LMFDB - Embedded newform 975.2.bt.m.68.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [975,2,Mod(68,975)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(975, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 9, 4]))

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

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

chi := DirichletCharacter("975.68");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 975 = 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	975.bt (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.78541419707$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$24$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 195)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			68.18
Character	$\chi$	$=$	975.68
Dual form			975.2.bt.m.932.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.395659 - 1.47662i) q^{2} +(1.07285 - 1.35978i) q^{3} +(-0.291809 - 0.168476i) q^{4} +(-1.58339 - 2.12220i) q^{6} +(-1.22324 - 4.56520i) q^{7} +(1.79769 - 1.79769i) q^{8} +(-0.697981 - 2.91767i) q^{9} +O(q^{10})$	\(q+(0.395659 - 1.47662i) q^{2} +(1.07285 - 1.35978i) q^{3} +(-0.291809 - 0.168476i) q^{4} +(-1.58339 - 2.12220i) q^{6} +(-1.22324 - 4.56520i) q^{7} +(1.79769 - 1.79769i) q^{8} +(-0.697981 - 2.91767i) q^{9} +(-1.33359 + 0.769949i) q^{11} +(-0.542158 + 0.216045i) q^{12} +(-0.402017 + 3.58307i) q^{13} -7.22505 q^{14} +(-2.28018 - 3.94939i) q^{16} +(-0.302869 + 0.0811535i) q^{17} +(-4.58446 - 0.123752i) q^{18} +(0.272564 + 0.157365i) q^{19} +(-7.52000 - 3.23444i) q^{21} +(0.609275 + 2.27384i) q^{22} +(4.55377 + 1.22018i) q^{23} +(-0.515801 - 4.37311i) q^{24} +(5.13177 + 2.01130i) q^{26} +(-4.71621 - 2.18113i) q^{27} +(-0.412174 + 1.53825i) q^{28} +(4.22484 + 7.31764i) q^{29} +0.517123 q^{31} +(-1.82255 + 0.488351i) q^{32} +(-0.383787 + 2.63943i) q^{33} +0.479331i q^{34} +(-0.287881 + 0.968998i) q^{36} +(-5.88304 - 1.57635i) q^{37} +(0.340210 - 0.340210i) q^{38} +(4.44087 + 4.39075i) q^{39} +(7.02151 - 4.05387i) q^{41} +(-7.75140 + 9.82445i) q^{42} +(-3.57884 + 0.958947i) q^{43} +0.518872 q^{44} +(3.60348 - 6.24141i) q^{46} +(0.501957 + 0.501957i) q^{47} +(-7.81659 - 1.13657i) q^{48} +(-13.2825 + 7.66868i) q^{49} +(-0.214583 + 0.498899i) q^{51} +(0.720974 - 0.977843i) q^{52} +(1.53186 - 1.53186i) q^{53} +(-5.08672 + 6.10107i) q^{54} +(-10.4058 - 6.00780i) q^{56} +(0.506401 - 0.201797i) q^{57} +(12.4770 - 3.34319i) q^{58} +(5.18876 - 8.98720i) q^{59} +(1.64018 - 2.84087i) q^{61} +(0.204604 - 0.763594i) q^{62} +(-12.4660 + 6.75544i) q^{63} -6.23630i q^{64} +(3.74558 + 1.61102i) q^{66} +(0.969129 + 0.259677i) q^{67} +(0.102052 + 0.0273448i) q^{68} +(6.54469 - 4.88303i) q^{69} +(2.97645 + 1.71845i) q^{71} +(-6.49982 - 3.99032i) q^{72} +(-2.93175 - 2.93175i) q^{73} +(-4.65535 + 8.06331i) q^{74} +(-0.0530244 - 0.0918409i) q^{76} +(5.14627 + 5.14627i) q^{77} +(8.24054 - 4.82023i) q^{78} -13.3966i q^{79} +(-8.02565 + 4.07296i) q^{81} +(-3.20790 - 11.9720i) q^{82} +(0.904137 - 0.904137i) q^{83} +(1.64948 + 2.21078i) q^{84} +5.66400i q^{86} +(14.4830 + 2.10590i) q^{87} +(-1.01325 + 3.78151i) q^{88} +(4.15720 + 7.20048i) q^{89} +(16.8492 - 2.54767i) q^{91} +(-1.12326 - 1.12326i) q^{92} +(0.554796 - 0.703171i) q^{93} +(0.939803 - 0.542595i) q^{94} +(-1.29128 + 3.00219i) q^{96} +(-1.32405 - 4.94142i) q^{97} +(6.06836 + 22.6474i) q^{98} +(3.17728 + 3.35357i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 2 q^{3} - 4 q^{6} + 4 q^{7}+O(q^{10}) $ 96 * q + 2 * q^3 - 4 * q^6 + 4 * q^7	$ 96 q + 2 q^{3} - 4 q^{6} + 4 q^{7} + 28 q^{12} + 24 q^{13} + 16 q^{16} - 16 q^{18} - 8 q^{21} + 12 q^{22} + 32 q^{27} + 44 q^{28} + 16 q^{31} + 46 q^{33} - 36 q^{36} - 20 q^{37} - 8 q^{42} + 16 q^{43} - 64 q^{48} + 48 q^{51} + 76 q^{52} - 68 q^{57} + 20 q^{58} + 18 q^{63} + 32 q^{66} + 52 q^{67} - 6 q^{72} - 64 q^{73} - 104 q^{76} - 144 q^{78} + 52 q^{82} - 14 q^{87} - 84 q^{88} + 64 q^{91} - 32 q^{93} - 240 q^{96} - 48 q^{97}+O(q^{100}) $ 96 * q + 2 * q^3 - 4 * q^6 + 4 * q^7 + 28 * q^12 + 24 * q^13 + 16 * q^16 - 16 * q^18 - 8 * q^21 + 12 * q^22 + 32 * q^27 + 44 * q^28 + 16 * q^31 + 46 * q^33 - 36 * q^36 - 20 * q^37 - 8 * q^42 + 16 * q^43 - 64 * q^48 + 48 * q^51 + 76 * q^52 - 68 * q^57 + 20 * q^58 + 18 * q^63 + 32 * q^66 + 52 * q^67 - 6 * q^72 - 64 * q^73 - 104 * q^76 - 144 * q^78 + 52 * q^82 - 14 * q^87 - 84 * q^88 + 64 * q^91 - 32 * q^93 - 240 * q^96 - 48 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/975\mathbb{Z}\right)^\times$.

