LMFDB - Embedded newform 756.2.ck.a.605.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(5,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 5, 15]))

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

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

chi := DirichletCharacter("756.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.ck (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$24$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			605.16
Character	$\chi$	$=$	756.605
Dual form			756.2.ck.a.5.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.727904 + 1.57167i) q^{3} +(-0.591212 - 3.35293i) q^{5} +(-1.25160 + 2.33098i) q^{7} +(-1.94031 + 2.28805i) q^{9} +O(q^{10})$	\(q+(0.727904 + 1.57167i) q^{3} +(-0.591212 - 3.35293i) q^{5} +(-1.25160 + 2.33098i) q^{7} +(-1.94031 + 2.28805i) q^{9} +(-5.13559 - 0.905544i) q^{11} +(2.56808 + 3.06052i) q^{13} +(4.83937 - 3.36980i) q^{15} -3.67787 q^{17} +7.57664i q^{19} +(-4.57459 - 0.270382i) q^{21} +(3.17546 + 3.78437i) q^{23} +(-6.19416 + 2.25449i) q^{25} +(-5.00843 - 1.38405i) q^{27} +(-5.50806 + 6.56425i) q^{29} +(-1.36807 + 3.75873i) q^{31} +(-2.31500 - 8.73062i) q^{33} +(8.55559 + 2.81844i) q^{35} +(3.11270 - 5.39136i) q^{37} +(-2.94082 + 6.26394i) q^{39} +(3.29135 - 2.76177i) q^{41} +(8.46720 - 3.08181i) q^{43} +(8.81882 + 5.15301i) q^{45} +(0.0867629 - 0.0315791i) q^{47} +(-3.86697 - 5.83494i) q^{49} +(-2.67714 - 5.78041i) q^{51} +(-0.822872 - 0.475085i) q^{53} +17.7547i q^{55} +(-11.9080 + 5.51507i) q^{57} +(0.157848 - 0.132450i) q^{59} +(-3.75967 - 10.3296i) q^{61} +(-2.90491 - 7.38658i) q^{63} +(8.74342 - 10.4200i) q^{65} +(0.114606 + 0.649962i) q^{67} +(-3.63636 + 7.74545i) q^{69} +(-4.63188 + 2.67422i) q^{71} +(-8.35033 + 4.82106i) q^{73} +(-8.05207 - 8.09414i) q^{75} +(8.53854 - 10.8376i) q^{77} +(-0.401358 + 2.27621i) q^{79} +(-1.47037 - 8.87908i) q^{81} +(-5.15096 - 4.32216i) q^{83} +(2.17440 + 12.3317i) q^{85} +(-14.3262 - 3.87873i) q^{87} +1.57358 q^{89} +(-10.3482 + 2.15559i) q^{91} +(-6.90332 + 0.585841i) q^{93} +(25.4040 - 4.47941i) q^{95} +(-1.25237 - 3.44085i) q^{97} +(12.0366 - 9.99347i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 6 q^{9}+O(q^{10}) $ 144 * q + 6 * q^9	$ 144 q + 6 q^{9} - 6 q^{11} + 12 q^{15} + 33 q^{21} + 21 q^{23} - 6 q^{29} + 27 q^{35} + 39 q^{39} - 54 q^{47} + 18 q^{49} - 9 q^{51} - 45 q^{53} + 3 q^{57} + 45 q^{59} + 39 q^{63} + 24 q^{65} - 36 q^{69} + 36 q^{71} + 45 q^{75} + 21 q^{77} - 18 q^{79} + 18 q^{81} + 36 q^{85} - 45 q^{87} + 9 q^{91} - 48 q^{93} - 66 q^{95}+O(q^{100}) $ 144 * q + 6 * q^9 - 6 * q^11 + 12 * q^15 + 33 * q^21 + 21 * q^23 - 6 * q^29 + 27 * q^35 + 39 * q^39 - 54 * q^47 + 18 * q^49 - 9 * q^51 - 45 * q^53 + 3 * q^57 + 45 * q^59 + 39 * q^63 + 24 * q^65 - 36 * q^69 + 36 * q^71 + 45 * q^75 + 21 * q^77 - 18 * q^79 + 18 * q^81 + 36 * q^85 - 45 * q^87 + 9 * q^91 - 48 * q^93 - 66 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.727904	+	1.57167i	0.420255	+	0.907406i
$3$	0.727904	+	1.57167i	0.420255	+	0.907406i
$4$		0			0
$5$	−0.591212	−	3.35293i	−0.264398	−	1.49948i	−0.770743	−	0.637146i	$-0.780115\pi$
$5$	−0.591212	−	3.35293i	−0.264398	−	1.49948i	0.506345	−	0.862331i	$-0.330996\pi$
$6$		0			0
$7$	−1.25160	+	2.33098i	−0.473062	+	0.881029i
$7$	−1.25160	+	2.33098i	−0.473062	+	0.881029i
$8$		0			0
$9$	−1.94031	+	2.28805i	−0.646771	+	0.762684i
$10$		0			0
$11$	−5.13559	−	0.905544i	−1.54844	−	0.273032i	−0.666902	−	0.745146i	$-0.732380\pi$
$11$	−5.13559	−	0.905544i	−1.54844	−	0.273032i	−0.881538	+	0.472114i	$0.843491\pi$
$12$		0			0
$13$	2.56808	+	3.06052i	0.712256	+	0.848834i	0.993854	−	0.110698i	$-0.0353088\pi$
$13$	2.56808	+	3.06052i	0.712256	+	0.848834i	−0.281598	+	0.959533i	$0.590864\pi$
$14$		0			0
$15$	4.83937	−	3.36980i	1.24952	−	0.870080i
$16$		0			0
$17$	−3.67787			−0.892015			−0.446008	−	0.895029i	$-0.647155\pi$
$17$	−3.67787			−0.892015			−0.446008	+	0.895029i	$0.647155\pi$
$18$		0			0
$19$			7.57664i			1.73820i	0.494635	+	0.869101i	$0.335302\pi$
$19$			7.57664i			1.73820i	−0.494635	+	0.869101i	$0.664698\pi$
$20$		0			0
$21$	−4.57459	−	0.270382i	−0.998258	−	0.0590022i
$22$		0			0
$23$	3.17546	+	3.78437i	0.662130	+	0.789096i	0.987690	−	0.156426i	$-0.0499972\pi$
$23$	3.17546	+	3.78437i	0.662130	+	0.789096i	−0.325560	+	0.945521i	$0.605553\pi$
$24$		0			0
$25$	−6.19416	+	2.25449i	−1.23883	+	0.450898i
$26$		0			0
$27$	−5.00843	−	1.38405i	−0.963873	−	0.266361i
$28$		0			0
$29$	−5.50806	+	6.56425i	−1.02282	+	1.21895i	−0.0473381	+	0.998879i	$0.515074\pi$
$29$	−5.50806	+	6.56425i	−1.02282	+	1.21895i	−0.975484	+	0.220072i	$0.929371\pi$
$30$		0			0
$31$	−1.36807	+	3.75873i	−0.245712	+	0.675088i	0.754120	+	0.656737i	$0.228064\pi$
$31$	−1.36807	+	3.75873i	−0.245712	+	0.675088i	−0.999832	+	0.0183509i	$0.994158\pi$
$32$		0			0
$33$	−2.31500	−	8.73062i	−0.402989	−	1.51981i
$34$		0			0
$35$	8.55559	+	2.81844i	1.44616	+	0.476403i
$36$		0			0
$37$	3.11270	−	5.39136i	0.511725	−	0.886334i	−0.488182	−	0.872742i	$-0.662340\pi$
$37$	3.11270	−	5.39136i	0.511725	−	0.886334i	0.999908	−	0.0135926i	$-0.00432679\pi$
$38$		0			0
$39$	−2.94082	+	6.26394i	−0.470908	+	1.00303i
$40$		0			0
$41$	3.29135	−	2.76177i	0.514022	−	0.431315i	−0.348520	−	0.937301i	$-0.613316\pi$
$41$	3.29135	−	2.76177i	0.514022	−	0.431315i	0.862542	+	0.505986i	$0.168871\pi$
$42$		0			0
$43$	8.46720	−	3.08181i	1.29124	−	0.469971i	0.397103	−	0.917774i	$-0.370015\pi$
$43$	8.46720	−	3.08181i	1.29124	−	0.469971i	0.894132	+	0.447803i	$0.147793\pi$
$44$		0			0
$45$	8.81882	+	5.15301i	1.31463	+	0.768165i
$46$		0			0
$47$	0.0867629	−	0.0315791i	0.0126557	−	0.00460629i	−0.335685	−	0.941974i	$-0.608968\pi$
$47$	0.0867629	−	0.0315791i	0.0126557	−	0.00460629i	0.348340	+	0.937368i	$0.386745\pi$
$48$		0			0
$49$	−3.86697	−	5.83494i	−0.552424	−	0.833563i
$50$		0			0
$51$	−2.67714	−	5.78041i	−0.374874	−	0.809420i
$52$		0			0
$53$	−0.822872	−	0.475085i	−0.113030	−	0.0652580i	0.442419	−	0.896808i	$-0.354120\pi$
$53$	−0.822872	−	0.475085i	−0.113030	−	0.0652580i	−0.555449	+	0.831550i	$0.687454\pi$
$54$		0			0
$55$			17.7547i			2.39404i
$56$		0			0
$57$	−11.9080	+	5.51507i	−1.57725	+	0.730488i
$58$		0			0
$59$	0.157848	−	0.132450i	0.0205500	−	0.0172435i	−0.632455	−	0.774597i	$-0.717953\pi$
$59$	0.157848	−	0.132450i	0.0205500	−	0.0172435i	0.653005	+	0.757354i	$0.273508\pi$
$60$		0			0
$61$	−3.75967	−	10.3296i	−0.481376	−	1.32257i	−0.908314	−	0.418289i	$-0.862630\pi$
$61$	−3.75967	−	10.3296i	−0.481376	−	1.32257i	0.426938	−	0.904281i	$-0.359592\pi$
$62$		0			0
$63$	−2.90491	−	7.38658i	−0.365984	−	0.930621i
$64$		0			0
$65$	8.74342	−	10.4200i	1.08449	−	1.29244i
$66$		0			0
$67$	0.114606	+	0.649962i	0.0140013	+	0.0794055i	0.991008	−	0.133804i	$-0.0427193\pi$
$67$	0.114606	+	0.649962i	0.0140013	+	0.0794055i	−0.977006	+	0.213210i	$0.931608\pi$
$68$		0			0
$69$	−3.63636	+	7.74545i	−0.437766	+	0.932442i
$70$		0			0
