LMFDB - Embedded newform 429.2.bd.b.76.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(76,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 6, 7]))

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

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

chi := DirichletCharacter("429.76");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.bd (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			76.1
Character	$\chi$	$=$	429.76
Dual form			429.2.bd.b.175.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.44393 - 0.654849i) q^{2} +(0.500000 + 0.866025i) q^{3} +(3.81192 + 2.20081i) q^{4} +(-0.748465 - 0.748465i) q^{5} +(-0.654849 - 2.44393i) q^{6} +(-0.270535 + 0.0724897i) q^{7} +(-4.29670 - 4.29670i) q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-2.44393 - 0.654849i) q^{2} +(0.500000 + 0.866025i) q^{3} +(3.81192 + 2.20081i) q^{4} +(-0.748465 - 0.748465i) q^{5} +(-0.654849 - 2.44393i) q^{6} +(-0.270535 + 0.0724897i) q^{7} +(-4.29670 - 4.29670i) q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.33906 + 2.31933i) q^{10} +(-2.59095 - 2.07050i) q^{11} +4.40162i q^{12} +(-2.42671 + 2.66666i) q^{13} +0.708639 q^{14} +(0.273957 - 1.02242i) q^{15} +(3.28552 + 5.69069i) q^{16} +(0.0934440 - 0.161850i) q^{17} +(1.78908 - 1.78908i) q^{18} +(-0.228087 - 0.851231i) q^{19} +(-1.20586 - 4.50032i) q^{20} +(-0.198045 - 0.198045i) q^{21} +(4.97623 + 6.75684i) q^{22} +(-1.93986 + 1.11998i) q^{23} +(1.57270 - 5.86940i) q^{24} -3.87960i q^{25} +(7.67697 - 4.92801i) q^{26} -1.00000 q^{27} +(-1.19079 - 0.319072i) q^{28} +(2.15228 - 1.24262i) q^{29} +(-1.33906 + 2.31933i) q^{30} +(-6.46328 - 6.46328i) q^{31} +(-1.15764 - 4.32037i) q^{32} +(0.497633 - 3.27908i) q^{33} +(-0.334358 + 0.334358i) q^{34} +(0.256742 + 0.148230i) q^{35} +(-3.81192 + 2.20081i) q^{36} +(4.61681 + 1.23707i) q^{37} +2.22971i q^{38} +(-3.52275 - 0.768259i) q^{39} +6.43185i q^{40} +(-11.4750 - 3.07471i) q^{41} +(0.354319 + 0.613699i) q^{42} +(-1.00862 + 1.74698i) q^{43} +(-5.31970 - 13.5948i) q^{44} +(1.02242 - 0.273957i) q^{45} +(5.47431 - 1.46684i) q^{46} +(-2.49262 + 2.49262i) q^{47} +(-3.28552 + 5.69069i) q^{48} +(-5.99424 + 3.46078i) q^{49} +(-2.54055 + 9.48148i) q^{50} +0.186888 q^{51} +(-15.1192 + 4.82437i) q^{52} -10.1750 q^{53} +(2.44393 + 0.654849i) q^{54} +(0.389537 + 3.48893i) q^{55} +(1.47387 + 0.850942i) q^{56} +(0.623145 - 0.623145i) q^{57} +(-6.07376 + 1.62746i) q^{58} +(-0.394865 - 1.47366i) q^{59} +(3.29446 - 3.29446i) q^{60} +(-6.06587 - 3.50213i) q^{61} +(11.5633 + 20.0283i) q^{62} +(0.0724897 - 0.270535i) q^{63} -1.82533i q^{64} +(3.81221 - 0.179598i) q^{65} +(-3.36348 + 7.68797i) q^{66} +(0.153377 - 0.572411i) q^{67} +(0.712401 - 0.411305i) q^{68} +(-1.93986 - 1.11998i) q^{69} +(-0.530391 - 0.530391i) q^{70} +(2.46664 - 0.660935i) q^{71} +(5.86940 - 1.57270i) q^{72} +(-3.86319 - 3.86319i) q^{73} +(-10.4731 - 6.04663i) q^{74} +(3.35983 - 1.93980i) q^{75} +(1.00395 - 3.74680i) q^{76} +(0.851033 + 0.372326i) q^{77} +(8.10627 + 4.18444i) q^{78} -9.45814i q^{79} +(1.80018 - 6.71838i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(26.0306 + 15.0288i) q^{82} +(-0.0514974 + 0.0514974i) q^{83} +(-0.319072 - 1.19079i) q^{84} +(-0.191078 + 0.0511993i) q^{85} +(3.60900 - 3.60900i) q^{86} +(2.15228 + 1.24262i) q^{87} +(2.23621 + 20.0289i) q^{88} +(12.9166 + 3.46100i) q^{89} -2.67813 q^{90} +(0.463204 - 0.897337i) q^{91} -9.85946 q^{92} +(2.36572 - 8.82900i) q^{93} +(7.72407 - 4.45949i) q^{94} +(-0.466402 + 0.807831i) q^{95} +(3.16273 - 3.16273i) q^{96} +(0.320398 - 0.0858504i) q^{97} +(16.9158 - 4.53258i) q^{98} +(3.08858 - 1.20858i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 28 q^{3} - 4 q^{5} - 28 q^{9}+O(q^{10}) $ 56 * q + 28 * q^3 - 4 * q^5 - 28 * q^9	$ 56 q + 28 q^{3} - 4 q^{5} - 28 q^{9} - 4 q^{11} - 24 q^{14} - 8 q^{15} + 4 q^{16} + 80 q^{20} - 10 q^{22} - 12 q^{23} + 40 q^{26} - 56 q^{27} - 12 q^{31} - 8 q^{33} - 16 q^{34} - 12 q^{37} - 12 q^{42} + 24 q^{44} - 4 q^{45} - 40 q^{47} - 4 q^{48} + 24 q^{49} - 88 q^{53} - 18 q^{55} + 72 q^{56} + 40 q^{58} + 8 q^{59} + 52 q^{60} - 20 q^{66} - 4 q^{67} - 12 q^{69} + 40 q^{70} - 24 q^{71} + 12 q^{75} - 4 q^{78} - 188 q^{80} - 28 q^{81} - 12 q^{82} + 32 q^{86} + 18 q^{88} - 16 q^{89} + 28 q^{91} - 96 q^{92} - 12 q^{93} - 28 q^{97} - 4 q^{99}+O(q^{100}) $ 56 * q + 28 * q^3 - 4 * q^5 - 28 * q^9 - 4 * q^11 - 24 * q^14 - 8 * q^15 + 4 * q^16 + 80 * q^20 - 10 * q^22 - 12 * q^23 + 40 * q^26 - 56 * q^27 - 12 * q^31 - 8 * q^33 - 16 * q^34 - 12 * q^37 - 12 * q^42 + 24 * q^44 - 4 * q^45 - 40 * q^47 - 4 * q^48 + 24 * q^49 - 88 * q^53 - 18 * q^55 + 72 * q^56 + 40 * q^58 + 8 * q^59 + 52 * q^60 - 20 * q^66 - 4 * q^67 - 12 * q^69 + 40 * q^70 - 24 * q^71 + 12 * q^75 - 4 * q^78 - 188 * q^80 - 28 * q^81 - 12 * q^82 + 32 * q^86 + 18 * q^88 - 16 * q^89 + 28 * q^91 - 96 * q^92 - 12 * q^93 - 28 * q^97 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$-1$	$1$

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 $

$2$	−2.44393	−	0.654849i	−1.72812	−	0.463048i	−0.748371	−	0.663280i	$-0.769164\pi$
$2$	−2.44393	−	0.654849i	−1.72812	−	0.463048i	−0.979749	+	0.200232i	$0.935830\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	3.81192	+	2.20081i	1.90596	+	1.10041i
$5$	−0.748465	−	0.748465i	−0.334724	−	0.334724i	0.519654	−	0.854377i	$-0.326061\pi$
$5$	−0.748465	−	0.748465i	−0.334724	−	0.334724i	−0.854377	+	0.519654i	$0.826061\pi$
$6$	−0.654849	−	2.44393i	−0.267341	−	0.997730i
$7$	−0.270535	+	0.0724897i	−0.102253	+	0.0273985i	−0.309583	−	0.950873i	$-0.600189\pi$
$7$	−0.270535	+	0.0724897i	−0.102253	+	0.0273985i	0.207330	+	0.978271i	$0.433523\pi$
$8$	−4.29670	−	4.29670i	−1.51911	−	1.51911i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	1.33906	+	2.31933i	0.423449	+	0.733436i
$11$	−2.59095	−	2.07050i	−0.781201	−	0.624280i
$11$	−2.59095	−	2.07050i	−0.781201	−	0.624280i
$12$			4.40162i			1.27064i
$13$	−2.42671	+	2.66666i	−0.673048	+	0.739599i
$13$	−2.42671	+	2.66666i	−0.673048	+	0.739599i
$14$	0.708639			0.189392
$15$	0.273957	−	1.02242i	0.0707354	−	0.263988i
$16$	3.28552	+	5.69069i	0.821380	+	1.42267i
$17$	0.0934440	−	0.161850i	0.0226635	−	0.0392543i	−0.854471	−	0.519499i	$-0.826119\pi$
$17$	0.0934440	−	0.161850i	0.0226635	−	0.0392543i	0.877135	+	0.480244i	$0.159452\pi$
$18$	1.78908	−	1.78908i	0.421690	−	0.421690i
$19$	−0.228087	−	0.851231i	−0.0523267	−	0.195286i	0.934815	−	0.355136i	$-0.115566\pi$
$19$	−0.228087	−	0.851231i	−0.0523267	−	0.195286i	−0.987141	+	0.159850i	$0.948899\pi$
$20$	−1.20586	−	4.50032i	−0.269638	−	1.00630i
$21$	−0.198045	−	0.198045i	−0.0432171	−	0.0432171i
$22$	4.97623	+	6.75684i	1.06094	+	1.44056i
$23$	−1.93986	+	1.11998i	−0.404489	+	0.233532i	−0.688419	−	0.725313i	$-0.741695\pi$
$23$	−1.93986	+	1.11998i	−0.404489	+	0.233532i	0.283930	+	0.958845i	$0.408362\pi$
$24$	1.57270	−	5.86940i	0.321026	−	1.19809i
$25$		−	3.87960i		−	0.775920i
$26$	7.67697	−	4.92801i	1.50558	−	0.966462i
$27$	−1.00000			−0.192450
$28$	−1.19079	−	0.319072i	−0.225039	−	0.0602990i
$29$	2.15228	−	1.24262i	0.399669	−	0.230749i	−0.286672	−	0.958029i	$-0.592549\pi$
$29$	2.15228	−	1.24262i	0.399669	−	0.230749i	0.686341	+	0.727280i	$0.259216\pi$
$30$	−1.33906	+	2.31933i	−0.244479	+	0.423449i
$31$	−6.46328	−	6.46328i	−1.16084	−	1.16084i	−0.984292	−	0.176547i	$-0.943507\pi$
$31$	−6.46328	−	6.46328i	−1.16084	−	1.16084i	−0.176547	−	0.984292i	$-0.556493\pi$
$32$	−1.15764	−	4.32037i	−0.204644	−	0.763740i
$33$	0.497633	−	3.27908i	0.0866267	−	0.570814i
$34$	−0.334358	+	0.334358i	−0.0573419	+	0.0573419i
$35$	0.256742	+	0.148230i	0.0433973	+	0.0250554i
$36$	−3.81192	+	2.20081i	−0.635320	+	0.366802i
$37$	4.61681	+	1.23707i	0.758999	+	0.203373i	0.617506	−	0.786566i	$-0.288143\pi$
$37$	4.61681	+	1.23707i	0.758999	+	0.203373i	0.141493	+	0.989939i	$0.454810\pi$
$38$			2.22971i			0.361707i
$39$	−3.52275	−	0.768259i	−0.564092	−	0.123020i
$40$			6.43185i			1.01697i
$41$	−11.4750	−	3.07471i	−1.79209	−	0.480189i	−0.799392	−	0.600810i	$-0.794845\pi$
$41$	−11.4750	−	3.07471i	−1.79209	−	0.480189i	−0.992699	+	0.120620i	$0.961512\pi$
$42$	0.354319	+	0.613699i	0.0546727	+	0.0946958i
$43$	−1.00862	+	1.74698i	−0.153813	+	0.266412i	−0.932626	−	0.360844i	$-0.882489\pi$
$43$	−1.00862	+	1.74698i	−0.153813	+	0.266412i	0.778813	+	0.627256i	$0.215822\pi$
$44$	−5.31970	−	13.5948i	−0.801975	−	2.04949i
$45$	1.02242	−	0.273957i	0.152414	−	0.0408391i
$46$	5.47431	−	1.46684i	0.807143	−	0.216273i
$47$	−2.49262	+	2.49262i	−0.363585	+	0.363585i	−0.865131	−	0.501546i	$-0.832765\pi$
$47$	−2.49262	+	2.49262i	−0.363585	+	0.363585i	0.501546	+	0.865131i	$0.332765\pi$
$48$	−3.28552	+	5.69069i	−0.474224	+	0.821380i
$49$	−5.99424	+	3.46078i	−0.856320	+	0.494397i
$50$	−2.54055	+	9.48148i	−0.359289	+	1.34088i
$51$	0.186888			0.0261695
$52$	−15.1192	+	4.82437i	−2.09666	+	0.669020i
$53$	−10.1750			−1.39765			−0.698824	−	0.715294i	$-0.746293\pi$
$53$	−10.1750			−1.39765			−0.698824	+	0.715294i	$0.746293\pi$
$54$	2.44393	+	0.654849i	0.332577	+	0.0891137i
$55$	0.389537	+	3.48893i	0.0525251	+	0.470448i
$56$	1.47387	+	0.850942i	0.196955	+	0.113712i
$57$	0.623145	−	0.623145i	0.0825375	−	0.0825375i
$58$	−6.07376	+	1.62746i	−0.797524	+	0.213696i
$59$	−0.394865	−	1.47366i	−0.0514071	−	0.191854i	0.935447	−	0.353466i	$-0.114997\pi$
$59$	−0.394865	−	1.47366i	−0.0514071	−	0.191854i	−0.986854	+	0.161613i	$0.948330\pi$
