LMFDB - Embedded newform 930.2.k.a.433.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(247,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 2]))

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

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

chi := DirichletCharacter("930.247");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.k (of order $4$, degree $2$, 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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			433.3
Character	$\chi$	$=$	930.433
Dual form			930.2.k.a.247.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(0.707107 - 0.707107i) q^{3} -1.00000i q^{4} +(-1.64980 + 1.50935i) q^{5} +1.00000i q^{6} +(2.19620 - 2.19620i) q^{7} +(0.707107 + 0.707107i) q^{8} -1.00000i q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(0.707107 - 0.707107i) q^{3} -1.00000i q^{4} +(-1.64980 + 1.50935i) q^{5} +1.00000i q^{6} +(2.19620 - 2.19620i) q^{7} +(0.707107 + 0.707107i) q^{8} -1.00000i q^{9} +(0.0993121 - 2.23386i) q^{10} -2.28592i q^{11} +(-0.707107 - 0.707107i) q^{12} +(-0.645595 + 0.645595i) q^{13} +3.10590i q^{14} +(-0.0993121 + 2.23386i) q^{15} -1.00000 q^{16} +(-1.02878 - 1.02878i) q^{17} +(0.707107 + 0.707107i) q^{18} -2.57080i q^{19} +(1.50935 + 1.64980i) q^{20} -3.10590i q^{21} +(1.61639 + 1.61639i) q^{22} +(-0.646450 + 0.646450i) q^{23} +1.00000 q^{24} +(0.443699 - 4.98027i) q^{25} -0.913009i q^{26} +(-0.707107 - 0.707107i) q^{27} +(-2.19620 - 2.19620i) q^{28} -6.94624 q^{29} +(-1.50935 - 1.64980i) q^{30} +(5.39846 - 1.36258i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-1.61639 - 1.61639i) q^{33} +1.45491 q^{34} +(-0.308453 + 6.93814i) q^{35} -1.00000 q^{36} +(-5.23746 - 5.23746i) q^{37} +(1.81783 + 1.81783i) q^{38} +0.913009i q^{39} +(-2.23386 - 0.0993121i) q^{40} +4.11753 q^{41} +(2.19620 + 2.19620i) q^{42} +(7.37606 - 7.37606i) q^{43} -2.28592 q^{44} +(1.50935 + 1.64980i) q^{45} -0.914219i q^{46} +(-2.53354 + 2.53354i) q^{47} +(-0.707107 + 0.707107i) q^{48} -2.64659i q^{49} +(3.20784 + 3.83533i) q^{50} -1.45491 q^{51} +(0.645595 + 0.645595i) q^{52} +(8.61614 - 8.61614i) q^{53} +1.00000 q^{54} +(3.45026 + 3.77131i) q^{55} +3.10590 q^{56} +(-1.81783 - 1.81783i) q^{57} +(4.91173 - 4.91173i) q^{58} -1.51768i q^{59} +(2.23386 + 0.0993121i) q^{60} -7.53156i q^{61} +(-2.85380 + 4.78078i) q^{62} +(-2.19620 - 2.19620i) q^{63} +1.00000i q^{64} +(0.0906728 - 2.03954i) q^{65} +2.28592 q^{66} +(-0.158559 + 0.158559i) q^{67} +(-1.02878 + 1.02878i) q^{68} +0.914219i q^{69} +(-4.68790 - 5.12412i) q^{70} +3.65076 q^{71} +(0.707107 - 0.707107i) q^{72} +(1.99695 - 1.99695i) q^{73} +7.40689 q^{74} +(-3.20784 - 3.83533i) q^{75} -2.57080 q^{76} +(-5.02033 - 5.02033i) q^{77} +(-0.645595 - 0.645595i) q^{78} -12.7157 q^{79} +(1.64980 - 1.50935i) q^{80} -1.00000 q^{81} +(-2.91153 + 2.91153i) q^{82} +(7.17507 - 7.17507i) q^{83} -3.10590 q^{84} +(3.25007 + 0.144490i) q^{85} +10.4313i q^{86} +(-4.91173 + 4.91173i) q^{87} +(1.61639 - 1.61639i) q^{88} -10.1718 q^{89} +(-2.23386 - 0.0993121i) q^{90} +2.83571i q^{91} +(0.646450 + 0.646450i) q^{92} +(2.85380 - 4.78078i) q^{93} -3.58297i q^{94} +(3.88026 + 4.24132i) q^{95} -1.00000i q^{96} +(-4.14245 + 4.14245i) q^{97} +(1.87142 + 1.87142i) q^{98} -2.28592 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 4 q^{7}+O(q^{10}) $ 32 * q - 4 * q^7	$ 32 q - 4 q^{7} + 4 q^{10} - 4 q^{15} - 32 q^{16} - 8 q^{17} + 4 q^{22} + 32 q^{24} + 8 q^{25} + 4 q^{28} - 8 q^{29} - 20 q^{31} - 4 q^{33} - 24 q^{35} - 32 q^{36} - 4 q^{37} + 16 q^{38} - 16 q^{41} - 4 q^{42} + 16 q^{43} + 8 q^{44} - 8 q^{47} - 16 q^{50} + 24 q^{53} + 32 q^{54} + 28 q^{55} - 16 q^{57} - 20 q^{58} + 16 q^{62} + 4 q^{63} - 56 q^{65} - 8 q^{66} + 32 q^{67} - 8 q^{68} - 28 q^{70} + 16 q^{71} + 20 q^{73} - 24 q^{74} + 16 q^{75} - 16 q^{76} + 40 q^{77} + 56 q^{79} - 32 q^{81} + 16 q^{82} - 72 q^{83} + 32 q^{85} + 20 q^{87} + 4 q^{88} + 64 q^{89} - 16 q^{93} + 32 q^{95} - 4 q^{97} + 16 q^{98} + 8 q^{99}+O(q^{100}) $ 32 * q - 4 * q^7 + 4 * q^10 - 4 * q^15 - 32 * q^16 - 8 * q^17 + 4 * q^22 + 32 * q^24 + 8 * q^25 + 4 * q^28 - 8 * q^29 - 20 * q^31 - 4 * q^33 - 24 * q^35 - 32 * q^36 - 4 * q^37 + 16 * q^38 - 16 * q^41 - 4 * q^42 + 16 * q^43 + 8 * q^44 - 8 * q^47 - 16 * q^50 + 24 * q^53 + 32 * q^54 + 28 * q^55 - 16 * q^57 - 20 * q^58 + 16 * q^62 + 4 * q^63 - 56 * q^65 - 8 * q^66 + 32 * q^67 - 8 * q^68 - 28 * q^70 + 16 * q^71 + 20 * q^73 - 24 * q^74 + 16 * q^75 - 16 * q^76 + 40 * q^77 + 56 * q^79 - 32 * q^81 + 16 * q^82 - 72 * q^83 + 32 * q^85 + 20 * q^87 + 4 * q^88 + 64 * q^89 - 16 * q^93 + 32 * q^95 - 4 * q^97 + 16 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$4$		−	1.00000i		−	0.500000i
$5$	−1.64980	+	1.50935i	−0.737814	+	0.675004i
$5$	−1.64980	+	1.50935i	−0.737814	+	0.675004i
$6$			1.00000i			0.408248i
$7$	2.19620	−	2.19620i	0.830086	−	0.830086i	−0.157443	−	0.987528i	$-0.550325\pi$
$7$	2.19620	−	2.19620i	0.830086	−	0.830086i	0.987528	+	0.157443i	$0.0503249\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$		−	1.00000i		−	0.333333i
$10$	0.0993121	−	2.23386i	0.0314052	−	0.706409i
$11$		−	2.28592i		−	0.689230i	−0.938744	−	0.344615i	$-0.888009\pi$
$11$		−	2.28592i		−	0.689230i	0.938744	−	0.344615i	$-0.111991\pi$
$12$	−0.707107	−	0.707107i	−0.204124	−	0.204124i
$13$	−0.645595	+	0.645595i	−0.179056	+	0.179056i	−0.790944	−	0.611888i	$-0.790410\pi$
$13$	−0.645595	+	0.645595i	−0.179056	+	0.179056i	0.611888	+	0.790944i	$0.290410\pi$
$14$			3.10590i			0.830086i
$15$	−0.0993121	+	2.23386i	−0.0256423	+	0.576781i
$16$	−1.00000			−0.250000
$17$	−1.02878	−	1.02878i	−0.249515	−	0.249515i	0.571257	−	0.820772i	$-0.306456\pi$
$17$	−1.02878	−	1.02878i	−0.249515	−	0.249515i	−0.820772	+	0.571257i	$0.806456\pi$
$18$	0.707107	+	0.707107i	0.166667	+	0.166667i
$19$		−	2.57080i		−	0.589783i	−0.955531	−	0.294892i	$-0.904716\pi$
$19$		−	2.57080i		−	0.589783i	0.955531	−	0.294892i	$-0.0952835\pi$
$20$	1.50935	+	1.64980i	0.337502	+	0.368907i
$21$		−	3.10590i		−	0.677762i
$22$	1.61639	+	1.61639i	0.344615	+	0.344615i
$23$	−0.646450	+	0.646450i	−0.134794	+	0.134794i	−0.771285	−	0.636490i	$-0.780385\pi$
$23$	−0.646450	+	0.646450i	−0.134794	+	0.134794i	0.636490	+	0.771285i	$0.280385\pi$
$24$	1.00000			0.204124
$25$	0.443699	−	4.98027i	0.0887398	−	0.996055i
$26$		−	0.913009i		−	0.179056i
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$	−2.19620	−	2.19620i	−0.415043	−	0.415043i
$29$	−6.94624			−1.28988			−0.644942	−	0.764231i	$-0.723119\pi$
$29$	−6.94624			−1.28988			−0.644942	+	0.764231i	$0.723119\pi$
$30$	−1.50935	−	1.64980i	−0.275569	−	0.301211i
$31$	5.39846	−	1.36258i	0.969592	−	0.244727i
$31$	5.39846	−	1.36258i	0.969592	−	0.244727i
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	−1.61639	−	1.61639i	−0.281377	−	0.281377i
$34$	1.45491			0.249515
$35$	−0.308453	+	6.93814i	−0.0521381	+	1.17276i
$36$	−1.00000			−0.166667
$37$	−5.23746	−	5.23746i	−0.861033	−	0.861033i	0.130425	−	0.991458i	$-0.458366\pi$
$37$	−5.23746	−	5.23746i	−0.861033	−	0.861033i	−0.991458	+	0.130425i	$0.958366\pi$
$38$	1.81783	+	1.81783i	0.294892	+	0.294892i
$39$			0.913009i			0.146198i
$40$	−2.23386	−	0.0993121i	−0.353205	−	0.0157026i
$41$	4.11753			0.643050			0.321525	−	0.946901i	$-0.395805\pi$
$41$	4.11753			0.643050			0.321525	+	0.946901i	$0.395805\pi$
$42$	2.19620	+	2.19620i	0.338881	+	0.338881i
$43$	7.37606	−	7.37606i	1.12484	−	1.12484i	0.133834	−	0.991004i	$-0.457271\pi$
$43$	7.37606	−	7.37606i	1.12484	−	1.12484i	0.991004	−	0.133834i	$-0.0427290\pi$
$44$	−2.28592			−0.344615
$45$	1.50935	+	1.64980i	0.225001	+	0.245938i
$46$		−	0.914219i		−	0.134794i
$47$	−2.53354	+	2.53354i	−0.369555	+	0.369555i	−0.867315	−	0.497760i	$-0.834156\pi$
$47$	−2.53354	+	2.53354i	−0.369555	+	0.369555i	0.497760	+	0.867315i	$0.334156\pi$
$48$	−0.707107	+	0.707107i	−0.102062	+	0.102062i
$49$		−	2.64659i		−	0.378084i
$50$	3.20784	+	3.83533i	0.453658	+	0.542397i
$51$	−1.45491			−0.203728
$52$	0.645595	+	0.645595i	0.0895279	+	0.0895279i
$53$	8.61614	−	8.61614i	1.18352	−	1.18352i	0.204692	−	0.978826i	$-0.434381\pi$
$53$	8.61614	−	8.61614i	1.18352	−	1.18352i	0.978826	−	0.204692i	$-0.0656192\pi$
$54$	1.00000			0.136083
$55$	3.45026	+	3.77131i	0.465233	+	0.508524i
$56$	3.10590			0.415043
$57$	−1.81783	−	1.81783i	−0.240778	−	0.240778i
$58$	4.91173	−	4.91173i	0.644942	−	0.644942i
$59$		−	1.51768i		−	0.197585i	−0.995108	−	0.0987923i	$-0.968502\pi$
$59$		−	1.51768i		−	0.197585i	0.995108	−	0.0987923i	$-0.0314980\pi$
$60$	2.23386	+	0.0993121i	0.288390	+	0.0128211i
