LMFDB - Embedded newform 224.2.u.b.29.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [224,2,Mod(29,224)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(224, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 3, 0]))

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

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

chi := DirichletCharacter("224.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 224 = 2^{5} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	224.u (of order $8$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.78864900528$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			29.9
Character	$\chi$	$=$	224.29
Dual form			224.2.u.b.85.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.27165 + 0.618795i) q^{2} +(2.04641 + 0.847650i) q^{3} +(1.23419 + 1.57378i) q^{4} +(-1.31439 - 3.17322i) q^{5} +(2.07779 + 2.34422i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(0.595604 + 2.76501i) q^{8} +(1.34795 + 1.34795i) q^{9} +O(q^{10})$	\(q+(1.27165 + 0.618795i) q^{2} +(2.04641 + 0.847650i) q^{3} +(1.23419 + 1.57378i) q^{4} +(-1.31439 - 3.17322i) q^{5} +(2.07779 + 2.34422i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(0.595604 + 2.76501i) q^{8} +(1.34795 + 1.34795i) q^{9} +(0.292129 - 4.84857i) q^{10} +(-3.26043 + 1.35052i) q^{11} +(1.19163 + 4.26675i) q^{12} +(1.07238 - 2.58896i) q^{13} +(-1.33675 + 0.461638i) q^{14} -7.60786i q^{15} +(-0.953572 + 3.88468i) q^{16} -3.99181i q^{17} +(0.880018 + 2.54823i) q^{18} +(-2.91342 + 7.03362i) q^{19} +(3.37176 - 5.98491i) q^{20} +(-2.04641 + 0.847650i) q^{21} +(-4.98182 - 0.300157i) q^{22} +(-1.47816 - 1.47816i) q^{23} +(-1.12491 + 6.16319i) q^{24} +(-4.80619 + 4.80619i) q^{25} +(2.96572 - 2.62866i) q^{26} +(-0.927079 - 2.23817i) q^{27} +(-1.98553 - 0.240130i) q^{28} +(-2.10649 - 0.872535i) q^{29} +(4.70770 - 9.67453i) q^{30} +7.19272 q^{31} +(-3.61643 + 4.34988i) q^{32} -7.81694 q^{33} +(2.47011 - 5.07618i) q^{34} +(3.17322 + 1.31439i) q^{35} +(-0.457759 + 3.78501i) q^{36} +(0.385477 + 0.930623i) q^{37} +(-8.05722 + 7.14149i) q^{38} +(4.38905 - 4.38905i) q^{39} +(7.99113 - 5.52429i) q^{40} +(6.37302 + 6.37302i) q^{41} +(-3.12684 - 0.188393i) q^{42} +(8.95733 - 3.71025i) q^{43} +(-6.14939 - 3.46442i) q^{44} +(2.50562 - 6.04910i) q^{45} +(-0.965022 - 2.79438i) q^{46} -4.31082i q^{47} +(-5.24424 + 7.14133i) q^{48} -1.00000i q^{49} +(-9.08584 + 3.13774i) q^{50} +(3.38366 - 8.16887i) q^{51} +(5.39796 - 1.50756i) q^{52} +(0.875431 - 0.362615i) q^{53} +(0.206047 - 3.41984i) q^{54} +(8.57097 + 8.57097i) q^{55} +(-2.37631 - 1.53400i) q^{56} +(-11.9241 + 11.9241i) q^{57} +(-2.13879 - 2.41304i) q^{58} +(0.860403 + 2.07720i) q^{59} +(11.9731 - 9.38951i) q^{60} +(-11.8976 - 4.92816i) q^{61} +(9.14662 + 4.45082i) q^{62} -1.90629 q^{63} +(-7.29051 + 3.29370i) q^{64} -9.62486 q^{65} +(-9.94040 - 4.83708i) q^{66} +(-1.95147 - 0.808326i) q^{67} +(6.28223 - 4.92663i) q^{68} +(-1.77195 - 4.27787i) q^{69} +(3.22189 + 3.63502i) q^{70} +(-5.27021 + 5.27021i) q^{71} +(-2.92425 + 4.52995i) q^{72} +(8.05861 + 8.05861i) q^{73} +(-0.0856736 + 1.42196i) q^{74} +(-13.9094 + 5.76146i) q^{75} +(-14.6651 + 4.09571i) q^{76} +(1.35052 - 3.26043i) q^{77} +(8.29726 - 2.86541i) q^{78} +9.04531i q^{79} +(13.5803 - 2.08009i) q^{80} -11.0849i q^{81} +(4.16065 + 12.0478i) q^{82} +(4.16535 - 10.0560i) q^{83} +(-3.85966 - 2.17444i) q^{84} +(-12.6669 + 5.24680i) q^{85} +(13.6865 + 0.824616i) q^{86} +(-3.57112 - 3.57112i) q^{87} +(-5.67611 - 8.21074i) q^{88} +(12.4833 - 12.4833i) q^{89} +(6.92942 - 6.14187i) q^{90} +(1.07238 + 2.58896i) q^{91} +(0.501976 - 4.15062i) q^{92} +(14.7192 + 6.09691i) q^{93} +(2.66752 - 5.48186i) q^{94} +26.1486 q^{95} +(-11.0879 + 5.83616i) q^{96} -3.17339 q^{97} +(0.618795 - 1.27165i) q^{98} +(-6.21534 - 2.57448i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 4 q^{2} + 4 q^{3} + 8 q^{5} + 12 q^{6} - 8 q^{8} + 8 q^{9}+O(q^{10}) $ 40 * q + 4 * q^2 + 4 * q^3 + 8 * q^5 + 12 * q^6 - 8 * q^8 + 8 * q^9	$ 40 q + 4 q^{2} + 4 q^{3} + 8 q^{5} + 12 q^{6} - 8 q^{8} + 8 q^{9} - 16 q^{10} + 12 q^{11} - 36 q^{12} + 8 q^{16} + 4 q^{19} - 4 q^{21} - 52 q^{22} + 16 q^{23} - 8 q^{24} - 16 q^{25} + 12 q^{26} - 32 q^{27} + 8 q^{28} + 16 q^{29} + 36 q^{30} + 24 q^{31} - 36 q^{32} + 8 q^{33} - 8 q^{34} - 8 q^{36} + 16 q^{37} - 12 q^{38} - 24 q^{39} + 36 q^{40} + 8 q^{41} + 52 q^{43} - 44 q^{44} - 64 q^{45} - 32 q^{46} - 36 q^{48} + 52 q^{50} + 16 q^{51} - 16 q^{52} - 32 q^{54} - 8 q^{55} + 12 q^{56} - 8 q^{57} + 40 q^{58} + 20 q^{59} + 52 q^{60} - 16 q^{61} - 12 q^{62} - 24 q^{63} - 48 q^{64} - 80 q^{65} - 40 q^{66} - 4 q^{67} - 4 q^{68} - 40 q^{69} + 32 q^{70} + 72 q^{72} - 24 q^{73} - 12 q^{74} + 20 q^{75} - 72 q^{76} + 4 q^{77} + 12 q^{78} + 60 q^{80} + 16 q^{82} + 4 q^{83} + 8 q^{84} - 64 q^{85} - 48 q^{86} - 32 q^{87} + 16 q^{88} + 32 q^{89} + 20 q^{90} + 108 q^{92} - 24 q^{93} + 68 q^{94} - 80 q^{95} - 40 q^{96} + 56 q^{97} + 4 q^{98} - 60 q^{99}+O(q^{100}) $ 40 * q + 4 * q^2 + 4 * q^3 + 8 * q^5 + 12 * q^6 - 8 * q^8 + 8 * q^9 - 16 * q^10 + 12 * q^11 - 36 * q^12 + 8 * q^16 + 4 * q^19 - 4 * q^21 - 52 * q^22 + 16 * q^23 - 8 * q^24 - 16 * q^25 + 12 * q^26 - 32 * q^27 + 8 * q^28 + 16 * q^29 + 36 * q^30 + 24 * q^31 - 36 * q^32 + 8 * q^33 - 8 * q^34 - 8 * q^36 + 16 * q^37 - 12 * q^38 - 24 * q^39 + 36 * q^40 + 8 * q^41 + 52 * q^43 - 44 * q^44 - 64 * q^45 - 32 * q^46 - 36 * q^48 + 52 * q^50 + 16 * q^51 - 16 * q^52 - 32 * q^54 - 8 * q^55 + 12 * q^56 - 8 * q^57 + 40 * q^58 + 20 * q^59 + 52 * q^60 - 16 * q^61 - 12 * q^62 - 24 * q^63 - 48 * q^64 - 80 * q^65 - 40 * q^66 - 4 * q^67 - 4 * q^68 - 40 * q^69 + 32 * q^70 + 72 * q^72 - 24 * q^73 - 12 * q^74 + 20 * q^75 - 72 * q^76 + 4 * q^77 + 12 * q^78 + 60 * q^80 + 16 * q^82 + 4 * q^83 + 8 * q^84 - 64 * q^85 - 48 * q^86 - 32 * q^87 + 16 * q^88 + 32 * q^89 + 20 * q^90 + 108 * q^92 - 24 * q^93 + 68 * q^94 - 80 * q^95 - 40 * q^96 + 56 * q^97 + 4 * q^98 - 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/224\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{8}\right)$

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 $

$2$	1.27165	+	0.618795i	0.899192	+	0.437554i
$2$	1.27165	+	0.618795i	0.899192	+	0.437554i
$3$	2.04641	+	0.847650i	1.18149	+	0.489391i	0.884976	−	0.465636i	$-0.154175\pi$
$3$	2.04641	+	0.847650i	1.18149	+	0.489391i	0.296518	+	0.955027i	$0.404175\pi$
$4$	1.23419	+	1.57378i	0.617093	+	0.786890i
$5$	−1.31439	−	3.17322i	−0.587814	−	1.41911i	−0.885588	−	0.464473i	$-0.846244\pi$
$5$	−1.31439	−	3.17322i	−0.587814	−	1.41911i	0.297773	−	0.954637i	$-0.403756\pi$
$6$	2.07779	+	2.34422i	0.848255	+	0.957024i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$8$	0.595604	+	2.76501i	0.210578	+	0.977577i
$9$	1.34795	+	1.34795i	0.449318	+	0.449318i
$10$	0.292129	−	4.84857i	0.0923792	−	1.53325i
$11$	−3.26043	+	1.35052i	−0.983057	+	0.407196i	−0.815557	−	0.578676i	$-0.803569\pi$
$11$	−3.26043	+	1.35052i	−0.983057	+	0.407196i	−0.167500	+	0.985872i	$0.553569\pi$
$12$	1.19163	+	4.26675i	0.343994	+	1.23171i
$13$	1.07238	−	2.58896i	0.297425	−	0.718047i	−0.702555	−	0.711630i	$-0.747957\pi$
$13$	1.07238	−	2.58896i	0.297425	−	0.718047i	0.999979	−	0.00641713i	$-0.00204265\pi$
$14$	−1.33675	+	0.461638i	−0.357260	+	0.123378i
$15$		−	7.60786i		−	1.96434i
$16$	−0.953572	+	3.88468i	−0.238393	+	0.971169i
$17$		−	3.99181i		−	0.968156i	−0.875025	−	0.484078i	$-0.839155\pi$
$17$		−	3.99181i		−	0.968156i	0.875025	−	0.484078i	$-0.160845\pi$
$18$	0.880018	+	2.54823i	0.207422	+	0.600624i
$19$	−2.91342	+	7.03362i	−0.668385	+	1.61362i	0.115928	+	0.993258i	$0.463016\pi$
$19$	−2.91342	+	7.03362i	−0.668385	+	1.61362i	−0.784312	+	0.620366i	$0.786984\pi$
$20$	3.37176	−	5.98491i	0.753947	−	1.33827i
$21$	−2.04641	+	0.847650i	−0.446563	+	0.184972i
$22$	−4.98182	−	0.300157i	−1.06213	−	0.0639937i
$23$	−1.47816	−	1.47816i	−0.308217	−	0.308217i	0.536000	−	0.844218i	$-0.319935\pi$
$23$	−1.47816	−	1.47816i	−0.308217	−	0.308217i	−0.844218	+	0.536000i	$0.819935\pi$
$24$	−1.12491	+	6.16319i	−0.229621	+	1.25806i
$25$	−4.80619	+	4.80619i	−0.961238	+	0.961238i
$26$	2.96572	−	2.62866i	0.581626	−	0.515523i
$27$	−0.927079	−	2.23817i	−0.178416	−	0.430735i
$28$	−1.98553	−	0.240130i	−0.375230	−	0.0453803i
$29$	−2.10649	−	0.872535i	−0.391164	−	0.162026i	0.178428	−	0.983953i	$-0.442899\pi$
$29$	−2.10649	−	0.872535i	−0.391164	−	0.162026i	−0.569592	+	0.821927i	$0.692899\pi$
$30$	4.70770	−	9.67453i	0.859505	−	1.76632i
$31$	7.19272			1.29185			0.645925	−	0.763401i	$-0.276472\pi$
$31$	7.19272			1.29185			0.645925	+	0.763401i	$0.276472\pi$
$32$	−3.61643	+	4.34988i	−0.639300	+	0.768957i
$33$	−7.81694			−1.36075
$34$	2.47011	−	5.07618i	0.423621	−	0.870558i
$35$	3.17322	+	1.31439i	0.536373	+	0.222173i
$36$	−0.457759	+	3.78501i	−0.0762931	+	0.630835i
$37$	0.385477	+	0.930623i	0.0633720	+	0.152993i	0.952393	−	0.304873i	$-0.0986139\pi$
$37$	0.385477	+	0.930623i	0.0633720	+	0.152993i	−0.889021	+	0.457866i	$0.848614\pi$
$38$	−8.05722	+	7.14149i	−1.30705	+	1.15850i
$39$	4.38905	−	4.38905i	0.702811	−	0.702811i
$40$	7.99113	−	5.52429i	1.26351	−	0.873467i
$41$	6.37302	+	6.37302i	0.995298	+	0.995298i	0.999989	−	0.00469080i	$-0.00149313\pi$
$41$	6.37302	+	6.37302i	0.995298	+	0.995298i	−0.00469080	+	0.999989i	$0.501493\pi$
$42$	−3.12684	−	0.188393i	−0.482481	−	0.0290697i
$43$	8.95733	−	3.71025i	1.36598	−	0.565808i	0.425285	−	0.905060i	$-0.360174\pi$
$43$	8.95733	−	3.71025i	1.36598	−	0.565808i	0.940695	+	0.339252i	$0.110174\pi$
$44$	−6.14939	−	3.46442i	−0.927056	−	0.522281i
$45$	2.50562	−	6.04910i	0.373516	−	0.901747i
