LMFDB - Embedded newform 378.2.u.d.43.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(43,378)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(378, base_ring=CyclotomicField(18))

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

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

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

chi := DirichletCharacter("378.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.u (of order $9$, 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:	$3.01834519640$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			43.4
Character	$\chi$	$=$	378.43
Dual form			378.2.u.d.211.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.766044 + 0.642788i) q^{2} +(0.503821 + 1.65716i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-4.01520 - 1.46142i) q^{5} +(-0.679250 + 1.59330i) q^{6} +(-0.173648 + 0.984808i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-2.49233 + 1.66982i) q^{9} +O(q^{10})$	\(q+(0.766044 + 0.642788i) q^{2} +(0.503821 + 1.65716i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-4.01520 - 1.46142i) q^{5} +(-0.679250 + 1.59330i) q^{6} +(-0.173648 + 0.984808i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-2.49233 + 1.66982i) q^{9} +(-2.13645 - 3.70043i) q^{10} +(-4.81620 + 1.75295i) q^{11} +(-1.54449 + 0.783929i) q^{12} +(0.991605 - 0.832055i) q^{13} +(-0.766044 + 0.642788i) q^{14} +(0.398849 - 7.39011i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(2.73186 + 4.73172i) q^{17} +(-2.98257 - 0.322884i) q^{18} +(1.05301 - 1.82386i) q^{19} +(0.741980 - 4.20798i) q^{20} +(-1.71947 + 0.208404i) q^{21} +(-4.81620 - 1.75295i) q^{22} +(0.926315 + 5.25340i) q^{23} +(-1.68705 - 0.392256i) q^{24} +(10.1559 + 8.52182i) q^{25} +1.29445 q^{26} +(-4.02284 - 3.28889i) q^{27} -1.00000 q^{28} +(0.526530 + 0.441811i) q^{29} +(5.05581 - 5.40478i) q^{30} +(-0.971570 - 5.51005i) q^{31} +(-0.939693 - 0.342020i) q^{32} +(-5.33141 - 7.09802i) q^{33} +(-0.948766 + 5.38072i) q^{34} +(2.13645 - 3.70043i) q^{35} +(-2.07724 - 2.16450i) q^{36} +(4.27290 + 7.40087i) q^{37} +(1.97900 - 0.720299i) q^{38} +(1.87844 + 1.22404i) q^{39} +(3.27322 - 2.74656i) q^{40} +(1.19874 - 1.00586i) q^{41} +(-1.45115 - 0.945605i) q^{42} +(-2.26818 + 0.825550i) q^{43} +(-2.56265 - 4.43863i) q^{44} +(12.4475 - 3.06233i) q^{45} +(-2.66722 + 4.61976i) q^{46} +(0.903202 - 5.12231i) q^{47} +(-1.04022 - 1.38490i) q^{48} +(-0.939693 - 0.342020i) q^{49} +(2.30216 + 13.0562i) q^{50} +(-6.46483 + 6.91106i) q^{51} +(0.991605 + 0.832055i) q^{52} +5.73848 q^{53} +(-0.967614 - 5.10526i) q^{54} +21.8998 q^{55} +(-0.766044 - 0.642788i) q^{56} +(3.55295 + 0.826097i) q^{57} +(0.119355 + 0.676894i) q^{58} +(-11.4995 - 4.18547i) q^{59} +(7.34710 - 0.890489i) q^{60} +(-0.404552 + 2.29433i) q^{61} +(2.79752 - 4.84545i) q^{62} +(-1.21166 - 2.74443i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-5.19748 + 1.89173i) q^{65} +(0.478416 - 8.86436i) q^{66} +(-7.73942 + 6.49415i) q^{67} +(-4.18546 + 3.51201i) q^{68} +(-8.23900 + 4.18182i) q^{69} +(4.01520 - 1.46142i) q^{70} +(2.20288 + 3.81550i) q^{71} +(-0.199940 - 2.99333i) q^{72} +(-7.78020 + 13.4757i) q^{73} +(-1.48396 + 8.41596i) q^{74} +(-9.00523 + 21.1234i) q^{75} +(1.97900 + 0.720299i) q^{76} +(-0.889997 - 5.04743i) q^{77} +(0.652170 + 2.14510i) q^{78} +(-0.893669 - 0.749877i) q^{79} +4.27289 q^{80} +(3.42341 - 8.32348i) q^{81} +1.56484 q^{82} +(9.57625 + 8.03543i) q^{83} +(-0.503821 - 1.65716i) q^{84} +(-4.05397 - 22.9912i) q^{85} +(-2.26818 - 0.825550i) q^{86} +(-0.466874 + 1.09514i) q^{87} +(0.889997 - 5.04743i) q^{88} +(-2.39651 + 4.15088i) q^{89} +(11.5038 + 5.65522i) q^{90} +(0.647224 + 1.12103i) q^{91} +(-5.01273 + 1.82448i) q^{92} +(8.64151 - 4.38612i) q^{93} +(3.98445 - 3.34335i) q^{94} +(-6.89345 + 5.78429i) q^{95} +(0.0933441 - 1.72953i) q^{96} +(9.60333 - 3.49533i) q^{97} +(-0.500000 - 0.866025i) q^{98} +(9.07644 - 12.4111i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 3 q^{3} + 3 q^{5} - 6 q^{6} - 15 q^{8} + 3 q^{9}+O(q^{10}) $ 30 * q - 3 * q^3 + 3 * q^5 - 6 * q^6 - 15 * q^8 + 3 * q^9	$ 30 q - 3 q^{3} + 3 q^{5} - 6 q^{6} - 15 q^{8} + 3 q^{9} - 3 q^{10} + 9 q^{11} + 3 q^{12} - 9 q^{13} + 12 q^{15} - 12 q^{18} - 15 q^{19} - 6 q^{20} - 3 q^{21} + 9 q^{22} - 12 q^{23} - 3 q^{24} + 21 q^{25} + 18 q^{26} + 3 q^{27} - 30 q^{28} - 30 q^{29} - 15 q^{30} + 18 q^{31} + 9 q^{33} + 12 q^{34} + 3 q^{35} - 12 q^{36} + 3 q^{37} - 3 q^{38} + 72 q^{39} + 3 q^{40} + 36 q^{41} - 3 q^{42} - 9 q^{43} - 3 q^{44} - 48 q^{45} - 15 q^{46} + 3 q^{48} + 3 q^{50} - 6 q^{51} - 9 q^{52} + 6 q^{53} + 45 q^{54} + 66 q^{55} - 51 q^{57} - 3 q^{58} - 48 q^{59} + 24 q^{60} + 57 q^{61} - 18 q^{62} - 15 q^{63} - 15 q^{64} + 24 q^{65} + 54 q^{66} + 6 q^{67} - 15 q^{68} - 48 q^{69} - 3 q^{70} - 24 q^{71} - 6 q^{72} - 36 q^{73} - 48 q^{74} - 129 q^{75} - 3 q^{76} + 9 q^{77} + 24 q^{78} - 21 q^{79} + 6 q^{80} + 27 q^{81} - 15 q^{83} + 3 q^{84} - 72 q^{85} - 9 q^{86} + 42 q^{87} - 9 q^{88} - 30 q^{89} - 30 q^{90} + 9 q^{91} + 6 q^{92} + 111 q^{93} - 45 q^{94} + 81 q^{95} - 6 q^{96} - 15 q^{97} - 15 q^{98} + 45 q^{99}+O(q^{100}) $ 30 * q - 3 * q^3 + 3 * q^5 - 6 * q^6 - 15 * q^8 + 3 * q^9 - 3 * q^10 + 9 * q^11 + 3 * q^12 - 9 * q^13 + 12 * q^15 - 12 * q^18 - 15 * q^19 - 6 * q^20 - 3 * q^21 + 9 * q^22 - 12 * q^23 - 3 * q^24 + 21 * q^25 + 18 * q^26 + 3 * q^27 - 30 * q^28 - 30 * q^29 - 15 * q^30 + 18 * q^31 + 9 * q^33 + 12 * q^34 + 3 * q^35 - 12 * q^36 + 3 * q^37 - 3 * q^38 + 72 * q^39 + 3 * q^40 + 36 * q^41 - 3 * q^42 - 9 * q^43 - 3 * q^44 - 48 * q^45 - 15 * q^46 + 3 * q^48 + 3 * q^50 - 6 * q^51 - 9 * q^52 + 6 * q^53 + 45 * q^54 + 66 * q^55 - 51 * q^57 - 3 * q^58 - 48 * q^59 + 24 * q^60 + 57 * q^61 - 18 * q^62 - 15 * q^63 - 15 * q^64 + 24 * q^65 + 54 * q^66 + 6 * q^67 - 15 * q^68 - 48 * q^69 - 3 * q^70 - 24 * q^71 - 6 * q^72 - 36 * q^73 - 48 * q^74 - 129 * q^75 - 3 * q^76 + 9 * q^77 + 24 * q^78 - 21 * q^79 + 6 * q^80 + 27 * q^81 - 15 * q^83 + 3 * q^84 - 72 * q^85 - 9 * q^86 + 42 * q^87 - 9 * q^88 - 30 * q^89 - 30 * q^90 + 9 * q^91 + 6 * q^92 + 111 * q^93 - 45 * q^94 + 81 * q^95 - 6 * q^96 - 15 * q^97 - 15 * q^98 + 45 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{2}{9}\right)$	$1$

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 $

$2$	0.766044	+	0.642788i	0.541675	+	0.454519i
$2$	0.766044	+	0.642788i	0.541675	+	0.454519i
$3$	0.503821	+	1.65716i	0.290881	+	0.956759i
$3$	0.503821	+	1.65716i	0.290881	+	0.956759i
$4$	0.173648	+	0.984808i	0.0868241	+	0.492404i
$5$	−4.01520	−	1.46142i	−1.79565	−	0.653565i	−0.998778	−	0.0494220i	$-0.984262\pi$
$5$	−4.01520	−	1.46142i	−1.79565	−	0.653565i	−0.796876	−	0.604143i	$-0.793516\pi$
$6$	−0.679250	+	1.59330i	−0.277303	+	0.650464i
$7$	−0.173648	+	0.984808i	−0.0656328	+	0.372222i
$7$	−0.173648	+	0.984808i	−0.0656328	+	0.372222i
$8$	−0.500000	+	0.866025i	−0.176777	+	0.306186i
$9$	−2.49233	+	1.66982i	−0.830777	+	0.556606i
$10$	−2.13645	−	3.70043i	−0.675603	−	1.17018i
$11$	−4.81620	+	1.75295i	−1.45214	+	0.528535i	−0.943188	−	0.332261i	$-0.892189\pi$
$11$	−4.81620	+	1.75295i	−1.45214	+	0.528535i	−0.508951	+	0.860796i	$0.669966\pi$
$12$	−1.54449	+	0.783929i	−0.445856	+	0.226301i
$13$	0.991605	−	0.832055i	0.275022	−	0.230771i	−0.494836	−	0.868987i	$-0.664772\pi$
$13$	0.991605	−	0.832055i	0.275022	−	0.230771i	0.769857	+	0.638216i	$0.220327\pi$
$14$	−0.766044	+	0.642788i	−0.204734	+	0.171792i
$15$	0.398849	−	7.39011i	0.102982	−	1.90812i
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$	2.73186	+	4.73172i	0.662574	+	1.14761i	0.979937	+	0.199307i	$0.0638692\pi$
$17$	2.73186	+	4.73172i	0.662574	+	1.14761i	−0.317363	+	0.948304i	$0.602797\pi$
$18$	−2.98257	−	0.322884i	−0.702999	−	0.0761044i
$19$	1.05301	−	1.82386i	0.241576	−	0.418422i	−0.719587	−	0.694402i	$-0.755669\pi$
$19$	1.05301	−	1.82386i	0.241576	−	0.418422i	0.961163	+	0.275980i	$0.0890023\pi$
$20$	0.741980	−	4.20798i	0.165912	−	0.940932i
$21$	−1.71947	+	0.208404i	−0.375219	+	0.0454776i
$22$	−4.81620	−	1.75295i	−1.02682	−	0.373731i
$23$	0.926315	+	5.25340i	0.193150	+	1.09541i	0.915029	+	0.403389i	$0.132168\pi$
$23$	0.926315	+	5.25340i	0.193150	+	1.09541i	−0.721879	+	0.692020i	$0.756721\pi$
$24$	−1.68705	−	0.392256i	−0.344367	−	0.0800690i
$25$	10.1559	+	8.52182i	2.03118	+	1.70436i
$26$	1.29445			0.253862
$27$	−4.02284	−	3.28889i	−0.774195	−	0.632947i
$28$	−1.00000			−0.188982
$29$	0.526530	+	0.441811i	0.0977742	+	0.0820423i	0.690364	−	0.723462i	$-0.257450\pi$
$29$	0.526530	+	0.441811i	0.0977742	+	0.0820423i	−0.592590	+	0.805504i	$0.701895\pi$
$30$	5.05581	−	5.40478i	0.923060	−	0.986773i
$31$	−0.971570	−	5.51005i	−0.174499	−	0.989633i	−0.938720	−	0.344679i	$-0.887988\pi$
$31$	−0.971570	−	5.51005i	−0.174499	−	0.989633i	0.764221	−	0.644954i	$-0.223123\pi$
$32$	−0.939693	−	0.342020i	−0.166116	−	0.0604612i
$33$	−5.33141	−	7.09802i	−0.928080	−	1.23561i
$34$	−0.948766	+	5.38072i	−0.162712	+	0.922785i
$35$	2.13645	−	3.70043i	0.361125	−	0.625487i
$36$	−2.07724	−	2.16450i	−0.346206	−	0.360751i
$37$	4.27290	+	7.40087i	0.702460	+	1.21670i	0.967600	+	0.252486i	$0.0812483\pi$
$37$	4.27290	+	7.40087i	0.702460	+	1.21670i	−0.265141	+	0.964210i	$0.585418\pi$
$38$	1.97900	−	0.720299i	0.321037	−	0.116848i
$39$	1.87844	+	1.22404i	0.300791	+	0.196003i
$40$	3.27322	−	2.74656i	0.517542	−	0.434270i
$41$	1.19874	−	1.00586i	0.187211	−	0.157089i	−0.544365	−	0.838848i	$-0.683229\pi$
$41$	1.19874	−	1.00586i	0.187211	−	0.157089i	0.731576	+	0.681760i	$0.238785\pi$
$42$	−1.45115	−	0.945605i	−0.223917	−	0.145910i
$43$	−2.26818	+	0.825550i	−0.345894	+	0.125895i	−0.509125	−	0.860693i	$-0.670031\pi$
$43$	−2.26818	+	0.825550i	−0.345894	+	0.125895i	0.163231	+	0.986588i	$0.447809\pi$
$44$	−2.56265	−	4.43863i	−0.386333	−	0.669149i
$45$	12.4475	−	3.06233i	1.85557	−	0.456506i