$n$	$301$	$326$	$352$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.395659	−	1.47662i	0.279773	−	1.04413i	−0.672801	−	0.739823i	$-0.734909\pi$
$2$	0.395659	−	1.47662i	0.279773	−	1.04413i	0.952575	−	0.304305i	$-0.0984241\pi$
$3$	1.07285	−	1.35978i	0.619411	−	0.785067i
$3$	1.07285	−	1.35978i	0.619411	−	0.785067i
$4$	−0.291809	−	0.168476i	−0.145905	−	0.0842381i
$5$		0			0
$5$		0			0
$6$	−1.58339	−	2.12220i	−0.646416	−	0.866385i
$7$	−1.22324	−	4.56520i	−0.462342	−	1.72548i	−0.665556	−	0.746348i	$-0.731805\pi$
$7$	−1.22324	−	4.56520i	−0.462342	−	1.72548i	0.203214	−	0.979134i	$-0.434861\pi$
$8$	1.79769	−	1.79769i	0.635579	−	0.635579i
$9$	−0.697981	−	2.91767i	−0.232660	−	0.972558i
$10$		0			0
$11$	−1.33359	+	0.769949i	−0.402093	+	0.232148i	−0.687387	−	0.726292i	$-0.741242\pi$
$11$	−1.33359	+	0.769949i	−0.402093	+	0.232148i	0.285294	+	0.958440i	$0.407909\pi$
$12$	−0.542158	+	0.216045i	−0.156507	+	0.0623669i
$13$	−0.402017	+	3.58307i	−0.111499	+	0.993765i
$13$	−0.402017	+	3.58307i	−0.111499	+	0.993765i
$14$	−7.22505			−1.93098
$15$		0			0
$16$	−2.28018	−	3.94939i	−0.570046	−	0.987349i
$17$	−0.302869	+	0.0811535i	−0.0734565	+	0.0196826i	−0.295360	−	0.955386i	$-0.595440\pi$
$17$	−0.302869	+	0.0811535i	−0.0734565	+	0.0196826i	0.221904	+	0.975069i	$0.428773\pi$
$18$	−4.58446	−	0.123752i	−1.08057	−	0.0291687i
$19$	0.272564	+	0.157365i	0.0625304	+	0.0361019i	0.530939	−	0.847410i	$-0.321839\pi$
$19$	0.272564	+	0.157365i	0.0625304	+	0.0361019i	−0.468409	+	0.883512i	$0.655173\pi$
$20$		0			0
$21$	−7.52000	−	3.23444i	−1.64100	−	0.705814i
$22$	0.609275	+	2.27384i	0.129898	+	0.484785i
$23$	4.55377	+	1.22018i	0.949526	+	0.254425i	0.700161	−	0.713985i	$-0.253111\pi$
$23$	4.55377	+	1.22018i	0.949526	+	0.254425i	0.249365	+	0.968410i	$0.419778\pi$
$24$	−0.515801	−	4.37311i	−0.105287	−	0.892657i
$25$		0			0
$26$	5.13177	+	2.01130i	1.00642	+	0.394448i
$27$	−4.71621	−	2.18113i	−0.907635	−	0.419759i
$28$	−0.412174	+	1.53825i	−0.0778936	+	0.290703i
$29$	4.22484	+	7.31764i	0.784534	+	1.35885i	0.929277	+	0.369383i	$0.120431\pi$
$29$	4.22484	+	7.31764i	0.784534	+	1.35885i	−0.144744	+	0.989469i	$0.546236\pi$
$30$		0			0
$31$	0.517123			0.0928780			0.0464390	−	0.998921i	$-0.485213\pi$
$31$	0.517123			0.0928780			0.0464390	+	0.998921i	$0.485213\pi$
$32$	−1.82255	+	0.488351i	−0.322185	+	0.0863291i
$33$	−0.383787	+	2.63943i	−0.0668087	+	0.459465i
$34$			0.479331i			0.0822046i
$35$		0			0
$36$	−0.287881	+	0.968998i	−0.0479802	+	0.161500i
$37$	−5.88304	−	1.57635i	−0.967165	−	0.259151i	−0.259535	−	0.965734i	$-0.583569\pi$
$37$	−5.88304	−	1.57635i	−0.967165	−	0.259151i	−0.707630	+	0.706583i	$0.750236\pi$
$38$	0.340210	−	0.340210i	0.0551894	−	0.0551894i
$39$	4.44087	+	4.39075i	0.711108	+	0.703083i
$40$		0			0
$41$	7.02151	−	4.05387i	1.09658	−	0.633108i	0.161256	−	0.986913i	$-0.448446\pi$
$41$	7.02151	−	4.05387i	1.09658	−	0.633108i	0.935319	+	0.353805i	$0.115112\pi$
$42$	−7.75140	+	9.82445i	−1.19607	+	1.51594i
$43$	−3.57884	+	0.958947i	−0.545768	+	0.146238i	−0.521160	−	0.853459i	$-0.674500\pi$
$43$	−3.57884	+	0.958947i	−0.545768	+	0.146238i	−0.0246079	+	0.999697i	$0.507834\pi$
$44$	0.518872			0.0782229
$45$		0			0
$46$	3.60348	−	6.24141i	0.531304	−	0.920246i
$47$	0.501957	+	0.501957i	0.0732179	+	0.0732179i	0.742767	−	0.669550i	$-0.233513\pi$
$47$	0.501957	+	0.501957i	0.0732179	+	0.0732179i	−0.669550	+	0.742767i	$0.733513\pi$
$48$	−7.81659	−	1.13657i	−1.12823	−	0.164050i
$49$	−13.2825	+	7.66868i	−1.89751	+	1.09553i
$50$		0			0
$51$	−0.214583	+	0.498899i	−0.0300476	+	0.0698599i
$52$	0.720974	−	0.977843i	0.0999811	−	0.135602i
$53$	1.53186	−	1.53186i	0.210417	−	0.210417i	−0.594028	−	0.804445i	$-0.702463\pi$
$53$	1.53186	−	1.53186i	0.210417	−	0.210417i	0.804445	+	0.594028i	$0.202463\pi$
$54$	−5.08672	+	6.10107i	−0.692215	+	0.830250i
$55$		0			0
$56$	−10.4058	−	6.00780i	−1.39054	−	0.802826i
$57$	0.506401	−	0.201797i	0.0670744	−	0.0267286i
$58$	12.4770	−	3.34319i	1.63831	−	0.438983i
$59$	5.18876	−	8.98720i	0.675519	−	1.17003i	−0.300797	−	0.953688i	$-0.597253\pi$
$59$	5.18876	−	8.98720i	0.675519	−	1.17003i	0.976317	−	0.216346i	$-0.0694139\pi$
