LMFDB - Embedded newform 546.2.cg.a.145.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(145,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 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("546.145");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.cg (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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			145.2
Character	$\chi$	$=$	546.145
Dual form			546.2.cg.a.241.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(0.866025 + 0.500000i) q^{3} -1.00000i q^{4} +(-0.622671 + 0.166844i) q^{5} +(-0.965926 + 0.258819i) q^{6} +(-1.49104 + 2.18559i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(0.866025 + 0.500000i) q^{3} -1.00000i q^{4} +(-0.622671 + 0.166844i) q^{5} +(-0.965926 + 0.258819i) q^{6} +(-1.49104 + 2.18559i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +(0.322318 - 0.558272i) q^{10} +(-0.187589 + 0.0502642i) q^{11} +(0.500000 - 0.866025i) q^{12} +(2.76090 + 2.31893i) q^{13} +(-0.491121 - 2.59977i) q^{14} +(-0.622671 - 0.166844i) q^{15} -1.00000 q^{16} -4.66105 q^{17} +(-0.965926 - 0.258819i) q^{18} +(-0.181008 + 0.675530i) q^{19} +(0.166844 + 0.622671i) q^{20} +(-2.38407 + 1.14726i) q^{21} +(0.0971030 - 0.168187i) q^{22} +5.88027i q^{23} +(0.258819 + 0.965926i) q^{24} +(-3.97024 + 2.29222i) q^{25} +(-3.59198 + 0.312523i) q^{26} +1.00000i q^{27} +(2.18559 + 1.49104i) q^{28} +(-3.99977 - 6.92780i) q^{29} +(0.558272 - 0.322318i) q^{30} +(-0.500334 + 1.86727i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-0.187589 - 0.0502642i) q^{33} +(3.29586 - 3.29586i) q^{34} +(0.563775 - 1.60968i) q^{35} +(0.866025 - 0.500000i) q^{36} +(8.11863 + 8.11863i) q^{37} +(-0.349680 - 0.605664i) q^{38} +(1.23155 + 3.38870i) q^{39} +(-0.558272 - 0.322318i) q^{40} +(-3.14978 + 11.7551i) q^{41} +(0.874562 - 2.49703i) q^{42} +(5.75363 + 3.32186i) q^{43} +(0.0502642 + 0.187589i) q^{44} +(-0.455827 - 0.455827i) q^{45} +(-4.15798 - 4.15798i) q^{46} +(-1.07444 - 4.00985i) q^{47} +(-0.866025 - 0.500000i) q^{48} +(-2.55360 - 6.51760i) q^{49} +(1.18654 - 4.42823i) q^{50} +(-4.03659 - 2.33053i) q^{51} +(2.31893 - 2.76090i) q^{52} +(-6.01682 - 10.4214i) q^{53} +(-0.707107 - 0.707107i) q^{54} +(0.108420 - 0.0625962i) q^{55} +(-2.59977 + 0.491121i) q^{56} +(-0.494522 + 0.494522i) q^{57} +(7.72696 + 2.07043i) q^{58} +(-2.72247 + 2.72247i) q^{59} +(-0.166844 + 0.622671i) q^{60} +(3.53462 - 2.04071i) q^{61} +(-0.966572 - 1.67415i) q^{62} +(-2.63830 - 0.198484i) q^{63} +1.00000i q^{64} +(-2.10603 - 0.983289i) q^{65} +(0.168187 - 0.0971030i) q^{66} +(-0.0733222 - 0.273642i) q^{67} +4.66105i q^{68} +(-2.94013 + 5.09246i) q^{69} +(0.739564 + 1.53686i) q^{70} +(2.34326 + 8.74517i) q^{71} +(-0.258819 + 0.965926i) q^{72} +(-0.854539 - 0.228973i) q^{73} -11.4815 q^{74} -4.58444 q^{75} +(0.675530 + 0.181008i) q^{76} +(0.169845 - 0.484938i) q^{77} +(-3.26701 - 1.52534i) q^{78} +(6.95881 - 12.0530i) q^{79} +(0.622671 - 0.166844i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-6.08491 - 10.5394i) q^{82} +(3.79021 + 3.79021i) q^{83} +(1.14726 + 2.38407i) q^{84} +(2.90231 - 0.777670i) q^{85} +(-6.41734 + 1.71952i) q^{86} -7.99954i q^{87} +(-0.168187 - 0.0971030i) q^{88} +(3.83517 - 3.83517i) q^{89} +0.644637 q^{90} +(-9.18484 + 2.57658i) q^{91} +5.88027 q^{92} +(-1.36694 + 1.36694i) q^{93} +(3.59513 + 2.07565i) q^{94} -0.450833i q^{95} +(0.965926 - 0.258819i) q^{96} +(6.54551 - 1.75386i) q^{97} +(6.41431 + 2.80297i) q^{98} +(-0.137324 - 0.137324i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 4 q^{7} + 16 q^{9}+O(q^{10}) $ 32 * q - 4 * q^7 + 16 * q^9	$ 32 q - 4 q^{7} + 16 q^{9} + 8 q^{11} + 16 q^{12} + 4 q^{14} - 32 q^{16} - 16 q^{17} + 24 q^{19} + 8 q^{21} - 4 q^{22} + 24 q^{25} - 8 q^{26} + 8 q^{28} - 12 q^{29} + 4 q^{31} + 8 q^{33} + 8 q^{34} + 40 q^{35} - 12 q^{37} - 8 q^{38} + 28 q^{39} + 28 q^{41} - 12 q^{42} + 84 q^{43} - 4 q^{44} - 40 q^{46} - 4 q^{47} - 36 q^{49} - 16 q^{50} - 20 q^{52} - 4 q^{53} - 48 q^{55} + 12 q^{56} + 12 q^{57} + 12 q^{58} - 24 q^{59} - 36 q^{61} + 40 q^{62} + 4 q^{63} + 44 q^{65} - 16 q^{67} + 8 q^{69} + 40 q^{70} + 20 q^{71} - 16 q^{73} - 40 q^{74} + 16 q^{75} - 36 q^{76} + 12 q^{77} - 20 q^{78} - 16 q^{81} - 24 q^{82} - 12 q^{83} - 8 q^{84} - 4 q^{85} - 20 q^{86} - 60 q^{89} - 48 q^{91} - 16 q^{92} - 32 q^{93} - 76 q^{97} - 8 q^{98} + 4 q^{99}+O(q^{100}) $ 32 * q - 4 * q^7 + 16 * q^9 + 8 * q^11 + 16 * q^12 + 4 * q^14 - 32 * q^16 - 16 * q^17 + 24 * q^19 + 8 * q^21 - 4 * q^22 + 24 * q^25 - 8 * q^26 + 8 * q^28 - 12 * q^29 + 4 * q^31 + 8 * q^33 + 8 * q^34 + 40 * q^35 - 12 * q^37 - 8 * q^38 + 28 * q^39 + 28 * q^41 - 12 * q^42 + 84 * q^43 - 4 * q^44 - 40 * q^46 - 4 * q^47 - 36 * q^49 - 16 * q^50 - 20 * q^52 - 4 * q^53 - 48 * q^55 + 12 * q^56 + 12 * q^57 + 12 * q^58 - 24 * q^59 - 36 * q^61 + 40 * q^62 + 4 * q^63 + 44 * q^65 - 16 * q^67 + 8 * q^69 + 40 * q^70 + 20 * q^71 - 16 * q^73 - 40 * q^74 + 16 * q^75 - 36 * q^76 + 12 * q^77 - 20 * q^78 - 16 * q^81 - 24 * q^82 - 12 * q^83 - 8 * q^84 - 4 * q^85 - 20 * q^86 - 60 * q^89 - 48 * q^91 - 16 * q^92 - 32 * q^93 - 76 * q^97 - 8 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{1}{12}\right)$

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 $

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$4$		−	1.00000i		−	0.500000i
$5$	−0.622671	+	0.166844i	−0.278467	+	0.0746150i	−0.395350	−	0.918531i	$-0.629377\pi$
$5$	−0.622671	+	0.166844i	−0.278467	+	0.0746150i	0.116883	+	0.993146i	$0.462710\pi$
$6$	−0.965926	+	0.258819i	−0.394338	+	0.105662i
$7$	−1.49104	+	2.18559i	−0.563560	+	0.826075i
$7$	−1.49104	+	2.18559i	−0.563560	+	0.826075i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	0.322318	−	0.558272i	0.101926	−	0.176541i
$11$	−0.187589	+	0.0502642i	−0.0565601	+	0.0151552i	−0.286988	−	0.957934i	$-0.592654\pi$
$11$	−0.187589	+	0.0502642i	−0.0565601	+	0.0151552i	0.230428	+	0.973089i	$0.425987\pi$
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	2.76090	+	2.31893i	0.765736	+	0.643155i
$13$	2.76090	+	2.31893i	0.765736	+	0.643155i
$14$	−0.491121	−	2.59977i	−0.131258	−	0.694818i
$15$	−0.622671	−	0.166844i	−0.160773	−	0.0430790i
$16$	−1.00000			−0.250000
$17$	−4.66105			−1.13047			−0.565236	−	0.824929i	$-0.691215\pi$
$17$	−4.66105			−1.13047			−0.565236	+	0.824929i	$0.691215\pi$
$18$	−0.965926	−	0.258819i	−0.227671	−	0.0610042i
$19$	−0.181008	+	0.675530i	−0.0415260	+	0.154977i	−0.983576	−	0.180496i	$-0.942230\pi$
$19$	−0.181008	+	0.675530i	−0.0415260	+	0.154977i	0.942050	+	0.335473i	$0.108896\pi$
$20$	0.166844	+	0.622671i	0.0373075	+	0.139234i
$21$	−2.38407	+	1.14726i	−0.520247	+	0.250352i
$22$	0.0971030	−	0.168187i	0.0207024	−	0.0358577i
$23$			5.88027i			1.22612i	0.790036	+	0.613061i	$0.210062\pi$
$23$			5.88027i			1.22612i	−0.790036	+	0.613061i	$0.789938\pi$
$24$	0.258819	+	0.965926i	0.0528312	+	0.197169i
$25$	−3.97024	+	2.29222i	−0.794049	+	0.458444i
$26$	−3.59198	+	0.312523i	−0.704445	+	0.0612908i
$27$			1.00000i			0.192450i
$28$	2.18559	+	1.49104i	0.413038	+	0.281780i
$29$	−3.99977	−	6.92780i	−0.742738	−	1.28646i	−0.951244	−	0.308439i	$-0.900193\pi$
$29$	−3.99977	−	6.92780i	−0.742738	−	1.28646i	0.208506	−	0.978021i	$-0.433140\pi$
$30$	0.558272	−	0.322318i	0.101926	−	0.0588470i
$31$	−0.500334	+	1.86727i	−0.0898627	+	0.335372i	−0.996191	−	0.0872031i	$-0.972207\pi$
$31$	−0.500334	+	1.86727i	−0.0898627	+	0.335372i	0.906328	+	0.422575i	$0.138874\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	−0.187589	−	0.0502642i	−0.0326550	−	0.00874988i
$34$	3.29586	−	3.29586i	0.565236	−	0.565236i
$35$	0.563775	−	1.60968i	0.0952953	−	0.272085i
$36$	0.866025	−	0.500000i	0.144338	−	0.0833333i
$37$	8.11863	+	8.11863i	1.33469	+	1.33469i	0.901116	+	0.433579i	$0.142749\pi$
$37$	8.11863	+	8.11863i	1.33469	+	1.33469i	0.433579	+	0.901116i	$0.357251\pi$
$38$	−0.349680	−	0.605664i	−0.0567256	−	0.0982516i
$39$	1.23155	+	3.38870i	0.197205	+	0.542626i
$40$	−0.558272	−	0.322318i	−0.0882705	−	0.0509630i
$41$	−3.14978	+	11.7551i	−0.491913	+	1.83584i	0.0547619	+	0.998499i	$0.482560\pi$
$41$	−3.14978	+	11.7551i	−0.491913	+	1.83584i	−0.546675	+	0.837345i	$0.684107\pi$
$42$	0.874562	−	2.49703i	0.134948	−	0.385300i
$43$	5.75363	+	3.32186i	0.877420	+	0.506579i	0.869807	−	0.493392i	$-0.164243\pi$
$43$	5.75363	+	3.32186i	0.877420	+	0.506579i	0.00761309	+	0.999971i	$0.497577\pi$
$44$	0.0502642	+	0.187589i	0.00757762	+	0.0282801i
$45$	−0.455827	−	0.455827i	−0.0679507	−	0.0679507i
$46$	−4.15798	−	4.15798i	−0.613061	−	0.613061i
$47$	−1.07444	−	4.00985i	−0.156723	−	0.584896i	−0.998952	−	0.0457768i	$-0.985424\pi$
$47$	−1.07444	−	4.00985i	−0.156723	−	0.584896i	0.842229	−	0.539120i	$-0.181243\pi$
$48$	−0.866025	−	0.500000i	−0.125000	−	0.0721688i
$49$	−2.55360	−	6.51760i	−0.364800	−	0.931086i
$50$	1.18654	−	4.42823i	0.167802	−	0.626247i
$51$	−4.03659	−	2.33053i	−0.565236	−	0.326339i
$52$	2.31893	−	2.76090i	0.321577	−	0.382868i
$53$	−6.01682	−	10.4214i	−0.826473	−	1.43149i	−0.900788	−	0.434259i	$-0.857010\pi$
$53$	−6.01682	−	10.4214i	−0.826473	−	1.43149i	0.0743148	−	0.997235i	$-0.476323\pi$
$54$	−0.707107	−	0.707107i	−0.0962250	−	0.0962250i
$55$	0.108420	−	0.0625962i	0.0146193	−	0.00844047i
$56$	−2.59977	+	0.491121i	−0.347409	+	0.0656288i
$57$	−0.494522	+	0.494522i	−0.0655011	+	0.0655011i
$58$	7.72696	+	2.07043i	1.01460	+	0.271861i
$59$	−2.72247	+	2.72247i	−0.354435	+	0.354435i	−0.861757	−	0.507322i	$-0.830636\pi$
$59$	−2.72247	+	2.72247i	−0.354435	+	0.354435i	0.507322	+	0.861757i	$0.330636\pi$