$46$	−2.66722	+	4.61976i	−0.393260	+	0.681146i
$47$	0.903202	−	5.12231i	0.131746	−	0.747166i	−0.845325	−	0.534252i	$-0.820593\pi$
$47$	0.903202	−	5.12231i	0.131746	−	0.747166i	0.977071	−	0.212914i	$-0.0682955\pi$
$48$	−1.04022	−	1.38490i	−0.150142	−	0.199893i
$49$	−0.939693	−	0.342020i	−0.134242	−	0.0488600i
$50$	2.30216	+	13.0562i	0.325574	+	1.84642i
$51$	−6.46483	+	6.91106i	−0.905258	+	0.967742i
$52$	0.991605	+	0.832055i	0.137511	+	0.115385i
$53$	5.73848			0.788241			0.394120	−	0.919059i	$-0.371049\pi$
$53$	5.73848			0.788241			0.394120	+	0.919059i	$0.371049\pi$
$54$	−0.967614	−	5.10526i	−0.131676	−	0.694738i
$55$	21.8998			2.95297
$56$	−0.766044	−	0.642788i	−0.102367	−	0.0858961i
$57$	3.55295	+	0.826097i	0.470599	+	0.109419i
$58$	0.119355	+	0.676894i	0.0156720	+	0.0888806i
$59$	−11.4995	−	4.18547i	−1.49711	−	0.544902i	−0.541797	−	0.840509i	$-0.682256\pi$
$59$	−11.4995	−	4.18547i	−1.49711	−	0.544902i	−0.955310	+	0.295607i	$0.904478\pi$
$60$	7.34710	−	0.890489i	0.948506	−	0.114962i
$61$	−0.404552	+	2.29433i	−0.0517976	+	0.293759i	−0.999692	−	0.0248266i	$-0.992097\pi$
$61$	−0.404552	+	2.29433i	−0.0517976	+	0.293759i	0.947894	+	0.318585i	$0.103208\pi$
$62$	2.79752	−	4.84545i	0.355286	−	0.615373i
$63$	−1.21166	−	2.74443i	−0.152655	−	0.345765i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	−5.19748	+	1.89173i	−0.644667	+	0.234640i
$66$	0.478416	−	8.86436i	0.0588889	−	1.09113i
$67$	−7.73942	+	6.49415i	−0.945521	+	0.793386i	−0.978538	−	0.206068i	$-0.933933\pi$
$67$	−7.73942	+	6.49415i	−0.945521	+	0.793386i	0.0330165	+	0.999455i	$0.489489\pi$
$68$	−4.18546	+	3.51201i	−0.507561	+	0.425894i
$69$	−8.23900	+	4.18182i	−0.991859	+	0.503432i
$70$	4.01520	−	1.46142i	0.479909	−	0.174673i
$71$	2.20288	+	3.81550i	0.261434	+	0.452816i	0.966623	−	0.256202i	$-0.0824714\pi$
$71$	2.20288	+	3.81550i	0.261434	+	0.452816i	−0.705189	+	0.709019i	$0.749138\pi$
$72$	−0.199940	−	2.99333i	−0.0235632	−	0.352767i
$73$	−7.78020	+	13.4757i	−0.910604	+	1.57721i	−0.0973904	+	0.995246i	$0.531050\pi$
$73$	−7.78020	+	13.4757i	−0.910604	+	1.57721i	−0.813213	+	0.581966i	$0.802284\pi$
$74$	−1.48396	+	8.41596i	−0.172507	+	0.978336i
$75$	−9.00523	+	21.1234i	−1.03983	+	2.43912i
$76$	1.97900	+	0.720299i	0.227007	+	0.0826239i
$77$	−0.889997	−	5.04743i	−0.101425	−	0.575208i
$78$	0.652170	+	2.14510i	0.0738437	+	0.242885i
$79$	−0.893669	−	0.749877i	−0.100546	−	0.0843678i	0.591129	−	0.806577i	$-0.298682\pi$
$79$	−0.893669	−	0.749877i	−0.100546	−	0.0843678i	−0.691675	+	0.722209i	$0.743127\pi$
$80$	4.27289			0.477724
$81$	3.42341	−	8.32348i	0.380379	−	0.924831i
$82$	1.56484			0.172808
$83$	9.57625	+	8.03543i	1.05113	+	0.882003i	0.993212	−	0.116318i	$-0.0371092\pi$
$83$	9.57625	+	8.03543i	1.05113	+	0.882003i	0.0579185	+	0.998321i	$0.481554\pi$
$84$	−0.503821	−	1.65716i	−0.0549713	−	0.180811i
$85$	−4.05397	−	22.9912i	−0.439715	−	2.49375i
$86$	−2.26818	−	0.825550i	−0.244584	−	0.0890213i
$87$	−0.466874	+	1.09514i	−0.0500541	+	0.117411i
$88$	0.889997	−	5.04743i	0.0948740	−	0.538057i
$89$	−2.39651	+	4.15088i	−0.254030	+	0.439992i	−0.964631	−	0.263602i	$-0.915089\pi$
$89$	−2.39651	+	4.15088i	−0.254030	+	0.439992i	0.710602	+	0.703594i	$0.248423\pi$
$90$	11.5038	+	5.65522i	1.21260	+	0.596113i
$91$	0.647224	+	1.12103i	0.0678475	+	0.117515i
$92$	−5.01273	+	1.82448i	−0.522613	+	0.190216i
$93$	8.64151	−	4.38612i	0.896082	−	0.454819i
$94$	3.98445	−	3.34335i	0.410965	−	0.344840i
$95$	−6.89345	+	5.78429i	−0.707253	+	0.593456i
$96$	0.0933441	−	1.72953i	0.00952689	−	0.176520i
$97$	9.60333	−	3.49533i	0.975070	−	0.354897i	0.195149	−	0.980774i	$-0.437481\pi$
$97$	9.60333	−	3.49533i	0.975070	−	0.354897i	0.779922	+	0.625877i	$0.215259\pi$
$98$	−0.500000	−	0.866025i	−0.0505076	−	0.0874818i
$99$	9.07644	−	12.4111i	0.912216	−	1.24736i
$100$	−6.62880	+	11.4814i	−0.662880	+	1.14814i
$101$	2.30126	−	13.0511i	0.228984	−	1.29863i	−0.625938	−	0.779873i	$-0.715284\pi$
$101$	2.30126	−	13.0511i	0.228984	−	1.29863i	0.854921	−	0.518757i	$-0.173605\pi$
$102$	−9.39469	+	1.13866i	−0.930213	+	0.112745i
$103$	7.22262	+	2.62882i	0.711666	+	0.259025i	0.672384	−	0.740203i	$-0.265271\pi$
$103$	7.22262	+	2.62882i	0.711666	+	0.259025i	0.0392825	+	0.999228i	$0.487493\pi$
$104$	0.224779	+	1.27478i	0.0220414	+	0.125003i
$105$	7.20858	+	1.67607i	0.703485	+	0.163568i
$106$	4.39593	+	3.68862i	0.426970	+	0.358271i
$107$	−2.52866			−0.244454			−0.122227	−	0.992502i	$-0.539004\pi$
$107$	−2.52866			−0.244454			−0.122227	+	0.992502i	$0.539004\pi$
$108$	2.54037	−	4.53283i	0.244447	−	0.436172i
$109$	−0.0820764			−0.00786149			−0.00393075	−	0.999992i	$-0.501251\pi$
$109$	−0.0820764			−0.00786149			−0.00393075	+	0.999992i	$0.501251\pi$
$110$	16.7762	+	14.0769i	1.59955	+	1.34218i
$111$	−10.1116	+	10.8096i	−0.959753	+	1.02600i
$112$	−0.173648	−	0.984808i	−0.0164082	−	0.0930556i
$113$	6.71500	+	2.44406i	0.631694	+	0.229918i	0.637969	−	0.770062i	$-0.279775\pi$
$113$	6.71500	+	2.44406i	0.631694	+	0.229918i	−0.00627429	+	0.999980i	$0.501997\pi$
$114$	2.19071	+	2.91662i	0.205179	+	0.273166i
$115$	3.95804	−	22.4472i	0.369090	−	2.09321i
$116$	−0.343668	+	0.595251i	−0.0319088	+	0.0552677i
$117$	−1.08203	+	3.72956i	−0.100033	+	0.344798i
$118$	−6.11875	−	10.5980i	−0.563277	−	0.975624i
$119$	−5.13422	+	1.86870i	−0.470653	+	0.171304i
$120$	6.20060	+	4.04047i	0.566035	+	0.368843i
$121$	11.6964	−	9.81447i	1.06331	−	0.892224i
$122$	−1.78467	+	1.49752i	−0.161577	+	0.135579i
$123$	2.27081	+	1.47972i	0.204752	+	0.133422i
$124$	5.25762	−	1.91362i	0.472149	−	0.171848i
$125$	−17.6419	−	30.5567i	−1.57794	−	2.73307i
$126$	0.835897	−	2.88119i	0.0744676	−	0.256677i
$127$	5.07561	−	8.79121i	0.450387	−	0.780094i	−0.548022	−	0.836464i	$-0.684619\pi$
$127$	5.07561	−	8.79121i	0.450387	−	0.780094i	0.998410	+	0.0563696i	$0.0179525\pi$
$128$	0.173648	−	0.984808i	0.0153485	−	0.0870455i
$129$	−2.51082	−	3.34280i	−0.221065	−	0.294317i
$130$	−5.19748	−	1.89173i	−0.455849	−	0.165915i
$131$	3.08930	+	17.5203i	0.269913	+	1.53075i	0.754670	+	0.656104i	$0.227797\pi$
$131$	3.08930	+	17.5203i	0.269913	+	1.53075i	−0.484757	+	0.874649i	$0.661092\pi$
$132$	6.06439	−	6.48298i	0.527837	−	0.564271i
$133$	1.61330	+	1.35372i	0.139891	+	0.117382i
$134$	−10.1031			−0.872775
$135$	11.3461	+	19.0846i	0.976515	+	1.64254i
$136$	−5.46372			−0.468510
$137$	−8.31257	−	6.97507i	−0.710191	−	0.595921i	0.214462	−	0.976732i	$-0.431200\pi$
$137$	−8.31257	−	6.97507i	−0.710191	−	0.595921i	−0.924653	+	0.380812i	$0.875645\pi$
$138$	−8.99946	−	2.09247i	−0.766085	−	0.178123i
$139$	−1.32456	−	7.51196i	−0.112348	−	0.637156i	−0.988029	−	0.154267i	$-0.950698\pi$
$139$	−1.32456	−	7.51196i	−0.112348	−	0.637156i	0.875681	−	0.482889i	$-0.160413\pi$
$140$	4.01520	+	1.46142i	0.339347	+	0.123512i
$141$	8.94352	−	1.08398i	0.753180	−	0.0912876i
$142$	−0.765052	+	4.33883i	−0.0642017	+	0.364106i
$143$	−3.31721	+	5.74558i	−0.277399	+	0.480469i
$144$	1.77091	−	2.42154i	0.147576	−	0.201795i
$145$	−1.46846	−	2.54344i	−0.121949	−	0.211221i
$146$	−14.6220	+	5.32197i	−1.21013	+	0.440449i
$147$	0.0933441	−	1.72953i	0.00769889	−	0.142650i
$148$	−6.54646	+	5.49313i	−0.538115	+	0.451533i
$149$	5.18609	−	4.35165i	0.424861	−	0.356501i	−0.405147	−	0.914251i	$-0.632780\pi$
$149$	5.18609	−	4.35165i	0.424861	−	0.356501i	0.830009	+	0.557750i	$0.188335\pi$
$150$	−20.4763	+	10.3930i	−1.67188	+	0.848586i
$151$	0.230134	−	0.0837618i	0.0187280	−	0.00681644i	−0.332639	−	0.943054i	$-0.607939\pi$
$151$	0.230134	−	0.0837618i	0.0187280	−	0.00681644i	0.351367	+	0.936238i	$0.385717\pi$
$152$	1.05301	+	1.82386i	0.0854101	+	0.147935i
$153$	−14.7098	−	7.23130i	−1.18922	−	0.584616i
$154$	2.56265	−	4.43863i	0.206504	−	0.357675i
$155$	−4.15141	+	23.5438i	−0.333449	+	1.89109i
$156$	−0.879254	+	2.06245i	−0.0703967	+	0.165128i
$157$	−3.62955	−	1.32105i	−0.289669	−	0.105431i	0.193099	−	0.981179i	$-0.438146\pi$
$157$	−3.62955	−	1.32105i	−0.289669	−	0.105431i	−0.482768	+	0.875748i	$0.660369\pi$
$158$	−0.202578	−	1.14888i	−0.0161163	−	0.0913999i
$159$	2.89116	+	9.50955i	0.229284	+	0.754156i
$160$	3.27322	+	2.74656i	0.258771	+	0.217135i
$161$	−5.33444			−0.420413
$162$	7.97271	−	4.17562i	0.626396	−	0.328068i
$163$	−20.2621			−1.58705			−0.793524	−	0.608539i	$-0.791756\pi$
$163$	−20.2621			−1.58705			−0.793524	+	0.608539i	$0.791756\pi$
$164$	1.19874	+	1.00586i	0.0936056	+	0.0785444i
$165$	11.0336	+	36.2914i	0.858963	+	2.82528i
$166$	2.17076	+	12.3110i	0.168484	+	0.955519i
$167$	−12.4961	−	4.54821i	−0.966978	−	0.351951i	−0.190214	−	0.981743i	$-0.560918\pi$
$167$	−12.4961	−	4.54821i	−0.966978	−	0.351951i	−0.776764	+	0.629792i	$0.783140\pi$
$168$	0.679250	−	1.59330i	0.0524053	−	0.122926i
$169$	−1.96646	+	11.1524i	−0.151266	+	0.857874i
$170$	11.6729	−	20.2181i	0.895274	−	1.55066i
$171$	0.421077	+	6.30399i	0.0322005	+	0.482078i
$172$	−1.20687	−	2.09037i	−0.0920232	−	0.159389i
$173$	12.1827	−	4.43414i	0.926234	−	0.337122i	0.165518	−	0.986207i	$-0.447070\pi$
$173$	12.1827	−	4.43414i	0.926234	−	0.337122i	0.760716	+	0.649085i	$0.224848\pi$
$174$	−1.06159	+	0.538823i	−0.0804786	+	0.0408481i
$175$	−10.1559	+	8.52182i	−0.767715	+	0.644189i
$176$	3.92620	−	3.29447i	0.295948	−	0.248330i
$177$	1.14230	−	21.1652i	0.0858604	−	1.59087i
$178$	−4.50397	+	1.63931i	−0.337587	+	0.122871i
$179$	−7.05409	−	12.2181i	−0.527248	−	0.913220i	−0.999496	−	0.0317542i	$-0.989891\pi$
$179$	−7.05409	−	12.2181i	−0.527248	−	0.913220i	0.472248	−	0.881466i	$-0.343443\pi$
$180$	5.17730	+	11.7266i	0.385893	+	0.874052i
$181$	−7.12894	+	12.3477i	−0.529890	+	0.917796i	0.469502	+	0.882931i	$0.344433\pi$
$181$	−7.12894	+	12.3477i	−0.529890	+	0.917796i	−0.999392	+	0.0348650i	$0.988900\pi$
$182$	−0.224779	+	1.27478i	−0.0166617	+	0.0944932i
$183$	−4.00588	+	0.485525i	−0.296123	+	0.0358910i
$184$	−5.01273	−	1.82448i	−0.369543	−	0.134503i
$185$	−6.34081	−	35.9605i	−0.466185	−	2.64387i