$61$		−	7.53156i		−	0.964318i	−0.876084	−	0.482159i	$-0.839853\pi$
$61$		−	7.53156i		−	0.964318i	0.876084	−	0.482159i	$-0.160147\pi$
$62$	−2.85380	+	4.78078i	−0.362433	+	0.607159i
$63$	−2.19620	−	2.19620i	−0.276695	−	0.276695i
$64$			1.00000i			0.125000i
$65$	0.0906728	−	2.03954i	0.0112466	−	0.252973i
$66$	2.28592			0.281377
$67$	−0.158559	+	0.158559i	−0.0193710	+	0.0193710i	−0.716726	−	0.697355i	$-0.754360\pi$
$67$	−0.158559	+	0.158559i	−0.0193710	+	0.0193710i	0.697355	+	0.716726i	$0.254360\pi$
$68$	−1.02878	+	1.02878i	−0.124757	+	0.124757i
$69$			0.914219i			0.110059i
$70$	−4.68790	−	5.12412i	−0.560311	−	0.612449i
$71$	3.65076			0.433265			0.216633	−	0.976253i	$-0.430493\pi$
$71$	3.65076			0.433265			0.216633	+	0.976253i	$0.430493\pi$
$72$	0.707107	−	0.707107i	0.0833333	−	0.0833333i
$73$	1.99695	−	1.99695i	0.233725	−	0.233725i	−0.580520	−	0.814246i	$-0.697151\pi$
$73$	1.99695	−	1.99695i	0.233725	−	0.233725i	0.814246	+	0.580520i	$0.197151\pi$
$74$	7.40689			0.861033
$75$	−3.20784	−	3.83533i	−0.370410	−	0.442866i
$76$	−2.57080			−0.294892
$77$	−5.02033	−	5.02033i	−0.572120	−	0.572120i
$78$	−0.645595	−	0.645595i	−0.0730992	−	0.0730992i
$79$	−12.7157			−1.43063			−0.715313	−	0.698804i	$-0.753716\pi$
$79$	−12.7157			−1.43063			−0.715313	+	0.698804i	$0.753716\pi$
$80$	1.64980	−	1.50935i	0.184454	−	0.168751i
$81$	−1.00000			−0.111111
$82$	−2.91153	+	2.91153i	−0.321525	+	0.321525i
$83$	7.17507	−	7.17507i	0.787566	−	0.787566i	−0.193529	−	0.981095i	$-0.561993\pi$
$83$	7.17507	−	7.17507i	0.787566	−	0.787566i	0.981095	+	0.193529i	$0.0619933\pi$
$84$	−3.10590			−0.338881
$85$	3.25007	+	0.144490i	0.352519	+	0.0156722i
$86$			10.4313i			1.12484i
$87$	−4.91173	+	4.91173i	−0.526593	+	0.526593i
$88$	1.61639	−	1.61639i	0.172308	−	0.172308i
$89$	−10.1718			−1.07821			−0.539103	−	0.842240i	$-0.681237\pi$
$89$	−10.1718			−1.07821			−0.539103	+	0.842240i	$0.681237\pi$
$90$	−2.23386	−	0.0993121i	−0.235470	−	0.0104684i
$91$			2.83571i			0.297263i
$92$	0.646450	+	0.646450i	0.0673971	+	0.0673971i
$93$	2.85380	−	4.78078i	0.295925	−	0.495744i
$94$		−	3.58297i		−	0.369555i
$95$	3.88026	+	4.24132i	0.398106	+	0.435150i
$96$		−	1.00000i		−	0.102062i
$97$	−4.14245	+	4.14245i	−0.420602	+	0.420602i	−0.885411	−	0.464809i	$-0.846123\pi$
$97$	−4.14245	+	4.14245i	−0.420602	+	0.420602i	0.464809	+	0.885411i	$0.346123\pi$
$98$	1.87142	+	1.87142i	0.189042	+	0.189042i
$99$	−2.28592			−0.229743
$100$	−4.98027	−	0.443699i	−0.498027	−	0.0443699i
$101$	−15.7111			−1.56331			−0.781657	−	0.623708i	$-0.785625\pi$
$101$	−15.7111			−1.56331			−0.781657	+	0.623708i	$0.785625\pi$
$102$	1.02878	−	1.02878i	0.101864	−	0.101864i
$103$	7.00278	+	7.00278i	0.690004	+	0.690004i	0.962233	−	0.272228i	$-0.0877606\pi$
$103$	7.00278	+	7.00278i	0.690004	+	0.690004i	−0.272228	+	0.962233i	$0.587761\pi$
$104$	−0.913009			−0.0895279
$105$	4.68790	+	5.12412i	0.457492	+	0.500063i
$106$			12.1851i			1.18352i
$107$	13.5469	−	13.5469i	1.30963	−	1.30963i	0.387946	−	0.921682i	$-0.373185\pi$
$107$	13.5469	−	13.5469i	1.30963	−	1.30963i	0.921682	−	0.387946i	$-0.126815\pi$
$108$	−0.707107	+	0.707107i	−0.0680414	+	0.0680414i
$109$		−	4.33911i		−	0.415612i	−0.978170	−	0.207806i	$-0.933368\pi$
$109$		−	4.33911i		−	0.415612i	0.978170	−	0.207806i	$-0.0666322\pi$
$110$	−5.10642	−	0.227019i	−0.486878	−	0.0216454i
$111$	−7.40689			−0.703031
$112$	−2.19620	+	2.19620i	−0.207521	+	0.207521i
$113$	2.73391	+	2.73391i	0.257185	+	0.257185i	0.823908	−	0.566723i	$-0.191789\pi$
$113$	2.73391	+	2.73391i	0.257185	+	0.257185i	−0.566723	+	0.823908i	$0.691789\pi$
$114$	2.57080			0.240778
$115$	0.0907930	−	2.04224i	0.00846649	−	0.190440i
$116$			6.94624i			0.644942i
$117$	0.645595	+	0.645595i	0.0596853	+	0.0596853i
$118$	1.07316	+	1.07316i	0.0987923	+	0.0987923i
$119$	−4.51880			−0.414238
$120$	−1.64980	+	1.50935i	−0.150606	+	0.137785i
$121$	5.77458			0.524962
$122$	5.32562	+	5.32562i	0.482159	+	0.482159i
$123$	2.91153	−	2.91153i	0.262524	−	0.262524i
$124$	−1.36258	−	5.39846i	−0.122363	−	0.484796i
$125$	6.78498	+	8.88617i	0.606867	+	0.794803i
$126$	3.10590			0.276695
$127$	6.59769	+	6.59769i	0.585450	+	0.585450i	0.936396	−	0.350946i	$-0.114140\pi$
$127$	6.59769	+	6.59769i	0.585450	+	0.585450i	−0.350946	+	0.936396i	$0.614140\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$		−	10.4313i		−	0.918426i
$130$	1.37805	+	1.50629i	0.120863	+	0.132110i
$131$	12.2505			1.07033			0.535166	−	0.844747i	$-0.320249\pi$
$131$	12.2505			1.07033			0.535166	+	0.844747i	$0.320249\pi$
$132$	−1.61639	+	1.61639i	−0.140689	+	0.140689i
$133$	−5.64600	−	5.64600i	−0.489570	−	0.489570i
$134$		−	0.224236i		−	0.0193710i
$135$	2.23386	+	0.0993121i	0.192260	+	0.00854742i
$136$		−	1.45491i		−	0.124757i
$137$	6.10844	+	6.10844i	0.521879	+	0.521879i	0.918138	−	0.396260i	$-0.129692\pi$
$137$	6.10844	+	6.10844i	0.521879	+	0.521879i	−0.396260	+	0.918138i	$0.629692\pi$
$138$	−0.646450	−	0.646450i	−0.0550295	−	0.0550295i
$139$	−13.2010			−1.11970			−0.559849	−	0.828595i	$-0.689141\pi$
$139$	−13.2010			−1.11970			−0.559849	+	0.828595i	$0.689141\pi$
$140$	6.93814	+	0.308453i	0.586380	+	0.0260690i
$141$			3.58297i			0.301741i
$142$	−2.58147	+	2.58147i	−0.216633	+	0.216633i
$143$	1.47578	+	1.47578i	0.123411	+	0.123411i
$144$			1.00000i			0.0833333i
$145$	11.4599	−	10.4843i	0.951695	−	0.870677i
$146$			2.82411i			0.233725i
$147$	−1.87142	−	1.87142i	−0.154352	−	0.154352i
$148$	−5.23746	+	5.23746i	−0.430517	+	0.430517i
$149$			14.6095i			1.19686i	0.801176	+	0.598429i	$0.204208\pi$
$149$			14.6095i			1.19686i	−0.801176	+	0.598429i	$0.795792\pi$
$150$	4.98027	+	0.443699i	0.406638	+	0.0362279i
$151$			10.6359i			0.865540i	0.901504	+	0.432770i	$0.142464\pi$
$151$			10.6359i			0.865540i	−0.901504	+	0.432770i	$0.857536\pi$
$152$	1.81783	−	1.81783i	0.147446	−	0.147446i
$153$	−1.02878	+	1.02878i	−0.0831717	+	0.0831717i
$154$	7.09982			0.572120
$155$	−6.84978	+	10.3962i	−0.550187	+	0.835041i
$156$	0.913009			0.0730992
$157$	5.40783	−	5.40783i	0.431592	−	0.431592i	−0.457578	−	0.889170i	$-0.651283\pi$
$157$	5.40783	−	5.40783i	0.431592	−	0.431592i	0.889170	+	0.457578i	$0.151283\pi$
$158$	8.99135	−	8.99135i	0.715313	−	0.715313i
$159$		−	12.1851i		−	0.966339i
$160$	−0.0993121	+	2.23386i	−0.00785131	+	0.176602i
$161$			2.83947i			0.223782i
$162$	0.707107	−	0.707107i	0.0555556	−	0.0555556i
$163$	3.47542	+	3.47542i	0.272216	+	0.272216i	0.829992	−	0.557776i	$-0.188345\pi$
$163$	3.47542	+	3.47542i	0.272216	+	0.272216i	−0.557776	+	0.829992i	$0.688345\pi$
$164$		−	4.11753i		−	0.321525i
$165$	5.10642	+	0.227019i	0.397535	+	0.0176734i
$166$			10.1471i			0.787566i
$167$	7.60389	+	7.60389i	0.588407	+	0.588407i	0.937200	−	0.348793i	$-0.113408\pi$
$167$	7.60389	+	7.60389i	0.588407	+	0.588407i	−0.348793	+	0.937200i	$0.613408\pi$
$168$	2.19620	−	2.19620i	0.169441	−	0.169441i
$169$			12.1664i			0.935878i
$170$	−2.40031	+	2.19597i	−0.184096	+	0.168424i
$171$	−2.57080			−0.196594
$172$	−7.37606	−	7.37606i	−0.562419	−	0.562419i
$173$	6.59906	+	6.59906i	0.501718	+	0.501718i	0.911971	−	0.410254i	$-0.134560\pi$
$173$	6.59906	+	6.59906i	0.501718	+	0.501718i	−0.410254	+	0.911971i	$0.634560\pi$
$174$		−	6.94624i		−	0.526593i
$175$	−9.96323	−	11.9121i	−0.753149	−	0.900472i
$176$			2.28592i			0.172308i
$177$	−1.07316	−	1.07316i	−0.0806636	−	0.0806636i
$178$	7.19253	−	7.19253i	0.539103	−	0.539103i
$179$	−17.9342			−1.34046			−0.670231	−	0.742153i	$-0.733805\pi$
$179$	−17.9342			−1.34046			−0.670231	+	0.742153i	$0.733805\pi$
$180$	1.64980	−	1.50935i	0.122969	−	0.112501i
$181$			10.9316i			0.812536i	0.913754	+	0.406268i	$0.133170\pi$
$181$			10.9316i			0.812536i	−0.913754	+	0.406268i	$0.866830\pi$
$182$	−2.00515	−	2.00515i	−0.148632	−	0.148632i
$183$	−5.32562	−	5.32562i	−0.393681	−	0.393681i
$184$	−0.914219			−0.0673971
$185$	16.5460	+	0.735593i	1.21648	+	0.0540819i
$186$	1.36258	+	5.39846i	0.0999093	+	0.395834i
$187$	−2.35170	+	2.35170i	−0.171973	+	0.171973i
$188$	2.53354	+	2.53354i	0.184778	+	0.184778i
$189$	−3.10590			−0.225921
$190$	−5.74282	−	0.255312i	−0.416628	−	0.0185223i
$191$	−16.5247			−1.19569			−0.597843	−	0.801613i	$-0.703976\pi$
$191$	−16.5247			−1.19569			−0.597843	+	0.801613i	$0.703976\pi$
$192$	0.707107	+	0.707107i	0.0510310	+	0.0510310i
$193$	−6.82452	−	6.82452i	−0.491239	−	0.491239i	0.417457	−	0.908697i	$-0.362921\pi$
$193$	−6.82452	−	6.82452i	−0.491239	−	0.491239i	−0.908697	+	0.417457i	$0.862921\pi$
$194$		−	5.85831i		−	0.420602i
$195$	−1.37805	−	1.50629i	−0.0986845	−	0.107867i
$196$	−2.64659			−0.189042
