LMFDB - Embedded newform 315.2.k.b.16.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(16,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0, 2]))

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

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

chi := DirichletCharacter("315.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.k (of order $3$, 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:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			16.5
Character	$\chi$	$=$	315.16
Dual form			315.2.k.b.256.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.259245 - 0.449026i) q^{2} +(-1.70948 + 0.278682i) q^{3} +(0.865584 - 1.49923i) q^{4} -1.00000 q^{5} +(0.568312 + 0.695356i) q^{6} +(-1.91816 + 1.82226i) q^{7} -1.93458 q^{8} +(2.84467 - 0.952806i) q^{9} +O(q^{10})$	\(q+(-0.259245 - 0.449026i) q^{2} +(-1.70948 + 0.278682i) q^{3} +(0.865584 - 1.49923i) q^{4} -1.00000 q^{5} +(0.568312 + 0.695356i) q^{6} +(-1.91816 + 1.82226i) q^{7} -1.93458 q^{8} +(2.84467 - 0.952806i) q^{9} +(0.259245 + 0.449026i) q^{10} -4.16739 q^{11} +(-1.06189 + 2.80414i) q^{12} +(2.27115 + 3.93375i) q^{13} +(1.31552 + 0.388893i) q^{14} +(1.70948 - 0.278682i) q^{15} +(-1.22964 - 2.12979i) q^{16} +(1.39573 + 2.41747i) q^{17} +(-1.16530 - 1.03032i) q^{18} +(-2.22814 + 3.85926i) q^{19} +(-0.865584 + 1.49923i) q^{20} +(2.77124 - 3.64969i) q^{21} +(1.08038 + 1.87127i) q^{22} -5.45501 q^{23} +(3.30713 - 0.539132i) q^{24} +1.00000 q^{25} +(1.17757 - 2.03961i) q^{26} +(-4.59739 + 2.42157i) q^{27} +(1.07167 + 4.45310i) q^{28} +(-2.18145 + 3.77837i) q^{29} +(-0.568312 - 0.695356i) q^{30} +(0.859688 - 1.48902i) q^{31} +(-2.57213 + 4.45506i) q^{32} +(7.12409 - 1.16138i) q^{33} +(0.723673 - 1.25344i) q^{34} +(1.91816 - 1.82226i) q^{35} +(1.03382 - 5.08956i) q^{36} +(-4.66225 + 8.07525i) q^{37} +2.31054 q^{38} +(-4.97876 - 6.09175i) q^{39} +1.93458 q^{40} +(0.217468 + 0.376665i) q^{41} +(-2.35724 - 0.298194i) q^{42} +(5.19296 - 8.99448i) q^{43} +(-3.60723 + 6.24790i) q^{44} +(-2.84467 + 0.952806i) q^{45} +(1.41419 + 2.44944i) q^{46} +(-3.75093 - 6.49681i) q^{47} +(2.69558 + 3.29817i) q^{48} +(0.358708 - 6.99080i) q^{49} +(-0.259245 - 0.449026i) q^{50} +(-3.05968 - 3.74367i) q^{51} +7.86348 q^{52} +(-4.17271 - 7.22734i) q^{53} +(2.27920 + 1.43657i) q^{54} +4.16739 q^{55} +(3.71084 - 3.52531i) q^{56} +(2.73347 - 7.21828i) q^{57} +2.26212 q^{58} +(-5.37076 + 9.30243i) q^{59} +(1.06189 - 2.80414i) q^{60} +(-2.05517 - 3.55966i) q^{61} -0.891481 q^{62} +(-3.72028 + 7.01138i) q^{63} -2.25129 q^{64} +(-2.27115 - 3.93375i) q^{65} +(-2.36838 - 2.89782i) q^{66} +(3.77921 - 6.54578i) q^{67} +4.83248 q^{68} +(9.32525 - 1.52022i) q^{69} +(-1.31552 - 0.388893i) q^{70} +15.1001 q^{71} +(-5.50324 + 1.84328i) q^{72} +(-1.11154 - 1.92524i) q^{73} +4.83467 q^{74} +(-1.70948 + 0.278682i) q^{75} +(3.85729 + 6.68102i) q^{76} +(7.99374 - 7.59409i) q^{77} +(-1.44463 + 3.81485i) q^{78} +(-0.495933 - 0.858981i) q^{79} +(1.22964 + 2.12979i) q^{80} +(7.18432 - 5.42084i) q^{81} +(0.112755 - 0.195298i) q^{82} +(0.763861 - 1.32305i) q^{83} +(-3.07300 - 7.31385i) q^{84} +(-1.39573 - 2.41747i) q^{85} -5.38501 q^{86} +(2.67618 - 7.06700i) q^{87} +8.06214 q^{88} +(1.04124 - 1.80348i) q^{89} +(1.16530 + 1.03032i) q^{90} +(-11.5248 - 3.40694i) q^{91} +(-4.72177 + 8.17834i) q^{92} +(-1.05466 + 2.78504i) q^{93} +(-1.94482 + 3.36853i) q^{94} +(2.22814 - 3.85926i) q^{95} +(3.15547 - 8.33267i) q^{96} +(-8.43928 + 14.6173i) q^{97} +(-3.23205 + 1.65126i) q^{98} +(-11.8549 + 3.97072i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - q^{2} + q^{3} - 7 q^{4} - 24 q^{5} + 3 q^{6} + 7 q^{7} + 12 q^{8} + 9 q^{9}+O(q^{10}) $ 24 * q - q^2 + q^3 - 7 * q^4 - 24 * q^5 + 3 * q^6 + 7 * q^7 + 12 * q^8 + 9 * q^9	\( 24 q - q^{2} + q^{3} - 7 q^{4} - 24 q^{5} + 3 q^{6} + 7 q^{7} + 12 q^{8} + 9 q^{9} + q^{10} - 2 q^{11} - 16 q^{12} - 4 q^{13} - 13 q^{14} - q^{15} - 5 q^{16} - 7 q^{17} - 12 q^{18} - 2 q^{19} + 7 q^{20} - 5 q^{21} + 19 q^{22} - 2 q^{23} - 30 q^{24} + 24 q^{25} + 11 q^{26} - 11 q^{27} - 28 q^{28} - 3 q^{30} + 8 q^{31} + 17 q^{32} + q^{33} + q^{34} - 7 q^{35} - 25 q^{36} + 17 q^{37} + 70 q^{38} - 8 q^{39} - 12 q^{40} + 20 q^{41} - 15 q^{42} + 31 q^{43} - 7 q^{44} - 9 q^{45} - 10 q^{46} - 31 q^{47} - 36 q^{48} - 11 q^{49} - q^{50} - 37 q^{51} + 8 q^{52} + 8 q^{53} + 111 q^{54} + 2 q^{55} + 45 q^{56} + 5 q^{57} - 90 q^{58} - 21 q^{59} + 16 q^{60} + 5 q^{61} + 14 q^{62} - 9 q^{63} - 56 q^{64} + 4 q^{65} + 46 q^{66} + 43 q^{67} + 96 q^{68} + 26 q^{69} + 13 q^{70} + 24 q^{71} - 69 q^{72} - 18 q^{73} - 18 q^{74} + q^{75} - 13 q^{76} + 5 q^{77} + 19 q^{78} + 40 q^{79} + 5 q^{80} - 39 q^{81} + 5 q^{82} - 60 q^{83} + 47 q^{84} + 7 q^{85} - 24 q^{86} - 61 q^{87} - 100 q^{88} - 4 q^{89} + 12 q^{90} - 33 q^{91} - 18 q^{92} - 8 q^{93} - 11 q^{94} + 2 q^{95} + 6 q^{96} + 6 q^{97} - 15 q^{98} - q^{99}+O(q^{100}) \) 24 * q - q^2 + q^3 - 7 * q^4 - 24 * q^5 + 3 * q^6 + 7 * q^7 + 12 * q^8 + 9 * q^9 + q^10 - 2 * q^11 - 16 * q^12 - 4 * q^13 - 13 * q^14 - q^15 - 5 * q^16 - 7 * q^17 - 12 * q^18 - 2 * q^19 + 7 * q^20 - 5 * q^21 + 19 * q^22 - 2 * q^23 - 30 * q^24 + 24 * q^25 + 11 * q^26 - 11 * q^27 - 28 * q^28 - 3 * q^30 + 8 * q^31 + 17 * q^32 + q^33 + q^34 - 7 * q^35 - 25 * q^36 + 17 * q^37 + 70 * q^38 - 8 * q^39 - 12 * q^40 + 20 * q^41 - 15 * q^42 + 31 * q^43 - 7 * q^44 - 9 * q^45 - 10 * q^46 - 31 * q^47 - 36 * q^48 - 11 * q^49 - q^50 - 37 * q^51 + 8 * q^52 + 8 * q^53 + 111 * q^54 + 2 * q^55 + 45 * q^56 + 5 * q^57 - 90 * q^58 - 21 * q^59 + 16 * q^60 + 5 * q^61 + 14 * q^62 - 9 * q^63 - 56 * q^64 + 4 * q^65 + 46 * q^66 + 43 * q^67 + 96 * q^68 + 26 * q^69 + 13 * q^70 + 24 * q^71 - 69 * q^72 - 18 * q^73 - 18 * q^74 + q^75 - 13 * q^76 + 5 * q^77 + 19 * q^78 + 40 * q^79 + 5 * q^80 - 39 * q^81 + 5 * q^82 - 60 * q^83 + 47 * q^84 + 7 * q^85 - 24 * q^86 - 61 * q^87 - 100 * q^88 - 4 * q^89 + 12 * q^90 - 33 * q^91 - 18 * q^92 - 8 * q^93 - 11 * q^94 + 2 * q^95 + 6 * q^96 + 6 * q^97 - 15 * q^98 - q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.259245	−	0.449026i	−0.183314	−	0.317510i	0.759693	−	0.650282i	$-0.225349\pi$
$2$	−0.259245	−	0.449026i	−0.183314	−	0.317510i	−0.943007	+	0.332772i	$0.892016\pi$
$3$	−1.70948	+	0.278682i	−0.986971	+	0.160897i
$3$	−1.70948	+	0.278682i	−0.986971	+	0.160897i
$4$	0.865584	−	1.49923i	0.432792	−	0.749617i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	0.568312	+	0.695356i	0.232012	+	0.283878i
$7$	−1.91816	+	1.82226i	−0.724998	+	0.688751i
$7$	−1.91816	+	1.82226i	−0.724998	+	0.688751i
$8$	−1.93458			−0.683976
$9$	2.84467	−	0.952806i	0.948224	−	0.317602i
$10$	0.259245	+	0.449026i	0.0819806	+	0.141995i
$11$	−4.16739			−1.25652			−0.628258	−	0.778005i	$-0.716232\pi$
$11$	−4.16739			−1.25652			−0.628258	+	0.778005i	$0.716232\pi$
$12$	−1.06189	+	2.80414i	−0.306542	+	0.809486i
$13$	2.27115	+	3.93375i	0.629904	+	1.09103i	0.987571	+	0.157176i	$0.0502390\pi$
$13$	2.27115	+	3.93375i	0.629904	+	1.09103i	−0.357667	+	0.933849i	$0.616428\pi$
$14$	1.31552	+	0.388893i	0.351588	+	0.103936i
$15$	1.70948	−	0.278682i	0.441387	−	0.0719555i
$16$	−1.22964	−	2.12979i	−0.307409	−	0.532448i
$17$	1.39573	+	2.41747i	0.338514	+	0.586323i	0.984153	−	0.177319i	$-0.0567425\pi$
$17$	1.39573	+	2.41747i	0.338514	+	0.586323i	−0.645640	+	0.763642i	$0.723409\pi$
$18$	−1.16530	−	1.03032i	−0.274665	−	0.242849i
$19$	−2.22814	+	3.85926i	−0.511171	+	0.885374i	0.488745	+	0.872427i	$0.337455\pi$
$19$	−2.22814	+	3.85926i	−0.511171	+	0.885374i	−0.999916	+	0.0129475i	$0.995879\pi$
$20$	−0.865584	+	1.49923i	−0.193550	+	0.335239i
$21$	2.77124	−	3.64969i	0.604734	−	0.796428i
$22$	1.08038	+	1.87127i	0.230337	+	0.398956i
$23$	−5.45501			−1.13745			−0.568724	−	0.822528i	$-0.692563\pi$
$23$	−5.45501			−1.13745			−0.568724	+	0.822528i	$0.692563\pi$
$24$	3.30713	−	0.539132i	0.675065	−	0.110050i
$25$	1.00000			0.200000
$26$	1.17757	−	2.03961i	0.230941	−	0.400001i
$27$	−4.59739	+	2.42157i	−0.884768	+	0.466031i
$28$	1.07167	+	4.45310i	0.202527	+	0.841557i
$29$	−2.18145	+	3.77837i	−0.405084	+	0.701627i	−0.994331	−	0.106326i	$-0.966091\pi$
$29$	−2.18145	+	3.77837i	−0.405084	+	0.701627i	0.589247	+	0.807953i	$0.299424\pi$
$30$	−0.568312	−	0.695356i	−0.103759	−	0.126954i
$31$	0.859688	−	1.48902i	0.154405	−	0.267437i	−0.778437	−	0.627722i	$-0.783987\pi$
$31$	0.859688	−	1.48902i	0.154405	−	0.267437i	0.932842	+	0.360286i	$0.117321\pi$
$32$	−2.57213	+	4.45506i	−0.454693	+	0.787551i
$33$	7.12409	−	1.16138i	1.24014	−	0.202170i
$34$	0.723673	−	1.25344i	0.124109	−	0.214963i
$35$	1.91816	−	1.82226i	0.324229	−	0.308019i
$36$	1.03382	−	5.08956i	0.172304	−	0.848261i
$37$	−4.66225	+	8.07525i	−0.766469	+	1.32756i	0.172998	+	0.984922i	$0.444655\pi$
$37$	−4.66225	+	8.07525i	−0.766469	+	1.32756i	−0.939466	+	0.342641i	$0.888679\pi$
$38$	2.31054			0.374820
$39$	−4.97876	−	6.09175i	−0.797240	−	0.975460i
$40$	1.93458			0.305883
$41$	0.217468	+	0.376665i	0.0339628	+	0.0588253i	0.882507	−	0.470299i	$-0.155854\pi$
$41$	0.217468	+	0.376665i	0.0339628	+	0.0588253i	−0.848544	+	0.529124i	$0.822521\pi$
$42$	−2.35724	−	0.298194i	−0.363730	−	0.0460123i
$43$	5.19296	−	8.99448i	0.791920	−	1.37165i	−0.132857	−	0.991135i	$-0.542415\pi$
$43$	5.19296	−	8.99448i	0.791920	−	1.37165i	0.924777	−	0.380510i	$-0.124252\pi$
$44$	−3.60723	+	6.24790i	−0.543810	+	0.941906i
$45$	−2.84467	+	0.952806i	−0.424059	+	0.142036i
$46$	1.41419	+	2.44944i	0.208510	+	0.361151i