$186$	9.43912	+	2.19469i	0.692110	+	0.160923i
$187$	−21.4517	−	18.0001i	−1.56870	−	1.31630i
$188$	5.20133			0.379346
$189$	3.93748	−	3.39061i	0.286410	−	0.246631i
$190$	−8.99876			−0.652839
$191$	18.8363	+	15.8055i	1.36295	+	1.14365i	0.975060	+	0.221939i	$0.0712387\pi$
$191$	18.8363	+	15.8055i	1.36295	+	1.14365i	0.387885	+	0.921708i	$0.373206\pi$
$192$	1.18323	−	1.26490i	0.0853922	−	0.0912862i
$193$	0.462813	+	2.62474i	0.0333140	+	0.188933i	0.996923	−	0.0783808i	$-0.0249750\pi$
$193$	0.462813	+	2.62474i	0.0333140	+	0.188933i	−0.963609	+	0.267314i	$0.913864\pi$
$194$	9.60333	+	3.49533i	0.689479	+	0.250950i
$195$	−5.75348	−	7.65993i	−0.412015	−	0.548539i
$196$	0.173648	−	0.984808i	0.0124034	−	0.0703434i
$197$	9.02399	−	15.6300i	0.642933	−	1.11359i	−0.341842	−	0.939757i	$-0.611051\pi$
$197$	9.02399	−	15.6300i	0.642933	−	1.11359i	0.984775	−	0.173835i	$-0.0556159\pi$
$198$	14.9307	−	3.67324i	1.06108	−	0.261046i
$199$	5.82769	+	10.0939i	0.413114	+	0.715534i	0.995228	−	0.0975725i	$-0.0311078\pi$
$199$	5.82769	+	10.0939i	0.413114	+	0.715534i	−0.582114	+	0.813107i	$0.697774\pi$
$200$	−12.4581	+	4.53437i	−0.880919	+	0.320628i
$201$	−14.6611	−	9.55354i	−1.03411	−	0.673855i
$202$	10.1519	−	8.51848i	0.714288	−	0.599358i
$203$	−0.526530	+	0.441811i	−0.0369552	+	0.0310091i
$204$	−7.92867	−	5.16653i	−0.555118	−	0.361729i
$205$	−6.28315	+	2.28688i	−0.438834	+	0.159723i
$206$	3.84308	+	6.65640i	0.267760	+	0.463774i
$207$	−11.0809	−	11.5464i	−0.770176	−	0.802531i
$208$	−0.647224	+	1.12103i	−0.0448769	+	0.0777291i
$209$	−1.87435	+	10.6299i	−0.129651	+	0.735288i
$210$	4.44474	+	5.91753i	0.306716	+	0.408348i
$211$	2.66815	+	0.971127i	0.183683	+	0.0668551i	0.432224	−	0.901766i	$-0.357729\pi$
$211$	2.66815	+	0.971127i	0.183683	+	0.0668551i	−0.248541	+	0.968621i	$0.579951\pi$
$212$	0.996476	+	5.65130i	0.0684383	+	0.388133i
$213$	−5.21302	+	5.57284i	−0.357190	+	0.381845i
$214$	−1.93706	−	1.62539i	−0.132415	−	0.111109i
$215$	10.3137			0.703387
$216$	4.85968	−	1.83943i	0.330659	−	0.125158i
$217$	5.59505			0.379817
$218$	−0.0628741	−	0.0527577i	−0.00425837	−	0.00357320i
$219$	−26.2512	−	6.10367i	−1.77389	−	0.412448i
$220$	3.80286	+	21.5671i	0.256389	+	1.45405i
$221$	6.64598	+	2.41894i	0.447057	+	0.162716i
$222$	−14.6942	+	1.78098i	−0.986211	+	0.119532i
$223$	−0.513295	+	2.91104i	−0.0343728	+	0.194938i	−0.997159	−	0.0753267i	$-0.976000\pi$
$223$	−0.513295	+	2.91104i	−0.0343728	+	0.194938i	0.962786	+	0.270265i	$0.0871112\pi$
$224$	0.500000	−	0.866025i	0.0334077	−	0.0578638i
$225$	−39.5418	−	4.28066i	−2.63612	−	0.285377i
$226$	3.57298	+	6.18858i	0.237671	+	0.411658i
$227$	17.1899	−	6.25661i	1.14093	−	0.415266i	0.298683	−	0.954352i	$-0.403453\pi$
$227$	17.1899	−	6.25661i	1.14093	−	0.415266i	0.842250	+	0.539087i	$0.181231\pi$
$228$	−0.196584	+	3.64242i	−0.0130191	+	0.241225i
$229$	−0.752830	+	0.631700i	−0.0497484	+	0.0417439i	−0.667323	−	0.744769i	$-0.732560\pi$
$229$	−0.752830	+	0.631700i	−0.0497484	+	0.0417439i	0.617574	+	0.786512i	$0.288115\pi$
$230$	17.4608	−	14.6514i	1.15133	−	0.966082i
$231$	7.91597	−	4.01786i	0.520833	−	0.264356i
$232$	−0.645885	+	0.235083i	−0.0424044	+	0.0154340i
$233$	8.44105	+	14.6203i	0.552992	+	0.957810i	0.998057	+	0.0623117i	$0.0198473\pi$
$233$	8.44105	+	14.6203i	0.552992	+	0.957810i	−0.445065	+	0.895498i	$0.646819\pi$
$234$	−3.22619	+	2.16149i	−0.210903	+	0.141301i
$235$	−11.1124	+	19.2472i	−0.724891	+	1.25555i
$236$	2.12502	−	12.0516i	0.138327	−	0.784492i
$237$	0.792414	−	1.85875i	0.0514729	−	0.120739i
$238$	−5.13422	−	1.86870i	−0.332802	−	0.121130i
$239$	−0.252887	−	1.43419i	−0.0163579	−	0.0927701i	0.975536	−	0.219841i	$-0.0705537\pi$
$239$	−0.252887	−	1.43419i	−0.0163579	−	0.0927701i	−0.991894	+	0.127070i	$0.959443\pi$
$240$	2.15277	+	7.08085i	0.138961	+	0.457067i
$241$	7.22633	+	6.06361i	0.465489	+	0.390592i	0.845146	−	0.534536i	$-0.179513\pi$
$241$	7.22633	+	6.06361i	0.465489	+	0.390592i	−0.379657	+	0.925127i	$0.623958\pi$
$242$	15.2686			0.981503
$243$	15.5181	+	1.47959i	0.995485	+	0.0949158i
$244$	−2.32972			−0.149145
$245$	3.27322	+	2.74656i	0.209119	+	0.175471i
$246$	0.788398	+	2.59318i	0.0502664	+	0.165335i
$247$	−0.473386	−	2.68471i	−0.0301209	−	0.170824i
$248$	5.25762	+	1.91362i	0.333859	+	0.121515i
$249$	−8.49125	+	19.9178i	−0.538111	+	1.26224i
$250$	6.12698	−	34.7478i	0.387504	−	2.19764i
$251$	1.88202	−	3.25976i	0.118792	−	0.205754i	−0.800497	−	0.599337i	$-0.795431\pi$
$251$	1.88202	−	3.25976i	0.118792	−	0.205754i	0.919289	+	0.393582i	$0.128764\pi$
$252$	2.49233	−	1.66982i	0.157002	−	0.105189i
$253$	−13.6703	−	23.6776i	−0.859442	−	1.48860i
$254$	9.53903	−	3.47192i	0.598532	−	0.217848i
$255$	36.0576	−	18.3015i	2.25801	−	1.14609i
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	−13.2068	+	11.0818i	−0.823816	+	0.691263i	−0.953862	−	0.300244i	$-0.902932\pi$
$257$	−13.2068	+	11.0818i	−0.823816	+	0.691263i	0.130047	+	0.991508i	$0.458487\pi$
$258$	0.225309	−	4.17465i	0.0140271	−	0.259903i
$259$	−8.03042	+	2.92283i	−0.498986	+	0.181616i
$260$	−2.76552	−	4.79002i	−0.171510	−	0.297064i
$261$	−2.05003	−	0.221930i	−0.126894	−	0.0137371i
$262$	−8.89528	+	15.4071i	−0.549552	+	0.951852i
$263$	3.83328	−	21.7396i	0.236370	−	1.34052i	−0.603340	−	0.797484i	$-0.706164\pi$
$263$	3.83328	−	21.7396i	0.236370	−	1.34052i	0.839709	−	0.543036i	$-0.182725\pi$
$264$	8.81277	−	1.06813i	0.542388	−	0.0657390i
$265$	−23.0412	−	8.38630i	−1.41541	−	0.515166i
$266$	0.365705	+	2.07402i	0.0224228	+	0.127166i
$267$	−8.08606	−	1.88009i	−0.494859	−	0.115060i
$268$	−7.73942	−	6.49415i	−0.472761	−	0.396693i
$269$	−10.2861			−0.627153			−0.313577	−	0.949563i	$-0.601527\pi$
$269$	−10.2861			−0.627153			−0.313577	+	0.949563i	$0.601527\pi$
$270$	−3.57574	+	21.9128i	−0.217613	+	1.33357i
$271$	−1.15605			−0.0702250			−0.0351125	−	0.999383i	$-0.511179\pi$
$271$	−1.15605			−0.0702250			−0.0351125	+	0.999383i	$0.511179\pi$
$272$	−4.18546	−	3.51201i	−0.253780	−	0.212947i
$273$	−1.53163	+	1.63735i	−0.0926984	+	0.0990967i
$274$	−1.88431	−	10.6864i	−0.113835	−	0.645591i
$275$	−63.8512	−	23.2399i	−3.85037	−	1.40142i
$276$	−5.54897	−	7.38766i	−0.334009	−	0.444685i
$277$	−4.22176	+	23.9428i	−0.253661	+	1.43858i	0.545825	+	0.837899i	$0.316216\pi$
$277$	−4.22176	+	23.9428i	−0.253661	+	1.43858i	−0.799486	+	0.600684i	$0.794895\pi$
$278$	3.81392	−	6.60591i	0.228744	−	0.396196i
$279$	11.6222	+	12.1105i	0.695806	+	0.725037i
$280$	2.13645	+	3.70043i	0.127677	+	0.221143i
$281$	19.0125	−	6.91997i	1.13419	−	0.412811i	0.294377	−	0.955689i	$-0.404888\pi$
$281$	19.0125	−	6.91997i	1.13419	−	0.412811i	0.839811	+	0.542879i	$0.182666\pi$
$282$	7.54790	+	4.91841i	0.449471	+	0.292887i
$283$	9.31265	−	7.81425i	0.553580	−	0.464509i	−0.322571	−	0.946545i	$-0.604547\pi$
$283$	9.31265	−	7.81425i	0.553580	−	0.464509i	0.876151	+	0.482037i	$0.160103\pi$
$284$	−3.37501	+	2.83197i	−0.200270	+	0.168046i
$285$	−13.0585	−	8.50928i	−0.773521	−	0.504046i
$286$	−6.23432	+	2.26911i	−0.368643	+	0.134175i
$287$	0.782420	+	1.35519i	0.0461848	+	0.0799944i
$288$	2.91314	−	0.716689i	0.171658	−	0.0422313i
$289$	−6.42614	+	11.1304i	−0.378008	+	0.654729i
$290$	0.509990	−	2.89230i	0.0299476	−	0.169842i
$291$	10.6307	+	14.1532i	0.623180	+	0.829675i
$292$	−14.6220	−	5.32197i	−0.855688	−	0.311445i
$293$	5.06490	+	28.7245i	0.295895	+	1.67810i	0.663543	+	0.748138i	$0.269052\pi$
$293$	5.06490	+	28.7245i	0.295895	+	1.67810i	−0.367648	+	0.929965i	$0.619837\pi$
$294$	1.18323	−	1.26490i	0.0690073	−	0.0737704i
$295$	40.0561	+	33.6111i	2.33216	+	1.95691i
$296$	−8.54579			−0.496714
$297$	25.1400	+	8.78810i	1.45877	+	0.509937i
$298$	6.76996			0.392173
$299$	5.28965	+	4.43855i	0.305909	+	0.256688i
$300$	−22.3662	−	5.20038i	−1.29131	−	0.300244i
$301$	−0.419143	−	2.37708i	−0.0241590	−	0.137012i
$302$	0.230134	+	0.0837618i	0.0132427	+	0.00481995i
$303$	22.7871	−	2.76186i	1.30908	−	0.158665i
$304$	−0.365705	+	2.07402i	−0.0209746	+	0.118953i
$305$	4.97733	−	8.62099i	0.285001	−	0.493636i
$306$	−6.62018	−	14.9948i	−0.378451	−	0.857195i
$307$	−6.34579	−	10.9912i	−0.362173	−	0.627303i	0.626145	−	0.779707i	$-0.284632\pi$
$307$	−6.34579	−	10.9912i	−0.362173	−	0.627303i	−0.988318	+	0.152404i	$0.951298\pi$
$308$	4.81620	−	1.75295i	0.274428	−	0.0998837i
$309$	−0.717457	+	13.2935i	−0.0408147	+	0.756239i
$310$	−18.3138	+	15.3671i	−1.04016	+	0.872795i
$311$	−18.3651	+	15.4101i	−1.04139	+	0.873829i	−0.992162	−	0.124958i	$-0.960120\pi$
$311$	−18.3651	+	15.4101i	−1.04139	+	0.873829i	−0.0492272	+	0.998788i	$0.515676\pi$
$312$	−1.99927	+	1.01475i	−0.113186	+	0.0574492i
$313$	13.4303	−	4.88824i	0.759128	−	0.276300i	0.0666863	−	0.997774i	$-0.478757\pi$
$313$	13.4303	−	4.88824i	0.759128	−	0.276300i	0.692441	+	0.721474i	$0.256535\pi$
$314$	−1.93124	−	3.34501i	−0.108986	−	0.188770i
$315$	0.854323	+	12.7902i	0.0481357	+	0.720645i
$316$	0.583301	−	1.01031i	0.0328132	−	0.0568342i
$317$	2.42580	−	13.7574i	0.136246	−	0.772691i	−0.837737	−	0.546073i	$-0.816122\pi$
$317$	2.42580	−	13.7574i	0.136246	−	0.772691i	0.973984	−	0.226618i	$-0.0727669\pi$
$318$	−3.89786	+	9.14314i	−0.218581	+	0.512722i
$319$	−3.31035	−	1.20487i	−0.185344	−	0.0674597i
$320$	0.741980	+	4.20798i	0.0414779	+	0.235233i
$321$	−1.27399	−	4.19038i	−0.0711071	−	0.233884i
$322$	−4.08642	−	3.42891i	−0.227727	−	0.191086i
$323$	11.5067			0.640248
$324$	8.79149	+	1.92605i	0.488416	+	0.107003i
$325$	17.1613			0.951937
$326$	−15.5216	−	13.0242i	−0.859664	−	0.721344i
$327$	−0.0413518	−	0.136013i	−0.00228676	−	0.00752155i
$328$	0.271732	+	1.54107i	0.0150039	+	0.0850911i
$329$	4.88765	+	1.77896i	0.269465	+	0.0980773i
$330$	−14.8754	+	34.8931i	−0.818866	+	1.92080i
$331$	−0.367194	+	2.08246i	−0.0201828	+	0.114463i	−0.993235	−	0.116123i	$-0.962953\pi$
$331$	−0.367194	+	2.08246i	−0.0201828	+	0.114463i	0.973052	+	0.230586i	$0.0740643\pi$
$332$	−6.25046	+	10.8261i	−0.343038	+	0.594160i
