LMFDB - Embedded newform 418.2.f.h.115.1

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:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - x^{19} + 11 x^{18} - 3 x^{17} + 103 x^{16} + 50 x^{15} + 1002 x^{14} + 1120 x^{13} + \cdots + 1936 $ x^20 - x^19 + 11x^18 - 3x^17 + 103x^16 + 50x^15 + 1002x^14 + 1120x^13 + 7288x^12 + 5704x^11 + 24392x^10 + 10376x^9 + 48880x^8 + 21224x^7 + 77528x^6 + 44616x^5 + 147848x^4 + 67728x^3 + 115472x^2 - 24464x + 1936
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			115.1
Root			$-0.657798 + 2.02449i$ of defining polynomial
Character	$\chi$	$=$	418.115
Dual form			418.2.f.h.229.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 - 0.951057i) q^{2} +(-1.72214 - 1.25121i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-0.137434 + 0.422980i) q^{5} +(-0.657798 + 2.02449i) q^{6} +(-0.658492 + 0.478423i) q^{7} +(0.809017 + 0.587785i) q^{8} +(0.473189 + 1.45633i) q^{9} +O(q^{10})$	\(q+(-0.309017 - 0.951057i) q^{2} +(-1.72214 - 1.25121i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-0.137434 + 0.422980i) q^{5} +(-0.657798 + 2.02449i) q^{6} +(-0.658492 + 0.478423i) q^{7} +(0.809017 + 0.587785i) q^{8} +(0.473189 + 1.45633i) q^{9} +0.444747 q^{10} +(-2.12947 + 2.54271i) q^{11} +2.12868 q^{12} +(0.164234 + 0.505460i) q^{13} +(0.658492 + 0.478423i) q^{14} +(0.765915 - 0.556470i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-1.81738 + 5.59332i) q^{17} +(1.23883 - 0.900059i) q^{18} +(0.809017 + 0.587785i) q^{19} +(-0.137434 - 0.422980i) q^{20} +1.73262 q^{21} +(3.07630 + 1.23951i) q^{22} +6.69536 q^{23} +(-0.657798 - 2.02449i) q^{24} +(3.88506 + 2.82266i) q^{25} +(0.429970 - 0.312391i) q^{26} +(-0.966126 + 2.97343i) q^{27} +(0.251522 - 0.774104i) q^{28} +(3.37106 - 2.44922i) q^{29} +(-0.765915 - 0.556470i) q^{30} +(-1.79257 - 5.51696i) q^{31} -1.00000 q^{32} +(6.84869 - 1.71448i) q^{33} +5.88116 q^{34} +(-0.111864 - 0.344281i) q^{35} +(-1.23883 - 0.900059i) q^{36} +(-1.92167 + 1.39618i) q^{37} +(0.309017 - 0.951057i) q^{38} +(0.349601 - 1.07596i) q^{39} +(-0.359808 + 0.261416i) q^{40} +(8.29803 + 6.02887i) q^{41} +(-0.535409 - 1.64782i) q^{42} -10.2461 q^{43} +(0.228214 - 3.30876i) q^{44} -0.681029 q^{45} +(-2.06898 - 6.36767i) q^{46} +(-5.12692 - 3.72493i) q^{47} +(-1.72214 + 1.25121i) q^{48} +(-1.95839 + 6.02732i) q^{49} +(1.48396 - 4.56716i) q^{50} +(10.1282 - 7.35854i) q^{51} +(-0.429970 - 0.312391i) q^{52} +(2.87949 + 8.86217i) q^{53} +3.12645 q^{54} +(-0.782850 - 1.25018i) q^{55} -0.813941 q^{56} +(-0.657798 - 2.02449i) q^{57} +(-3.37106 - 2.44922i) q^{58} +(-2.73342 + 1.98595i) q^{59} +(-0.292554 + 0.900388i) q^{60} +(-1.47351 + 4.53500i) q^{61} +(-4.69301 + 3.40967i) q^{62} +(-1.00833 - 0.732596i) q^{63} +(0.309017 + 0.951057i) q^{64} -0.236370 q^{65} +(-3.74693 - 5.98369i) q^{66} -1.23043 q^{67} +(-1.81738 - 5.59332i) q^{68} +(-11.5303 - 8.37728i) q^{69} +(-0.292863 + 0.212777i) q^{70} +(-3.57970 + 11.0172i) q^{71} +(-0.473189 + 1.45633i) q^{72} +(-9.98343 + 7.25339i) q^{73} +(1.92167 + 1.39618i) q^{74} +(-3.15888 - 9.72202i) q^{75} -1.00000 q^{76} +(0.185753 - 2.69314i) q^{77} -1.13133 q^{78} +(-1.07228 - 3.30013i) q^{79} +(0.359808 + 0.261416i) q^{80} +(9.10065 - 6.61201i) q^{81} +(3.16957 - 9.75492i) q^{82} +(-3.97579 + 12.2362i) q^{83} +(-1.40172 + 1.01841i) q^{84} +(-2.11609 - 1.53743i) q^{85} +(3.16622 + 9.74463i) q^{86} -8.86991 q^{87} +(-3.21734 + 0.805420i) q^{88} +7.40160 q^{89} +(0.210449 + 0.647697i) q^{90} +(-0.349970 - 0.254268i) q^{91} +(-5.41666 + 3.93543i) q^{92} +(-3.81580 + 11.7438i) q^{93} +(-1.95831 + 6.02706i) q^{94} +(-0.359808 + 0.261416i) q^{95} +(1.72214 + 1.25121i) q^{96} +(-4.39716 - 13.5331i) q^{97} +6.33750 q^{98} +(-4.71065 - 1.89803i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 5 q^{2} - q^{3} - 5 q^{4} - q^{5} + q^{6} + 13 q^{7} + 5 q^{8} - 6 q^{9}+O(q^{10}) $ 20 * q + 5 * q^2 - q^3 - 5 * q^4 - q^5 + q^6 + 13 * q^7 + 5 * q^8 - 6 * q^9	\( 20 q + 5 q^{2} - q^{3} - 5 q^{4} - q^{5} + q^{6} + 13 q^{7} + 5 q^{8} - 6 q^{9} + 6 q^{10} + q^{11} + 4 q^{12} - 2 q^{13} - 13 q^{14} - 8 q^{15} - 5 q^{16} + 11 q^{17} + 6 q^{18} + 5 q^{19} - q^{20} + 2 q^{21} + 4 q^{22} + 28 q^{23} + q^{24} - 30 q^{25} - 13 q^{26} - 31 q^{27} - 2 q^{28} + 28 q^{29} + 8 q^{30} - q^{31} - 20 q^{32} + 9 q^{33} + 24 q^{34} - 11 q^{35} - 6 q^{36} + 8 q^{37} - 5 q^{38} + 18 q^{39} - 4 q^{40} - 5 q^{41} - 22 q^{42} - 44 q^{43} + 11 q^{44} - 4 q^{45} + 7 q^{46} - 39 q^{47} - q^{48} + 4 q^{49} - 25 q^{50} - 11 q^{51} + 13 q^{52} - q^{53} - 4 q^{54} + 8 q^{55} + 22 q^{56} + q^{57} - 28 q^{58} + 6 q^{59} + 7 q^{60} + 10 q^{61} + 11 q^{62} + 34 q^{63} - 5 q^{64} - 8 q^{65} + 41 q^{66} + 18 q^{67} + 11 q^{68} - 63 q^{69} + q^{70} - 3 q^{71} + 6 q^{72} + 5 q^{73} - 8 q^{74} + 5 q^{75} - 20 q^{76} + 36 q^{77} + 22 q^{78} + 19 q^{79} + 4 q^{80} + 63 q^{81} - 9 q^{83} - 23 q^{84} + 30 q^{85} - 26 q^{86} - 16 q^{87} - q^{88} + 44 q^{89} + 14 q^{90} - 68 q^{91} - 7 q^{92} + 27 q^{93} - 31 q^{94} - 4 q^{95} + q^{96} - 71 q^{97} + 6 q^{98} + 20 q^{99}+O(q^{100}) \) 20 * q + 5 * q^2 - q^3 - 5 * q^4 - q^5 + q^6 + 13 * q^7 + 5 * q^8 - 6 * q^9 + 6 * q^10 + q^11 + 4 * q^12 - 2 * q^13 - 13 * q^14 - 8 * q^15 - 5 * q^16 + 11 * q^17 + 6 * q^18 + 5 * q^19 - q^20 + 2 * q^21 + 4 * q^22 + 28 * q^23 + q^24 - 30 * q^25 - 13 * q^26 - 31 * q^27 - 2 * q^28 + 28 * q^29 + 8 * q^30 - q^31 - 20 * q^32 + 9 * q^33 + 24 * q^34 - 11 * q^35 - 6 * q^36 + 8 * q^37 - 5 * q^38 + 18 * q^39 - 4 * q^40 - 5 * q^41 - 22 * q^42 - 44 * q^43 + 11 * q^44 - 4 * q^45 + 7 * q^46 - 39 * q^47 - q^48 + 4 * q^49 - 25 * q^50 - 11 * q^51 + 13 * q^52 - q^53 - 4 * q^54 + 8 * q^55 + 22 * q^56 + q^57 - 28 * q^58 + 6 * q^59 + 7 * q^60 + 10 * q^61 + 11 * q^62 + 34 * q^63 - 5 * q^64 - 8 * q^65 + 41 * q^66 + 18 * q^67 + 11 * q^68 - 63 * q^69 + q^70 - 3 * q^71 + 6 * q^72 + 5 * q^73 - 8 * q^74 + 5 * q^75 - 20 * q^76 + 36 * q^77 + 22 * q^78 + 19 * q^79 + 4 * q^80 + 63 * q^81 - 9 * q^83 - 23 * q^84 + 30 * q^85 - 26 * q^86 - 16 * q^87 - q^88 + 44 * q^89 + 14 * q^90 - 68 * q^91 - 7 * q^92 + 27 * q^93 - 31 * q^94 - 4 * q^95 + q^96 - 71 * q^97 + 6 * q^98 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$287$	$343$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$

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
$3$	−1.72214	−	1.25121i	−0.994276	−	0.722384i	−0.0334229	−	0.999441i	$-0.510641\pi$
$3$	−1.72214	−	1.25121i	−0.994276	−	0.722384i	−0.960853	+	0.277057i	$0.910641\pi$
$4$	−0.809017	+	0.587785i	−0.404508	+	0.293893i
$5$	−0.137434	+	0.422980i	−0.0614625	+	0.189162i	−0.977073	−	0.212904i	$-0.931708\pi$
$5$	−0.137434	+	0.422980i	−0.0614625	+	0.189162i	0.915611	+	0.402066i	$0.131708\pi$
$6$	−0.657798	+	2.02449i	−0.268545	+	0.826496i
$7$	−0.658492	+	0.478423i	−0.248887	+	0.180827i	−0.705233	−	0.708975i	$-0.749158\pi$
$7$	−0.658492	+	0.478423i	−0.248887	+	0.180827i	0.456347	+	0.889802i	$0.349158\pi$
$8$	0.809017	+	0.587785i	0.286031	+	0.207813i
$9$	0.473189	+	1.45633i	0.157730	+	0.485442i
$10$	0.444747			0.140641
$11$	−2.12947	+	2.54271i	−0.642060	+	0.766654i
$11$	−2.12947	+	2.54271i	−0.642060	+	0.766654i
$12$	2.12868			0.614497
$13$	0.164234	+	0.505460i	0.0455503	+	0.140189i	0.971245	−	0.238082i	$-0.0765187\pi$
$13$	0.164234	+	0.505460i	0.0455503	+	0.140189i	−0.925695	+	0.378271i	$0.876519\pi$
$14$	0.658492	+	0.478423i	0.175990	+	0.127864i
$15$	0.765915	−	0.556470i	0.197758	−	0.143680i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	−1.81738	+	5.59332i	−0.440779	+	1.35658i	0.446268	+	0.894899i	$0.352753\pi$
$17$	−1.81738	+	5.59332i	−0.440779	+	1.35658i	−0.887047	+	0.461679i	$0.847247\pi$
$18$	1.23883	−	0.900059i	0.291994	−	0.212146i
$19$	0.809017	+	0.587785i	0.185601	+	0.134847i
$19$	0.809017	+	0.587785i	0.185601	+	0.134847i
$20$	−0.137434	−	0.422980i	−0.0307313	−	0.0945811i
$21$	1.73262			0.378089
$22$	3.07630	+	1.23951i	0.655869	+	0.264264i
$23$	6.69536			1.39608			0.698040	−	0.716059i	$-0.254056\pi$
$23$	6.69536			1.39608			0.698040	+	0.716059i	$0.254056\pi$
$24$	−0.657798	−	2.02449i	−0.134272	−	0.413248i
$25$	3.88506	+	2.82266i	0.777012	+	0.564532i
$26$	0.429970	−	0.312391i	0.0843240	−	0.0612650i
$27$	−0.966126	+	2.97343i	−0.185931	+	0.572237i
$28$	0.251522	−	0.774104i	0.0475331	−	0.146292i
$29$	3.37106	−	2.44922i	0.625991	−	0.454809i	−0.229018	−	0.973422i	$-0.573552\pi$
$29$	3.37106	−	2.44922i	0.625991	−	0.454809i	0.855009	+	0.518613i	$0.173552\pi$
$30$	−0.765915	−	0.556470i	−0.139836	−	0.101597i
$31$	−1.79257	−	5.51696i	−0.321955	−	0.990876i	−0.972796	−	0.231662i	$-0.925584\pi$
$31$	−1.79257	−	5.51696i	−0.321955	−	0.990876i	0.650841	−	0.759214i	$-0.274416\pi$
$32$	−1.00000			−0.176777
$33$	6.84869	−	1.71448i	1.19220	−	0.298453i
$34$	5.88116			1.00861
$35$	−0.111864	−	0.344281i	−0.0189084	−	0.0581940i
$36$	−1.23883	−	0.900059i	−0.206471	−	0.150010i
$37$	−1.92167	+	1.39618i	−0.315921	+	0.229530i	−0.734433	−	0.678681i	$-0.762552\pi$
$37$	−1.92167	+	1.39618i	−0.315921	+	0.229530i	0.418512	+	0.908211i	$0.362552\pi$
$38$	0.309017	−	0.951057i	0.0501292	−	0.154282i
$39$	0.349601	−	1.07596i	0.0559809	−	0.172292i
$40$	−0.359808	+	0.261416i	−0.0568906	+	0.0413335i
$41$	8.29803	+	6.02887i	1.29594	+	0.941552i	0.999907	−	0.0136272i	$-0.00433781\pi$
$41$	8.29803	+	6.02887i	1.29594	+	0.941552i	0.296028	+	0.955179i	$0.404338\pi$
$42$	−0.535409	−	1.64782i	−0.0826154	−	0.254264i
$43$	−10.2461			−1.56252			−0.781258	−	0.624208i	$-0.785422\pi$
$43$	−10.2461			−1.56252			−0.781258	+	0.624208i	$0.785422\pi$
