LMFDB - Embedded newform 418.2.j.d.199.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(23,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([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("418.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.j (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			199.2
Character	$\chi$	$=$	418.199
Dual form			418.2.j.d.397.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.173648 + 0.984808i) q^{2} +(-1.16564 + 0.978092i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(2.75856 + 1.00403i) q^{5} +(-1.16564 - 0.978092i) q^{6} +(0.232407 - 0.402540i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-0.118881 + 0.674209i) q^{9} +(-0.509761 + 2.89100i) q^{10} +(0.500000 + 0.866025i) q^{11} +(0.760820 - 1.31778i) q^{12} +(3.44686 + 2.89226i) q^{13} +(0.436782 + 0.158976i) q^{14} +(-4.19754 + 1.52778i) q^{15} +(0.766044 - 0.642788i) q^{16} +(0.0327869 + 0.185944i) q^{17} -0.684609 q^{18} +(-4.22484 + 1.07272i) q^{19} -2.93560 q^{20} +(0.122818 + 0.696534i) q^{21} +(-0.766044 + 0.642788i) q^{22} +(-2.73507 + 0.995485i) q^{23} +(1.42987 + 0.520432i) q^{24} +(2.77135 + 2.32544i) q^{25} +(-2.24978 + 3.89673i) q^{26} +(-2.80333 - 4.85550i) q^{27} +(-0.0807140 + 0.457752i) q^{28} +(0.299660 - 1.69946i) q^{29} +(-2.23346 - 3.86847i) q^{30} +(0.937019 - 1.62296i) q^{31} +(0.766044 + 0.642788i) q^{32} +(-1.42987 - 0.520432i) q^{33} +(-0.177426 + 0.0645776i) q^{34} +(1.04527 - 0.877088i) q^{35} +(-0.118881 - 0.674209i) q^{36} -6.48294 q^{37} +(-1.79006 - 3.97438i) q^{38} -6.84672 q^{39} +(-0.509761 - 2.89100i) q^{40} +(-2.52894 + 2.12203i) q^{41} +(-0.664625 + 0.241904i) q^{42} +(10.0581 + 3.66086i) q^{43} +(-0.766044 - 0.642788i) q^{44} +(-1.00487 + 1.74048i) q^{45} +(-1.45530 - 2.52066i) q^{46} +(-0.699708 + 3.96824i) q^{47} +(-0.264230 + 1.49852i) q^{48} +(3.39197 + 5.87507i) q^{49} +(-1.80887 + 3.13306i) q^{50} +(-0.220088 - 0.184676i) q^{51} +(-4.22820 - 1.53894i) q^{52} +(1.27737 - 0.464925i) q^{53} +(4.29494 - 3.60389i) q^{54} +(0.509761 + 2.89100i) q^{55} -0.464814 q^{56} +(3.87544 - 5.38269i) q^{57} +1.72567 q^{58} +(-0.956207 - 5.42292i) q^{59} +(3.42187 - 2.87129i) q^{60} +(10.3050 - 3.75070i) q^{61} +(1.76102 + 0.640958i) q^{62} +(0.243767 + 0.204545i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(6.60445 + 11.4393i) q^{65} +(0.264230 - 1.49852i) q^{66} +(0.966729 - 5.48259i) q^{67} +(-0.0944062 - 0.163516i) q^{68} +(2.21445 - 3.83553i) q^{69} +(1.04527 + 0.877088i) q^{70} +(-3.74260 - 1.36219i) q^{71} +(0.643322 - 0.234150i) q^{72} +(8.35197 - 7.00813i) q^{73} +(-1.12575 - 6.38445i) q^{74} -5.50491 q^{75} +(3.60316 - 2.45301i) q^{76} +0.464814 q^{77} +(-1.18892 - 6.74270i) q^{78} +(4.24799 - 3.56449i) q^{79} +(2.75856 - 1.00403i) q^{80} +(6.08684 + 2.21543i) q^{81} +(-2.52894 - 2.12203i) q^{82} +(6.42325 - 11.1254i) q^{83} +(-0.353640 - 0.612522i) q^{84} +(-0.0962492 + 0.545857i) q^{85} +(-1.85867 + 10.5410i) q^{86} +(1.31293 + 2.27406i) q^{87} +(0.500000 - 0.866025i) q^{88} +(12.9777 + 10.8896i) q^{89} +(-1.88854 - 0.687371i) q^{90} +(1.96533 - 0.715321i) q^{91} +(2.22965 - 1.87090i) q^{92} +(0.495177 + 2.80829i) q^{93} -4.02946 q^{94} +(-12.7315 - 1.28272i) q^{95} -1.52164 q^{96} +(-2.10957 - 11.9640i) q^{97} +(-5.19681 + 4.36064i) q^{98} +(-0.643322 + 0.234150i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 15 q^{8} + 15 q^{11} - 3 q^{12} - 21 q^{13} - 9 q^{14} + 3 q^{15} + 6 q^{17} + 60 q^{18} - 9 q^{19} + 18 q^{20} - 39 q^{21} + 15 q^{23} + 24 q^{25} - 3 q^{27} + 9 q^{28} - 3 q^{29} - 21 q^{30} - 18 q^{31}+ \cdots + 9 q^{98}+O(q^{100}) $ 30 * q - 15 * q^8 + 15 * q^11 - 3 * q^12 - 21 * q^13 - 9 * q^14 + 3 * q^15 + 6 * q^17 + 60 * q^18 - 9 * q^19 + 18 * q^20 - 39 * q^21 + 15 * q^23 + 24 * q^25 - 3 * q^27 + 9 * q^28 - 3 * q^29 - 21 * q^30 - 18 * q^31 + 15 * q^34 + 51 * q^35 - 18 * q^37 - 6 * q^38 - 6 * q^41 + 51 * q^42 + 39 * q^43 - 54 * q^45 - 21 * q^46 - 3 * q^47 - 33 * q^49 - 24 * q^50 - 48 * q^51 - 12 * q^52 - 24 * q^53 - 9 * q^54 - 6 * q^57 - 18 * q^58 + 21 * q^59 + 3 * q^60 + 63 * q^61 - 27 * q^62 + 57 * q^63 - 15 * q^64 - 6 * q^65 - 45 * q^67 - 21 * q^68 + 42 * q^69 + 51 * q^70 - 48 * q^71 + 87 * q^73 + 9 * q^74 + 42 * q^75 - 9 * q^76 - 36 * q^78 - 57 * q^79 + 36 * q^81 - 6 * q^82 - 30 * q^83 + 9 * q^84 + 81 * q^85 - 24 * q^86 - 9 * q^87 + 15 * q^88 - 6 * q^89 - 114 * q^90 - 51 * q^91 - 3 * q^92 + 33 * q^93 + 78 * q^94 - 132 * q^95 + 6 * q^96 - 66 * q^97 + 9 * q^98

Character values

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

$n$	$287$	$343$
$\chi(n)$	$e\left(\frac{4}{9}\right)$	$1$

Coefficient data

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

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

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

$2$	0.173648	+	0.984808i	0.122788	+	0.696364i
$2$	0.173648	+	0.984808i	0.122788	+	0.696364i
$3$	−1.16564	+	0.978092i	−0.672985	+	0.564702i	−0.913947	−	0.405833i	$-0.866981\pi$
$3$	−1.16564	+	0.978092i	−0.672985	+	0.564702i	0.240962	+	0.970535i	$0.422537\pi$
$4$	−0.939693	+	0.342020i	−0.469846	+	0.171010i
$5$	2.75856	+	1.00403i	1.23367	+	0.449018i	0.874852	−	0.484391i	$-0.160959\pi$
$5$	2.75856	+	1.00403i	1.23367	+	0.449018i	0.358814	+	0.933409i	$0.383181\pi$
$6$	−1.16564	−	0.978092i	−0.475872	−	0.399304i
$7$	0.232407	−	0.402540i	0.0878415	−	0.152146i	−0.818757	−	0.574140i	$-0.805336\pi$
$7$	0.232407	−	0.402540i	0.0878415	−	0.152146i	0.906599	+	0.421994i	$0.138670\pi$
$8$	−0.500000	−	0.866025i	−0.176777	−	0.306186i
$9$	−0.118881	+	0.674209i	−0.0396271	+	0.224736i
$10$	−0.509761	+	2.89100i	−0.161201	+	0.914215i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$12$	0.760820	−	1.31778i	0.219630	−	0.380410i
$13$	3.44686	+	2.89226i	0.955988	+	0.802169i	0.980296	−	0.197535i	$-0.0632937\pi$
$13$	3.44686	+	2.89226i	0.955988	+	0.802169i	−0.0243077	+	0.999705i	$0.507738\pi$
$14$	0.436782	+	0.158976i	0.116735	+	0.0424880i
$15$	−4.19754	+	1.52778i	−1.08380	+	0.394471i
$16$	0.766044	−	0.642788i	0.191511	−	0.160697i
$17$	0.0327869	+	0.185944i	0.00795199	+	0.0450980i	0.988526	−	0.151054i	$-0.0482666\pi$
$17$	0.0327869	+	0.185944i	0.00795199	+	0.0450980i	−0.980574	+	0.196152i	$0.937156\pi$
$18$	−0.684609			−0.161364
$19$	−4.22484	+	1.07272i	−0.969245	+	0.246099i
$19$	−4.22484	+	1.07272i	−0.969245	+	0.246099i
$20$	−2.93560			−0.656420
$21$	0.122818	+	0.696534i	0.0268010	+	0.151996i
$22$	−0.766044	+	0.642788i	−0.163321	+	0.137043i
$23$	−2.73507	+	0.995485i	−0.570302	+	0.207573i	−0.611044	−	0.791597i	$-0.709250\pi$
$23$	−2.73507	+	0.995485i	−0.570302	+	0.207573i	0.0407417	+	0.999170i	$0.487028\pi$
$24$	1.42987	+	0.520432i	0.291872	+	0.106233i
$25$	2.77135	+	2.32544i	0.554270	+	0.465088i
$26$	−2.24978	+	3.89673i	−0.441218	+	0.764212i
$27$	−2.80333	−	4.85550i	−0.539500	−	0.934442i
$28$	−0.0807140	+	0.457752i	−0.0152535	+	0.0865070i
$29$	0.299660	−	1.69946i	0.0556455	−	0.315581i	−0.944262	−	0.329195i	$-0.893223\pi$
$29$	0.299660	−	1.69946i	0.0556455	−	0.315581i	0.999907	+	0.0136141i	$0.00433362\pi$
$30$	−2.23346	−	3.86847i	−0.407773	−	0.706283i
$31$	0.937019	−	1.62296i	0.168293	−	0.291493i	−0.769526	−	0.638615i	$-0.779508\pi$
$31$	0.937019	−	1.62296i	0.168293	−	0.291493i	0.937820	+	0.347122i	$0.112841\pi$
$32$	0.766044	+	0.642788i	0.135419	+	0.113630i
$33$	−1.42987	−	0.520432i	−0.248909	−	0.0905955i
$34$	−0.177426	+	0.0645776i	−0.0304282	+	0.0110750i
$35$	1.04527	−	0.877088i	0.176683	−	0.148255i
$36$	−0.118881	−	0.674209i	−0.0198135	−	0.112368i
$37$	−6.48294			−1.06579			−0.532894	−	0.846182i	$-0.678896\pi$
$37$	−6.48294			−1.06579			−0.532894	+	0.846182i	$0.678896\pi$
$38$	−1.79006	−	3.97438i	−0.290386	−	0.644730i
$39$	−6.84672			−1.09635
$40$	−0.509761	−	2.89100i	−0.0806004	−	0.457107i
$41$	−2.52894	+	2.12203i	−0.394953	+	0.331405i	−0.818539	−	0.574451i	$-0.805216\pi$
$41$	−2.52894	+	2.12203i	−0.394953	+	0.331405i	0.423586	+	0.905856i	$0.360771\pi$
$42$	−0.664625	+	0.241904i	−0.102554	+	0.0373266i
$43$	10.0581	+	3.66086i	1.53385	+	0.558276i	0.964561	−	0.263861i	$-0.0849960\pi$
$43$	10.0581	+	3.66086i	1.53385	+	0.558276i	0.569290	+	0.822137i	$0.307218\pi$
$44$	−0.766044	−	0.642788i	−0.115486	−	0.0969039i
$45$	−1.00487	+	1.74048i	−0.149797	+	0.259456i
$46$	−1.45530	−	2.52066i	−0.214573	−	0.371651i
$47$	−0.699708	+	3.96824i	−0.102063	+	0.578827i	0.890290	+	0.455394i	$0.150502\pi$
$47$	−0.699708	+	3.96824i	−0.102063	+	0.578827i	−0.992353	+	0.123433i	$0.960609\pi$
$48$	−0.264230	+	1.49852i	−0.0381383	+	0.216293i
$49$	3.39197	+	5.87507i	0.484568	+	0.839296i
$50$	−1.80887	+	3.13306i	−0.255813	+	0.443081i
$51$	−0.220088	−	0.184676i	−0.0308185	−	0.0258598i
$52$	−4.22820	−	1.53894i	−0.586346	−	0.213413i
$53$	1.27737	−	0.464925i	0.175460	−	0.0638623i	−0.252796	−	0.967520i	$-0.581350\pi$
$53$	1.27737	−	0.464925i	0.175460	−	0.0638623i	0.428256	+	0.903657i	$0.359128\pi$
$54$	4.29494	−	3.60389i	0.584468	−	0.490427i
$55$	0.509761	+	2.89100i	0.0687362	+	0.389822i
$56$	−0.464814			−0.0621133
$57$	3.87544	−	5.38269i	0.513315	−	0.712955i
$58$	1.72567			0.226592
$59$	−0.956207	−	5.42292i	−0.124488	−	0.706004i	−0.981611	−	0.190893i	$-0.938862\pi$
$59$	−0.956207	−	5.42292i	−0.124488	−	0.706004i	0.857123	−	0.515111i	$-0.172249\pi$
$60$	3.42187	−	2.87129i	0.441761	−	0.370681i
$61$	10.3050	−	3.75070i	1.31941	−	0.480227i	0.416144	−	0.909299i	$-0.363381\pi$
$61$	10.3050	−	3.75070i	1.31941	−	0.480227i	0.903271	+	0.429071i	$0.141159\pi$