$333$	−23.0076	−	11.3105i	−1.26081	−	0.619809i
$334$	−6.64904	−	11.5165i	−0.363819	−	0.630153i
$335$	40.5660	−	14.7648i	2.21636	−	0.806688i
$336$	1.54449	−	0.783929i	0.0842590	−	0.0427668i
$337$	10.0883	−	8.46509i	0.549545	−	0.461123i	−0.325242	−	0.945631i	$-0.605446\pi$
$337$	10.0883	−	8.46509i	0.549545	−	0.461123i	0.874787	+	0.484508i	$0.161001\pi$
$338$	−8.67500	+	7.27919i	−0.471858	+	0.395936i
$339$	−0.667033	+	12.3592i	−0.0362282	+	0.671258i
$340$	21.9380	−	7.98477i	1.18975	−	0.433035i
$341$	14.3381	+	24.8344i	0.776453	+	1.34486i
$342$	−3.72956	+	5.09980i	−0.201672	+	0.275766i
$343$	0.500000	−	0.866025i	0.0269975	−	0.0467610i
$344$	0.419143	−	2.37708i	0.0225987	−	0.128163i
$345$	39.1926	−	4.75026i	2.11006	−	0.255745i
$346$	12.1827	+	4.43414i	0.654946	+	0.238381i
$347$	−1.21733	−	6.90384i	−0.0653498	−	0.370617i	−0.999891	−	0.0147624i	$-0.995301\pi$
$347$	−1.21733	−	6.90384i	−0.0653498	−	0.370617i	0.934541	−	0.355855i	$-0.115810\pi$
$348$	−1.15957	−	0.269612i	−0.0621595	−	0.0144527i
$349$	−11.5680	−	9.70668i	−0.619219	−	0.519587i	0.278339	−	0.960483i	$-0.410216\pi$
$349$	−11.5680	−	9.70668i	−0.619219	−	0.519587i	−0.897558	+	0.440896i	$0.854661\pi$
$350$	−13.2576			−0.708649
$351$	−6.72560	+	0.0859434i	−0.358986	+	0.00458732i
$352$	5.12529			0.273179
$353$	−6.58608	−	5.52638i	−0.350542	−	0.294139i	0.450466	−	0.892794i	$-0.351258\pi$
$353$	−6.58608	−	5.52638i	−0.350542	−	0.294139i	−0.801008	+	0.598654i	$0.795702\pi$
$354$	14.4798	−	15.4792i	0.769591	−	0.822711i
$355$	−3.26898	−	18.5393i	−0.173500	−	0.983966i
$356$	−4.50397	−	1.63931i	−0.238710	−	0.0868832i
$357$	−5.68346	−	7.56671i	−0.300801	−	0.400473i
$358$	2.44986	−	13.8939i	0.129479	−	0.734313i
$359$	−8.04311	+	13.9311i	−0.424499	+	0.735254i	−0.996374	−	0.0850872i	$-0.972883\pi$
$359$	−8.04311	+	13.9311i	−0.424499	+	0.735254i	0.571874	+	0.820341i	$0.306216\pi$
$360$	−3.57170	+	12.3110i	−0.188245	+	0.648848i
$361$	7.28236	+	12.6134i	0.383282	+	0.663864i
$362$	−13.3980	+	4.87648i	−0.704185	+	0.256302i
$363$	22.1570	+	14.4381i	1.16294	+	0.757802i
$364$	−0.991605	+	0.832055i	−0.0519742	+	0.0436116i
$365$	50.9327	−	42.7376i	2.66594	−	2.23699i
$366$	−3.38077	−	2.20300i	−0.176716	−	0.115153i
$367$	−29.7812	+	10.8395i	−1.55456	+	0.565815i	−0.969483	−	0.245160i	$-0.921159\pi$
$367$	−29.7812	+	10.8395i	−1.55456	+	0.565815i	−0.585081	+	0.810975i	$0.698937\pi$
$368$	−2.66722	−	4.61976i	−0.139038	−	0.240822i
$369$	−1.30804	+	4.50861i	−0.0680941	+	0.234709i
$370$	18.2576	−	31.6231i	0.949169	−	1.64401i
$371$	−0.996476	+	5.65130i	−0.0517345	+	0.293401i
$372$	5.82006	+	7.74858i	0.301756	+	0.401745i
$373$	22.4425	+	8.16842i	1.16203	+	0.422945i	0.849822	−	0.527069i	$-0.176709\pi$
$373$	22.4425	+	8.16842i	1.16203	+	0.422945i	0.312208	+	0.950014i	$0.398931\pi$
$374$	−4.86270	−	27.5777i	−0.251444	−	1.42601i
$375$	41.7489	−	44.6305i	2.15590	−	2.30471i
$376$	3.98445	+	3.34335i	0.205482	+	0.172420i
$377$	0.889722			0.0458230
$378$	5.19573	−	0.0663939i	0.267239	−	0.00341493i
$379$	18.1766			0.933669			0.466834	−	0.884345i	$-0.345394\pi$
$379$	18.1766			0.933669			0.466834	+	0.884345i	$0.345394\pi$
$380$	−6.89345	−	5.78429i	−0.353627	−	0.296728i
$381$	17.1256	+	3.98188i	0.877371	+	0.203998i
$382$	4.26984	+	24.2155i	0.218464	+	1.23897i
$383$	14.9510	+	5.44173i	0.763962	+	0.278059i	0.694468	−	0.719523i	$-0.255640\pi$
$383$	14.9510	+	5.44173i	0.763962	+	0.278059i	0.0694931	+	0.997582i	$0.477862\pi$
$384$	1.71947	−	0.208404i	0.0877462	−	0.0106351i
$385$	−3.80286	+	21.5671i	−0.193812	+	1.09916i
$386$	−1.33262	+	2.30816i	−0.0678284	+	0.117482i
$387$	4.27453	−	5.84499i	0.217287	−	0.297117i
$388$	5.10982	+	8.85048i	0.259412	+	0.449315i
$389$	24.2577	−	8.82907i	1.22991	−	0.447652i	0.356345	−	0.934354i	$-0.384023\pi$
$389$	24.2577	−	8.82907i	1.22991	−	0.447652i	0.873568	+	0.486703i	$0.161801\pi$
$390$	0.516290	−	9.56612i	0.0261433	−	0.484399i
$391$	−22.3270	+	18.7346i	−1.12913	+	0.947450i
$392$	0.766044	−	0.642788i	0.0386911	−	0.0324657i
$393$	−27.4774	+	13.9465i	−1.38605	+	0.703509i
$394$	16.9596	−	6.17277i	0.854410	−	0.310980i
$395$	2.49238	+	4.31693i	0.125405	+	0.217208i
$396$	13.7987	+	6.78338i	0.693409	+	0.340878i
$397$	−0.519677	+	0.900106i	−0.0260818	+	0.0451750i	−0.878772	−	0.477242i	$-0.841636\pi$
$397$	−0.519677	+	0.900106i	−0.0260818	+	0.0451750i	0.852690	+	0.522417i	$0.174970\pi$
$398$	−2.02394	+	11.4783i	−0.101451	+	0.575356i
$399$	−1.43051	+	3.35552i	−0.0716150	+	0.167986i
$400$	−12.4581	−	4.53437i	−0.622904	−	0.226718i
$401$	4.56951	+	25.9150i	0.228190	+	1.29413i	0.856491	+	0.516162i	$0.172640\pi$
$401$	4.56951	+	25.9150i	0.228190	+	1.29413i	−0.628301	+	0.777971i	$0.716249\pi$
$402$	−5.09015	−	16.7424i	−0.253874	−	0.835036i
$403$	−5.54808	−	4.65539i	−0.276369	−	0.231901i
$404$	13.2524			0.659332
$405$	−25.9098	+	28.4174i	−1.28747	+	1.41207i
$406$	−0.687337			−0.0341119
$407$	−33.5525	−	28.1539i	−1.66314	−	1.39554i
$408$	−2.75274	−	9.05424i	−0.136281	−	0.448252i
$409$	−5.37641	−	30.4911i	−0.265846	−	1.50769i	−0.766614	−	0.642108i	$-0.778060\pi$
$409$	−5.37641	−	30.4911i	−0.265846	−	1.50769i	0.500768	−	0.865582i	$-0.333051\pi$
$410$	−6.28315	−	2.28688i	−0.310303	−	0.112941i
$411$	7.37074	−	17.2894i	0.363572	−	0.852824i
$412$	−1.33469	+	7.56938i	−0.0657553	+	0.372917i
$413$	6.11875	−	10.5980i	0.301084	−	0.521493i
$414$	−1.06657	−	15.9677i	−0.0524190	−	0.784771i
$415$	−26.7075	−	46.2588i	−1.31102	−	2.27075i
$416$	−1.21638	+	0.442727i	−0.0596381	+	0.0217065i
$417$	11.7812	−	5.97969i	0.576925	−	0.292827i
$418$	−8.26862	+	6.93820i	−0.404432	+	0.339358i
$419$	−5.23877	+	4.39585i	−0.255931	+	0.214751i	−0.761721	−	0.647905i	$-0.775645\pi$
$419$	−5.23877	+	4.39585i	−0.255931	+	0.214751i	0.505790	+	0.862656i	$0.331201\pi$
$420$	−0.398849	+	7.39011i	−0.0194618	+	0.360600i
$421$	6.31135	−	2.29714i	0.307597	−	0.111956i	−0.183610	−	0.982999i	$-0.558778\pi$
$421$	6.31135	−	2.29714i	0.307597	−	0.111956i	0.491206	+	0.871043i	$0.336556\pi$
$422$	1.41969	+	2.45898i	0.0691096	+	0.119701i
$423$	6.30226	+	14.2747i	0.306426	+	0.694059i
$424$	−2.86924	+	4.96967i	−0.139343	+	0.241348i
$425$	−12.5784	+	71.3354i	−0.610140	+	3.46028i
$426$	−7.57556	+	0.918180i	−0.367037	+	0.0444859i
$427$	−2.18922	−	0.796812i	−0.105944	−	0.0385605i
$428$	−0.439097	−	2.49024i	−0.0212245	−	0.120370i
$429$	−11.1926	−	2.60239i	−0.540384	−	0.125645i
$430$	7.90073	+	6.62950i	0.381007	+	0.319703i
$431$	−10.6609			−0.513515			−0.256758	−	0.966476i	$-0.582654\pi$
$431$	−10.6609			−0.513515			−0.256758	+	0.966476i	$0.582654\pi$
$432$	4.90510	+	1.71465i	0.235997	+	0.0824963i
$433$	22.1664			1.06525			0.532625	−	0.846351i	$-0.321206\pi$
$433$	22.1664			1.06525			0.532625	+	0.846351i	$0.321206\pi$
$434$	4.28605	+	3.59643i	0.205737	+	0.172634i
$435$	3.47504	−	3.71490i	0.166616	−	0.178116i
$436$	−0.0142524	−	0.0808294i	−0.000682567	−	0.00387103i
$437$	10.5569	+	3.84239i	0.505004	+	0.183806i
$438$	−16.1862	−	21.5496i	−0.773406	−	1.02968i
$439$	2.17434	−	12.3313i	0.103776	−	0.588541i	−0.887927	−	0.459985i	$-0.847855\pi$
$439$	2.17434	−	12.3313i	0.103776	−	0.588541i	0.991702	−	0.128556i	$-0.0410341\pi$
$440$	−10.9499	+	18.9658i	−0.522016	+	0.904159i
$441$	2.91314	−	0.716689i	0.138721	−	0.0341281i
$442$	3.53625	+	6.12497i	0.168202	+	0.291335i
$443$	29.4397	−	10.7152i	1.39872	−	0.509093i	0.470924	−	0.882174i	$-0.343921\pi$
$443$	29.4397	−	10.7152i	1.39872	−	0.509093i	0.927799	+	0.373080i	$0.121698\pi$
$444$	−12.4012	−	8.08095i	−0.588535	−	0.383505i
$445$	15.6886	−	13.1643i	0.743713	−	0.624049i
$446$	−2.26439	+	1.90005i	−0.107222	+	0.0899699i
$447$	9.82422	+	6.40171i	0.464670	+	0.302791i
$448$	0.939693	−	0.342020i	0.0443963	−	0.0161589i
$449$	18.1316	+	31.4048i	0.855682	+	1.48208i	0.876011	+	0.482291i	$0.160195\pi$
$449$	18.1316	+	31.4048i	0.855682	+	1.48208i	−0.0203295	+	0.999793i	$0.506472\pi$
$450$	−27.5392	−	28.6961i	−1.29821	−	1.35275i
$451$	−4.01013	+	6.94575i	−0.188830	+	0.327062i
$452$	−1.24088	+	7.03739i	−0.0583662	+	0.331011i
$453$	0.254752	+	0.339166i	0.0119693	+	0.0159354i
$454$	17.1899	+	6.25661i	0.806762	+	0.293637i
$455$	−0.960455	−	5.44701i	−0.0450268	−	0.255360i
$456$	−2.49189	+	2.66389i	−0.116694	+	0.124748i
$457$	−15.0727	−	12.6475i	−0.705072	−	0.591626i	0.218139	−	0.975918i	$-0.430001\pi$
$457$	−15.0727	−	12.6475i	−0.705072	−	0.591626i	−0.923212	+	0.384292i	$0.874446\pi$
$458$	−0.982750			−0.0459209
$459$	4.57228	−	28.0197i	0.213416	−	1.30785i
$460$	22.7935			1.06275
$461$	15.9402	+	13.3754i	0.742410	+	0.622956i	0.933484	−	0.358620i	$-0.116753\pi$
$461$	15.9402	+	13.3754i	0.742410	+	0.622956i	−0.191074	+	0.981576i	$0.561197\pi$
$462$	8.64662	+	2.01043i	0.402277	+	0.0935336i
$463$	1.17142	+	6.64343i	0.0544403	+	0.308746i	0.999853	−	0.0171284i	$-0.00545240\pi$
$463$	1.17142	+	6.64343i	0.0544403	+	0.308746i	−0.945413	+	0.325875i	$0.894341\pi$
$464$	−0.645885	−	0.235083i	−0.0299845	−	0.0109135i
$465$	−41.1074	+	4.98233i	−1.90631	+	0.231050i
$466$	−2.93155	+	16.6256i	−0.135801	+	0.770168i
$467$	−7.10359	+	12.3038i	−0.328715	+	0.569351i	−0.982257	−	0.187539i	$-0.939949\pi$
$467$	−7.10359	+	12.3038i	−0.328715	+	0.569351i	0.653542	+	0.756890i	$0.273282\pi$
$468$	−3.86079	−	0.417956i	−0.178465	−	0.0193200i
$469$	−5.05155	−	8.74954i	−0.233259	−	0.404016i
$470$	−20.8844	+	7.60131i	−0.963326	+	0.350622i
$471$	0.360540	−	6.68029i	0.0166128	−	0.307812i
$472$	9.37447	−	7.86612i	0.431495	−	0.362067i
$473$	9.47685	−	7.95202i	0.435746	−	0.365634i
$474$	1.80181	−	0.914532i	0.0827598	−	0.0420059i
$475$	26.2368	−	9.54943i	1.20383	−	0.438158i
$476$	−2.73186	−	4.73172i	−0.125215	−	0.216878i
$477$	−14.3022	+	9.58221i	−0.654852	+	0.438739i
$478$	0.728158	−	1.26121i	0.0333052	−	0.0576863i
$479$	−3.61586	+	20.5066i	−0.165213	+	0.936970i	0.783631	+	0.621226i	$0.213365\pi$