$47$	−3.75093	−	6.49681i	−0.547130	−	0.947656i	−0.998470	−	0.0553043i	$-0.982387\pi$
$47$	−3.75093	−	6.49681i	−0.547130	−	0.947656i	0.451340	−	0.892352i	$-0.350946\pi$
$48$	2.69558	+	3.29817i	0.389074	+	0.476050i
$49$	0.358708	−	6.99080i	0.0512441	−	0.998686i
$50$	−0.259245	−	0.449026i	−0.0366628	−	0.0635019i
$51$	−3.05968	−	3.74367i	−0.428441	−	0.524218i
$52$	7.86348			1.09047
$53$	−4.17271	−	7.22734i	−0.573165	−	0.992751i	−0.996238	−	0.0866556i	$-0.972382\pi$
$53$	−4.17271	−	7.22734i	−0.573165	−	0.992751i	0.423073	−	0.906096i	$-0.360951\pi$
$54$	2.27920	+	1.43657i	0.310160	+	0.195492i
$55$	4.16739			0.561931
$56$	3.71084	−	3.52531i	0.495881	−	0.471089i
$57$	2.73347	−	7.21828i	0.362057	−	0.956085i
$58$	2.26212			0.297031
$59$	−5.37076	+	9.30243i	−0.699214	+	1.21107i	0.269526	+	0.962993i	$0.413133\pi$
$59$	−5.37076	+	9.30243i	−0.699214	+	1.21107i	−0.968739	+	0.248080i	$0.920200\pi$
$60$	1.06189	−	2.80414i	0.137090	−	0.362013i
$61$	−2.05517	−	3.55966i	−0.263137	−	0.455767i	0.703937	−	0.710263i	$-0.251424\pi$
$61$	−2.05517	−	3.55966i	−0.263137	−	0.455767i	−0.967074	+	0.254496i	$0.918091\pi$
$62$	−0.891481			−0.113218
$63$	−3.72028	+	7.01138i	−0.468712	+	0.883351i
$64$	−2.25129			−0.281412
$65$	−2.27115	−	3.93375i	−0.281701	−	0.487921i
$66$	−2.36838	−	2.89782i	−0.291527	−	0.356697i
$67$	3.77921	−	6.54578i	0.461703	−	0.799694i	−0.537343	−	0.843364i	$-0.680572\pi$
$67$	3.77921	−	6.54578i	0.461703	−	0.799694i	0.999046	+	0.0436703i	$0.0139051\pi$
$68$	4.83248			0.586024
$69$	9.32525	−	1.52022i	1.12263	−	0.183012i
$70$	−1.31552	−	0.388893i	−0.157235	−	0.0464816i
$71$	15.1001			1.79205			0.896026	−	0.444003i	$-0.146442\pi$
$71$	15.1001			1.79205			0.896026	+	0.444003i	$0.146442\pi$
$72$	−5.50324	+	1.84328i	−0.648563	+	0.217232i
$73$	−1.11154	−	1.92524i	−0.130096	−	0.225332i	0.793618	−	0.608417i	$-0.208195\pi$
$73$	−1.11154	−	1.92524i	−0.130096	−	0.225332i	−0.923713	+	0.383085i	$0.874862\pi$
$74$	4.83467			0.562019
$75$	−1.70948	+	0.278682i	−0.197394	+	0.0321795i
$76$	3.85729	+	6.68102i	0.442461	+	0.766365i
$77$	7.99374	−	7.59409i	0.910971	−	0.865427i
$78$	−1.44463	+	3.81485i	−0.163573	+	0.431947i
$79$	−0.495933	−	0.858981i	−0.0557968	−	0.0966430i	0.836778	−	0.547543i	$-0.184437\pi$
$79$	−0.495933	−	0.858981i	−0.0557968	−	0.0966430i	−0.892575	+	0.450900i	$0.851103\pi$
$80$	1.22964	+	2.12979i	0.137478	+	0.238118i
$81$	7.18432	−	5.42084i	0.798258	−	0.602316i
$82$	0.112755	−	0.195298i	0.0124517	−	0.0215670i
$83$	0.763861	−	1.32305i	0.0838446	−	0.145223i	−0.821054	−	0.570851i	$-0.806613\pi$
$83$	0.763861	−	1.32305i	0.0838446	−	0.145223i	0.904898	+	0.425628i	$0.139947\pi$
$84$	−3.07300	−	7.31385i	−0.335292	−	0.798006i
$85$	−1.39573	−	2.41747i	−0.151388	−	0.262212i
$86$	−5.38501			−0.580681
$87$	2.67618	−	7.06700i	0.286917	−	0.757662i
$88$	8.06214			0.859427
$89$	1.04124	−	1.80348i	0.110371	−	0.191168i	−0.805549	−	0.592529i	$-0.798129\pi$
$89$	1.04124	−	1.80348i	0.110371	−	0.191168i	0.915920	+	0.401361i	$0.131463\pi$
$90$	1.16530	+	1.03032i	0.122834	+	0.108605i
$91$	−11.5248	−	3.40694i	−1.20812	−	0.357144i
$92$	−4.72177	+	8.17834i	−0.492278	+	0.852651i
$93$	−1.05466	+	2.78504i	−0.109363	+	0.288795i
$94$	−1.94482	+	3.36853i	−0.200593	+	0.347438i
$95$	2.22814	−	3.85926i	0.228603	−	0.395951i
$96$	3.15547	−	8.33267i	0.322054	−	0.850449i
$97$	−8.43928	+	14.6173i	−0.856879	+	1.48416i	0.0180116	+	0.999838i	$0.494266\pi$
$97$	−8.43928	+	14.6173i	−0.856879	+	1.48416i	−0.874891	+	0.484320i	$0.839067\pi$
$98$	−3.23205	+	1.65126i	−0.326486	+	0.166803i
$99$	−11.8549	+	3.97072i	−1.19146	+	0.399072i
$100$	0.865584	−	1.49923i	0.0865584	−	0.149923i
$101$	−7.86956			−0.783051			−0.391525	−	0.920167i	$-0.628052\pi$
$101$	−7.86956			−0.783051			−0.391525	+	0.920167i	$0.628052\pi$
$102$	−0.887796	+	2.34441i	−0.0879049	+	0.232131i
$103$	−16.4545			−1.62131			−0.810656	−	0.585523i	$-0.800889\pi$
$103$	−16.4545			−1.62131			−0.810656	+	0.585523i	$0.800889\pi$
$104$	−4.39371	−	7.61013i	−0.430839	−	0.746235i
$105$	−2.77124	+	3.64969i	−0.270445	+	0.356173i
$106$	−2.16351	+	3.74731i	−0.210139	+	0.363971i
$107$	−4.53367	+	7.85255i	−0.438286	+	0.759134i	−0.997557	−	0.0698504i	$-0.977748\pi$
$107$	−4.53367	+	7.85255i	−0.438286	+	0.759134i	0.559271	+	0.828985i	$0.311081\pi$
$108$	−0.348930	+	8.98864i	−0.0335758	+	0.864932i
$109$	5.37447	+	9.30885i	0.514780	+	0.891626i	0.999853	+	0.0171519i	$0.00545990\pi$
$109$	5.37447	+	9.30885i	0.514780	+	0.891626i	−0.485072	+	0.874474i	$0.661207\pi$
$110$	−1.08038	−	1.87127i	−0.103010	−	0.178418i
$111$	5.71961	−	15.1038i	0.542881	−	1.43359i
$112$	6.23969	+	1.84457i	0.589595	+	0.174296i
$113$	−4.68431	−	8.11346i	−0.440663	−	0.763250i	0.557076	−	0.830461i	$-0.311923\pi$
$113$	−4.68431	−	8.11346i	−0.440663	−	0.763250i	−0.997739	+	0.0672113i	$0.978590\pi$
$114$	−3.94984	+	0.643908i	−0.369936	+	0.0603075i
$115$	5.45501			0.508682
$116$	3.77645	+	6.54100i	0.350634	+	0.607316i
$117$	10.2088	+	9.02626i	0.943802	+	0.834478i
$118$	5.56938			0.512703
$119$	−7.08251	−	2.09372i	−0.649252	−	0.191931i
$120$	−3.30713	+	0.539132i	−0.301898	+	0.0492158i
$121$	6.36715			0.578832
$122$	−1.06559	+	1.84565i	−0.0964736	+	0.167097i
$123$	−0.476728	−	0.583299i	−0.0429851	−	0.0525943i
$124$	−1.48826	−	2.57775i	−0.133650	−	0.231489i
$125$	−1.00000			−0.0894427
$126$	4.11276	−	0.147163i	0.366394	−	0.0131104i
$127$	−4.33358			−0.384543			−0.192271	−	0.981342i	$-0.561585\pi$
$127$	−4.33358			−0.384543			−0.192271	+	0.981342i	$0.561585\pi$
$128$	5.72790	+	9.92102i	0.506280	+	0.876902i
$129$	−6.37069	+	16.8231i	−0.560908	+	1.48119i
$130$	−1.17757	+	2.03961i	−0.103280	+	0.178886i
$131$	9.92896			0.867498			0.433749	−	0.901034i	$-0.357191\pi$
$131$	9.92896			0.867498			0.433749	+	0.901034i	$0.357191\pi$
$132$	4.42532	−	11.6860i	0.385174	−	1.01713i
$133$	−2.75864	−	11.4630i	−0.239204	−	0.993964i
$134$	−3.91897			−0.338547
$135$	4.59739	−	2.42157i	0.395681	−	0.208415i
$136$	−2.70014	−	4.67679i	−0.231535	−	0.401031i
$137$	7.20522			0.615583			0.307792	−	0.951454i	$-0.400410\pi$
$137$	7.20522			0.615583			0.307792	+	0.951454i	$0.400410\pi$
$138$	−3.10015	−	3.79318i	−0.263902	−	0.322897i
$139$	7.04875	+	12.2088i	0.597868	+	1.03554i	0.993135	+	0.116971i	$0.0373185\pi$
$139$	7.04875	+	12.2088i	0.597868	+	1.03554i	−0.395268	+	0.918566i	$0.629348\pi$
$140$	−1.07167	−	4.45310i	−0.0905726	−	0.376356i
$141$	8.22270	+	10.0609i	0.692477	+	0.847278i
$142$	−3.91463	−	6.78034i	−0.328508	−	0.568993i
$143$	−9.46477	−	16.3935i	−0.791484	−	1.37089i
$144$	−5.52719	−	4.88696i	−0.460600	−	0.407247i
$145$	2.18145	−	3.77837i	0.181159	−	0.313777i
$146$	−0.576322	+	0.998219i	−0.0476967	+	0.0826132i
$147$	1.33501	+	12.0506i	0.110110	+	0.993919i
$148$	8.07113	+	13.9796i	0.663443	+	1.14912i
$149$	7.18954			0.588990			0.294495	−	0.955653i	$-0.404849\pi$
$149$	7.18954			0.588990			0.294495	+	0.955653i	$0.404849\pi$
$150$	0.568312	+	0.695356i	0.0464025	+	0.0567756i
$151$	−9.83779			−0.800588			−0.400294	−	0.916387i	$-0.631092\pi$
$151$	−9.83779			−0.800588			−0.400294	+	0.916387i	$0.631092\pi$
$152$	4.31051	−	7.46603i	0.349629	−	0.605575i
$153$	6.27377	+	5.54706i	0.507204	+	0.448453i
$154$	−5.48229	−	1.62067i	−0.441775	−	0.130597i
$155$	−0.859688	+	1.48902i	−0.0690518	+	0.119601i
$156$	−13.4425	+	2.19141i	−1.07626	+	0.175453i
$157$	−5.12162	+	8.87090i	−0.408750	+	0.707975i	−0.994750	−	0.102336i	$-0.967368\pi$
$157$	−5.12162	+	8.87090i	−0.408750	+	0.707975i	0.586000	+	0.810311i	$0.300702\pi$
$158$	−0.257137	+	0.445374i	−0.0204567	+	0.0354321i
$159$	9.14731	+	11.1922i	0.725428	+	0.887596i
$160$	2.57213	−	4.45506i	0.203345	−	0.352204i
$161$	10.4636	−	9.94047i	0.824648	−	0.783419i
$162$	−4.29660	−	1.82062i	−0.337573	−	0.143041i
$163$	−6.15718	+	10.6645i	−0.482268	+	0.835312i	−0.999793	−	0.0203561i	$-0.993520\pi$
$163$	−6.15718	+	10.6645i	−0.482268	+	0.835312i	0.517525	+	0.855668i	$0.326853\pi$
$164$	0.752947			0.0587952
$165$	−7.12409	+	1.16138i	−0.554610	+	0.0904132i
$166$	−0.792110			−0.0614797
$167$	7.25996	+	12.5746i	0.561793	+	0.973054i	0.997340	+	0.0728879i	$0.0232215\pi$
$167$	7.25996	+	12.5746i	0.561793	+	0.973054i	−0.435547	+	0.900166i	$0.643445\pi$
$168$	−5.36117	+	7.06060i	−0.413623	+	0.544737i
$169$	−3.81624	+	6.60993i	−0.293557	+	0.508456i
$170$	−0.723673	+	1.25344i	−0.0555031	+	0.0961343i
$171$	−2.66121	+	13.1013i	−0.203508	+	1.00188i
$172$	−8.98989	−	15.5709i	−0.685473	−	1.18727i
$173$	1.89564	+	3.28334i	0.144123	+	0.249628i	0.929045	−	0.369966i	$-0.120631\pi$
$173$	1.89564	+	3.28334i	0.144123	+	0.249628i	−0.784923	+	0.619594i	$0.787297\pi$
$174$	−3.86706	+	0.630413i	−0.293161	+	0.0477915i
$175$	−1.91816	+	1.82226i	−0.145000	+	0.137750i
$176$	5.12438	+	8.87568i	0.386265	+	0.669030i
$177$	6.58881	−	17.3991i	0.495245	−	1.30780i
$178$	−1.07975			−0.0809304
$179$	10.8720	+	18.8309i	0.812614	+	1.40749i	0.911029	+	0.412343i	$0.135289\pi$
$179$	10.8720	+	18.8309i	0.812614	+	1.40749i	−0.0984148	+	0.995145i	$0.531377\pi$
$180$	−1.03382	+	5.08956i	−0.0770565	+	0.379354i
$181$	−13.4199			−0.997494			−0.498747	−	0.866748i	$-0.666206\pi$
$181$	−13.4199			−0.997494			−0.498747	+	0.866748i	$0.666206\pi$
$182$	1.45794	+	6.05816i	0.108070	+	0.449060i
$183$	4.50529	+	5.51244i	0.333041	+	0.407491i
$184$	10.5531			0.777987
$185$	4.66225	−	8.07525i	0.342775	−	0.593704i
$186$	1.52397	−	0.248440i	0.111743	−	0.0182165i
$187$	−5.81655	−	10.0746i	−0.425348	−	0.736724i