$44$	0.228214	−	3.30876i	0.0344046	−	0.498815i
$45$	−0.681029			−0.101522
$46$	−2.06898	−	6.36767i	−0.305055	−	0.938861i
$47$	−5.12692	−	3.72493i	−0.747838	−	0.543336i	0.147318	−	0.989089i	$-0.452936\pi$
$47$	−5.12692	−	3.72493i	−0.747838	−	0.543336i	−0.895156	+	0.445753i	$0.852936\pi$
$48$	−1.72214	+	1.25121i	−0.248569	+	0.180596i
$49$	−1.95839	+	6.02732i	−0.279771	+	0.861046i
$50$	1.48396	−	4.56716i	0.209864	−	0.645894i
$51$	10.1282	−	7.35854i	1.41823	−	1.03040i
$52$	−0.429970	−	0.312391i	−0.0596261	−	0.0433209i
$53$	2.87949	+	8.86217i	0.395529	+	1.21731i	0.928549	+	0.371210i	$0.121057\pi$
$53$	2.87949	+	8.86217i	0.395529	+	1.21731i	−0.533020	+	0.846102i	$0.678943\pi$
$54$	3.12645			0.425456
$55$	−0.782850	−	1.25018i	−0.105559	−	0.168574i
$56$	−0.813941			−0.108768
$57$	−0.657798	−	2.02449i	−0.0871275	−	0.268151i
$58$	−3.37106	−	2.44922i	−0.442642	−	0.321598i
$59$	−2.73342	+	1.98595i	−0.355862	+	0.258549i	−0.751324	−	0.659934i	$-0.770584\pi$
$59$	−2.73342	+	1.98595i	−0.355862	+	0.258549i	0.395462	+	0.918482i	$0.370584\pi$
$60$	−0.292554	+	0.900388i	−0.0377685	+	0.116240i
$61$	−1.47351	+	4.53500i	−0.188664	+	0.580647i	−0.999992	−	0.00394334i	$-0.998745\pi$
$61$	−1.47351	+	4.53500i	−0.188664	+	0.580647i	0.811329	+	0.584590i	$0.198745\pi$
$62$	−4.69301	+	3.40967i	−0.596013	+	0.433029i
$63$	−1.00833	−	0.732596i	−0.127038	−	0.0922984i
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	−0.236370			−0.0293181
$66$	−3.74693	−	5.98369i	−0.461215	−	0.736541i
$67$	−1.23043			−0.150321			−0.0751604	−	0.997171i	$-0.523947\pi$
$67$	−1.23043			−0.150321			−0.0751604	+	0.997171i	$0.523947\pi$
$68$	−1.81738	−	5.59332i	−0.220390	−	0.678289i
$69$	−11.5303	−	8.37728i	−1.38809	−	1.00851i
$70$	−0.292863	+	0.212777i	−0.0350038	+	0.0254317i
$71$	−3.57970	+	11.0172i	−0.424832	+	1.30750i	0.478323	+	0.878184i	$0.341245\pi$
$71$	−3.57970	+	11.0172i	−0.424832	+	1.30750i	−0.903155	+	0.429315i	$0.858755\pi$
$72$	−0.473189	+	1.45633i	−0.0557659	+	0.171630i
$73$	−9.98343	+	7.25339i	−1.16847	+	0.848945i	−0.990825	−	0.135150i	$-0.956848\pi$
$73$	−9.98343	+	7.25339i	−1.16847	+	0.848945i	−0.177647	+	0.984094i	$0.556848\pi$
$74$	1.92167	+	1.39618i	0.223390	+	0.162302i
$75$	−3.15888	−	9.72202i	−0.364756	−	1.12260i
$76$	−1.00000			−0.114708
$77$	0.185753	−	2.69314i	0.0211685	−	0.306912i
$78$	−1.13133			−0.128098
$79$	−1.07228	−	3.30013i	−0.120640	−	0.371293i	0.872441	−	0.488719i	$-0.162536\pi$
$79$	−1.07228	−	3.30013i	−0.120640	−	0.371293i	−0.993082	+	0.117426i	$0.962536\pi$
$80$	0.359808	+	0.261416i	0.0402277	+	0.0292272i
$81$	9.10065	−	6.61201i	1.01118	−	0.734668i
$82$	3.16957	−	9.75492i	0.350020	−	1.07725i
$83$	−3.97579	+	12.2362i	−0.436400	+	1.34310i	0.455246	+	0.890366i	$0.349551\pi$
$83$	−3.97579	+	12.2362i	−0.436400	+	1.34310i	−0.891645	+	0.452735i	$0.850449\pi$
$84$	−1.40172	+	1.01841i	−0.152940	+	0.111117i
$85$	−2.11609	−	1.53743i	−0.229522	−	0.166757i
$86$	3.16622	+	9.74463i	0.341422	+	1.05079i
$87$	−8.86991			−0.950954
$88$	−3.21734	+	0.805420i	−0.342970	+	0.0858580i
$89$	7.40160			0.784568			0.392284	−	0.919844i	$-0.371685\pi$
$89$	7.40160			0.784568			0.392284	+	0.919844i	$0.371685\pi$
$90$	0.210449	+	0.647697i	0.0221833	+	0.0682733i
$91$	−0.349970	−	0.254268i	−0.0366868	−	0.0266545i
$92$	−5.41666	+	3.93543i	−0.564726	+	0.410297i
$93$	−3.81580	+	11.7438i	−0.395681	+	1.21778i
$94$	−1.95831	+	6.02706i	−0.201984	+	0.621643i
$95$	−0.359808	+	0.261416i	−0.0369155	+	0.0268207i
$96$	1.72214	+	1.25121i	0.175765	+	0.127701i
$97$	−4.39716	−	13.5331i	−0.446464	−	1.37408i	−0.880870	−	0.473359i	$-0.843041\pi$
$97$	−4.39716	−	13.5331i	−0.446464	−	1.37408i	0.434405	−	0.900718i	$-0.356959\pi$
$98$	6.33750			0.640184
$99$	−4.71065	−	1.89803i	−0.473438	−	0.190759i
$100$	−4.80220			−0.480220
$101$	1.08313	+	3.33352i	0.107775	+	0.331698i	0.990372	−	0.138433i	$-0.0442067\pi$
$101$	1.08313	+	3.33352i	0.107775	+	0.331698i	−0.882597	+	0.470131i	$0.844207\pi$
$102$	−10.1282	−	7.35854i	−1.00284	−	0.728604i
$103$	−0.561557	+	0.407995i	−0.0553319	+	0.0402009i	−0.615107	−	0.788443i	$-0.710887\pi$
$103$	−0.561557	+	0.407995i	−0.0553319	+	0.0402009i	0.559776	+	0.828644i	$0.310887\pi$
$104$	−0.164234	+	0.505460i	−0.0161044	+	0.0495644i
$105$	−0.238122	+	0.732863i	−0.0232383	+	0.0715201i
$106$	7.53861	−	5.47712i	0.732214	−	0.531985i
$107$	−6.98246	−	5.07306i	−0.675020	−	0.490431i	0.196682	−	0.980467i	$-0.436983\pi$
$107$	−6.98246	−	5.07306i	−0.675020	−	0.490431i	−0.871702	+	0.490037i	$0.836983\pi$
$108$	−0.966126	−	2.97343i	−0.0929655	−	0.286118i
$109$	8.10360			0.776184			0.388092	−	0.921621i	$-0.373134\pi$
$109$	8.10360			0.776184			0.388092	+	0.921621i	$0.373134\pi$
$110$	−0.947076	+	1.13086i	−0.0903002	+	0.107823i
$111$	5.05629			0.479922
$112$	0.251522	+	0.774104i	0.0237666	+	0.0731460i
$113$	−3.77212	−	2.74061i	−0.354851	−	0.257814i	0.396050	−	0.918229i	$-0.370381\pi$
$113$	−3.77212	−	2.74061i	−0.354851	−	0.257814i	−0.750901	+	0.660414i	$0.770381\pi$
$114$	−1.72214	+	1.25121i	−0.161293	+	0.117186i
$115$	−0.920173	+	2.83200i	−0.0858066	+	0.264085i
$116$	−1.28763	+	3.96292i	−0.119554	+	0.367948i
$117$	−0.658401	+	0.478356i	−0.0608692	+	0.0442240i
$118$	2.73342	+	1.98595i	0.251632	+	0.182821i
$119$	−1.47924	−	4.55263i	−0.135602	−	0.417339i
$120$	0.946723			0.0864236
$121$	−1.93070	−	10.8292i	−0.175518	−	0.984476i
$122$	4.76838			0.431709
$123$	−6.74699	−	20.7651i	−0.608356	−	1.87233i
$124$	4.69301	+	3.40967i	0.421445	+	0.306197i
$125$	−3.52691	+	2.56245i	−0.315456	+	0.229192i
$126$	−0.385148	+	1.18536i	−0.0343117	+	0.105601i
$127$	1.77843	−	5.47344i	0.157810	−	0.485689i	−0.840625	−	0.541618i	$-0.817812\pi$
$127$	1.77843	−	5.47344i	0.157810	−	0.485689i	0.998435	+	0.0559287i	$0.0178119\pi$
$128$	0.809017	−	0.587785i	0.0715077	−	0.0519534i
$129$	17.6452	+	12.8200i	1.55357	+	1.12874i
$130$	0.0730425	+	0.224802i	0.00640625	+	0.0197164i
$131$	−0.970302			−0.0847756			−0.0423878	−	0.999101i	$-0.513497\pi$
$131$	−0.970302			−0.0847756			−0.0423878	+	0.999101i	$0.513497\pi$
$132$	−4.53296	+	5.41260i	−0.394544	+	0.471107i
$133$	−0.813941			−0.0705777
$134$	0.380224	+	1.17021i	0.0328463	+	0.101091i
$135$	−1.12492	−	0.817303i	−0.0968178	−	0.0703422i
$136$	−4.75796	+	3.45686i	−0.407992	+	0.296423i
$137$	0.663405	−	2.04175i	0.0566785	−	0.174438i	−0.918709	−	0.394934i	$-0.870767\pi$
$137$	0.663405	−	2.04175i	0.0566785	−	0.174438i	0.975388	+	0.220496i	$0.0707674\pi$
$138$	−4.40419	+	13.5547i	−0.374910	+	1.15385i
$139$	7.91878	−	5.75333i	0.671663	−	0.487991i	−0.198919	−	0.980016i	$-0.563743\pi$
$139$	7.91878	−	5.75333i	0.671663	−	0.487991i	0.870581	+	0.492025i	$0.163743\pi$
$140$	0.292863	+	0.212777i	0.0247514	+	0.0179829i
$141$	4.16861	+	12.8297i	0.351060	+	1.08045i
$142$	11.5841			0.972120
$143$	−1.63497	−	0.658764i	−0.136723	−	0.0550886i
$144$	1.53127			0.127606
$145$	0.572670	+	1.76250i	0.0475577	+	0.146367i
$146$	9.98343	+	7.25339i	0.826234	+	0.600294i
$147$	10.9140	−	7.92952i	0.900175	−	0.654015i
$148$	0.734014	−	2.25906i	0.0603356	−	0.185694i
$149$	0.386032	−	1.18808i	0.0316250	−	0.0973316i	−0.933998	−	0.357278i	$-0.883705\pi$
$149$	0.386032	−	1.18808i	0.0316250	−	0.0973316i	0.965623	+	0.259946i	$0.0837049\pi$
$150$	−8.27005	+	6.00854i	−0.675247	+	0.490595i
$151$	11.2071	+	8.14242i	0.912020	+	0.662621i	0.941525	−	0.336944i	$-0.109393\pi$
$151$	11.2071	+	8.14242i	0.912020	+	0.662621i	−0.0295053	+	0.999565i	$0.509393\pi$
$152$	0.309017	+	0.951057i	0.0250646	+	0.0771409i
$153$	−9.00566			−0.728065
$154$	−2.61873	+	0.655564i	−0.211023	+	0.0528269i
$155$	2.57992			0.207224
$156$	0.349601	+	1.07596i	0.0279905	+	0.0861458i
$157$	−14.0038	−	10.1744i	−1.11763	−	0.812002i	−0.133778	−	0.991011i	$-0.542711\pi$
$157$	−14.0038	−	10.1744i	−1.11763	−	0.812002i	−0.983847	+	0.179009i	$0.942711\pi$
$158$	−2.80726	+	2.03959i	−0.223333	+	0.162261i
$159$	6.12951	−	18.8647i	0.486102	−	1.49607i
$160$	0.137434	−	0.422980i	0.0108651	−	0.0334395i
$161$	−4.40885	+	3.20321i	−0.347466	+	0.252449i
$162$	−9.10065	−	6.61201i	−0.715015	−	0.519489i
$163$	−3.08190	−	9.48513i	−0.241393	−	0.742932i	−0.996209	−	0.0869951i	$-0.972274\pi$
$163$	−3.08190	−	9.48513i	−0.241393	−	0.742932i	0.754815	−	0.655937i	$-0.227726\pi$
$164$	−10.2569			−0.800932
$165$	−0.216056	+	3.13248i	−0.0168199	+	0.243864i
$166$	12.8659			0.998590
$167$	7.07592	+	21.7774i	0.547551	+	1.68519i	0.714845	+	0.699282i	$0.246497\pi$
$167$	7.07592	+	21.7774i	0.547551	+	1.68519i	−0.167294	+	0.985907i	$0.553503\pi$
$168$	1.40172	+	1.01841i	0.108145	+	0.0785719i
$169$	10.2887	−	7.47518i	0.791439	−	0.575014i
$170$	−0.808274	+	2.48761i	−0.0619918	+	0.190791i
$171$	−0.473189	+	1.45633i	−0.0361857	+	0.111368i
$172$	8.28927	−	6.02251i	0.632051	−	0.459212i
$173$	6.26926	+	4.55488i	0.476643	+	0.346301i	0.800024	−	0.599967i	$-0.204820\pi$
$173$	6.26926	+	4.55488i	0.476643	+	0.346301i	−0.323382	+	0.946269i	$0.604820\pi$
$174$	2.74095	+	8.43579i	0.207791	+	0.639515i
$175$	−3.90871			−0.295471
$176$	1.76021	+	2.81099i	0.132681	+	0.211886i
$177$	7.19216			0.540596
$178$	−2.28722	−	7.03934i	−0.171434	−	0.527621i
$179$	−10.6619	−	7.74632i	−0.796908	−	0.578987i	0.113098	−	0.993584i	$-0.463923\pi$
$179$	−10.6619	−	7.74632i	−0.796908	−	0.578987i	−0.910005	+	0.414597i	$0.863923\pi$
$180$	0.550964	−	0.400299i	0.0410664	−	0.0298365i
$181$	−2.83113	+	8.71331i	−0.210436	+	0.647655i	0.789010	+	0.614380i	$0.210594\pi$
$181$	−2.83113	+	8.71331i	−0.210436	+	0.647655i	−0.999446	+	0.0332754i	$0.989406\pi$
$182$	−0.133677	+	0.411414i	−0.00990877	+	0.0304961i
$183$	8.21180	−	5.96623i	0.607034	−	0.441036i
