LMFDB - Embedded newform 385.2.i.c.221.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [385,2,Mod(221,385)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(385, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("385.221");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 385 = 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	385.i (of order $3$, 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:	$3.07424047782$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} + 17 x^{14} - 28 x^{13} + 127 x^{12} - 178 x^{11} + 612 x^{10} - 527 x^{9} + 1556 x^{8} + \cdots + 81 $ x^16 - 3x^15 + 17x^14 - 28x^13 + 127x^12 - 178x^11 + 612x^10 - 527x^9 + 1556x^8 - 1065x^7 + 2812x^6 - 1224x^5 + 2359x^4 - 1154x^3 + 1351x^2 - 333*x + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			221.7
Root			$-0.735245 - 1.27348i$ of defining polynomial
Character	$\chi$	$=$	385.221
Dual form			385.2.i.c.331.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.735245 + 1.27348i) q^{2} +(-0.359468 + 0.622616i) q^{3} +(-0.0811705 + 0.140591i) q^{4} +(-0.500000 - 0.866025i) q^{5} -1.05719 q^{6} +(2.24301 - 1.40318i) q^{7} +2.70226 q^{8} +(1.24157 + 2.15046i) q^{9} +O(q^{10})$	\(q+(0.735245 + 1.27348i) q^{2} +(-0.359468 + 0.622616i) q^{3} +(-0.0811705 + 0.140591i) q^{4} +(-0.500000 - 0.866025i) q^{5} -1.05719 q^{6} +(2.24301 - 1.40318i) q^{7} +2.70226 q^{8} +(1.24157 + 2.15046i) q^{9} +(0.735245 - 1.27348i) q^{10} +(0.500000 - 0.866025i) q^{11} +(-0.0583564 - 0.101076i) q^{12} -1.35223 q^{13} +(3.43609 + 1.82475i) q^{14} +0.718935 q^{15} +(2.14916 + 3.72246i) q^{16} +(0.271076 - 0.469517i) q^{17} +(-1.82571 + 3.16222i) q^{18} +(-0.0996235 - 0.172553i) q^{19} +0.162341 q^{20} +(0.0673544 + 1.90093i) q^{21} +1.47049 q^{22} +(1.98556 + 3.43910i) q^{23} +(-0.971375 + 1.68247i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-0.994221 - 1.72204i) q^{26} -3.94202 q^{27} +(0.0152091 + 0.429245i) q^{28} +2.25572 q^{29} +(0.528594 + 0.915551i) q^{30} +(-3.01637 + 5.22451i) q^{31} +(-0.458065 + 0.793391i) q^{32} +(0.359468 + 0.622616i) q^{33} +0.797229 q^{34} +(-2.33669 - 1.24091i) q^{35} -0.403114 q^{36} +(-3.88315 - 6.72581i) q^{37} +(0.146495 - 0.253737i) q^{38} +(0.486083 - 0.841921i) q^{39} +(-1.35113 - 2.34023i) q^{40} +4.07178 q^{41} +(-2.37128 + 1.48342i) q^{42} -9.85011 q^{43} +(0.0811705 + 0.140591i) q^{44} +(1.24157 - 2.15046i) q^{45} +(-2.91975 + 5.05716i) q^{46} +(-3.93074 - 6.80824i) q^{47} -3.09022 q^{48} +(3.06217 - 6.29469i) q^{49} -1.47049 q^{50} +(0.194886 + 0.337553i) q^{51} +(0.109761 - 0.190112i) q^{52} +(-4.51408 + 7.81862i) q^{53} +(-2.89835 - 5.02009i) q^{54} -1.00000 q^{55} +(6.06119 - 3.79176i) q^{56} +0.143246 q^{57} +(1.65851 + 2.87262i) q^{58} +(3.78709 - 6.55943i) q^{59} +(-0.0583564 + 0.101076i) q^{60} +(-3.75537 - 6.50448i) q^{61} -8.87109 q^{62} +(5.80232 + 3.08135i) q^{63} +7.24950 q^{64} +(0.676115 + 1.17107i) q^{65} +(-0.528594 + 0.915551i) q^{66} +(4.00602 - 6.93864i) q^{67} +(0.0440068 + 0.0762219i) q^{68} -2.85498 q^{69} +(-0.137765 - 3.88811i) q^{70} +6.96472 q^{71} +(3.35503 + 5.81109i) q^{72} +(-7.43549 + 12.8787i) q^{73} +(5.71013 - 9.89024i) q^{74} +(-0.359468 - 0.622616i) q^{75} +0.0323460 q^{76} +(-0.0936863 - 2.64409i) q^{77} +1.42956 q^{78} +(0.181768 + 0.314832i) q^{79} +(2.14916 - 3.72246i) q^{80} +(-2.30767 + 3.99700i) q^{81} +(2.99376 + 5.18534i) q^{82} +3.87173 q^{83} +(-0.272722 - 0.144830i) q^{84} -0.542152 q^{85} +(-7.24224 - 12.5439i) q^{86} +(-0.810858 + 1.40445i) q^{87} +(1.35113 - 2.34023i) q^{88} +(1.99114 + 3.44875i) q^{89} +3.65142 q^{90} +(-3.03306 + 1.89742i) q^{91} -0.644677 q^{92} +(-2.16858 - 3.75608i) q^{93} +(5.78011 - 10.0114i) q^{94} +(-0.0996235 + 0.172553i) q^{95} +(-0.329319 - 0.570397i) q^{96} -16.6867 q^{97} +(10.2676 - 0.728526i) q^{98} +2.48313 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 3 q^{2} - q^{3} - 9 q^{4} - 8 q^{5} - 6 q^{6} - q^{7} + 18 q^{8} - 19 q^{9}+O(q^{10}) $ 16 * q - 3 * q^2 - q^3 - 9 * q^4 - 8 * q^5 - 6 * q^6 - q^7 + 18 * q^8 - 19 * q^9	\( 16 q - 3 q^{2} - q^{3} - 9 q^{4} - 8 q^{5} - 6 q^{6} - q^{7} + 18 q^{8} - 19 q^{9} - 3 q^{10} + 8 q^{11} - 9 q^{12} + 28 q^{13} - 9 q^{14} + 2 q^{15} - 7 q^{16} - 5 q^{17} - 27 q^{18} - q^{19} + 18 q^{20} - 18 q^{21} - 6 q^{22} + 2 q^{23} + 24 q^{24} - 8 q^{25} - 21 q^{26} - 10 q^{27} + 32 q^{28} + 52 q^{29} + 3 q^{30} - 2 q^{31} - 16 q^{32} + q^{33} - 52 q^{34} + 5 q^{35} + 108 q^{36} + q^{37} + 31 q^{38} - 19 q^{39} - 9 q^{40} - 6 q^{41} + 44 q^{42} + 8 q^{43} + 9 q^{44} - 19 q^{45} - 10 q^{46} - q^{47} - 42 q^{48} + 17 q^{49} + 6 q^{50} - 3 q^{51} - 37 q^{52} - 26 q^{53} + 5 q^{54} - 16 q^{55} + 40 q^{57} + q^{58} + 19 q^{59} - 9 q^{60} - 52 q^{62} - 21 q^{63} + 2 q^{64} - 14 q^{65} - 3 q^{66} + 13 q^{67} - 15 q^{68} - 28 q^{69} + 15 q^{70} - 18 q^{71} - 32 q^{72} - 11 q^{73} - 24 q^{74} - q^{75} - 36 q^{76} + 4 q^{77} - 66 q^{78} + 8 q^{79} - 7 q^{80} - 52 q^{81} - 41 q^{82} + 64 q^{83} + 138 q^{84} + 10 q^{85} - 28 q^{86} + 16 q^{87} + 9 q^{88} - 5 q^{89} + 54 q^{90} + 13 q^{91} + 60 q^{92} + 14 q^{93} + 5 q^{94} - q^{95} - q^{96} + 18 q^{97} + 22 q^{98} - 38 q^{99}+O(q^{100}) \) 16 * q - 3 * q^2 - q^3 - 9 * q^4 - 8 * q^5 - 6 * q^6 - q^7 + 18 * q^8 - 19 * q^9 - 3 * q^10 + 8 * q^11 - 9 * q^12 + 28 * q^13 - 9 * q^14 + 2 * q^15 - 7 * q^16 - 5 * q^17 - 27 * q^18 - q^19 + 18 * q^20 - 18 * q^21 - 6 * q^22 + 2 * q^23 + 24 * q^24 - 8 * q^25 - 21 * q^26 - 10 * q^27 + 32 * q^28 + 52 * q^29 + 3 * q^30 - 2 * q^31 - 16 * q^32 + q^33 - 52 * q^34 + 5 * q^35 + 108 * q^36 + q^37 + 31 * q^38 - 19 * q^39 - 9 * q^40 - 6 * q^41 + 44 * q^42 + 8 * q^43 + 9 * q^44 - 19 * q^45 - 10 * q^46 - q^47 - 42 * q^48 + 17 * q^49 + 6 * q^50 - 3 * q^51 - 37 * q^52 - 26 * q^53 + 5 * q^54 - 16 * q^55 + 40 * q^57 + q^58 + 19 * q^59 - 9 * q^60 - 52 * q^62 - 21 * q^63 + 2 * q^64 - 14 * q^65 - 3 * q^66 + 13 * q^67 - 15 * q^68 - 28 * q^69 + 15 * q^70 - 18 * q^71 - 32 * q^72 - 11 * q^73 - 24 * q^74 - q^75 - 36 * q^76 + 4 * q^77 - 66 * q^78 + 8 * q^79 - 7 * q^80 - 52 * q^81 - 41 * q^82 + 64 * q^83 + 138 * q^84 + 10 * q^85 - 28 * q^86 + 16 * q^87 + 9 * q^88 - 5 * q^89 + 54 * q^90 + 13 * q^91 + 60 * q^92 + 14 * q^93 + 5 * q^94 - q^95 - q^96 + 18 * q^97 + 22 * q^98 - 38 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/385\mathbb{Z}\right)^\times$.

$n$	$211$	$232$	$276$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.735245	+	1.27348i	0.519897	+	0.900488i	0.999732	+	0.0231292i	$0.00736292\pi$
$2$	0.735245	+	1.27348i	0.519897	+	0.900488i	−0.479836	+	0.877358i	$0.659304\pi$
$3$	−0.359468	+	0.622616i	−0.207539	+	0.359468i	−0.950939	−	0.309380i	$-0.899879\pi$
$3$	−0.359468	+	0.622616i	−0.207539	+	0.359468i	0.743400	+	0.668847i	$0.233212\pi$
$4$	−0.0811705	+	0.140591i	−0.0405853	+	0.0702957i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	−1.05719			−0.431595
$7$	2.24301	−	1.40318i	0.847777	−	0.530352i
$7$	2.24301	−	1.40318i	0.847777	−	0.530352i
$8$	2.70226			0.955393
$9$	1.24157	+	2.15046i	0.413855	+	0.716818i
$10$	0.735245	−	1.27348i	0.232505	−	0.402710i
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$12$	−0.0583564	−	0.101076i	−0.0168460	−	0.0291782i
$13$	−1.35223			−0.375041			−0.187521	−	0.982261i	$-0.560045\pi$
$13$	−1.35223			−0.375041			−0.187521	+	0.982261i	$0.560045\pi$
$14$	3.43609	+	1.82475i	0.918332	+	0.487684i
$15$	0.718935			0.185628
$16$	2.14916	+	3.72246i	0.537291	+	0.930615i
$17$	0.271076	−	0.469517i	0.0657456	−	0.113875i	−0.831279	−	0.555856i	$-0.812391\pi$
$17$	0.271076	−	0.469517i	0.0657456	−	0.113875i	0.897024	+	0.441981i	$0.145724\pi$
$18$	−1.82571	+	3.16222i	−0.430324	+	0.745343i
$19$	−0.0996235	−	0.172553i	−0.0228552	−	0.0395863i	0.854372	−	0.519663i	$-0.173942\pi$
$19$	−0.0996235	−	0.172553i	−0.0228552	−	0.0395863i	−0.877227	+	0.480076i	$0.840609\pi$
$20$	0.162341			0.0363006
$21$	0.0673544	+	1.90093i	0.0146979	+	0.414817i
$22$	1.47049			0.313510
$23$	1.98556	+	3.43910i	0.414019	+	0.717102i	0.995325	−	0.0965834i	$-0.0307914\pi$
$23$	1.98556	+	3.43910i	0.414019	+	0.717102i	−0.581306	+	0.813685i	$0.697458\pi$
$24$	−0.971375	+	1.68247i	−0.198281	+	0.343433i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−0.994221	−	1.72204i	−0.194983	−	0.337720i
$27$	−3.94202			−0.758642
$28$	0.0152091	+	0.429245i	0.00287426	+	0.0811196i
$29$	2.25572			0.418876			0.209438	−	0.977822i	$-0.432837\pi$
$29$	2.25572			0.418876			0.209438	+	0.977822i	$0.432837\pi$
$30$	0.528594	+	0.915551i	0.0965076	+	0.167156i
$31$	−3.01637	+	5.22451i	−0.541756	+	0.938349i	0.457047	+	0.889443i	$0.348907\pi$
$31$	−3.01637	+	5.22451i	−0.541756	+	0.938349i	−0.998803	+	0.0489069i	$0.984426\pi$
$32$	−0.458065	+	0.793391i	−0.0809752	+	0.140253i
$33$	0.359468	+	0.622616i	0.0625753	+	0.108384i
$34$	0.797229			0.136724
$35$	−2.33669	−	1.24091i	−0.394973	−	0.209752i
$36$	−0.403114			−0.0671857
$37$	−3.88315	−	6.72581i	−0.638386	−	1.10572i	−0.985787	−	0.168000i	$-0.946269\pi$
$37$	−3.88315	−	6.72581i	−0.638386	−	1.10572i	0.347401	−	0.937717i	$-0.387064\pi$
$38$	0.146495	−	0.253737i	0.0237647	−	0.0411616i
$39$	0.486083	−	0.841921i	0.0778356	−	0.134815i
$40$	−1.35113	−	2.34023i	−0.213632	−	0.370022i
$41$	4.07178			0.635906			0.317953	−	0.948106i	$-0.397005\pi$
