LMFDB - Embedded newform 360.2.bm.b.11.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,2,Mod(11,360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(360, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1, 0]))

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

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

chi := DirichletCharacter("360.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	360.bm (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.87461447277$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.13
Character	$\chi$	$=$	360.11
Dual form			360.2.bm.b.131.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0418375 + 1.41359i) q^{2} +(1.46420 + 0.925262i) q^{3} +(-1.99650 - 0.118282i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-1.36920 + 2.03108i) q^{6} +(0.947055 + 0.546782i) q^{7} +(0.250732 - 2.81729i) q^{8} +(1.28778 + 2.70954i) q^{9} +O(q^{10})$	\(q+(-0.0418375 + 1.41359i) q^{2} +(1.46420 + 0.925262i) q^{3} +(-1.99650 - 0.118282i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-1.36920 + 2.03108i) q^{6} +(0.947055 + 0.546782i) q^{7} +(0.250732 - 2.81729i) q^{8} +(1.28778 + 2.70954i) q^{9} +(-1.24513 + 0.670565i) q^{10} +(2.31540 + 1.33679i) q^{11} +(-2.81384 - 2.02048i) q^{12} +(-2.12374 + 1.22614i) q^{13} +(-0.812551 + 1.31588i) q^{14} +(-0.0691995 + 1.73067i) q^{15} +(3.97202 + 0.472301i) q^{16} -0.124711i q^{17} +(-3.88407 + 1.70704i) q^{18} -5.84133 q^{19} +(-0.895814 - 1.78816i) q^{20} +(0.880763 + 1.67687i) q^{21} +(-1.98656 + 3.21710i) q^{22} +(-1.21152 - 2.09842i) q^{23} +(2.97386 - 3.89309i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-1.64441 - 3.05340i) q^{26} +(-0.621470 + 5.15885i) q^{27} +(-1.82612 - 1.20367i) q^{28} +(4.29490 - 7.43898i) q^{29} +(-2.44357 - 0.170227i) q^{30} +(2.54447 - 1.46905i) q^{31} +(-0.833822 + 5.59506i) q^{32} +(2.15332 + 4.09969i) q^{33} +(0.176291 + 0.00521759i) q^{34} +1.09356i q^{35} +(-2.25056 - 5.56192i) q^{36} +2.42896i q^{37} +(0.244386 - 8.25727i) q^{38} +(-4.24408 - 0.169696i) q^{39} +(2.56521 - 1.19151i) q^{40} +(7.57229 - 4.37186i) q^{41} +(-2.40727 + 1.17489i) q^{42} +(-2.14293 + 3.71166i) q^{43} +(-4.46457 - 2.94278i) q^{44} +(-1.70264 + 2.47002i) q^{45} +(3.01700 - 1.62481i) q^{46} +(3.32459 - 5.75836i) q^{47} +(5.37884 + 4.36670i) q^{48} +(-2.90206 - 5.02651i) q^{49} +(-1.20329 - 0.743030i) q^{50} +(0.115390 - 0.182602i) q^{51} +(4.38507 - 2.19679i) q^{52} +2.14097 q^{53} +(-7.26653 - 1.09434i) q^{54} +2.67359i q^{55} +(1.77790 - 2.53103i) q^{56} +(-8.55289 - 5.40476i) q^{57} +(10.3360 + 6.38247i) q^{58} +(-2.34413 + 1.35338i) q^{59} +(0.342864 - 3.44709i) q^{60} +(9.69518 + 5.59752i) q^{61} +(1.97018 + 3.65830i) q^{62} +(-0.261933 + 3.27022i) q^{63} +(-7.87427 - 1.41277i) q^{64} +(-2.12374 - 1.22614i) q^{65} +(-5.88538 + 2.87241i) q^{66} +(-0.707180 - 1.22487i) q^{67} +(-0.0147511 + 0.248986i) q^{68} +(0.167673 - 4.19348i) q^{69} +(-1.54586 - 0.0457520i) q^{70} -11.2346 q^{71} +(7.95646 - 2.94868i) q^{72} +5.35400 q^{73} +(-3.43356 - 0.101621i) q^{74} +(-1.53340 + 0.805405i) q^{75} +(11.6622 + 0.690927i) q^{76} +(1.46187 + 2.53203i) q^{77} +(0.417443 - 5.99231i) q^{78} +(2.07178 + 1.19614i) q^{79} +(1.57698 + 3.67602i) q^{80} +(-5.68325 + 6.97859i) q^{81} +(5.86323 + 10.8871i) q^{82} +(11.2212 + 6.47858i) q^{83} +(-1.56010 - 3.45206i) q^{84} +(0.108003 - 0.0623555i) q^{85} +(-5.15712 - 3.18452i) q^{86} +(13.1716 - 6.91827i) q^{87} +(4.34668 - 6.18797i) q^{88} -13.3875i q^{89} +(-3.42037 - 2.51019i) q^{90} -2.68172 q^{91} +(2.17060 + 4.33279i) q^{92} +(5.08487 + 0.203315i) q^{93} +(8.00089 + 4.94053i) q^{94} +(-2.92067 - 5.05874i) q^{95} +(-6.39779 + 7.42080i) q^{96} +(7.51249 - 13.0120i) q^{97} +(7.22687 - 3.89204i) q^{98} +(-0.640385 + 7.99516i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 24 q^{5} - q^{6} + 6 q^{8}+O(q^{10}) $ 48 * q + 24 * q^5 - q^6 + 6 * q^8	$ 48 q + 24 q^{5} - q^{6} + 6 q^{8} + 13 q^{12} + 15 q^{14} - 12 q^{16} + 7 q^{18} + 4 q^{21} - 21 q^{22} - 4 q^{24} - 24 q^{25} + 12 q^{27} - 2 q^{30} - 8 q^{33} - 27 q^{34} - 31 q^{36} - 27 q^{38} - 16 q^{39} + 12 q^{40} + 12 q^{41} - 9 q^{42} + 24 q^{44} - 6 q^{46} - 12 q^{47} + 7 q^{48} + 24 q^{49} - 20 q^{51} + 54 q^{52} - 32 q^{54} + 21 q^{56} + 4 q^{57} + 33 q^{58} - 36 q^{59} - q^{60} - 12 q^{61} - 42 q^{62} - 56 q^{63} - 12 q^{64} - 32 q^{66} + 51 q^{68} + 40 q^{69} + 15 q^{70} + 6 q^{72} + 54 q^{74} - 51 q^{76} - 24 q^{78} - 8 q^{81} - 18 q^{82} - 60 q^{83} + 41 q^{84} + 27 q^{86} - 36 q^{87} - 57 q^{88} - 22 q^{90} - 9 q^{92} - 75 q^{94} + 13 q^{96} - 42 q^{98} - 16 q^{99}+O(q^{100}) $ 48 * q + 24 * q^5 - q^6 + 6 * q^8 + 13 * q^12 + 15 * q^14 - 12 * q^16 + 7 * q^18 + 4 * q^21 - 21 * q^22 - 4 * q^24 - 24 * q^25 + 12 * q^27 - 2 * q^30 - 8 * q^33 - 27 * q^34 - 31 * q^36 - 27 * q^38 - 16 * q^39 + 12 * q^40 + 12 * q^41 - 9 * q^42 + 24 * q^44 - 6 * q^46 - 12 * q^47 + 7 * q^48 + 24 * q^49 - 20 * q^51 + 54 * q^52 - 32 * q^54 + 21 * q^56 + 4 * q^57 + 33 * q^58 - 36 * q^59 - q^60 - 12 * q^61 - 42 * q^62 - 56 * q^63 - 12 * q^64 - 32 * q^66 + 51 * q^68 + 40 * q^69 + 15 * q^70 + 6 * q^72 + 54 * q^74 - 51 * q^76 - 24 * q^78 - 8 * q^81 - 18 * q^82 - 60 * q^83 + 41 * q^84 + 27 * q^86 - 36 * q^87 - 57 * q^88 - 22 * q^90 - 9 * q^92 - 75 * q^94 + 13 * q^96 - 42 * q^98 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/360\mathbb{Z}\right)^\times$.

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$-1$	$1$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−0.0418375	+	1.41359i	−0.0295835	+	0.999562i
$2$	−0.0418375	+	1.41359i	−0.0295835	+	0.999562i
$3$	1.46420	+	0.925262i	0.845358	+	0.534201i
$3$	1.46420	+	0.925262i	0.845358	+	0.534201i
$4$	−1.99650	−	0.118282i	−0.998250	−	0.0591412i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	−1.36920	+	2.03108i	−0.558975	+	0.829184i
$7$	0.947055	+	0.546782i	0.357953	+	0.206664i	0.668182	−	0.743997i	$-0.267073\pi$
$7$	0.947055	+	0.546782i	0.357953	+	0.206664i	−0.310229	+	0.950662i	$0.600406\pi$
$8$	0.250732	−	2.81729i	0.0886471	−	0.996063i
$9$	1.28778	+	2.70954i	0.429260	+	0.903181i
$10$	−1.24513	+	0.670565i	−0.393744	+	0.212051i
$11$	2.31540	+	1.33679i	0.698118	+	0.403059i	0.806646	−	0.591035i	$-0.201280\pi$
$11$	2.31540	+	1.33679i	0.698118	+	0.403059i	−0.108528	+	0.994093i	$0.534614\pi$
$12$	−2.81384	−	2.02048i	−0.812285	−	0.583261i
$13$	−2.12374	+	1.22614i	−0.589018	+	0.340070i	−0.764709	−	0.644376i	$-0.777117\pi$
$13$	−2.12374	+	1.22614i	−0.589018	+	0.340070i	0.175691	+	0.984445i	$0.443784\pi$
$14$	−0.812551	+	1.31588i	−0.217163	+	0.351683i
$15$	−0.0691995	+	1.73067i	−0.0178672	+	0.446857i
$16$	3.97202	+	0.472301i	0.993005	+	0.118075i
$17$		−	0.124711i		−	0.0302469i	−0.999886	−	0.0151234i	$-0.995186\pi$
$17$		−	0.124711i		−	0.0302469i	0.999886	−	0.0151234i	$-0.00481412\pi$
$18$	−3.88407	+	1.70704i	−0.915485	+	0.402352i
$19$	−5.84133			−1.34009			−0.670047	−	0.742319i	$-0.733726\pi$
$19$	−5.84133			−1.34009			−0.670047	+	0.742319i	$0.733726\pi$
$20$	−0.895814	−	1.78816i	−0.200310	−	0.399845i
$21$	0.880763	+	1.67687i	0.192198	+	0.365924i
$22$	−1.98656	+	3.21710i	−0.423535	+	0.685889i
$23$	−1.21152	−	2.09842i	−0.252620	−	0.437550i	0.711627	−	0.702558i	$-0.247959\pi$
$23$	−1.21152	−	2.09842i	−0.252620	−	0.437550i	−0.964246	+	0.265008i	$0.914625\pi$
$24$	2.97386	−	3.89309i	0.607036	−	0.794674i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−1.64441	−	3.05340i	−0.322496	−	0.598821i
$27$	−0.621470	+	5.15885i	−0.119602	+	0.992822i
$28$	−1.82612	−	1.20367i	−0.345104	−	0.227472i
$29$	4.29490	−	7.43898i	0.797542	−	1.38138i	−0.123670	−	0.992323i	$-0.539466\pi$
$29$	4.29490	−	7.43898i	0.797542	−	1.38138i	0.921212	−	0.389060i	$-0.127200\pi$
$30$	−2.44357	−	0.170227i	−0.446132	−	0.0310790i
$31$	2.54447	−	1.46905i	0.457000	−	0.263849i	−0.253782	−	0.967261i	$-0.581675\pi$
$31$	2.54447	−	1.46905i	0.457000	−	0.263849i	0.710782	+	0.703413i	$0.248341\pi$
$32$	−0.833822	+	5.59506i	−0.147400	+	0.989077i
$33$	2.15332	+	4.09969i	0.374845	+	0.713664i
$34$	0.176291	+	0.00521759i	0.0302336	+	0.000894810i
$35$			1.09356i			0.184846i
$36$	−2.25056	−	5.56192i	−0.375093	−	0.926987i
$37$			2.42896i			0.399318i	0.979865	+	0.199659i	$0.0639835\pi$
$37$			2.42896i			0.399318i	−0.979865	+	0.199659i	$0.936017\pi$
$38$	0.244386	−	8.25727i	0.0396447	−	1.33951i
$39$	−4.24408	−	0.169696i	−0.679597	−	0.0271732i
$40$	2.56521	−	1.19151i	0.405596	−	0.188394i
$41$	7.57229	−	4.37186i	1.18259	−	0.682770i	0.225980	−	0.974132i	$-0.427442\pi$
$41$	7.57229	−	4.37186i	1.18259	−	0.682770i	0.956613	+	0.291362i	$0.0941084\pi$
$42$	−2.40727	+	1.17489i	−0.371450	+	0.181289i
$43$	−2.14293	+	3.71166i	−0.326793	+	0.566023i	−0.981874	−	0.189537i	$-0.939301\pi$
$43$	−2.14293	+	3.71166i	−0.326793	+	0.566023i	0.655080	+	0.755559i	$0.272635\pi$
$44$	−4.46457	−	2.94278i	−0.673059	−	0.443641i
$45$	−1.70264	+	2.47002i	−0.253815	+	0.368209i
$46$	3.01700	−	1.62481i	0.444832	−	0.239565i
$47$	3.32459	−	5.75836i	0.484941	−	0.839942i	−0.514909	−	0.857245i	$-0.672174\pi$
$47$	3.32459	−	5.75836i	0.484941	−	0.839942i	0.999850	+	0.0173022i	$0.00550774\pi$
$48$	5.37884	+	4.36670i	0.776368	+	0.630280i
$49$	−2.90206	−	5.02651i	−0.414580	−	0.718073i
$50$	−1.20329	−	0.743030i	−0.170171	−	0.105080i
$51$	0.115390	−	0.182602i	0.0161579	−	0.0255694i
$52$	4.38507	−	2.19679i	0.608099	−	0.304639i
$53$	2.14097			0.294084			0.147042	−	0.989130i	$-0.453025\pi$
$53$	2.14097			0.294084			0.147042	+	0.989130i	$0.453025\pi$
$54$	−7.26653	−	1.09434i	−0.988849	−	0.148921i
$55$			2.67359i			0.360507i
$56$	1.77790	−	2.53103i	0.237582	−	0.338224i