$60$	−0.166844	+	0.622671i	−0.0215395	+	0.0803865i
$61$	3.53462	−	2.04071i	0.452562	−	0.261287i	−0.256350	−	0.966584i	$-0.582520\pi$
$61$	3.53462	−	2.04071i	0.452562	−	0.261287i	0.708912	+	0.705297i	$0.249187\pi$
$62$	−0.966572	−	1.67415i	−0.122755	−	0.212617i
$63$	−2.63830	−	0.198484i	−0.332394	−	0.0250066i
$64$			1.00000i			0.125000i
$65$	−2.10603	−	0.983289i	−0.261221	−	0.121962i
$66$	0.168187	−	0.0971030i	0.0207024	−	0.0119526i
$67$	−0.0733222	−	0.273642i	−0.00895773	−	0.0334307i	0.961302	−	0.275496i	$-0.0888420\pi$
$67$	−0.0733222	−	0.273642i	−0.00895773	−	0.0334307i	−0.970260	+	0.242065i	$0.922175\pi$
$68$			4.66105i			0.565236i
$69$	−2.94013	+	5.09246i	−0.353951	+	0.613061i
$70$	0.739564	+	1.53686i	0.0883947	+	0.183690i
$71$	2.34326	+	8.74517i	0.278094	+	1.03786i	0.953739	+	0.300634i	$0.0971984\pi$
$71$	2.34326	+	8.74517i	0.278094	+	1.03786i	−0.675645	+	0.737227i	$0.736135\pi$
$72$	−0.258819	+	0.965926i	−0.0305021	+	0.113835i
$73$	−0.854539	−	0.228973i	−0.100016	−	0.0267993i	0.208464	−	0.978030i	$-0.433154\pi$
$73$	−0.854539	−	0.228973i	−0.100016	−	0.0267993i	−0.308480	+	0.951231i	$0.599820\pi$
$74$	−11.4815			−1.33469
$75$	−4.58444			−0.529366
$76$	0.675530	+	0.181008i	0.0774886	+	0.0207630i
$77$	0.169845	−	0.484938i	0.0193557	−	0.0552638i
$78$	−3.26701	−	1.52534i	−0.369916	−	0.172711i
$79$	6.95881	−	12.0530i	0.782927	−	1.35607i	−0.147302	−	0.989091i	$-0.547059\pi$
$79$	6.95881	−	12.0530i	0.782927	−	1.35607i	0.930230	−	0.366978i	$-0.119608\pi$
$80$	0.622671	−	0.166844i	0.0696168	−	0.0186538i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−6.08491	−	10.5394i	−0.671966	−	1.16388i
$83$	3.79021	+	3.79021i	0.416029	+	0.416029i	0.883833	−	0.467803i	$-0.154954\pi$
$83$	3.79021	+	3.79021i	0.416029	+	0.416029i	−0.467803	+	0.883833i	$0.654954\pi$
$84$	1.14726	+	2.38407i	0.125176	+	0.260124i
$85$	2.90231	−	0.777670i	0.314799	−	0.0843502i
$86$	−6.41734	+	1.71952i	−0.691999	+	0.185421i
$87$		−	7.99954i		−	0.857640i
$88$	−0.168187	−	0.0971030i	−0.0179288	−	0.0103512i
$89$	3.83517	−	3.83517i	0.406527	−	0.406527i	−0.473999	−	0.880526i	$-0.657190\pi$
$89$	3.83517	−	3.83517i	0.406527	−	0.406527i	0.880526	+	0.473999i	$0.157190\pi$
$90$	0.644637			0.0679507
$91$	−9.18484	+	2.57658i	−0.962832	+	0.270099i
$92$	5.88027			0.613061
$93$	−1.36694	+	1.36694i	−0.141745	+	0.141745i
$94$	3.59513	+	2.07565i	0.370809	+	0.214087i
$95$		−	0.450833i		−	0.0462545i
$96$	0.965926	−	0.258819i	0.0985844	−	0.0264156i
$97$	6.54551	−	1.75386i	0.664596	−	0.178078i	0.0892767	−	0.996007i	$-0.471544\pi$
$97$	6.54551	−	1.75386i	0.664596	−	0.178078i	0.575319	+	0.817929i	$0.304878\pi$
$98$	6.41431	+	2.80297i	0.647943	+	0.283143i
$99$	−0.137324	−	0.137324i	−0.0138016	−	0.0138016i
$100$	2.29222	+	3.97024i	0.229222	+	0.397024i
$101$	6.54013	−	11.3278i	0.650768	−	1.12716i	−0.332169	−	0.943220i	$-0.607781\pi$
$101$	6.54013	−	11.3278i	0.650768	−	1.12716i	0.982937	−	0.183943i	$-0.0588861\pi$
$102$	4.50223	−	1.20637i	0.445788	−	0.119448i
$103$	−6.00747	+	10.4052i	−0.591934	+	1.02526i	0.402038	+	0.915623i	$0.368302\pi$
$103$	−6.00747	+	10.4052i	−0.591934	+	1.02526i	−0.993972	+	0.109636i	$0.965031\pi$
$104$	0.312523	+	3.59198i	0.0306454	+	0.352223i
$105$	1.29308	−	1.11213i	0.126192	−	0.108533i
$106$	11.6236	+	3.11453i	1.12898	+	0.302510i
$107$	8.32137			0.804457			0.402228	−	0.915539i	$-0.368236\pi$
$107$	8.32137			0.804457			0.402228	+	0.915539i	$0.368236\pi$
$108$	1.00000			0.0962250
$109$	0.330520	+	0.0885625i	0.0316580	+	0.00848275i	0.274613	−	0.961555i	$-0.411450\pi$
$109$	0.330520	+	0.0885625i	0.0316580	+	0.00848275i	−0.242955	+	0.970037i	$0.578117\pi$
$110$	−0.0324022	+	0.120927i	−0.00308943	+	0.0115299i
$111$	2.97162	+	11.0903i	0.282054	+	1.05264i
$112$	1.49104	−	2.18559i	0.140890	−	0.206519i
$113$	4.79806	−	8.31049i	0.451364	−	0.781785i	−0.547107	−	0.837062i	$-0.684271\pi$
$113$	4.79806	−	8.31049i	0.451364	−	0.781785i	0.998471	+	0.0552776i	$0.0176044\pi$
$114$		−	0.699360i		−	0.0655011i
$115$	−0.981089	−	3.66148i	−0.0914871	−	0.341434i
$116$	−6.92780	+	3.99977i	−0.643230	+	0.371369i
$117$	−0.627799	+	3.55047i	−0.0580401	+	0.328241i
$118$		−	3.85015i		−	0.354435i
$119$	6.94982	−	10.1872i	0.637089	−	0.933855i
$120$	−0.322318	−	0.558272i	−0.0294235	−	0.0509630i
$121$	−9.49362	+	5.48114i	−0.863056	+	0.498286i
$122$	−1.05635	+	3.94236i	−0.0956376	+	0.356924i
$123$	−8.60536	+	8.60536i	−0.775919	+	0.775919i
$124$	1.86727	+	0.500334i	0.167686	+	0.0449313i
$125$	4.36885	−	4.36885i	0.390762	−	0.390762i
$126$	2.00591	−	1.72521i	0.178700	−	0.153694i
$127$	18.0075	−	10.3966i	1.59791	−	0.922552i	0.606016	−	0.795452i	$-0.292767\pi$
$127$	18.0075	−	10.3966i	1.59791	−	0.922552i	0.991890	−	0.127099i	$-0.0405666\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	3.32186	+	5.75363i	0.292473	+	0.506579i
$130$	2.18448	−	0.793901i	0.191592	−	0.0696297i
$131$	6.39529	+	3.69232i	0.558759	+	0.322600i	0.752647	−	0.658424i	$-0.228777\pi$
$131$	6.39529	+	3.69232i	0.558759	+	0.322600i	−0.193888	+	0.981024i	$0.562110\pi$
$132$	−0.0502642	+	0.187589i	−0.00437494	+	0.0163275i
$133$	−1.20654	−	1.40285i	−0.104620	−	0.121643i
$134$	0.245341	+	0.141648i	0.0211942	+	0.0122365i
$135$	−0.166844	−	0.622671i	−0.0143597	−	0.0535910i
$136$	−3.29586	−	3.29586i	−0.282618	−	0.282618i
$137$	11.2856	+	11.2856i	0.964194	+	0.964194i	0.999381	−	0.0351864i	$-0.0112025\pi$
$137$	11.2856	+	11.2856i	0.964194	+	0.964194i	−0.0351864	+	0.999381i	$0.511202\pi$
$138$	−1.52193	−	5.67990i	−0.129555	−	0.483506i
$139$	14.9928	+	8.65608i	1.27167	+	0.734199i	0.975302	−	0.220875i	$-0.0708912\pi$
$139$	14.9928	+	8.65608i	1.27167	+	0.734199i	0.296368	+	0.955074i	$0.404225\pi$
$140$	−1.60968	−	0.563775i	−0.136042	−	0.0476476i
$141$	1.07444	−	4.00985i	0.0904838	−	0.337690i
$142$	−7.84071	−	4.52684i	−0.657978	−	0.379884i
$143$	−0.634473	−	0.296230i	−0.0530573	−	0.0247720i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	3.64641	+	3.64641i	0.302817	+	0.302817i
$146$	0.766159	−	0.442342i	0.0634077	−	0.0366085i
$147$	1.04732	−	6.92121i	0.0863812	−	0.570852i
$148$	8.11863	−	8.11863i	0.667347	−	0.667347i
$149$	−1.79725	−	0.481571i	−0.147236	−	0.0394519i	0.184448	−	0.982842i	$-0.440950\pi$
$149$	−1.79725	−	0.481571i	−0.147236	−	0.0394519i	−0.331684	+	0.943390i	$0.607617\pi$
$150$	3.24169	−	3.24169i	0.264683	−	0.264683i
$151$	5.10073	−	19.0362i	0.415091	−	1.54914i	−0.369561	−	0.929207i	$-0.620492\pi$
$151$	5.10073	−	19.0362i	0.415091	−	1.54914i	0.784652	−	0.619936i	$-0.212841\pi$
$152$	−0.605664	+	0.349680i	−0.0491258	+	0.0283628i
$153$	−2.33053	−	4.03659i	−0.188412	−	0.326339i
$154$	0.222804	+	0.463001i	0.0179541	+	0.0373097i
$155$		−	1.24618i		−	0.100095i
$156$	3.38870	−	1.23155i	0.271313	−	0.0986027i
$157$	−6.16064	+	3.55685i	−0.491672	+	0.283867i	−0.725268	−	0.688467i	$-0.758284\pi$
$157$	−6.16064	+	3.55685i	−0.491672	+	0.283867i	0.233596	+	0.972334i	$0.424951\pi$
$158$	3.60214	+	13.4434i	0.286571	+	1.06950i
$159$		−	12.0336i		−	0.954329i
$160$	−0.322318	+	0.558272i	−0.0254815	+	0.0441353i
$161$	−12.8519	−	8.76772i	−1.01287	−	0.690993i
$162$	−0.258819	−	0.965926i	−0.0203347	−	0.0758903i
$163$	3.48860	−	13.0196i	0.273249	−	1.01978i	−0.683757	−	0.729709i	$-0.739655\pi$
$163$	3.48860	−	13.0196i	0.273249	−	1.01978i	0.957006	−	0.290068i	$-0.0936780\pi$
$164$	11.7551	+	3.14978i	0.917922	+	0.245957i
$165$	0.125192			0.00974621
$166$	−5.36016			−0.416029
$167$	9.84310	+	2.63745i	0.761682	+	0.204092i	0.618694	−	0.785632i	$-0.287662\pi$
$167$	9.84310	+	2.63745i	0.761682	+	0.204092i	0.142988	+	0.989724i	$0.454329\pi$
$168$	−2.49703	−	0.874562i	−0.192650	−	0.0674739i
$169$	2.24515	+	12.8047i	0.172704	+	0.984974i
$170$	−1.50234	+	2.60214i	−0.115225	+	0.199575i
$171$	−0.675530	+	0.181008i	−0.0516591	+	0.0138420i
$172$	3.32186	−	5.75363i	0.253289	−	0.438710i
$173$	4.90661	+	8.49850i	0.373043	+	0.646129i	0.990032	−	0.140843i	$-0.0449812\pi$
$173$	4.90661	+	8.49850i	0.373043	+	0.646129i	−0.616989	+	0.786971i	$0.711648\pi$
$174$	5.65653	+	5.65653i	0.428820	+	0.428820i
$175$	0.909936	−	12.0951i	0.0687847	−	0.914305i
$176$	0.187589	−	0.0502642i	0.0141400	−	0.00378881i
$177$	−3.71896	+	0.996492i	−0.279534	+	0.0749009i
$178$			5.42374i			0.406527i
$179$	−3.95348	−	2.28254i	−0.295497	−	0.170605i	0.344921	−	0.938632i	$-0.387906\pi$
$179$	−3.95348	−	2.28254i	−0.295497	−	0.170605i	−0.640418	+	0.768026i	$0.721239\pi$
$180$	−0.455827	+	0.455827i	−0.0339753	+	0.0339753i
$181$	−12.9946			−0.965885			−0.482942	−	0.875652i	$-0.660432\pi$
$181$	−12.9946			−0.965885			−0.482942	+	0.875652i	$0.660432\pi$
$182$	4.67274	−	8.31658i	0.346367	−	0.616466i
$183$	4.08143			0.301708
$184$	−4.15798	+	4.15798i	−0.306530	+	0.306530i
$185$	−6.40978	−	3.70069i	−0.471257	−	0.272080i
$186$		−	1.93314i		−	0.141745i
$187$	0.874361	−	0.234284i	0.0639396	−	0.0171326i
$188$	−4.00985	+	1.07444i	−0.292448	+	0.0783613i
$189$	−2.18559	−	1.49104i	−0.158978	−	0.108457i
$190$	0.318787	+	0.318787i	0.0231273	+	0.0231273i
$191$	−0.466746	−	0.808429i	−0.0337726	−	0.0584958i	0.848645	−	0.528963i	$-0.177419\pi$
$191$	−0.466746	−	0.808429i	−0.0337726	−	0.0584958i	−0.882418	+	0.470467i	$0.844086\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	−2.17840	+	0.583700i	−0.156805	+	0.0420156i	−0.336367	−	0.941731i	$-0.609198\pi$
$193$	−2.17840	+	0.583700i	−0.156805	+	0.0420156i	0.179563	+	0.983747i	$0.442532\pi$
$194$	−3.38821	+	5.86854i	−0.243259	+	0.421337i
$195$	−1.33223	−	1.90457i	−0.0954033	−	0.136389i
$196$	−6.51760	+	2.55360i	−0.465543	+	0.182400i