$60$	3.29446	−	3.29446i	0.425313	−	0.425313i
$61$	−6.06587	−	3.50213i	−0.776655	−	0.448402i	0.0585885	−	0.998282i	$-0.481340\pi$
$61$	−6.06587	−	3.50213i	−0.776655	−	0.448402i	−0.835244	+	0.549880i	$0.814673\pi$
$62$	11.5633	+	20.0283i	1.46854	+	2.54359i
$63$	0.0724897	−	0.270535i	0.00913284	−	0.0340842i
$64$		−	1.82533i		−	0.228166i
$65$	3.81221	−	0.179598i	0.472846	−	0.0222764i
$66$	−3.36348	+	7.68797i	−0.414016	+	0.946323i
$67$	0.153377	−	0.572411i	0.0187380	−	0.0699311i	−0.955924	−	0.293615i	$-0.905142\pi$
$67$	0.153377	−	0.572411i	0.0187380	−	0.0699311i	0.974662	+	0.223684i	$0.0718083\pi$
$68$	0.712401	−	0.411305i	0.0863913	−	0.0498781i
$69$	−1.93986	−	1.11998i	−0.233532	−	0.134830i
$70$	−0.530391	−	0.530391i	−0.0633939	−	0.0633939i
$71$	2.46664	−	0.660935i	0.292737	−	0.0784386i	−0.109462	−	0.993991i	$-0.534913\pi$
$71$	2.46664	−	0.660935i	0.292737	−	0.0784386i	0.402199	+	0.915552i	$0.368246\pi$
$72$	5.86940	−	1.57270i	0.691715	−	0.185345i
$73$	−3.86319	−	3.86319i	−0.452152	−	0.452152i	0.443916	−	0.896068i	$-0.353589\pi$
$73$	−3.86319	−	3.86319i	−0.452152	−	0.452152i	−0.896068	+	0.443916i	$0.853589\pi$
$74$	−10.4731	−	6.04663i	−1.21747	−	0.702906i
$75$	3.35983	−	1.93980i	0.387960	−	0.223989i
$76$	1.00395	−	3.74680i	0.115161	−	0.429787i
$77$	0.851033	+	0.372326i	0.0969842	+	0.0424305i
$78$	8.10627	+	4.18444i	0.917854	+	0.473795i
$79$		−	9.45814i		−	1.06412i	−0.846706	−	0.532062i	$-0.821417\pi$
$79$		−	9.45814i		−	1.06412i	0.846706	−	0.532062i	$-0.178583\pi$
$80$	1.80018	−	6.71838i	0.201267	−	0.751137i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	26.0306	+	15.0288i	2.87460	+	1.65965i
$83$	−0.0514974	+	0.0514974i	−0.00565257	+	0.00565257i	−0.709927	−	0.704275i	$-0.751272\pi$
$83$	−0.0514974	+	0.0514974i	−0.00565257	+	0.00565257i	0.704275	+	0.709927i	$0.251272\pi$
$84$	−0.319072	−	1.19079i	−0.0348136	−	0.129926i
$85$	−0.191078	+	0.0511993i	−0.0207253	+	0.00555334i
$86$	3.60900	−	3.60900i	0.389168	−	0.389168i
$87$	2.15228	+	1.24262i	0.230749	+	0.133223i
$88$	2.23621	+	20.0289i	0.238380	+	2.13508i
$89$	12.9166	+	3.46100i	1.36916	+	0.366866i	0.867172	−	0.498009i	$-0.165935\pi$
$89$	12.9166	+	3.46100i	1.36916	+	0.366866i	0.501989	+	0.864874i	$0.332602\pi$
$90$	−2.67813			−0.282299
$91$	0.463204	−	0.897337i	0.0485570	−	0.0940665i
$92$	−9.85946			−1.02792
$93$	2.36572	−	8.82900i	0.245314	−	0.915525i
$94$	7.72407	−	4.45949i	0.796677	−	0.459962i
$95$	−0.466402	+	0.807831i	−0.0478518	+	0.0828818i
$96$	3.16273	−	3.16273i	0.322795	−	0.322795i
$97$	0.320398	−	0.0858504i	0.0325315	−	0.00871679i	−0.242517	−	0.970147i	$-0.577973\pi$
$97$	0.320398	−	0.0858504i	0.0325315	−	0.00871679i	0.275048	+	0.961430i	$0.411306\pi$
$98$	16.9158	−	4.53258i	1.70875	−	0.457859i
$99$	3.08858	−	1.20858i	0.310414	−	0.121467i
$100$	8.53827	−	14.7887i	0.853827	−	1.47887i
$101$	5.60420	+	9.70675i	0.557638	+	0.965858i	0.997693	+	0.0678870i	$0.0216257\pi$
$101$	5.60420	+	9.70675i	0.557638	+	0.965858i	−0.440055	+	0.897971i	$0.645041\pi$
$102$	−0.456741	−	0.122383i	−0.0452241	−	0.0121178i
$103$		−	5.68987i		−	0.560640i	−0.959907	−	0.280320i	$-0.909559\pi$
$103$		−	5.68987i		−	0.560640i	0.959907	−	0.280320i	$-0.0904406\pi$
$104$	21.8847	−	1.03101i	2.14597	−	0.101099i
$105$			0.296460i			0.0289315i
$106$	24.8671	+	6.66311i	2.41530	+	0.647178i
$107$	13.0485	−	7.53358i	1.26145	−	0.728299i	0.288096	−	0.957602i	$-0.406978\pi$
$107$	13.0485	−	7.53358i	1.26145	−	0.728299i	0.973355	+	0.229303i	$0.0736445\pi$
$108$	−3.81192	−	2.20081i	−0.366802	−	0.211773i
$109$	−1.75786	+	1.75786i	−0.168373	+	0.168373i	−0.786264	−	0.617891i	$-0.787987\pi$
$109$	−1.75786	+	1.75786i	−0.168373	+	0.168373i	0.617891	+	0.786264i	$0.287987\pi$
$110$	1.33272	−	8.78179i	0.127070	−	0.837311i
$111$	1.23707	+	4.61681i	0.117418	+	0.438208i
$112$	−1.30136	−	1.30136i	−0.122967	−	0.122967i
$113$	−8.16542	+	14.1429i	−0.768138	+	1.33045i	0.170434	+	0.985369i	$0.445483\pi$
$113$	−8.16542	+	14.1429i	−0.768138	+	1.33045i	−0.938572	+	0.345084i	$0.887850\pi$
$114$	−1.93099	+	1.11486i	−0.180854	+	0.104416i
$115$	2.29018	+	0.613653i	0.213561	+	0.0572234i
$116$	10.9391			1.01567
$117$	−1.09604	−	3.43492i	−0.101329	−	0.317559i
$118$			3.86009i			0.355350i
$119$	−0.0135474	+	0.0505597i	−0.00124189	+	0.00463480i
$120$	−5.57015	+	3.21593i	−0.508483	+	0.293573i
$121$	2.42604	+	10.7291i	0.220549	+	0.975376i
$122$	12.5312	+	12.5312i	1.13452	+	1.13452i
$123$	−3.07471	−	11.4750i	−0.277237	−	1.03466i
$124$	−10.4130	−	38.8619i	−0.935117	−	3.48991i
$125$	−6.64607	+	6.64607i	−0.594442	+	0.594442i
$126$	−0.354319	+	0.613699i	−0.0315653	+	0.0546727i
$127$	2.63643	+	4.56642i	0.233945	+	0.405205i	0.958966	−	0.283523i	$-0.0915031\pi$
$127$	2.63643	+	4.56642i	0.233945	+	0.405205i	−0.725021	+	0.688727i	$0.758170\pi$
$128$	−3.51059	+	13.1017i	−0.310295	+	1.15804i
$129$	−2.01724			−0.177608
$130$	−9.43438	−	2.05750i	−0.827450	−	0.180454i
$131$		−	18.8707i		−	1.64874i	−0.566049	−	0.824372i	$-0.691529\pi$
$131$		−	18.8707i		−	1.64874i	0.566049	−	0.824372i	$-0.308471\pi$
$132$	9.11357	−	11.4044i	0.793235	−	0.992624i
$133$	0.123411	+	0.213754i	0.0107011	+	0.0185348i
$134$	−0.749686	+	1.29849i	−0.0647630	+	0.112173i
$135$	0.748465	+	0.748465i	0.0644176	+	0.0644176i
$136$	−1.09692	+	0.293919i	−0.0940601	+	0.0252033i
$137$	2.55530	+	9.53652i	0.218314	+	0.814760i	0.984973	+	0.172706i	$0.0552510\pi$
$137$	2.55530	+	9.53652i	0.218314	+	0.814760i	−0.766659	+	0.642054i	$0.778082\pi$
$138$	4.00747	+	4.00747i	0.341139	+	0.341139i
$139$	−11.7030	−	6.75670i	−0.992632	−	0.573096i	−0.0865718	−	0.996246i	$-0.527591\pi$
$139$	−11.7030	−	6.75670i	−0.992632	−	0.573096i	−0.906060	+	0.423149i	$0.860925\pi$
$140$	0.652453	+	1.13008i	0.0551423	+	0.0955093i
$141$	−3.40498	−	0.912361i	−0.286751	−	0.0768346i
$142$	−6.46112			−0.542205
$143$	11.8088	−	1.88468i	0.987502	−	0.157605i
$144$	−6.57104			−0.547587
$145$	−2.54097	−	0.680850i	−0.211016	−	0.0565415i
$146$	6.91156	+	11.9712i	0.572005	+	0.990741i
$147$	−5.99424	−	3.46078i	−0.494397	−	0.285440i
$148$	14.8763	+	14.8763i	1.22283	+	1.22283i
$149$	−0.366939	−	1.36944i	−0.0300608	−	0.112189i	0.949265	−	0.314477i	$-0.101829\pi$
$149$	−0.366939	−	1.36944i	−0.0300608	−	0.112189i	−0.979326	+	0.202288i	$0.935162\pi$
$150$	−9.48148	+	2.54055i	−0.774159	+	0.207435i
$151$	11.2855	+	11.2855i	0.918399	+	0.918399i	0.996913	−	0.0785141i	$-0.0250176\pi$
$151$	11.2855	+	11.2855i	0.918399	+	0.918399i	−0.0785141	+	0.996913i	$0.525018\pi$
$152$	−2.67746	+	4.63751i	−0.217171	+	0.376151i
$153$	0.0934440	+	0.161850i	0.00755450	+	0.0130848i
$154$	−1.83605	−	1.46724i	−0.147953	−	0.118233i
$155$			9.67507i			0.777120i
$156$	−11.7376	−	10.6815i	−0.939764	−	0.855201i
$157$	5.52193			0.440698			0.220349	−	0.975421i	$-0.429280\pi$
$157$	5.52193			0.440698			0.220349	+	0.975421i	$0.429280\pi$
$158$	−6.19365	+	23.1150i	−0.492741	+	1.83893i
$159$	−5.08752	−	8.81183i	−0.403466	−	0.698824i
$160$	−2.36719	+	4.10009i	−0.187143	+	0.324141i
$161$	0.443614	−	0.443614i	0.0349617	−	0.0349617i
$162$	0.654849	+	2.44393i	0.0514498	+	0.192013i
$163$	−1.09557	−	4.08871i	−0.0858115	−	0.320253i	0.909655	−	0.415364i	$-0.136346\pi$
$163$	−1.09557	−	4.08871i	−0.0858115	−	0.320253i	−0.995467	+	0.0951115i	$0.969679\pi$
$164$	−36.9748	−	36.9748i	−2.88725	−	2.88725i
$165$	−2.82674	+	2.08181i	−0.220061	+	0.162069i
$166$	0.159579	−	0.0921330i	0.0123857	−	0.00715091i
$167$	−6.12266	+	22.8501i	−0.473785	+	1.76819i	0.152193	+	0.988351i	$0.451366\pi$
$167$	−6.12266	+	22.8501i	−0.473785	+	1.76819i	−0.625979	+	0.779840i	$0.715300\pi$
$168$			1.70188i			0.131303i
$169$	−1.22218	−	12.9424i	−0.0940138	−	0.995571i
$170$	0.500510			0.0383873
$171$	0.851231	+	0.228087i	0.0650953	+	0.0174422i
$172$	−7.68954	+	4.43956i	−0.586322	+	0.338513i
$173$	5.52783	−	9.57449i	0.420273	−	0.727935i	−0.575693	−	0.817666i	$-0.695267\pi$
$173$	5.52783	−	9.57449i	0.420273	−	0.727935i	0.995966	+	0.0897313i	$0.0286008\pi$
$174$	−4.44630	−	4.44630i	−0.337073	−	0.337073i
$175$	0.281231	+	1.04957i	0.0212591	+	0.0793399i
$176$	3.26996	−	21.5470i	0.246483	−	1.62416i
$177$	1.07879	−	1.07879i	0.0810869	−	0.0810869i
$178$	−29.3009	−	16.9169i	−2.19620	−	1.26798i
$179$	4.12519	−	2.38168i	0.308331	−	0.178015i	−0.337848	−	0.941201i	$-0.609699\pi$
$179$	4.12519	−	2.38168i	0.308331	−	0.178015i	0.646179	+	0.763185i	$0.276366\pi$
$180$	4.50032	+	1.20586i	0.335434	+	0.0898792i
$181$			19.2838i			1.43335i	0.697406	+	0.716676i	$0.254337\pi$
$181$			19.2838i			1.43335i	−0.697406	+	0.716676i	$0.745663\pi$
$182$	−1.71966	+	1.88970i	−0.127470	+	0.140074i
$183$		−	7.00426i		−	0.517770i
$184$	13.1472	+	3.52279i	0.969226	+	0.259703i
$185$	−2.52962	−	4.38142i	−0.185981	−	0.322129i
$186$	−11.5633	+	20.0283i	−0.847865	+	1.46854i
$187$	−0.577219	+	0.225868i	−0.0422104	+	0.0165171i
$188$	−14.9874	+	4.01587i	−1.09307	+	0.292887i
$189$	0.270535	−	0.0724897i	0.0196785	−	0.00527285i
$190$	1.66886	−	1.66886i	0.121072	−	0.121072i
$191$	−7.30126	+	12.6461i	−0.528300	+	0.915043i	0.471155	+	0.882050i	$0.343837\pi$
$191$	−7.30126	+	12.6461i	−0.528300	+	0.915043i	−0.999456	+	0.0329927i	$0.989496\pi$
$192$	1.58078	−	0.912664i	0.114083	−	0.0658659i
$193$	−4.24728	+	15.8511i	−0.305726	+	1.14098i	0.626593	+	0.779347i	$0.284449\pi$
$193$	−4.24728	+	15.8511i	−0.305726	+	1.14098i	−0.932319	+	0.361638i	$0.882218\pi$
$194$	−0.839250			−0.0602546
$195$	2.06164	+	3.21167i	0.147637	+	0.229992i
$196$	−30.4661			−2.17615