$197$	−8.06466	−	8.06466i	−0.574583	−	0.574583i	0.358823	−	0.933406i	$-0.383178\pi$
$197$	−8.06466	−	8.06466i	−0.574583	−	0.574583i	−0.933406	+	0.358823i	$0.883178\pi$
$198$	1.61639	−	1.61639i	0.114872	−	0.114872i
$199$	−12.1211			−0.859245			−0.429622	−	0.903009i	$-0.641353\pi$
$199$	−12.1211			−0.859245			−0.429622	+	0.903009i	$0.641353\pi$
$200$	3.83533	−	3.20784i	0.271199	−	0.226829i
$201$			0.224236i			0.0158164i
$202$	11.1094	−	11.1094i	0.781657	−	0.781657i
$203$	−15.2553	+	15.2553i	−1.07071	+	1.07071i
$204$			1.45491i			0.101864i
$205$	−6.79311	+	6.21481i	−0.474451	+	0.434061i
$206$	−9.90342			−0.690004
$207$	0.646450	+	0.646450i	0.0449314	+	0.0449314i
$208$	0.645595	−	0.645595i	0.0447640	−	0.0447640i
$209$	−5.87665			−0.406496
$210$	−6.93814	−	0.308453i	−0.478777	−	0.0212853i
$211$	3.26766			0.224955			0.112478	−	0.993654i	$-0.464121\pi$
$211$	3.26766			0.224955			0.112478	+	0.993654i	$0.464121\pi$
$212$	−8.61614	−	8.61614i	−0.591759	−	0.591759i
$213$	2.58147	−	2.58147i	0.176880	−	0.176880i
$214$			19.1582i			1.30963i
$215$	−1.03596	+	23.3021i	−0.0706516	+	1.58919i
$216$		−	1.00000i		−	0.0680414i
$217$	8.86360	−	14.8486i	0.601700	−	1.00799i
$218$	3.06822	+	3.06822i	0.207806	+	0.207806i
$219$		−	2.82411i		−	0.190836i
$220$	3.77131	−	3.45026i	0.254262	−	0.232617i
$221$	1.32835			0.0893542
$222$	5.23746	−	5.23746i	0.351515	−	0.351515i
$223$	−8.64136	+	8.64136i	−0.578668	+	0.578668i	−0.934536	−	0.355868i	$-0.884185\pi$
$223$	−8.64136	+	8.64136i	−0.578668	+	0.578668i	0.355868	+	0.934536i	$0.384185\pi$
$224$		−	3.10590i		−	0.207521i
$225$	−4.98027	−	0.443699i	−0.332018	−	0.0295799i
$226$	−3.86633			−0.257185
$227$	4.77487	−	4.77487i	0.316920	−	0.316920i	−0.530663	−	0.847583i	$-0.678057\pi$
$227$	4.77487	−	4.77487i	0.316920	−	0.316920i	0.847583	+	0.530663i	$0.178057\pi$
$228$	−1.81783	+	1.81783i	−0.120389	+	0.120389i
$229$	20.6675			1.36575			0.682874	−	0.730537i	$-0.260730\pi$
$229$	20.6675			1.36575			0.682874	+	0.730537i	$0.260730\pi$
$230$	1.37988	+	1.50828i	0.0909866	+	0.0994531i
$231$	−7.09982			−0.467134
$232$	−4.91173	−	4.91173i	−0.322471	−	0.322471i
$233$	8.21359	+	8.21359i	0.538090	+	0.538090i	0.922968	−	0.384878i	$-0.125756\pi$
$233$	8.21359	+	8.21359i	0.538090	+	0.538090i	−0.384878	+	0.922968i	$0.625756\pi$
$234$	−0.913009			−0.0596853
$235$	0.355832	−	8.00386i	0.0232119	−	0.522114i
$236$	−1.51768			−0.0987923
$237$	−8.99135	+	8.99135i	−0.584051	+	0.584051i
$238$	3.19527	−	3.19527i	0.207119	−	0.207119i
$239$	−10.2135			−0.660658			−0.330329	−	0.943866i	$-0.607160\pi$
$239$	−10.2135			−0.660658			−0.330329	+	0.943866i	$0.607160\pi$
$240$	0.0993121	−	2.23386i	0.00641057	−	0.144195i
$241$			19.4861i			1.25521i	0.778531	+	0.627606i	$0.215965\pi$
$241$			19.4861i			1.25521i	−0.778531	+	0.627606i	$0.784035\pi$
$242$	−4.08324	+	4.08324i	−0.262481	+	0.262481i
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$	−7.53156			−0.482159
$245$	3.99464	+	4.36635i	0.255208	+	0.278956i
$246$			4.11753i			0.262524i
$247$	1.65970	+	1.65970i	0.105604	+	0.105604i
$248$	4.78078	+	2.85380i	0.303580	+	0.181216i
$249$		−	10.1471i		−	0.643045i
$250$	−11.0812	−	1.48576i	−0.700835	−	0.0939679i
$251$			14.4806i			0.914006i	0.889465	+	0.457003i	$0.151077\pi$
$251$			14.4806i			0.914006i	−0.889465	+	0.457003i	$0.848923\pi$
$252$	−2.19620	+	2.19620i	−0.138348	+	0.138348i
$253$	1.47773	+	1.47773i	0.0929043	+	0.0929043i
$254$	−9.33054			−0.585450
$255$	2.40031	−	2.19597i	0.150314	−	0.137517i
$256$	1.00000			0.0625000
$257$	−8.49349	+	8.49349i	−0.529809	+	0.529809i	−0.920515	−	0.390706i	$-0.872231\pi$
$257$	−8.49349	+	8.49349i	−0.529809	+	0.529809i	0.390706	+	0.920515i	$0.372231\pi$
$258$	7.37606	+	7.37606i	0.459213	+	0.459213i
$259$	−23.0050			−1.42946
$260$	−2.03954	−	0.0906728i	−0.126487	−	0.00562329i
$261$			6.94624i			0.429962i
$262$	−8.66242	+	8.66242i	−0.535166	+	0.535166i
$263$	−12.3291	+	12.3291i	−0.760245	+	0.760245i	−0.976366	−	0.216122i	$-0.930659\pi$
$263$	−12.3291	+	12.3291i	−0.760245	+	0.760245i	0.216122	+	0.976366i	$0.430659\pi$
$264$		−	2.28592i		−	0.140689i
$265$	−1.21012	+	27.2198i	−0.0743373	+	1.67210i
$266$	7.98465			0.489570
$267$	−7.19253	+	7.19253i	−0.440176	+	0.440176i
$268$	0.158559	+	0.158559i	0.00968551	+	0.00968551i
$269$	21.1061			1.28686			0.643432	−	0.765503i	$-0.277510\pi$
$269$	21.1061			1.28686			0.643432	+	0.765503i	$0.277510\pi$
$270$	−1.64980	+	1.50935i	−0.100404	+	0.0918564i
$271$			11.8564i			0.720223i	0.932909	+	0.360112i	$0.117261\pi$
$271$			11.8564i			0.720223i	−0.932909	+	0.360112i	$0.882739\pi$
$272$	1.02878	+	1.02878i	0.0623787	+	0.0623787i
$273$	2.00515	+	2.00515i	0.121357	+	0.121357i
$274$	−8.63863			−0.521879
$275$	−11.3845	−	1.01426i	−0.686511	−	0.0611621i
$276$	0.914219			0.0550295
$277$	5.27211	+	5.27211i	0.316771	+	0.316771i	0.847525	−	0.530755i	$-0.178091\pi$
$277$	5.27211	+	5.27211i	0.316771	+	0.316771i	−0.530755	+	0.847525i	$0.678091\pi$
$278$	9.33455	−	9.33455i	0.559849	−	0.559849i
$279$	−1.36258	−	5.39846i	−0.0815756	−	0.323197i
$280$	−5.12412	+	4.68790i	−0.306225	+	0.280155i
$281$	−14.1777			−0.845771			−0.422886	−	0.906183i	$-0.638983\pi$
$281$	−14.1777			−0.845771			−0.422886	+	0.906183i	$0.638983\pi$
$282$	−2.53354	−	2.53354i	−0.150870	−	0.150870i
$283$	−1.60325	−	1.60325i	−0.0953035	−	0.0953035i	0.657848	−	0.753151i	$-0.271467\pi$
$283$	−1.60325	−	1.60325i	−0.0953035	−	0.0953035i	−0.753151	+	0.657848i	$0.771467\pi$
$284$		−	3.65076i		−	0.216633i
$285$	5.74282	+	0.255312i	0.340175	+	0.0151234i
$286$	−2.08706			−0.123411
$287$	9.04292	−	9.04292i	0.533787	−	0.533787i
$288$	−0.707107	−	0.707107i	−0.0416667	−	0.0416667i
$289$		−	14.8832i		−	0.875485i
$290$	−0.689846	+	15.5169i	−0.0405091	+	0.911186i
$291$			5.85831i			0.343420i
$292$	−1.99695	−	1.99695i	−0.116863	−	0.116863i
$293$	−14.9272	−	14.9272i	−0.872056	−	0.872056i	0.120641	−	0.992696i	$-0.461505\pi$
$293$	−14.9272	−	14.9272i	−0.872056	−	0.872056i	−0.992696	+	0.120641i	$0.961505\pi$
$294$	2.64659			0.154352
$295$	2.29071	+	2.50387i	0.133370	+	0.145781i
$296$		−	7.40689i		−	0.430517i
$297$	−1.61639	+	1.61639i	−0.0937924	+	0.0937924i
$298$	−10.3305	−	10.3305i	−0.598429	−	0.598429i
$299$		−	0.834690i		−	0.0482714i
$300$	−3.83533	+	3.20784i	−0.221433	+	0.185205i
$301$		−	32.3986i		−	1.86742i
$302$	−7.52074	−	7.52074i	−0.432770	−	0.432770i
$303$	−11.1094	+	11.1094i	−0.638220	+	0.638220i
$304$			2.57080i			0.147446i
$305$	11.3678	+	12.4256i	0.650918	+	0.711487i
$306$		−	1.45491i		−	0.0831717i
$307$	4.84599	−	4.84599i	0.276575	−	0.276575i	−0.555165	−	0.831740i	$-0.687345\pi$
$307$	4.84599	−	4.84599i	0.276575	−	0.276575i	0.831740	+	0.555165i	$0.187345\pi$
$308$	−5.02033	+	5.02033i	−0.286060	+	0.286060i
$309$	9.90342			0.563386
$310$	−2.50768	−	12.1947i	−0.142427	−	0.692614i
$311$	−14.1416			−0.801896			−0.400948	−	0.916101i	$-0.631319\pi$
$311$	−14.1416			−0.801896			−0.400948	+	0.916101i	$0.631319\pi$
$312$	−0.645595	+	0.645595i	−0.0365496	+	0.0365496i
$313$	2.29684	−	2.29684i	0.129825	−	0.129825i	−0.639209	−	0.769033i	$-0.720738\pi$
$313$	2.29684	−	2.29684i	0.129825	−	0.129825i	0.769033	+	0.639209i	$0.220738\pi$
$314$			7.64783i			0.431592i
$315$	6.93814	+	0.308453i	0.390920	+	0.0173794i
$316$			12.7157i			0.715313i
$317$	2.60988	−	2.60988i	0.146586	−	0.146586i	−0.630005	−	0.776591i	$-0.716947\pi$
$317$	2.60988	−	2.60988i	0.146586	−	0.146586i	0.776591	+	0.630005i	$0.216947\pi$
$318$	8.61614	+	8.61614i	0.483169	+	0.483169i
$319$			15.8785i			0.889028i
$320$	−1.50935	−	1.64980i	−0.0843755	−	0.0922268i
$321$		−	19.1582i		−	1.06931i
$322$	−2.00781	−	2.00781i	−0.111891	−	0.111891i
$323$	−2.64478	+	2.64478i	−0.147160	+	0.147160i
$324$			1.00000i			0.0555556i
$325$	2.92879	+	3.50169i	0.162460	+	0.194239i
$326$	−4.91498			−0.272216
$327$	−3.06822	−	3.06822i	−0.169673	−	0.169673i
$328$	2.91153	+	2.91153i	0.160762	+	0.160762i
$329$			11.1283i			0.613525i
$330$	−3.77131	+	3.45026i	−0.207604	+	0.189931i
$331$		−	26.4727i		−	1.45507i	−0.686069	−	0.727537i	$-0.740665\pi$
$331$		−	26.4727i		−	1.45507i	0.686069	−	0.727537i	$-0.259335\pi$
$332$	−7.17507	−	7.17507i	−0.393783	−	0.393783i
$333$	−5.23746	+	5.23746i	−0.287011	+	0.287011i
$334$	−10.7535			−0.588407
$335$	0.0222693	−	0.500911i	0.00121670	−	0.0273677i
$336$			3.10590i			0.169441i
$337$	2.53291	+	2.53291i	0.137976	+	0.137976i	0.772721	−	0.634745i	$-0.218895\pi$
$337$	2.53291	+	2.53291i	0.137976	+	0.137976i	−0.634745	+	0.772721i	$0.718895\pi$
$338$	−8.60295	−	8.60295i	−0.467939	−	0.467939i
$339$	3.86633			0.209990
$340$	0.144490	−	3.25007i	0.00783608	−	0.176260i