$188$	−12.9870			−0.947173
$189$	4.40582	−	13.0226i	0.320476	−	0.947257i
$190$	−2.31054			−0.167624
$191$	5.30469	+	9.18799i	0.383834	+	0.664820i	0.991607	−	0.129291i	$-0.0412702\pi$
$191$	5.30469	+	9.18799i	0.383834	+	0.664820i	−0.607773	+	0.794111i	$0.707937\pi$
$192$	3.84855	−	0.627396i	0.277745	−	0.0452784i
$193$	11.0661	−	19.1670i	0.796552	−	1.37967i	−0.125297	−	0.992119i	$-0.539988\pi$
$193$	11.0661	−	19.1670i	0.796552	−	1.37967i	0.921849	−	0.387550i	$-0.126678\pi$
$194$	8.75138			0.628313
$195$	4.97876	+	6.09175i	0.356536	+	0.436239i
$196$	−10.1704	−	6.58891i	−0.726454	−	0.470637i
$197$	7.40378			0.527497			0.263749	−	0.964591i	$-0.415041\pi$
$197$	7.40378			0.527497			0.263749	+	0.964591i	$0.415041\pi$
$198$	4.85628	+	4.29376i	0.345121	+	0.305144i
$199$	−5.47597	−	9.48465i	−0.388181	−	0.672349i	0.604024	−	0.796966i	$-0.293563\pi$
$199$	−5.47597	−	9.48465i	−0.388181	−	0.672349i	−0.992205	+	0.124617i	$0.960230\pi$
$200$	−1.93458			−0.136795
$201$	−4.63630	+	12.2431i	−0.327019	+	0.863562i
$202$	2.04015	+	3.53364i	0.143544	+	0.248626i
$203$	−2.70082	−	11.2227i	−0.189561	−	0.787680i
$204$	−8.26104	+	1.34673i	−0.578389	+	0.0942897i
$205$	−0.217468	−	0.376665i	−0.0151886	−	0.0263075i
$206$	4.26576	+	7.38851i	0.297209	+	0.514782i
$207$	−15.5177	+	5.19757i	−1.07856	+	0.361256i
$208$	5.58538	−	9.67416i	0.387276	−	0.670782i
$209$	9.28554	−	16.0830i	0.642294	−	1.11249i
$210$	2.35724	+	0.298194i	0.162665	+	0.0205773i
$211$	−8.02408	−	13.8981i	−0.552401	−	0.956786i	−0.998101	−	0.0616037i	$-0.980379\pi$
$211$	−8.02408	−	13.8981i	−0.552401	−	0.956786i	0.445700	−	0.895182i	$-0.352955\pi$
$212$	−14.4473			−0.992245
$213$	−25.8134	+	4.20813i	−1.76870	+	0.288336i
$214$	4.70133			0.321377
$215$	−5.19296	+	8.99448i	−0.354157	+	0.613418i
$216$	8.89401	−	4.68471i	0.605160	−	0.318754i
$217$	1.06437	+	4.42277i	0.0722542	+	0.300237i
$218$	2.78661	−	4.82655i	0.188733	−	0.326895i
$219$	2.43669	+	2.98140i	0.164656	+	0.201464i
$220$	3.60723	−	6.24790i	0.243199	−	0.421233i
$221$	−6.33982	+	10.9809i	−0.426462	+	0.738654i
$222$	−8.26479	+	1.34734i	−0.554696	+	0.0904273i
$223$	0.311357	−	0.539286i	0.0208500	−	0.0361133i	−0.855412	−	0.517948i	$-0.826696\pi$
$223$	0.311357	−	0.539286i	0.0208500	−	0.0361133i	0.876262	+	0.481835i	$0.160029\pi$
$224$	−3.18453	−	13.2326i	−0.212775	−	0.884143i
$225$	2.84467	−	0.952806i	0.189645	−	0.0635204i
$226$	−2.42877	+	4.20676i	−0.161559	+	0.279829i
$227$	17.5136			1.16242			0.581208	−	0.813755i	$-0.302580\pi$
$227$	17.5136			1.16242			0.581208	+	0.813755i	$0.302580\pi$
$228$	−8.45585	−	10.3461i	−0.560003	−	0.685190i
$229$	9.50860			0.628346			0.314173	−	0.949366i	$-0.398273\pi$
$229$	9.50860			0.628346			0.314173	+	0.949366i	$0.398273\pi$
$230$	−1.41419	−	2.44944i	−0.0932487	−	0.161512i
$231$	−11.5488	+	15.2097i	−0.759858	+	1.00072i
$232$	4.22017	−	7.30955i	0.277068	−	0.479896i
$233$	−0.129981	+	0.225134i	−0.00851534	+	0.0147490i	−0.870252	−	0.492607i	$-0.836044\pi$
$233$	−0.129981	+	0.225134i	−0.00851534	+	0.0147490i	0.861736	+	0.507356i	$0.169377\pi$
$234$	1.40645	−	6.92403i	0.0919424	−	0.452638i
$235$	3.75093	+	6.49681i	0.244684	+	0.423805i
$236$	9.29769	+	16.1041i	0.605228	+	1.04829i
$237$	1.08717	+	1.33021i	0.0706195	+	0.0864062i
$238$	0.895971	+	3.72302i	0.0580772	+	0.241328i
$239$	1.90947	+	3.30730i	0.123514	+	0.213932i	0.921151	−	0.389206i	$-0.127250\pi$
$239$	1.90947	+	3.30730i	0.123514	+	0.213932i	−0.797637	+	0.603137i	$0.793917\pi$
$240$	−2.69558	−	3.29817i	−0.173999	−	0.212896i
$241$	−8.03593			−0.517639			−0.258820	−	0.965926i	$-0.583334\pi$
$241$	−8.03593			−0.517639			−0.258820	+	0.965926i	$0.583334\pi$
$242$	−1.65066	−	2.85902i	−0.106108	−	0.183785i
$243$	−10.7708	+	11.2690i	−0.690946	+	0.722906i
$244$	−7.11568			−0.455535
$245$	−0.358708	+	6.99080i	−0.0229170	+	0.446626i
$246$	−0.138327	+	0.365281i	−0.00881942	+	0.0232895i
$247$	−20.2418			−1.28795
$248$	−1.66313	+	2.88063i	−0.105609	+	0.182920i
$249$	−0.937099	+	2.47460i	−0.0593862	+	0.156821i
$250$	0.259245	+	0.449026i	0.0163961	+	0.0283989i
$251$	−16.7391			−1.05656			−0.528280	−	0.849070i	$-0.677163\pi$
$251$	−16.7391			−1.05656			−0.528280	+	0.849070i	$0.677163\pi$
$252$	7.29149	+	11.6465i	0.459321	+	0.733662i
$253$	22.7332			1.42922
$254$	1.12346	+	1.94589i	0.0704922	+	0.122096i
$255$	3.05968	+	3.74367i	0.191605	+	0.234437i
$256$	0.718573	−	1.24460i	0.0449108	−	0.0777878i
$257$	9.98747			0.623001			0.311501	−	0.950246i	$-0.399168\pi$
$257$	9.98747			0.623001			0.311501	+	0.950246i	$0.399168\pi$
$258$	9.20559	−	1.50071i	0.573115	−	0.0934300i
$259$	−5.77228	−	23.9855i	−0.358672	−	1.49039i
$260$	−7.86348			−0.487672
$261$	−2.60544	+	12.8267i	−0.161273	+	0.793955i
$262$	−2.57404	−	4.45837i	−0.159025	−	0.275439i
$263$	2.31996			0.143055			0.0715274	−	0.997439i	$-0.477213\pi$
$263$	2.31996			0.143055			0.0715274	+	0.997439i	$0.477213\pi$
$264$	−13.7821	+	2.24678i	−0.848229	+	0.138279i
$265$	4.17271	+	7.22734i	0.256327	+	0.443972i
$266$	−4.43200	+	4.21042i	−0.271744	+	0.258157i
$267$	−1.27738	+	3.37320i	−0.0781747	+	0.206436i
$268$	−6.54244	−	11.3318i	−0.399643	−	0.692202i
$269$	3.50368	+	6.06855i	0.213623	+	0.370006i	0.952846	−	0.303455i	$-0.0981402\pi$
$269$	3.50368	+	6.06855i	0.213623	+	0.370006i	−0.739223	+	0.673461i	$0.764807\pi$
$270$	−2.27920	−	1.43657i	−0.138708	−	0.0874269i
$271$	−1.38943	+	2.40656i	−0.0844016	+	0.146188i	−0.905136	−	0.425122i	$-0.860231\pi$
$271$	−1.38943	+	2.40656i	−0.0844016	+	0.146188i	0.820734	+	0.571310i	$0.193565\pi$
$272$	3.43248	−	5.94523i	0.208125	−	0.360482i
$273$	20.6509	+	2.61236i	1.24985	+	0.158107i
$274$	−1.86792	−	3.23533i	−0.112845	−	0.195454i
$275$	−4.16739			−0.251303
$276$	5.79263	−	15.2966i	0.348675	−	0.920748i
$277$	−7.23337			−0.434611			−0.217306	−	0.976104i	$-0.569727\pi$
$277$	−7.23337			−0.434611			−0.217306	+	0.976104i	$0.569727\pi$
$278$	3.65472	−	6.33015i	0.219195	−	0.379657i
$279$	1.02678	−	5.05490i	0.0614717	−	0.302629i
$280$	−3.71084	+	3.52531i	−0.221765	+	0.210678i
$281$	7.13246	−	12.3538i	0.425487	−	0.736965i	−0.570979	−	0.820965i	$-0.693436\pi$
$281$	7.13246	−	12.3538i	0.425487	−	0.736965i	0.996466	+	0.0839998i	$0.0267695\pi$
$282$	2.38590	−	6.30045i	0.142078	−	0.375186i
$283$	4.67580	−	8.09871i	0.277947	−	0.481419i	−0.692927	−	0.721007i	$-0.743679\pi$
$283$	4.67580	−	8.09871i	0.277947	−	0.481419i	0.970874	+	0.239589i	$0.0770126\pi$
$284$	13.0704	−	22.6386i	0.775585	−	1.34335i
$285$	−2.73347	+	7.21828i	−0.161917	+	0.427574i
$286$	−4.90740	+	8.49986i	−0.290181	+	0.502607i
$287$	−1.10352	−	0.326222i	−0.0651389	−	0.0192563i
$288$	−3.07206	+	15.1239i	−0.181023	+	0.891187i
$289$	4.60389	−	7.97416i	0.270817	−	0.469068i
$290$	−2.26212			−0.132836
$291$	10.3532	−	27.3399i	0.606918	−	1.60269i
$292$	−3.84851			−0.225217
$293$	−13.6282	−	23.6047i	−0.796166	−	1.37900i	−0.922096	−	0.386960i	$-0.873525\pi$
$293$	−13.6282	−	23.6047i	−0.796166	−	1.37900i	0.125931	−	0.992039i	$-0.459808\pi$
$294$	5.06496	−	3.72353i	0.295394	−	0.217160i
$295$	5.37076	−	9.30243i	0.312698	−	0.541609i
$296$	9.01948	−	15.6222i	0.524246	−	0.908021i
$297$	19.1591	−	10.0916i	1.11173	−	0.585575i
$298$	−1.86385	−	3.22829i	−0.107970	−	0.187010i
$299$	−12.3891	−	21.4586i	−0.716483	−	1.24098i
$300$	−1.06189	+	2.80414i	−0.0613083	+	0.161897i
$301$	6.42935	+	26.7158i	0.370582	+	1.53988i
$302$	2.55040	+	4.41743i	0.146759	+	0.254194i
$303$	13.4529	−	2.19311i	0.772848	−	0.125991i
$304$	10.9592			0.628555
$305$	2.05517	+	3.55966i	0.117679	+	0.203825i
$306$	0.864328	−	4.25514i	0.0494104	−	0.243250i
$307$	11.6773			0.666457			0.333228	−	0.942846i	$-0.391862\pi$
$307$	11.6773			0.666457			0.333228	+	0.942846i	$0.391862\pi$
$308$	−4.46607	−	18.5578i	−0.254478	−	1.05743i
$309$	28.1287	−	4.58558i	1.60019	−	0.260865i
$310$	0.891481			0.0506327
$311$	−0.511870	+	0.886585i	−0.0290255	+	0.0502736i	−0.880173	−	0.474653i	$-0.842574\pi$
$311$	−0.511870	+	0.886585i	−0.0290255	+	0.0502736i	0.851148	+	0.524926i	$0.175907\pi$
$312$	9.63179	+	11.7850i	0.545293	+	0.667192i
$313$	5.52917	+	9.57681i	0.312527	+	0.541313i	0.978909	−	0.204298i	$-0.0654911\pi$
$313$	5.52917	+	9.57681i	0.312527	+	0.541313i	−0.666381	+	0.745611i	$0.732158\pi$
$314$	5.31103			0.299719
$315$	3.72028	−	7.01138i	0.209614	−	0.395047i
$316$	−1.71709			−0.0965936
$317$	−4.74340	−	8.21580i	−0.266416	−	0.461445i	0.701518	−	0.712652i	$-0.252506\pi$
$317$	−4.74340	−	8.21580i	−0.266416	−	0.461445i	−0.967934	+	0.251206i	$0.919173\pi$
$318$	2.65418	−	7.00890i	0.148839	−	0.393039i
$319$	9.09094	−	15.7460i	0.508995	−	0.881605i
$320$	2.25129			0.125851
$321$	5.56187	−	14.6873i	0.310433	−	0.819763i
$322$	−7.17618	−	2.12141i	−0.399913	−	0.118222i
$323$	−12.4395			−0.692154
$324$	−1.90849	−	15.4632i	−0.106027	−	0.859065i
$325$	2.27115	+	3.93375i	0.125981	+	0.218205i
$326$	6.38488			0.353626
$327$	−11.7818	−	14.4156i	−0.651534	−	0.797182i
$328$	−0.420708	−	0.728688i	−0.0232297	−	0.0402351i
$329$	19.0338	+	5.62675i	1.04937	+	0.310213i
$330$	2.36838	+	2.89782i	0.130375	+	0.159520i
$331$	17.7162	+	30.6853i	0.973770	+	1.68662i	0.683935	+	0.729543i	$0.260267\pi$
$331$	17.7162	+	30.6853i	0.973770	+	1.68662i	0.289835	+	0.957077i	$0.406400\pi$
$332$	−1.32237	−	2.29041i	−0.0725745	−	0.125703i
$333$	−5.56842	+	27.4137i	−0.305148	+	1.50226i
$334$	3.76423	−	6.51983i	0.205969	−	0.356749i
$335$	−3.77921	+	6.54578i	−0.206480	+	0.357634i
$336$	−11.1807	−	1.41437i	−0.609957	−	0.0771604i