$197$	−4.04885	−	1.08489i	−0.288469	−	0.0772950i	0.111683	−	0.993744i	$-0.464376\pi$
$197$	−4.04885	−	1.08489i	−0.288469	−	0.0772950i	−0.400152	+	0.916449i	$0.631043\pi$
$198$	−8.33972	+	0.931123i	−0.592678	+	0.0661720i
$199$	10.8005	+	6.23568i	0.765628	+	0.442036i	0.831313	−	0.555805i	$-0.187590\pi$
$199$	10.8005	+	6.23568i	0.765628	+	0.442036i	−0.0656848	+	0.997840i	$0.520923\pi$
$200$	−16.6695	+	16.6695i	−1.17871	+	1.17871i
$201$	0.572411	−	0.153377i	0.0403748	−	0.0108184i
$202$	−7.33981	−	27.3925i	−0.516427	−	1.92733i
$203$	−0.492191	+	0.492191i	−0.0345451	+	0.0345451i
$204$	0.712401	+	0.411305i	0.0498781	+	0.0287971i
$205$	6.28730	+	10.8899i	0.439124	+	0.760586i
$206$	−3.72601	+	13.9057i	−0.259603	+	0.968853i
$207$		−	2.23996i		−	0.155688i
$208$	−23.1481	−	5.04826i	−1.60503	−	0.350034i
$209$	−1.17152	+	2.67775i	−0.0810354	+	0.185224i
$210$	0.194137	−	0.724528i	0.0133967	−	0.0499972i
$211$	20.4019	−	11.7790i	1.40452	−	0.810902i	0.409671	−	0.912233i	$-0.365643\pi$
$211$	20.4019	−	11.7790i	1.40452	−	0.810902i	0.994853	+	0.101331i	$0.0323101\pi$
$212$	−38.7864	−	22.3933i	−2.66386	−	1.53798i
$213$	1.80571	+	1.80571i	0.123725	+	0.123725i
$214$	−36.8231	+	9.86672i	−2.51718	+	0.674475i
$215$	2.06247	−	0.552636i	0.140659	−	0.0376895i
$216$	4.29670	+	4.29670i	0.292353	+	0.292353i
$217$	2.21706	+	1.28002i	0.150504	+	0.0868936i
$218$	5.44723	−	3.14496i	0.368933	−	0.213004i
$219$	1.41403	−	5.27721i	0.0955510	−	0.356601i
$220$	−6.19360	+	14.1568i	−0.417573	+	0.954452i
$221$	0.204837	+	0.641945i	0.0137788	+	0.0431819i
$222$		−	12.0933i		−	0.811646i
$223$	−2.00040	+	7.46560i	−0.133957	+	0.499933i	−1.00000		3.56387e-5i	$-0.999989\pi$
$223$	−2.00040	+	7.46560i	−0.133957	+	0.499933i	0.866043	+	0.499969i	$0.166655\pi$
$224$	0.626364	+	1.08489i	0.0418507	+	0.0724875i
$225$	3.35983	+	1.93980i	0.223989	+	0.129320i
$226$	29.2172	−	29.2172i	1.94350	−	1.94350i
$227$	−1.03567	−	3.86518i	−0.0687400	−	0.256541i	0.923001	−	0.384797i	$-0.125729\pi$
$227$	−1.03567	−	3.86518i	−0.0687400	−	0.256541i	−0.991741	+	0.128256i	$0.959062\pi$
$228$	3.74680	−	1.00395i	0.248138	−	0.0664883i
$229$	13.2463	−	13.2463i	0.875341	−	0.875341i	−0.117708	−	0.993048i	$-0.537555\pi$
$229$	13.2463	−	13.2463i	0.875341	−	0.875341i	0.993048	+	0.117708i	$0.0375545\pi$
$230$	−5.19520	−	2.99945i	−0.342561	−	0.197778i
$231$	0.103072	+	0.923179i	0.00678166	+	0.0607407i
$232$	−14.5869	−	3.90855i	−0.957677	−	0.256609i
$233$	18.6734			1.22334			0.611669	−	0.791114i	$-0.290498\pi$
$233$	18.6734			1.22334			0.611669	+	0.791114i	$0.290498\pi$
$234$	0.429299	+	9.11245i	0.0280641	+	0.595700i
$235$	3.73127			0.243401
$236$	1.73805	−	6.48648i	0.113137	−	0.422234i
$237$	8.19099	−	4.72907i	0.532062	−	0.307186i
$238$	0.0662180	−	0.114693i	0.00429228	−	0.00743444i
$239$	6.02314	−	6.02314i	0.389604	−	0.389604i	−0.484942	−	0.874546i	$-0.661159\pi$
$239$	6.02314	−	6.02314i	0.389604	−	0.389604i	0.874546	+	0.484942i	$0.161159\pi$
$240$	6.71838	−	1.80018i	0.433669	−	0.116201i
$241$	−13.9338	+	3.73354i	−0.897553	+	0.240499i	−0.677965	−	0.735094i	$-0.737138\pi$
$241$	−13.9338	+	3.73354i	−0.897553	+	0.240499i	−0.219588	+	0.975593i	$0.570471\pi$
$242$	1.09689	−	27.8099i	0.0705108	−	1.78769i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−15.4151	−	26.6997i	−0.986848	−	1.70927i
$245$	7.07675	+	1.89621i	0.452117	+	0.121144i
$246$			30.0575i			1.91640i
$247$	2.82345	+	1.45746i	0.179652	+	0.0927359i
$248$			55.5415i			3.52689i
$249$	−0.0703468	−	0.0188494i	−0.00445804	−	0.00119453i
$250$	20.5947	−	11.8904i	1.30252	−	0.752012i
$251$	−20.2960	−	11.7179i	−1.28107	−	0.739629i	−0.304029	−	0.952663i	$-0.598332\pi$
$251$	−20.2960	−	11.7179i	−1.28107	−	0.739629i	−0.977045	+	0.213034i	$0.931665\pi$
$252$	0.871721	−	0.871721i	0.0549133	−	0.0549133i
$253$	7.34501	+	1.11468i	0.461777	+	0.0700792i
$254$	−3.45292	−	12.8865i	−0.216656	−	0.808570i
$255$	−0.139879	−	0.139879i	−0.00875956	−	0.00875956i
$256$	15.3340	−	26.5592i	0.958372	−	1.65995i
$257$	22.2621	−	12.8530i	1.38867	−	0.801750i	0.395506	−	0.918463i	$-0.370569\pi$
$257$	22.2621	−	12.8530i	1.38867	−	0.801750i	0.993166	+	0.116713i	$0.0372359\pi$
$258$	4.92999	+	1.32099i	0.306927	+	0.0822410i
$259$	−1.33868			−0.0831818
$260$	14.9271	+	7.70534i	0.925738	+	0.477865i
$261$			2.48524i			0.153833i
$262$	−12.3575	+	46.1188i	−0.763448	+	2.84923i
$263$	−19.9874	+	11.5397i	−1.23248	+	0.711571i	−0.967546	−	0.252697i	$-0.918682\pi$
$263$	−19.9874	+	11.5397i	−1.23248	+	0.711571i	−0.264931	+	0.964267i	$0.585349\pi$
$264$	−16.2274	+	11.9510i	−0.998727	+	0.735536i
$265$	7.61565	+	7.61565i	0.467826	+	0.467826i
$266$	−0.161631	−	0.603216i	−0.00991024	−	0.0369855i
$267$	3.46100	+	12.9166i	0.211810	+	0.790485i
$268$	1.84443	−	1.84443i	0.112666	−	0.112666i
$269$	10.6666	−	18.4751i	0.650355	−	1.12645i	−0.332682	−	0.943039i	$-0.607953\pi$
$269$	10.6666	−	18.4751i	0.650355	−	1.12645i	0.983037	−	0.183409i	$-0.0587132\pi$
$270$	−1.33906	−	2.31933i	−0.0814928	−	0.141150i
$271$	5.11203	−	19.0784i	0.310534	−	1.15893i	−0.617542	−	0.786538i	$-0.711872\pi$
$271$	5.11203	−	19.0784i	0.310534	−	1.15893i	0.928076	−	0.372390i	$-0.121462\pi$
$272$	1.22805			0.0744614
$273$	1.00872	−	0.0475220i	0.0610504	−	0.00287616i
$274$		−	24.9799i		−	1.50909i
$275$	−8.03272	+	10.0519i	−0.484391	+	0.606149i
$276$	−4.92973	−	8.53854i	−0.296735	−	0.513960i
$277$	−14.4632	+	25.0511i	−0.869012	+	1.50517i	−0.00600516	+	0.999982i	$0.501912\pi$
$277$	−14.4632	+	25.0511i	−0.869012	+	1.50517i	−0.863007	+	0.505192i	$0.831422\pi$
$278$	24.1766	+	24.1766i	1.45002	+	1.45002i
$279$	8.82900	−	2.36572i	0.528579	−	0.141632i
$280$	−0.466243	−	1.74004i	−0.0278633	−	0.103987i
$281$	7.57512	+	7.57512i	0.451894	+	0.451894i	0.895983	−	0.444089i	$-0.146473\pi$
$281$	7.57512	+	7.57512i	0.451894	+	0.451894i	−0.444089	+	0.895983i	$0.646473\pi$
$282$	7.72407	+	4.45949i	0.459962	+	0.265559i
$283$	−6.39383	−	11.0744i	−0.380074	−	0.658307i	0.610999	−	0.791632i	$-0.290768\pi$
$283$	−6.39383	−	11.0744i	−0.380074	−	0.658307i	−0.991072	+	0.133325i	$0.957435\pi$
$284$	10.8572	+	2.90919i	0.644258	+	0.172628i
$285$	−0.932803			−0.0552545
$286$	−30.0941	−	3.12695i	−1.77950	−	0.184900i
$287$	3.32727			0.196403
$288$	4.32037	+	1.15764i	0.254580	+	0.0682145i
$289$	8.48254	+	14.6922i	0.498973	+	0.864246i
$290$	5.76409	+	3.32790i	0.338479	+	0.195421i
$291$	0.234548	+	0.234548i	0.0137494	+	0.0137494i
$292$	−6.22401	−	23.2283i	−0.364232	−	1.35933i
$293$	9.11447	−	2.44222i	0.532473	−	0.142676i	0.0174430	−	0.999848i	$-0.494447\pi$
$293$	9.11447	−	2.44222i	0.532473	−	0.142676i	0.515030	+	0.857172i	$0.327781\pi$
$294$	12.3832	+	12.3832i	0.722204	+	0.722204i
$295$	−0.807437	+	1.39852i	−0.0470108	+	0.0814251i
$296$	−14.5217	−	25.1524i	−0.844058	−	1.46195i
$297$	2.59095	+	2.07050i	0.150342	+	0.120143i
$298$			3.58709i			0.207795i
$299$	1.72087	−	7.89082i	0.0995205	−	0.456338i
$300$	17.0765			0.985915
$301$	0.146229	−	0.545733i	0.00842849	−	0.0314555i
$302$	−20.1906	−	34.9712i	−1.16184	−	2.01237i
$303$	−5.60420	+	9.70675i	−0.321953	+	0.557638i
$304$	4.09471	−	4.09471i	0.234848	−	0.234848i
$305$	1.91887	+	7.16131i	0.109874	+	0.410055i
$306$	−0.122383	−	0.456741i	−0.00699619	−	0.0261101i
$307$	−17.6330	−	17.6330i	−1.00637	−	1.00637i	−0.999980	−	0.00638873i	$-0.997966\pi$
$307$	−17.6330	−	17.6330i	−1.00637	−	1.00637i	−0.00638873	−	0.999980i	$-0.502034\pi$
$308$	2.42465	+	3.29224i	0.138157	+	0.187593i
$309$	4.92758	−	2.84494i	0.280320	−	0.161843i
$310$	6.33571	−	23.6452i	0.359844	−	1.34296i
$311$			5.23394i			0.296789i	0.988928	+	0.148395i	$0.0474106\pi$
$311$			5.23394i			0.296789i	−0.988928	+	0.148395i	$0.952589\pi$
$312$	11.8352	+	18.4372i	0.670038	+	1.04380i
$313$	−19.1637			−1.08320			−0.541599	−	0.840637i	$-0.682181\pi$
$313$	−19.1637			−1.08320			−0.541599	+	0.840637i	$0.682181\pi$
$314$	−13.4952	−	3.61603i	−0.761579	−	0.204064i
$315$	−0.256742	+	0.148230i	−0.0144658	+	0.00835181i
$316$	20.8156	−	36.0536i	1.17097	−	2.02818i
$317$	−12.9300	−	12.9300i	−0.726223	−	0.726223i	0.243642	−	0.969865i	$-0.421658\pi$
$317$	−12.9300	−	12.9300i	−0.726223	−	0.726223i	−0.969865	+	0.243642i	$0.921658\pi$
$318$	6.66311	+	24.8671i	0.373649	+	1.39448i
$319$	−8.14931	−	1.23674i	−0.456274	−	0.0692441i
$320$	−1.36619	+	1.36619i	−0.0763726	+	0.0763726i
$321$	13.0485	+	7.53358i	0.728299	+	0.420484i
$322$	−1.37466	+	0.793661i	−0.0766069	+	0.0442290i
$323$	−0.159085	−	0.0426267i	−0.00885172	−	0.00237181i
$324$		−	4.40162i		−	0.244535i
$325$	10.3456	+	9.41466i	0.573870	+	0.522231i
$326$			10.7100i			0.593170i
$327$	−2.40128	−	0.643422i	−0.132791	−	0.0355813i
$328$	36.0934	+	62.5156i	1.99293	+	3.45185i
$329$	0.493651	−	0.855029i	0.0272159	−	0.0471393i
$330$	8.27162	−	3.23672i	0.455338	−	0.178176i
$331$	−19.3111	+	5.17440i	−1.06144	+	0.284411i	−0.746970	−	0.664858i	$-0.768492\pi$
$331$	−19.3111	+	5.17440i	−1.06144	+	0.284411i	−0.314466	+	0.949269i	$0.601825\pi$
$332$	−0.309640	+	0.0829678i	−0.0169937	+	0.00455345i
$333$	−3.37974	+	3.37974i	−0.185209	+	0.185209i
$334$	29.9267	−	51.8346i	1.63752	−	2.83626i
$335$	−0.543227	+	0.313632i	−0.0296796	+	0.0171356i
$336$	0.476333	−	1.77770i	0.0259861	−	0.0969813i
$337$	−34.4099			−1.87443			−0.937214	−	0.348755i	$-0.886605\pi$
$337$	−34.4099			−1.87443			−0.937214	+	0.348755i	$0.886605\pi$
$338$	−5.48841	+	32.4307i	−0.298530	+	1.76400i
$339$	−16.3308			−0.886969
$340$	−0.841055	−	0.225360i	−0.0456126	−	0.0122219i