$341$	−3.11475	−	12.3404i	−0.168673	−	0.668272i
$342$	1.81783	−	1.81783i	0.0982972	−	0.0982972i
$343$	9.56096	+	9.56096i	0.516243	+	0.516243i
$344$	10.4313			0.562419
$345$	−1.37988	−	1.50828i	−0.0742903	−	0.0812031i
$346$	−9.33249			−0.501718
$347$	−1.28914	−	1.28914i	−0.0692049	−	0.0692049i	0.671657	−	0.740862i	$-0.265583\pi$
$347$	−1.28914	−	1.28914i	−0.0692049	−	0.0692049i	−0.740862	+	0.671657i	$0.765583\pi$
$348$	4.91173	+	4.91173i	0.263297	+	0.263297i
$349$			30.7364i			1.64528i	0.568563	+	0.822640i	$0.307500\pi$
$349$			30.7364i			1.64528i	−0.568563	+	0.822640i	$0.692500\pi$
$350$	15.4682	+	1.37808i	0.826811	+	0.0736616i
$351$	0.913009			0.0487328
$352$	−1.61639	−	1.61639i	−0.0861538	−	0.0861538i
$353$	5.12408	−	5.12408i	0.272727	−	0.272727i	−0.557470	−	0.830197i	$-0.688228\pi$
$353$	5.12408	−	5.12408i	0.272727	−	0.272727i	0.830197	+	0.557470i	$0.188228\pi$
$354$	1.51768			0.0806636
$355$	−6.02303	+	5.51029i	−0.319669	+	0.292456i
$356$			10.1718i			0.539103i
$357$	−3.19527	+	3.19527i	−0.169112	+	0.169112i
$358$	12.6814	−	12.6814i	0.670231	−	0.670231i
$359$		−	27.0240i		−	1.42627i	−0.701027	−	0.713135i	$-0.747275\pi$
$359$		−	27.0240i		−	1.42627i	0.701027	−	0.713135i	$-0.252725\pi$
$360$	−0.0993121	+	2.23386i	−0.00523421	+	0.117735i
$361$	12.3910			0.652156
$362$	−7.72978	−	7.72978i	−0.406268	−	0.406268i
$363$	4.08324	−	4.08324i	0.214315	−	0.214315i
$364$	2.83571			0.148632
$365$	−0.280469	+	6.30868i	−0.0146804	+	0.330211i
$366$	7.53156			0.393681
$367$	13.9530	+	13.9530i	0.728339	+	0.728339i	0.970289	−	0.241950i	$-0.0777870\pi$
$367$	13.9530	+	13.9530i	0.728339	+	0.728339i	−0.241950	+	0.970289i	$0.577787\pi$
$368$	0.646450	−	0.646450i	0.0336986	−	0.0336986i
$369$		−	4.11753i		−	0.214350i
$370$	−12.2199	+	11.1796i	−0.635283	+	0.581201i
$371$		−	37.8456i		−	1.96484i
$372$	−4.78078	−	2.85380i	−0.247872	−	0.147963i
$373$	1.02183	+	1.02183i	0.0529084	+	0.0529084i	0.733066	−	0.680158i	$-0.238089\pi$
$373$	1.02183	+	1.02183i	0.0529084	+	0.0529084i	−0.680158	+	0.733066i	$0.738089\pi$
$374$		−	3.32580i		−	0.171973i
$375$	11.0812	+	1.48576i	0.572230	+	0.0767245i
$376$	−3.58297			−0.184778
$377$	4.48446	−	4.48446i	0.230961	−	0.230961i
$378$	2.19620	−	2.19620i	0.112960	−	0.112960i
$379$			14.4008i			0.739717i	0.929088	+	0.369859i	$0.120594\pi$
$379$			14.4008i			0.739717i	−0.929088	+	0.369859i	$0.879406\pi$
$380$	4.24132	−	3.88026i	0.217575	−	0.199053i
$381$	9.33054			0.478018
$382$	11.6847	−	11.6847i	0.597843	−	0.597843i
$383$	26.2951	−	26.2951i	1.34361	−	1.34361i	0.451183	−	0.892431i	$-0.351002\pi$
$383$	26.2951	−	26.2951i	1.34361	−	1.34361i	0.892431	−	0.451183i	$-0.148998\pi$
$384$	−1.00000			−0.0510310
$385$	15.8600	+	0.705098i	0.808302	+	0.0359351i
$386$	9.65132			0.491239
$387$	−7.37606	−	7.37606i	−0.374946	−	0.374946i
$388$	4.14245	+	4.14245i	0.210301	+	0.210301i
$389$	32.3948			1.64248			0.821241	−	0.570581i	$-0.193282\pi$
$389$	32.3948			1.64248			0.821241	+	0.570581i	$0.193282\pi$
$390$	2.03954	+	0.0906728i	0.103276	+	0.00459140i
$391$	1.33011			0.0672664
$392$	1.87142	−	1.87142i	0.0945211	−	0.0945211i
$393$	8.66242	−	8.66242i	0.436961	−	0.436961i
$394$	11.4051			0.574583
$395$	20.9784	−	19.1925i	1.05554	−	0.965678i
$396$			2.28592i			0.114872i
$397$	7.11344	−	7.11344i	0.357013	−	0.357013i	−0.505698	−	0.862711i	$-0.668765\pi$
$397$	7.11344	−	7.11344i	0.357013	−	0.357013i	0.862711	+	0.505698i	$0.168765\pi$
$398$	8.57094	−	8.57094i	0.429622	−	0.429622i
$399$	−7.98465			−0.399733
$400$	−0.443699	+	4.98027i	−0.0221849	+	0.249014i
$401$		−	8.54129i		−	0.426532i	−0.976994	−	0.213266i	$-0.931590\pi$
$401$		−	8.54129i		−	0.426532i	0.976994	−	0.213266i	$-0.0684101\pi$
$402$	−0.158559	−	0.158559i	−0.00790818	−	0.00790818i
$403$	−2.60554	+	4.36489i	−0.129791	+	0.217431i
$404$			15.7111i			0.781657i
$405$	1.64980	−	1.50935i	0.0819794	−	0.0750004i
$406$		−	21.5743i		−	1.07071i
$407$	−11.9724	+	11.9724i	−0.593450	+	0.593450i
$408$	−1.02878	−	1.02878i	−0.0509320	−	0.0509320i
$409$	20.4495			1.01116			0.505581	−	0.862779i	$-0.331278\pi$
$409$	20.4495			1.01116			0.505581	+	0.862779i	$0.331278\pi$
$410$	0.408920	−	9.19799i	0.0201951	−	0.454256i
$411$	8.63863			0.426112
$412$	7.00278	−	7.00278i	0.345002	−	0.345002i
$413$	−3.33312	−	3.33312i	−0.164012	−	0.164012i
$414$	−0.914219			−0.0449314
$415$	−1.00773	+	22.6672i	−0.0494674	+	1.11269i
$416$			0.913009i			0.0447640i
$417$	−9.33455	+	9.33455i	−0.457115	+	0.457115i
$418$	4.15542	−	4.15542i	0.203248	−	0.203248i
$419$		−	13.4368i		−	0.656430i	−0.944603	−	0.328215i	$-0.893553\pi$
$419$		−	13.4368i		−	0.656430i	0.944603	−	0.328215i	$-0.106447\pi$
$420$	5.12412	−	4.68790i	0.250031	−	0.228746i
$421$	25.7542			1.25518			0.627592	−	0.778542i	$-0.284041\pi$
$421$	25.7542			1.25518			0.627592	+	0.778542i	$0.284041\pi$
$422$	−2.31059	+	2.31059i	−0.112478	+	0.112478i
$423$	2.53354	+	2.53354i	0.123185	+	0.123185i
$424$	12.1851			0.591759
$425$	−5.58006	+	4.66712i	−0.270672	+	0.226389i
$426$			3.65076i			0.176880i
$427$	−16.5408	−	16.5408i	−0.800466	−	0.800466i
$428$	−13.5469	−	13.5469i	−0.654814	−	0.654814i
$429$	2.08706			0.100764
$430$	−15.7446	−	17.2096i	−0.759270	−	0.829922i
$431$	13.2407			0.637781			0.318891	−	0.947792i	$-0.396690\pi$
$431$	13.2407			0.637781			0.318891	+	0.947792i	$0.396690\pi$
$432$	0.707107	+	0.707107i	0.0340207	+	0.0340207i
$433$	20.4880	−	20.4880i	0.984592	−	0.984592i	−0.0152909	−	0.999883i	$-0.504867\pi$
$433$	20.4880	−	20.4880i	0.984592	−	0.984592i	0.999883	+	0.0152909i	$0.00486743\pi$
$434$	4.23203	+	16.7671i	0.203144	+	0.804844i
$435$	0.689846	−	15.5169i	0.0330756	−	0.743980i
$436$	−4.33911			−0.207806
$437$	1.66190	+	1.66190i	0.0794994	+	0.0794994i
$438$	1.99695	+	1.99695i	0.0954180	+	0.0954180i
$439$			40.7603i			1.94538i	0.232103	+	0.972691i	$0.425439\pi$
$439$			40.7603i			1.94538i	−0.232103	+	0.972691i	$0.574561\pi$
$440$	−0.227019	+	5.10642i	−0.0108227	+	0.243439i
$441$	−2.64659			−0.126028
$442$	−0.939282	+	0.939282i	−0.0446771	+	0.0446771i
$443$	−2.75910	−	2.75910i	−0.131089	−	0.131089i	0.638518	−	0.769607i	$-0.279548\pi$
$443$	−2.75910	−	2.75910i	−0.131089	−	0.131089i	−0.769607	+	0.638518i	$0.779548\pi$
$444$			7.40689i			0.351515i
$445$	16.7814	−	15.3528i	0.795516	−	0.727793i
$446$		−	12.2207i		−	0.578668i
$447$	10.3305	+	10.3305i	0.488615	+	0.488615i
$448$	2.19620	+	2.19620i	0.103761	+	0.103761i
$449$	19.0399			0.898549			0.449275	−	0.893394i	$-0.351682\pi$
$449$	19.0399			0.898549			0.449275	+	0.893394i	$0.351682\pi$
$450$	3.83533	−	3.20784i	0.180799	−	0.151219i
$451$		−	9.41233i		−	0.443209i
$452$	2.73391	−	2.73391i	0.128592	−	0.128592i
$453$	7.52074	+	7.52074i	0.353355	+	0.353355i
$454$			6.75269i			0.316920i
$455$	−4.28009	−	4.67837i	−0.200654	−	0.219325i
$456$		−	2.57080i		−	0.120389i
$457$	−24.8241	−	24.8241i	−1.16122	−	1.16122i	−0.984208	−	0.177014i	$-0.943356\pi$
$457$	−24.8241	−	24.8241i	−1.16122	−	1.16122i	−0.177014	−	0.984208i	$-0.556644\pi$
$458$	−14.6141	+	14.6141i	−0.682874	+	0.682874i
$459$			1.45491i			0.0679094i
$460$	−2.04224	−	0.0907930i	−0.0952199	−	0.00423324i
$461$		−	3.00759i		−	0.140077i	−0.997544	−	0.0700387i	$-0.977688\pi$
$461$		−	3.00759i		−	0.140077i	0.997544	−	0.0700387i	$-0.0223123\pi$
$462$	5.02033	−	5.02033i	0.233567	−	0.233567i
$463$	−19.8731	+	19.8731i	−0.923583	+	0.923583i	−0.997281	−	0.0736979i	$-0.976520\pi$
$463$	−19.8731	+	19.8731i	−0.923583	+	0.923583i	0.0736979	+	0.997281i	$0.476520\pi$
$464$	6.94624			0.322471
$465$	2.50768	+	12.1947i	0.116291	+	0.565517i
$466$	−11.6158			−0.538090
$467$	2.52040	−	2.52040i	0.116630	−	0.116630i	−0.646383	−	0.763013i	$-0.723719\pi$
$467$	2.52040	−	2.52040i	0.116630	−	0.116630i	0.763013	+	0.646383i	$0.223719\pi$
$468$	0.645595	−	0.645595i	0.0298426	−	0.0298426i
$469$			0.696453i			0.0321592i
$470$	5.40797	+	5.91119i	0.249451	+	0.272663i
$471$		−	7.64783i		−	0.352393i
$472$	1.07316	−	1.07316i	0.0493962	−	0.0493962i
$473$	−16.8611	−	16.8611i	−0.775272	−	0.775272i
$474$		−	12.7157i		−	0.584051i
$475$	−12.8033	−	1.14066i	−0.587456	−	0.0523372i
$476$			4.51880i			0.207119i
$477$	−8.61614	−	8.61614i	−0.394506	−	0.394506i
$478$	7.22205	−	7.22205i	0.330329	−	0.330329i
$479$		−	33.9816i		−	1.55266i	−0.630329	−	0.776328i	$-0.717080\pi$
$479$		−	33.9816i		−	1.55266i	0.630329	−	0.776328i	$-0.282920\pi$
$480$	1.50935	+	1.64980i	0.0688923	+	0.0753029i
$481$	6.76256			0.308346
$482$	−13.7788	−	13.7788i	−0.627606	−	0.627606i
$483$	2.00781	+	2.00781i	0.0913584	+	0.0913584i
$484$		−	5.77458i		−	0.262481i
$485$	0.581801	−	13.0867i	0.0264182	−	0.594235i