$41$	4.07178			0.635906			0.317953	+	0.948106i	$0.397005\pi$
$42$	−2.37128	+	1.48342i	−0.365896	+	0.228897i
$43$	−9.85011			−1.50213			−0.751064	−	0.660230i	$-0.770459\pi$
$43$	−9.85011			−1.50213			−0.751064	+	0.660230i	$0.770459\pi$
$44$	0.0811705	+	0.140591i	0.0122369	+	0.0211950i
$45$	1.24157	−	2.15046i	0.185082	−	0.320571i
$46$	−2.91975	+	5.05716i	−0.430494	+	0.745638i
$47$	−3.93074	−	6.80824i	−0.573357	−	0.993084i	−0.996218	−	0.0868891i	$-0.972307\pi$
$47$	−3.93074	−	6.80824i	−0.573357	−	0.993084i	0.422861	−	0.906195i	$-0.361026\pi$
$48$	−3.09022			−0.446035
$49$	3.06217	−	6.29469i	0.437452	−	0.899242i
$50$	−1.47049			−0.207959
$51$	0.194886	+	0.337553i	0.0272895	+	0.0472668i
$52$	0.109761	−	0.190112i	0.0152211	−	0.0263638i
$53$	−4.51408	+	7.81862i	−0.620057	+	1.07397i	0.369417	+	0.929264i	$0.379557\pi$
$53$	−4.51408	+	7.81862i	−0.620057	+	1.07397i	−0.989475	+	0.144707i	$0.953776\pi$
$54$	−2.89835	−	5.02009i	−0.394415	−	0.683147i
$55$	−1.00000			−0.134840
$56$	6.06119	−	3.79176i	0.809960	−	0.506695i
$57$	0.143246			0.0189733
$58$	1.65851	+	2.87262i	0.217772	+	0.377193i
$59$	3.78709	−	6.55943i	0.493037	−	0.853965i	−0.506931	−	0.861987i	$-0.669220\pi$
$59$	3.78709	−	6.55943i	0.493037	−	0.853965i	0.999968	+	0.00802163i	$0.00255339\pi$
$60$	−0.0583564	+	0.101076i	−0.00753377	+	0.0130489i
$61$	−3.75537	−	6.50448i	−0.480825	−	0.832814i	0.518933	−	0.854815i	$-0.326330\pi$
$61$	−3.75537	−	6.50448i	−0.480825	−	0.832814i	−0.999758	+	0.0220013i	$0.992996\pi$
$62$	−8.87109			−1.12663
$63$	5.80232	+	3.08135i	0.731024	+	0.388213i
$64$	7.24950			0.906187
$65$	0.676115	+	1.17107i	0.0838618	+	0.145253i
$66$	−0.528594	+	0.915551i	−0.0650654	+	0.112697i
$67$	4.00602	−	6.93864i	0.489414	−	0.847689i	−0.510512	−	0.859871i	$-0.670544\pi$
$67$	4.00602	−	6.93864i	0.489414	−	0.847689i	0.999926	+	0.0121811i	$0.00387746\pi$
$68$	0.0440068	+	0.0762219i	0.00533660	+	0.00924327i
$69$	−2.85498			−0.343700
$70$	−0.137765	−	3.88811i	−0.0164660	−	0.464718i
$71$	6.96472			0.826560			0.413280	−	0.910604i	$-0.364383\pi$
$71$	6.96472			0.826560			0.413280	+	0.910604i	$0.364383\pi$
$72$	3.35503	+	5.81109i	0.395394	+	0.684843i
$73$	−7.43549	+	12.8787i	−0.870259	+	1.50733i	−0.00852971	+	0.999964i	$0.502715\pi$
$73$	−7.43549	+	12.8787i	−0.870259	+	1.50733i	−0.861729	+	0.507369i	$0.830618\pi$
$74$	5.71013	−	9.89024i	0.663790	−	1.14972i
$75$	−0.359468	−	0.622616i	−0.0415078	−	0.0718935i
$76$	0.0323460			0.00371034
$77$	−0.0936863	−	2.64409i	−0.0106765	−	0.301322i
$78$	1.42956			0.161866
$79$	0.181768	+	0.314832i	0.0204505	+	0.0354214i	0.876070	−	0.482185i	$-0.160157\pi$
$79$	0.181768	+	0.314832i	0.0204505	+	0.0354214i	−0.855619	+	0.517606i	$0.826823\pi$
$80$	2.14916	−	3.72246i	0.240284	−	0.416184i
$81$	−2.30767	+	3.99700i	−0.256408	+	0.444111i
$82$	2.99376	+	5.18534i	0.330605	+	0.572625i
$83$	3.87173			0.424978			0.212489	−	0.977163i	$-0.431843\pi$
$83$	3.87173			0.424978			0.212489	+	0.977163i	$0.431843\pi$
$84$	−0.272722	−	0.144830i	−0.0297564	−	0.0158023i
$85$	−0.542152			−0.0588046
$86$	−7.24224	−	12.5439i	−0.780951	−	1.35265i
$87$	−0.810858	+	1.40445i	−0.0869331	+	0.150572i
$88$	1.35113	−	2.34023i	0.144031	−	0.249469i
$89$	1.99114	+	3.44875i	0.211060	+	0.365567i	0.952047	−	0.305953i	$-0.0989751\pi$
$89$	1.99114	+	3.44875i	0.211060	+	0.365567i	−0.740986	+	0.671520i	$0.765642\pi$
$90$	3.65142			0.384894
$91$	−3.03306	+	1.89742i	−0.317951	+	0.198904i
$92$	−0.644677			−0.0672123
$93$	−2.16858	−	3.75608i	−0.224871	−	0.389488i
$94$	5.78011	−	10.0114i	0.596173	−	1.03260i
$95$	−0.0996235	+	0.172553i	−0.0102212	+	0.0177036i
$96$	−0.329319	−	0.570397i	−0.0336110	−	0.0582159i
$97$	−16.6867			−1.69427			−0.847137	−	0.531375i	$-0.821676\pi$
$97$	−16.6867			−1.69427			−0.847137	+	0.531375i	$0.821676\pi$
$98$	10.2676	−	0.728526i	1.03719	−	0.0735922i
$99$	2.48313			0.249564
$100$	−0.0811705	−	0.140591i	−0.00811705	−	0.0140591i
$101$	−2.41345	+	4.18022i	−0.240147	+	0.415947i	−0.960756	−	0.277395i	$-0.910529\pi$
$101$	−2.41345	+	4.18022i	−0.240147	+	0.415947i	0.720609	+	0.693342i	$0.243862\pi$
$102$	−0.286578	+	0.496368i	−0.0283755	+	0.0491477i
$103$	−8.28537	−	14.3507i	−0.816382	−	1.41401i	−0.908331	−	0.418251i	$-0.862643\pi$
$103$	−8.28537	−	14.3507i	−0.816382	−	1.41401i	0.0919498	−	0.995764i	$-0.470690\pi$
$104$	−3.65408			−0.358312
$105$	1.61258	−	1.00880i	0.157371	−	0.0984484i
$106$	−13.2758			−1.28946
$107$	−1.22575	−	2.12306i	−0.118498	−	0.205244i	0.800675	−	0.599099i	$-0.204475\pi$
$107$	−1.22575	−	2.12306i	−0.118498	−	0.205244i	−0.919173	+	0.393855i	$0.871141\pi$
$108$	0.319976	−	0.554214i	0.0307897	−	0.0533293i
$109$	−2.00770	+	3.47744i	−0.192303	+	0.333078i	−0.946013	−	0.324129i	$-0.894929\pi$
$109$	−2.00770	+	3.47744i	−0.192303	+	0.333078i	0.753710	+	0.657207i	$0.228262\pi$
$110$	−0.735245	−	1.27348i	−0.0701029	−	0.121422i
$111$	5.58347			0.529959
$112$	10.0439	+	5.33384i	0.949057	+	0.504001i
$113$	−13.6765			−1.28658			−0.643290	−	0.765622i	$-0.722431\pi$
$113$	−13.6765			−1.28658			−0.643290	+	0.765622i	$0.722431\pi$
$114$	0.105321	+	0.182421i	0.00986418	+	0.0170853i
$115$	1.98556	−	3.43910i	0.185155	−	0.320698i
$116$	−0.183098	+	0.317135i	−0.0170002	+	0.0294452i
$117$	−1.67888	−	2.90791i	−0.155213	−	0.268836i
$118$	11.1378			1.02531
$119$	−0.0507922	−	1.43350i	−0.00465611	−	0.131409i
$120$	1.94275			0.177348
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	5.52223	−	9.56478i	0.499959	−	0.865954i
$123$	−1.46367	+	2.53516i	−0.131975	+	0.228588i
$124$	−0.489681	−	0.848152i	−0.0439746	−	0.0761663i
$125$	1.00000			0.0894427
$126$	0.342088	+	9.65469i	0.0304756	+	0.860108i
$127$	15.7491			1.39750			0.698752	−	0.715364i	$-0.253739\pi$
$127$	15.7491			1.39750			0.698752	+	0.715364i	$0.253739\pi$
$128$	6.24629	+	10.8189i	0.552099	+	0.956263i
$129$	3.54080	−	6.13284i	0.311750	−	0.539966i
$130$	−0.994221	+	1.72204i	−0.0871989	+	0.151033i
$131$	3.66206	+	6.34288i	0.319956	+	0.554180i	0.980479	−	0.196626i	$-0.0629985\pi$
$131$	3.66206	+	6.34288i	0.319956	+	0.554180i	−0.660523	+	0.750806i	$0.729665\pi$
$132$	−0.116713			−0.0101585
$133$	−0.465579	−	0.247248i	−0.0403708	−	0.0214391i
$134$	11.7816			1.01778
$135$	1.97101	+	3.41389i	0.169637	+	0.293821i
$136$	0.732517	−	1.26876i	0.0628128	−	0.108795i
$137$	−3.85358	+	6.67459i	−0.329233	+	0.570249i	−0.982360	−	0.187000i	$-0.940124\pi$
$137$	−3.85358	+	6.67459i	−0.329233	+	0.570249i	0.653126	+	0.757249i	$0.273457\pi$
$138$	−2.09911	−	3.63577i	−0.178688	−	0.309497i
$139$	−16.6345			−1.41092			−0.705461	−	0.708749i	$-0.749260\pi$
$139$	−16.6345			−1.41092			−0.705461	+	0.708749i	$0.749260\pi$
$140$	0.364132	−	0.227794i	0.0307748	−	0.0192521i
$141$	5.65189			0.475975
$142$	5.12078	+	8.86945i	0.429726	+	0.744307i
$143$	−0.676115	+	1.17107i	−0.0565396	+	0.0979294i
$144$	−5.33666	+	9.24336i	−0.444721	+	0.770280i
$145$	−1.12786	−	1.95351i	−0.0936636	−	0.162230i
$146$	−21.8676			−1.80978
$147$	2.81843	+	4.16929i	0.232460	+	0.343877i
$148$	1.26079			0.103636
$149$	−4.15586	−	7.19816i	−0.340461	−	0.589696i	0.644057	−	0.764977i	$-0.277250\pi$
$149$	−4.15586	−	7.19816i	−0.340461	−	0.589696i	−0.984518	+	0.175281i	$0.943917\pi$
$150$	0.528594	−	0.915551i	0.0431595	−	0.0747544i
$151$	−3.79937	+	6.58071i	−0.309189	+	0.535530i	−0.978185	−	0.207735i	$-0.933391\pi$
$151$	−3.79937	+	6.58071i	−0.309189	+	0.535530i	0.668997	+	0.743266i	$0.266724\pi$
$152$	−0.269208	−	0.466283i	−0.0218357	−	0.0378205i
$153$	1.34623			0.108837
$154$	3.29832	−	2.06336i	0.265786	−	0.166271i
$155$	6.03274			0.484562
$156$	0.0789112	+	0.136678i	0.00631796	+	0.0109430i
$157$	−3.83556	+	6.64339i	−0.306111	+	0.530200i	−0.977508	−	0.210898i	$-0.932361\pi$
$157$	−3.83556	+	6.64339i	−0.306111	+	0.530200i	0.671397	+	0.741098i	$0.265695\pi$
$158$	−0.267289	+	0.462958i	−0.0212643	+	0.0368309i
$159$	−3.24533	−	5.62108i	−0.257372	−	0.445781i
$160$	0.916129			0.0724264
$161$	9.27931	+	4.92782i	0.731312	+	0.388367i
$162$	−6.78681			−0.533222
$163$	−8.47009	−	14.6706i	−0.663428	−	1.14909i	−0.979709	−	0.200426i	$-0.935767\pi$
$163$	−8.47009	−	14.6706i	−0.663428	−	1.14909i	0.316281	−	0.948666i	$-0.397566\pi$
$164$	−0.330509	+	0.572458i	−0.0258084	+	0.0447015i
$165$	0.359468	−	0.622616i	0.0279845	−	0.0484706i
$166$	2.84667	+	4.93058i	0.220945	+	0.382687i
$167$	12.0563			0.932945			0.466472	−	0.884536i	$-0.345525\pi$
$167$	12.0563			0.932945			0.466472	+	0.884536i	$0.345525\pi$
$168$	0.182009	+	5.13681i	0.0140423	+	0.396313i
$169$	−11.1715			−0.859344
$170$	−0.398614	−	0.690420i	−0.0305723	−	0.0529528i
$171$	0.247378	−	0.428472i	0.0189175	−	0.0327660i
$172$	0.799539	−	1.38484i	0.0609642	−	0.105593i
$173$	4.60695	+	7.97947i	0.350260	+	0.606668i	0.986295	−	0.164993i	$-0.0527600\pi$
$173$	4.60695	+	7.97947i	0.350260	+	0.606668i	−0.636035	+	0.771660i	$0.719427\pi$
$174$	−2.38472			−0.180785
$175$	0.0936863	+	2.64409i	0.00708202	+	0.199875i
$176$	4.29833			0.323999
$177$	2.72267	+	4.71581i	0.204649	+	0.354462i
$178$	−2.92795	+	5.07135i	−0.219459	+	0.380114i
$179$	−2.16076	+	3.74255i	−0.161503	+	0.279731i	−0.935408	−	0.353570i	$-0.884967\pi$
$179$	−2.16076	+	3.74255i	−0.161503	+	0.279731i	0.773905	+	0.633302i	$0.218301\pi$
$180$	0.201557	+	0.349107i	0.0150232	+	0.0260209i