$71$	−4.63188	+	2.67422i	−0.549703	+	0.317371i	−0.749002	−	0.662568i	$-0.769467\pi$
$71$	−4.63188	+	2.67422i	−0.549703	+	0.317371i	0.199299	+	0.979939i	$0.436133\pi$
$72$		0			0
$73$	−8.35033	+	4.82106i	−0.977332	+	0.564263i	−0.901464	−	0.432855i	$-0.857506\pi$
$73$	−8.35033	+	4.82106i	−0.977332	+	0.564263i	−0.0758684	+	0.997118i	$0.524173\pi$
$74$		0			0
$75$	−8.05207	−	8.09414i	−0.929773	−	0.934631i
$76$		0			0
$77$	8.53854	−	10.8376i	0.973057	−	1.23506i
$78$		0			0
$79$	−0.401358	+	2.27621i	−0.0451563	+	0.256094i	−0.999026	−	0.0441271i	$-0.985949\pi$
$79$	−0.401358	+	2.27621i	−0.0451563	+	0.256094i	0.953870	+	0.300221i	$0.0970605\pi$
$80$		0			0
$81$	−1.47037	−	8.87908i	−0.163375	−	0.986564i
$82$		0			0
$83$	−5.15096	−	4.32216i	−0.565391	−	0.474419i	0.314722	−	0.949184i	$-0.398089\pi$
$83$	−5.15096	−	4.32216i	−0.565391	−	0.474419i	−0.880113	+	0.474765i	$0.842533\pi$
$84$		0			0
$85$	2.17440	+	12.3317i	0.235847	+	1.33756i
$86$		0			0
$87$	−14.3262	−	3.87873i	−1.53593	−	0.415844i
$88$		0			0
$89$	1.57358			0.166799			0.0833997	−	0.996516i	$-0.473422\pi$
$89$	1.57358			0.166799			0.0833997	+	0.996516i	$0.473422\pi$
$90$		0			0
$91$	−10.3482	+	2.15559i	−1.08479	+	0.225967i
$92$		0			0
$93$	−6.90332	+	0.585841i	−0.715840	+	0.0607489i
$94$		0			0
$95$	25.4040	−	4.47941i	2.60639	−	0.459577i
$96$		0			0
$97$	−1.25237	−	3.44085i	−0.127159	−	0.349365i	0.859734	−	0.510741i	$-0.170629\pi$
$97$	−1.25237	−	3.44085i	−0.127159	−	0.349365i	−0.986893	+	0.161376i	$0.948407\pi$
$98$		0			0
$99$	12.0366	−	9.99347i	1.20972	−	1.00438i
$100$		0			0
$101$	1.45113	+	1.21764i	0.144393	+	0.121160i	0.712123	−	0.702055i	$-0.247734\pi$
$101$	1.45113	+	1.21764i	0.144393	+	0.121160i	−0.567730	+	0.823215i	$0.692178\pi$
$102$		0			0
$103$	−5.01468	+	0.884223i	−0.494111	+	0.0871251i	−0.415151	−	0.909753i	$-0.636271\pi$
$103$	−5.01468	+	0.884223i	−0.494111	+	0.0871251i	−0.0789603	+	0.996878i	$0.525160\pi$
$104$		0			0
$105$	1.79798	+	15.4981i	0.175465	+	1.51246i
$106$		0			0
$107$	5.57533	−	3.21892i	0.538987	−	0.311184i	−0.205681	−	0.978619i	$-0.565941\pi$
$107$	5.57533	−	3.21892i	0.538987	−	0.311184i	0.744668	+	0.667435i	$0.232608\pi$
$108$		0			0
$109$	−1.33104	+	2.30543i	−0.127491	+	0.220820i	−0.922704	−	0.385510i	$-0.874026\pi$
$109$	−1.33104	+	2.30543i	−0.127491	+	0.220820i	0.795213	+	0.606330i	$0.207359\pi$
$110$		0			0
$111$	10.7392	+	0.967761i	1.01932	+	0.0918558i
$112$		0			0
$113$	−1.42760	+	3.92229i	−0.134297	+	0.368978i	−0.988553	−	0.150875i	$-0.951791\pi$
$113$	−1.42760	+	3.92229i	−0.134297	+	0.368978i	0.854256	+	0.519853i	$0.174013\pi$
$114$		0			0
$115$	10.8114	−	12.8845i	1.00816	−	1.20148i
$116$		0			0
$117$	−11.9855	−	0.0624590i	−1.10806	−	0.00577434i
$118$		0			0
$119$	4.60324	−	8.57306i	0.421979	−	0.785891i
$120$		0			0
$121$	15.2177	+	5.53878i	1.38343	+	0.503526i
$122$		0			0
$123$	6.73638	+	3.16262i	0.607399	+	0.285164i
$124$		0			0
$125$	2.70957	+	4.69311i	0.242351	+	0.419765i
$126$		0			0
$127$	−1.14708	+	1.98680i	−0.101787	+	0.176300i	−0.912421	−	0.409253i	$-0.865789\pi$
$127$	−1.14708	+	1.98680i	−0.101787	+	0.176300i	0.810634	+	0.585553i	$0.199123\pi$
$128$		0			0
$129$	11.0069	+	11.0644i	0.969104	+	0.974167i
$130$		0			0
$131$	14.4895	−	12.1582i	1.26596	−	1.06226i	0.270936	−	0.962597i	$-0.412667\pi$
$131$	14.4895	−	12.1582i	1.26596	−	1.06226i	0.995021	−	0.0996665i	$-0.0317776\pi$
$132$		0			0
$133$	−17.6610	−	9.48296i	−1.53141	−	0.822277i
$134$		0			0
$135$	−1.67959	+	17.6112i	−0.144556	+	1.51573i
$136$		0			0
$137$	6.88509	+	18.9166i	0.588233	+	1.61616i	0.773732	+	0.633513i	$0.218388\pi$
$137$	6.88509	+	18.9166i	0.588233	+	1.61616i	−0.185499	+	0.982644i	$0.559390\pi$
$138$		0			0
$139$	8.88650	−	1.56693i	0.753743	−	0.132905i	0.216442	−	0.976296i	$-0.430555\pi$
$139$	8.88650	−	1.56693i	0.753743	−	0.132905i	0.537302	+	0.843390i	$0.319444\pi$
$140$		0			0
$141$	0.112787	+	0.113376i	0.00949838	+	0.00954801i
$142$		0			0
$143$	−10.4172	−	18.0431i	−0.871127	−	1.50884i
$144$		0			0
$145$	25.2659	+	14.5873i	2.09822	+	1.21141i
$146$		0			0
$147$	6.35584	−	10.3249i	0.524221	−	0.851582i
$148$		0			0
$149$	−5.94231	+	16.3264i	−0.486813	+	1.33751i	0.416737	+	0.909027i	$0.363174\pi$
$149$	−5.94231	+	16.3264i	−0.486813	+	1.33751i	−0.903551	+	0.428482i	$0.859049\pi$
$150$		0			0
$151$	−3.04228	+	17.2537i	−0.247578	+	1.40408i	0.566852	+	0.823820i	$0.308161\pi$
$151$	−3.04228	+	17.2537i	−0.247578	+	1.40408i	−0.814430	+	0.580262i	$0.802950\pi$
$152$		0			0
$153$	7.13622	−	8.41517i	0.576930	−	0.680326i
$154$		0			0
$155$	13.4116	+	2.36482i	1.07724	+	0.189947i
$156$		0			0
$157$	−11.4237	−	13.6142i	−0.911709	−	1.08653i	−0.995934	−	0.0900852i	$-0.971286\pi$
$157$	−11.4237	−	13.6142i	−0.911709	−	1.08653i	0.0842255	−	0.996447i	$-0.473158\pi$
$158$		0			0
$159$	0.147707	−	1.63910i	0.0117139	−	0.129989i
$160$		0			0
$161$	−12.7957	+	2.66542i	−1.00844	+	0.210064i
$162$		0			0
$163$	1.26841	+	2.19695i	0.0993497	+	0.172079i	0.911416	−	0.411487i	$-0.134990\pi$
$163$	1.26841	+	2.19695i	0.0993497	+	0.172079i	−0.812066	+	0.583566i	$0.801657\pi$
$164$		0			0
$165$	−27.9045	+	12.9237i	−2.17236	+	1.00611i
$166$		0			0
$167$	−9.64872	−	3.51185i	−0.746640	−	0.271755i	−0.0594489	−	0.998231i	$-0.518934\pi$
$167$	−9.64872	−	3.51185i	−0.746640	−	0.271755i	−0.687191	+	0.726477i	$0.741157\pi$
$168$		0			0
$169$	−0.514306	+	2.91678i	−0.0395620	+	0.224367i
$170$		0			0
$171$	−17.3358	−	14.7011i	−1.32570	−	1.12422i
$172$		0			0
$173$	17.4211	+	14.6180i	1.32450	+	1.11139i	0.985330	+	0.170662i	$0.0545905\pi$
$173$	17.4211	+	14.6180i	1.32450	+	1.11139i	0.339170	+	0.940725i	$0.389854\pi$
$174$		0			0
$175$	2.49746	−	17.2602i	0.188790	−	1.30475i
$176$		0			0
$177$	0.323066	+	0.151674i	0.0242831	+	0.0114005i
$178$		0			0
$179$			8.20144i			0.613004i	0.951870	+	0.306502i	$0.0991586\pi$
$179$			8.20144i			0.613004i	−0.951870	+	0.306502i	$0.900841\pi$
$180$		0			0
$181$	18.4566	+	10.6559i	1.37187	+	0.792050i	0.991164	−	0.132645i	$-0.0423471\pi$
$181$	18.4566	+	10.6559i	1.37187	+	0.792050i	0.380708	+	0.924695i	$0.375680\pi$
$182$		0			0
$183$	13.4981	−	13.4279i	0.997807	−	0.992621i
$184$		0			0
$185$	−19.9171	−	7.24924i	−1.46434	−	0.532975i
$186$		0			0
$187$	18.8881	+	3.33047i	1.38123	+	0.243548i
$188$		0			0
$189$	9.49479	−	9.94228i	0.690644	−	0.723195i
$190$		0			0
$191$	22.4547	+	3.95937i	1.62477	+	0.286490i	0.910539	−	0.413423i	$-0.135667\pi$
$191$	22.4547	+	3.95937i	1.62477	+	0.286490i	0.714228	+	0.699913i	$0.246778\pi$
$192$		0			0
$193$	18.1474	+	6.60512i	1.30628	+	0.475447i	0.899037	−	0.437873i	$-0.144268\pi$
$193$	18.1474	+	6.60512i	1.30628	+	0.475447i	0.407243	+	0.913320i	$0.366490\pi$
$194$		0			0
$195$	22.7412	+	6.15704i	1.62853	+	0.440915i
$196$		0			0
$197$	−1.31379	−	0.758514i	−0.0936033	−	0.0540419i	0.452468	−	0.891781i	$-0.350544\pi$
$197$	−1.31379	−	0.758514i	−0.0936033	−	0.0540419i	−0.546071	+	0.837739i	$0.683877\pi$
$198$		0			0
$199$		−	10.5673i		−	0.749099i	−0.927207	−	0.374549i	$-0.877797\pi$
