LMFDB - Embedded newform 154.2.f.a.141.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [154,2,Mod(15,154)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(154, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("154.15");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 154 = 2 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	154.f (of order $5$, 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:	$1.22969619113$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			141.1
Root			$-0.309017 - 0.951057i$ of defining polynomial
Character	$\chi$	$=$	154.141
Dual form			154.2.f.a.71.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 - 0.951057i) q^{2} +(0.809017 - 0.587785i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.809017 - 2.48990i) q^{5} +(-0.309017 - 0.951057i) q^{6} +(-0.809017 - 0.587785i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(-0.618034 + 1.90211i) q^{9} +O(q^{10})$	\(q+(0.309017 - 0.951057i) q^{2} +(0.809017 - 0.587785i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.809017 - 2.48990i) q^{5} +(-0.309017 - 0.951057i) q^{6} +(-0.809017 - 0.587785i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(-0.618034 + 1.90211i) q^{9} -2.61803 q^{10} +(3.23607 + 0.726543i) q^{11} -1.00000 q^{12} +(1.07295 - 3.30220i) q^{13} +(-0.809017 + 0.587785i) q^{14} +(-2.11803 - 1.53884i) q^{15} +(0.309017 + 0.951057i) q^{16} +(2.30902 + 7.10642i) q^{17} +(1.61803 + 1.17557i) q^{18} +(5.42705 - 3.94298i) q^{19} +(-0.809017 + 2.48990i) q^{20} -1.00000 q^{21} +(1.69098 - 2.85317i) q^{22} -8.23607 q^{23} +(-0.309017 + 0.951057i) q^{24} +(-1.50000 + 1.08981i) q^{25} +(-2.80902 - 2.04087i) q^{26} +(1.54508 + 4.75528i) q^{27} +(0.309017 + 0.951057i) q^{28} +(0.427051 + 0.310271i) q^{29} +(-2.11803 + 1.53884i) q^{30} +(-0.927051 + 2.85317i) q^{31} +1.00000 q^{32} +(3.04508 - 1.31433i) q^{33} +7.47214 q^{34} +(-0.809017 + 2.48990i) q^{35} +(1.61803 - 1.17557i) q^{36} +(6.35410 + 4.61653i) q^{37} +(-2.07295 - 6.37988i) q^{38} +(-1.07295 - 3.30220i) q^{39} +(2.11803 + 1.53884i) q^{40} +(2.00000 - 1.45309i) q^{41} +(-0.309017 + 0.951057i) q^{42} -7.38197 q^{43} +(-2.19098 - 2.48990i) q^{44} +5.23607 q^{45} +(-2.54508 + 7.83297i) q^{46} +(0.500000 - 0.363271i) q^{47} +(0.809017 + 0.587785i) q^{48} +(0.309017 + 0.951057i) q^{49} +(0.572949 + 1.76336i) q^{50} +(6.04508 + 4.39201i) q^{51} +(-2.80902 + 2.04087i) q^{52} +(-3.92705 + 12.0862i) q^{53} +5.00000 q^{54} +(-0.809017 - 8.64527i) q^{55} +1.00000 q^{56} +(2.07295 - 6.37988i) q^{57} +(0.427051 - 0.310271i) q^{58} +(-8.35410 - 6.06961i) q^{59} +(0.809017 + 2.48990i) q^{60} +(-2.20820 - 6.79615i) q^{61} +(2.42705 + 1.76336i) q^{62} +(1.61803 - 1.17557i) q^{63} +(0.309017 - 0.951057i) q^{64} -9.09017 q^{65} +(-0.309017 - 3.30220i) q^{66} -8.70820 q^{67} +(2.30902 - 7.10642i) q^{68} +(-6.66312 + 4.84104i) q^{69} +(2.11803 + 1.53884i) q^{70} +(-0.927051 - 2.85317i) q^{71} +(-0.618034 - 1.90211i) q^{72} +(5.54508 + 4.02874i) q^{73} +(6.35410 - 4.61653i) q^{74} +(-0.572949 + 1.76336i) q^{75} -6.70820 q^{76} +(-2.19098 - 2.48990i) q^{77} -3.47214 q^{78} +(1.21885 - 3.75123i) q^{79} +(2.11803 - 1.53884i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(-0.763932 - 2.35114i) q^{82} +(-1.95492 - 6.01661i) q^{83} +(0.809017 + 0.587785i) q^{84} +(15.8262 - 11.4984i) q^{85} +(-2.28115 + 7.02067i) q^{86} +0.527864 q^{87} +(-3.04508 + 1.31433i) q^{88} -3.09017 q^{89} +(1.61803 - 4.97980i) q^{90} +(-2.80902 + 2.04087i) q^{91} +(6.66312 + 4.84104i) q^{92} +(0.927051 + 2.85317i) q^{93} +(-0.190983 - 0.587785i) q^{94} +(-14.2082 - 10.3229i) q^{95} +(0.809017 - 0.587785i) q^{96} +(1.09017 - 3.35520i) q^{97} +1.00000 q^{98} +(-3.38197 + 5.70634i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{2} + q^{3} - q^{4} - q^{5} + q^{6} - q^{7} - q^{8} + 2 q^{9}+O(q^{10}) $ 4 * q - q^2 + q^3 - q^4 - q^5 + q^6 - q^7 - q^8 + 2 * q^9	\( 4 q - q^{2} + q^{3} - q^{4} - q^{5} + q^{6} - q^{7} - q^{8} + 2 q^{9} - 6 q^{10} + 4 q^{11} - 4 q^{12} + 11 q^{13} - q^{14} - 4 q^{15} - q^{16} + 7 q^{17} + 2 q^{18} + 15 q^{19} - q^{20} - 4 q^{21} + 9 q^{22} - 24 q^{23} + q^{24} - 6 q^{25} - 9 q^{26} - 5 q^{27} - q^{28} - 5 q^{29} - 4 q^{30} + 3 q^{31} + 4 q^{32} + q^{33} + 12 q^{34} - q^{35} + 2 q^{36} + 12 q^{37} - 15 q^{38} - 11 q^{39} + 4 q^{40} + 8 q^{41} + q^{42} - 34 q^{43} - 11 q^{44} + 12 q^{45} + q^{46} + 2 q^{47} + q^{48} - q^{49} + 9 q^{50} + 13 q^{51} - 9 q^{52} - 9 q^{53} + 20 q^{54} - q^{55} + 4 q^{56} + 15 q^{57} - 5 q^{58} - 20 q^{59} + q^{60} + 18 q^{61} + 3 q^{62} + 2 q^{63} - q^{64} - 14 q^{65} + q^{66} - 8 q^{67} + 7 q^{68} - 11 q^{69} + 4 q^{70} + 3 q^{71} + 2 q^{72} + 11 q^{73} + 12 q^{74} - 9 q^{75} - 11 q^{77} + 4 q^{78} + 25 q^{79} + 4 q^{80} - q^{81} - 12 q^{82} - 19 q^{83} + q^{84} + 32 q^{85} + 11 q^{86} + 20 q^{87} - q^{88} + 10 q^{89} + 2 q^{90} - 9 q^{91} + 11 q^{92} - 3 q^{93} - 3 q^{94} - 30 q^{95} + q^{96} - 18 q^{97} + 4 q^{98} - 18 q^{99}+O(q^{100}) \) 4 * q - q^2 + q^3 - q^4 - q^5 + q^6 - q^7 - q^8 + 2 * q^9 - 6 * q^10 + 4 * q^11 - 4 * q^12 + 11 * q^13 - q^14 - 4 * q^15 - q^16 + 7 * q^17 + 2 * q^18 + 15 * q^19 - q^20 - 4 * q^21 + 9 * q^22 - 24 * q^23 + q^24 - 6 * q^25 - 9 * q^26 - 5 * q^27 - q^28 - 5 * q^29 - 4 * q^30 + 3 * q^31 + 4 * q^32 + q^33 + 12 * q^34 - q^35 + 2 * q^36 + 12 * q^37 - 15 * q^38 - 11 * q^39 + 4 * q^40 + 8 * q^41 + q^42 - 34 * q^43 - 11 * q^44 + 12 * q^45 + q^46 + 2 * q^47 + q^48 - q^49 + 9 * q^50 + 13 * q^51 - 9 * q^52 - 9 * q^53 + 20 * q^54 - q^55 + 4 * q^56 + 15 * q^57 - 5 * q^58 - 20 * q^59 + q^60 + 18 * q^61 + 3 * q^62 + 2 * q^63 - q^64 - 14 * q^65 + q^66 - 8 * q^67 + 7 * q^68 - 11 * q^69 + 4 * q^70 + 3 * q^71 + 2 * q^72 + 11 * q^73 + 12 * q^74 - 9 * q^75 - 11 * q^77 + 4 * q^78 + 25 * q^79 + 4 * q^80 - q^81 - 12 * q^82 - 19 * q^83 + q^84 + 32 * q^85 + 11 * q^86 + 20 * q^87 - q^88 + 10 * q^89 + 2 * q^90 - 9 * q^91 + 11 * q^92 - 3 * q^93 - 3 * q^94 - 30 * q^95 + q^96 - 18 * q^97 + 4 * q^98 - 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/154\mathbb{Z}\right)^\times$.

$n$	$45$	$57$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	0.309017	−	0.951057i	0.218508	−	0.672499i
$2$	0.309017	−	0.951057i	0.218508	−	0.672499i
$3$	0.809017	−	0.587785i	0.467086	−	0.339358i	−0.329218	−	0.944254i	$-0.606785\pi$
$3$	0.809017	−	0.587785i	0.467086	−	0.339358i	0.796305	+	0.604896i	$0.206785\pi$
$4$	−0.809017	−	0.587785i	−0.404508	−	0.293893i
$5$	−0.809017	−	2.48990i	−0.361803	−	1.11352i	−0.951959	−	0.306227i	$-0.900933\pi$
$5$	−0.809017	−	2.48990i	−0.361803	−	1.11352i	0.590155	−	0.807290i	$-0.299067\pi$
$6$	−0.309017	−	0.951057i	−0.126156	−	0.388267i
$7$	−0.809017	−	0.587785i	−0.305780	−	0.222162i
$7$	−0.809017	−	0.587785i	−0.305780	−	0.222162i
$8$	−0.809017	+	0.587785i	−0.286031	+	0.207813i
$9$	−0.618034	+	1.90211i	−0.206011	+	0.634038i
$10$	−2.61803			−0.827895
$11$	3.23607	+	0.726543i	0.975711	+	0.219061i
$11$	3.23607	+	0.726543i	0.975711	+	0.219061i
$12$	−1.00000			−0.288675
$13$	1.07295	−	3.30220i	0.297583	−	0.915865i	−0.684759	−	0.728769i	$-0.740093\pi$
$13$	1.07295	−	3.30220i	0.297583	−	0.915865i	0.982342	−	0.187095i	$-0.0599074\pi$
$14$	−0.809017	+	0.587785i	−0.216219	+	0.157092i
$15$	−2.11803	−	1.53884i	−0.546874	−	0.397327i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	2.30902	+	7.10642i	0.560019	+	1.72356i	0.682307	+	0.731066i	$0.260977\pi$
$17$	2.30902	+	7.10642i	0.560019	+	1.72356i	−0.122288	+	0.992495i	$0.539023\pi$
$18$	1.61803	+	1.17557i	0.381374	+	0.277085i
$19$	5.42705	−	3.94298i	1.24505	−	0.904582i	0.247127	−	0.968983i	$-0.420514\pi$
$19$	5.42705	−	3.94298i	1.24505	−	0.904582i	0.997924	+	0.0644007i	$0.0205136\pi$
$20$	−0.809017	+	2.48990i	−0.180902	+	0.556758i
$21$	−1.00000			−0.218218
$22$	1.69098	−	2.85317i	0.360519	−	0.608298i
$23$	−8.23607			−1.71734			−0.858669	−	0.512530i	$-0.828708\pi$
$23$	−8.23607			−1.71734			−0.858669	+	0.512530i	$0.828708\pi$
$24$	−0.309017	+	0.951057i	−0.0630778	+	0.194134i
$25$	−1.50000	+	1.08981i	−0.300000	+	0.217963i
$26$	−2.80902	−	2.04087i	−0.550894	−	0.400248i
$27$	1.54508	+	4.75528i	0.297352	+	0.915155i
$28$	0.309017	+	0.951057i	0.0583987	+	0.179733i
$29$	0.427051	+	0.310271i	0.0793014	+	0.0576158i	0.626730	−	0.779237i	$-0.284393\pi$
$29$	0.427051	+	0.310271i	0.0793014	+	0.0576158i	−0.547428	+	0.836853i	$0.684393\pi$
$30$	−2.11803	+	1.53884i	−0.386698	+	0.280953i
$31$	−0.927051	+	2.85317i	−0.166503	+	0.512444i	−0.999144	−	0.0413693i	$-0.986828\pi$
$31$	−0.927051	+	2.85317i	−0.166503	+	0.512444i	0.832641	+	0.553814i	$0.186828\pi$
$32$	1.00000			0.176777
$33$	3.04508	−	1.31433i	0.530081	−	0.228795i
$34$	7.47214			1.28146
$35$	−0.809017	+	2.48990i	−0.136749	+	0.420870i
$36$	1.61803	−	1.17557i	0.269672	−	0.195928i
$37$	6.35410	+	4.61653i	1.04461	+	0.758952i	0.971180	−	0.238348i	$-0.0766060\pi$
$37$	6.35410	+	4.61653i	1.04461	+	0.758952i	0.0734282	+	0.997301i	$0.476606\pi$
$38$	−2.07295	−	6.37988i	−0.336277	−	1.03495i
$39$	−1.07295	−	3.30220i	−0.171809	−	0.528775i
$40$	2.11803	+	1.53884i	0.334891	+	0.243312i
$41$	2.00000	−	1.45309i	0.312348	−	0.226934i	−0.420556	−	0.907267i	$-0.638165\pi$
$41$	2.00000	−	1.45309i	0.312348	−	0.226934i	0.732903	+	0.680333i	$0.238165\pi$
$42$	−0.309017	+	0.951057i	−0.0476824	+	0.146751i
$43$	−7.38197			−1.12574			−0.562870	−	0.826546i	$-0.690303\pi$
$43$	−7.38197			−1.12574			−0.562870	+	0.826546i	$0.690303\pi$
$44$	−2.19098	−	2.48990i	−0.330303	−	0.375366i
$45$	5.23607			0.780547
