LMFDB - Embedded newform 804.2.j.a.499.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(499,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

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

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

chi := DirichletCharacter("804.499");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.j (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$34$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			499.3
Character	$\chi$	$=$	804.499
Dual form			804.2.j.a.775.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.38203 - 0.299971i) q^{2} -1.00000 q^{3} +(1.82004 + 0.829139i) q^{4} -2.35066i q^{5} +(1.38203 + 0.299971i) q^{6} +(1.38486 - 2.39864i) q^{7} +(-2.26663 - 1.69186i) q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(-1.38203 - 0.299971i) q^{2} -1.00000 q^{3} +(1.82004 + 0.829139i) q^{4} -2.35066i q^{5} +(1.38203 + 0.299971i) q^{6} +(1.38486 - 2.39864i) q^{7} +(-2.26663 - 1.69186i) q^{8} +1.00000 q^{9} +(-0.705129 + 3.24869i) q^{10} +(1.83264 - 3.17422i) q^{11} +(-1.82004 - 0.829139i) q^{12} +(4.15472 - 2.39873i) q^{13} +(-2.63344 + 2.89959i) q^{14} +2.35066i q^{15} +(2.62506 + 3.01812i) q^{16} +(0.648029 + 1.12242i) q^{17} +(-1.38203 - 0.299971i) q^{18} +(-0.898964 + 0.519017i) q^{19} +(1.94903 - 4.27829i) q^{20} +(-1.38486 + 2.39864i) q^{21} +(-3.48494 + 3.83715i) q^{22} +(-6.98551 + 4.03309i) q^{23} +(2.26663 + 1.69186i) q^{24} -0.525610 q^{25} +(-6.46151 + 2.06883i) q^{26} -1.00000 q^{27} +(4.50930 - 3.21738i) q^{28} +(2.95012 - 5.10975i) q^{29} +(0.705129 - 3.24869i) q^{30} +(1.23567 - 2.14024i) q^{31} +(-2.72257 - 4.95859i) q^{32} +(-1.83264 + 3.17422i) q^{33} +(-0.558905 - 1.74561i) q^{34} +(-5.63840 - 3.25533i) q^{35} +(1.82004 + 0.829139i) q^{36} +(3.79002 + 6.56450i) q^{37} +(1.39809 - 0.447636i) q^{38} +(-4.15472 + 2.39873i) q^{39} +(-3.97698 + 5.32809i) q^{40} +(6.36793 + 3.67652i) q^{41} +(2.63344 - 2.89959i) q^{42} -2.67928 q^{43} +(5.96734 - 4.25769i) q^{44} -2.35066i q^{45} +(10.8640 - 3.47841i) q^{46} +(-4.78379 - 2.76192i) q^{47} +(-2.62506 - 3.01812i) q^{48} +(-0.335658 - 0.581378i) q^{49} +(0.726410 + 0.157667i) q^{50} +(-0.648029 - 1.12242i) q^{51} +(9.55062 - 0.920930i) q^{52} -12.3998i q^{53} +(1.38203 + 0.299971i) q^{54} +(-7.46153 - 4.30792i) q^{55} +(-7.19712 + 3.09387i) q^{56} +(0.898964 - 0.519017i) q^{57} +(-5.60993 + 6.17690i) q^{58} +5.17955i q^{59} +(-1.94903 + 4.27829i) q^{60} +(-5.43091 + 3.13554i) q^{61} +(-2.34975 + 2.58722i) q^{62} +(1.38486 - 2.39864i) q^{63} +(2.27525 + 7.66963i) q^{64} +(-5.63860 - 9.76634i) q^{65} +(3.48494 - 3.83715i) q^{66} +(-7.40294 - 3.49234i) q^{67} +(0.248794 + 2.58015i) q^{68} +(6.98551 - 4.03309i) q^{69} +(6.81595 + 6.19033i) q^{70} +(-0.766921 - 0.442782i) q^{71} +(-2.26663 - 1.69186i) q^{72} +(-4.91258 - 8.50884i) q^{73} +(-3.26878 - 10.2093i) q^{74} +0.525610 q^{75} +(-2.06648 + 0.199263i) q^{76} +(-5.07589 - 8.79170i) q^{77} +(6.46151 - 2.06883i) q^{78} +(6.82671 - 11.8242i) q^{79} +(7.09459 - 6.17062i) q^{80} +1.00000 q^{81} +(-7.69784 - 6.99127i) q^{82} +(11.3909 - 6.57655i) q^{83} +(-4.50930 + 3.21738i) q^{84} +(2.63843 - 1.52330i) q^{85} +(3.70285 + 0.803704i) q^{86} +(-2.95012 + 5.10975i) q^{87} +(-9.52425 + 4.09424i) q^{88} -7.95359 q^{89} +(-0.705129 + 3.24869i) q^{90} -13.2876i q^{91} +(-16.0579 + 1.54840i) q^{92} +(-1.23567 + 2.14024i) q^{93} +(5.78287 + 5.25207i) q^{94} +(1.22003 + 2.11316i) q^{95} +(2.72257 + 4.95859i) q^{96} +(-6.87685 + 3.97035i) q^{97} +(0.289495 + 0.904171i) q^{98} +(1.83264 - 3.17422i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q - 68 q^{3} - 2 q^{4} + 4 q^{7} - 6 q^{8} + 68 q^{9}+O(q^{10}) $ 68 * q - 68 * q^3 - 2 * q^4 + 4 * q^7 - 6 * q^8 + 68 * q^9	$ 68 q - 68 q^{3} - 2 q^{4} + 4 q^{7} - 6 q^{8} + 68 q^{9} + 18 q^{10} + 2 q^{12} + 6 q^{13} + 10 q^{14} - 2 q^{16} - 36 q^{20} - 4 q^{21} - 22 q^{22} + 6 q^{24} - 68 q^{25} - q^{26} - 68 q^{27} + q^{28} - 8 q^{29} - 18 q^{30} + 2 q^{31} + 15 q^{32} - 2 q^{36} + 12 q^{37} - 22 q^{38} - 6 q^{39} + 18 q^{40} - 10 q^{42} - 4 q^{43} - 31 q^{44} + 32 q^{46} + 2 q^{48} - 46 q^{49} - 9 q^{50} - 28 q^{52} - 11 q^{56} + 4 q^{58} + 36 q^{60} + 6 q^{61} - 34 q^{62} + 4 q^{63} + 16 q^{64} + 22 q^{66} - 18 q^{67} + 34 q^{68} + 56 q^{70} - 36 q^{71} - 6 q^{72} + 6 q^{73} - 53 q^{74} + 68 q^{75} + 14 q^{76} - 4 q^{77} + q^{78} + 6 q^{79} + 55 q^{80} + 68 q^{81} - 26 q^{82} + 12 q^{83} - q^{84} - 21 q^{86} + 8 q^{87} - 50 q^{88} + 18 q^{90} + 10 q^{92} - 2 q^{93} - 16 q^{94} + 20 q^{95} - 15 q^{96} + 18 q^{97} - 70 q^{98}+O(q^{100}) $ 68 * q - 68 * q^3 - 2 * q^4 + 4 * q^7 - 6 * q^8 + 68 * q^9 + 18 * q^10 + 2 * q^12 + 6 * q^13 + 10 * q^14 - 2 * q^16 - 36 * q^20 - 4 * q^21 - 22 * q^22 + 6 * q^24 - 68 * q^25 - q^26 - 68 * q^27 + q^28 - 8 * q^29 - 18 * q^30 + 2 * q^31 + 15 * q^32 - 2 * q^36 + 12 * q^37 - 22 * q^38 - 6 * q^39 + 18 * q^40 - 10 * q^42 - 4 * q^43 - 31 * q^44 + 32 * q^46 + 2 * q^48 - 46 * q^49 - 9 * q^50 - 28 * q^52 - 11 * q^56 + 4 * q^58 + 36 * q^60 + 6 * q^61 - 34 * q^62 + 4 * q^63 + 16 * q^64 + 22 * q^66 - 18 * q^67 + 34 * q^68 + 56 * q^70 - 36 * q^71 - 6 * q^72 + 6 * q^73 - 53 * q^74 + 68 * q^75 + 14 * q^76 - 4 * q^77 + q^78 + 6 * q^79 + 55 * q^80 + 68 * q^81 - 26 * q^82 + 12 * q^83 - q^84 - 21 * q^86 + 8 * q^87 - 50 * q^88 + 18 * q^90 + 10 * q^92 - 2 * q^93 - 16 * q^94 + 20 * q^95 - 15 * q^96 + 18 * q^97 - 70 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.38203	−	0.299971i	−0.977246	−	0.212111i
$2$	−1.38203	−	0.299971i	−0.977246	−	0.212111i
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	1.82004	+	0.829139i	0.910018	+	0.414570i
$5$		−	2.35066i		−	1.05125i	−0.850717	−	0.525624i	$-0.823832\pi$
$5$		−	2.35066i		−	1.05125i	0.850717	−	0.525624i	$-0.176168\pi$
$6$	1.38203	+	0.299971i	0.564213	+	0.122462i
$7$	1.38486	−	2.39864i	0.523427	−	0.906602i	−0.476201	−	0.879336i	$-0.657987\pi$
$7$	1.38486	−	2.39864i	0.523427	−	0.906602i	0.999628	−	0.0272656i	$-0.00867998\pi$
$8$	−2.26663	−	1.69186i	−0.801376	−	0.598161i
$9$	1.00000			0.333333
$10$	−0.705129	+	3.24869i	−0.222981	+	1.02733i
$11$	1.83264	−	3.17422i	0.552562	−	0.957065i	−0.445527	−	0.895268i	$-0.646984\pi$
$11$	1.83264	−	3.17422i	0.552562	−	0.957065i	0.998089	−	0.0617964i	$-0.0196829\pi$
$12$	−1.82004	−	0.829139i	−0.525399	−	0.239352i
$13$	4.15472	−	2.39873i	1.15231	−	0.665288i	0.202862	−	0.979207i	$-0.434976\pi$
$13$	4.15472	−	2.39873i	1.15231	−	0.665288i	0.949450	+	0.313920i	$0.101642\pi$
$14$	−2.63344	+	2.89959i	−0.703817	+	0.774948i
$15$			2.35066i			0.606938i
$16$	2.62506	+	3.01812i	0.656264	+	0.754531i
$17$	0.648029	+	1.12242i	0.157170	+	0.272227i	0.933847	−	0.357672i	$-0.116430\pi$
$17$	0.648029	+	1.12242i	0.157170	+	0.272227i	−0.776677	+	0.629899i	$0.783096\pi$
$18$	−1.38203	−	0.299971i	−0.325749	−	0.0707037i
$19$	−0.898964	+	0.519017i	−0.206236	+	0.119071i	−0.599561	−	0.800329i	$-0.704658\pi$
$19$	−0.898964	+	0.519017i	−0.206236	+	0.119071i	0.393325	+	0.919400i	$0.371325\pi$
$20$	1.94903	−	4.27829i	0.435815	−	0.956654i
$21$	−1.38486	+	2.39864i	−0.302201	+	0.523427i
$22$	−3.48494	+	3.83715i	−0.742993	+	0.818083i
$23$	−6.98551	+	4.03309i	−1.45658	+	0.840957i	−0.998841	−	0.0481302i	$-0.984674\pi$
$23$	−6.98551	+	4.03309i	−1.45658	+	0.840957i	−0.457739	+	0.889087i	$0.651340\pi$
$24$	2.26663	+	1.69186i	0.462675	+	0.345349i
$25$	−0.525610			−0.105122
$26$	−6.46151	+	2.06883i	−1.26721	+	0.405731i
$27$	−1.00000			−0.192450
$28$	4.50930	−	3.21738i	0.852177	−	0.608027i
$29$	2.95012	−	5.10975i	0.547823	−	0.948857i	−0.450601	−	0.892726i	$-0.648790\pi$
$29$	2.95012	−	5.10975i	0.547823	−	0.948857i	0.998423	−	0.0561312i	$-0.0178765\pi$
$30$	0.705129	−	3.24869i	0.128738	−	0.593128i
$31$	1.23567	−	2.14024i	0.221933	−	0.384399i	−0.733462	−	0.679730i	$-0.762097\pi$
$31$	1.23567	−	2.14024i	0.221933	−	0.384399i	0.955395	+	0.295332i	$0.0954301\pi$
$32$	−2.72257	−	4.95859i	−0.481287	−	0.876563i
$33$	−1.83264	+	3.17422i	−0.319022	+	0.552562i
$34$	−0.558905	−	1.74561i	−0.0958514	−	0.299370i
$35$	−5.63840	−	3.25533i	−0.953063	−	0.550251i
$36$	1.82004	+	0.829139i	0.303339	+	0.138190i
$37$	3.79002	+	6.56450i	0.623075	+	1.07920i	0.988910	+	0.148518i	$0.0474503\pi$
$37$	3.79002	+	6.56450i	0.623075	+	1.07920i	−0.365834	+	0.930680i	$0.619216\pi$
$38$	1.39809	−	0.447636i	0.226800	−	0.0726162i
$39$	−4.15472	+	2.39873i	−0.665288	+	0.384104i
$40$	−3.97698	+	5.32809i	−0.628816	+	0.842445i
$41$	6.36793	+	3.67652i	0.994503	+	0.574176i	0.906617	−	0.421954i	$-0.138656\pi$
$41$	6.36793	+	3.67652i	0.994503	+	0.574176i	0.0878856	+	0.996131i	$0.471989\pi$
$42$	2.63344	−	2.89959i	0.406349	−	0.447416i
$43$	−2.67928			−0.408586			−0.204293	−	0.978910i	$-0.565489\pi$
$43$	−2.67928			−0.408586			−0.204293	+	0.978910i	$0.565489\pi$
$44$	5.96734	−	4.25769i	0.899611	−	0.641871i
$45$		−	2.35066i		−	0.350416i
$46$	10.8640	−	3.47841i	1.60181	−	0.512864i
$47$	−4.78379	−	2.76192i	−0.697788	−	0.402868i	0.108735	−	0.994071i	$-0.465320\pi$
$47$	−4.78379	−	2.76192i	−0.697788	−	0.402868i	−0.806523	+	0.591203i	$0.798653\pi$
$48$	−2.62506	−	3.01812i	−0.378894	−	0.435629i
$49$	−0.335658	−	0.581378i	−0.0479512	−	0.0830539i
$50$	0.726410	+	0.157667i	0.102730	+	0.0222975i
$51$	−0.648029	−	1.12242i	−0.0907422	−	0.157170i
$52$	9.55062	−	0.920930i	1.32443	−	0.127710i
