LMFDB - Embedded newform 343.2.e.d.99.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [343,2,Mod(50,343)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(343, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([12]))

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

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

chi := DirichletCharacter("343.50");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 343 = 7^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	343.e (of order $7$, degree $6$, not 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:	$2.73886878933$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{7})$
Twist minimal:	no (minimal twist has level 49)
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			99.1
Character	$\chi$	$=$	343.99
Dual form			343.2.e.d.246.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.525663 + 2.30308i) q^{2} +(-1.75326 + 2.19852i) q^{3} +(-3.22592 - 1.55352i) q^{4} +(-0.969239 + 1.21539i) q^{5} +(-4.14175 - 5.19359i) q^{6} +(2.32789 - 2.91908i) q^{8} +(-1.09201 - 4.78439i) q^{9} +O(q^{10})$	\(q+(-0.525663 + 2.30308i) q^{2} +(-1.75326 + 2.19852i) q^{3} +(-3.22592 - 1.55352i) q^{4} +(-0.969239 + 1.21539i) q^{5} +(-4.14175 - 5.19359i) q^{6} +(2.32789 - 2.91908i) q^{8} +(-1.09201 - 4.78439i) q^{9} +(-2.28964 - 2.87112i) q^{10} +(0.154470 - 0.676778i) q^{11} +(9.07134 - 4.36853i) q^{12} +(-0.928088 + 4.06622i) q^{13} +(-0.972725 - 4.26179i) q^{15} +(1.03437 + 1.29706i) q^{16} +(0.718981 - 0.346243i) q^{17} +11.5929 q^{18} -2.10874 q^{19} +(5.01482 - 2.41501i) q^{20} +(1.47747 + 0.711514i) q^{22} +(4.93736 + 2.37771i) q^{23} +(2.33626 + 10.2358i) q^{24} +(0.574863 + 2.51864i) q^{25} +(-8.87698 - 4.27493i) q^{26} +(4.83254 + 2.32723i) q^{27} +(0.0358031 - 0.0172419i) q^{29} +10.3266 q^{30} -2.43231 q^{31} +(3.19682 - 1.53951i) q^{32} +(1.21708 + 1.52618i) q^{33} +(0.419484 + 1.83788i) q^{34} +(-3.90993 + 17.1305i) q^{36} +(-8.68149 + 4.18078i) q^{37} +(1.10849 - 4.85660i) q^{38} +(-7.31249 - 9.16958i) q^{39} +(1.29153 + 5.65857i) q^{40} +(2.97571 - 3.73142i) q^{41} +(-4.04621 - 5.07379i) q^{43} +(-1.54970 + 1.94326i) q^{44} +(6.87330 + 3.31001i) q^{45} +(-8.07144 + 10.1213i) q^{46} +(1.24666 - 5.46199i) q^{47} -4.66515 q^{48} -6.10281 q^{50} +(-0.499340 + 2.18775i) q^{51} +(9.31091 - 11.6755i) q^{52} +(8.27149 + 3.98334i) q^{53} +(-7.90009 + 9.90640i) q^{54} +(0.672829 + 0.843700i) q^{55} +(3.69718 - 4.63611i) q^{57} +(0.0208891 + 0.0915209i) q^{58} +(-6.70433 - 8.40697i) q^{59} +(-3.48285 + 15.2593i) q^{60} +(4.29648 - 2.06908i) q^{61} +(1.27857 - 5.60180i) q^{62} +(2.60348 + 11.4066i) q^{64} +(-4.04249 - 5.06913i) q^{65} +(-4.15468 + 2.00079i) q^{66} -7.91320 q^{67} -2.85727 q^{68} +(-13.8839 + 6.68615i) q^{69} +(-3.10167 - 1.49368i) q^{71} +(-16.5081 - 7.94987i) q^{72} +(-0.560627 - 2.45627i) q^{73} +(-5.06515 - 22.1919i) q^{74} +(-6.54517 - 3.15199i) q^{75} +(6.80263 + 3.27598i) q^{76} +(24.9622 - 12.0212i) q^{78} -10.6304 q^{79} -2.57899 q^{80} +(-0.324859 + 0.156444i) q^{81} +(7.02954 + 8.81477i) q^{82} +(2.05809 + 9.01706i) q^{83} +(-0.276045 + 1.20943i) q^{85} +(13.8123 - 6.65165i) q^{86} +(-0.0248656 + 0.108944i) q^{87} +(-1.61598 - 2.02637i) q^{88} +(0.00588647 + 0.0257903i) q^{89} +(-11.2363 + 14.0898i) q^{90} +(-12.2337 - 15.3406i) q^{92} +(4.26447 - 5.34748i) q^{93} +(11.9241 + 5.74234i) q^{94} +(2.04387 - 2.56294i) q^{95} +(-2.22022 + 9.72743i) q^{96} -11.7290 q^{97} -3.40665 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 5 q^{2} + 7 q^{3} - 3 q^{4} + 7 q^{5} - 20 q^{8} + 9 q^{9}+O(q^{10}) $ 48 * q + 5 * q^2 + 7 * q^3 - 3 * q^4 + 7 * q^5 - 20 * q^8 + 9 * q^9	$ 48 q + 5 q^{2} + 7 q^{3} - 3 q^{4} + 7 q^{5} - 20 q^{8} + 9 q^{9} + 7 q^{10} + 6 q^{11} + 42 q^{12} - 14 q^{13} - 12 q^{15} - 15 q^{16} - 7 q^{17} - 4 q^{18} - 42 q^{19} + 14 q^{20} - 20 q^{22} + 12 q^{23} + 49 q^{24} - 13 q^{25} + 21 q^{26} + 7 q^{27} + 12 q^{29} - 22 q^{30} - 70 q^{31} + 15 q^{32} + 7 q^{33} + 70 q^{34} - 12 q^{36} - 9 q^{37} - 7 q^{38} - 28 q^{39} - 63 q^{40} - 42 q^{41} - 30 q^{43} + 37 q^{44} + 28 q^{45} + 9 q^{46} + 21 q^{47} - 84 q^{48} + 40 q^{50} - q^{51} + 77 q^{52} + 20 q^{53} + 7 q^{54} - 7 q^{55} - 12 q^{57} + 31 q^{58} - 7 q^{59} + 35 q^{60} + 7 q^{61} - 28 q^{62} - 32 q^{64} - 49 q^{65} - 119 q^{66} - 22 q^{67} - 154 q^{68} + 70 q^{69} + 19 q^{71} - 46 q^{72} + 28 q^{73} - 47 q^{74} + 7 q^{75} + 119 q^{76} + 28 q^{78} - 30 q^{79} - 140 q^{80} + 61 q^{81} + 112 q^{82} - 26 q^{85} + 24 q^{86} + 77 q^{87} + 28 q^{88} + 28 q^{89} - 182 q^{90} - 38 q^{92} + 34 q^{93} - 28 q^{94} - 67 q^{95} - 28 q^{96} - 16 q^{99}+O(q^{100}) $ 48 * q + 5 * q^2 + 7 * q^3 - 3 * q^4 + 7 * q^5 - 20 * q^8 + 9 * q^9 + 7 * q^10 + 6 * q^11 + 42 * q^12 - 14 * q^13 - 12 * q^15 - 15 * q^16 - 7 * q^17 - 4 * q^18 - 42 * q^19 + 14 * q^20 - 20 * q^22 + 12 * q^23 + 49 * q^24 - 13 * q^25 + 21 * q^26 + 7 * q^27 + 12 * q^29 - 22 * q^30 - 70 * q^31 + 15 * q^32 + 7 * q^33 + 70 * q^34 - 12 * q^36 - 9 * q^37 - 7 * q^38 - 28 * q^39 - 63 * q^40 - 42 * q^41 - 30 * q^43 + 37 * q^44 + 28 * q^45 + 9 * q^46 + 21 * q^47 - 84 * q^48 + 40 * q^50 - q^51 + 77 * q^52 + 20 * q^53 + 7 * q^54 - 7 * q^55 - 12 * q^57 + 31 * q^58 - 7 * q^59 + 35 * q^60 + 7 * q^61 - 28 * q^62 - 32 * q^64 - 49 * q^65 - 119 * q^66 - 22 * q^67 - 154 * q^68 + 70 * q^69 + 19 * q^71 - 46 * q^72 + 28 * q^73 - 47 * q^74 + 7 * q^75 + 119 * q^76 + 28 * q^78 - 30 * q^79 - 140 * q^80 + 61 * q^81 + 112 * q^82 - 26 * q^85 + 24 * q^86 + 77 * q^87 + 28 * q^88 + 28 * q^89 - 182 * q^90 - 38 * q^92 + 34 * q^93 - 28 * q^94 - 67 * q^95 - 28 * q^96 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/343\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{5}{7}\right)$

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 $

$2$	−0.525663	+	2.30308i	−0.371700	+	1.62852i	0.350304	+	0.936636i	$0.386078\pi$
$2$	−0.525663	+	2.30308i	−0.371700	+	1.62852i	−0.722004	+	0.691888i	$0.756779\pi$
$3$	−1.75326	+	2.19852i	−1.01225	+	1.26932i	−0.0495393	+	0.998772i	$0.515775\pi$
$3$	−1.75326	+	2.19852i	−1.01225	+	1.26932i	−0.962707	+	0.270545i	$0.912796\pi$
$4$	−3.22592	−	1.55352i	−1.61296	−	0.776761i
$5$	−0.969239	+	1.21539i	−0.433457	+	0.543538i	−0.949806	−	0.312841i	$-0.898719\pi$
$5$	−0.969239	+	1.21539i	−0.433457	+	0.543538i	0.516349	+	0.856378i	$0.327291\pi$
$6$	−4.14175	−	5.19359i	−1.69086	−	2.12027i
$7$		0			0
$7$		0			0
$8$	2.32789	−	2.91908i	0.823032	−	1.03205i
$9$	−1.09201	−	4.78439i	−0.364002	−	1.59480i
$10$	−2.28964	−	2.87112i	−0.724048	−	0.907928i
$11$	0.154470	−	0.676778i	0.0465745	−	0.204056i	−0.946287	−	0.323327i	$-0.895199\pi$
$11$	0.154470	−	0.676778i	0.0465745	−	0.204056i	0.992862	+	0.119271i	$0.0380557\pi$
$12$	9.07134	−	4.36853i	2.61867	−	1.26109i
$13$	−0.928088	+	4.06622i	−0.257405	+	1.12777i	0.666608	+	0.745408i	$0.267745\pi$
$13$	−0.928088	+	4.06622i	−0.257405	+	1.12777i	−0.924014	+	0.382359i	$0.875112\pi$
$14$		0			0
$15$	−0.972725	−	4.26179i	−0.251156	−	1.10039i
$16$	1.03437	+	1.29706i	0.258593	+	0.324266i
$17$	0.718981	−	0.346243i	0.174378	−	0.0839762i	−0.344658	−	0.938728i	$-0.612005\pi$
$17$	0.718981	−	0.346243i	0.174378	−	0.0839762i	0.519037	+	0.854752i	$0.326291\pi$
$18$	11.5929			2.73246
$19$	−2.10874			−0.483778			−0.241889	−	0.970304i	$-0.577767\pi$
$19$	−2.10874			−0.483778			−0.241889	+	0.970304i	$0.577767\pi$
$20$	5.01482	−	2.41501i	1.12135	−	0.540013i
$21$		0			0
$22$	1.47747	+	0.711514i	0.314999	+	0.151695i
$23$	4.93736	+	2.37771i	1.02951	+	0.495786i	0.870851	−	0.491547i	$-0.163568\pi$
$23$	4.93736	+	2.37771i	1.02951	+	0.495786i	0.158660	+	0.987333i	$0.449283\pi$
$24$	2.33626	+	10.2358i	0.476887	+	2.08938i
$25$	0.574863	+	2.51864i	0.114973	+	0.503728i
$26$	−8.87698	−	4.27493i	−1.74092	−	0.838382i
$27$	4.83254	+	2.32723i	0.930023	+	0.447875i
$28$		0			0
$29$	0.0358031	−	0.0172419i	0.00664847	−	0.00320174i	−0.430557	−	0.902564i	$-0.641683\pi$
$29$	0.0358031	−	0.0172419i	0.00664847	−	0.00320174i	0.437205	+	0.899362i	$0.355968\pi$
$30$	10.3266			1.88536
$31$	−2.43231			−0.436855			−0.218428	−	0.975853i	$-0.570093\pi$
$31$	−2.43231			−0.436855			−0.218428	+	0.975853i	$0.570093\pi$
$32$	3.19682	−	1.53951i	0.565123	−	0.272149i
$33$	1.21708	+	1.52618i	0.211867	+	0.265673i
$34$	0.419484	+	1.83788i	0.0719409	+	0.315194i
$35$		0			0
$36$	−3.90993	+	17.1305i	−0.651655	+	2.85509i
$37$	−8.68149	+	4.18078i	−1.42723	+	0.687317i	−0.978480	−	0.206342i	$-0.933844\pi$
$37$	−8.68149	+	4.18078i	−1.42723	+	0.687317i	−0.448748	+	0.893658i	$0.648130\pi$
$38$	1.10849	−	4.85660i	0.179820	−	0.787844i
$39$	−7.31249	−	9.16958i	−1.17094	−	1.46831i
$40$	1.29153	+	5.65857i	0.204209	+	0.894698i
$41$	2.97571	−	3.73142i	0.464728	−	0.582750i	−0.493144	−	0.869948i	$-0.664152\pi$
$41$	2.97571	−	3.73142i	0.464728	−	0.582750i	0.957871	+	0.287198i	$0.0927238\pi$
$42$		0			0
$43$	−4.04621	−	5.07379i	−0.617042	−	0.773746i	0.370883	−	0.928680i	$-0.379055\pi$
$43$	−4.04621	−	5.07379i	−0.617042	−	0.773746i	−0.987925	+	0.154933i	$0.950484\pi$