$199$		−	10.5673i		−	0.749099i	0.927207	−	0.374549i	$-0.122203\pi$
$200$		0			0
$201$	−0.938106	+	0.653233i	−0.0661689	+	0.0460755i
$202$		0			0
$203$	−8.40725	−	21.0551i	−0.590073	−	1.47778i
$204$		0			0
$205$	−11.2059	−	9.40287i	−0.782654	−	0.656725i
$206$		0			0
$207$	−14.8202	−	0.0772315i	−1.03008	−	0.00536796i
$208$		0			0
$209$	6.86098	−	38.9106i	0.474584	−	2.69150i
$210$		0			0
$211$	11.7963	+	4.29351i	0.812093	+	0.295578i	0.714488	−	0.699647i	$-0.246660\pi$
$211$	11.7963	+	4.29351i	0.812093	+	0.295578i	0.0976050	+	0.995225i	$0.468882\pi$
$212$		0			0
$213$	−7.57456	−	5.33323i	−0.519000	−	0.365427i
$214$		0			0
$215$	−15.3390	−	26.5679i	−1.04611	−	1.81192i
$216$		0			0
$217$	−7.04926	−	7.89338i	−0.478535	−	0.535838i
$218$		0			0
$219$	−13.6554	−	9.61472i	−0.922744	−	0.649702i
$220$		0			0
$221$	−9.44506	−	11.2562i	−0.635344	−	0.757173i
$222$		0			0
$223$	−17.7911	−	3.13705i	−1.19138	−	0.210073i	−0.457412	−	0.889255i	$-0.651223\pi$
$223$	−17.7911	−	3.13705i	−1.19138	−	0.210073i	−0.733970	+	0.679182i	$0.762335\pi$
$224$		0			0
$225$	6.86021	−	18.5470i	0.457347	−	1.23646i
$226$		0			0
$227$	−4.22816	+	23.9791i	−0.280633	+	1.59155i	0.439849	+	0.898072i	$0.355032\pi$
$227$	−4.22816	+	23.9791i	−0.280633	+	1.59155i	−0.720481	+	0.693474i	$0.756079\pi$
$228$		0			0
$229$	3.04053	−	8.35380i	0.200924	−	0.552034i	−0.797779	−	0.602950i	$-0.793992\pi$
$229$	3.04053	−	8.35380i	0.200924	−	0.552034i	0.998703	+	0.0509157i	$0.0162140\pi$
$230$		0			0
$231$	23.2484	+	5.53106i	1.52963	+	0.363917i
$232$		0			0
$233$	−3.32605	−	1.92030i	−0.217897	−	0.125803i	0.387079	−	0.922046i	$-0.373484\pi$
$233$	−3.32605	−	1.92030i	−0.217897	−	0.125803i	−0.604976	+	0.796244i	$0.706817\pi$
$234$		0			0
$235$	−0.157178	−	0.272240i	−0.0102532	−	0.0177590i
$236$		0			0
$237$	−3.86961	+	1.02606i	−0.251358	+	0.0666498i
$238$		0			0
$239$	3.15316	−	0.555987i	0.203961	−	0.0359638i	−0.0707342	−	0.997495i	$-0.522534\pi$
$239$	3.15316	−	0.555987i	0.203961	−	0.0359638i	0.274695	+	0.961531i	$0.411423\pi$
$240$		0			0
$241$	−0.279960	−	0.769183i	−0.0180338	−	0.0495474i	0.930349	−	0.366675i	$-0.119504\pi$
$241$	−0.279960	−	0.769183i	−0.0180338	−	0.0495474i	−0.948383	+	0.317128i	$0.897282\pi$
$242$		0			0
$243$	12.8847	−	8.77406i	0.826555	−	0.562856i
$244$		0			0
$245$	−17.2780	+	16.4154i	−1.10385	+	1.04874i
$246$		0			0
$247$	−23.1884	+	19.4574i	−1.47544	+	1.23805i
$248$		0			0
$249$	3.04363	−	11.2417i	0.192882	−	0.712416i
$250$		0			0
$251$	−1.58268	+	2.74129i	−0.0998981	+	0.173029i	−0.911642	−	0.410985i	$-0.865185\pi$
$251$	−1.58268	+	2.74129i	−0.0998981	+	0.173029i	0.811744	+	0.584013i	$0.198518\pi$
$252$		0			0
$253$	−12.8810	−	22.3105i	−0.809820	−	1.40265i
$254$		0			0
$255$	−17.7986	+	12.3937i	−1.11459	+	0.776124i
$256$		0			0
$257$	−7.10354	−	2.58548i	−0.443107	−	0.161278i	0.110825	−	0.993840i	$-0.464651\pi$
$257$	−7.10354	−	2.58548i	−0.443107	−	0.161278i	−0.553931	+	0.832562i	$0.686873\pi$
$258$		0			0
$259$	8.67130	+	14.0035i	0.538808	+	0.870136i
$260$		0			0
$261$	−4.33200	−	25.3394i	−0.268144	−	1.56847i
$262$		0			0
$263$	−11.3794	+	13.5615i	−0.701686	+	0.836237i	−0.992716	−	0.120477i	$-0.961558\pi$
$263$	−11.3794	+	13.5615i	−0.701686	+	0.836237i	0.291030	+	0.956714i	$0.406002\pi$
$264$		0			0
$265$	−1.10644	+	3.03991i	−0.0679678	+	0.186740i
$266$		0			0
$267$	1.14542	+	2.47316i	0.0700983	+	0.151355i
$268$		0			0
$269$	4.49490	−	7.78539i	0.274059	−	0.474683i	−0.695839	−	0.718198i	$-0.744967\pi$
$269$	4.49490	−	7.78539i	0.274059	−	0.474683i	0.969897	+	0.243515i	$0.0783004\pi$
$270$		0			0
$271$	−28.2099	+	16.2870i	−1.71363	+	0.989364i	−0.784083	+	0.620656i	$0.786866\pi$
$271$	−28.2099	+	16.2870i	−1.71363	+	0.989364i	−0.929545	+	0.368708i	$0.879800\pi$
$272$		0			0
$273$	−10.9204	−	14.6950i	−0.660932	−	0.889380i
$274$		0			0
$275$	33.8522	−	5.96906i	2.04136	−	0.359948i
$276$		0			0
$277$	22.9194	+	19.2317i	1.37709	+	1.15552i	0.970274	+	0.242009i	$0.0778064\pi$
$277$	22.9194	+	19.2317i	1.37709	+	1.15552i	0.406819	+	0.913509i	$0.366638\pi$
$278$		0			0
$279$	−5.94570	−	10.4233i	−0.355960	−	0.624028i
$280$		0			0
$281$	−4.56329	−	12.5375i	−0.272223	−	0.747926i	−0.998187	−	0.0601934i	$-0.980828\pi$
$281$	−4.56329	−	12.5375i	−0.272223	−	0.747926i	0.725964	−	0.687733i	$-0.241394\pi$
$282$		0			0
$283$	15.2606	−	2.69085i	0.907148	−	0.159955i	0.299440	−	0.954115i	$-0.403200\pi$
$283$	15.2606	−	2.69085i	0.907148	−	0.159955i	0.607708	+	0.794160i	$0.292089\pi$
$284$		0			0
$285$	25.5318	+	36.6662i	1.51237	+	2.17192i
$286$		0			0
$287$	2.31817	+	11.1287i	0.136837	+	0.656907i
$288$		0			0
$289$	−3.47325			−0.204309
$290$		0			0
$291$	4.49629	−	4.47292i	0.263577	−	0.262207i
$292$		0			0
$293$	1.97923	+	11.2248i	0.115628	+	0.655760i	0.986437	+	0.164138i	$0.0524844\pi$
$293$	1.97923	+	11.2248i	0.115628	+	0.655760i	−0.870809	+	0.491621i	$0.836405\pi$
$294$		0			0
$295$	−0.537417	−	0.450946i	−0.0312896	−	0.0262551i
$296$		0			0
$297$	24.4679	+	11.6433i	1.41977	+	0.675612i
$298$		0			0
$299$	−3.42729	+	19.4371i	−0.198205	+	1.12408i
$300$		0			0
$301$	−3.41394	+	23.5941i	−0.196776	+	1.35994i
$302$		0			0
$303$	−0.857453	+	3.16703i	−0.0492594	+	0.181941i
$304$		0			0
$305$	−32.4117	+	18.7129i	−1.85589	+	1.07150i
$306$		0			0
$307$	−2.53824	+	1.46546i	−0.144865	+	0.0836380i	−0.570681	−	0.821172i	$-0.693321\pi$
$307$	−2.53824	+	1.46546i	−0.144865	+	0.0836380i	0.425815	+	0.904810i	$0.359987\pi$
$308$		0			0
$309$	−5.03991	−	7.23781i	−0.286711	−	0.411744i
$310$		0			0
$311$	1.51071	+	8.56764i	0.0856643	+	0.485826i	0.997211	+	0.0746305i	$0.0237777\pi$
$311$	1.51071	+	8.56764i	0.0856643	+	0.485826i	−0.911547	+	0.411196i	$0.865111\pi$
$312$		0			0
$313$	3.79403	−	4.52155i	0.214451	−	0.255573i	−0.648085	−	0.761568i	$-0.724430\pi$
$313$	3.79403	−	4.52155i	0.214451	−	0.255573i	0.862537	+	0.505995i	$0.168874\pi$
$314$		0			0
$315$	−23.0493	+	14.1070i	−1.29868	+	0.794839i
$316$		0			0
$317$	11.6009	+	31.8731i	0.651569	+	1.79017i	0.611869	+	0.790959i	$0.290418\pi$
$317$	11.6009	+	31.8731i	0.651569	+	1.79017i	0.0396997	+	0.999212i	$0.487360\pi$
$318$		0			0
$319$	34.2314	−	28.7235i	1.91659	−	1.60821i
$320$		0			0
$321$	9.11738	+	6.41953i	0.508883	+	0.358303i
$322$		0			0
$323$		−	27.8659i		−	1.55050i
$324$		0			0
$325$	−22.8070	−	13.1676i	−1.26510	−	0.730408i
$326$		0			0
$327$	−4.59225	−	0.413830i	−0.253952	−	0.0228848i
$328$		0			0
$329$	−0.0349825	+	0.241767i	−0.00192865	+	0.0133291i
$330$		0			0
$331$	−23.4513	+	8.53558i	−1.28900	+	0.469158i	−0.893399	−	0.449265i	$-0.851686\pi$
$331$	−23.4513	+	8.53558i	−1.28900	+	0.469158i	−0.395601	+	0.918422i	$0.629464\pi$
$332$		0			0
$333$	6.29610	+	17.5830i	0.345024	+	0.963540i
$334$		0			0
$335$	2.11152	−	0.768531i	0.115365	−	0.0419894i
$336$		0			0
$337$	14.2082	−	11.9221i	0.773968	−	0.649436i	−0.167754	−	0.985829i	$-0.553651\pi$
$337$	14.2082	−	11.9221i	0.773968	−	0.649436i	0.941722	+	0.336393i	$0.109207\pi$