$341$	3.36380	+	30.1283i	0.182160	+	1.63154i
$342$	−1.93099	−	1.11486i	−0.104416	−	0.0602845i
$343$	2.75710	−	2.75710i	0.148869	−	0.148869i
$344$	11.8400	−	3.17251i	0.638368	−	0.171050i
$345$	0.613653	+	2.29018i	0.0330380	+	0.123299i
$346$	−19.7795	+	19.7795i	−1.06335	+	1.06335i
$347$	4.21522	+	2.43366i	0.226285	+	0.130646i	0.608857	−	0.793280i	$-0.291628\pi$
$347$	4.21522	+	2.43366i	0.226285	+	0.130646i	−0.382572	+	0.923926i	$0.624962\pi$
$348$	5.46956	+	9.47355i	0.293199	+	0.507835i
$349$	−6.78712	+	25.3299i	−0.363306	+	1.35588i	0.506396	+	0.862301i	$0.330977\pi$
$349$	−6.78712	+	25.3299i	−0.363306	+	1.35588i	−0.869702	+	0.493576i	$0.835689\pi$
$350$		−	2.74924i		−	0.146953i
$351$	2.42671	−	2.66666i	0.129528	−	0.142336i
$352$	−5.94594	+	13.5907i	−0.316920	+	0.724389i
$353$	4.90537	−	18.3071i	0.261086	−	0.974388i	−0.703516	−	0.710679i	$-0.748388\pi$
$353$	4.90537	−	18.3071i	0.261086	−	0.974388i	0.964602	−	0.263708i	$-0.0849457\pi$
$354$	−3.34294	+	1.93005i	−0.177675	+	0.102581i
$355$	−2.34088	−	1.35151i	−0.124241	−	0.0717306i
$356$	41.6201	+	41.6201i	2.20586	+	2.20586i
$357$	−0.0505597	+	0.0135474i	−0.00267590	+	0.000717007i
$358$	−11.6413	+	3.11928i	−0.615263	+	0.164859i
$359$	−8.76688	−	8.76688i	−0.462698	−	0.462698i	0.436841	−	0.899539i	$-0.356097\pi$
$359$	−8.76688	−	8.76688i	−0.462698	−	0.462698i	−0.899539	+	0.436841i	$0.856097\pi$
$360$	−5.57015	−	3.21593i	−0.293573	−	0.169494i
$361$	15.7819	−	9.11169i	0.830627	−	0.479563i
$362$	12.6280	−	47.1282i	0.663711	−	2.47700i
$363$	−8.07868	+	7.46558i	−0.424021	+	0.391841i
$364$	3.74057	−	2.40115i	0.196059	−	0.125854i
$365$			5.78292i			0.302692i
$366$	−4.58674	+	17.1179i	−0.239753	+	0.894769i
$367$	−14.1338	−	24.4805i	−0.737779	−	1.27787i	−0.953493	−	0.301414i	$-0.902541\pi$
$367$	−14.1338	−	24.4805i	−0.737779	−	1.27787i	0.215714	−	0.976457i	$-0.430792\pi$
$368$	−12.7469	−	7.35944i	−0.664479	−	0.383637i
$369$	8.40027	−	8.40027i	0.437301	−	0.437301i
$370$	3.31303	+	12.3644i	0.172236	+	0.642795i
$371$	2.75270	−	0.737584i	0.142913	−	0.0382935i
$372$	28.4489	−	28.4489i	1.47501	−	1.47501i
$373$	20.9884	+	12.1177i	1.08674	+	0.627429i	0.932706	−	0.360637i	$-0.117441\pi$
$373$	20.9884	+	12.1177i	1.08674	+	0.627429i	0.154033	+	0.988066i	$0.450774\pi$
$374$	1.55859	−	0.174016i	0.0805929	−	0.00899813i
$375$	−9.07870	−	2.43263i	−0.468822	−	0.125620i
$376$	21.4200			1.10465
$377$	−1.90931	+	8.75490i	−0.0983346	+	0.450900i
$378$	−0.708639			−0.0364484
$379$	−0.169900	+	0.634075i	−0.00872717	+	0.0325703i	−0.970152	−	0.242497i	$-0.922034\pi$
$379$	−0.169900	+	0.634075i	−0.00872717	+	0.0325703i	0.961425	+	0.275067i	$0.0887002\pi$
$380$	−3.55577	+	2.05292i	−0.182407	+	0.105313i
$381$	−2.63643	+	4.56642i	−0.135068	+	0.233945i
$382$	26.1251	−	26.1251i	1.33668	−	1.33668i
$383$	36.0341	−	9.65531i	1.84126	−	0.493363i	0.842299	−	0.539010i	$-0.181202\pi$
$383$	36.0341	−	9.65531i	1.84126	−	0.493363i	0.998958	+	0.0456472i	$0.0145350\pi$
$384$	−13.1017	+	3.51059i	−0.668594	+	0.179149i
$385$	−0.358295	−	0.915641i	−0.0182604	−	0.0466654i
$386$	20.7601	−	35.9576i	1.05666	−	1.83019i
$387$	−1.00862	−	1.74698i	−0.0512709	−	0.0888039i
$388$	1.41027	+	0.377881i	0.0715957	+	0.0191840i
$389$		−	21.7449i		−	1.10251i	−0.834337	−	0.551254i	$-0.814150\pi$
$389$		−	21.7449i		−	1.10251i	0.834337	−	0.551254i	$-0.185850\pi$
$390$	−2.93535	−	9.19916i	−0.148637	−	0.465818i
$391$			0.418622i			0.0211706i
$392$	40.6254	+	10.8855i	2.05189	+	0.549803i
$393$	16.3425	−	9.43537i	0.824372	−	0.475951i
$394$	9.18468	+	5.30278i	0.462717	+	0.267150i
$395$	−7.07908	+	7.07908i	−0.356187	+	0.356187i
$396$	14.4333	+	2.19039i	0.725299	+	0.110071i
$397$	8.11490	+	30.2852i	0.407275	+	1.51997i	0.799821	+	0.600239i	$0.204928\pi$
$397$	8.11490	+	30.2852i	0.407275	+	1.51997i	−0.392546	+	0.919732i	$0.628406\pi$
$398$	−22.3123	−	22.3123i	−1.11841	−	1.11841i
$399$	−0.123411	+	0.213754i	−0.00617827	+	0.0107011i
$400$	22.0776	−	12.7465i	1.10388	−	0.637325i
$401$	−26.2470	−	7.03286i	−1.31071	−	0.351204i	−0.465221	−	0.885194i	$-0.654025\pi$
$401$	−26.2470	−	7.03286i	−1.31071	−	0.351204i	−0.845491	+	0.533990i	$0.820692\pi$
$402$	−1.49937			−0.0747819
$403$	32.9199	−	1.55089i	1.63986	−	0.0772556i
$404$			49.3351i			2.45451i
$405$	−0.273957	+	1.02242i	−0.0136130	+	0.0508045i
$406$	1.52519	−	0.880570i	0.0756940	−	0.0437020i
$407$	−9.40056	−	12.7643i	−0.465969	−	0.632703i
$408$	−0.803001	−	0.803001i	−0.0397545	−	0.0397545i
$409$	6.00431	+	22.4084i	0.296894	+	1.10802i	0.939702	+	0.341996i	$0.111103\pi$
$409$	6.00431	+	22.4084i	0.296894	+	1.10802i	−0.642808	+	0.766028i	$0.722231\pi$
$410$	−8.23447	−	30.7315i	−0.406672	−	1.51772i
$411$	−6.98122	+	6.98122i	−0.344358	+	0.344358i
$412$	12.5223	−	21.6893i	0.616931	−	1.06856i
$413$	0.213650	+	0.370052i	0.0105130	+	0.0182091i
$414$	−1.46684	+	5.47431i	−0.0720911	+	0.269048i
$415$	0.0770880			0.00378410
$416$	14.3302	+	7.39723i	0.702596	+	0.362679i
$417$		−	13.5134i		−	0.661754i
$418$	4.61663	−	5.77707i	0.225807	−	0.282566i
$419$	−14.6051	−	25.2968i	−0.713507	−	1.23583i	−0.963533	−	0.267591i	$-0.913772\pi$
$419$	−14.6051	−	25.2968i	−0.713507	−	1.23583i	0.250026	−	0.968239i	$-0.419561\pi$
$420$	−0.652453	+	1.13008i	−0.0318364	+	0.0551423i
$421$	−0.263632	−	0.263632i	−0.0128487	−	0.0128487i	0.700653	−	0.713502i	$-0.252892\pi$
$421$	−0.263632	−	0.263632i	−0.0128487	−	0.0128487i	−0.713502	+	0.700653i	$0.752892\pi$
$422$	−57.5743	+	15.4270i	−2.80267	+	0.750974i
$423$	−0.912361	−	3.40498i	−0.0443605	−	0.165556i
$424$	43.7190	+	43.7190i	2.12318	+	2.12318i
$425$	−0.627912	−	0.362525i	−0.0304582	−	0.0175851i
$426$	−3.23056	−	5.59549i	−0.156521	−	0.271102i
$427$	1.89490	+	0.507737i	0.0917006	+	0.0245711i
$428$	66.3200			3.20570
$429$	7.53659	+	9.28439i	0.363870	+	0.448254i
$430$	−5.40242			−0.260528
$431$	−29.6837	−	7.95371i	−1.42981	−	0.383117i	−0.540858	−	0.841114i	$-0.681900\pi$
$431$	−29.6837	−	7.95371i	−1.42981	−	0.383117i	−0.888954	+	0.457997i	$0.848567\pi$
$432$	−3.28552	−	5.69069i	−0.158075	−	0.273793i
$433$	−18.3422	−	10.5899i	−0.881472	−	0.508918i	−0.0103286	−	0.999947i	$-0.503288\pi$
$433$	−18.3422	−	10.5899i	−0.881472	−	0.508918i	−0.871144	+	0.491028i	$0.836621\pi$
$434$	−4.58013	−	4.58013i	−0.219853	−	0.219853i
$435$	−0.680850	−	2.54097i	−0.0326443	−	0.121830i
$436$	−10.5696	+	2.83210i	−0.506190	+	0.135633i
$437$	1.39582	+	1.39582i	0.0667711	+	0.0667711i
$438$	−6.91156	+	11.9712i	−0.330247	+	0.572005i
$439$	10.2325	+	17.7231i	0.488369	+	0.845879i	0.999910	−	0.0133791i	$-0.00425884\pi$
$439$	10.2325	+	17.7231i	0.488369	+	0.845879i	−0.511542	+	0.859258i	$0.670926\pi$
$440$	13.3172	−	16.6646i	0.634871	−	0.794454i
$441$		−	6.92156i		−	0.329598i
$442$	−0.0802307	−	1.70301i	−0.00381619	−	0.0810038i
$443$	−1.83504			−0.0871854			−0.0435927	−	0.999049i	$-0.513880\pi$
$443$	−1.83504			−0.0871854			−0.0435927	+	0.999049i	$0.513880\pi$
$444$	−5.44512	+	20.3215i	−0.258414	+	0.964414i
$445$	−7.07721	−	12.2581i	−0.335492	−	0.581089i
$446$	9.77768	−	16.9354i	0.462987	−	0.801916i
$447$	1.00250	−	1.00250i	0.0474165	−	0.0474165i
$448$	0.132317	+	0.493815i	0.00625141	+	0.0233306i
$449$	−6.31978	−	23.5857i	−0.298249	−	1.11308i	−0.938603	−	0.345000i	$-0.887879\pi$
$449$	−6.31978	−	23.5857i	−0.298249	−	1.11308i	0.640354	−	0.768080i	$-0.278788\pi$
$450$	−6.94092	−	6.94092i	−0.327198	−	0.327198i
$451$	23.3649	+	31.7254i	1.10021	+	1.49389i
$452$	−62.2518	+	35.9411i	−2.92808	+	1.69053i
$453$	−4.13077	+	15.4162i	−0.194081	+	0.724318i
$454$			10.1244i			0.475164i
$455$	−1.01832	+	0.324933i	−0.0477394	+	0.0152331i
$456$	−5.35493			−0.250768
$457$	−15.4421	−	4.13770i	−0.722352	−	0.193554i	−0.121131	−	0.992637i	$-0.538652\pi$
$457$	−15.4421	−	4.13770i	−0.722352	−	0.193554i	−0.601221	+	0.799083i	$0.705319\pi$
$458$	−41.0474	+	23.6987i	−1.91802	+	1.10737i
$459$	−0.0934440	+	0.161850i	−0.00436159	+	0.00755450i
$460$	7.37946	+	7.37946i	0.344069	+	0.344069i
$461$	9.07241	+	33.8587i	0.422544	+	1.57696i	0.769228	+	0.638975i	$0.220641\pi$
$461$	9.07241	+	33.8587i	0.422544	+	1.57696i	−0.346683	+	0.937982i	$0.612692\pi$
$462$	0.352642	−	2.32368i	0.0164064	−	0.108107i
$463$	−8.93284	+	8.93284i	−0.415144	+	0.415144i	−0.883526	−	0.468382i	$-0.844837\pi$
$463$	−8.93284	+	8.93284i	−0.415144	+	0.415144i	0.468382	+	0.883526i	$0.344837\pi$
$464$	14.1428	+	8.16532i	0.656561	+	0.379066i
$465$	−8.37886	+	4.83754i	−0.388560	+	0.224335i
$466$	−45.6366	−	12.2283i	−2.11407	−	0.566465i
$467$		−	12.9587i		−	0.599658i	−0.953993	−	0.299829i	$-0.903070\pi$
$467$		−	12.9587i		−	0.599658i	0.953993	−	0.299829i	$-0.0969296\pi$
$468$	3.38159	−	15.5058i	0.156314	−	0.716757i
$469$			0.165976i			0.00766404i
$470$	−9.11897	−	2.44342i	−0.420627	−	0.112707i
$471$	2.76096	+	4.78213i	0.127219	+	0.220349i
$472$	−4.63524	+	8.02848i	−0.213354	+	0.369541i
$473$	6.23040	−	2.43799i	0.286474	−	0.112099i
$474$	−23.1150	+	6.19365i	−1.06171	+	0.284484i
$475$	−3.30244	+	0.884886i	−0.151526	+	0.0406013i
$476$	−0.162914	+	0.162914i	−0.00746716	+	0.00746716i
$477$	5.08752	−	8.81183i	0.232941	−	0.403466i
$478$	−18.6644	+	10.7759i	−0.853689	+	0.492877i
$479$	−5.46407	+	20.3922i	−0.249660	+	0.931742i	0.721324	+	0.692597i	$0.243534\pi$
$479$	−5.46407	+	20.3922i	−0.249660	+	0.931742i	−0.970984	+	0.239145i	$0.923133\pi$
$480$	−4.73438			−0.216094
$481$	−14.5025	+	9.30946i	−0.661257	+	0.424475i
$482$	36.4981			1.66244
$483$	0.605988	+	0.162374i	0.0275734	+	0.00738827i