$46$	−2.54508	+	7.83297i	−0.375252	+	1.15491i
$47$	0.500000	−	0.363271i	0.0729325	−	0.0529886i	−0.550722	−	0.834689i	$-0.685647\pi$
$47$	0.500000	−	0.363271i	0.0729325	−	0.0529886i	0.623654	+	0.781700i	$0.285647\pi$
$48$	0.809017	+	0.587785i	0.116772	+	0.0848395i
$49$	0.309017	+	0.951057i	0.0441453	+	0.135865i
$50$	0.572949	+	1.76336i	0.0810272	+	0.249376i
$51$	6.04508	+	4.39201i	0.846481	+	0.615005i
$52$	−2.80902	+	2.04087i	−0.389541	+	0.283018i
$53$	−3.92705	+	12.0862i	−0.539422	+	1.66017i	0.194474	+	0.980908i	$0.437700\pi$
$53$	−3.92705	+	12.0862i	−0.539422	+	1.66017i	−0.733896	+	0.679262i	$0.762300\pi$
$54$	5.00000			0.680414
$55$	−0.809017	−	8.64527i	−0.109088	−	1.16573i
$56$	1.00000			0.133631
$57$	2.07295	−	6.37988i	0.274569	−	0.845036i
$58$	0.427051	−	0.310271i	0.0560745	−	0.0407405i
$59$	−8.35410	−	6.06961i	−1.08761	−	0.790196i	−0.108617	−	0.994084i	$-0.534642\pi$
$59$	−8.35410	−	6.06961i	−1.08761	−	0.790196i	−0.978994	+	0.203888i	$0.934642\pi$
$60$	0.809017	+	2.48990i	0.104444	+	0.321444i
$61$	−2.20820	−	6.79615i	−0.282732	−	0.870158i	−0.987069	−	0.160293i	$-0.948756\pi$
$61$	−2.20820	−	6.79615i	−0.282732	−	0.870158i	0.704338	−	0.709865i	$-0.251244\pi$
$62$	2.42705	+	1.76336i	0.308236	+	0.223946i
$63$	1.61803	−	1.17557i	0.203853	−	0.148108i
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	−9.09017			−1.12750
$66$	−0.309017	−	3.30220i	−0.0380374	−	0.406472i
$67$	−8.70820			−1.06388			−0.531938	−	0.846783i	$-0.678536\pi$
$67$	−8.70820			−1.06388			−0.531938	+	0.846783i	$0.678536\pi$
$68$	2.30902	−	7.10642i	0.280009	−	0.861780i
$69$	−6.66312	+	4.84104i	−0.802145	+	0.582793i
$70$	2.11803	+	1.53884i	0.253153	+	0.183927i
$71$	−0.927051	−	2.85317i	−0.110021	−	0.338609i	0.880855	−	0.473386i	$-0.156968\pi$
$71$	−0.927051	−	2.85317i	−0.110021	−	0.338609i	−0.990876	+	0.134777i	$0.956968\pi$
$72$	−0.618034	−	1.90211i	−0.0728360	−	0.224166i
$73$	5.54508	+	4.02874i	0.649003	+	0.471528i	0.862931	−	0.505321i	$-0.168626\pi$
$73$	5.54508	+	4.02874i	0.649003	+	0.471528i	−0.213928	+	0.976849i	$0.568626\pi$
$74$	6.35410	−	4.61653i	0.738649	−	0.536660i
$75$	−0.572949	+	1.76336i	−0.0661585	+	0.203615i
$76$	−6.70820			−0.769484
$77$	−2.19098	−	2.48990i	−0.249686	−	0.283750i
$78$	−3.47214			−0.393142
$79$	1.21885	−	3.75123i	0.137131	−	0.422046i	−0.858784	−	0.512337i	$-0.828780\pi$
$79$	1.21885	−	3.75123i	0.137131	−	0.422046i	0.995915	+	0.0902913i	$0.0287798\pi$
$80$	2.11803	−	1.53884i	0.236803	−	0.172048i
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	−0.763932	−	2.35114i	−0.0843622	−	0.259640i
$83$	−1.95492	−	6.01661i	−0.214580	−	0.660409i	−0.999183	−	0.0404107i	$-0.987133\pi$
$83$	−1.95492	−	6.01661i	−0.214580	−	0.660409i	0.784603	−	0.619998i	$-0.212867\pi$
$84$	0.809017	+	0.587785i	0.0882710	+	0.0641326i
$85$	15.8262	−	11.4984i	1.71660	−	1.24718i
$86$	−2.28115	+	7.02067i	−0.245983	+	0.757058i
$87$	0.527864			0.0565930
$88$	−3.04508	+	1.31433i	−0.324607	+	0.140108i
$89$	−3.09017			−0.327557			−0.163779	−	0.986497i	$-0.552368\pi$
$89$	−3.09017			−0.327557			−0.163779	+	0.986497i	$0.552368\pi$
$90$	1.61803	−	4.97980i	0.170556	−	0.524917i
$91$	−2.80902	+	2.04087i	−0.294465	+	0.213941i
$92$	6.66312	+	4.84104i	0.694678	+	0.504713i
$93$	0.927051	+	2.85317i	0.0961307	+	0.295860i
$94$	−0.190983	−	0.587785i	−0.0196984	−	0.0606254i
$95$	−14.2082	−	10.3229i	−1.45773	−	1.05910i
$96$	0.809017	−	0.587785i	0.0825700	−	0.0599906i
$97$	1.09017	−	3.35520i	0.110690	−	0.340669i	−0.880334	−	0.474355i	$-0.842681\pi$
$97$	1.09017	−	3.35520i	0.110690	−	0.340669i	0.991024	+	0.133686i	$0.0426814\pi$
$98$	1.00000			0.101015
$99$	−3.38197	+	5.70634i	−0.339900	+	0.573509i
$100$	1.85410			0.185410
$101$	−0.927051	+	2.85317i	−0.0922450	+	0.283901i	−0.986526	−	0.163605i	$-0.947688\pi$
$101$	−0.927051	+	2.85317i	−0.0922450	+	0.283901i	0.894281	+	0.447506i	$0.147688\pi$
$102$	6.04508	−	4.39201i	0.598553	−	0.434874i
$103$	−3.92705	−	2.85317i	−0.386944	−	0.281131i	0.377258	−	0.926108i	$-0.376867\pi$
$103$	−3.92705	−	2.85317i	−0.386944	−	0.281131i	−0.764202	+	0.644977i	$0.776867\pi$
$104$	1.07295	+	3.30220i	0.105211	+	0.323807i
$105$	0.809017	+	2.48990i	0.0789520	+	0.242989i
$106$	10.2812	+	7.46969i	0.998594	+	0.725521i
$107$	4.11803	−	2.99193i	0.398105	−	0.289240i	−0.370663	−	0.928767i	$-0.620870\pi$
$107$	4.11803	−	2.99193i	0.398105	−	0.289240i	0.768769	+	0.639527i	$0.220870\pi$
$108$	1.54508	−	4.75528i	0.148676	−	0.457577i
$109$	5.32624			0.510161			0.255081	−	0.966920i	$-0.417898\pi$
$109$	5.32624			0.510161			0.255081	+	0.966920i	$0.417898\pi$
$110$	−8.47214	−	1.90211i	−0.807786	−	0.181359i
$111$	7.85410			0.745478
$112$	0.309017	−	0.951057i	0.0291994	−	0.0898664i
$113$	−8.23607	+	5.98385i	−0.774784	+	0.562914i	−0.903409	−	0.428780i	$-0.858944\pi$
$113$	−8.23607	+	5.98385i	−0.774784	+	0.562914i	0.128625	+	0.991693i	$0.458944\pi$
$114$	−5.42705	−	3.94298i	−0.508290	−	0.369294i
$115$	6.66312	+	20.5070i	0.621339	+	1.91228i
$116$	−0.163119	−	0.502029i	−0.0151452	−	0.0466122i
$117$	5.61803	+	4.08174i	0.519387	+	0.377357i
$118$	−8.35410	+	6.06961i	−0.769057	+	0.558753i
$119$	2.30902	−	7.10642i	0.211667	−	0.651445i
$120$	2.61803			0.238993
$121$	9.94427	+	4.70228i	0.904025	+	0.427480i
$122$	−7.14590			−0.646959
$123$	0.763932	−	2.35114i	0.0688814	−	0.211995i
$124$	2.42705	−	1.76336i	0.217956	−	0.158354i
$125$	−6.66312	−	4.84104i	−0.595967	−	0.432996i
$126$	−0.618034	−	1.90211i	−0.0550588	−	0.169454i
$127$	−0.354102	−	1.08981i	−0.0314215	−	0.0967053i	0.934116	−	0.356970i	$-0.116190\pi$
$127$	−0.354102	−	1.08981i	−0.0314215	−	0.0967053i	−0.965537	+	0.260265i	$0.916190\pi$
$128$	−0.809017	−	0.587785i	−0.0715077	−	0.0519534i
$129$	−5.97214	+	4.33901i	−0.525817	+	0.382029i
$130$	−2.80902	+	8.64527i	−0.246367	+	0.758240i
$131$	8.18034			0.714720			0.357360	−	0.933967i	$-0.383677\pi$
$131$	8.18034			0.714720			0.357360	+	0.933967i	$0.383677\pi$
$132$	−3.23607	−	0.726543i	−0.281664	−	0.0632374i
$133$	−6.70820			−0.581675
$134$	−2.69098	+	8.28199i	−0.232466	+	0.715455i
$135$	10.5902	−	7.69421i	0.911457	−	0.662212i
$136$	−6.04508	−	4.39201i	−0.518362	−	0.376612i
$137$	5.23607	+	16.1150i	0.447347	+	1.37679i	0.879889	+	0.475180i	$0.157617\pi$
$137$	5.23607	+	16.1150i	0.447347	+	1.37679i	−0.432541	+	0.901614i	$0.642383\pi$
$138$	2.54508	+	7.83297i	0.216652	+	0.666786i
$139$	0.854102	+	0.620541i	0.0724440	+	0.0526336i	0.623418	−	0.781889i	$-0.285744\pi$
$139$	0.854102	+	0.620541i	0.0724440	+	0.0526336i	−0.550974	+	0.834523i	$0.685744\pi$
$140$	2.11803	−	1.53884i	0.179007	−	0.130056i
$141$	0.190983	−	0.587785i	0.0160837	−	0.0495004i
$142$	−3.00000			−0.251754
$143$	5.87132	−	9.90659i	0.490985	−	0.828431i
$144$	−2.00000			−0.166667
$145$	0.427051	−	1.31433i	0.0354647	−	0.109149i
$146$	5.54508	−	4.02874i	0.458914	−	0.333421i
$147$	0.809017	+	0.587785i	0.0667266	+	0.0484797i
$148$	−2.42705	−	7.46969i	−0.199502	−	0.614005i
$149$	4.04508	+	12.4495i	0.331386	+	1.01990i	0.968475	+	0.249111i	$0.0801386\pi$
$149$	4.04508	+	12.4495i	0.331386	+	1.01990i	−0.637089	+	0.770791i	$0.719861\pi$
$150$	1.50000	+	1.08981i	0.122474	+	0.0889829i
$151$	6.47214	−	4.70228i	0.526695	−	0.382666i	−0.292425	−	0.956288i	$-0.594462\pi$
$151$	6.47214	−	4.70228i	0.526695	−	0.382666i	0.819120	+	0.573622i	$0.194462\pi$
$152$	−2.07295	+	6.37988i	−0.168138	+	0.517477i
$153$	−14.9443			−1.20817
$154$	−3.04508	+	1.31433i	−0.245380	+	0.105912i
$155$	7.85410			0.630857
$156$	−1.07295	+	3.30220i	−0.0859047	+	0.264387i
$157$	6.19098	−	4.49801i	0.494094	−	0.358980i	−0.312662	−	0.949864i	$-0.601221\pi$
$157$	6.19098	−	4.49801i	0.494094	−	0.358980i	0.806757	+	0.590884i	$0.201221\pi$
$158$	−3.19098	−	2.31838i	−0.253861	−	0.184441i
$159$	3.92705	+	12.0862i	0.311435	+	0.958500i
$160$	−0.809017	−	2.48990i	−0.0639584	−	0.196844i
$161$	6.66312	+	4.84104i	0.525127	+	0.381527i
$162$	−0.809017	+	0.587785i	−0.0635624	+	0.0461808i
$163$	−0.736068	+	2.26538i	−0.0576533	+	0.177439i	−0.975736	−	0.218950i	$-0.929737\pi$
$163$	−0.736068	+	2.26538i	−0.0576533	+	0.177439i	0.918083	+	0.396389i	$0.129737\pi$
$164$	−2.47214			−0.193041
$165$	−5.73607	−	6.51864i	−0.446552	−	0.507475i
$166$	−6.32624			−0.491011
$167$	−7.06231	+	21.7355i	−0.546498	+	1.68195i	0.170905	+	0.985288i	$0.445331\pi$
$167$	−7.06231	+	21.7355i	−0.546498	+	1.68195i	−0.717402	+	0.696659i	$0.754669\pi$
$168$	0.809017	−	0.587785i	0.0624170	−	0.0453486i
$169$	0.763932	+	0.555029i	0.0587640	+	0.0426945i
$170$	−6.04508	−	18.6049i	−0.463637	−	1.42693i
$171$	4.14590	+	12.7598i	0.317045	+	0.975763i
$172$	5.97214	+	4.33901i	0.455371	+	0.330846i
$173$	−4.19098	+	3.04493i	−0.318635	+	0.231502i	−0.735593	−	0.677424i	$-0.763096\pi$
$173$	−4.19098	+	3.04493i	−0.318635	+	0.231502i	0.416958	+	0.908926i	$0.363096\pi$
$174$	0.163119	−	0.502029i	0.0123660	−	0.0380587i
$175$	1.85410			0.140157
$176$	0.309017	+	3.30220i	0.0232930	+	0.248913i
$177$	−10.3262			−0.776168
$178$	−0.954915	+	2.93893i	−0.0715739	+	0.220282i
$179$	7.50000	−	5.44907i	0.560576	−	0.407283i	−0.271094	−	0.962553i	$-0.587385\pi$
$179$	7.50000	−	5.44907i	0.560576	−	0.407283i	0.831670	+	0.555270i	$0.187385\pi$
$180$	−4.23607	−	3.07768i	−0.315738	−	0.229397i
$181$	0.0901699	+	0.277515i	0.00670228	+	0.0206275i	0.954352	−	0.298685i	$-0.0965480\pi$
$181$	0.0901699	+	0.277515i	0.00670228	+	0.0206275i	−0.947649	+	0.319313i	$0.896548\pi$
$182$	1.07295	+	3.30220i	0.0795323	+	0.244775i
$183$	−5.78115	−	4.20025i	−0.427355	−	0.310492i
$184$	6.66312	−	4.84104i	0.491212	−	0.356886i