$44$	−1.54970	+	1.94326i	−0.233626	+	0.292958i
$45$	6.87330	+	3.31001i	1.02461	+	0.493427i
$46$	−8.07144	+	10.1213i	−1.19007	+	1.49230i
$47$	1.24666	−	5.46199i	0.181845	−	0.796714i	−0.798907	−	0.601455i	$-0.794588\pi$
$47$	1.24666	−	5.46199i	0.181845	−	0.796714i	0.980752	−	0.195259i	$-0.0625547\pi$
$48$	−4.66515			−0.673356
$49$		0			0
$50$	−6.10281			−0.863068
$51$	−0.499340	+	2.18775i	−0.0699215	+	0.306346i
$52$	9.31091	−	11.6755i	1.29119	−	1.61910i
$53$	8.27149	+	3.98334i	1.13618	+	0.547154i	0.904853	−	0.425723i	$-0.139980\pi$
$53$	8.27149	+	3.98334i	1.13618	+	0.547154i	0.231323	+	0.972877i	$0.425695\pi$
$54$	−7.90009	+	9.90640i	−1.07507	+	1.34809i
$55$	0.672829	+	0.843700i	0.0907242	+	0.113765i
$56$		0			0
$57$	3.69718	−	4.63611i	0.489703	−	0.614068i
$58$	0.0208891	+	0.0915209i	0.00274287	+	0.0120173i
$59$	−6.70433	−	8.40697i	−0.872830	−	1.09449i	−0.994789	−	0.101959i	$-0.967489\pi$
$59$	−6.70433	−	8.40697i	−0.872830	−	1.09449i	0.121959	−	0.992535i	$-0.461082\pi$
$60$	−3.48285	+	15.2593i	−0.449634	+	1.96997i
$61$	4.29648	−	2.06908i	0.550108	−	0.264918i	−0.138116	−	0.990416i	$-0.544105\pi$
$61$	4.29648	−	2.06908i	0.550108	−	0.264918i	0.688224	+	0.725498i	$0.258390\pi$
$62$	1.27857	−	5.60180i	0.162379	−	0.711429i
$63$		0			0
$64$	2.60348	+	11.4066i	0.325436	+	1.42583i
$65$	−4.04249	−	5.06913i	−0.501410	−	0.628748i
$66$	−4.15468	+	2.00079i	−0.511406	+	0.246280i
$67$	−7.91320			−0.966751			−0.483375	−	0.875413i	$-0.660589\pi$
$67$	−7.91320			−0.966751			−0.483375	+	0.875413i	$0.660589\pi$
$68$	−2.85727			−0.346495
$69$	−13.8839	+	6.68615i	−1.67143	+	0.804918i
$70$		0			0
$71$	−3.10167	−	1.49368i	−0.368100	−	0.177268i	0.240684	−	0.970603i	$-0.422628\pi$
$71$	−3.10167	−	1.49368i	−0.368100	−	0.177268i	−0.608784	+	0.793336i	$0.708342\pi$
$72$	−16.5081	−	7.94987i	−1.94549	−	0.936901i
$73$	−0.560627	−	2.45627i	−0.0656164	−	0.287484i	0.931465	−	0.363831i	$-0.118532\pi$
$73$	−0.560627	−	2.45627i	−0.0656164	−	0.287484i	−0.997081	+	0.0763468i	$0.975674\pi$
$74$	−5.06515	−	22.1919i	−0.588811	−	2.57975i
$75$	−6.54517	−	3.15199i	−0.755771	−	0.363960i
$76$	6.80263	+	3.27598i	0.780316	+	0.375780i
$77$		0			0
$78$	24.9622	−	12.0212i	2.82641	−	1.36113i
$79$	−10.6304			−1.19601			−0.598004	−	0.801493i	$-0.704039\pi$
$79$	−10.6304			−1.19601			−0.598004	+	0.801493i	$0.704039\pi$
$80$	−2.57899			−0.288340
$81$	−0.324859	+	0.156444i	−0.0360954	+	0.0173826i
$82$	7.02954	+	8.81477i	0.776283	+	0.973428i
$83$	2.05809	+	9.01706i	0.225904	+	0.989751i	0.952942	+	0.303154i	$0.0980395\pi$
$83$	2.05809	+	9.01706i	0.225904	+	0.989751i	−0.727037	+	0.686598i	$0.759103\pi$
$84$		0			0
$85$	−0.276045	+	1.20943i	−0.0299413	+	0.131181i
$86$	13.8123	−	6.65165i	1.48942	−	0.717266i
$87$	−0.0248656	+	0.108944i	−0.00266588	+	0.0116800i
$88$	−1.61598	−	2.02637i	−0.172264	−	0.216012i
$89$	0.00588647	+	0.0257903i	0.000623965	+	0.00273377i	0.975239	−	0.221154i	$-0.0709823\pi$
$89$	0.00588647	+	0.0257903i	0.000623965	+	0.00273377i	−0.974615	+	0.223888i	$0.928125\pi$
$90$	−11.2363	+	14.0898i	−1.18441	+	1.48520i
$91$		0			0
$92$	−12.2337	−	15.3406i	−1.27545	−	1.59937i
$93$	4.26447	−	5.34748i	0.442205	−	0.554508i
$94$	11.9241	+	5.74234i	1.22988	+	0.592277i
$95$	2.04387	−	2.56294i	0.209697	−	0.262952i
$96$	−2.22022	+	9.72743i	−0.226600	+	0.992802i
$97$	−11.7290			−1.19089			−0.595447	−	0.803394i	$-0.703025\pi$
$97$	−11.7290			−1.19089			−0.595447	+	0.803394i	$0.703025\pi$
$98$		0			0
$99$	−3.40665			−0.342381
$100$	2.05830	−	9.01800i	0.205830	−	0.901800i
$101$	−11.6644	+	14.6268i	−1.16066	+	1.45542i	−0.294494	+	0.955653i	$0.595151\pi$
$101$	−11.6644	+	14.6268i	−1.16066	+	1.45542i	−0.866162	+	0.499763i	$0.833420\pi$
$102$	−4.77608	−	2.30004i	−0.472903	−	0.227738i
$103$	4.69076	−	5.88202i	0.462194	−	0.579573i	−0.495047	−	0.868866i	$-0.664849\pi$
$103$	4.69076	−	5.88202i	0.462194	−	0.579573i	0.957240	+	0.289294i	$0.0934204\pi$
$104$	9.70913	+	12.1749i	0.952059	+	1.19384i
$105$		0			0
$106$	−13.5220	+	16.9560i	−1.31337	+	1.64691i
$107$	−1.07147	−	4.69444i	−0.103583	−	0.453828i	−0.999945	−	0.0105044i	$-0.996656\pi$
$107$	−1.07147	−	4.69444i	−0.103583	−	0.453828i	0.896361	−	0.443324i	$-0.146201\pi$
$108$	−11.9740	−	15.0149i	−1.15220	−	1.44481i
$109$	−2.62366	+	11.4950i	−0.251301	+	1.10102i	0.678975	+	0.734162i	$0.262425\pi$
$109$	−2.62366	+	11.4950i	−0.251301	+	1.10102i	−0.930276	+	0.366861i	$0.880433\pi$
$110$	−2.29679	+	1.10608i	−0.218991	+	0.105460i
$111$	6.02938	−	26.4165i	0.572284	−	2.50734i
$112$		0			0
$113$	2.44118	+	10.6955i	0.229647	+	1.00615i	0.949928	+	0.312468i	$0.101156\pi$
$113$	2.44118	+	10.6955i	0.229647	+	1.00615i	−0.720281	+	0.693682i	$0.755987\pi$
$114$	8.73387	+	10.9519i	0.818002	+	1.02574i
$115$	−7.67532	+	3.69624i	−0.715727	+	0.344676i
$116$	−0.142284			−0.0132107
$117$	20.4679			1.89225
$118$	22.8862	−	11.0214i	2.10684	−	1.01460i
$119$		0			0
$120$	−14.7049	−	7.08150i	−1.34237	−	0.646449i
$121$	9.47649	+	4.56364i	0.861499	+	0.414876i
$122$	2.50675	+	10.9828i	0.226950	+	0.994335i
$123$	2.98641	+	13.0843i	0.269276	+	1.17977i
$124$	7.84644	+	3.77864i	0.704631	+	0.339332i
$125$	−10.6213	−	5.11493i	−0.949994	−	0.457493i
$126$		0			0
$127$	−12.6746	+	6.10376i	−1.12469	+	0.541621i	−0.901337	−	0.433118i	$-0.857414\pi$
$127$	−12.6746	+	6.10376i	−1.12469	+	0.541621i	−0.223350	+	0.974738i	$0.571699\pi$
$128$	−20.5425			−1.81572
$129$	18.2489			1.60673
$130$	13.7996	−	6.64554i	1.21031	−	0.582852i
$131$	8.81382	+	11.0522i	0.770067	+	0.965633i	0.999971	−	0.00757994i	$-0.00241279\pi$
$131$	8.81382	+	11.0522i	0.770067	+	0.965633i	−0.229904	+	0.973213i	$0.573841\pi$
$132$	−1.55527	−	6.81409i	−0.135369	−	0.593091i
$133$		0			0
$134$	4.15968	−	18.2247i	0.359341	−	1.57438i
$135$	−7.51237	+	3.61777i	−0.646562	+	0.311368i
$136$	0.662996	−	2.90478i	0.0568515	−	0.249082i
$137$	1.54173	+	1.93326i	0.131719	+	0.165170i	0.843317	−	0.537417i	$-0.180600\pi$
$137$	1.54173	+	1.93326i	0.131719	+	0.165170i	−0.711598	+	0.702587i	$0.752028\pi$
$138$	−8.10047	−	35.4905i	−0.689558	−	3.02115i
$139$	−1.67222	+	2.09690i	−0.141836	+	0.177856i	−0.847675	−	0.530515i	$-0.821998\pi$
$139$	−1.67222	+	2.09690i	−0.141836	+	0.177856i	0.705840	+	0.708372i	$0.250570\pi$
$140$		0			0
$141$	9.82258	+	12.3171i	0.827211	+	1.03729i
$142$	5.07051	−	6.35821i	0.425507	−	0.533569i
$143$	2.60857	+	1.25622i	0.218139	+	0.105050i
$144$	5.07611	−	6.36524i	0.423009	−	0.530437i
$145$	−0.0137462	+	0.0602262i	−0.00114156	+	0.00500151i
$146$	5.95169			0.492565
$147$		0			0
$148$	34.5008			2.83595
$149$	−0.604675	+	2.64926i	−0.0495369	+	0.217036i	−0.993638	−	0.112620i	$-0.964076\pi$
$149$	−0.604675	+	2.64926i	−0.0495369	+	0.217036i	0.944101	+	0.329656i	$0.106933\pi$
$150$	10.6998	−	13.4172i	0.873638	−	1.09551i
$151$	−1.05507	−	0.508094i	−0.0858602	−	0.0413481i	0.390461	−	0.920620i	$-0.372316\pi$
$151$	−1.05507	−	0.508094i	−0.0858602	−	0.0413481i	−0.476321	+	0.879271i	$0.658030\pi$
$152$	−4.90891	+	6.15558i	−0.398165	+	0.499283i
$153$	−2.44169	−	3.06178i	−0.197399	−	0.247531i
$154$		0			0
$155$	2.35749	−	2.95620i	0.189358	−	0.237447i
$156$	9.34440	+	40.9405i	0.748151	+	3.27786i
$157$	6.37415	+	7.99293i	0.508712	+	0.637905i	0.968170	−	0.250295i	$-0.0805275\pi$
$157$	6.37415	+	7.99293i	0.508712	+	0.637905i	−0.459457	+	0.888200i	$0.651956\pi$
$158$	5.58799	−	24.4826i	0.444556	−	1.94773i
$159$	−23.2595	+	11.2012i	−1.84460	+	0.888314i
$160$	−1.22738	+	5.37752i	−0.0970332	+	0.425130i
$161$		0			0
$162$	−0.189536	−	0.830413i	−0.0148914	−	0.0652434i
$163$	3.32256	+	4.16636i	0.260243	+	0.326335i	0.894737	−	0.446593i	$-0.147363\pi$
$163$	3.32256	+	4.16636i	0.260243	+	0.326335i	−0.634494	+	0.772928i	$0.718791\pi$
$164$	−15.3963	+	7.41444i	−1.20225	+	0.578971i
$165$	−3.03454			−0.236239
$166$	−21.8489			−1.69580
$167$	1.38071	−	0.664915i	0.106843	−	0.0514526i	−0.379699	−	0.925110i	$-0.623972\pi$
$167$	1.38071	−	0.664915i	0.106843	−	0.0514526i	0.486542	+	0.873657i	$0.338258\pi$
$168$		0			0
$169$	−3.96021	−	1.90714i	−0.304632	−	0.146703i
$170$	−2.64031	−	1.27151i	−0.202503	−	0.0975202i
$171$	2.30276	+	10.0890i	0.176096	+	0.771528i
$172$	5.17053	+	22.6536i	0.394249	+	1.72732i
$173$	−4.99137	−	2.40371i	−0.379486	−	0.182751i	0.234410	−	0.972138i	$-0.424684\pi$
$173$	−4.99137	−	2.40371i	−0.379486	−	0.182751i	−0.613896	+	0.789387i	$0.710399\pi$
$174$	−0.237835	−	0.114535i	−0.0180302	−	0.00868289i
$175$		0			0
$176$	1.03760	−	0.499683i	0.0782123	−	0.0376650i
$177$	30.2374			2.27278
$178$	−0.0624915			−0.00468393
$179$	−11.4820	+	5.52942i	−0.858202	+	0.413288i	−0.810615	−	0.585579i	$-0.800867\pi$
$179$	−11.4820	+	5.52942i	−0.858202	+	0.413288i	−0.0475865	+	0.998867i	$0.515153\pi$
$180$	−17.0306	−	21.3557i	−1.26938	−	1.59176i
$181$	4.08394	+	17.8929i	0.303557	+	1.32997i	0.864716	+	0.502262i	$0.167499\pi$
$181$	4.08394	+	17.8929i	0.303557	+	1.32997i	−0.561158	+	0.827708i	$0.689644\pi$
$182$		0			0
$183$	−2.98395	+	13.0735i	−0.220580	+	0.966424i
$184$	18.4343	−	8.87751i	1.35900	−	0.654459i
$185$	3.33317	−	14.6036i	0.245059	−	1.07367i