$337$	−12.5415	−	21.7225i	−0.683179	−	1.18330i	−0.974005	−	0.226525i	$-0.927264\pi$
$337$	−12.5415	−	21.7225i	−0.683179	−	1.18330i	0.290827	−	0.956776i	$-0.406070\pi$
$338$	3.95738			0.215253
$339$	10.2688	+	12.5644i	0.557726	+	0.682404i
$340$	−4.83248			−0.262078
$341$	−3.58266	+	6.20535i	−0.194012	+	0.336038i
$342$	6.57274	−	2.20150i	0.355413	−	0.119044i
$343$	12.0510	+	14.0632i	0.650694	+	0.759340i
$344$	−10.0462	+	17.4005i	−0.541654	+	0.938173i
$345$	−9.32525	+	1.52022i	−0.502055	+	0.0818456i
$346$	0.982870	−	1.70238i	0.0528394	−	0.0915206i
$347$	−14.8844	+	25.7806i	−0.799038	+	1.38397i	0.121205	+	0.992627i	$0.461324\pi$
$347$	−14.8844	+	25.7806i	−0.799038	+	1.38397i	−0.920243	+	0.391347i	$0.872009\pi$
$348$	−8.27864	−	10.1293i	−0.443781	−	0.542988i
$349$	−8.66268	+	15.0042i	−0.463703	+	0.803157i	−0.999142	−	0.0414169i	$-0.986813\pi$
$349$	−8.66268	+	15.0042i	−0.463703	+	0.803157i	0.535439	+	0.844574i	$0.320146\pi$
$350$	1.31552	+	0.388893i	0.0703175	+	0.0207872i
$351$	−19.9672	−	12.5852i	−1.06577	−	0.671750i
$352$	10.7191	−	18.5660i	0.571329	−	0.989571i
$353$	17.3636			0.924173			0.462086	−	0.886835i	$-0.347101\pi$
$353$	17.3636			0.924173			0.462086	+	0.886835i	$0.347101\pi$
$354$	−9.52077	+	1.55209i	−0.506023	+	0.0824926i
$355$	−15.1001			−0.801430
$356$	−1.80256	−	3.12212i	−0.0955355	−	0.165472i
$357$	12.6909	+	1.60542i	0.671675	+	0.0849677i
$358$	5.63705	−	9.76366i	0.297927	−	0.516025i
$359$	−0.480637	+	0.832488i	−0.0253671	+	0.0439371i	−0.878430	−	0.477871i	$-0.841409\pi$
$359$	−0.480637	+	0.832488i	−0.0253671	+	0.0439371i	0.853063	+	0.521808i	$0.174742\pi$
$360$	5.50324	−	1.84328i	0.290046	−	0.0971492i
$361$	−0.429240	−	0.743465i	−0.0225916	−	0.0391297i
$362$	3.47905	+	6.02589i	0.182855	+	0.316714i
$363$	−10.8845	+	1.77441i	−0.571290	+	0.0931325i
$364$	−15.0834	+	14.3293i	−0.790587	+	0.751061i
$365$	1.11154	+	1.92524i	0.0581805	+	0.100772i
$366$	1.30725	−	3.45207i	0.0683312	−	0.180443i
$367$	20.6928			1.08016			0.540078	−	0.841615i	$-0.318395\pi$
$367$	20.6928			1.08016			0.540078	+	0.841615i	$0.318395\pi$
$368$	6.70768	+	11.6180i	0.349662	+	0.605633i
$369$	0.977514	+	0.864285i	0.0508873	+	0.0449929i
$370$	−4.83467			−0.251342
$371$	21.1741	+	6.25945i	1.09930	+	0.324974i
$372$	3.26254	+	3.99187i	0.169155	+	0.206969i
$373$	13.8541			0.717338			0.358669	−	0.933465i	$-0.383231\pi$
$373$	13.8541			0.717338			0.358669	+	0.933465i	$0.383231\pi$
$374$	−3.01583	+	5.22357i	−0.155945	+	0.270104i
$375$	1.70948	−	0.278682i	0.0882774	−	0.0143911i
$376$	7.25647	+	12.5686i	0.374224	+	0.648174i
$377$	−19.8176			−1.02066
$378$	−6.98969	+	1.39773i	−0.359511	+	0.0718914i
$379$	−32.8112			−1.68540			−0.842700	−	0.538383i	$-0.819035\pi$
$379$	−32.8112			−1.68540			−0.842700	+	0.538383i	$0.819035\pi$
$380$	−3.85729	−	6.68102i	−0.197875	−	0.342729i
$381$	7.40818	−	1.20769i	0.379533	−	0.0618719i
$382$	2.75043	−	4.76389i	0.140724	−	0.243742i
$383$	6.16912			0.315228			0.157614	−	0.987501i	$-0.449620\pi$
$383$	6.16912			0.315228			0.157614	+	0.987501i	$0.449620\pi$
$384$	−12.5566	−	15.3636i	−0.640775	−	0.784018i
$385$	−7.99374	+	7.59409i	−0.407399	+	0.387031i
$386$	−11.4753			−0.584078
$387$	6.20229	−	30.5342i	0.315280	−	1.55214i
$388$	14.6098	+	25.3049i	0.741700	+	1.28466i
$389$	−34.7597			−1.76239			−0.881194	−	0.472754i	$-0.843260\pi$
$389$	−34.7597			−1.76239			−0.881194	+	0.472754i	$0.843260\pi$
$390$	1.44463	−	3.81485i	0.0731519	−	0.193173i
$391$	−7.61371	−	13.1873i	−0.385042	−	0.666912i
$392$	−0.693949	+	13.5242i	−0.0350497	+	0.683077i
$393$	−16.9734	+	2.76703i	−0.856195	+	0.139578i
$394$	−1.91940	−	3.32449i	−0.0966978	−	0.167485i
$395$	0.495933	+	0.858981i	0.0249531	+	0.0432200i
$396$	−4.30834	+	21.2102i	−0.216502	+	1.06585i
$397$	2.98728	−	5.17412i	0.149927	−	0.259682i	−0.781273	−	0.624189i	$-0.785429\pi$
$397$	2.98728	−	5.17412i	0.149927	−	0.259682i	0.931200	+	0.364508i	$0.118763\pi$
$398$	−2.83924	+	4.91771i	−0.142318	+	0.246502i
$399$	7.91037	+	18.8270i	0.396014	+	0.942526i
$400$	−1.22964	−	2.12979i	−0.0614818	−	0.106490i
$401$	−19.6376			−0.980657			−0.490328	−	0.871538i	$-0.663123\pi$
$401$	−19.6376			−0.980657			−0.490328	+	0.871538i	$0.663123\pi$
$402$	6.69941	−	1.09215i	0.334136	−	0.0544714i
$403$	7.80992			0.389040
$404$	−6.81176	+	11.7983i	−0.338898	+	0.586988i
$405$	−7.18432	+	5.42084i	−0.356992	+	0.269364i
$406$	−4.33912	+	4.12218i	−0.215347	+	0.204580i
$407$	19.4294	−	33.6527i	0.963080	−	1.66810i
$408$	5.91919	+	7.24241i	0.293044	+	0.358553i
$409$	−11.7823	+	20.4075i	−0.582596	+	1.00909i	0.412574	+	0.910924i	$0.364630\pi$
$409$	−11.7823	+	20.4075i	−0.582596	+	1.00909i	−0.995170	+	0.0981622i	$0.968704\pi$
$410$	−0.112755	+	0.195298i	−0.00556858	+	0.00964506i
$411$	−12.3172	+	2.00797i	−0.607563	+	0.0990457i
$412$	−14.2428	+	24.6692i	−0.701690	+	1.21536i
$413$	−6.64948	−	27.6305i	−0.327200	−	1.35961i
$414$	6.35674	+	5.62042i	0.312417	+	0.276228i
$415$	−0.763861	+	1.32305i	−0.0374965	+	0.0649458i
$416$	−23.3668			−1.14565
$417$	−15.4521	−	18.9064i	−0.756693	−	0.925850i
$418$	−9.62894			−0.470967
$419$	−8.48897	−	14.7033i	−0.414713	−	0.718304i	0.580685	−	0.814128i	$-0.302785\pi$
$419$	−8.48897	−	14.7033i	−0.414713	−	0.718304i	−0.995398	+	0.0958239i	$0.969451\pi$
$420$	3.07300	+	7.31385i	0.149947	+	0.356879i
$421$	−4.80555	+	8.32346i	−0.234208	+	0.405660i	−0.959042	−	0.283263i	$-0.908583\pi$
$421$	−4.80555	+	8.32346i	−0.234208	+	0.405660i	0.724834	+	0.688923i	$0.241916\pi$
$422$	−4.16042	+	7.20605i	−0.202526	+	0.350785i
$423$	−16.8604	−	14.9074i	−0.819779	−	0.724821i
$424$	8.07242	+	13.9818i	0.392031	+	0.679018i
$425$	1.39573	+	2.41747i	0.0677028	+	0.117265i
$426$	8.58156	+	10.4999i	0.415778	+	0.508724i
$427$	10.4288	+	3.08295i	0.504684	+	0.149194i
$428$	7.84854	+	13.5941i	0.379374	+	0.657094i
$429$	20.7484	+	25.3867i	1.00174	+	1.22568i
$430$	5.38501			0.259688
$431$	17.4758	+	30.2689i	0.841778	+	1.45800i	0.888390	+	0.459090i	$0.151824\pi$
$431$	17.4758	+	30.2689i	0.841778	+	1.45800i	−0.0466114	+	0.998913i	$0.514842\pi$
$432$	10.8106	+	6.81385i	0.520123	+	0.327831i
$433$	−8.29330			−0.398551			−0.199275	−	0.979944i	$-0.563859\pi$
$433$	−8.29330			−0.398551			−0.199275	+	0.979944i	$0.563859\pi$
$434$	1.71001	−	1.62451i	0.0820830	−	0.0779792i
$435$	−2.67618	+	7.06700i	−0.128313	+	0.338837i
$436$	18.6082			0.891171
$437$	12.1545	−	21.0523i	0.581431	−	1.00707i
$438$	0.707027	−	1.86705i	0.0337831	−	0.0892111i
$439$	1.51253	+	2.61978i	0.0721893	+	0.125036i	0.899861	−	0.436178i	$-0.143668\pi$
$439$	1.51253	+	2.61978i	0.0721893	+	0.125036i	−0.827671	+	0.561213i	$0.810335\pi$
$440$	−8.06214			−0.384347
$441$	−5.64047	−	20.2283i	−0.268594	−	0.963254i
$442$	6.57428			0.312706
$443$	4.72696	+	8.18733i	0.224584	+	0.388992i	0.956195	−	0.292731i	$-0.0945642\pi$
$443$	4.72696	+	8.18733i	0.224584	+	0.388992i	−0.731610	+	0.681723i	$0.761231\pi$
$444$	−17.6933	−	21.6486i	−0.839689	−	1.02740i
$445$	−1.04124	+	1.80348i	−0.0493595	+	0.0854931i
$446$	−0.322872			−0.0152884
$447$	−12.2904	+	2.00360i	−0.581316	+	0.0947669i
$448$	4.31835	−	4.10245i	0.204023	−	0.193823i
$449$	27.0744			1.27772			0.638860	−	0.769323i	$-0.279406\pi$
$449$	27.0744			1.27772			0.638860	+	0.769323i	$0.279406\pi$
$450$	−1.16530	−	1.03032i	−0.0549329	−	0.0485699i
$451$	−0.906274	−	1.56971i	−0.0426748	−	0.0739149i
$452$	−16.2186			−0.762861
$453$	16.8175	−	2.74162i	0.790157	−	0.128813i
$454$	−4.54032	−	7.86406i	−0.213088	−	0.369078i
$455$	11.5248	+	3.40694i	0.540289	+	0.159720i
$456$	−5.28810	+	13.9643i	−0.247638	+	0.653939i
$457$	2.52031	+	4.36531i	0.117895	+	0.204200i	0.918933	−	0.394413i	$-0.129052\pi$
$457$	2.52031	+	4.36531i	0.117895	+	0.204200i	−0.801038	+	0.598613i	$0.795719\pi$
$458$	−2.46506	−	4.26961i	−0.115185	−	0.199506i
$459$	−12.2708	−	7.73422i	−0.572751	−	0.361002i
$460$	4.72177	−	8.17834i	0.220154	−	0.381317i
$461$	−16.0088	+	27.7281i	−0.745605	+	1.29143i	0.204306	+	0.978907i	$0.434506\pi$
$461$	−16.0088	+	27.7281i	−0.745605	+	1.29143i	−0.949911	+	0.312519i	$0.898827\pi$
$462$	9.82353	+	1.24269i	0.457032	+	0.0578151i
$463$	0.486386	+	0.842445i	0.0226043	+	0.0391517i	0.877106	−	0.480296i	$-0.159471\pi$
$463$	0.486386	+	0.842445i	0.0226043	+	0.0391517i	−0.854502	+	0.519448i	$0.826138\pi$
$464$	10.7295			0.498107
$465$	1.05466	−	2.78504i	0.0489086	−	0.129153i
$466$	0.134788			0.00624393
$467$	18.1325	−	31.4064i	0.839070	−	1.45331i	−0.0516023	−	0.998668i	$-0.516433\pi$
$467$	18.1325	−	31.4064i	0.839070	−	1.45331i	0.890673	−	0.454645i	$-0.150234\pi$
$468$	22.3690	−	7.49237i	1.03401	−	0.346335i
$469$	4.67899	+	19.4426i	0.216056	+	0.897775i
$470$	1.94482	−	3.36853i	0.0897081	−	0.155379i
$471$	6.28316	−	16.5920i	0.289513	−	0.764518i
$472$	10.3901	−	17.9963i	0.478245	−	0.828345i
$473$	−21.6411	+	37.4835i	−0.995060	+	1.72349i
$474$	0.315453	−	0.833019i	0.0144893	−	0.0382619i
$475$	−2.22814	+	3.85926i	−0.102234	+	0.177075i
$476$	−9.26949	+	8.80605i	−0.424866	+	0.403625i
$477$	−18.7562	−	16.5836i	−0.858789	−	0.759312i
$478$	0.990044	−	1.71481i	0.0452836	−	0.0784334i
$479$	−38.8769			−1.77633			−0.888167	−	0.459522i	$-0.848021\pi$
$479$	−38.8769			−1.77633			−0.888167	+	0.459522i	$0.848021\pi$
$480$	−3.15547	+	8.33267i	−0.144027	+	0.380333i
$481$	−42.3547			−1.93121
$482$	2.08328	+	3.60834i	0.0948907	+	0.164355i
$483$	−15.1171	+	19.9091i	−0.687854	+	0.905895i
$484$	5.51130	−	9.54585i	0.250514	−	0.433902i
$485$	8.43928	−	14.6173i	0.383208	−	0.663736i