$53$		−	12.3998i		−	1.70325i	−0.524155	−	0.851623i	$-0.675619\pi$
$53$		−	12.3998i		−	1.70325i	0.524155	−	0.851623i	$-0.324381\pi$
$54$	1.38203	+	0.299971i	0.188071	+	0.0408208i
$55$	−7.46153	−	4.30792i	−1.00611	−	0.580879i
$56$	−7.19712	+	3.09387i	−0.961756	+	0.413435i
$57$	0.898964	−	0.519017i	0.119071	−	0.0687455i
$58$	−5.60993	+	6.17690i	−0.736620	+	0.811067i
$59$			5.17955i			0.674320i	0.941447	+	0.337160i	$0.109466\pi$
$59$			5.17955i			0.674320i	−0.941447	+	0.337160i	$0.890534\pi$
$60$	−1.94903	+	4.27829i	−0.251618	+	0.552324i
$61$	−5.43091	+	3.13554i	−0.695357	+	0.401465i	−0.805616	−	0.592438i	$-0.798165\pi$
$61$	−5.43091	+	3.13554i	−0.695357	+	0.401465i	0.110259	+	0.993903i	$0.464832\pi$
$62$	−2.34975	+	2.58722i	−0.298418	+	0.328578i
$63$	1.38486	−	2.39864i	0.174476	−	0.302201i
$64$	2.27525	+	7.66963i	0.284406	+	0.958704i
$65$	−5.63860	−	9.76634i	−0.699382	−	1.21137i
$66$	3.48494	−	3.83715i	0.428967	−	0.472320i
$67$	−7.40294	−	3.49234i	−0.904414	−	0.426657i
$67$	−7.40294	−	3.49234i	−0.904414	−	0.426657i
$68$	0.248794	+	2.58015i	0.0301707	+	0.312889i
$69$	6.98551	−	4.03309i	0.840957	−	0.485527i
$70$	6.81595	+	6.19033i	0.814662	+	0.739886i
$71$	−0.766921	−	0.442782i	−0.0910168	−	0.0525486i	0.453801	−	0.891103i	$-0.350068\pi$
$71$	−0.766921	−	0.442782i	−0.0910168	−	0.0525486i	−0.544818	+	0.838555i	$0.683401\pi$
$72$	−2.26663	−	1.69186i	−0.267125	−	0.199387i
$73$	−4.91258	−	8.50884i	−0.574974	−	0.995884i	−0.996044	−	0.0888563i	$-0.971679\pi$
$73$	−4.91258	−	8.50884i	−0.574974	−	0.995884i	0.421070	−	0.907028i	$-0.361655\pi$
$74$	−3.26878	−	10.2093i	−0.379987	−	1.18680i
$75$	0.525610			0.0606922
$76$	−2.06648	+	0.199263i	−0.237042	+	0.0228571i
$77$	−5.07589	−	8.79170i	−0.578451	−	1.00191i
$78$	6.46151	−	2.06883i	0.731622	−	0.234249i
$79$	6.82671	−	11.8242i	0.768065	−	1.33033i	−0.170546	−	0.985350i	$-0.554553\pi$
$79$	6.82671	−	11.8242i	0.768065	−	1.33033i	0.938611	−	0.344977i	$-0.112113\pi$
$80$	7.09459	−	6.17062i	0.793199	−	0.689896i
$81$	1.00000			0.111111
$82$	−7.69784	−	6.99127i	−0.850084	−	0.772057i
$83$	11.3909	−	6.57655i	1.25032	−	0.721870i	0.279144	−	0.960249i	$-0.409949\pi$
$83$	11.3909	−	6.57655i	1.25032	−	0.721870i	0.971172	+	0.238379i	$0.0766161\pi$
$84$	−4.50930	+	3.21738i	−0.492005	+	0.351044i
$85$	2.63843	−	1.52330i	0.286178	−	0.165225i
$86$	3.70285	+	0.803704i	0.399289	+	0.0866656i
$87$	−2.95012	+	5.10975i	−0.316286	+	0.547823i
$88$	−9.52425	+	4.09424i	−1.01529	+	0.436448i
$89$	−7.95359			−0.843079			−0.421539	−	0.906810i	$-0.638510\pi$
$89$	−7.95359			−0.843079			−0.421539	+	0.906810i	$0.638510\pi$
$90$	−0.705129	+	3.24869i	−0.0743272	+	0.342442i
$91$		−	13.2876i		−	1.39292i
$92$	−16.0579	+	1.54840i	−1.67415	+	0.161432i
$93$	−1.23567	+	2.14024i	−0.128133	+	0.221933i
$94$	5.78287	+	5.25207i	0.596457	+	0.541710i
$95$	1.22003	+	2.11316i	0.125173	+	0.216806i
$96$	2.72257	+	4.95859i	0.277871	+	0.506084i
$97$	−6.87685	+	3.97035i	−0.698238	+	0.403128i	−0.806691	−	0.590974i	$-0.798744\pi$
$97$	−6.87685	+	3.97035i	−0.698238	+	0.403128i	0.108453	+	0.994102i	$0.465410\pi$
$98$	0.289495	+	0.904171i	0.0292434	+	0.0913351i
$99$	1.83264	−	3.17422i	0.184187	−	0.319022i
$100$	−0.956628	−	0.435803i	−0.0956628	−	0.0435803i
$101$	−4.06282	−	2.34567i	−0.404266	−	0.233403i	0.284057	−	0.958807i	$-0.408319\pi$
$101$	−4.06282	−	2.34567i	−0.404266	−	0.233403i	−0.688323	+	0.725404i	$0.741653\pi$
$102$	0.558905	+	1.74561i	0.0553399	+	0.172841i
$103$	−4.35385	−	2.51370i	−0.428998	−	0.247682i	0.269922	−	0.962882i	$-0.413002\pi$
$103$	−4.35385	−	2.51370i	−0.428998	−	0.247682i	−0.698920	+	0.715200i	$0.746335\pi$
$104$	−13.4755	−	1.59215i	−1.32138	−	0.156123i
$105$	5.63840	+	3.25533i	0.550251	+	0.317688i
$106$	−3.71958	+	17.1370i	−0.361278	+	1.66449i
$107$			16.0919i			1.55566i	0.628473	+	0.777831i	$0.283680\pi$
$107$			16.0919i			1.55566i	−0.628473	+	0.777831i	$0.716320\pi$
$108$	−1.82004	−	0.829139i	−0.175133	−	0.0797839i
$109$			9.75097i			0.933974i	0.884264	+	0.466987i	$0.154660\pi$
$109$			9.75097i			0.933974i	−0.884264	+	0.466987i	$0.845340\pi$
$110$	9.01984	+	8.19192i	0.860008	+	0.781069i
$111$	−3.79002	−	6.56450i	−0.359733	−	0.623075i
$112$	10.8747	−	2.11690i	1.02757	−	0.200028i
$113$	−9.90711	−	5.71987i	−0.931983	−	0.538080i	−0.0445446	−	0.999007i	$-0.514184\pi$
$113$	−9.90711	−	5.71987i	−0.931983	−	0.538080i	−0.887438	+	0.460927i	$0.847517\pi$
$114$	−1.39809	+	0.447636i	−0.130943	+	0.0419250i
$115$	9.48042	+	16.4206i	0.884054	+	1.53123i
$116$	9.60601	−	6.85387i	0.891895	−	0.636366i
$117$	4.15472	−	2.39873i	0.384104	−	0.221763i
$118$	1.55371	−	7.15832i	0.143031	−	0.658977i
$119$	3.58971			0.329068
$120$	3.97698	−	5.32809i	0.363047	−	0.486386i
$121$	−1.21714	−	2.10814i	−0.110649	−	0.191649i
$122$	8.44627	−	2.70431i	0.764690	−	0.244836i
$123$	−6.36793	−	3.67652i	−0.574176	−	0.331501i
$124$	4.02352	−	2.87077i	0.361323	−	0.257803i
$125$		−	10.5178i		−	0.940739i
$126$	−2.63344	+	2.89959i	−0.234606	+	0.258316i
$127$	−2.67054	−	1.54184i	−0.236972	−	0.136816i	0.376812	−	0.926290i	$-0.377020\pi$
$127$	−2.67054	−	1.54184i	−0.236972	−	0.136816i	−0.613784	+	0.789474i	$0.710354\pi$
$128$	−0.843810	−	11.2822i	−0.0745830	−	0.997215i
$129$	2.67928			0.235897
$130$	4.86312	+	15.1888i	0.426524	+	1.33215i
$131$			14.3495i			1.25372i	0.779130	+	0.626862i	$0.215661\pi$
$131$			14.3495i			1.25372i	−0.779130	+	0.626862i	$0.784339\pi$
$132$	−5.96734	+	4.25769i	−0.519391	+	0.370584i
$133$			2.87506i			0.249299i
$134$	9.18352	+	7.04719i	0.793335	+	0.608785i
$135$			2.35066i			0.202313i
$136$	0.430127	−	3.64048i	0.0368831	−	0.312169i
$137$			12.8058i			1.09408i	0.837108	+	0.547038i	$0.184245\pi$
$137$			12.8058i			1.09408i	−0.837108	+	0.547038i	$0.815755\pi$
$138$	−10.8640	+	3.47841i	−0.924807	+	0.296102i
$139$	−3.94727			−0.334803			−0.167402	−	0.985889i	$-0.553538\pi$
$139$	−3.94727			−0.334803			−0.167402	+	0.985889i	$0.553538\pi$
$140$	−7.56296	−	10.5998i	−0.639187	−	0.895849i
$141$	4.78379	+	2.76192i	0.402868	+	0.232596i
$142$	0.927089	+	0.841994i	0.0777996	+	0.0706585i
$143$		−	17.5840i		−	1.47045i
$144$	2.62506	+	3.01812i	0.218755	+	0.251510i
$145$	−12.0113	−	6.93472i	−0.997484	−	0.575897i
$146$	4.23695	+	13.2331i	0.350653	+	1.09518i
$147$	0.335658	+	0.581378i	0.0276846	+	0.0479512i
$148$	1.45508	+	15.0901i	0.119607	+	1.24040i
$149$	17.6801			1.44841			0.724204	−	0.689586i	$-0.242207\pi$
$149$	17.6801			1.44841			0.724204	+	0.689586i	$0.242207\pi$
$150$	−0.726410	−	0.157667i	−0.0593112	−	0.0128735i
$151$	12.6946	−	7.32922i	1.03307	−	0.596443i	0.115207	−	0.993341i	$-0.463247\pi$
$151$	12.6946	−	7.32922i	1.03307	−	0.596443i	0.917863	+	0.396898i	$0.129913\pi$
$152$	2.91572	+	0.344496i	0.236496	+	0.0279423i
$153$	0.648029	+	1.12242i	0.0523900	+	0.0907422i
$154$	4.37780	+	13.6730i	0.352773	+	1.10180i
$155$	−5.03098	−	2.90464i	−0.404098	−	0.233306i
$156$	−9.55062	+	0.920930i	−0.764661	+	0.0737334i
$157$	−0.694503	−	1.20291i	−0.0554274	−	0.0960030i	0.836980	−	0.547233i	$-0.184319\pi$
$157$	−0.694503	−	1.20291i	−0.0554274	−	0.0960030i	−0.892408	+	0.451230i	$0.850985\pi$
$158$	−12.9817	+	14.2936i	−1.03276	+	1.13714i
$159$			12.3998i			0.983370i
$160$	−11.6560	+	6.39984i	−0.921485	+	0.505952i
$161$			22.3410i			1.76072i
$162$	−1.38203	−	0.299971i	−0.108583	−	0.0235679i
$163$	18.2836	+	10.5561i	1.43208	+	0.826814i	0.997280	−	0.0737102i	$-0.0234840\pi$
$163$	18.2836	+	10.5561i	1.43208	+	0.826814i	0.434805	+	0.900525i	$0.356817\pi$
$164$	8.54150	+	11.9713i	0.666979	+	0.934801i
$165$	7.46153	+	4.30792i	0.580879	+	0.335371i
$166$	−17.7154	+	5.67207i	−1.37498	+	0.440238i
$167$	−14.7789	−	8.53260i	−1.14363	−	0.660273i	−0.196300	−	0.980544i	$-0.562893\pi$
$167$	−14.7789	−	8.53260i	−1.14363	−	0.660273i	−0.947326	+	0.320271i	$0.896226\pi$
$168$	7.19712	−	3.09387i	0.555270	−	0.238697i
$169$	5.00780	−	8.67376i	0.385215	−	0.667212i
$170$	−4.10334	+	1.31380i	−0.314712	+	0.100764i
$171$	−0.898964	+	0.519017i	−0.0687455	+	0.0396902i
$172$	−4.87638	−	2.22149i	−0.371820	−	0.169387i
$173$	9.07160	+	15.7125i	0.689701	+	1.19460i	0.971934	+	0.235252i	$0.0755914\pi$
$173$	9.07160	+	15.7125i	0.689701	+	1.19460i	−0.282233	+	0.959346i	$0.591075\pi$
$174$	5.60993	−	6.17690i	0.425288	−	0.468270i
$175$	−0.727894	+	1.26075i	−0.0550236	+	0.0953037i
$176$	14.3910	−	2.80139i	1.08476	−	0.211162i
$177$		−	5.17955i		−	0.389319i
$178$	10.9921	+	2.38584i	0.823895	+	0.178826i
$179$	5.91123			0.441826			0.220913	−	0.975293i	$-0.429096\pi$
$179$	5.91123			0.441826			0.220913	+	0.975293i	$0.429096\pi$
$180$	1.94903	−	4.27829i	0.145272	−	0.318885i
$181$	4.90958	−	8.50364i	0.364926	−	0.632070i	−0.623838	−	0.781553i	$-0.714428\pi$
$181$	4.90958	−	8.50364i	0.364926	−	0.632070i	0.988764	+	0.149483i	$0.0477610\pi$
$182$	−3.98589	+	18.3639i	−0.295453	+	1.36122i
$183$	5.43091	−	3.13554i	0.401465	−	0.231786i
$184$	22.6570	+	2.67695i	1.67030	+	0.197347i
$185$	15.4309	−	8.90905i	1.13450	−	0.655006i
$186$	2.34975	−	2.58722i	0.172292	−	0.189704i
$187$	4.75041			0.347385
$188$	−6.41665	−	8.99323i	−0.467982	−	0.655899i
$189$	−1.38486	+	2.39864i	−0.100734	+	0.174476i
$190$	−1.05224	−	3.28643i	−0.0763376	−	0.238423i
$191$	10.0471	+	17.4020i	0.726979	+	1.25917i	0.958154	+	0.286253i	$0.0924098\pi$
$191$	10.0471	+	17.4020i	0.726979	+	1.25917i	−0.231175	+	0.972912i	$0.574257\pi$
$192$	−2.27525	−	7.66963i	−0.164202	−	0.553508i