$62$	1.76102	+	0.640958i	0.223650	+	0.0814018i
$63$	0.243767	+	0.204545i	0.0307118	+	0.0257703i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	6.60445	+	11.4393i	0.819182	+	1.41886i
$66$	0.264230	−	1.49852i	0.0325245	−	0.184456i
$67$	0.966729	−	5.48259i	0.118105	−	0.669805i	−0.867061	−	0.498201i	$-0.833994\pi$
$67$	0.966729	−	5.48259i	0.118105	−	0.669805i	0.985166	−	0.171604i	$-0.0548949\pi$
$68$	−0.0944062	−	0.163516i	−0.0114484	−	0.0198293i
$69$	2.21445	−	3.83553i	0.266588	−	0.461744i
$70$	1.04527	+	0.877088i	0.124934	+	0.104832i
$71$	−3.74260	−	1.36219i	−0.444164	−	0.161663i	0.110249	−	0.993904i	$-0.464835\pi$
$71$	−3.74260	−	1.36219i	−0.444164	−	0.161663i	−0.554413	+	0.832241i	$0.687057\pi$
$72$	0.643322	−	0.234150i	0.0758163	−	0.0275949i
$73$	8.35197	−	7.00813i	0.977524	−	0.820240i	−0.00619030	−	0.999981i	$-0.501970\pi$
$73$	8.35197	−	7.00813i	0.977524	−	0.820240i	0.983714	+	0.179741i	$0.0575260\pi$
$74$	−1.12575	−	6.38445i	−0.130866	−	0.742177i
$75$	−5.50491			−0.635652
$76$	3.60316	−	2.45301i	0.413311	−	0.281379i
$77$	0.464814			0.0529704
$78$	−1.18892	−	6.74270i	−0.134619	−	0.763460i
$79$	4.24799	−	3.56449i	0.477936	−	0.401036i	−0.371743	−	0.928336i	$-0.621240\pi$
$79$	4.24799	−	3.56449i	0.477936	−	0.401036i	0.849680	+	0.527299i	$0.176795\pi$
$80$	2.75856	−	1.00403i	0.308416	−	0.112254i
$81$	6.08684	+	2.21543i	0.676316	+	0.246159i
$82$	−2.52894	−	2.12203i	−0.279274	−	0.234339i
$83$	6.42325	−	11.1254i	0.705043	−	1.22117i	−0.261632	−	0.965168i	$-0.584261\pi$
$83$	6.42325	−	11.1254i	0.705043	−	1.22117i	0.966676	−	0.256003i	$-0.0824059\pi$
$84$	−0.353640	−	0.612522i	−0.0385853	−	0.0668316i
$85$	−0.0962492	+	0.545857i	−0.0104397	+	0.0592065i
$86$	−1.85867	+	10.5410i	−0.200425	+	1.13667i
$87$	1.31293	+	2.27406i	0.140761	+	0.243805i
$88$	0.500000	−	0.866025i	0.0533002	−	0.0923186i
$89$	12.9777	+	10.8896i	1.37564	+	1.15430i	0.970795	+	0.239912i	$0.0771184\pi$
$89$	12.9777	+	10.8896i	1.37564	+	1.15430i	0.404843	+	0.914386i	$0.367326\pi$
$90$	−1.88854	−	0.687371i	−0.199069	−	0.0724553i
$91$	1.96533	−	0.715321i	0.206022	−	0.0749860i
$92$	2.22965	−	1.87090i	0.232457	−	0.195055i
$93$	0.495177	+	2.80829i	0.0513475	+	0.291206i
$94$	−4.02946			−0.415607
$95$	−12.7315	−	1.28272i	−1.30623	−	0.131605i
$96$	−1.52164			−0.155302
$97$	−2.10957	−	11.9640i	−0.214194	−	1.21476i	−0.882299	−	0.470689i	$-0.844005\pi$
$97$	−2.10957	−	11.9640i	−0.214194	−	1.21476i	0.668105	−	0.744067i	$-0.267106\pi$
$98$	−5.19681	+	4.36064i	−0.524957	+	0.440491i
$99$	−0.643322	+	0.234150i	−0.0646563	+	0.0235330i
$100$	−3.39957	−	1.23734i	−0.339957	−	0.123734i
$101$	6.82408	+	5.72608i	0.679021	+	0.569767i	0.915720	−	0.401817i	$-0.131621\pi$
$101$	6.82408	+	5.72608i	0.679021	+	0.569767i	−0.236699	+	0.971583i	$0.576065\pi$
$102$	0.143652	−	0.248813i	0.0142237	−	0.0246362i
$103$	−0.873352	−	1.51269i	−0.0860539	−	0.149050i	0.819786	−	0.572670i	$-0.194092\pi$
$103$	−0.873352	−	1.51269i	−0.0860539	−	0.149050i	−0.905840	+	0.423620i	$0.860759\pi$
$104$	0.781341	−	4.43120i	0.0766168	−	0.434515i
$105$	−0.360544	+	2.04475i	−0.0351855	+	0.199547i
$106$	0.679674	+	1.17723i	0.0660158	+	0.114343i
$107$	0.0331721	−	0.0574558i	0.00320687	−	0.00555446i	−0.864418	−	0.502775i	$-0.832313\pi$
$107$	0.0331721	−	0.0574558i	0.00320687	−	0.00555446i	0.867624	+	0.497220i	$0.165646\pi$
$108$	4.29494	+	3.60389i	0.413281	+	0.346784i
$109$	−3.58562	−	1.30506i	−0.343440	−	0.125002i	0.164541	−	0.986370i	$-0.447386\pi$
$109$	−3.58562	−	1.30506i	−0.343440	−	0.125002i	−0.507981	+	0.861368i	$0.669608\pi$
$110$	−2.75856	+	1.00403i	−0.263018	+	0.0957309i
$111$	7.55680	−	6.34091i	0.717260	−	0.601853i
$112$	−0.0807140	−	0.457752i	−0.00762676	−	0.0432535i
$113$	−0.0177717			−0.00167182			−0.000835908	−	1.00000i	$-0.500266\pi$
$113$	−0.0177717			−0.00167182			−0.000835908		1.00000i	$0.500266\pi$
$114$	5.97388	+	2.88187i	0.559505	+	0.269912i
$115$	−8.54437			−0.796766
$116$	0.299660	+	1.69946i	0.0278228	+	0.157791i
$117$	−2.35976	+	1.98007i	−0.218159	+	0.183058i
$118$	5.17449	−	1.88336i	0.476350	−	0.173377i
$119$	0.0824698	+	0.0300166i	0.00755999	+	0.00275161i
$120$	3.42187	+	2.87129i	0.312372	+	0.262111i
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	5.48315	+	9.49710i	0.496421	+	0.859827i
$123$	0.872301	−	4.94706i	0.0786527	−	0.446062i
$124$	−0.325423	+	1.84557i	−0.0292239	+	0.165737i
$125$	−2.02888	−	3.51412i	−0.181468	−	0.314312i
$126$	−0.159108	+	0.275583i	−0.0141745	+	0.0245509i
$127$	5.89110	+	4.94322i	0.522750	+	0.438640i	0.865589	−	0.500755i	$-0.166944\pi$
$127$	5.89110	+	4.94322i	0.522750	+	0.438640i	−0.342839	+	0.939394i	$0.611389\pi$
$128$	−0.939693	−	0.342020i	−0.0830579	−	0.0302306i
$129$	−15.3049	+	5.57051i	−1.34752	+	0.490456i
$130$	−10.1186	+	8.49052i	−0.887461	+	0.744668i
$131$	3.84086	+	21.7826i	0.335578	+	1.90316i	0.421454	+	0.906850i	$0.361520\pi$
$131$	3.84086	+	21.7826i	0.335578	+	1.90316i	−0.0858764	+	0.996306i	$0.527369\pi$
$132$	1.52164			0.132442
$133$	−0.550069	+	1.94998i	−0.0476970	+	0.169084i
$134$	5.56717			0.480930
$135$	−2.85806	−	16.2088i	−0.245982	−	1.39503i
$136$	0.144639	−	0.121366i	0.0124027	−	0.0104071i
$137$	−3.74905	+	1.36454i	−0.320303	+	0.116581i	−0.497168	−	0.867654i	$-0.665627\pi$
$137$	−3.74905	+	1.36454i	−0.320303	+	0.116581i	0.176865	+	0.984235i	$0.443405\pi$
$138$	4.16180	+	1.51477i	0.354276	+	0.128946i
$139$	1.13905	+	0.955779i	0.0966132	+	0.0810681i	0.689815	−	0.723986i	$-0.257692\pi$
$139$	1.13905	+	0.955779i	0.0966132	+	0.0810681i	−0.593202	+	0.805054i	$0.702136\pi$
$140$	−0.682253	+	1.18170i	−0.0576609	+	0.0998716i
$141$	−3.06569	−	5.30994i	−0.258178	−	0.447177i
$142$	0.691604	−	3.92228i	0.0580381	−	0.329150i
$143$	−0.781341	+	4.43120i	−0.0653390	+	0.370556i
$144$	0.342305	+	0.592889i	0.0285254	+	0.0494074i
$145$	2.53294	−	4.38719i	0.210350	−	0.364336i
$146$	8.35197	+	7.00813i	0.691214	+	0.579997i
$147$	−9.70020	−	3.53058i	−0.800059	−	0.291198i
$148$	6.09197	−	2.21730i	0.500757	−	0.182261i
$149$	6.20862	−	5.20965i	0.508630	−	0.426791i	−0.352017	−	0.935994i	$-0.614504\pi$
$149$	6.20862	−	5.20965i	0.508630	−	0.426791i	0.860647	+	0.509203i	$0.170060\pi$
$150$	−0.955917	−	5.42127i	−0.0780503	−	0.442645i
$151$	−16.0446			−1.30569			−0.652846	−	0.757490i	$-0.726425\pi$
$151$	−16.0446			−1.30569			−0.652846	+	0.757490i	$0.726425\pi$
$152$	3.04142	+	3.12246i	0.246692	+	0.253265i
$153$	−0.129263			−0.0104503
$154$	0.0807140	+	0.457752i	0.00650412	+	0.0368867i
$155$	4.21433	−	3.53625i	0.338503	−	0.284038i
$156$	6.43381	−	2.34171i	0.515117	−	0.187487i
$157$	−17.0547	−	6.20741i	−1.36111	−	0.495405i	−0.444716	−	0.895672i	$-0.646695\pi$
$157$	−17.0547	−	6.20741i	−1.36111	−	0.495405i	−0.916399	+	0.400266i	$0.868918\pi$
$158$	4.24799	+	3.56449i	0.337952	+	0.283575i
$159$	−1.03422	+	1.79132i	−0.0820190	+	0.142061i
$160$	1.46780	+	2.54230i	0.116040	+	0.200987i
$161$	−0.234927	+	1.33234i	−0.0185148	+	0.105003i
$162$	−1.12480	+	6.37907i	−0.0883729	+	0.501187i
$163$	−10.6935	−	18.5217i	−0.837579	−	1.45073i	−0.891913	−	0.452206i	$-0.850637\pi$
$163$	−10.6935	−	18.5217i	−0.837579	−	1.45073i	0.0543343	−	0.998523i	$-0.482696\pi$
$164$	1.65065	−	2.85900i	0.128894	−	0.223251i
$165$	−3.42187	−	2.87129i	−0.266392	−	0.223529i
$166$	12.0718	+	4.39376i	0.936951	+	0.341022i
$167$	−10.4015	+	3.78584i	−0.804892	+	0.292957i	−0.711512	−	0.702674i	$-0.751989\pi$
$167$	−10.4015	+	3.78584i	−0.804892	+	0.292957i	−0.0933800	+	0.995631i	$0.529767\pi$
$168$	0.541807	−	0.454630i	0.0418013	−	0.0350755i
$169$	1.25826	+	7.13597i	0.0967895	+	0.548921i
$170$	−0.554277			−0.0425111
$171$	−0.220982	−	2.97595i	−0.0168989	−	0.227577i
$172$	−10.7036			−0.816145
$173$	−1.51271	−	8.57900i	−0.115009	−	0.652249i	−0.986746	−	0.162274i	$-0.948117\pi$
$173$	−1.51271	−	8.57900i	−0.115009	−	0.652249i	0.871737	−	0.489975i	$-0.162994\pi$
$174$	−2.01152	+	1.68787i	−0.152493	+	0.127957i
$175$	1.58016	−	0.575133i	0.119449	−	0.0434760i
$176$	0.939693	+	0.342020i	0.0708320	+	0.0257807i
$177$	6.41871	+	5.38594i	0.482460	+	0.404832i
$178$	−8.47062	+	14.6715i	−0.634900	+	1.09968i
$179$	4.81361	+	8.33741i	0.359786	+	0.623167i	0.987925	−	0.154934i	$-0.0495164\pi$
$179$	4.81361	+	8.33741i	0.359786	+	0.623167i	−0.628139	+	0.778101i	$0.716183\pi$
$180$	0.348987	−	1.97921i	0.0260120	−	0.147521i
$181$	3.09282	−	17.5403i	0.229888	−	1.30376i	−0.623230	−	0.782038i	$-0.714180\pi$
$181$	3.09282	−	17.5403i	0.229888	−	1.30376i	0.853118	−	0.521719i	$-0.174709\pi$
$182$	1.04573	+	1.81126i	0.0775146	+	0.134259i
$183$	−8.34339	+	14.4512i	−0.616761	+	1.06826i
$184$	2.22965	+	1.87090i	0.164372	+	0.137925i
$185$	−17.8836	−	6.50909i	−1.31483	−	0.478558i
$186$	−2.67964	+	0.975308i	−0.196481	+	0.0715131i
$187$	−0.144639	+	0.121366i	−0.0105770	+	0.00887518i
$188$	−0.699708	−	3.96824i	−0.0510314	−	0.289414i
$189$	−2.60605			−0.189562
$190$	−0.947570	−	12.7608i	−0.0687440	−	0.925769i
$191$	25.2728			1.82868			0.914338	−	0.404952i	$-0.132712\pi$
$191$	25.2728			1.82868			0.914338	+	0.404952i	$0.132712\pi$
$192$	−0.264230	−	1.49852i	−0.0190692	−	0.108147i
$193$	12.8214	−	10.7584i	0.922901	−	0.774406i	−0.0516280	−	0.998666i	$-0.516441\pi$
$193$	12.8214	−	10.7584i	0.922901	−	0.774406i	0.974529	+	0.224260i	$0.0719966\pi$
$194$	11.4159	−	4.15504i	0.819613	−	0.298315i
$195$	−18.8871	−	6.87434i	−1.35253	−	0.492281i
$196$	−5.19681	−	4.36064i	−0.371200	−	0.311474i
$197$	−4.26264	+	7.38311i	−0.303700	+	0.526025i	−0.976971	−	0.213371i	$-0.931556\pi$