$57$	−8.55289	−	5.40476i	−1.13286	−	0.715879i
$58$	10.3360	+	6.38247i	1.35719	+	0.838060i
$59$	−2.34413	+	1.35338i	−0.305179	+	0.176195i	−0.644767	−	0.764379i	$-0.723046\pi$
$59$	−2.34413	+	1.35338i	−0.305179	+	0.176195i	0.339588	+	0.940574i	$0.389712\pi$
$60$	0.342864	−	3.44709i	0.0442636	−	0.445018i
$61$	9.69518	+	5.59752i	1.24134	+	0.716688i	0.969367	−	0.245616i	$-0.0789903\pi$
$61$	9.69518	+	5.59752i	1.24134	+	0.716688i	0.271974	+	0.962305i	$0.412324\pi$
$62$	1.97018	+	3.65830i	0.250214	+	0.464605i
$63$	−0.261933	+	3.27022i	−0.0330005	+	0.412009i
$64$	−7.87427	−	1.41277i	−0.984283	−	0.176596i
$65$	−2.12374	−	1.22614i	−0.263417	−	0.152084i
$66$	−5.88538	+	2.87241i	−0.724441	+	0.353569i
$67$	−0.707180	−	1.22487i	−0.0863958	−	0.149642i	0.819589	−	0.572951i	$-0.194202\pi$
$67$	−0.707180	−	1.22487i	−0.0863958	−	0.149642i	−0.905985	+	0.423309i	$0.860868\pi$
$68$	−0.0147511	+	0.248986i	−0.00178884	+	0.0301939i
$69$	0.167673	−	4.19348i	0.0201855	−	0.504836i
$70$	−1.54586	−	0.0457520i	−0.184765	−	0.00546840i
$71$	−11.2346			−1.33330			−0.666648	−	0.745372i	$-0.732272\pi$
$71$	−11.2346			−1.33330			−0.666648	+	0.745372i	$0.732272\pi$
$72$	7.95646	−	2.94868i	0.937678	−	0.347505i
$73$	5.35400			0.626639			0.313319	−	0.949648i	$-0.398559\pi$
$73$	5.35400			0.626639			0.313319	+	0.949648i	$0.398559\pi$
$74$	−3.43356	−	0.101621i	−0.399143	−	0.0118132i
$75$	−1.53340	+	0.805405i	−0.177062	+	0.0930002i
$76$	11.6622	+	0.690927i	1.33775	+	0.0792547i
$77$	1.46187	+	2.53203i	0.166596	+	0.288552i
$78$	0.417443	−	5.99231i	0.0472661	−	0.678495i
$79$	2.07178	+	1.19614i	0.233093	+	0.134577i	0.611998	−	0.790859i	$-0.290366\pi$
$79$	2.07178	+	1.19614i	0.233093	+	0.134577i	−0.378905	+	0.925436i	$0.623699\pi$
$80$	1.57698	+	3.67602i	0.176312	+	0.410991i
$81$	−5.68325	+	6.97859i	−0.631472	+	0.775398i
$82$	5.86323	+	10.8871i	0.647486	+	1.20227i
$83$	11.2212	+	6.47858i	1.23169	+	0.711116i	0.967382	−	0.253322i	$-0.0815232\pi$
$83$	11.2212	+	6.47858i	1.23169	+	0.711116i	0.264308	+	0.964438i	$0.414857\pi$
$84$	−1.56010	−	3.45206i	−0.170221	−	0.376650i
$85$	0.108003	−	0.0623555i	0.0117146	−	0.00676341i
$86$	−5.15712	−	3.18452i	−0.556107	−	0.343395i
$87$	13.1716	−	6.91827i	1.41214	−	0.741716i
$88$	4.34668	−	6.18797i	0.463358	−	0.659640i
$89$		−	13.3875i		−	1.41907i	−0.704671	−	0.709535i	$-0.748905\pi$
$89$		−	13.3875i		−	1.41907i	0.704671	−	0.709535i	$-0.251095\pi$
$90$	−3.42037	−	2.51019i	−0.360539	−	0.264597i
$91$	−2.68172			−0.281121
$92$	2.17060	+	4.33279i	0.226300	+	0.451724i
$93$	5.08487	+	0.203315i	0.527276	+	0.0210828i
$94$	8.00089	+	4.94053i	0.825229	+	0.509577i
$95$	−2.92067	−	5.05874i	−0.299654	−	0.519016i
$96$	−6.39779	+	7.42080i	−0.652971	+	0.757383i
$97$	7.51249	−	13.0120i	0.762778	−	1.32117i	−0.178636	−	0.983915i	$-0.557168\pi$
$97$	7.51249	−	13.0120i	0.762778	−	1.32117i	0.941413	−	0.337255i	$-0.109498\pi$
$98$	7.22687	−	3.89204i	0.730024	−	0.393155i
$99$	−0.640385	+	7.99516i	−0.0643611	+	0.803544i
$100$	1.10069	−	1.66988i	0.110069	−	0.166988i
$101$	9.34757	−	16.1905i	0.930117	−	1.61101i	0.147000	−	0.989136i	$-0.453038\pi$
$101$	9.34757	−	16.1905i	0.930117	−	1.61101i	0.783117	−	0.621874i	$-0.213629\pi$
$102$	0.253298	+	0.170755i	0.0250802	+	0.0169073i
$103$	−13.4232	+	7.74987i	−1.32262	+	0.763617i	−0.984147	−	0.177357i	$-0.943245\pi$
$103$	−13.4232	+	7.74987i	−1.32262	+	0.763617i	−0.338477	+	0.940975i	$0.609912\pi$
$104$	2.92190	+	6.29061i	0.286516	+	0.616845i
$105$	−1.01183	+	1.60120i	−0.0987449	+	0.156261i
$106$	−0.0895726	+	3.02646i	−0.00870006	+	0.293956i
$107$			16.6662i			1.61118i	0.592474	+	0.805590i	$0.298151\pi$
$107$			16.6662i			1.61118i	−0.592474	+	0.805590i	$0.701849\pi$
$108$	1.85097	−	10.2261i	0.178109	−	0.984011i
$109$			9.56196i			0.915870i	0.888986	+	0.457935i	$0.151411\pi$
$109$			9.56196i			0.915870i	−0.888986	+	0.457935i	$0.848589\pi$
$110$	−3.77937	−	0.111856i	−0.360349	−	0.0106651i
$111$	−2.24742	+	3.55649i	−0.213316	+	0.337567i
$112$	3.50347	+	2.61912i	0.331047	+	0.247484i
$113$	11.1943	−	6.46306i	1.05307	−	0.607993i	0.129566	−	0.991571i	$-0.458641\pi$
$113$	11.1943	−	6.46306i	1.05307	−	0.607993i	0.923509	+	0.383578i	$0.125308\pi$
$114$	7.99798	−	11.8642i	0.749079	−	1.11118i
$115$	1.21152	−	2.09842i	0.112975	−	0.195678i
$116$	−9.45466	+	14.3439i	−0.877843	+	1.33180i
$117$	−6.05718	−	4.17536i	−0.559986	−	0.386012i
$118$	−1.81506	−	3.37026i	−0.167090	−	0.310258i
$119$	0.0681898	−	0.118108i	0.00625095	−	0.0108270i
$120$	4.85845	+	0.628889i	0.443513	+	0.0574094i
$121$	−1.92596	−	3.33586i	−0.175087	−	0.303260i
$122$	−8.31824	+	13.4709i	−0.753098	+	1.21960i
$123$	15.1325	+	0.605061i	1.36445	+	0.0545565i
$124$	−5.25379	+	2.63199i	−0.471804	+	0.236360i
$125$	−1.00000			−0.0894427
$126$	−4.61181	−	0.507085i	−0.410852	−	0.0451748i
$127$		−	15.7987i		−	1.40191i	−0.713205	−	0.700956i	$-0.752757\pi$
$127$		−	15.7987i		−	1.40191i	0.713205	−	0.700956i	$-0.247243\pi$
$128$	2.32652	−	11.0719i	0.205637	−	0.978628i
$129$	−6.57194	+	3.45185i	−0.578627	+	0.303918i
$130$	1.82212	−	2.95080i	0.159810	−	0.258802i
$131$	−4.77387	+	2.75619i	−0.417095	+	0.240810i	−0.693834	−	0.720135i	$-0.744080\pi$
$131$	−4.77387	+	2.75619i	−0.417095	+	0.240810i	0.276739	+	0.960945i	$0.410746\pi$
$132$	−3.81419	−	8.43972i	−0.331982	−	0.734584i
$133$	−5.53206	−	3.19394i	−0.479690	−	0.276949i
$134$	1.76106	−	0.948421i	0.152132	−	0.0819311i
$135$	−4.77843	+	2.04122i	−0.411262	+	0.175680i
$136$	−0.351347	−	0.0312690i	−0.0301278	−	0.00268130i
$137$	−7.73347	−	4.46492i	−0.660715	−	0.381464i	0.131834	−	0.991272i	$-0.457913\pi$
$137$	−7.73347	−	4.46492i	−0.660715	−	0.381464i	−0.792549	+	0.609808i	$0.791247\pi$
$138$	5.92087	+	0.412467i	0.504018	+	0.0351115i
$139$	−7.69083	−	13.3209i	−0.652328	−	1.12987i	−0.982556	−	0.185964i	$-0.940459\pi$
$139$	−7.69083	−	13.3209i	−0.652328	−	1.12987i	0.330228	−	0.943901i	$-0.392874\pi$
$140$	0.129349	−	2.18330i	0.0109320	−	0.184523i
$141$	10.1959	−	5.35528i	0.858646	−	0.450996i
$142$	0.470025	−	15.8811i	0.0394436	−	1.33271i
$143$	−6.55638			−0.548272
$144$	3.83536	+	11.3706i	0.319613	+	0.947548i
$145$	8.58979			0.713344
$146$	−0.223998	+	7.56839i	−0.0185382	+	0.626364i
$147$	0.401642	−	10.0450i	0.0331269	−	0.828497i
$148$	0.287303	−	4.84941i	0.0236161	−	0.398619i
$149$	0.101779	+	0.176287i	0.00833810	+	0.0144420i	0.870164	−	0.492762i	$-0.164013\pi$
$149$	0.101779	+	0.176287i	0.00833810	+	0.0144420i	−0.861826	+	0.507204i	$0.830679\pi$
$150$	−1.07436	−	2.20131i	−0.0877214	−	0.179736i
$151$	−5.62686	−	3.24867i	−0.457908	−	0.264373i	0.253256	−	0.967399i	$-0.418498\pi$
$151$	−5.62686	−	3.24867i	−0.457908	−	0.264373i	−0.711164	+	0.703026i	$0.751832\pi$
$152$	−1.46461	+	16.4567i	−0.118795	+	1.33482i
$153$	0.337910	−	0.160600i	0.0273184	−	0.0129838i
$154$	−3.64043	+	1.96056i	−0.293354	+	0.157986i
$155$	2.54447	+	1.46905i	0.204376	+	0.117997i
$156$	8.45323	+	0.840798i	0.676800	+	0.0673177i
$157$	−19.7645	+	11.4110i	−1.57738	+	0.910700i	−0.582155	+	0.813078i	$0.697790\pi$
$157$	−19.7645	+	11.4110i	−1.57738	+	0.910700i	−0.995224	+	0.0976221i	$0.968876\pi$
$158$	−1.77754	+	2.87861i	−0.141413	+	0.229010i
$159$	3.13481	+	1.98096i	0.248606	+	0.157100i
$160$	−5.26238	+	2.07542i	−0.416028	+	0.164076i
$161$		−	2.64975i		−	0.208830i
$162$	−9.62712	−	8.32578i	−0.756378	−	0.654135i
$163$	−17.3974			−1.36267			−0.681334	−	0.731973i	$-0.738600\pi$
$163$	−17.3974			−1.36267			−0.681334	+	0.731973i	$0.738600\pi$
$164$	−15.6352	+	7.83275i	−1.22090	+	0.611635i
$165$	−2.47377	+	3.91468i	−0.192583	+	0.304757i
$166$	−9.62755	+	15.5912i	−0.747243	+	1.21011i
$167$	7.48004	+	12.9558i	0.578823	+	1.00255i	0.995615	+	0.0935486i	$0.0298211\pi$
$167$	7.48004	+	12.9558i	0.578823	+	1.00255i	−0.416792	+	0.909002i	$0.636846\pi$
$168$	4.94508	−	2.06092i	0.381521	−	0.159003i
$169$	−3.49317	+	6.05034i	−0.268705	+	0.465411i
$170$	0.0836269	+	0.155281i	0.00641389	+	0.0119095i
$171$	−7.52234	−	15.8273i	−0.575248	−	1.21035i
$172$	4.71738	−	7.15685i	0.359697	−	0.545705i
$173$	−12.9112	+	22.3629i	−0.981621	+	1.70022i	−0.325539	+	0.945529i	$0.605546\pi$
$173$	−12.9112	+	22.3629i	−0.981621	+	1.70022i	−0.656083	+	0.754689i	$0.727788\pi$
$174$	9.22856	+	18.9088i	0.699615	+	1.43347i
$175$	−0.947055	+	0.546782i	−0.0715906	+	0.0413329i
$176$	8.56543	+	6.40334i	0.645643	+	0.482670i
$177$	−4.68451	−	0.187307i	−0.352109	−	0.0140788i
$178$	18.9245	+	0.560098i	1.41845	+	0.0419811i
$179$		−	5.67678i		−	0.424303i	−0.977237	−	0.212151i	$-0.931953\pi$
$179$		−	5.67678i		−	0.424303i	0.977237	−	0.212151i	$-0.0680470\pi$
$180$	3.69149	−	4.73000i	0.275147	−	0.352554i
$181$		−	13.3860i		−	0.994971i	−0.867472	−	0.497485i	$-0.834257\pi$
$181$		−	13.3860i		−	0.994971i	0.867472	−	0.497485i	$-0.165743\pi$
$182$	0.112197	−	3.79087i	0.00831656	−	0.280998i
$183$	9.01654	+	17.1665i	0.666522	+	1.26898i
$184$	−6.21562	+	2.88707i	−0.458221	+	0.212838i
$185$	−2.10354	+	1.21448i	−0.154655	+	0.0892902i
$186$	−0.500143	+	7.17944i	−0.0366722	+	0.526422i
$187$	0.166713	−	0.288755i	0.0121913	−	0.0211159i
$188$	−7.31865	+	11.1033i	−0.533767	+	0.809792i
$189$	−3.40934	+	4.54591i	−0.247993	+	0.330666i
$190$	7.27320	−	3.91699i	0.527654	−	0.284168i
$191$	−2.24173	+	3.88280i	−0.162206	+	0.280949i	−0.935660	−	0.352904i	$-0.885194\pi$
$191$	−2.24173	+	3.88280i	−0.162206	+	0.280949i	0.773453	+	0.633853i	$0.218528\pi$
$192$	−10.2223	−	9.35434i	−0.737734	−	0.675092i
$193$	4.45569	+	7.71749i	0.320728	+	0.555517i	0.980638	−	0.195827i	$-0.0627392\pi$
$193$	4.45569	+	7.71749i	0.320728	+	0.555517i	−0.659911	+	0.751344i	$0.729406\pi$
$194$	18.0794	+	11.1640i	1.29803	+	0.801529i