$193$	−17.5735			−1.26497			−0.632485	−	0.774573i	$-0.717965\pi$
$193$	−17.5735			−1.26497			−0.632485	+	0.774573i	$0.717965\pi$
$194$	10.6950	−	3.42431i	0.767858	−	0.245851i
$195$	5.63860	+	9.76634i	0.403788	+	0.699382i
$196$	−0.128867	−	1.33644i	−0.00920482	−	0.0954597i
$197$	3.01823	+	1.74257i	0.215040	+	0.124153i	0.603651	−	0.797248i	$-0.293712\pi$
$197$	3.01823	+	1.74257i	0.215040	+	0.124153i	−0.388612	+	0.921402i	$0.627045\pi$
$198$	−3.48494	+	3.83715i	−0.247664	+	0.272694i
$199$	−3.32598	+	1.92025i	−0.235772	+	0.136123i	−0.613232	−	0.789903i	$-0.710131\pi$
$199$	−3.32598	+	1.92025i	−0.235772	+	0.136123i	0.377460	+	0.926026i	$0.376798\pi$
$200$	1.19136	+	0.889255i	0.0842422	+	0.0628799i
$201$	7.40294	+	3.49234i	0.522163	+	0.246330i
$202$	4.91132	+	4.46052i	0.345559	+	0.313841i
$203$	−8.17098	−	14.1525i	−0.573490	−	0.993314i
$204$	−0.248794	−	2.58015i	−0.0174191	−	0.180647i
$205$	8.64226	−	14.9688i	0.603602	−	1.04547i
$206$	5.26313	+	4.78004i	0.366700	+	0.333041i
$207$	−6.98551	+	4.03309i	−0.485527	+	0.280319i
$208$	18.1460	+	6.24266i	1.25820	+	0.432851i
$209$			3.80469i			0.263176i
$210$	−6.81595	−	6.19033i	−0.470345	−	0.427173i
$211$	−1.51419	+	0.874217i	−0.104241	+	0.0601836i	−0.551214	−	0.834364i	$-0.685835\pi$
$211$	−1.51419	+	0.874217i	−0.104241	+	0.0601836i	0.446973	+	0.894547i	$0.352502\pi$
$212$	10.2812	−	22.5681i	0.706114	−	1.54998i
$213$	0.766921	+	0.442782i	0.0525486	+	0.0303389i
$214$	4.82710	−	22.2395i	0.329973	−	1.52026i
$215$			6.29807i			0.429525i
$216$	2.26663	+	1.69186i	0.154225	+	0.115116i
$217$	−3.42245	−	5.92786i	−0.232331	−	0.402409i
$218$	2.92501	−	13.4762i	0.198106	−	0.912722i
$219$	4.91258	+	8.50884i	0.331961	+	0.574974i
$220$	−10.0084	−	14.0272i	−0.674765	−	0.945714i
$221$	5.38476	+	3.10889i	0.362218	+	0.209127i
$222$	3.26878	+	10.2093i	0.219386	+	0.685201i
$223$			8.44440i			0.565479i	0.959197	+	0.282740i	$0.0912432\pi$
$223$			8.44440i			0.565479i	−0.959197	+	0.282740i	$0.908757\pi$
$224$	−15.6643	−	0.336469i	−1.04661	−	0.0224813i
$225$	−0.525610			−0.0350406
$226$	11.9762	+	10.8769i	0.796643	+	0.723521i
$227$	7.79369	+	4.49969i	0.517285	+	0.298655i	0.735823	−	0.677174i	$-0.236795\pi$
$227$	7.79369	+	4.49969i	0.517285	+	0.298655i	−0.218538	+	0.975828i	$0.570129\pi$
$228$	2.06648	−	0.199263i	0.136856	−	0.0131965i
$229$	1.64455	−	0.949479i	0.108675	−	0.0627433i	−0.444678	−	0.895691i	$-0.646682\pi$
$229$	1.64455	−	0.949479i	0.108675	−	0.0627433i	0.553352	+	0.832947i	$0.313348\pi$
$230$	−8.17657	−	25.5376i	−0.539147	−	1.68390i
$231$	5.07589	+	8.79170i	0.333969	+	0.578451i
$232$	−15.3318	+	6.59076i	−1.00658	+	0.432705i
$233$	−2.26985	−	1.31050i	−0.148703	−	0.0858538i	0.423802	−	0.905755i	$-0.360695\pi$
$233$	−2.26985	−	1.31050i	−0.148703	−	0.0858538i	−0.572505	+	0.819901i	$0.694028\pi$
$234$	−6.46151	+	2.06883i	−0.422402	+	0.135244i
$235$	−6.49235	+	11.2451i	−0.423514	+	0.733548i
$236$	−4.29457	+	9.42697i	−0.279553	+	0.613644i
$237$	−6.82671	+	11.8242i	−0.443442	+	0.768065i
$238$	−4.96110	−	1.07681i	−0.321580	−	0.0697991i
$239$	−0.564399	+	0.977568i	−0.0365080	+	0.0632336i	−0.883702	−	0.468050i	$-0.844957\pi$
$239$	−0.564399	+	0.977568i	−0.0365080	+	0.0632336i	0.847194	+	0.531283i	$0.178290\pi$
$240$	−7.09459	+	6.17062i	−0.457954	+	0.398312i
$241$	14.5070			0.934475			0.467238	−	0.884132i	$-0.345249\pi$
$241$	14.5070			0.934475			0.467238	+	0.884132i	$0.345249\pi$
$242$	1.04974	+	3.27863i	0.0674800	+	0.210758i
$243$	−1.00000			−0.0641500
$244$	−12.4842	+	1.20381i	−0.799222	+	0.0770660i
$245$	−1.36662	+	0.789019i	−0.0873103	+	0.0504086i
$246$	7.69784	+	6.99127i	0.490796	+	0.445747i
$247$	−2.48996	+	4.31274i	−0.158433	+	0.274413i
$248$	−6.42179	+	2.76057i	−0.407784	+	0.175296i
$249$	−11.3909	+	6.57655i	−0.721870	+	0.416772i
$250$	−3.15502	+	14.5359i	−0.199541	+	0.919333i
$251$	5.94388	+	10.2951i	0.375174	+	0.649821i	0.990353	−	0.138567i	$-0.0442495\pi$
$251$	5.94388	+	10.2951i	0.375174	+	0.649821i	−0.615179	+	0.788388i	$0.710916\pi$
$252$	4.50930	−	3.21738i	0.284059	−	0.202676i
$253$			29.5648i			1.85872i
$254$	3.22828	+	2.93196i	0.202560	+	0.183967i
$255$	−2.63843	+	1.52330i	−0.165225	+	0.0953925i
$256$	−2.21815	+	15.8455i	−0.138635	+	0.990344i
$257$	5.22517	−	9.05026i	0.325937	−	0.564539i	−0.655765	−	0.754965i	$-0.727654\pi$
$257$	5.22517	−	9.05026i	0.325937	−	0.564539i	0.981702	+	0.190426i	$0.0609869\pi$
$258$	−3.70285	−	0.803704i	−0.230529	−	0.0500364i
$259$	20.9945			1.30454
$260$	−2.16480	−	22.4503i	−0.134255	−	1.39231i
$261$	2.95012	−	5.10975i	0.182608	−	0.316286i
$262$	4.30444	−	19.8315i	0.265929	−	1.22520i
$263$		−	6.65428i		−	0.410320i	−0.978728	−	0.205160i	$-0.934228\pi$
$263$		−	6.65428i		−	0.410320i	0.978728	−	0.205160i	$-0.0657715\pi$
$264$	9.52425	−	4.09424i	0.586177	−	0.251983i
$265$	−29.1478			−1.79053
$266$	0.862433	−	3.97343i	0.0528792	−	0.243626i
$267$	7.95359			0.486752
$268$	−10.5780	−	12.4942i	−0.646153	−	0.763208i
$269$	−28.7358			−1.75205			−0.876026	−	0.482264i	$-0.839815\pi$
$269$	−28.7358			−1.75205			−0.876026	+	0.482264i	$0.839815\pi$
$270$	0.705129	−	3.24869i	0.0429128	−	0.197709i
$271$	−8.94018			−0.543077			−0.271539	−	0.962428i	$-0.587532\pi$
$271$	−8.94018			−0.543077			−0.271539	+	0.962428i	$0.587532\pi$
$272$	−1.68649	+	4.90225i	−0.102258	+	0.297242i
$273$			13.2876i			0.804201i
$274$	3.84137	−	17.6981i	0.232066	−	1.06918i
$275$	−0.963253	+	1.66840i	−0.0580863	+	0.100608i
$276$	16.0579	−	1.54840i	0.966570	−	0.0932027i
$277$	−15.9968			−0.961155			−0.480577	−	0.876952i	$-0.659573\pi$
$277$	−15.9968			−0.961155			−0.480577	+	0.876952i	$0.659573\pi$
$278$	5.45526	+	1.18406i	0.327185	+	0.0710155i
$279$	1.23567	−	2.14024i	0.0739776	−	0.128133i
$280$	7.27263	+	16.9180i	0.434623	+	1.01104i
$281$	−21.6730	+	12.5129i	−1.29290	+	0.746457i	−0.979168	−	0.203054i	$-0.934913\pi$
$281$	−21.6730	+	12.5129i	−1.29290	+	0.746457i	−0.313734	+	0.949511i	$0.601580\pi$
$282$	−5.78287	−	5.25207i	−0.344365	−	0.312756i
$283$		−	30.4295i		−	1.80885i	−0.426637	−	0.904423i	$-0.640302\pi$
$283$		−	30.4295i		−	1.80885i	0.426637	−	0.904423i	$-0.359698\pi$
$284$	−1.02870	−	1.44176i	−0.0610419	−	0.0855529i
$285$	−1.22003	−	2.11316i	−0.0722686	−	0.125173i
$286$	−5.27469	+	24.3017i	−0.311899	+	1.43699i
$287$	17.6373	−	10.1829i	1.04110	−	0.601079i
$288$	−2.72257	−	4.95859i	−0.160429	−	0.292188i
$289$	7.66012	−	13.2677i	0.450595	−	0.780454i
$290$	14.5198	+	13.1871i	0.852632	+	0.774371i
$291$	6.87685	−	3.97035i	0.403128	−	0.232746i
$292$	−1.88606	−	19.5596i	−0.110373	−	1.14464i
$293$	22.0713			1.28942			0.644709	−	0.764428i	$-0.276979\pi$
$293$	22.0713			1.28942			0.644709	+	0.764428i	$0.276979\pi$
$294$	−0.289495	−	0.904171i	−0.0168837	−	0.0527323i
$295$	12.1754			0.708878
$296$	2.51561	−	21.2915i	0.146217	−	1.23754i
$297$	−1.83264	+	3.17422i	−0.106341	+	0.184187i
$298$	−24.4345	−	5.30350i	−1.41545	−	0.307224i
$299$	−19.3486	+	33.5127i	−1.11896	+	1.93809i
$300$	0.956628	+	0.435803i	0.0552309	+	0.0251611i
$301$	−3.71041	+	6.42663i	−0.213865	+	0.370425i
$302$	−19.7429	+	6.32123i	−1.13608	+	0.363746i
$303$	4.06282	+	2.34567i	0.233403	+	0.134755i
$304$	−3.92629	−	1.35074i	−0.225188	−	0.0774700i
$305$	7.37059	+	12.7662i	0.422039	+	0.730993i
$306$	−0.558905	−	1.74561i	−0.0319505	−	0.0997899i
$307$	−4.06763	+	2.34845i	−0.232152	+	0.134033i	−0.611564	−	0.791195i	$-0.709459\pi$
$307$	−4.06763	+	2.34845i	−0.232152	+	0.134033i	0.379412	+	0.925228i	$0.376126\pi$
$308$	−1.94876	−	20.2098i	−0.111041	−	1.15156i
$309$	4.35385	+	2.51370i	0.247682	+	0.142999i
$310$	6.08168	+	5.52346i	0.345416	+	0.313711i
$311$	−8.07394			−0.457831			−0.228916	−	0.973446i	$-0.573518\pi$
$311$	−8.07394			−0.457831			−0.228916	+	0.973446i	$0.573518\pi$
$312$	13.4755	+	1.59215i	0.762902	+	0.0901376i
$313$		−	24.2183i		−	1.36890i	−0.729059	−	0.684451i	$-0.760042\pi$
$313$		−	24.2183i		−	1.36890i	0.729059	−	0.684451i	$-0.239958\pi$
$314$	0.598988	+	1.87080i	0.0338028	+	0.105575i
$315$	−5.63840	−	3.25533i	−0.317688	−	0.183417i
$316$	22.2288	−	15.8602i	1.25047	−	0.892205i
$317$	8.71544	+	15.0956i	0.489508	+	0.847853i	0.999927	−	0.0120729i	$-0.00384301\pi$
$317$	8.71544	+	15.0956i	0.489508	+	0.847853i	−0.510419	+	0.859926i	$0.670510\pi$
$318$	3.71958	−	17.1370i	0.208584	−	0.960994i
$319$	−10.8130	−	18.7287i	−0.605412	−	1.04860i
$320$	18.0287	−	5.34835i	1.00784	−	0.298982i
$321$		−	16.0919i		−	0.898162i
$322$	6.70164	−	30.8760i	0.373468	−	1.72065i
$323$	−1.16511	−	0.672676i	−0.0648284	−	0.0374287i
$324$	1.82004	+	0.829139i	0.101113	+	0.0460633i
$325$	−2.18376	+	1.26079i	−0.121133	+	0.0699363i
$326$	−22.1021	−	20.0734i	−1.22412	−	1.11176i
$327$		−	9.75097i		−	0.539230i
$328$	−8.21360	−	19.1069i	−0.453520	−	1.05500i
$329$	−13.2497	+	7.64974i	−0.730482	+	0.421744i
$330$	−9.01984	−	8.19192i	−0.496526	−	0.450951i
$331$	−7.84025	+	13.5797i	−0.430939	+	0.746409i	−0.996954	−	0.0779861i	$-0.975151\pi$
$331$	−7.84025	+	13.5797i	−0.430939	+	0.746409i	0.566015	+	0.824395i	$0.308484\pi$
$332$	26.1847	−	2.52490i	1.43707	−	0.138572i
$333$	3.79002	+	6.56450i	0.207692	+	0.359733i
$334$	17.8654	+	16.2256i	0.977552	+	0.887825i
$335$	−8.20930	+	17.4018i	−0.448522	+	0.950763i
$336$	−10.8747	+	2.11690i	−0.593265	+	0.115487i
$337$	0.409934	−	0.236676i	0.0223305	−	0.0128925i	−0.488793	−	0.872400i	$-0.662563\pi$
$337$	0.409934	−	0.236676i	0.0223305	−	0.0128925i	0.511124	+	0.859507i	$0.329229\pi$