$197$	−19.1875	−	5.14128i	−1.36705	−	0.366301i	−0.500652	−	0.865649i	$-0.666906\pi$
$197$	−19.1875	−	5.14128i	−1.36705	−	0.366301i	−0.866402	+	0.499348i	$0.833573\pi$
$198$	0.194206			0.0138016
$199$	−5.19100			−0.367980			−0.183990	−	0.982928i	$-0.558901\pi$
$199$	−5.19100			−0.367980			−0.183990	+	0.982928i	$0.558901\pi$
$200$	−4.42823	−	1.18654i	−0.313123	−	0.0839011i
$201$	0.0733222	−	0.273642i	0.00517175	−	0.0193012i
$202$	3.38542	+	12.6346i	0.238197	+	0.888965i
$203$	21.1051	+	1.58778i	1.48129	+	0.111440i
$204$	−2.33053	+	4.03659i	−0.163170	+	0.282618i
$205$		−	7.84511i		−	0.547926i
$206$	−3.10970	−	11.6055i	−0.216663	−	0.808596i
$207$	−5.09246	+	2.94013i	−0.353951	+	0.204354i
$208$	−2.76090	−	2.31893i	−0.191434	−	0.160789i
$209$		−	0.135820i		−	0.00939486i
$210$	−0.127950	+	1.70074i	−0.00882937	+	0.117362i
$211$	10.8041	+	18.7132i	0.743783	+	1.28827i	0.950761	+	0.309925i	$0.100304\pi$
$211$	10.8041	+	18.7132i	0.743783	+	1.28827i	−0.206978	+	0.978346i	$0.566363\pi$
$212$	−10.4214	+	6.01682i	−0.715747	+	0.413237i
$213$	−2.34326	+	8.74517i	−0.160558	+	0.599209i
$214$	−5.88409	+	5.88409i	−0.402228	+	0.402228i
$215$	−4.13685	−	1.10847i	−0.282131	−	0.0755968i
$216$	−0.707107	+	0.707107i	−0.0481125	+	0.0481125i
$217$	−3.33507	−	3.87770i	−0.226400	−	0.263236i
$218$	−0.296336	+	0.171090i	−0.0200704	+	0.0115877i
$219$	−0.625566	−	0.625566i	−0.0422718	−	0.0422718i
$220$	−0.0625962	−	0.108420i	−0.00422023	−	0.00730966i
$221$	−12.8687	−	10.8086i	−0.865643	−	0.727068i
$222$	−9.94325	−	5.74074i	−0.667347	−	0.385293i
$223$	−3.24031	+	12.0930i	−0.216987	+	0.809806i	0.768471	+	0.639885i	$0.221018\pi$
$223$	−3.24031	+	12.0930i	−0.216987	+	0.809806i	−0.985458	+	0.169921i	$0.945649\pi$
$224$	0.491121	+	2.59977i	0.0328144	+	0.173704i
$225$	−3.97024	−	2.29222i	−0.264683	−	0.152815i
$226$	2.48366	+	9.26914i	0.165211	+	0.616574i
$227$	17.2746	+	17.2746i	1.14656	+	1.14656i	0.987225	+	0.159333i	$0.0509343\pi$
$227$	17.2746	+	17.2746i	1.14656	+	1.14656i	0.159333	+	0.987225i	$0.449066\pi$
$228$	0.494522	+	0.494522i	0.0327505	+	0.0327505i
$229$	−4.90630	−	18.3106i	−0.324218	−	1.21000i	−0.915096	−	0.403236i	$-0.867885\pi$
$229$	−4.90630	−	18.3106i	−0.324218	−	1.21000i	0.590879	−	0.806761i	$-0.298781\pi$
$230$	3.28279	+	1.89532i	0.216461	+	0.124974i
$231$	0.389559	−	0.335046i	0.0256311	−	0.0220444i
$232$	2.07043	−	7.72696i	0.135931	−	0.507300i
$233$	−3.27750	−	1.89226i	−0.214716	−	0.123966i	0.388785	−	0.921328i	$-0.372895\pi$
$233$	−3.27750	−	1.89226i	−0.214716	−	0.123966i	−0.603501	+	0.797362i	$0.706228\pi$
$234$	−2.06664	−	2.95449i	−0.135101	−	0.193141i
$235$	1.33804	+	2.31755i	0.0872841	+	0.151181i
$236$	2.72247	+	2.72247i	0.177217	+	0.177217i
$237$	12.0530	−	6.95881i	0.782927	−	0.452023i
$238$	2.28914	+	12.1177i	0.148383	+	0.785472i
$239$	11.3575	−	11.3575i	0.734657	−	0.734657i	−0.236882	−	0.971538i	$-0.576125\pi$
$239$	11.3575	−	11.3575i	0.734657	−	0.734657i	0.971538	+	0.236882i	$0.0761254\pi$
$240$	0.622671	+	0.166844i	0.0401933	+	0.0107698i
$241$	−18.1792	+	18.1792i	−1.17102	+	1.17102i	−0.189056	+	0.981966i	$0.560543\pi$
$241$	−18.1792	+	18.1792i	−1.17102	+	1.17102i	−0.981966	+	0.189056i	$0.939457\pi$
$242$	2.83725	−	10.5888i	0.182385	−	0.680671i
$243$	−0.866025	+	0.500000i	−0.0555556	+	0.0320750i
$244$	−2.04071	−	3.53462i	−0.130643	−	0.226281i
$245$	2.67748	+	3.63227i	0.171058	+	0.232057i
$246$		−	12.1698i		−	0.775919i
$247$	−2.06625	+	1.44533i	−0.131472	+	0.0919640i
$248$	−1.67415	+	0.966572i	−0.106309	+	0.0613774i
$249$	1.38731	+	5.17752i	0.0879173	+	0.328112i
$250$			6.17848i			0.390762i
$251$	−3.33196	+	5.77112i	−0.210311	+	0.364270i	−0.951812	−	0.306682i	$-0.900781\pi$
$251$	−3.33196	+	5.77112i	−0.210311	+	0.364270i	0.741501	+	0.670952i	$0.234114\pi$
$252$	−0.198484	+	2.63830i	−0.0125033	+	0.166197i
$253$	−0.295567	−	1.10307i	−0.0185822	−	0.0693495i
$254$	−5.38169	+	20.0847i	−0.337677	+	1.26023i
$255$	2.90231	+	0.777670i	0.181749	+	0.0486996i
$256$	1.00000			0.0625000
$257$	−4.58779			−0.286178			−0.143089	−	0.989710i	$-0.545704\pi$
$257$	−4.58779			−0.286178			−0.143089	+	0.989710i	$0.545704\pi$
$258$	−6.41734	−	1.71952i	−0.399526	−	0.107053i
$259$	−29.8492	+	5.63879i	−1.85474	+	0.350377i
$260$	−0.983289	+	2.10603i	−0.0609810	+	0.130611i
$261$	3.99977	−	6.92780i	0.247579	−	0.428820i
$262$	−7.13302	+	1.91129i	−0.440680	+	0.118080i
$263$	9.52299	−	16.4943i	0.587213	−	1.01708i	−0.407383	−	0.913257i	$-0.633559\pi$
$263$	9.52299	−	16.4943i	0.587213	−	1.01708i	0.994596	−	0.103825i	$-0.0331081\pi$
$264$	−0.0971030	−	0.168187i	−0.00597628	−	0.0103512i
$265$	5.48526	+	5.48526i	0.336957	+	0.336957i
$266$	1.84512	+	0.138811i	0.113131	+	0.00851108i
$267$	5.23893	−	1.40377i	0.320618	−	0.0859092i
$268$	−0.273642	+	0.0733222i	−0.0167153	+	0.00447886i
$269$			12.0075i			0.732109i	0.930593	+	0.366055i	$0.119292\pi$
$269$			12.0075i			0.732109i	−0.930593	+	0.366055i	$0.880708\pi$
$270$	0.558272	+	0.322318i	0.0339753	+	0.0196157i
$271$	−14.9596	+	14.9596i	−0.908731	+	0.908731i	−0.996170	−	0.0874385i	$-0.972132\pi$
$271$	−14.9596	+	14.9596i	−0.908731	+	0.908731i	0.0874385	+	0.996170i	$0.472132\pi$
$272$	4.66105			0.282618
$273$	−9.24259	−	2.36103i	−0.559387	−	0.142896i
$274$	−15.9603			−0.964194
$275$	0.629556	−	0.629556i	0.0379637	−	0.0379637i
$276$	5.09246	+	2.94013i	0.306530	+	0.176975i
$277$		−	18.6953i		−	1.12329i	−0.827377	−	0.561647i	$-0.810168\pi$
$277$		−	18.6953i		−	1.12329i	0.827377	−	0.561647i	$-0.189832\pi$
$278$	−16.7223	+	4.48072i	−1.00293	+	0.268736i
$279$	−1.86727	+	0.500334i	−0.111791	+	0.0299542i
$280$	1.53686	−	0.739564i	0.0918450	−	0.0441974i
$281$	−18.8108	−	18.8108i	−1.12216	−	1.12216i	−0.991416	−	0.130744i	$-0.958264\pi$
$281$	−18.8108	−	18.8108i	−1.12216	−	1.12216i	−0.130744	−	0.991416i	$-0.541736\pi$
$282$	2.07565	+	3.59513i	0.123603	+	0.214087i
$283$	−7.30041	+	12.6447i	−0.433965	+	0.751649i	−0.997211	−	0.0746406i	$-0.976219\pi$
$283$	−7.30041	+	12.6447i	−0.433965	+	0.751649i	0.563246	+	0.826289i	$0.309552\pi$
$284$	8.74517	−	2.34326i	0.518931	−	0.139047i
$285$	0.225417	−	0.390433i	0.0133525	−	0.0231273i
$286$	0.658106	−	0.239174i	0.0389146	−	0.0141427i
$287$	−20.9955	−	24.4115i	−1.23932	−	1.44097i
$288$	0.965926	+	0.258819i	0.0569177	+	0.0152511i
$289$	4.72543			0.277967
$290$	−5.15680			−0.302817
$291$	6.54551	+	1.75386i	0.383705	+	0.102813i
$292$	−0.228973	+	0.854539i	−0.0133996	+	0.0500081i
$293$	7.21239	+	26.9170i	0.421352	+	1.57251i	0.771762	+	0.635912i	$0.219376\pi$
$293$	7.21239	+	26.9170i	0.421352	+	1.57251i	−0.350409	+	0.936597i	$0.613957\pi$
$294$	4.15347	+	5.63460i	0.242235	+	0.328616i
$295$	1.24097	−	2.14943i	0.0722523	−	0.125145i
$296$			11.4815i			0.667347i
$297$	−0.0502642	−	0.187589i	−0.00291663	−	0.0108850i
$298$	1.61137	−	0.930324i	0.0933441	−	0.0538922i
$299$	−13.6359	+	16.2348i	−0.788586	+	0.938885i
$300$			4.58444i			0.264683i
$301$	−15.8391	+	7.62204i	−0.912951	+	0.439327i
$302$	9.85385	+	17.0674i	0.567026	+	0.982117i
$303$	11.3278	−	6.54013i	0.650768	−	0.375721i
$304$	0.181008	−	0.675530i	0.0103815	−	0.0387443i
$305$	−1.86043	+	1.86043i	−0.106528	+	0.106528i
$306$	4.50223	+	1.20637i	0.257376	+	0.0689636i
$307$	−1.42316	+	1.42316i	−0.0812241	+	0.0812241i	−0.746552	−	0.665327i	$-0.768292\pi$
$307$	−1.42316	+	1.42316i	−0.0812241	+	0.0812241i	0.665327	+	0.746552i	$0.268292\pi$
$308$	−0.484938	−	0.169845i	−0.0276319	−	0.00967783i
$309$	−10.4052	+	6.00747i	−0.591934	+	0.341753i
$310$	0.881179	+	0.881179i	0.0500476	+	0.0500476i
$311$	5.50785	+	9.53988i	0.312322	+	0.540957i	0.978865	−	0.204510i	$-0.0655600\pi$
$311$	5.50785	+	9.53988i	0.312322	+	0.540957i	−0.666543	+	0.745467i	$0.732227\pi$
$312$	−1.52534	+	3.26701i	−0.0863553	+	0.184958i
$313$	−5.06512	−	2.92435i	−0.286298	−	0.165294i	0.349973	−	0.936760i	$-0.386191\pi$
$313$	−5.06512	−	2.92435i	−0.286298	−	0.165294i	−0.636271	+	0.771466i	$0.719524\pi$
$314$	1.84116	−	6.87130i	0.103903	−	0.387770i
$315$	1.67591	−	0.316595i	0.0944267	−	0.0178381i
$316$	−12.0530	−	6.95881i	−0.678035	−	0.391464i
$317$	−4.74204	−	17.6975i	−0.266339	−	0.993992i	−0.961425	−	0.275066i	$-0.911300\pi$
$317$	−4.74204	−	17.6975i	−0.266339	−	0.993992i	0.695086	−	0.718927i	$-0.255366\pi$
$318$	8.50906	+	8.50906i	0.477165	+	0.477165i
$319$	1.09853	+	1.09853i	0.0615060	+	0.0615060i
$320$	−0.166844	−	0.622671i	−0.00932688	−	0.0348084i
$321$	7.20651	+	4.16068i	0.402228	+	0.232227i
$322$	15.2873	−	2.88792i	0.851930	−	0.160938i
$323$	0.843687	−	3.14868i	0.0469440	−	0.175197i
$324$	0.866025	+	0.500000i	0.0481125	+	0.0277778i
$325$	−16.2769	−	2.87811i	−0.902883	−	0.159649i
$326$	6.73947	+	11.6731i	0.373265	+	0.646513i
$327$	0.241957	+	0.241957i	0.0133803	+	0.0133803i
$328$	−10.5394	+	6.08491i	−0.581939	+	0.335983i
$329$	10.3659	+	3.63057i	0.571491	+	0.200160i
$330$	−0.0885244	+	0.0885244i	−0.00487311	+	0.00487311i
$331$	−15.8438	−	4.24534i	−0.870856	−	0.233345i	−0.204398	−	0.978888i	$-0.565524\pi$
$331$	−15.8438	−	4.24534i	−0.870856	−	0.233345i	−0.666458	+	0.745543i	$0.732190\pi$
$332$	3.79021	−	3.79021i	0.208015	−	0.208015i
$333$	−2.97162	+	11.0903i	−0.162844	+	0.607742i
$334$	−8.82508	+	5.09516i	−0.482887	+	0.278795i
$335$	0.0913112	+	0.158156i	0.00498886	+	0.00864097i
$336$	2.38407	−	1.14726i	0.130062	−	0.0625880i
$337$		−	2.60165i		−	0.141721i	−0.997486	−	0.0708603i	$-0.977426\pi$
$337$		−	2.60165i		−	0.141721i	0.997486	−	0.0708603i	$-0.0225745\pi$
$338$	−10.6418	−	7.46670i	−0.578839	−	0.406135i
$339$	8.31049	−	4.79806i	0.451364	−	0.260595i