$486$		−	1.00000i		−	0.0453609i
$487$	12.8096	+	12.8096i	0.580457	+	0.580457i	0.935029	−	0.354572i	$-0.115373\pi$
$487$	12.8096	+	12.8096i	0.580457	+	0.580457i	−0.354572	+	0.935029i	$0.615373\pi$
$488$	5.32562	−	5.32562i	0.241079	−	0.241079i
$489$	4.91498			0.222263
$490$	−5.91212	−	0.262838i	−0.267082	−	0.0118738i
$491$			23.8973i			1.07847i	0.842155	+	0.539236i	$0.181287\pi$
$491$			23.8973i			1.07847i	−0.842155	+	0.539236i	$0.818713\pi$
$492$	−2.91153	−	2.91153i	−0.131262	−	0.131262i
$493$	7.14613	+	7.14613i	0.321846	+	0.321846i
$494$	−2.34717			−0.105604
$495$	3.77131	−	3.45026i	0.169508	−	0.155078i
$496$	−5.39846	+	1.36258i	−0.242398	+	0.0611817i
$497$	8.01779	−	8.01779i	0.359647	−	0.359647i
$498$	7.17507	+	7.17507i	0.321522	+	0.321522i
$499$	−23.9868			−1.07380			−0.536898	−	0.843647i	$-0.680404\pi$
$499$	−23.9868			−1.07380			−0.536898	+	0.843647i	$0.680404\pi$
$500$	8.88617	−	6.78498i	0.397402	−	0.303434i
$501$	10.7535			0.480432
$502$	−10.2393	−	10.2393i	−0.457003	−	0.457003i
$503$	−0.770858	−	0.770858i	−0.0343709	−	0.0343709i	0.689712	−	0.724083i	$-0.257737\pi$
$503$	−0.770858	−	0.770858i	−0.0343709	−	0.0343709i	−0.724083	+	0.689712i	$0.757737\pi$
$504$		−	3.10590i		−	0.138348i
$505$	25.9202	−	23.7136i	1.15344	−	1.05524i
$506$	−2.08983			−0.0929043
$507$	8.60295	+	8.60295i	0.382071	+	0.382071i
$508$	6.59769	−	6.59769i	0.292725	−	0.292725i
$509$	6.48117			0.287273			0.143636	−	0.989631i	$-0.454120\pi$
$509$	6.48117			0.287273			0.143636	+	0.989631i	$0.454120\pi$
$510$	−0.144490	+	3.25007i	−0.00639813	+	0.143915i
$511$		−	8.77140i		−	0.388024i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−1.81783	+	1.81783i	−0.0802593	+	0.0802593i
$514$		−	12.0116i		−	0.529809i
$515$	−22.1229	−	0.983530i	−0.974850	−	0.0433395i
$516$	−10.4313			−0.459213
$517$	5.79147	+	5.79147i	0.254709	+	0.254709i
$518$	16.2670	−	16.2670i	0.714731	−	0.714731i
$519$	9.33249			0.409651
$520$	1.50629	−	1.37805i	0.0660550	−	0.0604317i
$521$	−37.3802			−1.63766			−0.818828	−	0.574039i	$-0.805376\pi$
$521$	−37.3802			−1.63766			−0.818828	+	0.574039i	$0.805376\pi$
$522$	−4.91173	−	4.91173i	−0.214981	−	0.214981i
$523$	8.80518	−	8.80518i	0.385024	−	0.385024i	−0.487885	−	0.872908i	$-0.662231\pi$
$523$	8.80518	−	8.80518i	0.385024	−	0.385024i	0.872908	+	0.487885i	$0.162231\pi$
$524$		−	12.2505i		−	0.535166i
$525$	−15.4682	−	1.37808i	−0.675088	−	0.0601445i
$526$		−	17.4360i		−	0.760245i
$527$	−6.95560	−	4.15202i	−0.302991	−	0.180865i
$528$	1.61639	+	1.61639i	0.0703443	+	0.0703443i
$529$			22.1642i			0.963661i
$530$	−18.3916	−	20.1030i	−0.798879	−	0.873217i
$531$	−1.51768			−0.0658616
$532$	−5.64600	+	5.64600i	−0.244785	+	0.244785i
$533$	−2.65826	+	2.65826i	−0.115142	+	0.115142i
$534$		−	10.1718i		−	0.440176i
$535$	−1.90264	+	42.7968i	−0.0822584	+	1.85027i
$536$	−0.224236			−0.00968551
$537$	−12.6814	+	12.6814i	−0.547241	+	0.547241i
$538$	−14.9243	+	14.9243i	−0.643432	+	0.643432i
$539$	−6.04989			−0.260587
$540$	0.0993121	−	2.23386i	0.00427371	−	0.0961301i
$541$	30.8938			1.32823			0.664114	−	0.747632i	$-0.268809\pi$
$541$	30.8938			1.32823			0.664114	+	0.747632i	$0.268809\pi$
$542$	−8.38372	−	8.38372i	−0.360112	−	0.360112i
$543$	7.72978	+	7.72978i	0.331716	+	0.331716i
$544$	−1.45491			−0.0623787
$545$	6.54926	+	7.15868i	0.280539	+	0.306644i
$546$	−2.83571			−0.121357
$547$	−5.61353	+	5.61353i	−0.240017	+	0.240017i	−0.816857	−	0.576840i	$-0.804286\pi$
$547$	−5.61353	+	5.61353i	−0.240017	+	0.240017i	0.576840	+	0.816857i	$0.304286\pi$
$548$	6.10844	−	6.10844i	0.260939	−	0.260939i
$549$	−7.53156			−0.321439
$550$	8.76725	−	7.33287i	0.373837	−	0.312674i
$551$			17.8574i			0.760752i
$552$	−0.646450	+	0.646450i	−0.0275148	+	0.0275148i
$553$	−27.9262	+	27.9262i	−1.18754	+	1.18754i
$554$	−7.45589			−0.316771
$555$	12.2199	−	11.1796i	0.518706	−	0.474548i
$556$			13.2010i			0.559849i
$557$	−12.1359	−	12.1359i	−0.514215	−	0.514215i	0.401600	−	0.915815i	$-0.368454\pi$
$557$	−12.1359	−	12.1359i	−0.514215	−	0.514215i	−0.915815	+	0.401600i	$0.868454\pi$
$558$	4.78078	+	2.85380i	0.202386	+	0.120811i
$559$			9.52389i			0.402818i
$560$	0.308453	−	6.93814i	0.0130345	−	0.293190i
$561$			3.32580i			0.140416i
$562$	10.0252	−	10.0252i	0.422886	−	0.422886i
$563$	−13.4460	−	13.4460i	−0.566681	−	0.566681i	0.364516	−	0.931197i	$-0.381235\pi$
$563$	−13.4460	−	13.4460i	−0.566681	−	0.566681i	−0.931197	+	0.364516i	$0.881235\pi$
$564$	3.58297			0.150870
$565$	−8.63685	−	0.383974i	−0.363355	−	0.0161539i
$566$	2.26734			0.0953035
$567$	−2.19620	+	2.19620i	−0.0922317	+	0.0922317i
$568$	2.58147	+	2.58147i	0.108316	+	0.108316i
$569$	−25.6031			−1.07334			−0.536668	−	0.843794i	$-0.680317\pi$
$569$	−25.6031			−1.07334			−0.536668	+	0.843794i	$0.680317\pi$
$570$	−4.24132	+	3.88026i	−0.177649	+	0.162526i
$571$			19.0268i			0.796247i	0.917332	+	0.398123i	$0.130338\pi$
$571$			19.0268i			0.796247i	−0.917332	+	0.398123i	$0.869662\pi$
$572$	1.47578	−	1.47578i	0.0617053	−	0.0617053i
$573$	−11.6847	+	11.6847i	−0.488137	+	0.488137i
$574$			12.7886i			0.533787i
$575$	2.93267	+	3.50633i	0.122301	+	0.146224i
$576$	1.00000			0.0416667
$577$	17.4177	−	17.4177i	0.725108	−	0.725108i	−0.244533	−	0.969641i	$-0.578635\pi$
$577$	17.4177	−	17.4177i	0.725108	−	0.725108i	0.969641	+	0.244533i	$0.0786347\pi$
$578$	10.5240	+	10.5240i	0.437742	+	0.437742i
$579$	−9.65132			−0.401095
$580$	−10.4843	−	11.4599i	−0.435339	−	0.475848i
$581$		−	31.5158i		−	1.30749i
$582$	−4.14245	−	4.14245i	−0.171710	−	0.171710i
$583$	−19.6958	−	19.6958i	−0.815717	−	0.815717i
$584$	2.82411			0.116863
$585$	−2.03954	−	0.0906728i	−0.0843244	−	0.00374886i
$586$	21.1102			0.872056
$587$	3.19035	+	3.19035i	0.131680	+	0.131680i	0.769875	−	0.638195i	$-0.220319\pi$
$587$	3.19035	+	3.19035i	0.131680	+	0.131680i	−0.638195	+	0.769875i	$0.720319\pi$
$588$	−1.87142	+	1.87142i	−0.0771762	+	0.0771762i
$589$	−3.50293	−	13.8784i	−0.144336	−	0.571849i
$590$	−3.39028	−	0.150724i	−0.139576	−	0.00620519i
$591$	−11.4051			−0.469145
$592$	5.23746	+	5.23746i	0.215258	+	0.215258i
$593$	19.4906	+	19.4906i	0.800384	+	0.800384i	0.983155	−	0.182772i	$-0.0585069\pi$
$593$	19.4906	+	19.4906i	0.800384	+	0.800384i	−0.182772	+	0.983155i	$0.558507\pi$
$594$		−	2.28592i		−	0.0937924i
$595$	7.45513	−	6.82047i	0.305630	−	0.279612i
$596$	14.6095			0.598429
$597$	−8.57094	+	8.57094i	−0.350785	+	0.350785i
$598$	0.590215	+	0.590215i	0.0241357	+	0.0241357i
$599$		−	28.7965i		−	1.17659i	−0.808645	−	0.588297i	$-0.799799\pi$
$599$		−	28.7965i		−	1.17659i	0.808645	−	0.588297i	$-0.200201\pi$
$600$	0.443699	−	4.98027i	0.0181139	−	0.203319i
$601$			21.3503i			0.870899i	0.900213	+	0.435449i	$0.143410\pi$
$601$			21.3503i			0.870899i	−0.900213	+	0.435449i	$0.856590\pi$
$602$	22.9093	+	22.9093i	0.933712	+	0.933712i
$603$	0.158559	+	0.158559i	0.00645700	+	0.00645700i
$604$	10.6359			0.432770
$605$	−9.52692	+	8.71589i	−0.387324	+	0.354351i
$606$		−	15.7111i		−	0.638220i
$607$	9.56787	−	9.56787i	0.388348	−	0.388348i	−0.485750	−	0.874098i	$-0.661453\pi$
$607$	9.56787	−	9.56787i	0.388348	−	0.388348i	0.874098	+	0.485750i	$0.161453\pi$
$608$	−1.81783	−	1.81783i	−0.0737229	−	0.0737229i
$609$			21.5743i			0.874235i
$610$	−16.8245	−	0.747975i	−0.681203	−	0.0302846i
$611$		−	3.27128i		−	0.132342i
$612$	1.02878	+	1.02878i	0.0415858	+	0.0415858i
$613$	−6.10160	+	6.10160i	−0.246441	+	0.246441i	−0.819508	−	0.573067i	$-0.805753\pi$
$613$	−6.10160	+	6.10160i	−0.246441	+	0.246441i	0.573067	+	0.819508i	$0.305753\pi$
$614$			6.85327i			0.276575i
$615$	−0.408920	+	9.19799i	−0.0164893	+	0.370899i
$616$		−	7.09982i		−	0.286060i
$617$	−4.45148	+	4.45148i	−0.179210	+	0.179210i	−0.791011	−	0.611801i	$-0.790445\pi$
$617$	−4.45148	+	4.45148i	−0.179210	+	0.179210i	0.611801	+	0.791011i	$0.290445\pi$
$618$	−7.00278	+	7.00278i	−0.281693	+	0.281693i
$619$	27.2826			1.09658			0.548290	−	0.836288i	$-0.315279\pi$
$619$	27.2826			1.09658			0.548290	+	0.836288i	$0.315279\pi$
$620$	10.3962	+	6.84978i	0.417521	+	0.275094i
$621$	0.914219			0.0366863
$622$	9.99961	−	9.99961i	0.400948	−	0.400948i
$623$	−22.3393	+	22.3393i	−0.895003	+	0.895003i
$624$		−	0.913009i		−	0.0365496i
$625$	−24.6063	−	4.41948i	−0.984251	−	0.176779i
$626$			3.24822i			0.129825i
$627$	−4.15542	+	4.15542i	−0.165951	+	0.165951i
$628$	−5.40783	−	5.40783i	−0.215796	−	0.215796i
$629$			10.7764i			0.429681i
$630$	−5.12412	+	4.68790i	−0.204150	+	0.186770i
$631$		−	5.74825i		−	0.228834i	−0.993433	−	0.114417i	$-0.963500\pi$
$631$		−	5.74825i		−	0.228834i	0.993433	−	0.114417i	$-0.0365000\pi$
$632$	−8.99135	−	8.99135i	−0.357657	−	0.357657i