$486$	7.85235	+	1.91493i	0.356190	+	0.0868632i
$487$	18.1746	+	31.4793i	0.823570	+	1.42647i	0.903007	+	0.429625i	$0.141354\pi$
$487$	18.1746	+	31.4793i	0.823570	+	1.42647i	−0.0794371	+	0.996840i	$0.525312\pi$
$488$	3.97588	+	6.88643i	0.179980	+	0.311734i
$489$	7.55358	−	19.9468i	0.341585	−	0.902024i
$490$	3.23205	−	1.65126i	0.146009	−	0.0745965i
$491$	3.11985	+	5.40374i	0.140797	+	0.243867i	0.927797	−	0.373086i	$-0.121700\pi$
$491$	3.11985	+	5.40374i	0.140797	+	0.243867i	−0.787000	+	0.616953i	$0.788367\pi$
$492$	−1.28715	+	0.209833i	−0.0580292	+	0.00946000i
$493$	−12.1788			−0.548506
$494$	5.24759	+	9.08909i	0.236100	+	0.408938i
$495$	11.8549	−	3.97072i	0.532836	−	0.178470i
$496$	−4.22842			−0.189862
$497$	−28.9645	+	27.5163i	−1.29923	+	1.23428i
$498$	1.35410	−	0.220747i	0.0606786	−	0.00989191i
$499$	5.55495			0.248674			0.124337	−	0.992240i	$-0.460320\pi$
$499$	5.55495			0.248674			0.124337	+	0.992240i	$0.460320\pi$
$500$	−0.865584	+	1.49923i	−0.0387101	+	0.0670478i
$501$	−15.9151	−	19.4729i	−0.711035	−	0.869985i
$502$	4.33953	+	7.51628i	0.193683	+	0.335468i
$503$	13.0787			0.583151			0.291576	−	0.956548i	$-0.405820\pi$
$503$	13.0787			0.583151			0.291576	+	0.956548i	$0.405820\pi$
$504$	7.19718	−	13.5641i	0.320588	−	0.604191i
$505$	7.86956			0.350191
$506$	−5.89347	−	10.2078i	−0.261997	−	0.453792i
$507$	4.68174	−	12.3631i	0.207923	−	0.549064i
$508$	−3.75107	+	6.49705i	−0.166427	+	0.288260i
$509$	−5.35315			−0.237274			−0.118637	−	0.992938i	$-0.537853\pi$
$509$	−5.35315			−0.237274			−0.118637	+	0.992938i	$0.537853\pi$
$510$	0.887796	−	2.34441i	0.0393123	−	0.103812i
$511$	5.64040	+	1.66741i	0.249517	+	0.0737619i
$512$	22.1665			0.979628
$513$	0.898197	−	23.1381i	0.0396564	−	1.02157i
$514$	−2.58921	−	4.48464i	−0.114205	−	0.197809i
$515$	16.4545			0.725072
$516$	19.7074	+	24.1130i	0.867571	+	1.06151i
$517$	15.6316	+	27.0747i	0.687477	+	1.19075i
$518$	−9.27369	+	8.81004i	−0.407462	+	0.387091i
$519$	−4.15557	−	5.08453i	−0.182409	−	0.223186i
$520$	4.39371	+	7.61013i	0.192677	+	0.333726i
$521$	−10.9063	−	18.8903i	−0.477815	−	0.827600i	0.521861	−	0.853030i	$-0.325238\pi$
$521$	−10.9063	−	18.8903i	−0.477815	−	0.827600i	−0.999677	+	0.0254300i	$0.991905\pi$
$522$	6.43499	−	2.15536i	0.281652	−	0.0943376i
$523$	8.20565	−	14.2126i	0.358808	−	0.621473i	−0.628954	−	0.777442i	$-0.716517\pi$
$523$	8.20565	−	14.2126i	0.358808	−	0.621473i	0.987762	+	0.155969i	$0.0498500\pi$
$524$	8.59435	−	14.8858i	0.375446	−	0.650291i
$525$	2.77124	−	3.64969i	0.120947	−	0.159286i
$526$	−0.601439	−	1.04172i	−0.0262240	−	0.0454212i
$527$	4.79957			0.209072
$528$	−11.2335	−	13.7448i	−0.488877	−	0.598164i
$529$	6.75714			0.293789
$530$	2.16351	−	3.74731i	0.0939769	−	0.162773i
$531$	−6.41464	+	31.5797i	−0.278372	+	1.37044i
$532$	−19.5735	−	5.78629i	−0.848618	−	0.250868i
$533$	−0.987804	+	1.71093i	−0.0427866	+	0.0741085i
$534$	1.84581	−	0.300906i	0.0798760	−	0.0130215i
$535$	4.53367	−	7.85255i	0.196008	−	0.339495i
$536$	−7.31116	+	12.6633i	−0.315794	+	0.546971i
$537$	−23.8334	−	29.1613i	−1.02849	−	1.25840i
$538$	1.81663	−	3.14649i	0.0783203	−	0.135655i
$539$	−1.49488	+	29.1334i	−0.0643890	+	1.25486i
$540$	0.348930	−	8.98864i	0.0150155	−	0.386809i
$541$	8.77183	−	15.1933i	0.377130	−	0.653209i	−0.613513	−	0.789685i	$-0.710244\pi$
$541$	8.77183	−	15.1933i	0.377130	−	0.653209i	0.990643	+	0.136476i	$0.0435775\pi$
$542$	1.44081			0.0618881
$543$	22.9411	−	3.73989i	0.984497	−	0.160494i
$544$	−14.3600			−0.615679
$545$	−5.37447	−	9.30885i	−0.230217	−	0.398747i
$546$	−4.18062	−	9.95002i	−0.178914	−	0.425822i
$547$	−8.72588	+	15.1137i	−0.373092	+	0.646214i	−0.990039	−	0.140790i	$-0.955036\pi$
$547$	−8.72588	+	15.1137i	−0.373092	+	0.646214i	0.616948	+	0.787004i	$0.288369\pi$
$548$	6.23672	−	10.8023i	0.266419	−	0.461452i
$549$	−9.23794	−	8.16788i	−0.394266	−	0.348596i
$550$	1.08038	+	1.87127i	0.0460674	+	0.0797912i
$551$	−9.72114	−	16.8375i	−0.414135	−	0.717302i
$552$	−18.0404	+	2.94097i	−0.767851	+	0.125176i
$553$	2.51657	+	0.743946i	0.107016	+	0.0316358i
$554$	1.87522	+	3.24797i	0.0796704	+	0.137993i
$555$	−5.71961	+	15.1038i	−0.242784	+	0.641121i
$556$	24.4051			1.03501
$557$	−6.58901	−	11.4125i	−0.279186	−	0.483564i	0.691997	−	0.721900i	$-0.256731\pi$
$557$	−6.58901	−	11.4125i	−0.279186	−	0.483564i	−0.971183	+	0.238337i	$0.923398\pi$
$558$	−2.53597	+	0.849409i	−0.107356	+	0.0359583i
$559$	47.1760			1.99533
$560$	−6.23969	−	1.84457i	−0.263675	−	0.0779474i
$561$	12.7509	+	15.6013i	0.538343	+	0.658688i
$562$	−7.39623			−0.311991
$563$	−22.7831	+	39.4616i	−0.960195	+	1.66311i	−0.238191	+	0.971218i	$0.576554\pi$
$563$	−22.7831	+	39.4616i	−0.960195	+	1.66311i	−0.722005	+	0.691888i	$0.756779\pi$
$564$	22.2010	−	3.61924i	0.934832	−	0.152398i
$565$	4.68431	+	8.11346i	0.197070	+	0.341336i
$566$	−4.84872			−0.203807
$567$	−3.90250	+	23.4898i	−0.163890	+	0.986479i
$568$	−29.2123			−1.22572
$569$	10.6230	+	18.3995i	0.445338	+	0.771348i	0.998076	−	0.0620074i	$-0.0197503\pi$
$569$	10.6230	+	18.3995i	0.445338	+	0.771348i	−0.552738	+	0.833355i	$0.686417\pi$
$570$	3.94984	−	0.643908i	0.165441	−	0.0269703i
$571$	16.8138	−	29.1223i	0.703634	−	1.21873i	−0.263548	−	0.964646i	$-0.584893\pi$
$571$	16.8138	−	29.1223i	0.703634	−	1.21873i	0.967182	−	0.254084i	$-0.0817740\pi$
$572$	−32.7702			−1.37019
$573$	−11.6288	−	14.2284i	−0.485801	−	0.594400i
$574$	0.139601	+	0.580083i	0.00582683	+	0.0242122i
$575$	−5.45501			−0.227490
$576$	−6.40419	+	2.14505i	−0.266841	+	0.0893769i
$577$	−2.15113	−	3.72587i	−0.0895527	−	0.155110i	0.817769	−	0.575546i	$-0.195210\pi$
$577$	−2.15113	−	3.72587i	−0.0895527	−	0.155110i	−0.907322	+	0.420436i	$0.861877\pi$
$578$	−4.77415			−0.198578
$579$	−13.5758	+	35.8496i	−0.564189	+	1.48986i
$580$	−3.77645	−	6.54100i	−0.156808	−	0.271600i
$581$	0.945728	+	3.92978i	0.0392354	+	0.163035i
$582$	−14.9603	+	2.43886i	−0.620126	+	0.101094i
$583$	17.3893	+	30.1191i	0.720191	+	1.24741i
$584$	2.15035	+	3.72452i	0.0889823	+	0.154122i
$585$	−10.2088	−	9.02626i	−0.422081	−	0.373190i
$586$	−7.06608	+	12.2388i	−0.291897	+	0.505580i
$587$	6.02889	−	10.4424i	0.248839	−	0.431002i	−0.714365	−	0.699773i	$-0.753284\pi$
$587$	6.02889	−	10.4424i	0.248839	−	0.431002i	0.963204	+	0.268771i	$0.0866176\pi$
$588$	19.2223	+	8.42934i	0.792714	+	0.347620i
$589$	3.83102	+	6.63551i	0.157854	+	0.273412i
$590$	−5.56938			−0.229288
$591$	−12.6566	+	2.06330i	−0.520625	+	0.0848729i
$592$	22.9315			0.942478
$593$	−10.6009	+	18.3612i	−0.435325	+	0.754005i	−0.997322	−	0.0731342i	$-0.976700\pi$
$593$	−10.6009	+	18.3612i	−0.435325	+	0.754005i	0.561997	+	0.827139i	$0.310033\pi$
$594$	−9.49832	−	5.98675i	−0.389721	−	0.245639i
$595$	7.08251	+	2.09372i	0.290355	+	0.0858343i
$596$	6.22314	−	10.7788i	0.254910	−	0.441517i
$597$	12.0043	+	14.6878i	0.491303	+	0.601132i
$598$	−6.42366	+	11.1261i	−0.262683	+	0.454980i
$599$	12.9157	−	22.3707i	0.527722	−	0.914041i	−0.471756	−	0.881729i	$-0.656380\pi$
$599$	12.9157	−	22.3707i	0.527722	−	0.914041i	0.999478	−	0.0323118i	$-0.0102870\pi$
$600$	3.30713	−	0.539132i	0.135013	−	0.0220100i
$601$	19.5434	−	33.8501i	0.797190	−	1.38077i	−0.124249	−	0.992251i	$-0.539652\pi$
$601$	19.5434	−	33.8501i	0.797190	−	1.38077i	0.921439	−	0.388523i	$-0.127014\pi$
$602$	10.3293	−	9.81291i	0.420992	−	0.399944i
$603$	4.51375	−	22.2214i	0.183814	−	0.904927i
$604$	−8.51543	+	14.7492i	−0.346488	+	0.600135i
$605$	−6.36715			−0.258862
$606$	−4.47236	−	5.47215i	−0.181677	−	0.222291i
$607$	−23.2068			−0.941936			−0.470968	−	0.882150i	$-0.656095\pi$
$607$	−23.2068			−0.941936			−0.470968	+	0.882150i	$0.656095\pi$
$608$	−11.4622	−	19.8530i	−0.464852	−	0.805147i
$609$	7.74459	+	18.4324i	0.313827	+	0.746918i
$610$	1.06559	−	1.84565i	0.0431443	−	0.0747282i
$611$	17.0379	−	29.5104i	0.689278	−	1.19386i
$612$	13.7468	−	4.60441i	0.555682	−	0.186122i
$613$	1.42443	+	2.46719i	0.0575324	+	0.0996490i	0.893357	−	0.449347i	$-0.148343\pi$
$613$	1.42443	+	2.46719i	0.0575324	+	0.0996490i	−0.835825	+	0.548996i	$0.815010\pi$
$614$	−3.02728	−	5.24340i	−0.122171	−	0.211606i
$615$	0.476728	+	0.583299i	0.0192235	+	0.0235209i
$616$	−15.4645	+	14.6913i	−0.623083	+	0.591931i
$617$	−14.3988	−	24.9394i	−0.579673	−	1.00402i	−0.995517	−	0.0945869i	$-0.969847\pi$
$617$	−14.3988	−	24.9394i	−0.579673	−	1.00402i	0.415844	−	0.909436i	$-0.363486\pi$
$618$	−9.35129	−	11.4417i	−0.376164	−	0.460255i
$619$	−36.4640			−1.46561			−0.732805	−	0.680439i	$-0.761789\pi$
$619$	−36.4640			−1.46561			−0.732805	+	0.680439i	$0.761789\pi$
$620$	1.48826	+	2.57775i	0.0597701	+	0.103525i
$621$	25.0788	−	13.2097i	1.00638	−	0.530086i
$622$	0.530800			0.0212831
$623$	1.28915	+	5.35678i	0.0516486	+	0.214615i
$624$	−6.85210	+	18.0944i	−0.274304	+	0.724355i
$625$	1.00000			0.0400000
$626$	2.86683	−	4.96549i	0.114581	−	0.198461i
$627$	−11.3914	+	30.0814i	−0.454930	+	1.20134i
$628$	8.86638	+	15.3570i	0.353807	+	0.612812i
$629$	−26.0289			−1.03784
$630$	−4.11276	+	0.147163i	−0.163856	+	0.00586313i
$631$	2.09147			0.0832602			0.0416301	−	0.999133i	$-0.486745\pi$
$631$	2.09147			0.0832602			0.0416301	+	0.999133i	$0.486745\pi$
$632$	0.959421	+	1.66177i	0.0381637	+	0.0661015i
$633$	17.5902	+	21.5224i	0.699148	+	0.855441i
$634$	−2.45941	+	4.25982i	−0.0976756	+	0.169179i
$635$	4.33358			0.171973
$636$	24.6974	−	4.02621i	0.979317	−	0.159650i
$637$	28.3147	−	14.4661i	1.12187	−	0.573167i
$638$	−9.42714			−0.373224
$639$	42.9548	−	14.3875i	1.69927	−	0.569159i