$340$	−0.777670	−	2.90231i	−0.0421751	−	0.157400i
$341$		−	0.375428i		−	0.0203306i
$342$	0.349680	−	0.605664i	0.0189085	−	0.0327505i
$343$	18.0523	+	4.13688i	0.974734	+	0.223370i
$344$	1.71952	+	6.41734i	0.0927103	+	0.346000i
$345$	0.981089	−	3.66148i	0.0528201	−	0.197127i
$346$	−9.47884	−	2.53985i	−0.509586	−	0.136543i
$347$	22.9641			1.23278			0.616388	−	0.787442i	$-0.288595\pi$
$347$	22.9641			1.23278			0.616388	+	0.787442i	$0.288595\pi$
$348$	−7.99954			−0.428820
$349$	−15.6485	−	4.19300i	−0.837644	−	0.224446i	−0.185598	−	0.982626i	$-0.559422\pi$
$349$	−15.6485	−	4.19300i	−0.837644	−	0.224446i	−0.652046	+	0.758180i	$0.726089\pi$
$350$	7.90912	+	9.19596i	0.422760	+	0.491545i
$351$	−2.31893	+	2.76090i	−0.123775	+	0.147366i
$352$	−0.0971030	+	0.168187i	−0.00517561	+	0.00896442i
$353$	−15.9586	+	4.27610i	−0.849392	+	0.227594i	−0.657156	−	0.753755i	$-0.728241\pi$
$353$	−15.9586	+	4.27610i	−0.849392	+	0.227594i	−0.192236	+	0.981349i	$0.561574\pi$
$354$	1.92507	−	3.33433i	0.102317	−	0.177217i
$355$	−2.91816	−	5.05441i	−0.154880	−	0.268260i
$356$	−3.83517	−	3.83517i	−0.203263	−	0.203263i
$357$	11.1123	−	5.34742i	0.588125	−	0.283016i
$358$	4.40954	−	1.18153i	0.233051	−	0.0624459i
$359$	11.9110	−	3.19154i	0.628638	−	0.168443i	0.0695863	−	0.997576i	$-0.477832\pi$
$359$	11.9110	−	3.19154i	0.628638	−	0.168443i	0.559051	+	0.829133i	$0.311165\pi$
$360$		−	0.644637i		−	0.0339753i
$361$	16.0309	+	9.25545i	0.843732	+	0.487129i
$362$	9.18860	−	9.18860i	0.482942	−	0.482942i
$363$	−10.9623			−0.575371
$364$	2.57658	+	9.18484i	0.135050	+	0.481416i
$365$	0.570300			0.0298509
$366$	−2.88601	+	2.88601i	−0.150854	+	0.150854i
$367$	−31.3456	−	18.0974i	−1.63623	−	0.944676i	−0.982116	−	0.188278i	$-0.939709\pi$
$367$	−31.3456	−	18.0974i	−1.63623	−	0.944676i	−0.654112	−	0.756398i	$-0.726957\pi$
$368$		−	5.88027i		−	0.306530i
$369$	−11.7551	+	3.14978i	−0.611948	+	0.163971i
$370$	7.14919	−	1.91562i	0.371668	−	0.0995883i
$371$	31.7483	+	2.38848i	1.64829	+	0.124004i
$372$	1.36694	+	1.36694i	0.0708725	+	0.0708725i
$373$	1.30565	+	2.26145i	0.0676041	+	0.117094i	0.897846	−	0.440309i	$-0.145131\pi$
$373$	1.30565	+	2.26145i	0.0676041	+	0.117094i	−0.830242	+	0.557403i	$0.811798\pi$
$374$	−0.452603	+	0.783931i	−0.0234035	+	0.0405361i
$375$	5.96796	−	1.59911i	0.308184	−	0.0825777i
$376$	2.07565	−	3.59513i	0.107043	−	0.185405i
$377$	5.02210	−	28.4022i	0.258651	−	1.46279i
$378$	2.59977	−	0.491121i	0.133718	−	0.0252605i
$379$	15.9583	+	4.27602i	0.819724	+	0.219644i	0.644226	−	0.764835i	$-0.277180\pi$
$379$	15.9583	+	4.27602i	0.819724	+	0.219644i	0.175498	+	0.984480i	$0.443846\pi$
$380$	−0.450833			−0.0231273
$381$	20.7933			1.06527
$382$	0.901685	+	0.241606i	0.0461342	+	0.0123616i
$383$	1.61437	−	6.02489i	0.0824902	−	0.307858i	−0.912337	−	0.409440i	$-0.865724\pi$
$383$	1.61437	−	6.02489i	0.0824902	−	0.307858i	0.994827	+	0.101583i	$0.0323906\pi$
$384$	−0.258819	−	0.965926i	−0.0132078	−	0.0492922i
$385$	−0.0248486	+	0.330295i	−0.00126640	+	0.0168334i
$386$	1.12762	−	1.95310i	0.0573944	−	0.0994101i
$387$			6.64372i			0.337719i
$388$	−1.75386	−	6.54551i	−0.0890390	−	0.332298i
$389$	−16.0767	+	9.28186i	−0.815119	+	0.470609i	−0.848730	−	0.528826i	$-0.822632\pi$
$389$	−16.0767	+	9.28186i	−0.815119	+	0.470609i	0.0336115	+	0.999435i	$0.489299\pi$
$390$	2.28877	+	0.404703i	0.115896	+	0.0204929i
$391$		−	27.4083i		−	1.38610i
$392$	2.80297	−	6.41431i	0.141571	−	0.323972i
$393$	3.69232	+	6.39529i	0.186253	+	0.322600i
$394$	17.2031	−	9.93219i	0.866677	−	0.500376i
$395$	−2.32207	+	8.66610i	−0.116836	+	0.436039i
$396$	−0.137324	+	0.137324i	−0.00690081	+	0.00690081i
$397$	12.9368	+	3.46639i	0.649277	+	0.173973i	0.568402	−	0.822751i	$-0.307562\pi$
$397$	12.9368	+	3.46639i	0.649277	+	0.173973i	0.0808752	+	0.996724i	$0.474228\pi$
$398$	3.67059	−	3.67059i	0.183990	−	0.183990i
$399$	−0.343470	−	1.81817i	−0.0171950	−	0.0910226i
$400$	3.97024	−	2.29222i	0.198512	−	0.114611i
$401$	5.95772	+	5.95772i	0.297515	+	0.297515i	0.840040	−	0.542525i	$-0.182532\pi$
$401$	5.95772	+	5.95772i	0.297515	+	0.297515i	−0.542525	+	0.840040i	$0.682532\pi$
$402$	0.141648	+	0.245341i	0.00706474	+	0.0122365i
$403$	−5.71144	+	3.99512i	−0.284507	+	0.199011i
$404$	−11.3278	−	6.54013i	−0.563581	−	0.325384i
$405$	0.166844	−	0.622671i	0.00829056	−	0.0309408i
$406$	−16.0463	+	13.8009i	−0.796365	+	0.684925i
$407$	−1.93104	−	1.11489i	−0.0957181	−	0.0552629i
$408$	−1.20637	−	4.50223i	−0.0597242	−	0.222894i
$409$	−15.8529	−	15.8529i	−0.783877	−	0.783877i	0.196606	−	0.980483i	$-0.437008\pi$
$409$	−15.8529	−	15.8529i	−0.783877	−	0.783877i	−0.980483	+	0.196606i	$0.937008\pi$
$410$	5.54733	+	5.54733i	0.273963	+	0.273963i
$411$	4.13082	+	15.4164i	0.203758	+	0.760436i
$412$	10.4052	+	6.00747i	0.512630	+	0.295967i
$413$	−1.89089	−	10.0095i	−0.0930445	−	0.492535i
$414$	1.52193	−	5.67990i	0.0747986	−	0.279152i
$415$	−2.99243	−	1.72768i	−0.146892	−	0.0848084i
$416$	3.59198	−	0.312523i	0.176111	−	0.0153227i
$417$	8.65608	+	14.9928i	0.423890	+	0.734199i
$418$	0.0960392	+	0.0960392i	0.00469743	+	0.00469743i
$419$	−17.3858	+	10.0377i	−0.849351	+	0.490373i	−0.860432	−	0.509566i	$-0.829806\pi$
$419$	−17.3858	+	10.0377i	−0.849351	+	0.490373i	0.0110810	+	0.999939i	$0.496473\pi$
$420$	−1.11213	−	1.29308i	−0.0542665	−	0.0630959i
$421$	5.85809	−	5.85809i	0.285506	−	0.285506i	−0.549794	−	0.835300i	$-0.685294\pi$
$421$	5.85809	−	5.85809i	0.285506	−	0.285506i	0.835300	+	0.549794i	$0.185294\pi$
$422$	−20.8719	−	5.59260i	−1.01603	−	0.272244i
$423$	2.93541	−	2.93541i	0.142725	−	0.142725i
$424$	3.11453	−	11.6236i	0.151255	−	0.564492i
$425$	18.5055	−	10.6842i	0.897650	−	0.518258i
$426$	−4.52684	−	7.84071i	−0.219326	−	0.379884i
$427$	−0.810096	+	10.7680i	−0.0392033	+	0.521101i
$428$		−	8.32137i		−	0.402228i
$429$	−0.401355	−	0.573779i	−0.0193776	−	0.0277023i
$430$	3.70900	−	2.14139i	0.178864	−	0.103267i
$431$	5.12017	+	19.1087i	0.246630	+	0.920436i	0.972557	+	0.232664i	$0.0747443\pi$
$431$	5.12017	+	19.1087i	0.246630	+	0.920436i	−0.725927	+	0.687772i	$0.758589\pi$
$432$		−	1.00000i		−	0.0481125i
$433$	1.55555	−	2.69429i	0.0747549	−	0.129479i	−0.826225	−	0.563341i	$-0.809516\pi$
$433$	1.55555	−	2.69429i	0.0747549	−	0.129479i	0.900980	+	0.433861i	$0.142849\pi$
$434$	5.10020	+	0.383697i	0.244818	+	0.0184180i
$435$	1.33468	+	4.98108i	0.0639929	+	0.238825i
$436$	0.0885625	−	0.330520i	0.00424137	−	0.0158290i
$437$	−3.97230	−	1.06437i	−0.190021	−	0.0509159i
$438$	0.884684			0.0422718
$439$	24.1830			1.15419			0.577095	−	0.816677i	$-0.304186\pi$
$439$	24.1830			1.15419			0.577095	+	0.816677i	$0.304186\pi$
$440$	0.120927	+	0.0324022i	0.00576495	+	0.00154471i
$441$	4.36761	−	5.47028i	0.207981	−	0.260490i
$442$	16.7424	−	1.45669i	0.796356	−	0.0692875i
$443$	−3.54398	+	6.13836i	−0.168380	+	0.291642i	−0.937850	−	0.347040i	$-0.887187\pi$
$443$	−3.54398	+	6.13836i	−0.168380	+	0.291642i	0.769471	+	0.638682i	$0.220520\pi$
$444$	11.0903	−	2.97162i	0.526320	−	0.141027i
$445$	−1.74817	+	3.02792i	−0.0828713	+	0.143537i
$446$	−6.25979	−	10.8423i	−0.296410	−	0.513396i
$447$	−1.31568	−	1.31568i	−0.0622294	−	0.0622294i
$448$	−2.18559	−	1.49104i	−0.103259	−	0.0704450i
$449$	5.40201	−	1.44746i	0.254936	−	0.0683100i	−0.129087	−	0.991633i	$-0.541205\pi$
$449$	5.40201	−	1.44746i	0.254936	−	0.0683100i	0.384024	+	0.923323i	$0.374538\pi$
$450$	4.42823	−	1.18654i	0.208749	−	0.0559341i
$451$		−	2.36345i		−	0.111291i
$452$	−8.31049	−	4.79806i	−0.390892	−	0.225682i
$453$	13.9355	−	13.9355i	0.654745	−	0.654745i
$454$	−24.4300			−1.14656
$455$	5.28925	−	3.13680i	0.247964	−	0.147056i
$456$	−0.699360			−0.0327505
$457$	12.1797	−	12.1797i	0.569742	−	0.569742i	−0.362314	−	0.932056i	$-0.618013\pi$
$457$	12.1797	−	12.1797i	0.569742	−	0.569742i	0.932056	+	0.362314i	$0.118013\pi$
$458$	16.4168	+	9.47825i	0.767107	+	0.442889i
$459$		−	4.66105i		−	0.217559i
$460$	−3.66148	+	0.981089i	−0.170717	+	0.0457435i
$461$	−1.99967	+	0.535809i	−0.0931338	+	0.0249551i	−0.305085	−	0.952325i	$-0.598685\pi$
$461$	−1.99967	+	0.535809i	−0.0931338	+	0.0249551i	0.211951	+	0.977280i	$0.432018\pi$
$462$	−0.0385467	+	0.512373i	−0.00179335	+	0.0238378i
$463$	0.348531	+	0.348531i	0.0161976	+	0.0161976i	0.715159	−	0.698962i	$-0.246354\pi$
$463$	0.348531	+	0.348531i	0.0161976	+	0.0161976i	−0.698962	+	0.715159i	$0.746354\pi$
$464$	3.99977	+	6.92780i	0.185685	+	0.321615i
$465$	0.623088	−	1.07922i	0.0288950	−	0.0500476i
$466$	3.65557	−	0.979508i	0.169341	−	0.0453748i
$467$	8.23209	−	14.2584i	0.380936	−	0.659800i	−0.610261	−	0.792201i	$-0.708935\pi$
$467$	8.23209	−	14.2584i	0.380936	−	0.659800i	0.991196	+	0.132401i	$0.0422686\pi$
$468$	3.55047	+	0.627799i	0.164121	+	0.0290200i
$469$	0.707395	+	0.247759i	0.0326645	+	0.0114404i
$470$	−2.58490	−	0.692621i	−0.119232	−	0.0319482i
$471$	−7.11369			−0.327782
$472$	−3.85015			−0.177217
$473$	−1.24629	−	0.333941i	−0.0573043	−	0.0153546i
$474$	−3.60214	+	13.4434i	−0.165452	+	0.617475i
$475$	−0.829820	−	3.09693i	−0.0380747	−	0.142097i
$476$	−10.1872	−	6.94982i	−0.466927	−	0.318544i
$477$	6.01682	−	10.4214i	0.275491	−	0.477165i
$478$			16.0620i			0.734657i
$479$	3.51104	+	13.1034i	0.160423	+	0.598708i	0.998580	+	0.0532780i	$0.0169669\pi$
$479$	3.51104	+	13.1034i	0.160423	+	0.598708i	−0.838156	+	0.545430i	$0.816366\pi$
$480$	−0.558272	+	0.322318i	−0.0254815	+	0.0147118i
$481$	3.58822	+	41.2412i	0.163609	+	1.88044i
$482$		−	25.7092i		−	1.17102i
$483$	−6.74618	−	14.0190i	−0.306962	−	0.637886i
$484$	5.48114	+	9.49362i	0.249143	+	0.431528i