$195$	−1.97508	−	3.76033i	−0.141438	−	0.269283i
$196$	5.19941	+	10.3787i	0.371386	+	0.741335i
$197$	−12.0147			−0.856014			−0.428007	−	0.903775i	$-0.640784\pi$
$197$	−12.0147			−0.856014			−0.428007	+	0.903775i	$0.640784\pi$
$198$	−11.2751	−	1.23974i	−0.801288	−	0.0881046i
$199$			12.4401i			0.881853i	0.897543	+	0.440927i	$0.145350\pi$
$199$			12.4401i			0.881853i	−0.897543	+	0.440927i	$0.854650\pi$
$200$	2.31448	+	1.62579i	0.163658	+	0.114960i
$201$	0.0978730	−	2.44779i	0.00690343	−	0.172654i
$202$	22.4957	+	13.8910i	1.58279	+	0.977370i
$203$	8.13501	−	4.69675i	0.570965	−	0.329647i
$204$	−0.251976	+	0.350917i	−0.0176418	+	0.0245691i
$205$	7.57229	+	4.37186i	0.528871	+	0.305344i
$206$	−10.3936	−	19.2991i	−0.724155	−	1.34464i
$207$	4.12558	−	5.98497i	0.286748	−	0.415984i
$208$	−9.01462	+	3.86720i	−0.625052	+	0.268142i
$209$	−13.5250	−	7.80866i	−0.935543	−	0.540136i
$210$	−2.22112	−	1.49731i	−0.153272	−	0.103324i
$211$	−11.2044	−	19.4065i	−0.771340	−	1.33600i	−0.936829	−	0.349788i	$-0.886254\pi$
$211$	−11.2044	−	19.4065i	−0.771340	−	1.33600i	0.165489	−	0.986212i	$-0.447080\pi$
$212$	−4.27444	−	0.253239i	−0.293570	−	0.0173925i
$213$	−16.4497	−	10.3949i	−1.12711	−	0.712248i
$214$	−23.5592	−	0.697270i	−1.61047	−	0.0476644i
$215$	−4.28585			−0.292293
$216$	14.3782	+	3.04435i	0.978311	+	0.207142i
$217$	3.21300			0.218113
$218$	−13.5167	−	0.400048i	−0.915469	−	0.0270947i
$219$	7.83935	+	4.95386i	0.529734	+	0.334751i
$220$	0.316239	−	5.33782i	0.0213208	−	0.359876i
$221$	0.152913	+	0.264853i	0.0102860	+	0.0178160i
$222$	−4.93340	−	3.32574i	−0.331108	−	0.223209i
$223$	−6.10284	−	3.52348i	−0.408677	−	0.235950i	0.281544	−	0.959548i	$-0.409153\pi$
$223$	−6.10284	−	3.52348i	−0.408677	−	0.235950i	−0.690221	+	0.723599i	$0.742487\pi$
$224$	−3.84896	+	4.84291i	−0.257169	+	0.323581i
$225$	−2.99042	−	0.239523i	−0.199362	−	0.0159682i
$226$	8.66780	+	16.0947i	0.576573	+	1.07060i
$227$	9.66735	+	5.58145i	0.641645	+	0.370454i	0.785248	−	0.619182i	$-0.212536\pi$
$227$	9.66735	+	5.58145i	0.641645	+	0.370454i	−0.143603	+	0.989635i	$0.545869\pi$
$228$	16.4366	+	11.8023i	1.08854	+	0.781624i
$229$	−5.60858	+	3.23812i	−0.370626	+	0.213981i	−0.673732	−	0.738976i	$-0.735310\pi$
$229$	−5.60858	+	3.23812i	−0.370626	+	0.213981i	0.303106	+	0.952957i	$0.401976\pi$
$230$	2.91562	+	1.80039i	0.192250	+	0.118714i
$231$	−0.202321	+	5.06003i	−0.0133118	+	0.332925i
$232$	−19.8809	−	13.9652i	−1.30525	−	0.916858i
$233$			7.74508i			0.507397i	0.967283	+	0.253699i	$0.0816471\pi$
$233$			7.74508i			0.507397i	−0.967283	+	0.253699i	$0.918353\pi$
$234$	6.15568	−	8.38771i	0.402409	−	0.548322i
$235$	6.64918			0.433744
$236$	4.84013	−	2.42476i	0.315065	−	0.157838i
$237$	1.92676	+	3.66834i	0.125157	+	0.238284i
$238$	0.164104	+	0.101334i	0.0106373	+	0.00656851i
$239$	−7.25239	−	12.5615i	−0.469118	−	0.812537i	0.530259	−	0.847836i	$-0.322095\pi$
$239$	−7.25239	−	12.5615i	−0.469118	−	0.812537i	−0.999377	+	0.0352993i	$0.988762\pi$
$240$	−1.09226	+	6.84156i	−0.0705050	+	0.441621i
$241$	−10.0033	+	17.3262i	−0.644368	+	1.11608i	0.340079	+	0.940397i	$0.389546\pi$
$241$	−10.0033	+	17.3262i	−0.644368	+	1.11608i	−0.984447	+	0.175681i	$0.943787\pi$
$242$	4.79613	−	2.58296i	0.308307	−	0.166039i
$243$	−14.7785	+	4.95956i	−0.948038	+	0.318156i
$244$	−18.6943	−	12.3222i	−1.19678	−	0.788848i
$245$	2.90206	−	5.02651i	0.185406	−	0.321132i
$246$	−1.48842	+	21.3659i	−0.0948979	+	1.36224i
$247$	12.4054	−	7.16228i	0.789339	−	0.455725i
$248$	−3.50076	−	7.53684i	−0.222298	−	0.478590i
$249$	10.4358	+	19.8685i	0.661340	+	1.25912i
$250$	0.0418375	−	1.41359i	0.00264603	−	0.0894036i
$251$		−	20.7692i		−	1.31094i	−0.755222	−	0.655469i	$-0.772471\pi$
$251$		−	20.7692i		−	1.31094i	0.755222	−	0.655469i	$-0.227529\pi$
$252$	0.909759	−	6.49801i	0.0573095	−	0.409336i
$253$		−	6.47822i		−	0.407282i
$254$	22.3330	+	0.660979i	1.40130	+	0.0414735i
$255$	0.215833	+	0.00862994i	0.0135160	+	0.000540428i
$256$	15.5539	+	3.75198i	0.972116	+	0.234499i
$257$	6.95814	−	4.01728i	0.434037	−	0.250591i	−0.267028	−	0.963689i	$-0.586042\pi$
$257$	6.95814	−	4.01728i	0.434037	−	0.250591i	0.701065	+	0.713097i	$0.252708\pi$
$258$	−4.60456	−	9.43447i	−0.286668	−	0.587364i
$259$	−1.32811	+	2.30036i	−0.0825248	+	0.142937i
$260$	4.09500	+	2.69919i	0.253961	+	0.167396i
$261$	25.6871	+	2.05745i	1.58999	+	0.127353i
$262$	−3.69642	−	6.86363i	−0.228365	−	0.424036i
$263$	−10.4995	+	18.1856i	−0.647425	+	1.12137i	0.336310	+	0.941751i	$0.390821\pi$
$263$	−10.4995	+	18.1856i	−0.647425	+	1.12137i	−0.983736	+	0.179622i	$0.942512\pi$
$264$	12.0899	−	5.03862i	0.744083	−	0.310105i
$265$	1.07048	+	1.85413i	0.0657592	+	0.113898i
$266$	4.74638	−	7.68646i	0.291019	−	0.471287i
$267$	12.3869	−	19.6020i	0.758067	−	1.19962i
$268$	1.26700	+	2.52910i	0.0773946	+	0.154490i
$269$	−1.50694			−0.0918795			−0.0459397	−	0.998944i	$-0.514628\pi$
$269$	−1.50694			−0.0918795			−0.0459397	+	0.998944i	$0.514628\pi$
$270$	−2.68554	−	6.84017i	−0.163437	−	0.416279i
$271$		−	25.3685i		−	1.54103i	−0.637423	−	0.770514i	$-0.720000\pi$
$271$		−	25.3685i		−	1.54103i	0.637423	−	0.770514i	$-0.280000\pi$
$272$	0.0589012	−	0.495355i	0.00357141	−	0.0300353i
$273$	−3.92659	−	2.48130i	−0.237648	−	0.150175i
$274$	6.63514	−	10.7452i	0.400843	−	0.649141i
$275$	−2.31540	+	1.33679i	−0.139624	+	0.0806117i
$276$	−0.830775	+	8.35245i	−0.0500068	+	0.502758i
$277$	−11.8303	−	6.83025i	−0.710816	−	0.410390i	0.100547	−	0.994932i	$-0.467941\pi$
$277$	−11.8303	−	6.83025i	−0.710816	−	0.410390i	−0.811363	+	0.584542i	$0.801274\pi$
$278$	19.1521	−	10.3144i	1.14867	−	0.618617i
$279$	7.25716	+	5.00253i	0.434475	+	0.299494i
$280$	3.08089	+	0.274191i	0.184118	+	0.0163861i
$281$	2.52130	+	1.45567i	0.150408	+	0.0868383i	0.573315	−	0.819335i	$-0.305657\pi$
$281$	2.52130	+	1.45567i	0.150408	+	0.0868383i	−0.422907	+	0.906173i	$0.638990\pi$
$282$	7.14363	+	14.6369i	0.425397	+	0.871613i
$283$	−4.83052	−	8.36671i	−0.287145	−	0.497349i	0.685982	−	0.727618i	$-0.259373\pi$
$283$	−4.83052	−	8.36671i	−0.287145	−	0.497349i	−0.973127	+	0.230269i	$0.926039\pi$
$284$	22.4298	+	1.32885i	1.33096	+	0.0788528i
$285$	0.404217	−	10.1094i	0.0239437	−	0.598829i
$286$	0.274302	−	9.26807i	0.0162198	−	0.548032i
$287$	9.56183			0.564417
$288$	−16.2338	+	4.94593i	−0.956589	+	0.291442i
$289$	16.9844			0.999085
$290$	−0.359375	+	12.1425i	−0.0211032	+	0.713031i
$291$	23.0393	−	12.1012i	1.35059	−	0.709385i
$292$	−10.6893	−	0.633284i	−0.625542	−	0.0370602i
$293$	11.9028	+	20.6162i	0.695367	+	1.20441i	0.970057	+	0.242878i	$0.0780914\pi$
$293$	11.9028	+	20.6162i	0.695367	+	1.20441i	−0.274690	+	0.961533i	$0.588575\pi$
$294$	14.1828	+	0.988016i	0.827155	+	0.0576223i
$295$	−2.34413	−	1.35338i	−0.136480	−	0.0787969i
$296$	6.84308	+	0.609017i	0.397746	+	0.0353984i
$297$	−8.33528	+	11.1140i	−0.483662	+	0.644900i
$298$	−0.253457	+	0.136499i	−0.0146824	+	0.00790720i
$299$	5.14590	+	2.97099i	0.297595	+	0.171817i
$300$	3.15670	−	1.42662i	0.182252	−	0.0823658i
$301$	−4.05894	+	2.34343i	−0.233953	+	0.135073i
$302$	4.82772	−	7.81819i	0.277804	−	0.449886i
$303$	28.6672	−	15.0572i	1.64688	−	0.865011i
$304$	−23.2019	−	2.75887i	−1.33072	−	0.158232i
$305$			11.1950i			0.641026i
$306$	0.212886	+	0.484387i	0.0121699	+	0.0276906i
$307$	17.7957			1.01565			0.507827	−	0.861459i	$-0.330449\pi$
$307$	17.7957			1.01565			0.507827	+	0.861459i	$0.330449\pi$
$308$	−2.61913	−	5.22812i	−0.149239	−	0.297900i
$309$	−26.8249	−	1.07257i	−1.52601	−	0.0610166i
$310$	−2.18309	+	3.53538i	−0.123991	+	0.200796i
$311$	8.19800	+	14.1993i	0.464866	+	0.805171i	0.999195	−	0.0401050i	$-0.0127692\pi$
$311$	8.19800	+	14.1993i	0.464866	+	0.805171i	−0.534330	+	0.845276i	$0.679436\pi$
$312$	−1.54221	+	11.9143i	−0.0873104	+	0.674512i
$313$	−10.7484	+	18.6168i	−0.607536	+	1.05228i	0.384109	+	0.923288i	$0.374509\pi$
$313$	−10.7484	+	18.6168i	−0.607536	+	1.05228i	−0.991645	+	0.128995i	$0.958825\pi$
$314$	−15.3037	−	28.4164i	−0.863637	−	1.60363i
$315$	−2.96306	+	1.40827i	−0.166950	+	0.0793470i
$316$	−3.99483	−	2.63315i	−0.224726	−	0.148126i
$317$	7.30418	−	12.6512i	0.410244	−	0.710563i	−0.584672	−	0.811270i	$-0.698777\pi$
$317$	7.30418	−	12.6512i	0.410244	−	0.710563i	0.994916	+	0.100706i	$0.0321103\pi$
$318$	−2.93142	+	4.34847i	−0.164386	+	0.243850i
$319$	19.8888	−	11.4828i	1.11356	−	0.642913i
$320$	−2.71364	−	7.52570i	−0.151697	−	0.420699i
$321$	−15.4206	+	24.4027i	−0.860693	+	1.36202i
$322$	3.74568	+	0.110859i	0.208738	+	0.00617793i
$323$			0.728479i			0.0405336i
$324$	12.1721	−	13.2605i	0.676225	−	0.736695i
$325$		−	2.45228i		−	0.136028i
$326$	0.727862	−	24.5928i	0.0403126	−	1.36207i
$327$	−8.84733	+	14.0007i	−0.489258	+	0.774238i
$328$	−10.4182	−	22.4295i	−0.575249	−	1.23846i
$329$	6.29713	−	3.63565i	0.347172	−	0.200440i
$330$	−5.43027	−	3.66069i	−0.298926	−	0.201514i
$331$	−15.6137	+	27.0437i	−0.858207	+	1.48646i	0.0154304	+	0.999881i	$0.495088\pi$
$331$	−15.6137	+	27.0437i	−0.858207	+	1.48646i	−0.873637	+	0.486577i	$0.838245\pi$
$332$	−21.6369	−	14.2618i	−1.18748	−	0.782715i
$333$	−6.58136	+	3.12796i	−0.360657	+	0.171411i
$334$	−18.6272	+	10.0317i	−1.01924	+	0.548910i
$335$	0.707180	−	1.22487i	0.0386374	−	0.0669219i
$336$	2.70642	+	7.07656i	0.147647	+	0.386058i
$337$	5.23636	+	9.06964i	0.285243	+	0.494055i	0.972668	−	0.232200i	$-0.0745925\pi$
$337$	5.23636	+	9.06964i	0.285243	+	0.494055i	−0.687425	+	0.726255i	$0.741259\pi$
$338$	−8.40658	−	5.19105i	−0.457258	−	0.282356i
$339$	22.3708	+	0.894480i	1.21502	+	0.0485815i
$340$	−0.223003	+	0.111718i	−0.0120941	+	0.00605876i
$341$	7.85526			0.425386
$342$	22.6882	−	9.97137i	1.22684	−	0.539190i
