LMFDB - Embedded newform 418.2.f.c.229.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(115,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("418.115");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.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:	$3.33774680449$
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			229.1
Root			$-0.309017 - 0.951057i$ of defining polynomial
Character	$\chi$	$=$	418.229
Dual form			418.2.f.c.115.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 - 0.951057i) q^{2} +(0.809017 - 0.587785i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.809017 - 2.48990i) q^{5} +(-0.309017 - 0.951057i) q^{6} +(-1.30902 - 0.951057i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(-0.618034 + 1.90211i) q^{9} +O(q^{10})$	\(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} +(-1.30902 - 0.951057i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(-0.618034 + 1.90211i) q^{9} -2.61803 q^{10} +(-3.30902 - 0.224514i) q^{11} -1.00000 q^{12} +(1.50000 - 4.61653i) q^{13} +(-1.30902 + 0.951057i) q^{14} +(-2.11803 - 1.53884i) q^{15} +(0.309017 + 0.951057i) q^{16} +(0.0729490 + 0.224514i) q^{17} +(1.61803 + 1.17557i) q^{18} +(0.809017 - 0.587785i) q^{19} +(-0.809017 + 2.48990i) q^{20} -1.61803 q^{21} +(-1.23607 + 3.07768i) q^{22} -1.00000 q^{23} +(-0.309017 + 0.951057i) q^{24} +(-1.50000 + 1.08981i) q^{25} +(-3.92705 - 2.85317i) q^{26} +(1.54508 + 4.75528i) q^{27} +(0.500000 + 1.53884i) q^{28} +(7.23607 + 5.25731i) q^{29} +(-2.11803 + 1.53884i) q^{30} +(2.69098 - 8.28199i) q^{31} +1.00000 q^{32} +(-2.80902 + 1.76336i) q^{33} +0.236068 q^{34} +(-1.30902 + 4.02874i) q^{35} +(1.61803 - 1.17557i) q^{36} +(-7.59017 - 5.51458i) q^{37} +(-0.309017 - 0.951057i) q^{38} +(-1.50000 - 4.61653i) q^{39} +(2.11803 + 1.53884i) q^{40} +(4.92705 - 3.57971i) q^{41} +(-0.500000 + 1.53884i) q^{42} -7.70820 q^{43} +(2.54508 + 2.12663i) q^{44} +5.23607 q^{45} +(-0.309017 + 0.951057i) q^{46} +(7.04508 - 5.11855i) q^{47} +(0.809017 + 0.587785i) q^{48} +(-1.35410 - 4.16750i) q^{49} +(0.572949 + 1.76336i) q^{50} +(0.190983 + 0.138757i) q^{51} +(-3.92705 + 2.85317i) q^{52} +(1.39919 - 4.30625i) q^{53} +5.00000 q^{54} +(2.11803 + 8.42075i) q^{55} +1.61803 q^{56} +(0.309017 - 0.951057i) q^{57} +(7.23607 - 5.25731i) q^{58} +(4.73607 + 3.44095i) q^{59} +(0.809017 + 2.48990i) q^{60} +(4.50000 + 13.8496i) q^{61} +(-7.04508 - 5.11855i) q^{62} +(2.61803 - 1.90211i) q^{63} +(0.309017 - 0.951057i) q^{64} -12.7082 q^{65} +(0.809017 + 3.21644i) q^{66} -5.61803 q^{67} +(0.0729490 - 0.224514i) q^{68} +(-0.809017 + 0.587785i) q^{69} +(3.42705 + 2.48990i) q^{70} +(3.01722 + 9.28605i) q^{71} +(-0.618034 - 1.90211i) q^{72} +(-0.309017 - 0.224514i) q^{73} +(-7.59017 + 5.51458i) q^{74} +(-0.572949 + 1.76336i) q^{75} -1.00000 q^{76} +(4.11803 + 3.44095i) q^{77} -4.85410 q^{78} +(4.63525 - 14.2658i) q^{79} +(2.11803 - 1.53884i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(-1.88197 - 5.79210i) q^{82} +(2.71885 + 8.36775i) q^{83} +(1.30902 + 0.951057i) q^{84} +(0.500000 - 0.363271i) q^{85} +(-2.38197 + 7.33094i) q^{86} +8.94427 q^{87} +(2.80902 - 1.76336i) q^{88} +18.4164 q^{89} +(1.61803 - 4.97980i) q^{90} +(-6.35410 + 4.61653i) q^{91} +(0.809017 + 0.587785i) q^{92} +(-2.69098 - 8.28199i) q^{93} +(-2.69098 - 8.28199i) q^{94} +(-2.11803 - 1.53884i) q^{95} +(0.809017 - 0.587785i) q^{96} +(2.83688 - 8.73102i) q^{97} -4.38197 q^{98} +(2.47214 - 6.15537i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{2} + q^{3} - q^{4} - q^{5} + q^{6} - 3 q^{7} - q^{8} + 2 q^{9}+O(q^{10}) $ 4 * q - q^2 + q^3 - q^4 - q^5 + q^6 - 3 * q^7 - q^8 + 2 * q^9	\( 4 q - q^{2} + q^{3} - q^{4} - q^{5} + q^{6} - 3 q^{7} - q^{8} + 2 q^{9} - 6 q^{10} - 11 q^{11} - 4 q^{12} + 6 q^{13} - 3 q^{14} - 4 q^{15} - q^{16} + 7 q^{17} + 2 q^{18} + q^{19} - q^{20} - 2 q^{21} + 4 q^{22} - 4 q^{23} + q^{24} - 6 q^{25} - 9 q^{26} - 5 q^{27} + 2 q^{28} + 20 q^{29} - 4 q^{30} + 13 q^{31} + 4 q^{32} - 9 q^{33} - 8 q^{34} - 3 q^{35} + 2 q^{36} - 8 q^{37} + q^{38} - 6 q^{39} + 4 q^{40} + 13 q^{41} - 2 q^{42} - 4 q^{43} - q^{44} + 12 q^{45} + q^{46} + 17 q^{47} + q^{48} + 8 q^{49} + 9 q^{50} + 3 q^{51} - 9 q^{52} - 19 q^{53} + 20 q^{54} + 4 q^{55} + 2 q^{56} - q^{57} + 20 q^{58} + 10 q^{59} + q^{60} + 18 q^{61} - 17 q^{62} + 6 q^{63} - q^{64} - 24 q^{65} + q^{66} - 18 q^{67} + 7 q^{68} - q^{69} + 7 q^{70} - 17 q^{71} + 2 q^{72} + q^{73} - 8 q^{74} - 9 q^{75} - 4 q^{76} + 12 q^{77} - 6 q^{78} - 15 q^{79} + 4 q^{80} - q^{81} - 12 q^{82} + 31 q^{83} + 3 q^{84} + 2 q^{85} - 14 q^{86} + 9 q^{88} + 20 q^{89} + 2 q^{90} - 12 q^{91} + q^{92} - 13 q^{93} - 13 q^{94} - 4 q^{95} + q^{96} + 27 q^{97} - 22 q^{98} - 8 q^{99}+O(q^{100}) \) 4 * q - q^2 + q^3 - q^4 - q^5 + q^6 - 3 * q^7 - q^8 + 2 * q^9 - 6 * q^10 - 11 * q^11 - 4 * q^12 + 6 * q^13 - 3 * q^14 - 4 * q^15 - q^16 + 7 * q^17 + 2 * q^18 + q^19 - q^20 - 2 * q^21 + 4 * q^22 - 4 * q^23 + q^24 - 6 * q^25 - 9 * q^26 - 5 * q^27 + 2 * q^28 + 20 * q^29 - 4 * q^30 + 13 * q^31 + 4 * q^32 - 9 * q^33 - 8 * q^34 - 3 * q^35 + 2 * q^36 - 8 * q^37 + q^38 - 6 * q^39 + 4 * q^40 + 13 * q^41 - 2 * q^42 - 4 * q^43 - q^44 + 12 * q^45 + q^46 + 17 * q^47 + q^48 + 8 * q^49 + 9 * q^50 + 3 * q^51 - 9 * q^52 - 19 * q^53 + 20 * q^54 + 4 * q^55 + 2 * q^56 - q^57 + 20 * q^58 + 10 * q^59 + q^60 + 18 * q^61 - 17 * q^62 + 6 * q^63 - q^64 - 24 * q^65 + q^66 - 18 * q^67 + 7 * q^68 - q^69 + 7 * q^70 - 17 * q^71 + 2 * q^72 + q^73 - 8 * q^74 - 9 * q^75 - 4 * q^76 + 12 * q^77 - 6 * q^78 - 15 * q^79 + 4 * q^80 - q^81 - 12 * q^82 + 31 * q^83 + 3 * q^84 + 2 * q^85 - 14 * q^86 + 9 * q^88 + 20 * q^89 + 2 * q^90 - 12 * q^91 + q^92 - 13 * q^93 - 13 * q^94 - 4 * q^95 + q^96 + 27 * q^97 - 22 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

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
$7$	−1.30902	−	0.951057i	−0.494762	−	0.359466i	0.312251	−	0.950000i	$-0.398917\pi$
$7$	−1.30902	−	0.951057i	−0.494762	−	0.359466i	−0.807013	+	0.590534i	$0.798917\pi$
$8$	−0.809017	+	0.587785i	−0.286031	+	0.207813i
$9$	−0.618034	+	1.90211i	−0.206011	+	0.634038i
$10$	−2.61803			−0.827895
$11$	−3.30902	−	0.224514i	−0.997706	−	0.0676935i
$11$	−3.30902	−	0.224514i	−0.997706	−	0.0676935i
$12$	−1.00000			−0.288675
$13$	1.50000	−	4.61653i	0.416025	−	1.28039i	−0.495306	−	0.868719i	$-0.664944\pi$
$13$	1.50000	−	4.61653i	0.416025	−	1.28039i	0.911331	−	0.411675i	$-0.135056\pi$
$14$	−1.30902	+	0.951057i	−0.349850	+	0.254181i
$15$	−2.11803	−	1.53884i	−0.546874	−	0.397327i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	0.0729490	+	0.224514i	0.0176927	+	0.0544526i	0.959513	−	0.281664i	$-0.0908864\pi$
$17$	0.0729490	+	0.224514i	0.0176927	+	0.0544526i	−0.941820	+	0.336117i	$0.890886\pi$
$18$	1.61803	+	1.17557i	0.381374	+	0.277085i
$19$	0.809017	−	0.587785i	0.185601	−	0.134847i
$19$	0.809017	−	0.587785i	0.185601	−	0.134847i
$20$	−0.809017	+	2.48990i	−0.180902	+	0.556758i
$21$	−1.61803			−0.353084
$22$	−1.23607	+	3.07768i	−0.263531	+	0.656164i
$23$	−1.00000			−0.208514			−0.104257	−	0.994550i	$-0.533247\pi$
$23$	−1.00000			−0.208514			−0.104257	+	0.994550i	$0.533247\pi$
$24$	−0.309017	+	0.951057i	−0.0630778	+	0.194134i
$25$	−1.50000	+	1.08981i	−0.300000	+	0.217963i
$26$	−3.92705	−	2.85317i	−0.770158	−	0.559553i
$27$	1.54508	+	4.75528i	0.297352	+	0.915155i
$28$	0.500000	+	1.53884i	0.0944911	+	0.290814i
$29$	7.23607	+	5.25731i	1.34370	+	0.976258i	0.999299	+	0.0374370i	$0.0119194\pi$
$29$	7.23607	+	5.25731i	1.34370	+	0.976258i	0.344405	+	0.938821i	$0.388081\pi$
$30$	−2.11803	+	1.53884i	−0.386698	+	0.280953i
$31$	2.69098	−	8.28199i	0.483315	−	1.48749i	−0.351092	−	0.936341i	$-0.614190\pi$
$31$	2.69098	−	8.28199i	0.483315	−	1.48749i	0.834407	−	0.551149i	$-0.185810\pi$
$32$	1.00000			0.176777
$33$	−2.80902	+	1.76336i	−0.488987	+	0.306961i
$34$	0.236068			0.0404853
$35$	−1.30902	+	4.02874i	−0.221264	+	0.680981i
$36$	1.61803	−	1.17557i	0.269672	−	0.195928i
$37$	−7.59017	−	5.51458i	−1.24782	−	0.906592i	−0.249723	−	0.968317i	$-0.580340\pi$
$37$	−7.59017	−	5.51458i	−1.24782	−	0.906592i	−0.998093	+	0.0617257i	$0.980340\pi$
$38$	−0.309017	−	0.951057i	−0.0501292	−	0.154282i
$39$	−1.50000	−	4.61653i	−0.240192	−	0.739236i
$40$	2.11803	+	1.53884i	0.334891	+	0.243312i
$41$	4.92705	−	3.57971i	0.769476	−	0.559057i	−0.132326	−	0.991206i	$-0.542245\pi$
$41$	4.92705	−	3.57971i	0.769476	−	0.559057i	0.901802	+	0.432149i	$0.142245\pi$
$42$	−0.500000	+	1.53884i	−0.0771517	+	0.237448i
$43$	−7.70820			−1.17549			−0.587745	−	0.809046i	$-0.699984\pi$
$43$	−7.70820			−1.17549			−0.587745	+	0.809046i	$0.699984\pi$
$44$	2.54508	+	2.12663i	0.383686	+	0.320601i
$45$	5.23607			0.780547
$46$	−0.309017	+	0.951057i	−0.0455621	+	0.140226i
$47$	7.04508	−	5.11855i	1.02763	−	0.746618i	0.0597980	−	0.998210i	$-0.480954\pi$
$47$	7.04508	−	5.11855i	1.02763	−	0.746618i	0.967833	+	0.251593i	$0.0809543\pi$
$48$	0.809017	+	0.587785i	0.116772	+	0.0848395i
$49$	−1.35410	−	4.16750i	−0.193443	−	0.595357i
$50$	0.572949	+	1.76336i	0.0810272	+	0.249376i
$51$	0.190983	+	0.138757i	0.0267430	+	0.0194299i
$52$	−3.92705	+	2.85317i	−0.544584	+	0.395663i
$53$	1.39919	−	4.30625i	0.192193	−	0.591510i	−0.807805	−	0.589450i	$-0.799344\pi$
$53$	1.39919	−	4.30625i	0.192193	−	0.591510i	0.999998	−	0.00205944i	$-0.000655539\pi$
$54$	5.00000			0.680414
$55$	2.11803	+	8.42075i	0.285596	+	1.13545i