$197$	−4.26264	+	7.38311i	−0.303700	+	0.526025i	0.673271	+	0.739396i	$0.264889\pi$
$198$	−0.342305	−	0.592889i	−0.0243265	−	0.0421348i
$199$	3.77453	−	21.4064i	0.267569	−	1.51746i	−0.494048	−	0.869435i	$-0.664483\pi$
$199$	3.77453	−	21.4064i	0.267569	−	1.51746i	0.761618	−	0.648027i	$-0.224406\pi$
$200$	0.628214	−	3.56278i	0.0444215	−	0.251927i
$201$	4.23562	+	7.33630i	0.298757	+	0.517463i
$202$	−4.45410	+	7.71473i	−0.313390	+	0.542807i
$203$	−0.614457	−	0.515591i	−0.0431264	−	0.0361874i
$204$	0.269978	+	0.0982639i	0.0189022	+	0.00687985i
$205$	−9.10681	+	3.31461i	−0.636047	+	0.231502i
$206$	1.33805	−	1.12276i	0.0932266	−	0.0782264i
$207$	−0.346016	−	1.96235i	−0.0240498	−	0.136393i
$208$	4.49956			0.311988
$209$	−3.04142	−	3.12246i	−0.210380	−	0.215985i
$210$	−2.07629			−0.143278
$211$	1.53236	+	8.69042i	0.105492	+	0.598273i	0.991023	+	0.133693i	$0.0426836\pi$
$211$	1.53236	+	8.69042i	0.105492	+	0.598273i	−0.885531	+	0.464580i	$0.846205\pi$
$212$	−1.04132	+	0.873773i	−0.0715183	+	0.0600109i
$213$	5.69489	−	2.07277i	0.390207	−	0.142024i
$214$	0.0623432	+	0.0226911i	0.00426169	+	0.00155113i
$215$	24.0703	+	20.1974i	1.64158	+	1.37745i
$216$	−2.80333	+	4.85550i	−0.190742	+	0.330375i
$217$	−0.435539	−	0.754376i	−0.0295663	−	0.0512104i
$218$	0.662595	−	3.75776i	0.0448766	−	0.254508i
$219$	−2.88083	+	16.3380i	−0.194668	+	1.10402i
$220$	−1.46780	−	2.54230i	−0.0989590	−	0.171402i
$221$	−0.424786	+	0.735751i	−0.0285742	+	0.0494920i
$222$	7.55680	+	6.34091i	0.507179	+	0.425574i
$223$	−6.01902	−	2.19074i	−0.403063	−	0.146703i	0.132530	−	0.991179i	$-0.457690\pi$
$223$	−6.01902	−	2.19074i	−0.403063	−	0.146703i	−0.535593	+	0.844476i	$0.679912\pi$
$224$	0.436782	−	0.158976i	0.0291837	−	0.0106220i
$225$	−1.89729	+	1.59202i	−0.126486	+	0.106135i
$226$	−0.00308602	−	0.0175017i	−0.000205279	−	0.00116419i
$227$	−13.8824			−0.921409			−0.460705	−	0.887554i	$-0.652403\pi$
$227$	−13.8824			−0.921409			−0.460705	+	0.887554i	$0.652403\pi$
$228$	−1.80074	+	6.38355i	−0.119257	+	0.422761i
$229$	−6.38691			−0.422059			−0.211030	−	0.977480i	$-0.567682\pi$
$229$	−6.38691			−0.422059			−0.211030	+	0.977480i	$0.567682\pi$
$230$	−1.48371	−	8.41456i	−0.0978332	−	0.554840i
$231$	−0.541807	+	0.454630i	−0.0356483	+	0.0299125i
$232$	−1.62160	+	0.590215i	−0.106463	+	0.0387495i
$233$	4.88223	+	1.77699i	0.319845	+	0.116414i	0.496953	−	0.867777i	$-0.334452\pi$
$233$	4.88223	+	1.77699i	0.319845	+	0.116414i	−0.177108	+	0.984191i	$0.556674\pi$
$234$	−2.35976	−	1.98007i	−0.154262	−	0.129441i
$235$	−5.91444	+	10.2441i	−0.385815	+	0.668252i
$236$	2.75329	+	4.76883i	0.179224	+	0.310425i
$237$	−1.46525	+	8.30985i	−0.0951783	+	0.539783i
$238$	−0.0152398	+	0.0864292i	−0.000987850	+	0.00560237i
$239$	4.10422	+	7.10873i	0.265480	+	0.459825i	0.967689	−	0.252146i	$-0.0811362\pi$
$239$	4.10422	+	7.10873i	0.265480	+	0.459825i	−0.702209	+	0.711971i	$0.747803\pi$
$240$	−2.23346	+	3.86847i	−0.144169	+	0.249709i
$241$	−13.7105	−	11.5045i	−0.883170	−	0.741068i	0.0836583	−	0.996494i	$-0.473340\pi$
$241$	−13.7105	−	11.5045i	−0.883170	−	0.741068i	−0.966828	+	0.255427i	$0.917784\pi$
$242$	−0.939693	−	0.342020i	−0.0604057	−	0.0219859i
$243$	6.54360	−	2.38168i	0.419772	−	0.152785i
$244$	−8.40068	+	7.04900i	−0.537798	+	0.451266i
$245$	3.45820	+	19.6124i	0.220936	+	1.25299i
$246$	5.02338			0.320279
$247$	−17.6650	−	8.52183i	−1.12400	−	0.542231i
$248$	−1.87404			−0.119001
$249$	3.39443	+	19.2508i	0.215113	+	1.21997i
$250$	3.10842	−	2.60827i	0.196594	−	0.164962i
$251$	−11.2269	+	4.08624i	−0.708633	+	0.257921i	−0.671092	−	0.741374i	$-0.734175\pi$
$251$	−11.2269	+	4.08624i	−0.708633	+	0.257921i	−0.0375405	+	0.999295i	$0.511952\pi$
$252$	−0.299025	−	0.108836i	−0.0188368	−	0.00685604i
$253$	−2.22965	−	1.87090i	−0.140177	−	0.117622i
$254$	−3.84514	+	6.65998i	−0.241266	+	0.417884i
$255$	−0.421705	−	0.730415i	−0.0264082	−	0.0457404i
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	0.707351	−	4.01159i	0.0441233	−	0.250236i	−0.954766	−	0.297359i	$-0.903894\pi$
$257$	0.707351	−	4.01159i	0.0441233	−	0.250236i	0.998889	+	0.0471231i	$0.0150053\pi$
$258$	−8.14355	−	14.1050i	−0.506995	−	0.878141i
$259$	−1.50668	+	2.60964i	−0.0936205	+	0.162155i
$260$	−10.1186	−	8.49052i	−0.627530	−	0.526560i
$261$	1.11016	+	0.404067i	0.0687175	+	0.0250111i
$262$	−20.7847	+	7.56502i	−1.28408	+	0.467369i
$263$	5.53215	−	4.64203i	0.341127	−	0.286240i	−0.456088	−	0.889934i	$-0.650750\pi$
$263$	5.53215	−	4.64203i	0.341127	−	0.286240i	0.797215	+	0.603695i	$0.206305\pi$
$264$	0.264230	+	1.49852i	0.0162622	+	0.0922278i
$265$	3.99050			0.245135
$266$	−2.01587	−	0.203102i	−0.123601	−	0.0124530i
$267$	−25.7785			−1.57762
$268$	0.966729	+	5.48259i	0.0590524	+	0.334903i
$269$	−24.3865	+	20.4627i	−1.48687	+	1.24764i	−0.588430	+	0.808548i	$0.700254\pi$
$269$	−24.3865	+	20.4627i	−1.48687	+	1.24764i	−0.898444	+	0.439087i	$0.855302\pi$
$270$	15.4663	−	5.62927i	0.941248	−	0.342586i
$271$	29.3563	+	10.6848i	1.78327	+	0.649057i	0.999612	+	0.0278621i	$0.00886992\pi$
$271$	29.3563	+	10.6848i	1.78327	+	0.649057i	0.783656	+	0.621194i	$0.213352\pi$
$272$	0.144639	+	0.121366i	0.00877000	+	0.00735891i
$273$	−1.59122	+	2.75608i	−0.0963052	+	0.166806i
$274$	−1.99483	−	3.45515i	−0.120512	−	0.208733i
$275$	−0.628214	+	3.56278i	−0.0378828	+	0.214844i
$276$	−0.769069	+	4.36161i	−0.0462925	+	0.262538i
$277$	−6.17888	−	10.7021i	−0.371253	−	0.643029i	0.618505	−	0.785781i	$-0.287738\pi$
$277$	−6.17888	−	10.7021i	−0.371253	−	0.643029i	−0.989759	+	0.142751i	$0.954405\pi$
$278$	−0.743464	+	1.28772i	−0.0445900	+	0.0772322i
$279$	0.982822	+	0.824686i	0.0588400	+	0.0493726i
$280$	−1.28222	−	0.466689i	−0.0766271	−	0.0278900i
$281$	6.33213	−	2.30471i	0.377743	−	0.137487i	−0.146169	−	0.989260i	$-0.546694\pi$
$281$	6.33213	−	2.30471i	0.377743	−	0.137487i	0.523912	+	0.851772i	$0.324472\pi$
$282$	4.69691	−	3.94118i	0.279697	−	0.234694i
$283$	0.638882	+	3.62328i	0.0379776	+	0.215382i	0.997891	−	0.0649160i	$-0.0206780\pi$
$283$	0.638882	+	3.62328i	0.0379776	+	0.215382i	−0.959913	+	0.280298i	$0.909567\pi$
$284$	3.98279			0.236335
$285$	16.0951	−	10.9574i	0.953389	−	0.649060i
$286$	−4.49956			−0.266065
$287$	0.266461	+	1.51117i	0.0157287	+	0.0892017i
$288$	−0.524441	+	0.440058i	−0.0309030	+	0.0259307i
$289$	15.9413	−	5.80215i	0.937722	−	0.341303i
$290$	4.76038	+	1.73264i	0.279539	+	0.101744i
$291$	14.1609	+	11.8824i	0.830125	+	0.696557i
$292$	−5.45136	+	9.44203i	−0.319017	+	0.552553i
$293$	−1.39756	−	2.42065i	−0.0816464	−	0.141416i	0.822311	−	0.569039i	$-0.192684\pi$
$293$	−1.39756	−	2.42065i	−0.0816464	−	0.141416i	−0.903957	+	0.427623i	$0.859351\pi$
$294$	1.79252	−	10.1659i	0.104542	−	0.592888i
$295$	2.80704	−	15.9195i	0.163432	−	0.926870i
$296$	3.24147	+	5.61439i	0.188407	+	0.326330i
$297$	2.80333	−	4.85550i	0.162665	−	0.281745i
$298$	6.20862	+	5.20965i	0.359655	+	0.301787i
$299$	−12.3066	−	4.47925i	−0.711711	−	0.259042i
$300$	5.17292	−	1.88279i	0.298659	−	0.108703i
$301$	3.81122	−	3.19799i	0.219675	−	0.184329i
$302$	−2.78612	−	15.8009i	−0.160323	−	0.909238i
$303$	−13.5551			−0.778719
$304$	−2.54689	+	3.53743i	−0.146074	+	0.202885i
$305$	32.1927			1.84335
$306$	−0.0224462	−	0.127299i	−0.00128317	−	0.00727719i
$307$	9.06777	−	7.60876i	0.517525	−	0.434255i	−0.346243	−	0.938145i	$-0.612543\pi$
$307$	9.06777	−	7.60876i	0.517525	−	0.434255i	0.863768	+	0.503890i	$0.168098\pi$
$308$	−0.436782	+	0.158976i	−0.0248880	+	0.00905848i
$309$	2.49757	+	0.909041i	0.142082	+	0.0517135i
$310$	4.21433	+	3.53625i	0.239358	+	0.200845i
$311$	−7.99915	+	13.8549i	−0.453590	+	0.785641i	−0.998606	−	0.0527846i	$-0.983190\pi$
$311$	−7.99915	+	13.8549i	−0.453590	+	0.785641i	0.545016	+	0.838426i	$0.316524\pi$
$312$	3.42336	+	5.92943i	0.193809	+	0.335688i
$313$	−3.03079	+	17.1885i	−0.171311	+	0.971551i	0.771006	+	0.636828i	$0.219754\pi$
$313$	−3.03079	+	17.1885i	−0.171311	+	0.971551i	−0.942317	+	0.334723i	$0.891357\pi$
$314$	3.15158	−	17.8735i	0.177854	−	1.00866i
$315$	0.467077	+	0.809001i	0.0263168	+	0.0455820i
$316$	−2.77268	+	4.80242i	−0.155975	+	0.270157i
$317$	−17.4289	−	14.6246i	−0.978906	−	0.821400i	0.00501780	−	0.999987i	$-0.498403\pi$
$317$	−17.4289	−	14.6246i	−0.978906	−	0.821400i	−0.983924	+	0.178588i	$0.942847\pi$
$318$	−1.94370	−	0.707448i	−0.108997	−	0.0396717i
$319$	1.62160	−	0.590215i	0.0907924	−	0.0330457i
$320$	−2.24880	+	1.88697i	−0.125712	+	0.105485i
$321$	0.0175302	+	0.0994184i	0.000978438	+	0.00554900i
$322$	−1.35289			−0.0753935
$323$	−0.337985	−	0.750412i	−0.0188060	−	0.0417540i
$324$	−6.47748			−0.359860
$325$	2.82669	+	16.0310i	0.156797	+	0.889237i
$326$	16.3834	−	13.7473i	0.907392	−	0.761392i
$327$	5.45602	−	1.98583i	0.301719	−	0.109817i
$328$	3.10220	+	1.12911i	0.171290	+	0.0623446i
$329$	1.43476	+	1.20391i	0.0791009	+	0.0663735i
$330$	2.23346	−	3.86847i	0.122948	−	0.212952i
$331$	4.97263	+	8.61285i	0.273320	+	0.473405i	0.969710	−	0.244259i	$-0.0785447\pi$
$331$	4.97263	+	8.61285i	0.273320	+	0.473405i	−0.696390	+	0.717664i	$0.745211\pi$
$332$	−2.23077	+	12.6513i	−0.122430	+	0.694332i
$333$	0.770699	−	4.37085i	0.0422341	−	0.239521i
$334$	−5.53452	−	9.58607i	−0.302836	−	0.524527i
$335$	8.17149	−	14.1534i	0.446456	−	0.773285i
$336$	0.541807	+	0.454630i	0.0295580	+	0.0248021i
$337$	25.4346	+	9.25744i	1.38551	+	0.504285i	0.923845	−	0.382768i	$-0.125029\pi$
$337$	25.4346	+	9.25744i	1.38551	+	0.504285i	0.461667	+	0.887053i	$0.347251\pi$
$338$	−6.80906	+	2.47830i	−0.370364	+	0.134802i
$339$	0.0207154	−	0.0173823i	0.00112511	−	0.000944078i