$185$	6.35410	−	19.5559i	0.467163	−	1.43778i
$186$	3.00000			0.219971
$187$	2.30902	+	24.6745i	0.168852	+	1.80438i
$188$	−0.618034			−0.0450748
$189$	1.54508	−	4.75528i	0.112388	−	0.345896i
$190$	−14.2082	+	10.3229i	−1.03077	+	0.748899i
$191$	1.30902	+	0.951057i	0.0947171	+	0.0688160i	0.634136	−	0.773222i	$-0.281356\pi$
$191$	1.30902	+	0.951057i	0.0947171	+	0.0688160i	−0.539419	+	0.842038i	$0.681356\pi$
$192$	−0.309017	−	0.951057i	−0.0223014	−	0.0686366i
$193$	−8.07295	−	24.8460i	−0.581104	−	1.78845i	−0.614384	−	0.789007i	$-0.710596\pi$
$193$	−8.07295	−	24.8460i	−0.581104	−	1.78845i	0.0332808	−	0.999446i	$-0.489404\pi$
$194$	−2.85410	−	2.07363i	−0.204913	−	0.148878i
$195$	−7.35410	+	5.34307i	−0.526638	+	0.382625i
$196$	0.309017	−	0.951057i	0.0220726	−	0.0679326i
$197$	−12.3262			−0.878208			−0.439104	−	0.898436i	$-0.644704\pi$
$197$	−12.3262			−0.878208			−0.439104	+	0.898436i	$0.644704\pi$
$198$	4.38197	+	4.97980i	0.311413	+	0.353899i
$199$	−1.70820			−0.121091			−0.0605457	−	0.998165i	$-0.519284\pi$
$199$	−1.70820			−0.121091			−0.0605457	+	0.998165i	$0.519284\pi$
$200$	0.572949	−	1.76336i	0.0405136	−	0.124688i
$201$	−7.04508	+	5.11855i	−0.496922	+	0.361035i
$202$	2.42705	+	1.76336i	0.170767	+	0.124069i
$203$	−0.163119	−	0.502029i	−0.0114487	−	0.0352355i
$204$	−2.30902	−	7.10642i	−0.161664	−	0.497549i
$205$	−5.23607	−	3.80423i	−0.365703	−	0.265699i
$206$	−3.92705	+	2.85317i	−0.273611	+	0.198790i
$207$	5.09017	−	15.6659i	0.353791	−	1.08886i
$208$	3.47214			0.240749
$209$	20.4271	−	8.81678i	1.41297	−	0.609869i
$210$	2.61803			0.180662
$211$	−1.98278	+	6.10237i	−0.136500	+	0.420104i	−0.995820	−	0.0913337i	$-0.970887\pi$
$211$	−1.98278	+	6.10237i	−0.136500	+	0.420104i	0.859320	+	0.511438i	$0.170887\pi$
$212$	10.2812	−	7.46969i	0.706112	−	0.513021i
$213$	−2.42705	−	1.76336i	−0.166299	−	0.120823i
$214$	−1.57295	−	4.84104i	−0.107525	−	0.330927i
$215$	5.97214	+	18.3803i	0.407296	+	1.25353i
$216$	−4.04508	−	2.93893i	−0.275233	−	0.199969i
$217$	2.42705	−	1.76336i	0.164759	−	0.119704i
$218$	1.64590	−	5.06555i	0.111474	−	0.343083i
$219$	6.85410			0.463157
$220$	−4.42705	+	7.46969i	−0.298472	+	0.503607i
$221$	25.9443			1.74520
$222$	2.42705	−	7.46969i	0.162893	−	0.501333i
$223$	−6.16312	+	4.47777i	−0.412713	+	0.299854i	−0.774699	−	0.632330i	$-0.782099\pi$
$223$	−6.16312	+	4.47777i	−0.412713	+	0.299854i	0.361986	+	0.932183i	$0.382099\pi$
$224$	−0.809017	−	0.587785i	−0.0540547	−	0.0392731i
$225$	−1.14590	−	3.52671i	−0.0763932	−	0.235114i
$226$	3.14590	+	9.68208i	0.209262	+	0.644042i
$227$	−15.6803	−	11.3924i	−1.04074	−	0.756142i	−0.0703107	−	0.997525i	$-0.522399\pi$
$227$	−15.6803	−	11.3924i	−1.04074	−	0.756142i	−0.970430	+	0.241383i	$0.922399\pi$
$228$	−5.42705	+	3.94298i	−0.359415	+	0.261130i
$229$	5.26393	−	16.2007i	0.347850	−	1.07057i	−0.612190	−	0.790711i	$-0.709711\pi$
$229$	5.26393	−	16.2007i	0.347850	−	1.07057i	0.960040	−	0.279863i	$-0.0902889\pi$
$230$	21.5623			1.42178
$231$	−3.23607	−	0.726543i	−0.212918	−	0.0478030i
$232$	−0.527864			−0.0346560
$233$	7.41641	−	22.8254i	0.485865	−	1.49534i	−0.344859	−	0.938654i	$-0.612073\pi$
$233$	7.41641	−	22.8254i	0.485865	−	1.49534i	0.830724	−	0.556684i	$-0.187927\pi$
$234$	5.61803	−	4.08174i	0.367262	−	0.266832i
$235$	−1.30902	−	0.951057i	−0.0853909	−	0.0620401i
$236$	3.19098	+	9.82084i	0.207715	+	0.639282i
$237$	−1.21885	−	3.75123i	−0.0791726	−	0.243668i
$238$	−6.04508	−	4.39201i	−0.391845	−	0.284692i
$239$	1.11803	−	0.812299i	0.0723196	−	0.0525433i	−0.551038	−	0.834480i	$-0.685768\pi$
$239$	1.11803	−	0.812299i	0.0723196	−	0.0525433i	0.623358	+	0.781937i	$0.285768\pi$
$240$	0.809017	−	2.48990i	0.0522218	−	0.160722i
$241$	−1.61803			−0.104227			−0.0521134	−	0.998641i	$-0.516596\pi$
$241$	−1.61803			−0.104227			−0.0521134	+	0.998641i	$0.516596\pi$
$242$	7.54508	−	8.00448i	0.485016	−	0.514547i
$243$	−16.0000			−1.02640
$244$	−2.20820	+	6.79615i	−0.141366	+	0.435079i
$245$	2.11803	−	1.53884i	0.135316	−	0.0983130i
$246$	−2.00000	−	1.45309i	−0.127515	−	0.0926453i
$247$	−7.19756	−	22.1518i	−0.457970	−	1.40949i
$248$	−0.927051	−	2.85317i	−0.0588678	−	0.181176i
$249$	−5.11803	−	3.71847i	−0.324342	−	0.235648i
$250$	−6.66312	+	4.84104i	−0.421413	+	0.306174i
$251$	−3.85410	+	11.8617i	−0.243269	+	0.748704i	0.752648	+	0.658424i	$0.228776\pi$
$251$	−3.85410	+	11.8617i	−0.243269	+	0.748704i	−0.995916	+	0.0902807i	$0.971224\pi$
$252$	−2.00000			−0.125988
$253$	−26.6525	−	5.98385i	−1.67563	−	0.376202i
$254$	−1.14590			−0.0719000
$255$	6.04508	−	18.6049i	0.378558	−	1.16508i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	−11.3713	−	8.26175i	−0.709324	−	0.515354i	0.173632	−	0.984811i	$-0.444450\pi$
$257$	−11.3713	−	8.26175i	−0.709324	−	0.515354i	−0.882955	+	0.469457i	$0.844450\pi$
$258$	2.28115	+	7.02067i	0.142018	+	0.437088i
$259$	−2.42705	−	7.46969i	−0.150810	−	0.464144i
$260$	7.35410	+	5.34307i	0.456082	+	0.331363i
$261$	−0.854102	+	0.620541i	−0.0528676	+	0.0384105i
$262$	2.52786	−	7.77997i	0.156172	−	0.480648i
$263$	22.6180			1.39469			0.697344	−	0.716737i	$-0.254365\pi$
$263$	22.6180			1.39469			0.697344	+	0.716737i	$0.254365\pi$
$264$	−1.69098	+	2.85317i	−0.104073	+	0.175600i
$265$	33.2705			2.04379
$266$	−2.07295	+	6.37988i	−0.127101	+	0.391176i
$267$	−2.50000	+	1.81636i	−0.152998	+	0.111159i
$268$	7.04508	+	5.11855i	0.430347	+	0.312665i
$269$	−1.48278	−	4.56352i	−0.0904066	−	0.278243i	0.895623	−	0.444814i	$-0.146730\pi$
$269$	−1.48278	−	4.56352i	−0.0904066	−	0.278243i	−0.986029	+	0.166571i	$0.946730\pi$
$270$	−4.04508	−	12.4495i	−0.246176	−	0.757652i
$271$	3.54508	+	2.57565i	0.215349	+	0.156460i	0.690230	−	0.723590i	$-0.257509\pi$
$271$	3.54508	+	2.57565i	0.215349	+	0.156460i	−0.474882	+	0.880050i	$0.657509\pi$
$272$	−6.04508	+	4.39201i	−0.366537	+	0.266305i
$273$	−1.07295	+	3.30220i	−0.0649378	+	0.199858i
$274$	16.9443			1.02364
$275$	−5.64590	+	2.43690i	−0.340460	+	0.146950i
$276$	8.23607			0.495753
$277$	−9.76393	+	30.0503i	−0.586658	+	1.80555i	0.00585065	+	0.999983i	$0.498138\pi$
$277$	−9.76393	+	30.0503i	−0.586658	+	1.80555i	−0.592508	+	0.805564i	$0.701862\pi$
$278$	0.854102	−	0.620541i	0.0512256	−	0.0372176i
$279$	−4.85410	−	3.52671i	−0.290607	−	0.211139i
$280$	−0.809017	−	2.48990i	−0.0483480	−	0.148800i
$281$	5.88197	+	18.1028i	0.350889	+	1.07992i	0.958355	+	0.285579i	$0.0921859\pi$
$281$	5.88197	+	18.1028i	0.350889	+	1.07992i	−0.607466	+	0.794345i	$0.707814\pi$
$282$	−0.500000	−	0.363271i	−0.0297746	−	0.0216325i
$283$	11.6631	−	8.47375i	0.693300	−	0.503712i	−0.184443	−	0.982843i	$-0.559048\pi$
$283$	11.6631	−	8.47375i	0.693300	−	0.503712i	0.877743	+	0.479131i	$0.159048\pi$
$284$	−0.927051	+	2.85317i	−0.0550104	+	0.169304i
$285$	−17.5623			−1.04030
$286$	−7.60739	−	8.64527i	−0.449834	−	0.511205i
$287$	−2.47214			−0.145926
$288$	−0.618034	+	1.90211i	−0.0364180	+	0.112083i
$289$	−31.4164	+	22.8254i	−1.84802	+	1.34267i
$290$	−1.11803	−	0.812299i	−0.0656532	−	0.0476999i
$291$	−1.09017	−	3.35520i	−0.0639069	−	0.196685i
$292$	−2.11803	−	6.51864i	−0.123949	−	0.381474i
$293$	−7.54508	−	5.48183i	−0.440789	−	0.320252i	0.345160	−	0.938544i	$-0.387825\pi$
$293$	−7.54508	−	5.48183i	−0.440789	−	0.320252i	−0.785948	+	0.618292i	$0.787825\pi$
$294$	0.809017	−	0.587785i	0.0471828	−	0.0342803i
$295$	−8.35410	+	25.7113i	−0.486395	+	1.49697i
$296$	−7.85410			−0.456510
$297$	1.54508	+	16.5110i	0.0896549	+	0.958065i
$298$	13.0902			0.758293
$299$	−8.83688	+	27.1971i	−0.511050	+	1.57285i
$300$	1.50000	−	1.08981i	0.0866025	−	0.0629204i
$301$	5.97214	+	4.33901i	0.344228	+	0.250096i
$302$	−2.47214	−	7.60845i	−0.142255	−	0.437817i
$303$	0.927051	+	2.85317i	0.0532577	+	0.163910i
$304$	5.42705	+	3.94298i	0.311263	+	0.226146i
$305$	−15.1353	+	10.9964i	−0.866642	+	0.629652i
$306$	−4.61803	+	14.2128i	−0.263995	+	0.812494i
$307$	16.4164			0.936934			0.468467	−	0.883481i	$-0.344807\pi$
$307$	16.4164			0.936934			0.468467	+	0.883481i	$0.344807\pi$
$308$	0.309017	+	3.30220i	0.0176079	+	0.188160i
$309$	−4.85410			−0.276140
$310$	2.42705	−	7.46969i	0.137847	−	0.424250i
$311$	7.42705	−	5.39607i	0.421149	−	0.305983i	−0.356951	−	0.934123i	$-0.616184\pi$
$311$	7.42705	−	5.39607i	0.421149	−	0.305983i	0.778100	+	0.628140i	$0.216184\pi$
$312$	2.80902	+	2.04087i	0.159029	+	0.115542i
$313$	−9.35410	−	28.7890i	−0.528725	−	1.62725i	−0.756830	−	0.653612i	$-0.773253\pi$
$313$	−9.35410	−	28.7890i	−0.528725	−	1.62725i	0.228105	−	0.973637i	$-0.426747\pi$
$314$	−2.36475	−	7.27794i	−0.133450	−	0.410718i
$315$	−4.23607	−	3.07768i	−0.238675	−	0.173408i
$316$	−3.19098	+	2.31838i	−0.179507	+	0.130419i
$317$	7.83688	−	24.1194i	0.440163	−	1.35468i	−0.447539	−	0.894264i	$-0.647699\pi$
$317$	7.83688	−	24.1194i	0.440163	−	1.35468i	0.887702	−	0.460418i	$-0.152301\pi$
$318$	12.7082			0.712641
$319$	1.15654	+	1.31433i	0.0647539	+	0.0735882i
$320$	−2.61803			−0.146353
$321$	1.57295	−	4.84104i	0.0877935	−	0.270200i
$322$	6.66312	−	4.84104i	0.371321	−	0.269781i
$323$	40.5517	+	29.4625i	2.25635	+	1.63934i
$324$	0.309017	+	0.951057i	0.0171676	+	0.0528365i
$325$	1.98936	+	6.12261i	0.110350	+	0.339621i
$326$	1.92705	+	1.40008i	0.106729	+	0.0775435i
$327$	4.30902	−	3.13068i	0.238289	−	0.173127i
$328$	−0.763932	+	2.35114i	−0.0421811	+	0.129820i
$329$	−0.618034			−0.0340733
$330$	−7.97214	+	3.44095i	−0.438852	+	0.189418i
$331$	−19.7082			−1.08326			−0.541630	−	0.840617i	$-0.682193\pi$
$331$	−19.7082			−1.08326			−0.541630	+	0.840617i	$0.682193\pi$
$332$	−1.95492	+	6.01661i	−0.107290	+	0.330204i