$46$	−0.965022	−	2.79438i	−0.142285	−	0.412008i
$47$		−	4.31082i		−	0.628798i	−0.949291	−	0.314399i	$-0.898197\pi$
$47$		−	4.31082i		−	0.628798i	0.949291	−	0.314399i	$-0.101803\pi$
$48$	−5.24424	+	7.14133i	−0.756941	+	1.03076i
$49$		−	1.00000i		−	0.142857i
$50$	−9.08584	+	3.13774i	−1.28493	+	0.443744i
$51$	3.38366	−	8.16887i	0.473807	−	1.14387i
$52$	5.39796	−	1.50756i	0.748563	−	0.209061i
$53$	0.875431	−	0.362615i	0.120250	−	0.0498091i	−0.321747	−	0.946826i	$-0.604270\pi$
$53$	0.875431	−	0.362615i	0.120250	−	0.0498091i	0.441997	+	0.897016i	$0.354270\pi$
$54$	0.206047	−	3.41984i	0.0280394	−	0.465381i
$55$	8.57097	+	8.57097i	1.15571	+	1.15571i
$56$	−2.37631	−	1.53400i	−0.317548	−	0.204989i
$57$	−11.9241	+	11.9241i	−1.57939	+	1.57939i
$58$	−2.13879	−	2.41304i	−0.280837	−	0.316848i
$59$	0.860403	+	2.07720i	0.112015	+	0.270428i	0.969939	−	0.243349i	$-0.0782460\pi$
$59$	0.860403	+	2.07720i	0.112015	+	0.270428i	−0.857924	+	0.513777i	$0.828246\pi$
$60$	11.9731	−	9.38951i	1.54572	−	1.21218i
$61$	−11.8976	−	4.92816i	−1.52334	−	0.630987i	−0.545080	−	0.838384i	$-0.683501\pi$
$61$	−11.8976	−	4.92816i	−1.52334	−	0.630987i	−0.978257	+	0.207397i	$0.933501\pi$
$62$	9.14662	+	4.45082i	1.16162	+	0.565255i
$63$	−1.90629			−0.240171
$64$	−7.29051	+	3.29370i	−0.911314	+	0.411712i
$65$	−9.62486			−1.19382
$66$	−9.94040	−	4.83708i	−1.22358	−	0.595404i
$67$	−1.95147	−	0.808326i	−0.238410	−	0.0987528i	0.260279	−	0.965533i	$-0.416185\pi$
$67$	−1.95147	−	0.808326i	−0.238410	−	0.0987528i	−0.498690	+	0.866781i	$0.666185\pi$
$68$	6.28223	−	4.92663i	0.761832	−	0.597442i
$69$	−1.77195	−	4.27787i	−0.213318	−	0.514996i
$70$	3.22189	+	3.63502i	0.385090	+	0.434468i
$71$	−5.27021	+	5.27021i	−0.625458	+	0.625458i	−0.946922	−	0.321463i	$-0.895825\pi$
$71$	−5.27021	+	5.27021i	−0.625458	+	0.625458i	0.321463	+	0.946922i	$0.395825\pi$
$72$	−2.92425	+	4.52995i	−0.344627	+	0.533859i
$73$	8.05861	+	8.05861i	0.943188	+	0.943188i	0.998471	−	0.0552824i	$-0.0176059\pi$
$73$	8.05861	+	8.05861i	0.943188	+	0.943188i	−0.0552824	+	0.998471i	$0.517606\pi$
$74$	−0.0856736	+	1.42196i	−0.00995935	+	0.165299i
$75$	−13.9094	+	5.76146i	−1.60612	+	0.665276i
$76$	−14.6651	+	4.09571i	−1.68220	+	0.469810i
$77$	1.35052	−	3.26043i	0.153905	−	0.371561i
$78$	8.29726	−	2.86541i	0.939480	−	0.324444i
$79$			9.04531i			1.01768i	0.860862	+	0.508839i	$0.169925\pi$
$79$			9.04531i			1.01768i	−0.860862	+	0.508839i	$0.830075\pi$
$80$	13.5803	−	2.08009i	1.51833	−	0.232561i
$81$		−	11.0849i		−	1.23166i
$82$	4.16065	+	12.0478i	0.459467	+	1.33046i
$83$	4.16535	−	10.0560i	0.457206	−	1.10379i	−0.512318	−	0.858796i	$-0.671213\pi$
$83$	4.16535	−	10.0560i	0.457206	−	1.10379i	0.969524	−	0.244997i	$-0.0787871\pi$
$84$	−3.85966	−	2.17444i	−0.421124	−	0.237251i
$85$	−12.6669	+	5.24680i	−1.37392	+	0.569096i
$86$	13.6865	+	0.824616i	1.47585	+	0.0889207i
$87$	−3.57112	−	3.57112i	−0.382865	−	0.382865i
$88$	−5.67611	−	8.21074i	−0.605075	−	0.875268i
$89$	12.4833	−	12.4833i	1.32323	−	1.32323i	0.412076	−	0.911149i	$-0.364804\pi$
$89$	12.4833	−	12.4833i	1.32323	−	1.32323i	0.911149	−	0.412076i	$-0.135196\pi$
$90$	6.92942	−	6.14187i	0.730425	−	0.647410i
$91$	1.07238	+	2.58896i	0.112416	+	0.271396i
$92$	0.501976	−	4.15062i	0.0523346	−	0.432732i
$93$	14.7192	+	6.09691i	1.52631	+	0.632220i
$94$	2.66752	−	5.48186i	0.275133	−	0.565410i
$95$	26.1486			2.68279
$96$	−11.0879	+	5.83616i	−1.13165	+	0.595651i
$97$	−3.17339			−0.322209			−0.161105	−	0.986937i	$-0.551506\pi$
$97$	−3.17339			−0.322209			−0.161105	+	0.986937i	$0.551506\pi$
$98$	0.618795	−	1.27165i	0.0625077	−	0.128456i
$99$	−6.21534	−	2.57448i	−0.624666	−	0.258745i
$100$	−13.4956	−	1.63216i	−1.34956	−	0.163216i
$101$	0.974224	+	2.35199i	0.0969389	+	0.234031i	0.964909	−	0.262586i	$-0.0845753\pi$
$101$	0.974224	+	2.35199i	0.0969389	+	0.234031i	−0.867970	+	0.496617i	$0.834575\pi$
$102$	9.35768	−	8.29415i	0.926548	−	0.821243i
$103$	−2.75763	+	2.75763i	−0.271718	+	0.271718i	−0.829791	−	0.558074i	$-0.811541\pi$
$103$	−2.75763	+	2.75763i	−0.271718	+	0.271718i	0.558074	+	0.829791i	$0.311541\pi$
$104$	7.79719	+	1.42315i	0.764577	+	0.139551i
$105$	5.37957	+	5.37957i	0.524992	+	0.524992i
$106$	1.33763	+	0.0805926i	0.129922	+	0.00782785i
$107$	−16.1940	+	6.70779i	−1.56554	+	0.648466i	−0.986040	−	0.166509i	$-0.946750\pi$
$107$	−16.1940	+	6.70779i	−1.56554	+	0.648466i	−0.579496	+	0.814975i	$0.696750\pi$
$108$	2.37820	−	4.22133i	0.228842	−	0.406198i
$109$	−3.93391	+	9.49731i	−0.376801	+	0.909677i	0.615761	+	0.787933i	$0.288849\pi$
$109$	−3.93391	+	9.49731i	−0.376801	+	0.909677i	−0.992562	+	0.121744i	$0.961151\pi$
$110$	5.59560	+	16.2030i	0.533520	+	1.54489i
$111$			2.23118i			0.211775i
$112$	−2.07260	−	3.42116i	−0.195843	−	0.323269i
$113$			12.0336i			1.13203i	0.824396	+	0.566013i	$0.191515\pi$
$113$			12.0336i			1.13203i	−0.824396	+	0.566013i	$0.808485\pi$
$114$	−22.5418	+	7.78470i	−2.11124	+	0.729104i
$115$	−2.74765	+	6.63341i	−0.256219	+	0.618568i
$116$	−1.22662	−	4.39202i	−0.113888	−	0.407788i
$117$	4.93531	−	2.04427i	0.456270	−	0.188993i
$118$	−0.191228	+	3.17388i	−0.0176039	+	0.292179i
$119$	2.82263	+	2.82263i	0.258750	+	0.258750i
$120$	21.0358	−	4.53127i	1.92029	−	0.413646i
$121$	1.02835	−	1.02835i	0.0934863	−	0.0934863i
$122$	−12.0801	−	13.6291i	−1.09368	−	1.23392i
$123$	7.63971	+	18.4439i	0.688849	+	1.66303i
$124$	8.87715	+	11.3198i	0.797192	+	1.01655i
$125$	5.70223	+	2.36194i	0.510023	+	0.211258i
$126$	−2.42414	−	1.17961i	−0.215959	−	0.105088i
$127$	14.6350			1.29865			0.649323	−	0.760513i	$-0.275052\pi$
$127$	14.6350			1.29865			0.649323	+	0.760513i	$0.275052\pi$
$128$	−11.3091	−	0.322905i	−0.999593	−	0.0285411i
$129$	21.4753			1.89080
$130$	−12.2395	−	5.95582i	−1.07347	−	0.522360i
$131$	−5.41172	−	2.24161i	−0.472824	−	0.195850i	0.133530	−	0.991045i	$-0.457369\pi$
$131$	−5.41172	−	2.24161i	−0.472824	−	0.195850i	−0.606354	+	0.795195i	$0.707369\pi$
$132$	−9.64755	−	12.3021i	−0.839711	−	1.07076i
$133$	−2.91342	−	7.03362i	−0.252626	−	0.609892i
$134$	−1.98140	−	2.23547i	−0.171167	−	0.193115i
$135$	−5.88366	+	5.88366i	−0.506385	+	0.506385i
$136$	11.0374	−	2.37754i	0.946447	−	0.203872i
$137$	0.680244	+	0.680244i	0.0581171	+	0.0581171i	0.735568	−	0.677451i	$-0.236915\pi$
$137$	0.680244	+	0.680244i	0.0581171	+	0.0581171i	−0.677451	+	0.735568i	$0.736915\pi$
$138$	0.393823	−	6.53643i	0.0335244	−	0.556418i
$139$	1.12425	−	0.465681i	0.0953580	−	0.0394986i	−0.334494	−	0.942398i	$-0.608566\pi$
$139$	1.12425	−	0.465681i	0.0953580	−	0.0394986i	0.429852	+	0.902899i	$0.358566\pi$
$140$	1.84778	+	6.61616i	0.156166	+	0.559168i
$141$	3.65407	−	8.82170i	0.307728	−	0.742921i
$142$	−9.96303	+	3.44068i	−0.836079	+	0.288735i
$143$			9.88938i			0.826991i
$144$	−6.52173	+	3.95099i	−0.543478	+	0.329249i
$145$			7.83120i			0.650346i
$146$	5.26110	+	15.2343i	0.435412	+	1.26080i
$147$	0.847650	−	2.04641i	0.0699130	−	0.168785i
$148$	−0.988847	+	1.75522i	−0.0812827	+	0.144278i
$149$	16.7481	−	6.93729i	1.37206	−	0.568325i	0.429712	−	0.902966i	$-0.358615\pi$
$149$	16.7481	−	6.93729i	1.37206	−	0.568325i	0.942346	+	0.334641i	$0.108615\pi$
$150$	−21.2530	−	1.28051i	−1.73530	−	0.104553i
$151$	−9.93052	−	9.93052i	−0.808134	−	0.808134i	0.176217	−	0.984351i	$-0.443614\pi$
$151$	−9.93052	−	9.93052i	−0.808134	−	0.808134i	−0.984351	+	0.176217i	$0.943614\pi$
$152$	−21.1833	−	3.86638i	−1.71819	−	0.313604i
$153$	5.38077	−	5.38077i	0.435010	−	0.435010i
$154$	3.73492	−	3.31043i	0.300968	−	0.266762i
$155$	−9.45406	−	22.8241i	−0.759368	−	1.83328i
$156$	12.3243	+	1.49050i	0.986735	+	0.119336i
$157$	−12.7161	−	5.26719i	−1.01486	−	0.420368i	−0.187633	−	0.982239i	$-0.560081\pi$
$157$	−12.7161	−	5.26719i	−1.01486	−	0.420368i	−0.827224	+	0.561872i	$0.810081\pi$
$158$	−5.59719	+	11.5025i	−0.445289	+	0.915087i
$159$	2.09886			0.166450
$160$	18.5566	+	5.75829i	1.46702	+	0.455232i
$161$	2.09043			0.164749
$162$	6.85930	−	14.0961i	0.538917	−	1.10750i
$163$	1.03878	+	0.430277i	0.0813636	+	0.0337019i	0.422994	−	0.906132i	$-0.360979\pi$
$163$	1.03878	+	0.430277i	0.0813636	+	0.0337019i	−0.341630	+	0.939834i	$0.610979\pi$
$164$	−2.16425	+	17.8952i	−0.168999	+	1.39738i
$165$	10.2745	+	24.8049i	0.799871	+	1.93106i
$166$	11.5195	−	10.2103i	0.894086	−	0.792470i
$167$	1.69327	−	1.69327i	0.131029	−	0.131029i	−0.638551	−	0.769580i	$-0.720466\pi$
$167$	1.69327	−	1.69327i	0.131029	−	0.131029i	0.769580	+	0.638551i	$0.220466\pi$
$168$	−3.56260	−	5.15347i	−0.274861	−	0.397598i
$169$	3.63970	+	3.63970i	0.279977	+	0.279977i
$170$	−19.3546	−	1.16612i	−1.48443	−	0.0894374i
$171$	−13.4082	+	5.55384i	−1.02535	+	0.424713i
$172$	16.8941	+	9.51774i	1.28817	+	0.725721i
$173$	−1.19903	+	2.89473i	−0.0911609	+	0.220082i	−0.962883	−	0.269918i	$-0.913003\pi$
$173$	−1.19903	+	2.89473i	−0.0911609	+	0.220082i	0.871722	+	0.490000i	$0.163003\pi$
$174$	−2.33142	−	6.75101i	−0.176745	−	0.511793i
$175$		−	6.79698i		−	0.513804i
$176$	−2.13725	−	13.9535i	−0.161102	−	1.05179i
$177$			4.98011i			0.374328i
$178$	23.5990	−	8.14977i	1.76882	−	0.610851i
$179$	7.32662	−	17.6880i	0.547617	−	1.32206i	−0.371629	−	0.928381i	$-0.621201\pi$
$179$	7.32662	−	17.6880i	0.547617	−	1.32206i	0.919246	−	0.393683i	$-0.128799\pi$
$180$	12.6124	−	3.52242i	0.940070	−	0.262545i
$181$	−17.1080	+	7.08636i	−1.27163	+	0.526725i	−0.913458	−	0.406932i	$-0.866599\pi$
$181$	−17.1080	+	7.08636i	−1.27163	+	0.526725i	−0.358168	+	0.933657i	$0.616599\pi$
$182$	−0.238340	+	3.95583i	−0.0176670	+	0.293225i
$183$	−20.1701	−	20.1701i	−1.49101	−	1.49101i
$184$	3.20672	−	4.96751i	0.236402	−	0.366210i
$185$	2.44641	−	2.44641i	0.179863	−	0.179863i
