LMFDB - Embedded newform 234.2.z.a.227.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [234,2,Mod(41,234)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(234, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 1]))

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

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

chi := DirichletCharacter("234.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 234 = 2 \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	234.z (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:	$1.86849940730$
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			227.3
Character	$\chi$	$=$	234.227
Dual form			234.2.z.a.167.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 + 0.965926i) q^{2} +(-0.788831 - 1.54199i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-0.707650 + 2.64098i) q^{5} +(1.69362 - 0.362854i) q^{6} +(-2.46440 - 2.46440i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-1.75549 + 2.43274i) q^{9} +O(q^{10})$	\(q+(-0.258819 + 0.965926i) q^{2} +(-0.788831 - 1.54199i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-0.707650 + 2.64098i) q^{5} +(1.69362 - 0.362854i) q^{6} +(-2.46440 - 2.46440i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-1.75549 + 2.43274i) q^{9} +(-2.36784 - 1.36707i) q^{10} +(-1.76278 - 0.472336i) q^{11} +(-0.0878497 + 1.72982i) q^{12} +(-3.37968 + 1.25609i) q^{13} +(3.01826 - 1.74260i) q^{14} +(4.63060 - 0.992098i) q^{15} +(0.500000 + 0.866025i) q^{16} +(0.419403 + 0.726428i) q^{17} +(-1.89550 - 2.32532i) q^{18} +(-6.94825 - 1.86178i) q^{19} +(1.93334 - 1.93334i) q^{20} +(-1.85610 + 5.74409i) q^{21} +(0.912483 - 1.58047i) q^{22} -6.37931 q^{23} +(-1.64814 - 0.532567i) q^{24} +(-2.14391 - 1.23778i) q^{25} +(-0.338562 - 3.58962i) q^{26} +(5.13606 + 0.787935i) q^{27} +(0.902034 + 3.36644i) q^{28} +(5.24032 - 3.02550i) q^{29} +(-0.240194 + 4.72959i) q^{30} +(7.43873 + 1.99320i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(0.662197 + 3.09079i) q^{33} +(-0.810225 + 0.217099i) q^{34} +(8.25239 - 4.76452i) q^{35} +(2.73667 - 1.22907i) q^{36} +(-4.09570 + 1.09744i) q^{37} +(3.59668 - 6.22963i) q^{38} +(4.60288 + 4.22061i) q^{39} +(1.36707 + 2.36784i) q^{40} +(2.93930 + 2.93930i) q^{41} +(-5.06797 - 3.27953i) q^{42} -8.62974i q^{43} +(1.29045 + 1.29045i) q^{44} +(-5.18257 - 6.35776i) q^{45} +(1.65109 - 6.16194i) q^{46} +(2.00059 + 7.46630i) q^{47} +(0.940991 - 1.45414i) q^{48} +5.14656i q^{49} +(1.75049 - 1.75049i) q^{50} +(0.789309 - 1.21975i) q^{51} +(3.55493 + 0.602036i) q^{52} -3.92979i q^{53} +(-2.09040 + 4.75712i) q^{54} +(2.49486 - 4.32123i) q^{55} -3.48519 q^{56} +(2.61014 + 12.1828i) q^{57} +(1.56612 + 5.84482i) q^{58} +(1.92746 + 7.19337i) q^{59} +(-4.50627 - 1.45612i) q^{60} -0.494876 q^{61} +(-3.85057 + 6.66938i) q^{62} +(10.3215 - 1.66902i) q^{63} -1.00000i q^{64} +(-0.925680 - 9.81456i) q^{65} +(-3.15687 - 0.160323i) q^{66} +(-3.91359 + 3.91359i) q^{67} -0.838806i q^{68} +(5.03219 + 9.83686i) q^{69} +(2.46630 + 9.20434i) q^{70} +(-1.48865 + 5.55573i) q^{71} +(0.478890 + 2.96153i) q^{72} +(-9.66963 - 9.66963i) q^{73} -4.24018i q^{74} +(-0.217478 + 4.28229i) q^{75} +(5.08647 + 5.08647i) q^{76} +(3.18018 + 5.50823i) q^{77} +(-5.26811 + 3.35366i) q^{78} +(-0.892374 + 1.54564i) q^{79} +(-2.64098 + 0.707650i) q^{80} +(-2.83649 - 8.54133i) q^{81} +(-3.59989 + 2.07840i) q^{82} +(-15.2034 + 4.07375i) q^{83} +(4.47947 - 4.04648i) q^{84} +(-2.21527 + 0.593581i) q^{85} +(8.33569 + 2.23354i) q^{86} +(-8.79903 - 5.69394i) q^{87} +(-1.58047 + 0.912483i) q^{88} +(-0.385644 - 1.43924i) q^{89} +(7.48247 - 3.36047i) q^{90} +(11.4244 + 5.23339i) q^{91} +(5.52464 + 3.18965i) q^{92} +(-2.79439 - 13.0428i) q^{93} -7.72968 q^{94} +(9.83385 - 17.0327i) q^{95} +(1.16105 + 1.28529i) q^{96} +(12.2984 - 12.2984i) q^{97} +(-4.97120 - 1.33203i) q^{98} +(4.24362 - 3.45922i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 8 q^{7}+O(q^{10}) $ 56 * q - 8 * q^7	$ 56 q - 8 q^{7} - 24 q^{11} + 28 q^{16} - 8 q^{19} - 24 q^{21} + 36 q^{27} - 4 q^{28} - 24 q^{30} - 4 q^{31} + 60 q^{33} - 24 q^{35} - 4 q^{37} + 36 q^{38} - 48 q^{41} - 36 q^{42} - 84 q^{45} - 36 q^{47} - 24 q^{50} + 8 q^{52} - 36 q^{54} + 36 q^{57} + 24 q^{60} - 48 q^{63} - 36 q^{65} + 28 q^{67} + 84 q^{69} - 24 q^{71} - 24 q^{72} + 28 q^{73} + 4 q^{76} + 24 q^{77} - 60 q^{78} - 24 q^{79} + 24 q^{81} - 96 q^{83} - 72 q^{85} + 4 q^{91} - 24 q^{92} - 36 q^{93} - 52 q^{97} + 48 q^{98} + 60 q^{99}+O(q^{100}) $ 56 * q - 8 * q^7 - 24 * q^11 + 28 * q^16 - 8 * q^19 - 24 * q^21 + 36 * q^27 - 4 * q^28 - 24 * q^30 - 4 * q^31 + 60 * q^33 - 24 * q^35 - 4 * q^37 + 36 * q^38 - 48 * q^41 - 36 * q^42 - 84 * q^45 - 36 * q^47 - 24 * q^50 + 8 * q^52 - 36 * q^54 + 36 * q^57 + 24 * q^60 - 48 * q^63 - 36 * q^65 + 28 * q^67 + 84 * q^69 - 24 * q^71 - 24 * q^72 + 28 * q^73 + 4 * q^76 + 24 * q^77 - 60 * q^78 - 24 * q^79 + 24 * q^81 - 96 * q^83 - 72 * q^85 + 4 * q^91 - 24 * q^92 - 36 * q^93 - 52 * q^97 + 48 * q^98 + 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/234\mathbb{Z}\right)^\times$.

$n$	$145$	$209$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$3$	−0.788831	−	1.54199i	−0.455432	−	0.890271i
$3$	−0.788831	−	1.54199i	−0.455432	−	0.890271i
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$	−0.707650	+	2.64098i	−0.316471	+	1.18108i	0.606142	+	0.795356i	$0.292716\pi$
$5$	−0.707650	+	2.64098i	−0.316471	+	1.18108i	−0.922613	+	0.385728i	$0.873950\pi$
$6$	1.69362	−	0.362854i	0.691416	−	0.148135i
$7$	−2.46440	−	2.46440i	−0.931457	−	0.931457i	0.0663403	−	0.997797i	$-0.478868\pi$
$7$	−2.46440	−	2.46440i	−0.931457	−	0.931457i	−0.997797	+	0.0663403i	$0.978868\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	−1.75549	+	2.43274i	−0.585164	+	0.810915i
$10$	−2.36784	−	1.36707i	−0.748777	−	0.432307i
$11$	−1.76278	−	0.472336i	−0.531499	−	0.142415i	−0.0169185	−	0.999857i	$-0.505386\pi$
$11$	−1.76278	−	0.472336i	−0.531499	−	0.142415i	−0.514580	+	0.857442i	$0.672052\pi$
$12$	−0.0878497	+	1.72982i	−0.0253600	+	0.499356i
$13$	−3.37968	+	1.25609i	−0.937355	+	0.348376i
$13$	−3.37968	+	1.25609i	−0.937355	+	0.348376i
$14$	3.01826	−	1.74260i	0.806665	−	0.465728i
$15$	4.63060	−	0.992098i	1.19562	−	0.256159i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	0.419403	+	0.726428i	0.101720	+	0.176185i	0.912393	−	0.409314i	$-0.134232\pi$
$17$	0.419403	+	0.726428i	0.101720	+	0.176185i	−0.810673	+	0.585499i	$0.800899\pi$
$18$	−1.89550	−	2.32532i	−0.446773	−	0.548082i
$19$	−6.94825	−	1.86178i	−1.59404	−	0.427121i	−0.650802	−	0.759247i	$-0.725567\pi$
$19$	−6.94825	−	1.86178i	−1.59404	−	0.427121i	−0.943235	+	0.332126i	$0.892234\pi$
$20$	1.93334	−	1.93334i	0.432307	−	0.432307i
$21$	−1.85610	+	5.74409i	−0.405034	+	1.25346i
$22$	0.912483	−	1.58047i	0.194542	−	0.336957i
$23$	−6.37931			−1.33018			−0.665089	−	0.746764i	$-0.731606\pi$
$23$	−6.37931			−1.33018			−0.665089	+	0.746764i	$0.731606\pi$
$24$	−1.64814	−	0.532567i	−0.336426	−	0.108710i
$25$	−2.14391	−	1.23778i	−0.428781	−	0.247557i
$26$	−0.338562	−	3.58962i	−0.0663975	−	0.703983i
$27$	5.13606	+	0.787935i	0.988436	+	0.151638i
$28$	0.902034	+	3.36644i	0.170468	+	0.636197i
$29$	5.24032	−	3.02550i	0.973104	−	0.561822i	0.0729226	−	0.997338i	$-0.476767\pi$
$29$	5.24032	−	3.02550i	0.973104	−	0.561822i	0.900181	+	0.435516i	$0.143434\pi$
$30$	−0.240194	+	4.72959i	−0.0438533	+	0.863501i
$31$	7.43873	+	1.99320i	1.33604	+	0.357990i	0.854962	−	0.518691i	$-0.173580\pi$
$31$	7.43873	+	1.99320i	1.33604	+	0.357990i	0.481074	+	0.876680i	$0.340247\pi$
$32$	−0.965926	+	0.258819i	−0.170753	+	0.0457532i