$484$	−14.3649	+	46.2378i	−0.652952	+	2.10172i
$485$	−0.304063	−	0.175551i	−0.0138068	−	0.00797134i
$486$	−1.78908	+	1.78908i	−0.0811544	+	0.0811544i
$487$	27.0709	−	7.25362i	1.22670	−	0.328693i	0.413405	−	0.910547i	$-0.364339\pi$
$487$	27.0709	−	7.25362i	1.22670	−	0.328693i	0.813293	+	0.581855i	$0.197673\pi$
$488$	11.0156	+	41.1108i	0.498653	+	1.86100i
$489$	2.99315	−	2.99315i	0.135355	−	0.135355i
$490$	−16.0534	−	9.26841i	−0.725217	−	0.418704i
$491$	−0.572806	−	0.992130i	−0.0258504	−	0.0447742i	0.852811	−	0.522220i	$-0.174896\pi$
$491$	−0.572806	−	0.992130i	−0.0258504	−	0.0447742i	−0.878661	+	0.477446i	$0.841563\pi$
$492$	13.5337	−	50.5085i	0.610147	−	2.27710i
$493$		−	0.464462i		−	0.0209183i
$494$	−5.94589	−	5.41086i	−0.267518	−	0.243446i
$495$	−3.21627	−	1.40712i	−0.144561	−	0.0632452i
$496$	15.5453	−	58.0157i	0.698003	−	2.60498i
$497$	−0.619403	+	0.357612i	−0.0277840	+	0.0160411i
$498$	0.159579	+	0.0921330i	0.00715091	+	0.00412858i
$499$	−21.9819	−	21.9819i	−0.984046	−	0.984046i	0.0158290	−	0.999875i	$-0.494961\pi$
$499$	−21.9819	−	21.9819i	−0.984046	−	0.984046i	−0.999875	+	0.0158290i	$0.994961\pi$
$500$	−39.9610	+	10.7075i	−1.78711	+	0.478855i
$501$	−22.8501	+	6.12266i	−1.02087	+	0.273540i
$502$	41.9286	+	41.9286i	1.87137	+	1.87137i
$503$	−25.6533	−	14.8109i	−1.14382	−	0.660387i	−0.196449	−	0.980514i	$-0.562941\pi$
$503$	−25.6533	−	14.8109i	−1.14382	−	0.660387i	−0.947375	+	0.320127i	$0.896274\pi$
$504$	−1.47387	+	0.850942i	−0.0656516	+	0.0379040i
$505$	3.07062	−	11.4597i	0.136641	−	0.509950i
$506$	−17.2207	−	7.53407i	−0.765555	−	0.334930i
$507$	10.5974	−	7.52965i	0.470646	−	0.334403i
$508$			23.2091i			1.02974i
$509$	−2.18354	+	8.14910i	−0.0967839	+	0.361202i	−0.997284	−	0.0736536i	$-0.976534\pi$
$509$	−2.18354	+	8.14910i	−0.0967839	+	0.361202i	0.900500	+	0.434856i	$0.143201\pi$
$510$	0.250255	+	0.433454i	0.0110815	+	0.0191937i
$511$	1.32517	+	0.765087i	0.0586220	+	0.0338455i
$512$	−35.6852	+	35.6852i	−1.57708	+	1.57708i
$513$	0.228087	+	0.851231i	0.0100703	+	0.0375828i
$514$	−62.8238	+	16.8336i	−2.77104	+	0.742498i
$515$	−4.25867	+	4.25867i	−0.187659	+	0.187659i
$516$	−7.68954	−	4.43956i	−0.338513	−	0.195441i
$517$	11.6192	−	1.29728i	0.511012	−	0.0570541i
$518$	3.27165	+	0.876636i	0.143748	+	0.0385172i
$519$	11.0557			0.485290
$520$	−17.1516	−	15.6082i	−0.752147	−	0.684466i
$521$	−40.3986			−1.76989			−0.884947	−	0.465692i	$-0.845805\pi$
$521$	−40.3986			−1.76989			−0.884947	+	0.465692i	$0.845805\pi$
$522$	1.62746	−	6.07376i	0.0712320	−	0.265841i
$523$	−1.46121	+	0.843630i	−0.0638942	+	0.0368893i	−0.531607	−	0.846991i	$-0.678412\pi$
$523$	−1.46121	+	0.843630i	−0.0638942	+	0.0368893i	0.467713	+	0.883881i	$0.345078\pi$
$524$	41.5309	−	71.9337i	1.81429	−	3.14244i
$525$	−0.768337	+	0.768337i	−0.0335330	+	0.0335330i
$526$	56.4046	−	15.1136i	2.45936	−	0.658983i
$527$	−1.65003	+	0.442125i	−0.0718766	+	0.0192593i
$528$	20.2952	−	7.94161i	0.883235	−	0.345614i
$529$	−8.99129	+	15.5734i	−0.390926	+	0.677103i
$530$	−13.6250	−	23.5992i	−0.591833	−	1.02508i
$531$	1.47366	+	0.394865i	0.0639512	+	0.0171357i
$532$			1.08642i			0.0471021i
$533$	36.0456	−	23.1385i	1.56131	−	1.00224i
$534$		−	33.8338i		−	1.46413i
$535$	−15.4050	−	4.12776i	−0.666016	−	0.178459i
$536$	−3.11849	+	1.80046i	−0.134698	+	0.0777681i
$537$	4.12519	+	2.38168i	0.178015	+	0.102777i
$538$	−38.1669	+	38.1669i	−1.64549	+	1.64549i
$539$	22.6963	+	3.44439i	0.977600	+	0.148360i
$540$	1.20586	+	4.50032i	0.0518918	+	0.193663i
$541$	14.9548	+	14.9548i	0.642958	+	0.642958i	0.951282	−	0.308323i	$-0.0997679\pi$
$541$	14.9548	+	14.9548i	0.642958	+	0.642958i	−0.308323	+	0.951282i	$0.599768\pi$
$542$	−24.9869	+	43.2786i	−1.07328	+	1.85897i
$543$	−16.7002	+	9.64189i	−0.716676	+	0.413773i
$544$	−0.807424	−	0.216349i	−0.0346180	−	0.00927587i
$545$	2.63140			0.112717
$546$	−2.49636	−	0.544418i	−0.106834	−	0.0232990i
$547$		−	34.2479i		−	1.46434i	−0.681124	−	0.732168i	$-0.738509\pi$
$547$		−	34.2479i		−	1.46434i	0.681124	−	0.732168i	$-0.261491\pi$
$548$	−11.2475	+	41.9762i	−0.480469	+	1.79313i
$549$	6.06587	−	3.50213i	0.258885	−	0.149467i
$550$	26.2139	−	19.3058i	1.11776	−	0.823202i
$551$	−1.54867	−	1.54867i	−0.0659754	−	0.0659754i
$552$	3.52279	+	13.1472i	0.149940	+	0.559583i
$553$	0.685617	+	2.55876i	0.0291554	+	0.108809i
$554$	51.7519	−	51.7519i	2.19873	−	2.19873i
$555$	2.52962	−	4.38142i	0.107376	−	0.185981i
$556$	−29.7405	−	51.5120i	−1.26128	−	2.18460i
$557$	3.79872	−	14.1770i	0.160957	−	0.600700i	−0.837564	−	0.546339i	$-0.816021\pi$
$557$	3.79872	−	14.1770i	0.160957	−	0.600700i	0.998521	−	0.0543610i	$-0.0173122\pi$
$558$	−23.1267			−0.979030
$559$	−2.21098	−	6.92905i	−0.0935145	−	0.293068i
$560$			1.94805i			0.0823202i
$561$	−0.484217	−	0.386952i	−0.0204437	−	0.0163371i
$562$	−13.5525	−	23.4736i	−0.571678	−	0.990175i
$563$	13.8604	−	24.0070i	0.584147	−	1.01177i	−0.410834	−	0.911710i	$-0.634762\pi$
$563$	13.8604	−	24.0070i	0.584147	−	1.01177i	0.994981	−	0.100063i	$-0.0319043\pi$
$564$	−10.9716	−	10.9716i	−0.461986	−	0.461986i
$565$	16.6970	−	4.47395i	0.702448	−	0.188220i
$566$	8.37399	+	31.2521i	0.351985	+	1.31363i
$567$	0.198045	+	0.198045i	0.00831713	+	0.00831713i
$568$	−13.4383	−	7.75858i	−0.563857	−	0.325543i
$569$	1.50257	+	2.60253i	0.0629911	+	0.109104i	0.895801	−	0.444455i	$-0.146603\pi$
$569$	1.50257	+	2.60253i	0.0629911	+	0.109104i	−0.832810	+	0.553559i	$0.813269\pi$
$570$	2.27971	+	0.610846i	0.0954864	+	0.0255855i
$571$	27.1145			1.13471			0.567354	−	0.823474i	$-0.307967\pi$
$571$	27.1145			1.13471			0.567354	+	0.823474i	$0.307967\pi$
$572$	49.1620	+	18.8047i	2.05557	+	0.786264i
$573$	−14.6025			−0.610029
$574$	−8.13162	−	2.17886i	−0.339407	−	0.0909438i
$575$	4.34508	+	7.52589i	0.181202	+	0.313851i
$576$	1.58078	+	0.912664i	0.0658659	+	0.0380277i
$577$	15.0421	+	15.0421i	0.626211	+	0.626211i	0.947113	−	0.320902i	$-0.103986\pi$
$577$	15.0421	+	15.0421i	0.626211	+	0.626211i	−0.320902	+	0.947113i	$0.603986\pi$
$578$	−11.1096	−	41.4615i	−0.462097	−	1.72457i
$579$	−15.8511	+	4.24728i	−0.658748	+	0.176511i
$580$	−8.18754	−	8.18754i	−0.339969	−	0.339969i
$581$	0.0101988	−	0.0176649i	0.000423119	−	0.000732863i
$582$	−0.419625	−	0.726812i	−0.0173940	−	0.0301273i
$583$	26.3630	+	21.0674i	1.09184	+	0.872524i
$584$			33.1979i			1.37374i
$585$	−1.75057	+	3.39127i	−0.0723771	+	0.140212i
$586$	−23.8744			−0.986243
$587$	5.36505	−	20.0226i	0.221439	−	0.826422i	−0.762361	−	0.647152i	$-0.775960\pi$
$587$	5.36505	−	20.0226i	0.221439	−	0.826422i	0.983800	−	0.179270i	$-0.0573735\pi$
$588$	−15.2330	−	26.3844i	−0.628200	−	1.08807i
$589$	−4.02756	+	6.97593i	−0.165953	+	0.287438i
$590$	2.88914	−	2.88914i	0.118944	−	0.118944i
$591$	−1.08489	−	4.04885i	−0.0446263	−	0.166548i
$592$	8.12884	+	30.3372i	0.334093	+	1.24685i
$593$	−5.93322	−	5.93322i	−0.243648	−	0.243648i	0.574709	−	0.818358i	$-0.305115\pi$
$593$	−5.93322	−	5.93322i	−0.243648	−	0.243648i	−0.818358	+	0.574709i	$0.805115\pi$
$594$	−4.97623	−	6.75684i	−0.204177	−	0.277237i
$595$	0.0479820	−	0.0277024i	0.00196707	−	0.00113569i
$596$	1.61513	−	6.02774i	0.0661582	−	0.246906i
$597$			12.4714i			0.510419i
$598$	−9.37299	+	18.1577i	−0.383290	+	0.742524i
$599$	23.2576			0.950280			0.475140	−	0.879910i	$-0.342397\pi$
$599$	23.2576			0.950280			0.475140	+	0.879910i	$0.342397\pi$
$600$	−22.7709	−	6.10145i	−0.929619	−	0.249091i
$601$	25.8836	−	14.9439i	1.05581	−	0.609574i	0.131542	−	0.991311i	$-0.458007\pi$
$601$	25.8836	−	14.9439i	1.05581	−	0.609574i	0.924271	+	0.381737i	$0.124674\pi$
$602$	−0.714746	+	1.23798i	−0.0291309	+	0.0504561i
$603$	0.419034	+	0.419034i	0.0170644	+	0.0170644i
$604$	18.1821	+	67.8565i	0.739819	+	2.76104i
$605$	6.21457	−	9.84618i	0.252658	−	0.400304i
$606$	20.0527	−	20.0527i	0.814586	−	0.814586i
$607$	−5.04566	−	2.91311i	−0.204797	−	0.118240i	0.394094	−	0.919070i	$-0.371058\pi$
$607$	−5.04566	−	2.91311i	−0.204797	−	0.118240i	−0.598891	+	0.800830i	$0.704392\pi$
$608$	−3.41359	+	1.97084i	−0.138439	+	0.0799280i
$609$	−0.672346	−	0.180155i	−0.0272448	−	0.00730023i
$610$		−	18.7583i		−	0.759502i
$611$	−0.598115	−	12.6958i	−0.0241972	−	0.513618i
$612$			0.822610i			0.0332520i
$613$	−21.5385	−	5.77123i	−0.869933	−	0.233098i	−0.203874	−	0.978997i	$-0.565353\pi$
$613$	−21.5385	−	5.77123i	−0.869933	−	0.233098i	−0.666059	+	0.745899i	$0.732020\pi$
$614$	31.5469	+	54.6408i	1.27313	+	2.20512i
$615$	−6.28730	+	10.8899i	−0.253529	+	0.439124i
$616$	−2.05686	−	5.25641i	−0.0828731	−	0.211787i
$617$	3.03997	−	0.814558i	0.122385	−	0.0327929i	−0.197107	−	0.980382i	$-0.563155\pi$
$617$	3.03997	−	0.814558i	0.122385	−	0.0327929i	0.319491	+	0.947589i	$0.396488\pi$
$618$	−13.9057	+	3.72601i	−0.559368	+	0.149882i
$619$	6.76152	−	6.76152i	0.271769	−	0.271769i	−0.558043	−	0.829812i	$-0.688448\pi$
$619$	6.76152	−	6.76152i	0.271769	−	0.271769i	0.829812	+	0.558043i	$0.188448\pi$
$620$	−21.2930	+	36.8806i	−0.855148	+	1.48116i
$621$	1.93986	−	1.11998i	0.0778440	−	0.0449433i
$622$	3.42744	−	12.7914i	0.137428	−	0.512888i
$623$	−3.74529			−0.150052
$624$	−7.20215	−	22.5710i	−0.288317	−	0.903564i
$625$	−9.44931			−0.377973
$626$	46.8349	+	12.5494i	1.87190	+	0.501573i
$627$	−2.90476	+	0.324314i	−0.116005	+	0.0129519i
$628$	21.0491	+	12.1527i	0.839952	+	0.484947i
$629$	0.631632	−	0.631632i	0.0251848	−	0.0251848i
$630$	0.724528	−	0.194137i	0.0288659	−	0.00773459i
$631$	6.90782	+	25.7803i	0.274996	+	1.02630i	0.955844	+	0.293874i	$0.0949447\pi$