$181$	−2.54375			−0.189075			−0.0945377	−	0.995521i	$-0.530137\pi$
$181$	−2.54375			−0.189075			−0.0945377	+	0.995521i	$0.530137\pi$
$182$	−4.64638	−	2.46748i	−0.344412	−	0.182902i
$183$	5.39973			0.399160
$184$	5.36551	+	9.29334i	0.395551	+	0.685114i
$185$	−3.88315	+	6.72581i	−0.285495	+	0.494492i
$186$	3.18887	−	5.52328i	0.233819	−	0.404987i
$187$	−0.271076	−	0.469517i	−0.0198230	−	0.0343345i
$188$	1.27624			0.0930794
$189$	−8.84198	+	5.53136i	−0.643159	+	0.402347i
$190$	−0.292991			−0.0212558
$191$	−1.46281	−	2.53367i	−0.105845	−	0.183330i	0.808238	−	0.588856i	$-0.200422\pi$
$191$	−1.46281	−	2.53367i	−0.105845	−	0.183330i	−0.914083	+	0.405526i	$0.867088\pi$
$192$	−2.60596	+	4.51365i	−0.188069	+	0.325745i
$193$	−6.67993	+	11.5700i	−0.480832	+	0.832825i	−0.999758	−	0.0219936i	$-0.992999\pi$
$193$	−6.67993	+	11.5700i	−0.480832	+	0.832825i	0.518926	+	0.854819i	$0.326332\pi$
$194$	−12.2688	−	21.2502i	−0.880847	−	1.52567i
$195$	−0.972166			−0.0696183
$196$	0.636422	+	0.941458i	0.0454587	+	0.0672470i
$197$	11.2489			0.801454			0.400727	−	0.916198i	$-0.368758\pi$
$197$	11.2489			0.801454			0.400727	+	0.916198i	$0.368758\pi$
$198$	1.82571	+	3.16222i	0.129748	+	0.224729i
$199$	5.24565	−	9.08574i	0.371855	−	0.644071i	−0.617996	−	0.786181i	$-0.712055\pi$
$199$	5.24565	−	9.08574i	0.371855	−	0.644071i	0.989851	+	0.142110i	$0.0453887\pi$
$200$	−1.35113	+	2.34023i	−0.0955393	+	0.165479i
$201$	2.88007	+	4.98843i	0.203145	+	0.351857i
$202$	−7.09791			−0.499407
$203$	5.05959	−	3.16518i	0.355114	−	0.222152i
$204$	−0.0632760			−0.00443021
$205$	−2.03589	−	3.52627i	−0.142193	−	0.246285i
$206$	12.1836	−	21.1025i	0.848868	−	1.47028i
$207$	−4.93042	+	8.53974i	−0.342688	+	0.593553i
$208$	−2.90616	−	5.03362i	−0.201506	−	0.349019i
$209$	−0.199247			−0.0137822
$210$	2.47032	+	1.31188i	0.170468	+	0.0905280i
$211$	8.48714			0.584279			0.292139	−	0.956376i	$-0.405633\pi$
$211$	8.48714			0.584279			0.292139	+	0.956376i	$0.405633\pi$
$212$	−0.732821	−	1.26928i	−0.0503304	−	0.0871747i
$213$	−2.50359	+	4.33635i	−0.171543	+	0.297122i
$214$	1.80246	−	3.12195i	0.123213	−	0.213412i
$215$	4.92505	+	8.53044i	0.335886	+	0.581771i
$216$	−10.6524			−0.724801
$217$	0.565185	+	15.9511i	0.0383673	+	1.08283i
$218$	−5.90461			−0.399911
$219$	−5.34564	−	9.25892i	−0.361225	−	0.625660i
$220$	0.0811705	−	0.140591i	0.00547252	−	0.00947868i
$221$	−0.366557	+	0.634895i	−0.0246573	+	0.0427077i
$222$	4.10522	+	7.11044i	0.275524	+	0.477222i
$223$	19.7906			1.32528			0.662640	−	0.748938i	$-0.269436\pi$
$223$	19.7906			1.32528			0.662640	+	0.748938i	$0.269436\pi$
$224$	0.0858288	+	2.42233i	0.00573468	+	0.161849i
$225$	−2.48313			−0.165542
$226$	−10.0556	−	17.4168i	−0.668889	−	1.15855i
$227$	1.14223	−	1.97839i	0.0758122	−	0.131311i	−0.825627	−	0.564216i	$-0.809178\pi$
$227$	1.14223	−	1.97839i	0.0758122	−	0.131311i	0.901439	+	0.432906i	$0.142512\pi$
$228$	−0.0116273	+	0.0201391i	−0.000770038	+	0.00133375i
$229$	13.1008	+	22.6912i	0.865723	+	1.49948i	0.866328	+	0.499476i	$0.166474\pi$
$229$	13.1008	+	22.6912i	0.865723	+	1.49948i	−0.000605448		1.00000i	$0.500193\pi$
$230$	5.83951			0.385046
$231$	1.67993	+	0.892135i	0.110531	+	0.0586982i
$232$	6.09553			0.400191
$233$	−9.01622	−	15.6166i	−0.590672	−	1.02307i	−0.994142	−	0.108081i	$-0.965529\pi$
$233$	−9.01622	−	15.6166i	−0.590672	−	1.02307i	0.403470	−	0.914993i	$-0.367804\pi$
$234$	2.46878	−	4.27605i	0.161389	−	0.279534i
$235$	−3.93074	+	6.80824i	−0.256413	+	0.444121i
$236$	0.614800	+	1.06486i	0.0400201	+	0.0693168i
$237$	−0.261359			−0.0169771
$238$	1.78819	−	1.11866i	0.115911	−	0.0725117i
$239$	26.4144			1.70861			0.854304	−	0.519774i	$-0.173984\pi$
$239$	26.4144			1.70861			0.854304	+	0.519774i	$0.173984\pi$
$240$	1.54511	+	2.67621i	0.0997364	+	0.172749i
$241$	−7.17106	+	12.4206i	−0.461928	+	0.800083i	−0.999057	−	0.0434170i	$-0.986176\pi$
$241$	−7.17106	+	12.4206i	−0.461928	+	0.800083i	0.537129	+	0.843500i	$0.319509\pi$
$242$	0.735245	−	1.27348i	0.0472633	−	0.0818625i
$243$	−7.57209	−	13.1152i	−0.485750	−	0.841344i
$244$	1.21930			0.0780577
$245$	−6.98245	+	0.495430i	−0.446092	+	0.0316519i
$246$	−4.30464			−0.274454
$247$	0.134714	+	0.233331i	0.00857164	+	0.0148465i
$248$	−8.15102	+	14.1180i	−0.517590	+	0.896492i
$249$	−1.39176	+	2.41060i	−0.0881994	+	0.152766i
$250$	0.735245	+	1.27348i	0.0465010	+	0.0805421i
$251$	7.73165			0.488018			0.244009	−	0.969773i	$-0.421537\pi$
$251$	7.73165			0.488018			0.244009	+	0.969773i	$0.421537\pi$
$252$	−0.904188	+	0.565642i	−0.0569585	+	0.0356321i
$253$	3.97113			0.249663
$254$	11.5794	+	20.0561i	0.726558	+	1.25843i
$255$	0.194886	−	0.337553i	0.0122042	−	0.0211384i
$256$	−1.93560	+	3.35257i	−0.120975	+	0.209535i
$257$	3.86407	+	6.69276i	0.241034	+	0.417483i	0.961009	−	0.276517i	$-0.0891802\pi$
$257$	3.86407	+	6.69276i	0.241034	+	0.417483i	−0.719975	+	0.694000i	$0.755847\pi$
$258$	10.4134			0.648311
$259$	−18.1475	−	9.63729i	−1.12763	−	0.598832i
$260$	−0.219522			−0.0136142
$261$	2.80062	+	4.85082i	0.173354	+	0.300258i
$262$	−5.38503	+	9.32714i	−0.332688	+	0.576233i
$263$	−11.4831	+	19.8892i	−0.708076	+	1.22642i	0.257494	+	0.966280i	$0.417103\pi$
$263$	−11.4831	+	19.8892i	−0.708076	+	1.22642i	−0.965570	+	0.260144i	$0.916230\pi$
$264$	0.971375	+	1.68247i	0.0597840	+	0.103549i
$265$	9.02817			0.554596
$266$	−0.0274492	−	0.774694i	−0.00168302	−	0.0474995i
$267$	−2.86300			−0.175213
$268$	0.650342	+	1.12643i	0.0397260	+	0.0688074i
$269$	10.7424	−	18.6064i	0.654975	−	1.13445i	−0.326925	−	0.945050i	$-0.606012\pi$
$269$	10.7424	−	18.6064i	0.654975	−	1.13445i	0.981900	−	0.189400i	$-0.0606543\pi$
$270$	−2.89835	+	5.02009i	−0.176388	+	0.305513i
$271$	10.5662	+	18.3012i	0.641851	+	1.11172i	0.985019	+	0.172445i	$0.0551667\pi$
$271$	10.5662	+	18.3012i	0.641851	+	1.11172i	−0.343168	+	0.939274i	$0.611500\pi$
$272$	2.33035			0.141298
$273$	−0.0910787	−	2.57050i	−0.00551233	−	0.155574i
$274$	−11.3333			−0.684670
$275$	0.500000	+	0.866025i	0.0301511	+	0.0522233i
$276$	0.231741	−	0.401387i	0.0139491	−	0.0241606i
$277$	5.91140	−	10.2388i	0.355181	−	0.615192i	−0.631968	−	0.774995i	$-0.717752\pi$
$277$	5.91140	−	10.2388i	0.355181	−	0.615192i	0.987149	+	0.159803i	$0.0510857\pi$
$278$	−12.2305	−	21.1838i	−0.733534	−	1.27052i
$279$	−14.9801			−0.896835
$280$	−6.31435	−	3.35326i	−0.377355	−	0.200396i
$281$	26.7399			1.59517			0.797584	−	0.603209i	$-0.206111\pi$
$281$	26.7399			1.59517			0.797584	+	0.603209i	$0.206111\pi$
$282$	4.15553	+	7.19758i	0.247458	+	0.428610i
$283$	5.86786	−	10.1634i	0.348808	−	0.604153i	−0.637230	−	0.770674i	$-0.719920\pi$
$283$	5.86786	−	10.1634i	0.348808	−	0.604153i	0.986038	+	0.166520i	$0.0532532\pi$
$284$	−0.565330	+	0.979180i	−0.0335462	+	0.0581037i
$285$	−0.0716228	−	0.124054i	−0.00424257	−	0.00734835i
$286$	−1.98844			−0.117579
$287$	9.13304	−	5.71345i	0.539107	−	0.337254i
$288$	−2.27487			−0.134048
$289$	8.35304	+	14.4679i	0.491355	+	0.851052i
$290$	1.65851	−	2.87262i	0.0973908	−	0.168686i
$291$	5.99832	−	10.3894i	0.351627	−	0.609037i
$292$	−1.20709	−	2.09073i	−0.0706394	−	0.122351i
$293$	14.9197			0.871621			0.435810	−	0.900039i	$-0.356462\pi$
$293$	14.9197			0.871621			0.435810	+	0.900039i	$0.356462\pi$
$294$	−3.23728	+	6.65467i	−0.188802	+	0.388108i
$295$	−7.57418			−0.440986
$296$	−10.4933	−	18.1749i	−0.609909	−	1.05639i
$297$	−1.97101	+	3.41389i	−0.114370	+	0.198094i
$298$	6.11115	−	10.5848i	0.354009	−	0.613162i
$299$	−2.68494	−	4.65045i	−0.155274	−	0.268943i
$300$	0.116713			0.00673841
$301$	−22.0939	+	13.8215i	−1.27347	+	0.796657i
$302$	−11.1739			−0.642985
$303$	−1.73512	−	3.00531i	−0.0996798	−	0.172650i
$304$	0.428214	−	0.741689i	0.0245598	−	0.0425388i
$305$	−3.75537	+	6.50448i	−0.215032	+	0.372446i
$306$	0.989812	+	1.71441i	0.0565838	+	0.0980060i
$307$	31.0065			1.76964			0.884818	−	0.465937i	$-0.154283\pi$
$307$	31.0065			1.76964			0.884818	+	0.465937i	$0.154283\pi$
$308$	0.379341	+	0.201451i	0.0216150	+	0.0114787i
$309$	11.9133			0.677723
$310$	4.43554	+	7.68259i	0.251922	+	0.436342i
$311$	11.3287	−	19.6220i	0.642394	−	1.11266i	−0.342503	−	0.939517i	$-0.611275\pi$
$311$	11.3287	−	19.6220i	0.642394	−	1.11266i	0.984897	−	0.173142i	$-0.0553921\pi$
$312$	1.31352	−	2.27509i	0.0743636	−	0.128801i
$313$	5.24515	+	9.08486i	0.296473	+	0.513507i	0.975327	−	0.220767i	$-0.0708561\pi$
$313$	5.24515	+	9.08486i	0.296473	+	0.513507i	−0.678853	+	0.734274i	$0.737523\pi$
$314$	−11.2803			−0.636585
$315$	−0.232635	−	6.56563i	−0.0131075	−	0.369931i
$316$	−0.0590170			−0.00331996
$317$	−16.9666	−	29.3870i	−0.952938	−	1.65054i	−0.739018	−	0.673685i	$-0.764710\pi$
$317$	−16.9666	−	29.3870i	−0.952938	−	1.65054i	−0.213919	−	0.976851i	$-0.568623\pi$
$318$	4.77223	−	8.26575i	0.267613	−	0.463520i
$319$	1.12786	−	1.95351i	0.0631480	−	0.109375i
$320$	−3.62475	−	6.27825i	−0.202630	−	0.350965i
$321$	1.76247			0.0983716
$322$	0.547082	+	15.4402i	0.0304877	+	0.860448i
$323$	−0.108022			−0.00601051
$324$	−0.374630	−	0.648878i	−0.0208128	−	0.0360488i
$325$	0.676115	−	1.17107i	0.0375041	−	0.0649590i
$326$	12.4552	−	21.5730i	0.689828	−	1.19482i
$327$	−1.44341	−	2.50005i	−0.0798206	−	0.138253i
$328$	11.0030			0.607540
$329$	−18.3699	−	9.75540i	−1.01276	−	0.537832i
$330$	1.05719			0.0581962