$186$	14.9450	+	16.8613i	1.09582	+	1.23633i
$187$	5.39100	+	13.0150i	0.394229	+	0.951752i
$188$	6.78429	−	5.32035i	0.494795	−	0.388027i
$189$	2.23817	+	0.927079i	0.162803	+	0.0674351i
$190$	33.2519	+	16.1806i	2.41235	+	1.17387i
$191$	−2.49496			−0.180529			−0.0902647	−	0.995918i	$-0.528771\pi$
$191$	−2.49496			−0.180529			−0.0902647	+	0.995918i	$0.528771\pi$
$192$	−17.7113	+	0.560443i	−1.27820	+	0.0404465i
$193$	17.1026			1.23107			0.615535	−	0.788109i	$-0.288940\pi$
$193$	17.1026			1.23107			0.615535	+	0.788109i	$0.288940\pi$
$194$	−4.03545	−	1.96368i	−0.289728	−	0.140984i
$195$	−19.6964	−	8.15851i	−1.41049	−	0.584243i
$196$	1.57378	−	1.23419i	0.112413	−	0.0881561i
$197$	0.959896	+	2.31739i	0.0683898	+	0.165107i	0.954379	−	0.298599i	$-0.0965193\pi$
$197$	0.959896	+	2.31739i	0.0683898	+	0.165107i	−0.885989	+	0.463706i	$0.846519\pi$
$198$	−6.31066	−	7.11986i	−0.448479	−	0.505986i
$199$	−5.21673	+	5.21673i	−0.369804	+	0.369804i	−0.867406	−	0.497601i	$-0.834214\pi$
$199$	−5.21673	+	5.21673i	−0.369804	+	0.369804i	0.497601	+	0.867406i	$0.334214\pi$
$200$	−16.1517	−	10.4266i	−1.14210	−	0.737269i
$201$	−3.30833	−	3.30833i	−0.233352	−	0.233352i
$202$	−0.216525	+	3.59375i	−0.0152346	+	0.252855i
$203$	2.10649	−	0.872535i	0.147846	−	0.0612399i
$204$	17.0321	−	4.75677i	1.19248	−	0.333040i
$205$	11.8464	−	28.5997i	0.827386	−	1.99749i
$206$	−5.21315	+	1.80033i	−0.363218	+	0.125435i
$207$		−	3.98498i		−	0.276975i
$208$	9.03466	+	6.63460i	0.626441	+	0.460027i
$209$		−	26.8673i		−	1.85845i
$210$	3.51207	+	10.1698i	0.242356	+	0.701781i
$211$	−4.71690	+	11.3876i	−0.324725	+	0.783955i	0.674242	+	0.738510i	$0.264470\pi$
$211$	−4.71690	+	11.3876i	−0.324725	+	0.783955i	−0.998967	+	0.0454443i	$0.985530\pi$
$212$	1.65112	+	0.930202i	0.113400	+	0.0638865i
$213$	−15.2523	+	6.31770i	−1.04507	+	0.432882i
$214$	−24.7439	−	1.49083i	−1.69146	−	0.101911i
$215$	−23.5469	−	23.5469i	−1.60589	−	1.60589i
$216$	5.63637	−	3.89644i	0.383507	−	0.265119i
$217$	−5.08602	+	5.08602i	−0.345262	+	0.345262i
$218$	−10.8794	+	9.64296i	−0.736849	+	0.653104i
$219$	9.66032	+	23.3221i	0.652784	+	1.57596i
$220$	−2.91066	+	24.0670i	−0.196237	+	1.62260i
$221$	−10.3346	−	4.28074i	−0.695181	−	0.287953i
$222$	−1.38064	+	2.83728i	−0.0926628	+	0.190426i
$223$	−11.4705			−0.768121			−0.384061	−	0.923308i	$-0.625475\pi$
$223$	−11.4705			−0.768121			−0.384061	+	0.923308i	$0.625475\pi$
$224$	−0.518629	−	5.63303i	−0.0346524	−	0.376373i
$225$	−12.9570			−0.863803
$226$	−7.44634	+	15.3025i	−0.495323	+	1.01791i
$227$	−7.74690	−	3.20887i	−0.514180	−	0.212980i	0.110479	−	0.993879i	$-0.464762\pi$
$227$	−7.74690	−	3.20887i	−0.514180	−	0.212980i	−0.624658	+	0.780898i	$0.714762\pi$
$228$	−33.4825	−	4.04937i	−2.21743	−	0.268176i
$229$	−9.93030	−	23.9739i	−0.656213	−	1.58424i	−0.803607	−	0.595160i	$-0.797089\pi$
$229$	−9.93030	−	23.9739i	−0.656213	−	1.58424i	0.147394	−	0.989078i	$-0.452911\pi$
$230$	−7.59876	+	6.73514i	−0.501048	+	0.444102i
$231$	5.52741	−	5.52741i	0.363677	−	0.363677i
$232$	1.15793	−	6.34413i	0.0760220	−	0.416512i
$233$	−8.83386	−	8.83386i	−0.578726	−	0.578726i	0.355826	−	0.934552i	$-0.384199\pi$
$233$	−8.83386	−	8.83386i	−0.578726	−	0.578726i	−0.934552	+	0.355826i	$0.884199\pi$
$234$	7.54097	+	0.454347i	0.492969	+	0.0297016i
$235$	−13.6792	+	5.66611i	−0.892333	+	0.369616i
$236$	−2.20716	+	3.91773i	−0.143674	+	0.255023i
$237$	−7.66726	+	18.5104i	−0.498042	+	1.20238i
$238$	1.84277	+	5.33603i	0.119449	+	0.345884i
$239$			18.9665i			1.22684i	0.789756	+	0.613421i	$0.210207\pi$
$239$			18.9665i			1.22684i	−0.789756	+	0.613421i	$0.789793\pi$
$240$	29.5540	+	7.25464i	1.90771	+	0.468285i
$241$		−	11.6622i		−	0.751230i	−0.926776	−	0.375615i	$-0.877432\pi$
$241$		−	11.6622i		−	0.751230i	0.926776	−	0.375615i	$-0.122568\pi$
$242$	1.94404	−	0.671363i	0.124967	−	0.0431568i
$243$	6.61490	−	15.9698i	0.424346	−	1.02446i
$244$	−6.92805	−	24.8065i	−0.443523	−	1.58808i
$245$	−3.17322	+	1.31439i	−0.202730	+	0.0839735i
$246$	−1.69795	+	28.1816i	−0.108257	+	1.79679i
$247$	15.0854	+	15.0854i	0.959863	+	0.959863i
$248$	4.28401	+	19.8879i	0.272035	+	1.26288i
$249$	17.0480	−	17.0480i	1.08037	−	1.08037i
$250$	5.78968	+	6.53207i	0.366171	+	0.413124i
$251$	−1.29530	−	3.12712i	−0.0817583	−	0.197382i	0.877714	−	0.479185i	$-0.159068\pi$
$251$	−1.29530	−	3.12712i	−0.0817583	−	0.197382i	−0.959472	+	0.281803i	$0.909068\pi$
$252$	−2.35272	−	3.00009i	−0.148208	−	0.188988i
$253$	6.81571	+	2.82316i	0.428500	+	0.177490i
$254$	18.6106	+	9.05607i	1.16773	+	0.568228i
$255$	−30.3691			−1.90179
$256$	−14.1814	−	7.40864i	−0.886337	−	0.463040i
$257$	−12.8155			−0.799406			−0.399703	−	0.916645i	$-0.630887\pi$
$257$	−12.8155			−0.799406			−0.399703	+	0.916645i	$0.630887\pi$
$258$	27.3091	+	13.2888i	1.70019	+	0.827327i
$259$	−0.930623	−	0.385477i	−0.0578261	−	0.0239524i
$260$	−11.8789	−	15.1474i	−0.736696	−	0.939404i
$261$	−1.66331	−	4.01558i	−0.102956	−	0.248558i
$262$	−5.49471	−	6.19928i	−0.339464	−	0.382993i
$263$	13.2241	−	13.2241i	0.815435	−	0.815435i	−0.170008	−	0.985443i	$-0.554379\pi$
$263$	13.2241	−	13.2241i	0.815435	−	0.815435i	0.985443	+	0.170008i	$0.0543793\pi$
$264$	−4.65580	−	21.6139i	−0.286545	−	1.33024i
$265$	−2.30132	−	2.30132i	−0.141369	−	0.141369i
$266$	0.647519	−	10.7471i	0.0397019	−	0.658948i
$267$	36.1273	−	14.9644i	2.21096	−	0.915809i
$268$	−1.13635	−	4.06881i	−0.0694136	−	0.248542i
$269$	11.5379	−	27.8549i	0.703478	−	1.69835i	−0.0122102	−	0.999925i	$-0.503887\pi$
$269$	11.5379	−	27.8549i	0.703478	−	1.69835i	0.715688	−	0.698420i	$-0.246113\pi$
$270$	−11.1227	+	3.84117i	−0.676908	+	0.233766i
$271$		−	7.52706i		−	0.457237i	−0.973516	−	0.228618i	$-0.926579\pi$
$271$		−	7.52706i		−	0.457237i	0.973516	−	0.228618i	$-0.0734208\pi$
$272$	15.5069	+	3.80648i	0.940243	+	0.230802i
$273$			6.20706i			0.375668i
$274$	0.444100	+	1.28596i	0.0268291	+	0.0776879i
$275$	9.17943	−	22.1611i	0.553540	−	1.33636i
$276$	4.54552	−	8.06836i	0.273608	−	0.485658i
$277$	2.07896	−	0.861132i	0.124912	−	0.0517404i	−0.319352	−	0.947636i	$-0.603465\pi$
$277$	2.07896	−	0.861132i	0.124912	−	0.0517404i	0.444264	+	0.895896i	$0.353465\pi$
$278$	1.71782	+	0.103499i	0.103028	+	0.00620748i
$279$	9.69546	+	9.69546i	0.580452	+	0.580452i
$280$	−1.74432	+	9.55684i	−0.104243	+	0.571130i
$281$	−8.87322	+	8.87322i	−0.529332	+	0.529332i	−0.920373	−	0.391041i	$-0.872115\pi$
$281$	−8.87322	+	8.87322i	−0.529332	+	0.529332i	0.391041	+	0.920373i	$0.372115\pi$
$282$	10.1055	−	8.95699i	0.601775	−	0.533381i
$283$	1.03578	+	2.50060i	0.0615709	+	0.148645i	0.951671	−	0.307121i	$-0.0993655\pi$
$283$	1.03578	+	2.50060i	0.0615709	+	0.148645i	−0.890100	+	0.455766i	$0.849365\pi$
$284$	−14.7986	−	1.78974i	−0.878133	−	0.106201i
$285$	53.5108	+	22.1649i	3.16971	+	1.31293i
$286$	−6.11950	+	12.5758i	−0.361853	+	0.743624i
$287$	−9.01281			−0.532009
$288$	−10.7382	+	0.988660i	−0.632755	+	0.0582574i
$289$	1.06547			0.0626746
$290$	−4.84591	+	9.95855i	−0.284562	+	0.584786i
$291$	−6.49406	−	2.68993i	−0.380689	−	0.157686i
$292$	−2.73666	+	22.6283i	−0.160151	+	1.32422i
$293$	1.01798	+	2.45762i	0.0594709	+	0.143575i	0.950822	−	0.309739i	$-0.100242\pi$
$293$	1.01798	+	2.45762i	0.0594709	+	0.143575i	−0.891351	+	0.453314i	$0.850242\pi$
$294$	2.34422	−	2.07779i	0.136718	−	0.121179i
$295$	5.46050	−	5.46050i	0.317923	−	0.317923i
$296$	−2.34359	+	1.62013i	−0.136218	+	0.0941680i
$297$	6.04536	+	6.04536i	0.350787	+	0.350787i
$298$	25.5905	+	1.54184i	1.48242	+	0.0893162i
$299$	−5.41203	+	2.24174i	−0.312986	+	0.129643i
$300$	−26.2340	−	14.7796i	−1.51462	−	0.853302i
$301$	−3.71025	+	8.95733i	−0.213855	+	0.516292i
$302$	−6.48319	−	18.7731i	−0.373065	−	1.08027i
$303$			5.63892i			0.323948i
$304$	−24.5452	−	18.0248i	−1.40776	−	1.03379i
$305$			44.2314i			2.53268i
$306$	10.1721	−	3.51286i	0.581498	−	0.200817i
$307$	−2.14695	+	5.18320i	−0.122533	+	0.295821i	−0.973229	−	0.229837i	$-0.926181\pi$
$307$	−2.14695	+	5.18320i	−0.122533	+	0.295821i	0.850696	+	0.525658i	$0.176181\pi$
$308$	6.79799	−	1.89856i	0.387351	−	0.108181i
$309$	−7.98075	+	3.30574i	−0.454009	+	0.188057i
$310$	2.10120	−	34.8744i	0.119340	−	1.98073i
$311$	0.0597239	+	0.0597239i	0.00338663	+	0.00338663i	0.708798	−	0.705411i	$-0.249238\pi$
$311$	0.0597239	+	0.0597239i	0.00338663	+	0.00338663i	−0.705411	+	0.708798i	$0.749238\pi$
$312$	14.7499	+	9.52162i	0.835049	+	0.539056i
$313$	−1.04454	+	1.04454i	−0.0590406	+	0.0590406i	−0.736011	−	0.676970i	$-0.763293\pi$
$313$	−1.04454	+	1.04454i	−0.0590406	+	0.0590406i	0.676970	+	0.736011i	$0.263293\pi$
$314$	−12.9111	−	14.5667i	−0.728618	−	0.822046i
$315$	2.50562	+	6.04910i	0.141176	+	0.340828i
$316$	−14.2353	+	11.1636i	−0.800800	+	0.628001i
$317$	−2.47028	−	1.02322i	−0.138745	−	0.0574699i	0.312231	−	0.950006i	$-0.398924\pi$
$317$	−2.47028	−	1.02322i	−0.138745	−	0.0574699i	−0.450975	+	0.892536i	$0.648924\pi$
$318$	2.66901	+	1.29876i	0.149671	+	0.0728311i
$319$	8.04642			0.450513
$320$	20.0342	+	18.8052i	1.11995	+	1.05124i
$321$	−38.8254			−2.16702
$322$	2.65830	+	1.29355i	0.148141	+	0.0720866i
$323$	28.0769	+	11.6298i	1.56224	+	0.647101i
$324$	17.4452	−	13.6809i	0.969180	−	0.760047i
$325$	7.28895	+	17.5971i	0.404318	+	0.976110i
$326$	1.05471	+	1.18995i	0.0584151	+	0.0659055i
$327$	−16.1008	+	16.1008i	−0.890375	+	0.890375i
$328$	−13.8256	+	21.4172i	−0.763393	+	1.18257i
$329$	3.04821	+	3.04821i	0.168053	+	0.168053i
$330$	−2.28355	+	37.9010i	−0.125705	+	2.08638i
$331$	26.9997	−	11.1836i	1.48404	−	0.614708i	0.514027	−	0.857774i	$-0.328153\pi$
$331$	26.9997	−	11.1836i	1.48404	−	0.614708i	0.970010	+	0.243065i	$0.0781530\pi$
$332$	20.9668	−	5.85567i	1.15070	−	0.321372i