$631$	6.90782	+	25.7803i	0.274996	+	1.02630i	−0.680848	+	0.732425i	$0.738389\pi$
$632$	−40.6388	+	40.6388i	−1.61652	+	1.61652i
$633$	20.4019	+	11.7790i	0.810902	+	0.468175i
$634$	23.1329	+	40.0673i	0.918725	+	1.59128i
$635$	1.44453	−	5.39108i	0.0573246	−	0.213938i
$636$		−	44.7867i		−	1.77591i
$637$	5.31755	−	24.3829i	0.210689	−	0.966087i
$638$	19.1065	+	8.35908i	0.756433	+	0.330939i
$639$	−0.660935	+	2.46664i	−0.0261462	+	0.0975789i
$640$	12.4337	−	7.17861i	0.491486	−	0.283760i
$641$	20.0459	+	11.5735i	0.791765	+	0.457126i	0.840584	−	0.541682i	$-0.182212\pi$
$641$	20.0459	+	11.5735i	0.791765	+	0.457126i	−0.0488184	+	0.998808i	$0.515546\pi$
$642$	−26.9564	−	26.9564i	−1.06388	−	1.06388i
$643$	−38.3344	+	10.2717i	−1.51176	+	0.405075i	−0.917019	−	0.398843i	$-0.869412\pi$
$643$	−38.3344	+	10.2717i	−1.51176	+	0.405075i	−0.594740	+	0.803918i	$0.702745\pi$
$644$	2.66733	−	0.714709i	0.105108	−	0.0281635i
$645$	1.50983	+	1.50983i	0.0594495	+	0.0594495i
$646$	0.360878	+	0.208353i	0.0141986	+	0.00819755i
$647$	−23.0636	+	13.3158i	−0.906725	+	0.523498i	−0.879376	−	0.476128i	$-0.842040\pi$
$647$	−23.0636	+	13.3158i	−0.906725	+	0.523498i	−0.0273491	+	0.999626i	$0.508707\pi$
$648$	−1.57270	+	5.86940i	−0.0617815	+	0.230572i
$649$	−2.02813	+	4.63574i	−0.0796112	+	0.181969i
$650$	−19.1187	−	29.7836i	−0.749898	−	1.16821i
$651$			2.56005i			0.100336i
$652$	4.82228	−	17.9970i	0.188855	−	0.704816i
$653$	5.84447	+	10.1229i	0.228712	+	0.396140i	0.957427	−	0.288677i	$-0.0932153\pi$
$653$	5.84447	+	10.1229i	0.228712	+	0.396140i	−0.728715	+	0.684817i	$0.759882\pi$
$654$	5.44723	+	3.14496i	0.213004	+	0.122978i
$655$	−14.1241	+	14.1241i	−0.551873	+	0.551873i
$656$	−20.2041	−	75.4026i	−0.788836	−	2.94398i
$657$	5.27721	−	1.41403i	0.205884	−	0.0551664i
$658$	−1.76636	+	1.76636i	−0.0688601	+	0.0688601i
$659$	4.96055	+	2.86397i	0.193235	+	0.111565i	0.593496	−	0.804837i	$-0.297747\pi$
$659$	4.96055	+	2.86397i	0.193235	+	0.111565i	−0.400261	+	0.916401i	$0.631080\pi$
$660$	−15.3570	+	1.71459i	−0.597769	+	0.0667404i
$661$	−39.2136	−	10.5073i	−1.52523	−	0.408685i	−0.603773	−	0.797156i	$-0.706337\pi$
$661$	−39.2136	−	10.5073i	−1.52523	−	0.408685i	−0.921461	+	0.388471i	$0.873003\pi$
$662$	50.5835			1.96598
$663$	−0.453522	+	0.498367i	−0.0176133	+	0.0193550i
$664$	0.442538			0.0171738
$665$	0.0676186	−	0.252356i	0.00262214	−	0.00978595i
$666$	10.4731	−	6.04663i	0.405823	−	0.234302i
$667$	−2.78342	+	4.82103i	−0.107775	+	0.186671i
$668$	−73.6277	+	73.6277i	−2.84874	+	2.84874i
$669$	−7.46560	+	2.00040i	−0.288637	+	0.0773400i
$670$	1.53299	−	0.410763i	0.0592246	−	0.0158692i
$671$	8.46519	+	21.6332i	0.326795	+	0.835142i
$672$	−0.626364	+	1.08489i	−0.0241625	+	0.0418507i
$673$	−10.9897	−	19.0347i	−0.423621	−	0.733733i	0.572670	−	0.819786i	$-0.305908\pi$
$673$	−10.9897	−	19.0347i	−0.423621	−	0.733733i	−0.996291	+	0.0860532i	$0.972574\pi$
$674$	84.0955	+	22.5333i	3.23924	+	0.867951i
$675$			3.87960i			0.149326i
$676$	23.8250	−	52.0252i	0.916346	−	2.00097i
$677$		−	1.44089i		−	0.0553779i	−0.999617	−	0.0276889i	$-0.991185\pi$
$677$		−	1.44089i		−	0.0553779i	0.999617	−	0.0276889i	$-0.00881479\pi$
$678$	39.9114	+	10.6942i	1.53279	+	0.410709i
$679$	−0.0804557	+	0.0464511i	−0.00308760	+	0.00178263i
$680$	1.04099	+	0.601018i	0.0399203	+	0.0230480i
$681$	2.82951	−	2.82951i	0.108427	−	0.108427i
$682$	11.5086	−	75.8342i	0.440686	−	2.90384i
$683$	2.49612	+	9.31565i	0.0955115	+	0.356454i	0.997097	−	0.0761483i	$-0.0242622\pi$
$683$	2.49612	+	9.31565i	0.0955115	+	0.356454i	−0.901585	+	0.432602i	$0.857596\pi$
$684$	2.74285	+	2.74285i	0.104875	+	0.104875i
$685$	5.22519	−	9.05030i	0.199644	−	0.345794i
$686$	−8.54365	+	4.93268i	−0.326198	+	0.188330i
$687$	18.0948	+	4.84849i	0.690360	+	0.184981i
$688$	−13.2553			−0.505355
$689$	24.6918	−	27.1334i	0.940684	−	1.03370i
$690$		−	5.99890i		−	0.228374i
$691$	11.4054	−	42.5657i	0.433883	−	1.61927i	−0.309842	−	0.950788i	$-0.600276\pi$
$691$	11.4054	−	42.5657i	0.433883	−	1.61927i	0.743725	−	0.668486i	$-0.233057\pi$
$692$	42.1433	−	24.3314i	1.60205	−	0.924943i
$693$	−0.747961	+	0.550853i	−0.0284127	+	0.0209252i
$694$	−8.70802	−	8.70802i	−0.330552	−	0.330552i
$695$	3.70209	+	13.8164i	0.140428	+	0.524086i
$696$	−3.90855	−	14.5869i	−0.148153	−	0.552915i
$697$	−1.56991	+	1.56991i	−0.0594645	+	0.0594645i
$698$	33.1745	−	57.4599i	1.25567	−	2.17489i
$699$	9.33672	+	16.1717i	0.353147	+	0.611669i
$700$	−1.23787	+	4.61980i	−0.0467872	+	0.174612i
$701$	−10.0232			−0.378569			−0.189285	−	0.981922i	$-0.560617\pi$
$701$	−10.0232			−0.378569			−0.189285	+	0.981922i	$0.560617\pi$
$702$	−7.67697	+	4.92801i	−0.289748	+	0.185996i
$703$		−	4.21213i		−	0.158864i
$704$	−3.77935	+	4.72933i	−0.142439	+	0.178243i
$705$	1.86564	+	3.23137i	0.0702639	+	0.121701i
$706$	−23.9768	+	41.5290i	−0.902377	+	1.56296i
$707$	−2.21977	−	2.21977i	−0.0834831	−	0.0834831i
$708$	6.48648	−	1.73805i	0.243777	−	0.0653198i
$709$	10.4860	+	39.1344i	0.393811	+	1.46972i	0.823796	+	0.566886i	$0.191852\pi$
$709$	10.4860	+	39.1344i	0.393811	+	1.46972i	−0.429985	+	0.902836i	$0.641481\pi$
$710$	4.83592	+	4.83592i	0.181489	+	0.181489i
$711$	8.19099	+	4.72907i	0.307186	+	0.177354i
$712$	−40.6280	−	70.3698i	−1.52260	−	2.63722i
$713$	19.7766	+	5.29913i	0.740640	+	0.198454i
$714$	0.132436			0.00495629
$715$	−10.2491	−	7.42786i	−0.383294	−	0.277786i
$716$	20.9665			0.783556
$717$	8.22776	+	2.20462i	0.307271	+	0.0823331i
$718$	15.6847	+	27.1666i	0.585347	+	1.01385i
$719$	7.59445	+	4.38466i	0.283225	+	0.163520i	0.634883	−	0.772609i	$-0.281048\pi$
$719$	7.59445	+	4.38466i	0.283225	+	0.163520i	−0.351657	+	0.936129i	$0.614382\pi$
$720$	4.91819	+	4.91819i	0.183290	+	0.183290i
$721$	0.412457	+	1.53931i	0.0153607	+	0.0573269i
$722$	−44.5367	+	11.9336i	−1.65748	+	0.444121i
$723$	−10.2002	−	10.2002i	−0.379351	−	0.379351i
$724$	−42.4400	+	73.5082i	−1.57727	+	2.73191i
$725$	−4.82088	−	8.35001i	−0.179043	−	0.310111i
$726$	24.6326	−	12.9550i	0.914200	−	0.480807i
$727$			9.35419i			0.346928i	0.984840	+	0.173464i	$0.0554960\pi$
$727$			9.35419i			0.346928i	−0.984840	+	0.173464i	$0.944504\pi$
$728$	−5.84584	+	1.86534i	−0.216661	+	0.0691340i
$729$	1.00000			0.0370370
$730$	3.78694	−	14.1331i	0.140161	−	0.523088i
$731$	0.188499	+	0.326489i	0.00697187	+	0.0120756i
$732$	15.4151	−	26.6997i	0.569757	−	0.986848i
$733$	−0.419471	+	0.419471i	−0.0154935	+	0.0154935i	−0.714811	−	0.699318i	$-0.753487\pi$
$733$	−0.419471	+	0.419471i	−0.0154935	+	0.0154935i	0.699318	+	0.714811i	$0.253487\pi$
$734$	18.5110	+	69.0841i	0.683255	+	2.54994i
$735$	1.89621	+	7.07675i	0.0699427	+	0.261030i
$736$	7.08438	+	7.08438i	0.261134	+	0.261134i
$737$	−1.58257	+	1.16552i	−0.0582947	+	0.0429325i
$738$	−26.0306	+	15.0288i	−0.958199	+	0.553216i
$739$	12.3624	−	46.1371i	0.454758	−	1.69718i	−0.234039	−	0.972227i	$-0.575194\pi$
$739$	12.3624	−	46.1371i	0.454758	−	1.69718i	0.688797	−	0.724954i	$-0.258139\pi$
$740$		−	22.2688i		−	0.818618i
$741$	0.149527	+	3.17391i	0.00549300	+	0.116596i
$742$	−7.21042			−0.264703
$743$	−16.5083	−	4.42338i	−0.605630	−	0.162278i	−0.0570430	−	0.998372i	$-0.518167\pi$
$743$	−16.5083	−	4.42338i	−0.605630	−	0.162278i	−0.548587	+	0.836094i	$0.684834\pi$
$744$	−48.1004	+	27.7708i	−1.76345	+	1.01813i
$745$	−0.750333	+	1.29962i	−0.0274901	+	0.0476142i
$746$	−43.3590	−	43.3590i	−1.58749	−	1.58749i
$747$	−0.0188494	−	0.0703468i	−0.000689662	−	0.00257385i
$748$	−2.69740	−	0.409358i	−0.0986269	−	0.0149676i
$749$	−2.98398	+	2.98398i	−0.109032	+	0.109032i
$750$	20.5947	+	11.8904i	0.752012	+	0.434174i
$751$	11.0208	−	6.36287i	0.402155	−	0.232184i	−0.285258	−	0.958451i	$-0.592079\pi$
$751$	11.0208	−	6.36287i	0.402155	−	0.232184i	0.687413	+	0.726266i	$0.258746\pi$
$752$	−22.3742	−	5.99516i	−0.815905	−	0.218621i
$753$		−	23.4358i		−	0.854049i
$754$	10.3994	−	20.1461i	0.378723	−	0.733676i
$755$		−	16.8936i		−	0.614820i
$756$	1.19079	+	0.319072i	0.0433087	+	0.0116045i
$757$	9.29878	+	16.1060i	0.337970	+	0.585381i	0.984051	−	0.177888i	$-0.0569264\pi$
$757$	9.29878	+	16.1060i	0.337970	+	0.585381i	−0.646081	+	0.763269i	$0.723593\pi$
$758$	0.830447	−	1.43838i	0.0301632	−	0.0522442i
$759$	2.70716	+	6.91830i	0.0982639	+	0.251118i
$760$	5.47500	−	1.46702i	0.198599	−	0.0532144i
$761$	−26.0492	+	6.97985i	−0.944281	+	0.253019i	−0.697934	−	0.716162i	$-0.745897\pi$
$761$	−26.0492	+	6.97985i	−0.944281	+	0.253019i	−0.246347	+	0.969182i	$0.579230\pi$
$762$	9.43356	−	9.43356i	0.341742	−	0.341742i
$763$	0.348137	−	0.602990i	0.0126034	−	0.0218297i
$764$	−55.6636	+	32.1374i	−2.01384	+	1.16269i
$765$	0.0511993	−	0.191078i	0.00185111	−	0.00690845i
$766$	−94.3876			−3.41036
$767$	4.88797	+	2.52316i	0.176494	+	0.0911061i
$768$	30.6679			1.10663
$769$	−19.0218	−	5.09687i	−0.685943	−	0.183798i	−0.101017	−	0.994885i	$-0.532210\pi$
$769$	−19.0218	−	5.09687i	−0.685943	−	0.183798i	−0.584926	+	0.811087i	$0.698876\pi$
$770$	0.276041	+	2.47239i	0.00994781	+	0.0890988i
$771$	22.2621	+	12.8530i	0.801750	+	0.462891i
$772$	−51.0755	+	51.0755i	−1.83825	+	1.83825i
$773$	31.1770	−	8.35386i	1.12136	−	0.300467i	0.349926	−	0.936777i	$-0.386207\pi$
$773$	31.1770	−	8.35386i	1.12136	−	0.300467i	0.771433	+	0.636310i	$0.219540\pi$
$774$	1.32099	+	4.92999i	0.0474818	+	0.177205i
$775$	−25.0749	+	25.0749i	−0.900719	+	0.900719i
$776$	−1.74553	−	1.00778i	−0.0626608	−	0.0361772i
$777$	−0.669342	−	1.15933i	−0.0240125	−	0.0415909i
$778$	−14.2396	+	53.1429i	−0.510514	+	1.90527i