$186$	10.0740	+	12.6324i	0.738662	+	0.926253i
$187$	−0.123268	−	0.540074i	−0.00901428	−	0.0394942i
$188$	−12.5070	+	15.6832i	−0.912165	+	1.14382i
$189$		0			0
$190$	4.82826	+	6.05445i	0.350279	+	0.439236i
$191$	−12.2728	+	15.3896i	−0.888031	+	1.11356i	0.104855	+	0.994488i	$0.466562\pi$
$191$	−12.2728	+	15.3896i	−0.888031	+	1.11356i	−0.992886	+	0.119068i	$0.962009\pi$
$192$	−29.6423	−	14.2750i	−2.13925	−	1.03021i
$193$	9.71472	−	12.1819i	0.699281	−	0.876871i	−0.297688	−	0.954663i	$-0.596216\pi$
$193$	9.71472	−	12.1819i	0.699281	−	0.876871i	0.996970	+	0.0777923i	$0.0247871\pi$
$194$	6.16548	−	27.0127i	0.442656	−	1.93940i
$195$	18.2321			1.30563
$196$		0			0
$197$	16.2192			1.15557			0.577786	−	0.816188i	$-0.303917\pi$
$197$	16.2192			1.15557			0.577786	+	0.816188i	$0.303917\pi$
$198$	1.79075	−	7.84579i	0.127263	−	0.557576i
$199$	13.6956	−	17.1738i	0.970856	−	1.21742i	−0.00522013	−	0.999986i	$-0.501662\pi$
$199$	13.6956	−	17.1738i	0.970856	−	1.21742i	0.976076	−	0.217429i	$-0.0697669\pi$
$200$	8.69032	+	4.18504i	0.614498	+	0.295927i
$201$	13.8739	−	17.3973i	0.978590	−	1.22711i
$202$	−27.5550	−	34.5529i	−1.93877	−	2.43113i
$203$		0			0
$204$	5.00955	−	6.28178i	0.350739	−	0.439812i
$205$	1.65095	+	7.23328i	0.115307	+	0.505194i
$206$	11.0810	+	13.8952i	0.772051	+	0.968121i
$207$	5.98425	−	26.2187i	0.415934	−	1.82233i
$208$	−6.23413	+	3.00220i	−0.432259	+	0.208165i
$209$	−0.325737	+	1.42715i	−0.0225317	+	0.0987179i
$210$		0			0
$211$	−6.15510	−	26.9673i	−0.423735	−	1.85650i	−0.509917	−	0.860224i	$-0.670324\pi$
$211$	−6.15510	−	26.9673i	−0.423735	−	1.85650i	0.0861819	−	0.996279i	$-0.472533\pi$
$212$	−20.4950	−	25.6999i	−1.40760	−	1.76508i
$213$	8.72193	−	4.20026i	0.597617	−	0.287797i
$214$	11.3749			0.777572
$215$	10.0884			0.688021
$216$	18.0430	−	8.68904i	1.22767	−	0.591214i
$217$		0			0
$218$	−25.0948	−	12.0850i	−1.69963	−	0.818500i
$219$	6.38309	+	3.07393i	0.431329	+	0.207717i
$220$	−0.859786	−	3.76697i	−0.0579667	−	0.253969i
$221$	0.740623	+	3.24488i	0.0498197	+	0.218274i
$222$	57.6698	+	27.7723i	3.87054	+	1.86396i
$223$	−2.05848	−	0.991311i	−0.137846	−	0.0663831i	0.363689	−	0.931520i	$-0.381517\pi$
$223$	−2.05848	−	0.991311i	−0.137846	−	0.0663831i	−0.501535	+	0.865137i	$0.667231\pi$
$224$		0			0
$225$	11.4224	−	5.50073i	0.761493	−	0.366716i
$226$	−25.9159			−1.72390
$227$	−25.8285			−1.71430			−0.857149	−	0.515068i	$-0.827767\pi$
$227$	−25.8285			−1.71430			−0.857149	+	0.515068i	$0.827767\pi$
$228$	−19.1291	+	9.21209i	−1.26686	+	0.610086i
$229$	−4.70943	−	5.90544i	−0.311208	−	0.390243i	0.601488	−	0.798882i	$-0.294575\pi$
$229$	−4.70943	−	5.90544i	−0.311208	−	0.390243i	−0.912696	+	0.408639i	$0.866003\pi$
$230$	−4.47811	−	19.6199i	−0.295278	−	1.29370i
$231$		0			0
$232$	0.0330153	−	0.144649i	0.00216756	−	0.00949669i
$233$	5.33701	−	2.57017i	0.349639	−	0.168377i	−0.250818	−	0.968034i	$-0.580700\pi$
$233$	5.33701	−	2.57017i	0.349639	−	0.168377i	0.600457	+	0.799657i	$0.294985\pi$
$234$	−10.7592	+	47.1391i	−0.703351	+	3.08158i
$235$	5.43012	+	6.80916i	0.354222	+	0.444180i
$236$	8.56725	+	37.5356i	0.557680	+	2.44336i
$237$	18.6378	−	23.3711i	1.21066	−	1.51811i
$238$		0			0
$239$	3.75792	+	4.71229i	0.243080	+	0.304813i	0.888373	−	0.459123i	$-0.151836\pi$
$239$	3.75792	+	4.71229i	0.243080	+	0.304813i	−0.645293	+	0.763935i	$0.723265\pi$
$240$	4.52164	−	5.66996i	0.291871	−	0.365994i
$241$	6.57839	+	3.16799i	0.423751	+	0.204068i	0.633591	−	0.773668i	$-0.281580\pi$
$241$	6.57839	+	3.16799i	0.423751	+	0.204068i	−0.209840	+	0.977736i	$0.567294\pi$
$242$	−15.4919	+	19.4262i	−0.995855	+	1.24876i
$243$	−3.35500	+	14.6992i	−0.215223	+	0.942955i
$244$	−17.0745			−1.09308
$245$		0			0
$246$	−31.7041			−2.02138
$247$	1.95710	−	8.57460i	0.124527	−	0.545589i
$248$	−5.66214	+	7.10010i	−0.359546	+	0.450857i
$249$	−23.4326	−	11.2845i	−1.48498	−	0.715128i
$250$	17.3633	−	21.7729i	1.09815	−	1.37704i
$251$	1.84792	+	2.31721i	0.116639	+	0.146261i	0.836723	−	0.547626i	$-0.184468\pi$
$251$	1.84792	+	2.31721i	0.116639	+	0.146261i	−0.720084	+	0.693887i	$0.755897\pi$
$252$		0			0
$253$	2.37185	−	2.97421i	0.149117	−	0.186987i
$254$	−7.39489	−	32.3991i	−0.463996	−	2.03290i
$255$	−2.17498	−	2.72734i	−0.136203	−	0.170793i
$256$	5.59147	−	24.4978i	0.349467	−	1.53112i
$257$	−23.5080	+	11.3209i	−1.46639	+	0.706177i	−0.985354	−	0.170523i	$-0.945454\pi$
$257$	−23.5080	+	11.3209i	−1.46639	+	0.706177i	−0.481038	+	0.876700i	$0.659740\pi$
$258$	−9.59279	+	42.0287i	−0.597221	+	2.61660i
$259$		0			0
$260$	5.16577	+	22.6327i	0.320368	+	1.40362i
$261$	−0.121589	−	0.152468i	−0.00752617	−	0.00943752i
$262$	−30.0872	+	14.4892i	−1.85879	+	0.895147i
$263$	−4.95415			−0.305486			−0.152743	−	0.988266i	$-0.548811\pi$
$263$	−4.95415			−0.305486			−0.152743	+	0.988266i	$0.548811\pi$
$264$	7.28826			0.448561
$265$	−12.8583	+	6.19225i	−0.789882	+	0.380387i
$266$		0			0
$267$	−0.0670211	−	0.0322757i	−0.00410162	−	0.00197524i
$268$	25.5274	+	12.2933i	1.55933	+	0.750935i
$269$	−3.59066	−	15.7317i	−0.218926	−	0.959180i	−0.958273	−	0.285855i	$-0.907723\pi$
$269$	−3.59066	−	15.7317i	−0.218926	−	0.959180i	0.739347	−	0.673325i	$-0.235135\pi$
$270$	−4.38304	−	19.2033i	−0.266743	−	1.16868i
$271$	1.57720	+	0.759539i	0.0958080	+	0.0461387i	0.481174	−	0.876625i	$-0.340211\pi$
$271$	1.57720	+	0.759539i	0.0958080	+	0.0461387i	−0.385366	+	0.922764i	$0.625925\pi$
$272$	1.19279	+	0.574419i	0.0723237	+	0.0348293i
$273$		0			0
$274$	−5.26289	+	2.53448i	−0.317943	+	0.153113i
$275$	1.79336			0.108144
$276$	55.1756			3.32118
$277$	−14.5725	+	7.01775i	−0.875577	+	0.421656i	−0.817007	−	0.576627i	$-0.804368\pi$
$277$	−14.5725	+	7.01775i	−0.875577	+	0.421656i	−0.0585702	+	0.998283i	$0.518654\pi$
$278$	−3.95030	−	4.95351i	−0.236923	−	0.297092i
$279$	2.65609	+	11.6371i	0.159016	+	0.696695i
$280$		0			0
$281$	−0.859518	+	3.76580i	−0.0512746	+	0.224649i	−0.994073	−	0.108715i	$-0.965326\pi$
$281$	−0.859518	+	3.76580i	−0.0512746	+	0.224649i	0.942798	+	0.333363i	$0.108184\pi$
$282$	−33.5307	+	16.1475i	−1.99672	+	0.961572i
$283$	−6.66341	+	29.1943i	−0.396099	+	1.73542i	0.246429	+	0.969161i	$0.420743\pi$
$283$	−6.66341	+	29.1943i	−0.396099	+	1.73542i	−0.642528	+	0.766262i	$0.722115\pi$
$284$	7.68527	+	9.63702i	0.456037	+	0.571852i
$285$	2.05122	+	8.98700i	0.121504	+	0.532344i
$286$	−4.26440	+	5.34739i	−0.252159	+	0.316198i
$287$		0			0
$288$	−10.8565	−	13.6137i	−0.639727	−	0.802193i
$289$	−10.2023	+	12.7933i	−0.600134	+	0.752544i
$290$	−0.131480	−	0.0633174i	−0.00772076	−	0.00371812i
$291$	20.5639	−	25.7864i	1.20548	−	1.51162i
$292$	−2.00733	+	8.79468i	−0.117470	+	0.514670i
$293$	12.3352			0.720633			0.360316	−	0.932830i	$-0.382669\pi$
$293$	12.3352			0.720633			0.360316	+	0.932830i	$0.382669\pi$
$294$		0			0
$295$	16.7158			0.973233
$296$	−8.00549	+	35.0743i	−0.465310	+	2.03865i
$297$	2.32150	−	2.91107i	0.134707	−	0.168917i
$298$	−5.78360	−	2.78523i	−0.335035	−	0.161344i
$299$	−14.2506	+	17.8697i	−0.824133	+	1.03343i
$300$	16.2175	+	20.3361i	0.936319	+	1.17411i
$301$		0			0
$302$	1.72479	−	2.16282i	0.0992506	−	0.124456i
$303$	−11.7064	−	51.2891i	−0.672515	−	2.94648i
$304$	−2.18122	−	2.73517i	−0.125102	−	0.156873i
$305$	−1.64959	+	7.22732i	−0.0944552	+	0.413835i
$306$	8.33505	−	4.01395i	0.476483	−	0.229462i
$307$	1.11320	−	4.87723i	0.0635334	−	0.278358i	−0.933176	−	0.359421i	$-0.882974\pi$
$307$	1.11320	−	4.87723i	0.0635334	−	0.278358i	0.996709	+	0.0810628i	$0.0258314\pi$
$308$		0			0
$309$	4.70763	+	20.6255i	0.267807	+	1.17334i
$310$	5.56911	+	6.98345i	0.316304	+	0.396633i
$311$	27.0284	−	13.0162i	1.53264	−	0.738079i	0.538142	−	0.842854i	$-0.319126\pi$
$311$	27.0284	−	13.0162i	1.53264	−	0.738079i	0.994496	+	0.104775i	$0.0334122\pi$
$312$	−43.7894			−2.47909
$313$	−1.02497			−0.0579345			−0.0289672	−	0.999580i	$-0.509222\pi$
$313$	−1.02497			−0.0579345			−0.0289672	+	0.999580i	$0.509222\pi$
$314$	−21.7590	+	10.4786i	−1.22793	+	0.591341i
$315$		0			0
$316$	34.2927	+	16.5145i	1.92912	+	0.929013i
$317$	0.421420	+	0.202945i	0.0236693	+	0.0113985i	0.445681	−	0.895192i	$-0.352962\pi$
$317$	0.421420	+	0.202945i	0.0236693	+	0.0113985i	−0.422012	+	0.906590i	$0.638676\pi$
$318$	−13.5706	−	59.4567i	−0.761002	−	3.33417i
$319$	−0.00613841	−	0.0268941i	−0.000343685	−	0.00150578i
$320$	−16.3868	−	7.89149i	−0.916053	−	0.441148i
$321$	12.1994	+	5.87492i	0.680904	+	0.327906i
$322$		0			0
$323$	−1.51614	+	0.730136i	−0.0843605	+	0.0406259i
$324$	1.29101			0.0717227
$325$	−10.7749			−0.597682
$326$	−11.3420	+	5.46203i	−0.628176	+	0.302514i
$327$	−20.6721	−	25.9219i	−1.14317	−	1.43349i
$328$	−3.96519	−	17.3726i	−0.218941	−	0.959244i
$329$		0			0
$330$	1.59515	−	6.98879i	0.0878099	−	0.384720i
$331$	11.5486	−	5.56152i	0.634770	−	0.305689i	−0.0886862	−	0.996060i	$-0.528267\pi$
$331$	11.5486	−	5.56152i	0.634770	−	0.305689i	0.723456	+	0.690371i	$0.242553\pi$
$332$	7.36899	−	32.2856i	0.404426	−	1.77190i
$333$	29.4827	+	36.9702i	1.61564	+	2.02595i
$334$	0.805564	+	3.52941i	0.0440785	+	0.193121i
$335$	7.66978	−	9.61760i	0.419045	−	0.525466i