$333$	−0.734832	+	1.77404i	−0.0402685	+	0.0972169i
$334$	3.20103	−	1.10546i	0.175152	−	0.0604879i
$335$			7.25492i			0.396378i
$336$	−1.34145	−	8.75792i	−0.0731819	−	0.477784i
$337$		−	34.3919i		−	1.87345i	−0.350071	−	0.936723i	$-0.613843\pi$
$337$		−	34.3919i		−	1.87345i	0.350071	−	0.936723i	$-0.386157\pi$
$338$	2.37619	+	6.88065i	0.129248	+	0.374258i
$339$	−10.2003	+	24.6257i	−0.554004	+	1.33748i
$340$	−23.8906	−	13.4594i	−1.29565	−	0.729939i
$341$	−23.4514	+	9.71388i	−1.26996	+	0.526036i
$342$	−20.4872	−	1.23436i	−1.10782	−	0.0667466i
$343$	0.707107	+	0.707107i	0.0381802	+	0.0381802i
$344$	15.5939	+	22.5572i	0.840766	+	1.21620i
$345$	−11.2456	+	11.2456i	−0.605443	+	0.605443i
$346$	−3.31599	+	2.93912i	−0.178269	+	0.158008i
$347$	−3.52396	−	8.50759i	−0.189176	−	0.456712i	0.800625	−	0.599165i	$-0.204501\pi$
$347$	−3.52396	−	8.50759i	−0.189176	−	0.456712i	−0.989801	+	0.142454i	$0.954501\pi$
$348$	1.21274	−	10.0276i	0.0650095	−	0.537536i
$349$	23.2371	+	9.62512i	1.24385	+	0.515221i	0.904917	−	0.425589i	$-0.139933\pi$
$349$	23.2371	+	9.62512i	1.24385	+	0.515221i	0.338936	+	0.940809i	$0.389933\pi$
$350$	4.20594	−	8.64338i	0.224817	−	0.462008i
$351$	−6.78870			−0.362354
$352$	5.91654	−	19.0665i	0.315352	−	1.01625i
$353$	8.11517			0.431927			0.215964	−	0.976401i	$-0.430711\pi$
$353$	8.11517			0.431927			0.215964	+	0.976401i	$0.430711\pi$
$354$	−3.08167	+	6.33296i	−0.163789	+	0.336593i
$355$	23.6507	+	9.79643i	1.25525	+	0.519940i
$356$	35.0526	+	4.23927i	1.85779	+	0.224681i
$357$	3.38366	+	8.16887i	0.179082	+	0.432342i
$358$	20.2621	−	17.9593i	1.07089	−	0.949178i
$359$	−10.0921	+	10.0921i	−0.532640	+	0.532640i	−0.921357	−	0.388717i	$-0.872918\pi$
$359$	−10.0921	+	10.0921i	−0.532640	+	0.532640i	0.388717	+	0.921357i	$0.372918\pi$
$360$	18.2182	+	3.32518i	0.960181	+	0.175253i
$361$	−27.5488	−	27.5488i	−1.44994	−	1.44994i
$362$	−26.1404	−	1.57497i	−1.37391	−	0.0827785i
$363$	2.97610	−	1.23274i	0.156205	−	0.0647022i
$364$	−2.75093	+	4.88294i	−0.144188	+	0.255936i
$365$	14.9796	−	36.1639i	0.784068	−	1.89291i
$366$	−13.1681	−	38.1304i	−0.688309	−	1.99311i
$367$		−	12.5748i		−	0.656401i	−0.944608	−	0.328200i	$-0.893558\pi$
$367$		−	12.5748i		−	0.656401i	0.944608	−	0.328200i	$-0.106442\pi$
$368$	7.15169	−	4.33263i	0.372808	−	0.225854i
$369$			17.1811i			0.894411i
$370$	4.62480	−	1.59715i	0.240432	−	0.0830318i
$371$	−0.362615	+	0.875431i	−0.0188261	+	0.0454501i
$372$	8.57107	+	30.6896i	0.444389	+	1.59118i
$373$	24.7506	−	10.2520i	1.28154	−	0.530830i	0.365085	−	0.930974i	$-0.381040\pi$
$373$	24.7506	−	10.2520i	1.28154	−	0.530830i	0.916452	+	0.400144i	$0.131040\pi$
$374$	−1.19817	+	19.8865i	−0.0619558	+	1.02830i
$375$	9.66698	+	9.66698i	0.499201	+	0.499201i
$376$	11.9194	−	2.56754i	0.614699	−	0.132411i
$377$	−4.51791	+	4.51791i	−0.232684	+	0.232684i
$378$	2.27249	+	2.56389i	0.116884	+	0.131872i
$379$	6.91773	+	16.7009i	0.355340	+	0.857866i	0.995942	+	0.0899936i	$0.0286847\pi$
$379$	6.91773	+	16.7009i	0.355340	+	0.857866i	−0.640602	+	0.767873i	$0.721315\pi$
$380$	32.2723	+	41.1522i	1.65553	+	2.11107i
$381$	29.9492	+	12.4054i	1.53434	+	0.635546i
$382$	−3.17272	−	1.54387i	−0.162331	−	0.0789914i
$383$	12.5811			0.642864			0.321432	−	0.946933i	$-0.395836\pi$
$383$	12.5811			0.642864			0.321432	+	0.946933i	$0.395836\pi$
$384$	−22.8693	−	10.2470i	−1.16704	−	0.522913i
$385$	−12.1212			−0.617753
$386$	21.7485	+	10.5830i	1.10697	+	0.538660i
$387$	17.0753	+	7.07283i	0.867987	+	0.359532i
$388$	−3.91656	−	4.99423i	−0.198833	−	0.253544i
$389$	2.35916	+	5.69552i	0.119614	+	0.288774i	0.972334	−	0.233594i	$-0.0750487\pi$
$389$	2.35916	+	5.69552i	0.119614	+	0.288774i	−0.852720	+	0.522368i	$0.825049\pi$
$390$	−19.9985	−	22.5628i	−1.01266	−	1.14251i
$391$	−5.90052	+	5.90052i	−0.298402	+	0.298402i
$392$	2.76501	−	0.595604i	0.139654	−	0.0300825i
$393$	−9.17448	−	9.17448i	−0.462791	−	0.462791i
$394$	−0.213340	+	3.54089i	−0.0107479	+	0.178388i
$395$	28.7028	−	11.8891i	1.44419	−	0.598205i
$396$	−3.61922	−	12.9590i	−0.181873	−	0.651213i
$397$	−8.45626	+	20.4152i	−0.424408	+	1.02461i	0.556624	+	0.830764i	$0.312096\pi$
$397$	−8.45626	+	20.4152i	−0.424408	+	1.02461i	−0.981032	+	0.193846i	$0.937904\pi$
$398$	−9.86195	+	3.40577i	−0.494335	+	0.170716i
$399$		−	16.8632i		−	0.844217i
$400$	−14.0874	−	23.2535i	−0.704372	−	1.16268i
$401$		−	6.12306i		−	0.305771i	−0.988244	−	0.152885i	$-0.951143\pi$
$401$		−	6.12306i		−	0.305771i	0.988244	−	0.152885i	$-0.0488565\pi$
$402$	−2.15986	−	6.25421i	−0.107724	−	0.311932i
$403$	7.71333	−	18.6216i	0.384228	−	0.927610i
$404$	−2.49914	+	4.43600i	−0.124337	+	0.220699i
$405$	−35.1750	+	14.5699i	−1.74786	+	0.723986i
$406$	3.21863	+	0.193924i	0.159738	+	0.00962429i
$407$	−2.51364	−	2.51364i	−0.124597	−	0.124597i
$408$	24.6023	+	4.49042i	1.21799	+	0.222309i
$409$	8.76516	−	8.76516i	0.433409	−	0.433409i	−0.456377	−	0.889786i	$-0.650853\pi$
$409$	8.76516	−	8.76516i	0.433409	−	0.433409i	0.889786	+	0.456377i	$0.150853\pi$
$410$	32.7618	−	29.0383i	1.61799	−	1.43410i
$411$	0.815447	+	1.96866i	0.0402231	+	0.0971070i
$412$	−7.74334	−	0.936480i	−0.381487	−	0.0461370i
$413$	−2.07720	−	0.860403i	−0.102212	−	0.0423377i
$414$	2.46588	−	5.06749i	0.121192	−	0.249054i
$415$	−37.3850			−1.83516
$416$	7.38346	+	14.0275i	0.362004	+	0.687754i
$417$	2.69542			0.131995
$418$	16.6253	−	34.1657i	0.813171	−	1.67110i
$419$	−13.9853	−	5.79289i	−0.683226	−	0.283001i	0.0139488	−	0.999903i	$-0.495560\pi$
$419$	−13.9853	−	5.79289i	−0.683226	−	0.283001i	−0.697175	+	0.716901i	$0.745560\pi$
$420$	−1.82688	+	15.1056i	−0.0891424	+	0.737080i
$421$	11.5803	+	27.9573i	0.564388	+	1.36255i	0.906226	+	0.422794i	$0.138951\pi$
$421$	11.5803	+	27.9573i	0.564388	+	1.36255i	−0.341838	+	0.939759i	$0.611049\pi$
$422$	−13.0448	+	11.5622i	−0.635012	+	0.562841i
$423$	5.81079	−	5.81079i	0.282530	−	0.282530i
$424$	1.52404	+	2.20460i	0.0740141	+	0.107065i
$425$	19.1854	+	19.1854i	0.930628	+	0.930628i
$426$	−23.3049	−	1.40413i	−1.12913	−	0.0680304i
$427$	11.8976	−	4.92816i	0.575767	−	0.238491i
$428$	−30.5430	−	17.2072i	−1.47635	−	0.831741i
$429$	−8.38273	+	20.2377i	−0.404722	+	0.977085i
$430$	−15.3727	−	44.5141i	−0.741338	−	2.14666i
$431$			21.2472i			1.02344i	0.859151	+	0.511721i	$0.170992\pi$
$431$			21.2472i			1.02344i	−0.859151	+	0.511721i	$0.829008\pi$
$432$	9.57859	−	1.46715i	0.460850	−	0.0705881i
$433$		−	13.9889i		−	0.672265i	−0.941815	−	0.336132i	$-0.890881\pi$
$433$		−	13.9889i		−	0.672265i	0.941815	−	0.336132i	$-0.109119\pi$
$434$	−9.61484	+	3.32043i	−0.461527	+	0.159386i
$435$	−6.63812	+	16.0258i	−0.318273	+	0.768380i
$436$	−19.8019	+	5.53032i	−0.948337	+	0.264854i
$437$	14.7033	−	6.09031i	0.703354	−	0.291339i
$438$	−2.14704	+	35.6353i	−0.102590	+	1.70272i
$439$	−4.52510	−	4.52510i	−0.215971	−	0.215971i	0.590827	−	0.806798i	$-0.298802\pi$
$439$	−4.52510	−	4.52510i	−0.215971	−	0.215971i	−0.806798	+	0.590827i	$0.798802\pi$
$440$	−18.5939	+	28.8037i	−0.886429	+	1.37316i
$441$	1.34795	−	1.34795i	0.0641883	−	0.0641883i
$442$	−10.4931	−	11.8386i	−0.499106	−	0.563105i
$443$	−1.28025	−	3.09080i	−0.0608265	−	0.146848i	0.890544	−	0.454897i	$-0.150324\pi$
$443$	−1.28025	−	3.09080i	−0.0608265	−	0.146848i	−0.951371	+	0.308049i	$0.900324\pi$
$444$	−3.51139	+	2.75369i	−0.166643	+	0.130685i
$445$	−56.0202	−	23.2043i	−2.65561	−	1.09999i
$446$	−14.5864	−	7.09788i	−0.690688	−	0.336095i
$447$	40.1538			1.89921
$448$	2.82618	−	7.48417i	0.133524	−	0.353594i
$449$	0.619029			0.0292138			0.0146069	−	0.999893i	$-0.495350\pi$
$449$	0.619029			0.0292138			0.0146069	+	0.999893i	$0.495350\pi$
$450$	−16.4768	−	8.01776i	−0.776725	−	0.377961i
$451$	−29.3856	−	12.1719i	−1.38372	−	0.573154i
$452$	−18.9383	+	14.8517i	−0.890781	+	0.698566i
$453$	−11.9043	−	28.7395i	−0.559312	−	1.35030i
$454$	−7.86571	−	8.87430i	−0.369156	−	0.416491i
$455$	6.80581	−	6.80581i	0.319061	−	0.319061i
$456$	−40.0722	−	25.8682i	−1.87655	−	1.21139i
$457$	8.97599	+	8.97599i	0.419879	+	0.419879i	0.885162	−	0.465283i	$-0.154047\pi$
$457$	8.97599	+	8.97599i	0.419879	+	0.419879i	−0.465283	+	0.885162i	$0.654047\pi$
$458$	2.20705	−	36.6312i	0.103128	−	1.71166i
$459$	−8.93433	+	3.70072i	−0.417019	+	0.172735i
$460$	−13.8306	+	3.86266i	−0.644857	+	0.180097i
$461$	−12.6076	+	30.4375i	−0.587196	+	1.41762i	0.298977	+	0.954260i	$0.403355\pi$
$461$	−12.6076	+	30.4375i	−0.587196	+	1.41762i	−0.886173	+	0.463355i	$0.846645\pi$
$462$	10.4493	−	3.60859i	0.486144	−	0.167887i
$463$			4.33434i			0.201434i	0.994915	+	0.100717i	$0.0321136\pi$
$463$			4.33434i			0.201434i	−0.994915	+	0.100717i	$0.967886\pi$
$464$	5.39820	−	7.35099i	0.250605	−	0.341261i
$465$		−	54.7212i		−	2.53763i
$466$	−5.76723	−	16.6999i	−0.267162	−	0.773609i
$467$	0.967591	−	2.33597i	0.0447748	−	0.108096i	−0.899910	−	0.436076i	$-0.856368\pi$
$467$	0.967591	−	2.33597i	0.0447748	−	0.108096i	0.944685	+	0.327980i	$0.106368\pi$
$468$	9.30833	+	5.24409i	0.430278	+	0.242408i
$469$	1.95147	−	0.808326i	0.0901106	−	0.0373250i
$470$	−20.9013	−	1.25931i	−0.964106	−	0.0580878i
$471$	−21.5576	−	21.5576i	−0.993323	−	0.993323i
$472$	−5.23100	+	3.61621i	−0.240776	+	0.166449i
$473$	−24.1940	+	24.1940i	−1.11244	+	1.11244i
$474$	−21.2042	+	18.7943i	−0.973941	+	0.863250i
$475$	−19.8025	−	47.8074i	−0.908600	−	2.19355i
$476$	−0.958554	+	7.92586i	−0.0439352	+	0.363281i
$477$	1.66883	+	0.691252i	0.0764105	+	0.0316503i
$478$	−11.7364	+	24.1188i	−0.536810	+	1.10317i
$479$	−1.81624			−0.0829862			−0.0414931	−	0.999139i	$-0.513211\pi$
$479$	−1.81624			−0.0829862			−0.0414931	+	0.999139i	$0.513211\pi$
$480$	33.0933	+	27.5133i	1.51049	+	1.25580i