$33$	0.662197	+	3.09079i	0.115274	+	0.538038i
$34$	−0.810225	+	0.217099i	−0.138952	+	0.0372322i
$35$	8.25239	−	4.76452i	1.39491	−	0.805350i
$36$	2.73667	−	1.22907i	0.456112	−	0.204845i
$37$	−4.09570	+	1.09744i	−0.673328	+	0.180418i	−0.579254	−	0.815147i	$-0.696656\pi$
$37$	−4.09570	+	1.09744i	−0.673328	+	0.180418i	−0.0940746	+	0.995565i	$0.529989\pi$
$38$	3.59668	−	6.22963i	0.583458	−	1.01058i
$39$	4.60288	+	4.22061i	0.737050	+	0.675838i
$40$	1.36707	+	2.36784i	0.216153	+	0.374389i
$41$	2.93930	+	2.93930i	0.459041	+	0.459041i	0.898341	−	0.439300i	$-0.144773\pi$
$41$	2.93930	+	2.93930i	0.459041	+	0.459041i	−0.439300	+	0.898341i	$0.644773\pi$
$42$	−5.06797	−	3.27953i	−0.782005	−	0.506043i
$43$		−	8.62974i		−	1.31602i	−0.753008	−	0.658011i	$-0.771398\pi$
$43$		−	8.62974i		−	1.31602i	0.753008	−	0.658011i	$-0.228602\pi$
$44$	1.29045	+	1.29045i	0.194542	+	0.194542i
$45$	−5.18257	−	6.35776i	−0.772572	−	0.947759i
$46$	1.65109	−	6.16194i	0.243439	−	0.908528i
$47$	2.00059	+	7.46630i	0.291816	+	1.08907i	0.943713	+	0.330765i	$0.107307\pi$
$47$	2.00059	+	7.46630i	0.291816	+	1.08907i	−0.651897	+	0.758307i	$0.726027\pi$
$48$	0.940991	−	1.45414i	0.135820	−	0.209888i
$49$			5.14656i			0.735223i
$50$	1.75049	−	1.75049i	0.247557	−	0.247557i
$51$	0.789309	−	1.21975i	0.110525	−	0.170799i
$52$	3.55493	+	0.602036i	0.492981	+	0.0834874i
$53$		−	3.92979i		−	0.539798i	−0.962889	−	0.269899i	$-0.913010\pi$
$53$		−	3.92979i		−	0.539798i	0.962889	−	0.269899i	$-0.0869903\pi$
$54$	−2.09040	+	4.75712i	−0.284467	+	0.647363i
$55$	2.49486	−	4.32123i	0.336408	−	0.582675i
$56$	−3.48519			−0.465728
$57$	2.61014	+	12.1828i	0.345722	+	1.61365i
$58$	1.56612	+	5.84482i	0.205641	+	0.767463i
$59$	1.92746	+	7.19337i	0.250934	+	0.936497i	0.970308	+	0.241874i	$0.0777622\pi$
$59$	1.92746	+	7.19337i	0.250934	+	0.936497i	−0.719374	+	0.694623i	$0.755571\pi$
$60$	−4.50627	−	1.45612i	−0.581756	−	0.187984i
$61$	−0.494876			−0.0633624			−0.0316812	−	0.999498i	$-0.510086\pi$
$61$	−0.494876			−0.0633624			−0.0316812	+	0.999498i	$0.510086\pi$
$62$	−3.85057	+	6.66938i	−0.489023	+	0.847013i
$63$	10.3215	−	1.66902i	1.30039	−	0.210277i
$64$		−	1.00000i		−	0.125000i
$65$	−0.925680	−	9.81456i	−0.114816	−	1.21735i
$66$	−3.15687	−	0.160323i	−0.388583	−	0.0197344i
$67$	−3.91359	+	3.91359i	−0.478121	+	0.478121i	−0.904530	−	0.426409i	$-0.859778\pi$
$67$	−3.91359	+	3.91359i	−0.478121	+	0.478121i	0.426409	+	0.904530i	$0.359778\pi$
$68$		−	0.838806i		−	0.101720i
$69$	5.03219	+	9.83686i	0.605805	+	1.18422i
$70$	2.46630	+	9.20434i	0.294779	+	1.10013i
$71$	−1.48865	+	5.55573i	−0.176671	+	0.659344i	0.819591	+	0.572950i	$0.194201\pi$
$71$	−1.48865	+	5.55573i	−0.176671	+	0.659344i	−0.996261	+	0.0863938i	$0.972466\pi$
$72$	0.478890	+	2.96153i	0.0564377	+	0.349020i
$73$	−9.66963	−	9.66963i	−1.13174	−	1.13174i	−0.989887	−	0.141858i	$-0.954693\pi$
$73$	−9.66963	−	9.66963i	−1.13174	−	1.13174i	−0.141858	−	0.989887i	$-0.545307\pi$
$74$		−	4.24018i		−	0.492910i
$75$	−0.217478	+	4.28229i	−0.0251122	+	0.494477i
$76$	5.08647	+	5.08647i	0.583458	+	0.583458i
$77$	3.18018	+	5.50823i	0.362415	+	0.627721i
$78$	−5.26811	+	3.35366i	−0.596496	+	0.379728i
$79$	−0.892374	+	1.54564i	−0.100400	+	0.173898i	−0.911849	−	0.410525i	$-0.865346\pi$
$79$	−0.892374	+	1.54564i	−0.100400	+	0.173898i	0.811450	+	0.584422i	$0.198679\pi$
$80$	−2.64098	+	0.707650i	−0.295271	+	0.0791177i
$81$	−2.83649	−	8.54133i	−0.315166	−	0.949037i
$82$	−3.59989	+	2.07840i	−0.397541	+	0.229520i
$83$	−15.2034	+	4.07375i	−1.66879	+	0.447152i	−0.964785	−	0.263039i	$-0.915275\pi$
$83$	−15.2034	+	4.07375i	−1.66879	+	0.447152i	−0.704009	+	0.710191i	$0.748609\pi$
$84$	4.47947	−	4.04648i	0.488751	−	0.441507i
$85$	−2.21527	+	0.593581i	−0.240280	+	0.0643829i
$86$	8.33569	+	2.23354i	0.898860	+	0.240849i
$87$	−8.79903	−	5.69394i	−0.943355	−	0.610454i
$88$	−1.58047	+	0.912483i	−0.168478	+	0.0972710i
$89$	−0.385644	−	1.43924i	−0.0408782	−	0.152559i	0.942470	−	0.334290i	$-0.108497\pi$
$89$	−0.385644	−	1.43924i	−0.0408782	−	0.152559i	−0.983348	+	0.181731i	$0.941830\pi$
$90$	7.48247	−	3.36047i	0.788722	−	0.354224i
$91$	11.4244	+	5.23339i	1.19760	+	0.548608i
$92$	5.52464	+	3.18965i	0.575984	+	0.332544i
$93$	−2.79439	−	13.0428i	−0.289765	−	1.35247i
$94$	−7.72968			−0.797256
$95$	9.83385	−	17.0327i	1.00893	−	1.74752i
$96$	1.16105	+	1.28529i	0.118499	+	0.131179i
$97$	12.2984	−	12.2984i	1.24872	−	1.24872i	0.292430	−	0.956287i	$-0.405536\pi$
$97$	12.2984	−	12.2984i	1.24872	−	1.24872i	0.956287	−	0.292430i	$-0.0944638\pi$
$98$	−4.97120	−	1.33203i	−0.502167	−	0.134555i
$99$	4.24362	−	3.45922i	0.426500	−	0.347664i
$100$	1.23778	+	2.14391i	0.123778	+	0.214391i
$101$	0.0423653	+	0.0733788i	0.00421550	+	0.00730146i	0.868125	−	0.496345i	$-0.165325\pi$
$101$	0.0423653	+	0.0733788i	0.00421550	+	0.00730146i	−0.863910	+	0.503646i	$0.831991\pi$
$102$	0.973896	+	1.07811i	0.0964300	+	0.106749i
$103$	7.73765	−	4.46733i	0.762413	−	0.440179i	−0.0677484	−	0.997702i	$-0.521582\pi$
$103$	7.73765	−	4.46733i	0.762413	−	0.440179i	0.830161	+	0.557523i	$0.188248\pi$
$104$	−1.50161	+	3.27798i	−0.147245	+	0.321433i
$105$	−13.8566	−	8.96673i	−1.35226	−	0.875064i
$106$	3.79588	+	1.01710i	0.368689	+	0.0987899i
$107$	−12.3692	−	7.14138i	−1.19578	−	0.690384i	−0.236168	−	0.971712i	$-0.575892\pi$
$107$	−12.3692	−	7.14138i	−1.19578	−	0.690384i	−0.959611	+	0.281329i	$0.909225\pi$
$108$	−4.05399	−	3.25040i	−0.390096	−	0.312770i
$109$	−9.68492	+	9.68492i	−0.927647	+	0.927647i	−0.997554	−	0.0699067i	$-0.977730\pi$
$109$	−9.68492	+	9.68492i	−0.927647	+	0.927647i	0.0699067	+	0.997554i	$0.477730\pi$
$110$	3.52827	+	3.52827i	0.336408	+	0.336408i
$111$	4.92305	+	5.44985i	0.467276	+	0.517276i
$112$	0.902034	−	3.36644i	0.0852342	−	0.318098i
$113$	−6.89055	−	3.97826i	−0.648209	−	0.374244i	0.139561	−	0.990213i	$-0.455431\pi$
$113$	−6.89055	−	3.97826i	−0.648209	−	0.374244i	−0.787770	+	0.615970i	$0.788764\pi$
$114$	−12.4432	−	0.631934i	−1.16541	−	0.0591860i
$115$	4.51432	−	16.8477i	0.420962	−	1.57105i
$116$	−6.05100			−0.561822
$117$	2.87726	−	10.4270i	0.266003	−	0.963972i
$118$	−7.44713			−0.685564
$119$	0.756632	−	2.82379i	0.0693603	−	0.258856i
$120$	2.57281	−	3.97585i	0.234864	−	0.362944i
$121$	−6.64198	−	3.83475i	−0.603816	−	0.348614i
$122$	0.128083	−	0.478014i	0.0115961	−	0.0432773i
$123$	2.21377	−	6.85099i	0.199609	−	0.617733i
$124$	−5.44553	−	5.44553i	−0.489023	−	0.489023i
$125$	−4.88057	+	4.88057i	−0.436531	+	0.436531i
$126$	−1.05925	+	10.4018i	−0.0943655	+	0.926664i
$127$	10.0640	+	5.81045i	0.893035	+	0.515594i	0.874934	−	0.484242i	$-0.160905\pi$
$127$	10.0640	+	5.81045i	0.893035	+	0.515594i	0.0181011	+	0.999836i	$0.494238\pi$
$128$	0.965926	+	0.258819i	0.0853766	+	0.0228766i
$129$	−13.3070	+	6.80740i	−1.17162	+	0.599358i
$130$	9.71972	+	1.64606i	0.852476	+	0.144369i
$131$	−4.16625	+	2.40538i	−0.364007	+	0.210159i	−0.670837	−	0.741605i	$-0.734065\pi$
$131$	−4.16625	+	2.40538i	−0.364007	+	0.210159i	0.306830	+	0.951764i	$0.400732\pi$
$132$	0.971917	−	3.00780i	0.0845945	−	0.261796i
$133$	12.5351	+	21.7114i	1.08693	+	1.88262i
$134$	−2.76733	−	4.79315i	−0.239061	−	0.414065i
$135$	−5.71546	+	13.0067i	−0.491909	+	1.11944i
$136$	0.810225	+	0.217099i	0.0694762	+	0.0186161i
$137$	−5.48363	+	5.48363i	−0.468498	+	0.468498i	−0.901428	−	0.432930i	$-0.857480\pi$
$137$	−5.48363	+	5.48363i	−0.468498	+	0.468498i	0.432930	+	0.901428i	$0.357480\pi$
$138$	−10.8041	+	2.31476i	−0.919706	+	0.197045i
$139$	2.41353	−	4.18036i	0.204713	−	0.354574i	−0.745328	−	0.666698i	$-0.767707\pi$