$333$	−12.7082	+	9.23305i	−0.696405	+	0.505968i
$334$	18.4894	+	13.4333i	1.01169	+	0.735038i
$335$	7.04508	+	21.6825i	0.384914	+	1.18464i
$336$	−0.309017	−	0.951057i	−0.0168583	−	0.0518844i
$337$	−10.3541	−	7.52270i	−0.564024	−	0.409787i	0.268906	−	0.963167i	$-0.413338\pi$
$337$	−10.3541	−	7.52270i	−0.564024	−	0.409787i	−0.832929	+	0.553379i	$0.813338\pi$
$338$	0.763932	−	0.555029i	0.0415524	−	0.0301896i
$339$	−3.14590	+	9.68208i	−0.170862	+	0.525858i
$340$	−19.5623			−1.06091
$341$	−5.07295	+	8.55951i	−0.274716	+	0.463523i
$342$	13.4164			0.725476
$343$	0.309017	−	0.951057i	0.0166853	−	0.0513522i
$344$	5.97214	−	4.33901i	0.321996	−	0.233944i
$345$	17.4443	+	12.6740i	0.939168	+	0.682346i
$346$	1.60081	+	4.92680i	0.0860602	+	0.264866i
$347$	1.25329	+	3.85723i	0.0672801	+	0.207067i	0.979044	−	0.203647i	$-0.0652795\pi$
$347$	1.25329	+	3.85723i	0.0672801	+	0.207067i	−0.911764	+	0.410714i	$0.865280\pi$
$348$	−0.427051	−	0.310271i	−0.0228923	−	0.0166323i
$349$	−21.7082	+	15.7719i	−1.16201	+	0.844252i	−0.990031	−	0.140848i	$-0.955017\pi$
$349$	−21.7082	+	15.7719i	−1.16201	+	0.844252i	−0.171982	+	0.985100i	$0.555017\pi$
$350$	0.572949	−	1.76336i	0.0306254	−	0.0942553i
$351$	17.3607			0.926645
$352$	3.23607	+	0.726543i	0.172483	+	0.0387248i
$353$	−12.9098			−0.687121			−0.343560	−	0.939131i	$-0.611633\pi$
$353$	−12.9098			−0.687121			−0.343560	+	0.939131i	$0.611633\pi$
$354$	−3.19098	+	9.82084i	−0.169599	+	0.521972i
$355$	−6.35410	+	4.61653i	−0.337241	+	0.245020i
$356$	2.50000	+	1.81636i	0.132500	+	0.0962667i
$357$	−2.30902	−	7.10642i	−0.122206	−	0.376112i
$358$	−2.86475	−	8.81678i	−0.151406	−	0.465981i
$359$	−9.63525	−	7.00042i	−0.508529	−	0.369468i	0.303736	−	0.952756i	$-0.401766\pi$
$359$	−9.63525	−	7.00042i	−0.508529	−	0.369468i	−0.812265	+	0.583288i	$0.801766\pi$
$360$	−4.23607	+	3.07768i	−0.223260	+	0.162208i
$361$	8.03444	−	24.7275i	0.422865	−	1.30145i
$362$	0.291796			0.0153365
$363$	10.8090	−	2.04087i	0.567326	−	0.107118i
$364$	3.47214			0.181989
$365$	5.54508	−	17.0660i	0.290243	−	0.893276i
$366$	−5.78115	+	4.20025i	−0.302186	+	0.219551i
$367$	−2.42705	−	1.76336i	−0.126691	−	0.0920464i	0.522635	−	0.852556i	$-0.324949\pi$
$367$	−2.42705	−	1.76336i	−0.126691	−	0.0920464i	−0.649326	+	0.760510i	$0.724949\pi$
$368$	−2.54508	−	7.83297i	−0.132672	−	0.408322i
$369$	1.52786	+	4.70228i	0.0795374	+	0.244791i
$370$	−16.6353	−	12.0862i	−0.864826	−	0.628333i
$371$	10.2812	−	7.46969i	0.533771	−	0.387807i
$372$	0.927051	−	2.85317i	0.0480654	−	0.147930i
$373$	19.6525			1.01757			0.508783	−	0.860895i	$-0.330095\pi$
$373$	19.6525			1.01757			0.508783	+	0.860895i	$0.330095\pi$
$374$	24.1803	+	5.42882i	1.25034	+	0.280718i
$375$	−8.23607			−0.425309
$376$	−0.190983	+	0.587785i	−0.00984920	+	0.0303127i
$377$	1.48278	−	1.07730i	0.0763670	−	0.0554839i
$378$	−4.04508	−	2.93893i	−0.208057	−	0.151162i
$379$	−4.96149	−	15.2699i	−0.254855	−	0.784362i	−0.993858	−	0.110661i	$-0.964703\pi$
$379$	−4.96149	−	15.2699i	−0.254855	−	0.784362i	0.739003	−	0.673702i	$-0.235297\pi$
$380$	5.42705	+	16.7027i	0.278402	+	0.856833i
$381$	−0.927051	−	0.673542i	−0.0474943	−	0.0345066i
$382$	1.30902	−	0.951057i	0.0669751	−	0.0486603i
$383$	4.95492	−	15.2497i	0.253184	−	0.779221i	−0.740998	−	0.671508i	$-0.765647\pi$
$383$	4.95492	−	15.2497i	0.253184	−	0.779221i	0.994182	−	0.107714i	$-0.0343530\pi$
$384$	−1.00000			−0.0510310
$385$	−4.42705	+	7.46969i	−0.225623	+	0.380691i
$386$	−26.1246			−1.32971
$387$	4.56231	−	14.0413i	0.231915	−	0.713761i
$388$	−2.85410	+	2.07363i	−0.144895	+	0.105272i
$389$	21.4443	+	15.5802i	1.08727	+	0.789946i	0.978936	−	0.204169i	$-0.0654491\pi$
$389$	21.4443	+	15.5802i	1.08727	+	0.789946i	0.108332	+	0.994115i	$0.465449\pi$
$390$	2.80902	+	8.64527i	0.142240	+	0.437770i
$391$	−19.0172	−	58.5290i	−0.961742	−	2.95994i
$392$	−0.809017	−	0.587785i	−0.0408615	−	0.0296876i
$393$	6.61803	−	4.80828i	0.333836	−	0.242546i
$394$	−3.80902	+	11.7229i	−0.191896	+	0.590594i
$395$	−10.3262			−0.519569
$396$	6.09017	−	2.62866i	0.306043	−	0.132095i
$397$	24.7082			1.24007			0.620035	−	0.784574i	$-0.287119\pi$
$397$	24.7082			1.24007			0.620035	+	0.784574i	$0.287119\pi$
$398$	−0.527864	+	1.62460i	−0.0264594	+	0.0814338i
$399$	−5.42705	+	3.94298i	−0.271692	+	0.197396i
$400$	−1.50000	−	1.08981i	−0.0750000	−	0.0544907i
$401$	3.87132	+	11.9147i	0.193325	+	0.594992i	0.999992	+	0.00398641i	$0.00126892\pi$
$401$	3.87132	+	11.9147i	0.193325	+	0.594992i	−0.806667	+	0.591006i	$0.798731\pi$
$402$	2.69098	+	8.28199i	0.134214	+	0.413068i
$403$	8.42705	+	6.12261i	0.419781	+	0.304989i
$404$	2.42705	−	1.76336i	0.120750	−	0.0877302i
$405$	−0.809017	+	2.48990i	−0.0402004	+	0.123724i
$406$	−0.527864			−0.0261975
$407$	17.2082	+	19.5559i	0.852979	+	0.969351i
$408$	−7.47214			−0.369926
$409$	2.07295	−	6.37988i	0.102501	−	0.315465i	−0.886635	−	0.462470i	$-0.846963\pi$
$409$	2.07295	−	6.37988i	0.102501	−	0.315465i	0.989136	+	0.147005i	$0.0469634\pi$
$410$	−5.23607	+	3.80423i	−0.258591	+	0.187877i
$411$	13.7082	+	9.95959i	0.676176	+	0.491271i
$412$	1.50000	+	4.61653i	0.0738997	+	0.227440i
$413$	3.19098	+	9.82084i	0.157018	+	0.483252i
$414$	−13.3262	−	9.68208i	−0.654949	−	0.475848i
$415$	−13.3992	+	9.73508i	−0.657740	+	0.477876i
$416$	1.07295	−	3.30220i	0.0526057	−	0.161904i
$417$	1.05573			0.0516992
$418$	−2.07295	−	22.1518i	−0.101391	−	1.08348i
$419$	11.5066			0.562133			0.281067	−	0.959688i	$-0.409312\pi$
$419$	11.5066			0.562133			0.281067	+	0.959688i	$0.409312\pi$
$420$	0.809017	−	2.48990i	0.0394760	−	0.121495i
$421$	13.6074	−	9.88635i	0.663184	−	0.481831i	−0.204553	−	0.978856i	$-0.565574\pi$
$421$	13.6074	−	9.88635i	0.663184	−	0.481831i	0.867737	+	0.497024i	$0.165574\pi$
$422$	5.19098	+	3.77147i	0.252693	+	0.183592i
$423$	0.381966	+	1.17557i	0.0185718	+	0.0571582i
$424$	−3.92705	−	12.0862i	−0.190714	−	0.586959i
$425$	−11.2082	−	8.14324i	−0.543678	−	0.395005i
$426$	−2.42705	+	1.76336i	−0.117591	+	0.0854349i
$427$	−2.20820	+	6.79615i	−0.106862	+	0.328889i
$428$	−5.09017			−0.246043
$429$	−1.07295	−	11.4657i	−0.0518025	−	0.553568i
$430$	19.3262			0.931994
$431$	8.21885	−	25.2950i	0.395888	−	1.21842i	−0.532380	−	0.846506i	$-0.678702\pi$
$431$	8.21885	−	25.2950i	0.395888	−	1.21842i	0.928268	−	0.371912i	$-0.121298\pi$
$432$	−4.04508	+	2.93893i	−0.194619	+	0.141399i
$433$	2.19098	+	1.59184i	0.105292	+	0.0764991i	0.639185	−	0.769053i	$-0.279272\pi$
$433$	2.19098	+	1.59184i	0.105292	+	0.0764991i	−0.533893	+	0.845552i	$0.679272\pi$
$434$	−0.927051	−	2.85317i	−0.0444999	−	0.136957i
$435$	−0.427051	−	1.31433i	−0.0204755	−	0.0630172i
$436$	−4.30902	−	3.13068i	−0.206364	−	0.149933i
$437$	−44.6976	+	32.4747i	−2.13817	+	1.55347i
$438$	2.11803	−	6.51864i	0.101204	−	0.311473i
$439$	−21.7082			−1.03608			−0.518038	−	0.855358i	$-0.673337\pi$
$439$	−21.7082			−1.03608			−0.518038	+	0.855358i	$0.673337\pi$
$440$	5.73607	+	6.51864i	0.273456	+	0.310764i
$441$	−2.00000			−0.0952381
$442$	8.01722	−	24.6745i	0.381340	−	1.17364i
$443$	20.3435	−	14.7804i	0.966547	−	0.702237i	0.0118849	−	0.999929i	$-0.496217\pi$
$443$	20.3435	−	14.7804i	0.966547	−	0.702237i	0.954662	+	0.297692i	$0.0962168\pi$
$444$	−6.35410	−	4.61653i	−0.301552	−	0.219091i
$445$	2.50000	+	7.69421i	0.118511	+	0.364740i
$446$	2.35410	+	7.24518i	0.111470	+	0.343069i
$447$	10.5902	+	7.69421i	0.500898	+	0.363924i
$448$	−0.809017	+	0.587785i	−0.0382225	+	0.0277702i
$449$	1.48278	−	4.56352i	0.0699767	−	0.215366i	−0.909952	−	0.414713i	$-0.863882\pi$
$449$	1.48278	−	4.56352i	0.0699767	−	0.215366i	0.979929	+	0.199347i	$0.0638820\pi$
$450$	−3.70820			−0.174806
$451$	7.52786	−	3.24920i	0.354473	−	0.152999i
$452$	10.1803			0.478843
$453$	2.47214	−	7.60845i	0.116151	−	0.357476i
$454$	−15.6803	+	11.3924i	−0.735915	+	0.534673i
$455$	7.35410	+	5.34307i	0.344766	+	0.250487i
$456$	2.07295	+	6.37988i	0.0970747	+	0.298765i
$457$	3.52786	+	10.8576i	0.165027	+	0.507899i	0.999038	−	0.0438473i	$-0.0139615\pi$
$457$	3.52786	+	10.8576i	0.165027	+	0.507899i	−0.834012	+	0.551747i	$0.813962\pi$
$458$	−13.7812	−	10.0126i	−0.643951	−	0.467858i
$459$	−30.2254	+	21.9601i	−1.41080	+	1.02501i
$460$	6.66312	−	20.5070i	0.310670	−	0.956142i
$461$	2.72949			0.127125			0.0635625	−	0.997978i	$-0.479754\pi$
$461$	2.72949			0.127125			0.0635625	+	0.997978i	$0.479754\pi$
$462$	−1.69098	+	2.85317i	−0.0786716	+	0.132741i
$463$	−21.9787			−1.02144			−0.510719	−	0.859748i	$-0.670621\pi$
$463$	−21.9787			−1.02144			−0.510719	+	0.859748i	$0.670621\pi$
$464$	−0.163119	+	0.502029i	−0.00757261	+	0.0233061i
$465$	6.35410	−	4.61653i	0.294664	−	0.214086i
$466$	−19.4164	−	14.1068i	−0.899448	−	0.653487i
$467$	−11.1074	−	34.1850i	−0.513989	−	1.58189i	−0.785114	−	0.619351i	$-0.787396\pi$
$467$	−11.1074	−	34.1850i	−0.513989	−	1.58189i	0.271126	−	0.962544i	$-0.412604\pi$
$468$	−2.14590	−	6.60440i	−0.0991942	−	0.305288i
$469$	7.04508	+	5.11855i	0.325312	+	0.236353i
$470$	−1.30902	+	0.951057i	−0.0603805	+	0.0438690i
$471$	2.36475	−	7.27794i	0.108962	−	0.335350i
$472$	10.3262			0.475304
$473$	−23.8885	−	5.36331i	−1.09840	−	0.246605i
$474$	−3.94427			−0.181166
$475$	−3.84346	+	11.8290i	−0.176350	+	0.542749i
$476$	−6.04508	+	4.39201i	−0.277076	+	0.201308i
$477$	−20.5623	−	14.9394i	−0.941483	−	0.684028i
$478$	−0.427051	−	1.31433i	−0.0195329	−	0.0601160i
$479$	−12.4377	−	38.2793i	−0.568293	−	1.74903i	−0.657959	−	0.753053i	$-0.728580\pi$
$479$	−12.4377	−	38.2793i	−0.568293	−	1.74903i	0.0896666	−	0.995972i	$-0.471420\pi$
$480$	−2.11803	−	1.53884i	−0.0966746	−	0.0702382i