$481$	2.82272			0.128705
$482$	7.21652	−	14.8303i	0.328704	−	0.675500i
$483$	4.27787	+	1.77195i	0.194650	+	0.0806267i
$484$	2.88757	+	0.349223i	0.131253	+	0.0158738i
$485$	4.17109	+	10.0699i	0.189399	+	0.457250i
$486$	18.2938	−	16.2147i	0.829826	−	0.735513i
$487$	−22.0815	+	22.0815i	−1.00061	+	1.00061i	−0.000609086		1.00000i	$0.500194\pi$
$487$	−22.0815	+	22.0815i	−1.00061	+	1.00061i	−1.00000		0.000609086i	$0.999806\pi$
$488$	6.54012	−	35.8323i	0.296057	−	1.62205i
$489$	1.76105	+	1.76105i	0.0796372	+	0.0796372i
$490$	−4.84857	−	0.292129i	−0.219036	−	0.0131970i
$491$	−28.1018	+	11.6402i	−1.26822	+	0.525313i	−0.912422	−	0.409251i	$-0.865790\pi$
$491$	−28.1018	+	11.6402i	−1.26822	+	0.525313i	−0.355796	+	0.934564i	$0.615790\pi$
$492$	−19.5978	+	34.7864i	−0.883538	+	1.56829i
$493$	−3.48299	+	8.40869i	−0.156866	+	0.378708i
$494$	9.84860	+	28.5182i	0.443109	+	1.28309i
$495$			23.1066i			1.03856i
$496$	−6.85878	+	27.9414i	−0.307968	+	1.25461i
$497$		−	7.45320i		−	0.334322i
$498$	32.2283	−	11.1299i	1.44418	−	0.498741i
$499$	−6.86233	+	16.5671i	−0.307200	+	0.741647i	0.692593	+	0.721328i	$0.256468\pi$
$499$	−6.86233	+	16.5671i	−0.307200	+	0.741647i	−0.999794	+	0.0203187i	$0.993532\pi$
$500$	3.32043	+	11.8891i	0.148494	+	0.531698i
$501$	4.90041	−	2.02982i	0.218934	−	0.0906856i
$502$	0.287884	−	4.77812i	0.0128489	−	0.213258i
$503$	25.4254	+	25.4254i	1.13366	+	1.13366i	0.989563	+	0.144100i	$0.0460285\pi$
$503$	25.4254	+	25.4254i	1.13366	+	1.13366i	0.144100	+	0.989563i	$0.453971\pi$
$504$	−1.13540	−	5.27092i	−0.0505746	−	0.234785i
$505$	6.18286	−	6.18286i	0.275134	−	0.275134i
$506$	6.92024	+	7.80759i	0.307642	+	0.347090i
$507$	4.36312	+	10.5335i	0.193773	+	0.467809i
$508$	18.0623	+	23.0323i	0.801385	+	1.02189i
$509$	−31.3793	−	12.9977i	−1.39086	−	0.576115i	−0.443501	−	0.896274i	$-0.646264\pi$
$509$	−31.3793	−	12.9977i	−1.39086	−	0.576115i	−0.947364	+	0.320159i	$0.896264\pi$
$510$	−38.6189	−	18.7922i	−1.71007	−	0.832135i
$511$	−11.3966			−0.504155
$512$	−13.4493	−	18.1966i	−0.594383	−	0.804182i
$513$	18.4434			0.814296
$514$	−16.2968	−	7.93014i	−0.718820	−	0.349783i
$515$	12.3752	+	5.12598i	0.545317	+	0.225878i
$516$	26.5046	+	33.7975i	1.16680	+	1.48785i
$517$	5.82183	+	14.0551i	0.256044	+	0.618144i
$518$	−0.944895	−	1.06606i	−0.0415163	−	0.0468398i
$519$	−4.90743	+	4.90743i	−0.215412	+	0.215412i
$520$	−5.73261	−	26.6128i	−0.251391	−	1.16705i
$521$	−10.0555	−	10.0555i	−0.440542	−	0.440542i	0.451652	−	0.892194i	$-0.350835\pi$
$521$	−10.0555	−	10.0555i	−0.440542	−	0.440542i	−0.892194	+	0.451652i	$0.850835\pi$
$522$	0.369676	−	6.13566i	0.0161803	−	0.268551i
$523$	37.5312	−	15.5459i	1.64113	−	0.679776i	0.644714	−	0.764424i	$-0.276976\pi$
$523$	37.5312	−	15.5459i	1.64113	−	0.679776i	0.996411	+	0.0846473i	$0.0269763\pi$
$524$	−3.15126	−	11.2834i	−0.137664	−	0.492918i
$525$	5.76146	−	13.9094i	0.251451	−	0.607056i
$526$	24.9995	−	8.63343i	1.09003	−	0.376436i
$527$		−	28.7120i		−	1.25071i
$528$	7.45401	−	30.3663i	0.324394	−	1.32152i
$529$		−	18.6301i		−	0.810004i
$530$	−1.50243	−	4.35052i	−0.0652613	−	0.188974i
$531$	−1.64018	+	3.95975i	−0.0711778	+	0.171838i
$532$	7.47368	−	13.2659i	0.324025	−	0.575149i
$533$	23.3338	−	9.66516i	1.01070	−	0.418644i
$534$	55.2012	+	3.32590i	2.38879	+	0.143926i
$535$	42.5706	+	42.5706i	1.84049	+	1.84049i
$536$	1.07272	−	5.87727i	0.0463345	−	0.253860i
$537$	29.9865	−	29.9865i	1.29401	−	1.29401i
$538$	31.9087	−	28.2821i	1.37568	−	1.21933i
$539$	1.35052	+	3.26043i	0.0581708	+	0.140437i
$540$	−16.5211	−	1.99806i	−0.710956	−	0.0859830i
$541$	−40.9479	−	16.9612i	−1.76049	−	0.729217i	−0.996463	−	0.0840290i	$-0.973221\pi$
$541$	−40.9479	−	16.9612i	−1.76049	−	0.729217i	−0.764023	−	0.645189i	$-0.776779\pi$
$542$	4.65771	−	9.57179i	0.200066	−	0.411143i
$543$	−41.0167			−1.76019
$544$	17.3639	+	14.4361i	0.744470	+	0.618942i
$545$	35.3078			1.51242
$546$	−3.84090	+	7.89321i	−0.164375	+	0.337798i
$547$	15.1849	+	6.28978i	0.649259	+	0.268932i	0.682911	−	0.730502i	$-0.260714\pi$
$547$	15.1849	+	6.28978i	0.649259	+	0.268932i	−0.0336520	+	0.999434i	$0.510714\pi$
$548$	−0.231008	+	1.91010i	−0.00986815	+	0.0815955i
$549$	−9.39453	−	22.6804i	−0.400949	−	0.967976i
$550$	25.3862	−	22.5010i	1.08247	−	0.959444i
$551$	12.2742	−	12.2742i	0.522897	−	0.522897i
$552$	10.7730	−	7.44738i	0.458528	−	0.316982i
$553$	−6.39600	−	6.39600i	−0.271986	−	0.271986i
$554$	3.17657	+	0.191390i	0.134960	+	0.00813137i
$555$	7.08004	−	2.93265i	0.300531	−	0.124484i
$556$	2.12042	+	1.19459i	0.0899258	+	0.0506620i
$557$	−12.4332	+	30.0164i	−0.526812	+	1.27184i	0.406790	+	0.913522i	$0.366648\pi$
$557$	−12.4332	+	30.0164i	−0.526812	+	1.27184i	−0.933601	+	0.358314i	$0.883352\pi$
$558$	6.32972	+	18.3287i	0.267959	+	0.775917i
$559$		−	27.1689i		−	1.14912i
$560$	−8.13189	+	11.0736i	−0.343635	+	0.467944i
$561$			31.2037i			1.31742i
$562$	−16.7743	+	5.79292i	−0.707582	+	0.244360i
$563$	−9.89235	+	23.8823i	−0.416913	+	1.00652i	0.566324	+	0.824183i	$0.308365\pi$
$563$	−9.89235	+	23.8823i	−0.416913	+	1.00652i	−0.983237	+	0.182334i	$0.941635\pi$
$564$	18.3932	−	5.13691i	0.774494	−	0.216303i
$565$	38.1854	−	15.8169i	1.60647	−	0.665422i
$566$	−0.230206	+	3.82082i	−0.00967630	+	0.160601i
$567$	7.83823	+	7.83823i	0.329175	+	0.329175i
$568$	−17.7111	−	11.4332i	−0.743142	−	0.479726i
$569$	−12.2649	+	12.2649i	−0.514173	+	0.514173i	−0.915802	−	0.401629i	$-0.868444\pi$
$569$	−12.2649	+	12.2649i	−0.514173	+	0.514173i	0.401629	+	0.915802i	$0.368444\pi$
$570$	54.3314	+	61.2982i	2.27569	+	2.56750i
$571$	2.37758	+	5.74000i	0.0994988	+	0.240211i	0.965789	−	0.259330i	$-0.0835018\pi$
$571$	2.37758	+	5.74000i	0.0994988	+	0.240211i	−0.866290	+	0.499542i	$0.833502\pi$
$572$	−15.5637	+	12.2053i	−0.650751	+	0.510330i
$573$	−5.10572	−	2.11486i	−0.213294	−	0.0883494i
$574$	−11.4611	−	5.57708i	−0.478379	−	0.232783i
$575$	14.2086			0.592540
$576$	−14.2670	−	5.38752i	−0.594459	−	0.224480i
$577$	−18.2599			−0.760171			−0.380086	−	0.924951i	$-0.624105\pi$
$577$	−18.2599			−0.760171			−0.380086	+	0.924951i	$0.624105\pi$
$578$	1.35490	+	0.659306i	0.0563565	+	0.0274235i
$579$	34.9988	+	14.4970i	1.45450	+	0.602474i
$580$	−12.3246	+	9.66516i	−0.511751	+	0.401324i
$581$	4.16535	+	10.0560i	0.172808	+	0.417195i
$582$	−6.59365	−	7.43914i	−0.273316	−	0.308362i
$583$	−2.36457	+	2.36457i	−0.0979303	+	0.0979303i
$584$	−17.4824	+	27.0818i	−0.723425	+	1.12065i
$585$	−12.9739	−	12.9739i	−0.536404	−	0.536404i
$586$	−0.226249	+	3.75515i	−0.00934627	+	0.155124i
$587$	−28.7686	+	11.9164i	−1.18741	+	0.491841i	−0.886910	−	0.461942i	$-0.847153\pi$
$587$	−28.7686	+	11.9164i	−1.18741	+	0.491841i	−0.300498	+	0.953782i	$0.597153\pi$
$588$	4.26675	−	1.19163i	0.175958	−	0.0491421i
$589$	−20.9554	+	50.5909i	−0.863453	+	2.08456i
$590$	10.3228	−	3.56492i	0.424982	−	0.146765i
$591$			5.55599i			0.228543i
$592$	−3.98275	+	0.610035i	−0.163690	+	0.0250723i
$593$			20.3865i			0.837175i	0.908176	+	0.418587i	$0.137475\pi$
$593$			20.3865i			0.837175i	−0.908176	+	0.418587i	$0.862525\pi$
$594$	3.94674	+	11.4284i	0.161937	+	0.468913i
$595$	5.24680	−	12.6669i	0.215098	−	0.519292i
$596$	31.5880	+	17.7959i	1.29390	+	0.728950i
$597$	−15.0975	+	6.25360i	−0.617901	+	0.255943i
$598$	−8.26938	−	0.498234i	−0.338160	−	0.0203743i
$599$	−8.05573	−	8.05573i	−0.329148	−	0.329148i	0.523114	−	0.852263i	$-0.324770\pi$
$599$	−8.05573	−	8.05573i	−0.329148	−	0.329148i	−0.852263	+	0.523114i	$0.824770\pi$
$600$	−24.2150	−	35.0280i	−0.988572	−	1.43001i
$601$	27.7400	−	27.7400i	1.13154	−	1.13154i	0.141617	−	0.989922i	$-0.454770\pi$
$601$	27.7400	−	27.7400i	1.13154	−	1.13154i	0.989922	−	0.141617i	$-0.0452300\pi$
$602$	−10.2609	+	9.09470i	−0.418203	+	0.370672i
$603$	−1.54091	−	3.72008i	−0.0627506	−	0.151493i
$604$	3.37236	−	27.8846i	0.137219	−	1.13461i
$605$	−4.61484	−	1.91153i	−0.187620	−	0.0777147i
$606$	−3.48934	+	7.17073i	−0.141745	+	0.291291i
$607$	27.7378			1.12584			0.562921	−	0.826511i	$-0.309677\pi$
$607$	27.7378			1.12584			0.562921	+	0.826511i	$0.309677\pi$
$608$	−20.0592	−	38.1096i	−0.813509	−	1.54555i
$609$	5.05033			0.204650
$610$	−27.3702	+	56.2469i	−1.10819	+	2.27737i
$611$	−11.1605	−	4.62284i	−0.451507	−	0.187020i
$612$	15.1090	+	1.82729i	0.610746	+	0.0738636i
$613$	1.16183	+	2.80491i	0.0469259	+	0.113289i	0.945604	−	0.325319i	$-0.105472\pi$
$613$	1.16183	+	2.80491i	0.0469259	+	0.113289i	−0.898678	+	0.438608i	$0.855472\pi$
$614$	−5.93750	+	5.26269i	−0.239618	+	0.212385i
$615$	48.4850	−	48.4850i	1.95510	−	1.95510i
$616$	9.81948	+	1.79226i	0.395638	+	0.0722121i
$617$	21.3712	+	21.3712i	0.860373	+	0.860373i	0.991381	−	0.131009i	$-0.0418216\pi$
$617$	21.3712	+	21.3712i	0.860373	+	0.860373i	−0.131009	+	0.991381i	$0.541822\pi$
$618$	−12.1943	−	0.734712i	−0.490526	−	0.0295544i
$619$	−27.8362	+	11.5301i	−1.11883	+	0.463435i	−0.863971	−	0.503542i	$-0.832030\pi$
$619$	−27.8362	+	11.5301i	−1.11883	+	0.463435i	−0.254861	+	0.966978i	$0.582030\pi$
$620$	24.2521	−	43.0478i	0.973988	−	1.72884i
$621$	−1.93799	+	4.67873i	−0.0777691	+	0.187751i
$622$	0.0389910	+	0.112905i	0.00156340	+	0.00452706i
$623$			17.6540i			0.707294i
$624$	12.8648	+	21.2353i	0.515003	+	0.850094i
$625$			12.7859i			0.511438i
$626$	−1.97464	+	0.681930i	−0.0789223	+	0.0272554i
$627$	22.7740	−	54.9814i	0.909507	−	2.19574i
$628$	−7.40465	−	26.5131i	−0.295478	−	1.05799i
$629$	3.71487	−	1.53875i	0.148121	−	0.0613539i
$630$	−0.556883	+	9.24280i	−0.0221868	+	0.368242i
$631$	−4.04695	−	4.04695i	−0.161106	−	0.161106i	0.621950	−	0.783057i	$-0.286341\pi$
$631$	−4.04695	−	4.04695i	−0.161106	−	0.161106i	−0.783057	+	0.621950i	$0.786341\pi$