$56$	1.61803			0.216219
$57$	0.309017	−	0.951057i	0.0409303	−	0.125971i
$58$	7.23607	−	5.25731i	0.950142	−	0.690319i
$59$	4.73607	+	3.44095i	0.616584	+	0.447974i	0.851726	−	0.523987i	$-0.175556\pi$
$59$	4.73607	+	3.44095i	0.616584	+	0.447974i	−0.235143	+	0.971961i	$0.575556\pi$
$60$	0.809017	+	2.48990i	0.104444	+	0.321444i
$61$	4.50000	+	13.8496i	0.576166	+	1.77326i	0.632174	+	0.774826i	$0.282163\pi$
$61$	4.50000	+	13.8496i	0.576166	+	1.77326i	−0.0560084	+	0.998430i	$0.517837\pi$
$62$	−7.04508	−	5.11855i	−0.894727	−	0.650057i
$63$	2.61803	−	1.90211i	0.329841	−	0.239644i
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	−12.7082			−1.57626
$66$	0.809017	+	3.21644i	0.0995831	+	0.395916i
$67$	−5.61803			−0.686352			−0.343176	−	0.939271i	$-0.611503\pi$
$67$	−5.61803			−0.686352			−0.343176	+	0.939271i	$0.611503\pi$
$68$	0.0729490	−	0.224514i	0.00884637	−	0.0272263i
$69$	−0.809017	+	0.587785i	−0.0973942	+	0.0707610i
$70$	3.42705	+	2.48990i	0.409611	+	0.297600i
$71$	3.01722	+	9.28605i	0.358078	+	1.10205i	0.954203	+	0.299160i	$0.0967063\pi$
$71$	3.01722	+	9.28605i	0.358078	+	1.10205i	−0.596125	+	0.802892i	$0.703294\pi$
$72$	−0.618034	−	1.90211i	−0.0728360	−	0.224166i
$73$	−0.309017	−	0.224514i	−0.0361677	−	0.0262774i	0.569555	−	0.821954i	$-0.307116\pi$
$73$	−0.309017	−	0.224514i	−0.0361677	−	0.0262774i	−0.605722	+	0.795676i	$0.707116\pi$
$74$	−7.59017	+	5.51458i	−0.882339	+	0.641057i
$75$	−0.572949	+	1.76336i	−0.0661585	+	0.203615i
$76$	−1.00000			−0.114708
$77$	4.11803	+	3.44095i	0.469294	+	0.392133i
$78$	−4.85410			−0.549619
$79$	4.63525	−	14.2658i	0.521507	−	1.60503i	−0.249615	−	0.968345i	$-0.580304\pi$
$79$	4.63525	−	14.2658i	0.521507	−	1.60503i	0.771122	−	0.636688i	$-0.219696\pi$
$80$	2.11803	−	1.53884i	0.236803	−	0.172048i
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	−1.88197	−	5.79210i	−0.207828	−	0.639630i
$83$	2.71885	+	8.36775i	0.298432	+	0.918480i	0.982047	+	0.188637i	$0.0604069\pi$
$83$	2.71885	+	8.36775i	0.298432	+	0.918480i	−0.683615	+	0.729843i	$0.739593\pi$
$84$	1.30902	+	0.951057i	0.142825	+	0.103769i
$85$	0.500000	−	0.363271i	0.0542326	−	0.0394023i
$86$	−2.38197	+	7.33094i	−0.256854	+	0.790515i
$87$	8.94427			0.958927
$88$	2.80902	−	1.76336i	0.299442	−	0.187974i
$89$	18.4164			1.95214			0.976068	−	0.217467i	$-0.0697795\pi$
$89$	18.4164			1.95214			0.976068	+	0.217467i	$0.0697795\pi$
$90$	1.61803	−	4.97980i	0.170556	−	0.524917i
$91$	−6.35410	+	4.61653i	−0.666091	+	0.483943i
$92$	0.809017	+	0.587785i	0.0843459	+	0.0612808i
$93$	−2.69098	−	8.28199i	−0.279042	−	0.858803i
$94$	−2.69098	−	8.28199i	−0.277554	−	0.854222i
$95$	−2.11803	−	1.53884i	−0.217306	−	0.157882i
$96$	0.809017	−	0.587785i	0.0825700	−	0.0599906i
$97$	2.83688	−	8.73102i	0.288042	−	0.886501i	−0.697429	−	0.716654i	$-0.745673\pi$
$97$	2.83688	−	8.73102i	0.288042	−	0.886501i	0.985470	−	0.169847i	$-0.0543273\pi$
$98$	−4.38197			−0.442645
$99$	2.47214	−	6.15537i	0.248459	−	0.618638i
$100$	1.85410			0.185410
$101$	−2.83688	+	8.73102i	−0.282280	+	0.868769i	0.704920	+	0.709286i	$0.250983\pi$
$101$	−2.83688	+	8.73102i	−0.282280	+	0.868769i	−0.987201	+	0.159483i	$0.949017\pi$
$102$	0.190983	−	0.138757i	0.0189101	−	0.0137390i
$103$	−7.54508	−	5.48183i	−0.743439	−	0.540140i	0.150347	−	0.988633i	$-0.451961\pi$
$103$	−7.54508	−	5.48183i	−0.743439	−	0.540140i	−0.893786	+	0.448493i	$0.851961\pi$
$104$	1.50000	+	4.61653i	0.147087	+	0.452688i
$105$	1.30902	+	4.02874i	0.127747	+	0.393165i
$106$	−3.66312	−	2.66141i	−0.355794	−	0.258499i
$107$	−4.66312	+	3.38795i	−0.450801	+	0.327526i	−0.789912	−	0.613220i	$-0.789874\pi$
$107$	−4.66312	+	3.38795i	−0.450801	+	0.327526i	0.339111	+	0.940746i	$0.389874\pi$
$108$	1.54508	−	4.75528i	0.148676	−	0.457577i
$109$	13.0902			1.25381			0.626905	−	0.779095i	$-0.284321\pi$
$109$	13.0902			1.25381			0.626905	+	0.779095i	$0.284321\pi$
$110$	8.66312	+	0.587785i	0.825996	+	0.0560431i
$111$	−9.38197			−0.890497
$112$	0.500000	−	1.53884i	0.0472456	−	0.145407i
$113$	5.80902	−	4.22050i	0.546466	−	0.397031i	−0.280015	−	0.959996i	$-0.590339\pi$
$113$	5.80902	−	4.22050i	0.546466	−	0.397031i	0.826481	+	0.562965i	$0.190339\pi$
$114$	−0.809017	−	0.587785i	−0.0757714	−	0.0550511i
$115$	0.809017	+	2.48990i	0.0754412	+	0.232184i
$116$	−2.76393	−	8.50651i	−0.256625	−	0.789809i
$117$	7.85410	+	5.70634i	0.726112	+	0.527551i
$118$	4.73607	−	3.44095i	0.435990	−	0.316766i
$119$	0.118034	−	0.363271i	0.0108202	−	0.0333010i
$120$	2.61803			0.238993
$121$	10.8992	+	1.48584i	0.990835	+	0.135076i
$122$	14.5623			1.31841
$123$	1.88197	−	5.79210i	0.169691	−	0.522256i
$124$	−7.04508	+	5.11855i	−0.632667	+	0.459660i
$125$	−6.66312	−	4.84104i	−0.595967	−	0.432996i
$126$	−1.00000	−	3.07768i	−0.0890871	−	0.274182i
$127$	4.54508	+	13.9883i	0.403311	+	1.24126i	0.922297	+	0.386481i	$0.126310\pi$
$127$	4.54508	+	13.9883i	0.403311	+	1.24126i	−0.518986	+	0.854783i	$0.673690\pi$
$128$	−0.809017	−	0.587785i	−0.0715077	−	0.0519534i
$129$	−6.23607	+	4.53077i	−0.549055	+	0.398912i
$130$	−3.92705	+	12.0862i	−0.344425	+	1.06003i
$131$	−10.7639			−0.940449			−0.470225	−	0.882547i	$-0.655827\pi$
$131$	−10.7639			−0.940449			−0.470225	+	0.882547i	$0.655827\pi$
$132$	3.30902	+	0.224514i	0.288013	+	0.0195414i
$133$	−1.61803			−0.140301
$134$	−1.73607	+	5.34307i	−0.149973	+	0.461571i
$135$	10.5902	−	7.69421i	0.911457	−	0.662212i
$136$	−0.190983	−	0.138757i	−0.0163767	−	0.0118983i
$137$	−0.781153	−	2.40414i	−0.0667384	−	0.205400i	0.912126	−	0.409910i	$-0.134440\pi$
$137$	−0.781153	−	2.40414i	−0.0667384	−	0.205400i	−0.978864	+	0.204510i	$0.934440\pi$
$138$	0.309017	+	0.951057i	0.0263053	+	0.0809593i
$139$	2.07295	+	1.50609i	0.175825	+	0.127745i	0.672217	−	0.740354i	$-0.265342\pi$
$139$	2.07295	+	1.50609i	0.175825	+	0.127745i	−0.496392	+	0.868099i	$0.665342\pi$
$140$	3.42705	−	2.48990i	0.289639	−	0.210435i
$141$	2.69098	−	8.28199i	0.226622	−	0.697470i
$142$	9.76393			0.819371
$143$	−6.00000	+	14.9394i	−0.501745	+	1.24929i
$144$	−2.00000			−0.166667
$145$	7.23607	−	22.2703i	0.600923	−	1.84945i
$146$	−0.309017	+	0.224514i	−0.0255744	+	0.0185809i
$147$	−3.54508	−	2.57565i	−0.292394	−	0.212436i
$148$	2.89919	+	8.92278i	0.238312	+	0.733448i
$149$	1.21885	+	3.75123i	0.0998518	+	0.307312i	0.988488	−	0.151301i	$-0.0483463\pi$
$149$	1.21885	+	3.75123i	0.0998518	+	0.307312i	−0.888636	+	0.458613i	$0.848346\pi$
$150$	1.50000	+	1.08981i	0.122474	+	0.0889829i
$151$	−7.47214	+	5.42882i	−0.608074	+	0.441791i	−0.848736	−	0.528818i	$-0.822636\pi$
$151$	−7.47214	+	5.42882i	−0.608074	+	0.441791i	0.240662	+	0.970609i	$0.422636\pi$
$152$	−0.309017	+	0.951057i	−0.0250646	+	0.0771409i
$153$	−0.472136			−0.0381699
$154$	4.54508	−	2.85317i	0.366253	−	0.229915i
$155$	−22.7984			−1.83121
$156$	−1.50000	+	4.61653i	−0.120096	+	0.369618i
$157$	−4.23607	+	3.07768i	−0.338075	+	0.245626i	−0.743849	−	0.668347i	$-0.767002\pi$
$157$	−4.23607	+	3.07768i	−0.338075	+	0.245626i	0.405774	+	0.913973i	$0.367002\pi$
$158$	−12.1353	−	8.81678i	−0.965429	−	0.701425i
$159$	−1.39919	−	4.30625i	−0.110963	−	0.341508i
$160$	−0.809017	−	2.48990i	−0.0639584	−	0.196844i
$161$	1.30902	+	0.951057i	0.103165	+	0.0749538i
$162$	−0.809017	+	0.587785i	−0.0635624	+	0.0461808i
$163$	−3.50000	+	10.7719i	−0.274141	+	0.843720i	0.715304	+	0.698813i	$0.246288\pi$
$163$	−3.50000	+	10.7719i	−0.274141	+	0.843720i	−0.989445	+	0.144907i	$0.953712\pi$
$164$	−6.09017			−0.475562
$165$	6.66312	+	5.56758i	0.518723	+	0.433436i
$166$	8.79837			0.682886
$167$	−0.881966	+	2.71441i	−0.0682486	+	0.210048i	−0.979364	−	0.202103i	$-0.935222\pi$
$167$	−0.881966	+	2.71441i	−0.0682486	+	0.210048i	0.911116	+	0.412151i	$0.135222\pi$
$168$	1.30902	−	0.951057i	0.100993	−	0.0733756i
$169$	−8.54508	−	6.20837i	−0.657314	−	0.477567i
$170$	−0.190983	−	0.587785i	−0.0146477	−	0.0450811i
$171$	0.618034	+	1.90211i	0.0472622	+	0.145458i
$172$	6.23607	+	4.53077i	0.475496	+	0.345468i
$173$	−6.59017	+	4.78804i	−0.501041	+	0.364028i	−0.809415	−	0.587238i	$-0.800215\pi$
$173$	−6.59017	+	4.78804i	−0.501041	+	0.364028i	0.308373	+	0.951265i	$0.400215\pi$
$174$	2.76393	−	8.50651i	0.209533	−	0.644877i
$175$	3.00000			0.226779
$176$	−0.809017	−	3.21644i	−0.0609820	−	0.242448i
$177$	5.85410			0.440021
$178$	5.69098	−	17.5150i	0.426557	−	1.31281i
$179$	−9.47214	+	6.88191i	−0.707981	+	0.514378i	−0.882522	−	0.470272i	$-0.844156\pi$
$179$	−9.47214	+	6.88191i	−0.707981	+	0.514378i	0.174541	+	0.984650i	$0.444156\pi$
$180$	−4.23607	−	3.07768i	−0.315738	−	0.229397i
$181$	−3.36475	−	10.3556i	−0.250100	−	0.769727i	−0.994756	−	0.102279i	$-0.967387\pi$
$181$	−3.36475	−	10.3556i	−0.250100	−	0.769727i	0.744656	−	0.667448i	$-0.232613\pi$
$182$	2.42705	+	7.46969i	0.179905	+	0.553691i
$183$	11.7812	+	8.55951i	0.870888	+	0.632737i
$184$	0.809017	−	0.587785i	0.0596415	−	0.0433321i
$185$	−7.59017	+	23.3601i	−0.558040	+	1.71747i
$186$	−8.70820			−0.638516
$187$	−0.190983	−	0.759299i	−0.0139661	−	0.0555254i
$188$	−8.70820			−0.635111
$189$	2.50000	−	7.69421i	0.181848	−	0.559671i
$190$	−2.11803	+	1.53884i	−0.153658	+	0.111639i
$191$	−7.04508	−	5.11855i	−0.509764	−	0.370366i	0.302970	−	0.953000i	$-0.402022\pi$
$191$	−7.04508	−	5.11855i	−0.509764	−	0.370366i	−0.812734	+	0.582635i	$0.802022\pi$
$192$	−0.309017	−	0.951057i	−0.0223014	−	0.0686366i
$193$	−0.0450850	−	0.138757i	−0.00324529	−	0.00998797i	0.949421	−	0.314007i	$-0.101671\pi$