$779$			10.4692i			0.375097i
$780$	0.790521	+	16.7799i	0.0283052	+	0.600817i
$781$	−7.75942	−	3.39474i	−0.277654	−	0.121473i
$782$	0.274134	−	1.02308i	0.00980301	−	0.0365853i
$783$	−2.15228	+	1.24262i	−0.0769164	+	0.0444077i
$784$	−39.3884	−	22.7409i	−1.40673	−	0.812175i
$785$	−4.13297	−	4.13297i	−0.147512	−	0.147512i
$786$	−46.1188	+	12.3575i	−1.64500	+	0.440777i
$787$	11.5604	−	3.09759i	0.412083	−	0.110417i	−0.0468209	−	0.998903i	$-0.514909\pi$
$787$	11.5604	−	3.09759i	0.412083	−	0.110417i	0.458904	+	0.888486i	$0.348242\pi$
$788$	−13.0463	−	13.0463i	−0.464754	−	0.464754i
$789$	−19.9874	−	11.5397i	−0.711571	−	0.410825i
$790$	21.9365	−	12.6651i	0.780466	−	0.450602i
$791$	1.18382	−	4.41806i	0.0420917	−	0.157088i
$792$	−18.4636	−	8.07782i	−0.656076	−	0.287033i
$793$	24.0591	−	7.67698i	0.854364	−	0.272617i
$794$		−	79.3290i		−	2.81528i
$795$	−2.78752	+	10.4032i	−0.0988632	+	0.368963i
$796$	27.4471	+	47.5398i	0.972837	+	1.68500i
$797$	−23.3585	−	13.4861i	−0.827402	−	0.477701i	0.0255605	−	0.999673i	$-0.491863\pi$
$797$	−23.3585	−	13.4861i	−0.827402	−	0.477701i	−0.852962	+	0.521973i	$0.825196\pi$
$798$	0.441584	−	0.441584i	0.0156319	−	0.0156319i
$799$	0.170509	+	0.636349i	0.00603218	+	0.0225124i
$800$	−16.7613	+	4.49118i	−0.592601	+	0.158787i
$801$	−9.45563	+	9.45563i	−0.334098	+	0.334098i
$802$	59.5403	+	34.3756i	2.10244	+	1.21385i
$803$	2.01059	+	18.0081i	0.0709521	+	0.635491i
$804$	2.51954	+	0.675108i	0.0888572	+	0.0238092i
$805$	−0.664059			−0.0234050
$806$	−81.4695	−	17.7673i	−2.86964	−	0.625825i
$807$	21.3332			0.750965
$808$	17.6275	−	65.7865i	0.620132	−	2.31436i
$809$	−26.4470	+	15.2692i	−0.929825	+	0.536835i	−0.886756	−	0.462237i	$-0.847047\pi$
$809$	−26.4470	+	15.2692i	−0.929825	+	0.536835i	−0.0430690	+	0.999072i	$0.513714\pi$
$810$	1.33906	−	2.31933i	0.0470499	−	0.0814928i
$811$	29.0949	−	29.0949i	1.02166	−	1.02166i	0.0219016	−	0.999760i	$-0.493028\pi$
$811$	29.0949	−	29.0949i	1.02166	−	1.02166i	0.999760	−	0.0219016i	$-0.00697206\pi$
$812$	−2.95941	+	0.792972i	−0.103855	+	0.0278279i
$813$	19.0784	−	5.11203i	0.669107	−	0.179287i
$814$	14.6156	+	37.3510i	0.512278	+	1.30915i
$815$	−2.24026	+	3.88025i	−0.0784730	+	0.135919i
$816$	0.614024	+	1.06352i	0.0214951	+	0.0372307i
$817$	1.71713	+	0.460105i	0.0600749	+	0.0160970i
$818$		−	58.6965i		−	2.05227i
$819$	0.545515	+	0.849815i	0.0190618	+	0.0296949i
$820$			55.3487i			1.93286i
$821$	−23.2267	−	6.22358i	−0.810619	−	0.217205i	−0.170378	−	0.985379i	$-0.554499\pi$
$821$	−23.2267	−	6.22358i	−0.810619	−	0.217205i	−0.640241	+	0.768174i	$0.721165\pi$
$822$	21.6333	−	12.4900i	0.754546	−	0.435638i
$823$	−40.0236	−	23.1076i	−1.39513	−	0.805481i	−0.401256	−	0.915966i	$-0.631426\pi$
$823$	−40.0236	−	23.1076i	−1.39513	−	0.805481i	−0.993878	+	0.110485i	$0.964760\pi$
$824$	−24.4477	+	24.4477i	−0.851675	+	0.851675i
$825$	−12.7215	−	1.93062i	−0.442906	−	0.0672154i
$826$	−0.279817	−	1.04429i	−0.00973607	−	0.0363355i
$827$	−7.35431	−	7.35431i	−0.255734	−	0.255734i	0.567582	−	0.823317i	$-0.307879\pi$
$827$	−7.35431	−	7.35431i	−0.255734	−	0.255734i	−0.823317	+	0.567582i	$0.807879\pi$
$828$	4.92973	−	8.53854i	0.171320	−	0.296735i
$829$	−0.689949	+	0.398342i	−0.0239629	+	0.0138350i	−0.511934	−	0.859025i	$-0.671071\pi$
$829$	−0.689949	+	0.398342i	−0.0239629	+	0.0138350i	0.487971	+	0.872860i	$0.337737\pi$
$830$	−0.188398	−	0.0504810i	−0.00653938	−	0.00175222i
$831$	−28.9265			−1.00345
$832$	4.86754	+	4.42954i	0.168751	+	0.153567i
$833$			1.29356i			0.0448190i
$834$	−8.84924	+	33.0258i	−0.306424	+	1.14359i
$835$	21.6851	−	12.5199i	0.750442	−	0.433268i
$836$	−10.3589	+	7.62909i	−0.358272	+	0.263857i
$837$	6.46328	+	6.46328i	0.223404	+	0.223404i
$838$	19.1283	+	71.3878i	0.660776	+	2.46605i
$839$	6.15459	+	22.9692i	0.212480	+	0.792986i	0.987038	+	0.160484i	$0.0513054\pi$
$839$	6.15459	+	22.9692i	0.212480	+	0.792986i	−0.774559	+	0.632502i	$0.782028\pi$
$840$	1.27380	−	1.27380i	0.0439503	−	0.0439503i
$841$	−11.4118	+	19.7658i	−0.393510	+	0.681579i
$842$	0.471660	+	0.816938i	0.0162545	+	0.0281536i
$843$	−2.77269	+	10.3478i	−0.0954964	+	0.356397i
$844$	103.694			3.56929
$845$	−8.77219	+	10.6017i	−0.301772	+	0.364710i
$846$			8.91899i			0.306641i
$847$	−1.43408	−	2.72674i	−0.0492756	−	0.0936920i
$848$	−33.4303	−	57.9029i	−1.14800	−	1.98839i
$849$	6.39383	−	11.0744i	0.219436	−	0.380074i
$850$	1.29717	+	1.29717i	0.0444927	+	0.0444927i
$851$	−10.3415	+	2.77099i	−0.354501	+	0.0949883i
$852$	2.90919	+	10.8572i	0.0996671	+	0.371963i
$853$	−17.8786	−	17.8786i	−0.612151	−	0.612151i	0.331355	−	0.943506i	$-0.392494\pi$
$853$	−17.8786	−	17.8786i	−0.612151	−	0.612151i	−0.943506	+	0.331355i	$0.892494\pi$
$854$	−4.29851	−	2.48175i	−0.147092	−	0.0849236i
$855$	−0.466402	−	0.807831i	−0.0159506	−	0.0276273i
$856$	−88.4352	−	23.6961i	−3.02265	−	0.809918i
$857$	−9.17853			−0.313533			−0.156766	−	0.987636i	$-0.550107\pi$
$857$	−9.17853			−0.313533			−0.156766	+	0.987636i	$0.550107\pi$
$858$	−12.3390	−	27.6257i	−0.421247	−	0.943127i
$859$	−11.0895			−0.378367			−0.189184	−	0.981942i	$-0.560584\pi$
$859$	−11.0895			−0.378367			−0.189184	+	0.981942i	$0.560584\pi$
$860$	9.07820	+	2.43250i	0.309564	+	0.0829474i
$861$	1.66363	+	2.88150i	0.0566965	+	0.0982013i
$862$	67.3363	+	38.8766i	2.29348	+	1.32414i
$863$	−11.7942	−	11.7942i	−0.401479	−	0.401479i	0.477275	−	0.878754i	$-0.341624\pi$
$863$	−11.7942	−	11.7942i	−0.401479	−	0.401479i	−0.878754	+	0.477275i	$0.841624\pi$
$864$	1.15764	+	4.32037i	0.0393837	+	0.146982i
$865$	−11.3036	+	3.02878i	−0.384332	+	0.102982i
$866$	37.8924	+	37.8924i	1.28764	+	1.28764i
$867$	−8.48254	+	14.6922i	−0.288082	+	0.498973i
$868$	5.63418	+	9.75868i	0.191236	+	0.331231i
$869$	−19.5831	+	24.5056i	−0.664311	+	0.831294i
$870$			6.65580i			0.225653i
$871$	1.15423	+	1.79808i	0.0391094	+	0.0609256i
$872$	15.1060			0.511554
$873$	−0.0858504	+	0.320398i	−0.00290560	+	0.0108438i
$874$	−2.49723	−	4.32534i	−0.0844702	−	0.146307i
$875$	1.31622	−	2.27977i	0.0444965	−	0.0770701i
$876$	17.0043	−	17.0043i	0.574522	−	0.574522i
$877$	−9.12001	−	34.0364i	−0.307961	−	1.14933i	−0.930366	−	0.366631i	$-0.880511\pi$
$877$	−9.12001	−	34.0364i	−0.307961	−	1.14933i	0.622405	−	0.782695i	$-0.286155\pi$
$878$	−13.4014	−	50.0148i	−0.452276	−	1.68792i
$879$	6.67226	+	6.67226i	0.225050	+	0.225050i
$880$	−18.5746	+	13.6797i	−0.626149	+	0.461142i
$881$	2.68348	−	1.54931i	0.0904087	−	0.0521975i	−0.454114	−	0.890944i	$-0.650044\pi$
$881$	2.68348	−	1.54931i	0.0904087	−	0.0521975i	0.544523	+	0.838746i	$0.316711\pi$
$882$	−4.53258	+	16.9158i	−0.152620	+	0.569585i
$883$			39.7425i			1.33744i	0.743514	+	0.668720i	$0.233158\pi$
$883$			39.7425i			1.33744i	−0.743514	+	0.668720i	$0.766842\pi$
$884$	−0.631978	+	2.89785i	−0.0212557	+	0.0974653i
$885$	−1.61487			−0.0542834
$886$	4.48471	+	1.20168i	0.150667	+	0.0403711i
$887$	−21.9346	+	12.6640i	−0.736493	+	0.425214i	−0.820793	−	0.571226i	$-0.806468\pi$
$887$	−21.9346	+	12.6640i	−0.736493	+	0.425214i	0.0843000	+	0.996440i	$0.473135\pi$
$888$	14.5217	−	25.1524i	0.487317	−	0.844058i
$889$	−1.04426	−	1.04426i	−0.0350235	−	0.0350235i
$890$	9.26901	+	34.5924i	0.310698	+	1.15954i
$891$	−0.497633	+	3.27908i	−0.0166713	+	0.109853i
$892$	−24.0557	+	24.0557i	−0.805446	+	0.805446i
$893$	2.69033	+	1.55326i	0.0900283	+	0.0519779i
$894$	−3.10652	+	1.79355i	−0.103897	+	0.0599852i
$895$	−4.87016	−	1.30496i	−0.162792	−	0.0436199i
$896$		−	3.79895i		−	0.126914i
$897$	7.69409	−	2.45509i	0.256898	−	0.0819732i
$898$			61.7804i			2.06164i
$899$	−21.9422	−	5.87940i	−0.731814	−	0.196089i
$900$	8.53827	+	14.7887i	0.284609	+	0.492957i
$901$	−0.950795	+	1.64683i	−0.0316756	+	0.0548637i
$902$	−36.3268	−	92.8351i	−1.20955	−	3.09107i
$903$	0.545733	−	0.146229i	0.0181609	−	0.00486619i
$904$	95.8522	−	25.6835i	3.18800	−	0.854221i
$905$	14.4332	−	14.4332i	0.479777	−	0.479777i
$906$	20.1906	−	34.9712i	0.670789	−	1.16184i
$907$	−0.445515	+	0.257218i	−0.0147931	+	0.00854079i	−0.507378	−	0.861723i	$-0.669385\pi$
$907$	−0.445515	+	0.257218i	−0.0147931	+	0.00854079i	0.492585	+	0.870264i	$0.336052\pi$
$908$	4.55864	−	17.0131i	0.151284	−	0.564599i
$909$	−11.2084			−0.371759
$910$	2.70148	−	0.127270i	0.0895531	−	0.00421896i
$911$	6.69235			0.221728			0.110864	−	0.993836i	$-0.464638\pi$
$911$	6.69235			0.221728			0.110864	+	0.993836i	$0.464638\pi$
$912$	5.59348	+	1.49877i	0.185219	+	0.0496291i
$913$	0.240053	−	0.0268017i	0.00794458	−	0.000887006i
$914$	35.0299	+	20.2245i	1.15869	+	0.668967i
$915$	−5.24244	+	5.24244i	−0.173310	+	0.173310i
$916$	79.6465	−	21.3412i	2.63159	−	0.705133i
$917$	1.36793	+	5.10520i	0.0451731	+	0.168588i
$918$	0.334358	−	0.334358i	0.0110354	−	0.0110354i
$919$	50.3854	+	29.0900i	1.66206	+	0.959591i	0.971729	+	0.236098i	$0.0758686\pi$
$919$	50.3854	+	29.0900i	1.66206	+	0.959591i	0.690331	+	0.723493i	$0.257465\pi$
$920$	−7.20355	−	12.4769i	−0.237494	−	0.411352i
$921$	6.45413	−	24.0871i	0.212671	−	0.793698i
$922$		−	88.6894i		−	2.92083i
$923$	−4.22333	+	8.18160i	−0.139013	+	0.269301i
$924$	−1.63884	+	3.74593i	−0.0539139	+	0.123232i
$925$	4.79934	−	17.9114i	0.157801	−	0.588923i
$926$	27.6809	−	15.9816i	0.909651	−	0.525187i
$927$	4.92758	+	2.84494i	0.161843	+	0.0934400i
$928$	−7.86015	−	7.86015i	−0.258022	−	0.258022i
$929$	9.28360	−	2.48753i	0.304585	−	0.0816133i	−0.103289	−	0.994651i	$-0.532937\pi$
$929$	9.28360	−	2.48753i	0.304585	−	0.0816133i	0.407874	+	0.913038i	$0.366270\pi$