$633$	2.31059	−	2.31059i	0.0918376	−	0.0918376i
$634$			3.69093i			0.146586i
$635$	−20.8431	−	0.926636i	−0.827135	−	0.0367724i
$636$	−12.1851			−0.483169
$637$	1.70863	+	1.70863i	0.0676982	+	0.0676982i
$638$	−11.2278	−	11.2278i	−0.444514	−	0.444514i
$639$		−	3.65076i		−	0.144422i
$640$	2.23386	+	0.0993121i	0.0883011	+	0.00392565i
$641$		−	28.8917i		−	1.14115i	−0.821244	−	0.570577i	$-0.806720\pi$
$641$		−	28.8917i		−	1.14115i	0.821244	−	0.570577i	$-0.193280\pi$
$642$	13.5469	+	13.5469i	0.534653	+	0.534653i
$643$	30.3015	−	30.3015i	1.19497	−	1.19497i	0.219321	−	0.975653i	$-0.429616\pi$
$643$	30.3015	−	30.3015i	1.19497	−	1.19497i	0.975653	−	0.219321i	$-0.0703842\pi$
$644$	2.83947			0.111891
$645$	15.7446	+	17.2096i	0.619941	+	0.677628i
$646$		−	3.74029i		−	0.147160i
$647$	26.0467	+	26.0467i	1.02400	+	1.02400i	0.999705	+	0.0242961i	$0.00773444\pi$
$647$	26.0467	+	26.0467i	1.02400	+	1.02400i	0.0242961	+	0.999705i	$0.492266\pi$
$648$	−0.707107	−	0.707107i	−0.0277778	−	0.0277778i
$649$	−3.46928			−0.136181
$650$	−4.54704	−	0.405101i	−0.178349	−	0.0158894i
$651$	−4.23203	−	16.7671i	−0.165867	−	0.657153i
$652$	3.47542	−	3.47542i	0.136108	−	0.136108i
$653$	9.71240	+	9.71240i	0.380076	+	0.380076i	0.871129	−	0.491054i	$-0.163388\pi$
$653$	9.71240	+	9.71240i	0.380076	+	0.380076i	−0.491054	+	0.871129i	$0.663388\pi$
$654$	4.33911			0.169673
$655$	−20.2109	+	18.4904i	−0.789706	+	0.722478i
$656$	−4.11753			−0.160762
$657$	−1.99695	−	1.99695i	−0.0779084	−	0.0779084i
$658$	−7.86892	−	7.86892i	−0.306762	−	0.306762i
$659$		−	45.4407i		−	1.77012i	−0.465477	−	0.885060i	$-0.654117\pi$
$659$		−	45.4407i		−	1.77012i	0.465477	−	0.885060i	$-0.345883\pi$
$660$	0.227019	−	5.10642i	0.00883671	−	0.198767i
$661$	6.33239			0.246302			0.123151	−	0.992388i	$-0.460700\pi$
$661$	6.33239			0.246302			0.123151	+	0.992388i	$0.460700\pi$
$662$	18.7191	+	18.7191i	0.727537	+	0.727537i
$663$	0.939282	−	0.939282i	0.0364787	−	0.0364787i
$664$	10.1471			0.393783
$665$	17.8366	+	0.792972i	0.691674	+	0.0307502i
$666$		−	7.40689i		−	0.287011i
$667$	4.49040	−	4.49040i	0.173869	−	0.173869i
$668$	7.60389	−	7.60389i	0.294204	−	0.294204i
$669$			12.2207i			0.472481i
$670$	0.338451	+	0.369945i	0.0130755	+	0.0142922i
$671$	−17.2165			−0.664637
$672$	−2.19620	−	2.19620i	−0.0847203	−	0.0847203i
$673$	22.0450	−	22.0450i	0.849773	−	0.849773i	−0.140331	−	0.990105i	$-0.544817\pi$
$673$	22.0450	−	22.0450i	0.849773	−	0.849773i	0.990105	+	0.140331i	$0.0448168\pi$
$674$	−3.58207			−0.137976
$675$	−3.83533	+	3.20784i	−0.147622	+	0.123470i
$676$	12.1664			0.467939
$677$	21.9954	+	21.9954i	0.845351	+	0.845351i	0.989549	−	0.144198i	$-0.0460601\pi$
$677$	21.9954	+	21.9954i	0.845351	+	0.845351i	−0.144198	+	0.989549i	$0.546060\pi$
$678$	−2.73391	+	2.73391i	−0.104995	+	0.104995i
$679$			18.1953i			0.698272i
$680$	2.19597	+	2.40031i	0.0842118	+	0.0920478i
$681$		−	6.75269i		−	0.258764i
$682$	10.9285	+	6.52355i	0.418473	+	0.249800i
$683$	27.4799	+	27.4799i	1.05149	+	1.05149i	0.998600	+	0.0528873i	$0.0168424\pi$
$683$	27.4799	+	27.4799i	1.05149	+	1.05149i	0.0528873	+	0.998600i	$0.483158\pi$
$684$			2.57080i			0.0982972i
$685$	−19.2975	−	0.857920i	−0.737320	−	0.0327795i
$686$	−13.5212			−0.516243
$687$	14.6141	−	14.6141i	0.557564	−	0.557564i
$688$	−7.37606	+	7.37606i	−0.281209	+	0.281209i
$689$			11.1251i			0.423832i
$690$	2.04224	+	0.0907930i	0.0777467	+	0.00345643i
$691$	−13.7723			−0.523924			−0.261962	−	0.965078i	$-0.584370\pi$
$691$	−13.7723			−0.523924			−0.261962	+	0.965078i	$0.584370\pi$
$692$	6.59906	−	6.59906i	0.250859	−	0.250859i
$693$	−5.02033	+	5.02033i	−0.190707	+	0.190707i
$694$	1.82313			0.0692049
$695$	21.7791	−	19.9251i	0.826129	−	0.755801i
$696$	−6.94624			−0.263297
$697$	−4.23602	−	4.23602i	−0.160451	−	0.160451i
$698$	−21.7339	−	21.7339i	−0.822640	−	0.822640i
$699$	11.6158			0.439349
$700$	−11.9121	+	9.96323i	−0.450236	+	0.376575i
$701$	−9.39133			−0.354706			−0.177353	−	0.984147i	$-0.556753\pi$
$701$	−9.39133			−0.354706			−0.177353	+	0.984147i	$0.556753\pi$
$702$	−0.645595	+	0.645595i	−0.0243664	+	0.0243664i
$703$	−13.4645	+	13.4645i	−0.507823	+	0.507823i
$704$	2.28592			0.0861538
$705$	−5.40797	−	5.91119i	−0.203676	−	0.222628i
$706$			7.24654i			0.272727i
$707$	−34.5048	+	34.5048i	−1.29768	+	1.29768i
$708$	−1.07316	+	1.07316i	−0.0403318	+	0.0403318i
$709$	−43.3559			−1.62827			−0.814133	−	0.580678i	$-0.802787\pi$
$709$	−43.3559			−1.62827			−0.814133	+	0.580678i	$0.802787\pi$
$710$	0.362564	−	8.15528i	0.0136068	−	0.306062i
$711$			12.7157i			0.476876i
$712$	−7.19253	−	7.19253i	−0.269552	−	0.269552i
$713$	−2.60900	+	4.37068i	−0.0977077	+	0.163683i
$714$		−	4.51880i		−	0.169112i
$715$	−4.66221	−	0.207271i	−0.174357	−	0.00775148i
$716$			17.9342i			0.670231i
$717$	−7.22205	+	7.22205i	−0.269712	+	0.269712i
$718$	19.1088	+	19.1088i	0.713135	+	0.713135i
$719$	35.6680			1.33019			0.665096	−	0.746758i	$-0.268391\pi$
$719$	35.6680			1.33019			0.665096	+	0.746758i	$0.268391\pi$
$720$	−1.50935	−	1.64980i	−0.0562503	−	0.0614845i
$721$	30.7590			1.14553
$722$	−8.76173	+	8.76173i	−0.326078	+	0.326078i
$723$	13.7788	+	13.7788i	0.512438	+	0.512438i
$724$	10.9316			0.406268
$725$	−3.08204	+	34.5942i	−0.114464	+	1.28480i
$726$			5.77458i			0.214315i
$727$	−24.3888	+	24.3888i	−0.904529	+	0.904529i	−0.995824	−	0.0912951i	$-0.970899\pi$
$727$	−24.3888	+	24.3888i	−0.904529	+	0.904529i	0.0912951	+	0.995824i	$0.470899\pi$
$728$	−2.00515	+	2.00515i	−0.0743158	+	0.0743158i
$729$			1.00000i			0.0370370i
$730$	−4.26259	−	4.65923i	−0.157765	−	0.172446i
$731$	−15.1766			−0.561328
$732$	−5.32562	+	5.32562i	−0.196841	+	0.196841i
$733$	−37.4630	−	37.4630i	−1.38373	−	1.38373i	−0.837892	−	0.545835i	$-0.816212\pi$
$733$	−37.4630	−	37.4630i	−1.38373	−	1.38373i	−0.545835	−	0.837892i	$-0.683788\pi$
$734$	−19.7325			−0.728339
$735$	5.91212	+	0.262838i	0.218072	+	0.00969494i
$736$			0.914219i			0.0336986i
$737$	0.362452	+	0.362452i	0.0133511	+	0.0133511i
$738$	2.91153	+	2.91153i	0.107175	+	0.107175i
$739$	−14.2026			−0.522449			−0.261225	−	0.965278i	$-0.584126\pi$
$739$	−14.2026			−0.522449			−0.261225	+	0.965278i	$0.584126\pi$
$740$	0.735593	−	16.5460i	0.0270410	−	0.608242i
$741$	2.34717			0.0862254
$742$	26.7608	+	26.7608i	0.982422	+	0.982422i
$743$	18.1308	−	18.1308i	0.665154	−	0.665154i	−0.291436	−	0.956590i	$-0.594133\pi$
$743$	18.1308	−	18.1308i	0.665154	−	0.665154i	0.956590	+	0.291436i	$0.0941331\pi$
$744$	5.39846	−	1.36258i	0.197917	−	0.0499546i
$745$	−22.0509	−	24.1028i	−0.807884	−	0.883059i
$746$	−1.44509			−0.0529084
$747$	−7.17507	−	7.17507i	−0.262522	−	0.262522i
$748$	2.35170	+	2.35170i	0.0859866	+	0.0859866i
$749$		−	59.5034i		−	2.17421i
$750$	−8.88617	+	6.78498i	−0.324477	+	0.247753i
$751$	1.13824			0.0415349			0.0207675	−	0.999784i	$-0.493389\pi$
$751$	1.13824			0.0415349			0.0207675	+	0.999784i	$0.493389\pi$
$752$	2.53354	−	2.53354i	0.0923888	−	0.0923888i
$753$	10.2393	+	10.2393i	0.373141	+	0.373141i
$754$			6.34198i			0.230961i
$755$	−16.0534	−	17.5472i	−0.584242	−	0.638607i
$756$			3.10590i			0.112960i
$757$	25.8080	+	25.8080i	0.938008	+	0.938008i	0.998188	−	0.0601796i	$-0.0191673\pi$
$757$	25.8080	+	25.8080i	0.938008	+	0.938008i	−0.0601796	+	0.998188i	$0.519167\pi$
$758$	−10.1829	−	10.1829i	−0.369859	−	0.369859i
$759$	2.08983			0.0758560
$760$	−0.255312	+	5.74282i	−0.00926114	+	0.208314i
$761$		−	46.5507i		−	1.68746i	−0.536766	−	0.843731i	$-0.680354\pi$
$761$		−	46.5507i		−	1.68746i	0.536766	−	0.843731i	$-0.319646\pi$
$762$	−6.59769	+	6.59769i	−0.239009	+	0.239009i
$763$	−9.52956	−	9.52956i	−0.344993	−	0.344993i
$764$			16.5247i			0.597843i
$765$	0.144490	−	3.25007i	0.00522405	−	0.117506i
$766$			37.1868i			1.34361i
$767$	0.979805	+	0.979805i	0.0353787	+	0.0353787i
$768$	0.707107	−	0.707107i	0.0255155	−	0.0255155i
$769$		−	33.1296i		−	1.19468i	−0.801987	−	0.597342i	$-0.796224\pi$
$769$		−	33.1296i		−	1.19468i	0.801987	−	0.597342i	$-0.203776\pi$
$770$	−11.7133	+	10.7162i	−0.422118	+	0.386183i
$771$			12.0116i			0.432587i
$772$	−6.82452	+	6.82452i	−0.245620	+	0.245620i
$773$	−38.5038	+	38.5038i	−1.38489	+	1.38489i	−0.549188	+	0.835699i	$0.685063\pi$
$773$	−38.5038	+	38.5038i	−1.38489	+	1.38489i	−0.835699	+	0.549188i	$0.814937\pi$
$774$	10.4313			0.374946
$775$	−4.39074	−	27.4904i	−0.157720	−	0.987484i
$776$	−5.85831			−0.210301
$777$	−16.2670	+	16.2670i	−0.583576	+	0.583576i
$778$	−22.9066	+	22.9066i	−0.821241	+	0.821241i
$779$		−	10.5854i		−	0.379260i
$780$	−1.50629	+	1.37805i	−0.0539337	+	0.0493423i
$781$		−	8.34533i		−	0.298619i