$640$	−5.72790	−	9.92102i	−0.226415	−	0.392163i
$641$	20.8503			0.823537			0.411769	−	0.911288i	$-0.364911\pi$
$641$	20.8503			0.823537			0.411769	+	0.911288i	$0.364911\pi$
$642$	−8.03686	+	1.31018i	−0.317189	+	0.0517086i
$643$	−19.8691	−	34.4143i	−0.783560	−	1.35717i	−0.929855	−	0.367925i	$-0.880068\pi$
$643$	−19.8691	−	34.4143i	−0.783560	−	1.35717i	0.146295	−	0.989241i	$-0.453265\pi$
$644$	−5.84597	−	24.2917i	−0.230363	−	0.957227i
$645$	6.37069	−	16.8231i	0.250846	−	0.662409i
$646$	3.22489	+	5.58568i	0.126882	+	0.219765i
$647$	12.4989	+	21.6487i	0.491381	+	0.851097i	0.999951	−	0.00992365i	$-0.00315885\pi$
$647$	12.4989	+	21.6487i	0.491381	+	0.851097i	−0.508570	+	0.861021i	$0.669826\pi$
$648$	−13.8986	+	10.4870i	−0.545989	+	0.411970i
$649$	22.3821	−	38.7669i	0.878573	−	1.52173i
$650$	1.17757	−	2.03961i	0.0461881	−	0.0800002i
$651$	−3.05207	−	7.26404i	−0.119620	−	0.284700i
$652$	10.6591	+	18.4621i	0.417443	+	0.723032i
$653$	−18.0250			−0.705375			−0.352687	−	0.935741i	$-0.614732\pi$
$653$	−18.0250			−0.705375			−0.352687	+	0.935741i	$0.614732\pi$
$654$	−3.41859	+	9.02750i	−0.133678	+	0.353003i
$655$	−9.92896			−0.387957
$656$	0.534813	−	0.926323i	0.0208809	−	0.0361669i
$657$	−4.99634	−	4.41759i	−0.194926	−	0.172347i
$658$	−2.40787	−	10.0054i	−0.0938684	−	0.390051i
$659$	−10.2791	+	17.8039i	−0.400417	+	0.693543i	−0.993776	−	0.111395i	$-0.964468\pi$
$659$	−10.2791	+	17.8039i	−0.400417	+	0.693543i	0.593359	+	0.804938i	$0.297801\pi$
$660$	−4.42532	+	11.6860i	−0.172255	+	0.454875i
$661$	−9.88014	+	17.1129i	−0.384293	+	0.665615i	−0.991671	−	0.128798i	$-0.958888\pi$
$661$	−9.88014	+	17.1129i	−0.384293	+	0.665615i	0.607378	+	0.794413i	$0.292221\pi$
$662$	9.18569	−	15.9101i	0.357012	−	0.618363i
$663$	7.77764	−	20.5384i	0.302058	−	0.797647i
$664$	−1.47775	+	2.55953i	−0.0573477	+	0.0993292i
$665$	2.75864	+	11.4630i	0.106975	+	0.444514i
$666$	13.7530	−	4.60650i	0.532920	−	0.178498i
$667$	11.8998	−	20.6111i	0.460762	−	0.798064i
$668$	25.1364			0.972557
$669$	−0.381971	+	1.00867i	−0.0147678	+	0.0389975i
$670$	3.91897			0.151403
$671$	8.56469	+	14.8345i	0.330636	+	0.572679i
$672$	9.13161	+	21.7335i	0.352259	+	0.838389i
$673$	−4.01350	+	6.95159i	−0.154709	+	0.267964i	−0.932953	−	0.359998i	$-0.882777\pi$
$673$	−4.01350	+	6.95159i	−0.154709	+	0.267964i	0.778244	+	0.627962i	$0.216111\pi$
$674$	−6.50265	+	11.2629i	−0.250473	+	0.433832i
$675$	−4.59739	+	2.42157i	−0.176954	+	0.0932062i
$676$	6.60655	+	11.4429i	0.254098	+	0.440111i
$677$	16.0138	+	27.7367i	0.615460	+	1.06601i	0.990304	+	0.138919i	$0.0443629\pi$
$677$	16.0138	+	27.7367i	0.615460	+	1.06601i	−0.374844	+	0.927088i	$0.622304\pi$
$678$	2.97960	−	7.86824i	0.114431	−	0.302178i
$679$	−10.4486	−	43.4169i	−0.400980	−	1.66619i
$680$	2.70014	+	4.67679i	0.103546	+	0.179347i
$681$	−29.9392	+	4.88072i	−1.14727	+	0.187030i
$682$	3.71515			0.142260
$683$	−11.3678	−	19.6895i	−0.434975	−	0.753399i	0.562318	−	0.826921i	$-0.309910\pi$
$683$	−11.3678	−	19.6895i	−0.434975	−	0.753399i	−0.997294	+	0.0735216i	$0.976576\pi$
$684$	17.3384	+	15.3301i	0.662952	+	0.586159i
$685$	−7.20522			−0.275297
$686$	3.19056	−	9.05704i	0.121816	−	0.345799i
$687$	−16.2548	+	2.64988i	−0.620159	+	0.101099i
$688$	−25.5418			−0.973774
$689$	18.9537	−	32.8287i	0.722078	−	1.25068i
$690$	3.10015	+	3.79318i	0.118021	+	0.144404i
$691$	−12.3393	−	21.3722i	−0.469408	−	0.813038i	0.529981	−	0.848010i	$-0.322199\pi$
$691$	−12.3393	−	21.3722i	−0.469408	−	0.813038i	−0.999388	+	0.0349719i	$0.988866\pi$
$692$	6.56332			0.249500
$693$	15.5039	−	29.2192i	0.588944	−	1.10994i
$694$	15.4349			0.585900
$695$	−7.04875	−	12.2088i	−0.267374	−	0.463106i
$696$	−5.17728	+	13.6717i	−0.196244	+	0.518223i
$697$	−0.607052	+	1.05145i	−0.0229937	+	0.0398263i
$698$	8.98305			0.340013
$699$	0.159460	−	0.421086i	0.00603132	−	0.0159269i
$700$	1.07167	+	4.45310i	0.0405053	+	0.168311i
$701$	−32.8193			−1.23957			−0.619785	−	0.784772i	$-0.712780\pi$
$701$	−32.8193			−1.23957			−0.619785	+	0.784772i	$0.712780\pi$
$702$	−0.474696	+	12.2285i	−0.0179163	+	0.461534i
$703$	−20.7763	−	35.9856i	−0.783593	−	1.35722i
$704$	9.38202			0.353598
$705$	−8.22270	−	10.0609i	−0.309685	−	0.378914i
$706$	−4.50144	−	7.79673i	−0.169414	−	0.293434i
$707$	15.0951	−	14.3404i	0.567710	−	0.539327i
$708$	−20.3822	−	24.9385i	−0.766009	−	0.937248i
$709$	21.1285	+	36.5957i	0.793499	+	1.37438i	0.923788	+	0.382904i	$0.125076\pi$
$709$	21.1285	+	36.5957i	0.793499	+	1.37438i	−0.130289	+	0.991476i	$0.541591\pi$
$710$	3.91463	+	6.78034i	0.146913	+	0.254462i
$711$	−2.22921	−	1.97099i	−0.0836019	−	0.0739180i
$712$	−2.01436	+	3.48897i	−0.0754912	+	0.130755i
$713$	−4.68961	+	8.12264i	−0.175627	+	0.304195i
$714$	−2.56919	−	6.11476i	−0.0961495	−	0.228839i
$715$	9.46477	+	16.3935i	0.353962	+	0.613081i
$716$	37.6426			1.40677
$717$	−4.18590	−	5.12165i	−0.156325	−	0.191271i
$718$	0.498412			0.0186006
$719$	−4.51490	+	7.82003i	−0.168377	+	0.291638i	−0.937849	−	0.347042i	$-0.887186\pi$
$719$	−4.51490	+	7.82003i	−0.168377	+	0.291638i	0.769472	+	0.638680i	$0.220519\pi$
$720$	5.52719	+	4.88696i	0.205986	+	0.182126i
$721$	31.5625	−	29.9845i	1.17545	−	1.11668i
$722$	−0.222557	+	0.385480i	−0.00828271	+	0.0143461i
$723$	13.7373	−	2.23947i	0.510895	−	0.0832868i
$724$	−11.6160	+	20.1196i	−0.431707	+	0.747738i
$725$	−2.18145	+	3.77837i	−0.0810169	+	0.140325i
$726$	3.61853	+	4.42744i	0.134296	+	0.164318i
$727$	−15.3705	+	26.6225i	−0.570061	+	0.987375i	0.426498	+	0.904489i	$0.359747\pi$
$727$	−15.3705	+	26.6225i	−0.570061	+	0.987375i	−0.996559	+	0.0828866i	$0.973586\pi$
$728$	22.2955	+	6.59098i	0.826328	+	0.244278i
$729$	15.2720	−	22.2658i	0.565631	−	0.824659i
$730$	0.576322	−	0.998219i	0.0213306	−	0.0369457i
$731$	28.9919			1.07230
$732$	12.1641	−	1.98301i	0.449600	−	0.0732943i
$733$	9.88435			0.365087			0.182543	−	0.983198i	$-0.441567\pi$
$733$	9.88435			0.365087			0.182543	+	0.983198i	$0.441567\pi$
$734$	−5.36452	−	9.29162i	−0.198008	−	0.342960i
$735$	−1.33501	−	12.0506i	−0.0492425	−	0.444494i
$736$	14.0310	−	24.3024i	0.517190	−	0.895799i
$737$	−15.7494	+	27.2788i	−0.580138	+	1.00483i
$738$	0.134671	−	0.662992i	0.00495729	−	0.0244051i
$739$	4.97735	+	8.62102i	0.183095	+	0.317129i	0.942933	−	0.332983i	$-0.108055\pi$
$739$	4.97735	+	8.62102i	0.183095	+	0.317129i	−0.759838	+	0.650112i	$0.774722\pi$
$740$	−8.07113	−	13.9796i	−0.296701	−	0.513901i
$741$	34.6030	−	5.64103i	1.27117	−	0.207228i
$742$	−2.67862	−	11.1304i	−0.0983352	−	0.408611i
$743$	3.72404	+	6.45022i	0.136622	+	0.236636i	0.926216	−	0.376994i	$-0.123042\pi$
$743$	3.72404	+	6.45022i	0.136622	+	0.236636i	−0.789594	+	0.613629i	$0.789709\pi$
$744$	2.04032	−	5.38788i	0.0748017	−	0.197529i
$745$	−7.18954			−0.263404
$746$	−3.59161	−	6.22085i	−0.131498	−	0.227762i
$747$	0.912328	−	4.49144i	0.0333803	−	0.164333i
$748$	−20.1388			−0.736348
$749$	−5.61309	−	23.3240i	−0.205098	−	0.852241i
$750$	−0.568312	−	0.695356i	−0.0207518	−	0.0253908i
$751$	36.2668			1.32339			0.661697	−	0.749771i	$-0.269836\pi$
$751$	36.2668			1.32339			0.661697	+	0.749771i	$0.269836\pi$
$752$	−9.22457	+	15.9774i	−0.336385	+	0.582637i
$753$	28.6152	−	4.66488i	1.04279	−	0.169998i
$754$	5.13761	+	8.89861i	0.187101	+	0.324068i
$755$	9.83779			0.358034
$756$	−15.7104	−	17.8775i	−0.571381	−	0.650199i
$757$	−9.90893			−0.360146			−0.180073	−	0.983653i	$-0.557633\pi$
$757$	−9.90893			−0.360146			−0.180073	+	0.983653i	$0.557633\pi$
$758$	8.50617	+	14.7331i	0.308958	+	0.535131i
$759$	−38.8620	+	6.33533i	−1.41060	+	0.229958i
$760$	−4.31051	+	7.46603i	−0.156359	+	0.270821i
$761$	−28.0659			−1.01739			−0.508694	−	0.860947i	$-0.669872\pi$
$761$	−28.0659			−1.01739			−0.508694	+	0.860947i	$0.669872\pi$
$762$	−2.46282	−	3.01338i	−0.0892187	−	0.109163i
$763$	−27.2723	−	8.06220i	−0.987323	−	0.291871i
$764$	18.3666			0.664481
$765$	−6.27377	−	5.54706i	−0.226829	−	0.200554i
$766$	−1.59932	−	2.77010i	−0.0577857	−	0.100088i
$767$	−48.7912			−1.76175
$768$	−0.881539	+	2.32789i	−0.0318098	+	0.0840003i
$769$	−15.0181	−	26.0121i	−0.541565	−	0.938019i	−0.998814	−	0.0486801i	$-0.984499\pi$
$769$	−15.0181	−	26.0121i	−0.541565	−	0.938019i	0.457249	−	0.889339i	$-0.348835\pi$
$770$	5.48229	+	1.62067i	0.197568	+	0.0584048i
$771$	−17.0734	+	2.78333i	−0.614884	+	0.100239i
$772$	−19.1572	−	33.1812i	−0.689483	−	1.19422i
$773$	12.5815	+	21.7918i	0.452524	+	0.783795i	0.998542	−	0.0539783i	$-0.0171902\pi$
$773$	12.5815	+	21.7918i	0.452524	+	0.783795i	−0.546018	+	0.837774i	$0.683857\pi$
$774$	−15.3186	+	5.13087i	−0.550615	+	0.184425i
$775$	0.859688	−	1.48902i	0.0308809	−	0.0534873i
$776$	16.3264	−	28.2782i	0.586085	−	1.01513i
$777$	16.5520	+	39.3942i	0.593798	+	1.41326i
$778$	9.01130	+	15.6080i	0.323071	+	0.559575i
$779$	−1.93820			−0.0694432
$780$	13.4425	−	2.19141i	0.481319	−	0.0784652i
$781$	−62.9280			−2.25174
$782$	−3.94764	+	6.83752i	−0.141167	+	0.244509i
$783$	0.879373	−	22.6532i	0.0314262	−	0.809559i
$784$	−15.3300	+	7.83217i	−0.547502	+	0.279721i
$785$	5.12162	−	8.87090i	0.182798	−	0.316616i
$786$	5.64275	+	6.90417i	0.201270	+	0.246263i
$787$	−2.58355	+	4.47484i	−0.0920935	+	0.159511i	−0.908392	−	0.418120i	$-0.862689\pi$
$787$	−2.58355	+	4.47484i	−0.0920935	+	0.159511i	0.816298	+	0.577631i	$0.196023\pi$
$788$	6.40859	−	11.1000i	0.228297	−	0.395421i
$789$	−3.96593	+	0.646531i	−0.141191	+	0.0230171i
$790$	0.257137	−	0.445374i	0.00914852	−	0.0158457i
$791$	23.7701	+	7.02690i	0.845169	+	0.249848i