$338$	−9.52282	+	10.4852i	−0.517973	+	0.570322i
$339$	9.90711	+	5.71987i	0.538080	+	0.310661i
$340$	6.06505	−	0.584831i	0.328924	−	0.0317169i
$341$	−4.52907	−	7.84458i	−0.245263	−	0.424808i
$342$	1.39809	−	0.447636i	0.0756000	−	0.0242054i
$343$	17.5286			0.946458
$344$	6.07294	+	4.53295i	0.327431	+	0.244400i
$345$	−9.48042	−	16.4206i	−0.510409	−	0.884054i
$346$	−7.82398	−	24.4364i	−0.420620	−	1.31371i
$347$	11.9179	−	20.6425i	0.639789	−	1.10815i	−0.345690	−	0.938349i	$-0.612355\pi$
$347$	11.9179	−	20.6425i	0.639789	−	1.10815i	0.985479	−	0.169798i	$-0.0543114\pi$
$348$	−9.60601	+	6.85387i	−0.514936	+	0.367406i
$349$	31.3226			1.67666			0.838330	−	0.545163i	$-0.183532\pi$
$349$	31.3226			1.67666			0.838330	+	0.545163i	$0.183532\pi$
$350$	1.38416	−	1.52405i	0.0739866	−	0.0814640i
$351$	−4.15472	+	2.39873i	−0.221763	+	0.128035i
$352$	−20.7292	−	0.445263i	−1.10487	−	0.0237326i
$353$	−10.4637	+	6.04123i	−0.556928	+	0.321542i	−0.751911	−	0.659264i	$-0.770868\pi$
$353$	−10.4637	+	6.04123i	−0.556928	+	0.321542i	0.194984	+	0.980806i	$0.437535\pi$
$354$	−1.55371	+	7.15832i	−0.0825790	+	0.380460i
$355$	−1.04083	+	1.80277i	−0.0552416	+	0.0956812i
$356$	−14.4758	−	6.59463i	−0.767216	−	0.349515i
$357$	−3.58971			−0.189988
$358$	−8.16952	−	1.77320i	−0.431773	−	0.0937163i
$359$			34.1767i			1.80378i	0.431967	+	0.901889i	$0.357820\pi$
$359$			34.1767i			1.80378i	−0.431967	+	0.901889i	$0.642180\pi$
$360$	−3.97698	+	5.32809i	−0.209605	+	0.280815i
$361$	−8.96124	+	15.5213i	−0.471644	+	0.816912i
$362$	−9.33604	+	10.2796i	−0.490691	+	0.540283i
$363$	1.21714	+	2.10814i	0.0638831	+	0.110649i
$364$	11.0173	−	24.1839i	0.577461	−	1.26758i
$365$	−20.0014	+	11.5478i	−1.04692	+	0.604440i
$366$	−8.44627	+	2.70431i	−0.441494	+	0.141356i
$367$	13.7004	−	23.7297i	0.715153	−	1.23868i	−0.247747	−	0.968825i	$-0.579690\pi$
$367$	13.7004	−	23.7297i	0.715153	−	1.23868i	0.962900	−	0.269857i	$-0.0869764\pi$
$368$	−30.5097	−	10.4961i	−1.59043	−	0.547145i
$369$	6.36793	+	3.67652i	0.331501	+	0.191392i
$370$	−23.9985	+	7.68379i	−1.24762	+	0.399461i
$371$	−29.7427	−	17.1720i	−1.54417	−	0.891525i
$372$	−4.02352	+	2.87077i	−0.208610	+	0.148843i
$373$	−16.4511	−	9.49803i	−0.851804	−	0.491790i	0.00945481	−	0.999955i	$-0.496990\pi$
$373$	−16.4511	−	9.49803i	−0.851804	−	0.491790i	−0.861259	+	0.508166i	$0.830324\pi$
$374$	−6.56523	−	1.42498i	−0.339480	−	0.0736842i
$375$			10.5178i			0.543136i
$376$	6.17033	+	14.3538i	0.318210	+	0.740238i
$377$		−	28.3061i		−	1.45784i
$378$	2.63344	−	2.89959i	0.135450	−	0.149139i
$379$	−10.1094	−	17.5100i	−0.519287	−	0.899431i	−0.999749	−	0.0224153i	$-0.992864\pi$
$379$	−10.1094	−	17.5100i	−0.519287	−	0.899431i	0.480462	−	0.877015i	$-0.340469\pi$
$380$	0.468401	+	4.85760i	0.0240284	+	0.249190i
$381$	2.67054	+	1.54184i	0.136816	+	0.0789908i
$382$	−8.66528	−	27.0640i	−0.443354	−	1.38471i
$383$	8.88351	+	15.3867i	0.453926	+	0.786223i	0.998626	−	0.0524083i	$-0.0166897\pi$
$383$	8.88351	+	15.3867i	0.453926	+	0.786223i	−0.544700	+	0.838631i	$0.683356\pi$
$384$	0.843810	+	11.2822i	0.0430605	+	0.575742i
$385$	−20.6663	+	11.9317i	−1.05325	+	0.608095i
$386$	24.2872	+	5.27154i	1.23619	+	0.268314i
$387$	−2.67928			−0.136195
$388$	−15.8081	+	1.52431i	−0.802533	+	0.0773853i
$389$	16.8606	+	29.2035i	0.854868	+	1.48067i	0.876768	+	0.480914i	$0.159695\pi$
$389$	16.8606	+	29.2035i	0.854868	+	1.48067i	−0.0218997	+	0.999760i	$0.506971\pi$
$390$	−4.86312	−	15.1888i	−0.246254	−	0.769116i
$391$	−9.05363	−	5.22711i	−0.457862	−	0.264346i
$392$	−0.222792	+	1.88566i	−0.0112527	+	0.0952400i
$393$		−	14.3495i		−	0.723838i
$394$	−3.64857	−	3.31367i	−0.183812	−	0.166941i
$395$	−27.7947	−	16.0473i	−1.39850	−	0.807426i
$396$	5.96734	−	4.25769i	0.299870	−	0.213957i
$397$	25.9535			1.30257			0.651286	−	0.758833i	$-0.274230\pi$
$397$	25.9535			1.30257			0.651286	+	0.758833i	$0.274230\pi$
$398$	5.17263	−	1.65616i	0.259281	−	0.0830158i
$399$		−	2.87506i		−	0.143933i
$400$	−1.37976	−	1.58636i	−0.0689878	−	0.0793178i
$401$			6.25356i			0.312288i	0.987734	+	0.156144i	$0.0499063\pi$
$401$			6.25356i			0.312288i	−0.987734	+	0.156144i	$0.950094\pi$
$402$	−9.18352	−	7.04719i	−0.458032	−	0.351482i
$403$		−	11.8561i		−	0.590596i
$404$	−5.44959	−	7.63785i	−0.271127	−	0.379997i
$405$		−	2.35066i		−	0.116805i
$406$	7.04722	+	22.0104i	0.349748	+	1.09236i
$407$	27.7830			1.37715
$408$	−0.430127	+	3.64048i	−0.0212944	+	0.180231i
$409$	7.95171	+	4.59092i	0.393187	+	0.227007i	0.683540	−	0.729913i	$-0.260439\pi$
$409$	7.95171	+	4.59092i	0.393187	+	0.227007i	−0.290353	+	0.956920i	$0.593773\pi$
$410$	−16.4341	+	18.0950i	−0.811623	+	0.893649i
$411$		−	12.8058i		−	0.631665i
$412$	−5.83996	−	8.18496i	−0.287714	−	0.403244i
$413$	12.4239	+	7.17294i	0.611340	+	0.352957i
$414$	10.8640	−	3.47841i	0.533937	−	0.170955i
$415$	−15.4592	−	26.7762i	−0.758864	−	1.31439i
$416$	−23.2058	−	14.0709i	−1.13776	−	0.689880i
$417$	3.94727			0.193299
$418$	1.14129	−	5.25820i	0.0558225	−	0.257187i
$419$	23.6128	−	13.6328i	1.15356	−	0.666007i	0.203807	−	0.979011i	$-0.434669\pi$
$419$	23.6128	−	13.6328i	1.15356	−	0.666007i	0.949752	+	0.313004i	$0.101335\pi$
$420$	7.56296	+	10.5998i	0.369035	+	0.517219i
$421$	−20.1730	−	34.9406i	−0.983170	−	1.70290i	−0.649801	−	0.760104i	$-0.725148\pi$
$421$	−20.1730	−	34.9406i	−0.983170	−	1.70290i	−0.333369	−	0.942796i	$-0.608185\pi$
$422$	2.35490	−	0.753986i	0.114635	−	0.0367034i
$423$	−4.78379	−	2.76192i	−0.232596	−	0.134289i
$424$	−20.9787	+	28.1058i	−1.01882	+	1.36494i
$425$	−0.340610	−	0.589954i	−0.0165220	−	0.0286170i
$426$	−0.927089	−	0.841994i	−0.0449176	−	0.0407947i
$427$			17.3691i			0.840549i
$428$	−13.3424	+	29.2878i	−0.644930	+	1.41568i
$429$			17.5840i			0.848965i
$430$	1.88924	−	8.70415i	0.0911071	−	0.419751i
$431$	18.4729	+	10.6653i	0.889806	+	0.513730i	0.873879	−	0.486143i	$-0.161597\pi$
$431$	18.4729	+	10.6653i	0.889806	+	0.513730i	0.0159272	+	0.999873i	$0.494930\pi$
$432$	−2.62506	−	3.01812i	−0.126298	−	0.145210i
$433$	−0.916164	−	0.528948i	−0.0440280	−	0.0254196i	0.477824	−	0.878455i	$-0.341426\pi$
$433$	−0.916164	−	0.528948i	−0.0440280	−	0.0254196i	−0.521852	+	0.853036i	$0.674759\pi$
$434$	2.95176	+	9.21914i	0.141689	+	0.442533i
$435$	12.0113	+	6.93472i	0.575897	+	0.332495i
$436$	−8.08491	+	17.7471i	−0.387197	+	0.849933i
$437$	4.18648	−	7.25120i	0.200267	−	0.346872i
$438$	−4.23695	−	13.2331i	−0.202449	−	0.632304i
$439$	1.28115	−	0.739672i	0.0611459	−	0.0353026i	−0.469115	−	0.883137i	$-0.655427\pi$
$439$	1.28115	−	0.739672i	0.0611459	−	0.0353026i	0.530261	+	0.847834i	$0.322094\pi$
$440$	9.62418	+	22.3883i	0.458815	+	1.06732i
$441$	−0.335658	−	0.581378i	−0.0159837	−	0.0276846i
$442$	−6.50934	−	5.91186i	−0.309618	−	0.281199i
$443$	10.9889	−	19.0333i	0.522097	−	0.904298i	−0.477573	−	0.878592i	$-0.658483\pi$
$443$	10.9889	−	19.0333i	0.522097	−	0.904298i	0.999670	−	0.0257060i	$-0.00818338\pi$
$444$	−1.45508	−	15.0901i	−0.0690551	−	0.716144i
$445$			18.6962i			0.886285i
$446$	2.53307	−	11.6705i	0.119944	−	0.552612i
$447$	−17.6801			−0.836239
$448$	21.5476	+	5.16383i	1.01803	+	0.243968i
$449$	−0.164189	+	0.284383i	−0.00774855	+	0.0134209i	−0.869874	−	0.493275i	$-0.835800\pi$
$449$	−0.164189	+	0.284383i	−0.00774855	+	0.0134209i	0.862125	+	0.506695i	$0.169133\pi$
$450$	0.726410	+	0.157667i	0.0342433	+	0.00743251i
$451$	23.3402	−	13.4755i	1.09905	−	0.634536i
$452$	−13.2887	−	18.6247i	−0.625049	−	0.876034i
$453$	−12.6946	+	7.32922i	−0.596443	+	0.344357i
$454$	−9.42137	−	8.55660i	−0.442167	−	0.401581i
$455$	−31.2346			−1.46430
$456$	−2.91572	−	0.344496i	−0.136541	−	0.0161325i
$457$	−20.1951	+	34.9789i	−0.944686	+	1.63624i	−0.188308	+	0.982110i	$0.560300\pi$
$457$	−20.1951	+	34.9789i	−0.944686	+	1.63624i	−0.756378	+	0.654134i	$0.773033\pi$
$458$	−2.55763	+	0.818896i	−0.119510	+	0.0382645i
$459$	−0.648029	−	1.12242i	−0.0302474	−	0.0523900i
$460$	3.63976	+	37.7466i	0.169705	+	1.75994i
$461$	29.7953			1.38770			0.693852	−	0.720118i	$-0.255912\pi$
$461$	29.7953			1.38770			0.693852	+	0.720118i	$0.255912\pi$
$462$	−4.37780	−	13.6730i	−0.203674	−	0.636127i
$463$	0.354213	+	0.613514i	0.0164617	+	0.0285124i	0.874139	−	0.485676i	$-0.161427\pi$
$463$	0.354213	+	0.613514i	0.0164617	+	0.0285124i	−0.857677	+	0.514188i	$0.828093\pi$
$464$	23.1661	−	4.50957i	1.07546	−	0.209351i
$465$	5.03098	+	2.90464i	0.233306	+	0.134699i
$466$	2.74390	+	2.49205i	0.127109	+	0.115442i
$467$	27.9080	−	16.1127i	1.29143	−	0.745607i	0.312521	−	0.949911i	$-0.398826\pi$
$467$	27.9080	−	16.1127i	1.29143	−	0.745607i	0.978908	+	0.204304i	$0.0654931\pi$
$468$	9.55062	−	0.920930i	0.441477	−	0.0425700i
$469$	−18.6289	+	12.9206i	−0.860202	+	0.596619i
$470$	12.3458	−	13.5936i	0.569471	−	0.627024i
$471$	0.694503	+	1.20291i	0.0320010	+	0.0554274i
$472$	8.76306	−	11.7401i	0.403352	−	0.540384i
$473$	−4.91015	+	8.50463i	−0.225769	+	0.391043i
$474$	12.9817	−	14.2936i	0.596267	−	0.656529i
$475$	0.472504	−	0.272800i	0.0216800	−	0.0125169i
$476$	6.53340	+	2.97637i	0.299458	+	0.136422i
$477$		−	12.3998i		−	0.567749i
$478$	1.07326	−	1.18173i	0.0490898	−	0.0540510i
$479$	5.97745	−	3.45108i	0.273117	−	0.157684i	−0.357187	−	0.934033i	$-0.616264\pi$
$479$	5.97745	−	3.45108i	0.273117	−	0.157684i	0.630303	+	0.776349i	$0.282931\pi$
$480$	11.6560	−	6.39984i	0.532020	−	0.292111i
$481$	31.4929	+	18.1825i	1.43595	+	0.829048i
$482$	−20.0491	−	4.35166i	−0.913212	−	0.198213i