$60$		0			0
$61$	1.64018	−	2.84087i	0.210003	−	0.363737i	−0.741712	−	0.670719i	$-0.765986\pi$
$61$	1.64018	−	2.84087i	0.210003	−	0.363737i	0.951715	+	0.306982i	$0.0993191\pi$
$62$	0.204604	−	0.763594i	0.0259848	−	0.0969765i
$63$	−12.4660	+	6.75544i	−1.57056	+	0.851105i
$64$		−	6.23630i		−	0.779537i
$65$		0			0
$66$	3.74558	+	1.61102i	0.461049	+	0.198303i
$67$	0.969129	+	0.259677i	0.118398	+	0.0317246i	0.317531	−	0.948248i	$-0.397146\pi$
$67$	0.969129	+	0.259677i	0.118398	+	0.0317246i	−0.199134	+	0.979972i	$0.563813\pi$
$68$	0.102052	+	0.0273448i	0.0123757	+	0.00331605i
$69$	6.54469	−	4.88303i	0.787888	−	0.587848i
$70$		0			0
$71$	2.97645	+	1.71845i	0.353239	+	0.203943i	0.666111	−	0.745853i	$-0.267958\pi$
$71$	2.97645	+	1.71845i	0.353239	+	0.203943i	−0.312872	+	0.949795i	$0.601291\pi$
$72$	−6.49982	−	3.99032i	−0.766012	−	0.470264i
$73$	−2.93175	−	2.93175i	−0.343135	−	0.343135i	0.514410	−	0.857545i	$-0.328011\pi$
$73$	−2.93175	−	2.93175i	−0.343135	−	0.343135i	−0.857545	+	0.514410i	$0.828011\pi$
$74$	−4.65535	+	8.06331i	−0.541174	+	0.937341i
$75$		0			0
$76$	−0.0530244	−	0.0918409i	−0.00608232	−	0.0105349i
$77$	5.14627	+	5.14627i	0.586472	+	0.586472i
$78$	8.24054	−	4.82023i	0.933058	−	0.545784i
$79$		−	13.3966i		−	1.50723i	−0.657315	−	0.753616i	$-0.728308\pi$
$79$		−	13.3966i		−	1.50723i	0.657315	−	0.753616i	$-0.271692\pi$
$80$		0			0
$81$	−8.02565	+	4.07296i	−0.891738	+	0.452551i
$82$	−3.20790	−	11.9720i	−0.354253	−	1.32209i
$83$	0.904137	−	0.904137i	0.0992420	−	0.0992420i	−0.655743	−	0.754985i	$-0.727644\pi$
$83$	0.904137	−	0.904137i	0.0992420	−	0.0992420i	0.754985	+	0.655743i	$0.227644\pi$
$84$	1.64948	+	2.21078i	0.179973	+	0.241216i
$85$		0			0
$86$			5.66400i			0.610765i
$87$	14.4830	+	2.10590i	1.55274	+	0.225776i
$88$	−1.01325	+	3.78151i	−0.108013	+	0.403111i
$89$	4.15720	+	7.20048i	0.440662	+	0.763249i	0.997739	−	0.0672121i	$-0.0214104\pi$
$89$	4.15720	+	7.20048i	0.440662	+	0.763249i	−0.557077	+	0.830461i	$0.688077\pi$
$90$		0			0
$91$	16.8492	−	2.54767i	1.76627	−	0.267069i
$92$	−1.12326	−	1.12326i	−0.117108	−	0.117108i
$93$	0.554796	−	0.703171i	0.0575296	−	0.0729154i
$94$	0.939803	−	0.542595i	0.0969332	−	0.0559644i
$95$		0			0
$96$	−1.29128	+	3.00219i	−0.131791	+	0.306410i
$97$	−1.32405	−	4.94142i	−0.134437	−	0.501725i	−1.00000		0.000924660i	$-0.999706\pi$
$97$	−1.32405	−	4.94142i	−0.134437	−	0.501725i	0.865563	−	0.500801i	$-0.166961\pi$
$98$	6.06836	+	22.6474i	0.612997	+	2.28774i
$99$	3.17728	+	3.35357i	0.319329	+	0.337047i
$100$		0			0
$101$	−9.43200	+	5.44557i	−0.938519	+	0.541854i	−0.889496	−	0.456943i	$-0.848944\pi$
$101$	−9.43200	+	5.44557i	−0.938519	+	0.541854i	−0.0490234	+	0.998798i	$0.515611\pi$
$102$	0.651783	+	0.514251i	0.0645361	+	0.0509184i
$103$	8.81215	+	8.81215i	0.868287	+	0.868287i	0.992283	−	0.123996i	$-0.0395710\pi$
$103$	8.81215	+	8.81215i	0.868287	+	0.868287i	−0.123996	+	0.992283i	$0.539571\pi$
$104$	5.71854	+	7.16395i	0.560749	+	0.702483i
$105$		0			0
$106$	−1.65588	−	2.86807i	−0.160833	−	0.278571i
$107$	0.892733	−	3.33172i	0.0863038	−	0.322090i	−0.909254	−	0.416241i	$-0.863347\pi$
$107$	0.892733	−	3.33172i	0.0863038	−	0.322090i	0.995558	+	0.0941514i	$0.0300138\pi$
$108$	1.00877	+	1.43104i	0.0970685	+	0.137702i
$109$		−	3.08340i		−	0.295336i	−0.989037	−	0.147668i	$-0.952823\pi$
$109$		−	3.08340i		−	0.295336i	0.989037	−	0.147668i	$-0.0471767\pi$
$110$		0			0
$111$	−8.45511	+	6.30842i	−0.802524	+	0.598768i
$112$	−15.2406	+	15.2406i	−1.44010	+	1.44010i
$113$	4.20709	+	15.7011i	0.395769	+	1.47703i	0.820466	+	0.571696i	$0.193714\pi$
$113$	4.20709	+	15.7011i	0.395769	+	1.47703i	−0.424696	+	0.905336i	$0.639619\pi$
$114$	−0.0976146	−	0.827604i	−0.00914245	−	0.0775122i
$115$		0			0
$116$		−	2.84714i		−	0.264350i
$117$	10.7348	−	1.32796i	0.992435	−	0.122770i
$118$	−11.2177	−	11.2177i	−1.03267	−	1.03267i
$119$	0.740963	+	1.28339i	0.0679240	+	0.117648i
$120$		0			0
$121$	−4.31436	+	7.47268i	−0.392214	+	0.679335i
$122$	−3.54594	−	3.54594i	−0.321034	−	0.321034i
$123$	2.02068	−	13.8969i	0.182199	−	1.25304i