$193$	−0.0450850	−	0.138757i	−0.00324529	−	0.00998797i	−0.952666	+	0.304019i	$0.901671\pi$
$194$	−7.42705	−	5.39607i	−0.533231	−	0.387415i
$195$	−10.2812	+	7.46969i	−0.736249	+	0.534916i
$196$	−1.35410	+	4.16750i	−0.0967216	+	0.297678i
$197$	23.0000			1.63868			0.819341	−	0.573306i	$-0.194340\pi$
$197$	23.0000			1.63868			0.819341	+	0.573306i	$0.194340\pi$
$198$	−5.09017	−	4.25325i	−0.361743	−	0.302266i
$199$	−3.41641			−0.242183			−0.121091	−	0.992641i	$-0.538639\pi$
$199$	−3.41641			−0.242183			−0.121091	+	0.992641i	$0.538639\pi$
$200$	0.572949	−	1.76336i	0.0405136	−	0.124688i
$201$	−4.54508	+	3.30220i	−0.320586	+	0.232919i
$202$	7.42705	+	5.39607i	0.522565	+	0.379666i
$203$	−4.47214	−	13.7638i	−0.313882	−	0.966031i
$204$	−0.0729490	−	0.224514i	−0.00510745	−	0.0157191i
$205$	−12.8992	−	9.37181i	−0.900918	−	0.654555i
$206$	−7.54508	+	5.48183i	−0.525691	+	0.381937i
$207$	0.618034	−	1.90211i	0.0429563	−	0.132206i
$208$	4.85410			0.336571
$209$	−2.80902	+	1.76336i	−0.194304	+	0.121974i
$210$	4.23607			0.292316
$211$	−5.92705	+	18.2416i	−0.408035	+	1.25580i	0.510299	+	0.859997i	$0.329535\pi$
$211$	−5.92705	+	18.2416i	−0.408035	+	1.25580i	−0.918334	+	0.395806i	$0.870465\pi$
$212$	−3.66312	+	2.66141i	−0.251584	+	0.182787i
$213$	7.89919	+	5.73910i	0.541243	+	0.393236i
$214$	1.78115	+	5.48183i	0.121757	+	0.374730i
$215$	6.23607	+	19.1926i	0.425296	+	1.30893i
$216$	−4.04508	−	2.93893i	−0.275233	−	0.199969i
$217$	−11.3992	+	8.28199i	−0.773827	+	0.562218i
$218$	4.04508	−	12.4495i	0.273968	−	0.843186i
$219$	−0.381966			−0.0258109
$220$	3.23607	−	8.05748i	0.218176	−	0.543235i
$221$	1.14590			0.0770814
$222$	−2.89919	+	8.92278i	−0.194581	+	0.598858i
$223$	−10.4721	+	7.60845i	−0.701266	+	0.509500i	−0.880344	−	0.474335i	$-0.842688\pi$
$223$	−10.4721	+	7.60845i	−0.701266	+	0.509500i	0.179078	+	0.983835i	$0.442688\pi$
$224$	−1.30902	−	0.951057i	−0.0874624	−	0.0635451i
$225$	−1.14590	−	3.52671i	−0.0763932	−	0.235114i
$226$	−2.21885	−	6.82891i	−0.147596	−	0.454252i
$227$	−13.8713	−	10.0781i	−0.920672	−	0.668907i	0.0230192	−	0.999735i	$-0.492672\pi$
$227$	−13.8713	−	10.0781i	−0.920672	−	0.668907i	−0.943691	+	0.330828i	$0.892672\pi$
$228$	−0.809017	+	0.587785i	−0.0535785	+	0.0389270i
$229$	5.42705	−	16.7027i	0.358630	−	1.10375i	−0.595245	−	0.803544i	$-0.702945\pi$
$229$	5.42705	−	16.7027i	0.358630	−	1.10375i	0.953875	−	0.300204i	$-0.0970549\pi$
$230$	2.61803			0.172628
$231$	5.35410	+	0.363271i	0.352274	+	0.0239015i
$232$	−8.94427			−0.587220
$233$	0.218847	−	0.673542i	0.0143371	−	0.0441252i	−0.943632	−	0.330996i	$-0.892615\pi$
$233$	0.218847	−	0.673542i	0.0143371	−	0.0441252i	0.957969	+	0.286871i	$0.0926152\pi$
$234$	7.85410	−	5.70634i	0.513439	−	0.373035i
$235$	−18.4443	−	13.4005i	−1.20317	−	0.874155i
$236$	−1.80902	−	5.56758i	−0.117757	−	0.362419i
$237$	−4.63525	−	14.2658i	−0.301092	−	0.926666i
$238$	−0.309017	−	0.224514i	−0.0200306	−	0.0145531i
$239$	−4.30902	+	3.13068i	−0.278727	+	0.202507i	−0.718362	−	0.695669i	$-0.755108\pi$
$239$	−4.30902	+	3.13068i	−0.278727	+	0.202507i	0.439635	+	0.898177i	$0.355108\pi$
$240$	0.809017	−	2.48990i	0.0522218	−	0.160722i
$241$	−6.09017			−0.392302			−0.196151	−	0.980574i	$-0.562844\pi$
$241$	−6.09017			−0.392302			−0.196151	+	0.980574i	$0.562844\pi$
$242$	4.78115	−	9.90659i	0.307344	−	0.636820i
$243$	−16.0000			−1.02640
$244$	4.50000	−	13.8496i	0.288083	−	0.886628i
$245$	−9.28115	+	6.74315i	−0.592951	+	0.430804i
$246$	−4.92705	−	3.57971i	−0.314137	−	0.228234i
$247$	−1.50000	−	4.61653i	−0.0954427	−	0.293742i
$248$	2.69098	+	8.28199i	0.170878	+	0.525907i
$249$	7.11803	+	5.17155i	0.451087	+	0.327734i
$250$	−6.66312	+	4.84104i	−0.421413	+	0.306174i
$251$	4.76393	−	14.6619i	0.300697	−	0.925449i	−0.680551	−	0.732700i	$-0.738260\pi$
$251$	4.76393	−	14.6619i	0.300697	−	0.925449i	0.981248	−	0.192749i	$-0.0617403\pi$
$252$	−3.23607			−0.203853
$253$	3.30902	+	0.224514i	0.208036	+	0.0141151i
$254$	14.7082			0.922875
$255$	0.190983	−	0.587785i	0.0119598	−	0.0368085i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	−13.9721	−	10.1514i	−0.871558	−	0.633224i	0.0594466	−	0.998231i	$-0.481066\pi$
$257$	−13.9721	−	10.1514i	−0.871558	−	0.633224i	−0.931005	+	0.365008i	$0.881066\pi$
$258$	2.38197	+	7.33094i	0.148295	+	0.456404i
$259$	4.69098	+	14.4374i	0.291484	+	0.897094i
$260$	10.2812	+	7.46969i	0.637610	+	0.463251i
$261$	−14.4721	+	10.5146i	−0.895803	+	0.650839i
$262$	−3.32624	+	10.2371i	−0.205496	+	0.632451i
$263$	−12.3820			−0.763505			−0.381752	−	0.924265i	$-0.624679\pi$
$263$	−12.3820			−0.763505			−0.381752	+	0.924265i	$0.624679\pi$
$264$	1.23607	−	3.07768i	0.0760747	−	0.189418i
$265$	−11.8541			−0.728192
$266$	−0.500000	+	1.53884i	−0.0306570	+	0.0943524i
$267$	14.8992	−	10.8249i	0.911815	−	0.662473i
$268$	4.54508	+	3.30220i	0.277635	+	0.201714i
$269$	6.01722	+	18.5191i	0.366876	+	1.12913i	0.948798	+	0.315884i	$0.102301\pi$
$269$	6.01722	+	18.5191i	0.366876	+	1.12913i	−0.581921	+	0.813245i	$0.697699\pi$
$270$	−4.04508	−	12.4495i	−0.246176	−	0.757652i
$271$	11.4721	+	8.33499i	0.696883	+	0.506315i	0.878915	−	0.476978i	$-0.158268\pi$
$271$	11.4721	+	8.33499i	0.696883	+	0.506315i	−0.182033	+	0.983292i	$0.558268\pi$
$272$	−0.190983	+	0.138757i	−0.0115800	+	0.00841340i
$273$	−2.42705	+	7.46969i	−0.146892	+	0.452086i
$274$	−2.52786			−0.152714
$275$	5.20820	−	3.26944i	0.314067	−	0.197155i
$276$	1.00000			0.0601929
$277$	5.29837	−	16.3067i	0.318348	−	0.979776i	−0.656006	−	0.754756i	$-0.727755\pi$
$277$	5.29837	−	16.3067i	0.318348	−	0.979776i	0.974354	−	0.225020i	$-0.0722447\pi$
$278$	2.07295	−	1.50609i	0.124327	−	0.0903290i
$279$	14.0902	+	10.2371i	0.843556	+	0.612880i
$280$	−1.30902	−	4.02874i	−0.0782287	−	0.240763i
$281$	6.53444	+	20.1109i	0.389812	+	1.19972i	0.932929	+	0.360061i	$0.117244\pi$
$281$	6.53444	+	20.1109i	0.389812	+	1.19972i	−0.543117	+	0.839657i	$0.682756\pi$
$282$	−7.04508	−	5.11855i	−0.419529	−	0.304805i
$283$	13.8992	−	10.0984i	0.826221	−	0.600285i	−0.0922667	−	0.995734i	$-0.529411\pi$
$283$	13.8992	−	10.0984i	0.826221	−	0.600285i	0.918488	+	0.395450i	$0.129411\pi$
$284$	3.01722	−	9.28605i	0.179039	−	0.551026i
$285$	−2.61803			−0.155079
$286$	12.3541	+	10.3229i	0.730513	+	0.610404i
$287$	−9.85410			−0.581669
$288$	−0.618034	+	1.90211i	−0.0364180	+	0.112083i
$289$	13.7082	−	9.95959i	0.806365	−	0.585858i
$290$	−18.9443	−	13.7638i	−1.11245	−	0.808239i
$291$	−2.83688	−	8.73102i	−0.166301	−	0.511822i
$292$	0.118034	+	0.363271i	0.00690742	+	0.0212588i
$293$	19.7533	+	14.3516i	1.15400	+	0.838430i	0.989008	−	0.147865i	$-0.0472402\pi$
$293$	19.7533	+	14.3516i	1.15400	+	0.838430i	0.164992	+	0.986295i	$0.447240\pi$
$294$	−3.54508	+	2.57565i	−0.206754	+	0.150215i
$295$	4.73607	−	14.5761i	0.275745	−	0.848654i
$296$	9.38197			0.545316
$297$	−4.04508	−	16.0822i	−0.234720	−	0.933184i
$298$	3.94427			0.228486
$299$	−1.50000	+	4.61653i	−0.0867472	+	0.266981i
$300$	1.50000	−	1.08981i	0.0866025	−	0.0629204i
$301$	10.0902	+	7.33094i	0.581588	+	0.422548i
$302$	2.85410	+	8.78402i	0.164235	+	0.505464i
$303$	2.83688	+	8.73102i	0.162975	+	0.501584i
$304$	0.809017	+	0.587785i	0.0464003	+	0.0337118i
$305$	30.8435	−	22.4091i	1.76609	−	1.28314i
$306$	−0.145898	+	0.449028i	−0.00834044	+	0.0256692i
$307$	23.0000			1.31268			0.656340	−	0.754466i	$-0.272104\pi$
$307$	23.0000			1.31268			0.656340	+	0.754466i	$0.272104\pi$
$308$	−1.30902	−	5.20431i	−0.0745882	−	0.296543i
$309$	−9.32624			−0.530551
$310$	−7.04508	+	21.6825i	−0.400134	+	1.23149i
$311$	−1.61803	+	1.17557i	−0.0917503	+	0.0666605i	−0.632715	−	0.774385i	$-0.718059\pi$
$311$	−1.61803	+	1.17557i	−0.0917503	+	0.0666605i	0.540964	+	0.841046i	$0.318059\pi$
$312$	3.92705	+	2.85317i	0.222325	+	0.161529i
$313$	−6.16312	−	18.9681i	−0.348360	−	1.07214i	−0.959760	−	0.280821i	$-0.909393\pi$
$313$	−6.16312	−	18.9681i	−0.348360	−	1.07214i	0.611400	−	0.791322i	$-0.290607\pi$
$314$	1.61803	+	4.97980i	0.0913109	+	0.281026i
$315$	−6.85410	−	4.97980i	−0.386185	−	0.280580i
$316$	−12.1353	+	8.81678i	−0.682661	+	0.495983i
$317$	−5.25329	+	16.1680i	−0.295054	+	0.908083i	0.688149	+	0.725569i	$0.258423\pi$
$317$	−5.25329	+	16.1680i	−0.295054	+	0.908083i	−0.983203	+	0.182514i	$0.941577\pi$
$318$	−4.52786			−0.253910
$319$	−22.7639	−	19.0211i	−1.27454	−	1.06498i
$320$	−2.61803			−0.146353
$321$	−1.78115	+	5.48183i	−0.0994143	+	0.305966i
$322$	1.30902	−	0.951057i	0.0729487	−	0.0530003i
$323$	0.190983	+	0.138757i	0.0106266	+	0.00772066i
$324$	0.309017	+	0.951057i	0.0171676	+	0.0528365i
$325$	2.78115	+	8.55951i	0.154271	+	0.474796i
$326$	9.16312	+	6.65740i	0.507498	+	0.368719i
$327$	10.5902	−	7.69421i	0.585638	−	0.425491i
$328$	−1.88197	+	5.79210i	−0.103914	+	0.319815i
$329$	−14.0902			−0.776816
$330$	7.35410	−	4.61653i	0.404830	−	0.254131i
$331$	−24.1803			−1.32907			−0.664536	−	0.747256i	$-0.731371\pi$
$331$	−24.1803			−1.32907			−0.664536	+	0.747256i	$0.731371\pi$
$332$	2.71885	−	8.36775i	0.149216	−	0.459240i
$333$	15.1803	−	11.0292i	0.831878	−	0.604394i
$334$	2.30902	+	1.67760i	0.126344	+	0.0917941i
$335$	4.54508	+	13.9883i	0.248325	+	0.764264i
$336$	−0.500000	−	1.53884i	−0.0272772	−	0.0839507i
$337$	5.66312	+	4.11450i	0.308490	+	0.224131i	0.731248	−	0.682111i	$-0.238938\pi$
$337$	5.66312	+	4.11450i	0.308490	+	0.224131i	−0.422758	+	0.906242i	$0.638938\pi$
$338$	−8.54508	+	6.20837i	−0.464791	+	0.337691i
$339$	2.21885	−	6.82891i	0.120511	−	0.370895i