$481$	22.0623	−	16.0292i	1.00595	−	0.730869i
$482$	−0.500000	+	1.53884i	−0.0227744	+	0.0700923i
$483$	8.23607			0.374754
$484$	−5.28115	−	9.64932i	−0.240052	−	0.438606i
$485$	−9.23607			−0.419388
$486$	−4.94427	+	15.2169i	−0.224277	+	0.690253i
$487$	−13.2812	+	9.64932i	−0.601826	+	0.437253i	−0.846527	−	0.532346i	$-0.821310\pi$
$487$	−13.2812	+	9.64932i	−0.601826	+	0.437253i	0.244700	+	0.969599i	$0.421310\pi$
$488$	5.78115	+	4.20025i	0.261700	+	0.190137i
$489$	0.736068	+	2.26538i	0.0332861	+	0.102444i
$490$	−0.809017	−	2.48990i	−0.0365477	−	0.112482i
$491$	11.6353	+	8.45351i	0.525092	+	0.381501i	0.818519	−	0.574480i	$-0.194796\pi$
$491$	11.6353	+	8.45351i	0.525092	+	0.381501i	−0.293427	+	0.955982i	$0.594796\pi$
$492$	−2.00000	+	1.45309i	−0.0901670	+	0.0655101i
$493$	−1.21885	+	3.75123i	−0.0548941	+	0.168947i
$494$	−23.2918			−1.04795
$495$	16.9443	+	3.80423i	0.761588	+	0.170987i
$496$	−3.00000			−0.134704
$497$	−0.927051	+	2.85317i	−0.0415839	+	0.127982i
$498$	−5.11803	+	3.71847i	−0.229345	+	0.166629i
$499$	6.80902	+	4.94704i	0.304813	+	0.221460i	0.729668	−	0.683802i	$-0.239675\pi$
$499$	6.80902	+	4.94704i	0.304813	+	0.221460i	−0.424854	+	0.905262i	$0.639675\pi$
$500$	2.54508	+	7.83297i	0.113820	+	0.350301i
$501$	7.06231	+	21.7355i	0.315521	+	0.971072i
$502$	10.0902	+	7.33094i	0.450346	+	0.327196i
$503$	−8.13525	+	5.91061i	−0.362733	+	0.263541i	−0.754191	−	0.656655i	$-0.771971\pi$
$503$	−8.13525	+	5.91061i	−0.362733	+	0.263541i	0.391458	+	0.920196i	$0.371971\pi$
$504$	−0.618034	+	1.90211i	−0.0275294	+	0.0847268i
$505$	7.85410			0.349503
$506$	−13.9271	+	23.4989i	−0.619133	+	1.04465i
$507$	0.944272			0.0419366
$508$	−0.354102	+	1.08981i	−0.0157107	+	0.0483527i
$509$	34.7984	−	25.2825i	1.54241	−	1.12063i	0.593610	−	0.804753i	$-0.297702\pi$
$509$	34.7984	−	25.2825i	1.54241	−	1.12063i	0.948801	−	0.315874i	$-0.102298\pi$
$510$	−15.8262	−	11.4984i	−0.700798	−	0.509159i
$511$	−2.11803	−	6.51864i	−0.0936963	−	0.288368i
$512$	0.309017	+	0.951057i	0.0136568	+	0.0420312i
$513$	27.1353	+	19.7149i	1.19805	+	0.870435i
$514$	−11.3713	+	8.26175i	−0.501568	+	0.364410i
$515$	−3.92705	+	12.0862i	−0.173047	+	0.532582i
$516$	7.38197			0.324973
$517$	1.88197	−	0.812299i	0.0827688	−	0.0357249i
$518$	−7.85410			−0.345089
$519$	−1.60081	+	4.92680i	−0.0702679	+	0.216262i
$520$	7.35410	−	5.34307i	0.322499	−	0.234309i
$521$	−23.4894	−	17.0660i	−1.02909	−	0.747676i	−0.0609616	−	0.998140i	$-0.519417\pi$
$521$	−23.4894	−	17.0660i	−1.02909	−	0.747676i	−0.968126	+	0.250464i	$0.919417\pi$
$522$	0.326238	+	1.00406i	0.0142790	+	0.0439464i
$523$	7.45492	+	22.9439i	0.325981	+	1.00327i	0.970996	+	0.239096i	$0.0768510\pi$
$523$	7.45492	+	22.9439i	0.325981	+	1.00327i	−0.645015	+	0.764170i	$0.723149\pi$
$524$	−6.61803	−	4.80828i	−0.289110	−	0.210051i
$525$	1.50000	−	1.08981i	0.0654654	−	0.0475634i
$526$	6.98936	−	21.5110i	0.304750	−	0.937925i
$527$	−22.4164			−0.976474
$528$	2.19098	+	2.48990i	0.0953503	+	0.108359i
$529$	44.8328			1.94925
$530$	10.2812	−	31.6421i	0.446585	−	1.37445i
$531$	16.7082	−	12.1392i	0.725074	−	0.526797i
$532$	5.42705	+	3.94298i	0.235293	+	0.170950i
$533$	−2.65248	−	8.16348i	−0.114891	−	0.353600i
$534$	0.954915	+	2.93893i	0.0413232	+	0.127180i
$535$	−10.7812	−	7.83297i	−0.466110	−	0.338649i
$536$	7.04508	−	5.11855i	0.304301	−	0.221088i
$537$	2.86475	−	8.81678i	0.123623	−	0.380472i
$538$	−4.79837			−0.206873
$539$	0.309017	+	3.30220i	0.0133103	+	0.142236i
$540$	−13.0902			−0.563311
$541$	−7.14590	+	21.9928i	−0.307226	+	0.945545i	0.671611	+	0.740904i	$0.265603\pi$
$541$	−7.14590	+	21.9928i	−0.307226	+	0.945545i	−0.978837	+	0.204641i	$0.934397\pi$
$542$	3.54508	−	2.57565i	0.152274	−	0.110634i
$543$	0.236068	+	0.171513i	0.0101306	+	0.00736035i
$544$	2.30902	+	7.10642i	0.0989983	+	0.304685i
$545$	−4.30902	−	13.2618i	−0.184578	−	0.568073i
$546$	2.80902	+	2.04087i	0.120215	+	0.0873412i
$547$	15.9894	−	11.6169i	0.683656	−	0.496705i	−0.190913	−	0.981607i	$-0.561145\pi$
$547$	15.9894	−	11.6169i	0.683656	−	0.496705i	0.874568	+	0.484902i	$0.161145\pi$
$548$	5.23607	−	16.1150i	0.223674	−	0.688397i
$549$	14.2918			0.609959
$550$	0.572949	+	6.12261i	0.0244306	+	0.261069i
$551$	3.54102			0.150853
$552$	2.54508	−	7.83297i	0.108326	−	0.333393i
$553$	−3.19098	+	2.31838i	−0.135694	+	0.0985878i
$554$	25.5623	+	18.5721i	1.08604	+	0.789053i
$555$	−6.35410	−	19.5559i	−0.269717	−	0.830102i
$556$	−0.326238	−	1.00406i	−0.0138356	−	0.0425815i
$557$	4.28115	+	3.11044i	0.181398	+	0.131794i	0.674779	−	0.738020i	$-0.264239\pi$
$557$	4.28115	+	3.11044i	0.181398	+	0.131794i	−0.493381	+	0.869814i	$0.664239\pi$
$558$	−4.85410	+	3.52671i	−0.205491	+	0.149298i
$559$	−7.92047	+	24.3767i	−0.335000	+	1.03102i
$560$	−2.61803			−0.110632
$561$	16.3713	+	18.6049i	0.691198	+	0.785498i
$562$	19.0344			0.802919
$563$	3.14590	−	9.68208i	0.132584	−	0.408051i	−0.862623	−	0.505848i	$-0.831180\pi$
$563$	3.14590	−	9.68208i	0.132584	−	0.408051i	0.995206	+	0.0977971i	$0.0311796\pi$
$564$	−0.500000	+	0.363271i	−0.0210538	+	0.0152965i
$565$	21.5623	+	15.6659i	0.907133	+	0.659071i
$566$	−4.45492	−	13.7108i	−0.187254	−	0.576309i
$567$	0.309017	+	0.951057i	0.0129775	+	0.0399406i
$568$	2.42705	+	1.76336i	0.101837	+	0.0739888i
$569$	10.0623	−	7.31069i	0.421834	−	0.306480i	−0.356541	−	0.934280i	$-0.616044\pi$
$569$	10.0623	−	7.31069i	0.421834	−	0.306480i	0.778375	+	0.627799i	$0.216044\pi$
$570$	−5.42705	+	16.7027i	−0.227314	+	0.699601i
$571$	−11.2918			−0.472547			−0.236273	−	0.971687i	$-0.575926\pi$
$571$	−11.2918			−0.472547			−0.236273	+	0.971687i	$0.575926\pi$
$572$	−10.5729	+	4.56352i	−0.442077	+	0.190811i
$573$	1.61803			0.0675943
$574$	−0.763932	+	2.35114i	−0.0318859	+	0.0981347i
$575$	12.3541	−	8.97578i	0.515202	−	0.374316i
$576$	1.61803	+	1.17557i	0.0674181	+	0.0489821i
$577$	8.75329	+	26.9399i	0.364404	+	1.12152i	0.950353	+	0.311173i	$0.100722\pi$
$577$	8.75329	+	26.9399i	0.364404	+	1.12152i	−0.585949	+	0.810348i	$0.699278\pi$
$578$	12.0000	+	36.9322i	0.499134	+	1.53618i
$579$	−21.1353	−	15.3557i	−0.878351	−	0.638160i
$580$	−1.11803	+	0.812299i	−0.0464238	+	0.0337289i
$581$	−1.95492	+	6.01661i	−0.0811035	+	0.249611i
$582$	−3.52786			−0.146235
$583$	−21.4894	+	36.2587i	−0.889998	+	1.50168i
$584$	−6.85410			−0.283625
$585$	5.61803	−	17.2905i	0.232277	−	0.714875i
$586$	−7.54508	+	5.48183i	−0.311685	+	0.226452i
$587$	−19.6631	−	14.2861i	−0.811584	−	0.589650i	0.102706	−	0.994712i	$-0.467250\pi$
$587$	−19.6631	−	14.2861i	−0.811584	−	0.589650i	−0.914289	+	0.405062i	$0.867250\pi$
$588$	−0.309017	−	0.951057i	−0.0127436	−	0.0392209i
$589$	6.21885	+	19.1396i	0.256243	+	0.788635i
$590$	21.8713	+	15.8904i	0.900428	+	0.654199i
$591$	−9.97214	+	7.24518i	−0.410199	+	0.298027i
$592$	−2.42705	+	7.46969i	−0.0997512	+	0.307003i
$593$	1.23607			0.0507592			0.0253796	−	0.999678i	$-0.491921\pi$
$593$	1.23607			0.0507592			0.0253796	+	0.999678i	$0.491921\pi$
$594$	16.1803	+	3.63271i	0.663887	+	0.149052i
$595$	−19.5623			−0.801976
$596$	4.04508	−	12.4495i	0.165693	−	0.509951i
$597$	−1.38197	+	1.00406i	−0.0565601	+	0.0410933i
$598$	23.1353	+	16.8087i	0.946071	+	0.687361i
$599$	9.96149	+	30.6583i	0.407016	+	1.25267i	0.919200	+	0.393790i	$0.128836\pi$
$599$	9.96149	+	30.6583i	0.407016	+	1.25267i	−0.512185	+	0.858875i	$0.671164\pi$
$600$	−0.572949	−	1.76336i	−0.0233905	−	0.0719887i
$601$	−19.2812	−	14.0086i	−0.786495	−	0.571422i	0.120426	−	0.992722i	$-0.461574\pi$
$601$	−19.2812	−	14.0086i	−0.786495	−	0.571422i	−0.906921	+	0.421300i	$0.861574\pi$
$602$	5.97214	−	4.33901i	0.243406	−	0.176845i
$603$	5.38197	−	16.5640i	0.219171	−	0.674538i
$604$	−8.00000			−0.325515
$605$	3.66312	−	28.5645i	0.148927	−	1.16131i
$606$	3.00000			0.121867
$607$	0.298374	−	0.918300i	0.0121106	−	0.0372727i	−0.944819	−	0.327594i	$-0.893762\pi$
$607$	0.298374	−	0.918300i	0.0121106	−	0.0372727i	0.956929	+	0.290321i	$0.0937622\pi$
$608$	5.42705	−	3.94298i	0.220096	−	0.159909i
$609$	−0.427051	−	0.310271i	−0.0173050	−	0.0125728i
$610$	5.78115	+	17.7926i	0.234072	+	0.720400i
$611$	−0.663119	−	2.04087i	−0.0268269	−	0.0825648i
$612$	12.0902	+	8.78402i	0.488716	+	0.355073i
$613$	−8.50000	+	6.17561i	−0.343312	+	0.249431i	−0.746058	−	0.665881i	$-0.768056\pi$
$613$	−8.50000	+	6.17561i	−0.343312	+	0.249431i	0.402746	+	0.915312i	$0.368056\pi$
$614$	5.07295	−	15.6129i	0.204728	−	0.630087i
$615$	−6.47214			−0.260982
$616$	3.23607	+	0.726543i	0.130385	+	0.0292732i
$617$	7.47214			0.300817			0.150408	−	0.988624i	$-0.451941\pi$
$617$	7.47214			0.300817			0.150408	+	0.988624i	$0.451941\pi$
$618$	−1.50000	+	4.61653i	−0.0603388	+	0.185704i
$619$	−12.9271	+	9.39205i	−0.519582	+	0.377498i	−0.816446	−	0.577421i	$-0.804059\pi$
$619$	−12.9271	+	9.39205i	−0.519582	+	0.377498i	0.296864	+	0.954920i	$0.404059\pi$
$620$	−6.35410	−	4.61653i	−0.255187	−	0.185404i
$621$	−12.7254	−	39.1648i	−0.510654	−	1.57163i
$622$	−2.83688	−	8.73102i	−0.113749	−	0.350082i
$623$	2.50000	+	1.81636i	0.100160	+	0.0727708i
$624$	2.80902	−	2.04087i	0.112451	−	0.0817002i
$625$	−9.52786	+	29.3238i	−0.381115	+	1.17295i
$626$	−30.2705			−1.20985
$627$	11.3435	−	19.1396i	0.453014	−	0.764364i
$628$	−7.65248			−0.305367
$629$	−18.1353	+	55.8146i	−0.723100	+	2.22547i
$630$	−4.23607	+	3.07768i	−0.168769	+	0.122618i
$631$	−0.0729490	−	0.0530006i	−0.00290405	−	0.00210992i	0.586332	−	0.810071i	$-0.300571\pi$
$631$	−0.0729490	−	0.0530006i	−0.00290405	−	0.00210992i	−0.589236	+	0.807961i	$0.700571\pi$
$632$	1.21885	+	3.75123i	0.0484831	+	0.149216i