$340$	−0.0962492	−	0.545857i	−0.00521985	−	0.0296032i
$341$	1.87404			0.101485
$342$	2.89237	−	0.734393i	0.156401	−	0.0397114i
$343$	6.40697			0.345944
$344$	−1.85867	−	10.5410i	−0.100213	−	0.568334i
$345$	9.95970	−	8.35718i	0.536212	−	0.449935i
$346$	8.18599	−	2.97946i	0.440081	−	0.160177i
$347$	−18.2689	−	6.64935i	−0.980728	−	0.356956i	−0.198605	−	0.980080i	$-0.563641\pi$
$347$	−18.2689	−	6.64935i	−0.980728	−	0.356956i	−0.782123	+	0.623124i	$0.785863\pi$
$348$	−2.01152	−	1.68787i	−0.107829	−	0.0904792i
$349$	−11.3028	+	19.5770i	−0.605025	+	1.04793i	0.387023	+	0.922070i	$0.373504\pi$
$349$	−11.3028	+	19.5770i	−0.605025	+	1.04793i	−0.992048	+	0.125864i	$0.959830\pi$
$350$	0.840788	+	1.45629i	0.0449420	+	0.0778419i
$351$	4.38070	−	24.8442i	0.233825	−	1.32609i
$352$	−0.173648	+	0.984808i	−0.00925548	+	0.0524904i
$353$	−12.0481	−	20.8679i	−0.641254	−	1.11068i	−0.985153	−	0.171678i	$-0.945081\pi$
$353$	−12.0481	−	20.8679i	−0.641254	−	1.11068i	0.343899	−	0.939007i	$-0.388252\pi$
$354$	−4.18951	+	7.25645i	−0.222670	+	0.385676i
$355$	−8.95649	−	7.51539i	−0.475361	−	0.398875i
$356$	−15.9196	−	5.79425i	−0.843735	−	0.307094i
$357$	−0.125489	+	0.0456744i	−0.00664160	+	0.00241735i
$358$	−7.37487	+	6.18825i	−0.389774	+	0.327059i
$359$	4.44864	+	25.2295i	0.234790	+	1.33156i	0.843055	+	0.537828i	$0.180755\pi$
$359$	4.44864	+	25.2295i	0.234790	+	1.33156i	−0.608264	+	0.793735i	$0.708134\pi$
$360$	2.00974			0.105923
$361$	16.6985	−	9.06413i	0.878871	−	0.477059i
$362$	17.8108			0.936117
$363$	−0.264230	−	1.49852i	−0.0138685	−	0.0786521i
$364$	−1.60215	+	1.34436i	−0.0839754	+	0.0704638i
$365$	30.0758	−	10.9467i	1.57424	−	0.572976i
$366$	−15.6804	−	5.70721i	−0.819630	−	0.298321i
$367$	−0.781166	−	0.655476i	−0.0407765	−	0.0342156i	0.622172	−	0.782881i	$-0.286251\pi$
$367$	−0.781166	−	0.655476i	−0.0407765	−	0.0342156i	−0.662948	+	0.748665i	$0.730695\pi$
$368$	−1.45530	+	2.52066i	−0.0758629	+	0.131398i
$369$	−1.13005	−	1.95730i	−0.0588279	−	0.101893i
$370$	3.30475	−	18.7422i	0.171806	−	0.974360i
$371$	0.109719	−	0.622245i	0.00569630	−	0.0323053i
$372$	−1.42581	−	2.46957i	−0.0739246	−	0.128041i
$373$	15.8682	−	27.4845i	0.821623	−	1.42309i	−0.0828501	−	0.996562i	$-0.526402\pi$
$373$	15.8682	−	27.4845i	0.821623	−	1.42309i	0.904473	−	0.426531i	$-0.140264\pi$
$374$	−0.144639	−	0.121366i	−0.00747908	−	0.00627570i
$375$	5.80208	+	2.11178i	0.299618	+	0.109052i
$376$	3.78645	−	1.37816i	0.195271	−	0.0710729i
$377$	5.94817	−	4.99110i	0.306346	−	0.257055i
$378$	−0.452535	−	2.56646i	−0.0232759	−	0.132004i
$379$	−19.0665			−0.979382			−0.489691	−	0.871896i	$-0.662890\pi$
$379$	−19.0665			−0.979382			−0.489691	+	0.871896i	$0.662890\pi$
$380$	12.4024	−	3.14907i	0.636232	−	0.161544i
$381$	−11.7018			−0.599504
$382$	4.38858	+	24.8889i	0.224539	+	1.27342i
$383$	−13.8994	+	11.6630i	−0.710228	+	0.595952i	−0.924663	−	0.380786i	$-0.875653\pi$
$383$	−13.8994	+	11.6630i	−0.710228	+	0.595952i	0.214435	+	0.976738i	$0.431209\pi$
$384$	1.42987	−	0.520432i	0.0729680	−	0.0265582i
$385$	1.28222	+	0.466689i	0.0653478	+	0.0237847i
$386$	12.8214	+	10.7584i	0.652590	+	0.547588i
$387$	−3.66391	+	6.34607i	−0.186247	+	0.322589i
$388$	6.07426	+	10.5209i	0.308374	+	0.534120i
$389$	0.674298	−	3.82413i	0.0341882	−	0.193891i	−0.962930	−	0.269750i	$-0.913059\pi$
$389$	0.674298	−	3.82413i	0.0341882	−	0.193891i	0.997119	+	0.0758592i	$0.0241699\pi$
$390$	3.49019	−	19.7939i	0.176733	−	1.00230i
$391$	−0.274779	−	0.475931i	−0.0138962	−	0.0240689i
$392$	3.39197	−	5.87507i	0.171321	−	0.296736i
$393$	−25.7825	−	21.6341i	−1.30055	−	1.09129i
$394$	−8.01114	−	2.91582i	−0.403595	−	0.146897i
$395$	15.2972	−	5.56773i	0.769686	−	0.280143i
$396$	0.524441	−	0.440058i	0.0263542	−	0.0221138i
$397$	3.10116	+	17.5876i	0.155643	+	0.882694i	0.958196	+	0.286113i	$0.0923633\pi$
$397$	3.10116	+	17.5876i	0.155643	+	0.882694i	−0.802553	+	0.596581i	$0.796526\pi$
$398$	21.7367			1.08956
$399$	−1.26607	−	2.81100i	−0.0633828	−	0.140726i
$400$	3.61774			0.180887
$401$	5.81792	+	32.9951i	0.290533	+	1.64770i	0.684823	+	0.728709i	$0.259880\pi$
$401$	5.81792	+	32.9951i	0.290533	+	1.64770i	−0.394290	+	0.918986i	$0.629009\pi$
$402$	−6.48934	+	5.44520i	−0.323659	+	0.271582i
$403$	7.92381	−	2.88403i	0.394713	−	0.143664i
$404$	−8.37097	−	3.04679i	−0.416471	−	0.151583i
$405$	14.5666	+	12.2228i	0.723818	+	0.607356i
$406$	0.401058	−	0.694654i	0.0199042	−	0.0344751i
$407$	−3.24147	−	5.61439i	−0.160674	−	0.278295i
$408$	−0.0498899	+	0.282940i	−0.00246992	+	0.0140076i
$409$	4.57191	−	25.9286i	0.226066	−	1.28209i	−0.634570	−	0.772865i	$-0.718823\pi$
$409$	4.57191	−	25.9286i	0.226066	−	1.28209i	0.860636	−	0.509220i	$-0.170066\pi$
$410$	−4.84563	−	8.39289i	−0.239309	−	0.414495i
$411$	3.03542	−	5.25749i	0.149726	−	0.259333i
$412$	1.33805	+	1.12276i	0.0659211	+	0.0553144i
$413$	−2.40517	−	0.875411i	−0.118351	−	0.0430762i
$414$	1.87246	−	0.681519i	0.0920262	−	0.0334948i
$415$	28.8892	−	24.2409i	1.41812	−	1.18994i
$416$	0.781341	+	4.43120i	0.0383084	+	0.217258i
$417$	−2.26257			−0.110799
$418$	2.54689	−	3.53743i	0.124572	−	0.173021i
$419$	−32.1866			−1.57242			−0.786209	−	0.617961i	$-0.787959\pi$
$419$	−32.1866			−1.57242			−0.786209	+	0.617961i	$0.787959\pi$
$420$	−0.360544	−	2.04475i	−0.0175927	−	0.0997733i
$421$	15.3365	−	12.8688i	0.747455	−	0.627189i	−0.187373	−	0.982289i	$-0.559997\pi$
$421$	15.3365	−	12.8688i	0.747455	−	0.627189i	0.934829	+	0.355099i	$0.115553\pi$
$422$	−8.29230	+	3.01815i	−0.403663	+	0.146921i
$423$	−2.59224	−	0.943498i	−0.126039	−	0.0458745i
$424$	−1.04132	−	0.873773i	−0.0505710	−	0.0424341i
$425$	−0.341537	+	0.591560i	−0.0165670	+	0.0286949i
$426$	3.03019	+	5.24844i	0.146813	+	0.254288i
$427$	0.885135	−	5.01985i	0.0428347	−	0.242927i
$428$	−0.0115206	+	0.0653363i	−0.000556867	+	0.00315815i
$429$	−3.42336	−	5.92943i	−0.165281	−	0.286276i
$430$	−15.7108	+	27.2119i	−0.757642	+	1.31227i
$431$	22.4001	+	18.7959i	1.07898	+	0.905369i	0.995835	−	0.0911689i	$-0.0290603\pi$
$431$	22.4001	+	18.7959i	1.07898	+	0.905369i	0.0831411	+	0.996538i	$0.473505\pi$
$432$	−5.26853	−	1.91759i	−0.253482	−	0.0922600i
$433$	−20.5516	+	7.48017i	−0.987647	+	0.359474i	−0.784809	−	0.619738i	$-0.787239\pi$
$433$	−20.5516	+	7.48017i	−0.987647	+	0.359474i	−0.202839	+	0.979212i	$0.565017\pi$
$434$	0.667284	−	0.559918i	0.0320307	−	0.0268769i
$435$	1.33856	+	7.59135i	0.0641791	+	0.363978i
$436$	3.81573			0.182741
$437$	10.4874	−	7.13973i	0.501679	−	0.341540i
$438$	−16.5900			−0.792702
$439$	4.48455	+	25.4331i	0.214036	+	1.21386i	0.882572	+	0.470177i	$0.155810\pi$
$439$	4.48455	+	25.4331i	0.214036	+	1.21386i	−0.668536	+	0.743680i	$0.733079\pi$
$440$	2.24880	−	1.88697i	0.107207	−	0.0899576i
$441$	−4.36427	+	1.58846i	−0.207822	+	0.0756411i
$442$	−0.798337	−	0.290571i	−0.0379730	−	0.0138210i
$443$	5.48127	+	4.59934i	0.260423	+	0.218521i	0.763645	−	0.645636i	$-0.223408\pi$
$443$	5.48127	+	4.59934i	0.260423	+	0.218521i	−0.503222	+	0.864157i	$0.667852\pi$
$444$	−4.93235	+	8.54308i	−0.234079	+	0.405437i
$445$	24.8664	+	43.0698i	1.17878	+	2.04170i
$446$	1.11227	−	6.30799i	0.0526675	−	0.298692i
$447$	−2.14153	+	12.1452i	−0.101291	+	0.574448i
$448$	0.232407	+	0.402540i	0.0109802	+	0.0190182i
$449$	−7.01591	+	12.1519i	−0.331101	+	0.573484i	−0.982728	−	0.185056i	$-0.940754\pi$
$449$	−7.01591	+	12.1519i	−0.331101	+	0.573484i	0.651627	+	0.758540i	$0.274087\pi$
$450$	−1.89729	−	1.59202i	−0.0894393	−	0.0750485i
$451$	−3.10220	−	1.12911i	−0.146077	−	0.0531676i
$452$	0.0166999	−	0.00607826i	0.000785497	−	0.000285898i
$453$	18.7023	−	15.6931i	0.878712	−	0.737327i
$454$	−2.41066	−	13.6715i	−0.113138	−	0.641636i
$455$	6.13968			0.287833
$456$	−6.59927	−	0.664888i	−0.309039	−	0.0311362i
$457$	−31.3113			−1.46468			−0.732340	−	0.680940i	$-0.761572\pi$
$457$	−31.3113			−1.46468			−0.732340	+	0.680940i	$0.761572\pi$
$458$	−1.10908	−	6.28988i	−0.0518237	−	0.293907i
$459$	0.810938	−	0.680458i	0.0378514	−	0.0317611i
$460$	8.02908	−	2.92235i	0.374358	−	0.136255i
$461$	−11.4923	−	4.18287i	−0.535252	−	0.194816i	0.0602299	−	0.998185i	$-0.480817\pi$
$461$	−11.4923	−	4.18287i	−0.535252	−	0.194816i	−0.595482	+	0.803369i	$0.703039\pi$
$462$	−0.541807	−	0.454630i	−0.0252072	−	0.0211513i
$463$	11.6386	−	20.1587i	0.540892	−	0.936852i	−0.457961	−	0.888972i	$-0.651420\pi$
$463$	11.6386	−	20.1587i	0.540892	−	0.936852i	0.998853	−	0.0478802i	$-0.0152466\pi$
$464$	−0.862837	−	1.49448i	−0.0400562	−	0.0693794i
$465$	−1.45364	+	8.24401i	−0.0674110	+	0.382307i
$466$	−0.902200	+	5.11663i	−0.0417936	+	0.237023i
$467$	−8.64566	−	14.9747i	−0.400073	−	0.692947i	0.593661	−	0.804715i	$-0.297682\pi$
$467$	−8.64566	−	14.9747i	−0.400073	−	0.692947i	−0.993734	+	0.111768i	$0.964349\pi$
$468$	1.54022	−	2.66774i	0.0711967	−	0.123316i
$469$	−1.98229	−	1.66334i	−0.0915337	−	0.0768059i
$470$	−11.1155	−	4.04571i	−0.512720	−	0.186615i
$471$	25.9512	−	9.44545i	1.19577	−	0.435223i
$472$	−4.21828	+	3.53956i	−0.194162	+	0.162921i
$473$	1.85867	+	10.5410i	0.0854616	+	0.484677i
$474$	−8.43804			−0.387572
$475$	−14.2031	−	6.85173i	−0.651681	−	0.314379i
$476$	−0.0877625			−0.00402259
$477$	0.161601	+	0.916485i	0.00739920	+	0.0419630i
$478$	−6.28804	+	5.27629i	−0.287608	+	0.241332i
$479$	12.4751	−	4.54057i	0.570002	−	0.207464i	−0.0409091	−	0.999163i	$-0.513025\pi$
$479$	12.4751	−	4.54057i	0.570002	−	0.207464i	0.610911	+	0.791699i	$0.290803\pi$
$480$	−4.19754	−	1.52778i	−0.191591	−	0.0697333i
$481$	−22.3458	−	18.7504i	−1.01888	−	0.854943i