$184$	5.41666	+	3.93543i	0.399322	+	0.290124i
$185$	−0.326450	−	1.00471i	−0.0240011	−	0.0738678i
$186$	12.3482			0.905414
$187$	−10.3521	−	16.5319i	−0.757020	−	1.20893i
$188$	6.33722			0.462189
$189$	−0.786370	−	2.42020i	−0.0572000	−	0.176043i
$190$	0.359808	+	0.261416i	0.0261032	+	0.0189651i
$191$	11.7816	−	8.55983i	0.852486	−	0.619367i	−0.0733442	−	0.997307i	$-0.523367\pi$
$191$	11.7816	−	8.55983i	0.852486	−	0.619367i	0.925830	+	0.377939i	$0.123367\pi$
$192$	0.657798	−	2.02449i	0.0474725	−	0.146105i
$193$	−0.751094	+	2.31163i	−0.0540649	+	0.166395i	−0.974443	−	0.224635i	$-0.927881\pi$
$193$	−0.751094	+	2.31163i	−0.0540649	+	0.166395i	0.920378	+	0.391030i	$0.127881\pi$
$194$	−11.5119	+	8.36390i	−0.826508	+	0.600493i
$195$	0.407062	+	0.295748i	0.0291503	+	0.0211790i
$196$	−1.95839	−	6.02732i	−0.139885	−	0.430523i
$197$	−10.9047			−0.776928			−0.388464	−	0.921464i	$-0.626994\pi$
$197$	−10.9047			−0.776928			−0.388464	+	0.921464i	$0.626994\pi$
$198$	−0.349458	+	5.06662i	−0.0248349	+	0.360069i
$199$	−15.3004			−1.08461			−0.542307	−	0.840180i	$-0.682449\pi$
$199$	−15.3004			−1.08461			−0.542307	+	0.840180i	$0.682449\pi$
$200$	1.48396	+	4.56716i	0.104932	+	0.322947i
$201$	2.11897	+	1.53952i	0.149460	+	0.108589i
$202$	2.83566	−	2.06023i	0.199516	−	0.144957i
$203$	−1.04806	+	3.22559i	−0.0735591	+	0.226392i
$204$	−3.86862	+	11.9064i	−0.270857	+	0.833613i
$205$	−3.69053	+	2.68132i	−0.257758	+	0.187272i
$206$	0.561557	+	0.407995i	0.0391255	+	0.0284264i
$207$	3.16817	+	9.75063i	0.220203	+	0.677716i
$208$	0.531472			0.0368509
$209$	−3.21734	+	0.805420i	−0.222548	+	0.0557120i
$210$	0.770577			0.0531749
$211$	−1.73393	−	5.33647i	−0.119368	−	0.367378i	0.873465	−	0.486887i	$-0.161868\pi$
$211$	−1.73393	−	5.33647i	−0.119368	−	0.367378i	−0.992833	+	0.119509i	$0.961868\pi$
$212$	−7.53861	−	5.47712i	−0.517754	−	0.376170i
$213$	19.9495	−	14.4942i	1.36692	−	0.993123i
$214$	−2.66706	+	8.20838i	−0.182317	+	0.561113i
$215$	1.40817	−	4.33389i	0.0960362	−	0.295569i
$216$	−2.52935	+	1.83768i	−0.172100	+	0.125038i
$217$	3.81983	+	2.77527i	0.259307	+	0.188398i
$218$	−2.50415	−	7.70698i	−0.169603	−	0.521983i
$219$	26.2683			1.77505
$220$	1.36817	+	0.551268i	0.0922423	+	0.0371665i
$221$	−3.12567			−0.210255
$222$	−1.56248	−	4.80882i	−0.104867	−	0.322747i
$223$	19.4052	+	14.0987i	1.29947	+	0.944121i	0.999950	−	0.00996822i	$-0.00317304\pi$
$223$	19.4052	+	14.0987i	1.29947	+	0.944121i	0.299521	+	0.954090i	$0.403173\pi$
$224$	0.658492	−	0.478423i	0.0439974	−	0.0319660i
$225$	−2.27235	+	6.99357i	−0.151490	+	0.466238i
$226$	−1.44082	+	4.43439i	−0.0958420	+	0.294971i
$227$	2.85398	−	2.07354i	0.189425	−	0.137625i	−0.489031	−	0.872267i	$-0.662649\pi$
$227$	2.85398	−	2.07354i	0.189425	−	0.137625i	0.678456	+	0.734641i	$0.262649\pi$
$228$	1.72214	+	1.25121i	0.114051	+	0.0828631i
$229$	−6.04800	−	18.6138i	−0.399663	−	1.23004i	−0.925270	−	0.379309i	$-0.876162\pi$
$229$	−6.04800	−	18.6138i	−0.399663	−	1.23004i	0.525607	−	0.850728i	$-0.323838\pi$
$230$	2.97774			0.196347
$231$	−3.68957	+	4.40554i	−0.242756	+	0.289863i
$232$	4.16686			0.273568
$233$	5.93372	+	18.2621i	0.388731	+	1.19639i	0.933737	+	0.357959i	$0.116527\pi$
$233$	5.93372	+	18.2621i	0.388731	+	1.19639i	−0.545007	+	0.838432i	$0.683473\pi$
$234$	0.658401	+	0.478356i	0.0430410	+	0.0312711i
$235$	2.28018	−	1.65665i	0.148743	−	0.108068i
$236$	1.04408	−	3.21333i	0.0679635	−	0.209170i
$237$	−2.28253	+	7.02491i	−0.148266	+	0.456317i
$238$	−3.87270	+	2.81368i	−0.251030	+	0.182384i
$239$	15.6786	+	11.3912i	1.01417	+	0.736836i	0.965079	−	0.261959i	$-0.0843684\pi$
$239$	15.6786	+	11.3912i	1.01417	+	0.736836i	0.0490884	+	0.998794i	$0.484368\pi$
$240$	−0.292554	−	0.900388i	−0.0188843	−	0.0581198i
$241$	5.20964			0.335582			0.167791	−	0.985823i	$-0.446337\pi$
$241$	5.20964			0.335582			0.167791	+	0.985823i	$0.446337\pi$
$242$	−9.70260	+	5.18262i	−0.623707	+	0.333152i
$243$	−14.5662			−0.934423
$244$	−1.47351	−	4.53500i	−0.0943318	−	0.290324i
$245$	−2.28028	−	1.65672i	−0.145682	−	0.105844i
$246$	−17.6638	+	12.8335i	−1.12621	+	0.818236i
$247$	−0.164234	+	0.505460i	−0.0104499	+	0.0321616i
$248$	1.79257	−	5.51696i	0.113828	−	0.350327i
$249$	22.1569	−	16.0979i	1.40414	−	1.02016i
$250$	3.52691	+	2.56245i	0.223061	+	0.162064i
$251$	4.20242	+	12.9337i	0.265255	+	0.816370i	0.991635	+	0.129077i	$0.0412013\pi$
$251$	4.20242	+	12.9337i	0.265255	+	0.816370i	−0.726380	+	0.687293i	$0.758799\pi$
$252$	1.24637			0.0785137
$253$	−14.2576	+	17.0243i	−0.896367	+	1.07031i
$254$	−5.75512			−0.361108
$255$	1.72056	+	5.29532i	0.107745	+	0.331606i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	8.86110	−	6.43797i	0.552740	−	0.401589i	−0.276055	−	0.961142i	$-0.589027\pi$
$257$	8.86110	−	6.43797i	0.552740	−	0.401589i	0.828795	+	0.559553i	$0.189027\pi$
$258$	6.73987	−	20.7432i	0.419606	−	1.29141i
$259$	0.597444	−	1.83874i	0.0371234	−	0.114254i
$260$	0.191228	−	0.138935i	0.0118594	−	0.00861639i
$261$	5.16201	+	3.75042i	0.319521	+	0.232145i
$262$	0.299840	+	0.922812i	0.0185242	+	0.0570115i
$263$	27.8602			1.71793			0.858966	−	0.512032i	$-0.171107\pi$
$263$	27.8602			1.71793			0.858966	+	0.512032i	$0.171107\pi$
$264$	6.54845	+	2.63852i	0.403029	+	0.162389i
$265$	−4.14426			−0.254580
$266$	0.251522	+	0.774104i	0.0154218	+	0.0474634i
$267$	−12.7466	−	9.26092i	−0.780077	−	0.566759i
$268$	0.995438	−	0.723228i	0.0608061	−	0.0441782i
$269$	3.99223	−	12.2868i	0.243411	−	0.749141i	−0.752483	−	0.658611i	$-0.771144\pi$
$269$	3.99223	−	12.2868i	0.243411	−	0.749141i	0.995894	−	0.0905294i	$-0.0288559\pi$
$270$	−0.429682	+	1.32242i	−0.0261496	+	0.0804802i
$271$	−6.55792	+	4.76461i	−0.398365	+	0.289429i	−0.768875	−	0.639399i	$-0.779183\pi$
$271$	−6.55792	+	4.76461i	−0.398365	+	0.289429i	0.370509	+	0.928829i	$0.379183\pi$
$272$	4.75796	+	3.45686i	0.288494	+	0.209603i
$273$	0.284555	+	0.875769i	0.0172220	+	0.0530040i
$274$	−2.14682			−0.129694
$275$	−15.4503	+	3.86779i	−0.931690	+	0.233236i
$276$	14.2523			0.857886
$277$	7.25063	+	22.3151i	0.435648	+	1.34079i	0.892421	+	0.451204i	$0.149005\pi$
$277$	7.25063	+	22.3151i	0.435648	+	1.34079i	−0.456773	+	0.889583i	$0.650995\pi$
$278$	−7.91878	−	5.75333i	−0.474937	−	0.345062i
$279$	7.18627	−	5.22113i	0.430231	−	0.312581i
$280$	0.111864	−	0.344281i	0.00668513	−	0.0205747i
$281$	−4.44071	+	13.6671i	−0.264911	+	0.815311i	0.726803	+	0.686846i	$0.241005\pi$
$281$	−4.44071	+	13.6671i	−0.264911	+	0.815311i	−0.991714	+	0.128465i	$0.958995\pi$
$282$	10.9136	−	7.92917i	0.649893	−	0.472175i
$283$	9.45652	+	6.87056i	0.562132	+	0.408412i	0.832238	−	0.554418i	$-0.187059\pi$
$283$	9.45652	+	6.87056i	0.562132	+	0.408412i	−0.270107	+	0.962830i	$0.587059\pi$
$284$	−3.57970	−	11.0172i	−0.212416	−	0.653749i
$285$	0.946723			0.0560791
$286$	−0.121289	+	1.75851i	−0.00717200	+	0.103983i
$287$	−8.34854			−0.492799
$288$	−0.473189	−	1.45633i	−0.0278829	−	0.0858149i
$289$	−14.2290	−	10.3380i	−0.837002	−	0.608118i
$290$	1.49927	−	1.08928i	0.0880402	−	0.0639649i
$291$	−9.36015	+	28.8076i	−0.548702	+	1.68873i
$292$	3.81333	−	11.7362i	0.223158	−	0.686811i
$293$	−19.9706	+	14.5095i	−1.16670	+	0.847656i	−0.990610	−	0.136719i	$-0.956344\pi$
$293$	−19.9706	+	14.5095i	−1.16670	+	0.847656i	−0.176088	+	0.984374i	$0.556344\pi$
$294$	−10.9140	−	7.92952i	−0.636520	−	0.462459i
$295$	−0.464349	−	1.42912i	−0.0270355	−	0.0832066i
$296$	−2.37532			−0.138063
$297$	−5.50322	−	8.78841i	−0.319329	−	0.509955i
$298$	−1.24923			−0.0723657
$299$	1.09960	+	3.38423i	0.0635918	+	0.195715i
$300$	8.27005	+	6.00854i	0.477471	+	0.346903i
$301$	6.74698	−	4.90197i	0.388890	−	0.282545i
$302$	4.28073	−	13.1747i	0.246328	−	0.758120i
$303$	2.30563	−	7.09599i	0.132455	−	0.407654i
$304$	0.809017	−	0.587785i	0.0464003	−	0.0337118i
$305$	−1.71570	−	1.24653i	−0.0982407	−	0.0713761i
$306$	2.78290	+	8.56489i	0.159088	+	0.489622i
$307$	−11.2527			−0.642226			−0.321113	−	0.947041i	$-0.604057\pi$
$307$	−11.2527			−0.642226			−0.321113	+	0.947041i	$0.604057\pi$
$308$	1.43271	+	2.28798i	0.0816363	+	0.130370i
$309$	1.47756			0.0840557
$310$	−0.797240	−	2.45365i	−0.0452802	−	0.139358i
$311$	−2.75641	−	2.00265i	−0.156302	−	0.113560i	0.506886	−	0.862013i	$-0.330797\pi$
$311$	−2.75641	−	2.00265i	−0.156302	−	0.113560i	−0.663187	+	0.748454i	$0.730797\pi$
$312$	0.915267	−	0.664980i	0.0518168	−	0.0376471i
$313$	6.37884	−	19.6321i	0.360554	−	1.10967i	−0.592165	−	0.805817i	$-0.701727\pi$
$313$	6.37884	−	19.6321i	0.360554	−	1.10967i	0.952719	−	0.303853i	$-0.0982733\pi$
$314$	−5.34898	+	16.4625i	−0.301860	+	0.929031i
$315$	0.448452	−	0.325820i	0.0252674	−	0.0183579i
$316$	2.80726	+	2.03959i	0.157920	+	0.114736i
$317$	−8.09693	−	24.9198i	−0.454769	−	1.39963i	−0.871406	−	0.490562i	$-0.836791\pi$
$317$	−8.09693	−	24.9198i	−0.454769	−	1.39963i	0.416637	−	0.909073i	$-0.363209\pi$
$318$	−19.8355			−1.11232
$319$	−0.950938	+	13.7872i	−0.0532423	+	0.771933i
$320$	−0.444747			−0.0248621
$321$	5.67732	+	17.4730i	0.316877	+	0.975248i
$322$	4.40885	+	3.20321i	0.245695	+	0.178508i
$323$	−4.75796	+	3.45686i	−0.264740	+	0.192345i
$324$	−3.47614	+	10.6985i	−0.193119	+	0.594359i
$325$	−0.788683	+	2.42732i	−0.0437483	+	0.134643i
$326$	−8.06853	+	5.86213i	−0.446875	+	0.324673i
$327$	−13.9555	−	10.1393i	−0.771742	−	0.560703i
$328$	3.16957	+	9.75492i	0.175010	+	0.538626i
$329$	5.15813			0.284377
$330$	3.04593	−	0.762510i	0.167673	−	0.0419748i
$331$	22.7831			1.25227			0.626137	−	0.779713i	$-0.284635\pi$
$331$	22.7831			1.25227			0.626137	+	0.779713i	$0.284635\pi$
$332$	−3.97579	−	12.2362i	−0.218200	−	0.671550i