$633$	1.98278	+	6.10237i	0.0788084	+	0.242547i
$634$	−20.5172	−	14.9066i	−0.814843	−	0.592018i
$635$	−2.42705	+	1.76336i	−0.0963146	+	0.0699766i
$636$	3.92705	−	12.0862i	0.155718	−	0.479250i
$637$	3.47214			0.137571
$638$	1.60739	−	0.693786i	0.0636372	−	0.0274673i
$639$	6.00000			0.237356
$640$	−0.809017	+	2.48990i	−0.0319792	+	0.0984219i
$641$	−25.4615	+	18.4989i	−1.00567	+	0.730661i	−0.963296	−	0.268441i	$-0.913492\pi$
$641$	−25.4615	+	18.4989i	−1.00567	+	0.730661i	−0.0423724	+	0.999102i	$0.513492\pi$
$642$	−4.11803	−	2.99193i	−0.162526	−	0.118082i
$643$	13.6353	+	41.9650i	0.537722	+	1.65494i	0.737693	+	0.675136i	$0.235915\pi$
$643$	13.6353	+	41.9650i	0.537722	+	1.65494i	−0.199971	+	0.979802i	$0.564085\pi$
$644$	−2.54508	−	7.83297i	−0.100290	−	0.308662i
$645$	15.6353	+	11.3597i	0.615638	+	0.447287i
$646$	40.5517	−	29.4625i	1.59548	−	1.15919i
$647$	−12.1631	+	37.4342i	−0.478182	+	1.47169i	0.363437	+	0.931619i	$0.381603\pi$
$647$	−12.1631	+	37.4342i	−0.478182	+	1.47169i	−0.841618	+	0.540073i	$0.818397\pi$
$648$	1.00000			0.0392837
$649$	−22.6246	−	25.7113i	−0.888094	−	1.00926i
$650$	6.43769			0.252507
$651$	0.927051	−	2.85317i	0.0363340	−	0.111825i
$652$	1.92705	−	1.40008i	0.0754691	−	0.0548315i
$653$	−27.7082	−	20.1312i	−1.08431	−	0.787794i	−0.105877	−	0.994379i	$-0.533765\pi$
$653$	−27.7082	−	20.1312i	−1.08431	−	0.787794i	−0.978429	+	0.206585i	$0.933765\pi$
$654$	−1.64590	−	5.06555i	−0.0643597	−	0.198079i
$655$	−6.61803	−	20.3682i	−0.258588	−	0.795852i
$656$	2.00000	+	1.45309i	0.0780869	+	0.0567334i
$657$	−11.0902	+	8.05748i	−0.432669	+	0.314352i
$658$	−0.190983	+	0.587785i	−0.00744529	+	0.0229143i
$659$	−17.5623			−0.684130			−0.342065	−	0.939676i	$-0.611126\pi$
$659$	−17.5623			−0.684130			−0.342065	+	0.939676i	$0.611126\pi$
$660$	0.809017	+	8.64527i	0.0314909	+	0.336516i
$661$	−27.2705			−1.06070			−0.530350	−	0.847779i	$-0.677939\pi$
$661$	−27.2705			−1.06070			−0.530350	+	0.847779i	$0.677939\pi$
$662$	−6.09017	+	18.7436i	−0.236701	+	0.728491i
$663$	20.9894	−	15.2497i	0.815159	−	0.592248i
$664$	5.11803	+	3.71847i	0.198618	+	0.144305i
$665$	5.42705	+	16.7027i	0.210452	+	0.647705i
$666$	4.85410	+	14.9394i	0.188093	+	0.578890i
$667$	−3.51722	−	2.55541i	−0.136187	−	0.0989459i
$668$	18.4894	−	13.4333i	0.715375	−	0.519750i
$669$	−2.35410	+	7.24518i	−0.0910148	+	0.280115i
$670$	22.7984			0.880778
$671$	−2.20820	−	23.5972i	−0.0852468	−	0.910959i
$672$	−1.00000			−0.0385758
$673$	−10.3090	+	31.7279i	−0.397383	+	1.22302i	0.529706	+	0.848181i	$0.322302\pi$
$673$	−10.3090	+	31.7279i	−0.397383	+	1.22302i	−0.927090	+	0.374839i	$0.877698\pi$
$674$	−10.3541	+	7.52270i	−0.398825	+	0.289763i
$675$	−7.50000	−	5.44907i	−0.288675	−	0.209735i
$676$	−0.291796	−	0.898056i	−0.0112229	−	0.0345406i
$677$	−7.12461	−	21.9273i	−0.273821	−	0.842735i	−0.989529	−	0.144335i	$-0.953896\pi$
$677$	−7.12461	−	21.9273i	−0.273821	−	0.842735i	0.715708	−	0.698400i	$-0.246104\pi$
$678$	8.23607	+	5.98385i	0.316304	+	0.229809i
$679$	−2.85410	+	2.07363i	−0.109530	+	0.0795785i
$680$	−6.04508	+	18.6049i	−0.231818	+	0.713464i
$681$	−19.3820			−0.742719
$682$	6.57295	+	7.46969i	0.251691	+	0.286029i
$683$	1.96556			0.0752100			0.0376050	−	0.999293i	$-0.488027\pi$
$683$	1.96556			0.0752100			0.0376050	+	0.999293i	$0.488027\pi$
$684$	4.14590	−	12.7598i	0.158522	−	0.487882i
$685$	35.8885	−	26.0746i	1.37123	−	0.996257i
$686$	−0.809017	−	0.587785i	−0.0308884	−	0.0224417i
$687$	−5.26393	−	16.2007i	−0.200832	−	0.618096i
$688$	−2.28115	−	7.02067i	−0.0869681	−	0.267660i
$689$	35.6976	+	25.9358i	1.35997	+	0.988075i
$690$	17.4443	−	12.6740i	0.664092	−	0.482491i
$691$	−12.5344	+	38.5770i	−0.476833	+	1.46754i	0.366637	+	0.930364i	$0.380509\pi$
$691$	−12.5344	+	38.5770i	−0.476833	+	1.46754i	−0.843470	+	0.537176i	$0.819491\pi$
$692$	5.18034			0.196927
$693$	6.09017	−	2.62866i	0.231346	−	0.0998544i
$694$	4.05573			0.153953
$695$	0.854102	−	2.62866i	0.0323979	−	0.0997106i
$696$	−0.427051	+	0.310271i	−0.0161873	+	0.0117608i
$697$	14.9443	+	10.8576i	0.566055	+	0.411263i
$698$	8.29180	+	25.5195i	0.313849	+	0.965928i
$699$	−7.41641	−	22.8254i	−0.280514	−	0.863334i
$700$	−1.50000	−	1.08981i	−0.0566947	−	0.0411911i
$701$	12.8541	−	9.33905i	0.485493	−	0.352731i	−0.317956	−	0.948106i	$-0.602996\pi$
$701$	12.8541	−	9.33905i	0.485493	−	0.352731i	0.803448	+	0.595374i	$0.202996\pi$
$702$	5.36475	−	16.5110i	0.202479	−	0.623167i
$703$	52.6869			1.98712
$704$	1.69098	−	2.85317i	0.0637313	−	0.107533i
$705$	−1.61803			−0.0609387
$706$	−3.98936	+	12.2780i	−0.150141	+	0.462088i
$707$	2.42705	−	1.76336i	0.0912786	−	0.0663178i
$708$	8.35410	+	6.06961i	0.313966	+	0.228110i
$709$	−9.20820	−	28.3399i	−0.345821	−	1.06433i	−0.961143	−	0.276052i	$-0.910974\pi$
$709$	−9.20820	−	28.3399i	−0.345821	−	1.06433i	0.615321	−	0.788276i	$-0.289026\pi$
$710$	2.42705	+	7.46969i	0.0910856	+	0.280333i
$711$	6.38197	+	4.63677i	0.239342	+	0.173892i
$712$	2.50000	−	1.81636i	0.0936915	−	0.0680708i
$713$	7.63525	−	23.4989i	0.285943	−	0.880041i
$714$	−7.47214			−0.279638
$715$	−29.4164	−	6.60440i	−1.10011	−	0.246990i
$716$	−9.27051			−0.346455
$717$	0.427051	−	1.31433i	0.0159485	−	0.0490845i
$718$	−9.63525	+	7.00042i	−0.359585	+	0.261253i
$719$	−15.1631	−	11.0167i	−0.565489	−	0.410852i	0.267975	−	0.963426i	$-0.413646\pi$
$719$	−15.1631	−	11.0167i	−0.565489	−	0.410852i	−0.833464	+	0.552574i	$0.813646\pi$
$720$	1.61803	+	4.97980i	0.0603006	+	0.185586i
$721$	1.50000	+	4.61653i	0.0558629	+	0.171928i
$722$	−21.0344	−	15.2824i	−0.782821	−	0.568753i
$723$	−1.30902	+	0.951057i	−0.0486829	+	0.0353702i
$724$	0.0901699	−	0.277515i	0.00335114	−	0.0103137i
$725$	−0.978714			−0.0363485
$726$	1.39919	−	10.9106i	0.0519287	−	0.404932i
$727$	28.1246			1.04308			0.521542	−	0.853226i	$-0.325357\pi$
$727$	28.1246			1.04308			0.521542	+	0.853226i	$0.325357\pi$
$728$	1.07295	−	3.30220i	0.0397661	−	0.122388i
$729$	−10.5172	+	7.64121i	−0.389527	+	0.283008i
$730$	−14.5172	−	10.5474i	−0.537306	−	0.390376i
$731$	−17.0451	−	52.4594i	−0.630435	−	1.94028i
$732$	2.20820	+	6.79615i	0.0816176	+	0.251193i
$733$	19.3885	+	14.0866i	0.716132	+	0.520301i	0.885146	−	0.465313i	$-0.154058\pi$
$733$	19.3885	+	14.0866i	0.716132	+	0.520301i	−0.169014	+	0.985614i	$0.554058\pi$
$734$	−2.42705	+	1.76336i	−0.0895841	+	0.0650866i
$735$	0.809017	−	2.48990i	0.0298410	−	0.0918413i
$736$	−8.23607			−0.303585
$737$	−28.1803	−	6.32688i	−1.03804	−	0.233054i
$738$	4.94427			0.182001
$739$	5.20163	−	16.0090i	0.191345	−	0.588899i	−0.808655	−	0.588283i	$-0.799804\pi$
$739$	5.20163	−	16.0090i	0.191345	−	0.588899i	1.00000		0.000615770i	$-0.000196006\pi$
$740$	−16.6353	+	12.0862i	−0.611524	+	0.444298i
$741$	−18.8435	−	13.6906i	−0.692232	−	0.502936i
$742$	−3.92705	−	12.0862i	−0.144167	−	0.443699i
$743$	−11.4894	−	35.3606i	−0.421504	−	1.29725i	−0.906303	−	0.422629i	$-0.861107\pi$
$743$	−11.4894	−	35.3606i	−0.421504	−	1.29725i	0.484799	−	0.874626i	$-0.338893\pi$
$744$	−2.42705	−	1.76336i	−0.0889800	−	0.0646478i
$745$	27.7254	−	20.1437i	1.01578	−	0.738008i
$746$	6.07295	−	18.6906i	0.222346	−	0.684312i
$747$	12.6525			0.462930
$748$	12.6353	−	21.3193i	0.461991	−	0.779510i
$749$	−5.09017			−0.185991
$750$	−2.54508	+	7.83297i	−0.0929334	+	0.286019i
$751$	−3.00000	+	2.17963i	−0.109472	+	0.0795357i	−0.641174	−	0.767395i	$-0.721552\pi$
$751$	−3.00000	+	2.17963i	−0.109472	+	0.0795357i	0.531703	+	0.846931i	$0.321552\pi$
$752$	0.500000	+	0.363271i	0.0182331	+	0.0132471i
$753$	3.85410	+	11.8617i	0.140451	+	0.432265i
$754$	−0.566371	−	1.74311i	−0.0206260	−	0.0634804i
$755$	−16.9443	−	12.3107i	−0.616665	−	0.448033i
$756$	−4.04508	+	2.93893i	−0.147118	+	0.106888i
$757$	8.46556	−	26.0543i	0.307686	−	0.946960i	−0.670975	−	0.741480i	$-0.734124\pi$
$757$	8.46556	−	26.0543i	0.307686	−	0.946960i	0.978661	−	0.205480i	$-0.0658756\pi$
$758$	−16.0557			−0.583170
$759$	−25.0795	+	10.8249i	−0.910329	+	0.392919i
$760$	17.5623			0.637052
$761$	−8.32624	+	25.6255i	−0.301826	+	0.928925i	0.679017	+	0.734123i	$0.262406\pi$
$761$	−8.32624	+	25.6255i	−0.301826	+	0.928925i	−0.980843	+	0.194802i	$0.937594\pi$
$762$	−0.927051	+	0.673542i	−0.0335835	+	0.0243999i
$763$	−4.30902	−	3.13068i	−0.155997	−	0.113338i
$764$	−0.500000	−	1.53884i	−0.0180894	−	0.0556733i
$765$	12.0902	+	37.2097i	0.437121	+	1.34532i
$766$	−12.9721	−	9.42481i	−0.468702	−	0.340532i
$767$	−29.0066	+	21.0745i	−1.04737	+	0.760957i
$768$	−0.309017	+	0.951057i	−0.0111507	+	0.0343183i
$769$	16.3820			0.590749			0.295374	−	0.955382i	$-0.404556\pi$
$769$	16.3820			0.590749			0.295374	+	0.955382i	$0.404556\pi$
$770$	5.73607	+	6.51864i	0.206714	+	0.234915i
$771$	−14.0557			−0.506205
$772$	−8.07295	+	24.8460i	−0.290552	+	0.894226i
$773$	−2.38197	+	1.73060i	−0.0856734	+	0.0622453i	−0.629797	−	0.776759i	$-0.716862\pi$
$773$	−2.38197	+	1.73060i	−0.0856734	+	0.0622453i	0.544124	+	0.839005i	$0.316862\pi$
$774$	−11.9443	−	8.67802i	−0.429328	−	0.311925i
$775$	−1.71885	−	5.29007i	−0.0617428	−	0.190025i
$776$	1.09017	+	3.35520i	0.0391348	+	0.120445i
$777$	−6.35410	−	4.61653i	−0.227952	−	0.165617i
$778$	21.4443	−	15.5802i	0.768814	−	0.558576i
$779$	5.12461	−	15.7719i	0.183608	−	0.565088i
$780$	9.09017			0.325480
$781$	−0.927051	−	9.90659i	−0.0331725	−	0.354486i
$782$	−61.5410			−2.20070
$783$	−0.815595	+	2.51014i	−0.0291470	+	0.0897052i
$784$	−0.809017	+	0.587785i	−0.0288935	+	0.0209923i
$785$	−16.2082	−	11.7759i	−0.578496	−	0.420302i
$786$	−2.52786	−	7.77997i	−0.0901659	−	0.277502i
$787$	−7.06231	−	21.7355i	−0.251744	−	0.774788i	−0.994454	−	0.105175i	$-0.966460\pi$