$485$	−3.78308	+	2.18416i	−0.171781	+	0.0991777i
$486$	0.258819	−	0.965926i	0.0117403	−	0.0438153i
$487$	14.4177	−	14.4177i	0.653329	−	0.653329i	−0.300464	−	0.953793i	$-0.597142\pi$
$487$	14.4177	−	14.4177i	0.653329	−	0.653329i	0.953793	+	0.300464i	$0.0971416\pi$
$488$	3.94236	+	1.05635i	0.178462	+	0.0478188i
$489$	9.53104	−	9.53104i	0.431009	−	0.431009i
$490$	−4.46167	−	0.675139i	−0.201558	−	0.0304997i
$491$	−0.616449	+	0.355907i	−0.0278200	+	0.0160619i	−0.513845	−	0.857883i	$-0.671780\pi$
$491$	−0.616449	+	0.355907i	−0.0278200	+	0.0160619i	0.486026	+	0.873945i	$0.338446\pi$
$492$	8.60536	+	8.60536i	0.387960	+	0.387960i
$493$	18.6431	+	32.2909i	0.839645	+	1.45431i
$494$	0.439058	−	2.48306i	0.0197541	−	0.111718i
$495$	0.108420	+	0.0625962i	0.00487311	+	0.00281349i
$496$	0.500334	−	1.86727i	0.0224657	−	0.0838430i
$497$	−22.6073	−	7.91799i	−1.01407	−	0.355170i
$498$	−4.64204	−	2.68008i	−0.208015	−	0.120097i
$499$	−2.71218	−	10.1220i	−0.121414	−	0.453122i	0.878273	−	0.478160i	$-0.158696\pi$
$499$	−2.71218	−	10.1220i	−0.121414	−	0.453122i	−0.999687	+	0.0250378i	$0.992029\pi$
$500$	−4.36885	−	4.36885i	−0.195381	−	0.195381i
$501$	7.20565	+	7.20565i	0.321925	+	0.321925i
$502$	−1.72475	−	6.43685i	−0.0769793	−	0.287291i
$503$	−11.4031	−	6.58360i	−0.508440	−	0.293548i	0.223752	−	0.974646i	$-0.428169\pi$
$503$	−11.4031	−	6.58360i	−0.508440	−	0.293548i	−0.732192	+	0.681098i	$0.761503\pi$
$504$	−1.72521	−	2.00591i	−0.0768469	−	0.0893501i
$505$	−2.18237	+	8.14471i	−0.0971141	+	0.362435i
$506$	0.988987	+	0.570992i	0.0439658	+	0.0253837i
$507$	−4.45797	+	12.2117i	−0.197985	+	0.542342i
$508$	−10.3966	−	18.0075i	−0.461276	−	0.798953i
$509$	6.53617	+	6.53617i	0.289711	+	0.289711i	0.836966	−	0.547255i	$-0.184327\pi$
$509$	6.53617	+	6.53617i	0.289711	+	0.289711i	−0.547255	+	0.836966i	$0.684327\pi$
$510$	−2.60214	+	1.50234i	−0.115225	+	0.0665249i
$511$	1.77459	−	1.52626i	0.0785034	−	0.0675179i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−0.675530	−	0.181008i	−0.0298254	−	0.00799169i
$514$	3.24406	−	3.24406i	0.143089	−	0.143089i
$515$	2.00462	−	7.48136i	0.0883343	−	0.329668i
$516$	5.75363	−	3.32186i	0.253289	−	0.146237i
$517$	0.403104	+	0.698196i	0.0177285	+	0.0307066i
$518$	17.1193	−	25.0938i	0.752180	−	1.10256i
$519$			9.81322i			0.430753i
$520$	−0.793901	−	2.18448i	−0.0348148	−	0.0957958i
$521$	21.4893	−	12.4068i	0.941462	−	0.543553i	0.0510434	−	0.998696i	$-0.483745\pi$
$521$	21.4893	−	12.4068i	0.941462	−	0.543553i	0.890418	+	0.455143i	$0.150412\pi$
$522$	2.07043	+	7.72696i	0.0906204	+	0.338200i
$523$			4.17951i			0.182757i	0.995816	+	0.0913787i	$0.0291274\pi$
$523$			4.17951i			0.182757i	−0.995816	+	0.0913787i	$0.970873\pi$
$524$	3.69232	−	6.39529i	0.161300	−	0.279380i
$525$	6.83559	−	10.0197i	0.298329	−	0.437296i
$526$	4.92946	+	18.3970i	0.214935	+	0.802147i
$527$	2.33209	−	8.70346i	0.101587	−	0.379129i
$528$	0.187589	+	0.0502642i	0.00816375	+	0.00218747i
$529$	−11.5776			−0.503373
$530$	−7.75732			−0.336957
$531$	−3.71896	−	0.996492i	−0.161389	−	0.0432441i
$532$	−1.40285	+	1.20654i	−0.0608213	+	0.0523102i
$533$	−35.9555	+	25.1507i	−1.55741	+	1.08940i
$534$	−2.71187	+	4.69710i	−0.117354	+	0.203263i
$535$	−5.18148	+	1.38837i	−0.224015	+	0.0600246i
$536$	0.141648	−	0.245341i	0.00611824	−	0.0105971i
$537$	−2.28254	−	3.95348i	−0.0984991	−	0.170605i
$538$	−8.49058	−	8.49058i	−0.366055	−	0.366055i
$539$	0.806629	+	1.09427i	0.0347440	+	0.0471337i
$540$	−0.622671	+	0.166844i	−0.0267955	+	0.00717983i
$541$	1.39468	−	0.373703i	0.0599619	−	0.0160667i	−0.228713	−	0.973494i	$-0.573452\pi$
$541$	1.39468	−	0.373703i	0.0599619	−	0.0160667i	0.288675	+	0.957427i	$0.406785\pi$
$542$		−	21.1561i		−	0.908731i
$543$	−11.2537	−	6.49732i	−0.482942	−	0.278827i
$544$	−3.29586	+	3.29586i	−0.141309	+	0.141309i
$545$	−0.220581			−0.00944867
$546$	8.20500	−	4.86600i	0.351142	−	0.208246i
$547$	−7.40341			−0.316547			−0.158273	−	0.987395i	$-0.550593\pi$
$547$	−7.40341			−0.316547			−0.158273	+	0.987395i	$0.550593\pi$
$548$	11.2856	−	11.2856i	0.482097	−	0.482097i
$549$	3.53462	+	2.04071i	0.150854	+	0.0870956i
$550$			0.890327i			0.0379637i
$551$	5.40393	−	1.44798i	0.230215	−	0.0616859i
$552$	−5.67990	+	1.52193i	−0.241753	+	0.0647775i
$553$	15.9671	+	33.1806i	0.678989	+	1.41098i
$554$	13.2196	+	13.2196i	0.561647	+	0.561647i
$555$	−3.70069	−	6.40978i	−0.157086	−	0.272080i
$556$	8.65608	−	14.9928i	0.367100	−	0.635835i
$557$	−8.41950	+	2.25600i	−0.356746	+	0.0955897i	−0.432741	−	0.901518i	$-0.642453\pi$
$557$	−8.41950	+	2.25600i	−0.356746	+	0.0955897i	0.0759949	+	0.997108i	$0.475787\pi$
$558$	0.966572	−	1.67415i	0.0409182	−	0.0708725i
$559$	8.18205	+	22.5136i	0.346064	+	0.952222i
$560$	−0.563775	+	1.60968i	−0.0238238	+	0.0680212i
$561$	0.874361	+	0.234284i	0.0369156	+	0.00989149i
$562$	26.6025			1.12216
$563$	36.1805			1.52483			0.762414	−	0.647090i	$-0.224014\pi$
$563$	36.1805			1.52483			0.762414	+	0.647090i	$0.224014\pi$
$564$	−4.00985	−	1.07444i	−0.168845	−	0.0452419i
$565$	−1.60106	+	5.97523i	−0.0673570	+	0.251380i
$566$	−3.77897	−	14.1033i	−0.158842	−	0.592807i
$567$	−1.14726	−	2.38407i	−0.0481802	−	0.100122i
$568$	−4.52684	+	7.84071i	−0.189942	+	0.328989i
$569$			29.6783i			1.24418i	0.782947	+	0.622088i	$0.213716\pi$
$569$			29.6783i			1.24418i	−0.782947	+	0.622088i	$0.786284\pi$
$570$	0.116684	+	0.435471i	0.00488736	+	0.0182399i
$571$	−13.1009	+	7.56384i	−0.548258	+	0.316537i	−0.748419	−	0.663226i	$-0.769187\pi$
$571$	−13.1009	+	7.56384i	−0.548258	+	0.316537i	0.200161	+	0.979763i	$0.435853\pi$
$572$	−0.296230	+	0.634473i	−0.0123860	+	0.0265286i
$573$		−	0.933493i		−	0.0389972i
$574$	32.1076	+	2.41551i	1.34014	+	0.100821i
$575$	−13.4789	−	23.3461i	−0.562108	−	0.973600i
$576$	−0.866025	+	0.500000i	−0.0360844	+	0.0208333i
$577$	5.15718	−	19.2468i	0.214696	−	0.801257i	−0.771577	−	0.636136i	$-0.780532\pi$
$577$	5.15718	−	19.2468i	0.214696	−	0.801257i	0.986273	−	0.165121i	$-0.0528015\pi$
$578$	−3.34139	+	3.34139i	−0.138983	+	0.138983i
$579$	−2.17840	−	0.583700i	−0.0905311	−	0.0242577i
$580$	3.64641	−	3.64641i	0.151409	−	0.151409i
$581$	−13.9352	+	2.63249i	−0.578129	+	0.109214i
$582$	−5.86854	+	3.38821i	−0.243259	+	0.140446i
$583$	1.65251	+	1.65251i	0.0684401	+	0.0684401i
$584$	−0.442342	−	0.766159i	−0.0183042	−	0.0317039i
$585$	−0.201464	−	2.31552i	−0.00832950	−	0.0957351i
$586$	−24.1331	−	13.9333i	−0.996931	−	0.575578i
$587$	−7.35518	+	27.4499i	−0.303581	+	1.13298i	0.630579	+	0.776125i	$0.282817\pi$
$587$	−7.35518	+	27.4499i	−0.303581	+	1.13298i	−0.934160	+	0.356854i	$0.883849\pi$
$588$	−6.92121	−	1.04732i	−0.285426	−	0.0431906i
$589$	−1.17083	−	0.675982i	−0.0482434	−	0.0278533i
$590$	0.642375	+	2.39738i	0.0264462	+	0.0986985i
$591$	−14.0462	−	14.0462i	−0.577785	−	0.577785i
$592$	−8.11863	−	8.11863i	−0.333674	−	0.333674i
$593$	8.50516	+	31.7417i	0.349265	+	1.30347i	0.887550	+	0.460712i	$0.152406\pi$
$593$	8.50516	+	31.7417i	0.349265	+	1.30347i	−0.538285	+	0.842763i	$0.680928\pi$
$594$	0.168187	+	0.0971030i	0.00690081	+	0.00398419i
$595$	−2.62778	+	7.50278i	−0.107729	+	0.307584i
$596$	−0.481571	+	1.79725i	−0.0197259	+	0.0736182i
$597$	−4.49554	−	2.59550i	−0.183990	−	0.106227i
$598$	−1.83772	−	21.1218i	−0.0751499	−	0.863735i
$599$	16.9713	+	29.3952i	0.693429	+	1.20105i	0.970707	+	0.240265i	$0.0772343\pi$
$599$	16.9713	+	29.3952i	0.693429	+	1.20105i	−0.277278	+	0.960790i	$0.589432\pi$
$600$	−3.24169	−	3.24169i	−0.132341	−	0.132341i
$601$	34.5158	−	19.9277i	1.40793	−	0.812868i	0.412741	−	0.910848i	$-0.364571\pi$
$601$	34.5158	−	19.9277i	1.40793	−	0.812868i	0.995188	+	0.0979799i	$0.0312381\pi$
$602$	5.81034	−	16.5895i	0.236812	−	0.676139i
$603$	0.200320	−	0.200320i	0.00815766	−	0.00815766i
$604$	−19.0362	−	5.10073i	−0.774571	−	0.207546i
$605$	4.99691	−	4.99691i	0.203153	−	0.203153i
$606$	−3.38542	+	12.6346i	−0.137523	+	0.513244i
$607$	39.2667	−	22.6707i	1.59379	−	0.920174i	0.601138	−	0.799145i	$-0.294714\pi$
$607$	39.2667	−	22.6707i	1.59379	−	0.920174i	0.992649	−	0.121028i	$-0.0386192\pi$
$608$	0.349680	+	0.605664i	0.0141814	+	0.0245629i
$609$	17.4837	+	11.9276i	0.708475	+	0.483332i
$610$		−	2.63104i		−	0.106528i
$611$	6.33214	−	13.5623i	0.256171	−	0.548673i
$612$	−4.03659	+	2.33053i	−0.163170	+	0.0942060i
$613$	3.07273	+	11.4676i	0.124106	+	0.463171i	0.999806	−	0.0196847i	$-0.00626624\pi$
$613$	3.07273	+	11.4676i	0.124106	+	0.463171i	−0.875700	+	0.482856i	$0.839600\pi$
$614$		−	2.01265i		−	0.0812241i
$615$	3.92256	−	6.79407i	0.158173	−	0.273963i
$616$	0.463001	−	0.222804i	0.0186549	−	0.00897703i
$617$	2.32942	+	8.69353i	0.0937791	+	0.349988i	0.996832	−	0.0795421i	$-0.0253458\pi$
$617$	2.32942	+	8.69353i	0.0937791	+	0.349988i	−0.903052	+	0.429530i	$0.858679\pi$
$618$	3.10970	−	11.6055i	0.125090	−	0.466843i
$619$	−42.1728	−	11.3002i	−1.69507	−	0.454193i	−0.723379	−	0.690451i	$-0.757412\pi$
$619$	−42.1728	−	11.3002i	−1.69507	−	0.454193i	−0.971690	+	0.236258i	$0.924079\pi$
$620$	−1.24618			−0.0500476
$621$	−5.88027			−0.235967
$622$	−10.6404	−	2.85107i	−0.426639	−	0.114318i
$623$	2.66371	+	14.1005i	0.106719	+	0.564924i
$624$	−1.23155	−	3.38870i	−0.0493013	−	0.135657i
$625$	9.46967	−	16.4019i	0.378787	−	0.656078i
$626$	5.64941	−	1.51376i	0.225796	−	0.0605018i
$627$	0.0679100	−	0.117624i	0.00271206	−	0.00469743i
$628$	3.55685	+	6.16064i	0.141934	+	0.245836i
$629$	−37.8414	−	37.8414i	−1.50883	−	1.50883i
$630$	−0.961179	+	1.40891i	−0.0382943	+	0.0561324i
$631$	−22.2577	+	5.96394i	−0.886066	+	0.237421i	−0.673023	−	0.739622i	$-0.735004\pi$