$340$	−0.618034			−0.0335176
$341$	−10.7639	+	26.8011i	−0.582900	+	1.45136i
$342$	2.00000			0.108148
$343$	−5.69098	+	17.5150i	−0.307284	+	0.945724i
$344$	6.23607	−	4.53077i	0.336226	−	0.244283i
$345$	2.11803	+	1.53884i	0.114031	+	0.0828485i
$346$	2.51722	+	7.74721i	0.135327	+	0.416493i
$347$	−3.90983	−	12.0332i	−0.209891	−	0.645977i	−0.999477	−	0.0323376i	$-0.989705\pi$
$347$	−3.90983	−	12.0332i	−0.209891	−	0.645977i	0.789586	−	0.613639i	$-0.210295\pi$
$348$	−7.23607	−	5.25731i	−0.387894	−	0.281821i
$349$	12.9271	−	9.39205i	0.691969	−	0.502745i	−0.185338	−	0.982675i	$-0.559338\pi$
$349$	12.9271	−	9.39205i	0.691969	−	0.502745i	0.877307	+	0.479930i	$0.159338\pi$
$350$	0.927051	−	2.85317i	0.0495530	−	0.152508i
$351$	24.2705			1.29546
$352$	−3.30902	−	0.224514i	−0.176371	−	0.0119666i
$353$	−26.0000			−1.38384			−0.691920	−	0.721974i	$-0.743235\pi$
$353$	−26.0000			−1.38384			−0.691920	+	0.721974i	$0.743235\pi$
$354$	1.80902	−	5.56758i	0.0961482	−	0.295914i
$355$	20.6803	−	15.0251i	1.09760	−	0.797452i
$356$	−14.8992	−	10.8249i	−0.789655	−	0.573718i
$357$	−0.118034	−	0.363271i	−0.00624702	−	0.0192264i
$358$	3.61803	+	11.1352i	0.191219	+	0.588512i
$359$	−21.4443	−	15.5802i	−1.13179	−	0.822290i	−0.145832	−	0.989309i	$-0.546586\pi$
$359$	−21.4443	−	15.5802i	−1.13179	−	0.822290i	−0.985954	+	0.167019i	$0.946586\pi$
$360$	−4.23607	+	3.07768i	−0.223260	+	0.162208i
$361$	0.309017	−	0.951057i	0.0162641	−	0.0500556i
$362$	−10.8885			−0.572289
$363$	9.69098	−	5.20431i	0.508645	−	0.273155i
$364$	7.85410			0.411667
$365$	−0.309017	+	0.951057i	−0.0161747	+	0.0497806i
$366$	11.7812	−	8.55951i	0.615811	−	0.447413i
$367$	11.2533	+	8.17599i	0.587417	+	0.426783i	0.841390	−	0.540428i	$-0.181738\pi$
$367$	11.2533	+	8.17599i	0.587417	+	0.426783i	−0.253973	+	0.967211i	$0.581738\pi$
$368$	−0.309017	−	0.951057i	−0.0161086	−	0.0495772i
$369$	3.76393	+	11.5842i	0.195942	+	0.603049i
$370$	19.8713	+	14.4374i	1.03306	+	0.750563i
$371$	−5.92705	+	4.30625i	−0.307717	+	0.223570i
$372$	−2.69098	+	8.28199i	−0.139521	+	0.429401i
$373$	21.2361			1.09956			0.549781	−	0.835309i	$-0.314711\pi$
$373$	21.2361			1.09956			0.549781	+	0.835309i	$0.314711\pi$
$374$	−0.781153	−	0.0530006i	−0.0403925	−	0.00274059i
$375$	−8.23607			−0.425309
$376$	−2.69098	+	8.28199i	−0.138777	+	0.427111i
$377$	35.1246	−	25.5195i	1.80901	−	1.31432i
$378$	−6.54508	−	4.75528i	−0.336643	−	0.244585i
$379$	7.86475	+	24.2052i	0.403985	+	1.24334i	0.921740	+	0.387809i	$0.126768\pi$
$379$	7.86475	+	24.2052i	0.403985	+	1.24334i	−0.517755	+	0.855529i	$0.673232\pi$
$380$	0.809017	+	2.48990i	0.0415017	+	0.127729i
$381$	11.8992	+	8.64527i	0.609614	+	0.442910i
$382$	−7.04508	+	5.11855i	−0.360458	+	0.261888i
$383$	4.42705	−	13.6251i	0.226212	−	0.696208i	−0.771955	−	0.635678i	$-0.780721\pi$
$383$	4.42705	−	13.6251i	0.226212	−	0.696208i	0.998166	−	0.0605305i	$-0.0192792\pi$
$384$	−1.00000			−0.0510310
$385$	5.23607	−	13.0373i	0.266855	−	0.664441i
$386$	−0.145898			−0.00742601
$387$	4.76393	−	14.6619i	0.242164	−	0.745305i
$388$	−7.42705	+	5.39607i	−0.377051	+	0.273944i
$389$	21.1803	+	15.3884i	1.07389	+	0.780224i	0.976607	−	0.215033i	$-0.0689860\pi$
$389$	21.1803	+	15.3884i	1.07389	+	0.780224i	0.0972792	+	0.995257i	$0.468986\pi$
$390$	3.92705	+	12.0862i	0.198854	+	0.612010i
$391$	−0.0729490	−	0.224514i	−0.00368919	−	0.0113542i
$392$	3.54508	+	2.57565i	0.179054	+	0.130090i
$393$	−8.70820	+	6.32688i	−0.439271	+	0.319149i
$394$	7.10739	−	21.8743i	0.358065	−	1.10201i
$395$	−39.2705			−1.97591
$396$	−5.61803	+	3.52671i	−0.282317	+	0.177224i
$397$	−10.8197			−0.543023			−0.271512	−	0.962435i	$-0.587524\pi$
$397$	−10.8197			−0.543023			−0.271512	+	0.962435i	$0.587524\pi$
$398$	−1.05573	+	3.24920i	−0.0529189	+	0.162868i
$399$	−1.30902	+	0.951057i	−0.0655328	+	0.0476124i
$400$	−1.50000	−	1.08981i	−0.0750000	−	0.0544907i
$401$	5.12868	+	15.7844i	0.256114	+	0.788238i	0.993608	+	0.112884i	$0.0360089\pi$
$401$	5.12868	+	15.7844i	0.256114	+	0.788238i	−0.737494	+	0.675353i	$0.763991\pi$
$402$	1.73607	+	5.34307i	0.0865872	+	0.266488i
$403$	−34.1976	−	24.8460i	−1.70350	−	1.23767i
$404$	7.42705	−	5.39607i	0.369510	−	0.268464i
$405$	−0.809017	+	2.48990i	−0.0402004	+	0.123724i
$406$	−14.4721			−0.718240
$407$	23.8779	+	19.9519i	1.18358	+	0.988981i
$408$	−0.236068			−0.0116871
$409$	1.01722	−	3.13068i	0.0502983	−	0.154802i	−0.922752	−	0.385393i	$-0.874066\pi$
$409$	1.01722	−	3.13068i	0.0502983	−	0.154802i	0.973051	+	0.230591i	$0.0740659\pi$
$410$	−12.8992	+	9.37181i	−0.637045	+	0.462841i
$411$	−2.04508	−	1.48584i	−0.100877	−	0.0732911i
$412$	2.88197	+	8.86978i	0.141984	+	0.436983i
$413$	−2.92705	−	9.00854i	−0.144031	−	0.443281i
$414$	−1.61803	−	1.17557i	−0.0795220	−	0.0577761i
$415$	18.6353	−	13.5393i	0.914769	−	0.664618i
$416$	1.50000	−	4.61653i	0.0735436	−	0.226344i
$417$	2.56231			0.125477
$418$	0.809017	+	3.21644i	0.0395703	+	0.157321i
$419$	25.5279			1.24712			0.623559	−	0.781776i	$-0.285686\pi$
$419$	25.5279			1.24712			0.623559	+	0.781776i	$0.285686\pi$
$420$	1.30902	−	4.02874i	0.0638735	−	0.196582i
$421$	−20.1353	+	14.6291i	−0.981332	+	0.712980i	−0.958006	−	0.286748i	$-0.907426\pi$
$421$	−20.1353	+	14.6291i	−0.981332	+	0.712980i	−0.0233263	+	0.999728i	$0.507426\pi$
$422$	15.5172	+	11.2739i	0.755366	+	0.548806i
$423$	5.38197	+	16.5640i	0.261680	+	0.805369i
$424$	1.39919	+	4.30625i	0.0679505	+	0.209130i
$425$	−0.354102	−	0.257270i	−0.0171765	−	0.0124794i
$426$	7.89919	−	5.73910i	0.382717	−	0.278060i
$427$	7.28115	−	22.4091i	0.352360	−	1.08445i
$428$	5.76393			0.278610
$429$	3.92705	+	15.6129i	0.189600	+	0.753799i
$430$	20.1803			0.973182
$431$	11.5344	−	35.4994i	0.555595	−	1.70994i	−0.138774	−	0.990324i	$-0.544316\pi$
$431$	11.5344	−	35.4994i	0.555595	−	1.70994i	0.694368	−	0.719620i	$-0.255684\pi$
$432$	−4.04508	+	2.93893i	−0.194619	+	0.141399i
$433$	19.3262	+	14.0413i	0.928760	+	0.674783i	0.945689	−	0.325073i	$-0.105389\pi$
$433$	19.3262	+	14.0413i	0.928760	+	0.674783i	−0.0169291	+	0.999857i	$0.505389\pi$
$434$	4.35410	+	13.4005i	0.209004	+	0.643247i
$435$	−7.23607	−	22.2703i	−0.346943	−	1.06778i
$436$	−10.5902	−	7.69421i	−0.507177	−	0.368486i
$437$	−0.809017	+	0.587785i	−0.0387005	+	0.0281176i
$438$	−0.118034	+	0.363271i	−0.00563988	+	0.0173578i
$439$	10.8541			0.518038			0.259019	−	0.965872i	$-0.416601\pi$
$439$	10.8541			0.518038			0.259019	+	0.965872i	$0.416601\pi$
$440$	−6.66312	−	5.56758i	−0.317652	−	0.265424i
$441$	8.76393			0.417330
$442$	0.354102	−	1.08981i	0.0168429	−	0.0518372i
$443$	8.73607	−	6.34712i	0.415063	−	0.301561i	−0.360585	−	0.932726i	$-0.617423\pi$
$443$	8.73607	−	6.34712i	0.415063	−	0.301561i	0.775648	+	0.631165i	$0.217423\pi$
$444$	7.59017	+	5.51458i	0.360214	+	0.261710i
$445$	−14.8992	−	45.8550i	−0.706289	−	2.17373i
$446$	4.00000	+	12.3107i	0.189405	+	0.582930i
$447$	3.19098	+	2.31838i	0.150928	+	0.109656i
$448$	−1.30902	+	0.951057i	−0.0618452	+	0.0449332i
$449$	3.98278	−	12.2577i	0.187959	−	0.578478i	−0.812028	−	0.583619i	$-0.801636\pi$
$449$	3.98278	−	12.2577i	0.187959	−	0.578478i	0.999987	+	0.00514051i	$0.00163628\pi$
$450$	−3.70820			−0.174806
$451$	−17.1074	+	10.7391i	−0.805556	+	0.505686i
$452$	−7.18034			−0.337735
$453$	−2.85410	+	8.78402i	−0.134097	+	0.412709i
$454$	−13.8713	+	10.0781i	−0.651013	+	0.472989i
$455$	16.6353	+	12.0862i	0.779873	+	0.566611i
$456$	0.309017	+	0.951057i	0.0144710	+	0.0445373i
$457$	0.600813	+	1.84911i	0.0281048	+	0.0864978i	0.964125	−	0.265448i	$-0.0855200\pi$
$457$	0.600813	+	1.84911i	0.0281048	+	0.0864978i	−0.936020	+	0.351946i	$0.885520\pi$
$458$	−14.2082	−	10.3229i	−0.663906	−	0.482356i
$459$	−0.954915	+	0.693786i	−0.0445716	+	0.0323832i
$460$	0.809017	−	2.48990i	0.0377206	−	0.116092i
$461$	−20.2361			−0.942488			−0.471244	−	0.882003i	$-0.656195\pi$
$461$	−20.2361			−0.942488			−0.471244	+	0.882003i	$0.656195\pi$
$462$	2.00000	−	4.97980i	0.0930484	−	0.231681i
$463$	29.8541			1.38744			0.693719	−	0.720246i	$-0.255971\pi$
$463$	29.8541			1.38744			0.693719	+	0.720246i	$0.255971\pi$
$464$	−2.76393	+	8.50651i	−0.128312	+	0.394905i
$465$	−18.4443	+	13.4005i	−0.855333	+	0.621436i
$466$	−0.572949	−	0.416272i	−0.0265414	−	0.0192834i
$467$	−0.718847	−	2.21238i	−0.0332643	−	0.102377i	0.933046	−	0.359758i	$-0.117141\pi$
$467$	−0.718847	−	2.21238i	−0.0332643	−	0.102377i	−0.966310	+	0.257381i	$0.917141\pi$
$468$	−3.00000	−	9.23305i	−0.138675	−	0.426798i
$469$	7.35410	+	5.34307i	0.339581	+	0.246720i
$470$	−18.4443	+	13.4005i	−0.850771	+	0.618121i
$471$	−1.61803	+	4.97980i	−0.0745551	+	0.229457i
$472$	−5.85410			−0.269457
$473$	25.5066	+	1.73060i	1.17279	+	0.0795731i
$474$	−15.0000			−0.688973
$475$	−0.572949	+	1.76336i	−0.0262887	+	0.0809083i
$476$	−0.309017	+	0.224514i	−0.0141638	+	0.0102906i
$477$	7.32624	+	5.32282i	0.335445	+	0.243715i
$478$	1.64590	+	5.06555i	0.0752816	+	0.231693i
$479$	5.69098	+	17.5150i	0.260028	+	0.800283i	0.992797	+	0.119806i	$0.0382273\pi$
$479$	5.69098	+	17.5150i	0.260028	+	0.800283i	−0.732770	+	0.680477i	$0.761773\pi$
$480$	−2.11803	−	1.53884i	−0.0966746	−	0.0702382i
$481$	−36.8435	+	26.7683i	−1.67992	+	1.22053i
$482$	−1.88197	+	5.79210i	−0.0857212	+	0.263823i
$483$	1.61803			0.0736231
$484$	−7.94427	−	7.60845i	−0.361103	−	0.345839i
$485$	−24.0344			−1.09135
$486$	−4.94427	+	15.2169i	−0.224277	+	0.690253i
$487$	30.9894	−	22.5151i	1.40426	−	1.02026i	0.410136	−	0.912024i	$-0.365481\pi$