$787$	−7.06231	−	21.7355i	−0.251744	−	0.774788i	0.742710	−	0.669614i	$-0.233540\pi$
$788$	9.97214	+	7.24518i	0.355243	+	0.258099i
$789$	18.2984	−	13.2945i	0.651439	−	0.473298i
$790$	−3.19098	+	9.82084i	−0.113530	+	0.349410i
$791$	10.1803			0.361971
$792$	−0.618034	−	6.60440i	−0.0219609	−	0.234677i
$793$	−24.8115			−0.881083
$794$	7.63525	−	23.4989i	0.270965	−	0.833945i
$795$	26.9164	−	19.5559i	0.954627	−	0.693577i
$796$	1.38197	+	1.00406i	0.0489825	+	0.0355879i
$797$	13.1246	+	40.3934i	0.464898	+	1.43081i	0.859111	+	0.511789i	$0.171017\pi$
$797$	13.1246	+	40.3934i	0.464898	+	1.43081i	−0.394214	+	0.919019i	$0.628983\pi$
$798$	2.07295	+	6.37988i	0.0733816	+	0.225845i
$799$	3.73607	+	2.71441i	0.132173	+	0.0960290i
$800$	−1.50000	+	1.08981i	−0.0530330	+	0.0385307i
$801$	1.90983	−	5.87785i	0.0674805	−	0.207684i
$802$	12.5279			0.442374
$803$	15.0172	+	17.0660i	0.529946	+	0.602247i
$804$	8.70820			0.307115
$805$	6.66312	−	20.5070i	0.234844	−	0.722776i
$806$	8.42705	−	6.12261i	0.296830	−	0.215660i
$807$	−3.88197	−	2.82041i	−0.136652	−	0.0992833i
$808$	−0.927051	−	2.85317i	−0.0326135	−	0.100374i
$809$	−7.92705	−	24.3970i	−0.278700	−	0.857751i	−0.988217	−	0.153062i	$-0.951087\pi$
$809$	−7.92705	−	24.3970i	−0.278700	−	0.857751i	0.709516	−	0.704689i	$-0.248913\pi$
$810$	2.11803	+	1.53884i	0.0744201	+	0.0540694i
$811$	43.5689	−	31.6546i	1.52991	−	1.11154i	0.573622	−	0.819120i	$-0.305538\pi$
$811$	43.5689	−	31.6546i	1.52991	−	1.11154i	0.956289	−	0.292425i	$-0.0944621\pi$
$812$	−0.163119	+	0.502029i	−0.00572435	+	0.0176177i
$813$	4.38197			0.153682
$814$	23.9164	−	10.3229i	0.838270	−	0.361816i
$815$	6.23607			0.218440
$816$	−2.30902	+	7.10642i	−0.0808318	+	0.248775i
$817$	−40.0623	+	29.1070i	−1.40160	+	1.01832i
$818$	−5.42705	−	3.94298i	−0.189752	−	0.137863i
$819$	−2.14590	−	6.60440i	−0.0749837	−	0.230776i
$820$	2.00000	+	6.15537i	0.0698430	+	0.214955i
$821$	21.2705	+	15.4539i	0.742346	+	0.539346i	0.893445	−	0.449173i	$-0.148281\pi$
$821$	21.2705	+	15.4539i	0.742346	+	0.539346i	−0.151099	+	0.988519i	$0.548281\pi$
$822$	13.7082	−	9.95959i	0.478129	−	0.347381i
$823$	−8.60081	+	26.4706i	−0.299805	+	0.922706i	0.681759	+	0.731577i	$0.261215\pi$
$823$	−8.60081	+	26.4706i	−0.299805	+	0.922706i	−0.981565	+	0.191130i	$0.938785\pi$
$824$	4.85410			0.169101
$825$	−3.13525	+	5.29007i	−0.109156	+	0.184177i
$826$	10.3262			0.359296
$827$	−1.47214	+	4.53077i	−0.0511912	+	0.157550i	−0.973384	−	0.229180i	$-0.926396\pi$
$827$	−1.47214	+	4.53077i	−0.0511912	+	0.157550i	0.922193	+	0.386730i	$0.126396\pi$
$828$	−13.3262	+	9.68208i	−0.463119	+	0.336475i
$829$	20.2254	+	14.6946i	0.702458	+	0.510366i	0.880732	−	0.473615i	$-0.157051\pi$
$829$	20.2254	+	14.6946i	0.702458	+	0.510366i	−0.178274	+	0.983981i	$0.557051\pi$
$830$	5.11803	+	15.7517i	0.177650	+	0.546749i
$831$	9.76393	+	30.0503i	0.338707	+	1.04243i
$832$	−2.80902	−	2.04087i	−0.0973851	−	0.0707544i
$833$	−6.04508	+	4.39201i	−0.209450	+	0.152174i
$834$	0.326238	−	1.00406i	0.0112967	−	0.0347677i
$835$	59.8328			2.07060
$836$	−21.7082	−	4.87380i	−0.750794	−	0.168564i
$837$	−15.0000			−0.518476
$838$	3.55573	−	10.9434i	0.122831	−	0.378034i
$839$	12.9271	−	9.39205i	0.446291	−	0.324250i	−0.341838	−	0.939759i	$-0.611050\pi$
$839$	12.9271	−	9.39205i	0.446291	−	0.324250i	0.788130	+	0.615509i	$0.211050\pi$
$840$	−2.11803	−	1.53884i	−0.0730791	−	0.0530951i
$841$	−8.87539	−	27.3156i	−0.306048	−	0.941918i
$842$	−5.19756	−	15.9964i	−0.179120	−	0.551274i
$843$	15.3992	+	11.1882i	0.530376	+	0.385341i
$844$	5.19098	−	3.77147i	0.178681	−	0.129819i
$845$	0.763932	−	2.35114i	0.0262801	−	0.0808817i
$846$	1.23607			0.0424969
$847$	−5.28115	−	9.64932i	−0.181463	−	0.331555i
$848$	−12.7082			−0.436402
$849$	4.45492	−	13.7108i	0.152892	−	0.470554i
$850$	−11.2082	+	8.14324i	−0.384438	+	0.279311i
$851$	−52.3328	−	38.0220i	−1.79395	−	1.30338i
$852$	0.927051	+	2.85317i	0.0317602	+	0.0977480i
$853$	11.5238	+	35.4666i	0.394567	+	1.21435i	0.929298	+	0.369331i	$0.120413\pi$
$853$	11.5238	+	35.4666i	0.394567	+	1.21435i	−0.534731	+	0.845023i	$0.679587\pi$
$854$	5.78115	+	4.20025i	0.197827	+	0.143730i
$855$	28.4164	−	20.6457i	0.971821	−	0.706069i
$856$	−1.57295	+	4.84104i	−0.0537623	+	0.165463i
$857$	−21.4721			−0.733474			−0.366737	−	0.930325i	$-0.619525\pi$
$857$	−21.4721			−0.733474			−0.366737	+	0.930325i	$0.619525\pi$
$858$	−11.2361	−	2.52265i	−0.383593	−	0.0861220i
$859$	23.2918			0.794706			0.397353	−	0.917666i	$-0.369929\pi$
$859$	23.2918			0.794706			0.397353	+	0.917666i	$0.369929\pi$
$860$	5.97214	−	18.3803i	0.203648	−	0.626765i
$861$	−2.00000	+	1.45309i	−0.0681598	+	0.0495210i
$862$	−21.5172	−	15.6332i	−0.732879	−	0.532468i
$863$	16.1353	+	49.6592i	0.549250	+	1.69042i	0.710663	+	0.703532i	$0.248395\pi$
$863$	16.1353	+	49.6592i	0.549250	+	1.69042i	−0.161413	+	0.986887i	$0.551605\pi$
$864$	1.54508	+	4.75528i	0.0525649	+	0.161778i
$865$	10.9721	+	7.97172i	0.373064	+	0.271047i
$866$	2.19098	−	1.59184i	0.0744526	−	0.0540930i
$867$	−12.0000	+	36.9322i	−0.407541	+	1.25428i
$868$	−3.00000			−0.101827
$869$	6.66970	−	11.2537i	0.226254	−	0.381755i
$870$	−1.38197			−0.0468530
$871$	−9.34346	+	28.7562i	−0.316591	+	0.974367i
$872$	−4.30902	+	3.13068i	−0.145922	+	0.106018i
$873$	5.70820	+	4.14725i	0.193193	+	0.140363i
$874$	17.0729	+	52.5451i	0.577501	+	1.77737i
$875$	2.54508	+	7.83297i	0.0860396	+	0.264803i
$876$	−5.54508	−	4.02874i	−0.187351	−	0.136119i
$877$	38.2254	−	27.7724i	1.29078	−	0.937807i	0.290960	−	0.956735i	$-0.406025\pi$
$877$	38.2254	−	27.7724i	1.29078	−	0.937807i	0.999821	+	0.0189280i	$0.00602533\pi$
$878$	−6.70820	+	20.6457i	−0.226391	+	0.696760i
$879$	−9.32624			−0.314566
$880$	7.97214	−	3.44095i	0.268741	−	0.115995i
$881$	57.6525			1.94236			0.971181	−	0.238345i	$-0.0766048\pi$
$881$	57.6525			1.94236			0.971181	+	0.238345i	$0.0766048\pi$
$882$	−0.618034	+	1.90211i	−0.0208103	+	0.0640475i
$883$	−36.6525	+	26.6296i	−1.23345	+	0.896157i	−0.997144	−	0.0755210i	$-0.975938\pi$
$883$	−36.6525	+	26.6296i	−1.23345	+	0.896157i	−0.236310	+	0.971678i	$0.575938\pi$
$884$	−20.9894	−	15.2497i	−0.705948	−	0.512902i
$885$	8.35410	+	25.7113i	0.280820	+	0.864275i
$886$	−7.77051	−	23.9152i	−0.261055	−	0.803446i
$887$	7.30902	+	5.31031i	0.245413	+	0.178303i	0.703691	−	0.710506i	$-0.251534\pi$
$887$	7.30902	+	5.31031i	0.245413	+	0.178303i	−0.458279	+	0.888809i	$0.651534\pi$
$888$	−6.35410	+	4.61653i	−0.213230	+	0.154920i
$889$	−0.354102	+	1.08981i	−0.0118762	+	0.0365512i
$890$	8.09017			0.271183
$891$	−2.19098	−	2.48990i	−0.0734007	−	0.0834147i
$892$	7.61803			0.255071
$893$	1.28115	−	3.94298i	0.0428721	−	0.131947i
$894$	10.5902	−	7.69421i	0.354188	−	0.257333i
$895$	−19.6353	−	14.2658i	−0.656334	−	0.476855i
$896$	0.309017	+	0.951057i	0.0103235	+	0.0317726i
$897$	8.83688	+	27.1971i	0.295055	+	0.908086i
$898$	−3.88197	−	2.82041i	−0.129543	−	0.0941184i
$899$	−1.28115	+	0.930812i	−0.0427288	+	0.0310443i
$900$	−1.14590	+	3.52671i	−0.0381966	+	0.117557i
$901$	−94.9574			−3.16349
$902$	−0.763932	−	8.16348i	−0.0254362	−	0.271814i
$903$	7.38197			0.245656
$904$	3.14590	−	9.68208i	0.104631	−	0.322021i
$905$	0.618034	−	0.449028i	0.0205441	−	0.0149262i
$906$	−6.47214	−	4.70228i	−0.215022	−	0.156223i
$907$	−4.82624	−	14.8536i	−0.160253	−	0.493207i	0.838403	−	0.545052i	$-0.183490\pi$
$907$	−4.82624	−	14.8536i	−0.160253	−	0.493207i	−0.998655	+	0.0518447i	$0.983490\pi$
$908$	5.98936	+	18.4333i	0.198764	+	0.611732i
$909$	−4.85410	−	3.52671i	−0.161000	−	0.116974i
$910$	7.35410	−	5.34307i	0.243786	−	0.177121i
$911$	−14.9721	+	46.0795i	−0.496049	+	1.52668i	0.319267	+	0.947665i	$0.396563\pi$
$911$	−14.9721	+	46.0795i	−0.496049	+	1.52668i	−0.815316	+	0.579017i	$0.803437\pi$
$912$	6.70820			0.222131
$913$	−1.95492	−	20.8905i	−0.0646982	−	0.691374i
$914$	11.4164			0.377621
$915$	−5.78115	+	17.7926i	−0.191119	+	0.588204i
$916$	−13.7812	+	10.0126i	−0.455342	+	0.330825i
$917$	−6.61803	−	4.80828i	−0.218547	−	0.158783i
$918$	11.5451	+	35.5321i	0.381045	+	1.17273i
$919$	−1.54508	−	4.75528i	−0.0509677	−	0.156862i	0.922333	−	0.386396i	$-0.126280\pi$
$919$	−1.54508	−	4.75528i	−0.0509677	−	0.156862i	−0.973301	+	0.229533i	$0.926280\pi$
$920$	−17.4443	−	12.6740i	−0.575121	−	0.417850i
$921$	13.2812	−	9.64932i	0.437629	−	0.317956i
$922$	0.843459	−	2.59590i	0.0277778	−	0.0854914i
$923$	−10.4164			−0.342860
$924$	2.19098	+	2.48990i	0.0720780	+	0.0819116i
$925$	−14.5623			−0.478806
$926$	−6.79180	+	20.9030i	−0.223192	+	0.686915i
$927$	7.85410	−	5.70634i	0.257963	−	0.187421i
$928$	0.427051	+	0.310271i	0.0140186	+	0.0101851i
$929$	10.1246	+	31.1604i	0.332178	+	1.02234i	0.968096	+	0.250581i	$0.0806217\pi$
$929$	10.1246	+	31.1604i	0.332178	+	1.02234i	−0.635918	+	0.771757i	$0.719378\pi$
$930$	−2.42705	−	7.46969i	−0.0795861	−	0.244941i
$931$	5.42705	+	3.94298i	0.177864	+	0.129226i
$932$	−19.4164	+	14.1068i	−0.636006	+	0.462085i
$933$	2.83688	−	8.73102i	0.0928753	−	0.285841i
$934$	−35.9443			−1.17613
$935$	59.5689	−	25.7113i	1.94811	−	0.840849i
$936$	−6.94427			−0.226981
$937$	12.7599	−	39.2708i	0.416847	−	1.28292i	−0.493742	−	0.869608i	$-0.664371\pi$
$937$	12.7599	−	39.2708i	0.416847	−	1.28292i	0.910589	−	0.413314i	$-0.135629\pi$
$938$	7.04508	−	5.11855i	0.230030	−	0.167127i
$939$	−24.4894	−	17.7926i	−0.799180	−	0.580638i
$940$	0.500000	+	1.53884i	0.0163082	+	0.0501915i
$941$	1.57295	+	4.84104i	0.0512767	+	0.157813i	0.973416	−	0.229045i	$-0.0735603\pi$