$479$	−3.61586	+	20.5066i	−0.165213	+	0.936970i	−0.948844	+	0.315744i	$0.897746\pi$
$480$	−2.90236	+	6.80802i	−0.132474	+	0.310742i
$481$	10.3950	+	3.78346i	0.473969	+	0.172511i
$482$	1.63808	+	9.29000i	0.0746124	+	0.423148i
$483$	−2.68760	−	8.83999i	−0.122290	−	0.402234i
$484$	11.6964	+	9.81447i	0.531656	+	0.446112i
$485$	−43.6675			−1.98284
$486$	10.9365	+	11.1083i	0.496089	+	0.503881i
$487$	−8.35169			−0.378451			−0.189226	−	0.981934i	$-0.560598\pi$
$487$	−8.35169			−0.378451			−0.189226	+	0.981934i	$0.560598\pi$
$488$	−1.78467	−	1.49752i	−0.0807883	−	0.0677894i
$489$	−10.2084	−	33.5774i	−0.461642	−	1.51842i
$490$	0.741980	+	4.20798i	0.0335192	+	0.190097i
$491$	1.92938	+	0.702239i	0.0870719	+	0.0316916i	0.385189	−	0.922838i	$-0.374136\pi$
$491$	1.92938	+	0.702239i	0.0870719	+	0.0316916i	−0.298117	+	0.954529i	$0.596359\pi$
$492$	−1.06292	+	2.49327i	−0.0479200	+	0.112405i
$493$	−0.652121	+	3.69836i	−0.0293701	+	0.166566i
$494$	1.36306	−	2.36089i	0.0613271	−	0.106222i
$495$	−54.5815	+	36.5687i	−2.45326	+	1.64364i
$496$	2.79752	+	4.84545i	0.125613	+	0.217567i
$497$	−4.14006	+	1.50686i	−0.185707	+	0.0675918i
$498$	−19.3076	+	9.79982i	−0.865193	+	0.439141i
$499$	−21.5689	+	18.0985i	−0.965557	+	0.810198i	−0.981848	−	0.189669i	$-0.939259\pi$
$499$	−21.5689	+	18.0985i	−0.965557	+	0.810198i	0.0162913	+	0.999867i	$0.494814\pi$
$500$	27.0290	−	22.6800i	1.20877	−	1.01428i
$501$	1.24130	−	22.9995i	0.0554571	−	1.02754i
$502$	3.53705	−	1.28738i	0.157866	−	0.0574586i
$503$	2.41217	+	4.17800i	0.107553	+	0.186288i	0.914779	−	0.403956i	$-0.132365\pi$
$503$	2.41217	+	4.17800i	0.107553	+	0.186288i	−0.807225	+	0.590244i	$0.799032\pi$
$504$	2.98257	+	0.322884i	0.132854	+	0.0143824i
$505$	−28.3131	+	49.0396i	−1.25991	+	2.18224i
$506$	4.74763	−	26.9252i	0.211058	−	1.19697i
$507$	−19.4719	+	2.36006i	−0.864779	+	0.104814i
$508$	9.53903	+	3.47192i	0.423226	+	0.154042i
$509$	−5.64945	−	32.0396i	−0.250407	−	1.42013i	−0.807592	−	0.589742i	$-0.799229\pi$
$509$	−5.64945	−	32.0396i	−0.250407	−	1.42013i	0.557184	−	0.830389i	$-0.311882\pi$
$510$	39.3857	+	9.15758i	1.74403	+	0.405504i
$511$	−11.9200	−	10.0020i	−0.527308	−	0.442464i
$512$	1.00000			0.0441942
$513$	−10.2345	+	3.87387i	−0.451866	+	0.171036i
$514$	−17.2402			−0.760433
$515$	−25.1585	−	21.1105i	−1.10862	−	0.930240i
$516$	2.85601	−	3.05315i	0.125729	−	0.134407i
$517$	4.62917	+	26.2533i	0.203591	+	1.15462i
$518$	−8.03042	−	2.92283i	−0.352836	−	0.128422i
$519$	13.4860	+	17.9546i	0.591968	+	0.788121i
$520$	0.960455	−	5.44701i	0.0421187	−	0.238867i
$521$	−12.0278	+	20.8327i	−0.526946	+	0.912697i	0.472561	+	0.881298i	$0.343330\pi$
$521$	−12.0278	+	20.8327i	−0.526946	+	0.912697i	−0.999507	+	0.0313993i	$0.990004\pi$
$522$	−1.42776	−	1.48774i	−0.0624915	−	0.0651168i
$523$	−9.61529	−	16.6542i	−0.420447	−	0.728236i	0.575536	−	0.817776i	$-0.304793\pi$
$523$	−9.61529	−	16.6542i	−0.420447	−	0.728236i	−0.995983	+	0.0895405i	$0.971460\pi$
$524$	−16.7177	+	6.08473i	−0.730314	+	0.265813i
$525$	−19.2387	−	12.5365i	−0.839648	−	0.547136i
$526$	16.9104	−	14.1895i	0.737328	−	0.618692i
$527$	23.4178	−	19.6499i	1.02010	−	0.855962i
$528$	7.43756	+	4.84650i	0.323678	+	0.210917i
$529$	−5.12717	+	1.86614i	−0.222920	+	0.0811364i
$530$	−12.2599	−	21.2348i	−0.532538	−	0.922383i
$531$	35.6495	−	8.77049i	1.54706	−	0.380607i
$532$	−1.05301	+	1.82386i	−0.0456536	+	0.0790744i
$533$	0.351742	−	1.99483i	0.0152357	−	0.0864057i
$534$	−4.98578	−	6.63786i	−0.215756	−	0.287248i
$535$	10.1531	+	3.69542i	0.438956	+	0.159767i
$536$	−1.75439	−	9.94961i	−0.0757779	−	0.429758i
$537$	16.6932	−	17.8454i	0.720365	−	0.770088i
$538$	−7.87959	−	6.61176i	−0.339713	−	0.285053i
$539$	5.12529			0.220762
$540$	−16.8244	+	14.4877i	−0.724008	+	0.623452i
$541$	24.6582			1.06014			0.530070	−	0.847954i	$-0.322166\pi$
$541$	24.6582			1.06014			0.530070	+	0.847954i	$0.322166\pi$
$542$	−0.885585	−	0.743094i	−0.0380391	−	0.0319186i
$543$	−24.0537	−	5.59274i	−1.03225	−	0.240008i
$544$	−0.948766	−	5.38072i	−0.0406780	−	0.230696i
$545$	0.329553	+	0.119948i	0.0141165	+	0.00513799i
$546$	−2.22576	+	0.269769i	−0.0952538	+	0.0115450i
$547$	−0.679846	+	3.85560i	−0.0290681	+	0.164854i	−0.995886	−	0.0906121i	$-0.971118\pi$
$547$	−0.679846	+	3.85560i	−0.0290681	+	0.164854i	0.966818	+	0.255466i	$0.0822288\pi$
$548$	5.42564	−	9.39749i	0.231772	−	0.401441i
$549$	−2.82284	−	6.39376i	−0.120476	−	0.272879i
$550$	−33.9745	−	58.8456i	−1.44868	−	2.50919i
$551$	1.36024	−	0.495088i	0.0579483	−	0.0210914i
$552$	0.497938	−	9.22609i	0.0211937	−	0.392688i
$553$	0.893669	−	0.749877i	0.0380027	−	0.0318880i
$554$	−18.6242	+	15.6276i	−0.791266	+	0.663951i
$555$	56.3975	−	28.6253i	2.39394	−	1.21508i
$556$	7.16783	−	2.60888i	0.303984	−	0.110641i
$557$	−0.353701	−	0.612629i	−0.0149868	−	0.0259579i	0.858435	−	0.512923i	$-0.171437\pi$
$557$	−0.353701	−	0.612629i	−0.0149868	−	0.0259579i	−0.873422	+	0.486965i	$0.838104\pi$
$558$	1.11868	+	16.7478i	0.0473573	+	0.708992i
$559$	−1.56223	+	2.70587i	−0.0660755	+	0.114446i
$560$	−0.741980	+	4.20798i	−0.0313544	+	0.177819i
$561$	19.0212	−	44.6176i	0.803074	−	1.88376i
$562$	19.0125	+	6.91997i	0.801992	+	0.291901i
$563$	3.92432	+	22.2559i	0.165390	+	0.937975i	0.948661	+	0.316294i	$0.102439\pi$
$563$	3.92432	+	22.2559i	0.165390	+	0.937975i	−0.783271	+	0.621681i	$0.786450\pi$
$564$	2.62054	+	8.61942i	0.110345	+	0.362943i
$565$	−23.3903	−	19.6268i	−0.984038	−	0.825706i
$566$	12.1568			0.510989
$567$	7.60255	+	4.81676i	0.319277	+	0.202285i
$568$	−4.40576			−0.184862
$569$	−32.3668	−	27.1590i	−1.35689	−	1.13856i	−0.976930	−	0.213562i	$-0.931494\pi$
$569$	−32.3668	−	27.1590i	−1.35689	−	1.13856i	−0.379959	−	0.925003i	$-0.624062\pi$
$570$	−4.53376	−	14.9123i	−0.189898	−	0.624610i
$571$	2.06965	+	11.7376i	0.0866122	+	0.491202i	0.996997	+	0.0774397i	$0.0246745\pi$
$571$	2.06965	+	11.7376i	0.0866122	+	0.491202i	−0.910385	+	0.413763i	$0.864214\pi$
$572$	−6.23432	−	2.26911i	−0.260670	−	0.0948761i
$573$	−16.7021	+	39.1778i	−0.697740	+	1.63668i
$574$	−0.271732	+	1.54107i	−0.0113419	+	0.0643229i
$575$	−35.3609	+	61.2469i	−1.47465	+	2.55417i
$576$	2.69227	+	1.32351i	0.112178	+	0.0551463i
$577$	−5.95903	−	10.3213i	−0.248078	−	0.429683i	0.714915	−	0.699212i	$-0.246465\pi$
$577$	−5.95903	−	10.3213i	−0.248078	−	0.429683i	−0.962992	+	0.269529i	$0.913132\pi$
$578$	−12.0772	+	4.39574i	−0.502345	+	0.182839i
$579$	−4.11643	+	2.08935i	−0.171073	+	0.0868306i
$580$	2.24981	−	1.88781i	0.0934182	−	0.0783872i
$581$	−9.57625	+	8.03543i	−0.397290	+	0.333366i
$582$	−0.953944	+	17.6752i	−0.0395422	+	0.732662i
$583$	−27.6376	+	10.0593i	−1.14463	+	0.416613i
$584$	−7.78020	−	13.4757i	−0.321947	−	0.557629i
$585$	9.79498	−	13.3936i	0.404973	−	0.553759i
$586$	−14.5838	+	25.2599i	−0.602452	+	1.04348i
$587$	−2.11274	+	11.9819i	−0.0872021	+	0.494548i	0.909658	+	0.415359i	$0.136344\pi$
$587$	−2.11274	+	11.9819i	−0.0872021	+	0.494548i	−0.996860	+	0.0791887i	$0.974767\pi$
$588$	1.71947	−	0.208404i	0.0709096	−	0.00859445i
$589$	−11.0726	−	4.03010i	−0.456239	−	0.166058i
$590$	9.07998	+	51.4951i	0.373817	+	2.12002i
$591$	30.4478	+	7.07944i	1.25246	+	0.291209i
$592$	−6.54646	−	5.49313i	−0.269058	−	0.225766i
$593$	40.5372			1.66466			0.832332	−	0.554277i	$-0.187005\pi$
$593$	40.5372			1.66466			0.832332	+	0.554277i	$0.187005\pi$
$594$	13.6095	+	22.8918i	0.558405	+	0.939261i
$595$	23.3459			0.957089
$596$	5.18609	+	4.35165i	0.212431	+	0.178250i
$597$	−13.7910	+	14.7429i	−0.564427	+	0.603386i
$598$	1.19907	+	6.80025i	0.0490335	+	0.278083i
$599$	16.2759	+	5.92395i	0.665016	+	0.242046i	0.652401	−	0.757874i	$-0.273762\pi$
$599$	16.2759	+	5.92395i	0.665016	+	0.242046i	0.0126156	+	0.999920i	$0.495984\pi$
$600$	−13.7908	−	18.3605i	−0.563006	−	0.749562i
$601$	−3.95798	+	22.4468i	−0.161449	+	0.915625i	0.791201	+	0.611556i	$0.209456\pi$
$601$	−3.95798	+	22.4468i	−0.161449	+	0.915625i	−0.952650	+	0.304068i	$0.901655\pi$
$602$	1.20687	−	2.09037i	0.0491885	−	0.0851969i
$603$	8.44515	−	29.1090i	0.343913	−	1.18541i
$604$	0.122452	+	0.212092i	0.00498248	+	0.00862991i
$605$	−61.3066	+	22.3138i	−2.49247	+	0.907183i
$606$	19.2312	+	12.5315i	0.781214	+	0.509059i
$607$	20.2842	−	17.0204i	0.823309	−	0.690838i	−0.130436	−	0.991457i	$-0.541638\pi$
$607$	20.2842	−	17.0204i	0.823309	−	0.690838i	0.953744	+	0.300619i	$0.0971931\pi$
$608$	−1.61330	+	1.35372i	−0.0654279	+	0.0549005i
$609$	−0.997427	−	0.649949i	−0.0404178	−	0.0263373i
$610$	9.35432	−	3.40469i	0.378745	−	0.137852i
$611$	−3.36643	−	5.83083i	−0.136191	−	0.235890i
$612$	4.56711	−	15.7420i	0.184614	−	0.636334i
$613$	4.90834	−	8.50149i	0.198246	−	0.343372i	−0.749714	−	0.661762i	$-0.769809\pi$
$613$	4.90834	−	8.50149i	0.198246	−	0.343372i	0.947960	+	0.318390i	$0.103142\pi$
$614$	2.20387	−	12.4988i	0.0889409	−	0.504409i
$615$	−6.95530	−	9.25998i	−0.280465	−	0.373398i
$616$	4.81620	+	1.75295i	0.194050	+	0.0706285i
$617$	−0.299581	−	1.69901i	−0.0120607	−	0.0683995i	0.978183	−	0.207743i	$-0.0666118\pi$
$617$	−0.299581	−	1.69901i	−0.0120607	−	0.0683995i	−0.990244	+	0.139344i	$0.955501\pi$
$618$	−9.09448	+	9.72221i	−0.365833	+	0.391085i
$619$	27.6054	+	23.1637i	1.10955	+	0.931027i	0.998030	−	0.0627346i	$-0.0199822\pi$
$619$	27.6054	+	23.1637i	1.10955	+	0.931027i	0.111525	+	0.993762i	$0.464427\pi$
$620$	−23.9070			−0.960129
$621$	13.5514	−	24.1801i	0.543800	−	0.970314i
$622$	−23.9739			−0.961267
$623$	−3.67167	−	3.08089i	−0.147102	−	0.123433i
$624$	−2.18380	−	0.507756i	−0.0874219	−	0.0203265i
$625$	14.6691	+	83.1926i	0.586764	+	3.32771i
$626$	13.4303	+	4.88824i	0.536784	+	0.195374i
$627$	−18.5598	+	2.24950i	−0.741207	+	0.0898364i
$628$	0.670713	−	3.80380i	0.0267644	−	0.151788i
$629$	−23.3459	+	40.4363i	−0.930863	+	1.61230i
$630$	−7.56692	+	10.3470i	−0.301473	+	0.412234i
$631$	−9.45744	−	16.3808i	−0.376495	−	0.652108i	0.614055	−	0.789263i	$-0.289537\pi$