$124$	−0.150901	−	0.0871229i	−0.0135513	−	0.00782386i
$125$		0			0
$126$	5.04294	+	21.0803i	0.449261	+	1.87799i
$127$	14.8348	+	3.97498i	1.31638	+	0.352722i	0.847620	−	0.530604i	$-0.178035\pi$
$127$	14.8348	+	3.97498i	1.31638	+	0.352722i	0.468758	+	0.883327i	$0.344702\pi$
$128$	−12.8537	−	3.44415i	−1.13612	−	0.304423i
$129$	−2.53561	+	5.89522i	−0.223248	+	0.519045i
$130$		0			0
$131$			10.3934i			0.908079i	0.890981	+	0.454040i	$0.150018\pi$
$131$			10.3934i			0.908079i	−0.890981	+	0.454040i	$0.849982\pi$
$132$	0.556673	−	0.705550i	0.0484522	−	0.0614103i
$133$	0.384990	−	1.43680i	0.0333829	−	0.124587i
$134$	0.766890	−	1.32829i	0.0662492	−	0.114747i
$135$		0			0
$136$	−0.398575	+	0.690353i	−0.0341776	+	0.0591973i
$137$	2.16793	−	0.580896i	0.185219	−	0.0496293i	−0.165017	−	0.986291i	$-0.552768\pi$
$137$	2.16793	−	0.580896i	0.185219	−	0.0496293i	0.350236	+	0.936661i	$0.386101\pi$
$138$	−4.62092	−	11.5960i	−0.393359	−	0.987120i
$139$	13.5163	+	7.80366i	1.14644	+	0.661898i	0.948018	−	0.318218i	$-0.103084\pi$
$139$	13.5163	+	7.80366i	1.14644	+	0.661898i	0.198424	+	0.980116i	$0.436418\pi$
$140$		0			0
$141$	1.22107	−	0.144024i	0.102833	−	0.0121290i
$142$	3.71516	−	3.71516i	0.311769	−	0.311769i
$143$	−2.22266	−	5.08788i	−0.185868	−	0.425470i
$144$	−9.93152	+	9.40943i	−0.827627	+	0.784120i
$145$		0			0
$146$	−5.48905	+	3.16910i	−0.454277	+	0.262277i
$147$	−3.82251	+	26.2886i	−0.315275	+	2.16825i
$148$	1.45115	+	1.45115i	0.119283	+	0.119283i
$149$	9.10942	−	15.7780i	0.746273	−	1.29258i	−0.203325	−	0.979111i	$-0.565175\pi$
$149$	9.10942	−	15.7780i	0.746273	−	1.29258i	0.949598	−	0.313471i	$-0.101492\pi$
$150$		0			0
$151$	1.15188			0.0937386			0.0468693	−	0.998901i	$-0.485076\pi$
$151$	1.15188			0.0937386			0.0468693	+	0.998901i	$0.485076\pi$
$152$	0.772877	−	0.207092i	0.0626886	−	0.0167974i
$153$	0.448176	+	0.827029i	0.0362329	+	0.0668613i
$154$	9.63526	−	5.56292i	0.776431	−	0.448273i
$155$		0			0
$156$	−0.556149	−	2.02944i	−0.0445275	−	0.162485i
$157$	14.1981	−	14.1981i	1.13313	−	1.13313i	0.143476	−	0.989654i	$-0.454172\pi$
$157$	14.1981	−	14.1981i	1.13313	−	1.13313i	0.989654	−	0.143476i	$-0.0458279\pi$
$158$	−19.7816	−	5.30048i	−1.57374	−	0.421683i
$159$	−0.439528	−	3.72644i	−0.0348568	−	0.295526i
$160$		0			0
$161$		−	22.2814i		−	1.75602i
$162$	2.83879	+	13.4623i	0.223037	+	1.05770i
$163$	11.9054	−	3.19005i	0.932506	−	0.249864i	0.239583	−	0.970876i	$-0.422989\pi$
$163$	11.9054	−	3.19005i	0.932506	−	0.249864i	0.692923	+	0.721012i	$0.256323\pi$
$164$	−2.73192			−0.213327
$165$		0			0
$166$	−0.977337	−	1.69280i	−0.0758561	−	0.131387i
$167$	−5.66579	+	21.1450i	−0.438432	+	1.63625i	0.294286	+	0.955717i	$0.404918\pi$
$167$	−5.66579	+	21.1450i	−0.438432	+	1.63625i	−0.732718	+	0.680532i	$0.761749\pi$
$168$	−19.3332	+	7.70410i	−1.49159	+	0.594384i
$169$	−12.6768	−	2.88091i	−0.975136	−	0.221608i
$170$		0			0
$171$	0.268895	−	0.905089i	0.0205629	−	0.0692139i
$172$	1.20590	+	0.323119i	0.0919488	+	0.0246376i
$173$	−1.61031	−	6.00977i	−0.122430	−	0.456915i	0.877305	−	0.479933i	$-0.159339\pi$
$173$	−1.61031	−	6.00977i	−0.122430	−	0.456915i	−0.999735	+	0.0230183i	$0.992672\pi$
$174$	8.83994	−	20.5526i	0.670154	−	1.55809i
$175$		0			0
$176$	6.08167	+	3.51125i	0.458423	+	0.264671i
$177$	−6.65381	−	16.6975i	−0.500131	−	1.25506i
$178$	12.2772	−	3.28967i	0.920215	−	0.246571i
$179$	−11.0651	−	19.1653i	−0.827043	−	1.43248i	−0.900348	−	0.435171i	$-0.856688\pi$
$179$	−11.0651	−	19.1653i	−0.827043	−	1.43248i	0.0733044	−	0.997310i	$-0.476646\pi$
$180$		0			0
$181$	1.45214			0.107937			0.0539685	−	0.998543i	$-0.482813\pi$
$181$	1.45214			0.107937			0.0539685	+	0.998543i	$0.482813\pi$
$182$	2.90459	−	25.8878i	0.215303	−	1.91893i
$183$	−2.10328	−	5.27811i	−0.155479	−	0.390169i
$184$	10.3798	−	5.99276i	0.765206	−	0.441792i
$185$		0			0
$186$	−0.818806	−	1.09744i	−0.0600378	−	0.0804681i
$187$	0.341419	−	0.341419i	0.0249670	−	0.0249670i
$188$	−0.0619079	−	0.231043i	−0.00451509	−	0.0168506i
$189$	−4.18824	+	24.1985i	−0.304650	+	1.76018i
$190$		0			0
$191$	6.15141	+	3.55152i	0.445100	+	0.256979i	0.705759	−	0.708452i	$-0.250606\pi$