$336$		0			0
$337$	−9.17474	−	11.5048i	−0.499780	−	0.626704i	0.466400	−	0.884574i	$-0.345551\pi$
$337$	−9.17474	−	11.5048i	−0.499780	−	0.626704i	−0.966180	+	0.257870i	$0.916979\pi$
$338$	6.47403	−	8.11818i	0.352141	−	0.441571i
$339$	−27.7944	−	13.3851i	−1.50958	−	0.726977i
$340$	2.76938	−	3.47269i	0.150191	−	0.188333i
$341$	−0.375719	+	1.64613i	−0.0203463	+	0.0891430i
$342$	−24.4463			−1.32191
$343$		0			0
$344$	−24.2299			−1.30639
$345$	5.33059	−	23.3548i	0.286989	−	1.25738i
$346$	8.15973	−	10.2320i	0.438670	−	0.550074i
$347$	29.6710	+	14.2888i	1.59282	+	0.767064i	0.999287	−	0.0377431i	$-0.0120169\pi$
$347$	29.6710	+	14.2888i	1.59282	+	0.767064i	0.593537	+	0.804807i	$0.297731\pi$
$348$	0.249461	−	0.312814i	0.0133725	−	0.0167686i
$349$	−5.15105	−	6.45921i	−0.275729	−	0.345754i	0.624614	−	0.780934i	$-0.285256\pi$
$349$	−5.15105	−	6.45921i	−0.275729	−	0.345754i	−0.900344	+	0.435180i	$0.856685\pi$
$350$		0			0
$351$	−13.9481	+	17.4903i	−0.744492	+	0.933564i
$352$	−0.548091	−	2.40134i	−0.0292133	−	0.127992i
$353$	−1.98723	−	2.49190i	−0.105769	−	0.132631i	0.726129	−	0.687558i	$-0.241317\pi$
$353$	−1.98723	−	2.49190i	−0.105769	−	0.132631i	−0.831899	+	0.554928i	$0.812746\pi$
$354$	−15.8947	+	69.6391i	−0.844792	+	3.70128i
$355$	4.82166	−	2.32199i	0.255907	−	0.123238i
$356$	0.0210765	−	0.0923423i	0.00111705	−	0.00489413i
$357$		0			0
$358$	−6.69906	−	29.3505i	−0.354056	−	1.55122i
$359$	2.66811	+	3.34571i	0.140818	+	0.176580i	0.847239	−	0.531212i	$-0.178263\pi$
$359$	2.66811	+	3.34571i	0.140818	+	0.176580i	−0.706422	+	0.707791i	$0.749692\pi$
$360$	25.6624	−	12.3584i	1.35253	−	0.651344i
$361$	−14.5532			−0.765959
$362$	−43.3556			−2.27872
$363$	−26.6480	+	12.8330i	−1.39866	+	0.673559i
$364$		0			0
$365$	3.52870	+	1.69933i	0.184701	+	0.0889471i
$366$	−28.5409	−	13.7446i	−1.49186	−	0.718440i
$367$	7.70119	+	33.7411i	0.401999	+	1.76127i	0.619287	+	0.785164i	$0.287422\pi$
$367$	7.70119	+	33.7411i	0.401999	+	1.76127i	−0.217289	+	0.976107i	$0.569721\pi$
$368$	2.02304	+	8.86350i	0.105458	+	0.462042i
$369$	−21.1021	−	10.1622i	−1.09853	−	0.529024i
$370$	31.8810	+	15.3531i	1.65742	+	0.798170i
$371$		0			0
$372$	−22.0643	+	10.6256i	−1.14398	+	0.550912i
$373$	21.8081			1.12918			0.564590	−	0.825371i	$-0.309034\pi$
$373$	21.8081			1.12918			0.564590	+	0.825371i	$0.309034\pi$
$374$	1.30863			0.0676678
$375$	29.8671	−	14.3833i	1.54233	−	0.742748i
$376$	−13.0419	−	16.3540i	−0.672584	−	0.843394i
$377$	0.0368808	+	0.161585i	0.00189946	+	0.00832207i
$378$		0			0
$379$	1.33904	−	5.86672i	0.0687819	−	0.301353i	−0.928823	−	0.370524i	$-0.879178\pi$
$379$	1.33904	−	5.86672i	0.0687819	−	0.301353i	0.997605	+	0.0691708i	$0.0220353\pi$
$380$	−10.5750	+	5.09263i	−0.542484	+	0.261246i
$381$	8.80263	−	38.5668i	0.450972	−	1.97584i
$382$	−28.9922	−	36.3551i	−1.48337	−	1.86009i
$383$	5.39754	+	23.6482i	0.275801	+	1.20836i	0.903047	+	0.429543i	$0.141325\pi$
$383$	5.39754	+	23.6482i	0.275801	+	1.20836i	−0.627245	+	0.778822i	$0.715818\pi$
$384$	36.0164	−	45.1632i	1.83796	−	2.30472i
$385$		0			0
$386$	22.9492	+	28.7774i	1.16808	+	1.46473i
$387$	−19.8565	+	24.8993i	−1.00936	+	1.26570i
$388$	37.8367	+	18.2212i	1.92087	+	0.925041i
$389$	12.7872	−	16.0346i	0.648337	−	0.812988i	−0.343681	−	0.939086i	$-0.611674\pi$
$389$	12.7872	−	16.0346i	0.648337	−	0.812988i	0.992018	+	0.126098i	$0.0402454\pi$
$390$	−9.58397	+	41.9901i	−0.485303	+	2.12625i
$391$	4.37313			0.221159
$392$		0			0
$393$	−39.7514			−2.00519
$394$	−8.52585	+	37.3542i	−0.429526	+	1.88188i
$395$	10.3034	−	12.9200i	0.518418	−	0.650076i
$396$	10.9896	+	5.29231i	0.552248	+	0.265949i
$397$	2.77868	−	3.48436i	0.139458	−	0.174875i	−0.707198	−	0.707016i	$-0.750041\pi$
$397$	2.77868	−	3.48436i	0.139458	−	0.174875i	0.846656	+	0.532141i	$0.178612\pi$
$398$	32.3533	+	40.5697i	1.62172	+	2.03358i
$399$		0			0
$400$	−2.67221	+	3.35084i	−0.133610	+	0.167542i
$401$	6.98361	+	30.5972i	0.348745	+	1.52795i	0.780034	+	0.625737i	$0.215202\pi$
$401$	6.98361	+	30.5972i	0.348745	+	1.52795i	−0.431289	+	0.902214i	$0.641941\pi$
$402$	32.7745	+	41.0979i	1.63464	+	2.04978i
$403$	2.25740	−	9.89030i	0.112449	−	0.492671i
$404$	60.3516	−	29.0638i	3.00261	−	1.44598i
$405$	0.124726	−	0.546460i	0.00619769	−	0.0271538i
$406$		0			0
$407$	1.48843	+	6.52125i	0.0737788	+	0.323246i
$408$	5.22381	+	6.55045i	0.258617	+	0.324295i
$409$	−12.5172	+	6.02796i	−0.618935	+	0.298063i	−0.716953	−	0.697121i	$-0.754464\pi$
$409$	−12.5172	+	6.02796i	−0.618935	+	0.298063i	0.0980182	+	0.995185i	$0.468750\pi$
$410$	−17.5267			−0.865580
$411$	−6.95337			−0.342985
$412$	−24.2699	+	11.6878i	−1.19569	+	0.575814i
$413$		0			0
$414$	57.2382	+	27.5644i	2.81310	+	1.35472i
$415$	−12.9540	−	6.23832i	−0.635887	−	0.306227i
$416$	3.29304	+	14.4278i	0.161455	+	0.707379i
$417$	−1.67823	−	7.35282i	−0.0821834	−	0.360069i
$418$	−3.11561	−	1.50040i	−0.152389	−	0.0733869i
$419$	12.4309	+	5.98640i	0.607289	+	0.292455i	0.712145	−	0.702033i	$-0.247724\pi$
$419$	12.4309	+	5.98640i	0.607289	+	0.292455i	−0.104856	+	0.994487i	$0.533438\pi$
$420$		0			0
$421$	−7.73392	+	3.72446i	−0.376928	+	0.181519i	−0.612749	−	0.790277i	$-0.709936\pi$
$421$	−7.73392	+	3.72446i	−0.376928	+	0.181519i	0.235821	+	0.971797i	$0.424222\pi$
$422$	65.3433			3.18086
$423$	−27.4937			−1.33679
$424$	30.8828	−	14.8724i	1.49980	−	0.722266i
$425$	1.28538	+	1.61181i	0.0623499	+	0.0781843i
$426$	5.08874	+	22.2952i	0.246550	+	1.08021i
$427$		0			0
$428$	−3.83642	+	16.8085i	−0.185440	+	0.812467i
$429$	−7.33533	+	3.53251i	−0.354153	+	0.170551i
$430$	−5.30309	+	23.2343i	−0.255738	+	1.12046i
$431$	−9.34514	−	11.7184i	−0.450139	−	0.564457i	0.504045	−	0.863678i	$-0.331845\pi$
$431$	−9.34514	−	11.7184i	−0.450139	−	0.564457i	−0.954184	+	0.299221i	$0.903273\pi$
$432$	1.98009	+	8.67533i	0.0952670	+	0.417392i
$433$	−7.66601	+	9.61287i	−0.368405	+	0.461965i	−0.931135	−	0.364676i	$-0.881180\pi$
$433$	−7.66601	+	9.61287i	−0.368405	+	0.461965i	0.562730	+	0.826641i	$0.309751\pi$
$434$		0			0
$435$	−0.108308	−	0.135814i	−0.00519296	−	0.00651177i
$436$	26.3215	−	33.0061i	1.26057	−	1.58071i
$437$	−10.4116	−	5.01397i	−0.498055	−	0.239851i
$438$	−10.4349	+	13.0849i	−0.498597	+	0.625221i
$439$	0.899282	−	3.94001i	0.0429204	−	0.188047i	−0.948923	−	0.315507i	$-0.897825\pi$
$439$	0.899282	−	3.94001i	0.0429204	−	0.188047i	0.991844	+	0.127460i	$0.0406826\pi$
$440$	4.02910			0.192080
$441$		0			0
$442$	−7.86254			−0.373983
$443$	2.76172	−	12.0999i	0.131213	−	0.574882i	−0.865985	−	0.500071i	$-0.833307\pi$
$443$	2.76172	−	12.0999i	0.131213	−	0.574882i	0.997198	−	0.0748115i	$-0.0238355\pi$
$444$	−60.4889	+	75.8507i	−2.87068	+	3.59971i
$445$	−0.0370506	−	0.0178426i	−0.00175637	−	0.000845822i
$446$	3.36514	−	4.21975i	0.159344	−	0.199811i
$447$	−4.76429	−	5.97423i	−0.225343	−	0.282572i
$448$		0			0
$449$	4.20919	−	5.27815i	0.198644	−	0.249092i	−0.672526	−	0.740074i	$-0.734791\pi$
$449$	4.20919	−	5.27815i	0.198644	−	0.249092i	0.871170	+	0.490982i	$0.163362\pi$
$450$	6.66430	+	29.1982i	0.314158	+	1.37642i
$451$	−2.06568	−	2.59029i	−0.0972693	−	0.121972i
$452$	8.74066	−	38.2953i	0.411126	−	1.80126i
$453$	2.96687	−	1.42877i	0.139396	−	0.0671294i
$454$	13.5771	−	59.4852i	0.637205	−	2.79178i
$455$		0			0
$456$	−4.92656	−	21.5847i	−0.230707	−	1.01080i
$457$	−3.09382	−	3.87953i	−0.144723	−	0.181477i	0.704187	−	0.710015i	$-0.251312\pi$
$457$	−3.09382	−	3.87953i	−0.144723	−	0.181477i	−0.848910	+	0.528538i	$0.822740\pi$
$458$	16.0763	−	7.74193i	0.751196	−	0.361757i
$459$	4.28029			0.199787
$460$	30.5022			1.42217
$461$	35.4998	−	17.0958i	1.65339	−	0.796231i	0.654188	−	0.756332i	$-0.273011\pi$
$461$	35.4998	−	17.0958i	1.65339	−	0.796231i	0.999204	−	0.0398990i	$-0.0127036\pi$
$462$		0			0
$463$	6.40555	+	3.08475i	0.297691	+	0.143360i	0.576767	−	0.816909i	$-0.304314\pi$
$463$	6.40555	+	3.08475i	0.297691	+	0.143360i	−0.279076	+	0.960269i	$0.590028\pi$
$464$	0.0593976	+	0.0286044i	0.00275746	+	0.00132792i
$465$	2.36597	+	10.3660i	0.109719	+	0.480711i
$466$	3.11384	+	13.6426i	0.144246	+	0.631982i
$467$	10.1186	+	4.87287i	0.468234	+	0.225490i	0.653096	−	0.757275i	$-0.273470\pi$
$467$	10.1186	+	4.87287i	0.468234	+	0.225490i	−0.184862	+	0.982764i	$0.559184\pi$
$468$	−66.0278	−	31.7973i	−3.05213	−	1.46983i
$469$		0			0
$470$	−18.5365	+	8.92669i	−0.855023	+	0.411757i
$471$	−28.7482			−1.32465
$472$	−40.1475			−1.84794
$473$	−4.05885	+	1.95464i	−0.186626	+	0.0898744i
$474$	44.0282	+	55.2097i	2.02228	+	2.53586i
$475$	−1.21224	−	5.31115i	−0.0556212	−	0.243692i
$476$		0			0
$477$	10.0253	−	43.9238i	0.459028	−	2.01113i
$478$	−12.8282	+	6.17773i	−0.586747	+	0.282563i
$479$	5.57937	−	24.4448i	0.254928	−	1.11691i	−0.671668	−	0.740853i	$-0.734422\pi$
$479$	5.57937	−	24.4448i	0.254928	−	1.11691i	0.926596	−	0.376059i	$-0.122721\pi$
$480$	−9.67067	−	12.1266i	−0.441404	−	0.553503i
$481$	−8.94281	−	39.1810i	−0.407757	−	1.78650i
$482$	−10.7541	+	13.4853i	−0.489838	+	0.614237i
$483$		0			0
$484$	−23.4807	−	29.4439i	−1.06731	−	1.33836i
$485$	11.3682	−	14.2552i	0.516202	−	0.647296i