$941$	1.57295	+	4.84104i	0.0512767	+	0.157813i	−0.922139	+	0.386858i	$0.873560\pi$
$942$	−6.19098	−	4.49801i	−0.201713	−	0.146553i
$943$	−16.4721	+	11.9677i	−0.536407	+	0.389722i
$944$	3.19098	−	9.82084i	0.103858	−	0.319641i
$945$	−13.0902			−0.425823
$946$	−12.4828	+	21.0620i	−0.405850	+	0.684785i
$947$	−54.1591			−1.75993			−0.879966	−	0.475036i	$-0.842435\pi$
$947$	−54.1591			−1.75993			−0.879966	+	0.475036i	$0.842435\pi$
$948$	−1.21885	+	3.75123i	−0.0395863	+	0.121834i
$949$	19.2533	−	13.9883i	0.624988	−	0.454081i
$950$	10.0623	+	7.31069i	0.326464	+	0.237190i
$951$	−7.83688	−	24.1194i	−0.254128	−	0.782126i
$952$	2.30902	+	7.10642i	0.0748357	+	0.230321i
$953$	24.1631	+	17.5555i	0.782720	+	0.568680i	0.905794	−	0.423718i	$-0.139275\pi$
$953$	24.1631	+	17.5555i	0.782720	+	0.568680i	−0.123074	+	0.992398i	$0.539275\pi$
$954$	−20.5623	+	14.9394i	−0.665729	+	0.483681i
$955$	1.30902	−	4.02874i	0.0423588	−	0.130367i
$956$	−1.38197			−0.0446960
$957$	1.70820	+	0.383516i	0.0552184	+	0.0123973i
$958$	−40.2492			−1.30039
$959$	5.23607	−	16.1150i	0.169081	−	0.520379i
$960$	−2.11803	+	1.53884i	−0.0683593	+	0.0496659i
$961$	17.7984	+	12.9313i	0.574141	+	0.417138i
$962$	−8.42705	−	25.9358i	−0.271699	−	0.836204i
$963$	3.14590	+	9.68208i	0.101375	+	0.312001i
$964$	1.30902	+	0.951057i	0.0421606	+	0.0306315i
$965$	−55.3328	+	40.2016i	−1.78123	+	1.29414i
$966$	2.54508	−	7.83297i	0.0818868	−	0.252022i
$967$	8.32624			0.267754			0.133877	−	0.990998i	$-0.457257\pi$
$967$	8.32624			0.267754			0.133877	+	0.990998i	$0.457257\pi$
$968$	−10.8090	+	2.04087i	−0.347415	+	0.0655961i
$969$	50.1246			1.61023
$970$	−2.85410	+	8.78402i	−0.0916397	+	0.282038i
$971$	21.5344	−	15.6457i	0.691073	−	0.502094i	−0.185940	−	0.982561i	$-0.559533\pi$
$971$	21.5344	−	15.6457i	0.691073	−	0.502094i	0.877013	+	0.480467i	$0.159533\pi$
$972$	12.9443	+	9.40456i	0.415188	+	0.301652i
$973$	−0.326238	−	1.00406i	−0.0104587	−	0.0321886i
$974$	5.07295	+	15.6129i	0.162548	+	0.500271i
$975$	5.20820	+	3.78398i	0.166796	+	0.121184i
$976$	5.78115	−	4.20025i	0.185050	−	0.134447i
$977$	6.74265	−	20.7517i	0.215716	−	0.663907i	−0.783386	−	0.621536i	$-0.786509\pi$
$977$	6.74265	−	20.7517i	0.215716	−	0.663907i	0.999102	−	0.0423707i	$-0.0134910\pi$
$978$	2.38197			0.0761669
$979$	−10.0000	−	2.24514i	−0.319601	−	0.0717550i
$980$	−2.61803			−0.0836300
$981$	−3.29180	+	10.1311i	−0.105099	+	0.323461i
$982$	11.6353	−	8.45351i	0.371296	−	0.269762i
$983$	34.1246	+	24.7930i	1.08841	+	0.790773i	0.979129	−	0.203238i	$-0.0651465\pi$
$983$	34.1246	+	24.7930i	1.08841	+	0.790773i	0.109277	+	0.994011i	$0.465147\pi$
$984$	0.763932	+	2.35114i	0.0243533	+	0.0749516i
$985$	9.97214	+	30.6911i	0.317739	+	0.977899i
$986$	3.19098	+	2.31838i	0.101622	+	0.0738324i
$987$	−0.500000	+	0.363271i	−0.0159152	+	0.0115631i
$988$	−7.19756	+	22.1518i	−0.228985	+	0.704743i
$989$	60.7984			1.93328
$990$	8.85410	−	14.9394i	0.281402	−	0.474805i
$991$	−28.0000			−0.889449			−0.444725	−	0.895667i	$-0.646698\pi$
$991$	−28.0000			−0.889449			−0.444725	+	0.895667i	$0.646698\pi$
$992$	−0.927051	+	2.85317i	−0.0294339	+	0.0905882i
$993$	−15.9443	+	11.5842i	−0.505976	+	0.367613i
$994$	2.42705	+	1.76336i	0.0769814	+	0.0559302i
$995$	1.38197	+	4.25325i	0.0438113	+	0.134837i
$996$	1.95492	+	6.01661i	0.0619439	+	0.190644i
$997$	−7.26393	−	5.27756i	−0.230051	−	0.167142i	0.466788	−	0.884369i	$-0.345411\pi$
$997$	−7.26393	−	5.27756i	−0.230051	−	0.167142i	−0.696839	+	0.717227i	$0.745411\pi$
$998$	6.80902	−	4.94704i	0.215536	−	0.156596i
$999$	−12.1353	+	37.3485i	−0.383942	+	1.18165i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	154.2.f.a.141.1	yes	4
11.4	even	5		1694.2.a.q.1.1		2
11.5	even	5	inner	154.2.f.a.71.1	✓	4
11.7	odd	10		1694.2.a.k.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
154.2.f.a.71.1	✓	4	11.5	even	5	inner
154.2.f.a.141.1	yes	4	1.1	even	1	trivial
1694.2.a.k.1.1		2	11.7	odd	10
1694.2.a.q.1.1		2	11.4	even	5

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:	\( N \)	\(=\)	\( 154 = 2 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	154.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.309017 - 0.951057i) q^{2} +(0.809017 - 0.587785i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.809017 - 2.48990i) q^{5} +(-0.309017 - 0.951057i) q^{6} +(-0.809017 - 0.587785i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(-0.618034 + 1.90211i) q^{9} +O(q^{10})\)	\(q+(0.309017 - 0.951057i) q^{2} +(0.809017 - 0.587785i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.809017 - 2.48990i) q^{5} +(-0.309017 - 0.951057i) q^{6} +(-0.809017 - 0.587785i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(-0.618034 + 1.90211i) q^{9} -2.61803 q^{10} +(3.23607 + 0.726543i) q^{11} -1.00000 q^{12} +(1.07295 - 3.30220i) q^{13} +(-0.809017 + 0.587785i) q^{14} +(-2.11803 - 1.53884i) q^{15} +(0.309017 + 0.951057i) q^{16} +(2.30902 + 7.10642i) q^{17} +(1.61803 + 1.17557i) q^{18} +(5.42705 - 3.94298i) q^{19} +(-0.809017 + 2.48990i) q^{20} -1.00000 q^{21} +(1.69098 - 2.85317i) q^{22} -8.23607 q^{23} +(-0.309017 + 0.951057i) q^{24} +(-1.50000 + 1.08981i) q^{25} +(-2.80902 - 2.04087i) q^{26} +(1.54508 + 4.75528i) q^{27} +(0.309017 + 0.951057i) q^{28} +(0.427051 + 0.310271i) q^{29} +(-2.11803 + 1.53884i) q^{30} +(-0.927051 + 2.85317i) q^{31} +1.00000 q^{32} +(3.04508 - 1.31433i) q^{33} +7.47214 q^{34} +(-0.809017 + 2.48990i) q^{35} +(1.61803 - 1.17557i) q^{36} +(6.35410 + 4.61653i) q^{37} +(-2.07295 - 6.37988i) q^{38} +(-1.07295 - 3.30220i) q^{39} +(2.11803 + 1.53884i) q^{40} +(2.00000 - 1.45309i) q^{41} +(-0.309017 + 0.951057i) q^{42} -7.38197 q^{43} +(-2.19098 - 2.48990i) q^{44} +5.23607 q^{45} +(-2.54508 + 7.83297i) q^{46} +(0.500000 - 0.363271i) q^{47} +(0.809017 + 0.587785i) q^{48} +(0.309017 + 0.951057i) q^{49} +(0.572949 + 1.76336i) q^{50} +(6.04508 + 4.39201i) q^{51} +(-2.80902 + 2.04087i) q^{52} +(-3.92705 + 12.0862i) q^{53} +5.00000 q^{54} +(-0.809017 - 8.64527i) q^{55} +1.00000 q^{56} +(2.07295 - 6.37988i) q^{57} +(0.427051 - 0.310271i) q^{58} +(-8.35410 - 6.06961i) q^{59} +(0.809017 + 2.48990i) q^{60} +(-2.20820 - 6.79615i) q^{61} +(2.42705 + 1.76336i) q^{62} +(1.61803 - 1.17557i) q^{63} +(0.309017 - 0.951057i) q^{64} -9.09017 q^{65} +(-0.309017 - 3.30220i) q^{66} -8.70820 q^{67} +(2.30902 - 7.10642i) q^{68} +(-6.66312 + 4.84104i) q^{69} +(2.11803 + 1.53884i) q^{70} +(-0.927051 - 2.85317i) q^{71} +(-0.618034 - 1.90211i) q^{72} +(5.54508 + 4.02874i) q^{73} +(6.35410 - 4.61653i) q^{74} +(-0.572949 + 1.76336i) q^{75} -6.70820 q^{76} +(-2.19098 - 2.48990i) q^{77} -3.47214 q^{78} +(1.21885 - 3.75123i) q^{79} +(2.11803 - 1.53884i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(-0.763932 - 2.35114i) q^{82} +(-1.95492 - 6.01661i) q^{83} +(0.809017 + 0.587785i) q^{84} +(15.8262 - 11.4984i) q^{85} +(-2.28115 + 7.02067i) q^{86} +0.527864 q^{87} +(-3.04508 + 1.31433i) q^{88} -3.09017 q^{89} +(1.61803 - 4.97980i) q^{90} +(-2.80902 + 2.04087i) q^{91} +(6.66312 + 4.84104i) q^{92} +(0.927051 + 2.85317i) q^{93} +(-0.190983 - 0.587785i) q^{94} +(-14.2082 - 10.3229i) q^{95} +(0.809017 - 0.587785i) q^{96} +(1.09017 - 3.35520i) q^{97} +1.00000 q^{98} +(-3.38197 + 5.70634i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} + q^{3} - q^{4} - q^{5} + q^{6} - q^{7} - q^{8} + 2 q^{9}+O(q^{10}) \) 4 * q - q^2 + q^3 - q^4 - q^5 + q^6 - q^7 - q^8 + 2 * q^9	\( 4 q - q^{2} + q^{3} - q^{4} - q^{5} + q^{6} - q^{7} - q^{8} + 2 q^{9} - 6 q^{10} + 4 q^{11} - 4 q^{12} + 11 q^{13} - q^{14} - 4 q^{15} - q^{16} + 7 q^{17} + 2 q^{18} + 15 q^{19} - q^{20} - 4 q^{21} + 9 q^{22} - 24 q^{23} + q^{24} - 6 q^{25} - 9 q^{26} - 5 q^{27} - q^{28} - 5 q^{29} - 4 q^{30} + 3 q^{31} + 4 q^{32} + q^{33} + 12 q^{34} - q^{35} + 2 q^{36} + 12 q^{37} - 15 q^{38} - 11 q^{39} + 4 q^{40} + 8 q^{41} + q^{42} - 34 q^{43} - 11 q^{44} + 12 q^{45} + q^{46} + 2 q^{47} + q^{48} - q^{49} + 9 q^{50} + 13 q^{51} - 9 q^{52} - 9 q^{53} + 20 q^{54} - q^{55} + 4 q^{56} + 15 q^{57} - 5 q^{58} - 20 q^{59} + q^{60} + 18 q^{61} + 3 q^{62} + 2 q^{63} - q^{64} - 14 q^{65} + q^{66} - 8 q^{67} + 7 q^{68} - 11 q^{69} + 4 q^{70} + 3 q^{71} + 2 q^{72} + 11 q^{73} + 12 q^{74} - 9 q^{75} - 11 q^{77} + 4 q^{78} + 25 q^{79} + 4 q^{80} - q^{81} - 12 q^{82} - 19 q^{83} + q^{84} + 32 q^{85} + 11 q^{86} + 20 q^{87} - q^{88} + 10 q^{89} + 2 q^{90} - 9 q^{91} + 11 q^{92} - 3 q^{93} - 3 q^{94} - 30 q^{95} + q^{96} - 18 q^{97} + 4 q^{98} - 18 q^{99}+O(q^{100}) \) 4 * q - q^2 + q^3 - q^4 - q^5 + q^6 - q^7 - q^8 + 2 * q^9 - 6 * q^10 + 4 * q^11 - 4 * q^12 + 11 * q^13 - q^14 - 4 * q^15 - q^16 + 7 * q^17 + 2 * q^18 + 15 * q^19 - q^20 - 4 * q^21 + 9 * q^22 - 24 * q^23 + q^24 - 6 * q^25 - 9 * q^26 - 5 * q^27 - q^28 - 5 * q^29 - 4 * q^30 + 3 * q^31 + 4 * q^32 + q^33 + 12 * q^34 - q^35 + 2 * q^36 + 12 * q^37 - 15 * q^38 - 11 * q^39 + 4 * q^40 + 8 * q^41 + q^42 - 34 * q^43 - 11 * q^44 + 12 * q^45 + q^46 + 2 * q^47 + q^48 - q^49 + 9 * q^50 + 13 * q^51 - 9 * q^52 - 9 * q^53 + 20 * q^54 - q^55 + 4 * q^56 + 15 * q^57 - 5 * q^58 - 20 * q^59 + q^60 + 18 * q^61 + 3 * q^62 + 2 * q^63 - q^64 - 14 * q^65 + q^66 - 8 * q^67 + 7 * q^68 - 11 * q^69 + 4 * q^70 + 3 * q^71 + 2 * q^72 + 11 * q^73 + 12 * q^74 - 9 * q^75 - 11 * q^77 + 4 * q^78 + 25 * q^79 + 4 * q^80 - q^81 - 12 * q^82 - 19 * q^83 + q^84 + 32 * q^85 + 11 * q^86 + 20 * q^87 - q^88 + 10 * q^89 + 2 * q^90 - 9 * q^91 + 11 * q^92 - 3 * q^93 - 3 * q^94 - 30 * q^95 + q^96 - 18 * q^97 + 4 * q^98 - 18 * q^99

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