$782$	−0.940527	+	0.940527i	−0.0336332	+	0.0336332i
$783$	4.91173	+	4.91173i	0.175531	+	0.175531i
$784$			2.64659i			0.0945211i
$785$	−0.759522	+	17.0842i	−0.0271085	+	0.609761i
$786$			12.2505i			0.436961i
$787$	6.24580	+	6.24580i	0.222639	+	0.222639i	0.809609	−	0.586970i	$-0.199679\pi$
$787$	6.24580	+	6.24580i	0.222639	+	0.222639i	−0.586970	+	0.809609i	$0.699679\pi$
$788$	−8.06466	+	8.06466i	−0.287291	+	0.287291i
$789$			17.4360i			0.620737i
$790$	−1.26282	+	28.4051i	−0.0449292	+	1.01061i
$791$	12.0084			0.426971
$792$	−1.61639	−	1.61639i	−0.0574359	−	0.0574359i
$793$	4.86234	+	4.86234i	0.172667	+	0.172667i
$794$			10.0599i			0.357013i
$795$	18.3916	+	20.1030i	0.652282	+	0.712978i
$796$			12.1211i			0.429622i
$797$	2.22757	+	2.22757i	0.0789046	+	0.0789046i	0.745458	−	0.666553i	$-0.232231\pi$
$797$	2.22757	+	2.22757i	0.0789046	+	0.0789046i	−0.666553	+	0.745458i	$0.732231\pi$
$798$	5.64600	−	5.64600i	0.199866	−	0.199866i
$799$	5.21290			0.184419
$800$	−3.20784	−	3.83533i	−0.113414	−	0.135599i
$801$			10.1718i			0.359402i
$802$	6.03961	+	6.03961i	0.213266	+	0.213266i
$803$	−4.56486	−	4.56486i	−0.161091	−	0.161091i
$804$	0.224236			0.00790818
$805$	−4.28577	−	4.68456i	−0.151053	−	0.165109i
$806$	−1.24405	−	4.92884i	−0.0438198	−	0.173611i
$807$	14.9243	−	14.9243i	0.525360	−	0.525360i
$808$	−11.1094	−	11.1094i	−0.390829	−	0.390829i
$809$	−18.4580			−0.648950			−0.324475	−	0.945894i	$-0.605188\pi$
$809$	−18.4580			−0.648950			−0.324475	+	0.945894i	$0.605188\pi$
$810$	−0.0993121	+	2.23386i	−0.00348947	+	0.0784899i
$811$	53.0711			1.86358			0.931789	−	0.363000i	$-0.118248\pi$
$811$	53.0711			1.86358			0.931789	+	0.363000i	$0.118248\pi$
$812$	15.2553	+	15.2553i	0.535357	+	0.535357i
$813$	8.38372	+	8.38372i	0.294030	+	0.294030i
$814$		−	16.9315i		−	0.593450i
$815$	−10.9794	−	0.488117i	−0.384591	−	0.0170980i
$816$	1.45491			0.0509320
$817$	−18.9624	−	18.9624i	−0.663410	−	0.663410i
$818$	−14.4600	+	14.4600i	−0.505581	+	0.505581i
$819$	2.83571			0.0990878
$820$	6.21481	+	6.79311i	0.217031	+	0.237226i
$821$		−	3.57101i		−	0.124629i	−0.998057	−	0.0623146i	$-0.980152\pi$
$821$		−	3.57101i		−	0.124629i	0.998057	−	0.0623146i	$-0.0198482\pi$
$822$	−6.10844	+	6.10844i	−0.213056	+	0.213056i
$823$	9.97403	−	9.97403i	0.347673	−	0.347673i	−0.511569	−	0.859242i	$-0.670936\pi$
$823$	9.97403	−	9.97403i	0.347673	−	0.347673i	0.859242	+	0.511569i	$0.170936\pi$
$824$			9.90342i			0.345002i
$825$	−8.76725	+	7.33287i	−0.305236	+	0.255298i
$826$	4.71375			0.164012
$827$	0.892928	+	0.892928i	0.0310501	+	0.0310501i	0.722461	−	0.691411i	$-0.243011\pi$
$827$	0.892928	+	0.892928i	0.0310501	+	0.0310501i	−0.691411	+	0.722461i	$0.743011\pi$
$828$	0.646450	−	0.646450i	0.0224657	−	0.0224657i
$829$	9.51575			0.330496			0.165248	−	0.986252i	$-0.447158\pi$
$829$	9.51575			0.330496			0.165248	+	0.986252i	$0.447158\pi$
$830$	−15.3155	−	16.7407i	−0.531610	−	0.581077i
$831$	7.45589			0.258642
$832$	−0.645595	−	0.645595i	−0.0223820	−	0.0223820i
$833$	−2.72275	+	2.72275i	−0.0943377	+	0.0943377i
$834$		−	13.2010i		−	0.457115i
$835$	−24.0219	−	1.06796i	−0.831312	−	0.0369581i
$836$			5.87665i			0.203248i
$837$	−4.78078	−	2.85380i	−0.165248	−	0.0986417i
$838$	9.50124	+	9.50124i	0.328215	+	0.328215i
$839$		−	16.4379i		−	0.567500i	−0.958898	−	0.283750i	$-0.908421\pi$
$839$		−	16.4379i		−	0.567500i	0.958898	−	0.283750i	$-0.0915785\pi$
$840$	−0.308453	+	6.93814i	−0.0106426	+	0.239389i
$841$	19.2503			0.663803
$842$	−18.2110	+	18.2110i	−0.627592	+	0.627592i
$843$	−10.0252	+	10.0252i	−0.345285	+	0.345285i
$844$		−	3.26766i		−	0.112478i
$845$	−18.3634	−	20.0722i	−0.631721	−	0.690504i
$846$	−3.58297			−0.123185
$847$	12.6821	−	12.6821i	0.435763	−	0.435763i
$848$	−8.61614	+	8.61614i	−0.295880	+	0.295880i
$849$	−2.26734			−0.0778150
$850$	0.645542	−	7.24585i	0.0221419	−	0.248531i
$851$	6.77152			0.232125
$852$	−2.58147	−	2.58147i	−0.0884399	−	0.0884399i
$853$	−33.3864	−	33.3864i	−1.14313	−	1.14313i	−0.987875	−	0.155253i	$-0.950381\pi$
$853$	−33.3864	−	33.3864i	−1.14313	−	1.14313i	−0.155253	−	0.987875i	$-0.549619\pi$
$854$	23.3922			0.800466
$855$	4.24132	−	3.88026i	0.145050	−	0.132702i
$856$	19.1582			0.654814
$857$	20.6509	−	20.6509i	0.705420	−	0.705420i	−0.260149	−	0.965569i	$-0.583772\pi$
$857$	20.6509	−	20.6509i	0.705420	−	0.705420i	0.965569	+	0.260149i	$0.0837716\pi$
$858$	−1.47578	+	1.47578i	−0.0503822	+	0.0503822i
$859$	−18.1246			−0.618403			−0.309201	−	0.950997i	$-0.600062\pi$
$859$	−18.1246			−0.618403			−0.309201	+	0.950997i	$0.600062\pi$
$860$	23.3021	+	1.03596i	0.794596	+	0.0353258i
$861$		−	12.7886i		−	0.435835i
$862$	−9.36258	+	9.36258i	−0.318891	+	0.318891i
$863$	−37.2310	+	37.2310i	−1.26736	+	1.26736i	−0.319912	+	0.947447i	$0.603653\pi$
$863$	−37.2310	+	37.2310i	−1.26736	+	1.26736i	−0.947447	+	0.319912i	$0.896347\pi$
$864$	−1.00000			−0.0340207
$865$	−20.8475	−	0.926829i	−0.708836	−	0.0315131i
$866$			28.9745i			0.984592i
$867$	−10.5240	−	10.5240i	−0.357415	−	0.357415i
$868$	−14.8486	−	8.86360i	−0.503994	−	0.300850i
$869$			29.0670i			0.986031i
$870$	10.4843	+	11.4599i	0.355452	+	0.388528i
$871$		−	0.204729i		−	0.00693699i
$872$	3.06822	−	3.06822i	0.103903	−	0.103903i
$873$	4.14245	+	4.14245i	0.140201	+	0.140201i
$874$	−2.35028			−0.0794994
$875$	34.4170	+	4.61463i	1.16351	+	0.156003i
$876$	−2.82411			−0.0954180
$877$	0.916616	−	0.916616i	0.0309519	−	0.0309519i	−0.691461	−	0.722413i	$-0.743033\pi$
$877$	0.916616	−	0.916616i	0.0309519	−	0.0309519i	0.722413	+	0.691461i	$0.243033\pi$
$878$	−28.8219	−	28.8219i	−0.972691	−	0.972691i
$879$	−21.1102			−0.712030
$880$	−3.45026	−	3.77131i	−0.116308	−	0.127131i
$881$			10.2655i			0.345855i	0.984935	+	0.172927i	$0.0553226\pi$
$881$			10.2655i			0.345855i	−0.984935	+	0.172927i	$0.944677\pi$
$882$	1.87142	−	1.87142i	0.0630141	−	0.0630141i
$883$	−40.4805	+	40.4805i	−1.36228	+	1.36228i	−0.491272	+	0.871006i	$0.663468\pi$
$883$	−40.4805	+	40.4805i	−1.36228	+	1.36228i	−0.871006	+	0.491272i	$0.836532\pi$
$884$		−	1.32835i		−	0.0446771i
$885$	3.39028	+	0.150724i	0.113963	+	0.00506652i
$886$	3.90196			0.131089
$887$	−10.8456	+	10.8456i	−0.364159	+	0.364159i	−0.865342	−	0.501182i	$-0.832899\pi$
$887$	−10.8456	+	10.8456i	−0.364159	+	0.364159i	0.501182	+	0.865342i	$0.332899\pi$
$888$	−5.23746	−	5.23746i	−0.175758	−	0.175758i
$889$	28.9797			0.971948
$890$	−1.01018	+	22.7223i	−0.0338613	+	0.761655i
$891$			2.28592i			0.0765811i
$892$	8.64136	+	8.64136i	0.289334	+	0.289334i
$893$	6.51324	+	6.51324i	0.217957	+	0.217957i
$894$	−14.6095			−0.488615
$895$	29.5878	−	27.0690i	0.989012	−	0.904817i
$896$	−3.10590			−0.103761
$897$	−0.590215	−	0.590215i	−0.0197067	−	0.0197067i
$898$	−13.4633	+	13.4633i	−0.449275	+	0.449275i
$899$	−37.4990	+	9.46482i	−1.25066	+	0.315669i
$900$	−0.443699	+	4.98027i	−0.0147900	+	0.166009i
$901$	−17.7282			−0.590611
$902$	6.65552	+	6.65552i	0.221605	+	0.221605i
$903$	−22.9093	−	22.9093i	−0.762373	−	0.762373i
$904$			3.86633i			0.128592i
$905$	−16.4996	−	18.0349i	−0.548465	−	0.599501i
$906$	−10.6359			−0.353355
$907$	−23.9271	+	23.9271i	−0.794488	+	0.794488i	−0.982220	−	0.187732i	$-0.939886\pi$
$907$	−23.9271	+	23.9271i	−0.794488	+	0.794488i	0.187732	+	0.982220i	$0.439886\pi$
$908$	−4.77487	−	4.77487i	−0.158460	−	0.158460i
$909$			15.7111i			0.521105i
$910$	6.33459	+	0.281620i	0.209990	+	0.00933563i
$911$			42.8751i			1.42052i	0.703942	+	0.710258i	$0.251422\pi$
$911$			42.8751i			1.42052i	−0.703942	+	0.710258i	$0.748578\pi$
$912$	1.81783	+	1.81783i	0.0601945	+	0.0601945i
$913$	−16.4016	−	16.4016i	−0.542814	−	0.542814i
$914$	35.1066			1.16122
$915$	16.8245	+	0.747975i	0.556200	+	0.0247273i
$916$		−	20.6675i		−	0.682874i
$917$	26.9046	−	26.9046i	0.888467	−	0.888467i
$918$	−1.02878	−	1.02878i	−0.0339547	−	0.0339547i
$919$		−	1.54947i		−	0.0511124i	−0.999673	−	0.0255562i	$-0.991864\pi$
$919$		−	1.54947i		−	0.0511124i	0.999673	−	0.0255562i	$-0.00813568\pi$
$920$	1.50828	−	1.37988i	0.0497266	−	0.0454933i
$921$		−	6.85327i		−	0.225823i
$922$	2.12669	+	2.12669i	0.0700387	+	0.0700387i
$923$	−2.35691	+	2.35691i	−0.0775786	+	0.0775786i
$924$			7.09982i			0.233567i
$925$	−28.4078	+	23.7601i	−0.934044	+	0.781228i
$926$		−	28.1049i		−	0.923583i
$927$	7.00278	−	7.00278i	0.230001	−	0.230001i
$928$	−4.91173	+	4.91173i	−0.161236	+	0.161236i
$929$	27.8938			0.915167			0.457584	−	0.889167i	$-0.348715\pi$
$929$	27.8938			0.915167			0.457584	+	0.889167i	$0.348715\pi$
$930$	−10.3962	−	6.84978i	−0.340904	−	0.224613i
$931$	−6.80387			−0.222988
$932$	8.21359	−	8.21359i	0.269045	−	0.269045i