$486$	−32.0899	−	15.4537i	−1.45563	−	0.700993i
$487$	−6.42889	+	8.06157i	−0.291321	+	0.365304i	−0.905857	−	0.423584i	$-0.860772\pi$
$487$	−6.42889	+	8.06157i	−0.291321	+	0.365304i	0.614536	+	0.788889i	$0.289343\pi$
$488$	3.96193	−	17.3583i	0.179348	−	0.785775i
$489$	−14.9852			−0.677652
$490$		0			0
$491$	−10.2368			−0.461979			−0.230989	−	0.972956i	$-0.574196\pi$
$491$	−10.2368			−0.461979			−0.230989	+	0.972956i	$0.574196\pi$
$492$	10.6929	−	46.8485i	0.482071	−	2.11209i
$493$	0.0197719	−	0.0247932i	0.000890481	−	0.00111663i
$494$	18.7192	+	9.01471i	0.842218	+	0.405591i
$495$	3.30186	−	4.14040i	0.148407	−	0.186097i
$496$	−2.51591	−	3.15485i	−0.112968	−	0.141657i
$497$		0			0
$498$	38.3068	−	48.0353i	1.71657	−	2.15251i
$499$	−5.41529	−	23.7259i	−0.242421	−	1.06212i	−0.938805	−	0.344448i	$-0.888066\pi$
$499$	−5.41529	−	23.7259i	−0.242421	−	1.06212i	0.696384	−	0.717670i	$-0.254791\pi$
$500$	26.3172	+	33.0007i	1.17694	+	1.47584i
$501$	−0.958917	+	4.20129i	−0.0428413	+	0.187700i
$502$	−6.30811	+	3.03783i	−0.281545	+	0.135585i
$503$	−3.01324	+	13.2019i	−0.134354	+	0.588642i	0.862264	+	0.506460i	$0.169046\pi$
$503$	−3.01324	+	13.2019i	−0.134354	+	0.588642i	−0.996617	+	0.0821824i	$0.973811\pi$
$504$		0			0
$505$	−6.47153	−	28.3536i	−0.287980	−	1.26172i
$506$	5.60305	+	7.02601i	0.249086	+	0.312344i
$507$	11.1362	−	5.36290i	0.494575	−	0.238175i
$508$	50.3696			2.23479
$509$	43.0758			1.90930			0.954650	−	0.297729i	$-0.0962293\pi$
$509$	43.0758			1.90930			0.954650	+	0.297729i	$0.0962293\pi$
$510$	7.42460	−	3.57550i	0.328767	−	0.158326i
$511$		0			0
$512$	16.4650	+	7.92911i	0.727656	+	0.350421i
$513$	−10.1906	−	4.90752i	−0.449925	−	0.216672i
$514$	−13.7156	−	60.0919i	−0.604968	−	2.65054i
$515$	2.60247	+	11.4022i	0.114679	+	0.502440i
$516$	−58.8696	−	28.3501i	−2.59159	−	1.24804i
$517$	−3.50398	−	1.68743i	−0.154105	−	0.0742131i
$518$		0			0
$519$	14.0358	−	6.75928i	0.616103	−	0.296700i
$520$	−24.2077			−1.06158
$521$	15.4258			0.675818			0.337909	−	0.941179i	$-0.390280\pi$
$521$	15.4258			0.675818			0.337909	+	0.941179i	$0.390280\pi$
$522$	0.415061	−	0.199883i	0.0181667	−	0.00874863i
$523$	9.01700	+	11.3070i	0.394286	+	0.494419i	0.938863	−	0.344292i	$-0.111881\pi$
$523$	9.01700	+	11.3070i	0.394286	+	0.494419i	−0.544577	+	0.838711i	$0.683310\pi$
$524$	−11.2629	−	49.3459i	−0.492022	−	2.15569i
$525$		0			0
$526$	2.60421	−	11.4098i	0.113549	−	0.497491i
$527$	−1.74878	+	0.842169i	−0.0761782	+	0.0366855i
$528$	−0.720626	+	3.15727i	−0.0313612	+	0.137402i
$529$	4.38378	+	5.49708i	0.190599	+	0.239004i
$530$	−7.50210	−	32.8689i	−0.325871	−	1.42773i
$531$	−32.9010	+	41.2566i	−1.42778	+	1.79038i
$532$		0			0
$533$	12.4111	+	15.5630i	0.537583	+	0.674107i
$534$	0.109564	−	0.137389i	0.00474130	−	0.00594540i
$535$	6.74407	+	3.24777i	0.291572	+	0.140414i
$536$	−18.4210	+	23.0992i	−0.795667	+	0.997735i
$537$	7.97434	−	34.9379i	0.344118	−	1.50768i
$538$	38.1189			1.64342
$539$		0			0
$540$	29.8546			1.28474
$541$	−2.06891	+	9.06447i	−0.0889492	+	0.389712i	−0.999731	−	0.0231751i	$-0.992622\pi$
$541$	−2.06891	+	9.06447i	−0.0889492	+	0.389712i	0.910782	+	0.412887i	$0.135480\pi$
$542$	−2.57835	+	3.23315i	−0.110750	+	0.138876i
$543$	−46.4982	−	22.3924i	−1.99543	−	0.960948i
$544$	1.76541	−	2.21375i	0.0756912	−	0.0949138i
$545$	−11.4279	−	14.3302i	−0.489519	−	0.613837i
$546$		0			0
$547$	−0.922752	+	1.15709i	−0.0394540	+	0.0494738i	−0.801167	−	0.598441i	$-0.795787\pi$
$547$	−0.922752	+	1.15709i	−0.0394540	+	0.0494738i	0.761713	+	0.647915i	$0.224359\pi$
$548$	−1.97012	−	8.63167i	−0.0841594	−	0.368727i
$549$	−14.5910	−	18.2966i	−0.622731	−	0.780880i
$550$	−0.942702	+	4.13025i	−0.0401969	+	0.176114i
$551$	−0.0754995	+	0.0363586i	−0.00321639	+	0.00154893i
$552$	−12.8028	+	56.0929i	−0.544925	+	2.38747i
$553$		0			0
$554$	−8.50222	−	37.2507i	−0.361225	−	1.58263i
$555$	26.2623	+	32.9319i	1.11477	+	1.39788i
$556$	8.65202	−	4.16659i	0.366927	−	0.176703i
$557$	15.0936			0.639536			0.319768	−	0.947496i	$-0.396395\pi$
$557$	15.0936			0.639536			0.319768	+	0.947496i	$0.396395\pi$
$558$	−28.1974			−1.19369
$559$	24.3864	−	11.7439i	1.03144	−	0.496713i
$560$		0			0
$561$	1.40349	+	0.675884i	0.0592553	+	0.0285358i
$562$	−8.22111	−	3.95908i	−0.346787	−	0.167004i
$563$	3.72086	+	16.3022i	0.156816	+	0.687054i	0.990808	+	0.135278i	$0.0431927\pi$
$563$	3.72086	+	16.3022i	0.156816	+	0.687054i	−0.833992	+	0.551776i	$0.813950\pi$
$564$	−12.5520	−	54.9937i	−0.528533	−	2.31565i
$565$	−15.3653	−	7.39953i	−0.646422	−	0.311301i
$566$	−63.7342	−	30.6928i	−2.67895	−	1.29011i
$567$		0			0
$568$	−11.5805	+	5.57688i	−0.485907	+	0.234001i
$569$	−28.8470			−1.20933			−0.604664	−	0.796480i	$-0.706693\pi$
$569$	−28.8470			−1.20933			−0.604664	+	0.796480i	$0.706693\pi$
$570$	−21.7760			−0.912098
$571$	−12.4055	+	5.97420i	−0.519156	+	0.250012i	−0.675064	−	0.737759i	$-0.735884\pi$
$571$	−12.4055	+	5.97420i	−0.519156	+	0.250012i	0.155908	+	0.987772i	$0.450170\pi$
$572$	−6.46347	−	8.10493i	−0.270251	−	0.338884i
$573$	−12.3170	−	53.9642i	−0.514549	−	2.25439i
$574$		0			0
$575$	−3.15028	+	13.8023i	−0.131376	+	0.575595i
$576$	51.7306	−	24.9122i	2.15544	−	1.03801i
$577$	−4.84581	+	21.2309i	−0.201734	+	0.883854i	0.768147	+	0.640274i	$0.221179\pi$
$577$	−4.84581	+	21.2309i	−0.201734	+	0.883854i	−0.969881	+	0.243580i	$0.921678\pi$
$578$	−24.1009	−	30.2216i	−1.00247	−	1.25705i
$579$	9.74966	+	42.7161i	0.405182	+	1.77522i
$580$	0.137907	−	0.172930i	0.00572628	−	0.00718052i
$581$		0			0
$582$	48.5784	+	60.9154i	2.01364	+	2.52502i
$583$	3.97353	−	4.98265i	0.164567	−	0.206360i
$584$	−8.47512	−	4.08140i	−0.350703	−	0.168890i
$585$	−19.8382	+	24.8764i	−0.820211	+	1.02851i
$586$	−6.48419	+	28.4091i	−0.267859	+	1.17357i
$587$	25.3416			1.04596			0.522979	−	0.852345i	$-0.324820\pi$
$587$	25.3416			1.04596			0.522979	+	0.852345i	$0.324820\pi$
$588$		0			0
$589$	5.12910			0.211341
$590$	−8.78689	+	38.4979i	−0.361751	+	1.58493i
$591$	−28.4366	+	35.6583i	−1.16972	+	1.46679i
$592$	−14.4026	−	6.93594i	−0.591945	−	0.285066i
$593$	−1.45328	+	1.82235i	−0.0596789	+	0.0748350i	−0.810775	−	0.585358i	$-0.800954\pi$
$593$	−1.45328	+	1.82235i	−0.0596789	+	0.0748350i	0.751096	+	0.660193i	$0.229525\pi$
$594$	5.48410	+	6.87685i	0.225015	+	0.282160i
$595$		0			0
$596$	6.06632	−	7.60692i	0.248486	−	0.311592i
$597$	13.7449	+	60.2202i	0.562540	+	2.46465i
$598$	−33.6643	−	42.2137i	−1.37664	−	1.72625i
$599$	−4.52045	+	19.8054i	−0.184701	+	0.809226i	0.794652	+	0.607065i	$0.207653\pi$
$599$	−4.52045	+	19.8054i	−0.184701	+	0.809226i	−0.979352	+	0.202161i	$0.935204\pi$
$600$	−24.4373	+	11.7684i	−0.997649	+	0.480442i
$601$	−5.83473	+	25.5636i	−0.238004	+	1.04276i	0.704798	+	0.709408i	$0.251038\pi$
$601$	−5.83473	+	25.5636i	−0.238004	+	1.04276i	−0.942802	+	0.333354i	$0.891820\pi$
$602$		0			0
$603$	8.64125	+	37.8598i	0.351899	+	1.54177i
$604$	2.61423	+	3.27814i	0.106372	+	0.133386i
$605$	−14.7316	+	7.09435i	−0.598924	+	0.288426i
$606$	124.277			5.04839
$607$	19.8727			0.806606			0.403303	−	0.915066i	$-0.367862\pi$
$607$	19.8727			0.806606			0.403303	+	0.915066i	$0.367862\pi$
$608$	−6.74126	+	3.24642i	−0.273394	+	0.131660i
$609$		0			0
$610$	−15.7780	−	7.59827i	−0.638832	−	0.307645i
$611$	21.0527	+	10.1384i	0.851699	+	0.410157i
$612$	3.12016	+	13.6703i	0.126125	+	0.552589i
$613$	−4.42685	−	19.3953i	−0.178799	−	0.783369i	−0.982186	−	0.187912i	$-0.939828\pi$
$613$	−4.42685	−	19.3953i	−0.178799	−	0.783369i	0.803387	−	0.595457i	$-0.203029\pi$
$614$	10.6475	+	5.12756i	0.429697	+	0.206931i
$615$	−18.7971	−	9.05219i	−0.757971	−	0.365019i
$616$		0			0
$617$	19.5919	−	9.43496i	0.788740	−	0.379837i	0.00425965	−	0.999991i	$-0.498644\pi$
$617$	19.5919	−	9.43496i	0.788740	−	0.379837i	0.784480	+	0.620154i	$0.212930\pi$
$618$	−49.9767			−2.01036
$619$	26.4883			1.06465			0.532327	−	0.846539i	$-0.321318\pi$
$619$	26.4883			1.06465			0.532327	+	0.846539i	$0.321318\pi$
$620$	−12.1976	+	5.87405i	−0.489867	+	0.235908i
$621$	18.3265	+	22.9807i	0.735418	+	0.922185i
$622$	15.7695	+	69.0906i	0.632299	+	2.77028i
$623$		0			0
$624$	4.32967	−	18.9695i	0.173326	−	0.759389i
$625$	4.87329	−	2.34686i	0.194932	−	0.0938742i
$626$	0.538787	−	2.36058i	0.0215343	−	0.0943477i
$627$	−2.56651	−	3.21831i	−0.102497	−	0.128527i
$628$	−8.14531	−	35.6870i	−0.325033	−	1.42406i
$629$	−4.79426	+	6.01181i	−0.191160	+	0.239707i
$630$		0			0
$631$	0.0524457	+	0.0657648i	0.00208783	+	0.00261806i	0.782874	−	0.622180i	$-0.213753\pi$
$631$	0.0524457	+	0.0657648i	0.00208783	+	0.00261806i	−0.780786	+	0.624798i	$0.785181\pi$
$632$	−24.7463	+	31.0308i	−0.984353	+	1.23434i
$633$	70.0796	+	33.7486i	2.78542	+	1.34139i
$634$	−0.688924	+	0.863883i	−0.0273607	+	0.0343092i
$635$	4.86627	−	21.3205i	0.193112	−	0.846079i
$636$	92.4349			3.66528
$637$		0			0
$638$	0.0651661			0.00257995
$639$	−3.75933	+	16.4707i	−0.148717	+	0.651570i
$640$	19.9106	−	24.9671i	0.787036	−	0.986912i
$641$	−29.8363	−	14.3684i	−1.17846	−	0.567518i	−0.260999	−	0.965339i	$-0.584052\pi$
$641$	−29.8363	−	14.3684i	−1.17846	−	0.567518i	−0.917463	+	0.397821i	$0.869766\pi$