$191$	6.15141	+	3.55152i	0.445100	+	0.256979i	−0.260658	+	0.965431i	$0.583940\pi$
$192$	−8.47997	−	6.69062i	−0.611989	−	0.482854i
$193$	−4.79987	+	17.9134i	−0.345502	+	1.28943i	0.546522	+	0.837445i	$0.315952\pi$
$193$	−4.79987	+	17.9134i	−0.345502	+	1.28943i	−0.892024	+	0.451987i	$0.850715\pi$
$194$	−7.82047			−0.561477
$195$		0			0
$196$	5.16796			0.369140
$197$	2.28337	−	8.52164i	0.162683	−	0.607141i	−0.835641	−	0.549276i	$-0.814904\pi$
$197$	2.28337	−	8.52164i	0.162683	−	0.607141i	0.998324	−	0.0578659i	$-0.0184296\pi$
$198$	6.20908	−	3.36476i	0.441260	−	0.239123i
$199$	−7.34287	−	4.23941i	−0.520522	−	0.300524i	0.216626	−	0.976255i	$-0.430495\pi$
$199$	−7.34287	−	4.23941i	−0.520522	−	0.300524i	−0.737148	+	0.675731i	$0.763828\pi$
$200$		0			0
$201$	1.39283	−	1.03920i	0.0982430	−	0.0732997i
$202$	4.30918	+	16.0821i	0.303193	+	1.13153i
$203$	28.2385	−	28.2385i	1.98195	−	1.98195i
$204$	0.146670	−	0.109431i	0.0102689	−	0.00766173i
$205$		0			0
$206$	16.4988	−	9.52559i	1.14953	−	0.663679i
$207$	0.381642	−	14.1381i	0.0265259	−	0.982664i
$208$	15.0676	−	6.58233i	1.04475	−	0.456403i
$209$	−0.484651			−0.0335240
$210$		0			0
$211$	−5.01025	−	8.67800i	−0.344920	−	0.597418i	0.640420	−	0.768025i	$-0.278761\pi$
$211$	−5.01025	−	8.67800i	−0.344920	−	0.597418i	−0.985339	+	0.170607i	$0.945427\pi$
$212$	−0.705092	+	0.188929i	−0.0484259	+	0.0129757i
$213$	5.52999	−	2.20366i	0.378909	−	0.150992i
$214$	−4.56647	−	2.63645i	−0.312158	−	0.180224i
$215$		0			0
$216$	−12.3993	+	4.55728i	−0.843664	+	0.310084i
$217$	−0.632566	−	2.36077i	−0.0429414	−	0.160259i
$218$	−4.55300	−	1.21997i	−0.308368	−	0.0826270i
$219$	−7.13184	+	0.841190i	−0.481925	+	0.0568424i
$220$		0			0
$221$	−0.169020	−	1.11782i	−0.0113695	−	0.0751930i
$222$	5.96979	+	14.9810i	0.400666	+	1.00546i
$223$	1.10003	−	4.10536i	0.0736633	−	0.274915i	−0.919264	−	0.393643i	$-0.871215\pi$
$223$	1.10003	−	4.10536i	0.0736633	−	0.274915i	0.992927	+	0.118727i	$0.0378814\pi$
$224$	4.45884	+	7.72294i	0.297919	+	0.516010i
$225$		0			0
$226$	24.8491			1.65294
$227$	17.0179	−	4.55994i	1.12952	−	0.302654i	0.354790	−	0.934946i	$-0.384552\pi$
$227$	17.0179	−	4.55994i	1.12952	−	0.302654i	0.774730	+	0.632292i	$0.217886\pi$
$228$	−0.181770	−	0.0264304i	−0.0120380	−	0.00175039i
$229$		−	2.21593i		−	0.146433i	−0.997316	−	0.0732163i	$-0.976674\pi$
$229$		−	2.21593i		−	0.146433i	0.997316	−	0.0732163i	$-0.0233263\pi$
$230$		0			0
$231$	12.5190	−	1.47659i	0.823687	−	0.0971527i
$232$	20.7498	+	5.55989i	1.36229	+	0.365025i
$233$	−13.0878	+	13.0878i	−0.857413	+	0.857413i	−0.991033	−	0.133620i	$-0.957340\pi$
$233$	−13.0878	+	13.0878i	−0.857413	+	0.857413i	0.133620	+	0.991033i	$0.457340\pi$
$234$	2.28644	−	16.3767i	0.149469	−	1.07058i
$235$		0			0
$236$	−3.02826	+	1.74837i	−0.197123	+	0.113809i
$237$	−18.2163	−	14.3725i	−1.18328	−	0.933596i
$238$	2.18824	−	0.586338i	0.141843	−	0.0380066i
$239$	−5.02287			−0.324902			−0.162451	−	0.986717i	$-0.551940\pi$
$239$	−5.02287			−0.324902			−0.162451	+	0.986717i	$0.551940\pi$
$240$		0			0
$241$	−6.12257	+	10.6046i	−0.394390	+	0.683103i	−0.993023	−	0.117920i	$-0.962377\pi$
$241$	−6.12257	+	10.6046i	−0.394390	+	0.683103i	0.598634	+	0.801023i	$0.295711\pi$
$242$	9.32730	+	9.32730i	0.599582	+	0.599582i
$243$	−3.07201	+	15.2828i	−0.197070	+	0.980389i
$244$	−0.957239	+	0.552662i	−0.0612810	+	0.0353806i
$245$		0			0
$246$	−19.7209	−	8.48220i	−1.25736	−	0.540805i
$247$	−0.673424	+	0.913351i	−0.0428489	+	0.0581151i
$248$	0.929626	−	0.929626i	0.0590313	−	0.0590313i
$249$	−0.259419	−	2.19943i	−0.0164400	−	0.139383i
$250$		0			0
$251$	6.21474	+	3.58808i	0.392271	+	0.226478i	0.683144	−	0.730284i	$-0.260612\pi$
$251$	6.21474	+	3.58808i	0.392271	+	0.226478i	−0.290873	+	0.956762i	$0.593946\pi$
$252$	4.77581	+	0.128918i	0.300848	+	0.00812106i
$253$	−7.01234	+	1.87895i	−0.440862	+	0.118129i
$254$	11.7391	−	20.3327i	0.736575	−	1.27578i
$255$		0			0
$256$	−3.93510	+	6.81580i	−0.245944	+	0.425987i
$257$	−7.38261	+	27.5523i	−0.460515	+	1.71866i	0.210834	+	0.977522i	$0.432382\pi$
$257$	−7.38261	+	27.5523i	−0.460515	+	1.71866i	−0.671349	+	0.741142i	$0.734285\pi$