$338$		0			0
$339$	−7.20371	+	0.611333i	−0.391252	+	0.0332031i
$340$		0			0
$341$	10.4295	−	18.0645i	0.564790	−	0.978246i
$342$		0			0
$343$	18.4411	−	1.71081i	0.995724	−	0.0923748i
$344$		0			0
$345$	28.1198	+	7.61327i	1.51392	+	0.409885i
$346$		0			0
$347$	8.00581	−	21.9958i	0.429774	−	1.18080i	−0.516175	−	0.856483i	$-0.672645\pi$
$347$	8.00581	−	21.9958i	0.429774	−	1.18080i	0.945950	−	0.324313i	$-0.105133\pi$
$348$		0			0
$349$	−14.0653	+	16.7624i	−0.752899	+	0.897270i	−0.997377	−	0.0723850i	$-0.976939\pi$
$349$	−14.0653	+	16.7624i	−0.752899	+	0.897270i	0.244478	+	0.969655i	$0.421383\pi$
$350$		0			0
$351$	−8.62612	−	18.8827i	−0.460428	−	1.00789i
$352$		0			0
$353$	−21.2118	+	7.72046i	−1.12899	+	0.410919i	−0.837925	−	0.545785i	$-0.816232\pi$
$353$	−21.2118	+	7.72046i	−1.12899	+	0.410919i	−0.291064	+	0.956703i	$0.594009\pi$
$354$		0			0
$355$	11.7049	+	13.9493i	0.621231	+	0.740354i
$356$		0			0
$357$	16.8248	+	0.994431i	0.890461	+	0.0526309i
$358$		0			0
$359$			26.0175i			1.37315i	0.727057	+	0.686577i	$0.240887\pi$
$359$			26.0175i			1.37315i	−0.727057	+	0.686577i	$0.759113\pi$
$360$		0			0
$361$	−38.4055			−2.02134
$362$		0			0
$363$	2.37185	+	27.9489i	0.124490	+	1.46694i
$364$		0			0
$365$	21.1015	+	25.1478i	1.10450	+	1.31630i
$366$		0			0
$367$	−20.7174	−	3.65303i	−1.08144	−	0.190687i	−0.395587	−	0.918428i	$-0.629459\pi$
$367$	−20.7174	−	3.65303i	−1.08144	−	0.190687i	−0.685852	+	0.727741i	$0.740570\pi$
$368$		0			0
$369$	−0.0671698	+	12.8895i	−0.00349672	+	0.670999i
$370$		0			0
$371$	2.13733	−	1.32348i	0.110964	−	0.0687117i
$372$		0			0
$373$	1.91950	+	10.8860i	0.0993881	+	0.563658i	0.993314	+	0.115443i	$0.0368288\pi$
$373$	1.91950	+	10.8860i	0.0993881	+	0.563658i	−0.893926	+	0.448215i	$0.852060\pi$
$374$		0			0
$375$	−5.40373	+	7.67469i	−0.279047	+	0.396319i
$376$		0			0
$377$	−34.2351			−1.76320
$378$		0			0
$379$	18.1091			0.930203			0.465102	−	0.885257i	$-0.346018\pi$
$379$	18.1091			0.930203			0.465102	+	0.885257i	$0.346018\pi$
$380$		0			0
$381$	−3.95757	−	0.356635i	−0.202752	−	0.0182710i
$382$		0			0
$383$	0.256321	+	1.45367i	0.0130974	+	0.0742791i	0.990656	−	0.136385i	$-0.0435485\pi$
$383$	0.256321	+	1.45367i	0.0130974	+	0.0742791i	−0.977558	+	0.210664i	$0.932437\pi$
$384$		0			0
$385$	−41.3858	−	22.2218i	−2.10922	−	1.13253i
$386$		0			0
$387$	−9.37767	+	25.3531i	−0.476694	+	1.28877i
$388$		0			0
$389$	−11.7473	−	2.07137i	−0.595614	−	0.105023i	−0.132289	−	0.991211i	$-0.542233\pi$
$389$	−11.7473	−	2.07137i	−0.595614	−	0.105023i	−0.463325	+	0.886189i	$0.653344\pi$
$390$		0			0
$391$	−11.6790	−	13.9184i	−0.590630	−	0.703886i
$392$		0			0
$393$	29.6557	+	13.9228i	1.49593	+	0.702315i
$394$		0			0
$395$	7.86928			0.395946
$396$		0			0
$397$		−	6.36679i		−	0.319540i	−0.987154	−	0.159770i	$-0.948925\pi$
$397$		−	6.36679i		−	0.319540i	0.987154	−	0.159770i	$-0.0510753\pi$
$398$		0			0
$399$	2.04859	−	34.6601i	0.102558	−	1.73517i
$400$		0			0
$401$	−16.3873	−	19.5296i	−0.818341	−	0.975261i	0.181626	−	0.983368i	$-0.441864\pi$
$401$	−16.3873	−	19.5296i	−0.818341	−	0.975261i	−0.999967	+	0.00810645i	$0.997420\pi$
$402$		0			0
$403$	−15.0170	+	5.46572i	−0.748048	+	0.272267i
$404$		0			0
$405$	−28.9016	+	10.1795i	−1.43613	+	0.505823i
$406$		0			0
$407$	−20.8677	+	24.8691i	−1.03437	+	1.23272i
$408$		0			0
$409$	6.72474	−	18.4761i	0.332517	−	0.913583i	−0.654938	−	0.755683i	$-0.727305\pi$
$409$	6.72474	−	18.4761i	0.332517	−	0.913583i	0.987455	−	0.157901i	$-0.0504726\pi$
$410$		0			0
$411$	−24.7191	+	24.5906i	−1.21930	+	1.21296i
$412$		0			0
$413$	0.111176	+	0.533715i	0.00547060	+	0.0262624i
$414$		0			0
$415$	−11.4466	+	19.8261i	−0.561892	+	0.973226i
$416$		0			0
$417$	8.93122	+	12.8261i	0.437364	+	0.628097i
$418$		0			0
$419$	−5.01894	+	4.21139i	−0.245191	+	0.205740i	−0.757098	−	0.653301i	$-0.773384\pi$
$419$	−5.01894	+	4.21139i	−0.245191	+	0.205740i	0.511907	+	0.859041i	$0.328939\pi$
$420$		0			0
$421$	27.0755	−	9.85467i	1.31958	−	0.480287i	0.416255	−	0.909248i	$-0.363342\pi$
$421$	27.0755	−	9.85467i	1.31958	−	0.480287i	0.903323	+	0.428960i	$0.141120\pi$
$422$		0			0
$423$	−0.0960924	+	0.259791i	−0.00467217	+	0.0126315i
$424$		0			0
$425$	22.7813	−	8.29172i	1.10506	−	0.402208i
$426$		0			0
$427$	28.7838	+	4.16486i	1.39294	+	0.201552i
$428$		0			0
$429$	20.7751	−	29.5060i	1.00303	−	1.42456i
$430$		0			0
$431$	30.0524	+	17.3507i	1.44757	+	0.835756i	0.998336	−	0.0576573i	$-0.0183631\pi$
$431$	30.0524	+	17.3507i	1.44757	+	0.835756i	0.449236	+	0.893413i	$0.351696\pi$
$432$		0			0
$433$		−	22.3944i		−	1.07620i	−0.842880	−	0.538102i	$-0.819141\pi$
$433$		−	22.3944i		−	1.07620i	0.842880	−	0.538102i	$-0.180859\pi$
$434$		0			0
$435$	−4.53529	+	50.3279i	−0.217451	+	2.41304i
$436$		0			0
$437$	−28.6728	+	24.0594i	−1.37161	+	1.15092i
$438$		0			0
$439$	−9.41439	−	25.8658i	−0.449324	−	1.23451i	−0.933195	−	0.359369i	$-0.882992\pi$
$439$	−9.41439	−	25.8658i	−0.449324	−	1.23451i	0.483871	−	0.875139i	$-0.339230\pi$
$440$		0			0
$441$	20.8538	+	2.47378i	0.993037	+	0.117799i
$442$		0			0
$443$	−3.01473	+	3.59281i	−0.143234	+	0.170700i	−0.832892	−	0.553436i	$-0.813316\pi$
$443$	−3.01473	+	3.59281i	−0.143234	+	0.170700i	0.689658	+	0.724135i	$0.257761\pi$
$444$		0			0
$445$	−0.930321	−	5.27611i	−0.0441014	−	0.250112i
$446$		0			0
$447$	−29.9852	+	2.54465i	−1.41825	+	0.120358i
$448$		0			0
$449$	1.49280	−	0.861866i	0.0704494	−	0.0406740i	−0.464362	−	0.885646i	$-0.653716\pi$
$449$	1.49280	−	0.861866i	0.0704494	−	0.0406740i	0.534811	+	0.844972i	$0.320383\pi$
$450$		0			0
$451$	−19.4039	+	11.2029i	−0.913694	+	0.527522i
$452$		0			0
$453$	−29.3316	+	7.77752i	−1.37812	+	0.365420i
$454$		0			0
$455$	13.3455	+	33.4225i	0.625649	+	1.56687i
$456$		0			0
$457$	1.98772	−	11.2729i	0.0929815	−	0.527324i	−0.902366	−	0.430971i	$-0.858171\pi$
$457$	1.98772	−	11.2729i	0.0929815	−	0.527324i	0.995347	−	0.0963531i	$-0.0307178\pi$
$458$		0			0
$459$	18.4204	+	5.09038i	0.859790	+	0.237599i
$460$		0			0
$461$	0.965463	+	0.810120i	0.0449661	+	0.0377310i	0.664994	−	0.746849i	$-0.268434\pi$
$461$	0.965463	+	0.810120i	0.0449661	+	0.0377310i	−0.620028	+	0.784580i	$0.712879\pi$
$462$		0			0
$463$	−6.39773	−	36.2833i	−0.297328	−	1.68623i	−0.657589	−	0.753377i	$-0.728424\pi$
$463$	−6.39773	−	36.2833i	−0.297328	−	1.68623i	0.360261	−	0.932851i	$-0.382687\pi$
$464$		0			0
$465$	6.04561	+	22.8000i	0.280358	+	1.05732i
$466$		0			0
$467$	−20.3672			−0.942483			−0.471242	−	0.882004i	$-0.656194\pi$
$467$	−20.3672			−0.942483			−0.471242	+	0.882004i	$0.656194\pi$
$468$		0			0
$469$	−1.65849	−	0.546351i	−0.0765821	−	0.0252282i
$470$		0			0
$471$	13.0817	−	27.8641i	0.602775	−	1.28391i
$472$		0			0
$473$	−46.2748	+	8.15950i	−2.12772	+	0.375174i
$474$		0			0
$475$	−17.0815	−	46.9309i	−0.783751	−	2.15334i
$476$		0			0
$477$	2.68365	−	0.960960i	0.122876	−	0.0439993i
$478$		0			0
$479$	21.7978	+	18.2905i	0.995968	+	0.835716i	0.986421	−	0.164238i	$-0.0525166\pi$