$333$	−2.94260	−	2.13793i	−0.161254	−	0.117158i
$334$	18.5250	−	13.4592i	1.01364	−	0.736455i
$335$	0.169103	−	0.520446i	0.00923910	−	0.0284350i
$336$	0.535409	−	1.64782i	0.0292090	−	0.0898959i
$337$	13.4952	−	9.80482i	0.735129	−	0.534103i	−0.156053	−	0.987749i	$-0.549877\pi$
$337$	13.4952	−	9.80482i	0.735129	−	0.534103i	0.891182	+	0.453646i	$0.149877\pi$
$338$	−10.2887	−	7.47518i	−0.559632	−	0.406596i
$339$	3.06705	+	9.43940i	0.166579	+	0.512678i
$340$	2.61563			0.141852
$341$	17.8452	+	7.19024i	0.966374	+	0.389373i
$342$	1.53127			0.0828017
$343$	−3.35467	−	10.3246i	−0.181135	−	0.557477i
$344$	−8.28927	−	6.02251i	−0.446928	−	0.324712i
$345$	5.12808	−	3.72577i	0.276087	−	0.200589i
$346$	2.39464	−	7.36995i	0.128737	−	0.396211i
$347$	7.68261	−	23.6447i	0.412424	−	1.26931i	−0.502110	−	0.864804i	$-0.667443\pi$
$347$	7.68261	−	23.6447i	0.412424	−	1.26931i	0.914534	−	0.404508i	$-0.132557\pi$
$348$	7.17591	−	5.21360i	0.384669	−	0.279478i
$349$	−15.8230	−	11.4961i	−0.846987	−	0.615372i	0.0773266	−	0.997006i	$-0.475362\pi$
$349$	−15.8230	−	11.4961i	−0.846987	−	0.615372i	−0.924314	+	0.381634i	$0.875362\pi$
$350$	1.20786	+	3.71740i	0.0645627	+	0.198704i
$351$	−1.66162			−0.0886907
$352$	2.12947	−	2.54271i	0.113501	−	0.135527i
$353$	−17.1793			−0.914360			−0.457180	−	0.889374i	$-0.651141\pi$
$353$	−17.1793			−0.914360			−0.457180	+	0.889374i	$0.651141\pi$
$354$	−2.22250	−	6.84015i	−0.118125	−	0.363550i
$355$	−4.16807	−	3.02828i	−0.221218	−	0.160724i
$356$	−5.98802	+	4.35055i	−0.317364	+	0.230579i
$357$	−3.14883	+	9.69109i	−0.166654	+	0.512907i
$358$	−4.07248	+	12.5338i	−0.215237	+	0.662432i
$359$	−15.3867	+	11.1791i	−0.812080	+	0.590011i	−0.914433	−	0.404738i	$-0.867363\pi$
$359$	−15.3867	+	11.1791i	−0.812080	+	0.590011i	0.102353	+	0.994748i	$0.467363\pi$
$360$	−0.550964	−	0.400299i	−0.0290383	−	0.0210976i
$361$	0.309017	+	0.951057i	0.0162641	+	0.0500556i
$362$	9.16172			0.481529
$363$	−10.2247	+	21.0651i	−0.536656	+	1.10563i
$364$	0.432587			0.0226737
$365$	−1.69597	−	5.21965i	−0.0887710	−	0.273209i
$366$	−8.21180	−	5.96623i	−0.429238	−	0.311860i
$367$	−3.39444	+	2.46621i	−0.177188	+	0.128735i	−0.672844	−	0.739784i	$-0.734928\pi$
$367$	−3.39444	+	2.46621i	−0.177188	+	0.128735i	0.495656	+	0.868519i	$0.334928\pi$
$368$	2.06898	−	6.36767i	0.107853	−	0.331938i
$369$	−4.85347	+	14.9374i	−0.252662	+	0.777612i
$370$	−0.854658	+	0.620946i	−0.0444316	+	0.0322814i
$371$	−6.13599	−	4.45806i	−0.318565	−	0.231451i
$372$	−3.81580	−	11.7438i	−0.197840	−	0.608890i
$373$	−30.5753			−1.58313			−0.791564	−	0.611086i	$-0.790733\pi$
$373$	−30.5753			−1.58313			−0.791564	+	0.611086i	$0.790733\pi$
$374$	−12.5238	+	14.9541i	−0.647589	+	0.773256i
$375$	9.27997			0.479216
$376$	−1.95831	−	6.02706i	−0.100992	−	0.310822i
$377$	1.79162	+	1.30169i	0.0922733	+	0.0670405i
$378$	−2.05874	+	1.49576i	−0.105890	+	0.0769338i
$379$	8.62627	−	26.5489i	0.443102	−	1.36373i	−0.441451	−	0.897286i	$-0.645536\pi$
$379$	8.62627	−	26.5489i	0.443102	−	1.36373i	0.884552	−	0.466441i	$-0.154464\pi$
$380$	0.137434	−	0.422980i	0.00705024	−	0.0216984i
$381$	−9.91110	+	7.20084i	−0.507761	+	0.368910i
$382$	−11.7816	−	8.55983i	−0.602799	−	0.437959i
$383$	−4.12024	−	12.6808i	−0.210535	−	0.647959i	−0.999441	−	0.0334448i	$-0.989352\pi$
$383$	−4.12024	−	12.6808i	−0.210535	−	0.647959i	0.788906	−	0.614514i	$-0.210648\pi$
$384$	−2.12868			−0.108629
$385$	1.11361	+	0.448700i	0.0567550	+	0.0228679i
$386$	2.43059			0.123714
$387$	−4.84835	−	14.9217i	−0.246455	−	0.758512i
$388$	11.5119	+	8.36390i	0.584430	+	0.424613i
$389$	4.85839	−	3.52983i	0.246330	−	0.178969i	−0.457769	−	0.889071i	$-0.651351\pi$
$389$	4.85839	−	3.52983i	0.246330	−	0.178969i	0.704099	+	0.710102i	$0.251351\pi$
$390$	0.155484	−	0.478530i	0.00787324	−	0.0242313i
$391$	−12.1680	+	37.4493i	−0.615363	+	1.89389i
$392$	−5.12714	+	3.72509i	−0.258960	+	0.188145i
$393$	1.67099	+	1.21405i	0.0842904	+	0.0612406i
$394$	3.36974	+	10.3710i	0.169765	+	0.522483i
$395$	1.54325			0.0776495
$396$	4.92663	−	1.23332i	0.247572	−	0.0619765i
$397$	−27.7223			−1.39134			−0.695671	−	0.718360i	$-0.744893\pi$
$397$	−27.7223			−1.39134			−0.695671	+	0.718360i	$0.744893\pi$
$398$	4.72807	+	14.5515i	0.236997	+	0.729402i
$399$	1.40172	+	1.01841i	0.0701737	+	0.0509842i
$400$	3.88506	−	2.82266i	0.194253	−	0.141133i
$401$	9.01192	−	27.7358i	0.450034	−	1.38506i	−0.426834	−	0.904330i	$-0.640371\pi$
$401$	9.01192	−	27.7358i	0.450034	−	1.38506i	0.876868	−	0.480732i	$-0.159629\pi$
$402$	0.809374	−	2.49100i	0.0403679	−	0.124240i
$403$	2.49420	−	1.81214i	0.124245	−	0.0902693i
$404$	−2.83566	−	2.06023i	−0.141079	−	0.102500i
$405$	1.54600	+	4.75811i	0.0768215	+	0.236432i
$406$	3.39158			0.168321
$407$	0.542082	−	7.85937i	0.0268700	−	0.389574i
$408$	12.5191			0.619788
$409$	3.47106	+	10.6828i	0.171633	+	0.528231i	0.999464	−	0.0327463i	$-0.0104253\pi$
$409$	3.47106	+	10.6828i	0.171633	+	0.528231i	−0.827831	+	0.560978i	$0.810425\pi$
$410$	3.69053	+	2.68132i	0.182262	+	0.132421i
$411$	−3.69712	+	2.68612i	−0.182366	+	0.132496i
$412$	0.214496	−	0.660150i	0.0105674	−	0.0325232i
$413$	0.849816	−	2.61547i	0.0418167	−	0.128699i
$414$	8.29438	−	6.02622i	0.407647	−	0.296173i
$415$	−4.62926	−	3.36336i	−0.227242	−	0.165101i
$416$	−0.164234	−	0.505460i	−0.00805222	−	0.0247822i
$417$	−20.8358			−1.02034
$418$	1.76021	+	2.81099i	0.0860948	+	0.137490i
$419$	−20.2013			−0.986897			−0.493449	−	0.869775i	$-0.664264\pi$
$419$	−20.2013			−0.986897			−0.493449	+	0.869775i	$0.664264\pi$
$420$	−0.238122	−	0.732863i	−0.0116191	−	0.0357600i
$421$	10.2803	+	7.46911i	0.501033	+	0.364022i	0.809412	−	0.587242i	$-0.199786\pi$
$421$	10.2803	+	7.46911i	0.501033	+	0.364022i	−0.308378	+	0.951264i	$0.599786\pi$
$422$	−4.53947	+	3.29812i	−0.220978	+	0.160550i
$423$	2.99871	−	9.22907i	0.145802	−	0.448733i
$424$	−2.87949	+	8.86217i	−0.139841	+	0.430385i
$425$	−22.8487	+	16.6005i	−1.10832	+	0.805244i
$426$	−19.9495	−	14.4942i	−0.966556	−	0.702244i
$427$	−1.19935	−	3.69122i	−0.0580407	−	0.178631i
$428$	8.63080			0.417185
$429$	1.99139	+	3.18016i	0.0961450	+	0.153540i
$430$	−4.55693			−0.219754
$431$	−9.75883	−	30.0346i	−0.470066	−	1.44672i	−0.852497	−	0.522731i	$-0.824913\pi$
$431$	−9.75883	−	30.0346i	−0.470066	−	1.44672i	0.382431	−	0.923984i	$-0.375087\pi$
$432$	2.52935	+	1.83768i	0.121693	+	0.0884154i
$433$	−17.1813	+	12.4830i	−0.825682	+	0.599893i	−0.918334	−	0.395806i	$-0.870465\pi$
$433$	−17.1813	+	12.4830i	−0.825682	+	0.599893i	0.0926526	+	0.995698i	$0.470465\pi$
$434$	1.45905	−	4.49048i	0.0700365	−	0.215550i
$435$	1.21903	−	3.75179i	0.0584480	−	0.179885i
$436$	−6.55595	+	4.76318i	−0.313973	+	0.228115i
$437$	5.41666	+	3.93543i	0.259114	+	0.188257i
$438$	−8.11735	−	24.9826i	−0.387862	−	1.19372i
$439$	23.1919			1.10689			0.553445	−	0.832886i	$-0.313313\pi$
$439$	23.1919			1.10689			0.553445	+	0.832886i	$0.313313\pi$
$440$	0.101498	−	1.47156i	0.00483871	−	0.0701540i
$441$	−9.70444			−0.462116
$442$	0.965885	+	2.97269i	0.0459425	+	0.141396i
$443$	13.4663	+	9.78387i	0.639805	+	0.464846i	0.859783	−	0.510659i	$-0.170599\pi$
$443$	13.4663	+	9.78387i	0.639805	+	0.464846i	−0.219978	+	0.975505i	$0.570599\pi$
$444$	−4.09062	+	2.97201i	−0.194132	+	0.141045i
$445$	−1.01723	+	3.13072i	−0.0482215	+	0.148411i
$446$	7.41215	−	22.8122i	0.350975	−	1.08019i
$447$	−2.15134	+	1.56304i	−0.101755	+	0.0739291i
$448$	−0.658492	−	0.478423i	−0.0311108	−	0.0226034i
$449$	−0.690204	−	2.12423i	−0.0325727	−	0.100249i	0.933448	−	0.358712i	$-0.116784\pi$
$449$	−0.690204	−	2.12423i	−0.0325727	−	0.100249i	−0.966021	+	0.258463i	$0.916784\pi$
$450$	7.35348			0.346646
$451$	−33.0001	+	8.26113i	−1.55391	+	0.389002i
$452$	4.66260			0.219310
$453$	−9.11229	−	28.0447i	−0.428133	−	1.31766i
$454$	−2.85398	−	2.07354i	−0.133944	−	0.0973159i
$455$	0.155648	−	0.113085i	0.00729690	−	0.00530151i
$456$	0.657798	−	2.02449i	0.0308042	−	0.0948056i
$457$	3.84000	−	11.8183i	0.179628	−	0.552837i	−0.820187	−	0.572096i	$-0.806131\pi$
$457$	3.84000	−	11.8183i	0.179628	−	0.552837i	0.999815	+	0.0192585i	$0.00613055\pi$
$458$	−15.8339	+	11.5040i	−0.739868	+	0.537546i
$459$	−14.8755	−	10.8077i	−0.694330	−	0.504460i
$460$	−0.920173	−	2.83200i	−0.0429033	−	0.132043i
$461$	31.8148			1.48176			0.740881	−	0.671636i	$-0.234408\pi$
$461$	31.8148			1.48176			0.740881	+	0.671636i	$0.234408\pi$
$462$	5.33006	+	2.14760i	0.247977	+	0.0999153i
$463$	−0.0722953			−0.00335985			−0.00167992	−	0.999999i	$-0.500535\pi$
$463$	−0.0722953			−0.00335985			−0.00167992	+	0.999999i	$0.500535\pi$
$464$	−1.28763	−	3.96292i	−0.0597768	−	0.183974i
$465$	−4.44298	−	3.22801i	−0.206038	−	0.149696i
$466$	15.5347	−	11.2866i	0.719630	−	0.522842i
$467$	−10.4480	+	32.1557i	−0.483476	+	1.48799i	0.350699	+	0.936488i	$0.385944\pi$
$467$	−10.4480	+	32.1557i	−0.483476	+	1.48799i	−0.834175	+	0.551499i	$0.814056\pi$
$468$	0.251487	−	0.773996i	0.0116250	−	0.0357780i
$469$	0.810228	−	0.588665i	0.0374129	−	0.0271820i
$470$	−2.28018	−	1.65665i	−0.105177	−	0.0764156i
$471$	11.3863	+	35.0433i	0.524651	+	1.61471i
$472$	−3.37870			−0.155517
$473$	21.8188	−	26.0528i	1.00323	−	1.19791i
$474$	7.38643			0.339270
$475$	1.48396	+	4.56716i	0.0680888	+	0.209556i
$476$	3.87270	+	2.81368i	0.177505	+	0.128965i
$477$	−11.5437	+	8.38696i	−0.528548	+	0.384013i
$478$	5.98871	−	18.4314i	0.273917	−	0.843031i
$479$	−2.37442	+	7.30771i	−0.108490	+	0.333898i	−0.990534	−	0.137270i	$-0.956167\pi$
$479$	−2.37442	+	7.30771i	−0.108490	+	0.333898i	0.882044	+	0.471167i	$0.156167\pi$
$480$	−0.765915	+	0.556470i	−0.0349591	+	0.0253993i