$258$	7.70177	+	6.07663i	0.479491	+	0.378314i
$259$			28.7855i			1.78864i
$260$		0			0
$261$	18.4016	−	17.4343i	1.13903	−	1.07916i
$262$	15.3472	+	4.11226i	0.948151	+	0.254056i
$263$	−6.13623	−	1.64420i	−0.378376	−	0.101386i	0.0646180	−	0.997910i	$-0.479417\pi$
$263$	−6.13623	−	1.64420i	−0.378376	−	0.101386i	−0.442994	+	0.896524i	$0.646084\pi$
$264$	4.05494	+	5.43480i	0.249564	+	0.334489i
$265$		0			0
$266$	−1.96929	−	1.13697i	−0.120745	−	0.0697119i
$267$	14.2511	+	2.07218i	0.872152	+	0.126816i
$268$	−0.239051	−	0.239051i	−0.0146024	−	0.0146024i
$269$	−11.4264	+	19.7912i	−0.696681	+	1.20669i	0.272929	+	0.962034i	$0.412008\pi$
$269$	−11.4264	+	19.7912i	−0.696681	+	1.20669i	−0.969611	+	0.244654i	$0.921326\pi$
$270$		0			0
$271$	1.77494	+	3.07429i	0.107820	+	0.186750i	0.914887	−	0.403710i	$-0.132280\pi$
$271$	1.77494	+	3.07429i	0.107820	+	0.186750i	−0.807067	+	0.590460i	$0.798946\pi$
$272$	1.01110	+	1.01110i	0.0613072	+	0.0613072i
$273$	14.6124	−	25.6444i	0.884383	−	1.55207i
$274$		−	3.43105i		−	0.207277i
$275$		0			0
$276$	−2.73247	+	0.322291i	−0.164476	+	0.0193996i
$277$	0.126003	+	0.470249i	0.00757078	+	0.0282545i	0.969608	−	0.244664i	$-0.0786777\pi$
$277$	0.126003	+	0.470249i	0.00757078	+	0.0282545i	−0.962037	+	0.272919i	$0.912011\pi$
$278$	16.8709	−	16.8709i	1.01185	−	1.01185i
$279$	−0.360942	−	1.50880i	−0.0216090	−	0.0903292i
$280$		0			0
$281$		−	6.41544i		−	0.382713i	−0.981521	−	0.191357i	$-0.938711\pi$
$281$		−	6.41544i		−	0.382713i	0.981521	−	0.191357i	$-0.0612887\pi$
$282$	0.270460	−	1.86004i	0.0161057	−	0.110764i
$283$	3.06672	−	11.4452i	0.182298	−	0.680344i	−0.812895	−	0.582410i	$-0.802110\pi$
$283$	3.06672	−	11.4452i	0.182298	−	0.680344i	0.995193	−	0.0979344i	$-0.0312235\pi$
$284$	−0.579037	−	1.00292i	−0.0343595	−	0.0595124i
$285$		0			0
$286$	−8.39228	+	1.26895i	−0.496246	+	0.0750346i
$287$	−27.0957	−	27.0957i	−1.59941	−	1.59941i
$288$	2.69695	+	4.97675i	0.158920	+	0.293258i
$289$	−14.6373	+	8.45084i	−0.861017	+	0.497108i
$290$		0			0
$291$	−8.13973	−	3.50100i	−0.477160	−	0.205232i
$292$	0.361581	+	1.34944i	0.0211599	+	0.0789700i
$293$	−3.32469	−	12.4079i	−0.194230	−	0.724878i	−0.992465	−	0.122531i	$-0.960899\pi$
$293$	−3.32469	−	12.4079i	−0.194230	−	0.724878i	0.798234	−	0.602347i	$-0.205768\pi$
$294$	37.3059	+	16.0457i	2.17572	+	0.935805i
$295$		0			0
$296$	−13.4097	+	7.74207i	−0.779421	+	0.449999i
$297$	7.96886	−	0.722504i	0.462400	−	0.0419239i
$298$	−19.6938	−	19.6938i	−1.14083	−	1.14083i
$299$	−6.20267	+	15.8259i	−0.358710	+	0.915237i
$300$		0			0
$301$	8.75556	+	15.1651i	0.504662	+	0.874101i
$302$	0.455751	−	1.70089i	0.0262255	−	0.0978750i
$303$	−2.71438	+	18.6677i	−0.155937	+	1.07243i
$304$		−	1.43528i		−	0.0823190i
$305$		0			0
$306$	1.39853	−	0.334564i	0.0799488	−	0.0191257i
$307$	−9.25135	+	9.25135i	−0.528003	+	0.528003i	−0.919976	−	0.391974i	$-0.871792\pi$
$307$	−9.25135	+	9.25135i	−0.528003	+	0.528003i	0.391974	+	0.919976i	$0.371792\pi$
$308$	−0.634706	−	2.36876i	−0.0361657	−	0.134972i
$309$	21.4367	−	2.52842i	1.21949	−	0.143837i
$310$		0			0
$311$			11.5380i			0.654259i	0.944979	+	0.327130i	$0.106081\pi$
$311$			11.5380i			0.654259i	−0.944979	+	0.327130i	$0.893919\pi$
$312$	15.8765	−	0.0900894i	0.898830	−	0.00510031i
$313$	8.37161	+	8.37161i	0.473192	+	0.473192i	0.902946	−	0.429754i	$-0.141400\pi$
$313$	8.37161	+	8.37161i	0.473192	+	0.473192i	−0.429754	+	0.902946i	$0.641400\pi$
$314$	−15.3476	−	26.5828i	−0.866113	−	1.50015i
$315$		0			0
$316$	−2.25700	+	3.90924i	−0.126966	+	0.219912i
$317$	−3.70998	−	3.70998i	−0.208373	−	0.208373i	0.595202	−	0.803576i	$-0.297072\pi$
$317$	−3.70998	−	3.70998i	−0.208373	−	0.208373i	−0.803576	+	0.595202i	$0.797072\pi$
$318$	−5.67644	−	0.825385i	−0.318319	−	0.0462853i
$319$	−11.2684	−	6.50583i	−0.630911	−	0.364256i
$320$		0			0
$321$	−3.57263	−	4.78836i	−0.199405	−	0.267260i
$322$	−32.9012	−	8.81585i	−1.83351	−	0.491288i
$323$	−0.0953217	−	0.0255414i	−0.00530384	−	0.00142116i
$324$	3.02815	+	0.163603i	0.168231	+	0.00908904i
$325$		0			0
$326$		−	18.8420i		−	1.04356i
$327$	−4.19273	−	3.30802i	−0.231858	−	0.182934i