$343$		−	14.0021i		−	0.756044i
$344$	9.91952	+	6.96788i	0.534825	+	0.375683i
$345$	3.71550	−	1.95153i	0.200036	−	0.105067i
$346$	−31.0719	−	19.1868i	−1.67043	−	1.03149i
$347$	−27.8626	+	16.0865i	−1.49574	+	0.863567i	−0.999988	−	0.00489628i	$-0.998441\pi$
$347$	−27.8626	+	16.0865i	−1.49574	+	0.863567i	−0.495754	+	0.868463i	$0.665108\pi$
$348$	−27.1154	+	12.2543i	−1.45354	+	0.656902i
$349$	14.7646	+	8.52433i	0.790330	+	0.456297i	0.840079	−	0.542465i	$-0.182509\pi$
$349$	14.7646	+	8.52433i	0.790330	+	0.456297i	−0.0497488	+	0.998762i	$0.515842\pi$
$350$	−0.733306	−	1.36163i	−0.0391969	−	0.0727820i
$351$	−5.00564	−	11.7180i	−0.267181	−	0.625463i
$352$	−9.41008	+	11.8401i	−0.501559	+	0.631082i
$353$	−16.3559	−	9.44311i	−0.870539	−	0.502606i	−0.00301183	−	0.999995i	$-0.500959\pi$
$353$	−16.3559	−	9.44311i	−0.870539	−	0.502606i	−0.867527	+	0.497389i	$0.834292\pi$
$354$	0.460763	−	6.61416i	0.0244893	−	0.351539i
$355$	−5.61728	−	9.72941i	−0.298134	−	0.516384i
$356$	−1.58350	+	26.7281i	−0.0839254	+	1.41659i
$357$	0.209125	−	0.109841i	0.0110681	−	0.00581340i
$358$	8.02467	+	0.237502i	0.424117	+	0.0125524i
$359$	24.5546			1.29594			0.647972	−	0.761664i	$-0.275618\pi$
$359$	24.5546			1.29594			0.647972	+	0.761664i	$0.275618\pi$
$360$	6.53186	+	5.41616i	0.344259	+	0.285457i
$361$	15.1211			0.795850
$362$	18.9223	+	0.560035i	0.994535	+	0.0294348i
$363$	0.266551	−	6.66640i	0.0139903	−	0.349895i
$364$	5.35406	+	0.317201i	0.280629	+	0.0166258i
$365$	2.67700	+	4.63670i	0.140121	+	0.242696i
$366$	−24.6437	+	12.0275i	−1.28815	+	0.628689i
$367$	16.6622	+	9.61992i	0.869759	+	0.502156i	0.867268	−	0.497841i	$-0.165874\pi$
$367$	16.6622	+	9.61992i	0.869759	+	0.502156i	0.00249084	+	0.999997i	$0.499207\pi$
$368$	−3.82110	−	8.90715i	−0.199189	−	0.464317i
$369$	21.5972	+	14.8874i	1.12430	+	0.775010i
$370$	−1.62877	−	3.02436i	−0.0846759	−	0.157229i
$371$	2.02761	+	1.17064i	0.105268	+	0.0607767i
$372$	−10.1279	−	1.00737i	−0.525107	−	0.0522296i
$373$	13.5653	−	7.83195i	0.702386	−	0.405523i	−0.105849	−	0.994382i	$-0.533756\pi$
$373$	13.5653	−	7.83195i	0.702386	−	0.405523i	0.808236	+	0.588859i	$0.200423\pi$
$374$	0.401208	+	0.247745i	0.0207460	+	0.0128106i
$375$	−1.46420	−	0.925262i	−0.0756111	−	0.0477803i
$376$	−15.3894	−	10.8101i	−0.793647	−	0.557490i
$377$			21.0646i			1.08488i
$378$	−6.28343	−	5.00961i	−0.323185	−	0.257666i
$379$	11.3447			0.582738			0.291369	−	0.956611i	$-0.405889\pi$
$379$	11.3447			0.582738			0.291369	+	0.956611i	$0.405889\pi$
$380$	5.23275	+	10.4452i	0.268434	+	0.535829i
$381$	14.6180	−	23.1326i	0.748902	−	1.18512i
$382$	−5.39491	−	3.33135i	−0.276028	−	0.170447i
$383$	−8.35938	−	14.4789i	−0.427145	−	0.739836i	0.569473	−	0.822010i	$-0.307147\pi$
$383$	−8.35938	−	14.4789i	−0.427145	−	0.739836i	−0.996618	+	0.0821736i	$0.973814\pi$
$384$	13.6509	−	14.0589i	0.696621	−	0.717439i
$385$	−1.46187	+	2.53203i	−0.0745038	+	0.129044i
$386$	−11.0958	+	5.97566i	−0.564762	+	0.304153i
$387$	−12.8165	−	1.02656i	−0.651500	−	0.0521829i
$388$	−16.5378	+	25.0899i	−0.839578	+	1.27375i
$389$	6.23931	−	10.8068i	0.316346	−	0.547927i	−0.663377	−	0.748285i	$-0.730877\pi$
$389$	6.23931	−	10.8068i	0.316346	−	0.547927i	0.979723	+	0.200359i	$0.0642108\pi$
$390$	5.39821	−	2.63464i	0.273349	−	0.133410i
$391$	−0.261696	+	0.151090i	−0.0132345	+	0.00764096i
$392$	−14.8888	+	6.91564i	−0.751997	+	0.349292i
$393$	−9.54011	−	0.381454i	−0.481235	−	0.0192418i
$394$	0.502666	−	16.9840i	0.0253239	−	0.855640i
$395$			2.39229i			0.120369i
$396$	2.22422	−	15.8866i	0.111771	−	0.798331i
$397$			0.465205i			0.0233480i	0.999932	+	0.0116740i	$0.00371603\pi$
$397$			0.465205i			0.0233480i	−0.999932	+	0.0116740i	$0.996284\pi$
$398$	−17.5852	−	0.520461i	−0.881467	−	0.0260883i
$399$	−5.14483	−	9.79518i	−0.257564	−	0.490372i
$400$	−2.39503	+	3.20372i	−0.119752	+	0.160186i
$401$	−11.4982	+	6.63849i	−0.574193	+	0.331510i	−0.758822	−	0.651298i	$-0.774225\pi$
$401$	−11.4982	+	6.63849i	−0.574193	+	0.331510i	0.184629	+	0.982808i	$0.440892\pi$
$402$	3.45609	+	0.240762i	0.172374	+	0.0120081i
$403$	−3.60251	+	6.23974i	−0.179454	+	0.310823i
$404$	−20.5775	+	31.2186i	−1.02377	+	1.55318i
$405$	−8.88526	−	1.43255i	−0.441512	−	0.0711839i
$406$	6.29895	+	11.6961i	0.312612	+	0.580468i
$407$	−3.24702	+	5.62400i	−0.160949	+	0.278771i
$408$	−0.485512	−	0.370873i	−0.0240364	−	0.0183609i
$409$	−0.111999	−	0.193987i	−0.00553798	−	0.00959206i	0.863243	−	0.504788i	$-0.168429\pi$
$409$	−0.111999	−	0.193987i	−0.00553798	−	0.00959206i	−0.868781	+	0.495196i	$0.835096\pi$
$410$	−6.49685	+	10.5212i	−0.320856	+	0.519607i
$411$	−7.19214	−	13.6930i	−0.354762	−	0.675428i
$412$	27.7160	−	13.8849i	1.36547	−	0.684059i
$413$	−2.96002			−0.145653
$414$	8.28771	+	6.08229i	0.407319	+	0.298928i
$415$			12.9572i			0.636042i
$416$	−5.08951	−	12.9048i	−0.249534	−	0.632711i
$417$	1.06440	−	26.6206i	0.0521241	−	1.30361i
$418$	11.6041	−	18.7922i	0.567577	−	0.919155i
$419$	−6.92393	+	3.99754i	−0.338256	+	0.195292i	−0.659501	−	0.751704i	$-0.729232\pi$
$419$	−6.92393	+	3.99754i	−0.338256	+	0.195292i	0.321244	+	0.946996i	$0.395899\pi$
$420$	2.20952	−	3.07711i	0.107814	−	0.150148i
$421$	−15.0227	−	8.67337i	−0.732162	−	0.422714i	0.0870505	−	0.996204i	$-0.472256\pi$
$421$	−15.0227	−	8.67337i	−0.732162	−	0.422714i	−0.819213	+	0.573490i	$0.805589\pi$
$422$	27.9017	−	15.0265i	1.35823	−	0.731478i
$423$	19.8838	+	1.59263i	0.966786	+	0.0774362i
$424$	0.536808	−	6.03173i	0.0260697	−	0.292926i
$425$	0.108003	+	0.0623555i	0.00523891	+	0.00302469i
$426$	15.3824	−	22.8183i	0.745280	−	1.10555i
$427$	6.12124	+	10.6023i	0.296228	+	0.513082i
$428$	1.97131	−	33.2740i	0.0952871	−	1.60836i
$429$	−9.59987	−	6.06638i	−0.463486	−	0.292887i
$430$	0.179309	−	6.05846i	0.00864706	−	0.292165i
$431$	−3.02918			−0.145910			−0.0729552	−	0.997335i	$-0.523243\pi$
$431$	−3.02918			−0.145910			−0.0729552	+	0.997335i	$0.523243\pi$
$432$	−4.90502	+	20.1975i	−0.235993	+	0.971755i
$433$	0.00546847			0.000262798			0.000131399	−	1.00000i	$-0.499958\pi$
$433$	0.00546847			0.000262798			0.000131399		1.00000i	$0.499958\pi$
$434$	−0.134424	+	4.54188i	−0.00645254	+	0.218017i
$435$	12.5772	+	7.94781i	0.603031	+	0.381069i
$436$	1.13101	−	19.0905i	0.0541656	−	0.914267i
$437$	7.07690	+	12.2575i	0.338534	+	0.586358i
$438$	−7.33073	+	10.8744i	−0.350276	+	0.519599i
$439$	22.4571	+	12.9656i	1.07182	+	0.618815i	0.928678	−	0.370887i	$-0.120946\pi$
$439$	22.4571	+	12.9656i	1.07182	+	0.618815i	0.143141	+	0.989702i	$0.454280\pi$
$440$	7.53228	+	0.670354i	0.359087	+	0.0319579i
$441$	9.88234	−	14.3363i	0.470588	−	0.682680i
$442$	−0.380793	+	0.205076i	−0.0181125	+	0.00975449i
$443$	13.0998	+	7.56316i	0.622389	+	0.359336i	0.777799	−	0.628514i	$-0.216336\pi$
$443$	13.0998	+	7.56316i	0.622389	+	0.359336i	−0.155409	+	0.987850i	$0.549670\pi$
$444$	4.90765	−	6.83469i	0.232907	−	0.324360i
$445$	11.5939	−	6.69374i	0.549603	−	0.317314i
$446$	5.23610	−	8.47953i	0.247936	−	0.401518i
$447$	−0.0140862	+	0.352293i	−0.000666253	+	0.0166629i
$448$	−6.68488	−	5.64348i	−0.315831	−	0.266629i
$449$		−	4.83214i		−	0.228043i	−0.993478	−	0.114021i	$-0.963627\pi$
$449$		−	4.83214i		−	0.228043i	0.993478	−	0.114021i	$-0.0363732\pi$
$450$	0.463700	−	4.21722i	0.0218590	−	0.198802i
$451$	23.3771			1.10079
$452$	−23.1140	+	11.5794i	−1.08719	+	0.544649i
$453$	−5.23299	−	9.96304i	−0.245868	−	0.468104i
$454$	−8.29436	+	13.4322i	−0.389274	+	0.630405i
$455$	−1.34086	−	2.32244i	−0.0628606	−	0.108878i
$456$	−17.3713	+	22.7408i	−0.813485	+	1.06494i
$457$	−0.817739	+	1.41637i	−0.0382522	+	0.0662548i	−0.884518	−	0.466507i	$-0.845512\pi$
$457$	−0.817739	+	1.41637i	−0.0382522	+	0.0662548i	0.846265	+	0.532761i	$0.178846\pi$
$458$	−4.34273	−	8.06374i	−0.202923	−	0.376794i
$459$	0.643366	+	0.0775042i	0.0300298	+	0.00361758i
$460$	−2.66701	+	4.04619i	−0.124350	+	0.188654i
$461$	4.05449	−	7.02259i	0.188837	−	0.327075i	−0.756026	−	0.654542i	$-0.772862\pi$
$461$	4.05449	−	7.02259i	0.188837	−	0.327075i	0.944863	+	0.327467i	$0.106195\pi$
$462$	−7.14436	−	0.497699i	−0.332386	−	0.0231551i
$463$	−19.0599	+	11.0043i	−0.885790	+	0.511411i	−0.872563	−	0.488501i	$-0.837544\pi$
$463$	−19.0599	+	11.0043i	−0.885790	+	0.511411i	−0.0132272	+	0.999913i	$0.504210\pi$
$464$	20.5729	−	27.5193i	0.955071	−	1.27755i
$465$	2.36636	+	4.50528i	0.109737	+	0.208928i
$466$	−10.9484	−	0.324034i	−0.507175	−	0.0150106i
$467$		−	4.66635i		−	0.215933i	−0.994155	−	0.107966i	$-0.965566\pi$
$467$		−	4.66635i		−	0.215933i	0.994155	−	0.107966i	$-0.0344339\pi$
$468$	11.5993	+	9.05255i	0.536177	+	0.418454i
$469$		−	1.54669i		−	0.0714197i
$470$	−0.278185	+	9.39924i	−0.0128317	+	0.433555i
$471$	−39.4974	−	1.57928i	−1.81995	−	0.0727692i
$472$	3.22512	+	6.94342i	0.148448	+	0.319597i
$473$	−9.92345	+	5.72931i	−0.456281	+	0.263434i
$474$	−5.26615	+	2.57018i	−0.241882	+	0.118052i
$475$	2.92067	−	5.05874i	0.134009	−	0.232111i
$476$	−0.150111	+	0.227737i	−0.00688033	+	0.0104383i
$477$	2.75709	+	5.80104i	0.126238	+	0.265611i
$478$	18.0603	−	9.72640i	0.826059	−	0.444875i
$479$	4.15142	−	7.19047i	0.189683	−	0.328541i	−0.755461	−	0.655193i	$-0.772587\pi$
$479$	4.15142	−	7.19047i	0.189683	−	0.328541i	0.945145	+	0.326652i	$0.105921\pi$
$480$	−9.62550	−	1.83024i	−0.439342	−	0.0835388i
$481$	−2.97824	−	5.15846i	−0.135796	−	0.235206i
$482$	−24.0737	−	14.8655i	−1.09653	−	0.677103i
$483$	2.45172	−	3.87978i	0.111557	−	0.176536i
$484$	3.45061	+	6.88785i	0.156846	+	0.313084i
$485$	15.0250			0.682249
$486$	−6.39252	−	21.0982i	−0.289971	−	0.957036i
$487$			12.1772i			0.551800i	0.961186	+	0.275900i	$0.0889759\pi$
$487$			12.1772i			0.551800i	−0.961186	+	0.275900i	$0.911024\pi$