$642$	−19.9432	+	25.0080i	−0.787095	+	0.986986i
$643$	−5.03595	−	6.31488i	−0.198598	−	0.249034i	0.672553	−	0.740049i	$-0.265198\pi$
$643$	−5.03595	−	6.31488i	−0.198598	−	0.249034i	−0.871151	+	0.491014i	$0.836626\pi$
$644$		0			0
$645$	−17.6876	+	22.1795i	−0.696447	+	0.873317i
$646$	−0.884582	−	3.87561i	−0.0348034	−	0.152484i
$647$	17.7209	+	22.2213i	0.696681	+	0.873611i	0.996771	−	0.0803005i	$-0.0255880\pi$
$647$	17.7209	+	22.2213i	0.696681	+	0.873611i	−0.300090	+	0.953911i	$0.597017\pi$
$648$	−0.299563	+	1.31247i	−0.0117679	+	0.0515587i
$649$	−6.72527	+	3.23872i	−0.263990	+	0.127131i
$650$	5.66395	−	24.8154i	0.222158	−	0.973339i
$651$		0			0
$652$	−4.24579	−	18.6020i	−0.166278	−	0.728512i
$653$	−10.1325	−	12.7057i	−0.396515	−	0.497214i	0.542995	−	0.839736i	$-0.317290\pi$
$653$	−10.1325	−	12.7057i	−0.396515	−	0.497214i	−0.939510	+	0.342522i	$0.888719\pi$
$654$	70.5669	−	33.9832i	2.75938	−	1.32885i
$655$	−21.9754			−0.858649
$656$	7.91788			0.309141
$657$	−11.1395	+	5.36452i	−0.434595	+	0.209290i
$658$		0			0
$659$	−16.7515	−	8.06711i	−0.652547	−	0.314250i	0.0781604	−	0.996941i	$-0.475095\pi$
$659$	−16.7515	−	8.06711i	−0.652547	−	0.314250i	−0.730707	+	0.682691i	$0.760810\pi$
$660$	9.78919	+	4.71423i	0.381044	+	0.183501i
$661$	−5.62299	−	24.6359i	−0.218709	−	0.958226i	−0.958433	−	0.285316i	$-0.907901\pi$
$661$	−5.62299	−	24.6359i	−0.218709	−	0.958226i	0.739725	−	0.672910i	$-0.234956\pi$
$662$	6.73795	+	29.5209i	0.261878	+	1.14736i
$663$	−8.43244	−	4.06085i	−0.327489	−	0.157710i
$664$	31.1125	+	14.9830i	1.20740	+	0.581453i
$665$		0			0
$666$	−100.643	+	48.4673i	−3.89985	+	1.87807i
$667$	0.217769			0.00843206
$668$	−5.48702			−0.212299
$669$	5.78847	−	2.78758i	0.223795	−	0.107774i
$670$	18.1184	+	22.7197i	0.699974	+	0.877740i
$671$	−0.736627	−	3.22737i	−0.0284372	−	0.124591i
$672$		0			0
$673$	−10.4442	+	45.7591i	−0.402595	+	1.76389i	0.214228	+	0.976784i	$0.431276\pi$
$673$	−10.4442	+	45.7591i	−0.402595	+	1.76389i	−0.616823	+	0.787102i	$0.711581\pi$
$674$	31.3192	−	15.0825i	1.20637	−	0.580958i
$675$	−3.08340	+	13.5093i	−0.118680	+	0.519972i
$676$	9.81256	+	12.3046i	0.377406	+	0.473252i
$677$	1.56139	+	6.84091i	0.0600092	+	0.262917i	0.996029	−	0.0890301i	$-0.0283767\pi$
$677$	1.56139	+	6.84091i	0.0600092	+	0.262917i	−0.936020	+	0.351947i	$0.885520\pi$
$678$	45.4373	−	56.9766i	1.74501	−	2.18817i
$679$		0			0
$680$	2.88783	+	3.62122i	0.110743	+	0.138867i
$681$	45.2842	−	56.7846i	1.73529	−	2.17599i
$682$	−3.59367	−	1.73062i	−0.137609	−	0.0662689i
$683$	−27.9858	+	35.0931i	−1.07085	+	1.34280i	−0.134821	+	0.990870i	$0.543046\pi$
$683$	−27.9858	+	35.0931i	−1.07085	+	1.34280i	−0.936026	+	0.351930i	$0.885525\pi$
$684$	8.24503	−	36.1238i	0.315257	−	1.38123i
$685$	−3.84397			−0.146870
$686$		0			0
$687$	21.2401			0.810361
$688$	2.39573	−	10.4964i	0.0913364	−	0.400171i
$689$	−23.8738	+	29.9368i	−0.909520	+	1.14050i
$690$	50.9860	+	24.5536i	1.94100	+	0.934738i
$691$	−31.6423	+	39.6782i	−1.20373	+	1.50943i	−0.397739	+	0.917499i	$0.630205\pi$
$691$	−31.6423	+	39.6782i	−1.20373	+	1.50943i	−0.805990	+	0.591929i	$0.798366\pi$
$692$	12.3675	+	15.5084i	0.470143	+	0.589541i
$693$		0			0
$694$	−48.5053	+	60.8237i	−1.84123	+	2.30884i
$695$	−0.927761	−	4.06479i	−0.0351920	−	0.154186i
$696$	0.260130	+	0.326193i	0.00986021	+	0.0123643i
$697$	0.847499	−	3.71314i	0.0321013	−	0.140645i
$698$	17.5838	−	8.46792i	0.665557	−	0.320515i
$699$	−3.70661	+	16.2397i	−0.140197	+	0.614243i
$700$		0			0
$701$	2.81197	+	12.3201i	0.106207	+	0.465322i	0.999863	+	0.0165696i	$0.00527450\pi$
$701$	2.81197	+	12.3201i	0.106207	+	0.465322i	−0.893656	+	0.448753i	$0.851868\pi$
$702$	−32.9496	−	41.3175i	−1.24360	−	1.55943i
$703$	18.3070	−	8.81619i	0.690462	−	0.332509i
$704$	8.12190			0.306106
$705$	−24.4905			−0.922366
$706$	6.78367	−	3.26684i	0.255307	−	0.122949i
$707$		0			0
$708$	−97.5434	−	46.9744i	−3.66591	−	1.76541i
$709$	−19.7954	−	9.53297i	−0.743433	−	0.358018i	0.0235187	−	0.999723i	$-0.492513\pi$
$709$	−19.7954	−	9.53297i	−0.743433	−	0.358018i	−0.766952	+	0.641705i	$0.778227\pi$
$710$	2.81316	+	12.3253i	0.105576	+	0.462559i
$711$	11.6084	+	50.8597i	0.435349	+	1.90739i
$712$	0.0889870	+	0.0428539i	0.00333493	+	0.00160602i
$713$	−12.0092	−	5.78332i	−0.449747	−	0.216587i
$714$		0			0
$715$	−4.05512	+	1.95284i	−0.151653	+	0.0730321i
$716$	45.6300			1.70527
$717$	−16.9487			−0.632961
$718$	−9.10796	+	4.38616i	−0.339906	+	0.163690i
$719$	−23.5893	−	29.5800i	−0.879732	−	1.10315i	−0.993965	−	0.109695i	$-0.965013\pi$
$719$	−23.5893	−	29.5800i	−0.879732	−	1.10315i	0.114233	−	0.993454i	$-0.463559\pi$
$720$	2.81627	+	12.3389i	0.104956	+	0.459843i
$721$		0			0
$722$	7.65009	−	33.5172i	0.284707	−	1.24738i
$723$	−18.4985	+	8.90842i	−0.687968	+	0.331308i
$724$	14.6226	−	64.0657i	0.543444	−	2.38098i
$725$	0.0640079	+	0.0802634i	0.00237719	+	0.00298091i
$726$	−15.5476	−	68.1184i	−0.577025	−	2.52811i
$727$	2.38311	−	2.98832i	0.0883846	−	0.110831i	−0.735673	−	0.677337i	$-0.763134\pi$
$727$	2.38311	−	2.98832i	0.0883846	−	0.110831i	0.824057	+	0.566506i	$0.191705\pi$
$728$		0			0
$729$	−27.1088	−	33.9933i	−1.00403	−	1.25901i
$730$	−5.76861	+	7.23360i	−0.213506	+	0.267728i
$731$	−4.66592	−	2.24699i	−0.172575	−	0.0831078i
$732$	29.9360	−	37.5386i	1.10647	−	1.38747i
$733$	−6.06406	+	26.5684i	−0.223981	+	0.981326i	0.730467	+	0.682948i	$0.239303\pi$
$733$	−6.06406	+	26.5684i	−0.223981	+	0.981326i	−0.954448	+	0.298378i	$0.903555\pi$
$734$	−81.7568			−3.01770
$735$		0			0
$736$	19.4443			0.716728
$737$	−1.22235	+	5.35548i	−0.0450259	+	0.197271i
$738$	34.4970	−	43.2578i	1.26985	−	1.59234i
$739$	28.5578	+	13.7527i	1.05052	+	0.505903i	0.877779	−	0.479065i	$-0.159024\pi$
$739$	28.5578	+	13.7527i	1.05052	+	0.505903i	0.172738	+	0.984968i	$0.444739\pi$
$740$	−33.4395	+	41.9318i	−1.22926	+	1.54144i
$741$	15.4201	+	19.3363i	0.566473	+	0.710335i
$742$		0			0
$743$	21.2921	−	26.6995i	0.781132	−	0.979509i	−0.218861	−	0.975756i	$-0.570234\pi$
$743$	21.2921	−	26.6995i	0.781132	−	0.979509i	0.999993	−	0.00375264i	$-0.00119451\pi$
$744$	−5.68250	−	24.8967i	−0.208331	−	0.912756i
$745$	−2.63380	−	3.30268i	−0.0964949	−	0.121001i
$746$	−11.4637	+	50.2258i	−0.419716	+	1.83890i
$747$	40.8937	−	19.6934i	1.49622	−	0.720543i
$748$	−0.441363	+	1.93374i	−0.0161378	+	0.0707045i
$749$		0			0
$750$	17.4257	+	76.3472i	0.636298	+	2.78780i
$751$	1.35198	+	1.69533i	0.0493344	+	0.0618633i	0.805887	−	0.592070i	$-0.201689\pi$
$751$	1.35198	+	1.69533i	0.0493344	+	0.0618633i	−0.756552	+	0.653933i	$0.773118\pi$
$752$	8.37406	−	4.03274i	0.305371	−	0.147059i
$753$	−8.33433			−0.303720
$754$	−0.391531			−0.0142587
$755$	1.64014	−	0.789852i	0.0596909	−	0.0287456i
$756$		0			0
$757$	40.7751	+	19.6363i	1.48200	+	0.713693i	0.987810	−	0.155663i	$-0.0497513\pi$
$757$	40.7751	+	19.6363i	1.48200	+	0.713693i	0.494188	+	0.869355i	$0.335466\pi$
$758$	12.8076	+	6.16784i	0.465195	+	0.224026i
$759$	2.38039	+	10.4291i	0.0864025	+	0.378554i
$760$	−2.72350	−	11.9325i	−0.0987919	−	0.432835i
$761$	42.6541	+	20.5411i	1.54621	+	0.744615i	0.995910	−	0.0903528i	$-0.0287995\pi$
$761$	42.6541	+	20.5411i	1.54621	+	0.744615i	0.550299	+	0.834968i	$0.314514\pi$
$762$	84.1953	+	40.5463i	3.05007	+	1.46884i
$763$		0			0
$764$	63.4994	−	30.5797i	2.29733	−	1.10633i
$765$	6.08784			0.220106
$766$	−57.3009			−2.07037
$767$	40.4068	−	19.4589i	1.45901	−	0.702620i
$768$	44.0557	+	55.2441i	1.58972	+	1.99345i
$769$	5.71133	+	25.0230i	0.205956	+	0.902351i	0.967226	+	0.253916i	$0.0817188\pi$
$769$	5.71133	+	25.0230i	0.205956	+	0.902351i	−0.761271	+	0.648434i	$0.775424\pi$
$770$		0			0
$771$	16.3266	−	71.5314i	0.587987	−	2.57614i
$772$	−50.2638	+	24.2058i	−1.80903	+	0.871184i
$773$	−5.10773	+	22.3784i	−0.183712	+	0.804896i	0.796130	+	0.605125i	$0.206877\pi$
$773$	−5.10773	+	22.3784i	−0.183712	+	0.804896i	−0.979843	+	0.199771i	$0.935980\pi$
$774$	−46.9072	−	58.8198i	−1.68604	−	2.11423i
$775$	−1.39824	−	6.12610i	−0.0502264	−	0.220056i
$776$	−27.3037	+	34.2377i	−0.980145	+	1.22906i
$777$		0			0
$778$	30.2073	+	37.8788i	1.08298	+	1.35802i
$779$	−6.27499	+	7.86859i	−0.224825	+	0.281922i
$780$	−58.8155	−	28.3240i	−2.10593	−	1.01416i
$781$	−1.49001	+	1.86841i	−0.0533166	+	0.0668569i
$782$	−2.29880	+	10.0717i	−0.0822048	+	0.360163i
$783$	0.213146			0.00761721
$784$		0			0
$785$	−15.8926			−0.567230
$786$	20.8958	−	91.5507i	0.745330	−	3.26550i
$787$	10.7300	−	13.4550i	0.382483	−	0.479618i	−0.552904	−	0.833245i	$-0.686480\pi$
$787$	10.7300	−	13.4550i	0.382483	−	0.479618i	0.935387	+	0.353627i	$0.115052\pi$
$788$	−52.3220	−	25.1969i	−1.86389	−	0.897604i
$789$	8.68592	−	10.8918i	0.309227	−	0.387758i
$790$	24.3397	+	30.5210i	0.865968	+	1.08589i
$791$		0			0
$792$	−7.93030	+	9.94428i	−0.281791	+	0.353355i
$793$	4.42581	+	19.3907i	0.157165	+	0.688585i
$794$	6.56411	+	8.23114i	0.232952	+	0.292112i
$795$	8.93026	−	39.1260i	0.316724	−	1.38766i
$796$	−70.8608	+	34.1248i	−2.51159	+	1.20952i
$797$	−5.96330	+	26.1269i	−0.211231	+	0.925464i	0.752501	+	0.658591i	$0.228847\pi$