$482$	8.94888	−	15.4999i	0.407611	−	0.706002i
$483$	−1.02931	−	1.78281i	−0.0468350	−	0.0811206i
$484$	0.173648	−	0.984808i	0.00789310	−	0.0447640i
$485$	6.19285	−	35.1214i	0.281203	−	1.59478i
$486$	3.48178	+	6.03062i	0.157937	+	0.273554i
$487$	13.6041	−	23.5629i	0.616459	−	1.06774i	−0.373667	−	0.927563i	$-0.621900\pi$
$487$	13.6041	−	23.5629i	0.616459	−	1.06774i	0.990127	−	0.140176i	$-0.0447668\pi$
$488$	−8.40068	−	7.04900i	−0.380281	−	0.319093i
$489$	30.5807	+	11.1305i	1.38291	+	0.503337i
$490$	−18.7139	+	6.81132i	−0.845409	+	0.307704i
$491$	27.2048	−	22.8276i	1.22774	−	1.03019i	0.229354	−	0.973343i	$-0.426339\pi$
$491$	27.2048	−	22.8276i	1.22774	−	1.03019i	0.998383	−	0.0568508i	$-0.0181059\pi$
$492$	0.872301	+	4.94706i	0.0393264	+	0.223031i
$493$	0.325829			0.0146746
$494$	5.32486	−	18.8765i	0.239577	−	0.849292i
$495$	−2.00974			−0.0903310
$496$	−0.325423	−	1.84557i	−0.0146119	−	0.0828684i
$497$	−1.41814	+	1.18996i	−0.0636124	+	0.0533771i
$498$	−18.3689	+	6.68573i	−0.823130	+	0.299595i
$499$	8.77449	+	3.19365i	0.392800	+	0.142968i	0.530867	−	0.847455i	$-0.321867\pi$
$499$	8.77449	+	3.19365i	0.392800	+	0.142968i	−0.138066	+	0.990423i	$0.544089\pi$
$500$	3.10842	+	2.60827i	0.139013	+	0.116646i
$501$	8.42155	−	14.5866i	0.376247	−	0.651679i
$502$	−5.97368	−	10.3467i	−0.266619	−	0.461797i
$503$	2.47219	−	14.0205i	0.110230	−	0.625143i	−0.878772	−	0.477241i	$-0.841637\pi$
$503$	2.47219	−	14.0205i	0.110230	−	0.625143i	0.989002	−	0.147902i	$-0.0472520\pi$
$504$	0.0552576	−	0.313381i	0.00246137	−	0.0139591i
$505$	13.0755	+	22.6474i	0.581850	+	1.00779i
$506$	1.45530	−	2.52066i	0.0646961	−	0.112057i
$507$	−8.44632	−	7.08730i	−0.375114	−	0.314758i
$508$	−7.22650	−	2.63023i	−0.320624	−	0.116698i
$509$	−19.3301	+	7.03558i	−0.856791	+	0.311846i	−0.732806	−	0.680438i	$-0.761790\pi$
$509$	−19.3301	+	7.03558i	−0.856791	+	0.311846i	−0.123985	+	0.992284i	$0.539567\pi$
$510$	0.646090	−	0.542134i	0.0286094	−	0.0240061i
$511$	−0.880002	−	4.99074i	−0.0389290	−	0.220777i
$512$	1.00000			0.0441942
$513$	17.0522	+	17.5065i	0.752873	+	0.772933i
$514$	4.07347			0.179673
$515$	−0.890403	−	5.04972i	−0.0392358	−	0.222517i
$516$	12.4766	−	10.4691i	0.549253	−	0.460878i
$517$	−3.78645	+	1.37816i	−0.166528	+	0.0606112i
$518$	−2.83163	−	1.03063i	−0.124415	−	0.0452832i
$519$	10.1543	+	8.52050i	0.445726	+	0.374008i
$520$	6.60445	−	11.4393i	0.289624	−	0.501644i
$521$	−18.0348	−	31.2371i	−0.790118	−	1.36852i	−0.925894	−	0.377784i	$-0.876686\pi$
$521$	−18.0348	−	31.2371i	−0.790118	−	1.36852i	0.135776	−	0.990740i	$-0.456647\pi$
$522$	−0.205150	+	1.16346i	−0.00897918	+	0.0509235i
$523$	−4.93650	+	27.9963i	−0.215858	+	1.22419i	0.663553	+	0.748129i	$0.269048\pi$
$523$	−4.93650	+	27.9963i	−0.215858	+	1.22419i	−0.879411	+	0.476063i	$0.842063\pi$
$524$	−11.0593	−	19.1553i	−0.483129	−	0.836803i
$525$	−1.27938	+	2.21595i	−0.0558366	+	0.0967118i
$526$	5.53215	+	4.64203i	0.241213	+	0.202402i
$527$	0.332502	+	0.121021i	0.0144840	+	0.00527175i
$528$	−1.42987	+	0.520432i	−0.0622273	+	0.0226489i
$529$	−11.1294	+	9.33866i	−0.483886	+	0.406029i
$530$	0.692944	+	3.92988i	0.0300995	+	0.170703i
$531$	3.76985			0.163598
$532$	−0.150035	−	2.02051i	−0.00650485	−	0.0876003i
$533$	−14.8544			−0.643414
$534$	−4.47639	−	25.3869i	−0.193712	−	1.09860i
$535$	0.149195	−	0.125189i	0.00645026	−	0.00541241i
$536$	−5.23143	+	1.90408i	−0.225963	+	0.0822439i
$537$	−13.7657	−	5.01031i	−0.594034	−	0.216211i
$538$	−24.3865	−	20.4627i	−1.05138	−	0.882212i
$539$	−3.39197	+	5.87507i	−0.146103	+	0.253057i
$540$	8.22944	+	14.2538i	0.354139	+	0.613386i
$541$	−2.35945	+	13.3811i	−0.101441	+	0.575298i	0.891142	+	0.453725i	$0.149905\pi$
$541$	−2.35945	+	13.3811i	−0.101441	+	0.575298i	−0.992582	+	0.121573i	$0.961206\pi$
$542$	−5.42482	+	30.7657i	−0.233016	+	1.32150i
$543$	13.5509	+	23.4708i	0.581523	+	1.00723i
$544$	−0.0944062	+	0.163516i	−0.00404763	+	0.00701070i
$545$	−8.58082	−	7.20016i	−0.367562	−	0.308421i
$546$	−2.99052	−	1.08846i	−0.127983	−	0.0465818i
$547$	−20.0995	+	7.31560i	−0.859391	+	0.312793i	−0.733863	−	0.679298i	$-0.762285\pi$
$547$	−20.0995	+	7.31560i	−0.859391	+	0.312793i	−0.125528	+	0.992090i	$0.540062\pi$
$548$	3.05626	−	2.56450i	0.130557	−	0.109550i
$549$	1.30369	+	7.39358i	0.0556400	+	0.315550i
$550$	−3.61774			−0.154261
$551$	0.557023	+	7.50139i	0.0237300	+	0.319570i
$552$	−4.42889			−0.188506
$553$	−0.447588	−	2.53840i	−0.0190334	−	0.107944i
$554$	9.46660	−	7.94342i	0.402197	−	0.337484i
$555$	27.2124	−	9.90450i	1.15510	−	0.420423i
$556$	−1.39726	−	0.508559i	−0.0592568	−	0.0215677i
$557$	−16.3886	−	13.7517i	−0.694407	−	0.582677i	0.225769	−	0.974181i	$-0.427511\pi$
$557$	−16.3886	−	13.7517i	−0.694407	−	0.582677i	−0.920176	+	0.391504i	$0.871955\pi$
$558$	−0.641492	+	1.11110i	−0.0271565	+	0.0470365i
$559$	24.0808	+	41.7092i	1.01851	+	1.76411i
$560$	0.236944	−	1.34378i	0.0100127	−	0.0567849i
$561$	0.0498899	−	0.282940i	0.00210635	−	0.0119457i
$562$	3.36926	+	5.83572i	0.142123	+	0.246165i
$563$	−10.0526	+	17.4117i	−0.423669	+	0.733816i	−0.996295	−	0.0860009i	$-0.972591\pi$
$563$	−10.0526	+	17.4117i	−0.423669	+	0.733816i	0.572626	+	0.819816i	$0.305925\pi$
$564$	4.69691	+	3.94118i	0.197776	+	0.165954i
$565$	−0.0490242	−	0.0178433i	−0.00206246	−	0.000750675i
$566$	−3.45729	+	1.25835i	−0.145321	+	0.0528925i
$567$	2.30642	−	1.93532i	0.0968607	−	0.0812758i
$568$	0.691604	+	3.92228i	0.0290191	+	0.164575i
$569$	−12.2391			−0.513089			−0.256544	−	0.966532i	$-0.582584\pi$
$569$	−12.2391			−0.513089			−0.256544	+	0.966532i	$0.582584\pi$
$570$	13.5858	+	13.9478i	0.569047	+	0.584209i
$571$	−8.38225			−0.350786			−0.175393	−	0.984498i	$-0.556120\pi$
$571$	−8.38225			−0.350786			−0.175393	+	0.984498i	$0.556120\pi$
$572$	−0.781341	−	4.43120i	−0.0326695	−	0.185278i
$573$	−29.4591	+	24.7191i	−1.23067	+	1.03266i
$574$	−1.44194	+	0.524825i	−0.0601856	+	0.0219058i
$575$	−9.89479	−	3.60141i	−0.412641	−	0.150189i
$576$	−0.524441	−	0.440058i	−0.0218517	−	0.0183358i
$577$	−10.1570	+	17.5924i	−0.422841	+	0.732383i	−0.996216	−	0.0869106i	$-0.972301\pi$
$577$	−10.1570	+	17.5924i	−0.422841	+	0.732383i	0.573375	+	0.819293i	$0.305634\pi$
$578$	8.48217	+	14.6916i	0.352812	+	0.611088i
$579$	−4.42244	+	25.0809i	−0.183790	+	1.04233i
$580$	−0.879682	+	4.98893i	−0.0365268	+	0.207154i
$581$	−2.98561	−	5.17124i	−0.123864	−	0.214539i
$582$	−9.24285	+	16.0091i	−0.383128	+	0.663598i
$583$	1.04132	+	0.873773i	0.0431271	+	0.0361880i
$584$	−10.2452	−	3.72895i	−0.423949	−	0.154305i
$585$	−8.49759	+	3.09287i	−0.351332	+	0.127874i
$586$	2.14119	−	1.79667i	0.0884516	−	0.0742197i
$587$	−1.06498	−	6.03982i	−0.0439565	−	0.249290i	0.954910	−	0.296897i	$-0.0959517\pi$
$587$	−1.06498	−	6.03982i	−0.0439565	−	0.249290i	−0.998866	+	0.0476067i	$0.984841\pi$
$588$	10.3227			0.425702
$589$	−2.21777	+	7.86192i	−0.0913816	+	0.323945i
$590$	16.1651			0.665507
$591$	−2.25264	−	12.7753i	−0.0926610	−	0.525507i
$592$	−4.96622	+	4.16715i	−0.204110	+	0.171269i
$593$	−41.2253	+	15.0048i	−1.69292	+	0.616173i	−0.994988	−	0.0999897i	$-0.968119\pi$
$593$	−41.2253	+	15.0048i	−1.69292	+	0.616173i	−0.697933	+	0.716163i	$0.745897\pi$
$594$	5.26853	+	1.91759i	0.216170	+	0.0786796i
$595$	0.197360	+	0.165605i	0.00809098	+	0.00678914i
$596$	−4.05239	+	7.01894i	−0.165992	+	0.287507i
$597$	16.5377	+	28.6441i	0.676843	+	1.17233i
$598$	2.27417	−	12.8975i	0.0929979	−	0.527417i
$599$	6.37423	−	36.1501i	0.260444	−	1.47705i	−0.521258	−	0.853399i	$-0.674537\pi$
$599$	6.37423	−	36.1501i	0.260444	−	1.47705i	0.781702	−	0.623652i	$-0.214352\pi$
$600$	2.75245	+	4.76739i	0.112368	+	0.194628i
$601$	−12.5362	+	21.7133i	−0.511361	+	0.885702i	0.488553	+	0.872534i	$0.337525\pi$
$601$	−12.5362	+	21.7133i	−0.511361	+	0.885702i	−0.999913	+	0.0131680i	$0.995808\pi$
$602$	3.81122	+	3.19799i	0.155334	+	0.130341i
$603$	3.58148	+	1.30355i	0.145849	+	0.0530848i
$604$	15.0770	−	5.48758i	0.613475	−	0.223287i
$605$	−2.24880	+	1.88697i	−0.0914267	+	0.0767161i
$606$	−2.35382	−	13.3492i	−0.0956172	−	0.542272i
$607$	11.3520			0.460765			0.230382	−	0.973100i	$-0.426002\pi$
$607$	11.3520			0.460765			0.230382	+	0.973100i	$0.426002\pi$
$608$	−3.92595	−	1.89392i	−0.159218	−	0.0768088i
$609$	1.22053			0.0494585
$610$	5.59020	+	31.7036i	0.226341	+	1.28364i
$611$	−13.8890	+	11.6542i	−0.561888	+	0.471480i
$612$	0.121467	−	0.0442104i	0.00491002	−	0.00178710i
$613$	18.2944	+	6.65862i	0.738904	+	0.268939i	0.683929	−	0.729549i	$-0.260270\pi$
$613$	18.2944	+	6.65862i	0.738904	+	0.268939i	0.0549749	+	0.998488i	$0.482492\pi$
$614$	9.06777	+	7.60876i	0.365945	+	0.307065i
$615$	7.37332	−	12.7710i	0.297321	−	0.514975i
$616$	−0.232407	−	0.402540i	−0.00936394	−	0.0162188i
$617$	−4.39145	+	24.9051i	−0.176793	+	1.00264i	0.759261	+	0.650786i	$0.225561\pi$
$617$	−4.39145	+	24.9051i	−0.176793	+	1.00264i	−0.936054	+	0.351856i	$0.885551\pi$
$618$	−0.461532	+	2.61748i	−0.0185655	+	0.105290i
$619$	−5.56045	−	9.63098i	−0.223493	−	0.387102i	0.732373	−	0.680904i	$-0.238413\pi$
$619$	−5.56045	−	9.63098i	−0.223493	−	0.387102i	−0.955866	+	0.293802i	$0.905079\pi$
$620$	−2.75071	+	4.76437i	−0.110471	+	0.191342i
$621$	12.5009	+	10.4895i	0.501643	+	0.420929i
$622$	−15.0335	−	5.47174i	−0.602788	−	0.219397i
$623$	7.39963	−	2.69324i	0.296460	−	0.107903i
$624$	−5.24489	+	4.40098i	−0.209964	+	0.176180i
$625$	−5.20956	−	29.5449i	−0.208382	−	1.18179i
$626$	−17.4536			−0.697588
$627$	6.59927	+	0.664888i	0.263549	+	0.0265531i
$628$	18.1493			0.724234
$629$	−0.212556	−	1.20546i	−0.00847514	−	0.0480649i