$631$	−22.2577	+	5.96394i	−0.886066	+	0.237421i	−0.213044	+	0.977043i	$0.568338\pi$
$632$	13.4434	−	3.60214i	0.534749	−	0.143286i
$633$			21.6082i			0.858847i
$634$	15.8672	+	9.16091i	0.630166	+	0.363826i
$635$	−9.47813	+	9.47813i	−0.376128	+	0.376128i
$636$	−12.0336			−0.477165
$637$	8.06360	−	23.9161i	0.319491	−	0.947589i
$638$	−1.55356			−0.0615060
$639$	−6.40191	+	6.40191i	−0.253256	+	0.253256i
$640$	0.558272	+	0.322318i	0.0220676	+	0.0127408i
$641$			6.66110i			0.263098i	0.991310	+	0.131549i	$0.0419950\pi$
$641$			6.66110i			0.263098i	−0.991310	+	0.131549i	$0.958005\pi$
$642$	−8.03782	+	2.15373i	−0.317228	+	0.0850009i
$643$	−23.5690	+	6.31530i	−0.929471	+	0.249051i	−0.691629	−	0.722253i	$-0.743107\pi$
$643$	−23.5690	+	6.31530i	−0.929471	+	0.249051i	−0.237842	+	0.971304i	$0.576440\pi$
$644$	−8.76772	+	12.8519i	−0.345496	+	0.506434i
$645$	−3.02839	−	3.02839i	−0.119243	−	0.119243i
$646$	1.62988	+	2.82303i	0.0641267	+	0.111071i
$647$	−16.7697	+	29.0460i	−0.659287	+	1.14192i	0.321514	+	0.946905i	$0.395808\pi$
$647$	−16.7697	+	29.0460i	−0.659287	+	1.14192i	−0.980801	+	0.195013i	$0.937525\pi$
$648$	−0.965926	+	0.258819i	−0.0379452	+	0.0101674i
$649$	0.373861	−	0.647547i	0.0146753	−	0.0254184i
$650$	13.5447	−	9.47441i	0.531266	−	0.371617i
$651$	−0.949407	−	5.02573i	−0.0372102	−	0.196974i
$652$	−13.0196	−	3.48860i	−0.509889	−	0.136624i
$653$	−26.2753			−1.02823			−0.514115	−	0.857721i	$-0.671880\pi$
$653$	−26.2753			−1.02823			−0.514115	+	0.857721i	$0.671880\pi$
$654$	−0.342179			−0.0133803
$655$	−4.59821	−	1.23209i	−0.179667	−	0.0481416i
$656$	3.14978	−	11.7551i	0.122978	−	0.458961i
$657$	−0.228973	−	0.854539i	−0.00893309	−	0.0333387i
$658$	−9.89700	+	4.76260i	−0.385825	+	0.185666i
$659$	−10.6194	+	18.3934i	−0.413674	+	0.716504i	−0.995288	−	0.0969604i	$-0.969088\pi$
$659$	−10.6194	+	18.3934i	−0.413674	+	0.716504i	0.581614	+	0.813465i	$0.302421\pi$
$660$		−	0.125192i		−	0.00487311i
$661$	11.2946	+	42.1521i	0.439310	+	1.63953i	0.730536	+	0.682874i	$0.239270\pi$
$661$	11.2946	+	42.1521i	0.439310	+	1.63953i	−0.291226	+	0.956654i	$0.594063\pi$
$662$	14.2052	−	8.20137i	0.552100	−	0.318755i
$663$	−5.74031	−	15.7949i	−0.222935	−	0.613424i
$664$			5.36016i			0.208015i
$665$	0.985336	+	0.672210i	0.0382097	+	0.0260672i
$666$	−5.74074	−	9.94325i	−0.222449	−	0.385293i
$667$	40.7373	−	23.5197i	1.57736	−	0.910687i
$668$	2.63745	−	9.84310i	0.102046	−	0.380841i
$669$	−8.85268	+	8.85268i	−0.342264	+	0.342264i
$670$	−0.176400	−	0.0472662i	−0.00681492	−	0.00182605i
$671$	−0.560480	+	0.560480i	−0.0216371	+	0.0216371i
$672$	−0.874562	+	2.49703i	−0.0337369	+	0.0963249i
$673$	0.332310	−	0.191859i	0.0128096	−	0.00739563i	−0.493582	−	0.869700i	$-0.664313\pi$
$673$	0.332310	−	0.191859i	0.0128096	−	0.00739563i	0.506391	+	0.862304i	$0.330979\pi$
$674$	1.83964	+	1.83964i	0.0708603	+	0.0708603i
$675$	−2.29222	−	3.97024i	−0.0882277	−	0.152815i
$676$	12.8047	−	2.24515i	0.492487	−	0.0863520i
$677$	18.6386	+	10.7610i	0.716340	+	0.413579i	0.813404	−	0.581699i	$-0.197612\pi$
$677$	18.6386	+	10.7610i	0.716340	+	0.413579i	−0.0970639	+	0.995278i	$0.530945\pi$
$678$	−2.48366	+	9.26914i	−0.0953844	+	0.355979i
$679$	−5.92639	+	16.9209i	−0.227434	+	0.649364i
$680$	2.60214	+	1.50234i	0.0997874	+	0.0576123i
$681$	6.32296	+	23.5976i	0.242296	+	0.904262i
$682$	0.265468	+	0.265468i	0.0101653	+	0.0101653i
$683$	−16.5674	−	16.5674i	−0.633935	−	0.633935i	0.315117	−	0.949053i	$-0.397956\pi$
$683$	−16.5674	−	16.5674i	−0.633935	−	0.633935i	−0.949053	+	0.315117i	$0.897956\pi$
$684$	0.181008	+	0.675530i	0.00692100	+	0.0258295i
$685$	−8.91016	−	5.14428i	−0.340440	−	0.196553i
$686$	−15.6901	+	9.83970i	−0.599052	+	0.375682i
$687$	4.90630	−	18.3106i	0.187187	−	0.698592i
$688$	−5.75363	−	3.32186i	−0.219355	−	0.126645i
$689$	7.55471	−	42.7251i	0.287811	−	1.62770i
$690$	1.89532	+	3.28279i	0.0721536	+	0.124974i
$691$	−22.1664	−	22.1664i	−0.843251	−	0.843251i	0.146029	−	0.989280i	$-0.453351\pi$
$691$	−22.1664	−	22.1664i	−0.843251	−	0.843251i	−0.989280	+	0.146029i	$0.953351\pi$
$692$	8.49850	−	4.90661i	0.323064	−	0.186521i
$693$	0.504891	−	0.0953787i	0.0191792	−	0.00362314i
$694$	−16.2381	+	16.2381i	−0.616388	+	0.616388i
$695$	−10.7798	−	2.88843i	−0.408901	−	0.109565i
$696$	5.65653	−	5.65653i	0.214410	−	0.214410i
$697$	14.6813	−	54.7914i	0.556094	−	2.07537i
$698$	14.0300	−	8.10025i	0.531045	−	0.306599i
$699$	−1.89226	−	3.27750i	−0.0715720	−	0.123966i
$700$	−12.0951	−	0.909936i	−0.457152	−	0.0343924i
$701$		−	17.4358i		−	0.658542i	−0.944235	−	0.329271i	$-0.893197\pi$
$701$		−	17.4358i		−	0.658542i	0.944235	−	0.329271i	$-0.106803\pi$
$702$	−0.312523	−	3.59198i	−0.0117954	−	0.135571i
$703$	−6.95391	+	4.01484i	−0.262272	+	0.151423i
$704$	−0.0502642	−	0.187589i	−0.00189440	−	0.00707001i
$705$			2.67608i			0.100787i
$706$	8.26080	−	14.3081i	0.310899	−	0.538493i
$707$	15.0064	+	31.1843i	0.564374	+	1.17281i
$708$	0.996492	+	3.71896i	0.0374505	+	0.139767i
$709$	2.44496	−	9.12472i	0.0918224	−	0.342686i	−0.904696	−	0.426057i	$-0.859902\pi$
$709$	2.44496	−	9.12472i	0.0918224	−	0.342686i	0.996519	+	0.0833714i	$0.0265688\pi$
$710$	5.63746	+	1.51055i	0.211570	+	0.0566901i
$711$	13.9176			0.521951
$712$	5.42374			0.203263
$713$	−10.9801	−	2.94210i	−0.411207	−	0.110183i
$714$	−4.07638	+	11.6388i	−0.152555	+	0.435570i
$715$	0.444492	+	0.0785957i	0.0166231	+	0.00293931i
$716$	−2.28254	+	3.95348i	−0.0853027	+	0.147749i
$717$	15.5147	−	4.15714i	0.579405	−	0.155251i
$718$	−6.16558	+	10.6791i	−0.230097	+	0.398540i
$719$	−15.7488	−	27.2776i	−0.587330	−	1.01728i	−0.994581	−	0.103968i	$-0.966846\pi$
$719$	−15.7488	−	27.2776i	−0.587330	−	1.01728i	0.407251	−	0.913316i	$-0.366487\pi$
$720$	0.455827	+	0.455827i	0.0169877	+	0.0169877i
$721$	−13.7842	−	28.6445i	−0.513351	−	1.06678i
$722$	−17.8802	+	4.79097i	−0.665430	+	0.178302i
$723$	−24.8332	+	6.65403i	−0.923556	+	0.247466i
$724$			12.9946i			0.482942i
$725$	31.7601	+	18.3367i	1.17954	+	0.681008i
$726$	7.75151	−	7.75151i	0.287685	−	0.287685i
$727$	−1.26745			−0.0470072			−0.0235036	−	0.999724i	$-0.507482\pi$
$727$	−1.26745			−0.0470072			−0.0235036	+	0.999724i	$0.507482\pi$
$728$	−8.31658	−	4.67274i	−0.308233	−	0.173183i
$729$	−1.00000			−0.0370370
$730$	−0.403263	+	0.403263i	−0.0149254	+	0.0149254i
$731$	−26.8180	−	15.4834i	−0.991899	−	0.572673i
$732$		−	4.08143i		−	0.150854i
$733$	29.9256	−	8.01854i	1.10533	−	0.296172i	0.340396	−	0.940282i	$-0.389439\pi$
$733$	29.9256	−	8.01854i	1.10533	−	0.296172i	0.764932	+	0.644111i	$0.222772\pi$
$734$	34.9615	−	9.36790i	1.29045	−	0.345776i
$735$	0.502630	+	4.48438i	0.0185398	+	0.165409i
$736$	4.15798	+	4.15798i	0.153265	+	0.153265i
$737$	0.0275088	+	0.0476467i	0.00101330	+	0.00175509i
$738$	6.08491	−	10.5394i	0.223989	−	0.387960i
$739$	−20.7109	+	5.54946i	−0.761861	+	0.204140i	−0.618773	−	0.785570i	$-0.712370\pi$
$739$	−20.7109	+	5.54946i	−0.761861	+	0.204140i	−0.143088	+	0.989710i	$0.545703\pi$
$740$	−3.70069	+	6.40978i	−0.136040	+	0.235628i
$741$	−2.51209	+	0.218566i	−0.0922839	+	0.00802922i
$742$	−24.1383	+	20.7605i	−0.886146	+	0.762143i
$743$	−26.2331	−	7.02915i	−0.962401	−	0.257875i	−0.256785	−	0.966469i	$-0.582663\pi$
$743$	−26.2331	−	7.02915i	−0.962401	−	0.257875i	−0.705616	+	0.708594i	$0.749330\pi$
$744$	−1.93314			−0.0708725
$745$	1.19944			0.0439442
$746$	−2.52232	−	0.675855i	−0.0923489	−	0.0247448i
$747$	−1.38731	+	5.17752i	−0.0507591	+	0.189435i
$748$	−0.234284	−	0.874361i	−0.00856628	−	0.0319698i
$749$	−12.4075	+	18.1871i	−0.453360	+	0.664542i
$750$	−3.08924	+	5.35072i	−0.112803	+	0.195381i
$751$			43.5089i			1.58766i	0.608137	+	0.793832i	$0.291917\pi$
$751$			43.5089i			1.58766i	−0.608137	+	0.793832i	$0.708083\pi$
$752$	1.07444	+	4.00985i	0.0391806	+	0.146224i
$753$	−5.77112	+	3.33196i	−0.210311	+	0.121423i
$754$	16.5322	+	23.6345i	0.602067	+	0.860718i
$755$			12.7043i			0.462357i
$756$	−1.49104	+	2.18559i	−0.0542286	+	0.0794891i
$757$	15.3805	+	26.6398i	0.559014	+	0.968240i	0.997579	+	0.0695407i	$0.0221534\pi$
$757$	15.3805	+	26.6398i	0.559014	+	0.968240i	−0.438566	+	0.898699i	$0.644513\pi$
$758$	−14.3078	+	8.26064i	−0.519684	+	0.300040i
$759$	0.295567	−	1.10307i	0.0107284	−	0.0400390i
$760$	0.318787	−	0.318787i	0.0115636	−	0.0115636i
$761$	37.9738	+	10.1751i	1.37655	+	0.368846i	0.869867	−	0.493286i	$-0.164205\pi$
$761$	37.9738	+	10.1751i	1.37655	+	0.368846i	0.506684	+	0.862132i	$0.330871\pi$
$762$	−14.7031	+	14.7031i	−0.532635	+	0.532635i
$763$	−0.686379	+	0.590330i	−0.0248486	+	0.0213714i
$764$	−0.808429	+	0.466746i	−0.0292479	+	0.0168863i
$765$	2.12463	+	2.12463i	0.0768163	+	0.0768163i
$766$	3.11871	+	5.40177i	0.112684	+	0.195174i
$767$	−13.8297	+	1.20326i	−0.499360	+	0.0434472i
$768$	0.866025	+	0.500000i	0.0312500	+	0.0180422i
$769$	1.23726	−	4.61753i	0.0446169	−	0.166513i	−0.940023	−	0.341112i	$-0.889196\pi$
$769$	1.23726	−	4.61753i	0.0446169	−	0.166513i	0.984640	+	0.174600i	$0.0558631\pi$
$770$	−0.215983	−	0.251124i	−0.00778348	−	0.00904989i
$771$	−3.97314	−	2.29389i	−0.143089	−	0.0826126i
$772$	0.583700	+	2.17840i	0.0210078	+	0.0784023i
$773$	18.3386	+	18.3386i	0.659595	+	0.659595i	0.955284	−	0.295689i	$-0.0955493\pi$
$773$	18.3386	+	18.3386i	0.659595	+	0.659595i	−0.295689	+	0.955284i	$0.595549\pi$
$774$	−4.69782	−	4.69782i	−0.168860	−	0.168860i
$775$	−2.29375	−	8.56041i	−0.0823941	−	0.307499i
$776$	5.86854	+	3.38821i	0.210668	+	0.121629i
$777$	−28.6695	−	10.0413i	−1.02851	−	0.360228i
$778$	4.80465	−	17.9312i	0.172255	−	0.642864i
$779$	−7.37081	−	4.25554i	−0.264087	−	0.152471i