$933$	−9.99961	+	9.99961i	−0.327372	+	0.327372i
$934$			3.56438i			0.116630i
$935$	0.330293	−	7.42939i	0.0108017	−	0.242967i
$936$			0.913009i			0.0298426i
$937$	39.7118	−	39.7118i	1.29733	−	1.29733i	0.367179	−	0.930150i	$-0.380324\pi$
$937$	39.7118	−	39.7118i	1.29733	−	1.29733i	0.930150	−	0.367179i	$-0.119676\pi$
$938$	−0.492466	−	0.492466i	−0.0160796	−	0.0160796i
$939$		−	3.24822i		−	0.106002i
$940$	−8.00386	−	0.355832i	−0.261057	−	0.0116060i
$941$			16.9430i			0.552326i	0.961111	+	0.276163i	$0.0890629\pi$
$941$			16.9430i			0.552326i	−0.961111	+	0.276163i	$0.910937\pi$
$942$	5.40783	+	5.40783i	0.176197	+	0.176197i
$943$	−2.66178	+	2.66178i	−0.0866794	+	0.0866794i
$944$			1.51768i			0.0493962i
$945$	5.12412	−	4.68790i	0.166688	−	0.152497i
$946$	23.8451			0.775272
$947$	−27.6824	−	27.6824i	−0.899557	−	0.899557i	0.0958398	−	0.995397i	$-0.469446\pi$
$947$	−27.6824	−	27.6824i	−0.899557	−	0.899557i	−0.995397	+	0.0958398i	$0.969446\pi$
$948$	8.99135	+	8.99135i	0.292025	+	0.292025i
$949$			2.57844i			0.0836998i
$950$	9.85988	−	8.24674i	0.319897	−	0.267560i
$951$		−	3.69093i		−	0.119687i
$952$	−3.19527	−	3.19527i	−0.103559	−	0.103559i
$953$	3.75045	−	3.75045i	0.121489	−	0.121489i	−0.643748	−	0.765237i	$-0.722622\pi$
$953$	3.75045	−	3.75045i	0.121489	−	0.121489i	0.765237	+	0.643748i	$0.222622\pi$
$954$	12.1851			0.394506
$955$	27.2625	−	24.9417i	0.882195	−	0.807093i
$956$			10.2135i			0.330329i
$957$	11.2278	+	11.2278i	0.362944	+	0.362944i
$958$	24.0286	+	24.0286i	0.776328	+	0.776328i
$959$	26.8307			0.866408
$960$	−2.23386	−	0.0993121i	−0.0720976	−	0.00320528i
$961$	27.2867	−	14.7117i	0.880218	−	0.474570i
$962$	−4.78185	+	4.78185i	−0.154173	+	0.154173i
$963$	−13.5469	−	13.5469i	−0.436543	−	0.436543i
$964$	19.4861			0.627606
$965$	21.5597	+	0.958493i	0.694032	+	0.0308550i
$966$	−2.83947			−0.0913584
$967$	38.6129	+	38.6129i	1.24171	+	1.24171i	0.959292	+	0.282416i	$0.0911359\pi$
$967$	38.6129	+	38.6129i	1.24171	+	1.24171i	0.282416	+	0.959292i	$0.408864\pi$
$968$	4.08324	+	4.08324i	0.131240	+	0.131240i
$969$			3.74029i			0.120155i
$970$	8.84227	+	9.66506i	0.283908	+	0.310326i
$971$	2.06489			0.0662656			0.0331328	−	0.999451i	$-0.489452\pi$
$971$	2.06489			0.0662656			0.0331328	+	0.999451i	$0.489452\pi$
$972$	0.707107	+	0.707107i	0.0226805	+	0.0226805i
$973$	−28.9921	+	28.9921i	−0.929445	+	0.929445i
$974$	−18.1155			−0.580457
$975$	4.54704	+	0.405101i	0.145622	+	0.0129736i
$976$			7.53156i			0.241079i
$977$	−10.3125	+	10.3125i	−0.329926	+	0.329926i	−0.852558	−	0.522632i	$-0.824950\pi$
$977$	−10.3125	+	10.3125i	−0.329926	+	0.329926i	0.522632	+	0.852558i	$0.324950\pi$
$978$	−3.47542	+	3.47542i	−0.111132	+	0.111132i
$979$			23.2518i			0.743132i
$980$	4.36635	−	3.99464i	0.139478	−	0.127604i
$981$	−4.33911			−0.138537
$982$	−16.8980	−	16.8980i	−0.539236	−	0.539236i
$983$	26.6917	−	26.6917i	0.851332	−	0.851332i	−0.138966	−	0.990297i	$-0.544378\pi$
$983$	26.6917	−	26.6917i	0.851332	−	0.851332i	0.990297	+	0.138966i	$0.0443777\pi$
$984$	4.11753			0.131262
$985$	25.4775	+	1.13267i	0.811781	+	0.0360898i
$986$	−10.1062			−0.321846
$987$	7.86892	+	7.86892i	0.250470	+	0.250470i
$988$	1.65970	−	1.65970i	0.0528021	−	0.0528021i
$989$			9.53651i			0.303243i
$990$	−0.227019	+	5.10642i	−0.00721515	+	0.162293i
$991$		−	37.3811i		−	1.18745i	−0.804668	−	0.593725i	$-0.797657\pi$
$991$		−	37.3811i		−	1.18745i	0.804668	−	0.593725i	$-0.202343\pi$
$992$	2.85380	−	4.78078i	0.0906082	−	0.151790i
$993$	−18.7191	−	18.7191i	−0.594031	−	0.594031i
$994$			11.3389i			0.359647i
$995$	19.9975	−	18.2951i	0.633963	−	0.579994i
$996$	−10.1471			−0.321522
$997$	−28.3442	+	28.3442i	−0.897670	+	0.897670i	−0.995230	−	0.0975598i	$-0.968896\pi$
$997$	−28.3442	+	28.3442i	−0.897670	+	0.897670i	0.0975598	+	0.995230i	$0.468896\pi$
$998$	16.9612	−	16.9612i	0.536898	−	0.536898i
$999$			7.40689i			0.234344i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.k.a.433.3	yes	32
5.2	odd	4		930.2.k.b.247.3	yes	32
31.30	odd	2		930.2.k.b.433.3	yes	32
155.92	even	4	inner	930.2.k.a.247.3	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.k.a.247.3	✓	32	155.92	even	4	inner
930.2.k.a.433.3	yes	32	1.1	even	1	trivial
930.2.k.b.247.3	yes	32	5.2	odd	4
930.2.k.b.433.3	yes	32	31.30	odd	2

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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(0.707107 - 0.707107i) q^{3} -1.00000i q^{4} +(-1.64980 + 1.50935i) q^{5} +1.00000i q^{6} +(2.19620 - 2.19620i) q^{7} +(0.707107 + 0.707107i) q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(0.707107 - 0.707107i) q^{3} -1.00000i q^{4} +(-1.64980 + 1.50935i) q^{5} +1.00000i q^{6} +(2.19620 - 2.19620i) q^{7} +(0.707107 + 0.707107i) q^{8} -1.00000i q^{9} +(0.0993121 - 2.23386i) q^{10} -2.28592i q^{11} +(-0.707107 - 0.707107i) q^{12} +(-0.645595 + 0.645595i) q^{13} +3.10590i q^{14} +(-0.0993121 + 2.23386i) q^{15} -1.00000 q^{16} +(-1.02878 - 1.02878i) q^{17} +(0.707107 + 0.707107i) q^{18} -2.57080i q^{19} +(1.50935 + 1.64980i) q^{20} -3.10590i q^{21} +(1.61639 + 1.61639i) q^{22} +(-0.646450 + 0.646450i) q^{23} +1.00000 q^{24} +(0.443699 - 4.98027i) q^{25} -0.913009i q^{26} +(-0.707107 - 0.707107i) q^{27} +(-2.19620 - 2.19620i) q^{28} -6.94624 q^{29} +(-1.50935 - 1.64980i) q^{30} +(5.39846 - 1.36258i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-1.61639 - 1.61639i) q^{33} +1.45491 q^{34} +(-0.308453 + 6.93814i) q^{35} -1.00000 q^{36} +(-5.23746 - 5.23746i) q^{37} +(1.81783 + 1.81783i) q^{38} +0.913009i q^{39} +(-2.23386 - 0.0993121i) q^{40} +4.11753 q^{41} +(2.19620 + 2.19620i) q^{42} +(7.37606 - 7.37606i) q^{43} -2.28592 q^{44} +(1.50935 + 1.64980i) q^{45} -0.914219i q^{46} +(-2.53354 + 2.53354i) q^{47} +(-0.707107 + 0.707107i) q^{48} -2.64659i q^{49} +(3.20784 + 3.83533i) q^{50} -1.45491 q^{51} +(0.645595 + 0.645595i) q^{52} +(8.61614 - 8.61614i) q^{53} +1.00000 q^{54} +(3.45026 + 3.77131i) q^{55} +3.10590 q^{56} +(-1.81783 - 1.81783i) q^{57} +(4.91173 - 4.91173i) q^{58} -1.51768i q^{59} +(2.23386 + 0.0993121i) q^{60} -7.53156i q^{61} +(-2.85380 + 4.78078i) q^{62} +(-2.19620 - 2.19620i) q^{63} +1.00000i q^{64} +(0.0906728 - 2.03954i) q^{65} +2.28592 q^{66} +(-0.158559 + 0.158559i) q^{67} +(-1.02878 + 1.02878i) q^{68} +0.914219i q^{69} +(-4.68790 - 5.12412i) q^{70} +3.65076 q^{71} +(0.707107 - 0.707107i) q^{72} +(1.99695 - 1.99695i) q^{73} +7.40689 q^{74} +(-3.20784 - 3.83533i) q^{75} -2.57080 q^{76} +(-5.02033 - 5.02033i) q^{77} +(-0.645595 - 0.645595i) q^{78} -12.7157 q^{79} +(1.64980 - 1.50935i) q^{80} -1.00000 q^{81} +(-2.91153 + 2.91153i) q^{82} +(7.17507 - 7.17507i) q^{83} -3.10590 q^{84} +(3.25007 + 0.144490i) q^{85} +10.4313i q^{86} +(-4.91173 + 4.91173i) q^{87} +(1.61639 - 1.61639i) q^{88} -10.1718 q^{89} +(-2.23386 - 0.0993121i) q^{90} +2.83571i q^{91} +(0.646450 + 0.646450i) q^{92} +(2.85380 - 4.78078i) q^{93} -3.58297i q^{94} +(3.88026 + 4.24132i) q^{95} -1.00000i q^{96} +(-4.14245 + 4.14245i) q^{97} +(1.87142 + 1.87142i) q^{98} -2.28592 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 4 q^{7}+O(q^{10}) \) 32 * q - 4 * q^7	\( 32 q - 4 q^{7} + 4 q^{10} - 4 q^{15} - 32 q^{16} - 8 q^{17} + 4 q^{22} + 32 q^{24} + 8 q^{25} + 4 q^{28} - 8 q^{29} - 20 q^{31} - 4 q^{33} - 24 q^{35} - 32 q^{36} - 4 q^{37} + 16 q^{38} - 16 q^{41} - 4 q^{42} + 16 q^{43} + 8 q^{44} - 8 q^{47} - 16 q^{50} + 24 q^{53} + 32 q^{54} + 28 q^{55} - 16 q^{57} - 20 q^{58} + 16 q^{62} + 4 q^{63} - 56 q^{65} - 8 q^{66} + 32 q^{67} - 8 q^{68} - 28 q^{70} + 16 q^{71} + 20 q^{73} - 24 q^{74} + 16 q^{75} - 16 q^{76} + 40 q^{77} + 56 q^{79} - 32 q^{81} + 16 q^{82} - 72 q^{83} + 32 q^{85} + 20 q^{87} + 4 q^{88} + 64 q^{89} - 16 q^{93} + 32 q^{95} - 4 q^{97} + 16 q^{98} + 8 q^{99}+O(q^{100}) \) 32 * q - 4 * q^7 + 4 * q^10 - 4 * q^15 - 32 * q^16 - 8 * q^17 + 4 * q^22 + 32 * q^24 + 8 * q^25 + 4 * q^28 - 8 * q^29 - 20 * q^31 - 4 * q^33 - 24 * q^35 - 32 * q^36 - 4 * q^37 + 16 * q^38 - 16 * q^41 - 4 * q^42 + 16 * q^43 + 8 * q^44 - 8 * q^47 - 16 * q^50 + 24 * q^53 + 32 * q^54 + 28 * q^55 - 16 * q^57 - 20 * q^58 + 16 * q^62 + 4 * q^63 - 56 * q^65 - 8 * q^66 + 32 * q^67 - 8 * q^68 - 28 * q^70 + 16 * q^71 + 20 * q^73 - 24 * q^74 + 16 * q^75 - 16 * q^76 + 40 * q^77 + 56 * q^79 - 32 * q^81 + 16 * q^82 - 72 * q^83 + 32 * q^85 + 20 * q^87 + 4 * q^88 + 64 * q^89 - 16 * q^93 + 32 * q^95 - 4 * q^97 + 16 * q^98 + 8 * q^99

Introduction

L-functions

Modular forms

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Database

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