$331$	−7.70042	−	13.3375i	−0.423253	−	0.733096i	0.573002	−	0.819554i	$-0.305779\pi$
$331$	−7.70042	−	13.3375i	−0.423253	−	0.733096i	−0.996256	+	0.0864575i	$0.972445\pi$
$332$	−0.314271	+	0.544333i	−0.0172478	+	0.0298741i
$333$	9.64237	−	16.7011i	0.528399	−	0.915214i
$334$	8.86434	+	15.3535i	0.485035	+	0.840105i
$335$	−8.01205			−0.437745
$336$	−6.93139	+	4.33614i	−0.378138	+	0.236556i
$337$	−14.6257			−0.796710			−0.398355	−	0.917231i	$-0.630419\pi$
$337$	−14.6257			−0.796710			−0.398355	+	0.917231i	$0.630419\pi$
$338$	−8.21377	−	14.2267i	−0.446770	−	0.773829i
$339$	4.91627	−	8.51523i	0.267015	−	0.462484i
$340$	0.0440068	−	0.0762219i	0.00238660	−	0.00413371i
$341$	3.01637	+	5.22451i	0.163346	+	0.282923i
$342$	0.727534			0.0393406
$343$	−1.96412	−	18.4158i	−0.106053	−	0.994361i
$344$	−26.6175			−1.43512
$345$	1.42749	+	2.47249i	0.0768536	+	0.133114i
$346$	−6.77447	+	11.7337i	−0.364198	+	0.630809i
$347$	−0.557832	+	0.966193i	−0.0299460	+	0.0518680i	−0.880610	−	0.473842i	$-0.842867\pi$
$347$	−0.557832	+	0.966193i	−0.0299460	+	0.0518680i	0.850664	+	0.525710i	$0.176200\pi$
$348$	−0.131635	−	0.227999i	−0.00705640	−	0.0122220i
$349$	25.7539			1.37858			0.689289	−	0.724487i	$-0.257923\pi$
$349$	25.7539			1.37858			0.689289	+	0.724487i	$0.257923\pi$
$350$	−3.29832	+	2.06336i	−0.176303	+	0.110291i
$351$	5.33051			0.284522
$352$	0.458065	+	0.793391i	0.0244149	+	0.0422879i
$353$	−7.64132	+	13.2352i	−0.406707	+	0.704436i	−0.994518	−	0.104561i	$-0.966656\pi$
$353$	−7.64132	+	13.2352i	−0.406707	+	0.704436i	0.587812	+	0.808998i	$0.299990\pi$
$354$	−4.00366	+	6.93455i	−0.212792	+	0.368567i
$355$	−3.48236	−	6.03163i	−0.184825	−	0.320125i
$356$	−0.646487			−0.0342637
$357$	0.910778	+	0.483673i	0.0482035	+	0.0255987i
$358$	−6.35476			−0.335859
$359$	−3.41465	−	5.91435i	−0.180218	−	0.312147i	0.761736	−	0.647887i	$-0.224347\pi$
$359$	−3.41465	−	5.91435i	−0.180218	−	0.312147i	−0.941955	+	0.335740i	$0.891014\pi$
$360$	3.35503	−	5.81109i	0.176826	−	0.306271i
$361$	9.48015	−	16.4201i	0.498955	−	0.864216i
$362$	−1.87028	−	3.23942i	−0.0982997	−	0.170260i
$363$	0.718935			0.0377343
$364$	−0.0205663	−	0.580438i	−0.00107796	−	0.0304232i
$365$	14.8710			0.778383
$366$	3.97012	+	6.87646i	0.207522	+	0.359438i
$367$	2.25814	−	3.91122i	0.117874	−	0.204164i	−0.801051	−	0.598596i	$-0.795725\pi$
$367$	2.25814	−	3.91122i	0.117874	−	0.204164i	0.918925	+	0.394432i	$0.129059\pi$
$368$	−8.53461	+	14.7824i	−0.444897	+	0.770584i
$369$	5.05539	+	8.75619i	0.263173	+	0.455829i
$370$	−11.4203			−0.593711
$371$	0.845816	+	23.8713i	0.0439126	+	1.23934i
$372$	0.704098			0.0365058
$373$	−2.12824	−	3.68622i	−0.110196	−	0.190865i	0.805653	−	0.592388i	$-0.201815\pi$
$373$	−2.12824	−	3.68622i	−0.110196	−	0.190865i	−0.915849	+	0.401522i	$0.868481\pi$
$374$	0.398614	−	0.690420i	0.0206119	−	0.0357008i
$375$	−0.359468	+	0.622616i	−0.0185628	+	0.0321518i
$376$	−10.6219	−	18.3976i	−0.547781	−	0.948785i
$377$	−3.05025			−0.157096
$378$	−13.5451	−	7.19319i	−0.696685	−	0.369978i
$379$	−12.2039			−0.626871			−0.313436	−	0.949609i	$-0.601480\pi$
$379$	−12.2039			−0.626871			−0.313436	+	0.949609i	$0.601480\pi$
$380$	−0.0161730	−	0.0280124i	−0.000829656	−	0.00143701i
$381$	−5.66128	+	9.80562i	−0.290036	+	0.502357i
$382$	2.15105	−	3.72573i	0.110057	−	0.190625i
$383$	−5.51232	−	9.54761i	−0.281666	−	0.487860i	0.690129	−	0.723686i	$-0.257554\pi$
$383$	−5.51232	−	9.54761i	−0.281666	−	0.487860i	−0.971795	+	0.235826i	$0.924220\pi$
$384$	−8.98135			−0.458328
$385$	−2.24301	+	1.40318i	−0.114314	+	0.0715127i
$386$	−19.6455			−0.999932
$387$	−12.2296	−	21.1822i	−0.621663	−	1.07675i
$388$	1.35447	−	2.34600i	0.0687626	−	0.119100i
$389$	−15.2836	+	26.4720i	−0.774911	+	1.34219i	0.159933	+	0.987128i	$0.448872\pi$
$389$	−15.2836	+	26.4720i	−0.774911	+	1.34219i	−0.934844	+	0.355058i	$0.884461\pi$
$390$	−0.714780	−	1.23804i	−0.0361943	−	0.0626904i
$391$	2.15295			0.108880
$392$	8.27477	−	17.0099i	0.417939	−	0.859129i
$393$	−5.26557			−0.265613
$394$	8.27073	+	14.3253i	0.416673	+	0.721699i
$395$	0.181768	−	0.314832i	0.00914576	−	0.0158409i
$396$	−0.201557	+	0.349107i	−0.0101286	+	0.0175433i
$397$	8.88315	+	15.3861i	0.445832	+	0.772204i	0.998110	−	0.0614560i	$-0.0195744\pi$
$397$	8.88315	+	15.3861i	0.445832	+	0.772204i	−0.552277	+	0.833660i	$0.686241\pi$
$398$	15.4274			0.773304
$399$	0.321301	−	0.201000i	0.0160852	−	0.0100626i
$400$	−4.29833			−0.214916
$401$	−12.5534	−	21.7432i	−0.626889	−	1.08580i	−0.988172	−	0.153348i	$-0.950995\pi$
$401$	−12.5534	−	21.7432i	−0.626889	−	1.08580i	0.361283	−	0.932456i	$-0.382339\pi$
$402$	−4.23512	+	7.33544i	−0.211228	+	0.365858i
$403$	4.07883	−	7.06474i	0.203181	−	0.351920i
$404$	−0.391802	−	0.678621i	−0.0194929	−	0.0337627i
$405$	4.61534			0.229338
$406$	7.75084	+	4.11612i	0.384668	+	0.204279i
$407$	−7.76630			−0.384961
$408$	0.526633	+	0.912154i	0.0260722	+	0.0451584i
$409$	−9.56236	+	16.5625i	−0.472828	+	0.818962i	−0.999516	−	0.0310962i	$-0.990100\pi$
$409$	−9.56236	+	16.5625i	−0.472828	+	0.818962i	0.526688	+	0.850058i	$0.323434\pi$
$410$	2.99376	−	5.18534i	0.147851	−	0.256086i
$411$	−2.77047	−	4.79860i	−0.136657	−	0.236698i
$412$	2.69011			0.132532
$413$	−0.709597	−	20.0268i	−0.0349170	−	0.985456i
$414$	−14.5003			−0.712649
$415$	−1.93587	−	3.35302i	−0.0950279	−	0.164593i
$416$	0.619409	−	1.07285i	0.0303690	−	0.0526007i
$417$	5.97957	−	10.3569i	0.292821	−	0.507181i
$418$	−0.146495	−	0.253737i	−0.00716532	−	0.0124107i
$419$	−34.2881			−1.67508			−0.837542	−	0.546372i	$-0.816008\pi$
$419$	−34.2881			−1.67508			−0.837542	+	0.546372i	$0.816008\pi$
$420$	0.0109344	+	0.308599i	0.000533543	+	0.0150581i
$421$	−13.2601			−0.646258			−0.323129	−	0.946355i	$-0.604735\pi$
$421$	−13.2601			−0.646258			−0.323129	+	0.946355i	$0.604735\pi$
$422$	6.24013	+	10.8082i	0.303765	+	0.526136i
$423$	9.76054	−	16.9058i	0.474574	−	0.821986i
$424$	−12.1982	+	21.1279i	−0.592398	+	1.02606i
$425$	0.271076	+	0.469517i	0.0131491	+	0.0227749i
$426$	−7.36301			−0.356739
$427$	−17.5503	−	9.32015i	−0.849318	−	0.451034i
$428$	0.397980			0.0192371
$429$	−0.486083	−	0.841921i	−0.0234683	−	0.0406483i
$430$	−7.24224	+	12.5439i	−0.349252	+	0.604922i
$431$	9.67826	−	16.7632i	0.466185	−	0.807457i	−0.533069	−	0.846072i	$-0.678961\pi$
$431$	9.67826	−	16.7632i	0.466185	−	0.807457i	0.999254	+	0.0386152i	$0.0122947\pi$
$432$	−8.47204	−	14.6740i	−0.407611	−	0.706003i
$433$	14.8600			0.714127			0.357064	−	0.934080i	$-0.383778\pi$
$433$	14.8600			0.714127			0.357064	+	0.934080i	$0.383778\pi$
$434$	−19.8979	+	12.4477i	−0.955131	+	0.597511i
$435$	1.62172			0.0777553
$436$	−0.325932	−	0.564531i	−0.0156093	−	0.0270361i
$437$	0.395618	−	0.685230i	0.0189250	−	0.0327790i
$438$	7.86071	−	13.6151i	0.375599	−	0.650557i
$439$	10.5297	+	18.2379i	0.502554	+	0.870448i	0.999996	+	0.00295114i	$0.000939379\pi$
$439$	10.5297	+	18.2379i	0.502554	+	0.870448i	−0.497442	+	0.867497i	$0.665727\pi$
$440$	−2.70226			−0.128825
$441$	17.3383	−	1.23022i	0.825635	−	0.0585819i
$442$	−1.07804			−0.0512770
$443$	4.05594	+	7.02509i	0.192704	+	0.333772i	0.946145	−	0.323742i	$-0.104941\pi$
$443$	4.05594	+	7.02509i	0.192704	+	0.333772i	−0.753442	+	0.657515i	$0.771608\pi$
$444$	−0.453213	+	0.784988i	−0.0215085	+	0.0372539i
$445$	1.99114	−	3.44875i	0.0943890	−	0.163487i
$446$	14.5510	+	25.2030i	0.689008	+	1.19340i
$447$	5.97559			0.282636
$448$	16.2607	−	10.1724i	0.768245	−	0.480599i
$449$	35.4379			1.67242			0.836209	−	0.548411i	$-0.184767\pi$
$449$	35.4379			1.67242			0.836209	+	0.548411i	$0.184767\pi$
$450$	−1.82571	−	3.16222i	−0.0860648	−	0.149069i
$451$	2.03589	−	3.52627i	0.0958664	−	0.166046i
$452$	1.11013	−	1.92280i	0.0522162	−	0.0904411i
$453$	−2.73150	−	4.73110i	−0.128337	−	0.222287i
$454$	3.35926			0.157658
$455$	3.15975	+	1.67800i	0.148131	+	0.0786657i
$456$	0.387087			0.0181270
$457$	−16.3267	−	28.2786i	−0.763730	−	1.32282i	−0.940915	−	0.338641i	$-0.890033\pi$
$457$	−16.3267	−	28.2786i	−0.763730	−	1.32282i	0.177186	−	0.984177i	$-0.443301\pi$
$458$	−19.2645	+	33.3672i	−0.900173	+	1.55914i
$459$	−1.06859	+	1.85085i	−0.0498773	+	0.0863901i
$460$	0.322339	+	0.558307i	0.0150291	+	0.0260312i
$461$	−1.18996			−0.0554219			−0.0277109	−	0.999616i	$-0.508822\pi$
$461$	−1.18996			−0.0554219			−0.0277109	+	0.999616i	$0.508822\pi$
$462$	0.0990440	+	2.79530i	0.00460794	+	0.130049i
$463$	−17.3660			−0.807068			−0.403534	−	0.914965i	$-0.632218\pi$
$463$	−17.3660			−0.807068			−0.403534	+	0.914965i	$0.632218\pi$
$464$	4.84791	+	8.39682i	0.225058	+	0.389813i
$465$	−2.16858	+	3.75608i	−0.100565	+	0.174184i
$466$	13.2583	−	22.9640i	0.614177	−	1.06379i
$467$	−6.54091	−	11.3292i	−0.302677	−	0.524252i	0.674064	−	0.738673i	$-0.264547\pi$
$467$	−6.54091	−	11.3292i	−0.302677	−	0.524252i	−0.976741	+	0.214421i	$0.931214\pi$
$468$	0.545103			0.0251974
$469$	−0.750619	−	21.1846i	−0.0346604	−	0.978214i
$470$	−11.5602			−0.533233
$471$	−2.75752	−	4.77617i	−0.127060	−	0.220074i
$472$	10.2337	−	17.7253i	0.471044	−	0.815872i
$473$	−4.92505	+	8.53044i	−0.226454	+	0.392230i
$474$	−0.192163	−	0.332837i	−0.00882635	−	0.0152877i
$475$	0.199247			0.00914208
$476$	0.205661	+	0.109217i	0.00942644	+	0.00500595i
$477$	−22.4181			−1.02646
$478$	19.4211	+	33.6383i	0.888299	+	1.53858i