$630$	−0.715603	+	0.600463i	−0.0285103	+	0.0239230i
$631$	−30.3547	+	11.0482i	−1.20840	+	0.439823i	−0.866150	−	0.499785i	$-0.833412\pi$
$631$	−30.3547	+	11.0482i	−1.20840	+	0.439823i	−0.342254	+	0.939608i	$0.611190\pi$
$632$	−5.21093	−	1.89662i	−0.207280	−	0.0754437i
$633$	−10.2862	−	8.63116i	−0.408840	−	0.343058i
$634$	11.3759	−	19.7037i	0.451796	−	0.782533i
$635$	11.2878	+	19.5510i	0.447942	+	0.775859i
$636$	0.359181	−	2.03702i	0.0142425	−	0.0807730i
$637$	−5.30057	+	30.0611i	−0.210016	+	1.19106i
$638$	0.862837	+	1.49448i	0.0341601	+	0.0591669i
$639$	1.36333	−	2.36135i	0.0539324	−	0.0934136i
$640$	−2.24880	−	1.88697i	−0.0888916	−	0.0745889i
$641$	36.2615	+	13.1981i	1.43224	+	0.521294i	0.937573	−	0.347788i	$-0.113067\pi$
$641$	36.2615	+	13.1981i	1.43224	+	0.521294i	0.494669	+	0.869081i	$0.335289\pi$
$642$	−0.0948640	+	0.0345277i	−0.00374398	+	0.00136270i
$643$	−31.9021	+	26.7690i	−1.25810	+	1.05567i	−0.262213	+	0.965010i	$0.584452\pi$
$643$	−31.9021	+	26.7690i	−1.25810	+	1.05567i	−0.995882	+	0.0906571i	$0.971103\pi$
$644$	−0.234927	−	1.33234i	−0.00925741	−	0.0525014i
$645$	−47.8124			−1.88261
$646$	0.680321	−	0.463158i	0.0267669	−	0.0182227i
$647$	11.2852			0.443667			0.221834	−	0.975085i	$-0.428796\pi$
$647$	11.2852			0.443667			0.221834	+	0.975085i	$0.428796\pi$
$648$	−1.12480	−	6.37907i	−0.0441864	−	0.250594i
$649$	4.21828	−	3.53956i	0.165582	−	0.138940i
$650$	−15.2966	+	5.56749i	−0.599980	+	0.218375i
$651$	1.24553	+	0.453337i	0.0488163	+	0.0177677i
$652$	16.3834	+	13.7473i	0.641623	+	0.538385i
$653$	−3.49176	+	6.04790i	−0.136643	+	0.236673i	−0.926224	−	0.376974i	$-0.876965\pi$
$653$	−3.49176	+	6.04790i	−0.136643	+	0.236673i	0.789581	+	0.613647i	$0.210298\pi$
$654$	2.90309	+	5.02830i	0.113520	+	0.196622i
$655$	−11.2752	+	63.9450i	−0.440560	+	2.49854i
$656$	−0.573263	+	3.25114i	−0.0223822	+	0.126936i
$657$	3.73205	+	6.46410i	0.145601	+	0.252189i
$658$	−0.936473	+	1.62202i	−0.0365075	+	0.0632329i
$659$	−26.5311	−	22.2622i	−1.03351	−	0.867214i	−0.0422414	−	0.999107i	$-0.513450\pi$
$659$	−26.5311	−	22.2622i	−1.03351	−	0.867214i	−0.991264	+	0.131894i	$0.957894\pi$
$660$	4.19754	+	1.52778i	0.163389	+	0.0594687i
$661$	4.03157	−	1.46737i	0.156810	−	0.0570741i	−0.262423	−	0.964953i	$-0.584521\pi$
$661$	4.03157	−	1.46737i	0.156810	−	0.0570741i	0.419232	+	0.907879i	$0.362299\pi$
$662$	−7.61851	+	6.39269i	−0.296102	+	0.248459i
$663$	−0.224483	−	1.27310i	−0.00871818	−	0.0494433i
$664$	−12.8465			−0.498541
$665$	−3.47524	+	4.82684i	−0.134764	+	0.187177i
$666$	4.43828			0.171980
$667$	0.872192	+	4.94645i	0.0337714	+	0.191527i
$668$	8.47938	−	7.11504i	0.328077	−	0.275289i
$669$	9.15878	−	3.33352i	0.354099	−	0.128881i
$670$	15.3574	+	5.58963i	0.593307	+	0.215946i
$671$	8.40068	+	7.04900i	0.324304	+	0.272124i
$672$	−0.353640	+	0.612522i	−0.0136419	+	0.0236285i
$673$	−22.8757	−	39.6218i	−0.881792	−	1.52731i	−0.849346	−	0.527836i	$-0.823004\pi$
$673$	−22.8757	−	39.6218i	−0.881792	−	1.52731i	−0.0324459	−	0.999473i	$-0.510330\pi$
$674$	−4.70013	+	26.6557i	−0.181042	+	1.02674i
$675$	3.52218	−	19.9753i	0.135569	−	0.768849i
$676$	−3.62303	−	6.27527i	−0.139347	−	0.241356i
$677$	−3.05858	+	5.29761i	−0.117551	+	0.203604i	−0.918796	−	0.394732i	$-0.870838\pi$
$677$	−3.05858	+	5.29761i	−0.117551	+	0.203604i	0.801246	+	0.598335i	$0.204171\pi$
$678$	0.0207154	+	0.0173823i	0.000795571	+	0.000667564i
$679$	−5.30626	−	1.93132i	−0.203635	−	0.0741173i
$680$	0.520850	−	0.189574i	0.0199737	−	0.00726983i
$681$	16.1820	−	13.5783i	0.620095	−	0.520321i
$682$	0.325423	+	1.84557i	0.0124611	+	0.0706704i
$683$	8.43385			0.322712			0.161356	−	0.986896i	$-0.448413\pi$
$683$	8.43385			0.322712			0.161356	+	0.986896i	$0.448413\pi$
$684$	1.22549	+	2.72090i	0.0468578	+	0.104036i
$685$	−11.7120			−0.447494
$686$	1.11256	+	6.30963i	0.0424777	+	0.240903i
$687$	7.44487	−	6.24699i	0.284039	−	0.238337i
$688$	10.0581	−	3.66086i	0.383463	−	0.139569i
$689$	5.74761	+	2.09196i	0.218966	+	0.0796972i
$690$	9.95970	+	8.35718i	0.379159	+	0.318152i
$691$	−0.143675	+	0.248853i	−0.00546566	+	0.00946680i	−0.868745	−	0.495259i	$-0.835073\pi$
$691$	−0.143675	+	0.248853i	−0.00546566	+	0.00946680i	0.863280	+	0.504726i	$0.168406\pi$
$692$	4.35567	+	7.54425i	0.165578	+	0.286789i
$693$	−0.0552576	+	0.313381i	−0.00209906	+	0.0119044i
$694$	3.37596	−	19.1460i	0.128150	−	0.726774i
$695$	2.18251	+	3.78022i	0.0827874	+	0.143392i
$696$	1.31293	−	2.27406i	0.0497664	−	0.0861980i
$697$	−0.477494	−	0.400665i	−0.0180864	−	0.0151763i
$698$	−21.2423	−	7.73157i	−0.804033	−	0.292644i
$699$	−7.42900	+	2.70393i	−0.280991	+	0.102272i
$700$	−1.28816	+	1.08090i	−0.0486880	+	0.0408540i
$701$	−0.499937	−	2.83529i	−0.0188824	−	0.107087i	0.973910	−	0.226935i	$-0.0728705\pi$
$701$	−0.499937	−	2.83529i	−0.0188824	−	0.107087i	−0.992792	+	0.119848i	$0.961759\pi$
$702$	25.2275			0.952150
$703$	27.3894	−	6.95437i	1.03301	−	0.262289i
$704$	−1.00000			−0.0376889
$705$	−3.12554	−	17.7258i	−0.117715	−	0.667594i
$706$	18.4587	−	15.4887i	0.694703	−	0.582925i
$707$	3.89094	−	1.41619i	0.146334	−	0.0532612i
$708$	−7.87371	−	2.86580i	−0.295912	−	0.107703i
$709$	−28.9099	−	24.2583i	−1.08573	−	0.911038i	−0.0893485	−	0.996000i	$-0.528478\pi$
$709$	−28.9099	−	24.2583i	−1.08573	−	0.911038i	−0.996384	+	0.0849626i	$0.972923\pi$
$710$	5.84593	−	10.1255i	0.219394	−	0.380002i
$711$	1.89820	+	3.28778i	0.0711881	+	0.123301i
$712$	2.94182	−	16.6839i	0.110249	−	0.625254i
$713$	−0.947178	+	5.37171i	−0.0354721	+	0.201172i
$714$	−0.0667715	−	0.115652i	−0.00249886	−	0.00432815i
$715$	−6.60445	+	11.4393i	−0.246993	+	0.427804i
$716$	−7.37487	−	6.18825i	−0.275612	−	0.231266i
$717$	−11.7371	−	4.27194i	−0.438328	−	0.159538i
$718$	−24.0737	+	8.76212i	−0.898423	+	0.326999i
$719$	33.9117	−	28.4553i	1.26469	−	1.06120i	0.269526	−	0.962993i	$-0.413133\pi$
$719$	33.9117	−	28.4553i	1.26469	−	1.06120i	0.995166	−	0.0982097i	$-0.0313116\pi$
$720$	0.348987	+	1.97921i	0.0130060	+	0.0737607i
$721$	−0.811892			−0.0302364
$722$	11.8261	+	14.8709i	0.440122	+	0.553437i
$723$	27.2340			1.01284
$724$	3.09282	+	17.5403i	0.114944	+	0.651878i
$725$	4.78245	−	4.01295i	0.177616	−	0.149037i
$726$	1.42987	−	0.520432i	0.0530676	−	0.0193150i
$727$	10.2593	+	3.73409i	0.380497	+	0.138490i	0.525186	−	0.850988i	$-0.323996\pi$
$727$	10.2593	+	3.73409i	0.380497	+	0.138490i	−0.144689	+	0.989477i	$0.546218\pi$
$728$	−1.60215	−	1.34436i	−0.0593796	−	0.0498254i
$729$	−15.0142	+	26.0054i	−0.556083	+	0.963164i
$730$	16.0030	+	27.7180i	0.592298	+	1.02589i
$731$	−0.350939	+	1.99028i	−0.0129800	+	0.0736130i
$732$	2.89763	−	16.4333i	0.107099	−	0.607391i
$733$	−17.6633	−	30.5938i	−0.652409	−	1.13001i	−0.982537	−	0.186070i	$-0.940425\pi$
$733$	−17.6633	−	30.5938i	−0.652409	−	1.13001i	0.330127	−	0.943936i	$-0.392908\pi$
$734$	0.509870	−	0.883121i	0.0188196	−	0.0325966i
$735$	−23.2138	−	19.4787i	−0.856252	−	0.718481i
$736$	−2.73507	−	0.995485i	−0.100816	−	0.0366941i
$737$	5.23143	−	1.90408i	0.192702	−	0.0701378i
$738$	1.73133	−	1.45276i	0.0637313	−	0.0534769i
$739$	0.199338	+	1.13050i	0.00733275	+	0.0415861i	0.988255	−	0.152816i	$-0.0488343\pi$
$739$	0.199338	+	1.13050i	0.00733275	+	0.0415861i	−0.980922	+	0.194403i	$0.937723\pi$
$740$	19.0313			0.699605
$741$	28.9263	−	7.34460i	1.06263	−	0.269811i
$742$	0.631844			0.0231957
$743$	1.90333	+	10.7943i	0.0698264	+	0.396005i	0.999611	+	0.0279005i	$0.00888215\pi$
$743$	1.90333	+	10.7943i	0.0698264	+	0.396005i	−0.929784	+	0.368105i	$0.880007\pi$
$744$	2.18446	−	1.83298i	0.0800862	−	0.0672003i
$745$	22.3575	−	8.13747i	0.819116	−	0.298134i
$746$	29.8224	+	10.8545i	1.09188	+	0.397410i
$747$	6.73724	+	5.65321i	0.246503	+	0.206840i
$748$	0.0944062	−	0.163516i	0.00345183	−	0.00597875i
$749$	−0.0154189	−	0.0267062i	−0.000563393	−	0.000975825i
$750$	−1.07218	+	6.08064i	−0.0391505	+	0.222033i
$751$	3.57783	−	20.2909i	0.130557	−	0.740424i	−0.847294	−	0.531123i	$-0.821770\pi$
$751$	3.57783	−	20.2909i	0.130557	−	0.740424i	0.977851	−	0.209301i	$-0.0671188\pi$
$752$	2.01473	+	3.48961i	0.0734696	+	0.127253i
$753$	9.08980	−	15.7440i	0.331251	−	0.573743i
$754$	5.94817	+	4.99110i	0.216619	+	0.181765i
$755$	−44.2601	−	16.1093i	−1.61079	−	0.586279i
$756$	2.44888	−	0.891321i	0.0890651	−	0.0324170i
$757$	26.2269	−	22.0070i	0.953233	−	0.799857i	−0.0266063	−	0.999646i	$-0.508470\pi$
$757$	26.2269	−	22.0070i	0.953233	−	0.799857i	0.979839	+	0.199789i	$0.0640256\pi$
$758$	−3.31087	−	18.7769i	−0.120256	−	0.682006i
$759$	4.42889			0.160759
$760$	5.25489	+	11.6672i	0.190615	+	0.423213i
$761$	−43.6051			−1.58069			−0.790343	−	0.612665i	$-0.790097\pi$
$761$	−43.6051			−1.58069			−0.790343	+	0.612665i	$0.790097\pi$
$762$	−2.03200	−	11.5241i	−0.0736117	−	0.417473i
$763$	−1.35866	+	1.14005i	−0.0491868	+	0.0412726i
$764$	−23.7487	+	8.64381i	−0.859197	+	0.312722i
$765$	−0.356579	−	0.129784i	−0.0128921	−	0.00469235i
$766$	−13.8994	−	11.6630i	−0.502207	−	0.421402i
$767$	12.3886	−	21.4577i	0.447326	−	0.774791i
$768$	0.760820	+	1.31778i	0.0274537	+	0.0475513i
$769$	6.33751	−	35.9418i	0.228536	−	1.29609i	−0.627271	−	0.778801i	$-0.715828\pi$
$769$	6.33751	−	35.9418i	0.228536	−	1.29609i	0.855808	−	0.517294i	$-0.173061\pi$
$770$	−0.236944	+	1.34378i	−0.00853887	+	0.0484263i
$771$	3.09918	+	5.36794i	0.111614	+	0.193321i
$772$	−8.36854	+	14.4947i	−0.301190	+	0.521677i
$773$	35.3572	+	29.6682i	1.27171	+	1.06709i	0.994331	+	0.106330i	$0.0339100\pi$
$773$	35.3572	+	29.6682i	1.27171	+	1.06709i	0.277379	+	0.960761i	$0.410534\pi$