$481$	−1.02131	−	0.742029i	−0.0465679	−	0.0338336i
$482$	−1.60987	−	4.95466i	−0.0733275	−	0.225679i
$483$	11.6005			0.527842
$484$	7.92723	+	7.62620i	0.360329	+	0.346646i
$485$	6.32854			0.287364
$486$	4.50121	+	13.8533i	0.204179	+	0.628398i
$487$	24.5685	+	17.8500i	1.11330	+	0.808862i	0.983181	−	0.182636i	$-0.0584628\pi$
$487$	24.5685	+	17.8500i	1.11330	+	0.808862i	0.130123	+	0.991498i	$0.458463\pi$
$488$	−3.85770	+	2.80278i	−0.174630	+	0.126876i
$489$	−6.56038	+	20.1908i	−0.296671	+	0.913059i
$490$	−0.870990	+	2.68063i	−0.0393473	+	0.121099i
$491$	−8.18301	+	5.94531i	−0.369294	+	0.268308i	−0.756918	−	0.653510i	$-0.773296\pi$
$491$	−8.18301	+	5.94531i	−0.369294	+	0.268308i	0.387624	+	0.921818i	$0.373296\pi$
$492$	17.6638	+	12.8335i	0.796348	+	0.578580i
$493$	7.57277	+	23.3066i	0.341060	+	1.04968i
$494$	0.531472			0.0239120
$495$	1.45023	−	1.73166i	0.0651831	−	0.0778321i
$496$	−5.80088			−0.260467
$497$	−2.91366	−	8.96734i	−0.130696	−	0.402240i
$498$	−22.1569	−	16.0979i	−0.992874	−	0.721365i
$499$	15.0982	−	10.9695i	0.675890	−	0.491063i	−0.196102	−	0.980584i	$-0.562828\pi$
$499$	15.0982	−	10.9695i	0.675890	−	0.491063i	0.871992	+	0.489521i	$0.162828\pi$
$500$	1.34716	−	4.14613i	0.0602468	−	0.185421i
$501$	15.0624	−	46.3572i	0.672937	−	2.07109i
$502$	11.0021	−	7.99349i	0.491047	−	0.356767i
$503$	10.7921	+	7.84090i	0.481195	+	0.349609i	0.801788	−	0.597608i	$-0.203882\pi$
$503$	10.7921	+	7.84090i	0.481195	+	0.349609i	−0.320593	+	0.947217i	$0.603882\pi$
$504$	−0.385148	−	1.18536i	−0.0171559	−	0.0528003i
$505$	−1.55887			−0.0693688
$506$	20.5969	+	8.29896i	0.915646	+	0.368934i
$507$	−27.0716			−1.20229
$508$	1.77843	+	5.47344i	0.0789050	+	0.242845i
$509$	−28.4656	−	20.6815i	−1.26172	−	0.916691i	−0.262877	−	0.964829i	$-0.584671\pi$
$509$	−28.4656	−	20.6815i	−1.26172	−	0.916691i	−0.998841	+	0.0481379i	$0.984671\pi$
$510$	4.50447	−	3.27269i	0.199461	−	0.144917i
$511$	3.10383	−	9.55260i	0.137305	−	0.422582i
$512$	−0.309017	+	0.951057i	−0.0136568	+	0.0420312i
$513$	−2.52935	+	1.83768i	−0.111674	+	0.0811356i
$514$	−8.86110	−	6.43797i	−0.390846	−	0.283966i
$515$	−0.0953963	−	0.293600i	−0.00420366	−	0.0129375i
$516$	−21.8107			−0.960161
$517$	20.3890	−	5.10412i	0.896708	−	0.224479i
$518$	−1.93337			−0.0849474
$519$	−5.09742	−	15.6883i	−0.223752	−	0.688638i
$520$	−0.191228	−	0.138935i	−0.00838589	−	0.00609270i
$521$	21.9260	−	15.9301i	0.960593	−	0.697912i	0.00730498	−	0.999973i	$-0.497675\pi$
$521$	21.9260	−	15.9301i	0.960593	−	0.697912i	0.953289	+	0.302061i	$0.0976747\pi$
$522$	1.97171	−	6.06831i	0.0862996	−	0.265603i
$523$	3.78202	−	11.6399i	0.165376	−	0.508976i	−0.833688	−	0.552236i	$-0.813775\pi$
$523$	3.78202	−	11.6399i	0.165376	−	0.508976i	0.999064	+	0.0432606i	$0.0137746\pi$
$524$	0.784990	−	0.570329i	0.0342925	−	0.0249149i
$525$	6.73133	+	4.89060i	0.293780	+	0.213443i
$526$	−8.60927	−	26.4966i	−0.375382	−	1.15531i
$527$	34.1159			1.48611
$528$	0.485795	−	7.04329i	0.0211415	−	0.306520i
$529$	21.8279			0.949038
$530$	1.28065	+	3.94142i	0.0556277	+	0.171204i
$531$	−4.18562	−	3.04103i	−0.181640	−	0.131969i
$532$	0.658492	−	0.478423i	0.0285493	−	0.0207423i
$533$	−1.68453	+	5.18447i	−0.0729653	+	0.224564i
$534$	−4.86875	+	14.9845i	−0.210692	+	0.648442i
$535$	3.10543	−	2.25623i	0.134259	−	0.0975452i
$536$	−0.995438	−	0.723228i	−0.0429964	−	0.0312387i
$537$	8.66901	+	26.6805i	0.374095	+	1.15135i
$538$	−12.9191			−0.556983
$539$	−11.1554	−	17.8146i	−0.480495	−	0.767330i
$540$	1.39048			0.0598367
$541$	13.8116	+	42.5078i	0.593808	+	1.82755i	0.560573	+	0.828105i	$0.310581\pi$
$541$	13.8116	+	42.5078i	0.593808	+	1.82755i	0.0332353	+	0.999448i	$0.489419\pi$
$542$	6.55792	+	4.76461i	0.281687	+	0.204657i
$543$	15.7777	−	11.4632i	0.677088	−	0.491933i
$544$	1.81738	−	5.59332i	0.0779195	−	0.239811i
$545$	−1.11371	+	3.42766i	−0.0477063	+	0.146825i
$546$	0.744974	−	0.541255i	0.0318819	−	0.0231636i
$547$	2.29936	+	1.67058i	0.0983133	+	0.0714288i	0.635856	−	0.771808i	$-0.280647\pi$
$547$	2.29936	+	1.67058i	0.0983133	+	0.0714288i	−0.537543	+	0.843237i	$0.680647\pi$
$548$	0.663405	+	2.04175i	0.0283392	+	0.0872192i
$549$	−7.30169			−0.311629
$550$	8.45290	+	13.4989i	0.360433	+	0.575596i
$551$	4.16686			0.177514
$552$	−4.40419	−	13.5547i	−0.187455	−	0.576927i
$553$	2.28494	+	1.66011i	0.0971656	+	0.0705949i
$554$	18.9824	−	13.7915i	0.806485	−	0.585945i
$555$	−0.694908	+	2.13871i	−0.0294972	+	0.0907831i
$556$	−3.02471	+	9.30909i	−0.128276	+	0.394793i
$557$	25.5925	−	18.5940i	1.08439	−	0.787855i	0.105946	−	0.994372i	$-0.466213\pi$
$557$	25.5925	−	18.5940i	1.08439	−	0.787855i	0.978443	+	0.206517i	$0.0662129\pi$
$558$	−7.18627	−	5.22113i	−0.304219	−	0.221028i
$559$	−1.68276	−	5.17899i	−0.0711730	−	0.219048i
$560$	−0.361998			−0.0152972
$561$	−2.85704	+	41.4228i	−0.120624	+	1.74887i
$562$	14.3704			0.606180
$563$	−1.35629	−	4.17422i	−0.0571606	−	0.175922i	0.918400	−	0.395654i	$-0.129482\pi$
$563$	−1.35629	−	4.17422i	−0.0571606	−	0.175922i	−0.975560	+	0.219731i	$0.929482\pi$
$564$	−10.9136	−	7.92917i	−0.459544	−	0.333878i
$565$	1.67764	−	1.21888i	0.0705788	−	0.0512785i
$566$	3.61207	−	11.1168i	0.151827	−	0.467274i
$567$	−2.82937	+	8.70792i	−0.118823	+	0.365698i
$568$	−9.37177	+	6.80899i	−0.393231	+	0.285699i
$569$	31.3993	+	22.8129i	1.31633	+	0.956367i	0.999970	+	0.00772642i	$0.00245942\pi$
$569$	31.3993	+	22.8129i	1.31633	+	0.956367i	0.316356	+	0.948641i	$0.397541\pi$
$570$	−0.292554	−	0.900388i	−0.0122537	−	0.0377131i
$571$	−22.3077			−0.933547			−0.466774	−	0.884377i	$-0.654584\pi$
$571$	−22.3077			−0.933547			−0.466774	+	0.884377i	$0.654584\pi$
$572$	1.70993	−	0.428058i	0.0714956	−	0.0178980i
$573$	−30.9996			−1.29503
$574$	2.57984	+	7.93994i	0.107681	+	0.331407i
$575$	26.0119	+	18.8987i	1.08477	+	0.788132i
$576$	−1.23883	+	0.900059i	−0.0516177	+	0.0375025i
$577$	6.07195	−	18.6875i	0.252779	−	0.777973i	−0.741481	−	0.670974i	$-0.765876\pi$
$577$	6.07195	−	18.6875i	0.252779	−	0.777973i	0.994259	−	0.106998i	$-0.0341240\pi$
$578$	−5.43501	+	16.7272i	−0.226067	+	0.695761i
$579$	4.18581	−	3.04117i	0.173956	−	0.126387i
$580$	−1.49927	−	1.08928i	−0.0622538	−	0.0452300i
$581$	−3.23606	−	9.95957i	−0.134254	−	0.413193i
$582$	30.2901			1.25556
$583$	−28.6657	−	11.5500i	−1.18721	−	0.478354i
$584$	−12.3402			−0.510641
$585$	−0.111848	−	0.344233i	−0.00462434	−	0.0142323i
$586$	19.9706	+	14.5095i	0.824980	+	0.599383i
$587$	−32.7802	+	23.8162i	−1.35298	+	0.983001i	−0.354128	+	0.935197i	$0.615222\pi$
$587$	−32.7802	+	23.8162i	−1.35298	+	0.983001i	−0.998857	+	0.0478041i	$0.984778\pi$
$588$	−4.16879	+	12.8302i	−0.171918	+	0.529110i
$589$	1.79257	−	5.51696i	0.0738615	−	0.227322i
$590$	−1.21568	+	0.883245i	−0.0500489	+	0.0363626i
$591$	18.7794	+	13.6440i	0.772481	+	0.561241i
$592$	0.734014	+	2.25906i	0.0301678	+	0.0928469i
$593$	−11.8720			−0.487525			−0.243762	−	0.969835i	$-0.578382\pi$
$593$	−11.8720			−0.487525			−0.243762	+	0.969835i	$0.578382\pi$
$594$	−6.65768	+	7.94964i	−0.273168	+	0.326178i
$595$	2.12897			0.0872792
$596$	0.386032	+	1.18808i	0.0158125	+	0.0486658i
$597$	26.3493	+	19.1439i	1.07841	+	0.783508i
$598$	2.87880	−	2.09157i	0.117723	−	0.0855307i
$599$	−11.4996	+	35.3921i	−0.469861	+	1.44608i	0.382905	+	0.923788i	$0.374924\pi$
$599$	−11.4996	+	35.3921i	−0.469861	+	1.44608i	−0.852765	+	0.522294i	$0.825076\pi$
$600$	3.15888	−	9.72202i	0.128961	−	0.396900i
$601$	14.0134	−	10.1813i	0.571619	−	0.415305i	−0.264074	−	0.964502i	$-0.585066\pi$
$601$	14.0134	−	10.1813i	0.571619	−	0.415305i	0.835693	+	0.549197i	$0.185066\pi$
$602$	−6.74698	−	4.90197i	−0.274987	−	0.199789i
$603$	−0.582226	−	1.79191i	−0.0237101	−	0.0729721i
$604$	−13.8527			−0.563659
$605$	4.84589	+	0.671664i	0.197013	+	0.0273070i
$606$	−7.46117			−0.303089
$607$	0.291352	+	0.896689i	0.0118256	+	0.0363955i	0.956795	−	0.290763i	$-0.0939090\pi$
$607$	0.291352	+	0.896689i	0.0118256	+	0.0363955i	−0.944970	+	0.327158i	$0.893909\pi$
$608$	−0.809017	−	0.587785i	−0.0328100	−	0.0238378i
$609$	5.84077	−	4.24357i	0.236680	−	0.171958i
$610$	−0.655339	+	2.01693i	−0.0265339	+	0.0816630i
$611$	1.04079	−	3.20321i	0.0421057	−	0.129588i
$612$	7.28573	−	5.29339i	0.294508	−	0.213973i
$613$	27.5265	+	19.9992i	1.11178	+	0.807759i	0.982944	−	0.183906i	$-0.0588743\pi$
$613$	27.5265	+	19.9992i	1.11178	+	0.807759i	0.128841	+	0.991665i	$0.458874\pi$
$614$	3.47728	+	10.7020i	0.140331	+	0.431896i
$615$	9.71048			0.391564
$616$	1.73327	−	2.06961i	0.0698353	−	0.0833871i
$617$	−12.4983			−0.503162			−0.251581	−	0.967836i	$-0.580950\pi$
$617$	−12.4983			−0.503162			−0.251581	+	0.967836i	$0.580950\pi$
$618$	−0.456592	−	1.40525i	−0.0183668	−	0.0565273i
$619$	23.8010	+	17.2924i	0.956642	+	0.695041i	0.952368	−	0.304950i	$-0.0986397\pi$
$619$	23.8010	+	17.2924i	0.956642	+	0.695041i	0.00427361	+	0.999991i	$0.498640\pi$
$620$	−2.08720	+	1.51644i	−0.0838240	+	0.0609017i
$621$	−6.46856	+	19.9082i	−0.259574	+	0.798888i
$622$	−1.05285	+	3.24035i	−0.0422156	+	0.129926i
$623$	−4.87390	+	3.54109i	−0.195269	+	0.141871i
$624$	−0.915267	−	0.664980i	−0.0366400	−	0.0266205i
$625$	6.82066	+	20.9918i	0.272826	+	0.839674i
$626$	−20.6424			−0.825035
$627$	6.54845	+	2.63852i	0.261520	+	0.105372i
$628$	17.3097			0.690731
$629$	−4.31685	−	13.2859i	−0.172124	−	0.529744i
$630$	−0.448452	−	0.325820i	−0.0178668	−	0.0129810i
$631$	−6.27948	+	4.56231i	−0.249982	+	0.181623i	−0.705719	−	0.708492i	$-0.749376\pi$
$631$	−6.27948	+	4.56231i	−0.249982	+	0.181623i	0.455737	+	0.890115i	$0.349376\pi$
$632$	1.07228	−	3.30013i	0.0426529	−	0.131272i