$479$	−17.2054	+	29.8007i	−0.786136	+	1.36163i	0.142181	+	0.989841i	$0.454588\pi$
$479$	−17.2054	+	29.8007i	−0.786136	+	1.36163i	−0.928318	+	0.371788i	$0.878745\pi$
$480$	−0.329319	+	0.570397i	−0.0150313	+	0.0260349i
$481$	5.25091	+	9.09485i	0.239421	+	0.414689i
$482$	−21.0899			−0.960620
$483$	−6.40375	+	4.00606i	−0.291381	+	0.182282i
$484$	0.162341			0.00737914
$485$	8.34333	+	14.4511i	0.378851	+	0.656189i
$486$	11.1347	−	19.2858i	0.505080	−	0.874824i
$487$	13.4835	−	23.3541i	0.610994	−	1.05827i	−0.380079	−	0.924954i	$-0.624103\pi$
$487$	13.4835	−	23.3541i	0.610994	−	1.05827i	0.991073	−	0.133319i	$-0.0425636\pi$
$488$	−10.1480	−	17.5768i	−0.459377	−	0.795664i
$489$	12.1789			0.550748
$490$	−5.76473	−	8.52775i	−0.260424	−	0.385245i
$491$	34.2270			1.54464			0.772322	−	0.635232i	$-0.219095\pi$
$491$	34.2270			1.54464			0.772322	+	0.635232i	$0.219095\pi$
$492$	−0.237615	−	0.411560i	−0.0107125	−	0.0185546i
$493$	0.611471	−	1.05910i	0.0275393	−	0.0476994i
$494$	−0.198095	+	0.343111i	−0.00891273	+	0.0154373i
$495$	−1.24157	−	2.15046i	−0.0558042	−	0.0966558i
$496$	−25.9307			−1.16432
$497$	15.6219	−	9.77276i	0.700739	−	0.438368i
$498$	−4.09315			−0.183418
$499$	17.6946	+	30.6480i	0.792120	+	1.37199i	0.924652	+	0.380813i	$0.124356\pi$
$499$	17.6946	+	30.6480i	0.792120	+	1.37199i	−0.132533	+	0.991179i	$0.542311\pi$
$500$	−0.0811705	+	0.140591i	−0.00363006	+	0.00628744i
$501$	−4.33385	+	7.50645i	−0.193622	+	0.335363i
$502$	5.68466	+	9.84612i	0.253719	+	0.439454i
$503$	15.5682			0.694154			0.347077	−	0.937837i	$-0.387174\pi$
$503$	15.5682			0.694154			0.347077	+	0.937837i	$0.387174\pi$
$504$	15.6794	+	8.32660i	0.698415	+	0.370896i
$505$	4.82690			0.214794
$506$	2.91975	+	5.05716i	0.129799	+	0.224818i
$507$	4.01578	−	6.95554i	0.178347	−	0.308906i
$508$	−1.27836	+	2.21418i	−0.0567181	+	0.0982386i
$509$	6.04740	+	10.4744i	0.268046	+	0.464270i	0.968357	−	0.249568i	$-0.0802887\pi$
$509$	6.04740	+	10.4744i	0.268046	+	0.464270i	−0.700311	+	0.713838i	$0.746955\pi$
$510$	0.573156			0.0253798
$511$	1.39321	+	39.3203i	0.0616319	+	1.73943i
$512$	19.2926			0.852619
$513$	0.392717	+	0.680206i	0.0173389	+	0.0300318i
$514$	−5.68207	+	9.84163i	−0.250625	+	0.434096i
$515$	−8.28537	+	14.3507i	−0.365097	+	0.632367i
$516$	0.574817	+	0.995611i	0.0253049	+	0.0438293i
$517$	−7.86148			−0.345747
$518$	−1.06992	−	30.1962i	−0.0470097	−	1.32675i
$519$	−6.62419			−0.290770
$520$	1.82704	+	3.16452i	0.0801209	+	0.138774i
$521$	−4.77090	+	8.26345i	−0.209017	+	0.362028i	−0.951405	−	0.307942i	$-0.900360\pi$
$521$	−4.77090	+	8.26345i	−0.209017	+	0.362028i	0.742388	+	0.669970i	$0.233693\pi$
$522$	−4.11829	+	7.13308i	−0.180253	+	0.312207i
$523$	17.3082	+	29.9787i	0.756835	+	1.31088i	0.944457	+	0.328636i	$0.106589\pi$
$523$	17.3082	+	29.9787i	0.756835	+	1.31088i	−0.187621	+	0.982241i	$0.560078\pi$
$524$	−1.18901			−0.0519420
$525$	−1.67993	−	0.892135i	−0.0733182	−	0.0389360i
$526$	−33.7715			−1.47251
$527$	1.63533	+	2.83248i	0.0712361	+	0.123385i
$528$	−1.54511	+	2.67621i	−0.0672423	+	0.116467i
$529$	3.61507	−	6.26148i	0.157177	−	0.272238i
$530$	6.63792	+	11.4972i	0.288333	+	0.499407i
$531$	18.8077			0.816184
$532$	0.0725522	−	0.0453872i	0.00314554	−	0.00196779i
$533$	−5.50599			−0.238491
$534$	−2.10501	−	3.64598i	−0.0910925	−	0.157777i
$535$	−1.22575	+	2.12306i	−0.0529939	+	0.0917881i
$536$	10.8253	−	18.7500i	0.467582	−	0.809877i
$537$	−1.55345	−	2.69065i	−0.0670362	−	0.116110i
$538$	31.5932			1.36208
$539$	−3.92028	−	5.79926i	−0.168858	−	0.249792i
$540$	−0.639951			−0.0275391
$541$	−1.24370	−	2.15415i	−0.0534708	−	0.0926141i	0.838051	−	0.545592i	$-0.183695\pi$
$541$	−1.24370	−	2.15415i	−0.0534708	−	0.0926141i	−0.891522	+	0.452978i	$0.850362\pi$
$542$	−15.5375	+	26.9117i	−0.667393	+	1.15596i
$543$	0.914396	−	1.58378i	0.0392405	−	0.0679665i
$544$	0.248341	+	0.430139i	0.0106475	+	0.0184420i
$545$	4.01540			0.172001
$546$	3.20652	−	2.00593i	0.137226	−	0.0858460i
$547$	−27.1185			−1.15950			−0.579751	−	0.814794i	$-0.696850\pi$
$547$	−27.1185			−1.15950			−0.579751	+	0.814794i	$0.696850\pi$
$548$	−0.625594	−	1.08356i	−0.0267241	−	0.0462874i
$549$	9.32507	−	16.1515i	0.397984	−	0.689329i
$550$	−0.735245	+	1.27348i	−0.0313510	+	0.0543014i
$551$	−0.224722	−	0.389231i	−0.00957350	−	0.0165818i
$552$	−7.71491			−0.328368
$553$	0.849474	+	0.451117i	0.0361233	+	0.0191834i
$554$	17.3853			0.738631
$555$	−2.79173	−	4.83543i	−0.118503	−	0.205252i
$556$	1.35023	−	2.33867i	0.0572626	−	0.0991818i
$557$	−11.1540	+	19.3194i	−0.472612	+	0.818587i	−0.999509	−	0.0313416i	$-0.990022\pi$
$557$	−11.1540	+	19.3194i	−0.472612	+	0.818587i	0.526897	+	0.849929i	$0.323355\pi$
$558$	−11.0140	−	19.0769i	−0.466262	−	0.807589i
$559$	13.3196			0.563360
$560$	−0.402694	−	11.3652i	−0.0170169	−	0.480266i
$561$	0.389772			0.0164562
$562$	19.6604	+	34.0527i	0.829322	+	1.43643i
$563$	4.40534	−	7.63027i	0.185663	−	0.321577i	−0.758137	−	0.652095i	$-0.773890\pi$
$563$	4.40534	−	7.63027i	0.185663	−	0.321577i	0.943800	+	0.330518i	$0.107223\pi$
$564$	−0.458767	+	0.794608i	−0.0193176	+	0.0334590i
$565$	6.83827	+	11.8442i	0.287688	+	0.498290i
$566$	17.2573			0.725377
$567$	0.432394	+	12.2034i	0.0181589	+	0.512494i
$568$	18.8205			0.789690
$569$	8.94245	+	15.4888i	0.374887	+	0.649323i	0.990310	−	0.138874i	$-0.0443482\pi$
$569$	8.94245	+	15.4888i	0.374887	+	0.649323i	−0.615423	+	0.788197i	$0.711015\pi$
$570$	0.105321	−	0.182421i	0.00441140	−	0.00764076i
$571$	2.72561	−	4.72090i	0.114063	−	0.197563i	−0.803342	−	0.595518i	$-0.796947\pi$
$571$	2.72561	−	4.72090i	0.114063	−	0.197563i	0.917405	+	0.397955i	$0.130280\pi$
$572$	−0.109761	−	0.190112i	−0.00458935	−	0.00794898i
$573$	2.10334			0.0878682
$574$	13.9910	+	7.42998i	0.583973	+	0.310121i
$575$	−3.97113			−0.165608
$576$	9.00073	+	15.5897i	0.375030	+	0.649572i
$577$	18.7699	−	32.5105i	0.781403	−	1.35343i	−0.149721	−	0.988728i	$-0.547838\pi$
$577$	18.7699	−	32.5105i	0.781403	−	1.35343i	0.931124	−	0.364702i	$-0.118829\pi$
$578$	−12.2831	+	21.2749i	−0.510908	+	0.884918i
$579$	−4.80244	−	8.31807i	−0.199583	−	0.345687i
$580$	0.366196			0.0152054
$581$	8.68433	−	5.43274i	0.360287	−	0.225388i
$582$	17.6409			0.731240
$583$	4.51408	+	7.81862i	0.186954	+	0.323814i
$584$	−20.0926	+	34.8015i	−0.831439	+	1.44009i
$585$	−1.67888	+	2.90791i	−0.0694133	+	0.120227i
$586$	10.9697	+	19.0000i	0.453153	+	0.784884i
$587$	−8.73112			−0.360372			−0.180186	−	0.983633i	$-0.557670\pi$
$587$	−8.73112			−0.360372			−0.180186	+	0.983633i	$0.557670\pi$
$588$	−0.814940	+	0.0578230i	−0.0336076	+	0.00238458i
$589$	1.20201			0.0495278
$590$	−5.56888	−	9.64558i	−0.229267	−	0.397102i
$591$	−4.04363	+	7.00377i	−0.166333	+	0.288097i
$592$	16.6911	−	28.9097i	0.685998	−	1.18818i
$593$	9.50761	+	16.4677i	0.390431	+	0.676246i	0.992506	−	0.122193i	$-0.0389927\pi$
$593$	9.50761	+	16.4677i	0.390431	+	0.676246i	−0.602076	+	0.798439i	$0.705659\pi$
$594$	−5.79670			−0.237841
$595$	−1.21605	+	0.760737i	−0.0498532	+	0.0311872i
$596$	1.34933			0.0552708
$597$	3.77129	+	6.53206i	0.154348	+	0.267339i
$598$	3.94818	−	6.83844i	0.161453	−	0.279645i
$599$	6.18177	−	10.7071i	0.252580	−	0.437482i	−0.711655	−	0.702529i	$-0.752054\pi$
$599$	6.18177	−	10.7071i	0.252580	−	0.437482i	0.964235	+	0.265047i	$0.0853875\pi$
$600$	−0.971375	−	1.68247i	−0.0396562	−	0.0686866i
$601$	−25.2886			−1.03154			−0.515772	−	0.856726i	$-0.672495\pi$
$601$	−25.2886			−1.03154			−0.515772	+	0.856726i	$0.672495\pi$
$602$	−33.8458	−	17.9740i	−1.37945	−	0.732564i
$603$	19.8950			0.810186
$604$	−0.616794	−	1.06832i	−0.0250970	−	0.0434693i
$605$	−0.500000	+	0.866025i	−0.0203279	+	0.0352089i
$606$	2.55147	−	4.41928i	0.103646	−	0.179521i
$607$	4.78467	+	8.28730i	0.194204	+	0.336371i	0.946639	−	0.322295i	$-0.104454\pi$
$607$	4.78467	+	8.28730i	0.194204	+	0.336371i	−0.752435	+	0.658666i	$0.771121\pi$
$608$	0.182536			0.00740281
$609$	0.151933	+	4.28796i	0.00615662	+	0.173757i
$610$	−11.0445			−0.447177
$611$	5.31526	+	9.20631i	0.215033	+	0.372447i
$612$	−0.109275	+	0.189269i	−0.00441716	+	0.00765075i
$613$	−0.826926	+	1.43228i	−0.0333992	+	0.0578492i	−0.882242	−	0.470796i	$-0.843967\pi$
$613$	−0.826926	+	1.43228i	−0.0333992	+	0.0578492i	0.848843	+	0.528646i	$0.177300\pi$
$614$	22.7974	+	39.4863i	0.920028	+	1.59354i
$615$	2.92735			0.118042
$616$	−0.253165	−	7.14502i	−0.0102003	−	0.287881i
$617$	4.35949			0.175506			0.0877531	−	0.996142i	$-0.472031\pi$
$617$	4.35949			0.175506			0.0877531	+	0.996142i	$0.472031\pi$
$618$	8.75919	+	15.1714i	0.352346	+	0.610282i
$619$	18.5995	−	32.2154i	0.747579	−	1.29484i	−0.201401	−	0.979509i	$-0.564550\pi$
$619$	18.5995	−	32.2154i	0.747579	−	1.29484i	0.948980	−	0.315336i	$-0.102117\pi$
$620$	−0.489681	+	0.848152i	−0.0196661	+	0.0340626i
$621$	−7.82713	−	13.5570i	−0.314092	−	0.544023i
$622$	33.3176			1.33591
$623$	9.30536	+	4.94165i	0.372811	+	0.197983i
$624$	4.17869			0.167281
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−7.71294	+	13.3592i	−0.308271	+	0.533941i
$627$	0.0716228	−	0.124054i	0.00286034	−	0.00495425i
$628$	−0.622669	−	1.07849i	−0.0248472	−	0.0430366i
$629$	−4.21051			−0.167884
$630$	8.19017	−	5.12360i	0.326304	−	0.204129i
$631$	−35.1684			−1.40003			−0.700017	−	0.714126i	$-0.746824\pi$
$631$	−35.1684			−1.40003			−0.700017	+	0.714126i	$0.746824\pi$