$139$	2.41353	−	4.18036i	0.204713	−	0.354574i	0.950041	+	0.312124i	$0.101040\pi$
$140$	−9.52903			−0.805350
$141$	9.93487	−	8.97454i	0.836667	−	0.755793i
$142$	−4.98113	−	2.87586i	−0.418007	−	0.241336i
$143$	6.55094	−	0.617865i	0.547817	−	0.0516685i
$144$	−2.98456	−	0.303929i	−0.248714	−	0.0253274i
$145$	4.28199	+	15.9806i	0.355600	+	1.32712i
$146$	11.8428	−	6.83746i	0.980120	−	0.565872i
$147$	7.93597	−	4.05977i	0.654548	−	0.334844i
$148$	4.09570	+	1.09744i	0.336664	+	0.0902089i
$149$	−12.6085	+	3.37842i	−1.03292	+	0.276771i	−0.735178	−	0.677874i	$-0.762902\pi$
$149$	−12.6085	+	3.37842i	−1.03292	+	0.276771i	−0.297746	+	0.954645i	$0.596235\pi$
$150$	−4.08009	−	1.31841i	−0.333138	−	0.107647i
$151$	−11.0213	+	2.95315i	−0.896900	+	0.240324i	−0.677685	−	0.735353i	$-0.737016\pi$
$151$	−11.0213	+	2.95315i	−0.896900	+	0.240324i	−0.219216	+	0.975676i	$0.570350\pi$
$152$	−6.22963	+	3.59668i	−0.505289	+	0.291729i
$153$	−2.50347	−	0.254937i	−0.202394	−	0.0206105i
$154$	−6.14363	+	1.64618i	−0.495068	+	0.132653i
$155$	−10.5280	+	18.2351i	−0.845632	+	1.46468i
$156$	−1.87590	−	5.95659i	−0.150193	−	0.476909i
$157$	2.16879	+	3.75646i	0.173089	+	0.299798i	0.939498	−	0.342554i	$-0.111292\pi$
$157$	2.16879	+	3.75646i	0.173089	+	0.299798i	−0.766409	+	0.642352i	$0.777959\pi$
$158$	−1.26201	−	1.26201i	−0.100400	−	0.100400i
$159$	−6.05971	+	3.09994i	−0.480566	+	0.245841i
$160$		−	2.73415i		−	0.216153i
$161$	15.7212	+	15.7212i	1.23900	+	1.23900i
$162$	8.98443	−	0.529183i	0.705883	−	0.0415766i
$163$	4.75149	−	17.7328i	0.372166	−	1.38894i	−0.485277	−	0.874361i	$-0.661281\pi$
$163$	4.75149	−	17.7328i	0.372166	−	1.38894i	0.857442	−	0.514580i	$-0.172052\pi$
$164$	−1.07586	−	4.01515i	−0.0840103	−	0.313531i
$165$	−8.63134	−	0.438346i	−0.671949	−	0.0341252i
$166$		−	15.7398i		−	1.22164i
$167$	1.72148	−	1.72148i	0.133212	−	0.133212i	−0.637357	−	0.770569i	$-0.719972\pi$
$167$	1.72148	−	1.72148i	0.133212	−	0.133212i	0.770569	+	0.637357i	$0.219972\pi$
$168$	2.74923	+	5.37415i	0.212107	+	0.414624i
$169$	9.84448	−	8.49035i	0.757268	−	0.653104i
$170$		−	2.29342i		−	0.175897i
$171$	16.7268	−	13.6350i	1.27913	−	1.04269i
$172$	−4.31487	+	7.47357i	−0.329006	+	0.569855i
$173$	10.1751			0.773602			0.386801	−	0.922163i	$-0.373580\pi$
$173$	10.1751			0.773602			0.386801	+	0.922163i	$0.373580\pi$
$174$	7.77728	−	7.02551i	0.589594	−	0.532603i
$175$	2.23305	+	8.33385i	0.168803	+	0.629980i
$176$	−0.472336	−	1.76278i	−0.0356037	−	0.132875i
$177$	9.57170	−	8.64648i	0.719453	−	0.649909i
$178$	1.49001			0.111681
$179$	−6.54598	+	11.3380i	−0.489270	+	0.847440i	−0.999924	−	0.0123463i	$-0.996070\pi$
$179$	−6.54598	+	11.3380i	−0.489270	+	0.847440i	0.510654	+	0.859786i	$0.329403\pi$
$180$	1.30936	+	8.09727i	0.0975936	+	0.603535i
$181$			10.0606i			0.747798i	0.927469	+	0.373899i	$0.121979\pi$
$181$			10.0606i			0.747798i	−0.927469	+	0.373899i	$0.878021\pi$
$182$	−8.01192	+	9.68063i	−0.593883	+	0.717576i
$183$	0.390373	+	0.763096i	0.0288572	+	0.0564097i
$184$	−4.51085	+	4.51085i	−0.332544	+	0.332544i
$185$		−	11.5933i		−	0.852354i
$186$	13.3216	+	0.676543i	0.976787	+	0.0496065i
$187$	−0.396198	−	1.47863i	−0.0289729	−	0.108128i
$188$	2.00059	−	7.46630i	0.145908	−	0.544536i
$189$	−10.7155	−	14.5991i	−0.779441	−	1.06193i
$190$	13.9072	+	13.9072i	1.00893	+	1.00893i
$191$			18.6945i			1.35269i	0.736587	+	0.676343i	$0.236436\pi$
$191$			18.6945i			1.35269i	−0.736587	+	0.676343i	$0.763564\pi$
$192$	−1.54199	+	0.788831i	−0.111284	+	0.0569289i
$193$	−3.65707	−	3.65707i	−0.263242	−	0.263242i	0.563128	−	0.826370i	$-0.309598\pi$
$193$	−3.65707	−	3.65707i	−0.263242	−	0.263242i	−0.826370	+	0.563128i	$0.809598\pi$
$194$	8.69631	+	15.0624i	0.624358	+	1.08142i
$195$	−14.4038	+	9.16942i	−1.03148	+	0.656636i
$196$	2.57328	−	4.45706i	0.183806	−	0.318361i
$197$	−8.85907	+	2.37378i	−0.631183	+	0.169125i	−0.560206	−	0.828353i	$-0.689278\pi$
$197$	−8.85907	+	2.37378i	−0.631183	+	0.169125i	−0.0709764	+	0.997478i	$0.522612\pi$
$198$	2.24302	+	4.99434i	0.159404	+	0.354932i
$199$	−11.5728	+	6.68158i	−0.820376	+	0.473644i	−0.850546	−	0.525900i	$-0.823728\pi$
$199$	−11.5728	+	6.68158i	−0.820376	+	0.473644i	0.0301700	+	0.999545i	$0.490395\pi$
$200$	−2.39122	+	0.640725i	−0.169085	+	0.0453061i
$201$	9.12190	+	2.94758i	0.643409	+	0.207906i
$202$	−0.0818434	+	0.0219299i	−0.00575848	+	0.00154298i
$203$	−20.3703	−	5.45821i	−1.42972	−	0.383091i
$204$	−1.29343	+	0.661676i	−0.0905585	+	0.0463266i
$205$	−9.84263	+	5.68265i	−0.687439	+	0.396893i
$206$	2.31246	+	8.63023i	0.161117	+	0.601296i
$207$	11.1988	−	15.5192i	0.778372	−	1.07866i
$208$	−2.77764	−	2.29885i	−0.192595	−	0.159396i
$209$	11.3689	+	6.56381i	0.786401	+	0.454029i
$210$	12.2475	−	11.0637i	0.845161	−	0.763466i
$211$	−11.9791			−0.824672			−0.412336	−	0.911032i	$-0.635287\pi$
$211$	−11.9791			−0.824672			−0.412336	+	0.911032i	$0.635287\pi$
$212$	−1.96489	+	3.40330i	−0.134949	+	0.233739i
$213$	9.74119	−	2.08703i	0.667456	−	0.143001i
$214$	10.0994	−	10.0994i	0.690384	−	0.690384i
$215$	22.7910	+	6.10683i	1.55433	+	0.416483i
$216$	4.18890	−	3.07459i	0.285019	−	0.209199i
$217$	−13.4200	−	23.2441i	−0.911007	−	1.57791i
$218$	−6.84827	−	11.8616i	−0.463823	−	0.803366i
$219$	−7.28281	+	22.5382i	−0.492127	+	1.52299i
$220$	−4.32123	+	2.49486i	−0.291337	+	0.168204i
$221$	−2.32991	−	1.92829i	−0.156726	−	0.129711i
$222$	−6.53833	+	3.34478i	−0.438824	+	0.224487i
$223$	1.69696	+	0.454698i	0.113637	+	0.0304489i	0.315189	−	0.949029i	$-0.397932\pi$
$223$	1.69696	+	0.454698i	0.113637	+	0.0304489i	−0.201553	+	0.979478i	$0.564599\pi$
$224$	3.01826	+	1.74260i	0.201666	+	0.116432i
$225$	6.77483	−	3.04265i	0.451655	−	0.202844i
$226$	5.62611	−	5.62611i	0.374244	−	0.374244i
$227$	7.63479	+	7.63479i	0.506739	+	0.506739i	0.913524	−	0.406785i	$-0.133350\pi$
$227$	7.63479	+	7.63479i	0.506739	+	0.506739i	−0.406785	+	0.913524i	$0.633350\pi$
$228$	3.83094	−	11.8557i	0.253710	−	0.785161i
$229$	−0.614457	+	2.29318i	−0.0406044	+	0.151538i	−0.983252	−	0.182253i	$-0.941661\pi$
$229$	−0.614457	+	2.29318i	−0.0406044	+	0.151538i	0.942647	+	0.333790i	$0.108328\pi$
$230$	15.1052	+	8.72099i	0.996007	+	0.575045i
$231$	5.98504	−	9.24888i	0.393787	−	0.608532i
$232$	1.56612	−	5.84482i	0.102820	−	0.383731i
$233$	14.8461			0.972602			0.486301	−	0.873791i	$-0.338346\pi$
$233$	14.8461			0.972602			0.486301	+	0.873791i	$0.338346\pi$
$234$	9.32697	+	5.47792i	0.609723	+	0.358103i
$235$	−21.1341			−1.37864
$236$	1.92746	−	7.19337i	0.125467	−	0.468249i
$237$	3.08729	+	0.156790i	0.200541	+	0.0101846i
$238$	2.53174	+	1.46170i	0.164108	+	0.0947480i
$239$	7.64464	−	28.5302i	0.494491	−	1.84546i	−0.0383723	−	0.999264i	$-0.512217\pi$
$239$	7.64464	−	28.5302i	0.494491	−	1.84546i	0.532863	−	0.846201i	$-0.321116\pi$
$240$	3.17448	+	3.51417i	0.204912	+	0.226839i
$241$	14.5621	+	14.5621i	0.938026	+	0.938026i	0.998189	−	0.0601623i	$-0.0191618\pi$
$241$	14.5621	+	14.5621i	0.938026	+	0.938026i	−0.0601623	+	0.998189i	$0.519162\pi$
$242$	5.42315	−	5.42315i	0.348614	−	0.348614i
$243$	−10.9332	+	11.1115i	−0.701363	+	0.712804i
$244$	0.428575	+	0.247438i	0.0274367	+	0.0158406i
$245$	−13.5920	−	3.64197i	−0.868361	−	0.232677i
$246$	6.04458	+	3.91150i	0.385388	+	0.249388i
$247$	25.8214	−	2.43540i	1.64298	−	0.154961i
$248$	6.66938	−	3.85057i	0.423506	−	0.244511i
$249$	18.2746	+	20.2301i	1.15811	+	1.28203i
$250$	−3.45108	−	5.97745i	−0.218266	−	0.378047i
$251$	−10.3116	−	17.8602i	−0.650861	−	1.12732i	−0.982914	−	0.184064i	$-0.941075\pi$
$251$	−10.3116	−	17.8602i	−0.650861	−	1.12732i	0.332053	−	0.943261i	$-0.392259\pi$
$252$	−9.77320	−	3.71534i	−0.615653	−	0.234044i