$487$	30.9894	−	22.5151i	1.40426	−	1.02026i	0.994126	−	0.108232i	$-0.0345188\pi$
$488$	−11.7812	−	8.55951i	−0.533308	−	0.387471i
$489$	3.50000	+	10.7719i	0.158275	+	0.487122i
$490$	3.54508	+	10.9106i	0.160151	+	0.492893i
$491$	5.78115	+	4.20025i	0.260900	+	0.189555i	0.710544	−	0.703653i	$-0.248449\pi$
$491$	5.78115	+	4.20025i	0.260900	+	0.189555i	−0.449644	+	0.893208i	$0.648449\pi$
$492$	−4.92705	+	3.57971i	−0.222129	+	0.161386i
$493$	−0.652476	+	2.00811i	−0.0293860	+	0.0904409i
$494$	−4.85410			−0.218396
$495$	−17.3262	−	1.17557i	−0.778756	−	0.0528380i
$496$	8.70820			0.391010
$497$	4.88197	−	15.0251i	0.218986	−	0.673970i
$498$	7.11803	−	5.17155i	0.318967	−	0.231743i
$499$	26.6074	+	19.3314i	1.19111	+	0.865392i	0.993381	−	0.114864i	$-0.0366433\pi$
$499$	26.6074	+	19.3314i	1.19111	+	0.865392i	0.197729	+	0.980257i	$0.436643\pi$
$500$	2.54508	+	7.83297i	0.113820	+	0.350301i
$501$	0.881966	+	2.71441i	0.0394033	+	0.121271i
$502$	−12.4721	−	9.06154i	−0.556659	−	0.404436i
$503$	21.8262	−	15.8577i	0.973184	−	0.707059i	0.0170089	−	0.999855i	$-0.494586\pi$
$503$	21.8262	−	15.8577i	0.973184	−	0.707059i	0.956175	+	0.292796i	$0.0945856\pi$
$504$	−1.00000	+	3.07768i	−0.0445435	+	0.137091i
$505$	24.0344			1.06952
$506$	1.23607	−	3.07768i	0.0549499	−	0.136820i
$507$	−10.5623			−0.469088
$508$	4.54508	−	13.9883i	0.201656	−	0.620632i
$509$	3.51722	−	2.55541i	0.155898	−	0.113267i	−0.507102	−	0.861886i	$-0.669283\pi$
$509$	3.51722	−	2.55541i	0.155898	−	0.113267i	0.663000	+	0.748620i	$0.269283\pi$
$510$	−0.500000	−	0.363271i	−0.0221404	−	0.0160859i
$511$	0.190983	+	0.587785i	0.00844859	+	0.0260021i
$512$	0.309017	+	0.951057i	0.0136568	+	0.0420312i
$513$	4.04508	+	2.93893i	0.178595	+	0.129757i
$514$	−13.9721	+	10.1514i	−0.616284	+	0.447757i
$515$	−7.54508	+	23.2214i	−0.332476	+	1.02326i
$516$	7.70820			0.339335
$517$	−24.4615	+	15.3557i	−1.07582	+	0.675341i
$518$	15.1803			0.666986
$519$	−2.51722	+	7.74721i	−0.110494	+	0.340065i
$520$	10.2812	−	7.46969i	0.450858	−	0.327568i
$521$	−5.13525	−	3.73098i	−0.224980	−	0.163457i	0.469586	−	0.882887i	$-0.344403\pi$
$521$	−5.13525	−	3.73098i	−0.224980	−	0.163457i	−0.694565	+	0.719430i	$0.744403\pi$
$522$	5.52786	+	17.0130i	0.241948	+	0.744639i
$523$	−0.774575	−	2.38390i	−0.0338698	−	0.104241i	0.932692	−	0.360673i	$-0.117453\pi$
$523$	−0.774575	−	2.38390i	−0.0338698	−	0.104241i	−0.966562	+	0.256432i	$0.917453\pi$
$524$	8.70820	+	6.32688i	0.380420	+	0.276391i
$525$	2.42705	−	1.76336i	0.105925	−	0.0769592i
$526$	−3.82624	+	11.7759i	−0.166832	+	0.513456i
$527$	2.05573			0.0895489
$528$	−2.54508	−	2.12663i	−0.110761	−	0.0925496i
$529$	−22.0000			−0.956522
$530$	−3.66312	+	11.2739i	−0.159116	+	0.489708i
$531$	−9.47214	+	6.88191i	−0.411056	+	0.298649i
$532$	1.30902	+	0.951057i	0.0567531	+	0.0412335i
$533$	−9.13525	−	28.1154i	−0.395692	−	1.21781i
$534$	−5.69098	−	17.5150i	−0.246273	−	0.757950i
$535$	12.2082	+	8.86978i	0.527807	+	0.383474i
$536$	4.54508	−	3.30220i	0.196318	−	0.142633i
$537$	−3.61803	+	11.1352i	−0.156130	+	0.480518i
$538$	19.4721			0.839503
$539$	3.54508	+	14.0943i	0.152698	+	0.607086i
$540$	−13.0902			−0.563311
$541$	12.2254	−	37.6260i	0.525612	−	1.61767i	−0.237490	−	0.971390i	$-0.576325\pi$
$541$	12.2254	−	37.6260i	0.525612	−	1.61767i	0.763102	−	0.646278i	$-0.223675\pi$
$542$	11.4721	−	8.33499i	0.492770	−	0.358019i
$543$	−8.80902	−	6.40013i	−0.378031	−	0.274656i
$544$	0.0729490	+	0.224514i	0.00312766	+	0.00962596i
$545$	−10.5902	−	32.5932i	−0.453633	−	1.39614i
$546$	6.35410	+	4.61653i	0.271930	+	0.197569i
$547$	1.88197	−	1.36733i	0.0804671	−	0.0584627i	−0.546824	−	0.837247i	$-0.684163\pi$
$547$	1.88197	−	1.36733i	0.0804671	−	0.0584627i	0.627291	+	0.778785i	$0.284163\pi$
$548$	−0.781153	+	2.40414i	−0.0333692	+	0.102700i
$549$	−29.1246			−1.24301
$550$	−1.50000	−	5.96361i	−0.0639602	−	0.254289i
$551$	8.94427			0.381039
$552$	0.309017	−	0.951057i	0.0131526	−	0.0404797i
$553$	−19.6353	+	14.2658i	−0.834976	+	0.606646i
$554$	−13.8713	−	10.0781i	−0.589336	−	0.428178i
$555$	7.59017	+	23.3601i	0.322185	+	0.991583i
$556$	−0.791796	−	2.43690i	−0.0335796	−	0.103347i
$557$	−12.8541	−	9.33905i	−0.544646	−	0.395708i	0.281162	−	0.959660i	$-0.409280\pi$
$557$	−12.8541	−	9.33905i	−0.544646	−	0.395708i	−0.825808	+	0.563952i	$0.809280\pi$
$558$	14.0902	−	10.2371i	0.596484	−	0.433371i
$559$	−11.5623	+	35.5851i	−0.489033	+	1.50509i
$560$	−4.23607			−0.179007
$561$	−0.600813	−	0.502029i	−0.0253663	−	0.0211957i
$562$	21.1459			0.891986
$563$	−7.54508	+	23.2214i	−0.317987	+	0.978665i	0.656520	+	0.754309i	$0.272028\pi$
$563$	−7.54508	+	23.2214i	−0.317987	+	0.978665i	−0.974507	+	0.224356i	$0.927972\pi$
$564$	−7.04508	+	5.11855i	−0.296652	+	0.215530i
$565$	−15.2082	−	11.0494i	−0.639814	−	0.464852i
$566$	−5.30902	−	16.3395i	−0.223155	−	0.686799i
$567$	0.500000	+	1.53884i	0.0209980	+	0.0646253i
$568$	−7.89919	−	5.73910i	−0.331443	−	0.240807i
$569$	16.1803	−	11.7557i	0.678315	−	0.492825i	−0.194483	−	0.980906i	$-0.562303\pi$
$569$	16.1803	−	11.7557i	0.678315	−	0.492825i	0.872798	+	0.488081i	$0.162303\pi$
$570$	−0.809017	+	2.48990i	−0.0338860	+	0.104290i
$571$	19.3607			0.810219			0.405110	−	0.914268i	$-0.367233\pi$
$571$	19.3607			0.810219			0.405110	+	0.914268i	$0.367233\pi$
$572$	13.6353	−	8.55951i	0.570119	−	0.357891i
$573$	−8.70820			−0.363790
$574$	−3.04508	+	9.37181i	−0.127099	+	0.391172i
$575$	1.50000	−	1.08981i	0.0625543	−	0.0454484i
$576$	1.61803	+	1.17557i	0.0674181	+	0.0489821i
$577$	1.19098	+	3.66547i	0.0495813	+	0.152595i	0.972782	−	0.231723i	$-0.0744364\pi$
$577$	1.19098	+	3.66547i	0.0495813	+	0.152595i	−0.923200	+	0.384319i	$0.874436\pi$
$578$	−5.23607	−	16.1150i	−0.217792	−	0.670294i
$579$	−0.118034	−	0.0857567i	−0.00490533	−	0.00356393i
$580$	−18.9443	+	13.7638i	−0.786618	+	0.571511i
$581$	4.39919	−	13.5393i	0.182509	−	0.561705i
$582$	−9.18034			−0.380537
$583$	−5.59675	+	13.9353i	−0.231794	+	0.577143i
$584$	0.381966			0.0158059
$585$	7.85410	−	24.1724i	0.324727	−	0.999407i
$586$	19.7533	−	14.3516i	0.816001	−	0.592859i
$587$	−4.13525	−	3.00444i	−0.170680	−	0.124006i	0.499166	−	0.866507i	$-0.333640\pi$
$587$	−4.13525	−	3.00444i	−0.170680	−	0.124006i	−0.669846	+	0.742500i	$0.733640\pi$
$588$	1.35410	+	4.16750i	0.0558422	+	0.171865i
$589$	−2.69098	−	8.28199i	−0.110880	−	0.341254i
$590$	−12.3992	−	9.00854i	−0.510466	−	0.370876i
$591$	18.6074	−	13.5191i	0.765406	−	0.556100i
$592$	2.89919	−	8.92278i	0.119156	−	0.366724i
$593$	−19.9443			−0.819013			−0.409507	−	0.912307i	$-0.634299\pi$
$593$	−19.9443			−0.819013			−0.409507	+	0.912307i	$0.634299\pi$
$594$	−16.5451	−	1.12257i	−0.678853	−	0.0460596i
$595$	−1.00000			−0.0409960
$596$	1.21885	−	3.75123i	0.0499259	−	0.153656i
$597$	−2.76393	+	2.00811i	−0.113120	+	0.0821866i
$598$	3.92705	+	2.85317i	0.160589	+	0.116675i
$599$	4.40983	+	13.5721i	0.180181	+	0.554539i	0.999832	−	0.0183233i	$-0.00583282\pi$
$599$	4.40983	+	13.5721i	0.180181	+	0.554539i	−0.819651	+	0.572863i	$0.805833\pi$
$600$	−0.572949	−	1.76336i	−0.0233905	−	0.0719887i
$601$	−23.5902	−	17.1393i	−0.962263	−	0.699125i	−0.00858786	−	0.999963i	$-0.502734\pi$
$601$	−23.5902	−	17.1393i	−0.962263	−	0.699125i	−0.953675	+	0.300838i	$0.902734\pi$
$602$	10.0902	−	7.33094i	0.411245	−	0.298787i
$603$	3.47214	−	10.6861i	0.141396	−	0.435173i
$604$	9.23607			0.375810
$605$	−5.11803	−	28.3399i	−0.208078	−	1.15218i
$606$	9.18034			0.372926
$607$	−10.1287	+	31.1729i	−0.411110	+	1.26527i	0.504574	+	0.863369i	$0.331650\pi$
$607$	−10.1287	+	31.1729i	−0.411110	+	1.26527i	−0.915684	+	0.401899i	$0.868350\pi$
$608$	0.809017	−	0.587785i	0.0328100	−	0.0238378i
$609$	−11.7082	−	8.50651i	−0.474440	−	0.344701i
$610$	−11.7812	−	36.2587i	−0.477005	−	1.46807i
$611$	−13.0623	−	40.2016i	−0.528444	−	1.62638i
$612$	0.381966	+	0.277515i	0.0154401	+	0.0112179i
$613$	−4.61803	+	3.35520i	−0.186521	+	0.135515i	−0.677127	−	0.735866i	$-0.736775\pi$
$613$	−4.61803	+	3.35520i	−0.186521	+	0.135515i	0.490606	+	0.871381i	$0.336775\pi$
$614$	7.10739	−	21.8743i	0.286831	−	0.882775i
$615$	−15.9443			−0.642935
$616$	−5.35410	−	0.363271i	−0.215723	−	0.0146366i
$617$	22.2705			0.896577			0.448288	−	0.893889i	$-0.352034\pi$
$617$	22.2705			0.896577			0.448288	+	0.893889i	$0.352034\pi$
$618$	−2.88197	+	8.86978i	−0.115930	+	0.356795i
$619$	14.2082	−	10.3229i	0.571076	−	0.414911i	−0.264420	−	0.964408i	$-0.585181\pi$
$619$	14.2082	−	10.3229i	0.571076	−	0.414911i	0.835496	+	0.549497i	$0.185181\pi$
$620$	18.4443	+	13.4005i	0.740740	+	0.538179i
$621$	−1.54508	−	4.75528i	−0.0620021	−	0.190823i
$622$	0.618034	+	1.90211i	0.0247809	+	0.0762678i
$623$	−24.1074	−	17.5150i	−0.965842	−	0.701725i
$624$	3.92705	−	2.85317i	0.157208	−	0.114218i
$625$	−9.52786	+	29.3238i	−0.381115	+	1.17295i
$626$	−19.9443			−0.797133
$627$	−1.23607	+	3.07768i	−0.0493638	+	0.122911i
$628$	5.23607			0.208942
$629$	0.684405	−	2.10638i	0.0272890	−	0.0839870i
$630$	−6.85410	+	4.97980i	−0.273074	+	0.198400i
$631$	−15.2984	−	11.1149i	−0.609019	−	0.442478i	0.240050	−	0.970761i	$-0.422836\pi$
$631$	−15.2984	−	11.1149i	−0.609019	−	0.442478i	−0.849069	+	0.528283i	$0.822836\pi$
$632$	4.63525	+	14.2658i	0.184381	+	0.567465i
$633$	5.92705	+	18.2416i	0.235579	+	0.725038i
$634$	13.7533	+	9.99235i	0.546213	+	0.396847i
$635$	31.1525	−	22.6336i	1.23625	−	0.898187i
$636$	−1.39919	+	4.30625i	−0.0554814	+	0.170754i