$632$	0.491185	+	0.850758i	0.0195383	+	0.0338413i
$633$	−3.05085	+	5.28423i	−0.121260	+	0.210029i
$634$	24.9492	−	43.2132i	0.990859	−	1.71622i
$635$	−7.87453	−	13.6391i	−0.312491	−	0.541251i
$636$	1.05370			0.0417820
$637$	−4.14076	+	8.51187i	−0.164063	+	0.337253i
$638$	3.31701			0.131322
$639$	8.64716	+	14.9773i	0.342076	+	0.592494i
$640$	6.24629	−	10.8189i	0.246906	−	0.427654i
$641$	7.95259	−	13.7743i	0.314108	−	0.544052i	−0.665139	−	0.746719i	$-0.731628\pi$
$641$	7.95259	−	13.7743i	0.314108	−	0.544052i	0.979248	+	0.202668i	$0.0649612\pi$
$642$	1.29585	+	2.24448i	0.0511431	+	0.0885824i
$643$	42.0439			1.65805			0.829024	−	0.559213i	$-0.188897\pi$
$643$	42.0439			1.65805			0.829024	+	0.559213i	$0.188897\pi$
$644$	−1.44602	+	0.904599i	−0.0569810	+	0.0356462i
$645$	−7.08159			−0.278837
$646$	−0.0794227	−	0.137564i	−0.00312484	−	0.00541239i
$647$	−15.4828	+	26.8170i	−0.608692	+	1.05429i	0.382764	+	0.923846i	$0.374972\pi$
$647$	−15.4828	+	26.8170i	−0.608692	+	1.05429i	−0.991456	+	0.130439i	$0.958361\pi$
$648$	−6.23592	+	10.8009i	−0.244970	+	0.424301i
$649$	−3.78709	−	6.55943i	−0.148656	−	0.257480i
$650$	1.98844			0.0779931
$651$	−10.1346	−	5.38202i	−0.397206	−	0.210938i
$652$	2.75009			0.107702
$653$	8.41697	+	14.5786i	0.329381	+	0.570505i	0.982389	−	0.186846i	$-0.0598265\pi$
$653$	8.41697	+	14.5786i	0.329381	+	0.570505i	−0.653008	+	0.757351i	$0.726493\pi$
$654$	2.12252	−	3.67631i	0.0829969	−	0.143755i
$655$	3.66206	−	6.34288i	0.143089	−	0.247837i
$656$	8.75093	+	15.1571i	0.341667	+	0.591784i
$657$	−36.9266			−1.44064
$658$	−1.08303	−	30.5663i	−0.0422211	−	1.19160i
$659$	−37.5268			−1.46184			−0.730918	−	0.682465i	$-0.760908\pi$
$659$	−37.5268			−1.46184			−0.730918	+	0.682465i	$0.760908\pi$
$660$	0.0583564	+	0.101076i	0.00227152	+	0.00393439i
$661$	−3.99088	+	6.91240i	−0.155227	+	0.268861i	−0.933142	−	0.359509i	$-0.882944\pi$
$661$	−3.99088	+	6.91240i	−0.155227	+	0.268861i	0.777915	+	0.628370i	$0.216278\pi$
$662$	11.3234	−	19.6127i	0.440096	−	0.762269i
$663$	−0.263531	−	0.456449i	−0.0102347	−	0.0177270i
$664$	10.4624			0.406021
$665$	0.0186667	+	0.526827i	0.000723864	+	0.0204295i
$666$	28.3580			1.09885
$667$	4.47887	+	7.75764i	0.173423	+	0.300377i
$668$	−0.978617	+	1.69501i	−0.0378638	+	0.0655820i
$669$	−7.11409	+	12.3220i	−0.275047	+	0.476395i
$670$	−5.89082	−	10.2032i	−0.227582	−	0.394184i
$671$	−7.51073			−0.289949
$672$	−1.53904	−	0.817311i	−0.0593696	−	0.0315285i
$673$	−30.3125			−1.16846			−0.584230	−	0.811588i	$-0.698603\pi$
$673$	−30.3125			−1.16846			−0.584230	+	0.811588i	$0.698603\pi$
$674$	−10.7534	−	18.6255i	−0.414207	−	0.717428i
$675$	1.97101	−	3.41389i	0.0758642	−	0.131401i
$676$	0.906794	−	1.57061i	0.0348767	−	0.0604082i
$677$	8.70847	+	15.0835i	0.334694	+	0.579706i	0.983426	−	0.181310i	$-0.0580339\pi$
$677$	8.70847	+	15.0835i	0.334694	+	0.579706i	−0.648732	+	0.761017i	$0.724701\pi$
$678$	14.4587			0.555282
$679$	−37.4283	+	23.4144i	−1.43637	+	0.898562i
$680$	−1.46503			−0.0561815
$681$	0.821187	+	1.42234i	0.0314679	+	0.0545041i
$682$	−4.43554	+	7.68259i	−0.169846	+	0.294181i
$683$	5.00212	−	8.66393i	0.191401	−	0.331516i	−0.754314	−	0.656514i	$-0.772030\pi$
$683$	5.00212	−	8.66393i	0.191401	−	0.331516i	0.945715	+	0.324998i	$0.105364\pi$
$684$	0.0401596	+	0.0695585i	0.00153554	+	0.00265964i
$685$	7.70716			0.294475
$686$	22.0081	−	16.0414i	0.840273	−	0.612464i
$687$	−18.8372			−0.718684
$688$	−21.1695	−	36.6666i	−0.807079	−	1.39790i
$689$	6.10408	−	10.5726i	0.232547	−	0.402783i
$690$	−2.09911	+	3.63577i	−0.0799119	+	0.138411i
$691$	−15.6377	−	27.0852i	−0.594884	−	1.03037i	−0.993563	−	0.113279i	$-0.963864\pi$
$691$	−15.6377	−	27.0852i	−0.594884	−	1.03037i	0.398679	−	0.917091i	$-0.369469\pi$
$692$	−1.49579			−0.0568615
$693$	5.56968	−	3.48428i	0.211575	−	0.132357i
$694$	−1.64057			−0.0622753
$695$	8.31726	+	14.4059i	0.315492	+	0.546448i
$696$	−2.19115	+	3.79518i	−0.0830552	+	0.143856i
$697$	1.10376	−	1.91177i	0.0418080	−	0.0724136i
$698$	18.9355	+	32.7972i	0.716718	+	1.24139i
$699$	12.9642			0.490350
$700$	−0.379341	−	0.201451i	−0.0143378	−	0.00761413i
$701$	−14.8672			−0.561528			−0.280764	−	0.959777i	$-0.590588\pi$
$701$	−14.8672			−0.561528			−0.280764	+	0.959777i	$0.590588\pi$
$702$	3.91923	+	6.78831i	0.147922	+	0.256208i
$703$	−0.773706	+	1.34010i	−0.0291809	+	0.0505427i
$704$	3.62475	−	6.27825i	0.136613	−	0.236620i
$705$	−2.82595	−	4.89468i	−0.106431	−	0.184344i
$706$	−22.4730			−0.845782
$707$	0.452215	+	12.7628i	0.0170073	+	0.479994i
$708$	−0.884003			−0.0332229
$709$	−12.9287	−	22.3932i	−0.485549	−	0.840995i	0.514314	−	0.857602i	$-0.328047\pi$
$709$	−12.9287	−	22.3932i	−0.485549	−	0.840995i	−0.999862	+	0.0166075i	$0.994713\pi$
$710$	5.12078	−	8.86945i	0.192179	−	0.332864i
$711$	−0.451355	+	0.781770i	−0.0169271	+	0.0293187i
$712$	5.38057	+	9.31942i	0.201645	+	0.349260i
$713$	−23.9568			−0.897189
$714$	0.0536969	+	1.51548i	0.00200956	+	0.0567153i
$715$	1.35223			0.0505705
$716$	−0.350780	−	0.607569i	−0.0131093	−	0.0227059i
$717$	−9.49513	+	16.4461i	−0.354602	+	0.614189i
$718$	5.02121	−	8.69699i	0.187390	−	0.324569i
$719$	5.45539	+	9.44901i	0.203452	+	0.352388i	0.949638	−	0.313348i	$-0.101451\pi$
$719$	5.45539	+	9.44901i	0.203452	+	0.352388i	−0.746187	+	0.665737i	$0.768117\pi$
$720$	10.6733			0.397771
$721$	−38.7207	−	20.5628i	−1.44204	−	0.765799i
$722$	27.8809			1.03762
$723$	−5.15553	−	8.92963i	−0.191736	−	0.332097i
$724$	0.206478	−	0.357630i	0.00767368	−	0.0132912i
$725$	−1.12786	+	1.95351i	−0.0418876	+	0.0725515i
$726$	0.528594	+	0.915551i	0.0196179	+	0.0339793i
$727$	−30.6727			−1.13759			−0.568794	−	0.822480i	$-0.692590\pi$
$727$	−30.6727			−1.13759			−0.568794	+	0.822480i	$0.692590\pi$
$728$	−8.19612	+	5.12733i	−0.303768	+	0.190031i
$729$	−2.95833			−0.109568
$730$	10.9338	+	18.9379i	0.404679	+	0.700924i
$731$	−2.67013	+	4.62480i	−0.0987582	+	0.171054i
$732$	−0.438299	+	0.759156i	−0.0162000	+	0.0280592i
$733$	−19.4276	−	33.6497i	−0.717576	−	1.24288i	−0.961957	−	0.273199i	$-0.911918\pi$
$733$	−19.4276	−	33.6497i	−0.717576	−	1.24288i	0.244381	−	0.969679i	$-0.421415\pi$
$734$	6.64116			0.245130
$735$	2.20150	−	4.52548i	0.0812036	−	0.166925i
$736$	−3.63807			−0.134101
$737$	−4.00602	−	6.93864i	−0.147564	−	0.255588i
$738$	−7.43390	+	12.8759i	−0.273646	+	0.473968i
$739$	12.0520	−	20.8747i	0.443341	−	0.767888i	−0.554594	−	0.832121i	$-0.687127\pi$
$739$	12.0520	−	20.8747i	0.443341	−	0.767888i	0.997935	+	0.0642324i	$0.0204599\pi$
$740$	−0.630395	−	1.09188i	−0.0231738	−	0.0401382i
$741$	−0.193701			−0.00711579
$742$	−29.7778	+	18.6284i	−1.09318	+	0.683870i
$743$	1.57531			0.0577925			0.0288962	−	0.999582i	$-0.490801\pi$
$743$	1.57531			0.0577925			0.0288962	+	0.999582i	$0.490801\pi$
$744$	−5.86005	−	10.1499i	−0.214840	−	0.372114i
$745$	−4.15586	+	7.19816i	−0.152259	+	0.263720i
$746$	3.12956	−	5.42056i	0.114581	−	0.198461i
$747$	4.80701	+	8.32599i	0.175879	+	0.304632i
$748$	0.0880135			0.00321809
$749$	−5.72841	−	3.04210i	−0.209312	−	0.111156i
$750$	−1.05719			−0.0386030
$751$	23.3817	+	40.4984i	0.853212	+	1.47781i	0.878294	+	0.478121i	$0.158682\pi$
$751$	23.3817	+	40.4984i	0.853212	+	1.47781i	−0.0250821	+	0.999685i	$0.507985\pi$
$752$	16.8956	−	29.2640i	0.616119	−	1.06715i
$753$	−2.77928	+	4.81385i	−0.101283	+	0.175427i
$754$	−2.24268	−	3.88444i	−0.0816736	−	0.141463i
$755$	7.59875			0.276547
$756$	−0.0599547	−	1.69209i	−0.00218053	−	0.0615407i
$757$	28.7476			1.04485			0.522425	−	0.852686i	$-0.325028\pi$
$757$	28.7476			1.04485			0.522425	+	0.852686i	$0.325028\pi$
$758$	−8.97285	−	15.5414i	−0.325908	−	0.564490i
$759$	−1.42749	+	2.47249i	−0.0518147	+	0.0897457i
$760$	−0.269208	+	0.466283i	−0.00976522	+	0.0169138i
$761$	14.3758	+	24.8996i	0.521121	+	0.902608i	0.999698	+	0.0245626i	$0.00781931\pi$
$761$	14.3758	+	24.8996i	0.521121	+	0.902608i	−0.478577	+	0.878045i	$0.658847\pi$
$762$	−16.6497			−0.603155
$763$	0.376188	+	10.6171i	0.0136189	+	0.384365i
$764$	0.474949			0.0171831
$765$	−0.673117	−	1.16587i	−0.0243366	−	0.0421522i
$766$	8.10581	−	14.0397i	0.292875	−	0.507274i
$767$	−5.12102	+	8.86986i	−0.184909	+	0.320272i
$768$	−1.39157	−	2.41028i	−0.0502141	−	0.0869734i
$769$	−40.5398			−1.46190			−0.730951	−	0.682430i	$-0.760923\pi$
$769$	−40.5398			−1.46190			−0.730951	+	0.682430i	$0.760923\pi$
$770$	−3.43609	−	1.82475i	−0.123828	−	0.0657593i
$771$	−5.55603			−0.200095
$772$	−1.08443	−	1.87828i	−0.0390294	−	0.0676009i
$773$	−17.6643	+	30.5954i	−0.635339	+	1.10044i	0.351104	+	0.936336i	$0.385806\pi$
$773$	−17.6643	+	30.5954i	−0.635339	+	1.10044i	−0.986443	+	0.164103i	$0.947527\pi$
$774$	17.9834	−	31.1482i	0.646402	−	1.11960i
$775$	−3.01637	−	5.22451i	−0.108351	−	0.187670i
$776$	−45.0917			−1.61870
$777$	12.5238	−	7.83461i	0.449287	−	0.281065i
$778$	−44.9489			−1.61150
$779$	−0.405645	−	0.702598i	−0.0145338	−	0.0251732i
$780$	0.0789112	−	0.136678i	0.00282548	−	0.00489387i
$781$	3.48236	−	6.03163i	0.124609	−	0.215829i
$782$	1.58295	+	2.74175i	0.0566062	+	0.0980447i
$783$	−8.89208			−0.317777
$784$	30.0128	−	2.12952i	1.07189	−	0.0760544i
$785$	7.67112			0.273794
$786$	−3.87149	−	6.70561i	−0.138091	−	0.239181i
$787$	8.93406	−	15.4742i	0.318465	−	0.551597i	−0.661703	−	0.749766i	$-0.730166\pi$