$488$	18.2007	−	25.9107i	0.823908	−	1.17292i
$489$	−25.4733	−	16.0971i	−1.15194	−	0.727938i
$490$	6.98404	+	4.31263i	0.315507	+	0.194825i
$491$	−22.4724	+	12.9744i	−1.01416	+	0.585528i	−0.912408	−	0.409281i	$-0.865779\pi$
$491$	−22.4724	+	12.9744i	−1.01416	+	0.585528i	−0.101756	+	0.994809i	$0.532446\pi$
$492$	−30.1404	−	2.99791i	−1.35884	−	0.135156i
$493$	−0.927723	−	0.535621i	−0.0417825	−	0.0241232i
$494$	9.60555	+	17.8359i	0.432174	+	0.802476i
$495$	−7.24421	+	3.44299i	−0.325603	+	0.154751i
$496$	10.8005	−	4.63333i	0.484957	−	0.208043i
$497$	−10.6397	−	6.14286i	−0.477258	−	0.275545i
$498$	−28.5227	+	13.9207i	−1.27813	+	0.623801i
$499$	21.1249	+	36.5894i	0.945680	+	1.63797i	0.754384	+	0.656433i	$0.227936\pi$
$499$	21.1249	+	36.5894i	0.945680	+	1.63797i	0.191296	+	0.981532i	$0.438731\pi$
$500$	1.99650	+	0.118282i	0.0892862	+	0.00528975i
$501$	−1.03523	+	25.8909i	−0.0462506	+	1.15672i
$502$	29.3592	+	0.868930i	1.31037	+	0.0387822i
$503$	15.7960			0.704311			0.352156	−	0.935942i	$-0.385449\pi$
$503$	15.7960			0.704311			0.352156	+	0.935942i	$0.385449\pi$
$504$	9.14749	+	1.55789i	0.407462	+	0.0693940i
$505$	18.6951			0.831922
$506$	9.15758	+	0.271032i	0.407104	+	0.0120489i
$507$	−10.7129	+	5.62683i	−0.475775	+	0.249896i
$508$	−1.86871	+	31.5422i	−0.0829107	+	1.39946i
$509$	−16.1458	−	27.9654i	−0.715651	−	1.23954i	−0.962708	−	0.270543i	$-0.912797\pi$
$509$	−16.1458	−	27.9654i	−0.715651	−	1.23954i	0.247057	−	0.969001i	$-0.420537\pi$
$510$	−0.0212292	+	0.304740i	−0.000940043	+	0.0134941i
$511$	5.07053	+	2.92747i	0.224307	+	0.129504i
$512$	−5.95451	+	21.8299i	−0.263155	+	0.964754i
$513$	3.63021	−	30.1346i	0.160278	−	1.33047i
$514$	5.38770	+	10.0041i	0.237641	+	0.441260i
$515$	−13.4232	−	7.74987i	−0.591495	−	0.341500i
$516$	13.5292	−	6.11427i	0.595588	−	0.269166i
$517$	15.3955	−	8.88858i	0.677092	−	0.390919i
$518$	−3.19620	−	1.97365i	−0.140433	−	0.0867172i
$519$	−39.5962	+	20.7975i	−1.73808	+	0.912910i
$520$	−3.98688	+	5.67575i	−0.174836	+	0.248898i
$521$			10.9201i			0.478418i	0.970968	+	0.239209i	$0.0768881\pi$
$521$			10.9201i			0.478418i	−0.970968	+	0.239209i	$0.923112\pi$
$522$	−3.98308	+	36.2251i	−0.174335	+	1.58553i
$523$	5.69579			0.249059			0.124530	−	0.992216i	$-0.460258\pi$
$523$	5.69579			0.249059			0.124530	+	0.992216i	$0.460258\pi$
$524$	9.85703	−	4.93808i	0.430607	−	0.215721i
$525$	−1.89260	−	0.0756741i	−0.0825997	−	0.00330269i
$526$	−25.2678	−	15.6028i	−1.10173	−	0.680316i
$527$	−0.183207	−	0.317323i	−0.00798060	−	0.0138228i
$528$	6.61675	+	17.3011i	0.287957	+	0.752932i
$529$	8.56443	−	14.8340i	0.372367	−	0.644958i
$530$	−2.66578	+	1.43566i	−0.115794	+	0.0623609i
$531$	−6.68576	−	4.60865i	−0.290137	−	0.199999i
$532$	10.6670	+	7.03104i	0.462472	+	0.304834i
$533$	−10.7210	+	18.5694i	−0.464379	+	0.804328i
$534$	27.1910	+	18.3302i	1.17667	+	0.793225i
$535$	−14.4333	+	8.33308i	−0.624007	+	0.360271i
$536$	−3.62814	+	1.68522i	−0.156712	+	0.0727904i
$537$	5.25251	−	8.31196i	0.226663	−	0.358688i
$538$	0.0630463	−	2.13020i	0.00271812	−	0.0918392i
$539$		−	15.5178i		−	0.668400i
$540$	9.78158	−	3.51009i	0.420932	−	0.151050i
$541$			40.7008i			1.74987i	0.484244	+	0.874933i	$0.339095\pi$
$541$			40.7008i			1.74987i	−0.484244	+	0.874933i	$0.660905\pi$
$542$	35.8608	+	1.06135i	1.54035	+	0.0455891i
$543$	12.3855	−	19.5998i	0.531514	−	0.841106i
$544$	0.697766	+	0.103987i	0.0299165	+	0.00445840i
$545$	−8.28090	+	4.78098i	−0.354715	+	0.204795i
$546$	3.67183	−	5.44679i	0.157140	−	0.233101i
$547$	−4.03253	+	6.98454i	−0.172418	+	0.298637i	−0.939265	−	0.343193i	$-0.888491\pi$
$547$	−4.03253	+	6.98454i	−0.172418	+	0.298637i	0.766846	+	0.641831i	$0.221825\pi$
$548$	14.9117	+	9.82895i	0.636998	+	0.419872i
$549$	−2.68146	+	33.4779i	−0.114442	+	1.42880i
$550$	−1.79282	−	3.32896i	−0.0764459	−	0.141947i
$551$	−25.0879	+	43.4535i	−1.06878	+	1.85118i
$552$	−11.7722	−	1.52382i	−0.501059	−	0.0648582i
$553$	1.30806	+	2.26563i	0.0556243	+	0.0963442i
$554$	10.1502	−	16.4375i	0.431239	−	0.698364i
$555$	−4.20372	−	0.168083i	−0.178438	−	0.00713471i
$556$	13.7791	+	27.5049i	0.584365	+	1.16647i
$557$	−33.6992			−1.42788			−0.713940	−	0.700207i	$-0.753091\pi$
$557$	−33.6992			−1.42788			−0.713940	+	0.700207i	$0.753091\pi$
$558$	−7.37517	+	10.0494i	−0.312216	+	0.425425i
$559$		−	10.5101i		−	0.444530i
$560$	−0.516492	+	4.34366i	−0.0218258	+	0.183553i
$561$	0.511276	−	0.268543i	0.0215861	−	0.0113379i
$562$	−2.16322	+	3.50320i	−0.0912499	+	0.147774i
$563$	−6.59410	+	3.80710i	−0.277908	+	0.160450i	−0.632476	−	0.774580i	$-0.717961\pi$
$563$	−6.59410	+	3.80710i	−0.277908	+	0.160450i	0.354568	+	0.935030i	$0.384628\pi$
$564$	−20.9895	+	9.48583i	−0.883816	+	0.399425i
$565$	11.1943	+	6.46306i	0.470949	+	0.271903i
$566$	12.0292	−	6.47836i	0.505627	−	0.272306i
$567$	−9.19812	+	3.50160i	−0.386285	+	0.147053i
$568$	−2.81686	+	31.6510i	−0.118193	+	1.32805i
$569$	−11.5746	−	6.68257i	−0.485231	−	0.280148i	0.237363	−	0.971421i	$-0.423717\pi$
$569$	−11.5746	−	6.68257i	−0.485231	−	0.280148i	−0.722594	+	0.691273i	$0.757050\pi$
$570$	14.2737	+	0.994351i	0.597859	+	0.0416488i
$571$	1.37959	+	2.38951i	0.0577339	+	0.0999980i	0.893448	−	0.449167i	$-0.148279\pi$
$571$	1.37959	+	2.38951i	0.0577339	+	0.0999980i	−0.835714	+	0.549165i	$0.814946\pi$
$572$	13.0898	+	0.775505i	0.547313	+	0.0324255i
$573$	−6.87496	+	3.61101i	−0.287206	+	0.150852i
$574$	−0.400042	+	13.5165i	−0.0166974	+	0.564170i
$575$	2.42304			0.101048
$576$	−6.31235	−	23.1550i	−0.263015	−	0.964792i
$577$	−5.91800			−0.246369			−0.123185	−	0.992384i	$-0.539311\pi$
$577$	−5.91800			−0.246369			−0.123185	+	0.992384i	$0.539311\pi$
$578$	−0.710586	+	24.0091i	−0.0295565	+	0.998648i
$579$	−0.616663	+	15.4226i	−0.0256276	+	0.640943i
$580$	−17.1495	−	1.01602i	−0.712095	−	0.0421880i
$581$	7.08474	+	12.2711i	0.293925	+	0.509093i
$582$	16.1423	+	33.0746i	0.669119	+	1.37098i
$583$	4.95718	+	2.86203i	0.205306	+	0.118533i
$584$	1.34242	−	15.0838i	0.0555497	−	0.624172i
$585$	0.587376	−	7.33335i	0.0242850	−	0.303197i
$586$	−29.6409	+	15.9631i	−1.22445	+	0.659432i
$587$	−0.615419	−	0.355312i	−0.0254011	−	0.0146653i	0.487246	−	0.873265i	$-0.338002\pi$
$587$	−0.615419	−	0.355312i	−0.0254011	−	0.0146653i	−0.512647	+	0.858600i	$0.671335\pi$
$588$	−1.99002	+	20.0073i	−0.0820672	+	0.825088i
$589$	−14.8631	+	8.58120i	−0.612422	+	0.353582i
$590$	2.01120	−	3.25702i	0.0828000	−	0.134089i
$591$	−17.5920	−	11.1168i	−0.723638	−	0.457283i
$592$	−1.14720	+	9.64786i	−0.0471496	+	0.396525i
$593$			5.76716i			0.236829i	0.992964	+	0.118414i	$0.0377811\pi$
$593$			5.76716i			0.236829i	−0.992964	+	0.118414i	$0.962219\pi$
$594$	−15.3620	−	12.2477i	−0.630310	−	0.502529i
$595$	0.136380			0.00559102
$596$	−0.182351	−	0.363996i	−0.00746938	−	0.0149099i
$597$	−11.5103	+	18.2148i	−0.471086	+	0.745481i
$598$	−4.41506	+	7.14992i	−0.180545	+	0.292382i
$599$	−16.9465	−	29.3522i	−0.692416	−	1.19930i	−0.971044	−	0.238901i	$-0.923213\pi$
$599$	−16.9465	−	29.3522i	−0.692416	−	1.19930i	0.278628	−	0.960399i	$-0.410120\pi$
$600$	1.88459	+	4.52198i	0.0769380	+	0.184609i
$601$	1.86493	−	3.23015i	0.0760719	−	0.131760i	−0.825480	−	0.564431i	$-0.809095\pi$
$601$	1.86493	−	3.23015i	0.0760719	−	0.131760i	0.901552	+	0.432671i	$0.142429\pi$
$602$	−3.14284	−	5.83574i	−0.128093	−	0.237847i
$603$	2.40815	−	3.49350i	0.0980676	−	0.142266i
$604$	10.8498	+	7.15153i	0.441471	+	0.290992i
$605$	1.92596	−	3.33586i	0.0783015	−	0.135622i
$606$	20.0854	+	41.1537i	0.815912	+	1.67175i
$607$	15.0247	−	8.67454i	0.609836	−	0.352089i	−0.163066	−	0.986615i	$-0.552138\pi$
$607$	15.0247	−	8.67454i	0.609836	−	0.352089i	0.772901	+	0.634526i	$0.218805\pi$
$608$	4.87063	−	32.6826i	0.197530	−	1.32546i
$609$	16.2570	+	0.650025i	0.658768	+	0.0263403i
$610$	−15.8252	−	0.468372i	−0.640745	−	0.0189638i
$611$			16.3056i			0.659655i
$612$	−0.693633	+	0.280669i	−0.0280385	+	0.0113454i
$613$		−	29.3264i		−	1.18448i	−0.805761	−	0.592241i	$-0.798243\pi$
$613$		−	29.3264i		−	1.18448i	0.805761	−	0.592241i	$-0.201757\pi$
$614$	−0.744526	+	25.1559i	−0.0300466	+	1.01521i
$615$	7.04224	+	13.4076i	0.283971	+	0.540648i
$616$	7.50002	−	3.48366i	0.302184	−	0.140360i
$617$	13.3388	−	7.70113i	0.536998	−	0.310036i	−0.206863	−	0.978370i	$-0.566326\pi$
$617$	13.3388	−	7.70113i	0.536998	−	0.310036i	0.743861	+	0.668334i	$0.232992\pi$
$618$	2.63847	−	37.8747i	0.106135	−	1.52354i
$619$	14.0738	−	24.3766i	0.565675	−	0.979778i	−0.431311	−	0.902203i	$-0.641949\pi$
$619$	14.0738	−	24.3766i	0.565675	−	0.979778i	0.996987	−	0.0775751i	$-0.0247178\pi$
$620$	−4.90626	−	3.23392i	−0.197040	−	0.129877i
$621$	11.5783	−	4.94596i	0.464623	−	0.198475i
$622$	−20.4151	+	10.9946i	−0.818571	+	0.440843i
$623$	7.32003	−	12.6787i	0.293271	−	0.507960i
$624$	−16.7774	−	2.67852i	−0.671634	−	0.107227i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−25.8669	−	15.9728i	−1.03385	−	0.638400i
$627$	−12.5783	−	23.9476i	−0.502328	−	0.956376i
$628$	40.8095	−	20.4443i	1.62848	−	0.815818i
$629$	0.302918			0.0120781
$630$	−1.86675	−	4.24749i	−0.0743733	−	0.169224i
$631$			11.3112i			0.450292i	0.974325	+	0.225146i	$0.0722859\pi$
$631$			11.3112i			0.450292i	−0.974325	+	0.225146i	$0.927714\pi$
$632$	3.88934	−	5.53690i	0.154710	−	0.220246i
$633$	1.55067	−	38.7820i	0.0616336	−	1.54145i
$634$	17.5781	+	10.8544i	0.698116	+	0.431085i
$635$	13.6821	−	7.89937i	0.542958	−	0.313477i
$636$	−6.02433	−	4.32577i	−0.238880	−	0.171528i
$637$	12.3264	+	7.11665i	0.488390	+	0.281972i
$638$	15.3999	+	28.5951i	0.609688	+	1.13209i
$639$	−14.4676	−	30.4405i	−0.572330	−	1.20421i
$640$	10.7518	−	3.52113i	0.425003	−	0.139185i