$792$	22.9341	−	7.68165i	0.814929	−	0.272956i
$793$	9.33519	−	16.1690i	0.331502	−	0.574179i
$794$	−3.09775			−0.109935
$795$	−9.14731	−	11.1922i	−0.324421	−	0.396945i
$796$	−18.9596			−0.672006
$797$	3.35427	+	5.80977i	0.118814	+	0.205793i	0.919298	−	0.393562i	$-0.128757\pi$
$797$	3.35427	+	5.80977i	0.118814	+	0.205793i	−0.800484	+	0.599355i	$0.795424\pi$
$798$	6.40307	−	8.43277i	0.226666	−	0.298517i
$799$	10.4706	−	18.1355i	0.370422	−	0.641590i
$800$	−2.57213	+	4.45506i	−0.0909386	+	0.157510i
$801$	1.24362	−	6.12241i	0.0439411	−	0.216325i
$802$	5.09097	+	8.81782i	0.179768	+	0.311368i
$803$	4.63221	+	8.02322i	0.163467	+	0.283133i
$804$	14.3422	+	17.5483i	0.505809	+	0.618882i
$805$	−10.4636	+	9.94047i	−0.368794	+	0.350355i
$806$	−2.02469	−	3.50686i	−0.0713166	−	0.123524i
$807$	−7.68068	−	9.39768i	−0.270373	−	0.330814i
$808$	15.2243			0.535588
$809$	−3.33325	−	5.77336i	−0.117191	−	0.202981i	0.801462	−	0.598045i	$-0.204056\pi$
$809$	−3.33325	−	5.77336i	−0.117191	−	0.202981i	−0.918653	+	0.395064i	$0.870722\pi$
$810$	4.29660	+	1.82062i	0.150967	+	0.0639701i
$811$	43.9145			1.54205			0.771024	−	0.636806i	$-0.219745\pi$
$811$	43.9145			1.54205			0.771024	+	0.636806i	$0.219745\pi$
$812$	−19.1633	−	5.66503i	−0.672499	−	0.198803i
$813$	1.70454	−	4.50118i	0.0597807	−	0.157863i
$814$	−20.1480			−0.706185
$815$	6.15718	−	10.6645i	0.215677	−	0.373563i
$816$	−4.21094	+	11.1198i	−0.147412	+	0.389272i
$817$	23.1413	+	40.0820i	0.809613	+	1.40229i
$818$	12.2180			0.427193
$819$	−36.0303	+	1.28924i	−1.25900	+	0.0450498i
$820$	−0.752947			−0.0262940
$821$	−14.3895	−	24.9233i	−0.502196	−	0.869830i	−0.999997	−	0.00253813i	$-0.999192\pi$
$821$	−14.3895	−	24.9233i	−0.502196	−	0.869830i	0.497800	−	0.867292i	$-0.334141\pi$
$822$	4.09481	+	5.01020i	0.142823	+	0.174751i
$823$	6.28560	−	10.8870i	0.219102	−	0.379496i	−0.735432	−	0.677599i	$-0.763021\pi$
$823$	6.28560	−	10.8870i	0.219102	−	0.379496i	0.954534	+	0.298103i	$0.0963538\pi$
$824$	31.8325			1.10894
$825$	7.12409	−	1.16138i	0.248029	−	0.0404340i
$826$	−10.6830	+	10.1489i	−0.371709	+	0.353125i
$827$	−30.9917			−1.07769			−0.538844	−	0.842405i	$-0.681139\pi$
$827$	−30.9917			−1.07769			−0.538844	+	0.842405i	$0.681139\pi$
$828$	−5.63951	+	27.7636i	−0.195986	+	0.964853i
$829$	−13.8314	−	23.9566i	−0.480383	−	0.832048i	0.519364	−	0.854553i	$-0.326169\pi$
$829$	−13.8314	−	23.9566i	−0.480383	−	0.832048i	−0.999747	+	0.0225055i	$0.992836\pi$
$830$	0.792110			0.0274945
$831$	12.3653	−	2.01581i	0.428949	−	0.0699278i
$832$	−5.11302	−	8.85602i	−0.177262	−	0.307027i
$833$	17.4007	−	8.89009i	0.602900	−	0.308023i
$834$	−4.48358	+	11.8398i	−0.155254	+	0.409979i
$835$	−7.25996	−	12.5746i	−0.251241	−	0.435163i
$836$	−16.0748	−	27.8424i	−0.555959	−	0.962950i
$837$	−0.346553	+	8.92742i	−0.0119786	+	0.308577i
$838$	−4.40145	+	7.62354i	−0.152046	+	0.263351i
$839$	−17.3283	+	30.0134i	−0.598238	+	1.03618i	0.394843	+	0.918748i	$0.370799\pi$
$839$	−17.3283	+	30.0134i	−0.598238	+	1.03618i	−0.993081	+	0.117430i	$0.962534\pi$
$840$	5.36117	−	7.06060i	0.184978	−	0.243614i
$841$	4.98259	+	8.63010i	0.171813	+	0.297590i
$842$	4.98327			0.171735
$843$	−8.75005	+	23.1063i	−0.301368	+	0.795823i
$844$	−27.7821			−0.956298
$845$	3.81624	−	6.60993i	0.131283	−	0.227388i
$846$	−2.32283	+	11.4354i	−0.0798605	+	0.393158i
$847$	−12.2132	+	11.6026i	−0.419652	+	0.398671i
$848$	−10.2618	+	17.7740i	−0.352392	+	0.610362i
$849$	−5.73623	+	15.1477i	−0.196867	+	0.519867i
$850$	0.723673	−	1.25344i	0.0248218	−	0.0429926i
$851$	25.4326	−	44.0506i	0.871819	−	1.51003i
$852$	−16.0347	+	42.3428i	−0.549338	+	1.45064i
$853$	−14.8192	+	25.6676i	−0.507400	+	0.878842i	0.492564	+	0.870276i	$0.336060\pi$
$853$	−14.8192	+	25.6676i	−0.507400	+	0.878842i	−0.999963	+	0.00856569i	$0.997273\pi$
$854$	−1.31929	−	5.48204i	−0.0451452	−	0.187591i
$855$	2.66121	−	13.1013i	0.0910115	−	0.448055i
$856$	8.77073	−	15.1914i	0.299777	−	0.519230i
$857$	49.8331			1.70227			0.851133	−	0.524951i	$-0.175916\pi$
$857$	49.8331			1.70227			0.851133	+	0.524951i	$0.175916\pi$
$858$	6.02036	−	15.8980i	0.205532	−	0.542748i
$859$	26.3010			0.897377			0.448689	−	0.893688i	$-0.351891\pi$
$859$	26.3010			0.897377			0.448689	+	0.893688i	$0.351891\pi$
$860$	8.98989	+	15.5709i	0.306553	+	0.530965i
$861$	1.97737	+	0.250139i	0.0673885	+	0.00852473i
$862$	9.06103	−	15.6942i	0.308620	−	0.534545i
$863$	14.6857	−	25.4363i	0.499906	−	0.865862i	−0.500094	−	0.865971i	$-0.666701\pi$
$863$	14.6857	−	25.4363i	0.499906	−	0.865862i	1.00000		0.000108680i	$3.45940e-5\pi$
$864$	1.03686	−	26.7103i	0.0352749	−	0.908702i
$865$	−1.89564	−	3.28334i	−0.0644535	−	0.111637i
$866$	2.15000	+	3.72391i	0.0730600	+	0.126544i
$867$	−5.64801	+	14.9147i	−0.191816	+	0.506531i
$868$	7.55207	+	2.23254i	0.256334	+	0.0757772i
$869$	2.06675	+	3.57971i	0.0701096	+	0.121433i
$870$	3.86706	−	0.630413i	0.131106	−	0.0213730i
$871$	34.3326			1.16331
$872$	−10.3973	−	18.0087i	−0.352098	−	0.609851i
$873$	−10.0796	+	49.6223i	−0.341142	+	1.67946i
$874$	−12.6040			−0.426338
$875$	1.91816	−	1.82226i	0.0648458	−	0.0616038i
$876$	6.57897	−	1.07251i	0.222283	−	0.0362368i
$877$	−50.8198			−1.71606			−0.858032	−	0.513596i	$-0.828313\pi$
$877$	−50.8198			−1.71606			−0.858032	+	0.513596i	$0.828313\pi$
$878$	0.784235	−	1.35833i	0.0264666	−	0.0458416i
$879$	29.8753	+	36.5539i	1.00767	+	1.23293i
$880$	−5.12438	−	8.87568i	−0.172743	−	0.299199i
$881$	−57.2561			−1.92901			−0.964504	−	0.264068i	$-0.914936\pi$
$881$	−57.2561			−1.92901			−0.964504	+	0.264068i	$0.914936\pi$
$882$	−7.62078	+	7.77682i	−0.256605	+	0.261859i
$883$	−13.4051			−0.451118			−0.225559	−	0.974230i	$-0.572421\pi$
$883$	−13.4051			−0.451118			−0.225559	+	0.974230i	$0.572421\pi$
$884$	10.9753	+	19.0097i	0.369139	+	0.639367i
$885$	−6.58881	+	17.3991i	−0.221480	+	0.584864i
$886$	2.45088	−	4.24506i	0.0823391	−	0.142615i
$887$	−27.2243			−0.914103			−0.457052	−	0.889440i	$-0.651095\pi$
$887$	−27.2243			−0.914103			−0.457052	+	0.889440i	$0.651095\pi$
$888$	−11.0650	+	29.2195i	−0.371318	+	0.980541i
$889$	8.31251	−	7.89692i	0.278793	−	0.264854i
$890$	1.07975			0.0361932
$891$	−29.9399	+	22.5908i	−1.00302	+	0.756819i
$892$	−0.539011	−	0.933595i	−0.0180474	−	0.0312591i
$893$	33.4304			1.11871
$894$	4.08590	+	4.99929i	0.136653	+	0.167201i
$895$	−10.8720	−	18.8309i	−0.363412	−	0.629448i
$896$	−29.0658	−	8.59239i	−0.971019	−	0.287052i
$897$	27.1592	+	33.2306i	0.906819	+	1.10954i
$898$	−7.01891	−	12.1571i	−0.234224	−	0.405688i
$899$	3.75073	+	6.49645i	0.125094	+	0.216669i
$900$	1.03382	−	5.08956i	0.0344607	−	0.169652i
$901$	11.6479	−	20.1748i	0.388049	−	0.672120i
$902$	−0.469895	+	0.813882i	−0.0156458	+	0.0270993i
$903$	−18.4361	−	43.8786i	−0.613515	−	1.46019i
$904$	9.06215	+	15.6961i	0.301403	+	0.522045i
$905$	13.4199			0.446093
$906$	−5.59093	−	6.84077i	−0.185746	−	0.227269i
$907$	−5.43501			−0.180467			−0.0902333	−	0.995921i	$-0.528761\pi$
$907$	−5.43501			−0.180467			−0.0902333	+	0.995921i	$0.528761\pi$
$908$	15.1595	−	26.2570i	0.503084	−	0.871368i
$909$	−22.3863	+	7.49817i	−0.742507	+	0.248698i
$910$	−1.45794	−	6.05816i	−0.0483302	−	0.200826i
$911$	−19.9220	+	34.5060i	−0.660047	+	1.14323i	0.320556	+	0.947230i	$0.396130\pi$
$911$	−19.9220	+	34.5060i	−0.660047	+	1.14323i	−0.980603	+	0.196005i	$0.937203\pi$
$912$	−18.7346	+	3.05414i	−0.620365	+	0.101133i
$913$	−3.18331	+	5.51365i	−0.105352	+	0.182475i
$914$	1.30676	−	2.26337i	0.0432237	−	0.0748657i
$915$	−4.50529	−	5.51244i	−0.148940	−	0.182236i
$916$	8.23049	−	14.2556i	0.271943	−	0.471019i
$917$	−19.0454	+	18.0932i	−0.628934	+	0.597490i
$918$	−0.291723	+	7.51497i	−0.00962830	+	0.248031i
$919$	2.17725	−	3.77110i	0.0718207	−	0.124397i	−0.827879	−	0.560907i	$-0.810452\pi$
$919$	2.17725	−	3.77110i	0.0718207	−	0.124397i	0.899699	+	0.436510i	$0.143786\pi$
$920$	−10.5531			−0.347927
$921$	−19.9621	+	3.25425i	−0.657773	+	0.107231i
$922$	16.6009			0.546720
$923$	34.2946	+	59.3999i	1.12882	+	1.95517i
$924$	12.8064	+	30.4797i	0.421300	+	1.00271i
$925$	−4.66225	+	8.07525i	−0.153294	+	0.265513i
$926$	0.252187	−	0.436800i	0.00828737	−	0.0143541i
$927$	−46.8077	+	15.6780i	−1.53737	+	0.514932i
$928$	−11.2219	−	19.4370i	−0.368378	−	0.638049i
$929$	−17.1482	−	29.7015i	−0.562613	−	0.974475i	−0.997267	−	0.0738772i	$-0.976463\pi$
$929$	−17.1482	−	29.7015i	−0.562613	−	0.974475i	0.434654	−	0.900597i	$-0.356871\pi$
$930$	−1.52397	+	0.248440i	−0.0499730	+	0.00814667i
$931$	26.1800	+	16.9609i	0.858016	+	0.555870i
$932$	0.225019	+	0.389744i	0.00737074	+	0.0127665i
$933$	0.627958	−	1.65825i	0.0205584	−	0.0542887i
$934$	−18.8030			−0.615254
$935$	5.81655	+	10.0746i	0.190221	+	0.329473i
$936$	−19.7497	−	17.4620i	−0.645538	−	0.570763i
$937$	12.8590			0.420084			0.210042	−	0.977692i	$-0.432640\pi$
$937$	12.8590			0.420084			0.210042	+	0.977692i	$0.432640\pi$
$938$	7.51722	−	7.14139i	0.245446	−	0.233175i
$939$	−12.1209	−	14.8305i	−0.395551	−	0.483976i
$940$	12.9870			0.423589
$941$	−15.1313	+	26.2082i	−0.493267	+	0.854363i	−0.999970	−	0.00775729i	$-0.997531\pi$
$941$	−15.1313	+	26.2082i	−0.493267	+	0.854363i	0.506703	+	0.862121i	$0.330864\pi$
$942$	−9.07911	+	1.48009i	−0.295814	+	0.0482239i
$943$	−1.18629	−	2.05471i	−0.0386309	−	0.0669107i
$944$	26.4163			0.859779
$945$	−4.40582	+	13.0226i	−0.143321	+	0.423626i
$946$	22.4414			0.729634
$947$	24.6104	+	42.6264i	0.799730	+	1.38517i	0.919792	+	0.392407i	$0.128357\pi$