$787$	8.93406	−	15.4742i	0.318465	−	0.551597i	0.980168	+	0.198169i	$0.0634994\pi$
$788$	−0.913082	+	1.58150i	−0.0325272	+	0.0563388i
$789$	−8.25558	−	14.2991i	−0.293906	−	0.509061i
$790$	0.534577			0.0190194
$791$	−30.6766	+	19.1907i	−1.09073	+	0.682341i
$792$	6.71007			0.238432
$793$	5.07812	+	8.79556i	0.180329	+	0.312340i
$794$	−13.0626	+	22.6251i	−0.463574	+	0.802933i
$795$	−3.24533	+	5.62108i	−0.115100	+	0.199359i
$796$	0.851585	+	1.47499i	0.0301836	+	0.0522796i
$797$	10.2292			0.362336			0.181168	−	0.983452i	$-0.442012\pi$
$797$	10.2292			0.362336			0.181168	+	0.983452i	$0.442012\pi$
$798$	0.492204	+	0.261387i	0.0174238	+	0.00925301i
$799$	−4.26211			−0.150783
$800$	−0.458065	−	0.793391i	−0.0161950	−	0.0280506i
$801$	−4.94426	+	8.56371i	−0.174697	+	0.302584i
$802$	18.4597	−	31.9732i	0.651835	−	1.12901i
$803$	7.43549	+	12.8787i	0.262393	+	0.454478i
$804$	−0.935108			−0.0329787
$805$	−0.372040	−	10.5000i	−0.0131127	−	0.370077i
$806$	11.9958			0.422532
$807$	7.72309	+	13.3768i	0.271866	+	0.470885i
$808$	−6.52177	+	11.2960i	−0.229435	+	0.397393i
$809$	4.65584	−	8.06415i	0.163691	−	0.283521i	−0.772499	−	0.635016i	$-0.780993\pi$
$809$	4.65584	−	8.06415i	0.163691	−	0.283521i	0.936190	+	0.351496i	$0.114327\pi$
$810$	3.39341	+	5.87755i	0.119232	+	0.206516i
$811$	−19.7720			−0.694291			−0.347145	−	0.937811i	$-0.612849\pi$
$811$	−19.7720			−0.694291			−0.347145	+	0.937811i	$0.612849\pi$
$812$	0.0343075	+	0.968255i	0.00120396	+	0.0339791i
$813$	−15.1928			−0.532836
$814$	−5.71013	−	9.89024i	−0.200140	−	0.346653i
$815$	−8.47009	+	14.6706i	−0.296694	+	0.513889i
$816$	−0.837684	+	1.45091i	−0.0293248	+	0.0507921i
$817$	0.981302	+	1.69966i	0.0343314	+	0.0594637i
$818$	−28.1227			−0.983287
$819$	−7.84607	−	4.16669i	−0.274164	−	0.145596i
$820$	0.661018			0.0230837
$821$	11.2507	+	19.4867i	0.392651	+	0.680091i	0.992798	−	0.119798i	$-0.0382248\pi$
$821$	11.2507	+	19.4867i	0.392651	+	0.680091i	−0.600148	+	0.799889i	$0.704891\pi$
$822$	4.07395	−	7.05630i	0.142095	−	0.246117i
$823$	9.92317	−	17.1874i	0.345900	−	0.599116i	−0.639617	−	0.768694i	$-0.720907\pi$
$823$	9.92317	−	17.1874i	0.345900	−	0.599116i	0.985517	+	0.169578i	$0.0542404\pi$
$824$	−22.3892	−	38.7793i	−0.779965	−	1.35094i
$825$	−0.718935			−0.0250301
$826$	24.9821	−	15.6283i	0.869237	−	0.543777i
$827$	−39.2944			−1.36640			−0.683200	−	0.730231i	$-0.739412\pi$
$827$	−39.2944			−1.36640			−0.683200	+	0.730231i	$0.739412\pi$
$828$	−0.800409	−	1.38635i	−0.0278161	−	0.0481790i
$829$	5.13644	−	8.89657i	0.178396	−	0.308991i	−0.762935	−	0.646475i	$-0.776243\pi$
$829$	5.13644	−	8.89657i	0.178396	−	0.308991i	0.941331	+	0.337484i	$0.109576\pi$
$830$	2.84667	−	4.93058i	0.0988094	−	0.171143i
$831$	4.24991	+	7.36106i	0.147428	+	0.255353i
$832$	−9.80299			−0.339857
$833$	−2.12539	−	3.14408i	−0.0736403	−	0.108936i
$834$	17.5858			0.608947
$835$	−6.02815	−	10.4411i	−0.208613	−	0.361328i
$836$	0.0161730	−	0.0280124i	0.000559354	−	0.000968830i
$837$	11.8906	−	20.5951i	0.410999	−	0.711871i
$838$	−25.2102	−	43.6653i	−0.870871	−	1.50839i
$839$	−15.4080			−0.531942			−0.265971	−	0.963981i	$-0.585693\pi$
$839$	−15.4080			−0.531942			−0.265971	+	0.963981i	$0.585693\pi$
$840$	4.35760	−	2.72603i	0.150352	−	0.0940569i
$841$	−23.9117			−0.824543
$842$	−9.74943	−	16.8865i	−0.335988	−	0.581947i
$843$	−9.61212	+	16.6487i	−0.331059	+	0.573411i
$844$	−0.688906	+	1.19322i	−0.0237131	+	0.0410723i
$845$	5.58574	+	9.67478i	0.192155	+	0.332823i
$846$	28.7056			0.986918
$847$	−2.33669	−	1.24091i	−0.0802898	−	0.0426382i
$848$	−38.8060			−1.33260
$849$	4.21861	+	7.30685i	0.144782	+	0.250770i
$850$	−0.398614	+	0.690420i	−0.0136724	+	0.0236812i
$851$	15.4205	−	26.7091i	0.528608	−	0.915575i
$852$	−0.406436	−	0.703967i	−0.0139243	−	0.0241175i
$853$	26.8003			0.917624			0.458812	−	0.888533i	$-0.348275\pi$
$853$	26.8003			0.917624			0.458812	+	0.888533i	$0.348275\pi$
$854$	−1.03471	−	29.2026i	−0.0354072	−	0.999291i
$855$	−0.494756			−0.0169203
$856$	−3.31230	−	5.73707i	−0.113212	−	0.196089i
$857$	1.42206	−	2.46309i	0.0485768	−	0.0841374i	−0.840715	−	0.541478i	$-0.817865\pi$
$857$	1.42206	−	2.46309i	0.0485768	−	0.0841374i	0.889291	+	0.457341i	$0.151198\pi$
$858$	0.714780	−	1.23804i	0.0244022	−	0.0422658i
$859$	−20.4657	−	35.4476i	−0.698279	−	1.20946i	−0.969063	−	0.246815i	$-0.920616\pi$
$859$	−20.4657	−	35.4476i	−0.698279	−	1.20946i	0.270783	−	0.962640i	$-0.412717\pi$
$860$	−1.59908			−0.0545281
$861$	0.274253	+	7.74018i	0.00934650	+	0.263785i
$862$	28.4636			0.969473
$863$	11.8307	+	20.4914i	0.402721	+	0.697534i	0.994053	−	0.108894i	$-0.0347310\pi$
$863$	11.8307	+	20.4914i	0.402721	+	0.697534i	−0.591332	+	0.806428i	$0.701398\pi$
$864$	1.80570	−	3.12756i	0.0614311	−	0.106402i
$865$	4.60695	−	7.97947i	0.156641	−	0.271310i
$866$	10.9258	+	18.9240i	0.371272	+	0.643063i
$867$	−12.0106			−0.407901
$868$	−2.28847	−	1.21530i	−0.0776757	−	0.0412500i
$869$	0.363537			0.0123321
$870$	1.19236	+	2.06522i	0.0404247	+	0.0700177i
$871$	−5.41707	+	9.38264i	−0.183550	+	0.317918i
$872$	−5.42533	+	9.39695i	−0.183725	+	0.318221i
$873$	−20.7176	−	35.8839i	−0.701184	−	1.21449i
$874$	1.16350			0.0393561
$875$	2.24301	−	1.40318i	0.0758275	−	0.0474362i
$876$	1.73563			0.0586416
$877$	−11.1901	−	19.3818i	−0.377862	−	0.654476i	0.612889	−	0.790169i	$-0.290007\pi$
$877$	−11.1901	−	19.3818i	−0.377862	−	0.654476i	−0.990751	+	0.135693i	$0.956674\pi$
$878$	−15.4838	+	26.8187i	−0.522552	+	0.905087i
$879$	−5.36316	+	9.28927i	−0.180895	+	0.313319i
$880$	−2.14916	−	3.72246i	−0.0724483	−	0.125484i
$881$	−37.3337			−1.25780			−0.628902	−	0.777485i	$-0.716495\pi$
$881$	−37.3337			−1.25780			−0.628902	+	0.777485i	$0.716495\pi$
$882$	14.3146	+	21.1755i	0.481997	+	0.713018i
$883$	1.75761			0.0591482			0.0295741	−	0.999563i	$-0.490585\pi$
$883$	1.75761			0.0591482			0.0295741	+	0.999563i	$0.490585\pi$
$884$	−0.0595073	−	0.103070i	−0.00200145	−	0.00346661i
$885$	2.72267	−	4.71581i	0.0915216	−	0.158520i
$886$	−5.96422	+	10.3303i	−0.200372	+	0.347054i
$887$	21.5115	+	37.2590i	0.722286	+	1.25104i	0.960081	+	0.279721i	$0.0902419\pi$
$887$	21.5115	+	37.2590i	0.722286	+	1.25104i	−0.237795	+	0.971315i	$0.576425\pi$
$888$	15.0880			0.506319
$889$	35.3253	−	22.0988i	1.18477	−	0.741169i
$890$	5.85590			0.196290
$891$	2.30767	+	3.99700i	0.0773099	+	0.133905i
$892$	−1.60642	+	2.78240i	−0.0537868	+	0.0931615i
$893$	−0.783188	+	1.35652i	−0.0262084	+	0.0453942i
$894$	4.39352	+	7.60980i	0.146941	+	0.254510i
$895$	4.32152			0.144453
$896$	29.1913	+	15.5022i	0.975213	+	0.517891i
$897$	3.86060			0.128902
$898$	26.0555	+	45.1295i	0.869485	+	1.50599i
$899$	−6.80408	+	11.7850i	−0.226929	+	0.393052i
$900$	0.201557	−	0.349107i	0.00671857	−	0.0116369i
$901$	2.44732	+	4.23888i	0.0815320	+	0.141218i
$902$	5.98752			0.199363
$903$	−0.663448	−	18.7244i	−0.0220782	−	0.623108i
$904$	−36.9576			−1.22919
$905$	1.27188	+	2.20295i	0.0422786	+	0.0732286i
$906$	4.01665	−	6.95704i	0.133444	−	0.231132i
$907$	−3.67556	+	6.36626i	−0.122045	+	0.211388i	−0.920574	−	0.390568i	$-0.872279\pi$
$907$	−3.67556	+	6.36626i	−0.122045	+	0.211388i	0.798529	+	0.601956i	$0.205612\pi$
$908$	0.185430	+	0.321174i	0.00615372	+	0.0106585i
$909$	−11.9858			−0.397545
$910$	0.186290	+	5.25762i	0.00617544	+	0.174288i
$911$	55.4043			1.83563			0.917813	−	0.397014i	$-0.129953\pi$
$911$	55.4043			1.83563			0.917813	+	0.397014i	$0.129953\pi$
$912$	0.307858	+	0.533226i	0.0101942	+	0.0176569i
$913$	1.93587	−	3.35302i	0.0640678	−	0.110969i
$914$	24.0082	−	41.5835i	0.794121	−	1.37546i
$915$	−2.69987	−	4.67630i	−0.0892548	−	0.154594i
$916$	−4.25358			−0.140542
$917$	17.1142	+	9.08859i	0.565162	+	0.300132i
$918$	−3.14269			−0.103724
$919$	−20.9476	−	36.2823i	−0.690997	−	1.19684i	−0.971512	−	0.236992i	$-0.923838\pi$
$919$	−20.9476	−	36.2823i	−0.690997	−	1.19684i	0.280514	−	0.959850i	$-0.409495\pi$
$920$	5.36551	−	9.29334i	0.176896	−	0.306392i
$921$	−11.1458	+	19.3052i	−0.367268	+	0.636127i
$922$	−0.874910	−	1.51539i	−0.0288136	−	0.0499067i
$923$	−9.41791			−0.309994
$924$	−0.261788	+	0.163769i	−0.00861218	+	0.00538761i
$925$	7.76630			0.255354
$926$	−12.7683	−	22.1153i	−0.419592	−	0.726755i
$927$	20.5737	−	35.6346i	0.675728	−	1.17039i
$928$	−1.03326	+	1.78967i	−0.0339186	+	0.0587487i
$929$	−16.5737	−	28.7065i	−0.543767	−	0.941831i	−0.998683	−	0.0512974i	$-0.983664\pi$
$929$	−16.5737	−	28.7065i	−0.543767	−	0.941831i	0.454917	−	0.890534i	$-0.349669\pi$
$930$	−6.37774			−0.209134
$931$	−1.39123	+	0.0987130i	−0.0455957	+	0.00323519i
$932$	2.92741			0.0958904
$933$	8.14463	+	14.1069i	0.266643	+	0.461840i
$934$	9.61834	−	16.6594i	0.314722	−	0.545114i
$935$	−0.271076	+	0.469517i	−0.00886513	+	0.0153549i
$936$	−4.53678	−	7.85793i	−0.148289	−	0.256844i
$937$	41.2006			1.34597			0.672983	−	0.739658i	$-0.265013\pi$
$937$	41.2006			1.34597			0.672983	+	0.739658i	$0.265013\pi$
$938$	26.4263	−	16.5318i	0.862849	−	0.539781i
$939$	−7.54184			−0.246119
$940$	−0.638120	−	1.10526i	−0.0208132	−	0.0360495i
$941$	11.7212	−	20.3018i	0.382101	−	0.661818i	−0.609261	−	0.792969i	$-0.708534\pi$
$941$	11.7212	−	20.3018i	0.382101	−	0.661818i	0.991362	+	0.131151i	$0.0418673\pi$
$942$	4.05491	−	7.02331i	0.132116	−	0.228832i
$943$	8.08479	+	14.0033i	0.263277	+	0.456009i