$641$	18.5045	+	10.6836i	0.730882	+	0.421975i	0.818745	−	0.574158i	$-0.194670\pi$
$641$	18.5045	+	10.6836i	0.730882	+	0.421975i	−0.0878627	+	0.996133i	$0.528004\pi$
$642$	−33.8503	−	22.8194i	−1.33596	−	0.900610i
$643$	−8.54544	−	14.8011i	−0.336999	−	0.583700i	0.646867	−	0.762602i	$-0.276079\pi$
$643$	−8.54544	−	14.8011i	−0.336999	−	0.583700i	−0.983867	+	0.178902i	$0.942745\pi$
$644$	−0.313419	+	5.29023i	−0.0123504	+	0.208464i
$645$	−6.27536	−	3.96554i	−0.247092	−	0.156143i
$646$	−1.02977	−	0.0304777i	−0.0405159	−	0.00119913i
$647$	−20.5113			−0.806383			−0.403192	−	0.915116i	$-0.632099\pi$
$647$	−20.5113			−0.806383			−0.403192	+	0.915116i	$0.632099\pi$
$648$	18.2357	+	17.7611i	0.716367	+	0.697723i
$649$	−7.23677			−0.284068
$650$	3.46653	+	0.102597i	0.135968	+	0.00402419i
$651$	4.70448	+	2.97287i	0.184383	+	0.116516i
$652$	34.7339	+	2.05780i	1.36028	+	0.0805898i
$653$	−1.44882	−	2.50943i	−0.0566968	−	0.0982017i	0.836284	−	0.548297i	$-0.184723\pi$
$653$	−1.44882	−	2.50943i	−0.0566968	−	0.0982017i	−0.892981	+	0.450095i	$0.851390\pi$
$654$	−19.4211	−	13.0923i	−0.759425	−	0.511949i
$655$	−4.77387	−	2.75619i	−0.186530	−	0.107693i
$656$	32.1421	−	13.7887i	1.25494	−	0.538359i
$657$	6.89477	+	14.5069i	0.268991	+	0.565968i
$658$	4.87588	+	9.05370i	0.190082	+	0.352950i
$659$	−16.4080	−	9.47318i	−0.639166	−	0.369023i	0.145127	−	0.989413i	$-0.453641\pi$
$659$	−16.4080	−	9.47318i	−0.639166	−	0.369023i	−0.784293	+	0.620390i	$0.786974\pi$
$660$	5.40192	−	7.52304i	0.210269	−	0.292834i
$661$	−12.1534	+	7.01678i	−0.472713	+	0.272921i	−0.717375	−	0.696688i	$-0.754656\pi$
$661$	−12.1534	+	7.01678i	−0.472713	+	0.272921i	0.244662	+	0.969608i	$0.421323\pi$
$662$	−37.5756	−	23.2029i	−1.46042	−	0.901806i
$663$	−0.0211630	+	0.529284i	−0.000821903	+	0.0205557i
$664$	21.0656	−	29.9891i	0.817502	−	1.16380i
$665$		−	6.38787i		−	0.247711i
$666$	−4.14632	−	9.43425i	−0.160667	−	0.365570i
$667$	−20.8134			−0.805899
$668$	−13.4014	−	26.7510i	−0.518518	−	1.03503i
$669$	−5.67566	−	10.8058i	−0.219434	−	0.417777i
$670$	1.70189	+	1.05091i	0.0657496	+	0.0406003i
$671$	14.9655	+	25.9209i	0.577735	+	1.00067i
$672$	−10.1166	+	3.52971i	−0.390257	+	0.136162i
$673$	−4.84513	+	8.39201i	−0.186766	+	0.323488i	−0.944170	−	0.329458i	$-0.893134\pi$
$673$	−4.84513	+	8.39201i	−0.186766	+	0.323488i	0.757404	+	0.652946i	$0.226467\pi$
$674$	−13.0399	+	7.02264i	−0.502277	+	0.270502i
$675$	−4.15696	−	3.11764i	−0.160002	−	0.119998i
$676$	7.68975	−	11.6663i	0.295760	−	0.448705i
$677$	9.97234	−	17.2726i	0.383268	−	0.663840i	−0.608259	−	0.793739i	$-0.708132\pi$
$677$	9.97234	−	17.2726i	0.383268	−	0.663840i	0.991527	+	0.129898i	$0.0414651\pi$
$678$	−2.20037	+	31.5858i	−0.0845047	+	1.21305i
$679$	14.2295	−	8.21539i	0.546077	−	0.315278i
$680$	−0.148594	−	0.319910i	−0.00569832	−	0.0122680i
$681$	8.99066	+	17.1172i	0.344523	+	0.655933i
$682$	−0.328644	+	11.1042i	−0.0125844	+	0.425200i
$683$		−	30.2801i		−	1.15864i	−0.815101	−	0.579318i	$-0.803319\pi$
$683$		−	30.2801i		−	1.15864i	0.815101	−	0.579318i	$-0.196681\pi$
$684$	13.1463	+	32.4890i	0.502660	+	1.24225i
$685$		−	8.92984i		−	0.341192i
$686$	19.7933	+	0.585813i	0.755713	+	0.0223665i
$687$	−11.2082	−	0.448152i	−0.427620	−	0.0170981i
$688$	−10.2648	+	13.7307i	−0.391341	+	0.523477i
$689$	−4.54684	+	2.62512i	−0.173221	+	0.100009i
$690$	2.60323	+	5.33386i	0.0991032	+	0.203056i
$691$	3.89324	−	6.74329i	0.148106	−	0.256527i	−0.782422	−	0.622749i	$-0.786016\pi$
$691$	3.89324	−	6.74329i	0.148106	−	0.256527i	0.930527	+	0.366222i	$0.119349\pi$
$692$	28.4224	−	43.1203i	1.08046	−	1.63919i
$693$	−4.97809	+	7.22170i	−0.189102	+	0.274330i
$694$	−21.5740	−	40.0594i	−0.818940	−	1.52063i
$695$	7.69083	−	13.3209i	0.291730	−	0.505291i
$696$	−16.1882	−	38.8429i	−0.613614	−	1.47234i
$697$	−0.545220	−	0.944348i	−0.0206517	−	0.0357697i
$698$	−12.6677	+	20.5145i	−0.479478	+	0.776485i
$699$	−7.16623	+	11.3404i	−0.271052	+	0.428932i
$700$	1.95547	−	0.979631i	0.0739098	−	0.0370266i
$701$	−19.9020			−0.751687			−0.375843	−	0.926683i	$-0.622647\pi$
$701$	−19.9020			−0.751687			−0.375843	+	0.926683i	$0.622647\pi$
$702$	16.7740	−	6.58569i	0.633094	−	0.248561i
$703$		−	14.1883i		−	0.535123i
$704$	−16.3435	−	13.7974i	−0.615967	−	0.520009i
$705$	9.73574	+	6.15223i	0.366669	+	0.231706i
$706$	14.0330	−	22.7256i	0.528140	−	0.855289i
$707$	17.7053	−	10.2222i	0.665877	−	0.384444i
$708$	9.33046	+	0.928052i	0.350660	+	0.0348783i
$709$	33.0445	+	19.0782i	1.24101	+	0.716498i	0.969300	−	0.245881i	$-0.0790771\pi$
$709$	33.0445	+	19.0782i	1.24101	+	0.716498i	0.271711	+	0.962379i	$0.412410\pi$
$710$	13.9885	−	7.53350i	0.524977	−	0.282727i
$711$	−0.573007	+	7.15395i	−0.0214894	+	0.268294i
$712$	−37.7164	−	3.35666i	−1.41348	−	0.125796i
$713$	−6.16535	−	3.55957i	−0.230894	−	0.133307i
$714$	0.146521	+	0.300213i	0.00548342	+	0.0112352i
$715$	−3.27819	−	5.67799i	−0.122597	−	0.212345i
$716$	−0.671464	+	11.3337i	−0.0250938	+	0.423560i
$717$	1.00372	−	25.1030i	0.0374847	−	0.937487i
$718$	−1.02730	+	34.7103i	−0.0383386	+	1.29538i
$719$	42.2205			1.57456			0.787280	−	0.616596i	$-0.211489\pi$
$719$	42.2205			1.57456			0.787280	+	0.616596i	$0.211489\pi$
$720$	−7.92953	+	9.00681i	−0.295516	+	0.335664i
$721$	−16.9500			−0.631250
$722$	−0.632630	+	21.3752i	−0.0235441	+	0.795502i
$723$	−30.6781	+	16.1134i	−1.14093	+	0.599263i
$724$	−1.58332	+	26.7251i	−0.0588438	+	0.993229i
$725$	4.29490	+	7.43898i	0.159508	+	0.276277i
$726$	9.41243	+	0.655700i	0.349328	+	0.0243353i
$727$	−22.2634	−	12.8538i	−0.825703	−	0.476720i	0.0266764	−	0.999644i	$-0.491508\pi$
$727$	−22.2634	−	12.8538i	−0.825703	−	0.476720i	−0.852379	+	0.522924i	$0.824841\pi$
$728$	−0.672394	+	7.55520i	−0.0249206	+	0.280014i
$729$	−26.2276	−	6.41214i	−0.971391	−	0.237487i
$730$	−6.66642	+	3.59021i	−0.246735	+	0.132880i
$731$	0.462885	+	0.267247i	0.0171204	+	0.00988448i
$732$	−15.9710	−	35.3394i	−0.590306	−	1.30618i
$733$	44.6422	−	25.7742i	1.64890	−	0.951991i	0.671385	−	0.741109i	$-0.265700\pi$
$733$	44.6422	−	25.7742i	1.64890	−	0.951991i	0.977512	−	0.210882i	$-0.0676335\pi$
$734$	−14.2958	+	23.1511i	−0.527666	+	0.854523i
$735$	8.90004	−	4.67467i	0.328283	−	0.172428i
$736$	12.7510	−	5.02883i	0.470007	−	0.185365i
$737$		−	3.78142i		−	0.139290i
$738$	−21.9484	+	29.9068i	−0.807931	+	1.10088i
$739$	−13.1324			−0.483085			−0.241542	−	0.970390i	$-0.577653\pi$
$739$	−13.1324			−0.483085			−0.241542	+	0.970390i	$0.577653\pi$
$740$	4.34336	−	2.17589i	0.159665	−	0.0799874i
$741$	24.7911	+	0.991252i	0.910723	+	0.0364146i
$742$	−1.73964	+	2.81724i	−0.0638643	+	0.103424i
$743$	−19.9804	−	34.6070i	−0.733009	−	1.26961i	−0.955591	−	0.294695i	$-0.904782\pi$
$743$	−19.9804	−	34.6070i	−0.733009	−	1.26961i	0.222582	−	0.974914i	$-0.428552\pi$
$744$	1.84774	−	14.2746i	0.0677413	−	0.523332i
$745$	−0.101779	+	0.176287i	−0.00372891	+	0.00645866i
$746$	10.5037	+	19.5036i	0.384566	+	0.714076i
$747$	−3.10353	+	38.7474i	−0.113552	+	1.41769i
$748$	−0.366997	+	0.556781i	−0.0134187	+	0.0203579i
$749$	−9.11277	+	15.7838i	−0.332973	+	0.576727i
$750$	1.36920	−	2.03108i	0.0499963	−	0.0741645i
$751$	−27.3738	+	15.8043i	−0.998885	+	0.576707i	−0.907918	−	0.419147i	$-0.862329\pi$
$751$	−27.3738	+	15.8043i	−0.998885	+	0.576707i	−0.0909671	+	0.995854i	$0.528996\pi$
$752$	15.9250	−	21.3021i	0.580725	−	0.776807i
$753$	19.2169	−	30.4103i	0.700304	−	1.10821i
$754$	−29.7768	−	0.881288i	−1.08441	−	0.0320946i
$755$		−	6.49734i		−	0.236462i
$756$	7.34444	−	8.67264i	0.267115	−	0.315421i
$757$		−	10.1899i		−	0.370357i	−0.982705	−	0.185178i	$-0.940714\pi$
$757$		−	10.1899i		−	0.370357i	0.982705	−	0.185178i	$-0.0592863\pi$
$758$	−0.474633	+	16.0368i	−0.0172394	+	0.582483i
$759$	5.99405	−	9.48543i	0.217570	−	0.344299i
$760$	−14.9843	+	6.95998i	−0.543536	+	0.252465i
$761$	45.8686	−	26.4823i	1.66274	−	0.959981i	0.691337	−	0.722533i	$-0.257022\pi$
$761$	45.8686	−	26.4823i	1.66274	−	0.959981i	0.971400	−	0.237449i	$-0.0763111\pi$
$762$	32.0885	+	21.6317i	1.16244	+	0.783634i
$763$	−5.22831	+	9.05570i	−0.189278	+	0.327838i
$764$	4.93489	−	7.48685i	0.178538	−	0.270865i
$765$	0.308039	+	0.212339i	0.0111372	+	0.00767712i
$766$	20.8170	−	11.2110i	0.752149	−	0.405071i
$767$	3.31887	−	5.74845i	0.119837	−	0.207564i
$768$	19.3024	+	19.8851i	0.696517	+	0.717540i
$769$	−17.1669	−	29.7339i	−0.619053	−	1.07223i	−0.989659	−	0.143441i	$-0.954183\pi$
$769$	−17.1669	−	29.7339i	−0.619053	−	1.07223i	0.370606	−	0.928790i	$-0.379150\pi$
$770$	−3.51811	−	2.17243i	−0.126784	−	0.0782888i
$771$	13.9052	+	0.555988i	0.500782	+	0.0200234i
$772$	−7.98294	−	15.9350i	−0.287312	−	0.573513i
$773$	49.7288			1.78862			0.894310	−	0.447447i	$-0.147667\pi$
$773$	49.7288			1.78862			0.894310	+	0.447447i	$0.147667\pi$
$774$	1.98735	−	18.0744i	0.0714338	−	0.649671i
$775$			2.93810i			0.105540i
$776$	−34.7750	−	24.4274i	−1.24835	−	0.876893i
$777$	−4.07306	+	2.13934i	−0.146120	+	0.0767482i
$778$	15.0154	+	9.27198i	0.538328	+	0.332417i
$779$	−44.2322	+	25.5375i	−1.58478	+	0.914976i
$780$	3.49846	+	7.74111i	0.125265	+	0.277176i
$781$	−26.0124	−	15.0183i	−0.930799	−	0.537397i
$782$	−0.202631	−	0.376253i	−0.00724609	−	0.0134548i
$783$	35.7075	+	26.7798i	1.27608	+	0.957034i
$784$	−9.15300	−	21.3360i	−0.326893	−	0.762002i
$785$	−19.7645	−	11.4110i	−0.705425	−	0.407277i
$786$	0.938356	−	13.4699i	0.0334700	−	0.480455i
$787$	16.3098	+	28.2495i	0.581383	+	1.00698i	0.995316	+	0.0966772i	$0.0308215\pi$
$787$	16.3098	+	28.2495i	0.581383	+	1.00698i	−0.413933	+	0.910307i	$0.635845\pi$
$788$	23.9874	+	1.42113i	0.854516	+	0.0506257i
$789$	−32.1998	+	16.9127i	−1.14634	+	0.602107i
$790$	−3.38172	−	0.100087i	−0.120316	−	0.00356094i