$253$	11.2453	+	3.01318i	0.706988	+	0.189437i
$254$	−8.21722	+	8.21722i	−0.515594	+	0.515594i
$255$	2.66278	+	2.94771i	0.166749	+	0.184593i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−8.53934			−0.532669			−0.266335	−	0.963881i	$-0.585813\pi$
$257$	−8.53934			−0.532669			−0.266335	+	0.963881i	$0.585813\pi$
$258$	−3.13134	−	14.6155i	−0.194949	−	0.909919i
$259$	12.7980	+	7.38891i	0.795227	+	0.459125i
$260$	−4.10562	+	8.96250i	−0.254620	+	0.555830i
$261$	−1.83907	+	18.0596i	−0.113836	+	1.11786i
$262$	−1.24512	−	4.64685i	−0.0769237	−	0.287083i
$263$	−2.29077	+	1.32258i	−0.141255	+	0.0815535i	−0.568962	−	0.822364i	$-0.692655\pi$
$263$	−2.29077	+	1.32258i	−0.141255	+	0.0815535i	0.427707	+	0.903917i	$0.359321\pi$
$264$	2.65376	+	1.71728i	0.163328	+	0.105691i
$265$	10.3785	+	2.78091i	0.637547	+	0.170830i
$266$	−24.2160	+	6.48865i	−1.48478	+	0.397845i
$267$	−1.91510	+	1.72998i	−0.117202	+	0.105873i
$268$	5.34607	−	1.43247i	0.326563	−	0.0875023i
$269$	14.9308	−	8.62028i	0.910345	−	0.525588i	0.0298029	−	0.999556i	$-0.490512\pi$
$269$	14.9308	−	8.62028i	0.910345	−	0.525588i	0.880542	+	0.473968i	$0.157179\pi$
$270$	−11.0842	−	8.88709i	−0.674564	−	0.540851i
$271$	14.5522	−	3.89924i	0.883981	−	0.236862i	0.211857	−	0.977301i	$-0.432049\pi$
$271$	14.5522	−	3.89924i	0.883981	−	0.236862i	0.672124	+	0.740439i	$0.265382\pi$
$272$	−0.419403	+	0.726428i	−0.0254301	+	0.0440461i
$273$	−0.942066	−	21.7446i	−0.0570164	−	1.31604i
$274$	−3.87751	−	6.71604i	−0.234249	−	0.405731i
$275$	3.19459	+	3.19459i	0.192641	+	0.192641i
$276$	0.560420	−	11.0351i	0.0337333	−	0.664233i
$277$			13.6780i			0.821833i	0.911673	+	0.410916i	$0.134791\pi$
$277$			13.6780i			0.821833i	−0.911673	+	0.410916i	$0.865209\pi$
$278$	3.41325	+	3.41325i	0.204713	+	0.204713i
$279$	−17.9076	+	14.5975i	−1.07210	+	0.873928i
$280$	2.46630	−	9.20434i	0.147389	−	0.550065i
$281$	−3.44720	−	12.8651i	−0.205643	−	0.767468i	−0.989253	−	0.146216i	$-0.953291\pi$
$281$	−3.44720	−	12.8651i	−0.205643	−	0.767468i	0.783610	−	0.621253i	$-0.213376\pi$
$282$	6.09741	+	11.9191i	0.363096	+	0.709774i
$283$		−	2.53856i		−	0.150902i	−0.997150	−	0.0754510i	$-0.975960\pi$
$283$		−	2.53856i		−	0.150902i	0.997150	−	0.0754510i	$-0.0240396\pi$
$284$	4.06707	−	4.06707i	0.241336	−	0.241336i
$285$	−34.0216	−	1.72780i	−2.01527	−	0.102346i
$286$	−1.09870	+	6.48763i	−0.0649672	+	0.383622i
$287$		−	14.4872i		−	0.855154i
$288$	1.06603	−	2.80421i	0.0628167	−	0.165239i
$289$	8.14820	−	14.1131i	0.479306	−	0.830182i
$290$	−16.5443			−0.971517
$291$	−28.6655	−	9.26273i	−1.68040	−	0.542991i
$292$	3.53933	+	13.2090i	0.207124	+	0.772996i
$293$	3.60679	+	13.4607i	0.210711	+	0.786385i	0.987632	+	0.156787i	$0.0501136\pi$
$293$	3.60679	+	13.4607i	0.210711	+	0.786385i	−0.776921	+	0.629598i	$0.783220\pi$
$294$	1.86745	+	8.71631i	0.108912	+	0.508345i
$295$	−20.3616			−1.18550
$296$	−2.12009	+	3.67210i	−0.123228	+	0.213436i
$297$	−8.68159	−	3.81491i	−0.503757	−	0.221363i
$298$		−	13.0532i		−	0.756153i
$299$	21.5600	−	8.01297i	1.24685	−	0.463402i
$300$	2.32949	−	3.59984i	0.134493	−	0.207837i
$301$	−21.2672	+	21.2672i	−1.22582	+	1.22582i
$302$		−	11.4101i		−	0.656576i
$303$	0.0797307	−	0.123210i	0.00458041	−	0.00707826i
$304$	−1.86178	−	6.94825i	−0.106780	−	0.398509i
$305$	0.350199	−	1.30696i	0.0200523	−	0.0748363i
$306$	0.894197	−	2.35219i	0.0511178	−	0.134465i
$307$	−6.54395	−	6.54395i	−0.373483	−	0.373483i	0.495261	−	0.868744i	$-0.335072\pi$
$307$	−6.54395	−	6.54395i	−0.373483	−	0.373483i	−0.868744	+	0.495261i	$0.835072\pi$
$308$		−	6.36036i		−	0.362415i
$309$	−12.9923	−	8.40744i	−0.739106	−	0.478283i
$310$	−14.8889	−	14.8889i	−0.845632	−	0.845632i
$311$	8.02003	+	13.8911i	0.454774	+	0.787692i	0.998675	−	0.0514573i	$-0.0163866\pi$
$311$	8.02003	+	13.8911i	0.454774	+	0.787692i	−0.543901	+	0.839149i	$0.683053\pi$
$312$	6.23915	−	0.270305i	0.353222	−	0.0153030i
$313$	−9.30369	+	16.1145i	−0.525875	+	0.910843i	0.473670	+	0.880702i	$0.342929\pi$
$313$	−9.30369	+	16.1145i	−0.525875	+	0.910843i	−0.999546	+	0.0301408i	$0.990404\pi$
$314$	−4.18979	+	1.12265i	−0.236444	+	0.0633549i
$315$	−2.89615	+	28.4400i	−0.163179	+	1.60241i
$316$	1.54564	−	0.892374i	0.0869489	−	0.0501999i
$317$	7.22395	−	1.93565i	0.405737	−	0.108717i	−0.0501776	−	0.998740i	$-0.515979\pi$
$317$	7.22395	−	1.93565i	0.405737	−	0.108717i	0.455915	+	0.890023i	$0.349312\pi$
$318$	−1.42594	−	6.65555i	−0.0799628	−	0.373225i
$319$	−10.6666	+	2.85811i	−0.597215	+	0.160023i
$320$	2.64098	+	0.707650i	0.147636	+	0.0395588i
$321$	−1.25474	+	24.7066i	−0.0700326	+	1.37899i
$322$	−19.2544	+	11.1166i	−1.07301	+	0.619501i
$323$	−1.56167	−	5.82823i	−0.0868937	−	0.324292i
$324$	−1.81419	+	8.81525i	−0.100788	+	0.489736i
$325$	8.80049	+	1.49038i	0.488163	+	0.0826715i
$326$	15.8988	+	9.17918i	0.880553	+	0.508388i
$327$	22.5738	+	7.29433i	1.24834	+	0.403377i
$328$	4.15679			0.229520
$329$	13.4697	−	23.3302i	0.742609	−	1.28624i
$330$	2.65737	−	8.22378i	0.146283	−	0.452704i
$331$	−8.05567	+	8.05567i	−0.442779	+	0.442779i	−0.892945	−	0.450166i	$-0.851365\pi$
$331$	−8.05567	+	8.05567i	−0.442779	+	0.442779i	0.450166	+	0.892945i	$0.351365\pi$
$332$	15.2034	+	4.07375i	0.834397	+	0.223576i
$333$	4.52017	−	11.8903i	0.247704	−	0.651586i
$334$	1.21727	+	2.10838i	0.0666062	+	0.115365i
$335$	−7.56629	−	13.1052i	−0.413390	−	0.716013i
$336$	−5.90258	+	1.26462i	−0.322012	+	0.0689905i
$337$	14.3804	−	8.30252i	0.783349	−	0.452267i	−0.0542666	−	0.998526i	$-0.517282\pi$
$337$	14.3804	−	8.30252i	0.783349	−	0.452267i	0.837616	+	0.546259i	$0.183949\pi$
$338$	5.65311	+	11.7065i	0.307489	+	0.636750i
$339$	−0.698979	+	13.7634i	−0.0379633	+	0.747524i
$340$	2.21527	+	0.593581i	0.120140	+	0.0321915i
$341$	−12.1714	−	7.02716i	−0.659118	−	0.380542i
$342$	8.84115	+	19.6859i	0.478075	+	1.06449i
$343$	−4.56761	+	4.56761i	−0.246628	+	0.246628i
$344$	−6.10215	−	6.10215i	−0.329006	−	0.329006i
$345$	−29.5400	+	6.32890i	−1.59038	+	0.340736i
$346$	−2.63352	+	9.82844i	−0.141579	+	0.528380i
$347$	−12.1916	−	7.03881i	−0.654478	−	0.377863i	0.135692	−	0.990751i	$-0.456674\pi$
$347$	−12.1916	−	7.03881i	−0.654478	−	0.377863i	−0.790170	+	0.612888i	$0.790008\pi$
$348$	4.77322	+	9.33061i	0.255871	+	0.500173i
$349$	−0.665385	+	2.48325i	−0.0356172	+	0.132925i	−0.981445	−	0.191743i	$-0.938586\pi$
$349$	−0.665385	+	2.48325i	−0.0356172	+	0.132925i	0.945828	+	0.324668i	$0.105253\pi$
$350$	−8.62784			−0.461177
$351$	−18.3480	+	3.78838i	−0.979342	+	0.202209i
$352$	1.82497			0.0972710
$353$	−1.64048	+	6.12235i	−0.0873139	+	0.325860i	−0.995742	−	0.0921806i	$-0.970616\pi$
$353$	−1.64048	+	6.12235i	−0.0873139	+	0.325860i	0.908428	+	0.418040i	$0.137283\pi$
$354$	5.87452	+	11.4834i	0.312227	+	0.610337i
$355$	−13.6191	−	7.86302i	−0.722829	−	0.417326i
$356$	−0.385644	+	1.43924i	−0.0204391	+	0.0762797i
$357$	−4.95112	+	1.06077i	−0.262041	+	0.0561419i
$358$	−9.25742	−	9.25742i	−0.489270	−	0.489270i
$359$	15.0107	−	15.0107i	0.792236	−	0.792236i	−0.189622	−	0.981857i	$-0.560726\pi$
$359$	15.0107	−	15.0107i	0.792236	−	0.792236i	0.981857	+	0.189622i	$0.0607261\pi$
$360$	−8.16024	−	0.830986i	−0.430083	−	0.0437968i
$361$	28.3574	+	16.3722i	1.49250	+	0.861693i
$362$	−9.71779	−	2.60387i	−0.510756	−	0.136857i
$363$	−0.673763	+	13.2669i	−0.0353634	+	0.696330i
$364$	−7.27713	−	10.2444i	−0.381425	−	0.536955i
$365$	32.3801	−	18.6946i	1.69485	−	0.978522i
$366$	−0.838130	+	0.179568i	−0.0438098	+	0.00938617i
$367$	−8.38757	−	14.5277i	−0.437828	−	0.758340i	0.559694	−	0.828699i	$-0.310919\pi$
$367$	−8.38757	−	14.5277i	−0.437828	−	0.758340i	−0.997522	+	0.0703596i	$0.977585\pi$