$328$	5.33489	−	19.9101i	0.294570	−	1.09935i
$329$	1.67752	−	2.90554i	0.0924845	−	0.160188i
$330$		0			0
$331$	−2.45578	+	4.25354i	−0.134982	+	0.233796i	−0.925591	−	0.378526i	$-0.876431\pi$
$331$	−2.45578	+	4.25354i	−0.134982	+	0.233796i	0.790609	+	0.612322i	$0.209764\pi$
$332$	−0.416161	+	0.111510i	−0.0228398	+	0.00611991i
$333$	−0.493045	+	18.2650i	−0.0270187	+	1.00092i
$334$	28.9814	+	16.7324i	1.58579	+	0.915558i
$335$		0			0
$336$	4.37289	+	37.0746i	0.238561	+	2.02258i
$337$	−7.56647	+	7.56647i	−0.412172	+	0.412172i	−0.882495	−	0.470323i	$-0.844138\pi$
$337$	−7.56647	+	7.56647i	−0.412172	+	0.412172i	0.470323	+	0.882495i	$0.344138\pi$
$338$	−9.26968	+	17.5789i	−0.504204	+	0.956166i
$339$	25.8635	+	11.1242i	1.40471	+	0.604184i
$340$		0			0
$341$	−0.689630	+	0.398158i	−0.0373456	+	0.0215615i
$342$	−1.23008	−	0.755162i	−0.0665152	−	0.0408345i
$343$	27.8631	+	27.8631i	1.50446	+	1.50446i
$344$	−4.70975	+	8.15753i	−0.253933	+	0.439824i
$345$		0			0
$346$	−9.51129			−0.511330
$347$	13.2917	−	3.56149i	0.713534	−	0.191191i	0.116249	−	0.993220i	$-0.462913\pi$
$347$	13.2917	−	3.56149i	0.713534	−	0.191191i	0.597285	+	0.802029i	$0.296246\pi$
$348$	−3.87147	−	3.05456i	−0.207533	−	0.163742i
$349$	−6.13180	+	3.54020i	−0.328228	+	0.189502i	−0.655054	−	0.755582i	$-0.727354\pi$
$349$	−6.13180	+	3.54020i	−0.328228	+	0.189502i	0.326826	+	0.945084i	$0.394021\pi$
$350$		0			0
$351$	9.71115	−	16.0217i	0.518343	−	0.855173i
$352$	2.05453	−	2.05453i	0.109507	−	0.109507i
$353$	28.7628	+	7.70698i	1.53089	+	0.410201i	0.923310	−	0.384056i	$-0.125473\pi$
$353$	28.7628	+	7.70698i	1.53089	+	0.410201i	0.607582	+	0.794257i	$0.292140\pi$
$354$	−27.2885	+	3.21863i	−1.45037	+	0.171068i
$355$		0			0
$356$		−	2.80155i		−	0.148482i
$357$	2.54006	+	0.369338i	0.134434	+	0.0195475i
$358$	−32.6778	+	8.75600i	−1.72708	+	0.462769i
$359$	8.75552			0.462098			0.231049	−	0.972942i	$-0.425784\pi$
$359$	8.75552			0.462098			0.231049	+	0.972942i	$0.425784\pi$
$360$		0			0
$361$	−9.45047	−	16.3687i	−0.497393	−	0.861510i
$362$	0.574554	−	2.14426i	0.0301979	−	0.112700i
$363$	5.53251	+	13.8836i	0.290382	+	0.728702i
$364$	−5.34597	−	2.09525i	−0.280205	−	0.109821i
$365$		0			0
$366$	−8.62595	+	1.01742i	−0.450886	+	0.0531813i
$367$	−12.8730	−	3.44930i	−0.671963	−	0.180052i	−0.0933241	−	0.995636i	$-0.529749\pi$
$367$	−12.8730	−	3.44930i	−0.671963	−	0.180052i	−0.578639	+	0.815584i	$0.696416\pi$
$368$	−5.56446	−	20.7669i	−0.290068	−	1.08255i
$369$	−16.7287	−	17.6569i	−0.870864	−	0.919184i
$370$		0			0
$371$	−8.86707	−	5.11941i	−0.460356	−	0.265786i
$372$	−0.280362	+	0.111722i	−0.0145361	+	0.00579251i
$373$	0.892984	−	0.239274i	0.0462369	−	0.0123892i	−0.235626	−	0.971844i	$-0.575714\pi$
$373$	0.892984	−	0.239274i	0.0462369	−	0.0123892i	0.281863	+	0.959455i	$0.409048\pi$
$374$	−0.369061	−	0.639232i	−0.0190837	−	0.0330539i
$375$		0			0
$376$	1.80472			0.0930715
$377$	−27.9181	+	12.1961i	−1.43785	+	0.628130i
$378$	34.0749	+	15.7588i	1.75262	+	0.810545i
$379$	19.9811	−	11.5361i	1.02636	−	0.592569i	0.110420	−	0.993885i	$-0.464780\pi$
$379$	19.9811	−	11.5361i	1.02636	−	0.592569i	0.915940	+	0.401316i	$0.131447\pi$
$380$		0			0
$381$	21.3206	−	15.9075i	1.09229	−	0.814965i
$382$	7.67810	−	7.67810i	0.392846	−	0.392846i
$383$	−3.89025	−	14.5186i	−0.198782	−	0.741866i	−0.991255	−	0.131959i	$-0.957873\pi$
$383$	−3.89025	−	14.5186i	−0.198782	−	0.741866i	0.792473	−	0.609907i	$-0.208793\pi$
$384$	−18.4734	+	13.7832i	−0.942718	+	0.703369i
$385$		0			0
$386$	24.5521	+	14.1752i	1.24967	+	0.721497i
$387$	5.29585	+	9.77256i	0.269203	+	0.496767i
$388$	−0.446142	+	1.66502i	−0.0226494	+	0.0845287i
$389$	−3.16731			−0.160589			−0.0802944	−	0.996771i	$-0.525586\pi$
$389$	−3.16731			−0.160589			−0.0802944	+	0.996771i	$0.525586\pi$
$390$		0			0
$391$	−1.47822			−0.0747566
$392$	−10.0920	+	37.6638i	−0.509722	+	1.90231i
$393$	14.1328	+	11.1506i	0.712903	+	0.562474i
$394$	−11.6798	−	6.74333i	−0.588419	−	0.339724i
$395$		0			0
$396$	−0.362163	−	1.51390i	−0.0181994	−	0.0760764i
$397$	0.698672	+	2.60748i	0.0350653	+	0.130866i	0.981240	−	0.192792i	$-0.0617542\pi$