$631$	−9.45744	−	16.3808i	−0.376495	−	0.652108i	−0.990550	+	0.137155i	$0.956204\pi$
$632$	1.09625	−	0.399001i	0.0436064	−	0.0158714i
$633$	−0.265040	+	4.91081i	−0.0105344	+	0.195187i
$634$	10.7013	−	8.97949i	0.425004	−	0.356621i
$635$	−33.2272	+	27.8809i	−1.31858	+	1.10642i
$636$	−8.86303	+	4.49856i	−0.351442	+	0.178379i
$637$	−1.21638	+	0.442727i	−0.0481949	+	0.0175415i
$638$	−1.76140	−	3.05083i	−0.0697345	−	0.120784i
$639$	−11.8615	−	5.83107i	−0.469233	−	0.230674i
$640$	−2.13645	+	3.70043i	−0.0844504	+	0.146272i
$641$	0.731098	−	4.14626i	0.0288766	−	0.163768i	−0.966959	−	0.254931i	$-0.917947\pi$
$641$	0.731098	−	4.14626i	0.0288766	−	0.163768i	0.995836	+	0.0911631i	$0.0290585\pi$
$642$	1.71759	−	4.02892i	0.0677879	−	0.159009i
$643$	−27.5906	−	10.0422i	−1.08807	−	0.396024i	−0.265163	−	0.964204i	$-0.585426\pi$
$643$	−27.5906	−	10.0422i	−1.08807	−	0.396024i	−0.822905	+	0.568179i	$0.807648\pi$
$644$	−0.926315	−	5.25340i	−0.0365019	−	0.207013i
$645$	5.19624	+	17.0914i	0.204602	+	0.672972i
$646$	8.81462	+	7.39634i	0.346807	+	0.291005i
$647$	−29.7315			−1.16887			−0.584433	−	0.811442i	$-0.698683\pi$
$647$	−29.7315			−1.16887			−0.584433	+	0.811442i	$0.698683\pi$
$648$	5.49663	+	7.12650i	0.215928	+	0.279955i
$649$	62.7208			2.46201
$650$	13.1463	+	11.0311i	0.515641	+	0.432674i
$651$	2.81890	+	9.27186i	0.110481	+	0.363393i
$652$	−3.51847	−	19.9542i	−0.137794	−	0.781468i
$653$	−27.7507	−	10.1004i	−1.08597	−	0.395261i	−0.263843	−	0.964566i	$-0.584990\pi$
$653$	−27.7507	−	10.1004i	−1.08597	−	0.395261i	−0.822127	+	0.569305i	$0.807212\pi$
$654$	0.0557504	−	0.130773i	0.00218001	−	0.00511362i
$655$	13.2002	−	74.8622i	0.515776	−	2.92511i
$656$	−0.782420	+	1.35519i	−0.0305484	+	0.0529113i
$657$	−3.11115	−	46.5774i	−0.121378	−	1.81716i
$658$	2.60067	+	4.50449i	0.101385	+	0.175603i
$659$	−34.8968	+	12.7014i	−1.35938	+	0.494776i	−0.915864	−	0.401488i	$-0.868493\pi$
$659$	−34.8968	+	12.7014i	−1.35938	+	0.494776i	−0.443521	+	0.896264i	$0.646271\pi$
$660$	−33.8241	+	17.1679i	−1.31660	+	0.668259i
$661$	−5.75157	+	4.82614i	−0.223710	+	0.187715i	−0.747753	−	0.663977i	$-0.768867\pi$
$661$	−5.75157	+	4.82614i	−0.223710	+	0.187715i	0.524043	+	0.851692i	$0.324423\pi$
$662$	−1.61987	+	1.35923i	−0.0629580	+	0.0528280i
$663$	−0.660177	+	12.2321i	−0.0256391	+	0.475057i
$664$	−11.7470	+	4.27556i	−0.455873	+	0.165924i
$665$	−4.49938	−	7.79316i	−0.174478	−	0.302206i
$666$	−10.3546	−	23.4533i	−0.401233	−	0.908797i
$667$	−1.83328	+	3.17533i	−0.0709848	+	0.122949i
$668$	2.30919	−	13.0961i	0.0893451	−	0.506701i
$669$	−5.08266	+	0.616033i	−0.196507	+	0.0238172i
$670$	40.5660	+	14.7648i	1.56720	+	0.570415i
$671$	−2.07345	−	11.7591i	−0.0800446	−	0.453955i
$672$	1.68705	+	0.392256i	0.0650793	+	0.0151316i
$673$	−38.1041	−	31.9731i	−1.46880	−	1.23247i	−0.917237	−	0.398342i	$-0.869586\pi$
$673$	−38.1041	−	31.9731i	−1.46880	−	1.23247i	−0.551567	−	0.834130i	$-0.685970\pi$
$674$	13.1693			0.507264
$675$	−12.8282	−	67.6836i	−0.493759	−	2.60514i
$676$	−11.3244			−0.435554
$677$	−12.8190	−	10.7565i	−0.492676	−	0.413404i	0.362308	−	0.932058i	$-0.381989\pi$
$677$	−12.8190	−	10.7565i	−0.492676	−	0.413404i	−0.854984	+	0.518654i	$0.826433\pi$
$678$	−8.45530	+	9.03891i	−0.324724	+	0.347137i
$679$	1.77462	+	10.0644i	0.0681038	+	0.386236i
$680$	21.9380	+	7.98477i	0.841283	+	0.306202i
$681$	19.0288	+	25.3341i	0.729185	+	0.970805i
$682$	−4.97958	+	28.2406i	−0.190678	+	1.08139i
$683$	7.15735	−	12.3969i	0.273868	−	0.474354i	−0.695981	−	0.718061i	$-0.745030\pi$
$683$	7.15735	−	12.3969i	0.273868	−	0.474354i	0.969849	+	0.243707i	$0.0783634\pi$
$684$	−6.13510	+	1.50936i	−0.234581	+	0.0577117i
$685$	23.1832	+	40.1545i	0.885784	+	1.53422i
$686$	0.939693	−	0.342020i	0.0358776	−	0.0130584i
$687$	−1.42612	−	0.929294i	−0.0544097	−	0.0354548i
$688$	1.84904	−	1.55153i	0.0704939	−	0.0591514i
$689$	5.69030	−	4.77473i	0.216783	−	0.181903i
$690$	33.0767	+	21.5536i	1.25921	+	0.820533i
$691$	−7.56895	+	2.75487i	−0.287937	+	0.104800i	−0.481951	−	0.876198i	$-0.660072\pi$
$691$	−7.56895	+	2.75487i	−0.287937	+	0.104800i	0.194014	+	0.980999i	$0.437849\pi$
$692$	6.48228	+	11.2276i	0.246419	+	0.426811i
$693$	10.6465	+	11.0937i	0.404425	+	0.421415i
$694$	3.50517	−	6.07113i	0.133054	−	0.230457i
$695$	−5.65971	+	32.0978i	−0.214685	+	1.21754i
$696$	−0.714979	−	0.951893i	−0.0271012	−	0.0360814i
$697$	8.03423	+	2.92422i	0.304318	+	0.110763i
$698$	−2.62225	−	14.8715i	−0.0992535	−	0.562894i
$699$	−19.9754	+	21.3542i	−0.755539	+	0.807689i
$700$	−10.1559	−	8.52182i	−0.383857	−	0.322095i
$701$	−3.16382			−0.119496			−0.0597479	−	0.998213i	$-0.519030\pi$
$701$	−3.16382			−0.119496			−0.0597479	+	0.998213i	$0.519030\pi$
$702$	−5.20735	−	4.25730i	−0.196539	−	0.160681i
$703$	17.9975			0.678790
$704$	3.92620	+	3.29447i	0.147974	+	0.124165i
$705$	−37.4942	−	8.71779i	−1.41211	−	0.328331i
$706$	−1.49294	−	8.46690i	−0.0561876	−	0.318656i
$707$	12.4532	+	4.53259i	0.468350	+	0.170466i
$708$	21.0420	−	2.55035i	0.790806	−	0.0958480i
$709$	4.90163	−	27.7985i	0.184085	−	1.04400i	−0.743041	−	0.669246i	$-0.766617\pi$
$709$	4.90163	−	27.7985i	0.184085	−	1.04400i	0.927126	−	0.374750i	$-0.122272\pi$
$710$	9.41267	−	16.3032i	0.353251	−	0.611849i
$711$	3.47948	+	0.376677i	0.130491	+	0.0141265i
$712$	−2.39651	−	4.15088i	−0.0898130	−	0.155561i
$713$	28.0465	−	10.2081i	1.05035	−	0.382296i
$714$	0.510006	−	9.44969i	0.0190865	−	0.353646i
$715$	21.7160	−	18.2219i	0.812131	−	0.681459i
$716$	10.8075	−	9.06857i	0.403895	−	0.338908i
$717$	2.24927	−	1.14165i	0.0840005	−	0.0426356i
$718$	−15.1161	+	5.50181i	−0.564128	+	0.205326i
$719$	−18.9914	−	32.8940i	−0.708259	−	1.22674i	−0.965503	−	0.260394i	$-0.916148\pi$
$719$	−18.9914	−	32.8940i	−0.708259	−	1.22674i	0.257244	−	0.966347i	$-0.417186\pi$
$720$	−10.6495	+	7.13495i	−0.396882	+	0.265904i
$721$	−3.84308	+	6.65640i	−0.143124	+	0.247897i
$722$	−2.52914	+	14.3434i	−0.0941247	+	0.533808i
$723$	−6.40758	+	15.0301i	−0.238300	+	0.558977i
$724$	−13.3980	−	4.87648i	−0.497934	−	0.181233i
$725$	1.58236	+	8.97400i	0.0587673	+	0.333286i
$726$	7.69264	+	25.3024i	0.285500	+	0.939062i
$727$	−24.4230	−	20.4933i	−0.905799	−	0.760056i	0.0655160	−	0.997852i	$-0.479131\pi$
$727$	−24.4230	−	20.4933i	−0.905799	−	0.760056i	−0.971315	+	0.237796i	$0.923575\pi$
$728$	−1.29445			−0.0479754
$729$	5.36642	+	26.4613i	0.198756	+	0.980049i
$730$	66.4879			2.46083
$731$	−10.1026	−	8.47711i	−0.373659	−	0.313537i
$732$	−1.17376	−	3.86071i	−0.0433835	−	0.142696i
$733$	−0.825147	−	4.67964i	−0.0304775	−	0.172847i	0.965770	−	0.259402i	$-0.0835253\pi$
$733$	−0.825147	−	4.67964i	−0.0304775	−	0.172847i	−0.996247	+	0.0865550i	$0.972414\pi$
$734$	−29.7812	−	10.8395i	−1.09924	−	0.400091i
$735$	−2.90236	+	6.80802i	−0.107055	+	0.251118i
$736$	0.926315	−	5.25340i	0.0341444	−	0.193643i
$737$	25.8907	−	44.8439i	0.953695	−	1.65185i
$738$	−3.90010	+	2.61300i	−0.143564	+	0.0961858i
$739$	12.3553	+	21.3999i	0.454496	+	0.787209i	0.998659	−	0.0517698i	$-0.0164862\pi$
$739$	12.3553	+	21.3999i	0.454496	+	0.787209i	−0.544163	+	0.838979i	$0.683153\pi$
$740$	34.3131	−	12.4890i	1.26137	−	0.459103i
$741$	4.21048	−	2.13709i	0.154676	−	0.0785078i
$742$	−4.39593	+	3.68862i	−0.161380	+	0.135414i
$743$	35.5910	−	29.8644i	1.30571	−	1.09562i	0.316578	−	0.948566i	$-0.397466\pi$
$743$	35.5910	−	29.8644i	1.30571	−	1.09562i	0.989129	−	0.147052i	$-0.0469784\pi$
$744$	−0.522265	+	9.67682i	−0.0191471	+	0.354770i
$745$	−27.1828	+	9.89373i	−0.995900	+	0.362478i
$746$	11.9414	+	20.6832i	0.437207	+	0.757264i
$747$	−37.2849	−	4.03634i	−1.36418	−	0.147682i
$748$	14.0016	−	24.2515i	0.511949	−	0.886721i
$749$	0.439097	−	2.49024i	0.0160442	−	0.0909914i
$750$	60.6694	−	7.35331i	2.21533	−	0.268505i
$751$	29.2634	+	10.6510i	1.06784	+	0.388660i	0.815367	−	0.578945i	$-0.196535\pi$
$751$	29.2634	+	10.6510i	1.06784	+	0.388660i	0.252468	+	0.967605i	$0.418758\pi$
$752$	0.903202	+	5.12231i	0.0329364	+	0.186792i
$753$	6.35013	+	1.47647i	0.231412	+	0.0538056i
$754$	0.681566	+	0.571902i	0.0248212	+	0.0208274i
$755$	−1.04644			−0.0380840
$756$	4.02284	+	3.28889i	0.146309	+	0.119616i
$757$	−19.5364			−0.710064			−0.355032	−	0.934854i	$-0.615530\pi$
$757$	−19.5364			−0.710064			−0.355032	+	0.934854i	$0.615530\pi$
$758$	13.9241	+	11.6837i	0.505745	+	0.424371i
$759$	32.3501	−	34.5830i	1.17423	−	1.25528i
$760$	−1.56262	−	8.86205i	−0.0566821	−	0.321460i
$761$	40.8303	+	14.8610i	1.48010	+	0.538711i	0.950822	−	0.309738i	$-0.100241\pi$
$761$	40.8303	+	14.8610i	1.48010	+	0.538711i	0.529276	+	0.848450i	$0.322464\pi$
$762$	10.5595	+	14.0584i	0.382529	+	0.509283i
$763$	0.0142524	−	0.0808294i	0.000515972	−	0.00292622i
$764$	−12.2945	+	21.2947i	−0.444800	+	0.770416i
$765$	48.4950	+	50.5323i	1.75334	+	1.82700i
$766$	7.95527	+	13.7789i	0.287436	+	0.497853i
$767$	−14.8855	+	5.41788i	−0.537484	+	0.195628i
$768$	1.45115	+	0.945605i	0.0523638	+	0.0341216i
$769$	9.44827	−	7.92804i	0.340714	−	0.285893i	−0.456335	−	0.889808i	$-0.650838\pi$
$769$	9.44827	−	7.92804i	0.340714	−	0.285893i	0.797048	+	0.603916i	$0.206394\pi$
$770$	−16.7762	+	14.0769i	−0.604573	+	0.507297i
$771$	−25.0181	−	16.3024i	−0.901005	−	0.587118i
$772$	−2.50450	+	0.911564i	−0.0901390	+	0.0328079i
$773$	4.41669	+	7.64993i	0.158857	+	0.275149i	0.934457	−	0.356076i	$-0.115886\pi$
$773$	4.41669	+	7.64993i	0.158857	+	0.275149i	−0.775600	+	0.631225i	$0.782552\pi$
$774$	7.03157	−	1.72991i	0.252744	−	0.0621802i
$775$	37.0885	−	64.2391i	1.33226	−	2.30754i
$776$	−1.77462	+	10.0644i	−0.0637053	+	0.361291i
$777$	−8.88948	−	11.8351i	−0.318908	−	0.424581i
$778$	24.2577	+	8.82907i	0.869679	+	0.316537i
$779$	−0.572270	−	3.24550i	−0.0205037	−	0.116282i
$780$	6.54448	−	6.99621i	0.234330	−	0.250504i
$781$	−17.2979	−	14.5147i	−0.618967	−	0.519375i
$782$	−29.1459			−1.04225
$783$	−0.665077	−	3.50904i	−0.0237679	−	0.125403i
$784$	1.00000			0.0357143
$785$	12.6428	+	10.6085i	0.451240	+	0.378635i