$633$	−3.69097	+	11.3596i	−0.146703	+	0.451505i
$634$	−21.1980	+	15.4013i	−0.841882	+	0.611663i
$635$	2.07074	+	1.50448i	0.0821747	+	0.0597034i
$636$	6.12951	+	18.8647i	0.243051	+	0.748034i
$637$	−3.36820			−0.133453
$638$	13.4062	−	3.35607i	0.530758	−	0.132868i
$639$	−17.7385			−0.701724
$640$	0.137434	+	0.422980i	0.00543257	+	0.0167197i
$641$	−15.7958	−	11.4763i	−0.623898	−	0.453288i	0.230383	−	0.973100i	$-0.426002\pi$
$641$	−15.7958	−	11.4763i	−0.623898	−	0.453288i	−0.854281	+	0.519812i	$0.826002\pi$
$642$	14.8634	−	10.7989i	0.586612	−	0.426199i
$643$	−14.9691	+	46.0701i	−0.590323	+	1.81683i	−0.0135697	+	0.999908i	$0.504319\pi$
$643$	−14.9691	+	46.0701i	−0.590323	+	1.81683i	−0.576753	+	0.816919i	$0.695681\pi$
$644$	1.68403	−	5.18291i	0.0663600	−	0.204235i
$645$	−7.84765	+	5.70165i	−0.309001	+	0.224502i
$646$	4.75796	+	3.45686i	0.187199	+	0.136008i
$647$	9.90054	+	30.4707i	0.389230	+	1.19793i	0.933364	+	0.358930i	$0.116858\pi$
$647$	9.90054	+	30.4707i	0.389230	+	1.19793i	−0.544134	+	0.838998i	$0.683142\pi$
$648$	11.2490			0.441903
$649$	0.771068	−	11.1793i	0.0302671	−	0.438827i
$650$	2.55223			0.100107
$651$	−3.10584	−	9.55880i	−0.121728	−	0.374639i
$652$	8.06853	+	5.86213i	0.315988	+	0.229579i
$653$	29.7434	−	21.6098i	1.16395	−	0.845658i	0.173676	−	0.984803i	$-0.444435\pi$
$653$	29.7434	−	21.6098i	1.16395	−	0.845658i	0.990272	+	0.139145i	$0.0444355\pi$
$654$	−5.33053	+	16.4057i	−0.208440	+	0.641513i
$655$	0.133353	−	0.410418i	0.00521053	−	0.0160363i
$656$	8.29803	−	6.02887i	0.323984	−	0.235388i
$657$	−15.2873	−	11.1069i	−0.596416	−	0.433322i
$658$	−1.59395	−	4.90567i	−0.0621386	−	0.191243i
$659$	−1.92517			−0.0749940			−0.0374970	−	0.999297i	$-0.511938\pi$
$659$	−1.92517			−0.0749940			−0.0374970	+	0.999297i	$0.511938\pi$
$660$	−1.66644	−	2.66123i	−0.0648659	−	0.103588i
$661$	−0.375942			−0.0146225			−0.00731123	−	0.999973i	$-0.502327\pi$
$661$	−0.375942			−0.0146225			−0.00731123	+	0.999973i	$0.502327\pi$
$662$	−7.04037	−	21.6680i	−0.273632	−	0.842152i
$663$	5.38283	+	3.91086i	0.209052	+	0.151885i
$664$	−10.4088	+	7.56240i	−0.403938	+	0.293478i
$665$	0.111864	−	0.344281i	0.00433788	−	0.0133506i
$666$	−1.12398	+	3.45924i	−0.0435531	+	0.134043i
$667$	22.5705	−	16.3984i	0.873932	−	0.634949i
$668$	−18.5250	−	13.4592i	−0.716754	−	0.520752i
$669$	−15.7781	−	48.5599i	−0.610016	−	1.87744i
$670$	−0.547230			−0.0211413
$671$	−8.39337	−	13.4039i	−0.324022	−	0.517450i
$672$	−1.73262			−0.0668373
$673$	−4.19012	−	12.8959i	−0.161517	−	0.497099i	0.837245	−	0.546827i	$-0.184165\pi$
$673$	−4.19012	−	12.8959i	−0.161517	−	0.497099i	−0.998763	+	0.0497281i	$0.984165\pi$
$674$	−13.4952	−	9.80482i	−0.519815	−	0.377668i
$675$	−12.1464	+	8.82491i	−0.467517	+	0.339671i
$676$	−3.92994	+	12.0951i	−0.151151	+	0.465196i
$677$	14.2656	−	43.9051i	0.548273	−	1.68741i	−0.164804	−	0.986326i	$-0.552699\pi$
$677$	14.2656	−	43.9051i	0.548273	−	1.68741i	0.713077	−	0.701085i	$-0.247301\pi$
$678$	8.02963	−	5.83387i	0.308376	−	0.224048i
$679$	9.37003	+	6.80773i	0.359589	+	0.261257i
$680$	−0.808274	−	2.48761i	−0.0309959	−	0.0953955i
$681$	−7.50937			−0.287759
$682$	1.32384	−	19.1937i	0.0506926	−	0.734966i
$683$	13.2284			0.506170			0.253085	−	0.967444i	$-0.418555\pi$
$683$	13.2284			0.506170			0.253085	+	0.967444i	$0.418555\pi$
$684$	−0.473189	−	1.45633i	−0.0180928	−	0.0556840i
$685$	0.772444	+	0.561213i	0.0295136	+	0.0214429i
$686$	−8.78264	+	6.38096i	−0.335323	+	0.243626i
$687$	−12.8742	+	39.6229i	−0.491183	+	1.51171i
$688$	−3.16622	+	9.74463i	−0.120711	+	0.371510i
$689$	−4.00656	+	2.91093i	−0.152638	+	0.110898i
$690$	−5.12808	−	3.72577i	−0.195223	−	0.141838i
$691$	9.53953	+	29.3597i	0.362901	+	1.11689i	0.951285	+	0.308312i	$0.0997642\pi$
$691$	9.53953	+	29.3597i	0.362901	+	1.11689i	−0.588384	+	0.808581i	$0.700236\pi$
$692$	−7.74923			−0.294581
$693$	4.00999	−	1.00385i	0.152327	−	0.0381330i
$694$	−24.8615			−0.943728
$695$	1.34523	+	4.14019i	0.0510275	+	0.157046i
$696$	−7.17591	−	5.21360i	−0.272002	−	0.197621i
$697$	−48.8021	+	35.4568i	−1.84851	+	1.34302i
$698$	−6.04386	+	18.6011i	−0.228763	+	0.704061i
$699$	12.6310	−	38.8741i	0.477747	−	1.47036i
$700$	3.16221	−	2.29748i	0.119520	−	0.0868367i
$701$	39.3647	+	28.6001i	1.48678	+	1.08021i	0.975291	+	0.220925i	$0.0709074\pi$
$701$	39.3647	+	28.6001i	1.48678	+	1.08021i	0.511493	+	0.859287i	$0.329093\pi$
$702$	0.513468	+	1.58029i	0.0193796	+	0.0596443i
$703$	−2.37532			−0.0895868
$704$	−3.07630	−	1.23951i	−0.115942	−	0.0467158i
$705$	−5.99960			−0.225958
$706$	5.30869	+	16.3385i	0.199795	+	0.614906i
$707$	−2.30806	−	1.67691i	−0.0868036	−	0.0630665i
$708$	−5.81858	+	4.22745i	−0.218676	+	0.158877i
$709$	−1.31869	+	4.05852i	−0.0495246	+	0.152421i	−0.972760	−	0.231813i	$-0.925534\pi$
$709$	−1.31869	+	4.05852i	−0.0495246	+	0.152421i	0.923236	+	0.384234i	$0.125534\pi$
$710$	−1.59206	+	4.89986i	−0.0597490	+	0.183888i
$711$	4.29867	−	3.12317i	0.161213	−	0.117128i
$712$	5.98802	+	4.35055i	0.224410	+	0.163044i
$713$	−12.0019	−	36.9381i	−0.449475	−	1.38334i
$714$	10.1898			0.381344
$715$	0.503344	−	0.601020i	0.0188240	−	0.0224769i
$716$	13.1788			0.492516
$717$	−12.7480	−	39.2344i	−0.476084	−	1.46524i
$718$	15.3867	+	11.1791i	0.574227	+	0.417200i
$719$	−24.7032	+	17.9479i	−0.921275	+	0.669345i	−0.943841	−	0.330400i	$-0.892816\pi$
$719$	−24.7032	+	17.9479i	−0.921275	+	0.669345i	0.0225663	+	0.999745i	$0.492816\pi$
$720$	−0.210449	+	0.647697i	−0.00784299	+	0.0241382i
$721$	0.174587	−	0.537323i	0.00650196	−	0.0200110i
$722$	0.809017	−	0.587785i	0.0301085	−	0.0218751i
$723$	−8.97172	−	6.51833i	−0.333662	−	0.242419i
$724$	−2.83113	−	8.71331i	−0.105218	−	0.323828i
$725$	20.0101			0.743157
$726$	23.1937	+	3.21476i	0.860800	+	0.119311i
$727$	−3.87417			−0.143685			−0.0718425	−	0.997416i	$-0.522888\pi$
$727$	−3.87417			−0.143685			−0.0718425	+	0.997416i	$0.522888\pi$
$728$	−0.133677	−	0.411414i	−0.00495439	−	0.0152480i
$729$	−2.21695	−	1.61071i	−0.0821091	−	0.0596558i
$730$	−4.44010	+	3.22592i	−0.164335	+	0.119397i
$731$	18.6211	−	57.3097i	0.688725	−	2.11968i
$732$	−3.13663	+	9.65356i	−0.115933	+	0.356806i
$733$	−18.6740	+	13.5675i	−0.689740	+	0.501125i	−0.876575	−	0.481266i	$-0.840177\pi$
$733$	−18.6740	+	13.5675i	−0.689740	+	0.501125i	0.186835	+	0.982391i	$0.440177\pi$
$734$	3.39444	+	2.46621i	0.125291	+	0.0910294i
$735$	1.85406	+	5.70621i	0.0683880	+	0.210477i
$736$	−6.69536			−0.246794
$737$	2.62016	−	3.12862i	0.0965150	−	0.115244i
$738$	15.7062			0.578152
$739$	−9.21373	−	28.3570i	−0.338933	−	1.04313i	−0.964752	−	0.263160i	$-0.915235\pi$
$739$	−9.21373	−	28.3570i	−0.338933	−	1.04313i	0.625820	−	0.779968i	$-0.284765\pi$
$740$	0.854658	+	0.620946i	0.0314179	+	0.0228264i
$741$	0.915267	−	0.664980i	0.0336232	−	0.0244287i
$742$	−2.34374	+	7.21329i	−0.0860413	+	0.264808i
$743$	0.884905	−	2.72346i	0.0324640	−	0.0999140i	−0.933512	−	0.358547i	$-0.883272\pi$
$743$	0.884905	−	2.72346i	0.0324640	−	0.0999140i	0.965976	+	0.258633i	$0.0832722\pi$
$744$	−9.98991	+	7.25809i	−0.366248	+	0.266095i
$745$	0.449481	+	0.326567i	0.0164677	+	0.0119645i
$746$	9.44828	+	29.0788i	0.345926	+	1.06465i
$747$	−19.7012			−0.720831
$748$	18.0922	+	7.28975i	0.661517	+	0.266540i
$749$	7.02496			0.256687
$750$	−2.86767	−	8.82578i	−0.104712	−	0.322272i
$751$	39.1192	+	28.4218i	1.42748	+	1.03713i	0.990479	+	0.137665i	$0.0439598\pi$
$751$	39.1192	+	28.4218i	1.42748	+	1.03713i	0.437002	+	0.899460i	$0.356040\pi$
$752$	−5.12692	+	3.72493i	−0.186960	+	0.135834i
$753$	8.94561	−	27.5318i	0.325996	−	1.00331i
$754$	0.684339	−	2.10618i	0.0249222	−	0.0767026i
$755$	−4.98432	+	3.62132i	−0.181398	+	0.131793i
$756$	2.05874	+	1.49576i	0.0748758	+	0.0544004i
$757$	7.05841	+	21.7236i	0.256542	+	0.789556i	0.993522	+	0.113641i	$0.0362514\pi$
$757$	7.05841	+	21.7236i	0.256542	+	0.789556i	−0.736980	+	0.675915i	$0.763749\pi$
$758$	−27.9152			−1.01393
$759$	45.8545	−	11.4791i	1.66441	−	0.416663i
$760$	−0.444747			−0.0161327
$761$	7.31760	+	22.5213i	0.265263	+	0.816395i	0.991633	+	0.129091i	$0.0412059\pi$
$761$	7.31760	+	22.5213i	0.265263	+	0.816395i	−0.726370	+	0.687304i	$0.758794\pi$
$762$	9.91110	+	7.20084i	0.359041	+	0.260859i
$763$	−5.33616	+	3.87695i	−0.193182	+	0.140355i
$764$	−4.50017	+	13.8501i	−0.162810	+	0.501079i
$765$	1.23769	−	3.80921i	0.0447487	−	0.137722i
$766$	−10.7869	+	7.83717i	−0.389748	+	0.283168i
$767$	−1.45274	−	1.05548i	−0.0524553	−	0.0381110i
$768$	0.657798	+	2.02449i	0.0237362	+	0.0730526i
$769$	−49.9760			−1.80218			−0.901090	−	0.433633i	$-0.857231\pi$
$769$	−49.9760			−1.80218			−0.901090	+	0.433633i	$0.857231\pi$
$770$	0.0826132	−	1.19777i	0.00297717	−	0.0431645i
$771$	−23.3152			−0.839678
$772$	−0.751094	−	2.31163i	−0.0270325	−	0.0831974i
$773$	27.0838	+	19.6775i	0.974135	+	0.707751i	0.956390	−	0.292092i	$-0.0943513\pi$
$773$	27.0838	+	19.6775i	0.974135	+	0.707751i	0.0177449	+	0.999843i	$0.494351\pi$
$774$	−12.6931	+	9.22210i	−0.456245	+	0.331482i
$775$	8.60828	−	26.4936i	0.309218	−	0.951677i
$776$	4.39716	−	13.5331i	0.157849	−	0.485809i
$777$	−3.32953	+	2.41904i	−0.119446	+	0.0867827i
$778$	−4.85839	−	3.52983i	−0.174182	−	0.126551i
$779$	3.16957	+	9.75492i	0.113562	+	0.349506i
$780$	−0.503157			−0.0180159
$781$	−20.3906	−	32.5629i	−0.729632	−	1.16519i
$782$	39.3765			1.40810
$783$	4.02571	+	12.3899i	0.143867	+	0.442778i
$784$	5.12714	+	3.72509i	0.183112	+	0.133039i
$785$	6.22815	−	4.52502i	0.222292	−	0.161505i
$786$	0.638262	−	1.96437i	0.0227661	−	0.0700667i
$787$	5.18358	−	15.9534i	0.184775	−	0.568678i	−0.815170	−	0.579222i	$-0.803356\pi$