$944$	32.5563			1.05962
$945$	9.21129	+	4.89169i	0.299643	+	0.159127i
$946$	−14.4845			−0.470931
$947$	7.15527	+	12.3933i	0.232515	+	0.402728i	0.958548	−	0.284932i	$-0.0919712\pi$
$947$	7.15527	+	12.3933i	0.232515	+	0.402728i	−0.726033	+	0.687660i	$0.758638\pi$
$948$	0.0212147	−	0.0367449i	0.000689021	−	0.00119342i
$949$	10.0545	−	17.4149i	0.326383	−	0.565312i
$950$	0.146495	+	0.253737i	0.00475294	+	0.00823233i
$951$	24.3957			0.791086
$952$	−0.137254	−	3.87369i	−0.00444842	−	0.125547i
$953$	46.5779			1.50881			0.754403	−	0.656412i	$-0.227927\pi$
$953$	46.5779			1.50881			0.754403	+	0.656412i	$0.227927\pi$
$954$	−16.4828	−	28.5491i	−0.533651	−	0.924311i
$955$	−1.46281	+	2.53367i	−0.0473355	+	0.0819876i
$956$	−2.14407	+	3.71364i	−0.0693443	+	0.120108i
$957$	0.810858	+	1.40445i	0.0262113	+	0.0453993i
$958$	−50.6008			−1.63484
$959$	0.722055	+	20.3784i	0.0233164	+	0.658054i
$960$	5.21192			0.168214
$961$	−2.69699	−	4.67132i	−0.0869997	−	0.150688i
$962$	−7.72142	+	13.3739i	−0.248948	+	0.431191i
$963$	3.04370	−	5.27185i	0.0980820	−	0.169883i
$964$	−1.16416	−	2.01638i	−0.0374950	−	0.0649432i
$965$	13.3599			0.430069
$966$	−9.80997	−	5.20963i	−0.315631	−	0.167617i
$967$	14.4707			0.465347			0.232674	−	0.972555i	$-0.425253\pi$
$967$	14.4707			0.465347			0.232674	+	0.972555i	$0.425253\pi$
$968$	−1.35113	−	2.34023i	−0.0434270	−	0.0752177i
$969$	0.0388304	−	0.0672563i	0.00124741	−	0.00216058i
$970$	−12.2688	+	21.2502i	−0.393927	+	0.682302i
$971$	−24.5176	−	42.4658i	−0.786809	−	1.36279i	−0.927913	−	0.372798i	$-0.878398\pi$
$971$	−24.5176	−	42.4658i	−0.786809	−	1.36279i	0.141104	−	0.989995i	$-0.454935\pi$
$972$	2.45852			0.0788572
$973$	−37.3114	+	23.3412i	−1.19615	+	0.748286i
$974$	39.6546			1.27062
$975$	0.486083	+	0.841921i	0.0155671	+	0.0269630i
$976$	16.1418	−	27.9584i	0.516686	−	0.894927i
$977$	−25.6596	+	44.4438i	−0.820924	+	1.42188i	0.0840712	+	0.996460i	$0.473208\pi$
$977$	−25.6596	+	44.4438i	−0.820924	+	1.42188i	−0.904995	+	0.425422i	$0.860126\pi$
$978$	8.95447	+	15.5096i	0.286332	+	0.495942i
$979$	3.98228			0.127274
$980$	0.497116	−	1.02189i	0.0158798	−	0.0326430i
$981$	−9.97077			−0.318342
$982$	25.1652	+	43.5875i	0.803055	+	1.39093i
$983$	25.8656	−	44.8004i	0.824983	−	1.42891i	−0.0769494	−	0.997035i	$-0.524518\pi$
$983$	25.8656	−	44.8004i	0.824983	−	1.42891i	0.901932	−	0.431877i	$-0.142149\pi$
$984$	−3.95523	+	6.85066i	−0.126088	+	0.218391i
$985$	−5.62447	−	9.74187i	−0.179210	−	0.310402i
$986$	1.79832			0.0572703
$987$	12.6772	−	7.93063i	0.403521	−	0.252435i
$988$	−0.0437392			−0.00139153
$989$	−19.5580	−	33.8755i	−0.621909	−	1.07718i
$990$	1.82571	−	3.16222i	0.0580249	−	0.100502i
$991$	8.20598	−	14.2132i	0.260672	−	0.451497i	−0.705749	−	0.708462i	$-0.749389\pi$
$991$	8.20598	−	14.2132i	0.260672	−	0.451497i	0.966421	+	0.256965i	$0.0827227\pi$
$992$	−2.76339	−	4.78633i	−0.0877376	−	0.151966i
$993$	11.0722			0.351366
$994$	23.9314	+	12.7089i	0.759057	+	0.403101i
$995$	−10.4913			−0.332597
$996$	−0.225940	−	0.391340i	−0.00715919	−	0.0124001i
$997$	−19.3502	+	33.5155i	−0.612827	+	1.06145i	0.377935	+	0.925832i	$0.376634\pi$
$997$	−19.3502	+	33.5155i	−0.612827	+	1.06145i	−0.990762	+	0.135615i	$0.956699\pi$
$998$	−26.0197	+	45.0675i	−0.823641	+	1.42659i
$999$	15.3074	+	26.5133i	0.484306	+	0.838843i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	385.2.i.c.221.7	✓	16
7.2	even	3	inner	385.2.i.c.331.7	yes	16
7.3	odd	6		2695.2.a.s.1.2		8
7.4	even	3		2695.2.a.t.1.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
385.2.i.c.221.7	✓	16	1.1	even	1	trivial
385.2.i.c.331.7	yes	16	7.2	even	3	inner
2695.2.a.s.1.2		8	7.3	odd	6
2695.2.a.t.1.2		8	7.4	even	3

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:	\( N \)	\(=\)	\( 385 = 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	385.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.735245 + 1.27348i) q^{2} +(-0.359468 + 0.622616i) q^{3} +(-0.0811705 + 0.140591i) q^{4} +(-0.500000 - 0.866025i) q^{5} -1.05719 q^{6} +(2.24301 - 1.40318i) q^{7} +2.70226 q^{8} +(1.24157 + 2.15046i) q^{9} +O(q^{10})\)	\(q+(0.735245 + 1.27348i) q^{2} +(-0.359468 + 0.622616i) q^{3} +(-0.0811705 + 0.140591i) q^{4} +(-0.500000 - 0.866025i) q^{5} -1.05719 q^{6} +(2.24301 - 1.40318i) q^{7} +2.70226 q^{8} +(1.24157 + 2.15046i) q^{9} +(0.735245 - 1.27348i) q^{10} +(0.500000 - 0.866025i) q^{11} +(-0.0583564 - 0.101076i) q^{12} -1.35223 q^{13} +(3.43609 + 1.82475i) q^{14} +0.718935 q^{15} +(2.14916 + 3.72246i) q^{16} +(0.271076 - 0.469517i) q^{17} +(-1.82571 + 3.16222i) q^{18} +(-0.0996235 - 0.172553i) q^{19} +0.162341 q^{20} +(0.0673544 + 1.90093i) q^{21} +1.47049 q^{22} +(1.98556 + 3.43910i) q^{23} +(-0.971375 + 1.68247i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-0.994221 - 1.72204i) q^{26} -3.94202 q^{27} +(0.0152091 + 0.429245i) q^{28} +2.25572 q^{29} +(0.528594 + 0.915551i) q^{30} +(-3.01637 + 5.22451i) q^{31} +(-0.458065 + 0.793391i) q^{32} +(0.359468 + 0.622616i) q^{33} +0.797229 q^{34} +(-2.33669 - 1.24091i) q^{35} -0.403114 q^{36} +(-3.88315 - 6.72581i) q^{37} +(0.146495 - 0.253737i) q^{38} +(0.486083 - 0.841921i) q^{39} +(-1.35113 - 2.34023i) q^{40} +4.07178 q^{41} +(-2.37128 + 1.48342i) q^{42} -9.85011 q^{43} +(0.0811705 + 0.140591i) q^{44} +(1.24157 - 2.15046i) q^{45} +(-2.91975 + 5.05716i) q^{46} +(-3.93074 - 6.80824i) q^{47} -3.09022 q^{48} +(3.06217 - 6.29469i) q^{49} -1.47049 q^{50} +(0.194886 + 0.337553i) q^{51} +(0.109761 - 0.190112i) q^{52} +(-4.51408 + 7.81862i) q^{53} +(-2.89835 - 5.02009i) q^{54} -1.00000 q^{55} +(6.06119 - 3.79176i) q^{56} +0.143246 q^{57} +(1.65851 + 2.87262i) q^{58} +(3.78709 - 6.55943i) q^{59} +(-0.0583564 + 0.101076i) q^{60} +(-3.75537 - 6.50448i) q^{61} -8.87109 q^{62} +(5.80232 + 3.08135i) q^{63} +7.24950 q^{64} +(0.676115 + 1.17107i) q^{65} +(-0.528594 + 0.915551i) q^{66} +(4.00602 - 6.93864i) q^{67} +(0.0440068 + 0.0762219i) q^{68} -2.85498 q^{69} +(-0.137765 - 3.88811i) q^{70} +6.96472 q^{71} +(3.35503 + 5.81109i) q^{72} +(-7.43549 + 12.8787i) q^{73} +(5.71013 - 9.89024i) q^{74} +(-0.359468 - 0.622616i) q^{75} +0.0323460 q^{76} +(-0.0936863 - 2.64409i) q^{77} +1.42956 q^{78} +(0.181768 + 0.314832i) q^{79} +(2.14916 - 3.72246i) q^{80} +(-2.30767 + 3.99700i) q^{81} +(2.99376 + 5.18534i) q^{82} +3.87173 q^{83} +(-0.272722 - 0.144830i) q^{84} -0.542152 q^{85} +(-7.24224 - 12.5439i) q^{86} +(-0.810858 + 1.40445i) q^{87} +(1.35113 - 2.34023i) q^{88} +(1.99114 + 3.44875i) q^{89} +3.65142 q^{90} +(-3.03306 + 1.89742i) q^{91} -0.644677 q^{92} +(-2.16858 - 3.75608i) q^{93} +(5.78011 - 10.0114i) q^{94} +(-0.0996235 + 0.172553i) q^{95} +(-0.329319 - 0.570397i) q^{96} -16.6867 q^{97} +(10.2676 - 0.728526i) q^{98} +2.48313 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 3 q^{2} - q^{3} - 9 q^{4} - 8 q^{5} - 6 q^{6} - q^{7} + 18 q^{8} - 19 q^{9}+O(q^{10}) \) 16 * q - 3 * q^2 - q^3 - 9 * q^4 - 8 * q^5 - 6 * q^6 - q^7 + 18 * q^8 - 19 * q^9	\( 16 q - 3 q^{2} - q^{3} - 9 q^{4} - 8 q^{5} - 6 q^{6} - q^{7} + 18 q^{8} - 19 q^{9} - 3 q^{10} + 8 q^{11} - 9 q^{12} + 28 q^{13} - 9 q^{14} + 2 q^{15} - 7 q^{16} - 5 q^{17} - 27 q^{18} - q^{19} + 18 q^{20} - 18 q^{21} - 6 q^{22} + 2 q^{23} + 24 q^{24} - 8 q^{25} - 21 q^{26} - 10 q^{27} + 32 q^{28} + 52 q^{29} + 3 q^{30} - 2 q^{31} - 16 q^{32} + q^{33} - 52 q^{34} + 5 q^{35} + 108 q^{36} + q^{37} + 31 q^{38} - 19 q^{39} - 9 q^{40} - 6 q^{41} + 44 q^{42} + 8 q^{43} + 9 q^{44} - 19 q^{45} - 10 q^{46} - q^{47} - 42 q^{48} + 17 q^{49} + 6 q^{50} - 3 q^{51} - 37 q^{52} - 26 q^{53} + 5 q^{54} - 16 q^{55} + 40 q^{57} + q^{58} + 19 q^{59} - 9 q^{60} - 52 q^{62} - 21 q^{63} + 2 q^{64} - 14 q^{65} - 3 q^{66} + 13 q^{67} - 15 q^{68} - 28 q^{69} + 15 q^{70} - 18 q^{71} - 32 q^{72} - 11 q^{73} - 24 q^{74} - q^{75} - 36 q^{76} + 4 q^{77} - 66 q^{78} + 8 q^{79} - 7 q^{80} - 52 q^{81} - 41 q^{82} + 64 q^{83} + 138 q^{84} + 10 q^{85} - 28 q^{86} + 16 q^{87} + 9 q^{88} - 5 q^{89} + 54 q^{90} + 13 q^{91} + 60 q^{92} + 14 q^{93} + 5 q^{94} - q^{95} - q^{96} + 18 q^{97} + 22 q^{98} - 38 q^{99}+O(q^{100}) \) 16 * q - 3 * q^2 - q^3 - 9 * q^4 - 8 * q^5 - 6 * q^6 - q^7 + 18 * q^8 - 19 * q^9 - 3 * q^10 + 8 * q^11 - 9 * q^12 + 28 * q^13 - 9 * q^14 + 2 * q^15 - 7 * q^16 - 5 * q^17 - 27 * q^18 - q^19 + 18 * q^20 - 18 * q^21 - 6 * q^22 + 2 * q^23 + 24 * q^24 - 8 * q^25 - 21 * q^26 - 10 * q^27 + 32 * q^28 + 52 * q^29 + 3 * q^30 - 2 * q^31 - 16 * q^32 + q^33 - 52 * q^34 + 5 * q^35 + 108 * q^36 + q^37 + 31 * q^38 - 19 * q^39 - 9 * q^40 - 6 * q^41 + 44 * q^42 + 8 * q^43 + 9 * q^44 - 19 * q^45 - 10 * q^46 - q^47 - 42 * q^48 + 17 * q^49 + 6 * q^50 - 3 * q^51 - 37 * q^52 - 26 * q^53 + 5 * q^54 - 16 * q^55 + 40 * q^57 + q^58 + 19 * q^59 - 9 * q^60 - 52 * q^62 - 21 * q^63 + 2 * q^64 - 14 * q^65 - 3 * q^66 + 13 * q^67 - 15 * q^68 - 28 * q^69 + 15 * q^70 - 18 * q^71 - 32 * q^72 - 11 * q^73 - 24 * q^74 - q^75 - 36 * q^76 + 4 * q^77 - 66 * q^78 + 8 * q^79 - 7 * q^80 - 52 * q^81 - 41 * q^82 + 64 * q^83 + 138 * q^84 + 10 * q^85 - 28 * q^86 + 16 * q^87 + 9 * q^88 - 5 * q^89 + 54 * q^90 + 13 * q^91 + 60 * q^92 + 14 * q^93 + 5 * q^94 - q^95 - q^96 + 18 * q^97 + 22 * q^98 - 38 * q^99

Introduction

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