$479$	21.7978	+	18.2905i	0.995968	+	0.835716i	0.00954704	+	0.999954i	$0.496961\pi$
$480$		0			0
$481$	24.4940	−	4.31895i	1.11683	−	0.196927i
$482$		0			0
$483$	−13.5032	−	18.1705i	−0.614418	−	0.826788i
$484$		0			0
$485$	−10.7965	+	6.23337i	−0.490245	+	0.283043i
$486$		0			0
$487$	0.199066	−	0.344792i	0.00902053	−	0.0156240i	−0.861480	−	0.507792i	$-0.830462\pi$
$487$	0.199066	−	0.344792i	0.00902053	−	0.0156240i	0.870500	+	0.492168i	$0.163795\pi$
$488$		0			0
$489$	−2.52961	+	3.59270i	−0.114393	+	0.162468i
$490$		0			0
$491$	5.68427	−	15.6174i	0.256528	−	0.704804i	−0.742848	−	0.669461i	$-0.766525\pi$
$491$	5.68427	−	15.6174i	0.256528	−	0.704804i	0.999375	−	0.0353434i	$-0.0112525\pi$
$492$		0			0
$493$	20.2580	−	24.1425i	0.912373	−	1.08732i
$494$		0			0
$495$	−40.6236	−	34.4496i	−1.82590	−	1.54839i
$496$		0			0
$497$	−0.436273	−	14.1439i	−0.0195695	−	0.634441i
$498$		0			0
$499$	−12.1474	−	4.42128i	−0.543791	−	0.197924i	0.0554945	−	0.998459i	$-0.482326\pi$
$499$	−12.1474	−	4.42128i	−0.543791	−	0.197924i	−0.599286	+	0.800535i	$0.704549\pi$
$500$		0			0
$501$	−1.50386	−	17.7209i	−0.0671876	−	0.791712i
$502$		0			0
$503$	−13.1104	−	22.7079i	−0.584565	−	1.01250i	−0.994930	−	0.100574i	$-0.967932\pi$
$503$	−13.1104	−	22.7079i	−0.584565	−	1.01250i	0.410365	−	0.911921i	$-0.365401\pi$
$504$		0			0
$505$	3.22474	−	5.58542i	0.143499	−	0.248548i
$506$		0			0
$507$	−4.95858	+	1.31481i	−0.220218	+	0.0583928i
$508$		0			0
$509$	8.78538	−	7.37181i	0.389405	−	0.326750i	−0.426976	−	0.904263i	$-0.640421\pi$
$509$	8.78538	−	7.37181i	0.389405	−	0.326750i	0.816381	+	0.577513i	$0.195977\pi$
$510$		0			0
$511$	−0.786511	−	25.4985i	−0.0347932	−	1.12799i
$512$		0			0
$513$	10.4865	−	37.9471i	0.462990	−	1.67541i
$514$		0			0
$515$	5.92948	+	16.2911i	0.261284	+	0.717872i
$516$		0			0
$517$	−0.474175	+	0.0836099i	−0.0208542	+	0.00367716i
$518$		0			0
$519$	−10.2939	+	38.0207i	−0.451851	+	1.66892i
$520$		0			0
$521$	−3.75886	−	6.51053i	−0.164679	−	0.285232i	0.771863	−	0.635789i	$-0.219325\pi$
$521$	−3.75886	−	6.51053i	−0.164679	−	0.285232i	−0.936541	+	0.350558i	$0.885992\pi$
$522$		0			0
$523$	30.3709	+	17.5346i	1.32803	+	0.766736i	0.984994	−	0.172588i	$-0.0552129\pi$
$523$	30.3709	+	17.5346i	1.32803	+	0.766736i	0.343031	+	0.939324i	$0.388546\pi$
$524$		0			0
$525$	28.9453	−	8.63858i	1.26328	−	0.377018i
$526$		0			0
$527$	5.03157	−	13.8241i	0.219179	−	0.602189i
$528$		0			0
$529$	−0.243980	+	1.38368i	−0.0106078	+	0.0601600i
$530$		0			0
$531$	−0.00322136	+	0.618158i	−0.000139795	+	0.0268258i
$532$		0			0
$533$	16.9049	+	2.98078i	0.732231	+	0.129112i
$534$		0			0
$535$	−14.0890	−	16.7906i	−0.609121	−	0.725922i
$536$		0			0
$537$	−12.8900	+	5.96986i	−0.556244	+	0.257618i
$538$		0			0
$539$	14.5754	+	33.4676i	0.627807	+	1.44155i
$540$		0			0
$541$	9.21190	+	15.9555i	0.396050	+	0.685979i	0.993235	−	0.116125i	$-0.0370472\pi$
$541$	9.21190	+	15.9555i	0.396050	+	0.685979i	−0.597184	+	0.802104i	$0.703714\pi$
$542$		0			0
$543$	−3.31301	+	36.7643i	−0.142175	+	1.57771i
$544$		0			0
$545$	8.51688	+	3.09989i	0.364823	+	0.132785i
$546$		0			0
$547$	−2.17800	+	12.3520i	−0.0931245	+	0.528135i	0.902181	+	0.431357i	$0.141965\pi$
$547$	−2.17800	+	12.3520i	−0.0931245	+	0.528135i	−0.995306	+	0.0967786i	$0.969146\pi$
$548$		0			0
$549$	30.9296	+	11.4403i	1.32004	+	0.488262i
$550$		0			0
$551$	−49.7350	−	41.7326i	−2.11878	−	1.77787i
$552$		0			0
$553$	−4.80348	−	3.78448i	−0.204265	−	0.160932i
$554$		0			0
$555$	−3.10431	−	36.5800i	−0.131771	−	1.55273i
$556$		0			0
$557$		−	12.2848i		−	0.520524i	−0.965538	−	0.260262i	$-0.916191\pi$
$557$		−	12.2848i		−	0.520524i	0.965538	−	0.260262i	$-0.0838089\pi$
$558$		0			0
$559$	31.1763	+	17.9997i	1.31862	+	0.761305i
$560$		0			0
$561$	8.51427	+	32.1101i	0.359473	+	1.35569i
$562$		0			0
$563$	−27.3440	−	9.95240i	−1.15241	−	0.419444i	−0.306031	−	0.952022i	$-0.599001\pi$
$563$	−27.3440	−	9.95240i	−1.15241	−	0.419444i	−0.846381	+	0.532578i	$0.821223\pi$
$564$		0			0
$565$	13.9952	+	2.46773i	0.588781	+	0.103818i
$566$		0			0
$567$	22.5373	+	7.68568i	0.946478	+	0.322768i
$568$		0			0
$569$	13.2725	+	2.34030i	0.556412	+	0.0981104i	0.444781	−	0.895639i	$-0.353282\pi$
$569$	13.2725	+	2.34030i	0.556412	+	0.0981104i	0.111631	+	0.993750i	$0.464393\pi$
$570$		0			0
$571$	12.8860	+	4.69011i	0.539261	+	0.196275i	0.597269	−	0.802041i	$-0.296253\pi$
$571$	12.8860	+	4.69011i	0.539261	+	0.196275i	−0.0580075	+	0.998316i	$0.518475\pi$
$572$		0			0
$573$	10.1220	+	38.1735i	0.422854	+	1.59472i
$574$		0			0
$575$	−28.2011	−	16.2819i	−1.17607	−	0.679004i
$576$		0			0
$577$			32.2107i			1.34095i	0.741932	+	0.670476i	$0.233910\pi$
$577$			32.2107i			1.34095i	−0.741932	+	0.670476i	$0.766090\pi$
$578$		0			0
$579$	2.82848	+	33.3297i	0.117548	+	1.38514i
$580$		0			0
$581$	16.5219	−	6.59715i	0.685442	−	0.273696i
$582$		0			0
$583$	3.79572	+	3.18499i	0.157203	+	0.131909i
$584$		0			0
$585$	6.87655	+	40.2235i	0.284310	+	1.66304i
$586$		0			0
$587$	−4.81253	+	27.2932i	−0.198634	+	1.12651i	0.708513	+	0.705698i	$0.249366\pi$
$587$	−4.81253	+	27.2932i	−0.198634	+	1.12651i	−0.907147	+	0.420813i	$0.861745\pi$
$588$		0			0
$589$	−28.4786	−	10.3653i	−1.17344	−	0.427097i
$590$		0			0
$591$	0.235827	−	2.61697i	0.00970064	−	0.107648i
$592$		0			0
$593$	−9.73131	−	16.8551i	−0.399617	−	0.692157i	0.594061	−	0.804420i	$-0.297524\pi$
$593$	−9.73131	−	16.8551i	−0.399617	−	0.692157i	−0.993679	+	0.112262i	$0.964190\pi$
$594$		0			0
$595$	−31.4664	−	10.3659i	−1.29000	−	0.424959i
$596$		0			0
$597$	16.6084	−	7.69201i	0.679737	−	0.314813i
$598$		0			0
$599$	−14.9010	−	17.7583i	−0.608839	−	0.725586i	0.370270	−	0.928924i	$-0.379265\pi$
$599$	−14.9010	−	17.7583i	−0.608839	−	0.725586i	−0.979108	+	0.203339i	$0.934821\pi$
$600$		0			0
$601$	37.4177	+	6.59776i	1.52630	+	0.269128i	0.872906	−	0.487889i	$-0.162233\pi$
$601$	37.4177	+	6.59776i	1.52630	+	0.269128i	0.653395	+	0.757017i	$0.273344\pi$
$602$		0			0
$603$	−1.70952	−	0.998906i	−0.0696170	−	0.0406786i
$604$		0			0
$605$	9.57428	−	54.2985i	0.389250	−	2.20755i
$606$		0			0
$607$	−12.4714	+	34.2648i	−0.506197	+	1.39077i	0.378933	+	0.925424i	$0.376291\pi$
$607$	−12.4714	+	34.2648i	−0.506197	+	1.39077i	−0.885131	+	0.465342i	$0.845931\pi$
$608$		0			0
$609$	26.9720	−	28.5395i	1.09296	−	1.15648i
$610$		0			0
$611$	0.319462	+	0.184442i	0.0129241	+	0.00746171i
$612$		0			0
$613$	5.58435	+	9.67238i	0.225550	+	0.390664i	0.956484	−	0.291784i	$-0.0942488\pi$
$613$	5.58435	+	9.67238i	0.225550	+	0.390664i	−0.730934	+	0.682448i	$0.760915\pi$
$614$		0			0
$615$	6.62142	−	24.4564i	0.267001	−	0.986177i
$616$		0			0
$617$	21.5546	−	3.80066i	0.867756	−	0.153009i	0.277991	−	0.960584i	$-0.410332\pi$
$617$	21.5546	−	3.80066i	0.867756	−	0.153009i	0.589765	+	0.807575i	$0.299220\pi$
$618$		0			0
$619$	9.62741	+	26.4511i	0.386958	+	1.06316i	0.968363	+	0.249545i	$0.0802810\pi$
$619$	9.62741	+	26.4511i	0.386958	+	1.06316i	−0.581405	+	0.813614i	$0.697497\pi$