$632$	−25.0103	+	5.38742i	−0.994858	+	0.214300i
$633$	−19.3054	+	19.3054i	−0.767320	+	0.767320i
$634$	−2.50816	−	2.82978i	−0.0996119	−	0.112385i
$635$	−19.2361	−	46.4401i	−0.763363	−	1.84292i
$636$	2.59038	+	3.30315i	0.102715	+	0.130978i
$637$	−2.58896	−	1.07238i	−0.102578	−	0.0424893i
$638$	10.2322	+	4.97909i	0.405098	+	0.197124i
$639$	−14.2080			−0.562059
$640$	13.8399	+	36.3107i	0.547072	+	1.43531i
$641$	18.9525			0.748581			0.374290	−	0.927312i	$-0.377886\pi$
$641$	18.9525			0.748581			0.374290	+	0.927312i	$0.377886\pi$
$642$	−49.3723	−	24.0250i	−1.94857	−	0.948190i
$643$	28.2538	+	11.7031i	1.11422	+	0.461526i	0.862390	−	0.506245i	$-0.168967\pi$
$643$	28.2538	+	11.7031i	1.11422	+	0.461526i	0.251833	+	0.967771i	$0.418967\pi$
$644$	2.57998	+	3.28988i	0.101665	+	0.129639i
$645$	−28.2270	−	68.1461i	−1.11144	−	2.68325i
$646$	28.5075	+	32.1629i	1.12161	+	1.26543i
$647$	−5.94836	+	5.94836i	−0.233854	+	0.233854i	−0.814299	−	0.580445i	$-0.802879\pi$
$647$	−5.94836	+	5.94836i	−0.233854	+	0.233854i	0.580445	+	0.814299i	$0.302879\pi$
$648$	30.6499	−	6.60222i	1.20404	−	0.259360i
$649$	−5.61057	−	5.61057i	−0.220234	−	0.220234i
$650$	−1.62000	+	26.8877i	−0.0635415	+	1.05462i
$651$	−14.7192	+	6.09691i	−0.576892	+	0.238957i
$652$	0.604887	+	2.16586i	0.0236892	+	0.0848215i
$653$	2.47787	−	5.98211i	0.0969665	−	0.234098i	−0.867952	−	0.496649i	$-0.834564\pi$
$653$	2.47787	−	5.98211i	0.0969665	−	0.234098i	0.964918	+	0.262551i	$0.0845637\pi$
$654$	−30.4376	+	10.5115i	−1.19021	+	0.411031i
$655$			20.1189i			0.786112i
$656$	−30.8342	+	18.6800i	−1.20387	+	0.729330i
$657$			21.7253i			0.847583i
$658$	1.99004	+	5.76248i	0.0775798	+	0.224645i
$659$	−7.76365	+	18.7431i	−0.302429	+	0.730128i	0.697480	+	0.716605i	$0.254305\pi$
$659$	−7.76365	+	18.7431i	−0.302429	+	0.730128i	−0.999909	+	0.0135233i	$0.995695\pi$
$660$	−26.3568	+	46.7837i	−1.02594	+	1.82105i
$661$	−4.04730	+	1.67645i	−0.157422	+	0.0652062i	−0.460003	−	0.887917i	$-0.652152\pi$
$661$	−4.04730	+	1.67645i	−0.157422	+	0.0652062i	0.302581	+	0.953124i	$0.402152\pi$
$662$	41.2545	+	2.48560i	1.60340	+	0.0966058i
$663$	−17.5203	−	17.5203i	−0.680431	−	0.680431i
$664$	30.2859	+	5.52779i	1.17532	+	0.214520i
$665$	−18.4899	+	18.4899i	−0.717007	+	0.717007i
$666$	−2.03222	+	1.80125i	−0.0787468	+	0.0697970i
$667$	1.82397	+	4.40346i	0.0706245	+	0.170503i
$668$	4.75464	+	0.575026i	0.183962	+	0.0222484i
$669$	−23.4733	−	9.72296i	−0.907530	−	0.375911i
$670$	−4.48931	+	9.22571i	−0.173437	+	0.356420i
$671$	45.4470			1.75446
$672$	3.71351	−	11.9671i	0.143252	−	0.461641i
$673$	−6.98324			−0.269184			−0.134592	−	0.990901i	$-0.542972\pi$
$673$	−6.98324			−0.269184			−0.134592	+	0.990901i	$0.542972\pi$
$674$	21.2815	−	43.7344i	0.819734	−	1.68459i
$675$	15.2128	+	6.30134i	0.585540	+	0.242539i
$676$	−1.23602	+	10.2202i	−0.0475394	+	0.393083i
$677$	3.11331	+	7.51619i	0.119654	+	0.288871i	0.972347	−	0.233543i	$-0.0750318\pi$
$677$	3.11331	+	7.51619i	0.119654	+	0.288871i	−0.852692	+	0.522413i	$0.825032\pi$
$678$	−28.2094	+	25.0033i	−1.08338	+	0.960248i
$679$	2.24393	−	2.24393i	0.0861141	−	0.0861141i
$680$	−22.0519	−	31.8990i	−0.845652	−	1.22327i
$681$	−13.1333	−	13.1333i	−0.503270	−	0.503270i
$682$	−35.8328	−	2.15894i	−1.37211	−	0.0826703i
$683$	−11.0798	+	4.58941i	−0.423958	+	0.175609i	−0.584453	−	0.811428i	$-0.698691\pi$
$683$	−11.0798	+	4.58941i	−0.423958	+	0.175609i	0.160495	+	0.987037i	$0.448691\pi$
$684$	−25.2887	−	14.2470i	−0.966937	−	0.544749i
$685$	1.26446	−	3.05267i	0.0483125	−	0.116637i
$686$	0.461638	+	1.33675i	0.0176254	+	0.0510372i
$687$		−	57.4777i		−	2.19291i
$688$	5.87165	+	38.3343i	0.223854	+	1.46148i
$689$		−	2.65531i		−	0.101159i
$690$	−21.2592	+	7.34175i	−0.809324	+	0.279496i
$691$	−13.6069	+	32.8500i	−0.517632	+	1.24967i	0.421722	+	0.906725i	$0.361426\pi$
$691$	−13.6069	+	32.8500i	−0.517632	+	1.24967i	−0.939354	+	0.342949i	$0.888574\pi$
$692$	−6.03549	+	1.68561i	−0.229435	+	0.0640773i
$693$	6.21534	−	2.57448i	0.236101	−	0.0977964i
$694$	0.783213	−	12.9993i	0.0297304	−	0.493446i
$695$	−2.95542	−	2.95542i	−0.112106	−	0.112106i
$696$	7.74720	−	12.0012i	0.293657	−	0.454902i
$697$	25.4399	−	25.4399i	0.963604	−	0.963604i
$698$	23.5935	+	26.6188i	0.893026	+	1.00754i
$699$	−10.5897	−	25.5657i	−0.400538	−	0.966984i
$700$	10.6970	−	8.38874i	0.404307	−	0.317064i
$701$	25.8652	+	10.7137i	0.976913	+	0.404651i	0.813281	−	0.581871i	$-0.197679\pi$
$701$	25.8652	+	10.7137i	0.976913	+	0.404651i	0.163632	+	0.986521i	$0.447679\pi$
$702$	−8.63284	−	4.20081i	−0.325826	−	0.158549i
$703$	−7.66871			−0.289231
$704$	19.3220	−	20.5848i	0.728226	−	0.775819i
$705$	−32.7961			−1.23517
$706$	10.3197	+	5.02163i	0.388385	+	0.188992i
$707$	−2.35199	−	0.974224i	−0.0884555	−	0.0366395i
$708$	−7.83760	+	6.14638i	−0.294555	+	0.230995i
$709$	1.60084	+	3.86477i	0.0601208	+	0.145145i	0.951085	−	0.308929i	$-0.0999704\pi$
$709$	1.60084	+	3.86477i	0.0601208	+	0.145145i	−0.890964	+	0.454073i	$0.849970\pi$
$710$	24.0134	+	27.0925i	0.901206	+	1.01676i
$711$	−12.1927	+	12.1927i	−0.457261	+	0.457261i
$712$	41.9514	+	27.0813i	1.57220	+	1.01491i
$713$	−10.6320	−	10.6320i	−0.398171	−	0.398171i
$714$	−0.752030	+	12.4817i	−0.0281440	+	0.467117i
$715$	31.3812	−	12.9985i	1.17359	−	0.486117i
$716$	36.8795	−	10.2998i	1.37825	−	0.384922i
$717$	−16.0770	+	38.8132i	−0.600405	+	1.44951i
$718$	−19.0785	+	6.58867i	−0.712005	+	0.245887i
$719$			18.8294i			0.702217i	0.936335	+	0.351109i	$0.114195\pi$
$719$			18.8294i			0.702217i	−0.936335	+	0.351109i	$0.885805\pi$
$720$	21.1095	+	15.5018i	0.786705	+	0.577717i
$721$		−	3.89988i		−	0.145239i
$722$	−17.9854	−	52.0795i	−0.669346	−	1.93820i
$723$	9.88548	−	23.8657i	0.367645	−	0.887573i
$724$	−32.2668	−	18.1783i	−1.19919	−	0.675593i
$725$	14.3177	−	5.93060i	0.531748	−	0.220257i
$726$	4.54737	+	0.273981i	0.168769	+	0.0101684i
$727$	−11.3323	−	11.3323i	−0.420293	−	0.420293i	0.465011	−	0.885305i	$-0.346050\pi$
$727$	−11.3323	−	11.3323i	−0.420293	−	0.420293i	−0.885305	+	0.465011i	$0.846050\pi$
$728$	−6.51976	+	4.50713i	−0.241638	+	0.167045i
$729$	3.55888	−	3.55888i	0.131810	−	0.131810i
$730$	41.4269	−	36.7186i	1.53328	−	1.35901i
$731$	−14.8106	−	35.7559i	−0.547790	−	1.32248i
$732$	6.84966	−	56.6369i	0.253171	−	2.09336i
$733$	11.8615	+	4.91318i	0.438113	+	0.181472i	0.590827	−	0.806798i	$-0.298801\pi$
$733$	11.8615	+	4.91318i	0.438113	+	0.181472i	−0.152714	+	0.988270i	$0.548801\pi$
$734$	7.78124	−	15.9908i	0.287211	−	0.590230i
$735$	−7.60786			−0.280620
$736$	11.7755	−	1.08416i	0.434049	−	0.0399626i
$737$	7.45430			0.274583
$738$	−10.6316	+	21.8483i	−0.391353	+	0.804247i
$739$	−14.2986	−	5.92268i	−0.525983	−	0.217869i	0.103860	−	0.994592i	$-0.466881\pi$
$739$	−14.2986	−	5.92268i	−0.525983	−	0.217869i	−0.629843	+	0.776723i	$0.716881\pi$
$740$	6.86943	+	0.830789i	0.252525	+	0.0305404i
$741$	18.0838	+	43.6581i	0.664324	+	1.60382i
$742$	−1.00283	+	0.888857i	−0.0368151	+	0.0326310i
$743$	−17.1104	+	17.1104i	−0.627719	+	0.627719i	−0.947494	−	0.319774i	$-0.896393\pi$
$743$	−17.1104	+	17.1104i	−0.627719	+	0.627719i	0.319774	+	0.947494i	$0.396393\pi$
$744$	−8.09115	+	44.3301i	−0.296636	+	1.62522i
$745$	−44.0271	−	44.0271i	−1.61303	−	1.61303i
$746$	37.8180	+	2.27855i	1.38462	+	0.0834237i
$747$	19.1698	−	7.94038i	0.701385	−	0.290523i
$748$	−13.8293	+	24.5472i	−0.505649	+	0.897534i
$749$	6.70779	−	16.1940i	0.245097	−	0.591717i
$750$	6.31113	+	18.2749i	0.230450	+	0.667305i
$751$		−	28.1209i		−	1.02615i	−0.858345	−	0.513073i	$-0.828507\pi$
$751$		−	28.1209i		−	1.02615i	0.858345	−	0.513073i	$-0.171493\pi$
$752$	16.7461	+	4.11068i	0.610669	+	0.149901i
$753$		−	7.49732i		−	0.273217i
$754$	−8.54085	+	2.94954i	−0.311039	+	0.107416i
$755$	−18.4592	+	44.5644i	−0.671798	+	1.62186i
$756$	1.30329	+	4.66657i	0.0474003	+	0.169722i
$757$	31.5409	−	13.0647i	1.14637	−	0.474843i	0.273057	−	0.961998i	$-0.411965\pi$
$757$	31.5409	−	13.0647i	1.14637	−	0.474843i	0.873316	+	0.487155i	$0.161965\pi$
$758$	−1.53749	+	25.5183i	−0.0558442	+	0.926867i
$759$	11.5547	+	11.5547i	0.419408	+	0.419408i
$760$	15.5742	+	72.3011i	0.564937	+	2.62264i
$761$	−11.4071	+	11.4071i	−0.413507	+	0.413507i	−0.882958	−	0.469451i	$-0.844452\pi$
$761$	−11.4071	+	11.4071i	−0.413507	+	0.413507i	0.469451	+	0.882958i	$0.344452\pi$
$762$	30.4085	+	34.3077i	1.10158	+	1.24284i
$763$	−3.93391	−	9.49731i	−0.142417	−	0.343826i
$764$	−3.07925	−	3.92653i	−0.111403	−	0.142057i
$765$	−24.1469	−	10.0020i	−0.873031	−	0.361621i
$766$	15.9987	+	7.78512i	0.578058	+	0.281288i
$767$	6.30045			0.227496
$768$	−22.7410	−	27.1820i	−0.820595	−	0.980844i
$769$	17.2975			0.623763			0.311881	−	0.950121i	$-0.399041\pi$
$769$	17.2975			0.623763			0.311881	+	0.950121i	$0.399041\pi$
$770$	−15.4139	−	7.50053i	−0.555479	−	0.270300i
$771$	−26.2256	−	10.8630i	−0.944494	−	0.391222i
$772$	21.1077	+	26.9157i	0.759684	+	0.968717i
$773$	0.948593	+	2.29011i	0.0341185	+	0.0823694i	0.940020	−	0.341118i	$-0.110806\pi$
$773$	0.948593	+	2.29011i	0.0341185	+	0.0823694i	−0.905902	+	0.423488i	$0.860806\pi$
$774$	17.3372	+	19.5603i	0.623172	+	0.703080i
$775$	−34.5696	+	34.5696i	−1.24178	+	1.24178i
$776$	−1.89009	−	8.77445i	−0.0678501	−	0.314985i
$777$	−1.57768	−	1.57768i	−0.0565991	−	0.0565991i
$778$	−0.524332	+	8.70254i	−0.0187982	+	0.312001i
$779$	−63.3927	+	26.2581i	−2.27128	+	0.940795i
$780$	−11.4693	−	41.0669i	−0.410667	−	1.47043i
$781$	10.0657	−	24.3006i	0.360177	−	0.869545i
$782$	−11.1546	+	3.85218i	−0.398888	+	0.137754i
$783$			5.52357i			0.197396i
$784$	3.88468	+	0.953572i	0.138738	+	0.0340562i
$785$			47.2743i			1.68729i
$786$	−5.98960	−	17.3438i	−0.213642	−	0.618635i