$947$	24.6104	+	42.6264i	0.799730	+	1.38517i	−0.120061	+	0.992766i	$0.538309\pi$
$948$	2.93533	−	0.478522i	0.0953351	−	0.0155417i
$949$	5.04893	−	8.74501i	0.163895	−	0.283875i
$950$	2.31054			0.0749639
$951$	10.3984	+	12.7229i	0.337190	+	0.412568i
$952$	13.7017	+	4.05047i	0.444073	+	0.131276i
$953$	23.7257			0.768552			0.384276	−	0.923218i	$-0.374451\pi$
$953$	23.7257			0.768552			0.384276	+	0.923218i	$0.374451\pi$
$954$	−2.58402	+	12.7213i	−0.0836607	+	0.411866i
$955$	−5.30469	−	9.18799i	−0.171656	−	0.297316i
$956$	6.61123			0.213823
$957$	−11.1527	+	29.4510i	−0.360515	+	0.952014i
$958$	10.0787	+	17.4568i	0.325627	+	0.564003i
$959$	−13.8208	+	13.1298i	−0.446297	+	0.423984i
$960$	−3.84855	+	0.627396i	−0.124211	+	0.0202491i
$961$	14.0219	+	24.2866i	0.452318	+	0.783439i
$962$	10.9803	+	19.0184i	0.354018	+	0.613177i
$963$	−5.41485	+	26.6576i	−0.174491	+	0.859030i
$964$	−6.95576	+	12.0477i	−0.224030	+	0.388031i
$965$	−11.0661	+	19.1670i	−0.356229	+	0.617007i
$966$	12.8588	+	1.62665i	0.413724	+	0.0523366i
$967$	8.60234	+	14.8997i	0.276632	+	0.479141i	0.970546	−	0.240917i	$-0.0774482\pi$
$967$	8.60234	+	14.8997i	0.276632	+	0.479141i	−0.693913	+	0.720059i	$0.744115\pi$
$968$	−12.3177			−0.395907
$969$	21.2652	−	3.46668i	0.683136	−	0.111366i
$970$	−8.75138			−0.280990
$971$	17.7098	−	30.6742i	0.568333	−	0.984382i	−0.428398	−	0.903590i	$-0.640922\pi$
$971$	17.7098	−	30.6742i	0.568333	−	0.984382i	0.996731	−	0.0807916i	$-0.0257448\pi$
$972$	7.57184	+	25.9022i	0.242867	+	0.830813i
$973$	−35.7683	−	10.5738i	−1.14668	−	0.338980i
$974$	9.42337	−	16.3218i	0.301944	−	0.522983i
$975$	−4.97876	−	6.09175i	−0.159448	−	0.195092i
$976$	−5.05422	+	8.75417i	−0.161782	+	0.280214i
$977$	18.8484	−	32.6463i	0.603012	−	1.04445i	−0.389350	−	0.921090i	$-0.627300\pi$
$977$	18.8484	−	32.6463i	0.603012	−	1.04445i	0.992362	−	0.123358i	$-0.0393663\pi$
$978$	−10.9149	+	1.77935i	−0.349019	+	0.0568975i
$979$	−4.33925	+	7.51581i	−0.138683	+	0.240206i
$980$	10.1704	+	6.58891i	0.324880	+	0.210475i
$981$	24.1581	+	21.3598i	0.771309	+	0.681966i
$982$	1.61761	−	2.80179i	0.0516201	−	0.0894087i
$983$	25.9521			0.827742			0.413871	−	0.910336i	$-0.364176\pi$
$983$	25.9521			0.827742			0.413871	+	0.910336i	$0.364176\pi$
$984$	0.922267	+	1.12844i	0.0294008	+	0.0359733i
$985$	−7.40378			−0.235904
$986$	3.15730	+	5.46861i	0.100549	+	0.174156i
$987$	−34.1061	−	4.31446i	−1.08561	−	0.137331i
$988$	−17.5210	+	30.3472i	−0.557416	+	0.965473i
$989$	−28.3277	+	49.0650i	−0.900768	+	1.56018i
$990$	−4.85628	−	4.29376i	−0.154343	−	0.136465i
$991$	19.7117	+	34.1418i	0.626164	+	1.08455i	0.988314	+	0.152429i	$0.0487094\pi$
$991$	19.7117	+	34.1418i	0.626164	+	1.08455i	−0.362150	+	0.932120i	$0.617957\pi$
$992$	4.42246	+	7.65993i	0.140413	+	0.243203i
$993$	−38.8370	−	47.5189i	−1.23246	−	1.50797i
$994$	19.8645	+	5.87231i	0.630063	+	0.186258i
$995$	5.47597	+	9.48465i	0.173600	+	0.300684i
$996$	2.89887	+	3.54690i	0.0918542	+	0.112388i
$997$	−37.3818			−1.18389			−0.591947	−	0.805977i	$-0.701641\pi$
$997$	−37.3818			−1.18389			−0.591947	+	0.805977i	$0.701641\pi$
$998$	−1.44009	−	2.49432i	−0.0455854	−	0.0789562i
$999$	1.87942	−	48.4150i	0.0594623	−	1.53178i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.k.b.16.5	✓	24
3.2	odd	2		945.2.k.b.856.8		24
7.4	even	3		315.2.l.b.151.8	yes	24
9.4	even	3		315.2.l.b.121.8	yes	24
9.5	odd	6		945.2.l.b.226.5		24
21.11	odd	6		945.2.l.b.46.5		24
63.4	even	3	inner	315.2.k.b.256.5	yes	24
63.32	odd	6		945.2.k.b.361.8		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.k.b.16.5	✓	24	1.1	even	1	trivial
315.2.k.b.256.5	yes	24	63.4	even	3	inner
315.2.l.b.121.8	yes	24	9.4	even	3
315.2.l.b.151.8	yes	24	7.4	even	3
945.2.k.b.361.8		24	63.32	odd	6
945.2.k.b.856.8		24	3.2	odd	2
945.2.l.b.46.5		24	21.11	odd	6
945.2.l.b.226.5		24	9.5	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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.k (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.259245 - 0.449026i) q^{2} +(-1.70948 + 0.278682i) q^{3} +(0.865584 - 1.49923i) q^{4} -1.00000 q^{5} +(0.568312 + 0.695356i) q^{6} +(-1.91816 + 1.82226i) q^{7} -1.93458 q^{8} +(2.84467 - 0.952806i) q^{9} +O(q^{10})\)	\(q+(-0.259245 - 0.449026i) q^{2} +(-1.70948 + 0.278682i) q^{3} +(0.865584 - 1.49923i) q^{4} -1.00000 q^{5} +(0.568312 + 0.695356i) q^{6} +(-1.91816 + 1.82226i) q^{7} -1.93458 q^{8} +(2.84467 - 0.952806i) q^{9} +(0.259245 + 0.449026i) q^{10} -4.16739 q^{11} +(-1.06189 + 2.80414i) q^{12} +(2.27115 + 3.93375i) q^{13} +(1.31552 + 0.388893i) q^{14} +(1.70948 - 0.278682i) q^{15} +(-1.22964 - 2.12979i) q^{16} +(1.39573 + 2.41747i) q^{17} +(-1.16530 - 1.03032i) q^{18} +(-2.22814 + 3.85926i) q^{19} +(-0.865584 + 1.49923i) q^{20} +(2.77124 - 3.64969i) q^{21} +(1.08038 + 1.87127i) q^{22} -5.45501 q^{23} +(3.30713 - 0.539132i) q^{24} +1.00000 q^{25} +(1.17757 - 2.03961i) q^{26} +(-4.59739 + 2.42157i) q^{27} +(1.07167 + 4.45310i) q^{28} +(-2.18145 + 3.77837i) q^{29} +(-0.568312 - 0.695356i) q^{30} +(0.859688 - 1.48902i) q^{31} +(-2.57213 + 4.45506i) q^{32} +(7.12409 - 1.16138i) q^{33} +(0.723673 - 1.25344i) q^{34} +(1.91816 - 1.82226i) q^{35} +(1.03382 - 5.08956i) q^{36} +(-4.66225 + 8.07525i) q^{37} +2.31054 q^{38} +(-4.97876 - 6.09175i) q^{39} +1.93458 q^{40} +(0.217468 + 0.376665i) q^{41} +(-2.35724 - 0.298194i) q^{42} +(5.19296 - 8.99448i) q^{43} +(-3.60723 + 6.24790i) q^{44} +(-2.84467 + 0.952806i) q^{45} +(1.41419 + 2.44944i) q^{46} +(-3.75093 - 6.49681i) q^{47} +(2.69558 + 3.29817i) q^{48} +(0.358708 - 6.99080i) q^{49} +(-0.259245 - 0.449026i) q^{50} +(-3.05968 - 3.74367i) q^{51} +7.86348 q^{52} +(-4.17271 - 7.22734i) q^{53} +(2.27920 + 1.43657i) q^{54} +4.16739 q^{55} +(3.71084 - 3.52531i) q^{56} +(2.73347 - 7.21828i) q^{57} +2.26212 q^{58} +(-5.37076 + 9.30243i) q^{59} +(1.06189 - 2.80414i) q^{60} +(-2.05517 - 3.55966i) q^{61} -0.891481 q^{62} +(-3.72028 + 7.01138i) q^{63} -2.25129 q^{64} +(-2.27115 - 3.93375i) q^{65} +(-2.36838 - 2.89782i) q^{66} +(3.77921 - 6.54578i) q^{67} +4.83248 q^{68} +(9.32525 - 1.52022i) q^{69} +(-1.31552 - 0.388893i) q^{70} +15.1001 q^{71} +(-5.50324 + 1.84328i) q^{72} +(-1.11154 - 1.92524i) q^{73} +4.83467 q^{74} +(-1.70948 + 0.278682i) q^{75} +(3.85729 + 6.68102i) q^{76} +(7.99374 - 7.59409i) q^{77} +(-1.44463 + 3.81485i) q^{78} +(-0.495933 - 0.858981i) q^{79} +(1.22964 + 2.12979i) q^{80} +(7.18432 - 5.42084i) q^{81} +(0.112755 - 0.195298i) q^{82} +(0.763861 - 1.32305i) q^{83} +(-3.07300 - 7.31385i) q^{84} +(-1.39573 - 2.41747i) q^{85} -5.38501 q^{86} +(2.67618 - 7.06700i) q^{87} +8.06214 q^{88} +(1.04124 - 1.80348i) q^{89} +(1.16530 + 1.03032i) q^{90} +(-11.5248 - 3.40694i) q^{91} +(-4.72177 + 8.17834i) q^{92} +(-1.05466 + 2.78504i) q^{93} +(-1.94482 + 3.36853i) q^{94} +(2.22814 - 3.85926i) q^{95} +(3.15547 - 8.33267i) q^{96} +(-8.43928 + 14.6173i) q^{97} +(-3.23205 + 1.65126i) q^{98} +(-11.8549 + 3.97072i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - q^{2} + q^{3} - 7 q^{4} - 24 q^{5} + 3 q^{6} + 7 q^{7} + 12 q^{8} + 9 q^{9}+O(q^{10}) \) 24 * q - q^2 + q^3 - 7 * q^4 - 24 * q^5 + 3 * q^6 + 7 * q^7 + 12 * q^8 + 9 * q^9	\( 24 q - q^{2} + q^{3} - 7 q^{4} - 24 q^{5} + 3 q^{6} + 7 q^{7} + 12 q^{8} + 9 q^{9} + q^{10} - 2 q^{11} - 16 q^{12} - 4 q^{13} - 13 q^{14} - q^{15} - 5 q^{16} - 7 q^{17} - 12 q^{18} - 2 q^{19} + 7 q^{20} - 5 q^{21} + 19 q^{22} - 2 q^{23} - 30 q^{24} + 24 q^{25} + 11 q^{26} - 11 q^{27} - 28 q^{28} - 3 q^{30} + 8 q^{31} + 17 q^{32} + q^{33} + q^{34} - 7 q^{35} - 25 q^{36} + 17 q^{37} + 70 q^{38} - 8 q^{39} - 12 q^{40} + 20 q^{41} - 15 q^{42} + 31 q^{43} - 7 q^{44} - 9 q^{45} - 10 q^{46} - 31 q^{47} - 36 q^{48} - 11 q^{49} - q^{50} - 37 q^{51} + 8 q^{52} + 8 q^{53} + 111 q^{54} + 2 q^{55} + 45 q^{56} + 5 q^{57} - 90 q^{58} - 21 q^{59} + 16 q^{60} + 5 q^{61} + 14 q^{62} - 9 q^{63} - 56 q^{64} + 4 q^{65} + 46 q^{66} + 43 q^{67} + 96 q^{68} + 26 q^{69} + 13 q^{70} + 24 q^{71} - 69 q^{72} - 18 q^{73} - 18 q^{74} + q^{75} - 13 q^{76} + 5 q^{77} + 19 q^{78} + 40 q^{79} + 5 q^{80} - 39 q^{81} + 5 q^{82} - 60 q^{83} + 47 q^{84} + 7 q^{85} - 24 q^{86} - 61 q^{87} - 100 q^{88} - 4 q^{89} + 12 q^{90} - 33 q^{91} - 18 q^{92} - 8 q^{93} - 11 q^{94} + 2 q^{95} + 6 q^{96} + 6 q^{97} - 15 q^{98} - q^{99}+O(q^{100}) \) 24 * q - q^2 + q^3 - 7 * q^4 - 24 * q^5 + 3 * q^6 + 7 * q^7 + 12 * q^8 + 9 * q^9 + q^10 - 2 * q^11 - 16 * q^12 - 4 * q^13 - 13 * q^14 - q^15 - 5 * q^16 - 7 * q^17 - 12 * q^18 - 2 * q^19 + 7 * q^20 - 5 * q^21 + 19 * q^22 - 2 * q^23 - 30 * q^24 + 24 * q^25 + 11 * q^26 - 11 * q^27 - 28 * q^28 - 3 * q^30 + 8 * q^31 + 17 * q^32 + q^33 + q^34 - 7 * q^35 - 25 * q^36 + 17 * q^37 + 70 * q^38 - 8 * q^39 - 12 * q^40 + 20 * q^41 - 15 * q^42 + 31 * q^43 - 7 * q^44 - 9 * q^45 - 10 * q^46 - 31 * q^47 - 36 * q^48 - 11 * q^49 - q^50 - 37 * q^51 + 8 * q^52 + 8 * q^53 + 111 * q^54 + 2 * q^55 + 45 * q^56 + 5 * q^57 - 90 * q^58 - 21 * q^59 + 16 * q^60 + 5 * q^61 + 14 * q^62 - 9 * q^63 - 56 * q^64 + 4 * q^65 + 46 * q^66 + 43 * q^67 + 96 * q^68 + 26 * q^69 + 13 * q^70 + 24 * q^71 - 69 * q^72 - 18 * q^73 - 18 * q^74 + q^75 - 13 * q^76 + 5 * q^77 + 19 * q^78 + 40 * q^79 + 5 * q^80 - 39 * q^81 + 5 * q^82 - 60 * q^83 + 47 * q^84 + 7 * q^85 - 24 * q^86 - 61 * q^87 - 100 * q^88 - 4 * q^89 + 12 * q^90 - 33 * q^91 - 18 * q^92 - 8 * q^93 - 11 * q^94 + 2 * q^95 + 6 * q^96 + 6 * q^97 - 15 * q^98 - q^99

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