$483$		−	22.3410i		−	1.01655i
$484$	−0.467288	−	4.84607i	−0.0212404	−	0.220276i
$485$	9.33295	+	16.1651i	0.423787	+	0.734021i
$486$	1.38203	+	0.299971i	0.0626903	+	0.0136069i
$487$	18.8625	+	32.6707i	0.854739	+	1.48045i	0.876887	+	0.480697i	$0.159616\pi$
$487$	18.8625	+	32.6707i	0.854739	+	1.48045i	−0.0221474	+	0.999755i	$0.507050\pi$
$488$	17.6148	+	2.08120i	0.797383	+	0.0942116i
$489$	−18.2836	−	10.5561i	−0.826814	−	0.477362i
$490$	2.12540	−	0.680505i	0.0960158	−	0.0307421i
$491$		−	27.1918i		−	1.22715i	−0.789637	−	0.613574i	$-0.789731\pi$
$491$		−	27.1918i		−	1.22715i	0.789637	−	0.613574i	$-0.210269\pi$
$492$	−8.54150	−	11.9713i	−0.385081	−	0.539708i
$493$	7.64704			0.344405
$494$	4.73491	−	5.21344i	0.213034	−	0.234564i
$495$	−7.46153	−	4.30792i	−0.335371	−	0.193626i
$496$	9.70322	−	1.88885i	0.435687	−	0.0848120i
$497$	−2.12415	+	1.22638i	−0.0952813	+	0.0550107i
$498$	17.7154	−	5.67207i	0.793846	−	0.254172i
$499$	2.52661	+	4.37622i	0.113107	+	0.195906i	0.917021	−	0.398838i	$-0.130587\pi$
$499$	2.52661	+	4.37622i	0.113107	+	0.195906i	−0.803915	+	0.594745i	$0.797253\pi$
$500$	8.72070	−	19.1427i	0.390002	−	0.856089i
$501$	14.7789	+	8.53260i	0.660273	+	0.381209i
$502$	−5.12641	−	16.0112i	−0.228803	−	0.714613i
$503$	6.13385	−	10.6241i	0.273495	−	0.473707i	−0.696259	−	0.717790i	$-0.745154\pi$
$503$	6.13385	−	10.6241i	0.273495	−	0.473707i	0.969754	+	0.244083i	$0.0784869\pi$
$504$	−7.19712	+	3.09387i	−0.320585	+	0.137812i
$505$	−5.51388	+	9.55031i	−0.245364	+	0.424983i
$506$	8.86856	−	40.8595i	0.394256	−	1.81643i
$507$	−5.00780	+	8.67376i	−0.222404	+	0.385215i
$508$	−3.58208	−	5.02045i	−0.158929	−	0.222747i
$509$	−17.1174			−0.758715			−0.379358	−	0.925250i	$-0.623855\pi$
$509$	−17.1174			−0.758715			−0.379358	+	0.925250i	$0.623855\pi$
$510$	4.10334	−	1.31380i	0.181699	−	0.0581759i
$511$	−27.2129			−1.20383
$512$	7.81875	−	21.2336i	0.345543	−	0.938403i
$513$	0.898964	−	0.519017i	0.0396902	−	0.0229152i
$514$	−9.93617	+	10.9404i	−0.438266	+	0.482559i
$515$	−5.90885	+	10.2344i	−0.260375	+	0.450983i
$516$	4.87638	+	2.22149i	0.214671	+	0.0977958i
$517$	−17.5339	+	10.1232i	−0.771142	+	0.445219i
$518$	−29.0152	−	6.29774i	−1.27485	−	0.276707i
$519$	−9.07160	−	15.7125i	−0.398199	−	0.689701i
$520$	−3.74260	+	31.6764i	−0.164124	+	1.38910i
$521$		−	13.0867i		−	0.573337i	−0.958030	−	0.286669i	$-0.907452\pi$
$521$		−	13.0867i		−	0.573337i	0.958030	−	0.286669i	$-0.0925479\pi$
$522$	−5.60993	+	6.17690i	−0.245540	+	0.270356i
$523$	−10.6752	+	6.16333i	−0.466794	+	0.269503i	−0.714897	−	0.699230i	$-0.753526\pi$
$523$	−10.6752	+	6.16333i	−0.466794	+	0.269503i	0.248103	+	0.968734i	$0.420193\pi$
$524$	−11.8978	+	26.1167i	−0.519756	+	1.14091i
$525$	0.727894	−	1.26075i	0.0317679	−	0.0550236i
$526$	−1.99609	+	9.19644i	−0.0870335	+	0.400984i
$527$	3.20300			0.139525
$528$	−14.3910	+	2.80139i	−0.626287	+	0.121915i
$529$	21.0316	−	36.4278i	0.914416	−	1.58382i
$530$	40.2832	+	8.74348i	1.74979	+	0.379792i
$531$			5.17955i			0.224773i
$532$	−2.38382	+	5.23271i	−0.103352	+	0.226867i
$533$	35.2759			1.52797
$534$	−10.9921	−	2.38584i	−0.475676	−	0.103246i
$535$	37.8266			1.63539
$536$	10.8712	+	20.4406i	0.469566	+	0.882898i
$537$	−5.91123			−0.255088
$538$	39.7138	+	8.61989i	1.71218	+	0.371630i
$539$	−2.46056			−0.105984
$540$	−1.94903	+	4.27829i	−0.0838727	+	0.184108i
$541$			2.81447i			0.121004i	0.998168	+	0.0605018i	$0.0192701\pi$
$541$			2.81447i			0.121004i	−0.998168	+	0.0605018i	$0.980730\pi$
$542$	12.3556	+	2.68179i	0.530720	+	0.115193i
$543$	−4.90958	+	8.50364i	−0.210690	+	0.364926i
$544$	3.80131	−	6.26917i	0.162980	−	0.268789i
$545$	22.9212			0.981838
$546$	3.98589	−	18.3639i	0.170580	−	0.785902i
$547$	−9.56837	+	16.5729i	−0.409114	+	0.708606i	−0.994791	−	0.101939i	$-0.967495\pi$
$547$	−9.56837	+	16.5729i	−0.409114	+	0.708606i	0.585677	+	0.810545i	$0.300829\pi$
$548$	−10.6178	+	23.3071i	−0.453571	+	0.995629i
$549$	−5.43091	+	3.13554i	−0.231786	+	0.133822i
$550$	1.83172	−	2.01684i	0.0781048	−	0.0859984i
$551$			6.12464i			0.260919i
$552$	−22.6570	−	2.67695i	−0.964345	−	0.113938i
$553$	−18.9080	−	32.7497i	−0.804051	−	1.39266i
$554$	22.1081	+	4.79857i	0.939284	+	0.203872i
$555$	−15.4309	+	8.90905i	−0.655006	+	0.378168i
$556$	−7.18417	−	3.27284i	−0.304677	−	0.138799i
$557$	−10.3069	+	17.8520i	−0.436716	+	0.756415i	−0.997434	−	0.0715922i	$-0.977192\pi$
$557$	−10.3069	+	17.8520i	−0.436716	+	0.756415i	0.560718	+	0.828007i	$0.310525\pi$
$558$	−2.34975	+	2.58722i	−0.0994727	+	0.109526i
$559$	−11.1316	+	6.42686i	−0.470818	+	0.271827i
$560$	−4.97612	−	25.5628i	−0.210280	−	1.08023i
$561$	−4.75041			−0.200563
$562$	33.7063	−	10.7920i	1.42181	−	0.455233i
$563$	−10.6406			−0.448450			−0.224225	−	0.974537i	$-0.571985\pi$
$563$	−10.6406			−0.448450			−0.224225	+	0.974537i	$0.571985\pi$
$564$	6.41665	+	8.99323i	0.270190	+	0.378683i
$565$	−13.4455	+	23.2883i	−0.565656	+	0.979745i
$566$	−9.12796	+	42.0546i	−0.383677	+	1.76769i
$567$	1.38486	−	2.39864i	0.0581585	−	0.100734i
$568$	0.989206	+	2.30114i	0.0415061	+	0.0965539i
$569$	12.9488	−	22.4280i	0.542844	−	0.940233i	−0.455896	−	0.890033i	$-0.650681\pi$
$569$	12.9488	−	22.4280i	0.542844	−	0.940233i	0.998739	−	0.0501994i	$-0.0159857\pi$
$570$	1.05224	+	3.28643i	0.0440736	+	0.137654i
$571$	15.4044	+	8.89371i	0.644652	+	0.372190i	0.786404	−	0.617712i	$-0.211940\pi$
$571$	15.4044	+	8.89371i	0.644652	+	0.372190i	−0.141752	+	0.989902i	$0.545274\pi$
$572$	14.5796	−	32.0035i	0.609604	−	1.33814i
$573$	−10.0471	−	17.4020i	−0.419722	−	0.726979i
$574$	−27.4300	+	8.78246i	−1.14490	+	0.366573i
$575$	3.67165	−	2.11983i	0.153118	−	0.0884030i
$576$	2.27525	+	7.66963i	0.0948021	+	0.319568i
$577$	15.3947	+	8.88813i	0.640889	+	0.370018i	0.784957	−	0.619550i	$-0.212685\pi$
$577$	15.3947	+	8.88813i	0.640889	+	0.370018i	−0.144068	+	0.989568i	$0.546018\pi$
$578$	−14.5665	+	16.0386i	−0.605885	+	0.667119i
$579$	17.5735			0.730330
$580$	−16.1111	−	22.5805i	−0.668978	−	0.937603i
$581$		−	36.4303i		−	1.51138i
$582$	−10.6950	+	3.42431i	−0.443323	+	0.141942i
$583$	−39.3598	−	22.7244i	−1.63012	−	0.941149i
$584$	−3.26071	+	27.5978i	−0.134929	+	1.14200i
$585$	−5.63860	−	9.76634i	−0.233127	−	0.403788i
$586$	−30.5032	−	6.62073i	−1.26008	−	0.273500i
$587$	12.7123	+	22.0183i	0.524692	+	0.908793i	0.999587	+	0.0287501i	$0.00915269\pi$
$587$	12.7123	+	22.0183i	0.524692	+	0.908793i	−0.474895	+	0.880042i	$0.657514\pi$
$588$	0.128867	+	1.33644i	0.00531440	+	0.0551137i
$589$			2.56533i			0.105703i
$590$	−16.8268	−	3.65226i	−0.692748	−	0.150361i
$591$	−3.01823	−	1.74257i	−0.124153	−	0.0716799i
$592$	−9.86348	+	28.6709i	−0.405386	+	1.17837i
$593$	6.69149	−	3.86333i	0.274787	−	0.158648i	−0.356274	−	0.934381i	$-0.615953\pi$
$593$	6.69149	−	3.86333i	0.274787	−	0.158648i	0.631061	+	0.775733i	$0.282620\pi$
$594$	3.48494	−	3.83715i	0.142989	−	0.157440i
$595$		−	8.43819i		−	0.345932i
$596$	32.1784	+	14.6592i	1.31808	+	0.600466i
$597$	3.32598	−	1.92025i	0.136123	−	0.0785907i
$598$	36.7932	−	40.5117i	1.50459	−	1.65665i
$599$	4.28782	−	7.42672i	0.175196	−	0.303448i	−0.765033	−	0.643991i	$-0.777278\pi$
$599$	4.28782	−	7.42672i	0.175196	−	0.303448i	0.940229	+	0.340543i	$0.110611\pi$
$600$	−1.19136	−	0.889255i	−0.0486372	−	0.0363037i
$601$	−12.4819	−	21.6193i	−0.509149	−	0.881871i	−0.999944	−	0.0105963i	$-0.996627\pi$
$601$	−12.4819	−	21.6193i	−0.509149	−	0.881871i	0.490795	−	0.871275i	$-0.336706\pi$
$602$	7.05572	−	7.76880i	0.287570	−	0.316633i
$603$	−7.40294	−	3.49234i	−0.301471	−	0.142219i
$604$	29.1815	−	2.81386i	1.18738	−	0.114495i
$605$	−4.95553	+	2.86108i	−0.201471	+	0.116319i
$606$	−4.91132	−	4.46052i	−0.199509	−	0.181196i
$607$	−5.57552	−	3.21903i	−0.226303	−	0.130656i	0.382562	−	0.923930i	$-0.375042\pi$
$607$	−5.57552	−	3.21903i	−0.226303	−	0.130656i	−0.608866	+	0.793273i	$0.708375\pi$
$608$	5.02108	+	3.04453i	0.203632	+	0.123472i
$609$	8.17098	+	14.1525i	0.331105	+	0.573490i
$610$	−6.35691	−	19.8543i	−0.257384	−	0.803878i
$611$	−26.5004			−1.07209
$612$	0.248794	+	2.58015i	0.0100569	+	0.104296i
$613$	−6.94855	−	12.0352i	−0.280649	−	0.486099i	0.690896	−	0.722955i	$-0.257216\pi$
$613$	−6.94855	−	12.0352i	−0.280649	−	0.486099i	−0.971545	+	0.236856i	$0.923883\pi$
$614$	6.32607	−	2.02547i	0.255299	−	0.0817411i
$615$	−8.64226	+	14.9688i	−0.348490	+	0.603602i
$616$	−3.36910	+	28.5152i	−0.135745	+	1.14891i
$617$	−27.2822			−1.09834			−0.549169	−	0.835711i	$-0.685056\pi$
$617$	−27.2822			−1.09834			−0.549169	+	0.835711i	$0.685056\pi$
$618$	−5.26313	−	4.78004i	−0.211714	−	0.192281i
$619$	−1.91791	+	1.10731i	−0.0770874	+	0.0445064i	−0.538048	−	0.842914i	$-0.680838\pi$
$619$	−1.91791	+	1.10731i	−0.0770874	+	0.0445064i	0.460961	+	0.887420i	$0.347505\pi$
$620$	−6.74822	−	9.45793i	−0.271015	−	0.379840i
$621$	6.98551	−	4.03309i	0.280319	−	0.161842i
$622$	11.1585	+	2.42195i	0.447414	+	0.0971112i
$623$	−11.0146	+	19.0778i	−0.441290	+	0.764337i
$624$	−18.1460	−	6.24266i	−0.726423	−	0.249907i
$625$	−27.3518			−1.09407
$626$	−7.26479	+	33.4706i	−0.290359	+	1.33775i
$627$		−	3.80469i		−	0.151944i
$628$	−0.266637	−	2.76519i	−0.0106400	−	0.110343i
$629$	−4.91208	+	8.50798i	−0.195858	+	0.339235i
$630$	6.81595	+	6.19033i	0.271554	+	0.246629i
$631$	−6.23063	−	10.7918i	−0.248037	−	0.429613i	0.714944	−	0.699182i	$-0.246452\pi$
$631$	−6.23063	−	10.7918i	−0.248037	−	0.429613i	−0.962981	+	0.269569i	$0.913119\pi$