$787$	13.8991	−	33.5555i	0.495450	−	1.19612i	−0.456459	−	0.889744i	$-0.650883\pi$
$787$	13.8991	−	33.5555i	0.495450	−	1.19612i	0.951910	−	0.306379i	$-0.0991174\pi$
$788$	−2.46238	+	4.37076i	−0.0877187	+	0.155702i
$789$	38.2714	−	15.8525i	1.36250	−	0.564365i
$790$	43.8568	+	2.64239i	1.56036	+	0.0940122i
$791$	−8.50905	−	8.50905i	−0.302547	−	0.302547i
$792$	3.41657	−	18.7188i	0.121402	−	0.665145i
$793$	−25.5176	+	25.5176i	−0.906156	+	0.906156i
$794$	−23.3862	+	20.7283i	−0.829947	+	0.735620i
$795$	−2.75873	−	6.66015i	−0.0978419	−	0.236211i
$796$	−14.6484	−	1.77158i	−0.519199	−	0.0627919i
$797$	6.59106	+	2.73011i	0.233467	+	0.0967054i	0.496350	−	0.868122i	$-0.334673\pi$
$797$	6.59106	+	2.73011i	0.233467	+	0.0967054i	−0.262883	+	0.964828i	$0.584673\pi$
$798$	10.4349	−	21.4441i	0.369391	−	0.759113i
$799$	−17.2080			−0.608774
$800$	−3.52511	−	38.2876i	−0.124632	−	1.35367i
$801$	33.6538			1.18910
$802$	3.78892	−	7.78638i	0.133791	−	0.274947i
$803$	−37.1578	−	15.3913i	−1.31127	−	0.543146i
$804$	1.12349	−	9.28968i	0.0396226	−	0.327622i
$805$	−2.74765	−	6.63341i	−0.0968418	−	0.233797i
$806$	21.3316	−	18.9072i	0.751375	−	0.665978i
$807$	47.2225	−	47.2225i	1.66231	−	1.66231i
$808$	−5.92300	+	4.09459i	−0.208370	+	0.144047i
$809$	18.0406	+	18.0406i	0.634272	+	0.634272i	0.949137	−	0.314864i	$-0.101959\pi$
$809$	18.0406	+	18.0406i	0.634272	+	0.634272i	−0.314864	+	0.949137i	$0.601959\pi$
$810$	−53.7460	−	3.23822i	−1.88844	−	0.113780i
$811$	28.2026	−	11.6819i	0.990328	−	0.410207i	0.172086	−	0.985082i	$-0.444949\pi$
$811$	28.2026	−	11.6819i	0.990328	−	0.410207i	0.818241	+	0.574875i	$0.194949\pi$
$812$	3.97297	+	2.23828i	0.139424	+	0.0785481i
$813$	6.38031	−	15.4034i	0.223767	−	0.540222i
$814$	−1.64104	−	4.75190i	−0.0575185	−	0.166554i
$815$		−	3.86184i		−	0.135274i
$816$	28.5068	+	20.9340i	0.997939	+	0.732837i
$817$			73.8120i			2.58236i
$818$	16.5701	−	5.72238i	0.579358	−	0.200078i
$819$	−2.04427	+	4.93531i	−0.0714327	+	0.172454i
$820$	59.6302	−	16.6537i	2.08238	−	0.581573i
$821$	36.3237	−	15.0458i	1.26770	−	0.525100i	0.355439	−	0.934700i	$-0.384331\pi$
$821$	36.3237	−	15.0458i	1.26770	−	0.525100i	0.912266	+	0.409599i	$0.134331\pi$
$822$	−0.181236	+	3.00805i	−0.00632134	+	0.104918i
$823$	9.75716	+	9.75716i	0.340113	+	0.340113i	0.856410	−	0.516297i	$-0.172690\pi$
$823$	9.75716	+	9.75716i	0.340113	+	0.340113i	−0.516297	+	0.856410i	$0.672690\pi$
$824$	−9.26733	−	5.98242i	−0.322843	−	0.208407i
$825$	37.5697	−	37.5697i	1.30801	−	1.30801i
$826$	−2.10905	−	2.37949i	−0.0733834	−	0.0827931i
$827$	5.21633	+	12.5933i	0.181390	+	0.437913i	0.988253	−	0.152824i	$-0.0488369\pi$
$827$	5.21633	+	12.5933i	0.181390	+	0.437913i	−0.806864	+	0.590737i	$0.798837\pi$
$828$	6.27148	−	4.91820i	0.217949	−	0.170919i
$829$	6.80814	+	2.82003i	0.236457	+	0.0979435i	0.497765	−	0.867312i	$-0.334154\pi$
$829$	6.80814	+	2.82003i	0.236457	+	0.0979435i	−0.261309	+	0.965255i	$0.584154\pi$
$830$	−47.5406	−	23.1336i	−1.65016	−	0.802980i
$831$	4.98433			0.172905
$832$	0.709029	+	22.4069i	0.0245812	+	0.776820i
$833$	−3.99181			−0.138308
$834$	3.42763	+	1.66791i	0.118689	+	0.0577550i
$835$	−7.59873	−	3.14750i	−0.262965	−	0.108924i
$836$	42.2832	−	33.1592i	1.46239	−	1.14683i
$837$	−6.66822	−	16.0985i	−0.230487	−	0.556446i
$838$	−14.1998	−	16.0206i	−0.490523	−	0.553421i
$839$	−28.8291	+	28.8291i	−0.995292	+	0.995292i	−0.999989	−	0.00469670i	$-0.998505\pi$
$839$	−28.8291	+	28.8291i	−0.995292	+	0.995292i	0.00469670	+	0.999989i	$0.498505\pi$
$840$	−11.6704	+	18.0786i	−0.402668	+	0.623772i
$841$	−16.8301	−	16.8301i	−0.580349	−	0.580349i
$842$	−2.57376	+	42.7177i	−0.0886976	+	1.47215i
$843$	−25.6796	+	10.6368i	−0.884453	+	0.366352i
$844$	−23.7431	+	6.63105i	−0.817272	+	0.228250i
$845$	6.76559	−	16.3336i	0.232743	−	0.561892i
$846$	10.9850	−	3.79360i	0.377671	−	0.130427i
$847$			1.45431i			0.0499705i
$848$	0.573856	+	3.74655i	0.0197063	+	0.128657i
$849$			5.99523i			0.205756i
$850$	12.5253	+	36.2689i	0.429613	+	1.24401i
$851$	0.805812	−	1.94540i	0.0276229	−	0.0666875i
$852$	−28.7668	−	16.2065i	−0.985535	−	0.555227i
$853$	13.9681	−	5.78577i	0.478258	−	0.198101i	−0.130514	−	0.991447i	$-0.541663\pi$
$853$	13.9681	−	5.78577i	0.478258	−	0.198101i	0.608771	+	0.793346i	$0.291663\pi$
$854$	18.1792	+	1.09530i	0.622078	+	0.0374805i
$855$	35.2472	+	35.2472i	1.20543	+	1.20543i
$856$	−28.1923	−	40.7814i	−0.963593	−	1.39388i
$857$	−12.9470	+	12.9470i	−0.442260	+	0.442260i	−0.892771	−	0.450511i	$-0.851242\pi$
$857$	−12.9470	+	12.9470i	−0.442260	+	0.442260i	0.450511	+	0.892771i	$0.351242\pi$
$858$	−23.1829	+	20.5481i	−0.791450	+	0.701500i
$859$	4.00715	+	9.67412i	0.136722	+	0.330077i	0.977380	−	0.211490i	$-0.0678315\pi$
$859$	4.00715	+	9.67412i	0.136722	+	0.330077i	−0.840658	+	0.541566i	$0.817831\pi$
$860$	7.99642	−	66.1189i	0.272676	−	2.25464i
$861$	−18.4439	−	7.63971i	−0.628566	−	0.260360i
$862$	−13.1477	+	27.0190i	−0.447812	+	0.920272i
$863$	−34.8143			−1.18509			−0.592546	−	0.805537i	$-0.701877\pi$
$863$	−34.8143			−1.18509			−0.592546	+	0.805537i	$0.701877\pi$
$864$	13.0885	+	4.06149i	0.445279	+	0.138175i
$865$	10.7616			0.365906
$866$	8.65628	−	17.7890i	0.294152	−	0.604495i
$867$	2.18038	+	0.903143i	0.0740496	+	0.0306724i
$868$	−14.2814	−	1.72719i	−0.484742	−	0.0586246i
$869$	−12.2158	−	29.4916i	−0.414394	−	1.00043i
$870$	−18.3581	+	16.2716i	−0.622397	+	0.551659i
$871$	−4.18544	+	4.18544i	−0.141818	+	0.141818i
$872$	−28.6032	−	5.22066i	−0.968625	−	0.176794i
$873$	−4.27759	−	4.27759i	−0.144774	−	0.144774i
$874$	22.4661	+	1.35359i	0.759927	+	0.0457860i
$875$	−5.70223	+	2.36194i	−0.192770	+	0.0798481i
$876$	−24.7812	+	43.9870i	−0.837279	+	1.48618i
$877$	9.63779	−	23.2677i	0.325445	−	0.785694i	−0.673474	−	0.739211i	$-0.735199\pi$
$877$	9.63779	−	23.2677i	0.325445	−	0.785694i	0.998919	−	0.0464831i	$-0.0148014\pi$
$878$	−2.95423	−	8.55444i	−0.0997004	−	0.288699i
$879$			5.89217i			0.198738i
$880$	−41.4685	+	25.1224i	−1.39790	+	0.846876i
$881$		−	33.7808i		−	1.13810i	−0.822302	−	0.569051i	$-0.807311\pi$
$881$		−	33.7808i		−	1.13810i	0.822302	−	0.569051i	$-0.192689\pi$
$882$	2.54823	−	0.880018i	0.0858034	−	0.0296317i
$883$	−2.65935	+	6.42025i	−0.0894944	+	0.216059i	−0.962289	−	0.272029i	$-0.912305\pi$
$883$	−2.65935	+	6.42025i	−0.0894944	+	0.216059i	0.872795	+	0.488088i	$0.162305\pi$
$884$	−6.01789	−	21.5476i	−0.202403	−	0.724725i
$885$	15.8030	−	6.54582i	0.531212	−	0.220035i
$886$	0.284540	−	4.72262i	0.00955931	−	0.158660i
$887$	21.4970	+	21.4970i	0.721800	+	0.721800i	0.968972	−	0.247172i	$-0.0795011\pi$
$887$	21.4970	+	21.4970i	0.721800	+	0.721800i	−0.247172	+	0.968972i	$0.579501\pi$
$888$	−6.16923	+	1.32890i	−0.207026	+	0.0445950i
$889$	−10.3485	+	10.3485i	−0.347078	+	0.347078i
$890$	−56.8793	−	64.1728i	−1.90660	−	2.15108i
$891$	14.9704	+	36.1416i	0.501526	+	1.21079i
$892$	−14.1567	−	18.0520i	−0.474002	−	0.604427i
$893$	30.3207	+	12.5592i	1.01464	+	0.420279i
$894$	51.0616	+	24.8470i	1.70775	+	0.831007i
$895$	−65.7581			−2.19805
$896$	8.22507	−	7.76841i	0.274780	−	0.259524i
$897$	−12.9754			−0.433237
$898$	0.787189	+	0.383052i	0.0262688	+	0.0127826i
$899$	−15.1514	−	6.27590i	−0.505326	−	0.209313i
$900$	−15.9914	−	20.3916i	−0.533047	−	0.679719i
$901$	−1.44749	−	3.49455i	−0.0482229	−	0.116420i
$902$	−29.8363	−	33.6621i	−0.993441	−	1.12083i
$903$	−15.1854	+	15.1854i	−0.505337	+	0.505337i
$904$	−33.2730	+	7.16726i	−1.10664	+	0.238380i
$905$	44.9732	+	44.9732i	1.49496	+	1.49496i
$906$	2.64577	−	43.9129i	0.0878999	−	1.45891i
$907$	−8.90614	+	3.68904i	−0.295724	+	0.122493i	−0.525612	−	0.850724i	$-0.676164\pi$
$907$	−8.90614	+	3.68904i	−0.295724	+	0.122493i	0.229889	+	0.973217i	$0.426164\pi$
$908$	−4.51105	−	16.1523i	−0.149704	−	0.536031i
$909$	−1.85716	+	4.48358i	−0.0615980	+	0.148711i
$910$	12.8660	−	4.44320i	0.426504	−	0.147291i
$911$		−	3.54631i		−	0.117495i	−0.998273	−	0.0587473i	$-0.981289\pi$
$911$		−	3.54631i		−	0.117495i	0.998273	−	0.0587473i	$-0.0187106\pi$
$912$	−34.9508	−	57.6917i	−1.15734	−	1.91036i
$913$			38.4124i			1.27126i
$914$	5.86002	+	16.9686i	0.193832	+	0.561272i
$915$	−37.4928	+	90.5155i	−1.23947	+	2.99235i
$916$	25.4738	−	45.2163i	0.841677	−	1.49399i
$917$	5.41172	−	2.24161i	0.178711	−	0.0740244i
$918$	−13.6513	−	0.822499i	−0.450561	−	0.0271465i
$919$	−20.9848	−	20.9848i	−0.692224	−	0.692224i	0.270497	−	0.962721i	$-0.412812\pi$
$919$	−20.9848	−	20.9848i	−0.692224	−	0.692224i	−0.962721	+	0.270497i	$0.912812\pi$
$920$	−19.9779	−	3.64638i	−0.658652	−	0.120217i
$921$	−8.78707	+	8.78707i	−0.289544	+	0.289544i
$922$	−34.8670	+	30.9043i	−1.14829	+	1.01778i
$923$	7.99266	+	19.2960i	0.263082	+	0.635135i
$924$	15.5208	+	1.87708i	0.510596	+	0.0617515i
$925$	−6.32543	−	2.62008i	−0.207979	−	0.0861476i
$926$	−2.68207	+	5.51176i	−0.0881382	+	0.181128i
$927$	−7.43433			−0.244175
$928$	11.4134	−	6.00750i	0.374662	−	0.197206i
$929$	14.2322			0.466943			0.233471	−	0.972364i	$-0.424991\pi$
$929$	14.2322			0.466943			0.233471	+	0.972364i	$0.424991\pi$
$930$	33.8612	−	69.5862i	1.11035	−	2.28182i
$931$	7.03362	+	2.91342i	0.230518	+	0.0954835i
$932$	2.99994	−	24.8052i	0.0982663	−	0.812521i
$933$	0.0715944	+	0.172844i	0.00234390	+	0.00565867i
$934$	2.67592	−	2.37180i	0.0875589	−	0.0776075i
$935$	34.2137	−	34.2137i	1.11891	−	1.11891i
$936$	8.59192	+	12.4286i	0.280836	+	0.406241i
$937$	5.16566	+	5.16566i	0.168755	+	0.168755i	0.786432	−	0.617677i	$-0.211926\pi$
$937$	5.16566	+	5.16566i	0.168755	+	0.168755i	−0.617677	+	0.786432i	$0.711926\pi$
$938$	2.98178	+	0.179653i	0.0973585	+	0.00586589i
$939$	−3.02295	+	1.25215i	−0.0986501	+	0.0408622i