$791$	14.1355			0.502602
$792$	22.3641	+	3.80879i	0.794675	+	0.135340i
$793$	−27.4533			−0.974896
$794$	−0.657611	−	0.0194630i	−0.0233378	−	0.000690716i
$795$	−0.148154	+	3.70530i	−0.00525447	+	0.131413i
$796$	1.47144	−	24.8366i	0.0521538	−	0.880309i
$797$	−12.3771	−	21.4377i	−0.438419	−	0.759363i	0.559149	−	0.829067i	$-0.311128\pi$
$797$	−12.3771	−	21.4377i	−0.438419	−	0.759363i	−0.997568	+	0.0697039i	$0.977795\pi$
$798$	14.0617	−	6.86290i	0.497777	−	0.242944i
$799$	−0.718131	−	0.414613i	−0.0254056	−	0.0146679i
$800$	−4.42856	−	3.51964i	−0.156573	−	0.124438i
$801$	36.2739	−	17.2401i	1.28168	−	0.609149i
$802$	−8.90308	−	16.5315i	−0.314379	−	0.583749i
$803$	12.3966	+	7.15720i	0.437468	+	0.252572i
$804$	−0.484934	+	4.87543i	−0.0171023	+	0.171943i
$805$	2.29475	−	1.32488i	0.0808794	−	0.0466958i
$806$	−8.66974	−	5.35355i	−0.305379	−	0.188571i
$807$	−2.20646	−	1.39431i	−0.0776710	−	0.0490821i
$808$	−43.2695	−	30.3943i	−1.52222	−	1.06927i
$809$			31.2048i			1.09710i	0.836116	+	0.548552i	$0.184821\pi$
$809$			31.2048i			1.09710i	−0.836116	+	0.548552i	$0.815179\pi$
$810$	2.39678	−	12.5002i	0.0842142	−	0.439213i
$811$	37.9198			1.33155			0.665773	−	0.746155i	$-0.268102\pi$
$811$	37.9198			1.33155			0.665773	+	0.746155i	$0.268102\pi$
$812$	−16.7971	+	8.41482i	−0.589462	+	0.295302i
$813$	23.4725	−	37.1446i	0.823218	−	1.30272i
$814$	−7.81421	−	4.82526i	−0.273888	−	0.169125i
$815$	−8.69869	−	15.0666i	−0.304702	−	0.527759i
$816$	0.544576	−	0.670801i	0.0190640	−	0.0234827i
$817$	12.5175	−	21.6810i	0.437933	−	0.758523i
$818$	0.278905	−	0.150205i	0.00975169	−	0.00525178i
$819$	−3.45347	−	7.26625i	−0.120674	−	0.253903i
$820$	−14.6009	−	9.62409i	−0.509887	−	0.336088i
$821$	−10.9987	+	19.0504i	−0.383859	+	0.664863i	−0.991610	−	0.129264i	$-0.958738\pi$
$821$	−10.9987	+	19.0504i	−0.383859	+	0.664863i	0.607751	+	0.794127i	$0.292072\pi$
$822$	19.6573	−	9.59389i	0.685627	−	0.334625i
$823$	−30.4982	+	17.6082i	−1.06310	+	0.613782i	−0.926289	−	0.376815i	$-0.877019\pi$
$823$	−30.4982	+	17.6082i	−1.06310	+	0.613782i	−0.136813	+	0.990597i	$0.543686\pi$
$824$	18.4680	+	39.7601i	0.643364	+	1.38511i
$825$	−4.62709	−	0.185011i	−0.161095	−	0.00644125i
$826$	0.123840	−	4.18427i	0.00430893	−	0.145589i
$827$		−	26.5196i		−	0.922178i	−0.887354	−	0.461089i	$-0.847459\pi$
$827$		−	26.5196i		−	0.922178i	0.887354	−	0.461089i	$-0.152541\pi$
$828$	−8.94463	+	11.4610i	−0.310847	+	0.398297i
$829$			3.51213i			0.121981i	0.998138	+	0.0609907i	$0.0194260\pi$
$829$			3.51213i			0.121981i	−0.998138	+	0.0609907i	$0.980574\pi$
$830$	−18.3162	−	0.542094i	−0.635763	−	0.0188164i
$831$	−11.0022	−	20.9470i	−0.381664	−	0.726645i
$832$	18.4551	−	6.65460i	0.639816	−	0.230707i
$833$	−0.626862	+	0.361919i	−0.0217195	+	0.0125397i
$834$	37.5861	+	2.61837i	1.30150	+	0.0906668i
$835$	−7.48004	+	12.9558i	−0.258857	+	0.448354i
$836$	26.0790	+	17.1898i	0.901962	+	0.594520i
$837$	5.99730	+	14.0395i	0.207297	+	0.485276i
$838$	−5.36121	−	9.95488i	−0.185200	−	0.343886i
$839$	−6.16894	+	10.6849i	−0.212975	+	0.368884i	−0.952644	−	0.304087i	$-0.901649\pi$
$839$	−6.16894	+	10.6849i	−0.212975	+	0.368884i	0.739669	+	0.672971i	$0.234982\pi$
$840$	4.25735	+	3.25210i	0.146893	+	0.112208i
$841$	−22.3923	−	38.7846i	−0.772148	−	1.33740i
$842$	12.8891	−	20.8732i	0.444189	−	0.719336i
$843$	2.34482	+	4.46427i	0.0807598	+	0.153758i
$844$	20.0740	+	40.0704i	0.690977	+	1.37928i
$845$	−6.98633			−0.240337
$846$	−3.08322	+	28.0411i	−0.106003	+	0.964072i
$847$		−	4.21233i		−	0.144737i
$848$	8.50396	+	1.01118i	0.292027	+	0.0347241i
$849$	0.668539	−	16.7201i	0.0229442	−	0.573831i
$850$	−0.0926640	+	0.150064i	−0.00317835	+	0.00514714i
$851$	5.09696	−	2.94273i	0.174722	−	0.100876i
$852$	31.6122	+	22.6991i	1.08302	+	0.777660i
$853$	−28.9822	−	16.7329i	−0.992330	−	0.572922i	−0.0863602	−	0.996264i	$-0.527524\pi$
$853$	−28.9822	−	16.7329i	−0.992330	−	0.572922i	−0.905970	+	0.423342i	$0.860857\pi$
$854$	−15.2435	+	8.20939i	−0.521621	+	0.280919i
$855$	9.94571	−	14.4282i	0.340136	−	0.493434i
$856$	46.9535	+	4.17874i	1.60484	+	0.142826i
$857$	3.00409	+	1.73441i	0.102618	+	0.0592464i	0.550431	−	0.834881i	$-0.314464\pi$
$857$	3.00409	+	1.73441i	0.102618	+	0.0592464i	−0.447813	+	0.894127i	$0.647797\pi$
$858$	8.97703	−	13.3165i	0.306471	−	0.454619i
$859$	11.4262	+	19.7907i	0.389855	+	0.675250i	0.992430	−	0.122813i	$-0.0391916\pi$
$859$	11.4262	+	19.7907i	0.389855	+	0.675250i	−0.602574	+	0.798063i	$0.705858\pi$
$860$	8.55670	+	0.506941i	0.291781	+	0.0172865i
$861$	14.0005	+	8.84720i	0.477134	+	0.301512i
$862$	0.126733	−	4.28203i	0.00431655	−	0.145847i
$863$	22.0525			0.750677			0.375338	−	0.926888i	$-0.377526\pi$
$863$	22.0525			0.750677			0.375338	+	0.926888i	$0.377526\pi$
$864$	−28.3459	−	7.77873i	−0.964348	−	0.264638i
$865$	−25.8224			−0.877989
$866$	−0.000228787		0.00773021i	−7.77450e−6		0.000262683i
$867$	24.8687	+	15.7151i	0.844584	+	0.533712i
$868$	−6.41475	−	0.380041i	−0.217731	−	0.0128994i
$869$	3.19799	+	5.53909i	0.108485	+	0.187901i
$870$	−11.7612	+	17.4465i	−0.398742	+	0.591493i
$871$	3.00373	+	1.73420i	0.101777	+	0.0587612i
$872$	26.9388	+	2.39749i	0.912264	+	0.0811892i
$873$	44.9310	+	3.59882i	1.52069	+	0.121802i
$874$	−17.6233	+	9.49104i	−0.596116	+	0.321039i
$875$	−0.947055	−	0.546782i	−0.0320163	−	0.0184846i
$876$	−15.0653	−	10.8176i	−0.509009	−	0.365494i
$877$	−7.13379	+	4.11870i	−0.240891	+	0.139079i	−0.615586	−	0.788070i	$-0.711081\pi$
$877$	−7.13379	+	4.11870i	−0.240891	+	0.139079i	0.374695	+	0.927148i	$0.377747\pi$
$878$	−19.2677	+	31.2028i	−0.650253	+	1.05304i
$879$	−1.64733	+	41.1995i	−0.0555630	+	1.38962i
$880$	−1.26274	+	10.6195i	−0.0425670	+	0.357985i
$881$			32.8817i			1.10781i	0.832578	+	0.553907i	$0.186864\pi$
$881$			32.8817i			1.10781i	−0.832578	+	0.553907i	$0.813136\pi$
$882$	19.8522	+	14.5694i	0.668460	+	0.490578i
$883$	−11.4139			−0.384109			−0.192054	−	0.981384i	$-0.561515\pi$
$883$	−11.4139			−0.384109			−0.192054	+	0.981384i	$0.561515\pi$
$884$	−0.273963	−	0.546866i	−0.00921439	−	0.0183931i
$885$	−2.18004	−	4.15056i	−0.0732813	−	0.139519i
$886$	−11.2393	+	18.2013i	−0.377592	+	0.611486i
$887$	15.2731	+	26.4538i	0.512821	+	0.888232i	0.999889	+	0.0148681i	$0.00473284\pi$
$887$	15.2731	+	26.4538i	0.512821	+	0.888232i	−0.487069	+	0.873364i	$0.661934\pi$
$888$	9.45616	+	7.22337i	0.317328	+	0.242400i
$889$	8.63847	−	14.9623i	0.289725	−	0.501819i
$890$	8.97717	+	16.6691i	0.300915	+	0.558750i
$891$	−22.4879	+	8.56085i	−0.753373	+	0.286799i
$892$	11.7676	+	7.75648i	0.394007	+	0.259706i
$893$	−19.4200	+	33.6365i	−0.649866	+	1.12560i
$894$	−0.497410	−	0.0346512i	−0.0166359	−	0.00115891i
$895$	4.91624	−	2.83839i	0.164332	−	0.0948770i
$896$	8.25727	−	9.21361i	0.275856	−	0.307805i
$897$	4.78570	+	9.11144i	0.159790	+	0.304222i
$898$	6.83068	+	0.202164i	0.227943	+	0.00674631i
$899$		−	25.2376i		−	0.841723i
$900$	5.94205	+	0.831921i	0.198068	+	0.0277307i
$901$		−	0.267002i		−	0.00889513i
$902$	−0.978039	+	33.0458i	−0.0325651	+	1.10030i
$903$	−8.11139	−	0.324328i	−0.269930	−	0.0107930i
$904$	−15.4015	−	33.1582i	−0.512247	−	1.10283i
$905$	11.5926	−	6.69298i	0.385351	−	0.222482i
$906$	14.3026	−	6.98050i	0.475173	−	0.231912i
$907$	7.61694	−	13.1929i	0.252916	−	0.438064i	−0.711411	−	0.702776i	$-0.751944\pi$
$907$	7.61694	−	13.1929i	0.252916	−	0.438064i	0.964328	+	0.264712i	$0.0852769\pi$
$908$	−18.6407	−	12.2868i	−0.618613	−	0.407753i
$909$	55.9063	+	4.47791i	1.85430	+	0.148523i
$910$	3.33909	−	1.79827i	0.110690	−	0.0596121i
$911$	−10.3048	+	17.8485i	−0.341414	+	0.591346i	−0.984695	−	0.174284i	$-0.944239\pi$
$911$	−10.3048	+	17.8485i	−0.341414	+	0.591346i	0.643282	+	0.765629i	$0.277572\pi$
$912$	−31.4196	−	25.5074i	−1.04041	−	0.844633i
$913$	17.3211	+	30.0009i	0.573243	+	0.992887i
$914$	−1.96796	−	1.21521i	−0.0650942	−	0.0401955i
$915$	−10.3583	+	16.3918i	−0.342436	+	0.541896i
$916$	11.5805	−	5.80150i	0.382632	−	0.191687i
$917$	−6.02815			−0.199067
$918$	−0.136476	+	0.906216i	−0.00450439	+	0.0299096i
$919$			53.6801i			1.77074i	0.464884	+	0.885371i	$0.346096\pi$
$919$			53.6801i			1.77074i	−0.464884	+	0.885371i	$0.653904\pi$
$920$	−5.60808	−	3.93935i	−0.184893	−	0.129876i
$921$	26.0565	+	16.4657i	0.858591	+	0.542563i
$922$	9.75747	+	6.02522i	0.321345	+	0.198430i
$923$	23.8592	−	13.7751i	0.785336	−	0.453414i
$924$	1.00245	−	10.0784i	0.0329781	−	0.331555i
$925$	−2.10354	−	1.21448i	−0.0691639	−	0.0399318i
$926$	−14.7581	−	27.4034i	−0.484983	−	0.900532i
$927$	−38.2847	−	26.3905i	−1.25743	−	0.866779i
$928$	38.0404	+	30.2330i	1.24874	+	0.992447i
$929$	15.9508	+	9.20921i	0.523329	+	0.302144i	0.738296	−	0.674477i	$-0.235631\pi$
$929$	15.9508	+	9.20921i	0.523329	+	0.302144i	−0.214966	+	0.976621i	$0.568964\pi$
$930$	−6.46765	+	3.15658i	−0.212082	+	0.103508i
$931$	16.9519	+	29.3615i	0.555576	+	0.962285i
$932$	0.916107	−	15.4630i	0.0300081	−	0.506509i
$933$	−1.13459	+	28.3760i	−0.0371449	+	0.928989i
$934$	6.59632	+	0.195228i	0.215838	+	0.00638806i
$935$	0.333426			0.0109042
$936$	−13.2819	+	16.0179i	−0.434133	+	0.523563i
$937$	−50.9610			−1.66482			−0.832412	−	0.554157i	$-0.813041\pi$
$937$	−50.9610			−1.66482			−0.832412	+	0.554157i	$0.813041\pi$
$938$	2.18640	+	0.0647098i	0.0713885	+	0.00211285i
$939$	−32.9633	+	17.3137i	−1.07572	+	0.565010i
$940$	−13.2751	−	0.786480i	−0.432985	−	0.0256522i
$941$	−21.4122	−	37.0870i	−0.698018	−	1.20900i	−0.969153	−	0.246461i	$-0.920732\pi$
$941$	−21.4122	−	37.0870i	−0.698018	−	1.20900i	0.271135	−	0.962541i	$-0.412601\pi$
$942$	3.88493	−	55.7673i	0.126578	−	1.81700i
$943$	−18.3480	−	10.5932i	−0.597492	−	0.344962i