$632$	−35.4785	+	15.2513i	−1.41126	+	0.606665i
$633$	1.51419	−	0.874217i	0.0601836	−	0.0347470i
$634$	−7.51681	−	23.4770i	−0.298531	−	0.932391i
$635$	−3.62434	+	6.27754i	−0.143828	+	0.249117i
$636$	−10.2812	+	22.5681i	−0.407675	+	0.894884i
$637$	−2.78913	−	1.61031i	−0.110510	−	0.0638027i
$638$	9.32588	+	29.1272i	0.369215	+	1.15316i
$639$	−0.766921	−	0.442782i	−0.0303389	−	0.0175162i
$640$	−26.5206	+	1.98351i	−1.04832	+	0.0784052i
$641$	20.8534	+	12.0397i	0.823660	+	0.475540i	0.851677	−	0.524067i	$-0.175586\pi$
$641$	20.8534	+	12.0397i	0.823660	+	0.475540i	−0.0280172	+	0.999607i	$0.508919\pi$
$642$	−4.82710	+	22.2395i	−0.190510	+	0.877725i
$643$		−	41.9416i		−	1.65402i	−0.562191	−	0.827008i	$-0.690041\pi$
$643$		−	41.9416i		−	1.65402i	0.562191	−	0.827008i	$-0.309959\pi$
$644$	−18.5238	+	40.6614i	−0.729940	+	1.60228i
$645$		−	6.29807i		−	0.247986i
$646$	1.40844	+	1.27916i	0.0554142	+	0.0503279i
$647$	23.2422	+	40.2567i	0.913745	+	1.58265i	0.808728	+	0.588183i	$0.200157\pi$
$647$	23.2422	+	40.2567i	0.913745	+	1.58265i	0.105018	+	0.994470i	$0.466510\pi$
$648$	−2.26663	−	1.69186i	−0.0890418	−	0.0664624i
$649$	16.4411	+	9.49226i	0.645368	+	0.372604i
$650$	3.39623	−	1.08740i	0.133211	−	0.0426512i
$651$	3.42245	+	5.92786i	0.134136	+	0.232331i
$652$	24.5244	+	34.3721i	0.960450	+	1.34611i
$653$	11.0539	−	6.38196i	0.432572	−	0.249745i	−0.267870	−	0.963455i	$-0.586320\pi$
$653$	11.0539	−	6.38196i	0.432572	−	0.249745i	0.700442	+	0.713710i	$0.252986\pi$
$654$	−2.92501	+	13.4762i	−0.114377	+	0.526960i
$655$	33.7309			1.31798
$656$	5.61996	+	28.8703i	0.219423	+	1.12719i
$657$	−4.91258	−	8.50884i	−0.191658	−	0.331961i
$658$	20.6063	−	6.59767i	0.803317	−	0.257204i
$659$	10.7755	+	6.22124i	0.419754	+	0.242345i	0.694972	−	0.719037i	$-0.255417\pi$
$659$	10.7755	+	6.22124i	0.419754	+	0.242345i	−0.275218	+	0.961382i	$0.588750\pi$
$660$	10.0084	+	14.0272i	0.389576	+	0.546008i
$661$		−	45.3214i		−	1.76280i	−0.472372	−	0.881399i	$-0.656602\pi$
$661$		−	45.3214i		−	1.76280i	0.472372	−	0.881399i	$-0.343398\pi$
$662$	14.9090	−	16.4158i	0.579455	−	0.638017i
$663$	−5.38476	−	3.10889i	−0.209127	−	0.120739i
$664$	−36.9456	−	4.36516i	−1.43377	−	0.169401i
$665$	6.75829			0.262075
$666$	−3.26878	−	10.2093i	−0.126662	−	0.395601i
$667$			47.5923i			1.84278i
$668$	−19.8234	−	27.7834i	−0.766991	−	1.07497i
$669$		−	8.44440i		−	0.326480i
$670$	16.5656	−	21.5873i	0.639984	−	0.833992i
$671$			22.9852i			0.887336i
$672$	15.6643	+	0.336469i	0.604262	+	0.0129796i
$673$			1.54683i			0.0596261i	0.999555	+	0.0298130i	$0.00949119\pi$
$673$			1.54683i			0.0596261i	−0.999555	+	0.0298130i	$0.990509\pi$
$674$	−0.637539	+	0.204125i	−0.0245571	+	0.00786262i
$675$	0.525610			0.0202307
$676$	16.3061	−	11.6344i	0.627159	−	0.447477i
$677$	9.67983	+	5.58865i	0.372026	+	0.214789i	0.674343	−	0.738418i	$-0.264427\pi$
$677$	9.67983	+	5.58865i	0.372026	+	0.214789i	−0.302317	+	0.953207i	$0.597760\pi$
$678$	−11.9762	−	10.8769i	−0.459942	−	0.417725i
$679$			21.9935i			0.844032i
$680$	−8.55754	−	1.01108i	−0.328167	−	0.0387732i
$681$	−7.79369	−	4.49969i	−0.298655	−	0.172428i
$682$	3.90619	+	12.2001i	0.149576	+	0.467165i
$683$	−12.6933	−	21.9855i	−0.485696	−	0.841251i	0.514169	−	0.857689i	$-0.328101\pi$
$683$	−12.6933	−	21.9855i	−0.485696	−	0.841251i	−0.999865	+	0.0164384i	$0.994767\pi$
$684$	−2.06648	+	0.199263i	−0.0790140	+	0.00761902i
$685$	30.1022			1.15015
$686$	−24.2252	−	5.25808i	−0.924922	−	0.200754i
$687$	−1.64455	+	0.949479i	−0.0627433	+	0.0362249i
$688$	−7.03325	−	8.08639i	−0.268140	−	0.308291i
$689$	−29.7438	−	51.5178i	−1.13315	−	1.96267i
$690$	8.17657	+	25.5376i	0.311277	+	0.972201i
$691$	34.5555	+	19.9506i	1.31455	+	0.758958i	0.982847	−	0.184424i	$-0.0590419\pi$
$691$	34.5555	+	19.9506i	1.31455	+	0.758958i	0.331708	+	0.943382i	$0.392375\pi$
$692$	3.48281	+	36.1189i	0.132397	+	1.37303i
$693$	−5.07589	−	8.79170i	−0.192817	−	0.333969i
$694$	−22.6631	+	24.9536i	−0.860281	+	0.947225i
$695$			9.27870i			0.351961i
$696$	15.3318	−	6.59076i	0.581150	−	0.249822i
$697$			9.52997i			0.360973i
$698$	−43.2889	−	9.39586i	−1.63851	−	0.355639i
$699$	2.26985	+	1.31050i	0.0858538	+	0.0495677i
$700$	−2.37013	+	1.69108i	−0.0895825	+	0.0639169i
$701$	−20.5109	−	11.8420i	−0.774687	−	0.447266i	0.0598573	−	0.998207i	$-0.480935\pi$
$701$	−20.5109	−	11.8420i	−0.774687	−	0.447266i	−0.834544	+	0.550941i	$0.814269\pi$
$702$	6.46151	−	2.06883i	0.243874	−	0.0780830i
$703$	−6.81418	−	3.93417i	−0.257002	−	0.148380i
$704$	28.5148	+	6.83351i	1.07469	+	0.257548i
$705$	6.49235	−	11.2451i	0.244516	−	0.423514i
$706$	16.2734	−	5.21038i	0.612458	−	0.196095i
$707$	−11.2529	+	6.49684i	−0.423207	+	0.244339i
$708$	4.29457	−	9.42697i	0.161400	−	0.354287i
$709$	13.4519	+	23.2993i	0.505195	+	0.875024i	0.999982	+	0.00600948i	$0.00191289\pi$
$709$	13.4519	+	23.2993i	0.505195	+	0.875024i	−0.494787	+	0.869015i	$0.664754\pi$
$710$	1.97924	−	2.17927i	0.0742796	−	0.0817867i
$711$	6.82671	−	11.8242i	0.256022	−	0.443442i
$712$	18.0279	+	13.4563i	0.675623	+	0.504297i
$713$			19.9342i			0.746543i
$714$	4.96110	+	1.07681i	0.185665	+	0.0402985i
$715$	−41.3341			−1.54581
$716$	10.7587	+	4.90123i	0.402070	+	0.183168i
$717$	0.564399	−	0.977568i	0.0210779	−	0.0365080i
$718$	10.2520	−	47.2334i	0.382602	−	1.76273i
$719$	29.2447	−	16.8844i	1.09064	−	0.629682i	0.156894	−	0.987615i	$-0.449852\pi$
$719$	29.2447	−	16.8844i	1.09064	−	0.629682i	0.933747	+	0.357933i	$0.116518\pi$
$720$	7.09459	−	6.17062i	0.264400	−	0.229965i
$721$	−12.0589	+	6.96222i	−0.449098	+	0.259287i
$722$	17.0407	−	18.7629i	0.634189	−	0.698282i
$723$	−14.5070			−0.539519
$724$	15.9863	−	11.4062i	0.594126	−	0.423908i
$725$	−1.55061	+	2.68573i	−0.0575882	+	0.0997456i
$726$	−1.04974	−	3.27863i	−0.0389596	−	0.121681i
$727$	10.8162	+	18.7343i	0.401152	+	0.694816i	0.993865	−	0.110598i	$-0.0352766\pi$
$727$	10.8162	+	18.7343i	0.401152	+	0.694816i	−0.592713	+	0.805414i	$0.701943\pi$
$728$	−22.4807	+	30.1181i	−0.833189	+	1.11625i
$729$	1.00000			0.0370370
$730$	31.1066	−	9.95964i	1.15131	−	0.368623i
$731$	−1.73625	−	3.00727i	−0.0642175	−	0.111228i
$732$	12.4842	−	1.20381i	0.461431	−	0.0444941i
$733$	−16.0077	−	9.24206i	−0.591259	−	0.341363i	0.174336	−	0.984686i	$-0.444222\pi$
$733$	−16.0077	−	9.24206i	−0.591259	−	0.341363i	−0.765595	+	0.643323i	$0.777555\pi$
$734$	−26.0526	+	28.6856i	−0.961619	+	1.05880i
$735$	1.36662	−	0.789019i	0.0504086	−	0.0291034i
$736$	39.0170	+	23.6579i	1.43818	+	0.872043i
$737$	−24.6524	+	17.0984i	−0.908083	+	0.629828i
$738$	−7.69784	−	6.99127i	−0.283361	−	0.257352i
$739$	6.92586	+	11.9959i	0.254772	+	0.441278i	0.964834	−	0.262862i	$-0.0846663\pi$
$739$	6.92586	+	11.9959i	0.254772	+	0.441278i	−0.710062	+	0.704140i	$0.751333\pi$
$740$	35.4717	−	3.42040i	1.30396	−	0.125736i
$741$	2.48996	−	4.31274i	0.0914711	−	0.158433i
$742$	35.9544	+	32.6542i	1.31993	+	1.19877i
$743$	16.4484	−	9.49649i	0.603433	−	0.348392i	−0.166958	−	0.985964i	$-0.553394\pi$
$743$	16.4484	−	9.49649i	0.603433	−	0.348392i	0.770391	+	0.637572i	$0.220061\pi$
$744$	6.42179	−	2.76057i	0.235434	−	0.101207i
$745$		−	41.5599i		−	1.52264i
$746$	19.8868	+	18.0614i	0.728108	+	0.661276i
$747$	11.3909	−	6.57655i	0.416772	−	0.240623i
$748$	8.64592	+	3.93875i	0.316126	+	0.144015i
$749$	38.5987	+	22.2850i	1.41037	+	0.814275i
$750$	3.15502	−	14.5359i	0.115205	−	0.530777i
$751$			40.7347i			1.48643i	0.669053	+	0.743215i	$0.266700\pi$
$751$			40.7347i			1.48643i	−0.669053	+	0.743215i	$0.733300\pi$
$752$	−4.22190	−	21.6883i	−0.153957	−	0.790890i
$753$	−5.94388	−	10.2951i	−0.216607	−	0.375174i
$754$	−8.49100	+	39.1200i	−0.309224	+	1.42467i
$755$	−17.2285	−	29.8406i	−0.627010	−	1.08601i
$756$	−4.50930	+	3.21738i	−0.164002	+	0.117015i
$757$	37.9194	+	21.8928i	1.37820	+	0.795706i	0.991943	−	0.126683i	$-0.0404332\pi$
$757$	37.9194	+	21.8928i	1.37820	+	0.795706i	0.386261	+	0.922390i	$0.373766\pi$
$758$	8.71908	+	27.2320i	0.316691	+	0.989111i
$759$		−	29.5648i		−	1.07313i
$760$	0.809793	−	6.85388i	0.0293743	−	0.248616i
$761$	29.7038			1.07676			0.538380	−	0.842702i	$-0.319036\pi$
$761$	29.7038			1.07676			0.538380	+	0.842702i	$0.319036\pi$
$762$	−3.22828	−	2.93196i	−0.116948	−	0.106214i
$763$	23.3891	+	13.5037i	0.846742	+	0.488867i
$764$	3.85731	+	40.0027i	0.139553	+	1.44725i
$765$	2.63843	−	1.52330i	0.0953925	−	0.0550749i
$766$	−7.66175	−	23.9297i	−0.276830	−	0.864615i
$767$	12.4243	+	21.5196i	0.448617	+	0.777028i
$768$	2.21815	−	15.8455i	0.0800407	−	0.571775i
$769$	1.88624	+	1.08902i	0.0680194	+	0.0392710i	0.533624	−	0.845722i	$-0.320830\pi$
$769$	1.88624	+	1.08902i	0.0680194	+	0.0392710i	−0.465605	+	0.884993i	$0.654163\pi$
$770$	32.1407	−	10.2907i	1.15827	−	0.370852i
$771$	−5.22517	+	9.05026i	−0.188180	+	0.325937i
$772$	−31.9844	−	14.5709i	−1.15114	−	0.524418i
$773$	−4.97209	+	8.61191i	−0.178834	+	0.309749i	−0.941481	−	0.337065i	$-0.890566\pi$
$773$	−4.97209	+	8.61191i	−0.178834	+	0.309749i	0.762648	+	0.646814i	$0.223899\pi$
$774$	3.70285	+	0.803704i	0.133096	+	0.0288885i
$775$	−0.649480	+	1.12493i	−0.0233300	+	0.0404087i
$776$	22.3045	+	2.63530i	0.800686	+	0.0946019i
$777$	−20.9945			−0.753175
$778$	−14.5418	−	45.4179i	−0.521348	−	1.62831i
$779$	−7.63271			−0.273470
$780$	2.16480	+	22.4503i	0.0775121	+	0.803848i
$781$	−2.81098	+	1.62292i	−0.100585	+	0.0580727i
$782$	10.9444	+	9.93987i	0.391372	+	0.355449i