$786$	−30.0135	−	6.97846i	−1.07055	−	0.248913i
$787$	−0.973148	−	5.51900i	−0.0346890	−	0.196731i	0.962538	−	0.271145i	$-0.0874024\pi$
$787$	−0.973148	−	5.51900i	−0.0346890	−	0.196731i	−0.997227	+	0.0744143i	$0.976291\pi$
$788$	16.9596	+	6.17277i	0.604159	+	0.219896i
$789$	37.9572	−	4.60052i	1.35131	−	0.163783i
$790$	−0.865595	+	4.90903i	−0.0307965	+	0.174656i
$791$	−3.57298	+	6.18858i	−0.127040	+	0.220041i
$792$	6.21012	+	14.0660i	0.220667	+	0.499813i
$793$	1.50785	+	2.61168i	0.0535454	+	0.0927434i
$794$	−0.976673	+	0.355480i	−0.0346608	+	0.0126155i
$795$	2.28879	−	42.4080i	0.0811749	−	1.50406i
$796$	−8.92854	+	7.49193i	−0.316464	+	0.265545i
$797$	−15.8088	+	13.2651i	−0.559975	+	0.469875i	−0.878302	−	0.478106i	$-0.841323\pi$
$797$	−15.8088	+	13.2651i	−0.559975	+	0.469875i	0.318327	+	0.947981i	$0.396879\pi$
$798$	−3.25272	+	1.65096i	−0.115145	+	0.0584435i
$799$	26.7048	−	9.71975i	0.944748	−	0.343860i
$800$	−6.62880	−	11.4814i	−0.234364	−	0.405930i
$801$	−0.958318	−	14.3471i	−0.0338605	−	0.506930i
$802$	−13.1574	+	22.7892i	−0.464603	+	0.804716i
$803$	13.8487	−	78.5400i	0.488711	−	2.77162i
$804$	6.86253	−	16.0973i	0.242023	−	0.567709i
$805$	21.4189	+	7.79583i	0.754916	+	0.274767i
$806$	−1.25765	−	7.13247i	−0.0442987	−	0.251231i
$807$	−5.18234	−	17.0456i	−0.182427	−	0.600034i
$808$	10.1519	+	8.51848i	0.357144	+	0.299679i
$809$	19.0835			0.670942			0.335471	−	0.942051i	$-0.391105\pi$
$809$	19.0835			0.670942			0.335471	+	0.942051i	$0.391105\pi$
$810$	−38.1144	+	5.11454i	−1.33920	+	0.179707i
$811$	15.6737			0.550378			0.275189	−	0.961390i	$-0.411260\pi$
$811$	15.6737			0.550378			0.275189	+	0.961390i	$0.411260\pi$
$812$	−0.526530	−	0.441811i	−0.0184776	−	0.0155045i
$813$	−0.582441	−	1.91575i	−0.0204271	−	0.0671884i
$814$	−7.60573	−	43.1343i	−0.266581	−	1.51185i
$815$	81.3563	+	29.6113i	2.84979	+	1.03724i
$816$	3.71123	−	8.70538i	0.129919	−	0.304749i
$817$	−0.882719	+	5.00615i	−0.0308824	+	0.175143i
$818$	15.4808	−	26.8135i	0.541272	−	0.937511i
$819$	−3.48500	−	1.71322i	−0.121776	−	0.0598647i
$820$	−3.34319	−	5.79058i	−0.116749	−	0.202216i
$821$	−16.0553	+	5.84364i	−0.560333	+	0.203944i	−0.606631	−	0.794983i	$-0.707480\pi$
$821$	−16.0553	+	5.84364i	−0.560333	+	0.203944i	0.0462988	+	0.998928i	$0.485257\pi$
$822$	16.7597	−	8.50664i	0.584563	−	0.296703i
$823$	−21.1651	+	17.7597i	−0.737770	+	0.619062i	−0.932238	−	0.361846i	$-0.882146\pi$
$823$	−21.1651	+	17.7597i	−0.737770	+	0.619062i	0.194468	+	0.980909i	$0.437702\pi$
$824$	−5.88794	+	4.94056i	−0.205116	+	0.172113i
$825$	6.34264	−	117.520i	0.220823	−	4.09153i
$826$	11.4995	−	4.18547i	0.400119	−	0.145631i
$827$	20.8941	+	36.1897i	0.726560	+	1.25844i	0.958329	+	0.285668i	$0.0922156\pi$
$827$	20.8941	+	36.1897i	0.726560	+	1.25844i	−0.231768	+	0.972771i	$0.574451\pi$
$828$	9.44682	−	12.9176i	0.328300	−	0.448917i
$829$	22.3865	−	38.7745i	0.777514	−	1.34669i	−0.155856	−	0.987780i	$-0.549814\pi$
$829$	22.3865	−	38.7745i	0.777514	−	1.34669i	0.933370	−	0.358914i	$-0.116853\pi$
$830$	9.27543	−	52.6036i	0.321955	−	1.82590i
$831$	−41.8039	+	5.06676i	−1.45016	+	0.175764i
$832$	−1.21638	−	0.442727i	−0.0421705	−	0.0153488i
$833$	−0.948766	−	5.38072i	−0.0328728	−	0.186431i
$834$	12.8686	+	2.99207i	0.445602	+	0.103607i
$835$	43.5276	+	36.5240i	1.50633	+	1.26397i
$836$	−10.7939			−0.373316
$837$	−14.2135	+	25.3614i	−0.491289	+	0.876618i
$838$	−6.83873			−0.236240
$839$	3.84279	+	3.22449i	0.132668	+	0.111322i	0.706707	−	0.707506i	$-0.250180\pi$
$839$	3.84279	+	3.22449i	0.132668	+	0.111322i	−0.574039	+	0.818828i	$0.694624\pi$
$840$	−5.05581	+	5.40478i	−0.174442	+	0.186483i
$841$	−4.95376	−	28.0942i	−0.170819	−	0.968764i
$842$	6.31135	+	2.29714i	0.217504	+	0.0791648i
$843$	21.0463	+	28.0202i	0.724874	+	0.965066i
$844$	−0.493054	+	2.79625i	−0.0169716	+	0.0962509i
$845$	24.1940	−	41.9052i	0.832298	−	1.44158i
$846$	−4.34778	+	14.9860i	−0.149480	+	0.515231i
$847$	7.63430	+	13.2230i	0.262318	+	0.454347i
$848$	−5.39240	+	1.96267i	−0.185176	+	0.0673985i
$849$	17.6413	+	11.4955i	0.605449	+	0.394526i
$850$	−55.4891	+	46.5609i	−1.90326	+	1.59703i
$851$	−34.9217	+	29.3028i	−1.19710	+	1.00449i
$852$	−6.39341	−	4.16611i	−0.219035	−	0.142729i
$853$	−36.1142	+	13.1445i	−1.23653	+	0.450059i	−0.875828	−	0.482623i	$-0.839684\pi$
$853$	−36.1142	+	13.1445i	−1.23653	+	0.450059i	−0.360699	+	0.932682i	$0.617462\pi$
$854$	−1.16486	−	2.01760i	−0.0398608	−	0.0690408i
$855$	7.52203	−	25.9272i	0.257248	−	0.886691i
$856$	1.26433	−	2.18988i	0.0432138	−	0.0748486i
$857$	−2.99830	+	17.0042i	−0.102420	+	0.580853i	0.889799	+	0.456352i	$0.150844\pi$
$857$	−2.99830	+	17.0042i	−0.102420	+	0.580853i	−0.992219	+	0.124501i	$0.960267\pi$
$858$	−6.90124	−	9.18801i	−0.235604	−	0.313674i
$859$	−21.4014	−	7.78949i	−0.730208	−	0.265774i	−0.0499551	−	0.998751i	$-0.515908\pi$
$859$	−21.4014	−	7.78949i	−0.730208	−	0.265774i	−0.680253	+	0.732977i	$0.738130\pi$
$860$	1.79095	+	10.1570i	0.0610709	+	0.346350i
$861$	−1.85156	+	1.97936i	−0.0631011	+	0.0674566i
$862$	−8.16669	−	6.85267i	−0.278159	−	0.233403i
$863$	37.8052			1.28690			0.643452	−	0.765486i	$-0.277502\pi$
$863$	37.8052			1.28690			0.643452	+	0.765486i	$0.277502\pi$
$864$	2.65536	+	4.46644i	0.0903373	+	0.151951i
$865$	−55.3962			−1.88353
$866$	16.9805	+	14.2483i	0.577020	+	0.484177i
$867$	−21.6824	−	5.04139i	−0.736374	−	0.171214i
$868$	0.971570	+	5.51005i	0.0329772	+	0.187023i
$869$	5.61859	+	2.04500i	0.190597	+	0.0693718i
$870$	5.04993	−	0.612066i	0.171209	−	0.0207510i
$871$	−2.27096	+	12.8793i	−0.0769486	+	0.436397i
$872$	0.0410382	−	0.0710802i	0.00138973	−	0.00240708i
$873$	−18.0981	+	24.7473i	−0.612528	+	0.837570i
$874$	5.61719	+	9.72927i	0.190004	+	0.329097i
$875$	33.1560	−	12.0678i	1.12088	−	0.407966i
$876$	1.45247	−	26.9122i	0.0490745	−	0.909280i
$877$	−5.80050	+	4.86719i	−0.195869	+	0.164353i	−0.735447	−	0.677582i	$-0.763028\pi$
$877$	−5.80050	+	4.86719i	−0.195869	+	0.164353i	0.539579	+	0.841935i	$0.318584\pi$
$878$	9.59204	−	8.04868i	0.323716	−	0.271630i
$879$	−45.0492	+	22.8653i	−1.51947	+	0.771228i
$880$	−20.5791	+	7.49018i	−0.693721	+	0.252494i
$881$	−23.8211	−	41.2593i	−0.802553	−	1.39006i	−0.917931	−	0.396741i	$-0.870141\pi$
$881$	−23.8211	−	41.2593i	−0.802553	−	1.39006i	0.115378	−	0.993322i	$-0.463192\pi$
$882$	2.69227	+	1.32351i	0.0906534	+	0.0445650i
$883$	−23.7809	+	41.1897i	−0.800291	+	1.38614i	0.119134	+	0.992878i	$0.461988\pi$
$883$	−23.7809	+	41.1897i	−0.800291	+	1.38614i	−0.919425	+	0.393266i	$0.871345\pi$
$884$	−1.22813	+	6.96506i	−0.0413064	+	0.234260i
$885$	−35.5177	+	83.3131i	−1.19391	+	2.80054i
$886$	29.4397	+	10.7152i	0.989046	+	0.359983i
$887$	−3.77791	−	21.4256i	−0.126850	−	0.719401i	−0.980192	−	0.198050i	$-0.936539\pi$
$887$	−3.77791	−	21.4256i	−0.126850	−	0.719401i	0.853342	−	0.521351i	$-0.174572\pi$
$888$	−4.30555	−	14.1617i	−0.144485	−	0.475236i
$889$	7.77628	+	6.52508i	0.260808	+	0.218844i
$890$	20.4801			0.686493
$891$	−1.89718	+	46.0886i	−0.0635579	+	1.54403i
$892$	−2.95595			−0.0989725
$893$	−8.39130	−	7.04114i	−0.280804	−	0.235623i
$894$	3.41085	+	11.2189i	0.114076	+	0.375216i
$895$	10.4680	+	59.3669i	0.349906	+	1.98442i
$896$	0.939693	+	0.342020i	0.0313929	+	0.0114261i
$897$	−4.69033	+	11.0020i	−0.156605	+	0.367346i
$898$	−6.29703	+	35.7122i	−0.210135	+	1.19173i
$899$	1.92284	−	3.33046i	0.0641303	−	0.111077i
$900$	−2.65073	−	39.6844i	−0.0883576	−	1.32281i
$901$	15.6767	+	27.1529i	0.522268	+	0.904594i
$902$	−7.53658	+	2.74309i	−0.250941	+	0.0913349i
$903$	3.72801	−	1.89220i	0.124060	−	0.0629686i
$904$	−5.47412	+	4.59333i	−0.182067	+	0.152772i
$905$	46.6693	−	39.1602i	1.55134	−	1.30173i
$906$	−0.0228603	+	0.423568i	−0.000759481	+	0.0140721i
$907$	3.80815	−	1.38605i	0.126448	−	0.0460231i	−0.278021	−	0.960575i	$-0.589679\pi$
$907$	3.80815	−	1.38605i	0.126448	−	0.0460231i	0.404469	+	0.914552i	$0.367456\pi$
$908$	9.14655	+	15.8423i	0.303539	+	0.525745i
$909$	16.0574	+	36.3703i	0.532591	+	1.20633i
$910$	2.76552	−	4.79002i	0.0916761	−	0.158788i
$911$	6.66123	−	37.7777i	0.220697	−	1.25163i	−0.650047	−	0.759894i	$-0.725251\pi$
$911$	6.66123	−	37.7777i	0.220697	−	1.25163i	0.870743	−	0.491738i	$-0.163638\pi$
$912$	−3.62122	+	0.438902i	−0.119911	+	0.0145335i
$913$	−60.2069	−	21.9135i	−1.99256	−	0.725231i
$914$	−3.41671	−	19.3771i	−0.113015	−	0.640938i
$915$	16.7940	+	3.90478i	0.555192	+	0.129088i
$916$	−0.752830	−	0.631700i	−0.0248742	−	0.0208719i
$917$	−17.7906			−0.587496
$918$	21.5133	−	18.5254i	0.710045	−	0.611428i
$919$	−12.3500			−0.407388			−0.203694	−	0.979035i	$-0.565295\pi$
$919$	−12.3500			−0.407388			−0.203694	+	0.979035i	$0.565295\pi$
$920$	17.4608	+	14.6514i	0.575666	+	0.483041i
$921$	15.0170	−	16.0536i	0.494828	−	0.528983i
$922$	3.61335	+	20.4924i	0.118999	+	0.674880i
$923$	5.35909	+	1.95055i	0.176397	+	0.0642031i
$924$	5.33141	+	7.09802i	0.175391	+	0.233508i
$925$	−19.6738	+	111.576i	−0.646870	+	3.66858i
$926$	−3.37296	+	5.84213i	−0.110842	+	0.191984i
$927$	−22.3908	+	5.50858i	−0.735410	+	0.180926i
$928$	−0.343668	−	0.595251i	−0.0112815	−	0.0195401i
$929$	−1.32646	+	0.482793i	−0.0435198	+	0.0158399i	−0.363688	−	0.931521i	$-0.618483\pi$
$929$	−1.32646	+	0.482793i	−0.0435198	+	0.0158399i	0.320169	+	0.947361i	$0.396260\pi$
$930$	−34.6926	−	22.6066i	−1.13762	−	0.741300i
$931$	−1.61330	+	1.35372i	−0.0528737	+	0.0443663i
$932$	−12.9324	+	10.8516i	−0.423616	+	0.355456i
$933$	−34.7897	−	22.6699i	−1.13896	−	0.742178i
$934$	−13.3504	+	4.85914i	−0.436838	+	0.158996i
$935$	59.8273	+	103.624i	1.95656	+	3.38886i
$936$	−2.68888	−	2.80184i	−0.0878887	−	0.0915810i
$937$	12.0877	−	20.9365i	0.394888	−	0.683965i	−0.598199	−	0.801347i	$-0.704117\pi$
$937$	12.0877	−	20.9365i	0.394888	−	0.683965i	0.993087	+	0.117382i	$0.0374502\pi$
$938$	1.75439	−	9.94961i	0.0572827	−	0.324866i
$939$	14.8671	+	19.7934i	0.485168	+	0.645932i