$368$	−3.18965	−	5.52464i	−0.166272	−	0.287992i
$369$	−12.3105	+	1.99065i	−0.640857	+	0.103629i
$370$	11.1982	+	3.00056i	0.582169	+	0.155992i
$371$	−9.68458	+	9.68458i	−0.502798	+	0.502798i
$372$	−4.10137	+	12.6926i	−0.212646	+	0.658079i
$373$	5.46023	−	9.45739i	0.282720	−	0.489685i	−0.689334	−	0.724444i	$-0.742097\pi$
$373$	5.46023	−	9.45739i	0.282720	−	0.489685i	0.972054	+	0.234759i	$0.0754300\pi$
$374$	1.53079			0.0791554
$375$	11.3758	+	3.67587i	0.587441	+	0.189821i
$376$	6.69410	+	3.86484i	0.345222	+	0.199314i
$377$	−13.9103	+	16.8075i	−0.716418	+	0.865632i
$378$	16.8751	−	6.57189i	0.867959	−	0.338021i
$379$	1.57730	+	5.88656i	0.0810203	+	0.302372i	0.994531	−	0.104443i	$-0.0333060\pi$
$379$	1.57730	+	5.88656i	0.0810203	+	0.302372i	−0.913511	+	0.406815i	$0.866639\pi$
$380$	−17.0327	+	9.83385i	−0.873760	+	0.504466i
$381$	1.02089	−	20.1021i	0.0523019	−	1.02986i
$382$	−18.0575	−	4.83849i	−0.923901	−	0.247559i
$383$	−30.9806	+	8.30124i	−1.58304	+	0.424173i	−0.939864	−	0.341548i	$-0.889049\pi$
$383$	−30.9806	+	8.30124i	−1.58304	+	0.424173i	−0.643172	+	0.765722i	$0.722382\pi$
$384$	−0.362854	−	1.69362i	−0.0185168	−	0.0864270i
$385$	−16.7976	+	4.50091i	−0.856086	+	0.229387i
$386$	4.47898	−	2.58594i	0.227974	−	0.131621i
$387$	20.9939	+	15.1494i	1.06718	+	0.770089i
$388$	−16.8000	+	4.50154i	−0.852889	+	0.228531i
$389$	16.7063	−	28.9362i	0.847043	−	1.46712i	−0.0367925	−	0.999323i	$-0.511714\pi$
$389$	16.7063	−	28.9362i	0.847043	−	1.46712i	0.883835	−	0.467798i	$-0.154953\pi$
$390$	−5.12900	−	16.2862i	−0.259717	−	0.824684i
$391$	−2.67550	−	4.63411i	−0.135306	−	0.234357i
$392$	3.63917	+	3.63917i	0.183806	+	0.183806i
$393$	6.99555	+	4.52689i	0.352879	+	0.228351i
$394$		−	9.17159i		−	0.462058i
$395$	−3.45052	−	3.45052i	−0.173614	−	0.173614i
$396$	−5.40469	+	0.873958i	−0.271596	+	0.0439180i
$397$	−5.37105	+	20.0450i	−0.269565	+	1.00603i	0.689832	+	0.723970i	$0.257685\pi$
$397$	−5.37105	+	20.0450i	−0.269565	+	1.00603i	−0.959397	+	0.282061i	$0.908982\pi$
$398$	−3.45864	−	12.9078i	−0.173366	−	0.647010i
$399$	23.5908	−	36.4557i	1.18102	−	1.82507i
$400$		−	2.47557i		−	0.123778i
$401$	14.3386	−	14.3386i	0.716037	−	0.716037i	−0.251754	−	0.967791i	$-0.581007\pi$
$401$	14.3386	−	14.3386i	0.716037	−	0.716037i	0.967791	+	0.251754i	$0.0810074\pi$
$402$	−5.20806	+	8.04819i	−0.259754	+	0.401407i
$403$	−27.6442	+	2.60732i	−1.37705	+	0.129880i
$404$		−	0.0847306i		−	0.00421550i
$405$	24.5648	−	1.44687i	1.22063	−	0.0718954i
$406$	10.5445	−	18.2635i	0.523313	−	0.906404i
$407$	7.73818			0.383567
$408$	−0.304365	−	1.42062i	−0.0150683	−	0.0703310i
$409$	1.44482	+	5.39214i	0.0714418	+	0.266624i	0.992403	−	0.123030i	$-0.0392611\pi$
$409$	1.44482	+	5.39214i	0.0714418	+	0.266624i	−0.920961	+	0.389654i	$0.872594\pi$
$410$	−2.94155	−	10.9780i	−0.145273	−	0.542166i
$411$	12.7814	+	4.13007i	0.630459	+	0.203721i
$412$	−8.93467			−0.440179
$413$	12.9773	−	22.4774i	0.638573	−	1.10604i
$414$	12.0920	+	14.8339i	0.594287	+	0.729047i
$415$		−	43.0348i		−	2.11250i
$416$	2.93942	−	2.08801i	0.144117	−	0.102373i
$417$	−8.34997	−	0.424057i	−0.408900	−	0.0207661i
$418$	−9.28264	+	9.28264i	−0.454029	+	0.454029i
$419$			31.3420i			1.53116i	0.643343	+	0.765578i	$0.277547\pi$
$419$			31.3420i			1.53116i	−0.643343	+	0.765578i	$0.722453\pi$
$420$	7.51679	+	14.6937i	0.366782	+	0.716980i
$421$	−7.11743	−	26.5626i	−0.346882	−	1.29458i	−0.890398	−	0.455183i	$-0.849574\pi$
$421$	−7.11743	−	26.5626i	−0.346882	−	1.29458i	0.543516	−	0.839399i	$-0.317093\pi$
$422$	3.10041	−	11.5709i	0.150925	−	0.563261i
$423$	−21.6756	−	8.24011i	−1.05390	−	0.400648i
$424$	−2.77878	−	2.77878i	−0.134949	−	0.134949i
$425$		−	2.07652i		−	0.100726i
$426$	−0.505286	+	9.94944i	−0.0244812	+	0.482052i
$427$	1.21957	+	1.21957i	0.0590193	+	0.0590193i
$428$	7.14138	+	12.3692i	0.345192	+	0.597890i
$429$	−6.12032	−	9.61412i	−0.295492	−	0.464174i
$430$	−11.7975	+	20.4339i	−0.568926	+	0.985408i
$431$	−26.7454	+	7.16641i	−1.28828	+	0.345194i	−0.837007	−	0.547192i	$-0.815697\pi$
$431$	−26.7454	+	7.16641i	−1.28828	+	0.345194i	−0.451274	+	0.892386i	$0.649030\pi$
$432$	1.88566	+	4.84193i	0.0907239	+	0.232957i
$433$	−27.2596	+	15.7383i	−1.31001	+	0.756336i	−0.982098	−	0.188372i	$-0.939679\pi$
$433$	−27.2596	+	15.7383i	−1.31001	+	0.756336i	−0.327914	+	0.944708i	$0.606346\pi$
$434$	25.9254	−	6.94669i	1.24446	−	0.333452i
$435$	21.2642	−	19.2088i	1.01954	−	0.920992i
$436$	13.2298	−	3.54493i	0.633595	−	0.169771i
$437$	44.3250	+	11.8768i	2.12035	+	0.568147i
$438$	−19.8853	−	12.8680i	−0.950157	−	0.614856i
$439$	22.7395	−	13.1286i	1.08530	−	0.626596i	0.152976	−	0.988230i	$-0.451114\pi$
$439$	22.7395	−	13.1286i	1.08530	−	0.626596i	0.932320	+	0.361634i	$0.117781\pi$
$440$	−1.29144	−	4.81971i	−0.0615669	−	0.229771i
$441$	−12.5203	−	9.03475i	−0.596204	−	0.430226i
$442$	2.46561	−	1.75144i	0.117277	−	0.0833075i
$443$	−23.2806	−	13.4410i	−1.10609	−	0.638604i	−0.168279	−	0.985739i	$-0.553821\pi$
$443$	−23.2806	−	13.4410i	−1.10609	−	0.638604i	−0.937815	+	0.347136i	$0.887154\pi$
$444$	−1.53857	−	7.18123i	−0.0730171	−	0.340806i
$445$	4.07392			0.193122
$446$	−0.878410	+	1.52145i	−0.0415939	+	0.0720428i
$447$	15.1554	+	16.7772i	0.716828	+	0.793532i
$448$	−2.46440	+	2.46440i	−0.116432	+	0.116432i
$449$	1.60200	+	0.429254i	0.0756029	+	0.0202577i	0.296422	−	0.955057i	$-0.404206\pi$
$449$	1.60200	+	0.429254i	0.0756029	+	0.0202577i	−0.220819	+	0.975315i	$0.570873\pi$
$450$	1.18552	+	7.33148i	0.0558862	+	0.345609i
$451$	−3.79300	−	6.56968i	−0.178606	−	0.309354i
$452$	3.97826	+	6.89055i	0.187122	+	0.324104i
$453$	13.2477	+	14.6652i	0.622430	+	0.689033i
$454$	−9.35067	+	5.39861i	−0.438849	+	0.253369i
$455$	−21.9058	+	26.4683i	−1.02696	+	1.24085i
$456$	10.4602	+	6.76888i	0.489843	+	0.316982i
$457$	−35.0473	−	9.39089i	−1.63944	−	0.439287i	−0.682812	−	0.730594i	$-0.739243\pi$
$457$	−35.0473	−	9.39089i	−1.63944	−	0.439287i	−0.956630	+	0.291307i	$0.905910\pi$
$458$	−2.05601	−	1.18704i	−0.0960711	−	0.0554667i
$459$	1.58170	+	4.06144i	0.0738276	+	0.189572i
$460$	−12.3333	+	12.3333i	−0.575045	+	0.575045i
$461$	−15.6720	−	15.6720i	−0.729919	−	0.729919i	0.240685	−	0.970603i	$-0.422628\pi$
$461$	−15.6720	−	15.6720i	−0.729919	−	0.729919i	−0.970603	+	0.240685i	$0.922628\pi$
$462$	7.38469	+	8.17489i	0.343567	+	0.380330i
$463$	7.73679	−	28.8741i	0.359559	−	1.34189i	−0.515090	−	0.857136i	$-0.672242\pi$
$463$	7.73679	−	28.8741i	0.359559	−	1.34189i	0.874649	−	0.484756i	$-0.161092\pi$
$464$	5.24032	+	3.02550i	0.243276	+	0.140455i
$465$	36.4232	+	1.84977i	1.68909	+	0.0857810i
$466$	−3.84246	+	14.3403i	−0.177999	+	0.664300i
$467$	36.5666			1.69210			0.846051	−	0.533102i	$-0.178974\pi$
$467$	36.5666			1.69210			0.846051	+	0.533102i	$0.178974\pi$
$468$	−7.70526	+	7.59138i	−0.356176	+	0.350911i
$469$	19.2893			0.890699
$470$	5.46991	−	20.4140i	0.252308	−	0.941627i
$471$	4.08163	−	6.30748i	0.188072	−	0.290633i
$472$	6.44940	+	3.72356i	0.296858	+	0.171391i
$473$	−4.07614	+	15.2123i	−0.187421	+	0.699465i
$474$	−0.950498	+	2.94152i	−0.0436578	+	0.135108i
$475$	12.5919	+	12.5919i	0.577756	+	0.577756i
$476$	−2.06716	+	2.06716i	−0.0947480	+	0.0947480i
$477$	9.56017	+	6.89871i	0.437730	+	0.315870i
$478$	25.5795	+	14.7683i	1.16998	+	0.675487i
$479$	32.8503	+	8.80222i	1.50097	+	0.402184i	0.913425	−	0.407007i	$-0.133428\pi$
$479$	32.8503	+	8.80222i	1.50097	+	0.402184i	0.587545	+	0.809191i	$0.300094\pi$
$480$	−4.21604	+	2.15678i	−0.192435	+	0.0984431i
$481$	12.4637	−	8.85355i	0.568294	−	0.403687i
$482$	−17.8348	+	10.2969i	−0.812355	+	0.469013i
$483$	11.8406	−	36.6433i	0.538767	−	1.66733i