$783$	−2.95012	+	5.10975i	−0.105429	+	0.182608i
$784$	0.873547	−	2.53921i	0.0311981	−	0.0906860i
$785$	−2.82764	+	1.63254i	−0.100923	+	0.0582679i
$786$	−4.30444	+	19.8315i	−0.153534	+	0.707368i
$787$	1.54969	+	2.68414i	0.0552404	+	0.0956791i	0.892323	−	0.451397i	$-0.149074\pi$
$787$	1.54969	+	2.68414i	0.0552404	+	0.0956791i	−0.837083	+	0.547076i	$0.815741\pi$
$788$	4.04844	+	5.67407i	0.144220	+	0.202131i
$789$			6.65428i			0.236899i
$790$	33.5995	+	30.5155i	1.19542	+	1.08569i
$791$	−27.4399	+	15.8424i	−0.975649	+	0.563291i
$792$	−9.52425	+	4.09424i	−0.338430	+	0.145483i
$793$	−15.0426	+	26.0546i	−0.534179	+	0.925225i
$794$	−35.8687	−	7.78530i	−1.27293	−	0.276290i
$795$	29.1478			1.03377
$796$	−7.64555	+	0.737232i	−0.270989	+	0.0261305i
$797$	−5.86395	+	10.1567i	−0.207712	+	0.359768i	−0.950993	−	0.309211i	$-0.899935\pi$
$797$	−5.86395	+	10.1567i	−0.207712	+	0.359768i	0.743281	+	0.668979i	$0.233268\pi$
$798$	−0.862433	+	3.97343i	−0.0305298	+	0.140658i
$799$		−	7.15923i		−	0.253275i
$800$	1.43101	+	2.60628i	0.0505938	+	0.0921460i
$801$	−7.95359			−0.281026
$802$	1.87588	−	8.64263i	0.0662397	−	0.305182i
$803$	−36.0120			−1.27083
$804$	10.5780	+	12.4942i	0.373057	+	0.440638i
$805$	52.5161			1.85095
$806$	−3.55649	+	16.3856i	−0.125272	+	0.577158i
$807$	28.7358			1.01155
$808$	5.24039	+	12.1905i	0.184356	+	0.428859i
$809$			10.1074i			0.355358i	0.984088	+	0.177679i	$0.0568589\pi$
$809$			10.1074i			0.355358i	−0.984088	+	0.177679i	$0.943141\pi$
$810$	−0.705129	+	3.24869i	−0.0247757	+	0.114147i
$811$	−13.7485	+	23.8131i	−0.482774	+	0.836190i	−0.999804	−	0.0197775i	$-0.993704\pi$
$811$	−13.7485	+	23.8131i	−0.482774	+	0.836190i	0.517030	+	0.855967i	$0.327038\pi$
$812$	−3.13704	−	32.5330i	−0.110088	−	1.14168i
$813$	8.94018			0.313546
$814$	−38.3970	−	8.33407i	−1.34581	−	0.292109i
$815$	24.8137	−	42.9786i	0.869187	−	1.50548i
$816$	1.68649	−	4.90225i	0.0590389	−	0.171613i
$817$	2.40857	−	1.39059i	0.0842653	−	0.0486506i
$818$	−9.61239	−	8.73009i	−0.336089	−	0.305241i
$819$		−	13.2876i		−	0.464306i
$820$	28.1405	−	20.0782i	0.982708	−	0.701160i
$821$	−3.48216	−	6.03128i	−0.121528	−	0.210493i	0.798842	−	0.601541i	$-0.205446\pi$
$821$	−3.48216	−	6.03128i	−0.121528	−	0.210493i	−0.920371	+	0.391047i	$0.872113\pi$
$822$	−3.84137	+	17.6981i	−0.133983	+	0.617292i
$823$	16.3468	−	9.43783i	0.569814	−	0.328982i	−0.187261	−	0.982310i	$-0.559961\pi$
$823$	16.3468	−	9.43783i	0.569814	−	0.328982i	0.757075	+	0.653328i	$0.226628\pi$
$824$	5.61577	+	13.0637i	0.195635	+	0.455096i
$825$	0.963253	−	1.66840i	0.0335362	−	0.0580863i
$826$	−15.0186	−	13.6401i	−0.522563	−	0.474598i
$827$	−10.1156	+	5.84027i	−0.351755	+	0.203086i	−0.665458	−	0.746435i	$-0.731764\pi$
$827$	−10.1156	+	5.84027i	−0.351755	+	0.203086i	0.313703	+	0.949521i	$0.398430\pi$
$828$	−16.0579	+	1.54840i	−0.558049	+	0.0538106i
$829$	39.7595			1.38091			0.690453	−	0.723378i	$-0.257411\pi$
$829$	39.7595			1.38091			0.690453	+	0.723378i	$0.257411\pi$
$830$	13.3331	+	41.6429i	0.462800	+	1.44545i
$831$	15.9968			0.554923
$832$	27.8504	+	26.4075i	0.965539	+	0.915514i
$833$	0.435033	−	0.753499i	0.0150730	−	0.0261072i
$834$	−5.45526	−	1.18406i	−0.188900	−	0.0410008i
$835$	−20.0573	+	34.7402i	−0.694110	+	1.20223i
$836$	−3.15461	+	6.92466i	−0.109105	+	0.239494i
$837$	−1.23567	+	2.14024i	−0.0427110	+	0.0739776i
$838$	−36.7231	+	11.7579i	−1.26858	+	0.406170i
$839$	13.3504	+	7.70787i	0.460908	+	0.266105i	0.712426	−	0.701747i	$-0.247596\pi$
$839$	13.3504	+	7.70787i	0.460908	+	0.266105i	−0.251518	+	0.967853i	$0.580930\pi$
$840$	−7.27263	−	16.9180i	−0.250930	−	0.583726i
$841$	−2.90636	−	5.03397i	−0.100219	−	0.173585i
$842$	17.3986	+	54.3404i	0.599594	+	1.87269i
$843$	21.6730	−	12.5129i	0.746457	−	0.430967i
$844$	−3.48072	+	0.335633i	−0.119811	+	0.0115530i
$845$	−20.3891	−	11.7716i	−0.701406	−	0.404957i
$846$	5.78287	+	5.25207i	0.198819	+	0.180570i
$847$	−6.74224			−0.231666
$848$	37.4242	−	32.5502i	1.28515	−	1.11778i
$849$			30.4295i			1.04434i
$850$	0.293766	+	0.917510i	0.0100761	+	0.0314703i
$851$	−52.9504	−	30.5709i	−1.81512	−	1.04796i
$852$	1.02870	+	1.44176i	0.0352425	+	0.0493940i
$853$	8.53127	+	14.7766i	0.292105	+	0.505941i	0.974307	−	0.225223i	$-0.0723109\pi$
$853$	8.53127	+	14.7766i	0.292105	+	0.505941i	−0.682202	+	0.731164i	$0.738978\pi$
$854$	5.21022	−	24.0047i	0.178290	−	0.821423i
$855$	1.22003	+	2.11316i	0.0417243	+	0.0722686i
$856$	27.2252	−	36.4744i	0.930537	−	1.24667i
$857$		−	4.43888i		−	0.151629i	−0.997122	−	0.0758147i	$-0.975844\pi$
$857$		−	4.43888i		−	0.151629i	0.997122	−	0.0758147i	$-0.0241557\pi$
$858$	5.27469	−	24.3017i	0.180075	−	0.829647i
$859$	−21.8358	−	12.6069i	−0.745028	−	0.430142i	0.0788665	−	0.996885i	$-0.474870\pi$
$859$	−21.8358	−	12.6069i	−0.745028	−	0.430142i	−0.823895	+	0.566743i	$0.808203\pi$
$860$	−5.22198	+	11.4627i	−0.178068	+	0.390875i
$861$	−17.6373	+	10.1829i	−0.601079	+	0.347033i
$862$	−22.3308	−	20.2811i	−0.760591	−	0.690778i
$863$		−	23.8422i		−	0.811599i	−0.913962	−	0.405799i	$-0.866993\pi$
$863$		−	23.8422i		−	0.811599i	0.913962	−	0.405799i	$-0.133007\pi$
$864$	2.72257	+	4.95859i	0.0926237	+	0.168695i
$865$	36.9347	−	21.3243i	1.25582	−	0.725047i
$866$	1.10750	+	1.00585i	0.0376344	+	0.0341800i
$867$	−7.66012	+	13.2677i	−0.260151	+	0.450595i
$868$	−1.31396	−	13.6266i	−0.0445988	−	0.462517i
$869$	−25.0218	−	43.3390i	−0.848806	−	1.47018i
$870$	−14.5198	−	13.1871i	−0.492267	−	0.447083i
$871$	−39.1343	+	3.24797i	−1.32602	+	0.110053i
$872$	16.4972	−	22.1019i	0.558667	−	0.748464i
$873$	−6.87685	+	3.97035i	−0.232746	+	0.134376i
$874$	−7.96101	+	8.76558i	−0.269285	+	0.296500i
$875$	−25.2284	−	14.5656i	−0.852875	−	0.492408i
$876$	1.88606	+	19.5596i	0.0637240	+	0.660858i
$877$	26.2081	+	45.3937i	0.884983	+	1.53284i	0.845733	+	0.533606i	$0.179164\pi$
$877$	26.2081	+	45.3937i	0.884983	+	1.53284i	0.0392502	+	0.999229i	$0.487503\pi$
$878$	−1.99247	+	0.637945i	−0.0672427	+	0.0215296i
$879$	−22.0713			−0.744445
$880$	−6.58511	−	33.8283i	−0.221984	−	1.14035i
$881$	−23.7201	−	41.0845i	−0.799152	−	1.38417i	−0.920169	−	0.391521i	$-0.871949\pi$
$881$	−23.7201	−	41.0845i	−0.799152	−	1.38417i	0.121018	−	0.992650i	$-0.461384\pi$
$882$	0.289495	+	0.904171i	0.00974781	+	0.0304450i
$883$	−5.96060	+	10.3241i	−0.200590	+	0.347432i	−0.948719	−	0.316122i	$-0.897619\pi$
$883$	−5.96060	+	10.3241i	−0.200590	+	0.347432i	0.748129	+	0.663554i	$0.230953\pi$
$884$	7.22274	+	10.1230i	0.242927	+	0.340473i
$885$	−12.1754			−0.409271
$886$	−20.8964	+	23.0083i	−0.702029	+	0.772979i
$887$	−25.9889	+	15.0047i	−0.872622	+	0.503809i	−0.868219	−	0.496182i	$-0.834735\pi$
$887$	−25.9889	+	15.0047i	−0.872622	+	0.503809i	−0.00440346	+	0.999990i	$0.501402\pi$
$888$	−2.51561	+	21.2915i	−0.0844184	+	0.714496i
$889$	−7.39664	+	4.27045i	−0.248075	+	0.143226i
$890$	5.60831	−	25.8388i	0.187991	−	0.866118i
$891$	1.83264	−	3.17422i	0.0613957	−	0.106341i
$892$	−7.00158	+	15.3691i	−0.234430	+	0.514596i
$893$	5.73394			0.191879
$894$	24.4345	+	5.30350i	0.817210	+	0.177376i
$895$		−	13.8953i		−	0.464469i
$896$	−28.2305	−	13.6002i	−0.943115	−	0.454352i
$897$	19.3486	−	33.5127i	0.646030	−	1.11896i
$898$	0.312221	−	0.343776i	0.0104190	−	0.0114719i
$899$	−7.29073	−	12.6279i	−0.243160	−	0.421165i
$900$	−0.956628	−	0.435803i	−0.0318876	−	0.0145268i
$901$	13.9178	−	8.03544i	0.463669	−	0.267699i
$902$	−36.2992	+	11.6222i	−1.20863	+	0.386977i
$903$	3.71041	−	6.42663i	0.123475	−	0.213865i
$904$	12.7786	+	29.7263i	0.425010	+	0.988681i
$905$	−19.9892	−	11.5408i	−0.664463	−	0.383628i
$906$	19.7429	−	6.32123i	0.655913	−	0.210009i
$907$	22.4529	+	12.9632i	0.745535	+	0.430435i	0.824078	−	0.566476i	$-0.191693\pi$
$907$	22.4529	+	12.9632i	0.745535	+	0.430435i	−0.0785430	+	0.996911i	$0.525027\pi$
$908$	10.4539	+	14.6516i	0.346925	+	0.486232i
$909$	−4.06282	−	2.34567i	−0.134755	−	0.0778010i
$910$	43.1673	+	9.36947i	1.43098	+	0.310595i
$911$		−	54.6788i		−	1.81159i	−0.423717	−	0.905794i	$-0.639275\pi$
$911$		−	54.6788i		−	1.81159i	0.423717	−	0.905794i	$-0.360725\pi$
$912$	3.92629	+	1.35074i	0.130012	+	0.0447273i
$913$		−	48.2098i		−	1.59551i
$914$	38.4029	−	42.2841i	1.27026	−	1.39863i
$915$	−7.37059	−	12.7662i	−0.243664	−	0.422039i
$916$	3.78038	−	0.364528i	0.124907	−	0.0120443i
$917$	34.4194	+	19.8721i	1.13663	+	0.656233i
$918$	0.558905	+	1.74561i	0.0184466	+	0.0576137i
$919$	−14.5053	−	25.1240i	−0.478487	−	0.828764i	0.521209	−	0.853429i	$-0.325481\pi$
$919$	−14.5053	−	25.1240i	−0.478487	−	0.828764i	−0.999696	+	0.0246656i	$0.992148\pi$
$920$	6.29259	−	53.2589i	0.207461	−	1.75589i
$921$	4.06763	−	2.34845i	0.134033	−	0.0773840i
$922$	−41.1781	−	8.93770i	−1.35613	−	0.294348i
$923$	−4.24846			−0.139840
$924$	1.94876	+	20.2098i	0.0641094	+	0.664854i
$925$	−1.99207	−	3.45037i	−0.0654989	−	0.113447i
$926$	−0.305498	−	0.954151i	−0.0100393	−	0.0313553i
$927$	−4.35385	−	2.51370i	−0.142999	−	0.0825606i
$928$	−33.3691	−	0.716768i	−1.09539	−	0.0235291i
$929$		−	50.1280i		−	1.64465i	−0.569021	−	0.822323i	$-0.692678\pi$
$929$		−	50.1280i		−	1.64465i	0.569021	−	0.822323i	$-0.307322\pi$
$930$	−6.08168	−	5.52346i	−0.199426	−	0.181121i
$931$	0.603490	+	0.348425i	0.0197786	+	0.0114192i
$932$	−3.04463	−	4.26718i	−0.0997301	−	0.139776i
$933$	8.07394			0.264329
$934$	−43.4032	+	13.8967i	−1.42019	+	0.454714i
$935$		−	11.1666i		−	0.365187i
$936$	−13.4755	−	1.59215i	−0.440461	−	0.0520410i