$774$	−6.88589	−	2.50626i	−0.247508	−	0.0900856i
$775$	6.37091	−	2.31882i	0.228850	−	0.0832946i
$776$	−9.30631	+	7.80892i	−0.334077	+	0.280324i
$777$	−0.796220	−	4.51559i	−0.0285642	−	0.161996i
$778$	3.88312			0.139217
$779$	8.40801	−	11.6781i	0.301248	−	0.418410i
$780$	20.0992			0.719667
$781$	−0.691604	−	3.92228i	−0.0247475	−	0.140350i
$782$	0.420986	−	0.353249i	0.0150544	−	0.0126322i
$783$	−9.09177	+	3.30913i	−0.324913	+	0.118259i
$784$	6.37483	+	2.32025i	0.227672	+	0.0828660i
$785$	−40.8140	−	34.2470i	−1.45672	−	1.22233i
$786$	16.8283	−	29.1475i	0.600246	−	1.03966i
$787$	−14.9215	−	25.8448i	−0.531893	−	0.921266i	−0.999307	−	0.0372274i	$-0.988147\pi$
$787$	−14.9215	−	25.8448i	−0.531893	−	0.921266i	0.467414	−	0.884039i	$-0.345186\pi$
$788$	1.48040	−	8.39576i	0.0527370	−	0.299087i
$789$	−1.90819	+	10.8219i	−0.0679335	+	0.385270i
$790$	8.13948	+	14.0980i	0.289590	+	0.501584i
$791$	−0.00413025	+	0.00715381i	−0.000146855	+	0.000254360i
$792$	0.524441	+	0.440058i	0.0186352	+	0.0156368i
$793$	46.3678	+	16.8765i	1.64657	+	0.599302i
$794$	−16.7818	+	6.10809i	−0.595565	+	0.216768i
$795$	−4.65151	+	3.90308i	−0.164972	+	0.138428i
$796$	3.77453	+	21.4064i	0.133785	+	0.758731i
$797$	−26.9999			−0.956386			−0.478193	−	0.878255i	$-0.658708\pi$
$797$	−26.9999			−0.956386			−0.478193	+	0.878255i	$0.658708\pi$
$798$	2.54844	−	1.73496i	0.0902138	−	0.0614169i
$799$	−0.760811			−0.0269156
$800$	0.628214	+	3.56278i	0.0222107	+	0.125963i
$801$	−8.88469	+	7.45514i	−0.313925	+	0.263414i
$802$	−31.4835	+	11.4591i	−1.11172	+	0.404634i
$803$	10.2452	+	3.72895i	0.361545	+	0.131592i
$804$	−6.48934	−	5.44520i	−0.228861	−	0.192038i
$805$	−1.98577	+	3.43945i	−0.0699892	+	0.121225i
$806$	4.21617	+	7.30262i	0.148508	+	0.257224i
$807$	8.41160	−	47.7046i	0.296102	−	1.67928i
$808$	1.54689	−	8.77287i	0.0544195	−	0.308628i
$809$	−20.8081	−	36.0407i	−0.731575	−	1.26712i	−0.956210	−	0.292682i	$-0.905452\pi$
$809$	−20.8081	−	36.0407i	−0.731575	−	1.26712i	0.224635	−	0.974443i	$-0.427881\pi$
$810$	−9.50765	+	16.4677i	−0.334065	+	0.578617i
$811$	13.0443	+	10.9454i	0.458046	+	0.384346i	0.842412	−	0.538835i	$-0.181135\pi$
$811$	13.0443	+	10.9454i	0.458046	+	0.384346i	−0.384365	+	0.923181i	$0.625580\pi$
$812$	0.753743	+	0.274340i	0.0264512	+	0.00962745i
$813$	−44.6697	+	16.2585i	−1.56664	+	0.570209i
$814$	4.96622	−	4.16715i	0.174066	−	0.146059i
$815$	−10.9023	−	61.8298i	−0.381890	−	2.16580i
$816$	−0.287304			−0.0100577
$817$	−46.4211	−	4.67700i	−1.62407	−	0.163628i
$818$	26.3286			0.920556
$819$	0.248635	+	1.41008i	0.00868801	+	0.0492721i
$820$	7.42394	−	6.22943i	0.259255	−	0.217541i
$821$	−23.3648	+	8.50410i	−0.815438	+	0.296795i	−0.715868	−	0.698235i	$-0.753969\pi$
$821$	−23.3648	+	8.50410i	−0.815438	+	0.296795i	−0.0995697	+	0.995031i	$0.531747\pi$
$822$	5.70471	+	2.07635i	0.198975	+	0.0724209i
$823$	29.3389	+	24.6183i	1.02269	+	0.858140i	0.989963	−	0.141325i	$-0.0451361\pi$
$823$	29.3389	+	24.6183i	1.02269	+	0.858140i	0.0327278	+	0.999464i	$0.489581\pi$
$824$	−0.873352	+	1.51269i	−0.0304247	+	0.0526971i
$825$	−2.75245	−	4.76739i	−0.0958281	−	0.165979i
$826$	0.444458	−	2.52065i	0.0154647	−	0.0877045i
$827$	−0.718910	+	4.07714i	−0.0249989	+	0.141776i	−0.994753	−	0.102310i	$-0.967377\pi$
$827$	−0.718910	+	4.07714i	−0.0249989	+	0.141776i	0.969754	+	0.244086i	$0.0784878\pi$
$828$	0.996313	+	1.72567i	0.0346243	+	0.0599710i
$829$	11.3141	−	19.5966i	0.392955	−	0.680617i	−0.599883	−	0.800088i	$-0.704786\pi$
$829$	11.3141	−	19.5966i	0.392955	−	0.680617i	0.992838	+	0.119470i	$0.0381196\pi$
$830$	28.8892	+	24.2409i	1.00276	+	0.841415i
$831$	17.6701	+	6.43138i	0.612968	+	0.223102i
$832$	−4.22820	+	1.53894i	−0.146587	+	0.0533532i
$833$	−0.981221	+	0.823342i	−0.0339973	+	0.0285271i
$834$	−0.392891	−	2.22820i	−0.0136047	−	0.0771562i
$835$	−32.4943			−1.12451
$836$	3.92595	+	1.89392i	0.135782	+	0.0655028i
$837$	−10.5071			−0.363178
$838$	−5.58914	−	31.6976i	−0.193074	−	1.09498i
$839$	−11.8210	+	9.91902i	−0.408107	+	0.342443i	−0.823617	−	0.567146i	$-0.808048\pi$
$839$	−11.8210	+	9.91902i	−0.408107	+	0.342443i	0.415510	+	0.909589i	$0.363603\pi$
$840$	1.95107	−	0.710133i	0.0673184	−	0.0245019i
$841$	24.4527	+	8.90006i	0.843197	+	0.306899i
$842$	15.3365	+	12.8688i	0.528531	+	0.443490i
$843$	−5.12680	+	8.87987i	−0.176576	+	0.305839i
$844$	−4.41224	−	7.64223i	−0.151876	−	0.263056i
$845$	−3.69376	+	20.9483i	−0.127069	+	0.720645i
$846$	0.479027	−	2.71669i	0.0164693	−	0.0934019i
$847$	0.232407	+	0.402540i	0.00798559	+	0.0138315i
$848$	0.679674	−	1.17723i	0.0233401	−	0.0404263i
$849$	−4.28861	−	3.59857i	−0.147185	−	0.123503i
$850$	−0.641880	−	0.233625i	−0.0220163	−	0.00801328i
$851$	17.7313	−	6.45367i	0.607822	−	0.221229i
$852$	−4.64251	+	3.89553i	−0.159050	+	0.133459i
$853$	−6.00862	−	34.0766i	−0.205731	−	1.16676i	−0.896285	−	0.443478i	$-0.853744\pi$
$853$	−6.00862	−	34.0766i	−0.205731	−	1.16676i	0.690554	−	0.723281i	$-0.257367\pi$
$854$	5.09729			0.174426
$855$	2.37836	−	8.43121i	0.0813383	−	0.288341i
$856$	−0.0663443			−0.00226760
$857$	8.23874	+	46.7242i	0.281430	+	1.59607i	0.717766	+	0.696285i	$0.245165\pi$
$857$	8.23874	+	46.7242i	0.281430	+	1.59607i	−0.436336	+	0.899784i	$0.643724\pi$
$858$	5.24489	−	4.40098i	0.179058	−	0.150247i
$859$	−39.1762	+	14.2590i	−1.33668	+	0.486510i	−0.908764	−	0.417311i	$-0.862973\pi$
$859$	−39.1762	+	14.2590i	−1.33668	+	0.486510i	−0.427911	+	0.903821i	$0.640750\pi$
$860$	−29.5266	−	10.7468i	−1.00685	−	0.366463i
$861$	−1.78866	−	1.50087i	−0.0609575	−	0.0511494i
$862$	−14.6207	+	25.3237i	−0.497981	+	0.862529i
$863$	19.5396	+	33.8436i	0.665136	+	1.15205i	0.979248	+	0.202663i	$0.0649597\pi$
$863$	19.5396	+	33.8436i	0.665136	+	1.15205i	−0.314113	+	0.949386i	$0.601707\pi$
$864$	0.973585	−	5.52147i	0.0331220	−	0.187844i
$865$	4.44071	−	25.1845i	0.150989	−	0.856299i
$866$	−10.9353	−	18.9405i	−0.371596	−	0.643623i
$867$	−12.9068	+	22.3553i	−0.438339	+	0.759225i
$868$	0.667284	+	0.559918i	0.0226491	+	0.0190049i
$869$	5.21093	+	1.89662i	0.176769	+	0.0643386i
$870$	−7.24359	+	2.63645i	−0.245581	+	0.0893840i
$871$	19.1893	−	16.1017i	0.650204	−	0.545586i
$872$	0.662595	+	3.75776i	0.0224383	+	0.127254i
$873$	8.31700			0.281488
$874$	8.85238	+	9.08824i	0.299436	+	0.307414i
$875$	−1.88610			−0.0637618
$876$	−2.88083	−	16.3380i	−0.0973341	−	0.552009i
$877$	4.29784	−	3.60632i	0.145128	−	0.121777i	−0.567333	−	0.823488i	$-0.692025\pi$
$877$	4.29784	−	3.60632i	0.145128	−	0.121777i	0.712461	+	0.701712i	$0.247580\pi$
$878$	−24.2680	+	8.83283i	−0.819006	+	0.298094i
$879$	3.99667	+	1.45467i	0.134804	+	0.0490648i
$880$	2.24880	+	1.88697i	0.0758070	+	0.0636096i
$881$	−7.27987	+	12.6091i	−0.245265	+	0.424811i	−0.962206	−	0.272322i	$-0.912208\pi$
$881$	−7.27987	+	12.6091i	−0.245265	+	0.424811i	0.716941	+	0.697134i	$0.245542\pi$
$882$	−2.32218	−	4.02213i	−0.0781918	−	0.135432i
$883$	0.132065	−	0.748977i	0.00444433	−	0.0252051i	−0.982505	−	0.186236i	$-0.940371\pi$
$883$	0.132065	−	0.748977i	0.00444433	−	0.0252051i	0.986949	+	0.161031i	$0.0514820\pi$
$884$	0.147527	−	0.836666i	0.00496186	−	0.0281401i
$885$	12.2987	+	21.3020i	0.413417	+	0.716060i
$886$	−3.57765	+	6.19667i	−0.120193	+	0.208181i
$887$	28.4002	+	23.8306i	0.953586	+	0.800153i	0.979898	−	0.199500i	$-0.0639319\pi$
$887$	28.4002	+	23.8306i	0.953586	+	0.800153i	−0.0263122	+	0.999654i	$0.508376\pi$
$888$	−9.26979	−	3.37393i	−0.311074	−	0.113222i
$889$	3.35898	−	1.22257i	0.112656	−	0.0410036i
$890$	−38.0975	+	31.9676i	−1.27703	+	1.07156i
$891$	1.12480	+	6.37907i	0.0376823	+	0.213707i
$892$	6.40530			0.214465
$893$	−1.30065	−	17.5158i	−0.0435247	−	0.586143i
$894$	−12.3326			−0.412462
$895$	4.90758	+	27.8323i	0.164042	+	0.930330i
$896$	−0.356068	+	0.298776i	−0.0118954	+	0.00998142i
$897$	18.7263	−	6.81581i	0.625252	−	0.227573i
$898$	−13.1856	−	4.79916i	−0.440009	−	0.160150i
$899$	−2.47737	−	2.07876i	−0.0826249	−	0.0693306i
$900$	1.23837	−	2.14492i	0.0412790	−	0.0714973i
$901$	0.128331	+	0.222276i	0.00427532	+	0.00740507i
$902$	0.573263	−	3.25114i	0.0190876	−	0.108251i
$903$	−1.31460	+	7.45545i	−0.0437470	+	0.248102i
$904$	0.00888583	+	0.0153907i	0.000295538	+	0.000511887i
$905$	26.1427	−	45.2806i	0.869014	−	1.50518i
$906$	18.7023	+	15.6931i	0.621343	+	0.521369i
$907$	15.2915	+	5.56566i	0.507747	+	0.184805i	0.583175	−	0.812347i	$-0.301810\pi$
$907$	15.2915	+	5.56566i	0.507747	+	0.184805i	−0.0754284	+	0.997151i	$0.524032\pi$
$908$	13.0452	−	4.74807i	0.432921	−	0.157570i
$909$	−4.67183	+	3.92013i	−0.154955	+	0.130023i
$910$	1.06614	+	6.04640i	0.0353423	+	0.200436i
$911$	−17.9183			−0.593659			−0.296830	−	0.954930i	$-0.595929\pi$
$911$	−17.9183			−0.593659			−0.296830	+	0.954930i	$0.595929\pi$
$912$	−0.491164	−	6.61447i	−0.0162641	−	0.219027i
$913$	12.8465			0.425157
$914$	−5.43714	−	30.8356i	−0.179845	−	1.01995i
$915$	−37.5252	+	31.4874i	−1.24055	+	1.04094i
$916$	6.00173	−	2.18445i	0.198303	−	0.0721763i
$917$	9.66102	+	3.51632i	0.319035	+	0.116119i
$918$	0.810938	+	0.680458i	0.0267650	+	0.0224585i
$919$	17.2887	−	29.9450i	0.570303	−	0.987793i	−0.426232	−	0.904614i	$-0.640159\pi$
$919$	17.2887	−	29.9450i	0.570303	−	0.987793i	0.996535	−	0.0831794i	$-0.0265074\pi$
$920$	4.27218	+	7.39964i	0.140850	+	0.243959i
$921$	−3.12773	+	17.7382i	−0.103062	+	0.584494i
$922$	2.12370	−	12.0441i	0.0699403	−	0.396651i
$923$	−8.96040	−	15.5199i	−0.294935	−	0.510843i
$924$	0.353640	−	0.612522i	0.0116339	−	0.0201505i
$925$	−17.9665	−	15.0757i	−0.590735	−	0.495686i