$484$	3.83475	+	6.64198i	0.174307	+	0.301908i
$485$	23.7770	+	41.1830i	1.07966	+	1.87002i
$486$	−7.90319	−	13.4365i	−0.358496	−	0.609492i
$487$	12.0435	+	3.22705i	0.545744	+	0.146232i	0.521149	−	0.853466i	$-0.325504\pi$
$487$	12.0435	+	3.22705i	0.545744	+	0.146232i	0.0245951	+	0.999697i	$0.492170\pi$
$488$	−0.349930	+	0.349930i	−0.0158406	+	0.0158406i
$489$	−31.0920	+	6.66141i	−1.40603	+	0.301239i
$490$	7.03574	−	12.1863i	0.317842	−	0.550519i
$491$	−5.53351			−0.249724			−0.124862	−	0.992174i	$-0.539849\pi$
$491$	−5.53351			−0.249724			−0.124862	+	0.992174i	$0.539849\pi$
$492$	−5.34267	+	4.82624i	−0.240866	+	0.217584i
$493$	4.39562	+	2.53781i	0.197969	+	0.114297i
$494$	−4.33066	+	25.5719i	−0.194846	+	1.15053i
$495$	6.13274	+	13.6553i	0.275646	+	0.613758i
$496$	1.99320	+	7.43873i	0.0894974	+	0.334009i
$497$	17.3602	−	10.0229i	0.778711	−	0.449589i
$498$	−24.2706	+	12.4160i	−1.08759	+	0.556374i
$499$	2.39294	+	0.641188i	0.107123	+	0.0287035i	0.311982	−	0.950088i	$-0.399007\pi$
$499$	2.39294	+	0.641188i	0.107123	+	0.0287035i	−0.204859	+	0.978791i	$0.565674\pi$
$500$	6.66698	−	1.78641i	0.298157	−	0.0798908i
$501$	−4.01248	−	1.29656i	−0.179264	−	0.0579260i
$502$	19.9204	−	5.33767i	0.889093	−	0.238232i
$503$	−32.0788	+	18.5207i	−1.43032	+	0.825798i	−0.997145	−	0.0755096i	$-0.975942\pi$
$503$	−32.0788	+	18.5207i	−1.43032	+	0.825798i	−0.433179	+	0.901308i	$0.642608\pi$
$504$	6.11823	−	8.47858i	0.272528	−	0.377666i
$505$	−0.223772	+	0.0599596i	−0.00995773	+	0.00266817i
$506$	−5.82101	+	10.0823i	−0.258776	+	0.448212i
$507$	−20.8577	−	8.48269i	−0.926323	−	0.376729i
$508$	−5.81045	−	10.0640i	−0.257797	−	0.446518i
$509$	−23.6343	−	23.6343i	−1.04757	−	1.04757i	−0.998810	−	0.0487610i	$-0.984473\pi$
$509$	−23.6343	−	23.6343i	−1.04757	−	1.04757i	−0.0487610	−	0.998810i	$-0.515527\pi$
$510$	−3.53644	+	1.80912i	−0.156596	+	0.0801092i
$511$			47.6597i			2.10834i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−34.2197	−	15.0370i	−1.51084	−	0.663899i
$514$	2.21014	−	8.24837i	0.0974853	−	0.363820i
$515$	6.32261	+	23.5963i	0.278608	+	1.03978i
$516$	14.9279	+	0.758120i	0.657164	+	0.0333744i
$517$		−	14.1064i		−	0.620399i
$518$	−10.4495	+	10.4495i	−0.459125	+	0.459125i
$519$	−8.02647	−	15.6900i	−0.352323	−	0.688715i
$520$	−7.59449	−	6.28539i	−0.333041	−	0.275632i
$521$			6.65944i			0.291755i	0.989303	+	0.145878i	$0.0466006\pi$
$521$			6.65944i			0.291755i	−0.989303	+	0.145878i	$0.953399\pi$
$522$	−16.9683	−	6.45058i	−0.742681	−	0.282334i
$523$	0.581243	−	1.00674i	0.0254160	−	0.0440218i	−0.853038	−	0.521849i	$-0.825242\pi$
$523$	0.581243	−	1.00674i	0.0254160	−	0.0440218i	0.878454	+	0.477828i	$0.158576\pi$
$524$	4.81077			0.210159
$525$	11.0893	−	10.0173i	0.483975	−	0.437193i
$526$	−0.684615	−	2.55502i	−0.0298506	−	0.111404i
$527$	1.67191	+	6.23965i	0.0728296	+	0.271804i
$528$	−2.34561	+	2.11888i	−0.102079	+	0.0922123i
$529$	17.6956			0.769373
$530$	−5.37231	+	9.30512i	−0.233358	+	0.404189i
$531$	−20.8833	−	7.93890i	−0.906257	−	0.344519i
$532$		−	25.0702i		−	1.08693i
$533$	−13.6259	−	6.24187i	−0.590203	−	0.270365i
$534$	−1.17537	−	2.29759i	−0.0508632	−	0.0994266i
$535$	27.6134	−	27.6134i	1.19383	−	1.19383i
$536$			5.53466i			0.239061i
$537$	22.6468	+	1.15013i	0.977280	+	0.0496316i
$538$	4.46219	+	16.6531i	0.192379	+	0.717967i
$539$	2.43091	−	9.07227i	0.104707	−	0.390770i
$540$	11.4531	−	8.40639i	0.492862	−	0.361753i
$541$	15.5641	+	15.5641i	0.669152	+	0.669152i	0.957520	−	0.288368i	$-0.0931126\pi$
$541$	15.5641	+	15.5641i	0.669152	+	0.669152i	−0.288368	+	0.957520i	$0.593113\pi$
$542$			15.0655i			0.647119i
$543$	15.5134	−	7.93611i	0.665743	−	0.340571i
$544$	−0.593126	−	0.593126i	−0.0254301	−	0.0254301i
$545$	−18.7242	−	32.4313i	−0.802056	−	1.38920i
$546$	21.2475	+	4.71796i	0.909310	+	0.201910i
$547$	−4.14533	+	7.17992i	−0.177241	+	0.306991i	−0.940935	−	0.338588i	$-0.890051\pi$
$547$	−4.14533	+	7.17992i	−0.177241	+	0.306991i	0.763693	+	0.645579i	$0.223384\pi$
$548$	7.49077	−	2.00715i	0.319990	−	0.0857411i
$549$	0.868751	−	1.20391i	0.0370774	−	0.0513815i
$550$	−3.91256	+	2.25892i	−0.166832	+	0.0963205i
$551$	−42.0439	+	11.2656i	−1.79113	+	0.479932i
$552$	10.5140	+	3.39741i	0.447506	+	0.144603i
$553$	6.00824	−	1.60990i	0.255496	−	0.0684600i
$554$	−13.2120	−	3.54013i	−0.561322	−	0.150406i
$555$	−17.8768	+	9.14513i	−0.758826	+	0.388189i
$556$	−4.18036	+	2.41353i	−0.177287	+	0.102357i
$557$	−5.76476	−	21.5144i	−0.244261	−	0.911594i	−0.973754	−	0.227605i	$-0.926910\pi$
$557$	−5.76476	−	21.5144i	−0.244261	−	0.911594i	0.729493	−	0.683989i	$-0.239756\pi$
$558$	−9.46526	−	21.0755i	−0.400696	−	0.892197i
$559$	10.8397	+	29.1658i	0.458471	+	1.23358i
$560$	8.25239	+	4.76452i	0.348727	+	0.201338i
$561$	−1.96751	+	1.77733i	−0.0830683	+	0.0750388i
$562$	13.3189			0.561826
$563$	14.0872	−	24.3998i	0.593707	−	1.02833i	−0.400021	−	0.916506i	$-0.630997\pi$
$563$	14.0872	−	24.3998i	0.593707	−	1.02833i	0.993728	−	0.111824i	$-0.0356693\pi$
$564$	−13.0911	+	2.80475i	−0.551236	+	0.118101i
$565$	15.3826	−	15.3826i	0.647152	−	0.647152i
$566$	2.45206	+	0.657028i	0.103068	+	0.0276170i
$567$	−14.0590	+	28.0395i	−0.590423	+	1.17755i
$568$	2.87586	+	4.98113i	0.120668	+	0.209004i
$569$	14.5939	+	25.2774i	0.611808	+	1.05968i	0.990936	+	0.134338i	$0.0428907\pi$
$569$	14.5939	+	25.2774i	0.611808	+	1.05968i	−0.379128	+	0.925344i	$0.623776\pi$
$570$	10.4744	−	32.4152i	0.438723	−	1.35772i
$571$	−36.5099	+	21.0790i	−1.52789	+	0.882129i	−0.528443	+	0.848969i	$0.677224\pi$
$571$	−36.5099	+	21.0790i	−1.52789	+	0.882129i	−0.999450	+	0.0331604i	$0.989443\pi$
$572$	−5.98221	−	2.74038i	−0.250129	−	0.114581i
$573$	28.8268	−	14.7468i	1.20426	−	0.616056i
$574$	13.9936	+	3.74957i	0.584081	+	0.156504i
$575$	13.6766	+	7.89621i	0.570355	+	0.329295i
$576$	2.43274	+	1.75549i	0.101364	+	0.0731455i
$577$	13.8702	−	13.8702i	0.577425	−	0.577425i	−0.356768	−	0.934193i	$-0.616121\pi$
$577$	13.8702	−	13.8702i	0.577425	−	0.577425i	0.934193	+	0.356768i	$0.116121\pi$
$578$	11.5233	+	11.5233i	0.479306	+	0.479306i
$579$	−2.75438	+	8.52400i	−0.114468	+	0.354245i
$580$	4.28199	−	15.9806i	0.177800	−	0.663559i
$581$	47.5068	+	27.4280i	1.97091	+	1.13791i
$582$	16.3663	−	25.2914i	0.678405	−	1.04836i
$583$	−1.85618	+	6.92736i	−0.0768752	+	0.286902i
$584$	−13.6749			−0.565872
$585$	25.5013	+	14.9774i	1.05435	+	0.619241i
$586$	−13.9356			−0.575674
$587$	2.05358	−	7.66407i	0.0847604	−	0.316330i	−0.910508	−	0.413491i	$-0.864309\pi$
$587$	2.05358	−	7.66407i	0.0847604	−	0.316330i	0.995269	+	0.0971607i	$0.0309761\pi$
$588$	−8.90264	−	0.452124i	−0.367139	−	0.0186453i
$589$	−47.9752	−	27.6985i	−1.97679	−	1.14130i
$590$	5.26996	−	19.6678i	0.216961	−	0.809708i
$591$	10.6487	+	11.7881i	0.438028	+	0.484899i
$592$	−2.99826	−	2.99826i	−0.123228	−	0.123228i
$593$	−23.8412	+	23.8412i	−0.979040	+	0.979040i	−0.999785	−	0.0207452i	$-0.993396\pi$
$593$	−23.8412	+	23.8412i	−0.979040	+	0.979040i	0.0207452	+	0.999785i	$0.493396\pi$
$594$	5.93188	−	7.39840i	0.243388	−	0.303560i
$595$	6.92215	+	3.99651i	0.283781	+	0.163841i
$596$	12.6085	+	3.37842i	0.516462	+	0.138386i
$597$	19.4320	+	12.5746i	0.795297	+	0.514644i
$598$	2.15979	+	22.8993i	0.0883205	+	0.936422i
$599$	5.64668	−	3.26011i	0.230717	−	0.133205i	−0.380186	−	0.924910i	$-0.624140\pi$
$599$	5.64668	−	3.26011i	0.230717	−	0.133205i	0.610903	+	0.791706i	$0.290807\pi$
$600$	2.87426	+	3.18182i	0.117341	+	0.129897i
$601$	13.7872	+	23.8801i	0.562390	+	0.974088i	0.997287	+	0.0736083i	$0.0234515\pi$
$601$	13.7872	+	23.8801i	0.562390	+	0.974088i	−0.434897	+	0.900480i	$0.643215\pi$
$602$	−15.0381	−	26.0468i	−0.612909	−	1.06159i
