
$998$	−35.7661	−	25.9856i	−1.13216	−	0.822559i
$999$	4.02287	+	12.3811i	0.127278	+	0.391721i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.n.h.71.1	✓	12
11.3	even	5		8470.2.a.da.1.6		6
11.8	odd	10		8470.2.a.cu.1.6		6
11.9	even	5	inner	770.2.n.h.141.1	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.n.h.71.1	✓	12	1.1	even	1	trivial
770.2.n.h.141.1	yes	12	11.9	even	5	inner
8470.2.a.cu.1.6		6	11.8	odd	10
8470.2.a.da.1.6		6	11.3	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:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.309017 + 0.951057i) q^{2} +(-1.75015 - 1.27156i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-0.309017 + 0.951057i) q^{5} +(0.668497 - 2.05742i) q^{6} +(-0.809017 + 0.587785i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(0.519111 + 1.59766i) q^{9} +O(q^{10})\)	\(q+(0.309017 + 0.951057i) q^{2} +(-1.75015 - 1.27156i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-0.309017 + 0.951057i) q^{5} +(0.668497 - 2.05742i) q^{6} +(-0.809017 + 0.587785i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(0.519111 + 1.59766i) q^{9} -1.00000 q^{10} +(2.65784 - 1.98390i) q^{11} +2.16330 q^{12} +(-1.21150 - 3.72860i) q^{13} +(-0.809017 - 0.587785i) q^{14} +(1.75015 - 1.27156i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-1.87268 + 5.76352i) q^{17} +(-1.35905 + 0.987408i) q^{18} +(4.66837 + 3.39177i) q^{19} +(-0.309017 - 0.951057i) q^{20} +2.16330 q^{21} +(2.70812 + 1.91470i) q^{22} +1.51437 q^{23} +(0.668497 + 2.05742i) q^{24} +(-0.809017 - 0.587785i) q^{25} +(3.17174 - 2.30440i) q^{26} +(-0.882497 + 2.71605i) q^{27} +(0.309017 - 0.951057i) q^{28} +(3.33657 - 2.42416i) q^{29} +(1.75015 + 1.27156i) q^{30} +(1.78375 + 5.48982i) q^{31} +1.00000 q^{32} +(-7.17427 + 0.0925250i) q^{33} -6.06013 q^{34} +(-0.309017 - 0.951057i) q^{35} +(-1.35905 - 0.987408i) q^{36} +(3.68791 - 2.67942i) q^{37} +(-1.78316 + 5.48799i) q^{38} +(-2.62083 + 8.06610i) q^{39} +(0.809017 - 0.587785i) q^{40} +(4.48370 + 3.25760i) q^{41} +(0.668497 + 2.05742i) q^{42} +6.51122 q^{43} +(-0.984131 + 3.16725i) q^{44} -1.67988 q^{45} +(0.467965 + 1.44025i) q^{46} +(8.83643 + 6.42004i) q^{47} +(-1.75015 + 1.27156i) q^{48} +(0.309017 - 0.951057i) q^{49} +(0.309017 - 0.951057i) q^{50} +(10.6061 - 7.70580i) q^{51} +(3.17174 + 2.30440i) q^{52} +(1.15609 + 3.55809i) q^{53} -2.85582 q^{54} +(1.06549 + 3.14082i) q^{55} +1.00000 q^{56} +(-3.85751 - 11.8722i) q^{57} +(3.33657 + 2.42416i) q^{58} +(3.05324 - 2.21831i) q^{59} +(-0.668497 + 2.05742i) q^{60} +(-0.164673 + 0.506812i) q^{61} +(-4.66992 + 3.39290i) q^{62} +(-1.35905 - 0.987408i) q^{63} +(0.309017 + 0.951057i) q^{64} +3.92049 q^{65} +(-2.30497 - 6.79454i) q^{66} -1.15993 q^{67} +(-1.87268 - 5.76352i) q^{68} +(-2.65037 - 1.92560i) q^{69} +(0.809017 - 0.587785i) q^{70} +(0.192823 - 0.593448i) q^{71} +(0.519111 - 1.59766i) q^{72} +(-2.51213 + 1.82517i) q^{73} +(3.68791 + 2.67942i) q^{74} +(0.668497 + 2.05742i) q^{75} -5.77042 q^{76} +(-0.984131 + 3.16725i) q^{77} -8.48120 q^{78} +(1.16415 + 3.58288i) q^{79} +(0.809017 + 0.587785i) q^{80} +(9.07526 - 6.59357i) q^{81} +(-1.71262 + 5.27091i) q^{82} +(-3.82374 + 11.7683i) q^{83} +(-1.75015 + 1.27156i) q^{84} +(-4.90275 - 3.56205i) q^{85} +(2.01208 + 6.19254i) q^{86} -8.92194 q^{87} +(-3.31635 + 0.0427703i) q^{88} +3.59309 q^{89} +(-0.519111 - 1.59766i) q^{90} +(3.17174 + 2.30440i) q^{91} +(-1.22515 + 0.890122i) q^{92} +(3.85879 - 11.8761i) q^{93} +(-3.37522 + 10.3879i) q^{94} +(-4.66837 + 3.39177i) q^{95} +(-1.75015 - 1.27156i) q^{96} +(-4.83375 - 14.8768i) q^{97} +1.00000 q^{98} +(4.54932 + 3.21646i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{2} - 3 q^{4} + 3 q^{5} + 5 q^{6} - 3 q^{7} - 3 q^{8} - 3 q^{9}+O(q^{10}) \) 12 * q - 3 * q^2 - 3 * q^4 + 3 * q^5 + 5 * q^6 - 3 * q^7 - 3 * q^8 - 3 * q^9	\( 12 q - 3 q^{2} - 3 q^{4} + 3 q^{5} + 5 q^{6} - 3 q^{7} - 3 q^{8} - 3 q^{9} - 12 q^{10} - q^{11} - 10 q^{12} - 3 q^{14} - 3 q^{16} - 8 q^{18} - q^{19} + 3 q^{20} - 10 q^{21} - q^{22} - 4 q^{23} + 5 q^{24} - 3 q^{25} + 3 q^{27} - 3 q^{28} + 22 q^{29} + 6 q^{31} + 12 q^{32} - 29 q^{33} - 30 q^{34} + 3 q^{35} - 8 q^{36} - 10 q^{37} + 14 q^{38} + 20 q^{39} + 3 q^{40} + 16 q^{41} + 5 q^{42} + 30 q^{43} + 14 q^{44} - 22 q^{45} - 4 q^{46} + 34 q^{47} - 3 q^{49} - 3 q^{50} + 37 q^{51} - 26 q^{53} - 52 q^{54} + 11 q^{55} + 12 q^{56} - 19 q^{57} + 22 q^{58} + q^{59} - 5 q^{60} + 40 q^{61} - 4 q^{62} - 8 q^{63} - 3 q^{64} + 16 q^{66} - 58 q^{67} + 14 q^{69} + 3 q^{70} - 14 q^{71} - 3 q^{72} + 32 q^{73} - 10 q^{74} + 5 q^{75} - 26 q^{76} + 14 q^{77} - 60 q^{78} + 16 q^{79} + 3 q^{80} - 46 q^{81} + q^{82} + 35 q^{83} - 15 q^{85} + 5 q^{86} - q^{88} - 58 q^{89} + 3 q^{90} + 6 q^{92} + 46 q^{93} - 16 q^{94} + q^{95} + 57 q^{97} + 12 q^{98} + 69 q^{99}+O(q^{100}) \) 12 * q - 3 * q^2 - 3 * q^4 + 3 * q^5 + 5 * q^6 - 3 * q^7 - 3 * q^8 - 3 * q^9 - 12 * q^10 - q^11 - 10 * q^12 - 3 * q^14 - 3 * q^16 - 8 * q^18 - q^19 + 3 * q^20 - 10 * q^21 - q^22 - 4 * q^23 + 5 * q^24 - 3 * q^25 + 3 * q^27 - 3 * q^28 + 22 * q^29 + 6 * q^31 + 12 * q^32 - 29 * q^33 - 30 * q^34 + 3 * q^35 - 8 * q^36 - 10 * q^37 + 14 * q^38 + 20 * q^39 + 3 * q^40 + 16 * q^41 + 5 * q^42 + 30 * q^43 + 14 * q^44 - 22 * q^45 - 4 * q^46 + 34 * q^47 - 3 * q^49 - 3 * q^50 + 37 * q^51 - 26 * q^53 - 52 * q^54 + 11 * q^55 + 12 * q^56 - 19 * q^57 + 22 * q^58 + q^59 - 5 * q^60 + 40 * q^61 - 4 * q^62 - 8 * q^63 - 3 * q^64 + 16 * q^66 - 58 * q^67 + 14 * q^69 + 3 * q^70 - 14 * q^71 - 3 * q^72 + 32 * q^73 - 10 * q^74 + 5 * q^75 - 26 * q^76 + 14 * q^77 - 60 * q^78 + 16 * q^79 + 3 * q^80 - 46 * q^81 + q^82 + 35 * q^83 - 15 * q^85 + 5 * q^86 - q^88 - 58 * q^89 + 3 * q^90 + 6 * q^92 + 46 * q^93 - 16 * q^94 + q^95 + 57 * q^97 + 12 * q^98 + 69 * q^99

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