$787$	5.18358	−	15.9534i	0.184775	−	0.568678i	0.999944	+	0.0105440i	$0.00335633\pi$
$788$	8.82209	−	6.40963i	0.314274	−	0.228334i
$789$	−47.9791	−	34.8588i	−1.70810	−	1.24101i
$790$	−0.476892	−	1.46772i	−0.0169670	−	0.0522192i
$791$	3.79508			0.134938
$792$	−2.69537	−	4.30439i	−0.0957757	−	0.152950i
$793$	−2.53426			−0.0899942
$794$	8.56666	+	26.3655i	0.304019	+	0.935676i
$795$	7.13698	+	5.18532i	0.253123	+	0.183904i
$796$	12.3783	−	8.99333i	0.438736	−	0.318760i
$797$	6.82448	−	21.0036i	0.241736	−	0.743985i	−0.754421	−	0.656391i	$-0.772082\pi$
$797$	6.82448	−	21.0036i	0.241736	−	0.743985i	0.996156	−	0.0875942i	$-0.0279179\pi$
$798$	0.535409	−	1.64782i	0.0189533	−	0.0583322i
$799$	30.1522	−	21.9069i	1.06671	−	0.775010i
$800$	−3.88506	−	2.82266i	−0.137358	−	0.0997962i
$801$	3.50236	+	10.7791i	0.123750	+	0.380862i
$802$	−29.1632			−1.02979
$803$	2.81621	−	40.8308i	0.0993819	−	1.44089i
$804$	−2.61919			−0.0923716
$805$	−0.748967	−	2.30508i	−0.0263976	−	0.0812435i
$806$	−2.49420	−	1.81214i	−0.0878545	−	0.0638300i
$807$	−22.2485	+	16.1645i	−0.783185	+	0.569017i
$808$	−1.08313	+	3.33352i	−0.0381042	+	0.117273i
$809$	9.00008	−	27.6994i	0.316426	−	0.973859i	−0.658738	−	0.752373i	$-0.728909\pi$
$809$	9.00008	−	27.6994i	0.316426	−	0.973859i	0.975164	−	0.221486i	$-0.0710907\pi$
$810$	4.04749	−	2.94067i	0.142214	−	0.103325i
$811$	−24.5497	−	17.8364i	−0.862056	−	0.626320i	0.0663874	−	0.997794i	$-0.478853\pi$
$811$	−24.5497	−	17.8364i	−0.862056	−	0.626320i	−0.928444	+	0.371473i	$0.878853\pi$
$812$	−1.04806	−	3.22559i	−0.0367796	−	0.113196i
$813$	17.2551			0.605164
$814$	−7.64222	+	1.91313i	−0.267860	+	0.0670551i
$815$	4.43557			0.155371
$816$	−3.86862	−	11.9064i	−0.135429	−	0.416806i
$817$	−8.28927	−	6.02251i	−0.290005	−	0.210701i
$818$	9.08735	−	6.60235i	0.317732	−	0.230846i
$819$	0.204695	−	0.629988i	0.00715264	−	0.0220136i
$820$	1.40966	−	4.33847i	0.0492273	−	0.151506i
$821$	−5.72340	+	4.15829i	−0.199748	+	0.145125i	−0.683163	−	0.730266i	$-0.739396\pi$
$821$	−5.72340	+	4.15829i	−0.199748	+	0.145125i	0.483415	+	0.875391i	$0.339396\pi$
$822$	3.69712	+	2.68612i	0.128952	+	0.0936891i
$823$	−9.21619	−	28.3645i	−0.321256	−	0.988725i	−0.973102	−	0.230374i	$-0.926005\pi$
$823$	−9.21619	−	28.3645i	−0.321256	−	0.988725i	0.651846	−	0.758351i	$-0.273995\pi$
$824$	−0.694123			−0.0241809
$825$	31.4470	+	12.6707i	1.09484	+	0.441137i
$826$	−2.75006			−0.0956869
$827$	12.5743	+	38.6999i	0.437253	+	1.34573i	0.890760	+	0.454473i	$0.150173\pi$
$827$	12.5743	+	38.6999i	0.437253	+	1.34573i	−0.453507	+	0.891253i	$0.649827\pi$
$828$	−8.29438	−	6.02622i	−0.288250	−	0.209426i
$829$	−11.3922	+	8.27694i	−0.395668	+	0.287470i	−0.767774	−	0.640720i	$-0.778636\pi$
$829$	−11.3922	+	8.27694i	−0.395668	+	0.287470i	0.372106	+	0.928190i	$0.378636\pi$
$830$	−1.76822	+	5.44203i	−0.0613759	+	0.188895i
$831$	15.4343	−	47.5018i	0.535408	−	1.64782i
$832$	−0.429970	+	0.312391i	−0.0149065	+	0.0108302i
$833$	−30.1536	−	21.9078i	−1.04476	−	0.759062i
$834$	6.43863	+	19.8161i	0.222951	+	0.686174i
$835$	−10.1839			−0.352428
$836$	2.12947	−	2.54271i	0.0736493	−	0.0879413i
$837$	18.1361			0.626877
$838$	6.24254	+	19.2126i	0.215645	+	0.663687i
$839$	−40.0321	−	29.0850i	−1.38206	−	1.00413i	−0.996684	−	0.0813688i	$-0.974071\pi$
$839$	−40.0321	−	29.0850i	−1.38206	−	1.00413i	−0.385379	−	0.922759i	$-0.625929\pi$
$840$	−0.623410	+	0.452934i	−0.0215097	+	0.0156277i
$841$	−3.59611	+	11.0677i	−0.124004	+	0.381645i
$842$	3.92674	−	12.0853i	0.135325	−	0.416486i
$843$	24.7479	−	17.9804i	0.852362	−	0.619277i
$844$	4.53947	+	3.29812i	0.156255	+	0.113526i
$845$	1.74783	+	5.37926i	0.0601271	+	0.185052i
$846$	−9.70401			−0.333631
$847$	6.45231	+	6.20728i	0.221704	+	0.213285i
$848$	9.31823			0.319989
$849$	−7.68893	−	23.6641i	−0.263883	−	0.812150i
$850$	22.8487	+	16.6005i	0.783703	+	0.569394i
$851$	−12.8663	+	9.34791i	−0.441051	+	0.320442i
$852$	−7.62003	+	23.4520i	−0.261058	+	0.803453i
$853$	7.31294	−	22.5069i	0.250390	−	0.770622i	−0.744313	−	0.667831i	$-0.767223\pi$
$853$	7.31294	−	22.5069i	0.250390	−	0.770622i	0.994703	−	0.102791i	$-0.0327773\pi$
$854$	−3.13994	+	2.28130i	−0.107447	+	0.0780645i
$855$	−0.550964	−	0.400299i	−0.0188426	−	0.0136899i
$856$	−2.66706	−	8.20838i	−0.0911583	−	0.280557i
$857$	−17.6097			−0.601535			−0.300768	−	0.953697i	$-0.597243\pi$
$857$	−17.6097			−0.601535			−0.300768	+	0.953697i	$0.597243\pi$
$858$	2.40914	−	2.87664i	0.0822467	−	0.0982070i
$859$	35.6398			1.21602			0.608008	−	0.793931i	$-0.291969\pi$
$859$	35.6398			1.21602			0.608008	+	0.793931i	$0.291969\pi$
$860$	1.40817	+	4.33389i	0.0480181	+	0.147785i
$861$	14.3773	+	10.4457i	0.489978	+	0.355990i
$862$	−25.5490	+	18.5624i	−0.870201	+	0.632238i
$863$	9.94672	−	30.6128i	0.338590	−	1.04207i	−0.626336	−	0.779553i	$-0.715446\pi$
$863$	9.94672	−	30.6128i	0.338590	−	1.04207i	0.964926	−	0.262520i	$-0.0845537\pi$
$864$	0.966126	−	2.97343i	0.0328683	−	0.101158i
$865$	−2.78823	+	2.02577i	−0.0948028	+	0.0688782i
$866$	17.1813	+	12.4830i	0.583845	+	0.424188i
$867$	11.5694	+	35.6069i	0.392917	+	1.20927i
$868$	−4.72157			−0.160261
$869$	10.6746	+	4.30104i	0.362112	+	0.145903i
$870$	−3.94487			−0.133743
$871$	−0.202078	−	0.621932i	−0.00684715	−	0.0210734i
$872$	6.55595	+	4.76318i	0.222013	+	0.161302i
$873$	17.6279	−	12.8074i	0.596614	−	0.433465i
$874$	2.06898	−	6.36767i	0.0699843	−	0.215390i
$875$	1.09651	−	3.37471i	0.0370688	−	0.114086i
$876$	−21.2515	+	15.4401i	−0.718022	+	0.521674i
$877$	−23.5808	−	17.1324i	−0.796265	−	0.578521i	0.113551	−	0.993532i	$-0.463778\pi$
$877$	−23.5808	−	17.1324i	−0.796265	−	0.578521i	−0.909816	+	0.415012i	$0.863778\pi$
$878$	−7.16670	−	22.0568i	−0.241864	−	0.744382i
$879$	52.5466			1.77235
$880$	−1.43090	+	0.358208i	−0.0482358	+	0.0120752i
$881$	−17.4611			−0.588279			−0.294139	−	0.955763i	$-0.595033\pi$
$881$	−17.4611			−0.588279			−0.294139	+	0.955763i	$0.595033\pi$
$882$	2.99884	+	9.22947i	0.100976	+	0.310772i
$883$	−8.27556	−	6.01255i	−0.278495	−	0.202338i	0.439766	−	0.898113i	$-0.355061\pi$
$883$	−8.27556	−	6.01255i	−0.278495	−	0.202338i	−0.718261	+	0.695774i	$0.755061\pi$
$884$	2.52872	−	1.83722i	0.0850501	−	0.0617925i
$885$	−0.988451	+	3.04214i	−0.0332264	+	0.102260i
$886$	5.14368	−	15.8306i	0.172805	−	0.531841i
$887$	23.9251	−	17.3826i	0.803326	−	0.583651i	−0.108562	−	0.994090i	$-0.534625\pi$
$887$	23.9251	−	17.3826i	0.803326	−	0.583651i	0.911888	+	0.410439i	$0.134625\pi$
$888$	4.09062	+	2.97201i	0.137272	+	0.0997342i
$889$	1.44754	+	4.45506i	0.0485488	+	0.149418i
$890$	3.29184			0.110343
$891$	−2.56719	+	37.2204i	−0.0860040	+	1.24693i
$892$	−23.9862			−0.803118
$893$	−1.95831	−	6.02706i	−0.0655323	−	0.201688i
$894$	2.15134	+	1.56304i	0.0719515	+	0.0522758i
$895$	4.74185	−	3.44515i	0.158502	−	0.115159i
$896$	−0.251522	+	0.774104i	−0.00840275	+	0.0258610i
$897$	2.34070	−	7.20395i	0.0781538	−	0.240533i
$898$	−1.80698	+	1.31285i	−0.0602996	+	0.0438102i
$899$	−19.5551	−	14.2076i	−0.652200	−	0.473851i
$900$	−2.27235	−	6.99357i	−0.0757450	−	0.233119i
$901$	−54.8020			−1.82572
$902$	18.0544	+	28.8321i	0.601145	+	0.960004i
$903$	−17.7526			−0.590770
$904$	−1.44082	−	4.43439i	−0.0479210	−	0.147486i
$905$	−3.29646	−	2.39502i	−0.109578	−	0.0796131i
$906$	−23.8563	+	17.3326i	−0.792572	+	0.575837i
$907$	−3.64126	+	11.2066i	−0.120906	+	0.372110i	−0.993133	−	0.116991i	$-0.962675\pi$
$907$	−3.64126	+	11.2066i	−0.120906	+	0.372110i	0.872227	+	0.489101i	$0.162675\pi$
$908$	−1.09012	+	3.35505i	−0.0361770	+	0.111341i
$909$	−4.34217	+	3.15477i	−0.144021	+	0.104637i
$910$	−0.155648	−	0.113085i	−0.00515969	−	0.00374873i
$911$	−15.0388	−	46.2847i	−0.498258	−	1.53348i	−0.811818	−	0.583911i	$-0.801522\pi$
$911$	−15.0388	−	46.2847i	−0.498258	−	1.53348i	0.313560	−	0.949568i	$-0.398478\pi$
$912$	−2.12868			−0.0704876
$913$	−22.6468	−	36.1660i	−0.749499	−	1.19692i
$914$	−12.4265			−0.411032
$915$	1.39501	+	4.29339i	0.0461175	+	0.141935i
$916$	15.8339	+	11.5040i	0.523166	+	0.380102i
$917$	0.638936	−	0.464214i	0.0210995	−	0.0153297i
$918$	−5.68194	+	17.4872i	−0.187532	+	0.577164i
$919$	−13.8401	+	42.5953i	−0.456542	+	1.40509i	0.412774	+	0.910833i	$0.364560\pi$
$919$	−13.8401	+	42.5953i	−0.456542	+	1.40509i	−0.869316	+	0.494257i	$0.835440\pi$
$920$	−2.40904	+	1.75027i	−0.0794238	+	0.0577048i
$921$	19.3787	+	14.0794i	0.638550	+	0.463933i
$922$	−9.83131	−	30.2577i	−0.323777	−	0.996483i
$923$	−6.15665			−0.202648
$924$	0.395409	−	5.73283i	0.0130080	−	0.188596i
$925$	−11.4068			−0.375052
$926$	0.0223405	+	0.0687569i	0.000734153	+	0.00225949i
$927$	−0.859897	−	0.624752i	−0.0282427	−	0.0205195i
$928$	−3.37106	+	2.44922i	−0.110661	+	0.0803996i
$929$	12.6548	−	38.9475i	0.415191	−	1.27783i	−0.496889	−	0.867814i	$-0.665524\pi$
$929$	12.6548	−	38.9475i	0.415191	−	1.27783i	0.912080	−	0.410012i	$-0.134476\pi$
$930$	−1.69707	+	5.22304i	−0.0556490	+	0.171270i
$931$	−5.12714	+	3.72509i	−0.168035	+	0.122085i
$932$	−15.5347	−	11.2866i	−0.508855	−	0.369705i
$933$	2.24119	+	6.89767i	0.0733732	+	0.225819i
$934$	33.8105			1.10631
$935$	8.41538	−	2.10668i	0.275212	−	0.0688958i
$936$	−0.813828			−0.0266008
$937$	1.74918	+	5.38343i	0.0571433	+	0.175869i	0.975554	−	0.219759i	$-0.0705270\pi$
$937$	1.74918	+	5.38343i	0.0571433	+	0.175869i	−0.918411	+	0.395628i	$0.870527\pi$
$938$	−0.810228	−	0.588665i	−0.0264549	−	0.0192206i
$939$	−35.5490	+	25.8279i	−1.16010	+	0.842860i
$940$	−0.870952	+	2.68052i	−0.0284073	+	0.0874288i
$941$	−4.46157	+	13.7313i	−0.145443	+	0.447628i	−0.997068	−	0.0765243i	$-0.975618\pi$