$603$	−2.65049	−	16.3911i	−0.107936	−	0.667495i
$604$	11.0213	+	2.95315i	0.448450	+	0.120162i
$605$	14.8277	−	14.8277i	0.602832	−	0.602832i
$606$	0.0983764	+	0.108903i	0.00399627	+	0.00442389i
$607$	−2.95810	+	5.12359i	−0.120066	+	0.207960i	−0.919793	−	0.392403i	$-0.871644\pi$
$607$	−2.95810	+	5.12359i	−0.120066	+	0.207960i	0.799728	+	0.600363i	$0.204977\pi$
$608$	7.19335			0.291729
$609$	7.65221	+	35.7165i	0.310083	+	1.44731i
$610$	1.17179	+	0.676532i	0.0474443	+	0.0273920i
$611$	−16.1397	−	22.7208i	−0.652942	−	0.919185i
$612$	2.04060	+	1.47252i	0.0824864	+	0.0595230i
$613$	4.10104	+	15.3053i	0.165639	+	0.618175i	0.997958	+	0.0638768i	$0.0203465\pi$
$613$	4.10104	+	15.3053i	0.165639	+	0.618175i	−0.832318	+	0.554298i	$0.812987\pi$
$614$	8.01466	−	4.62727i	0.323445	−	0.186741i
$615$	16.5268	+	10.6946i	0.666424	+	0.431249i
$616$	6.14363	+	1.64618i	0.247534	+	0.0663266i
$617$	−25.2301	+	6.76037i	−1.01572	+	0.272162i	−0.728019	−	0.685557i	$-0.759559\pi$
$617$	−25.2301	+	6.76037i	−1.01572	+	0.272162i	−0.287705	+	0.957719i	$0.592892\pi$
$618$	11.4836	−	10.3736i	0.461939	−	0.417287i
$619$	11.8178	−	3.16658i	0.474999	−	0.127276i	−0.0133740	−	0.999911i	$-0.504257\pi$
$619$	11.8178	−	3.16658i	0.474999	−	0.127276i	0.488373	+	0.872635i	$0.337591\pi$
$620$	18.2351	−	10.5280i	0.732339	−	0.422816i
$621$	−32.7645	−	5.02648i	−1.31480	−	0.201706i
$622$	−15.4935	+	4.15147i	−0.621233	+	0.166459i
$623$	−2.59649	+	4.49726i	−0.104026	+	0.180179i
$624$	−1.35371	+	6.09651i	−0.0541920	+	0.244056i
$625$	−15.6247	−	27.0628i	−0.624988	−	1.08251i
$626$	−13.1574	−	13.1574i	−0.525875	−	0.525875i
$627$	1.15326	−	22.7085i	0.0460567	−	0.906888i
$628$		−	4.33759i		−	0.173089i
$629$	−2.51496	−	2.51496i	−0.100278	−	0.100278i
$630$	−26.7214	−	10.1583i	−1.06460	−	0.404716i
$631$	2.72399	−	10.1661i	0.108440	−	0.404704i	−0.890272	−	0.455428i	$-0.849486\pi$
$631$	2.72399	−	10.1661i	0.108440	−	0.404704i	0.998713	+	0.0507238i	$0.0161528\pi$
$632$	0.461927	+	1.72393i	0.0183745	+	0.0685744i
$633$	9.44944	+	18.4716i	0.375582	+	0.734181i
$634$			7.47878i			0.297020i
$635$	−22.4671	+	22.4671i	−0.891580	+	0.891580i
$636$	6.79783	+	0.345231i	0.269552	+	0.0136893i
$637$	−6.46454	−	17.3937i	−0.256134	−	0.689165i
$638$		−	11.0429i		−	0.437192i
$639$	−10.9023	−	13.3745i	−0.431290	−	0.529089i
$640$	−1.36707	+	2.36784i	−0.0540384	+	0.0935972i
$641$	4.92012			0.194333			0.0971666	−	0.995268i	$-0.469022\pi$
$641$	4.92012			0.194333			0.0971666	+	0.995268i	$0.469022\pi$
$642$	−23.5400	−	7.60653i	−0.929051	−	0.300206i
$643$	8.73497	+	32.5993i	0.344473	+	1.28559i	0.893226	+	0.449608i	$0.148436\pi$
$643$	8.73497	+	32.5993i	0.344473	+	1.28559i	−0.548753	+	0.835985i	$0.684897\pi$
$644$	−5.75435	−	21.4755i	−0.226753	−	0.846255i
$645$	−8.56155	−	39.9609i	−0.337111	−	1.57346i
$646$	6.03383			0.237398
$647$	2.54755	−	4.41248i	0.100154	−	0.173473i	−0.811594	−	0.584222i	$-0.801400\pi$
$647$	2.54755	−	4.41248i	0.100154	−	0.173473i	0.911748	+	0.410750i	$0.134733\pi$
$648$	−8.04534	−	4.03393i	−0.316051	−	0.158468i
$649$		−	13.5908i		−	0.533484i
$650$	−3.71733	+	8.11488i	−0.145806	+	0.318292i
$651$	−25.2562	+	39.0292i	−0.989867	+	1.52967i
$652$	−12.9813	+	12.9813i	−0.508388	+	0.508388i
$653$			39.5640i			1.54826i	0.633028	+	0.774129i	$0.281812\pi$
$653$			39.5640i			1.54826i	−0.633028	+	0.774129i	$0.718188\pi$
$654$	−12.8883	+	19.9168i	−0.503973	+	0.778807i
$655$	−3.40434	−	12.7052i	−0.133019	−	0.496432i
$656$	−1.07586	+	4.01515i	−0.0420052	+	0.156765i
$657$	40.4987	−	6.54878i	1.58000	−	0.255492i
$658$	19.0491	+	19.0491i	0.742609	+	0.742609i
$659$			15.2097i			0.592484i	0.955113	+	0.296242i	$0.0957335\pi$
$659$			15.2097i			0.592484i	−0.955113	+	0.296242i	$0.904267\pi$
$660$	7.25579	+	4.69529i	0.282431	+	0.182764i
$661$	8.36737	+	8.36737i	0.325453	+	0.325453i	0.850854	−	0.525401i	$-0.176085\pi$
$661$	8.36737	+	8.36737i	0.325453	+	0.325453i	−0.525401	+	0.850854i	$0.676085\pi$
$662$	−5.69622	−	9.86614i	−0.221390	−	0.383458i
$663$	−1.13550	+	5.11379i	−0.0440993	+	0.198603i
$664$	−7.86988	+	13.6310i	−0.305411	+	0.528987i
$665$	−66.2101	+	17.7409i	−2.56752	+	0.687964i
$666$	10.3153	+	7.44360i	0.399708	+	0.288434i
$667$	−33.4296	+	19.3006i	−1.29440	+	0.747323i
$668$	−2.35159	+	0.630107i	−0.0909858	+	0.0243796i
$669$	−0.637470	−	2.97538i	−0.0246460	−	0.115035i
$670$	14.6169	−	3.91660i	0.564702	−	0.151311i
$671$	0.872359	+	0.233748i	0.0336770	+	0.00902373i
$672$	0.306173	−	6.02876i	0.0118109	−	0.232564i
$673$	16.9241	−	9.77114i	0.652376	−	0.376650i	−0.136990	−	0.990572i	$-0.543743\pi$
$673$	16.9241	−	9.77114i	0.652376	−	0.376650i	0.789366	+	0.613923i	$0.210409\pi$
$674$	4.29770	+	16.0392i	0.165541	+	0.617808i
$675$	−10.0359	−	8.04660i	−0.386284	−	0.309714i
$676$	−12.7708	+	2.43062i	−0.491183	+	0.0934854i
$677$	−7.33732	−	4.23620i	−0.281996	−	0.162811i	0.352331	−	0.935876i	$-0.385389\pi$
$677$	−7.33732	−	4.23620i	−0.281996	−	0.162811i	−0.634327	+	0.773065i	$0.718723\pi$
$678$	−13.1135	−	4.23738i	−0.503620	−	0.162736i
$679$	−60.6166			−2.32625
$680$	−1.14671	+	1.98616i	−0.0439743	+	0.0761658i
$681$	5.75024	−	17.7954i	0.220350	−	0.681919i
$682$	9.93791	−	9.93791i	0.380542	−	0.380542i
$683$	−13.4051	−	3.59188i	−0.512930	−	0.137439i	−0.00693584	−	0.999976i	$-0.502208\pi$
$683$	−13.4051	−	3.59188i	−0.512930	−	0.137439i	−0.505995	+	0.862537i	$0.668874\pi$
$684$	−21.3033	+	3.44482i	−0.814554	+	0.131716i
$685$	−10.6017	−	18.3627i	−0.405070	−	0.701601i
$686$	−3.22979	−	5.59416i	−0.123314	−	0.213586i
$687$	4.02078	−	0.861445i	0.153402	−	0.0328662i
$688$	7.47357	−	4.31487i	0.284927	−	0.164503i
$689$	4.93616	+	13.2814i	0.188053	+	0.505982i
$690$	1.53227	−	30.1715i	0.0583326	−	1.14861i
$691$	−4.44039	−	1.18980i	−0.168920	−	0.0452620i	0.173368	−	0.984857i	$-0.444535\pi$
$691$	−4.44039	−	1.18980i	−0.168920	−	0.0452620i	−0.342288	+	0.939595i	$0.611202\pi$
$692$	−8.81194	−	5.08757i	−0.334980	−	0.193401i
$693$	−18.9829	−	1.93310i	−0.721101	−	0.0734322i
$694$	9.95438	−	9.95438i	0.377863	−	0.377863i
$695$	9.33234	+	9.33234i	0.353996	+	0.353996i
$696$	−10.2481	+	2.19563i	−0.388452	+	0.0832253i
$697$	−0.902436	+	3.36794i	−0.0341822	+	0.127570i
$698$	−2.22642	−	1.28542i	−0.0842712	−	0.0486540i
$699$	−11.7111	−	22.8926i	−0.442954	−	0.865880i
$700$	2.23305	−	8.33385i	0.0844013	−	0.314990i
$701$	3.27106			0.123546			0.0617731	−	0.998090i	$-0.480324\pi$
$701$	3.27106			0.123546			0.0617731	+	0.998090i	$0.480324\pi$
$702$	1.08951	−	18.7033i	0.0411210	−	0.705910i
$703$	30.5011			1.15037
$704$	−0.472336	+	1.76278i	−0.0178018	+	0.0664374i
$705$	16.6712	+	32.5887i	0.627875	+	1.22736i
$706$	−5.48915	−	3.16916i	−0.206587	−	0.119273i
$707$	0.0764298	−	0.285240i	0.00287444	−	0.0107276i
$708$	−12.6126	+	2.70222i	−0.474010	+	0.101556i
$709$	−13.1692	−	13.1692i	−0.494578	−	0.494578i	0.415167	−	0.909745i	$-0.363723\pi$
$709$	−13.1692	−	13.1692i	−0.494578	−	0.494578i	−0.909745	+	0.415167i	$0.863723\pi$
$710$	11.1200	−	11.1200i	0.417326	−	0.417326i
$711$	−2.19358	−	4.88427i	−0.0822658	−	0.183174i
$712$	−1.29039	−	0.745007i	−0.0483594	−	0.0279203i
$713$	−47.4540	−	12.7152i	−1.77716	−	0.476190i
$714$	0.256820	−	5.05696i	0.00961125	−	0.189252i
$715$	−3.00400	+	17.7382i	−0.112343	+	0.663370i
$716$	11.3380	−	6.54598i	0.423720	−	0.244635i
$717$	−50.0237	+	10.7175i	−1.86817	+	0.400252i
$718$	10.6142	+	18.3843i	0.396118	+	0.686096i
$719$	6.22658	+	10.7848i	0.232212	+	0.402204i	0.958459	−	0.285231i	$-0.0920703\pi$
$719$	6.22658	+	10.7848i	0.232212	+	0.402204i	−0.726247	+	0.687434i	$0.758737\pi$
$720$	2.91470	−	7.66712i	0.108624	−	0.285737i