$944$	−9.95011	+	4.26852i	−0.323849	+	0.138929i
$945$	−5.64154	−	0.679617i	−0.183519	−	0.0221080i
$946$	−7.68374	−	14.2674i	−0.249820	−	0.463874i
$947$	−18.4862	−	10.6730i	−0.600720	−	0.346826i	0.168604	−	0.985684i	$-0.446074\pi$
$947$	−18.4862	−	10.6730i	−0.600720	−	0.346826i	−0.769325	+	0.638858i	$0.779407\pi$
$948$	−3.41288	−	7.55173i	−0.110845	−	0.245269i
$949$	−11.3705	+	6.56475i	−0.369102	+	0.213101i
$950$	7.02882	+	4.34028i	0.228045	+	0.140817i
$951$	22.4005	−	11.7657i	0.726386	−	0.381528i
$952$	−0.315648	−	0.221724i	−0.0102302	−	0.00718612i
$953$		−	0.717198i		−	0.0232323i	−0.999933	−	0.0116162i	$-0.996302\pi$
$953$		−	0.717198i		−	0.0232323i	0.999933	−	0.0116162i	$-0.00369762\pi$
$954$	−8.31567	+	3.65471i	−0.269230	+	0.118326i
$955$	−4.48347			−0.145082
$956$	12.9936	+	25.9369i	0.420243	+	0.838859i
$957$	39.7458	+	1.58921i	1.28480	+	0.0513717i
$958$	9.99072	+	6.16925i	0.322786	+	0.199320i
$959$	−4.88268	−	8.45705i	−0.157670	−	0.273092i
$960$	2.98993	−	13.5300i	0.0964996	−	0.436678i
$961$	−11.1838	+	19.3709i	−0.360768	+	0.624868i
$962$	7.41657	−	3.99421i	0.239120	−	0.128778i
$963$	−45.1577	+	21.4623i	−1.45519	+	0.691614i
$964$	22.0209	−	33.4085i	0.709246	−	1.07602i
$965$	−4.45569	+	7.71749i	−0.143434	+	0.248435i
$966$	5.38186	+	3.62805i	0.173158	+	0.116731i
$967$	−1.20100	+	0.693395i	−0.0386214	+	0.0222981i	−0.519186	−	0.854661i	$-0.673765\pi$
$967$	−1.20100	+	0.693395i	−0.0386214	+	0.0222981i	0.480565	+	0.876959i	$0.340432\pi$
$968$	−9.88100	+	4.58959i	−0.317587	+	0.147515i
$969$	−0.674034	+	1.06664i	−0.0216531	+	0.0342654i
$970$	−0.628607	+	21.2392i	−0.0201834	+	0.681951i
$971$		−	6.74126i		−	0.216337i	−0.994133	−	0.108169i	$-0.965501\pi$
$971$		−	6.74126i		−	0.216337i	0.994133	−	0.108169i	$-0.0344987\pi$
$972$	30.0918	−	8.15373i	0.965195	−	0.261531i
$973$		−	16.8208i		−	0.539252i
$974$	−17.2136	−	0.509462i	−0.551559	−	0.0163242i
$975$	2.26900	−	3.59063i	0.0726662	−	0.114992i
$976$	35.8657	+	26.8125i	1.14803	+	0.858247i
$977$	45.1870	−	26.0887i	1.44566	−	0.834652i	0.447441	−	0.894313i	$-0.352335\pi$
$977$	45.1870	−	26.0887i	1.44566	−	0.834652i	0.998219	+	0.0596612i	$0.0190020\pi$
$978$	23.8206	−	35.3354i	0.761698	−	1.12990i
$979$	17.8963	−	30.9973i	0.571968	−	0.990678i
$980$	−6.38851	+	9.69217i	−0.204073	+	0.309605i
$981$	−25.9086	+	12.3137i	−0.827197	+	0.393146i
$982$	−17.4004	−	32.3097i	−0.555269	−	1.03104i
$983$	12.0449	−	20.8624i	0.384173	−	0.665407i	−0.607481	−	0.794334i	$-0.707820\pi$
$983$	12.0449	−	20.8624i	0.384173	−	0.665407i	0.991654	+	0.128927i	$0.0411534\pi$
$984$	5.49883	−	42.4809i	0.175296	−	1.35424i
$985$	−6.00737	−	10.4051i	−0.191411	−	0.331533i
$986$	0.795965	−	1.28902i	0.0253487	−	0.0410506i
$987$	12.5842	+	0.503170i	0.400560	+	0.0160161i
$988$	−25.6146	+	12.8321i	−0.814910	+	0.408245i
$989$	10.3848			0.330218
$990$	−4.56391	−	10.3844i	−0.145051	−	0.330038i
$991$		−	59.3927i		−	1.88667i	−0.331840	−	0.943336i	$-0.607669\pi$
$991$		−	59.3927i		−	1.88667i	0.331840	−	0.943336i	$-0.392331\pi$
$992$	6.09779	+	15.4614i	0.193605	+	0.490899i
$993$	−47.8842	+	25.1507i	−1.51956	+	0.798134i
$994$	9.12865	−	14.7833i	0.289543	−	0.468897i
$995$	−10.7734	+	6.22003i	−0.341540	+	0.197188i
$996$	−18.4849	−	40.9019i	−0.585716	−	1.29603i
$997$	−20.5450	−	11.8616i	−0.650665	−	0.375662i	0.138046	−	0.990426i	$-0.455918\pi$
$997$	−20.5450	−	11.8616i	−0.650665	−	0.375662i	−0.788711	+	0.614764i	$0.789251\pi$
$998$	−52.6064	+	28.3312i	−1.66523	+	0.896809i
$999$	−12.5306	−	1.50952i	−0.396452	−	0.0477592i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.2.bm.b.11.13	yes	48
3.2	odd	2		1080.2.bm.a.251.12		48
4.3	odd	2		1440.2.cc.b.911.5		48
8.3	odd	2		360.2.bm.a.11.20	✓	48
8.5	even	2		1440.2.cc.a.911.5		48
9.4	even	3		1080.2.bm.b.611.5		48
9.5	odd	6		360.2.bm.a.131.20	yes	48
12.11	even	2		4320.2.cc.a.1871.11		48
24.5	odd	2		4320.2.cc.b.1871.14		48
24.11	even	2		1080.2.bm.b.251.5		48
36.23	even	6		1440.2.cc.a.1391.5		48
36.31	odd	6		4320.2.cc.b.3311.14		48
72.5	odd	6		1440.2.cc.b.1391.5		48
72.13	even	6		4320.2.cc.a.3311.11		48
72.59	even	6	inner	360.2.bm.b.131.13	yes	48
72.67	odd	6		1080.2.bm.a.611.12		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.bm.a.11.20	✓	48	8.3	odd	2
360.2.bm.a.131.20	yes	48	9.5	odd	6
360.2.bm.b.11.13	yes	48	1.1	even	1	trivial
360.2.bm.b.131.13	yes	48	72.59	even	6	inner
1080.2.bm.a.251.12		48	3.2	odd	2
1080.2.bm.a.611.12		48	72.67	odd	6
1080.2.bm.b.251.5		48	24.11	even	2
1080.2.bm.b.611.5		48	9.4	even	3
1440.2.cc.a.911.5		48	8.5	even	2
1440.2.cc.a.1391.5		48	36.23	even	6
1440.2.cc.b.911.5		48	4.3	odd	2
1440.2.cc.b.1391.5		48	72.5	odd	6
4320.2.cc.a.1871.11		48	12.11	even	2
4320.2.cc.a.3311.11		48	72.13	even	6
4320.2.cc.b.1871.14		48	24.5	odd	2
4320.2.cc.b.3311.14		48	36.31	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	360.bm (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0418375 + 1.41359i) q^{2} +(1.46420 + 0.925262i) q^{3} +(-1.99650 - 0.118282i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-1.36920 + 2.03108i) q^{6} +(0.947055 + 0.546782i) q^{7} +(0.250732 - 2.81729i) q^{8} +(1.28778 + 2.70954i) q^{9} +O(q^{10})\)	\(q+(-0.0418375 + 1.41359i) q^{2} +(1.46420 + 0.925262i) q^{3} +(-1.99650 - 0.118282i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-1.36920 + 2.03108i) q^{6} +(0.947055 + 0.546782i) q^{7} +(0.250732 - 2.81729i) q^{8} +(1.28778 + 2.70954i) q^{9} +(-1.24513 + 0.670565i) q^{10} +(2.31540 + 1.33679i) q^{11} +(-2.81384 - 2.02048i) q^{12} +(-2.12374 + 1.22614i) q^{13} +(-0.812551 + 1.31588i) q^{14} +(-0.0691995 + 1.73067i) q^{15} +(3.97202 + 0.472301i) q^{16} -0.124711i q^{17} +(-3.88407 + 1.70704i) q^{18} -5.84133 q^{19} +(-0.895814 - 1.78816i) q^{20} +(0.880763 + 1.67687i) q^{21} +(-1.98656 + 3.21710i) q^{22} +(-1.21152 - 2.09842i) q^{23} +(2.97386 - 3.89309i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-1.64441 - 3.05340i) q^{26} +(-0.621470 + 5.15885i) q^{27} +(-1.82612 - 1.20367i) q^{28} +(4.29490 - 7.43898i) q^{29} +(-2.44357 - 0.170227i) q^{30} +(2.54447 - 1.46905i) q^{31} +(-0.833822 + 5.59506i) q^{32} +(2.15332 + 4.09969i) q^{33} +(0.176291 + 0.00521759i) q^{34} +1.09356i q^{35} +(-2.25056 - 5.56192i) q^{36} +2.42896i q^{37} +(0.244386 - 8.25727i) q^{38} +(-4.24408 - 0.169696i) q^{39} +(2.56521 - 1.19151i) q^{40} +(7.57229 - 4.37186i) q^{41} +(-2.40727 + 1.17489i) q^{42} +(-2.14293 + 3.71166i) q^{43} +(-4.46457 - 2.94278i) q^{44} +(-1.70264 + 2.47002i) q^{45} +(3.01700 - 1.62481i) q^{46} +(3.32459 - 5.75836i) q^{47} +(5.37884 + 4.36670i) q^{48} +(-2.90206 - 5.02651i) q^{49} +(-1.20329 - 0.743030i) q^{50} +(0.115390 - 0.182602i) q^{51} +(4.38507 - 2.19679i) q^{52} +2.14097 q^{53} +(-7.26653 - 1.09434i) q^{54} +2.67359i q^{55} +(1.77790 - 2.53103i) q^{56} +(-8.55289 - 5.40476i) q^{57} +(10.3360 + 6.38247i) q^{58} +(-2.34413 + 1.35338i) q^{59} +(0.342864 - 3.44709i) q^{60} +(9.69518 + 5.59752i) q^{61} +(1.97018 + 3.65830i) q^{62} +(-0.261933 + 3.27022i) q^{63} +(-7.87427 - 1.41277i) q^{64} +(-2.12374 - 1.22614i) q^{65} +(-5.88538 + 2.87241i) q^{66} +(-0.707180 - 1.22487i) q^{67} +(-0.0147511 + 0.248986i) q^{68} +(0.167673 - 4.19348i) q^{69} +(-1.54586 - 0.0457520i) q^{70} -11.2346 q^{71} +(7.95646 - 2.94868i) q^{72} +5.35400 q^{73} +(-3.43356 - 0.101621i) q^{74} +(-1.53340 + 0.805405i) q^{75} +(11.6622 + 0.690927i) q^{76} +(1.46187 + 2.53203i) q^{77} +(0.417443 - 5.99231i) q^{78} +(2.07178 + 1.19614i) q^{79} +(1.57698 + 3.67602i) q^{80} +(-5.68325 + 6.97859i) q^{81} +(5.86323 + 10.8871i) q^{82} +(11.2212 + 6.47858i) q^{83} +(-1.56010 - 3.45206i) q^{84} +(0.108003 - 0.0623555i) q^{85} +(-5.15712 - 3.18452i) q^{86} +(13.1716 - 6.91827i) q^{87} +(4.34668 - 6.18797i) q^{88} -13.3875i q^{89} +(-3.42037 - 2.51019i) q^{90} -2.68172 q^{91} +(2.17060 + 4.33279i) q^{92} +(5.08487 + 0.203315i) q^{93} +(8.00089 + 4.94053i) q^{94} +(-2.92067 - 5.05874i) q^{95} +(-6.39779 + 7.42080i) q^{96} +(7.51249 - 13.0120i) q^{97} +(7.22687 - 3.89204i) q^{98} +(-0.640385 + 7.99516i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 24 q^{5} - q^{6} + 6 q^{8}+O(q^{10}) \) 48 * q + 24 * q^5 - q^6 + 6 * q^8	\( 48 q + 24 q^{5} - q^{6} + 6 q^{8} + 13 q^{12} + 15 q^{14} - 12 q^{16} + 7 q^{18} + 4 q^{21} - 21 q^{22} - 4 q^{24} - 24 q^{25} + 12 q^{27} - 2 q^{30} - 8 q^{33} - 27 q^{34} - 31 q^{36} - 27 q^{38} - 16 q^{39} + 12 q^{40} + 12 q^{41} - 9 q^{42} + 24 q^{44} - 6 q^{46} - 12 q^{47} + 7 q^{48} + 24 q^{49} - 20 q^{51} + 54 q^{52} - 32 q^{54} + 21 q^{56} + 4 q^{57} + 33 q^{58} - 36 q^{59} - q^{60} - 12 q^{61} - 42 q^{62} - 56 q^{63} - 12 q^{64} - 32 q^{66} + 51 q^{68} + 40 q^{69} + 15 q^{70} + 6 q^{72} + 54 q^{74} - 51 q^{76} - 24 q^{78} - 8 q^{81} - 18 q^{82} - 60 q^{83} + 41 q^{84} + 27 q^{86} - 36 q^{87} - 57 q^{88} - 22 q^{90} - 9 q^{92} - 75 q^{94} + 13 q^{96} - 42 q^{98} - 16 q^{99}+O(q^{100}) \) 48 * q + 24 * q^5 - q^6 + 6 * q^8 + 13 * q^12 + 15 * q^14 - 12 * q^16 + 7 * q^18 + 4 * q^21 - 21 * q^22 - 4 * q^24 - 24 * q^25 + 12 * q^27 - 2 * q^30 - 8 * q^33 - 27 * q^34 - 31 * q^36 - 27 * q^38 - 16 * q^39 + 12 * q^40 + 12 * q^41 - 9 * q^42 + 24 * q^44 - 6 * q^46 - 12 * q^47 + 7 * q^48 + 24 * q^49 - 20 * q^51 + 54 * q^52 - 32 * q^54 + 21 * q^56 + 4 * q^57 + 33 * q^58 - 36 * q^59 - q^60 - 12 * q^61 - 42 * q^62 - 56 * q^63 - 12 * q^64 - 32 * q^66 + 51 * q^68 + 40 * q^69 + 15 * q^70 + 6 * q^72 + 54 * q^74 - 51 * q^76 - 24 * q^78 - 8 * q^81 - 18 * q^82 - 60 * q^83 + 41 * q^84 + 27 * q^86 - 36 * q^87 - 57 * q^88 - 22 * q^90 - 9 * q^92 - 75 * q^94 + 13 * q^96 - 42 * q^98 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more