$941$	−4.46157	+	13.7313i	−0.145443	+	0.447628i	0.851625	+	0.524152i	$0.175618\pi$
$942$	29.8096	−	21.6579i	0.971249	−	0.705654i
$943$	55.5583	+	40.3655i	1.80923	+	1.31448i
$944$	1.04408	+	3.21333i	0.0339818	+	0.104585i
$945$	1.13177			0.0368164
$946$	−31.5201	−	12.7001i	−1.02481	−	0.412917i
$947$	6.99025			0.227153			0.113576	−	0.993529i	$-0.463769\pi$
$947$	6.99025			0.227153			0.113576	+	0.993529i	$0.463769\pi$
$948$	−2.28253	−	7.02491i	−0.0741332	−	0.228158i
$949$	−5.30591	−	3.85497i	−0.172237	−	0.125138i
$950$	3.88506	−	2.82266i	0.126048	−	0.0915793i
$951$	−17.2358	+	53.0462i	−0.558908	+	1.72014i
$952$	1.47924	−	4.55263i	0.0479424	−	0.147552i
$953$	−13.4794	+	9.79336i	−0.436641	+	0.317238i	−0.784299	−	0.620383i	$-0.786977\pi$
$953$	−13.4794	+	9.79336i	−0.436641	+	0.317238i	0.347658	+	0.937621i	$0.386977\pi$
$954$	11.5437	+	8.38696i	0.373740	+	0.271538i
$955$	2.00144	+	6.15979i	0.0647650	+	0.199326i
$956$	−19.3799			−0.626790
$957$	18.8882	−	22.5536i	0.610570	−	0.729053i
$958$	7.68378			0.248252
$959$	0.539973	+	1.66187i	0.0174366	+	0.0536644i
$960$	0.765915	+	0.556470i	0.0247198	+	0.0179600i
$961$	−2.14404	+	1.55774i	−0.0691626	+	0.0502496i
$962$	−0.390107	+	1.20063i	−0.0125776	+	0.0387098i
$963$	4.08400	−	12.5693i	0.131605	−	0.405039i
$964$	−4.21469	+	3.06215i	−0.135746	+	0.0986252i
$965$	−0.874546	−	0.635395i	−0.0281526	−	0.0204541i
$966$	−3.58476	−	11.0327i	−0.115338	−	0.354973i
$967$	8.50933			0.273642			0.136821	−	0.990596i	$-0.456312\pi$
$967$	8.50933			0.273642			0.136821	+	0.990596i	$0.456312\pi$
$968$	4.80330	−	9.89587i	0.154384	−	0.318065i
$969$	12.5191			0.402172
$970$	−1.95563	−	6.01880i	−0.0627914	−	0.193252i
$971$	15.1071	+	10.9759i	0.484809	+	0.352234i	0.803185	−	0.595730i	$-0.203137\pi$
$971$	15.1071	+	10.9759i	0.484809	+	0.352234i	−0.318376	+	0.947965i	$0.603137\pi$
$972$	11.7843	−	8.56180i	0.377982	−	0.274620i
$973$	−2.46193	+	7.57705i	−0.0789260	+	0.242909i
$974$	9.38432	−	28.8820i	0.300693	−	0.925438i
$975$	4.39530	−	3.19337i	0.140762	−	0.102270i
$976$	3.85770	+	2.80278i	0.123482	+	0.0897149i
$977$	−0.0938749	−	0.288917i	−0.00300333	−	0.00924329i	0.949544	−	0.313635i	$-0.101547\pi$
$977$	−0.0938749	−	0.288917i	−0.00300333	−	0.00924329i	−0.952547	+	0.304392i	$0.901547\pi$
$978$	21.2298			0.678856
$979$	−15.7615	+	18.8201i	−0.503739	+	0.601492i
$980$	2.81858			0.0900364
$981$	3.83454	+	11.8015i	0.122427	+	0.376793i
$982$	8.18301	+	5.94531i	0.261130	+	0.189722i
$983$	−37.1995	+	27.0270i	−1.18648	+	0.862028i	−0.992888	−	0.119054i	$-0.962014\pi$
$983$	−37.1995	+	27.0270i	−1.18648	+	0.862028i	−0.193592	+	0.981082i	$0.562014\pi$
$984$	6.74699	−	20.7651i	0.215086	−	0.661967i
$985$	1.49868	−	4.61247i	0.0477520	−	0.146965i
$986$	19.8258	−	14.4043i	0.631381	−	0.458725i
$987$	−8.88300	−	6.45388i	−0.282749	−	0.205429i
$988$	−0.164234	−	0.505460i	−0.00522497	−	0.0160808i
$989$	−68.6014			−2.18140
$990$	−2.09505	−	0.844141i	−0.0665850	−	0.0268286i
$991$	19.4299			0.617210			0.308605	−	0.951190i	$-0.400138\pi$
$991$	19.4299			0.617210			0.308605	+	0.951190i	$0.400138\pi$
$992$	1.79257	+	5.51696i	0.0569141	+	0.175164i
$993$	−39.2356	−	28.5064i	−1.24511	−	0.904622i
$994$	−7.62807	+	5.54212i	−0.241948	+	0.175785i
$995$	2.10280	−	6.47174i	0.0666631	−	0.205168i
$996$	−8.46318	+	26.0470i	−0.268166	+	0.825331i
$997$	18.2400	−	13.2521i	0.577667	−	0.419699i	−0.260215	−	0.965551i	$-0.583794\pi$
$997$	18.2400	−	13.2521i	0.577667	−	0.419699i	0.837882	+	0.545851i	$0.183794\pi$
$998$	−15.0982	−	10.9695i	−0.477926	−	0.347234i
$999$	−2.29486	−	7.06284i	−0.0726060	−	0.223458i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.f.h.115.1	✓	20
11.3	even	5		4598.2.a.cc.1.9		10
11.8	odd	10		4598.2.a.cd.1.9		10
11.9	even	5	inner	418.2.f.h.229.1	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.f.h.115.1	✓	20	1.1	even	1	trivial
418.2.f.h.229.1	yes	20	11.9	even	5	inner
4598.2.a.cc.1.9		10	11.3	even	5
4598.2.a.cd.1.9		10	11.8	odd	10

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)

\(f(q)\)	\(=\)	\(q+(-0.309017 - 0.951057i) q^{2} +(-1.72214 - 1.25121i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-0.137434 + 0.422980i) q^{5} +(-0.657798 + 2.02449i) q^{6} +(-0.658492 + 0.478423i) q^{7} +(0.809017 + 0.587785i) q^{8} +(0.473189 + 1.45633i) q^{9} +O(q^{10})\)	\(q+(-0.309017 - 0.951057i) q^{2} +(-1.72214 - 1.25121i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-0.137434 + 0.422980i) q^{5} +(-0.657798 + 2.02449i) q^{6} +(-0.658492 + 0.478423i) q^{7} +(0.809017 + 0.587785i) q^{8} +(0.473189 + 1.45633i) q^{9} +0.444747 q^{10} +(-2.12947 + 2.54271i) q^{11} +2.12868 q^{12} +(0.164234 + 0.505460i) q^{13} +(0.658492 + 0.478423i) q^{14} +(0.765915 - 0.556470i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-1.81738 + 5.59332i) q^{17} +(1.23883 - 0.900059i) q^{18} +(0.809017 + 0.587785i) q^{19} +(-0.137434 - 0.422980i) q^{20} +1.73262 q^{21} +(3.07630 + 1.23951i) q^{22} +6.69536 q^{23} +(-0.657798 - 2.02449i) q^{24} +(3.88506 + 2.82266i) q^{25} +(0.429970 - 0.312391i) q^{26} +(-0.966126 + 2.97343i) q^{27} +(0.251522 - 0.774104i) q^{28} +(3.37106 - 2.44922i) q^{29} +(-0.765915 - 0.556470i) q^{30} +(-1.79257 - 5.51696i) q^{31} -1.00000 q^{32} +(6.84869 - 1.71448i) q^{33} +5.88116 q^{34} +(-0.111864 - 0.344281i) q^{35} +(-1.23883 - 0.900059i) q^{36} +(-1.92167 + 1.39618i) q^{37} +(0.309017 - 0.951057i) q^{38} +(0.349601 - 1.07596i) q^{39} +(-0.359808 + 0.261416i) q^{40} +(8.29803 + 6.02887i) q^{41} +(-0.535409 - 1.64782i) q^{42} -10.2461 q^{43} +(0.228214 - 3.30876i) q^{44} -0.681029 q^{45} +(-2.06898 - 6.36767i) q^{46} +(-5.12692 - 3.72493i) q^{47} +(-1.72214 + 1.25121i) q^{48} +(-1.95839 + 6.02732i) q^{49} +(1.48396 - 4.56716i) q^{50} +(10.1282 - 7.35854i) q^{51} +(-0.429970 - 0.312391i) q^{52} +(2.87949 + 8.86217i) q^{53} +3.12645 q^{54} +(-0.782850 - 1.25018i) q^{55} -0.813941 q^{56} +(-0.657798 - 2.02449i) q^{57} +(-3.37106 - 2.44922i) q^{58} +(-2.73342 + 1.98595i) q^{59} +(-0.292554 + 0.900388i) q^{60} +(-1.47351 + 4.53500i) q^{61} +(-4.69301 + 3.40967i) q^{62} +(-1.00833 - 0.732596i) q^{63} +(0.309017 + 0.951057i) q^{64} -0.236370 q^{65} +(-3.74693 - 5.98369i) q^{66} -1.23043 q^{67} +(-1.81738 - 5.59332i) q^{68} +(-11.5303 - 8.37728i) q^{69} +(-0.292863 + 0.212777i) q^{70} +(-3.57970 + 11.0172i) q^{71} +(-0.473189 + 1.45633i) q^{72} +(-9.98343 + 7.25339i) q^{73} +(1.92167 + 1.39618i) q^{74} +(-3.15888 - 9.72202i) q^{75} -1.00000 q^{76} +(0.185753 - 2.69314i) q^{77} -1.13133 q^{78} +(-1.07228 - 3.30013i) q^{79} +(0.359808 + 0.261416i) q^{80} +(9.10065 - 6.61201i) q^{81} +(3.16957 - 9.75492i) q^{82} +(-3.97579 + 12.2362i) q^{83} +(-1.40172 + 1.01841i) q^{84} +(-2.11609 - 1.53743i) q^{85} +(3.16622 + 9.74463i) q^{86} -8.86991 q^{87} +(-3.21734 + 0.805420i) q^{88} +7.40160 q^{89} +(0.210449 + 0.647697i) q^{90} +(-0.349970 - 0.254268i) q^{91} +(-5.41666 + 3.93543i) q^{92} +(-3.81580 + 11.7438i) q^{93} +(-1.95831 + 6.02706i) q^{94} +(-0.359808 + 0.261416i) q^{95} +(1.72214 + 1.25121i) q^{96} +(-4.39716 - 13.5331i) q^{97} +6.33750 q^{98} +(-4.71065 - 1.89803i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 5 q^{2} - q^{3} - 5 q^{4} - q^{5} + q^{6} + 13 q^{7} + 5 q^{8} - 6 q^{9}+O(q^{10}) \) 20 * q + 5 * q^2 - q^3 - 5 * q^4 - q^5 + q^6 + 13 * q^7 + 5 * q^8 - 6 * q^9	\( 20 q + 5 q^{2} - q^{3} - 5 q^{4} - q^{5} + q^{6} + 13 q^{7} + 5 q^{8} - 6 q^{9} + 6 q^{10} + q^{11} + 4 q^{12} - 2 q^{13} - 13 q^{14} - 8 q^{15} - 5 q^{16} + 11 q^{17} + 6 q^{18} + 5 q^{19} - q^{20} + 2 q^{21} + 4 q^{22} + 28 q^{23} + q^{24} - 30 q^{25} - 13 q^{26} - 31 q^{27} - 2 q^{28} + 28 q^{29} + 8 q^{30} - q^{31} - 20 q^{32} + 9 q^{33} + 24 q^{34} - 11 q^{35} - 6 q^{36} + 8 q^{37} - 5 q^{38} + 18 q^{39} - 4 q^{40} - 5 q^{41} - 22 q^{42} - 44 q^{43} + 11 q^{44} - 4 q^{45} + 7 q^{46} - 39 q^{47} - q^{48} + 4 q^{49} - 25 q^{50} - 11 q^{51} + 13 q^{52} - q^{53} - 4 q^{54} + 8 q^{55} + 22 q^{56} + q^{57} - 28 q^{58} + 6 q^{59} + 7 q^{60} + 10 q^{61} + 11 q^{62} + 34 q^{63} - 5 q^{64} - 8 q^{65} + 41 q^{66} + 18 q^{67} + 11 q^{68} - 63 q^{69} + q^{70} - 3 q^{71} + 6 q^{72} + 5 q^{73} - 8 q^{74} + 5 q^{75} - 20 q^{76} + 36 q^{77} + 22 q^{78} + 19 q^{79} + 4 q^{80} + 63 q^{81} - 9 q^{83} - 23 q^{84} + 30 q^{85} - 26 q^{86} - 16 q^{87} - q^{88} + 44 q^{89} + 14 q^{90} - 68 q^{91} - 7 q^{92} + 27 q^{93} - 31 q^{94} - 4 q^{95} + q^{96} - 71 q^{97} + 6 q^{98} + 20 q^{99}+O(q^{100}) \) 20 * q + 5 * q^2 - q^3 - 5 * q^4 - q^5 + q^6 + 13 * q^7 + 5 * q^8 - 6 * q^9 + 6 * q^10 + q^11 + 4 * q^12 - 2 * q^13 - 13 * q^14 - 8 * q^15 - 5 * q^16 + 11 * q^17 + 6 * q^18 + 5 * q^19 - q^20 + 2 * q^21 + 4 * q^22 + 28 * q^23 + q^24 - 30 * q^25 - 13 * q^26 - 31 * q^27 - 2 * q^28 + 28 * q^29 + 8 * q^30 - q^31 - 20 * q^32 + 9 * q^33 + 24 * q^34 - 11 * q^35 - 6 * q^36 + 8 * q^37 - 5 * q^38 + 18 * q^39 - 4 * q^40 - 5 * q^41 - 22 * q^42 - 44 * q^43 + 11 * q^44 - 4 * q^45 + 7 * q^46 - 39 * q^47 - q^48 + 4 * q^49 - 25 * q^50 - 11 * q^51 + 13 * q^52 - q^53 - 4 * q^54 + 8 * q^55 + 22 * q^56 + q^57 - 28 * q^58 + 6 * q^59 + 7 * q^60 + 10 * q^61 + 11 * q^62 + 34 * q^63 - 5 * q^64 - 8 * q^65 + 41 * q^66 + 18 * q^67 + 11 * q^68 - 63 * q^69 + q^70 - 3 * q^71 + 6 * q^72 + 5 * q^73 - 8 * q^74 + 5 * q^75 - 20 * q^76 + 36 * q^77 + 22 * q^78 + 19 * q^79 + 4 * q^80 + 63 * q^81 - 9 * q^83 - 23 * q^84 + 30 * q^85 - 26 * q^86 - 16 * q^87 - q^88 + 44 * q^89 + 14 * q^90 - 68 * q^91 - 7 * q^92 + 27 * q^93 - 31 * q^94 - 4 * q^95 + q^96 - 71 * q^97 + 6 * q^98 + 20 * q^99

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