$620$		0			0
$621$	−10.6663	−	23.3488i	−0.428025	−	0.936954i
$622$		0			0
$623$	−1.96950	+	3.66799i	−0.0789064	+	0.146955i
$624$		0			0
$625$	−11.1139	+	9.32564i	−0.444555	+	0.373026i
$626$		0			0
$627$	66.1488	−	17.5399i	2.64173	−	0.700477i
$628$		0			0
$629$	−11.4481	+	19.8287i	−0.456467	+	0.790624i
$630$		0			0
$631$	14.2798	+	24.7334i	0.568472	+	0.984622i	0.996717	+	0.0809596i	$0.0257985\pi$
$631$	14.2798	+	24.7334i	0.568472	+	0.984622i	−0.428246	+	0.903662i	$0.640868\pi$
$632$		0			0
$633$	1.83859	+	21.6652i	0.0730775	+	0.861116i
$634$		0			0
$635$	7.33978	+	2.67146i	0.291270	+	0.106014i
$636$		0			0
$637$	7.92725	−	26.8195i	0.314089	−	1.06263i
$638$		0			0
$639$	2.86854	−	15.7868i	0.113478	−	0.624516i
$640$		0			0
$641$	−5.54412	+	6.60722i	−0.218979	+	0.260969i	−0.864339	−	0.502909i	$-0.832263\pi$
$641$	−5.54412	+	6.60722i	−0.218979	+	0.260969i	0.645360	+	0.763879i	$0.276707\pi$
$642$		0			0
$643$	9.28376	−	25.5069i	0.366116	−	1.00589i	−0.610709	−	0.791855i	$-0.709116\pi$
$643$	9.28376	−	25.5069i	0.366116	−	1.00589i	0.976825	−	0.214040i	$-0.0686623\pi$
$644$		0			0
$645$	30.5908	−	43.4468i	1.20451	−	1.71072i
$646$		0			0
$647$	−19.4819	+	33.7436i	−0.765912	+	1.32660i	0.173850	+	0.984772i	$0.444379\pi$
$647$	−19.4819	+	33.7436i	−0.765912	+	1.32660i	−0.939763	+	0.341827i	$0.888954\pi$
$648$		0			0
$649$	−0.930580	+	0.537271i	−0.0365285	+	0.0210897i
$650$		0			0
$651$	7.27464	−	16.8248i	0.285116	−	0.659414i
$652$		0			0
$653$	8.30041	−	1.46359i	0.324820	−	0.0572745i	−0.00886048	−	0.999961i	$-0.502820\pi$
$653$	8.30041	−	1.46359i	0.324820	−	0.0572745i	0.333681	+	0.942686i	$0.391709\pi$
$654$		0			0
$655$	−49.3319	−	41.3944i	−1.92756	−	1.61741i
$656$		0			0
$657$	5.17140	−	28.4604i	0.201755	−	1.11034i
$658$		0			0
$659$	−7.86933	−	21.6208i	−0.306546	−	0.842227i	−0.993324	−	0.115360i	$-0.963198\pi$
$659$	−7.86933	−	21.6208i	−0.306546	−	0.842227i	0.686778	−	0.726867i	$-0.259024\pi$
$660$		0			0
$661$	−9.02230	+	1.59088i	−0.350927	+	0.0618779i	−0.346333	−	0.938112i	$-0.612573\pi$
$661$	−9.02230	+	1.59088i	−0.350927	+	0.0618779i	−0.00459369	+	0.999989i	$0.501462\pi$
$662$		0			0
$663$	10.8160	−	23.0380i	0.420057	−	0.894721i
$664$		0			0
$665$	−21.3543	+	64.8227i	−0.828085	+	2.51372i
$666$		0			0
$667$	−42.3322			−1.63911
$668$		0			0
$669$	−8.01980	−	30.2453i	−0.310063	−	1.16935i
$670$		0			0
$671$	9.95422	+	56.4532i	0.384278	+	2.17935i
$672$		0			0
$673$	−36.6890	−	30.7857i	−1.41426	−	1.18670i	−0.954333	−	0.298743i	$-0.903433\pi$
$673$	−36.6890	−	30.7857i	−1.41426	−	1.18670i	−0.459923	−	0.887959i	$-0.652123\pi$
$674$		0			0
$675$	34.1434	−	2.71840i	1.31418	−	0.104631i
$676$		0			0
$677$	−1.43912	+	8.16168i	−0.0553101	+	0.313679i	−0.999894	−	0.0145924i	$-0.995355\pi$
$677$	−1.43912	+	8.16168i	−0.0553101	+	0.313679i	0.944583	+	0.328271i	$0.106466\pi$
$678$		0			0
$679$	9.58803	+	1.38734i	0.367955	+	0.0532411i
$680$		0			0
$681$	−40.7649	+	10.8092i	−1.56212	+	0.414208i
$682$		0			0
$683$	20.7981	−	12.0078i	0.795818	−	0.459466i	−0.0461886	−	0.998933i	$-0.514708\pi$
$683$	20.7981	−	12.0078i	0.795818	−	0.459466i	0.842007	+	0.539467i	$0.181374\pi$
$684$		0			0
$685$	59.3556	−	34.2690i	2.26786	−	1.30935i
$686$		0			0
$687$	15.3427	−	1.30203i	0.585359	−	0.0496757i
$688$		0			0
$689$	−0.659192	−	3.73847i	−0.0251132	−	0.142424i
$690$		0			0
$691$	−7.68069	+	9.15348i	−0.292187	+	0.348215i	−0.892090	−	0.451858i	$-0.850761\pi$
$691$	−7.68069	+	9.15348i	−0.292187	+	0.348215i	0.599903	+	0.800073i	$0.295206\pi$
$692$		0			0
$693$	8.22957	+	40.5650i	0.312615	+	1.54094i
$694$		0			0
$695$	−10.5076	−	28.8694i	−0.398577	−	1.09508i
$696$		0			0
$697$	−12.1052	+	10.1574i	−0.458515	+	0.384740i
$698$		0			0
$699$	0.597034	−	6.62526i	0.0225819	−	0.250590i
$700$		0			0
$701$		−	23.0672i		−	0.871236i	−0.900132	−	0.435618i	$-0.856530\pi$
$701$		−	23.0672i		−	0.871236i	0.900132	−	0.435618i	$-0.143470\pi$
$702$		0			0
$703$	40.8484	+	23.5838i	1.54063	+	0.889482i
$704$		0			0
$705$	0.313462	−	0.445197i	0.0118057	−	0.0167671i
$706$		0			0
$707$	−4.65454	+	1.85855i	−0.175052	+	0.0698980i
$708$		0			0
$709$	33.8202	−	12.3095i	1.27014	−	0.462295i	0.382983	−	0.923755i	$-0.374897\pi$
$709$	33.8202	−	12.3095i	1.27014	−	0.462295i	0.887161	+	0.461461i	$0.152674\pi$
$710$		0			0
$711$	−4.42934	−	5.33489i	−0.166113	−	0.200074i
$712$		0			0
$713$	−18.5687	+	6.75844i	−0.695402	+	0.253106i
$714$		0			0
$715$	−54.3384	+	45.5953i	−2.03214	+	1.70517i
$716$		0			0
$717$	3.16903	+	4.55103i	0.118349	+	0.169961i
$718$		0			0
$719$	11.8984	−	20.6086i	0.443736	−	0.768573i	−0.554228	−	0.832365i	$-0.686986\pi$
$719$	11.8984	−	20.6086i	0.443736	−	0.768573i	0.997963	+	0.0637925i	$0.0203196\pi$
$720$		0			0
$721$	4.21529	−	12.7958i	0.156985	−	0.476542i
$722$		0			0
$723$	1.00512	−	0.999896i	0.0373808	−	0.0371865i
$724$		0			0
$725$	19.3188	−	53.0779i	0.717481	−	1.97126i
$726$		0			0
$727$	−3.48709	+	4.15575i	−0.129329	+	0.154128i	−0.826823	−	0.562463i	$-0.809854\pi$
$727$	−3.48709	+	4.15575i	−0.129329	+	0.154128i	0.697494	+	0.716591i	$0.254298\pi$
$728$		0			0
$729$	23.1688	+	13.8639i	0.858103	+	0.513477i
$730$		0			0
$731$	−31.1413	+	11.3345i	−1.15180	+	0.419222i
$732$		0			0
$733$	3.72206	+	4.43578i	0.137478	+	0.163839i	0.830390	−	0.557182i	$-0.188117\pi$
$733$	3.72206	+	4.43578i	0.137478	+	0.163839i	−0.692913	+	0.721021i	$0.743673\pi$
$734$		0			0
$735$	−38.3763	−	15.2065i	−1.41553	−	0.560900i
$736$		0			0
$737$		−	3.44172i		−	0.126777i
$738$		0			0
$739$	−16.9316			−0.622838			−0.311419	−	0.950273i	$-0.600804\pi$
$739$	−16.9316			−0.622838			−0.311419	+	0.950273i	$0.600804\pi$
$740$		0			0
$741$	−47.4596	−	22.2815i	−1.74347	−	0.818532i
$742$		0			0
$743$	14.8397	+	17.6852i	0.544415	+	0.648808i	0.966171	−	0.257901i	$-0.0830308\pi$
$743$	14.8397	+	17.6852i	0.544415	+	0.648808i	−0.421757	+	0.906709i	$0.638586\pi$
$744$		0			0
$745$	58.2544	+	10.2718i	2.13428	+	0.376330i
$746$		0			0
$747$	19.8838	−	3.39931i	0.727510	−	0.124374i
$748$		0			0
$749$	0.525136	+	17.0248i	0.0191880	+	0.622073i
$750$		0			0
$751$	7.05220	+	39.9950i	0.257338	+	1.45944i	0.789999	+	0.613109i	$0.210081\pi$
$751$	7.05220	+	39.9950i	0.257338	+	1.45944i	−0.532660	+	0.846329i	$0.678808\pi$
$752$		0			0
$753$	−5.46045	−	0.492067i	−0.198990	−	0.0179319i
$754$		0			0
$755$	59.6490			2.17085
$756$		0			0
$757$	−17.6945			−0.643118			−0.321559	−	0.946890i	$-0.604207\pi$
$757$	−17.6945			−0.643118			−0.321559	+	0.946890i	$0.604207\pi$
$758$		0			0
$759$	25.6887	−	36.4846i	0.932441	−	1.32431i
$760$		0			0
$761$	−1.35890	−	7.70670i	−0.0492601	−	0.279368i	0.950221	−	0.311576i	$-0.100857\pi$
$761$	−1.35890	−	7.70670i	−0.0492601	−	0.279368i	−0.999481	+	0.0322086i	$0.989746\pi$
$762$		0			0
$763$	−3.70798	−	5.98812i	−0.134238	−	0.216785i
$764$		0			0
$765$	−32.4345	−	18.9521i	−1.17267	−	0.685215i
$766$		0			0
$767$	0.810730	+	0.142954i	0.0292738	+	0.00516175i
$768$		0			0