$937$			44.5098i			1.45407i	0.686600	+	0.727035i	$0.259102\pi$
$937$			44.5098i			1.45407i	−0.686600	+	0.727035i	$0.740898\pi$
$938$	29.6216	−	12.2686i	0.967178	−	0.400585i
$939$			24.2183i			0.790335i
$940$	−21.1400	+	15.0834i	−0.689512	+	0.491965i
$941$			46.2225i			1.50681i	0.657557	+	0.753405i	$0.271590\pi$
$941$			46.2225i			1.50681i	−0.657557	+	0.753405i	$0.728410\pi$
$942$	−0.598988	−	1.87080i	−0.0195161	−	0.0609539i
$943$	−59.3109			−1.93143
$944$	−15.6325	+	13.5966i	−0.508796	+	0.442532i
$945$	5.63840	+	3.25533i	0.183417	+	0.105896i
$946$	9.33713	−	10.2808i	0.303576	−	0.334257i
$947$			1.37149i			0.0445673i	0.999752	+	0.0222836i	$0.00709369\pi$
$947$			1.37149i			0.0445673i	−0.999752	+	0.0222836i	$0.992906\pi$
$948$	−22.2288	+	15.8602i	−0.721956	+	0.515115i
$949$	−40.8208	−	23.5679i	−1.32510	−	0.765046i
$950$	−0.734849	+	0.235282i	−0.0238416	+	0.00763356i
$951$	−8.71544	−	15.0956i	−0.282618	−	0.489508i
$952$	−8.13655	−	6.07327i	−0.263707	−	0.196836i
$953$	5.26987			0.170708			0.0853539	−	0.996351i	$-0.472798\pi$
$953$	5.26987			0.170708			0.0853539	+	0.996351i	$0.472798\pi$
$954$	−3.71958	+	17.1370i	−0.120426	+	0.554830i
$955$	40.9062	−	23.6172i	1.32369	−	0.764236i
$956$	−1.83777	+	1.31124i	−0.0594376	+	0.0424086i
$957$	10.8130	+	18.7287i	0.349535	+	0.605412i
$958$	−9.29626	+	2.97645i	−0.300348	+	0.0961648i
$959$	30.7166	+	17.7343i	0.991892	+	0.572669i
$960$	−18.0287	+	5.34835i	−0.581874	+	0.172617i
$961$	12.4462	+	21.5575i	0.401492	+	0.695404i
$962$	−38.0701	−	34.5757i	−1.22743	−	1.11477i
$963$			16.0919i			0.518554i
$964$	26.4032	+	12.0283i	0.850389	+	0.387405i
$965$			41.3094i			1.32980i
$966$	−6.70164	+	30.8760i	−0.215622	+	0.993419i
$967$	−2.52786	−	1.45946i	−0.0812906	−	0.0469331i	0.458804	−	0.888538i	$-0.348278\pi$
$967$	−2.52786	−	1.45946i	−0.0812906	−	0.0469331i	−0.540094	+	0.841605i	$0.681611\pi$
$968$	−0.807870	+	6.83760i	−0.0259659	+	0.219769i
$969$	1.16511	+	0.672676i	0.0374287	+	0.0216095i
$970$	−8.04938	−	25.1404i	−0.258450	−	0.807209i
$971$	−13.2754	−	7.66457i	−0.426029	−	0.245968i	0.271625	−	0.962403i	$-0.412439\pi$
$971$	−13.2754	−	7.66457i	−0.426029	−	0.245968i	−0.697653	+	0.716435i	$0.745772\pi$
$972$	−1.82004	−	0.829139i	−0.0583777	−	0.0265946i
$973$	−5.46641	+	9.46809i	−0.175245	+	0.303533i
$974$	−16.2683	−	50.8102i	−0.521270	−	1.62806i
$975$	2.18376	−	1.26079i	0.0699363	−	0.0403777i
$976$	−23.7199	−	8.16020i	−0.759255	−	0.261202i
$977$	−11.7652	−	20.3779i	−0.376401	−	0.651946i	0.614134	−	0.789201i	$-0.289505\pi$
$977$	−11.7652	−	20.3779i	−0.376401	−	0.651946i	−0.990536	+	0.137255i	$0.956172\pi$
$978$	22.1021	+	20.0734i	0.706747	+	0.641876i
$979$	−14.5761	+	25.2465i	−0.465853	+	0.806881i
$980$	−3.14151	+	0.302924i	−0.100352	+	0.00967654i
$981$			9.75097i			0.311325i
$982$	−8.15673	+	37.5800i	−0.260292	+	1.19922i
$983$	−18.5252			−0.590862			−0.295431	−	0.955364i	$-0.595463\pi$
$983$	−18.5252			−0.590862			−0.295431	+	0.955364i	$0.595463\pi$
$984$	8.21360	+	19.1069i	0.261840	+	0.609107i
$985$	4.09620	−	7.09483i	0.130516	−	0.226060i
$986$	−10.5685	−	2.29389i	−0.336569	−	0.0730523i
$987$	13.2497	−	7.64974i	0.421744	−	0.243494i
$988$	−8.10768	+	5.78482i	−0.257940	+	0.184040i
$989$	18.7161	−	10.8058i	0.595138	−	0.343603i
$990$	9.01984	+	8.19192i	0.286669	+	0.260356i
$991$	32.6683			1.03774			0.518871	−	0.854852i	$-0.326352\pi$
$991$	32.6683			1.03774			0.518871	+	0.854852i	$0.326352\pi$
$992$	−13.9768	−	0.300222i	−0.443763	−	0.00953205i
$993$	7.84025	−	13.5797i	0.248803	−	0.430939i
$994$	3.30353	−	1.05772i	0.104782	−	0.0335487i
$995$	4.51386	+	7.81824i	0.143099	+	0.247855i
$996$	−26.1847	+	2.52490i	−0.829695	+	0.0800044i
$997$	53.0333			1.67958			0.839791	−	0.542909i	$-0.182677\pi$
$997$	53.0333			1.67958			0.839791	+	0.542909i	$0.182677\pi$
$998$	−2.17912	−	6.80599i	−0.0689790	−	0.215440i
$999$	−3.79002	−	6.56450i	−0.119911	−	0.207692i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.j.a.499.3	✓	68
4.3	odd	2		804.2.j.b.499.14	yes	68
67.38	odd	6		804.2.j.b.775.14	yes	68
268.239	even	6	inner	804.2.j.a.775.3	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.j.a.499.3	✓	68	1.1	even	1	trivial
804.2.j.a.775.3	yes	68	268.239	even	6	inner
804.2.j.b.499.14	yes	68	4.3	odd	2
804.2.j.b.775.14	yes	68	67.38	odd	6

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:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.j (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.38203 - 0.299971i) q^{2} -1.00000 q^{3} +(1.82004 + 0.829139i) q^{4} -2.35066i q^{5} +(1.38203 + 0.299971i) q^{6} +(1.38486 - 2.39864i) q^{7} +(-2.26663 - 1.69186i) q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(-1.38203 - 0.299971i) q^{2} -1.00000 q^{3} +(1.82004 + 0.829139i) q^{4} -2.35066i q^{5} +(1.38203 + 0.299971i) q^{6} +(1.38486 - 2.39864i) q^{7} +(-2.26663 - 1.69186i) q^{8} +1.00000 q^{9} +(-0.705129 + 3.24869i) q^{10} +(1.83264 - 3.17422i) q^{11} +(-1.82004 - 0.829139i) q^{12} +(4.15472 - 2.39873i) q^{13} +(-2.63344 + 2.89959i) q^{14} +2.35066i q^{15} +(2.62506 + 3.01812i) q^{16} +(0.648029 + 1.12242i) q^{17} +(-1.38203 - 0.299971i) q^{18} +(-0.898964 + 0.519017i) q^{19} +(1.94903 - 4.27829i) q^{20} +(-1.38486 + 2.39864i) q^{21} +(-3.48494 + 3.83715i) q^{22} +(-6.98551 + 4.03309i) q^{23} +(2.26663 + 1.69186i) q^{24} -0.525610 q^{25} +(-6.46151 + 2.06883i) q^{26} -1.00000 q^{27} +(4.50930 - 3.21738i) q^{28} +(2.95012 - 5.10975i) q^{29} +(0.705129 - 3.24869i) q^{30} +(1.23567 - 2.14024i) q^{31} +(-2.72257 - 4.95859i) q^{32} +(-1.83264 + 3.17422i) q^{33} +(-0.558905 - 1.74561i) q^{34} +(-5.63840 - 3.25533i) q^{35} +(1.82004 + 0.829139i) q^{36} +(3.79002 + 6.56450i) q^{37} +(1.39809 - 0.447636i) q^{38} +(-4.15472 + 2.39873i) q^{39} +(-3.97698 + 5.32809i) q^{40} +(6.36793 + 3.67652i) q^{41} +(2.63344 - 2.89959i) q^{42} -2.67928 q^{43} +(5.96734 - 4.25769i) q^{44} -2.35066i q^{45} +(10.8640 - 3.47841i) q^{46} +(-4.78379 - 2.76192i) q^{47} +(-2.62506 - 3.01812i) q^{48} +(-0.335658 - 0.581378i) q^{49} +(0.726410 + 0.157667i) q^{50} +(-0.648029 - 1.12242i) q^{51} +(9.55062 - 0.920930i) q^{52} -12.3998i q^{53} +(1.38203 + 0.299971i) q^{54} +(-7.46153 - 4.30792i) q^{55} +(-7.19712 + 3.09387i) q^{56} +(0.898964 - 0.519017i) q^{57} +(-5.60993 + 6.17690i) q^{58} +5.17955i q^{59} +(-1.94903 + 4.27829i) q^{60} +(-5.43091 + 3.13554i) q^{61} +(-2.34975 + 2.58722i) q^{62} +(1.38486 - 2.39864i) q^{63} +(2.27525 + 7.66963i) q^{64} +(-5.63860 - 9.76634i) q^{65} +(3.48494 - 3.83715i) q^{66} +(-7.40294 - 3.49234i) q^{67} +(0.248794 + 2.58015i) q^{68} +(6.98551 - 4.03309i) q^{69} +(6.81595 + 6.19033i) q^{70} +(-0.766921 - 0.442782i) q^{71} +(-2.26663 - 1.69186i) q^{72} +(-4.91258 - 8.50884i) q^{73} +(-3.26878 - 10.2093i) q^{74} +0.525610 q^{75} +(-2.06648 + 0.199263i) q^{76} +(-5.07589 - 8.79170i) q^{77} +(6.46151 - 2.06883i) q^{78} +(6.82671 - 11.8242i) q^{79} +(7.09459 - 6.17062i) q^{80} +1.00000 q^{81} +(-7.69784 - 6.99127i) q^{82} +(11.3909 - 6.57655i) q^{83} +(-4.50930 + 3.21738i) q^{84} +(2.63843 - 1.52330i) q^{85} +(3.70285 + 0.803704i) q^{86} +(-2.95012 + 5.10975i) q^{87} +(-9.52425 + 4.09424i) q^{88} -7.95359 q^{89} +(-0.705129 + 3.24869i) q^{90} -13.2876i q^{91} +(-16.0579 + 1.54840i) q^{92} +(-1.23567 + 2.14024i) q^{93} +(5.78287 + 5.25207i) q^{94} +(1.22003 + 2.11316i) q^{95} +(2.72257 + 4.95859i) q^{96} +(-6.87685 + 3.97035i) q^{97} +(0.289495 + 0.904171i) q^{98} +(1.83264 - 3.17422i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 68 q^{3} - 2 q^{4} + 4 q^{7} - 6 q^{8} + 68 q^{9}+O(q^{10}) \) 68 * q - 68 * q^3 - 2 * q^4 + 4 * q^7 - 6 * q^8 + 68 * q^9	\( 68 q - 68 q^{3} - 2 q^{4} + 4 q^{7} - 6 q^{8} + 68 q^{9} + 18 q^{10} + 2 q^{12} + 6 q^{13} + 10 q^{14} - 2 q^{16} - 36 q^{20} - 4 q^{21} - 22 q^{22} + 6 q^{24} - 68 q^{25} - q^{26} - 68 q^{27} + q^{28} - 8 q^{29} - 18 q^{30} + 2 q^{31} + 15 q^{32} - 2 q^{36} + 12 q^{37} - 22 q^{38} - 6 q^{39} + 18 q^{40} - 10 q^{42} - 4 q^{43} - 31 q^{44} + 32 q^{46} + 2 q^{48} - 46 q^{49} - 9 q^{50} - 28 q^{52} - 11 q^{56} + 4 q^{58} + 36 q^{60} + 6 q^{61} - 34 q^{62} + 4 q^{63} + 16 q^{64} + 22 q^{66} - 18 q^{67} + 34 q^{68} + 56 q^{70} - 36 q^{71} - 6 q^{72} + 6 q^{73} - 53 q^{74} + 68 q^{75} + 14 q^{76} - 4 q^{77} + q^{78} + 6 q^{79} + 55 q^{80} + 68 q^{81} - 26 q^{82} + 12 q^{83} - q^{84} - 21 q^{86} + 8 q^{87} - 50 q^{88} + 18 q^{90} + 10 q^{92} - 2 q^{93} - 16 q^{94} + 20 q^{95} - 15 q^{96} + 18 q^{97} - 70 q^{98}+O(q^{100}) \) 68 * q - 68 * q^3 - 2 * q^4 + 4 * q^7 - 6 * q^8 + 68 * q^9 + 18 * q^10 + 2 * q^12 + 6 * q^13 + 10 * q^14 - 2 * q^16 - 36 * q^20 - 4 * q^21 - 22 * q^22 + 6 * q^24 - 68 * q^25 - q^26 - 68 * q^27 + q^28 - 8 * q^29 - 18 * q^30 + 2 * q^31 + 15 * q^32 - 2 * q^36 + 12 * q^37 - 22 * q^38 - 6 * q^39 + 18 * q^40 - 10 * q^42 - 4 * q^43 - 31 * q^44 + 32 * q^46 + 2 * q^48 - 46 * q^49 - 9 * q^50 - 28 * q^52 - 11 * q^56 + 4 * q^58 + 36 * q^60 + 6 * q^61 - 34 * q^62 + 4 * q^63 + 16 * q^64 + 22 * q^66 - 18 * q^67 + 34 * q^68 + 56 * q^70 - 36 * q^71 - 6 * q^72 + 6 * q^73 - 53 * q^74 + 68 * q^75 + 14 * q^76 - 4 * q^77 + q^78 + 6 * q^79 + 55 * q^80 + 68 * q^81 - 26 * q^82 + 12 * q^83 - q^84 - 21 * q^86 + 8 * q^87 - 50 * q^88 + 18 * q^90 + 10 * q^92 - 2 * q^93 - 16 * q^94 + 20 * q^95 - 15 * q^96 + 18 * q^97 - 70 * q^98

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