$637$	−21.2705			−0.842768
$638$	−25.1246	+	15.7719i	−0.994693	+	0.624417i
$639$	−19.5279			−0.772510
$640$	−0.809017	+	2.48990i	−0.0319792	+	0.0984219i
$641$	−18.3262	+	13.3148i	−0.723843	+	0.525903i	−0.887610	−	0.460596i	$-0.847636\pi$
$641$	−18.3262	+	13.3148i	−0.723843	+	0.525903i	0.163767	+	0.986499i	$0.447636\pi$
$642$	4.66312	+	3.38795i	0.184039	+	0.133712i
$643$	−5.27051	−	16.2210i	−0.207849	−	0.639692i	−0.999584	−	0.0288285i	$-0.990822\pi$
$643$	−5.27051	−	16.2210i	−0.207849	−	0.639692i	0.791736	−	0.610864i	$-0.209178\pi$
$644$	−0.500000	−	1.53884i	−0.0197028	−	0.0606389i
$645$	16.3262	+	11.8617i	0.642845	+	0.467054i
$646$	0.190983	−	0.138757i	0.00751413	−	0.00545933i
$647$	7.37132	−	22.6866i	0.289797	−	0.891902i	−0.695123	−	0.718891i	$-0.744650\pi$
$647$	7.37132	−	22.6866i	0.289797	−	0.891902i	0.984920	−	0.173012i	$-0.0553498\pi$
$648$	1.00000			0.0392837
$649$	−14.8992	−	12.4495i	−0.584844	−	0.488685i
$650$	9.00000			0.353009
$651$	−4.35410	+	13.4005i	−0.170651	+	0.525209i
$652$	9.16312	−	6.65740i	0.358855	−	0.260724i
$653$	31.2984	+	22.7396i	1.22480	+	0.889869i	0.996489	−	0.0837190i	$-0.0266798\pi$
$653$	31.2984	+	22.7396i	1.22480	+	0.889869i	0.228311	+	0.973588i	$0.426680\pi$
$654$	−4.04508	−	12.4495i	−0.158175	−	0.486814i
$655$	8.70820	+	26.8011i	0.340258	+	1.04721i
$656$	4.92705	+	3.57971i	0.192369	+	0.139764i
$657$	0.618034	−	0.449028i	0.0241118	−	0.0175182i
$658$	−4.35410	+	13.4005i	−0.169741	+	0.522408i
$659$	−15.6525			−0.609734			−0.304867	−	0.952395i	$-0.598612\pi$
$659$	−15.6525			−0.609734			−0.304867	+	0.952395i	$0.598612\pi$
$660$	−2.11803	−	8.42075i	−0.0824444	−	0.327777i
$661$	−23.8541			−0.927817			−0.463909	−	0.885883i	$-0.653553\pi$
$661$	−23.8541			−0.927817			−0.463909	+	0.885883i	$0.653553\pi$
$662$	−7.47214	+	22.9969i	−0.290413	+	0.893799i
$663$	0.927051	−	0.673542i	0.0360037	−	0.0261582i
$664$	−7.11803	−	5.17155i	−0.276233	−	0.200695i
$665$	1.30902	+	4.02874i	0.0507615	+	0.156228i
$666$	−5.79837	−	17.8456i	−0.224682	−	0.691501i
$667$	−7.23607	−	5.25731i	−0.280182	−	0.203564i
$668$	2.30902	−	1.67760i	0.0893385	−	0.0649083i
$669$	−4.00000	+	12.3107i	−0.154649	+	0.475960i
$670$	14.7082			0.568227
$671$	−11.7812	−	46.8388i	−0.454806	−	1.80819i
$672$	−1.61803			−0.0624170
$673$	4.42705	−	13.6251i	0.170650	−	0.525208i	−0.828758	−	0.559607i	$-0.810952\pi$
$673$	4.42705	−	13.6251i	0.170650	−	0.525208i	0.999408	+	0.0343998i	$0.0109520\pi$
$674$	5.66312	−	4.11450i	0.218135	−	0.158484i
$675$	−7.50000	−	5.44907i	−0.288675	−	0.209735i
$676$	3.26393	+	10.0453i	0.125536	+	0.386360i
$677$	−1.83688	−	5.65334i	−0.0705971	−	0.217275i	0.909533	−	0.415632i	$-0.136440\pi$
$677$	−1.83688	−	5.65334i	−0.0705971	−	0.217275i	−0.980130	+	0.198357i	$0.936440\pi$
$678$	−5.80902	−	4.22050i	−0.223094	−	0.162087i
$679$	−12.0172	+	8.73102i	−0.461179	+	0.335066i
$680$	−0.190983	+	0.587785i	−0.00732386	+	0.0225405i
$681$	−17.1459			−0.657032
$682$	22.1631	+	18.5191i	0.848670	+	0.709133i
$683$	−1.97871			−0.0757134			−0.0378567	−	0.999283i	$-0.512053\pi$
$683$	−1.97871			−0.0757134			−0.0378567	+	0.999283i	$0.512053\pi$
$684$	0.618034	−	1.90211i	0.0236311	−	0.0727291i
$685$	−5.35410	+	3.88998i	−0.204570	+	0.148629i
$686$	14.8992	+	10.8249i	0.568854	+	0.413296i
$687$	−5.42705	−	16.7027i	−0.207055	−	0.637249i
$688$	−2.38197	−	7.33094i	−0.0908116	−	0.279489i
$689$	−17.7812	−	12.9188i	−0.677408	−	0.492166i
$690$	2.11803	−	1.53884i	0.0806322	−	0.0585827i
$691$	3.58359	−	11.0292i	0.136326	−	0.419569i	−0.859468	−	0.511190i	$-0.829205\pi$
$691$	3.58359	−	11.0292i	0.136326	−	0.419569i	0.995794	+	0.0916210i	$0.0292048\pi$
$692$	8.14590			0.309661
$693$	−9.09017	+	5.70634i	−0.345307	+	0.216766i
$694$	−12.6525			−0.480281
$695$	2.07295	−	6.37988i	0.0786314	−	0.242003i
$696$	−7.23607	+	5.25731i	−0.274282	+	0.199278i
$697$	1.16312	+	0.845055i	0.0440563	+	0.0320088i
$698$	−4.93769	−	15.1967i	−0.186894	−	0.575202i
$699$	−0.218847	−	0.673542i	−0.00827756	−	0.0254757i
$700$	−2.42705	−	1.76336i	−0.0917339	−	0.0666486i
$701$	−21.2533	+	15.4414i	−0.802726	+	0.583214i	−0.911712	−	0.410829i	$-0.865239\pi$
$701$	−21.2533	+	15.4414i	−0.802726	+	0.583214i	0.108987	+	0.994043i	$0.465239\pi$
$702$	7.50000	−	23.0826i	0.283069	−	0.871198i
$703$	−9.38197			−0.353848
$704$	−1.23607	+	3.07768i	−0.0465861	+	0.115995i
$705$	−22.7984			−0.858636
$706$	−8.03444	+	24.7275i	−0.302380	+	0.930631i
$707$	12.0172	−	8.73102i	0.451954	−	0.328364i
$708$	−4.73607	−	3.44095i	−0.177992	−	0.129319i
$709$	−14.9615	−	46.0467i	−0.561891	−	1.72932i	−0.677014	−	0.735970i	$-0.736726\pi$
$709$	−14.9615	−	46.0467i	−0.561891	−	1.72932i	0.115123	−	0.993351i	$-0.463274\pi$
$710$	−7.89919	−	24.3112i	−0.296451	−	0.912383i
$711$	24.2705	+	17.6336i	0.910215	+	0.661310i
$712$	−14.8992	+	10.8249i	−0.558371	+	0.405680i
$713$	−2.69098	+	8.28199i	−0.100778	+	0.310163i
$714$	−0.381966			−0.0142947
$715$	42.0517	+	2.85317i	1.57264	+	0.106702i
$716$	11.7082			0.437556
$717$	−1.64590	+	5.06555i	−0.0614672	+	0.189177i
$718$	−21.4443	+	15.5802i	−0.800293	+	0.581447i
$719$	11.0172	+	8.00448i	0.410873	+	0.298517i	0.773955	−	0.633240i	$-0.218276\pi$
$719$	11.0172	+	8.00448i	0.410873	+	0.298517i	−0.363082	+	0.931757i	$0.618276\pi$
$720$	1.61803	+	4.97980i	0.0603006	+	0.185586i
$721$	4.66312	+	14.3516i	0.173664	+	0.534482i
$722$	−0.809017	−	0.587785i	−0.0301085	−	0.0218751i
$723$	−4.92705	+	3.57971i	−0.183239	+	0.133131i
$724$	−3.36475	+	10.3556i	−0.125050	+	0.384864i
$725$	−16.5836			−0.615899
$726$	−1.95492	−	10.8249i	−0.0725537	−	0.401749i
$727$	31.2918			1.16055			0.580274	−	0.814421i	$-0.302945\pi$
$727$	31.2918			1.16055			0.580274	+	0.814421i	$0.302945\pi$
$728$	2.42705	−	7.46969i	0.0899525	−	0.276845i
$729$	−10.5172	+	7.64121i	−0.389527	+	0.283008i
$730$	0.809017	+	0.587785i	0.0299431	+	0.0217549i
$731$	−0.562306	−	1.73060i	−0.0207976	−	0.0640085i
$732$	−4.50000	−	13.8496i	−0.166325	−	0.511895i
$733$	−17.8713	−	12.9843i	−0.660092	−	0.479585i	0.206602	−	0.978425i	$-0.433760\pi$
$733$	−17.8713	−	12.9843i	−0.660092	−	0.479585i	−0.866694	+	0.498840i	$0.833760\pi$
$734$	11.2533	−	8.17599i	0.415366	−	0.301781i
$735$	−3.54508	+	10.9106i	−0.130762	+	0.402445i
$736$	−1.00000			−0.0368605
$737$	18.5902	+	1.26133i	0.684778	+	0.0464616i
$738$	12.1803			0.448365
$739$	−9.79837	+	30.1563i	−0.360439	+	1.10932i	0.592349	+	0.805681i	$0.298201\pi$
$739$	−9.79837	+	30.1563i	−0.360439	+	1.10932i	−0.952788	+	0.303636i	$0.901799\pi$
$740$	19.8713	−	14.4374i	0.730484	−	0.530728i
$741$	−3.92705	−	2.85317i	−0.144264	−	0.104814i
$742$	2.26393	+	6.96767i	0.0831116	+	0.255791i
$743$	4.52786	+	13.9353i	0.166111	+	0.511238i	0.999116	−	0.0420273i	$-0.0133817\pi$
$743$	4.52786	+	13.9353i	0.166111	+	0.511238i	−0.833005	+	0.553265i	$0.813382\pi$
$744$	7.04508	+	5.11855i	0.258285	+	0.187655i
$745$	8.35410	−	6.06961i	0.306071	−	0.222373i
$746$	6.56231	−	20.1967i	0.240263	−	0.739454i
$747$	−17.5967			−0.643831
$748$	−0.291796	+	0.726543i	−0.0106691	+	0.0265650i
$749$	9.32624			0.340773
$750$	−2.54508	+	7.83297i	−0.0929334	+	0.286019i
$751$	−9.28115	+	6.74315i	−0.338674	+	0.246061i	−0.744102	−	0.668066i	$-0.767122\pi$
$751$	−9.28115	+	6.74315i	−0.338674	+	0.246061i	0.405428	+	0.914127i	$0.367122\pi$
$752$	7.04508	+	5.11855i	0.256908	+	0.186654i
$753$	−4.76393	−	14.6619i	−0.173607	−	0.534308i
$754$	−13.4164	−	41.2915i	−0.488597	−	1.50375i
$755$	19.5623	+	14.2128i	0.711945	+	0.517258i
$756$	−6.54508	+	4.75528i	−0.238042	+	0.172948i
$757$	−14.9894	+	46.1325i	−0.544797	+	1.67671i	0.176674	+	0.984269i	$0.443466\pi$
$757$	−14.9894	+	46.1325i	−0.544797	+	1.67671i	−0.721471	+	0.692445i	$0.756534\pi$
$758$	25.4508			0.924416
$759$	2.80902	−	1.76336i	0.101961	−	0.0640058i
$760$	2.61803			0.0949661
$761$	−15.7254	+	48.3979i	−0.570046	+	1.75442i	0.0824133	+	0.996598i	$0.473737\pi$
$761$	−15.7254	+	48.3979i	−0.570046	+	1.75442i	−0.652460	+	0.757824i	$0.726263\pi$
$762$	11.8992	−	8.64527i	0.431062	−	0.313185i
$763$	−17.1353	−	12.4495i	−0.620338	−	0.450702i
$764$	2.69098	+	8.28199i	0.0973563	+	0.299632i
$765$	0.381966	+	1.17557i	0.0138100	+	0.0425028i
$766$	−11.5902	−	8.42075i	−0.418770	−	0.304254i
$767$	22.9894	−	16.7027i	0.830098	−	0.603101i
$768$	−0.309017	+	0.951057i	−0.0111507	+	0.0343183i
$769$	3.29180			0.118705			0.0593526	−	0.998237i	$-0.481096\pi$
$769$	3.29180			0.118705			0.0593526	+	0.998237i	$0.481096\pi$
$770$	−10.7812	−	9.00854i	−0.388526	−	0.324645i
$771$	−17.2705			−0.621982
$772$	−0.0450850	+	0.138757i	−0.00162264	+	0.00499398i
$773$	14.9164	−	10.8374i	0.536506	−	0.389794i	−0.286280	−	0.958146i	$-0.592419\pi$
$773$	14.9164	−	10.8374i	0.536506	−	0.389794i	0.822786	+	0.568352i	$0.192419\pi$
$774$	−12.4721	−	9.06154i	−0.448302	−	0.325710i
$775$	4.98936	+	15.3557i	0.179223	+	0.551592i
$776$	2.83688	+	8.73102i	0.101838	+	0.313425i
$777$	12.2812	+	8.92278i	0.440584	+	0.320103i
$778$	21.1803	−	15.3884i	0.759352	−	0.551702i
$779$	1.88197	−	5.79210i	0.0674284	−	0.207523i
$780$	12.7082			0.455027
$781$	−7.89919	−	31.4051i	−0.282655	−	1.12376i
$782$	−0.236068			−0.00844177
$783$	−13.8197	+	42.5325i	−0.493874	+	1.51999i
$784$	3.54508	−	2.57565i	0.126610	−	0.0919877i
$785$	11.0902	+	8.05748i	0.395825	+	0.287584i
$786$	3.32624	+	10.2371i	0.118643	+	0.365146i
$787$	10.9656	+	33.7485i	0.390880	+	1.20300i	0.932124	+	0.362139i	$0.117954\pi$