$797$	−5.96330	+	26.1269i	−0.211231	+	0.925464i	−0.963732	+	0.266872i	$0.914010\pi$
$798$		0			0
$799$	−0.994849	−	4.35872i	−0.0351952	−	0.154200i
$800$	5.71519	+	7.16662i	0.202062	+	0.253378i
$801$	0.116963	−	0.0563263i	0.00413268	−	0.00199019i
$802$	−74.1388			−2.61793
$803$	−1.74895			−0.0617190
$804$	−71.7833	+	34.5690i	−2.53160	+	1.21916i
$805$		0			0
$806$	21.5915	+	10.3979i	0.760529	+	0.366252i
$807$	40.8819	+	19.6877i	1.43911	+	0.693039i
$808$	15.5431	+	68.0989i	0.546805	+	2.39571i
$809$	−4.77388	−	20.9157i	−0.167841	−	0.735358i	−0.986858	−	0.161589i	$-0.948338\pi$
$809$	−4.77388	−	20.9157i	−0.167841	−	0.735358i	0.819017	−	0.573769i	$-0.194519\pi$
$810$	1.19298	+	0.574508i	0.0419170	+	0.0201862i
$811$	−28.1304	−	13.5469i	−0.987791	−	0.475695i	−0.131013	−	0.991381i	$-0.541823\pi$
$811$	−28.1304	−	13.5469i	−0.987791	−	0.475695i	−0.856778	+	0.515686i	$0.827537\pi$
$812$		0			0
$813$	−4.43510	+	2.13583i	−0.155546	+	0.0749070i
$814$	−15.8014			−0.553838
$815$	−8.28410			−0.290179
$816$	−3.35415	+	1.61527i	−0.117419	+	0.0565459i
$817$	8.53241	+	10.6993i	0.298511	+	0.374321i
$818$	−7.30306	−	31.9968i	−0.255345	−	1.11874i
$819$		0			0
$820$	5.91123	−	25.8988i	0.206429	−	0.904425i
$821$	−19.9814	+	9.62254i	−0.697356	+	0.335829i	−0.748753	−	0.662849i	$-0.769347\pi$
$821$	−19.9814	+	9.62254i	−0.697356	+	0.335829i	0.0513966	+	0.998678i	$0.483633\pi$
$822$	3.65513	−	16.0142i	0.127487	−	0.558559i
$823$	0.495691	+	0.621577i	0.0172787	+	0.0216668i	0.790396	−	0.612597i	$-0.209875\pi$
$823$	0.495691	+	0.621577i	0.0172787	+	0.0216668i	−0.773117	+	0.634263i	$0.781304\pi$
$824$	−6.25053	−	27.3854i	−0.217748	−	0.954014i
$825$	−3.14423	+	3.94273i	−0.109468	+	0.137268i
$826$		0			0
$827$	−2.16118	−	2.71004i	−0.0751516	−	0.0942372i	0.742835	−	0.669475i	$-0.233481\pi$
$827$	−2.16118	−	2.71004i	−0.0751516	−	0.0942372i	−0.817986	+	0.575238i	$0.804909\pi$
$828$	−60.0361	+	75.2829i	−2.08640	+	2.61626i
$829$	22.4813	+	10.8264i	0.780808	+	0.376017i	0.781438	−	0.623982i	$-0.214486\pi$
$829$	22.4813	+	10.8264i	0.780808	+	0.376017i	−0.000630251		1.00000i	$0.500201\pi$
$830$	21.1768	−	26.5549i	0.735057	−	0.921733i
$831$	10.1208	−	44.3419i	0.351085	−	1.53821i
$832$	−48.7981			−1.69177
$833$		0			0
$834$	17.8163			0.616929
$835$	−0.530109	+	2.32256i	−0.0183452	+	0.0803754i
$836$	3.26791	−	4.09783i	0.113023	−	0.141726i
$837$	−11.7542	−	5.66054i	−0.406285	−	0.195657i
$838$	−20.3216	+	25.4825i	−0.701999	+	0.880279i
$839$	7.60123	+	9.53164i	0.262424	+	0.329069i	0.895534	−	0.444992i	$-0.146794\pi$
$839$	7.60123	+	9.53164i	0.262424	+	0.329069i	−0.633111	+	0.774061i	$0.718222\pi$
$840$		0			0
$841$	−18.0802	+	22.6719i	−0.623456	+	0.781789i
$842$	−4.51230	−	19.7697i	−0.155504	−	0.681307i
$843$	−6.77222	−	8.49210i	−0.233248	−	0.292483i
$844$	−22.0384	+	96.5564i	−0.758592	+	3.32361i
$845$	6.15630	−	2.96472i	0.211783	−	0.101989i
$846$	14.4524	−	63.3201i	0.496884	−	2.17699i
$847$		0			0
$848$	3.38916	+	14.8489i	0.116384	+	0.509913i
$849$	−52.5016	−	65.8350i	−1.80185	−	2.25945i
$850$	−4.38780	+	2.11306i	−0.150500	+	0.0724772i
$851$	−52.8043			−1.81011
$852$	−34.6615			−1.18748
$853$	16.8204	−	8.10030i	0.575921	−	0.277349i	−0.123165	−	0.992386i	$-0.539305\pi$
$853$	16.8204	−	8.10030i	0.575921	−	0.277349i	0.699086	+	0.715037i	$0.253590\pi$
$854$		0			0
$855$	−14.4940	−	6.97994i	−0.495684	−	0.238709i
$856$	−16.1977	−	7.80040i	−0.553626	−	0.266612i
$857$	−8.95744	−	39.2451i	−0.305980	−	1.34059i	−0.860939	−	0.508709i	$-0.830123\pi$
$857$	−8.95744	−	39.2451i	−0.305980	−	1.34059i	0.554958	−	0.831878i	$-0.312734\pi$
$858$	−4.27974	−	18.7508i	−0.146108	−	0.640141i
$859$	−4.23172	−	2.03789i	−0.144384	−	0.0695319i	0.360296	−	0.932838i	$-0.382676\pi$
$859$	−4.23172	−	2.03789i	−0.144384	−	0.0695319i	−0.504681	+	0.863306i	$0.668390\pi$
$860$	−32.5443	−	15.6725i	−1.10975	−	0.534428i
$861$		0			0
$862$	31.9009	−	15.3627i	1.08655	−	0.523254i
$863$	−1.75083			−0.0595988			−0.0297994	−	0.999556i	$-0.509487\pi$
$863$	−1.75083			−0.0595988			−0.0297994	+	0.999556i	$0.509487\pi$
$864$	19.0315			0.647466
$865$	7.75927	−	3.73667i	0.263823	−	0.127051i
$866$	−18.1095	−	22.7086i	−0.615385	−	0.771669i
$867$	−10.2390	−	44.8599i	−0.347734	−	1.52352i
$868$		0			0
$869$	−1.64207	+	7.19439i	−0.0557035	+	0.244053i
$870$	0.369723	−	0.178049i	0.0125348	−	0.00603644i
$871$	7.34415	−	32.1768i	0.248847	−	1.09027i
$872$	27.4472	+	34.4178i	0.929481	+	1.16553i
$873$	12.8081	+	56.1159i	0.433488	+	1.89923i
$874$	17.0206	−	21.3431i	0.575730	−	0.721942i
$875$		0			0
$876$	−15.8159	−	19.8325i	−0.534370	−	0.670079i
$877$	−10.6073	+	13.3011i	−0.358183	+	0.449147i	−0.927975	−	0.372642i	$-0.878452\pi$
$877$	−10.6073	+	13.3011i	−0.358183	+	0.449147i	0.569793	+	0.821788i	$0.307024\pi$
$878$	8.60145	+	4.14224i	0.290285	+	0.139794i
$879$	−21.6269	+	27.1193i	−0.729458	+	0.914712i
$880$	−0.398377	+	1.74540i	−0.0134293	+	0.0588375i
$881$	−39.7542			−1.33935			−0.669676	−	0.742653i	$-0.733567\pi$
$881$	−39.7542			−1.33935			−0.669676	+	0.742653i	$0.733567\pi$
$882$		0			0
$883$	−36.2060			−1.21843			−0.609215	−	0.793005i	$-0.708515\pi$
$883$	−36.2060			−1.21843			−0.609215	+	0.793005i	$0.708515\pi$
$884$	2.65180	−	11.6183i	0.0891898	−	0.390766i
$885$	−29.3072	+	36.7501i	−0.985152	+	1.23534i
$886$	26.4153	+	12.7209i	0.887438	+	0.427367i
$887$	18.5005	−	23.1989i	0.621187	−	0.778944i	−0.367324	−	0.930093i	$-0.619726\pi$
$887$	18.5005	−	23.1989i	0.621187	−	0.778944i	0.988511	+	0.151149i	$0.0482974\pi$
$888$	−63.0760	−	79.0948i	−2.11669	−	2.65425i
$889$		0			0
$890$	0.0605692	−	0.0759513i	0.00203028	−	0.00254589i
$891$	0.0556967	+	0.244023i	0.00186591	+	0.00817508i
$892$	5.10047	+	6.39579i	0.170776	+	0.214147i
$893$	−2.62889	+	11.5179i	−0.0879725	+	0.385433i
$894$	16.2636	−	7.83212i	0.543935	−	0.261945i
$895$	4.40838	−	19.3144i	0.147356	−	0.645608i
$896$		0			0
$897$	−14.3018	−	62.6605i	−0.477525	−	2.09217i
$898$	9.94340	+	12.4686i	0.331816	+	0.416084i
$899$	−0.0870842	+	0.0419375i	−0.00290442	+	0.00139870i
$900$	−45.3933			−1.51311
$901$	7.32624			0.244073
$902$	7.05149	−	3.39582i	0.234789	−	0.113068i
$903$		0			0
$904$	36.9038	+	17.7720i	1.22740	+	0.591086i
$905$	−25.7051	−	12.3789i	−0.854468	−	0.411490i
$906$	1.73100	+	7.58399i	0.0575085	+	0.251961i
$907$	−9.91220	−	43.4282i	−0.329129	−	1.44201i	−0.820794	−	0.571225i	$-0.806469\pi$
$907$	−9.91220	−	43.4282i	−0.329129	−	1.44201i	0.491665	−	0.870785i	$-0.336389\pi$
$908$	83.3208	+	40.1252i	2.76510	+	1.33160i
$909$	82.7177	+	39.8348i	2.74357	+	1.32124i
$910$		0			0
$911$	−9.62759	+	4.63640i	−0.318976	+	0.153611i	−0.586520	−	0.809935i	$-0.699502\pi$
$911$	−9.62759	+	4.63640i	−0.318976	+	0.153611i	0.267544	+	0.963546i	$0.413788\pi$
$912$	9.83758			0.325755
$913$	6.42046			0.212486
$914$	10.5612	−	5.08599i	0.349332	−	0.168230i
$915$	−12.9973	−	16.2980i	−0.429676	−	0.538797i
$916$	6.01803	+	26.3667i	0.198841	+	0.871181i
$917$		0			0
$918$	−2.24999	+	9.85786i	−0.0742608	+	0.325358i
$919$	28.9246	−	13.9294i	0.954136	−	0.459488i	0.109002	−	0.994042i	$-0.465235\pi$
$919$	28.9246	−	13.9294i	0.954136	−	0.459488i	0.845134	+	0.534554i	$0.179520\pi$
$920$	−7.07767	+	31.0093i	−0.233344	+	1.02235i
$921$	8.77096	+	10.9984i	0.289013	+	0.362411i
$922$	20.7121	+	90.7456i	0.682116	+	2.98855i
$923$	8.95227	−	11.2258i	0.294668	−	0.369501i
$924$		0			0
$925$	−15.5205	−	19.4622i	−0.510312	−	0.639912i
$926$	−10.4716	+	13.1310i	−0.344118	+	0.431510i
$927$	−33.2642	−	16.0192i	−1.09254	−	0.526139i
$928$	0.0879121	−	0.110238i	0.00288586	−	0.00361875i
$929$	−1.15363	+	5.05438i	−0.0378493	+	0.165829i	−0.990320	−	0.138800i	$-0.955675\pi$
$929$	−1.15363	+	5.05438i	−0.0378493	+	0.165829i	0.952471	+	0.304629i	$0.0985325\pi$
$930$	−25.1174			−0.823631
$931$		0			0
$932$	−21.2096			−0.694744
$933$	−18.7715	+	82.2432i	−0.614551	+	2.69252i
$934$	−16.5416	+	20.7425i	−0.541258	+	0.678716i
$935$	0.775876	+	0.373642i	0.0253739	+	0.0122194i
$936$	47.6469	−	59.7473i	1.55739	−	1.95290i
$937$	−21.3291	−	26.7458i	−0.696791	−	0.873748i	0.299988	−	0.953943i	$-0.403017\pi$
$937$	−21.3291	−	26.7458i	−0.696791	−	0.873748i	−0.996779	+	0.0801945i	$0.974446\pi$
$938$		0			0
$939$	1.79703	−	2.25341i	0.0586440	−	0.0735373i
$940$	−6.93897	−	30.4016i	−0.226324	−	0.991592i
$941$	−15.0644	−	18.8902i	−0.491086	−	0.615802i	0.473107	−	0.881005i	$-0.343133\pi$
$941$	−15.0644	−	18.8902i	−0.491086	−	0.615802i	−0.964193	+	0.265203i	$0.914561\pi$
$942$	15.1119	−	66.2094i	0.492371	−	2.15722i
$943$	23.5644	−	11.3480i	0.767362	−	0.369542i
$944$	3.96958	−	17.3919i	0.129199	−	0.566057i
$945$		0			0
$946$	−2.36810	−	10.3753i	−0.0769937	−	0.337331i
$947$	−11.1317	−	13.9588i	−0.361733	−	0.453599i	0.567347	−	0.823479i	$-0.307970\pi$
$947$	−11.1317	−	13.9588i	−0.361733	−	0.453599i	−0.929079	+	0.369881i	$0.879399\pi$
$948$	−96.4316	+	46.4390i	−3.13195	+	1.50827i
$949$	10.5080			0.341105
$950$	12.8692			0.417533
$951$	−1.18504	+	0.570685i	−0.0384275	+	0.0185057i
$952$		0			0
$953$	17.5916	+	8.47169i	0.569849	+	0.274425i	0.696541	−	0.717517i	$-0.254722\pi$