$926$	21.8734	+	7.96128i	0.718805	+	0.261624i
$927$	1.12369	−	0.408991i	0.0369070	−	0.0134330i
$928$	1.32194	−	1.10924i	0.0433949	−	0.0364127i
$929$	−3.31072	−	18.7760i	−0.108621	−	0.616021i	−0.989712	−	0.143074i	$-0.954301\pi$
$929$	−3.31072	−	18.7760i	−0.108621	−	0.616021i	0.881091	−	0.472947i	$-0.156810\pi$
$930$	−8.37119			−0.274502
$931$	−20.6328	−	21.1826i	−0.676214	−	0.694232i
$932$	−5.19556			−0.170186
$933$	−4.22723	−	23.9738i	−0.138393	−	0.784868i
$934$	13.2459	−	11.1146i	0.433420	−	0.363682i
$935$	−0.520850	+	0.189574i	−0.0170336	+	0.00619973i
$936$	2.89467	+	1.05357i	0.0946152	+	0.0344371i
$937$	−37.5890	−	31.5410i	−1.22798	−	1.03040i	−0.998368	−	0.0571161i	$-0.981809\pi$
$937$	−37.5890	−	31.5410i	−1.22798	−	1.03040i	−0.229613	−	0.973282i	$-0.573746\pi$
$938$	1.29385	−	2.24101i	0.0422456	−	0.0731716i
$939$	−13.2791	−	23.0001i	−0.433347	−	0.750579i
$940$	2.05406	−	11.6492i	0.0669961	−	0.379954i
$941$	4.53582	−	25.7239i	0.147864	−	0.838576i	−0.817160	−	0.576411i	$-0.804453\pi$
$941$	4.53582	−	25.7239i	0.147864	−	0.838576i	0.965023	−	0.262164i	$-0.0844363\pi$
$942$	13.8083	+	23.9167i	0.449899	+	0.779249i
$943$	4.80438	−	8.32142i	0.156452	−	0.270983i
$944$	−4.21828	−	3.53956i	−0.137293	−	0.115203i
$945$	−7.18894	−	2.61656i	−0.233856	−	0.0851167i
$946$	−10.0581	+	3.66086i	−0.327018	+	0.119025i
$947$	12.6660	−	10.6281i	0.411591	−	0.345366i	−0.413363	−	0.910567i	$-0.635646\pi$
$947$	12.6660	−	10.6281i	0.411591	−	0.345366i	0.824953	+	0.565201i	$0.191201\pi$
$948$	−1.46525	−	8.30985i	−0.0475891	−	0.269891i
$949$	49.0574			1.59247
$950$	4.28130	−	15.1771i	0.138904	−	0.492409i
$951$	34.6201			1.12264
$952$	−0.0152398	−	0.0864292i	−0.000493925	−	0.00280119i
$953$	−11.1417	+	9.34901i	−0.360916	+	0.302844i	−0.805156	−	0.593064i	$-0.797918\pi$
$953$	−11.1417	+	9.34901i	−0.360916	+	0.302844i	0.444240	+	0.895908i	$0.353474\pi$
$954$	−0.874500	+	0.318292i	−0.0283130	+	0.0103051i
$955$	69.7166	+	25.3748i	2.25598	+	0.821108i
$956$	−6.28804	−	5.27629i	−0.203370	−	0.170647i
$957$	−1.31293	+	2.27406i	−0.0424409	+	0.0735099i
$958$	6.63787	+	11.4971i	0.214460	+	0.371455i
$959$	−0.322022	+	1.82628i	−0.0103986	+	0.0589735i
$960$	0.775674	−	4.39906i	0.0250348	−	0.141979i
$961$	13.7440	+	23.8053i	0.443355	+	0.767913i
$962$	14.5852	−	25.2623i	0.470245	−	0.814489i
$963$	0.0347937	+	0.0291953i	0.00112121	+	0.000940807i
$964$	16.8184	+	6.12140i	0.541684	+	0.197157i
$965$	46.1703	−	16.8046i	1.48627	−	0.540959i
$966$	1.57699	−	1.32325i	0.0507387	−	0.0425748i
$967$	−2.97193	−	16.8547i	−0.0955709	−	0.542010i	−0.994571	−	0.104061i	$-0.966816\pi$
$967$	−2.97193	−	16.8547i	−0.0955709	−	0.542010i	0.899000	−	0.437949i	$-0.144295\pi$
$968$	1.00000			0.0321412
$969$	1.12794	+	0.544133i	0.0362347	+	0.0174801i
$970$	35.6632			1.14508
$971$	−2.96443	−	16.8121i	−0.0951332	−	0.539527i	−0.994706	−	0.102757i	$-0.967233\pi$
$971$	−2.96443	−	16.8121i	−0.0951332	−	0.539527i	0.899573	−	0.436770i	$-0.143878\pi$
$972$	−5.33439	+	4.47609i	−0.171101	+	0.143571i
$973$	0.649463	−	0.236385i	0.0208208	−	0.00757817i
$974$	25.5673	+	9.30573i	0.819229	+	0.298175i
$975$	−18.9747	−	15.9216i	−0.607675	−	0.509900i
$976$	5.48315	−	9.49710i	0.175511	−	0.303995i
$977$	−10.9305	−	18.9322i	−0.349698	−	0.605695i	0.636498	−	0.771279i	$-0.280382\pi$
$977$	−10.9305	−	18.9322i	−0.349698	−	0.605695i	−0.986196	+	0.165584i	$0.947049\pi$
$978$	−5.65109	+	32.0489i	−0.180702	+	1.02481i
$979$	−2.94182	+	16.6839i	−0.0940208	+	0.533219i
$980$	−9.95748	−	17.2469i	−0.318080	−	0.550931i
$981$	1.30614	−	2.26231i	0.0417020	−	0.0722299i
$982$	27.2048	+	22.8276i	0.868141	+	0.728457i
$983$	−27.7848	−	10.1128i	−0.886198	−	0.322550i	−0.141490	−	0.989940i	$-0.545189\pi$
$983$	−27.7848	−	10.1128i	−0.886198	−	0.322550i	−0.744708	+	0.667390i	$0.767411\pi$
$984$	−4.72043	+	1.71810i	−0.150482	+	0.0547709i
$985$	−19.1716	+	16.0869i	−0.610859	+	0.512572i
$986$	0.0565795	+	0.320879i	0.00180186	+	0.0102189i
$987$	−2.84995			−0.0907150
$988$	19.5143	+	1.96610i	0.620834	+	0.0625501i
$989$	−31.1541			−0.990641
$990$	−0.348987	−	1.97921i	−0.0110915	−	0.0629033i
$991$	−25.7691	+	21.6229i	−0.818583	+	0.686873i	−0.952640	−	0.304101i	$-0.901644\pi$
$991$	−25.7691	+	21.6229i	−0.818583	+	0.686873i	0.134057	+	0.990974i	$0.457200\pi$
$992$	1.76102	−	0.640958i	0.0559124	−	0.0203505i
$993$	−14.2205	−	5.17583i	−0.451273	−	0.164250i
$994$	−1.41814	−	1.18996i	−0.0449808	−	0.0377433i
$995$	31.9051	−	55.2612i	1.01146	−	1.75190i
$996$	−9.77388	−	16.9289i	−0.309697	−	0.536411i
$997$	8.82809	−	50.0666i	0.279589	−	1.58563i	−0.444410	−	0.895824i	$-0.646587\pi$
$997$	8.82809	−	50.0666i	0.279589	−	1.58563i	0.723998	−	0.689802i	$-0.242302\pi$
$998$	−1.62146	+	9.19576i	−0.0513264	+	0.291087i
$999$	18.1738	+	31.4779i	0.574993	+	0.995918i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.j.d.199.2	✓	30
19.6	even	9		7942.2.a.ca.1.5		15
19.13	odd	18		7942.2.a.by.1.11		15
19.17	even	9	inner	418.2.j.d.397.2	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.j.d.199.2	✓	30	1.1	even	1	trivial
418.2.j.d.397.2	yes	30	19.17	even	9	inner
7942.2.a.by.1.11		15	19.13	odd	18
7942.2.a.ca.1.5		15	19.6	even	9

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.j (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.173648 + 0.984808i) q^{2} +(-1.16564 + 0.978092i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(2.75856 + 1.00403i) q^{5} +(-1.16564 - 0.978092i) q^{6} +(0.232407 - 0.402540i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-0.118881 + 0.674209i) q^{9} +(-0.509761 + 2.89100i) q^{10} +(0.500000 + 0.866025i) q^{11} +(0.760820 - 1.31778i) q^{12} +(3.44686 + 2.89226i) q^{13} +(0.436782 + 0.158976i) q^{14} +(-4.19754 + 1.52778i) q^{15} +(0.766044 - 0.642788i) q^{16} +(0.0327869 + 0.185944i) q^{17} -0.684609 q^{18} +(-4.22484 + 1.07272i) q^{19} -2.93560 q^{20} +(0.122818 + 0.696534i) q^{21} +(-0.766044 + 0.642788i) q^{22} +(-2.73507 + 0.995485i) q^{23} +(1.42987 + 0.520432i) q^{24} +(2.77135 + 2.32544i) q^{25} +(-2.24978 + 3.89673i) q^{26} +(-2.80333 - 4.85550i) q^{27} +(-0.0807140 + 0.457752i) q^{28} +(0.299660 - 1.69946i) q^{29} +(-2.23346 - 3.86847i) q^{30} +(0.937019 - 1.62296i) q^{31} +(0.766044 + 0.642788i) q^{32} +(-1.42987 - 0.520432i) q^{33} +(-0.177426 + 0.0645776i) q^{34} +(1.04527 - 0.877088i) q^{35} +(-0.118881 - 0.674209i) q^{36} -6.48294 q^{37} +(-1.79006 - 3.97438i) q^{38} -6.84672 q^{39} +(-0.509761 - 2.89100i) q^{40} +(-2.52894 + 2.12203i) q^{41} +(-0.664625 + 0.241904i) q^{42} +(10.0581 + 3.66086i) q^{43} +(-0.766044 - 0.642788i) q^{44} +(-1.00487 + 1.74048i) q^{45} +(-1.45530 - 2.52066i) q^{46} +(-0.699708 + 3.96824i) q^{47} +(-0.264230 + 1.49852i) q^{48} +(3.39197 + 5.87507i) q^{49} +(-1.80887 + 3.13306i) q^{50} +(-0.220088 - 0.184676i) q^{51} +(-4.22820 - 1.53894i) q^{52} +(1.27737 - 0.464925i) q^{53} +(4.29494 - 3.60389i) q^{54} +(0.509761 + 2.89100i) q^{55} -0.464814 q^{56} +(3.87544 - 5.38269i) q^{57} +1.72567 q^{58} +(-0.956207 - 5.42292i) q^{59} +(3.42187 - 2.87129i) q^{60} +(10.3050 - 3.75070i) q^{61} +(1.76102 + 0.640958i) q^{62} +(0.243767 + 0.204545i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(6.60445 + 11.4393i) q^{65} +(0.264230 - 1.49852i) q^{66} +(0.966729 - 5.48259i) q^{67} +(-0.0944062 - 0.163516i) q^{68} +(2.21445 - 3.83553i) q^{69} +(1.04527 + 0.877088i) q^{70} +(-3.74260 - 1.36219i) q^{71} +(0.643322 - 0.234150i) q^{72} +(8.35197 - 7.00813i) q^{73} +(-1.12575 - 6.38445i) q^{74} -5.50491 q^{75} +(3.60316 - 2.45301i) q^{76} +0.464814 q^{77} +(-1.18892 - 6.74270i) q^{78} +(4.24799 - 3.56449i) q^{79} +(2.75856 - 1.00403i) q^{80} +(6.08684 + 2.21543i) q^{81} +(-2.52894 - 2.12203i) q^{82} +(6.42325 - 11.1254i) q^{83} +(-0.353640 - 0.612522i) q^{84} +(-0.0962492 + 0.545857i) q^{85} +(-1.85867 + 10.5410i) q^{86} +(1.31293 + 2.27406i) q^{87} +(0.500000 - 0.866025i) q^{88} +(12.9777 + 10.8896i) q^{89} +(-1.88854 - 0.687371i) q^{90} +(1.96533 - 0.715321i) q^{91} +(2.22965 - 1.87090i) q^{92} +(0.495177 + 2.80829i) q^{93} -4.02946 q^{94} +(-12.7315 - 1.28272i) q^{95} -1.52164 q^{96} +(-2.10957 - 11.9640i) q^{97} +(-5.19681 + 4.36064i) q^{98} +(-0.643322 + 0.234150i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 15 q^{8} + 15 q^{11} - 3 q^{12} - 21 q^{13} - 9 q^{14} + 3 q^{15} + 6 q^{17} + 60 q^{18} - 9 q^{19} + 18 q^{20} - 39 q^{21} + 15 q^{23} + 24 q^{25} - 3 q^{27} + 9 q^{28} - 3 q^{29} - 21 q^{30} - 18 q^{31}+ \cdots + 9 q^{98}+O(q^{100}) \) 30 * q - 15 * q^8 + 15 * q^11 - 3 * q^12 - 21 * q^13 - 9 * q^14 + 3 * q^15 + 6 * q^17 + 60 * q^18 - 9 * q^19 + 18 * q^20 - 39 * q^21 + 15 * q^23 + 24 * q^25 - 3 * q^27 + 9 * q^28 - 3 * q^29 - 21 * q^30 - 18 * q^31 + 15 * q^34 + 51 * q^35 - 18 * q^37 - 6 * q^38 - 6 * q^41 + 51 * q^42 + 39 * q^43 - 54 * q^45 - 21 * q^46 - 3 * q^47 - 33 * q^49 - 24 * q^50 - 48 * q^51 - 12 * q^52 - 24 * q^53 - 9 * q^54 - 6 * q^57 - 18 * q^58 + 21 * q^59 + 3 * q^60 + 63 * q^61 - 27 * q^62 + 57 * q^63 - 15 * q^64 - 6 * q^65 - 45 * q^67 - 21 * q^68 + 42 * q^69 + 51 * q^70 - 48 * q^71 + 87 * q^73 + 9 * q^74 + 42 * q^75 - 9 * q^76 - 36 * q^78 - 57 * q^79 + 36 * q^81 - 6 * q^82 - 30 * q^83 + 9 * q^84 + 81 * q^85 - 24 * q^86 - 9 * q^87 + 15 * q^88 - 6 * q^89 - 114 * q^90 - 51 * q^91 - 3 * q^92 + 33 * q^93 + 78 * q^94 - 132 * q^95 + 6 * q^96 - 66 * q^97 + 9 * q^98

Introduction

L-functions

Modular forms

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Database

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