$780$	−1.90457	+	1.33223i	−0.0681946	+	0.0477016i
$781$	−0.879139	−	1.52271i	−0.0314581	−	0.0544870i
$782$	19.3806	+	19.3806i	0.693048	+	0.693048i
$783$	6.92780	−	3.99977i	0.247579	−	0.142940i
$784$	2.55360	+	6.51760i	0.0912001	+	0.232771i
$785$	3.24261	−	3.24261i	0.115734	−	0.115734i
$786$	−7.13302	−	1.91129i	−0.254426	−	0.0681734i
$787$	8.16111	−	8.16111i	0.290912	−	0.290912i	−0.546528	−	0.837441i	$-0.684051\pi$
$787$	8.16111	−	8.16111i	0.290912	−	0.290912i	0.837441	+	0.546528i	$0.184051\pi$
$788$	−5.14128	+	19.1875i	−0.183150	+	0.683527i
$789$	16.4943	−	9.52299i	0.587213	−	0.339027i
$790$	−4.48590	−	7.76981i	−0.159601	−	0.276438i
$791$	11.0092	+	22.8779i	0.391442	+	0.813443i
$792$		−	0.194206i		−	0.00690081i
$793$	14.4910	+	2.56232i	0.514591	+	0.0909906i
$794$	−11.5988	+	6.69656i	−0.411625	+	0.237652i
$795$	2.00774	+	7.49300i	0.0712073	+	0.265749i
$796$			5.19100i			0.183990i
$797$	−25.0479	+	43.3843i	−0.887244	+	1.53675i	−0.0441234	+	0.999026i	$0.514049\pi$
$797$	−25.0479	+	43.3843i	−0.887244	+	1.53675i	−0.843120	+	0.537725i	$0.819284\pi$
$798$	1.52851	+	1.04277i	0.0541088	+	0.0369138i
$799$	5.00800	+	18.6901i	0.177170	+	0.661209i
$800$	−1.18654	+	4.42823i	−0.0419506	+	0.156562i
$801$	5.23893	+	1.40377i	0.185109	+	0.0495997i
$802$	−8.42549			−0.297515
$803$	0.171811			0.00606308
$804$	−0.273642	−	0.0733222i	−0.00965061	−	0.00258587i
$805$	9.46533	+	3.31515i	0.333609	+	0.116844i
$806$	1.21363	−	6.86358i	0.0427481	−	0.241759i
$807$	−6.00374	+	10.3988i	−0.211342	+	0.366055i
$808$	12.6346	−	3.38542i	0.444483	−	0.119099i
$809$	−7.45613	+	12.9144i	−0.262143	+	0.454046i	−0.966811	−	0.255492i	$-0.917763\pi$
$809$	−7.45613	+	12.9144i	−0.262143	+	0.454046i	0.704668	+	0.709537i	$0.251096\pi$
$810$	0.322318	+	0.558272i	0.0113251	+	0.0196157i
$811$	20.0144	+	20.0144i	0.702802	+	0.702802i	0.965011	−	0.262209i	$-0.0844510\pi$
$811$	20.0144	+	20.0144i	0.702802	+	0.702802i	−0.262209	+	0.965011i	$0.584451\pi$
$812$	1.58778	−	21.1051i	0.0557200	−	0.740645i
$813$	−20.4352	+	5.47560i	−0.716694	+	0.192038i
$814$	2.15379	−	0.577108i	0.0754905	−	0.0202276i
$815$			8.68902i			0.304363i
$816$	4.03659	+	2.33053i	0.141309	+	0.0815848i
$817$	−3.28547	+	3.28547i	−0.114944	+	0.114944i
$818$	22.4194			0.783877
$819$	−6.82381	−	6.66601i	−0.238443	−	0.232929i
$820$	−7.84511			−0.273963
$821$	33.3684	−	33.3684i	1.16456	−	1.16456i	0.181100	−	0.983465i	$-0.442034\pi$
$821$	33.3684	−	33.3684i	1.16456	−	1.16456i	0.983465	−	0.181100i	$-0.0579659\pi$
$822$	−13.8220	−	7.98013i	−0.482097	−	0.278339i
$823$		−	47.3640i		−	1.65100i	−0.564399	−	0.825502i	$-0.690892\pi$
$823$		−	47.3640i		−	1.65100i	0.564399	−	0.825502i	$-0.309108\pi$
$824$	−11.6055	+	3.10970i	−0.404298	+	0.108331i
$825$	0.859990	−	0.230434i	0.0299410	−	0.00802267i
$826$	8.41485	+	5.74073i	0.292790	+	0.199745i
$827$	−3.14751	−	3.14751i	−0.109450	−	0.109450i	0.650261	−	0.759711i	$-0.274659\pi$
$827$	−3.14751	−	3.14751i	−0.109450	−	0.109450i	−0.759711	+	0.650261i	$0.774659\pi$
$828$	2.94013	+	5.09246i	0.102177	+	0.176975i
$829$	19.3840	−	33.5741i	0.673235	−	1.16608i	−0.303746	−	0.952753i	$-0.598237\pi$
$829$	19.3840	−	33.5741i	0.673235	−	1.16608i	0.976981	−	0.213325i	$-0.0684293\pi$
$830$	3.33762	−	0.894312i	0.115850	−	0.0310420i
$831$	9.34767	−	16.1906i	0.324267	−	0.561647i
$832$	−2.31893	+	2.76090i	−0.0803943	+	0.0957170i
$833$	11.9025	+	30.3789i	0.412396	+	1.05257i
$834$	−16.7223	−	4.48072i	−0.579045	−	0.155155i
$835$	−6.56906			−0.227332
$836$	−0.135820			−0.00469743
$837$	−1.86727	−	0.500334i	−0.0645424	−	0.0172941i
$838$	5.19589	−	19.3913i	0.179489	−	0.669862i
$839$	1.52601	+	5.69516i	0.0526838	+	0.196619i	0.987252	−	0.159166i	$-0.0508804\pi$
$839$	1.52601	+	5.69516i	0.0526838	+	0.196619i	−0.934568	+	0.355784i	$0.884214\pi$
$840$	1.70074	+	0.127950i	0.0586812	+	0.00441469i
$841$	−17.4963	+	30.3045i	−0.603321	+	1.04498i
$842$			8.28460i			0.285506i
$843$	−6.88524	−	25.6961i	−0.237140	−	0.885019i
$844$	18.7132	−	10.8041i	0.644135	−	0.371892i
$845$	−3.53438	−	7.59850i	−0.121586	−	0.261396i
$846$			4.15130i			0.142725i
$847$	2.17583	−	28.9217i	0.0747625	−	0.993763i
$848$	6.01682	+	10.4214i	0.206618	+	0.357873i
$849$	−12.6447	+	7.30041i	−0.433965	+	0.250550i
$850$	−5.53053	+	20.6402i	−0.189696	+	0.707954i
$851$	−47.7397	+	47.7397i	−1.63650	+	1.63650i
$852$	8.74517	+	2.34326i	0.299605	+	0.0802788i
$853$	32.7838	−	32.7838i	1.12250	−	1.12250i	0.131130	−	0.991365i	$-0.458139\pi$
$853$	32.7838	−	32.7838i	1.12250	−	1.12250i	0.991365	−	0.131130i	$-0.0418606\pi$
$854$	−7.04131	−	8.18696i	−0.240949	−	0.280152i
$855$	0.390433	−	0.225417i	0.0133525	−	0.00770909i
$856$	5.88409	+	5.88409i	0.201114	+	0.201114i
$857$	1.36374	+	2.36206i	0.0465844	+	0.0806865i	0.888377	−	0.459114i	$-0.151833\pi$
$857$	1.36374	+	2.36206i	0.0465844	+	0.0806865i	−0.841793	+	0.539800i	$0.818500\pi$
$858$	0.689524	+	0.121922i	0.0235400	+	0.00416236i
$859$	16.6381	+	9.60599i	0.567683	+	0.327752i	0.756223	−	0.654313i	$-0.227042\pi$
$859$	16.6381	+	9.60599i	0.567683	+	0.327752i	−0.188540	+	0.982065i	$0.560376\pi$
$860$	−1.10847	+	4.13685i	−0.0377984	+	0.141065i
$861$	−5.97685	−	31.6387i	−0.203691	−	1.07824i
$862$	−17.1324	−	9.89142i	−0.583533	−	0.336903i
$863$	−1.85333	−	6.91673i	−0.0630881	−	0.235448i	0.927181	−	0.374614i	$-0.122225\pi$
$863$	−1.85333	−	6.91673i	−0.0630881	−	0.235448i	−0.990269	+	0.139166i	$0.955558\pi$
$864$	0.707107	+	0.707107i	0.0240563	+	0.0240563i
$865$	−4.47313	−	4.47313i	−0.152091	−	0.152091i
$866$	0.805211	+	3.00509i	0.0273622	+	0.102117i
$867$	4.09234	+	2.36272i	0.138983	+	0.0802421i
$868$	−3.87770	+	3.33507i	−0.131618	+	0.113200i
$869$	−0.699558	+	2.61079i	−0.0237309	+	0.0885649i
$870$	−4.46592	−	2.57840i	−0.151409	−	0.0874159i
$871$	0.432121	−	0.925527i	0.0146419	−	0.0313603i
$872$	0.171090	+	0.296336i	0.00579383	+	0.0100352i
$873$	4.79165	+	4.79165i	0.162173	+	0.162173i
$874$	3.56147	−	2.05621i	0.120468	−	0.0695524i
$875$	3.03438	+	16.0626i	0.102581	+	0.543016i
$876$	−0.625566	+	0.625566i	−0.0211359	+	0.0211359i
$877$	2.84031	+	0.761059i	0.0959105	+	0.0256991i	0.306455	−	0.951885i	$-0.400857\pi$
$877$	2.84031	+	0.761059i	0.0959105	+	0.0256991i	−0.210545	+	0.977584i	$0.567524\pi$
$878$	−17.0999	+	17.0999i	−0.577095	+	0.577095i
$879$	−7.21239	+	26.9170i	−0.243268	+	0.907888i
$880$	−0.108420	+	0.0625962i	−0.00365483	+	0.00211012i
$881$	−29.3876	−	50.9008i	−0.990093	−	1.71489i	−0.616647	−	0.787240i	$-0.711509\pi$
$881$	−29.3876	−	50.9008i	−0.990093	−	1.71489i	−0.373447	−	0.927652i	$-0.621824\pi$
$882$	0.779711	+	6.95644i	0.0262542	+	0.234236i
$883$			36.4558i			1.22684i	0.789759	+	0.613418i	$0.210206\pi$
$883$			36.4558i			1.22684i	−0.789759	+	0.613418i	$0.789794\pi$
$884$	−10.8086	+	12.8687i	−0.363534	+	0.432822i
$885$	2.14943	−	1.24097i	0.0722523	−	0.0417149i
$886$	−1.83450	−	6.84645i	−0.0616313	−	0.230011i
$887$		−	31.3849i		−	1.05380i	−0.849927	−	0.526900i	$-0.823354\pi$
$887$		−	31.3849i		−	1.05380i	0.849927	−	0.526900i	$-0.176646\pi$
$888$	−5.74074	+	9.94325i	−0.192647	+	0.333674i
$889$	−4.12712	+	54.8588i	−0.138419	+	1.83990i
$890$	−0.904921	−	3.37721i	−0.0303330	−	0.113204i
$891$	0.0502642	−	0.187589i	0.00168392	−	0.00628446i
$892$	12.0930	+	3.24031i	0.404903	+	0.108493i
$893$	2.90325			0.0971537
$894$	1.86065			0.0622294
$895$	2.84255	+	0.761659i	0.0950160	+	0.0254595i
$896$	2.59977	−	0.491121i	0.0868522	−	0.0164072i
$897$	−19.9265	+	7.24183i	−0.665326	+	0.241798i
$898$	−2.79628	+	4.84331i	−0.0933132	+	0.161623i
$899$	14.9373	−	4.00244i	0.498187	−	0.133489i
$900$	−2.29222	+	3.97024i	−0.0764074	+	0.132341i
$901$	28.0447	+	48.5749i	0.934305	+	1.61826i
$902$	1.67121	+	1.67121i	0.0556453	+	0.0556453i
$903$	−17.5281	−	1.31867i	−0.583298	−	0.0438825i
$904$	9.26914	−	2.48366i	0.308287	−	0.0826053i
$905$	8.09140	−	2.16808i	0.268967	−	0.0720695i
$906$			19.7077i			0.654745i
$907$	43.2767	+	24.9858i	1.43698	+	0.829641i	0.997639	−	0.0686797i	$-0.0218786\pi$
$907$	43.2767	+	24.9858i	1.43698	+	0.829641i	0.439341	+	0.898320i	$0.355212\pi$
$908$	17.2746	−	17.2746i	0.573279	−	0.573279i
$909$	13.0803			0.433845
$910$	−1.52201	+	5.95812i	−0.0504540	+	0.197510i
$911$	14.0084			0.464120			0.232060	−	0.972702i	$-0.425453\pi$
$911$	14.0084			0.464120			0.232060	+	0.972702i	$0.425453\pi$
$912$	0.494522	−	0.494522i	0.0163753	−	0.0163753i
$913$	−0.901511	−	0.520488i	−0.0298357	−	0.0172256i
$914$			17.2247i			0.569742i
$915$	−2.54139	+	0.680963i	−0.0840157	+	0.0225119i
$916$	−18.3106	+	4.90630i	−0.604998	+	0.162109i
$917$	−17.6055	+	8.47208i	−0.581386	+	0.279773i
$918$	3.29586	+	3.29586i	0.108780	+	0.108780i
$919$	−12.7871	−	22.1478i	−0.421806	−	0.730590i	0.574310	−	0.818638i	$-0.305270\pi$
$919$	−12.7871	−	22.1478i	−0.421806	−	0.730590i	−0.996116	+	0.0880479i	$0.971937\pi$
$920$	1.89532	−	3.28279i	0.0624868	−	0.108230i
$921$	−1.94407	+	0.520913i	−0.0640594	+	0.0171647i
$922$	1.03510	−	1.79285i	0.0340893	−	0.0590445i
$923$	−13.8099	+	29.5784i	−0.454559	+	0.973586i
$924$	−0.335046	−	0.389559i	−0.0110222	−	0.0128156i
$925$	−50.8426	−	13.6232i	−1.67170	−	0.447929i
$926$	−0.492897			−0.0161976
$927$	−12.0149			−0.394622
$928$	−7.72696	−	2.07043i	−0.253650	−	0.0679653i
$929$	8.87430	−	33.1193i	0.291156	−	1.08661i	−0.653066	−	0.757301i	$-0.726518\pi$
$929$	8.87430	−	33.1193i	0.291156	−	1.08661i	0.944222	−	0.329309i	$-0.106816\pi$
$930$	0.322534	+	1.20371i	0.0105763	+	0.0394713i
$931$	4.86506	−	0.545298i	0.159446	−	0.0178714i
$932$	−1.89226	+	3.27750i	−0.0619832	+	0.107358i
$933$			11.0157i			0.360638i