$930$	23.6452	−	6.33571i	0.775357	−	0.207756i
$931$	4.31313	+	4.31313i	0.141357	+	0.141357i
$932$	71.1816	+	41.0967i	2.33163	+	1.34617i
$933$	−4.53272	+	2.61697i	−0.148395	+	0.0856757i
$934$	−8.48601	+	31.6702i	−0.277671	+	1.03628i
$935$	0.601082	+	0.262973i	0.0196575	+	0.00860014i
$936$	−10.0495	+	19.4682i	−0.328477	+	0.636338i
$937$			38.3153i			1.25171i	0.779941	+	0.625853i	$0.215249\pi$
$937$			38.3153i			1.25171i	−0.779941	+	0.625853i	$0.784751\pi$
$938$	0.108689	−	0.405633i	0.00354882	−	0.0132444i
$939$	−9.58187	−	16.5963i	−0.312693	−	0.541599i
$940$	14.2233	+	8.21182i	0.463913	+	0.267840i
$941$	35.8498	−	35.8498i	1.16867	−	1.16867i	0.186150	−	0.982521i	$-0.440399\pi$
$941$	35.8498	−	35.8498i	1.16867	−	1.16867i	0.982521	−	0.186150i	$-0.0596011\pi$
$942$	−3.61603	−	13.4952i	−0.117817	−	0.439698i
$943$	25.7035	−	6.88723i	0.837021	−	0.224279i
$944$	7.08878	−	7.08878i	0.230720	−	0.230720i
$945$	−0.256742	−	0.148230i	−0.00835181	−	0.00482192i
$946$	−16.8232	+	1.87829i	−0.546969	+	0.0610686i
$947$	31.9585	+	8.56326i	1.03851	+	0.278269i	0.737497	−	0.675351i	$-0.236008\pi$
$947$	31.9585	+	8.56326i	1.03851	+	0.278269i	0.301016	+	0.953619i	$0.402674\pi$
$948$	41.6312			1.35212
$949$	19.6767	−	0.926991i	0.638731	−	0.0300914i
$950$	8.65040			0.280656
$951$	4.73272	−	17.6628i	0.153469	−	0.572754i
$952$	0.275449	−	0.159031i	0.00892736	−	0.00515421i
$953$	24.8550	−	43.0502i	0.805133	−	1.39453i	−0.111068	−	0.993813i	$-0.535427\pi$
$953$	24.8550	−	43.0502i	0.805133	−	1.39453i	0.916201	−	0.400719i	$-0.131240\pi$
$954$	−18.2040	+	18.2040i	−0.589375	+	0.589375i
$955$	14.9299	−	4.00046i	0.483121	−	0.129452i
$956$	36.2155	−	9.70391i	1.17129	−	0.313847i
$957$	−3.00361	−	7.67588i	−0.0970929	−	0.248126i
$958$	26.7076	−	46.2589i	0.862883	−	1.49456i
$959$	−1.38260	−	2.39473i	−0.0446464	−	0.0773299i
$960$	−1.86626	−	0.500062i	−0.0602331	−	0.0161394i
$961$			52.5479i			1.69509i
$962$	41.5394	−	13.2547i	1.33928	−	0.427350i
$963$			15.0672i			0.485533i
$964$	−61.3312	−	16.4336i	−1.97534	−	0.529292i
$965$	15.0429	−	8.68502i	0.484248	−	0.279581i
$966$	−1.37466	−	0.793661i	−0.0442290	−	0.0255356i
$967$	−12.3750	+	12.3750i	−0.397954	+	0.397954i	−0.877511	−	0.479557i	$-0.840797\pi$
$967$	−12.3750	+	12.3750i	−0.397954	+	0.397954i	0.479557	+	0.877511i	$0.340797\pi$
$968$	35.6759	−	56.5238i	1.14667	−	1.81674i
$969$	−0.0426267	−	0.159085i	−0.00136937	−	0.00511054i
$970$	0.628149	+	0.628149i	0.0201686	+	0.0201686i
$971$	−8.36478	+	14.4882i	−0.268438	+	0.464949i	−0.968459	−	0.249174i	$-0.919841\pi$
$971$	−8.36478	+	14.4882i	−0.268438	+	0.464949i	0.700020	+	0.714123i	$0.253174\pi$
$972$	3.81192	−	2.20081i	0.122267	−	0.0705911i
$973$	3.65585	+	0.979582i	0.117201	+	0.0314040i
$974$	−70.9093			−2.27208
$975$	−2.98054	+	13.6669i	−0.0954537	+	0.437690i
$976$		−	46.0253i		−	1.47323i
$977$	−9.13756	+	34.1018i	−0.292336	+	1.09101i	0.650973	+	0.759101i	$0.274361\pi$
$977$	−9.13756	+	34.1018i	−0.292336	+	1.09101i	−0.943310	+	0.331914i	$0.892306\pi$
$978$	−9.27510	+	5.35498i	−0.296585	+	0.171233i
$979$	−26.3003	−	35.7112i	−0.840563	−	1.14134i
$980$	22.8028	+	22.8028i	0.728408	+	0.728408i
$981$	−0.643422	−	2.40128i	−0.0205429	−	0.0766671i
$982$	0.750204	+	2.79980i	0.0239400	+	0.0893451i
$983$	21.4490	−	21.4490i	0.684118	−	0.684118i	−0.276808	−	0.960925i	$-0.589276\pi$
$983$	21.4490	−	21.4490i	0.684118	−	0.684118i	0.960925	+	0.276808i	$0.0892765\pi$
$984$	−36.0934	+	62.5156i	−1.15062	+	1.99293i
$985$	2.21842	+	3.84242i	0.0706849	+	0.122430i
$986$	−0.304153	+	1.13511i	−0.00968619	+	0.0361494i
$987$	0.987303			0.0314262
$988$	7.55515	+	11.7696i	0.240361	+	0.374441i
$989$		−	4.51853i		−	0.143681i
$990$	6.93890	+	5.54507i	0.220533	+	0.176234i
$991$	−9.56048	−	16.5592i	−0.303699	−	0.526022i	0.673272	−	0.739395i	$-0.264888\pi$
$991$	−9.56048	−	16.5592i	−0.303699	−	0.526022i	−0.976971	+	0.213373i	$0.931555\pi$
$992$	−20.4416	+	35.4059i	−0.649021	+	1.12414i
$993$	−14.1367	−	14.1367i	−0.448615	−	0.448615i
$994$	1.74796	−	0.468364i	0.0554419	−	0.0148556i
$995$	−3.41662	−	12.7510i	−0.108314	−	0.404233i
$996$	−0.226672	−	0.226672i	−0.00718238	−	0.00718238i
$997$	−20.3493	−	11.7487i	−0.644470	−	0.372085i	0.141864	−	0.989886i	$-0.454690\pi$
$997$	−20.3493	−	11.7487i	−0.644470	−	0.372085i	−0.786334	+	0.617801i	$0.788024\pi$
$998$	39.3274	+	68.1171i	1.24489	+	2.15621i
$999$	−4.61681	−	1.23707i	−0.146069	−	0.0391392i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.bd.b.76.1	✓	56
11.10	odd	2	inner	429.2.bd.b.76.14	yes	56
13.6	odd	12	inner	429.2.bd.b.175.14	yes	56
143.32	even	12	inner	429.2.bd.b.175.1	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.bd.b.76.1	✓	56	1.1	even	1	trivial
429.2.bd.b.76.14	yes	56	11.10	odd	2	inner
429.2.bd.b.175.1	yes	56	143.32	even	12	inner
429.2.bd.b.175.14	yes	56	13.6	odd	12	inner

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:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.bd (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.44393 - 0.654849i) q^{2} +(0.500000 + 0.866025i) q^{3} +(3.81192 + 2.20081i) q^{4} +(-0.748465 - 0.748465i) q^{5} +(-0.654849 - 2.44393i) q^{6} +(-0.270535 + 0.0724897i) q^{7} +(-4.29670 - 4.29670i) q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-2.44393 - 0.654849i) q^{2} +(0.500000 + 0.866025i) q^{3} +(3.81192 + 2.20081i) q^{4} +(-0.748465 - 0.748465i) q^{5} +(-0.654849 - 2.44393i) q^{6} +(-0.270535 + 0.0724897i) q^{7} +(-4.29670 - 4.29670i) q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.33906 + 2.31933i) q^{10} +(-2.59095 - 2.07050i) q^{11} +4.40162i q^{12} +(-2.42671 + 2.66666i) q^{13} +0.708639 q^{14} +(0.273957 - 1.02242i) q^{15} +(3.28552 + 5.69069i) q^{16} +(0.0934440 - 0.161850i) q^{17} +(1.78908 - 1.78908i) q^{18} +(-0.228087 - 0.851231i) q^{19} +(-1.20586 - 4.50032i) q^{20} +(-0.198045 - 0.198045i) q^{21} +(4.97623 + 6.75684i) q^{22} +(-1.93986 + 1.11998i) q^{23} +(1.57270 - 5.86940i) q^{24} -3.87960i q^{25} +(7.67697 - 4.92801i) q^{26} -1.00000 q^{27} +(-1.19079 - 0.319072i) q^{28} +(2.15228 - 1.24262i) q^{29} +(-1.33906 + 2.31933i) q^{30} +(-6.46328 - 6.46328i) q^{31} +(-1.15764 - 4.32037i) q^{32} +(0.497633 - 3.27908i) q^{33} +(-0.334358 + 0.334358i) q^{34} +(0.256742 + 0.148230i) q^{35} +(-3.81192 + 2.20081i) q^{36} +(4.61681 + 1.23707i) q^{37} +2.22971i q^{38} +(-3.52275 - 0.768259i) q^{39} +6.43185i q^{40} +(-11.4750 - 3.07471i) q^{41} +(0.354319 + 0.613699i) q^{42} +(-1.00862 + 1.74698i) q^{43} +(-5.31970 - 13.5948i) q^{44} +(1.02242 - 0.273957i) q^{45} +(5.47431 - 1.46684i) q^{46} +(-2.49262 + 2.49262i) q^{47} +(-3.28552 + 5.69069i) q^{48} +(-5.99424 + 3.46078i) q^{49} +(-2.54055 + 9.48148i) q^{50} +0.186888 q^{51} +(-15.1192 + 4.82437i) q^{52} -10.1750 q^{53} +(2.44393 + 0.654849i) q^{54} +(0.389537 + 3.48893i) q^{55} +(1.47387 + 0.850942i) q^{56} +(0.623145 - 0.623145i) q^{57} +(-6.07376 + 1.62746i) q^{58} +(-0.394865 - 1.47366i) q^{59} +(3.29446 - 3.29446i) q^{60} +(-6.06587 - 3.50213i) q^{61} +(11.5633 + 20.0283i) q^{62} +(0.0724897 - 0.270535i) q^{63} -1.82533i q^{64} +(3.81221 - 0.179598i) q^{65} +(-3.36348 + 7.68797i) q^{66} +(0.153377 - 0.572411i) q^{67} +(0.712401 - 0.411305i) q^{68} +(-1.93986 - 1.11998i) q^{69} +(-0.530391 - 0.530391i) q^{70} +(2.46664 - 0.660935i) q^{71} +(5.86940 - 1.57270i) q^{72} +(-3.86319 - 3.86319i) q^{73} +(-10.4731 - 6.04663i) q^{74} +(3.35983 - 1.93980i) q^{75} +(1.00395 - 3.74680i) q^{76} +(0.851033 + 0.372326i) q^{77} +(8.10627 + 4.18444i) q^{78} -9.45814i q^{79} +(1.80018 - 6.71838i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(26.0306 + 15.0288i) q^{82} +(-0.0514974 + 0.0514974i) q^{83} +(-0.319072 - 1.19079i) q^{84} +(-0.191078 + 0.0511993i) q^{85} +(3.60900 - 3.60900i) q^{86} +(2.15228 + 1.24262i) q^{87} +(2.23621 + 20.0289i) q^{88} +(12.9166 + 3.46100i) q^{89} -2.67813 q^{90} +(0.463204 - 0.897337i) q^{91} -9.85946 q^{92} +(2.36572 - 8.82900i) q^{93} +(7.72407 - 4.45949i) q^{94} +(-0.466402 + 0.807831i) q^{95} +(3.16273 - 3.16273i) q^{96} +(0.320398 - 0.0858504i) q^{97} +(16.9158 - 4.53258i) q^{98} +(3.08858 - 1.20858i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 28 q^{3} - 4 q^{5} - 28 q^{9}+O(q^{10}) \) 56 * q + 28 * q^3 - 4 * q^5 - 28 * q^9	\( 56 q + 28 q^{3} - 4 q^{5} - 28 q^{9} - 4 q^{11} - 24 q^{14} - 8 q^{15} + 4 q^{16} + 80 q^{20} - 10 q^{22} - 12 q^{23} + 40 q^{26} - 56 q^{27} - 12 q^{31} - 8 q^{33} - 16 q^{34} - 12 q^{37} - 12 q^{42} + 24 q^{44} - 4 q^{45} - 40 q^{47} - 4 q^{48} + 24 q^{49} - 88 q^{53} - 18 q^{55} + 72 q^{56} + 40 q^{58} + 8 q^{59} + 52 q^{60} - 20 q^{66} - 4 q^{67} - 12 q^{69} + 40 q^{70} - 24 q^{71} + 12 q^{75} - 4 q^{78} - 188 q^{80} - 28 q^{81} - 12 q^{82} + 32 q^{86} + 18 q^{88} - 16 q^{89} + 28 q^{91} - 96 q^{92} - 12 q^{93} - 28 q^{97} - 4 q^{99}+O(q^{100}) \) 56 * q + 28 * q^3 - 4 * q^5 - 28 * q^9 - 4 * q^11 - 24 * q^14 - 8 * q^15 + 4 * q^16 + 80 * q^20 - 10 * q^22 - 12 * q^23 + 40 * q^26 - 56 * q^27 - 12 * q^31 - 8 * q^33 - 16 * q^34 - 12 * q^37 - 12 * q^42 + 24 * q^44 - 4 * q^45 - 40 * q^47 - 4 * q^48 + 24 * q^49 - 88 * q^53 - 18 * q^55 + 72 * q^56 + 40 * q^58 + 8 * q^59 + 52 * q^60 - 20 * q^66 - 4 * q^67 - 12 * q^69 + 40 * q^70 - 24 * q^71 + 12 * q^75 - 4 * q^78 - 188 * q^80 - 28 * q^81 - 12 * q^82 + 32 * q^86 + 18 * q^88 - 16 * q^89 + 28 * q^91 - 96 * q^92 - 12 * q^93 - 28 * q^97 - 4 * q^99

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