$953$	17.5916	+	8.47169i	0.569849	+	0.274425i	−0.126692	+	0.991942i	$0.540436\pi$
$954$	95.8902	+	46.1783i	3.10456	+	1.49508i
$955$	−6.80907	−	29.8325i	−0.220336	−	0.965357i
$956$	−4.80213	−	21.0395i	−0.155312	−	0.680466i
$957$	0.0698895	+	0.0336570i	0.00225921	+	0.00108798i
$958$	53.3655	+	25.6995i	1.72416	+	0.830313i
$959$		0			0
$960$	46.0801	−	22.1910i	1.48723	−	0.716211i
$961$	−25.0839			−0.809157
$962$	94.9379			3.06092
$963$	−21.2899	+	10.2527i	−0.686059	+	0.330389i
$964$	−16.2998	−	20.4394i	−0.524983	−	0.658307i
$965$	5.38981	+	23.6143i	0.173504	+	0.760171i
$966$		0			0
$967$	−1.14669	+	5.02398i	−0.0368751	+	0.161560i	−0.990013	−	0.140976i	$-0.954976\pi$
$967$	−1.14669	+	5.02398i	−0.0368751	+	0.161560i	0.953138	+	0.302536i	$0.0978332\pi$
$968$	35.3818	−	17.0390i	1.13721	−	0.547654i
$969$	1.05298	−	4.61340i	0.0338265	−	0.148204i
$970$	26.8551	+	33.6752i	0.862266	+	1.08125i
$971$	−12.7171	−	55.7172i	−0.408111	−	1.78805i	−0.592905	−	0.805273i	$-0.702019\pi$
$971$	−12.7171	−	55.7172i	−0.408111	−	1.78805i	0.184794	−	0.982777i	$-0.440838\pi$
$972$	33.6585	−	42.2065i	1.07960	−	1.35377i
$973$		0			0
$974$	−15.1870	−	19.0439i	−0.486623	−	0.610206i
$975$	18.8912	−	23.6888i	0.605001	−	0.758648i
$976$	7.12789	+	3.43261i	0.228158	+	0.109875i
$977$	35.2005	−	44.1401i	1.12617	−	1.41217i	0.227364	−	0.973810i	$-0.426989\pi$
$977$	35.2005	−	44.1401i	1.12617	−	1.41217i	0.898801	−	0.438357i	$-0.144439\pi$
$978$	7.87715	−	34.5120i	0.251883	−	1.10357i
$979$	0.0183636			0.000586903
$980$		0			0
$981$	57.8616			1.84738
$982$	5.38109	−	23.5761i	0.171717	−	0.752344i
$983$	−2.09047	+	2.62137i	−0.0666758	+	0.0836088i	−0.814051	−	0.580793i	$-0.802742\pi$
$983$	−2.09047	+	2.62137i	−0.0666758	+	0.0836088i	0.747375	+	0.664402i	$0.231314\pi$
$984$	45.1462	+	21.7413i	1.43921	+	0.693086i
$985$	−15.7203	+	19.7126i	−0.500891	+	0.628097i
$986$	0.0467073	+	0.0585691i	0.00148746	+	0.00186522i
$987$		0			0
$988$	−19.6343	+	24.6206i	−0.624650	+	0.783286i
$989$	−7.91363	−	34.6719i	−0.251639	−	1.10250i
$990$	7.80001	+	9.78090i	0.247901	+	0.310858i
$991$	7.41047	−	32.4674i	0.235401	−	1.03136i	−0.709680	−	0.704524i	$-0.751160\pi$
$991$	7.41047	−	32.4674i	0.235401	−	1.03136i	0.945081	−	0.326836i	$-0.105983\pi$
$992$	−7.77564	+	3.74455i	−0.246877	+	0.118890i
$993$	−8.02064	+	35.1407i	−0.254527	+	1.11516i
$994$		0			0
$995$	7.59844	+	33.2909i	0.240887	+	1.05539i
$996$	58.0609	+	72.8061i	1.83973	+	2.30695i
$997$	−35.3973	+	17.0464i	−1.12104	+	0.539866i	−0.900215	−	0.435447i	$-0.856591\pi$
$997$	−35.3973	+	17.0464i	−1.12104	+	0.539866i	−0.220829	+	0.975313i	$0.570876\pi$
$998$	57.4893			1.81979
$999$	−51.6833			−1.63519

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	343.2.e.d.99.1		48
7.2	even	3		343.2.g.i.67.4		48
7.3	odd	6		343.2.g.g.177.1		48
7.4	even	3		49.2.g.a.9.1	✓	48
7.5	odd	6		343.2.g.h.67.4		48
7.6	odd	2		343.2.e.c.99.1		48
21.11	odd	6		441.2.bb.d.352.4		48
28.11	odd	6		784.2.bg.c.401.1		48
49.2	even	21		49.2.g.a.11.1	yes	48
49.6	odd	14		2401.2.a.i.1.22		24
49.11	even	21		343.2.g.i.128.4		48
49.13	odd	14		343.2.e.c.246.1		48
49.36	even	7	inner	343.2.e.d.246.1		48
49.38	odd	42		343.2.g.h.128.4		48
49.43	even	7		2401.2.a.h.1.22		24
49.47	odd	42		343.2.g.g.312.1		48
147.2	odd	42		441.2.bb.d.109.4		48
196.51	odd	42		784.2.bg.c.305.1		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
49.2.g.a.9.1	✓	48	7.4	even	3
49.2.g.a.11.1	yes	48	49.2	even	21
343.2.e.c.99.1		48	7.6	odd	2
343.2.e.c.246.1		48	49.13	odd	14
343.2.e.d.99.1		48	1.1	even	1	trivial
343.2.e.d.246.1		48	49.36	even	7	inner
343.2.g.g.177.1		48	7.3	odd	6
343.2.g.g.312.1		48	49.47	odd	42
343.2.g.h.67.4		48	7.5	odd	6
343.2.g.h.128.4		48	49.38	odd	42
343.2.g.i.67.4		48	7.2	even	3
343.2.g.i.128.4		48	49.11	even	21
441.2.bb.d.109.4		48	147.2	odd	42
441.2.bb.d.352.4		48	21.11	odd	6
784.2.bg.c.305.1		48	196.51	odd	42
784.2.bg.c.401.1		48	28.11	odd	6
2401.2.a.h.1.22		24	49.43	even	7
2401.2.a.i.1.22		24	49.6	odd	14

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:	\( N \)	\(=\)	\( 343 = 7^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	343.e (of order \(7\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.525663 + 2.30308i) q^{2} +(-1.75326 + 2.19852i) q^{3} +(-3.22592 - 1.55352i) q^{4} +(-0.969239 + 1.21539i) q^{5} +(-4.14175 - 5.19359i) q^{6} +(2.32789 - 2.91908i) q^{8} +(-1.09201 - 4.78439i) q^{9} +O(q^{10})\)	\(q+(-0.525663 + 2.30308i) q^{2} +(-1.75326 + 2.19852i) q^{3} +(-3.22592 - 1.55352i) q^{4} +(-0.969239 + 1.21539i) q^{5} +(-4.14175 - 5.19359i) q^{6} +(2.32789 - 2.91908i) q^{8} +(-1.09201 - 4.78439i) q^{9} +(-2.28964 - 2.87112i) q^{10} +(0.154470 - 0.676778i) q^{11} +(9.07134 - 4.36853i) q^{12} +(-0.928088 + 4.06622i) q^{13} +(-0.972725 - 4.26179i) q^{15} +(1.03437 + 1.29706i) q^{16} +(0.718981 - 0.346243i) q^{17} +11.5929 q^{18} -2.10874 q^{19} +(5.01482 - 2.41501i) q^{20} +(1.47747 + 0.711514i) q^{22} +(4.93736 + 2.37771i) q^{23} +(2.33626 + 10.2358i) q^{24} +(0.574863 + 2.51864i) q^{25} +(-8.87698 - 4.27493i) q^{26} +(4.83254 + 2.32723i) q^{27} +(0.0358031 - 0.0172419i) q^{29} +10.3266 q^{30} -2.43231 q^{31} +(3.19682 - 1.53951i) q^{32} +(1.21708 + 1.52618i) q^{33} +(0.419484 + 1.83788i) q^{34} +(-3.90993 + 17.1305i) q^{36} +(-8.68149 + 4.18078i) q^{37} +(1.10849 - 4.85660i) q^{38} +(-7.31249 - 9.16958i) q^{39} +(1.29153 + 5.65857i) q^{40} +(2.97571 - 3.73142i) q^{41} +(-4.04621 - 5.07379i) q^{43} +(-1.54970 + 1.94326i) q^{44} +(6.87330 + 3.31001i) q^{45} +(-8.07144 + 10.1213i) q^{46} +(1.24666 - 5.46199i) q^{47} -4.66515 q^{48} -6.10281 q^{50} +(-0.499340 + 2.18775i) q^{51} +(9.31091 - 11.6755i) q^{52} +(8.27149 + 3.98334i) q^{53} +(-7.90009 + 9.90640i) q^{54} +(0.672829 + 0.843700i) q^{55} +(3.69718 - 4.63611i) q^{57} +(0.0208891 + 0.0915209i) q^{58} +(-6.70433 - 8.40697i) q^{59} +(-3.48285 + 15.2593i) q^{60} +(4.29648 - 2.06908i) q^{61} +(1.27857 - 5.60180i) q^{62} +(2.60348 + 11.4066i) q^{64} +(-4.04249 - 5.06913i) q^{65} +(-4.15468 + 2.00079i) q^{66} -7.91320 q^{67} -2.85727 q^{68} +(-13.8839 + 6.68615i) q^{69} +(-3.10167 - 1.49368i) q^{71} +(-16.5081 - 7.94987i) q^{72} +(-0.560627 - 2.45627i) q^{73} +(-5.06515 - 22.1919i) q^{74} +(-6.54517 - 3.15199i) q^{75} +(6.80263 + 3.27598i) q^{76} +(24.9622 - 12.0212i) q^{78} -10.6304 q^{79} -2.57899 q^{80} +(-0.324859 + 0.156444i) q^{81} +(7.02954 + 8.81477i) q^{82} +(2.05809 + 9.01706i) q^{83} +(-0.276045 + 1.20943i) q^{85} +(13.8123 - 6.65165i) q^{86} +(-0.0248656 + 0.108944i) q^{87} +(-1.61598 - 2.02637i) q^{88} +(0.00588647 + 0.0257903i) q^{89} +(-11.2363 + 14.0898i) q^{90} +(-12.2337 - 15.3406i) q^{92} +(4.26447 - 5.34748i) q^{93} +(11.9241 + 5.74234i) q^{94} +(2.04387 - 2.56294i) q^{95} +(-2.22022 + 9.72743i) q^{96} -11.7290 q^{97} -3.40665 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 5 q^{2} + 7 q^{3} - 3 q^{4} + 7 q^{5} - 20 q^{8} + 9 q^{9}+O(q^{10}) \) 48 * q + 5 * q^2 + 7 * q^3 - 3 * q^4 + 7 * q^5 - 20 * q^8 + 9 * q^9	\( 48 q + 5 q^{2} + 7 q^{3} - 3 q^{4} + 7 q^{5} - 20 q^{8} + 9 q^{9} + 7 q^{10} + 6 q^{11} + 42 q^{12} - 14 q^{13} - 12 q^{15} - 15 q^{16} - 7 q^{17} - 4 q^{18} - 42 q^{19} + 14 q^{20} - 20 q^{22} + 12 q^{23} + 49 q^{24} - 13 q^{25} + 21 q^{26} + 7 q^{27} + 12 q^{29} - 22 q^{30} - 70 q^{31} + 15 q^{32} + 7 q^{33} + 70 q^{34} - 12 q^{36} - 9 q^{37} - 7 q^{38} - 28 q^{39} - 63 q^{40} - 42 q^{41} - 30 q^{43} + 37 q^{44} + 28 q^{45} + 9 q^{46} + 21 q^{47} - 84 q^{48} + 40 q^{50} - q^{51} + 77 q^{52} + 20 q^{53} + 7 q^{54} - 7 q^{55} - 12 q^{57} + 31 q^{58} - 7 q^{59} + 35 q^{60} + 7 q^{61} - 28 q^{62} - 32 q^{64} - 49 q^{65} - 119 q^{66} - 22 q^{67} - 154 q^{68} + 70 q^{69} + 19 q^{71} - 46 q^{72} + 28 q^{73} - 47 q^{74} + 7 q^{75} + 119 q^{76} + 28 q^{78} - 30 q^{79} - 140 q^{80} + 61 q^{81} + 112 q^{82} - 26 q^{85} + 24 q^{86} + 77 q^{87} + 28 q^{88} + 28 q^{89} - 182 q^{90} - 38 q^{92} + 34 q^{93} - 28 q^{94} - 67 q^{95} - 28 q^{96} - 16 q^{99}+O(q^{100}) \) 48 * q + 5 * q^2 + 7 * q^3 - 3 * q^4 + 7 * q^5 - 20 * q^8 + 9 * q^9 + 7 * q^10 + 6 * q^11 + 42 * q^12 - 14 * q^13 - 12 * q^15 - 15 * q^16 - 7 * q^17 - 4 * q^18 - 42 * q^19 + 14 * q^20 - 20 * q^22 + 12 * q^23 + 49 * q^24 - 13 * q^25 + 21 * q^26 + 7 * q^27 + 12 * q^29 - 22 * q^30 - 70 * q^31 + 15 * q^32 + 7 * q^33 + 70 * q^34 - 12 * q^36 - 9 * q^37 - 7 * q^38 - 28 * q^39 - 63 * q^40 - 42 * q^41 - 30 * q^43 + 37 * q^44 + 28 * q^45 + 9 * q^46 + 21 * q^47 - 84 * q^48 + 40 * q^50 - q^51 + 77 * q^52 + 20 * q^53 + 7 * q^54 - 7 * q^55 - 12 * q^57 + 31 * q^58 - 7 * q^59 + 35 * q^60 + 7 * q^61 - 28 * q^62 - 32 * q^64 - 49 * q^65 - 119 * q^66 - 22 * q^67 - 154 * q^68 + 70 * q^69 + 19 * q^71 - 46 * q^72 + 28 * q^73 - 47 * q^74 + 7 * q^75 + 119 * q^76 + 28 * q^78 - 30 * q^79 - 140 * q^80 + 61 * q^81 + 112 * q^82 - 26 * q^85 + 24 * q^86 + 77 * q^87 + 28 * q^88 + 28 * q^89 - 182 * q^90 - 38 * q^92 + 34 * q^93 - 28 * q^94 - 67 * q^95 - 28 * q^96 - 16 * q^99

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