$769$	−27.7523	−	33.0738i	−1.00077	−	1.19267i	−0.981225	−	0.192865i	$-0.938222\pi$
$769$	−27.7523	−	33.0738i	−1.00077	−	1.19267i	−0.0195465	−	0.999809i	$-0.506222\pi$
$770$		0			0
$771$	−1.10717	−	13.0464i	−0.0398737	−	0.469856i
$772$		0			0
$773$	−0.416923			−0.0149957			−0.00749783	−	0.999972i	$-0.502387\pi$
$773$	−0.416923			−0.0149957			−0.00749783	+	0.999972i	$0.502387\pi$
$774$		0			0
$775$		−	26.3665i		−	0.947111i
$776$		0			0
$777$	−15.6971	+	23.8217i	−0.563130	+	0.854597i
$778$		0			0
$779$	20.9249	+	24.9374i	0.749713	+	0.893473i
$780$		0			0
$781$	26.2091	−	9.53932i	0.937834	−	0.341344i
$782$		0			0
$783$	36.6720	−	25.2532i	1.31055	−	0.902474i
$784$		0			0
$785$	−38.8937	+	46.3517i	−1.38818	+	1.65436i
$786$		0			0
$787$	16.9745	−	46.6370i	0.605075	−	1.66243i	−0.135759	−	0.990742i	$-0.543347\pi$
$787$	16.9745	−	46.6370i	0.605075	−	1.66243i	0.740834	−	0.671688i	$-0.234431\pi$
$788$		0			0
$789$	−29.5973	−	8.01330i	−1.05369	−	0.285281i
$790$		0			0
$791$	−7.35600	−	8.23686i	−0.261549	−	0.292869i
$792$		0			0
$793$	21.9588	−	38.0337i	0.779779	−	1.35062i
$794$		0			0
$795$	−5.58312	+	0.473804i	−0.198013	+	0.0168041i
$796$		0			0
$797$	−7.06498	+	5.92823i	−0.250255	+	0.209989i	−0.759282	−	0.650762i	$-0.774450\pi$
$797$	−7.06498	+	5.92823i	−0.250255	+	0.209989i	0.509027	+	0.860750i	$0.330005\pi$
$798$		0			0
$799$	−0.319103	+	0.116144i	−0.0112890	+	0.00410888i
$800$		0			0
$801$	−3.05324	+	3.60044i	−0.107881	+	0.127215i
$802$		0			0
$803$	47.2496	−	17.1974i	1.66740	−	0.606884i
$804$		0			0
$805$	16.5020	+	41.3274i	0.581618	+	1.45660i
$806$		0			0
$807$	15.5079	+	1.39749i	0.545905	+	0.0491941i
$808$		0			0
$809$	−7.87854	−	4.54868i	−0.276995	−	0.159923i	0.355067	−	0.934841i	$-0.384458\pi$
$809$	−7.87854	−	4.54868i	−0.276995	−	0.159923i	−0.632062	+	0.774918i	$0.717791\pi$
$810$		0			0
$811$			5.06978i			0.178024i	0.996031	+	0.0890120i	$0.0283710\pi$
$811$			5.06978i			0.178024i	−0.996031	+	0.0890120i	$0.971629\pi$
$812$		0			0
$813$	−46.1319	−	32.4814i	−1.61792	−	1.13917i
$814$		0			0
$815$	6.61634	−	5.55177i	0.231760	−	0.194470i
$816$		0			0
$817$	23.3498	+	64.1530i	0.816905	+	2.24443i
$818$		0			0
$819$	15.1467	−	27.8598i	0.529268	−	0.973501i
$820$		0			0
$821$	11.1948	−	13.3415i	0.390702	−	0.465621i	−0.534460	−	0.845194i	$-0.679485\pi$
$821$	11.1948	−	13.3415i	0.390702	−	0.465621i	0.925162	+	0.379573i	$0.123929\pi$
$822$		0			0
$823$	4.79691	+	27.2046i	0.167210	+	0.948294i	0.946757	+	0.321950i	$0.104338\pi$
$823$	4.79691	+	27.2046i	0.167210	+	0.948294i	−0.779547	+	0.626344i	$0.784551\pi$
$824$		0			0
$825$	34.0225	+	48.8597i	1.18451	+	1.70108i
$826$		0			0
$827$	14.3776	−	8.30090i	0.499957	−	0.288650i	−0.228739	−	0.973488i	$-0.573460\pi$
$827$	14.3776	−	8.30090i	0.499957	−	0.288650i	0.728696	+	0.684837i	$0.240127\pi$
$828$		0			0
$829$	−11.5716	+	6.68085i	−0.401897	+	0.232035i	−0.687302	−	0.726372i	$-0.741205\pi$
$829$	−11.5716	+	6.68085i	−0.401897	+	0.232035i	0.285405	+	0.958407i	$0.407872\pi$
$830$		0			0
$831$	−13.5428	+	50.0206i	−0.469793	+	1.73519i
$832$		0			0
$833$	14.2222	+	21.4602i	0.492771	+	0.743551i
$834$		0			0
$835$	−6.07054	+	34.4277i	−0.210080	+	1.19142i
$836$		0			0
$837$	12.0542	−	16.9319i	0.416653	−	0.585251i
$838$		0			0
$839$	6.63830	+	5.57020i	0.229180	+	0.192305i	0.750145	−	0.661273i	$-0.229984\pi$
$839$	6.63830	+	5.57020i	0.229180	+	0.192305i	−0.520966	+	0.853578i	$0.674428\pi$
$840$		0			0
$841$	−7.71487	−	43.7532i	−0.266030	−	1.50873i
$842$		0			0
$843$	16.3833	−	16.2981i	0.564270	−	0.561337i
$844$		0			0
$845$	10.0838			0.346894
$846$		0			0
$847$	−31.9573	+	28.5398i	−1.09807	+	0.980639i
$848$		0			0
$849$	15.3374	+	22.0260i	0.526378	+	0.755930i
$850$		0			0
$851$	30.2872	−	5.34045i	1.03823	−	0.183068i
$852$		0			0
$853$	−0.536334	−	1.47357i	−0.0183637	−	0.0504539i	0.930172	−	0.367124i	$-0.119657\pi$
$853$	−0.536334	−	1.47357i	−0.0183637	−	0.0504539i	−0.948536	+	0.316670i	$0.897435\pi$
$854$		0			0
$855$	−39.0425	+	66.8171i	−1.33523	+	2.28510i
$856$		0			0
$857$	2.54071	+	2.13191i	0.0867889	+	0.0728246i	0.685150	−	0.728402i	$-0.259737\pi$
$857$	2.54071	+	2.13191i	0.0867889	+	0.0728246i	−0.598361	+	0.801227i	$0.704181\pi$
$858$		0			0
$859$	−4.13266	+	0.728700i	−0.141005	+	0.0248629i	−0.243705	−	0.969849i	$-0.578363\pi$
$859$	−4.13266	+	0.728700i	−0.141005	+	0.0248629i	0.102700	+	0.994712i	$0.467252\pi$
$860$		0			0
$861$	−15.8033	+	11.7440i	−0.538575	+	0.400236i
$862$		0			0
$863$	−19.0212	+	10.9819i	−0.647491	+	0.373829i	−0.787494	−	0.616322i	$-0.788622\pi$
$863$	−19.0212	+	10.9819i	−0.647491	+	0.373829i	0.140004	+	0.990151i	$0.455289\pi$
$864$		0			0
$865$	38.7136	−	67.0540i	1.31630	−	2.27990i
$866$		0			0
$867$	−2.52819	−	5.45881i	−0.0858618	−	0.185391i
$868$		0			0
$869$	4.12242	−	11.3263i	0.139844	−	0.384217i
$870$		0			0
$871$	−1.69490	+	2.01991i	−0.0574296	+	0.0684419i
$872$		0			0
$873$	10.3028	+	3.81084i	0.348698	+	0.128977i
$874$		0			0
$875$	−14.3309	+	0.442041i	−0.484472	+	0.0149437i
$876$		0			0
$877$	−10.4737	−	3.81213i	−0.353673	−	0.128726i	0.159073	−	0.987267i	$-0.449149\pi$
$877$	−10.4737	−	3.81213i	−0.353673	−	0.128726i	−0.512746	+	0.858540i	$0.671372\pi$
$878$		0			0
$879$	−16.2010	+	11.2813i	−0.546447	+	0.380508i
$880$		0			0
$881$	16.4795	+	28.5434i	0.555209	+	0.961650i	0.997887	+	0.0649695i	$0.0206950\pi$
$881$	16.4795	+	28.5434i	0.555209	+	0.961650i	−0.442678	+	0.896680i	$0.645972\pi$
$882$		0			0
$883$	−3.53887	+	6.12951i	−0.119093	+	0.206274i	−0.919408	−	0.393304i	$-0.871332\pi$
$883$	−3.53887	+	6.12951i	−0.119093	+	0.206274i	0.800316	+	0.599579i	$0.204665\pi$
$884$		0			0
$885$	0.317552	−	1.17289i	0.0106744	−	0.0394262i
$886$		0			0
$887$	16.0443	−	13.4627i	0.538713	−	0.452034i	−0.332384	−	0.943144i	$-0.607853\pi$
$887$	16.0443	−	13.4627i	0.538713	−	0.452034i	0.871098	+	0.491110i	$0.163409\pi$
$888$		0			0
$889$	−3.19551	−	5.16052i	−0.107174	−	0.173078i
$890$		0			0
$891$	−0.489147	+	46.9308i	−0.0163870	+	1.57224i
$892$		0			0
$893$	0.239264	+	0.657371i	0.00800665	+	0.0219981i
$894$		0			0
$895$	27.4989	−	4.84879i	0.919185	−	0.162077i
$896$		0			0
$897$	−33.0435	+	8.76177i	−1.10329	+	0.292547i
$898$		0			0
$899$	−17.1379	−	29.6837i	−0.571580	−	0.990005i
$900$		0			0
$901$	3.02642	+	1.74730i	0.100825	+	0.0582111i
$902$		0			0
$903$	−39.5673	+	11.8086i	−1.31672	+	0.392967i
$904$		0			0
$905$	24.8169	−	68.1838i	0.824941	−	2.26651i
$906$		0			0
$907$	−0.493825	+	2.80062i	−0.0163972	+	0.0929932i	−0.991908	−	0.126958i	$-0.959479\pi$
$907$	−0.493825	+	2.80062i	−0.0163972	+	0.0929932i	0.975511	+	0.219951i	$0.0705898\pi$
$908$		0			0
$909$	−5.60167	+	0.957654i	−0.185796	+	0.0317634i
$910$		0			0
$911$	−24.5632	−	4.33115i	−0.813814	−	0.143497i	−0.248775	−	0.968561i	$-0.580028\pi$
$911$	−24.5632	−	4.33115i	−0.813814	−	0.143497i	−0.565039	+	0.825064i	$0.691139\pi$
$912$		0			0
$913$	22.5393	+	26.8613i	0.745942	+	0.888979i
$914$		0			0