$721$	−30.0780	−	8.05937i	−1.12016	−	0.300147i
$722$	−23.1537	+	23.1537i	−0.861693	+	0.861693i
$723$	10.9676	−	33.9417i	0.407891	−	1.26230i
$724$	5.03030	−	8.71273i	0.186950	−	0.323806i
$725$	−14.9797			−0.556331
$726$	−12.6404	−	4.08452i	−0.469130	−	0.151591i
$727$	−0.202128	−	0.116699i	−0.00749650	−	0.00432811i	0.496247	−	0.868181i	$-0.334711\pi$
$727$	−0.202128	−	0.116699i	−0.00749650	−	0.00432811i	−0.503744	+	0.863853i	$0.668044\pi$
$728$	11.7788	−	4.37771i	0.436553	−	0.162249i
$729$	25.7583	+	8.09377i	0.954012	+	0.299769i
$730$	9.67706	+	36.1153i	0.358164	+	1.33669i
$731$	6.26888	−	3.61934i	0.231863	−	0.133866i
$732$	0.0434747	−	0.856047i	0.00160687	−	0.0316404i
$733$	27.3080	+	7.31715i	1.00864	+	0.270265i	0.725062	−	0.688684i	$-0.241811\pi$
$733$	27.3080	+	7.31715i	1.00864	+	0.270265i	0.283580	+	0.958948i	$0.408478\pi$
$734$	16.2035	−	4.34173i	0.598084	−	0.160256i
$735$	5.10590	+	23.8317i	0.188334	+	0.879045i
$736$	6.16194	−	1.65109i	0.227132	−	0.0608599i
$737$	8.74734	−	5.05028i	0.322213	−	0.186030i
$738$	1.26337	−	12.4062i	0.0465052	−	0.456679i
$739$	34.3558	−	9.20561i	1.26380	−	0.338634i	0.436146	−	0.899876i	$-0.356343\pi$
$739$	34.3558	−	9.20561i	1.26380	−	0.338634i	0.827652	+	0.561242i	$0.189676\pi$
$740$	−5.79664	+	10.0401i	−0.213089	+	0.369080i
$741$	−24.1241	−	37.8953i	−0.886221	−	1.39212i
$742$	−6.84803	−	11.8611i	−0.251399	−	0.435436i
$743$	−18.5235	−	18.5235i	−0.679560	−	0.679560i	0.280340	−	0.959901i	$-0.409553\pi$
$743$	−18.5235	−	18.5235i	−0.679560	−	0.679560i	−0.959901	+	0.280340i	$0.909553\pi$
$744$	−11.1986	−	7.24670i	−0.410560	−	0.265677i
$745$		−	35.6895i		−	1.30756i
$746$	7.72193	+	7.72193i	0.282720	+	0.282720i
$747$	16.7791	−	44.1375i	0.613916	−	1.61491i
$748$	−0.396198	+	1.47863i	−0.0144865	+	0.0540642i
$749$	12.8835	+	48.0820i	0.470754	+	1.75688i
$750$	−6.49488	+	10.0367i	−0.237159	+	0.366490i
$751$			29.2381i			1.06691i	0.845827	+	0.533457i	$0.179108\pi$
$751$			29.2381i			1.06691i	−0.845827	+	0.533457i	$0.820892\pi$
$752$	−5.46571	+	5.46571i	−0.199314	+	0.199314i
$753$	−19.4062	+	29.9891i	−0.707201	+	1.09286i
$754$	−12.6346	−	17.7865i	−0.460124	−	0.647744i
$755$		−	31.1969i		−	1.13537i
$756$	1.98037	+	18.0010i	0.0720254	+	0.654689i
$757$	0.560080	−	0.970087i	0.0203565	−	0.0352584i	−0.855668	−	0.517526i	$-0.826853\pi$
$757$	0.560080	−	0.970087i	0.0203565	−	0.0352584i	0.876024	+	0.482267i	$0.160187\pi$
$758$	−6.09421			−0.221352
$759$	−4.22436	−	19.7171i	−0.153335	−	0.715686i
$760$	−5.09038	−	18.9975i	−0.184647	−	0.689113i
$761$	3.20044	+	11.9442i	0.116016	+	0.432977i	0.999361	−	0.0357464i	$-0.0113809\pi$
$761$	3.20044	+	11.9442i	0.116016	+	0.432977i	−0.883345	+	0.468723i	$0.844714\pi$
$762$	19.1529	+	6.18891i	0.693836	+	0.224201i
$763$	47.7351			1.72813
$764$	9.34724	−	16.1899i	0.338171	−	0.585730i
$765$	2.44487	−	6.43123i	0.0883943	−	0.232521i
$766$		−	32.0735i		−	1.15886i
$767$	−15.5497	−	21.8902i	−0.561467	−	0.790411i
$768$	1.72982	+	0.0878497i	0.0624196	+	0.00317000i
$769$	15.5698	−	15.5698i	0.561462	−	0.561462i	−0.368261

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:	\( N \)	\(=\)	\( 234 = 2 \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	234.z (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.258819 + 0.965926i) q^{2} +(-0.788831 - 1.54199i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-0.707650 + 2.64098i) q^{5} +(1.69362 - 0.362854i) q^{6} +(-2.46440 - 2.46440i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-1.75549 + 2.43274i) q^{9} +O(q^{10})\)	\(q+(-0.258819 + 0.965926i) q^{2} +(-0.788831 - 1.54199i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-0.707650 + 2.64098i) q^{5} +(1.69362 - 0.362854i) q^{6} +(-2.46440 - 2.46440i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-1.75549 + 2.43274i) q^{9} +(-2.36784 - 1.36707i) q^{10} +(-1.76278 - 0.472336i) q^{11} +(-0.0878497 + 1.72982i) q^{12} +(-3.37968 + 1.25609i) q^{13} +(3.01826 - 1.74260i) q^{14} +(4.63060 - 0.992098i) q^{15} +(0.500000 + 0.866025i) q^{16} +(0.419403 + 0.726428i) q^{17} +(-1.89550 - 2.32532i) q^{18} +(-6.94825 - 1.86178i) q^{19} +(1.93334 - 1.93334i) q^{20} +(-1.85610 + 5.74409i) q^{21} +(0.912483 - 1.58047i) q^{22} -6.37931 q^{23} +(-1.64814 - 0.532567i) q^{24} +(-2.14391 - 1.23778i) q^{25} +(-0.338562 - 3.58962i) q^{26} +(5.13606 + 0.787935i) q^{27} +(0.902034 + 3.36644i) q^{28} +(5.24032 - 3.02550i) q^{29} +(-0.240194 + 4.72959i) q^{30} +(7.43873 + 1.99320i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(0.662197 + 3.09079i) q^{33} +(-0.810225 + 0.217099i) q^{34} +(8.25239 - 4.76452i) q^{35} +(2.73667 - 1.22907i) q^{36} +(-4.09570 + 1.09744i) q^{37} +(3.59668 - 6.22963i) q^{38} +(4.60288 + 4.22061i) q^{39} +(1.36707 + 2.36784i) q^{40} +(2.93930 + 2.93930i) q^{41} +(-5.06797 - 3.27953i) q^{42} -8.62974i q^{43} +(1.29045 + 1.29045i) q^{44} +(-5.18257 - 6.35776i) q^{45} +(1.65109 - 6.16194i) q^{46} +(2.00059 + 7.46630i) q^{47} +(0.940991 - 1.45414i) q^{48} +5.14656i q^{49} +(1.75049 - 1.75049i) q^{50} +(0.789309 - 1.21975i) q^{51} +(3.55493 + 0.602036i) q^{52} -3.92979i q^{53} +(-2.09040 + 4.75712i) q^{54} +(2.49486 - 4.32123i) q^{55} -3.48519 q^{56} +(2.61014 + 12.1828i) q^{57} +(1.56612 + 5.84482i) q^{58} +(1.92746 + 7.19337i) q^{59} +(-4.50627 - 1.45612i) q^{60} -0.494876 q^{61} +(-3.85057 + 6.66938i) q^{62} +(10.3215 - 1.66902i) q^{63} -1.00000i q^{64} +(-0.925680 - 9.81456i) q^{65} +(-3.15687 - 0.160323i) q^{66} +(-3.91359 + 3.91359i) q^{67} -0.838806i q^{68} +(5.03219 + 9.83686i) q^{69} +(2.46630 + 9.20434i) q^{70} +(-1.48865 + 5.55573i) q^{71} +(0.478890 + 2.96153i) q^{72} +(-9.66963 - 9.66963i) q^{73} -4.24018i q^{74} +(-0.217478 + 4.28229i) q^{75} +(5.08647 + 5.08647i) q^{76} +(3.18018 + 5.50823i) q^{77} +(-5.26811 + 3.35366i) q^{78} +(-0.892374 + 1.54564i) q^{79} +(-2.64098 + 0.707650i) q^{80} +(-2.83649 - 8.54133i) q^{81} +(-3.59989 + 2.07840i) q^{82} +(-15.2034 + 4.07375i) q^{83} +(4.47947 - 4.04648i) q^{84} +(-2.21527 + 0.593581i) q^{85} +(8.33569 + 2.23354i) q^{86} +(-8.79903 - 5.69394i) q^{87} +(-1.58047 + 0.912483i) q^{88} +(-0.385644 - 1.43924i) q^{89} +(7.48247 - 3.36047i) q^{90} +(11.4244 + 5.23339i) q^{91} +(5.52464 + 3.18965i) q^{92} +(-2.79439 - 13.0428i) q^{93} -7.72968 q^{94} +(9.83385 - 17.0327i) q^{95} +(1.16105 + 1.28529i) q^{96} +(12.2984 - 12.2984i) q^{97} +(-4.97120 - 1.33203i) q^{98} +(4.24362 - 3.45922i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 8 q^{7}+O(q^{10}) \) 56 * q - 8 * q^7	\( 56 q - 8 q^{7} - 24 q^{11} + 28 q^{16} - 8 q^{19} - 24 q^{21} + 36 q^{27} - 4 q^{28} - 24 q^{30} - 4 q^{31} + 60 q^{33} - 24 q^{35} - 4 q^{37} + 36 q^{38} - 48 q^{41} - 36 q^{42} - 84 q^{45} - 36 q^{47} - 24 q^{50} + 8 q^{52} - 36 q^{54} + 36 q^{57} + 24 q^{60} - 48 q^{63} - 36 q^{65} + 28 q^{67} + 84 q^{69} - 24 q^{71} - 24 q^{72} + 28 q^{73} + 4 q^{76} + 24 q^{77} - 60 q^{78} - 24 q^{79} + 24 q^{81} - 96 q^{83} - 72 q^{85} + 4 q^{91} - 24 q^{92} - 36 q^{93} - 52 q^{97} + 48 q^{98} + 60 q^{99}+O(q^{100}) \) 56 * q - 8 * q^7 - 24 * q^11 + 28 * q^16 - 8 * q^19 - 24 * q^21 + 36 * q^27 - 4 * q^28 - 24 * q^30 - 4 * q^31 + 60 * q^33 - 24 * q^35 - 4 * q^37 + 36 * q^38 - 48 * q^41 - 36 * q^42 - 84 * q^45 - 36 * q^47 - 24 * q^50 + 8 * q^52 - 36 * q^54 + 36 * q^57 + 24 * q^60 - 48 * q^63 - 36 * q^65 + 28 * q^67 + 84 * q^69 - 24 * q^71 - 24 * q^72 + 28 * q^73 + 4 * q^76 + 24 * q^77 - 60 * q^78 - 24 * q^79 + 24 * q^81 - 96 * q^83 - 72 * q^85 + 4 * q^91 - 24 * q^92 - 36 * q^93 - 52 * q^97 + 48 * q^98 + 60 * q^99

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