$940$	−20.8844	−	7.60131i	−0.681175	−	0.247927i
$941$	−0.699198	−	3.96535i	−0.0227932	−	0.129267i	0.971288	−	0.237907i	$-0.0764614\pi$
$941$	−0.699198	−	3.96535i	−0.0227932	−	0.129267i	−0.994081	+	0.108640i	$0.965350\pi$
$942$	4.57020	−	4.88565i	0.148905	−	0.159183i
$943$	6.39458	+	5.36569i	0.208236	+	0.174731i
$944$	12.2375			0.398297
$945$	−20.7649	+	7.85970i	−0.675482	+	0.255676i
$946$	12.3711			0.402221
$947$	−13.2092	−	11.0838i	−0.429240	−	0.360175i	0.402425	−	0.915453i	$-0.368168\pi$
$947$	−13.2092	−	11.0838i	−0.429240	−	0.360175i	−0.831665	+	0.555278i	$0.812612\pi$
$948$	1.96811	+	0.457607i	0.0639214	+	0.0148624i
$949$	3.49765	+	19.8361i	0.113538	+	0.643908i
$950$	26.2368	+	9.54943i	0.851236	+	0.309824i
$951$	24.0203	−	2.91133i	0.778911	−	0.0944063i
$952$	0.948766	−	5.38072i	0.0307497	−	0.174390i
$953$	−16.5936	+	28.7410i	−0.537520	+	0.931012i	0.461517	+	0.887132i	$0.347305\pi$
$953$	−16.5936	+	28.7410i	−0.537520	+	0.931012i	−0.999037	+	0.0438806i	$0.986028\pi$
$954$	−17.1154	−	1.85286i	−0.554133	−	0.0599885i
$955$	−52.5331	−	90.9900i	−1.69993	−	2.94437i
$956$	1.36849	−	0.498089i	0.0442601	−	0.0161094i
$957$	0.328833	−	6.09280i	0.0106296	−	0.196952i
$958$	−15.9513	+	13.3847i	−0.515363	+	0.432441i
$959$	8.31257	−	6.97507i	0.268427	−	0.225237i
$960$	−6.59945	+	3.34964i	−0.212996	+	0.108109i
$961$	−0.286185	+	0.104163i	−0.00923179	+	0.00336010i
$962$	5.53104	+	9.58005i	0.178328	+	0.308873i
$963$	6.30224	−	4.22240i	0.203087	−	0.136065i
$964$	−4.71665	+	8.16948i	−0.151913	+	0.263121i
$965$	1.97755	−	11.2152i	0.0636596	−	0.361032i
$966$	3.62342	−	8.49938i	0.116582	−	0.273463i
$967$	25.9846	+	9.45763i	0.835609	+	0.304137i	0.724159	−	0.689633i	$-0.242228\pi$
$967$	25.9846	+	9.45763i	0.835609	+	0.304137i	0.111450	+	0.993770i	$0.464450\pi$
$968$	2.65136	+	15.0366i	0.0852181	+	0.483296i
$969$	5.79730	+	19.0683i	0.186236	+	0.612563i
$970$	−33.4512	−	28.0689i	−1.07405	−	0.901238i
$971$	15.0451			0.482820			0.241410	−	0.970423i	$-0.422390\pi$
$971$	15.0451			0.482820			0.241410	+	0.970423i	$0.422390\pi$
$972$	1.23757	+	15.5393i	0.0396952	+	0.498422i
$973$	7.62785			0.244538
$974$	−6.39777	−	5.36837i	−0.204998	−	0.172014i
$975$	8.64621	+	28.4389i	0.276900	+	0.910774i
$976$	−0.404552	−	2.29433i	−0.0129494	−	0.0734397i
$977$	−0.159751	−	0.0581445i	−0.00511088	−	0.00186021i	0.339463	−	0.940619i	$-0.389755\pi$
$977$	−0.159751	−	0.0581445i	−0.00511088	−	0.00186021i	−0.344574	+	0.938759i	$0.611977\pi$
$978$	13.7630	−	32.2836i	0.440092	−	1.03232i
$979$	4.26578	−	24.1924i	0.136335	−	0.773193i
$980$	−2.13645	+	3.70043i	−0.0682463	+	0.118206i
$981$	0.204561	−	0.137053i	0.00653114	−	0.00437575i
$982$	1.02660	+	1.77813i	0.0327603	+	0.0567424i
$983$	−20.0056	+	7.28146i	−0.638081	+	0.232242i	−0.640745	−	0.767754i	$-0.721374\pi$
$983$	−20.0056	+	7.28146i	−0.638081	+	0.232242i	0.00266383	+	0.999996i	$0.499152\pi$
$984$	−2.41688	+	1.22672i	−0.0770474	+	0.0391065i
$985$	−59.0751	+	49.5699i	−1.88229	+	1.57943i
$986$	−2.87682	+	2.41394i	−0.0916165	+	0.0768754i
$987$	−0.485514	+	8.99588i	−0.0154541	+	0.286342i
$988$	2.56172	−	0.932389i	0.0814991	−	0.0296633i
$989$	−6.43799	−	11.1509i	−0.204716	−	0.354579i
$990$	−65.3178	−	7.07109i	−2.07594	−	0.224734i
$991$	12.9904	−	22.5000i	0.412653	−	0.714736i	−0.582526	−	0.812812i	$-0.697935\pi$
$991$	12.9904	−	22.5000i	0.412653	−	0.714736i	0.995179	+	0.0980758i	$0.0312688\pi$
$992$	−0.971570	+	5.51005i	−0.0308474	+	0.174944i
$993$	−3.63597	+	0.440689i	−0.115384	+	0.0139849i
$994$	−4.14006	−	1.50686i	−0.131315	−	0.0477946i
$995$	−8.64806	−	49.0456i	−0.274162	−	1.55485i
$996$	−21.0897	−	4.90356i	−0.668251	−	0.155375i
$997$	3.64741	+	3.06054i	0.115515	+	0.0969283i	0.698715	−	0.715400i	$-0.253755\pi$
$997$	3.64741	+	3.06054i	0.115515	+	0.0969283i	−0.583201	+	0.812328i	$0.698200\pi$
$998$	−28.1562			−0.891269
$999$	7.15149	−	43.8256i	0.226263	−	1.38658i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.u.d.43.4	✓	30
27.22	even	9	inner	378.2.u.d.211.4	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.u.d.43.4	✓	30	1.1	even	1	trivial
378.2.u.d.211.4	yes	30	27.22	even	9	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	378.u (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.766044 + 0.642788i) q^{2} +(0.503821 + 1.65716i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-4.01520 - 1.46142i) q^{5} +(-0.679250 + 1.59330i) q^{6} +(-0.173648 + 0.984808i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-2.49233 + 1.66982i) q^{9} +O(q^{10})\)	\(q+(0.766044 + 0.642788i) q^{2} +(0.503821 + 1.65716i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-4.01520 - 1.46142i) q^{5} +(-0.679250 + 1.59330i) q^{6} +(-0.173648 + 0.984808i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-2.49233 + 1.66982i) q^{9} +(-2.13645 - 3.70043i) q^{10} +(-4.81620 + 1.75295i) q^{11} +(-1.54449 + 0.783929i) q^{12} +(0.991605 - 0.832055i) q^{13} +(-0.766044 + 0.642788i) q^{14} +(0.398849 - 7.39011i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(2.73186 + 4.73172i) q^{17} +(-2.98257 - 0.322884i) q^{18} +(1.05301 - 1.82386i) q^{19} +(0.741980 - 4.20798i) q^{20} +(-1.71947 + 0.208404i) q^{21} +(-4.81620 - 1.75295i) q^{22} +(0.926315 + 5.25340i) q^{23} +(-1.68705 - 0.392256i) q^{24} +(10.1559 + 8.52182i) q^{25} +1.29445 q^{26} +(-4.02284 - 3.28889i) q^{27} -1.00000 q^{28} +(0.526530 + 0.441811i) q^{29} +(5.05581 - 5.40478i) q^{30} +(-0.971570 - 5.51005i) q^{31} +(-0.939693 - 0.342020i) q^{32} +(-5.33141 - 7.09802i) q^{33} +(-0.948766 + 5.38072i) q^{34} +(2.13645 - 3.70043i) q^{35} +(-2.07724 - 2.16450i) q^{36} +(4.27290 + 7.40087i) q^{37} +(1.97900 - 0.720299i) q^{38} +(1.87844 + 1.22404i) q^{39} +(3.27322 - 2.74656i) q^{40} +(1.19874 - 1.00586i) q^{41} +(-1.45115 - 0.945605i) q^{42} +(-2.26818 + 0.825550i) q^{43} +(-2.56265 - 4.43863i) q^{44} +(12.4475 - 3.06233i) q^{45} +(-2.66722 + 4.61976i) q^{46} +(0.903202 - 5.12231i) q^{47} +(-1.04022 - 1.38490i) q^{48} +(-0.939693 - 0.342020i) q^{49} +(2.30216 + 13.0562i) q^{50} +(-6.46483 + 6.91106i) q^{51} +(0.991605 + 0.832055i) q^{52} +5.73848 q^{53} +(-0.967614 - 5.10526i) q^{54} +21.8998 q^{55} +(-0.766044 - 0.642788i) q^{56} +(3.55295 + 0.826097i) q^{57} +(0.119355 + 0.676894i) q^{58} +(-11.4995 - 4.18547i) q^{59} +(7.34710 - 0.890489i) q^{60} +(-0.404552 + 2.29433i) q^{61} +(2.79752 - 4.84545i) q^{62} +(-1.21166 - 2.74443i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-5.19748 + 1.89173i) q^{65} +(0.478416 - 8.86436i) q^{66} +(-7.73942 + 6.49415i) q^{67} +(-4.18546 + 3.51201i) q^{68} +(-8.23900 + 4.18182i) q^{69} +(4.01520 - 1.46142i) q^{70} +(2.20288 + 3.81550i) q^{71} +(-0.199940 - 2.99333i) q^{72} +(-7.78020 + 13.4757i) q^{73} +(-1.48396 + 8.41596i) q^{74} +(-9.00523 + 21.1234i) q^{75} +(1.97900 + 0.720299i) q^{76} +(-0.889997 - 5.04743i) q^{77} +(0.652170 + 2.14510i) q^{78} +(-0.893669 - 0.749877i) q^{79} +4.27289 q^{80} +(3.42341 - 8.32348i) q^{81} +1.56484 q^{82} +(9.57625 + 8.03543i) q^{83} +(-0.503821 - 1.65716i) q^{84} +(-4.05397 - 22.9912i) q^{85} +(-2.26818 - 0.825550i) q^{86} +(-0.466874 + 1.09514i) q^{87} +(0.889997 - 5.04743i) q^{88} +(-2.39651 + 4.15088i) q^{89} +(11.5038 + 5.65522i) q^{90} +(0.647224 + 1.12103i) q^{91} +(-5.01273 + 1.82448i) q^{92} +(8.64151 - 4.38612i) q^{93} +(3.98445 - 3.34335i) q^{94} +(-6.89345 + 5.78429i) q^{95} +(0.0933441 - 1.72953i) q^{96} +(9.60333 - 3.49533i) q^{97} +(-0.500000 - 0.866025i) q^{98} +(9.07644 - 12.4111i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 3 q^{3} + 3 q^{5} - 6 q^{6} - 15 q^{8} + 3 q^{9}+O(q^{10}) \) 30 * q - 3 * q^3 + 3 * q^5 - 6 * q^6 - 15 * q^8 + 3 * q^9	\( 30 q - 3 q^{3} + 3 q^{5} - 6 q^{6} - 15 q^{8} + 3 q^{9} - 3 q^{10} + 9 q^{11} + 3 q^{12} - 9 q^{13} + 12 q^{15} - 12 q^{18} - 15 q^{19} - 6 q^{20} - 3 q^{21} + 9 q^{22} - 12 q^{23} - 3 q^{24} + 21 q^{25} + 18 q^{26} + 3 q^{27} - 30 q^{28} - 30 q^{29} - 15 q^{30} + 18 q^{31} + 9 q^{33} + 12 q^{34} + 3 q^{35} - 12 q^{36} + 3 q^{37} - 3 q^{38} + 72 q^{39} + 3 q^{40} + 36 q^{41} - 3 q^{42} - 9 q^{43} - 3 q^{44} - 48 q^{45} - 15 q^{46} + 3 q^{48} + 3 q^{50} - 6 q^{51} - 9 q^{52} + 6 q^{53} + 45 q^{54} + 66 q^{55} - 51 q^{57} - 3 q^{58} - 48 q^{59} + 24 q^{60} + 57 q^{61} - 18 q^{62} - 15 q^{63} - 15 q^{64} + 24 q^{65} + 54 q^{66} + 6 q^{67} - 15 q^{68} - 48 q^{69} - 3 q^{70} - 24 q^{71} - 6 q^{72} - 36 q^{73} - 48 q^{74} - 129 q^{75} - 3 q^{76} + 9 q^{77} + 24 q^{78} - 21 q^{79} + 6 q^{80} + 27 q^{81} - 15 q^{83} + 3 q^{84} - 72 q^{85} - 9 q^{86} + 42 q^{87} - 9 q^{88} - 30 q^{89} - 30 q^{90} + 9 q^{91} + 6 q^{92} + 111 q^{93} - 45 q^{94} + 81 q^{95} - 6 q^{96} - 15 q^{97} - 15 q^{98} + 45 q^{99}+O(q^{100}) \) 30 * q - 3 * q^3 + 3 * q^5 - 6 * q^6 - 15 * q^8 + 3 * q^9 - 3 * q^10 + 9 * q^11 + 3 * q^12 - 9 * q^13 + 12 * q^15 - 12 * q^18 - 15 * q^19 - 6 * q^20 - 3 * q^21 + 9 * q^22 - 12 * q^23 - 3 * q^24 + 21 * q^25 + 18 * q^26 + 3 * q^27 - 30 * q^28 - 30 * q^29 - 15 * q^30 + 18 * q^31 + 9 * q^33 + 12 * q^34 + 3 * q^35 - 12 * q^36 + 3 * q^37 - 3 * q^38 + 72 * q^39 + 3 * q^40 + 36 * q^41 - 3 * q^42 - 9 * q^43 - 3 * q^44 - 48 * q^45 - 15 * q^46 + 3 * q^48 + 3 * q^50 - 6 * q^51 - 9 * q^52 + 6 * q^53 + 45 * q^54 + 66 * q^55 - 51 * q^57 - 3 * q^58 - 48 * q^59 + 24 * q^60 + 57 * q^61 - 18 * q^62 - 15 * q^63 - 15 * q^64 + 24 * q^65 + 54 * q^66 + 6 * q^67 - 15 * q^68 - 48 * q^69 - 3 * q^70 - 24 * q^71 - 6 * q^72 - 36 * q^73 - 48 * q^74 - 129 * q^75 - 3 * q^76 + 9 * q^77 + 24 * q^78 - 21 * q^79 + 6 * q^80 + 27 * q^81 - 15 * q^83 + 3 * q^84 - 72 * q^85 - 9 * q^86 + 42 * q^87 - 9 * q^88 - 30 * q^89 - 30 * q^90 + 9 * q^91 + 6 * q^92 + 111 * q^93 - 45 * q^94 + 81 * q^95 - 6 * q^96 - 15 * q^97 - 15 * q^98 + 45 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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