$915$	−53.0032	−	37.3194i	−1.75223	−	1.23374i
$916$		0			0
$917$	10.2053	+	48.9921i	0.337009	+	1.61786i
$918$		0			0
$919$	14.8003	+	25.6349i	0.488218	+	0.845619i	0.999908	−	0.0135513i	$-0.00431366\pi$
$919$	14.8003	+	25.6349i	0.488218	+	0.845619i	−0.511690	+	0.859170i	$0.670980\pi$
$920$		0			0
$921$	−4.15082	−	2.92258i	−0.136774	−	0.0963023i
$922$		0			0
$923$	−20.0795	−	7.30834i	−0.660925	−	0.240557i
$924$		0			0
$925$	−7.12581	+	40.4125i	−0.234295	+	1.32875i
$926$		0			0
$927$	7.70689	−	13.1895i	0.253128	−	0.433201i
$928$		0			0
$929$	−14.7619	−	12.3867i	−0.484322	−	0.406394i	0.367664	−	0.929959i	$-0.380158\pi$
$929$	−14.7619	−	12.3867i	−0.484322	−	0.406394i	−0.851986	+	0.523564i	$0.824602\pi$
$930$		0			0
$931$	44.2093	−	29.2987i	1.44890	−	0.960225i
$932$		0			0
$933$	−12.3659	+	8.61076i	−0.404841	+	0.281903i
$934$		0			0
$935$		−	65.2994i		−	2.13552i
$936$		0			0
$937$	22.0886	+	12.7529i	0.721604	+	0.416618i	0.815343	−	0.578979i	$-0.196549\pi$
$937$	22.0886	+	12.7529i	0.721604	+	0.416618i	−0.0937389	+	0.995597i	$0.529882\pi$
$938$		0			0
$939$	9.86809	+	2.67172i	0.322033	+	0.0871884i
$940$		0			0
$941$	−29.8447	−	10.8626i	−0.972911	−	0.354111i	−0.193831	−	0.981035i	$-0.562091\pi$
$941$	−29.8447	−	10.8626i	−0.972911	−	0.354111i	−0.779080	+	0.626924i	$0.784314\pi$
$942$		0			0
$943$	20.9031	+	3.68578i	0.680698	+	0.120025i
$944$		0			0
$945$	−38.9492	−	25.9574i	−1.26702	−	0.844393i
$946$		0			0
$947$	−27.9922	−	4.93578i	−0.909625	−	0.160391i	−0.300792	−	0.953690i	$-0.597251\pi$
$947$	−27.9922	−	4.93578i	−0.909625	−	0.160391i	−0.608833	+	0.793298i	$0.708362\pi$
$948$		0			0
$949$	−36.1992	−	13.1754i	−1.17508	−	0.427693i
$950$		0			0
$951$	−41.6498	+	41.4333i	−1.35059	+	1.34357i
$952$		0			0
$953$	41.9982	+	24.2477i	1.36046	+	0.785459i	0.989684	−	0.143265i	$-0.0457601\pi$
$953$	41.9982	+	24.2477i	1.36046	+	0.785459i	0.370771	+	0.928724i	$0.379093\pi$
$954$		0			0
$955$		−	77.6300i		−	2.51205i
$956$		0			0
$957$	70.0612	+	32.8926i	2.26476	+	1.06327i
$958$		0			0
$959$	−52.7118	−	7.62711i	−1.70215	−	0.246292i
$960$		0			0
$961$	11.4909	+	9.64203i	0.370675	+	0.311033i
$962$		0			0
$963$	−3.45282	+	19.0023i	−0.111266	+	0.612342i
$964$		0			0
$965$	11.4175	−	64.7521i	0.367544	−	2.08444i
$966$		0			0
$967$	−31.8353	−	11.5871i	−1.02375	−	0.372616i	−0.225054	−	0.974346i	$-0.572256\pi$
$967$	−31.8353	−	11.5871i	−1.02375	−	0.372616i	−0.798699	+	0.601731i	$0.794478\pi$
$968$		0			0
$969$	43.7961	−	20.2837i	1.40693	−	0.651607i
$970$		0			0
$971$	17.4445	+	30.2147i	0.559820	+	0.969637i	0.997511	+	0.0705115i	$0.0224632\pi$
$971$	17.4445	+	30.2147i	0.559820	+	0.969637i	−0.437691	+	0.899126i	$0.644204\pi$
$972$		0			0
$973$	−7.46990	+	22.6755i	−0.239474	+	0.726942i
$974$		0			0
$975$	4.09390	−	45.4299i	0.131110	−	1.45492i
$976$		0			0
$977$	7.41030	+	8.83125i	0.237077	+	0.282537i	0.871444	−	0.490495i	$-0.163184\pi$
$977$	7.41030	+	8.83125i	0.237077	+	0.282537i	−0.634368	+	0.773031i	$0.718739\pi$
$978$		0			0
$979$	−8.08127	−	1.42495i	−0.258279	−	0.0455415i
$980$		0			0
$981$	−2.69231	−	7.51875i	−0.0859589	−	0.240055i
$982$		0			0
$983$	−1.78163	+	10.1041i	−0.0568252	+	0.322272i	−0.999948	−	0.0101720i	$-0.996762\pi$
$983$	−1.78163	+	10.1041i	−0.0568252	+	0.322272i	0.943123	+	0.332444i	$0.107873\pi$
$984$		0			0
$985$	−1.76652	+	4.85348i	−0.0562860	+	0.154645i
$986$		0			0
$987$	−0.405443	+	0.121002i	−0.0129054	+	0.00385155i
$988$		0			0
$989$	38.5500	+	22.2568i	1.22582	+	0.707727i
$990$		0			0
$991$	4.77906	+	8.27757i	0.151812	+	0.262946i	0.931894	−	0.362732i	$-0.118156\pi$
$991$	4.77906	+	8.27757i	0.151812	+	0.262946i	−0.780082	+	0.625678i	$0.784823\pi$
$992$		0			0
$993$	−30.4854	−	30.6447i	−0.967426	−	0.972480i
$994$		0			0
$995$	−35.4316	+	6.24754i	−1.12326	+	0.198060i
$996$		0			0
$997$	−16.1256	−	44.3048i	−0.510704	−	1.40315i	−0.880505	−	0.474036i	$-0.842797\pi$
$997$	−16.1256	−	44.3048i	−0.510704	−	1.40315i	0.369802	−	0.929111i	$-0.379426\pi$
$998$		0			0
$999$	−23.0517	+	22.6941i	−0.729324	+	0.718010i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.ck.a.605.16	yes	144
7.5	odd	6		756.2.ca.a.173.24	✓	144
27.5	odd	18		756.2.ca.a.437.24	yes	144
189.5	even	18	inner	756.2.ck.a.5.16	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.ca.a.173.24	✓	144	7.5	odd	6
756.2.ca.a.437.24	yes	144	27.5	odd	18
756.2.ck.a.5.16	yes	144	189.5	even	18	inner
756.2.ck.a.605.16	yes	144	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.ck (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.727904 + 1.57167i) q^{3} +(-0.591212 - 3.35293i) q^{5} +(-1.25160 + 2.33098i) q^{7} +(-1.94031 + 2.28805i) q^{9} +O(q^{10})\)	\(q+(0.727904 + 1.57167i) q^{3} +(-0.591212 - 3.35293i) q^{5} +(-1.25160 + 2.33098i) q^{7} +(-1.94031 + 2.28805i) q^{9} +(-5.13559 - 0.905544i) q^{11} +(2.56808 + 3.06052i) q^{13} +(4.83937 - 3.36980i) q^{15} -3.67787 q^{17} +7.57664i q^{19} +(-4.57459 - 0.270382i) q^{21} +(3.17546 + 3.78437i) q^{23} +(-6.19416 + 2.25449i) q^{25} +(-5.00843 - 1.38405i) q^{27} +(-5.50806 + 6.56425i) q^{29} +(-1.36807 + 3.75873i) q^{31} +(-2.31500 - 8.73062i) q^{33} +(8.55559 + 2.81844i) q^{35} +(3.11270 - 5.39136i) q^{37} +(-2.94082 + 6.26394i) q^{39} +(3.29135 - 2.76177i) q^{41} +(8.46720 - 3.08181i) q^{43} +(8.81882 + 5.15301i) q^{45} +(0.0867629 - 0.0315791i) q^{47} +(-3.86697 - 5.83494i) q^{49} +(-2.67714 - 5.78041i) q^{51} +(-0.822872 - 0.475085i) q^{53} +17.7547i q^{55} +(-11.9080 + 5.51507i) q^{57} +(0.157848 - 0.132450i) q^{59} +(-3.75967 - 10.3296i) q^{61} +(-2.90491 - 7.38658i) q^{63} +(8.74342 - 10.4200i) q^{65} +(0.114606 + 0.649962i) q^{67} +(-3.63636 + 7.74545i) q^{69} +(-4.63188 + 2.67422i) q^{71} +(-8.35033 + 4.82106i) q^{73} +(-8.05207 - 8.09414i) q^{75} +(8.53854 - 10.8376i) q^{77} +(-0.401358 + 2.27621i) q^{79} +(-1.47037 - 8.87908i) q^{81} +(-5.15096 - 4.32216i) q^{83} +(2.17440 + 12.3317i) q^{85} +(-14.3262 - 3.87873i) q^{87} +1.57358 q^{89} +(-10.3482 + 2.15559i) q^{91} +(-6.90332 + 0.585841i) q^{93} +(25.4040 - 4.47941i) q^{95} +(-1.25237 - 3.44085i) q^{97} +(12.0366 - 9.99347i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 6 q^{9}+O(q^{10}) \) 144 * q + 6 * q^9	\( 144 q + 6 q^{9} - 6 q^{11} + 12 q^{15} + 33 q^{21} + 21 q^{23} - 6 q^{29} + 27 q^{35} + 39 q^{39} - 54 q^{47} + 18 q^{49} - 9 q^{51} - 45 q^{53} + 3 q^{57} + 45 q^{59} + 39 q^{63} + 24 q^{65} - 36 q^{69} + 36 q^{71} + 45 q^{75} + 21 q^{77} - 18 q^{79} + 18 q^{81} + 36 q^{85} - 45 q^{87} + 9 q^{91} - 48 q^{93} - 66 q^{95}+O(q^{100}) \) 144 * q + 6 * q^9 - 6 * q^11 + 12 * q^15 + 33 * q^21 + 21 * q^23 - 6 * q^29 + 27 * q^35 + 39 * q^39 - 54 * q^47 + 18 * q^49 - 9 * q^51 - 45 * q^53 + 3 * q^57 + 45 * q^59 + 39 * q^63 + 24 * q^65 - 36 * q^69 + 36 * q^71 + 45 * q^75 + 21 * q^77 - 18 * q^79 + 18 * q^81 + 36 * q^85 - 45 * q^87 + 9 * q^91 - 48 * q^93 - 66 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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