$787$	10.9656	+	33.7485i	0.390880	+	1.20300i	−0.541244	+	0.840866i	$0.682046\pi$
$788$	−18.6074	−	13.5191i	−0.662861	−	0.481597i
$789$	−10.0172	+	7.27794i	−0.356623	+	0.259101i
$790$	−12.1353	+	37.3485i	−0.431753	+	1.32880i
$791$	−11.6180			−0.413090
$792$	1.61803	+	6.43288i	0.0574943	+	0.228582i
$793$	70.6869			2.51017
$794$	−3.34346	+	10.2901i	−0.118655	+	0.365182i
$795$	−9.59017	+	6.96767i	−0.340128	+	0.247118i
$796$	2.76393	+	2.00811i	0.0979650	+	0.0711757i
$797$	−4.50000	−	13.8496i	−0.159398	−	0.490577i	0.839182	−	0.543851i	$-0.183034\pi$
$797$	−4.50000	−	13.8496i	−0.159398	−	0.490577i	−0.998580	+	0.0532739i	$0.983034\pi$
$798$	0.500000	+	1.53884i	0.0176998	+	0.0544744i
$799$	1.66312	+	1.20833i	0.0588369	+	0.0427475i
$800$	−1.50000	+	1.08981i	−0.0530330	+	0.0385307i
$801$	−11.3820	+	35.0301i	−0.402162	+	1.23773i
$802$	16.5967			0.586052
$803$	0.972136	+	0.812299i	0.0343059	+	0.0286654i
$804$	5.61803			0.198133
$805$	1.30902	−	4.02874i	0.0461368	−	0.141994i
$806$	−34.1976	+	24.8460i	−1.20456	+	0.875162i
$807$	15.7533	+	11.4454i	0.554542	+	0.402898i
$808$	−2.83688	−	8.73102i	−0.0998011	−	0.307156i
$809$	−5.52786	−	17.0130i	−0.194349	−	0.598146i	−0.999984	−	0.00573251i	$-0.998175\pi$
$809$	−5.52786	−	17.0130i	−0.194349	−	0.598146i	0.805634	−	0.592413i	$-0.201825\pi$
$810$	2.11803	+	1.53884i	0.0744201	+	0.0540694i
$811$	−21.4164	+	15.5599i	−0.752032	+	0.546383i	−0.896456	−	0.443133i	$-0.853867\pi$
$811$	−21.4164	+	15.5599i	−0.752032	+	0.546383i	0.144424	+	0.989516i	$0.453867\pi$
$812$	−4.47214	+	13.7638i	−0.156941	+	0.483015i
$813$	14.1803			0.497326
$814$	26.3541	−	16.5437i	0.923711	−	0.579858i
$815$	29.6525			1.03868
$816$	−0.0729490	+	0.224514i	−0.00255373	+	0.00785956i
$817$	−6.23607	+	4.53077i	−0.218172	+	0.158512i
$818$	−2.66312	−	1.93487i	−0.0931138	−	0.0676511i
$819$	−4.85410	−	14.9394i	−0.169616	−	0.522025i
$820$	4.92705	+	15.1639i	0.172060	+	0.529546i
$821$	11.2082	+	8.14324i	0.391169	+	0.284201i	0.765934	−	0.642919i	$-0.222277\pi$
$821$	11.2082	+	8.14324i	0.391169	+	0.284201i	−0.374765	+	0.927120i	$0.622277\pi$
$822$	−2.04508	+	1.48584i	−0.0713305	+	0.0518247i
$823$	1.76393	−	5.42882i	0.0614868	−	0.189237i	−0.915595	−	0.402102i	$-0.868280\pi$
$823$	1.76393	−	5.42882i	0.0614868	−	0.189237i	0.977082	+	0.212865i	$0.0682796\pi$
$824$	9.32624			0.324895
$825$	2.29180	−	5.70634i	0.0797901	−	0.198669i
$826$	−9.47214			−0.329578
$827$	6.68034	−	20.5600i	0.232298	−	0.714940i	−0.765170	−	0.643828i	$-0.777345\pi$
$827$	6.68034	−	20.5600i	0.232298	−	0.714940i	0.997468	−	0.0711122i	$-0.0226548\pi$
$828$	−1.61803	+	1.17557i	−0.0562306	+	0.0408539i
$829$	35.1246	+	25.5195i	1.21993	+	0.886330i	0.996094	−	0.0882976i	$-0.0281426\pi$
$829$	35.1246	+	25.5195i	1.21993	+	0.886330i	0.223834	+	0.974627i	$0.428143\pi$
$830$	−7.11803	−	21.9071i	−0.247071	−	0.760405i
$831$	−5.29837	−	16.3067i	−0.183799	−	0.565674i
$832$	−3.92705	−	2.85317i	−0.136146	−	0.0989159i
$833$	0.836881	−	0.608030i	0.0289962	−	0.0210670i
$834$	0.791796	−	2.43690i	0.0274177	−	0.0843829i
$835$	7.47214			0.258584
$836$	3.30902	+	0.224514i	0.114445	+	0.00776498i
$837$	43.5410			1.50500
$838$	7.88854	−	24.2784i	0.272505	−	0.838685i
$839$	−4.73607	+	3.44095i	−0.163507	+	0.118795i	−0.666530	−	0.745478i	$-0.732221\pi$
$839$	−4.73607	+	3.44095i	−0.163507	+	0.118795i	0.503023	+	0.864273i	$0.332221\pi$
$840$	−3.42705	−	2.48990i	−0.118244	−	0.0859097i
$841$	15.7599	+	48.5039i	0.543444	+	1.67255i
$842$	7.69098	+	23.6704i	0.265049	+	0.815736i
$843$	17.1074	+	12.4292i	0.589210	+	0.428086i
$844$	15.5172	−	11.2739i	0.534125	−	0.388064i
$845$	−8.54508	+	26.2991i	−0.293960	+	0.904715i
$846$	17.4164			0.598788
$847$	−12.8541	−	12.3107i	−0.441672	−	0.423002i
$848$	4.52786			0.155487
$849$	5.30902	−	16.3395i	0.182205	−	0.560769i
$850$	−0.354102	+	0.257270i	−0.0121456	+	0.00882429i
$851$	7.59017	+	5.51458i	0.260188	+	0.189037i
$852$	−3.01722	−	9.28605i	−0.103368	−	0.318135i
$853$	7.15248	+	22.0131i	0.244896	+	0.753713i	0.995654	+	0.0931347i	$0.0296887\pi$
$853$	7.15248	+	22.0131i	0.244896	+	0.753713i	−0.750757	+	0.660578i	$0.770311\pi$
$854$	−19.0623	−	13.8496i	−0.652299	−	0.473923i
$855$	4.23607	−	3.07768i	0.144870	−	0.105255i
$856$	1.78115	−	5.48183i	0.0608786	−	0.187365i
$857$	33.8541			1.15643			0.578217	−	0.815883i	$-0.303749\pi$
$857$	33.8541			1.15643			0.578217	+	0.815883i	$0.303749\pi$
$858$	16.0623	+	1.08981i	0.548358	+	0.0372056i
$859$	−16.3050			−0.556318			−0.278159	−	0.960535i	$-0.589724\pi$
$859$	−16.3050			−0.556318			−0.278159	+	0.960535i	$0.589724\pi$
$860$	6.23607	−	19.1926i	0.212648	−	0.654464i
$861$	−7.97214	+	5.79210i	−0.271690	+	0.197394i
$862$	−30.1976	−	21.9398i	−1.02853	−	0.747273i
$863$	0.381966	+	1.17557i	0.0130023	+	0.0400169i	0.957347	−	0.288940i	$-0.0933029\pi$
$863$	0.381966	+	1.17557i	0.0130023	+	0.0400169i	−0.944345	+	0.328957i	$0.893303\pi$
$864$	1.54508	+	4.75528i	0.0525649	+	0.161778i
$865$	17.2533	+	12.5352i	0.586629	+	0.426211i
$866$	19.3262	−	14.0413i	0.656732	−	0.477144i
$867$	5.23607	−	16.1150i	0.177826	−	0.547293i
$868$	14.0902			0.478252
$869$	−18.5410	+	46.1653i	−0.628961	+	1.56605i
$870$	−23.4164			−0.793891
$871$	−8.42705	+	25.9358i	−0.285540	+	0.878801i
$872$	−10.5902	+	7.69421i	−0.358628	+	0.260559i
$873$	14.8541	+	10.7921i	0.502735	+	0.365258i
$874$	0.309017	+	0.951057i	0.0104527	+	0.0321700i
$875$	4.11803	+	12.6740i	0.139215	+	0.428460i
$876$	0.309017	+	0.224514i	0.0104407	+	0.00758562i
$877$	12.7361	−	9.25330i	0.430066	−	0.312462i	−0.351609	−	0.936147i	$-0.614365\pi$
$877$	12.7361	−	9.25330i	0.430066	−	0.312462i	0.781675	+	0.623685i	$0.214365\pi$
$878$	3.35410	−	10.3229i	0.113195	−	0.348380i
$879$	24.4164			0.823545
$880$	−7.35410	+	4.61653i	−0.247907	+	0.155623i
$881$	−31.4164			−1.05845			−0.529223	−	0.848483i	$-0.677516\pi$
$881$	−31.4164			−1.05845			−0.529223	+	0.848483i	$0.677516\pi$
$882$	2.70820	−	8.33499i	0.0911900	−	0.280654i
$883$	−42.5066	+	30.8828i	−1.43046	+	1.03929i	−0.440529	+	0.897738i	$0.645209\pi$
$883$	−42.5066	+	30.8828i	−1.43046	+	1.03929i	−0.989931	+	0.141552i	$0.954791\pi$
$884$	−0.927051	−	0.673542i	−0.0311801	−	0.0226537i
$885$	−4.73607	−	14.5761i	−0.159201	−	0.489971i
$886$	−3.33688	−	10.2699i	−0.112105	−	0.345023i
$887$	−25.5172	−	18.5393i	−0.856784	−	0.622490i	0.0702238	−	0.997531i	$-0.477629\pi$
$887$	−25.5172	−	18.5393i	−0.856784	−	0.622490i	−0.927008	+	0.375041i	$0.877629\pi$
$888$	7.59017	−	5.51458i	0.254709	−	0.185057i
$889$	7.35410	−	22.6336i	0.246649	−	0.759107i
$890$	−48.2148			−1.61616
$891$	2.54508	+	2.12663i	0.0852636	+	0.0712447i
$892$	12.9443			0.433406
$893$	2.69098	−	8.28199i	0.0900503	−	0.277146i
$894$	3.19098	−	2.31838i	0.106722	−	0.0775384i
$895$	24.7984	+	18.0171i	0.828918	+	0.602244i
$896$	0.500000	+	1.53884i	0.0167038	+	0.0514091i
$897$	1.50000	+	4.61653i	0.0500835	+	0.154141i
$898$	−10.4271	−	7.57570i	−0.347955	−	0.252804i
$899$	63.0132	−	45.7817i	2.10161	−	1.52691i
$900$	−1.14590	+	3.52671i	−0.0381966	+	0.117557i
$901$	1.06888			0.0356097
$902$	4.92705	+	19.5887i	0.164053	+	0.652231i
$903$	12.4721			0.415047
$904$	−2.21885	+	6.82891i	−0.0737978	+	0.227126i
$905$	−23.0623	+	16.7557i	−0.766617	+	0.556980i
$906$	7.47214	+	5.42882i	0.248245	+	0.180361i
$907$	−14.8262	−	45.6305i	−0.492297	−	1.51513i	−0.821127	−	0.570746i	$-0.806654\pi$
$907$	−14.8262	−	45.6305i	−0.492297	−	1.51513i	0.328830	−	0.944389i	$-0.393346\pi$
$908$	5.29837	+	16.3067i	0.175833	+	0.541157i
$909$	−14.8541	−	10.7921i	−0.492679	−	0.357953i
$910$	16.6353	−	12.0862i	0.551453	−	0.400654i
$911$	9.88854	−	30.4338i	0.327622	−	1.00832i	−0.642621	−	0.766184i	$-0.722153\pi$
$911$	9.88854	−	30.4338i	0.327622	−	1.00832i	0.970243	−	0.242133i	$-0.0778470\pi$
$912$	1.00000			0.0331133
$913$	−7.11803	−	28.2994i	−0.235573	−	0.936575i
$914$	1.94427			0.0643108
$915$	11.7812	−	36.2587i	0.389473	−	1.19867i
$916$	−14.2082	+	10.3229i	−0.469452	+	0.341077i
$917$	14.0902	+	10.2371i	0.465298	+	0.338059i
$918$	0.364745	+	1.12257i	0.0120384	+	0.0370503i
$919$	8.90576	+	27.4091i	0.293774	+	0.904144i	0.983630	+	0.180197i	$0.0576737\pi$
$919$	8.90576	+	27.4091i	0.293774	+	0.904144i	−0.689856	+	0.723946i	$0.742326\pi$
$920$	−2.11803	−	1.53884i	−0.0698295	−	0.0507341i
$921$	18.6074	−	13.5191i	0.613134	−	0.445468i
$922$	−6.25329	+	19.2456i	−0.205941	+	0.633822i
$923$	47.3951			1.56003
$924$	−4.11803	−	3.44095i	−0.135473	−	0.113199i
$925$	17.3951			0.571948
$926$	9.22542	−	28.3929i	0.303166	−	0.933050i
$927$	15.0902	−	10.9637i	0.495626	−	0.360094i
$928$	7.23607	+	5.25731i	0.237536	+	0.172580i
$929$	12.6008	+	38.7813i	0.413419	+	1.27237i	0.913657	+	0.406486i	$0.133246\pi$
$929$	12.6008	+	38.7813i	0.413419	+	1.27237i	−0.500238	+	0.865888i	$0.666754\pi$
$930$	7.04508	+	21.6825i	0.231017	+	0.710999i
$931$	−3.54508	−	2.57565i	−0.116185	−	0.0844137i
$932$	−0.572949	+	0.416272i	−0.0187676	+	0.0136354i
$933$	−0.618034	+	1.90211i	−0.0202335	+	0.0622724i
$934$	−2.32624			−0.0761168
$935$	−1.73607	+	1.08981i	−0.0567755	+	0.0356407i
$936$	−9.70820			−0.317323
$937$	−16.6738	+	51.3166i	−0.544708	+	1.67644i	0.176975	+	0.984215i	$0.443369\pi$
$937$	−16.6738	+	51.3166i	−0.544708	+	1.67644i	−0.721683	+	0.692224i	$0.756631\pi$
$938$	7.35410	−	5.34307i	0.240120	−	0.174457i
$939$	−16.1353	−	11.7229i	−0.526554	−	0.382564i
$940$	7.04508	+	21.6825i	0.229785	+	0.707207i
$941$	−3.28773	−	10.1186i	−0.107177	−	0.329857i	0.883058	−	0.469263i	$-0.155481\pi$