$934$	4.26124	+	15.9032i	0.139432	+	0.520368i
$935$	−0.505351	+	0.291764i	−0.0165267	+	0.00954171i
$936$	−2.95449	+	2.06664i	−0.0965704	+	0.0675504i
$937$		−	32.4063i		−	1.05867i	−0.848414	−	0.529333i	$-0.822442\pi$
$937$		−	32.4063i		−	1.05867i	0.848414	−	0.529333i	$-0.177558\pi$
$938$	−0.675396	+	0.325012i	−0.0220525	+	0.0106120i
$939$	−2.92435	−	5.06512i	−0.0954326	−	0.165294i
$940$	2.31755	−	1.33804i	0.0755903	−	0.0436421i
$941$	−5.68046	+	21.1998i	−0.185178	+	0.691093i	0.809415	+	0.587238i	$0.199785\pi$
$941$	−5.68046	+	21.1998i	−0.185178	+	0.691093i	−0.994592	+	0.103855i	$0.966882\pi$
$942$	5.03014	−	5.03014i	0.163891	−	0.163891i
$943$	−69.1234	−	18.5216i	−2.25097	−	0.603145i
$944$	2.72247	−	2.72247i	0.0886087	−	0.0886087i
$945$	1.60968	+	0.563775i	0.0523627	+	0.0183396i
$946$	1.11739	−	0.645125i	0.0363295	−	0.0209748i
$947$	24.5587	+	24.5587i	0.798049	+	0.798049i	0.982788	−	0.184739i	$-0.0591439\pi$
$947$	24.5587	+	24.5587i	0.798049	+	0.798049i	−0.184739	+	0.982788i	$0.559144\pi$
$948$	−6.95881	−	12.0530i	−0.226012	−	0.391464i
$949$	−1.82833	−	2.61379i	−0.0593500	−	0.0848471i
$950$	2.77663	+	1.60309i	0.0900858	+	0.0520111i
$951$	4.74204	−	17.6975i	0.153771	−	0.573882i
$952$	12.1177	−	2.28914i	0.392736	−	0.0741915i
$953$	−20.1372	−	11.6262i	−0.652308	−	0.376610i	0.137032	−	0.990567i	$-0.456244\pi$
$953$	−20.1372	−	11.6262i	−0.652308	−	0.376610i	−0.789340	+	0.613957i	$0.789577\pi$
$954$	3.11453	+	11.6236i	0.100837	+	0.376328i
$955$	0.425511	+	0.425511i	0.0137692	+	0.0137692i
$956$	−11.3575	−	11.3575i	−0.367328	−	0.367328i
$957$	0.402091	+	1.50062i	0.0129977	+	0.0485082i
$958$	−11.7482	−	6.78280i	−0.379566	−	0.219142i
$959$	−41.4930	+	7.83841i	−1.33988	+	0.253116i
$960$	0.166844	−	0.622671i	0.00538488	−	0.0200966i
$961$	23.6104	+	13.6315i	0.761626	+	0.439725i
$962$	−31.6992	−	26.6247i	−1.02202	−	0.858415i
$963$	4.16068	+	7.20651i	0.134076	+	0.232227i
$964$	18.1792	+	18.1792i	0.585511	+	0.585511i
$965$	1.25904	−	0.726907i	0.0405299	−	0.0233999i
$966$	14.6832	+	5.14266i	0.472424	+	0.165462i
$967$	36.7896	−	36.7896i	1.18307	−	1.18307i	0.204130	−	0.978944i	$-0.434563\pi$
$967$	36.7896	−	36.7896i	1.18307	−	1.18307i	0.978944	−	0.204130i	$-0.0654366\pi$
$968$	−10.5888	−	2.83725i	−0.340335	−	0.0911926i
$969$	2.30500	−	2.30500i	0.0740471	−	0.0740471i
$970$	1.13061	−	4.21948i	0.0363016	−	0.135479i
$971$	−29.7072	+	17.1515i	−0.953350	+	0.550417i	−0.894120	−	0.447827i	$-0.852198\pi$
$971$	−29.7072	+	17.1515i	−0.953350	+	0.550417i	−0.0592304	+	0.998244i	$0.518865\pi$
$972$	0.500000	+	0.866025i	0.0160375	+	0.0277778i
$973$	−41.2734	+	19.8615i	−1.32317	+	0.636730i
$974$			20.3897i			0.653329i
$975$	−12.6572	−	10.6310i	−0.405355	−	0.340464i
$976$	−3.53462	+	2.04071i	−0.113140	+	0.0653217i
$977$	−3.26882	−	12.1994i	−0.104579	−	0.390294i	0.893718	−	0.448629i	$-0.148088\pi$
$977$	−3.26882	−	12.1994i	−0.104579	−	0.390294i	−0.998297	+	0.0583350i	$0.981421\pi$
$978$			13.4789i			0.431009i
$979$	−0.526662	+	0.912205i	−0.0168322	+	0.0291542i
$980$	3.63227	−	2.67748i	0.116029	−	0.0855289i
$981$	0.0885625	+	0.330520i	0.00282758	+	0.0105527i
$982$	0.184231	−	0.687560i	0.00587905	−	0.0219409i
$983$	0.954990	+	0.255889i	0.0304595	+	0.00816159i	0.274017	−	0.961725i	$-0.411648\pi$
$983$	0.954990	+	0.255889i	0.0304595	+	0.00816159i	−0.243557	+	0.969887i	$0.578314\pi$
$984$	−12.1698			−0.387960
$985$	12.8053			0.408011
$986$	−36.0158	−	9.65040i	−1.14698	−	0.307331i
$987$	7.16186	+	8.32712i	0.227964	+	0.265055i
$988$	1.44533	+	2.06625i	0.0459820	+	0.0657361i
$989$	−19.5334	+	33.8329i	−0.621127	+	1.07582i
$990$	−0.120927	+	0.0324022i	−0.00384330	+	0.00102981i
$991$	22.8043	−	39.4982i	0.724402	−	1.25470i	−0.234817	−	0.972040i	$-0.575449\pi$
$991$	22.8043	−	39.4982i	0.724402	−	1.25470i	0.959220	−	0.282662i	$-0.0912176\pi$
$992$	0.966572	+	1.67415i	0.0306887	+	0.0531544i
$993$	−11.5985	−	11.5985i	−0.368067	−	0.368067i
$994$	21.5846	−	10.3869i	0.684622	−	0.329452i
$995$	3.23229	−	0.866089i	0.102470	−	0.0274569i
$996$	5.17752	−	1.38731i	0.164056	−	0.0439587i
$997$		−	33.2657i		−	1.05354i	−0.850009	−	0.526768i	$-0.823404\pi$
$997$		−	33.2657i		−	1.05354i	0.850009	−	0.526768i	$-0.176596\pi$
$998$	9.07512	+	5.23952i	0.287268	+	0.165854i
$999$	−8.11863	+	8.11863i	−0.256862	+	0.256862i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.cg.a.145.2	yes	32
7.3	odd	6		546.2.by.a.535.2	yes	32
13.7	odd	12		546.2.by.a.397.2	✓	32
91.59	even	12	inner	546.2.cg.a.241.2	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.by.a.397.2	✓	32	13.7	odd	12
546.2.by.a.535.2	yes	32	7.3	odd	6
546.2.cg.a.145.2	yes	32	1.1	even	1	trivial
546.2.cg.a.241.2	yes	32	91.59	even	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.cg (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(0.866025 + 0.500000i) q^{3} -1.00000i q^{4} +(-0.622671 + 0.166844i) q^{5} +(-0.965926 + 0.258819i) q^{6} +(-1.49104 + 2.18559i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(0.866025 + 0.500000i) q^{3} -1.00000i q^{4} +(-0.622671 + 0.166844i) q^{5} +(-0.965926 + 0.258819i) q^{6} +(-1.49104 + 2.18559i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +(0.322318 - 0.558272i) q^{10} +(-0.187589 + 0.0502642i) q^{11} +(0.500000 - 0.866025i) q^{12} +(2.76090 + 2.31893i) q^{13} +(-0.491121 - 2.59977i) q^{14} +(-0.622671 - 0.166844i) q^{15} -1.00000 q^{16} -4.66105 q^{17} +(-0.965926 - 0.258819i) q^{18} +(-0.181008 + 0.675530i) q^{19} +(0.166844 + 0.622671i) q^{20} +(-2.38407 + 1.14726i) q^{21} +(0.0971030 - 0.168187i) q^{22} +5.88027i q^{23} +(0.258819 + 0.965926i) q^{24} +(-3.97024 + 2.29222i) q^{25} +(-3.59198 + 0.312523i) q^{26} +1.00000i q^{27} +(2.18559 + 1.49104i) q^{28} +(-3.99977 - 6.92780i) q^{29} +(0.558272 - 0.322318i) q^{30} +(-0.500334 + 1.86727i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-0.187589 - 0.0502642i) q^{33} +(3.29586 - 3.29586i) q^{34} +(0.563775 - 1.60968i) q^{35} +(0.866025 - 0.500000i) q^{36} +(8.11863 + 8.11863i) q^{37} +(-0.349680 - 0.605664i) q^{38} +(1.23155 + 3.38870i) q^{39} +(-0.558272 - 0.322318i) q^{40} +(-3.14978 + 11.7551i) q^{41} +(0.874562 - 2.49703i) q^{42} +(5.75363 + 3.32186i) q^{43} +(0.0502642 + 0.187589i) q^{44} +(-0.455827 - 0.455827i) q^{45} +(-4.15798 - 4.15798i) q^{46} +(-1.07444 - 4.00985i) q^{47} +(-0.866025 - 0.500000i) q^{48} +(-2.55360 - 6.51760i) q^{49} +(1.18654 - 4.42823i) q^{50} +(-4.03659 - 2.33053i) q^{51} +(2.31893 - 2.76090i) q^{52} +(-6.01682 - 10.4214i) q^{53} +(-0.707107 - 0.707107i) q^{54} +(0.108420 - 0.0625962i) q^{55} +(-2.59977 + 0.491121i) q^{56} +(-0.494522 + 0.494522i) q^{57} +(7.72696 + 2.07043i) q^{58} +(-2.72247 + 2.72247i) q^{59} +(-0.166844 + 0.622671i) q^{60} +(3.53462 - 2.04071i) q^{61} +(-0.966572 - 1.67415i) q^{62} +(-2.63830 - 0.198484i) q^{63} +1.00000i q^{64} +(-2.10603 - 0.983289i) q^{65} +(0.168187 - 0.0971030i) q^{66} +(-0.0733222 - 0.273642i) q^{67} +4.66105i q^{68} +(-2.94013 + 5.09246i) q^{69} +(0.739564 + 1.53686i) q^{70} +(2.34326 + 8.74517i) q^{71} +(-0.258819 + 0.965926i) q^{72} +(-0.854539 - 0.228973i) q^{73} -11.4815 q^{74} -4.58444 q^{75} +(0.675530 + 0.181008i) q^{76} +(0.169845 - 0.484938i) q^{77} +(-3.26701 - 1.52534i) q^{78} +(6.95881 - 12.0530i) q^{79} +(0.622671 - 0.166844i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-6.08491 - 10.5394i) q^{82} +(3.79021 + 3.79021i) q^{83} +(1.14726 + 2.38407i) q^{84} +(2.90231 - 0.777670i) q^{85} +(-6.41734 + 1.71952i) q^{86} -7.99954i q^{87} +(-0.168187 - 0.0971030i) q^{88} +(3.83517 - 3.83517i) q^{89} +0.644637 q^{90} +(-9.18484 + 2.57658i) q^{91} +5.88027 q^{92} +(-1.36694 + 1.36694i) q^{93} +(3.59513 + 2.07565i) q^{94} -0.450833i q^{95} +(0.965926 - 0.258819i) q^{96} +(6.54551 - 1.75386i) q^{97} +(6.41431 + 2.80297i) q^{98} +(-0.137324 - 0.137324i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 4 q^{7} + 16 q^{9}+O(q^{10}) \) 32 * q - 4 * q^7 + 16 * q^9	\( 32 q - 4 q^{7} + 16 q^{9} + 8 q^{11} + 16 q^{12} + 4 q^{14} - 32 q^{16} - 16 q^{17} + 24 q^{19} + 8 q^{21} - 4 q^{22} + 24 q^{25} - 8 q^{26} + 8 q^{28} - 12 q^{29} + 4 q^{31} + 8 q^{33} + 8 q^{34} + 40 q^{35} - 12 q^{37} - 8 q^{38} + 28 q^{39} + 28 q^{41} - 12 q^{42} + 84 q^{43} - 4 q^{44} - 40 q^{46} - 4 q^{47} - 36 q^{49} - 16 q^{50} - 20 q^{52} - 4 q^{53} - 48 q^{55} + 12 q^{56} + 12 q^{57} + 12 q^{58} - 24 q^{59} - 36 q^{61} + 40 q^{62} + 4 q^{63} + 44 q^{65} - 16 q^{67} + 8 q^{69} + 40 q^{70} + 20 q^{71} - 16 q^{73} - 40 q^{74} + 16 q^{75} - 36 q^{76} + 12 q^{77} - 20 q^{78} - 16 q^{81} - 24 q^{82} - 12 q^{83} - 8 q^{84} - 4 q^{85} - 20 q^{86} - 60 q^{89} - 48 q^{91} - 16 q^{92} - 32 q^{93} - 76 q^{97} - 8 q^{98} + 4 q^{99}+O(q^{100}) \) 32 * q - 4 * q^7 + 16 * q^9 + 8 * q^11 + 16 * q^12 + 4 * q^14 - 32 * q^16 - 16 * q^17 + 24 * q^19 + 8 * q^21 - 4 * q^22 + 24 * q^25 - 8 * q^26 + 8 * q^28 - 12 * q^29 + 4 * q^31 + 8 * q^33 + 8 * q^34 + 40 * q^35 - 12 * q^37 - 8 * q^38 + 28 * q^39 + 28 * q^41 - 12 * q^42 + 84 * q^43 - 4 * q^44 - 40 * q^46 - 4 * q^47 - 36 * q^49 - 16 * q^50 - 20 * q^52 - 4 * q^53 - 48 * q^55 + 12 * q^56 + 12 * q^57 + 12 * q^58 - 24 * q^59 - 36 * q^61 + 40 * q^62 + 4 * q^63 + 44 * q^65 - 16 * q^67 + 8 * q^69 + 40 * q^70 + 20 * q^71 - 16 * q^73 - 40 * q^74 + 16 * q^75 - 36 * q^76 + 12 * q^77 - 20 * q^78 - 16 * q^81 - 24 * q^82 - 12 * q^83 - 8 * q^84 - 4 * q^85 - 20 * q^86 - 60 * q^89 - 48 * q^91 - 16 * q^92 - 32 * q^93 - 76 * q^97 - 8 * q^98 + 4 * q^99

Introduction

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