$940$	−25.7999	−	14.5350i	−0.841500	−	0.474081i
$941$	16.2217	−	39.1626i	0.528812	−	1.27666i	−0.403490	−	0.914984i	$-0.632203\pi$
$941$	16.2217	−	39.1626i	0.528812	−	1.27666i	0.932302	−	0.361681i	$-0.117797\pi$
$942$	−14.0740	−	40.7535i	−0.458556	−	1.32782i
$943$		−	18.8407i		−	0.613536i
$944$	−8.88969	+	1.36163i	−0.289335	+	0.0443173i
$945$		−	8.32075i		−	0.270674i
$946$	−45.7375	+	15.7952i	−1.48705	+	0.513546i
$947$	−12.4420	+	30.0377i	−0.404312	+	0.976094i	0.582295	+	0.812977i	$0.302155\pi$
$947$	−12.4420	+	30.0377i	−0.404312	+	0.976094i	−0.986607	+	0.163117i	$0.947845\pi$
$948$	−38.5941	+	10.7787i	−1.25348	+	0.350075i
$949$	29.5053	−	12.2215i	0.957781	−	0.396726i
$950$	4.40117	−	73.0479i	0.142793	−	2.36999i
$951$	−4.18786	−	4.18786i	−0.135801	−	0.135801i
$952$	−6.12343	+	9.48577i	−0.198461	+	0.307436i
$953$	23.5096	−	23.5096i	0.761551	−	0.761551i	−0.215052	−	0.976603i	$-0.568992\pi$
$953$	23.5096	−	23.5096i	0.761551	−	0.761551i	0.976603	+	0.215052i	$0.0689920\pi$
$954$	1.69442	+	1.91169i	0.0548590	+	0.0618934i
$955$	3.27936	+	7.91708i	0.106118	+	0.256191i
$956$	−29.8491	+	23.4082i	−0.965390	+	0.757075i
$957$	16.4663	+	6.82055i	0.532279	+	0.220477i
$958$	−2.30962	−	1.12388i	−0.0746206	−	0.0363110i
$959$	−0.962010			−0.0310649
$960$	25.0580	+	55.4652i	0.808742	+	1.79013i
$961$	20.7352			0.668879
$962$	3.58951	+	1.74668i	0.115730	+	0.0563154i
$963$	−30.8706	−	12.7870i	−0.994791	−	0.412056i
$964$	18.3538	−	14.3933i	0.591135	−	0.463578i
$965$	−22.4795	−	54.2703i	−0.723641	−	1.74702i
$966$	4.34348	+	4.90043i	0.139749	+	0.157669i
$967$	43.6038	−	43.6038i	1.40220	−	1.40220i	0.609145	−	0.793059i	$-0.291513\pi$
$967$	43.6038	−	43.6038i	1.40220	−	1.40220i	0.793059	−	0.609145i	$-0.208487\pi$
$968$	3.45588	+	2.23090i	0.111076	+	0.0717039i
$969$	47.5987	+	47.5987i	1.52909	+	1.52909i
$970$	−0.927039	+	15.3864i	−0.0297654	+	0.494028i
$971$	36.4216	−	15.0863i	1.16882	−	0.484142i	0.288020	−	0.957624i	$-0.407003\pi$
$971$	36.4216	−	15.0863i	1.16882	−	0.484142i	0.880803	+	0.473482i	$0.157003\pi$
$972$	33.2969	−	9.29927i	1.06800	−	0.298274i
$973$	−0.465681	+	1.12425i	−0.0149291	+	0.0360419i
$974$	−41.7439	+	14.4160i	−1.33756	+	0.461919i
$975$			42.1893i			1.35114i
$976$	30.4896	−	41.5191i	0.975948	−	1.32899i
$977$		−	28.5955i		−	0.914850i	−0.889248	−	0.457425i	$-0.848772\pi$
$977$		−	28.5955i		−	0.914850i	0.889248	−	0.457425i	$-0.151228\pi$
$978$	1.14971	+	3.32916i	0.0367636	+	0.106455i
$979$	−23.8420	+	57.5598i	−0.761995	+	1.83962i
$980$	−5.98491	−	3.37176i	−0.191181	−	0.107707i
$981$	−18.1047	+	7.49920i	−0.578038	+	0.239431i
$982$	−42.9386	−	2.58707i	−1.37022	−	0.0825566i
$983$	−16.7253	−	16.7253i	−0.533456	−	0.533456i	0.388143	−	0.921599i	$-0.373117\pi$
$983$	−16.7253	−	16.7253i	−0.533456	−	0.533456i	−0.921599	+	0.388143i	$0.873117\pi$
$984$	−46.4472	+	32.1091i	−1.48068	+	1.02360i
$985$	6.09193	−	6.09193i	0.194105	−	0.194105i
$986$	−9.63240	+	8.53764i	−0.306758	+	0.271894i
$987$	3.65407	+	8.82170i	0.116310	+	0.280798i
$988$	−5.12294	+	42.3594i	−0.162983	+	1.34763i
$989$	−18.7247	−	7.75602i	−0.595410	−	0.246627i
$990$	−14.2982	+	29.3834i	−0.454427	+	0.933867i
$991$	12.5759			0.399486			0.199743	−	0.979848i	$-0.435989\pi$
$991$	12.5759			0.399486			0.199743	+	0.979848i	$0.435989\pi$
$992$	−26.0120	+	31.2875i	−0.825880	+	0.993378i
$993$	64.7322			2.05421
$994$	4.61200	−	9.47786i	0.146284	−	0.300619i
$995$	23.4107	+	9.69703i	0.742169	+	0.307417i
$996$	47.8702	+	5.78942i	1.51683	+	0.183445i
$997$	21.6842	+	52.3503i	0.686746	+	1.65795i	0.751236	+	0.660033i	$0.229458\pi$
$997$	21.6842	+	52.3503i	0.686746	+	1.65795i	−0.0644902	+	0.997918i	$0.520542\pi$
$998$	−18.9781	+	16.8212i	−0.600743	+	0.532466i
$999$	1.72552	−	1.72552i	0.0545931	−	0.0545931i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	224.2.u.b.29.9	✓	40
4.3	odd	2		896.2.u.b.337.3		40
32.11	odd	8		896.2.u.b.561.3		40
32.21	even	8	inner	224.2.u.b.85.9	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.2.u.b.29.9	✓	40	1.1	even	1	trivial
224.2.u.b.85.9	yes	40	32.21	even	8	inner
896.2.u.b.337.3		40	4.3	odd	2
896.2.u.b.561.3		40	32.11	odd	8

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:	\( N \)	\(=\)	\( 224 = 2^{5} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	224.u (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.27165 + 0.618795i) q^{2} +(2.04641 + 0.847650i) q^{3} +(1.23419 + 1.57378i) q^{4} +(-1.31439 - 3.17322i) q^{5} +(2.07779 + 2.34422i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(0.595604 + 2.76501i) q^{8} +(1.34795 + 1.34795i) q^{9} +O(q^{10})\)	\(q+(1.27165 + 0.618795i) q^{2} +(2.04641 + 0.847650i) q^{3} +(1.23419 + 1.57378i) q^{4} +(-1.31439 - 3.17322i) q^{5} +(2.07779 + 2.34422i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(0.595604 + 2.76501i) q^{8} +(1.34795 + 1.34795i) q^{9} +(0.292129 - 4.84857i) q^{10} +(-3.26043 + 1.35052i) q^{11} +(1.19163 + 4.26675i) q^{12} +(1.07238 - 2.58896i) q^{13} +(-1.33675 + 0.461638i) q^{14} -7.60786i q^{15} +(-0.953572 + 3.88468i) q^{16} -3.99181i q^{17} +(0.880018 + 2.54823i) q^{18} +(-2.91342 + 7.03362i) q^{19} +(3.37176 - 5.98491i) q^{20} +(-2.04641 + 0.847650i) q^{21} +(-4.98182 - 0.300157i) q^{22} +(-1.47816 - 1.47816i) q^{23} +(-1.12491 + 6.16319i) q^{24} +(-4.80619 + 4.80619i) q^{25} +(2.96572 - 2.62866i) q^{26} +(-0.927079 - 2.23817i) q^{27} +(-1.98553 - 0.240130i) q^{28} +(-2.10649 - 0.872535i) q^{29} +(4.70770 - 9.67453i) q^{30} +7.19272 q^{31} +(-3.61643 + 4.34988i) q^{32} -7.81694 q^{33} +(2.47011 - 5.07618i) q^{34} +(3.17322 + 1.31439i) q^{35} +(-0.457759 + 3.78501i) q^{36} +(0.385477 + 0.930623i) q^{37} +(-8.05722 + 7.14149i) q^{38} +(4.38905 - 4.38905i) q^{39} +(7.99113 - 5.52429i) q^{40} +(6.37302 + 6.37302i) q^{41} +(-3.12684 - 0.188393i) q^{42} +(8.95733 - 3.71025i) q^{43} +(-6.14939 - 3.46442i) q^{44} +(2.50562 - 6.04910i) q^{45} +(-0.965022 - 2.79438i) q^{46} -4.31082i q^{47} +(-5.24424 + 7.14133i) q^{48} -1.00000i q^{49} +(-9.08584 + 3.13774i) q^{50} +(3.38366 - 8.16887i) q^{51} +(5.39796 - 1.50756i) q^{52} +(0.875431 - 0.362615i) q^{53} +(0.206047 - 3.41984i) q^{54} +(8.57097 + 8.57097i) q^{55} +(-2.37631 - 1.53400i) q^{56} +(-11.9241 + 11.9241i) q^{57} +(-2.13879 - 2.41304i) q^{58} +(0.860403 + 2.07720i) q^{59} +(11.9731 - 9.38951i) q^{60} +(-11.8976 - 4.92816i) q^{61} +(9.14662 + 4.45082i) q^{62} -1.90629 q^{63} +(-7.29051 + 3.29370i) q^{64} -9.62486 q^{65} +(-9.94040 - 4.83708i) q^{66} +(-1.95147 - 0.808326i) q^{67} +(6.28223 - 4.92663i) q^{68} +(-1.77195 - 4.27787i) q^{69} +(3.22189 + 3.63502i) q^{70} +(-5.27021 + 5.27021i) q^{71} +(-2.92425 + 4.52995i) q^{72} +(8.05861 + 8.05861i) q^{73} +(-0.0856736 + 1.42196i) q^{74} +(-13.9094 + 5.76146i) q^{75} +(-14.6651 + 4.09571i) q^{76} +(1.35052 - 3.26043i) q^{77} +(8.29726 - 2.86541i) q^{78} +9.04531i q^{79} +(13.5803 - 2.08009i) q^{80} -11.0849i q^{81} +(4.16065 + 12.0478i) q^{82} +(4.16535 - 10.0560i) q^{83} +(-3.85966 - 2.17444i) q^{84} +(-12.6669 + 5.24680i) q^{85} +(13.6865 + 0.824616i) q^{86} +(-3.57112 - 3.57112i) q^{87} +(-5.67611 - 8.21074i) q^{88} +(12.4833 - 12.4833i) q^{89} +(6.92942 - 6.14187i) q^{90} +(1.07238 + 2.58896i) q^{91} +(0.501976 - 4.15062i) q^{92} +(14.7192 + 6.09691i) q^{93} +(2.66752 - 5.48186i) q^{94} +26.1486 q^{95} +(-11.0879 + 5.83616i) q^{96} -3.17339 q^{97} +(0.618795 - 1.27165i) q^{98} +(-6.21534 - 2.57448i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 4 q^{2} + 4 q^{3} + 8 q^{5} + 12 q^{6} - 8 q^{8} + 8 q^{9}+O(q^{10}) \) 40 * q + 4 * q^2 + 4 * q^3 + 8 * q^5 + 12 * q^6 - 8 * q^8 + 8 * q^9	\( 40 q + 4 q^{2} + 4 q^{3} + 8 q^{5} + 12 q^{6} - 8 q^{8} + 8 q^{9} - 16 q^{10} + 12 q^{11} - 36 q^{12} + 8 q^{16} + 4 q^{19} - 4 q^{21} - 52 q^{22} + 16 q^{23} - 8 q^{24} - 16 q^{25} + 12 q^{26} - 32 q^{27} + 8 q^{28} + 16 q^{29} + 36 q^{30} + 24 q^{31} - 36 q^{32} + 8 q^{33} - 8 q^{34} - 8 q^{36} + 16 q^{37} - 12 q^{38} - 24 q^{39} + 36 q^{40} + 8 q^{41} + 52 q^{43} - 44 q^{44} - 64 q^{45} - 32 q^{46} - 36 q^{48} + 52 q^{50} + 16 q^{51} - 16 q^{52} - 32 q^{54} - 8 q^{55} + 12 q^{56} - 8 q^{57} + 40 q^{58} + 20 q^{59} + 52 q^{60} - 16 q^{61} - 12 q^{62} - 24 q^{63} - 48 q^{64} - 80 q^{65} - 40 q^{66} - 4 q^{67} - 4 q^{68} - 40 q^{69} + 32 q^{70} + 72 q^{72} - 24 q^{73} - 12 q^{74} + 20 q^{75} - 72 q^{76} + 4 q^{77} + 12 q^{78} + 60 q^{80} + 16 q^{82} + 4 q^{83} + 8 q^{84} - 64 q^{85} - 48 q^{86} - 32 q^{87} + 16 q^{88} + 32 q^{89} + 20 q^{90} + 108 q^{92} - 24 q^{93} + 68 q^{94} - 80 q^{95} - 40 q^{96} + 56 q^{97} + 4 q^{98} - 60 q^{99}+O(q^{100}) \) 40 * q + 4 * q^2 + 4 * q^3 + 8 * q^5 + 12 * q^6 - 8 * q^8 + 8 * q^9 - 16 * q^10 + 12 * q^11 - 36 * q^12 + 8 * q^16 + 4 * q^19 - 4 * q^21 - 52 * q^22 + 16 * q^23 - 8 * q^24 - 16 * q^25 + 12 * q^26 - 32 * q^27 + 8 * q^28 + 16 * q^29 + 36 * q^30 + 24 * q^31 - 36 * q^32 + 8 * q^33 - 8 * q^34 - 8 * q^36 + 16 * q^37 - 12 * q^38 - 24 * q^39 + 36 * q^40 + 8 * q^41 + 52 * q^43 - 44 * q^44 - 64 * q^45 - 32 * q^46 - 36 * q^48 + 52 * q^50 + 16 * q^51 - 16 * q^52 - 32 * q^54 - 8 * q^55 + 12 * q^56 - 8 * q^57 + 40 * q^58 + 20 * q^59 + 52 * q^60 - 16 * q^61 - 12 * q^62 - 24 * q^63 - 48 * q^64 - 80 * q^65 - 40 * q^66 - 4 * q^67 - 4 * q^68 - 40 * q^69 + 32 * q^70 + 72 * q^72 - 24 * q^73 - 12 * q^74 + 20 * q^75 - 72 * q^76 + 4 * q^77 + 12 * q^78 + 60 * q^80 + 16 * q^82 + 4 * q^83 + 8 * q^84 - 64 * q^85 - 48 * q^86 - 32 * q^87 + 16 * q^88 + 32 * q^89 + 20 * q^90 + 108 * q^92 - 24 * q^93 + 68 * q^94 - 80 * q^95 - 40 * q^96 + 56 * q^97 + 4 * q^98 - 60 * q^99

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