$941$	−3.28773	−	10.1186i	−0.107177	−	0.329857i	−0.990235	+	0.139407i	$0.955481\pi$
$942$	4.23607	+	3.07768i	0.138019	+	0.100276i
$943$	−4.92705	+	3.57971i	−0.160447	+	0.116571i
$944$	−1.80902	+	5.56758i	−0.0588785	+	0.181209i
$945$	−21.1803			−0.688997
$946$	9.52786	−	23.7234i	0.309778	−	0.771315i
$947$	20.8885			0.678786			0.339393	−	0.940645i	$-0.389778\pi$
$947$	20.8885			0.678786			0.339393	+	0.940645i	$0.389778\pi$
$948$	−4.63525	+	14.2658i	−0.150546	+	0.463333i
$949$	−1.50000	+	1.08981i	−0.0486921	+	0.0353769i
$950$	1.50000	+	1.08981i	0.0486664	+	0.0353582i
$951$	5.25329	+	16.1680i	0.170350	+	0.524282i
$952$	0.118034	+	0.363271i	0.00382550	+	0.0117737i
$953$	−0.145898	−	0.106001i	−0.00472610	−	0.00343371i	0.585420	−	0.810730i	$-0.300930\pi$
$953$	−0.145898	−	0.106001i	−0.00472610	−	0.00343371i	−0.590146	+	0.807297i	$0.700930\pi$
$954$	7.32624	−	5.32282i	0.237196	−	0.172333i
$955$	−7.04508	+	21.6825i	−0.227974	+	0.701631i
$956$	5.32624			0.172263
$957$	−29.5967	−	2.00811i	−0.956727	−	0.0649131i
$958$	18.4164			0.595007
$959$	−1.26393	+	3.88998i	−0.0408145	+	0.125614i
$960$	−2.11803	+	1.53884i	−0.0683593	+	0.0496659i
$961$	−36.2705	−	26.3521i	−1.17002	−	0.850067i
$962$	14.0729	+	43.3121i	0.453730	+	1.39644i
$963$	−3.56231	−	10.9637i	−0.114794	−	0.353299i
$964$	4.92705	+	3.57971i	0.158690	+	0.115295i
$965$	−0.309017	+	0.224514i	−0.00994761	+	0.00722736i
$966$	0.500000	−	1.53884i	0.0160872	−	0.0495114i
$967$	11.7426			0.377618			0.188809	−	0.982014i	$-0.439537\pi$
$967$	11.7426			0.377618			0.188809	+	0.982014i	$0.439537\pi$
$968$	−9.69098	+	5.20431i	−0.311480	+	0.167273i
$969$	0.236068			0.00758360
$970$	−7.42705	+	22.8581i	−0.238468	+	0.733930i
$971$	−13.2639	+	9.63681i	−0.425660	+	0.309260i	−0.779911	−	0.625890i	$-0.784736\pi$
$971$	−13.2639	+	9.63681i	−0.425660	+	0.309260i	0.354251	+	0.935150i	$0.384736\pi$
$972$	12.9443	+	9.40456i	0.415188	+	0.301652i
$973$	−1.28115	−	3.94298i	−0.0410719	−	0.126406i
$974$	−11.8369	−	36.4302i	−0.379278	−	1.16730i
$975$	7.28115	+	5.29007i	0.233184	+	0.169418i
$976$	−11.7812	+	8.55951i	−0.377106	+	0.273983i
$977$	1.61803	−	4.97980i	0.0517655	−	0.159318i	−0.921832	−	0.387590i	$-0.873308\pi$
$977$	1.61803	−	4.97980i	0.0517655	−	0.159318i	0.973597	+	0.228272i	$0.0733076\pi$
$978$	11.3262			0.362173
$979$	−60.9402	−	4.13474i	−1.94766	−	0.132147i
$980$	11.4721			0.366464
$981$	−8.09017	+	24.8990i	−0.258299	+	0.794963i
$982$	5.78115	−	4.20025i	0.184484	−	0.134035i
$983$	−9.94427	−	7.22494i	−0.317173	−	0.230440i	0.417795	−	0.908541i	$-0.362803\pi$
$983$	−9.94427	−	7.22494i	−0.317173	−	0.230440i	−0.734968	+	0.678102i	$0.762803\pi$
$984$	1.88197	+	5.79210i	0.0599949	+	0.184645i
$985$	−18.6074	−	57.2677i	−0.592881	−	1.82470i
$986$	1.70820	+	1.24108i	0.0544003	+	0.0395241i
$987$	−11.3992	+	8.28199i	−0.362840	+	0.263619i
$988$	−1.50000	+	4.61653i	−0.0477214	+	0.146871i
$989$	7.70820			0.245107
$990$	−6.47214	+	16.1150i	−0.205698	+	0.512167i
$991$	47.0000			1.49300			0.746502	−	0.665383i	$-0.231732\pi$
$991$	47.0000			1.49300			0.746502	+	0.665383i	$0.231732\pi$
$992$	2.69098	−	8.28199i	0.0854388	−	0.262954i
$993$	−19.5623	+	14.2128i	−0.620791	+	0.451031i
$994$	−12.7812	−	9.28605i	−0.405394	−	0.294536i
$995$	2.76393	+	8.50651i	0.0876225	+	0.269674i
$996$	−2.71885	−	8.36775i	−0.0861500	−	0.265142i
$997$	15.1353	+	10.9964i	0.479338	+	0.348260i	0.801069	−	0.598571i	$-0.204265\pi$
$997$	15.1353	+	10.9964i	0.479338	+	0.348260i	−0.321731	+	0.946831i	$0.604265\pi$
$998$	26.6074	−	19.3314i	0.842242	−	0.611925i
$999$	14.4959	−	44.6139i	0.458631	−	1.41152i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.f.c.229.1	yes	4
11.4	even	5		4598.2.a.bd.1.1		2
11.5	even	5	inner	418.2.f.c.115.1	✓	4
11.7	odd	10		4598.2.a.u.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.f.c.115.1	✓	4	11.5	even	5	inner
418.2.f.c.229.1	yes	4	1.1	even	1	trivial
4598.2.a.u.1.1		2	11.7	odd	10
4598.2.a.bd.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:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.309017 - 0.951057i) q^{2} +(0.809017 - 0.587785i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.809017 - 2.48990i) q^{5} +(-0.309017 - 0.951057i) q^{6} +(-1.30902 - 0.951057i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(-0.618034 + 1.90211i) q^{9} +O(q^{10})\)	\(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} +(-1.30902 - 0.951057i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(-0.618034 + 1.90211i) q^{9} -2.61803 q^{10} +(-3.30902 - 0.224514i) q^{11} -1.00000 q^{12} +(1.50000 - 4.61653i) q^{13} +(-1.30902 + 0.951057i) q^{14} +(-2.11803 - 1.53884i) q^{15} +(0.309017 + 0.951057i) q^{16} +(0.0729490 + 0.224514i) q^{17} +(1.61803 + 1.17557i) q^{18} +(0.809017 - 0.587785i) q^{19} +(-0.809017 + 2.48990i) q^{20} -1.61803 q^{21} +(-1.23607 + 3.07768i) q^{22} -1.00000 q^{23} +(-0.309017 + 0.951057i) q^{24} +(-1.50000 + 1.08981i) q^{25} +(-3.92705 - 2.85317i) q^{26} +(1.54508 + 4.75528i) q^{27} +(0.500000 + 1.53884i) q^{28} +(7.23607 + 5.25731i) q^{29} +(-2.11803 + 1.53884i) q^{30} +(2.69098 - 8.28199i) q^{31} +1.00000 q^{32} +(-2.80902 + 1.76336i) q^{33} +0.236068 q^{34} +(-1.30902 + 4.02874i) q^{35} +(1.61803 - 1.17557i) q^{36} +(-7.59017 - 5.51458i) q^{37} +(-0.309017 - 0.951057i) q^{38} +(-1.50000 - 4.61653i) q^{39} +(2.11803 + 1.53884i) q^{40} +(4.92705 - 3.57971i) q^{41} +(-0.500000 + 1.53884i) q^{42} -7.70820 q^{43} +(2.54508 + 2.12663i) q^{44} +5.23607 q^{45} +(-0.309017 + 0.951057i) q^{46} +(7.04508 - 5.11855i) q^{47} +(0.809017 + 0.587785i) q^{48} +(-1.35410 - 4.16750i) q^{49} +(0.572949 + 1.76336i) q^{50} +(0.190983 + 0.138757i) q^{51} +(-3.92705 + 2.85317i) q^{52} +(1.39919 - 4.30625i) q^{53} +5.00000 q^{54} +(2.11803 + 8.42075i) q^{55} +1.61803 q^{56} +(0.309017 - 0.951057i) q^{57} +(7.23607 - 5.25731i) q^{58} +(4.73607 + 3.44095i) q^{59} +(0.809017 + 2.48990i) q^{60} +(4.50000 + 13.8496i) q^{61} +(-7.04508 - 5.11855i) q^{62} +(2.61803 - 1.90211i) q^{63} +(0.309017 - 0.951057i) q^{64} -12.7082 q^{65} +(0.809017 + 3.21644i) q^{66} -5.61803 q^{67} +(0.0729490 - 0.224514i) q^{68} +(-0.809017 + 0.587785i) q^{69} +(3.42705 + 2.48990i) q^{70} +(3.01722 + 9.28605i) q^{71} +(-0.618034 - 1.90211i) q^{72} +(-0.309017 - 0.224514i) q^{73} +(-7.59017 + 5.51458i) q^{74} +(-0.572949 + 1.76336i) q^{75} -1.00000 q^{76} +(4.11803 + 3.44095i) q^{77} -4.85410 q^{78} +(4.63525 - 14.2658i) q^{79} +(2.11803 - 1.53884i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(-1.88197 - 5.79210i) q^{82} +(2.71885 + 8.36775i) q^{83} +(1.30902 + 0.951057i) q^{84} +(0.500000 - 0.363271i) q^{85} +(-2.38197 + 7.33094i) q^{86} +8.94427 q^{87} +(2.80902 - 1.76336i) q^{88} +18.4164 q^{89} +(1.61803 - 4.97980i) q^{90} +(-6.35410 + 4.61653i) q^{91} +(0.809017 + 0.587785i) q^{92} +(-2.69098 - 8.28199i) q^{93} +(-2.69098 - 8.28199i) q^{94} +(-2.11803 - 1.53884i) q^{95} +(0.809017 - 0.587785i) q^{96} +(2.83688 - 8.73102i) q^{97} -4.38197 q^{98} +(2.47214 - 6.15537i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} + q^{3} - q^{4} - q^{5} + q^{6} - 3 q^{7} - q^{8} + 2 q^{9}+O(q^{10}) \) 4 * q - q^2 + q^3 - q^4 - q^5 + q^6 - 3 * q^7 - q^8 + 2 * q^9	\( 4 q - q^{2} + q^{3} - q^{4} - q^{5} + q^{6} - 3 q^{7} - q^{8} + 2 q^{9} - 6 q^{10} - 11 q^{11} - 4 q^{12} + 6 q^{13} - 3 q^{14} - 4 q^{15} - q^{16} + 7 q^{17} + 2 q^{18} + q^{19} - q^{20} - 2 q^{21} + 4 q^{22} - 4 q^{23} + q^{24} - 6 q^{25} - 9 q^{26} - 5 q^{27} + 2 q^{28} + 20 q^{29} - 4 q^{30} + 13 q^{31} + 4 q^{32} - 9 q^{33} - 8 q^{34} - 3 q^{35} + 2 q^{36} - 8 q^{37} + q^{38} - 6 q^{39} + 4 q^{40} + 13 q^{41} - 2 q^{42} - 4 q^{43} - q^{44} + 12 q^{45} + q^{46} + 17 q^{47} + q^{48} + 8 q^{49} + 9 q^{50} + 3 q^{51} - 9 q^{52} - 19 q^{53} + 20 q^{54} + 4 q^{55} + 2 q^{56} - q^{57} + 20 q^{58} + 10 q^{59} + q^{60} + 18 q^{61} - 17 q^{62} + 6 q^{63} - q^{64} - 24 q^{65} + q^{66} - 18 q^{67} + 7 q^{68} - q^{69} + 7 q^{70} - 17 q^{71} + 2 q^{72} + q^{73} - 8 q^{74} - 9 q^{75} - 4 q^{76} + 12 q^{77} - 6 q^{78} - 15 q^{79} + 4 q^{80} - q^{81} - 12 q^{82} + 31 q^{83} + 3 q^{84} + 2 q^{85} - 14 q^{86} + 9 q^{88} + 20 q^{89} + 2 q^{90} - 12 q^{91} + q^{92} - 13 q^{93} - 13 q^{94} - 4 q^{95} + q^{96} + 27 q^{97} - 22 q^{98} - 8 q^{99}+O(q^{100}) \) 4 * q - q^2 + q^3 - q^4 - q^5 + q^6 - 3 * q^7 - q^8 + 2 * q^9 - 6 * q^10 - 11 * q^11 - 4 * q^12 + 6 * q^13 - 3 * q^14 - 4 * q^15 - q^16 + 7 * q^17 + 2 * q^18 + q^19 - q^20 - 2 * q^21 + 4 * q^22 - 4 * q^23 + q^24 - 6 * q^25 - 9 * q^26 - 5 * q^27 + 2 * q^28 + 20 * q^29 - 4 * q^30 + 13 * q^31 + 4 * q^32 - 9 * q^33 - 8 * q^34 - 3 * q^35 + 2 * q^36 - 8 * q^37 + q^38 - 6 * q^39 + 4 * q^40 + 13 * q^41 - 2 * q^42 - 4 * q^43 - q^44 + 12 * q^45 + q^46 + 17 * q^47 + q^48 + 8 * q^49 + 9 * q^50 + 3 * q^51 - 9 * q^52 - 19 * q^53 + 20 * q^54 + 4 * q^55 + 2 * q^56 - q^57 + 20 * q^58 + 10 * q^59 + q^60 + 18 * q^61 - 17 * q^62 + 6 * q^63 - q^64 - 24 * q^65 + q^66 - 18 * q^67 + 7 * q^68 - q^69 + 7 * q^70 - 17 * q^71 + 2 * q^72 + q^73 - 8 * q^74 - 9 * q^75 - 4 * q^76 + 12 * q^77 - 6 * q^78 - 15 * q^79 + 4 * q^80 - q^81 - 12 * q^82 + 31 * q^83 + 3 * q^84 + 2 * q^85 - 14 * q^86 + 9 * q^88 + 20 * q^89 + 2 * q^90 - 12 * q^91 + q^92 - 13 * q^93 - 13 * q^94 - 4 * q^95 + q^96 + 27 * q^97 - 22 * q^98 - 8 * q^99

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