$397$	0.698672	+	2.60748i	0.0350653	+	0.130866i	−0.946174	+	0.323657i	$0.895088\pi$
$398$	−9.16527	+	9.16527i	−0.459414	+	0.459414i
$399$	−1.54069	−	2.06497i	−0.0771311	−	0.103378i
$400$		0			0
$401$	−15.5372	+	8.97040i	−0.775890	+	0.447960i	−0.834972	−	0.550293i	$-0.814516\pi$
$401$	−15.5372	+	8.97040i	−0.775890	+	0.447960i	0.0590816	+	0.998253i	$0.481183\pi$
$402$	−0.983420	−	2.46786i	−0.0490486	−	0.123086i
$403$	−0.207892	+	1.85289i	−0.0103558	+	0.0922988i
$404$	3.66979			0.182579
$405$		0			0
$406$	−30.5247	−	52.8703i	−1.51492	−	2.62391i
$407$	9.05928	−	2.42743i	0.449052	−	0.120323i
$408$	0.511113	+	1.28262i	0.0253039	+	0.0634991i
$409$	−7.81117	−	4.50978i	−0.386238	−	0.222994i	0.294291	−	0.955716i	$-0.404916\pi$
$409$	−7.81117	−	4.50978i	−0.386238	−	0.222994i	−0.680529	+	0.732721i	$0.738250\pi$
$410$		0			0
$411$	1.53598	−	3.57112i	0.0757644	−	0.176150i
$412$	−1.08683	−	4.05610i	−0.0535443	−	0.199830i
$413$	−47.3755	−	12.6942i	−2.33119	−	0.624642i
$414$	−20.7256	−	6.15740i	−1.01861	−	0.302620i
$415$		0			0
$416$	−1.01710	−	6.72665i	−0.0498674	−	0.329801i
$417$	25.1123	−	10.0070i	1.22975	−	0.490046i
$418$	−0.191757	+	0.715646i	−0.00937913	+	0.0350034i
$419$	15.5348	+	26.9070i	0.758923	+	1.31449i	0.943400	+	0.331657i	$0.107608\pi$
$419$	15.5348	+	26.9070i	0.758923	+	1.31449i	−0.184477	+	0.982837i	$0.559059\pi$
$420$		0			0
$421$	32.1771			1.56822			0.784108	−	0.620625i	$-0.213121\pi$
$421$	32.1771			1.56822			0.784108	+	0.620625i	$0.213121\pi$
$422$	−14.7965	+	3.96470i	−0.720280	+	0.192999i
$423$	1.11419	−	1.81490i	0.0541738	−	0.0882435i
$424$		−	5.50761i		−	0.267473i
$425$		0			0
$426$	−1.06597	−	9.03760i	−0.0516464	−	0.437873i
$427$	−14.9755	−	4.01267i	−0.724715	−	0.194187i
$428$	−0.821824	+	0.821824i	−0.0397244	+	0.0397244i
$429$	−9.30296	−	2.43623i	−0.449151	−	0.117622i
$430$		0			0
$431$	−22.6638	+	13.0849i	−1.09168	+	0.630279i	−0.934022	−	0.357216i	$-0.883726\pi$
$431$	−22.6638	+	13.0849i	−1.09168	+	0.630279i	−0.157653	+	0.987495i	$0.550393\pi$
$432$	2.13968	+	23.5996i	0.102945	+	1.13543i
$433$	−5.97090	+	1.59990i	−0.286943	+	0.0768861i	−0.399420	−	0.916768i	$-0.630788\pi$
$433$	−5.97090	+	1.59990i	−0.286943	+	0.0768861i	0.112477	+	0.993654i	$0.464122\pi$
$434$	−3.73624			−0.179345
$435$		0			0
$436$	−0.519479	+	0.899763i	−0.0248785	+	0.0430909i
$437$	1.04918	+	1.04918i	0.0501890	+	0.0501890i
$438$	−1.57966	+	10.8638i	−0.0754791	+	0.519095i
$439$	13.8795	−	8.01336i	0.662434	−	0.382457i	−0.130770	−	0.991413i	$-0.541745\pi$
$439$	13.8795	−	8.01336i	0.662434	−	0.382457i	0.793204	+	0.608956i	$0.208411\pi$
$440$		0			0
$441$	31.6457	+	33.4015i	1.50694	+	1.59055i
$442$	−1.71748	−	0.192699i	−0.0816920	−	0.00916576i
$443$	−20.0198	+	20.0198i	−0.951169	+	0.951169i	−0.998862	−	0.0476927i	$-0.984813\pi$
$443$	−20.0198	+	20.0198i	−0.951169	+	0.951169i	0.0476927	+	0.998862i	$0.484813\pi$
$444$	3.53010	−	0.416370i	0.167531	−	0.0197600i
$445$		0			0
$446$	−5.62682	−	3.24865i	−0.266438	−	0.153828i
$447$	−11.6815	−	29.3142i	−0.552514	−	1.38651i
$448$	−28.4699	+	7.62850i	−1.34508	+	0.360413i
$449$	0.678048	−	1.17441i	0.0319991	−	0.0554240i	−0.849582	−	0.527456i	$-0.823146\pi$
$449$	0.678048	−	1.17441i	0.0319991	−	0.0554240i	0.881581	+	0.472032i	$0.156479\pi$
$450$		0			0
$451$	−6.24255	+	10.8124i	−0.293950	+	0.509136i
$452$	1.41759	−	5.29051i	0.0666777	−	0.248845i
$453$	1.23579	−	1.56630i	0.0580627	−	0.0735910i
$454$		−	26.9332i		−	1.26404i
$455$		0			0
$456$	0.547584	−	1.27312i	0.0256430	−	0.0596193i
$457$	2.94651	+	0.789516i	0.137832	+	0.0369320i	0.327076	−	0.944998i	$-0.393937\pi$
$457$	2.94651	+	0.789516i	0.137832	+	0.0369320i	−0.189243	+	0.981930i	$0.560604\pi$
$458$	−3.27208	−	0.876751i	−0.152894	−	0.0409679i
$459$	1.60540	+	0.277860i	0.0749337	+	0.0129694i
$460$		0			0
$461$	16.1818	+	9.34255i	0.753660	+	0.435126i	0.827015	−	0.562180i	$-0.190037\pi$
$461$	16.1818	+	9.34255i	0.753660	+	0.435126i	−0.0733547	+	0.997306i	$0.523371\pi$
$462$	2.77288	−	19.0700i	0.129006	−	0.887216i
$463$	−19.4337	−	19.4337i	−0.903163	−	0.903163i	0.0925456	−	0.995708i	$-0.470500\pi$
$463$	−19.4337	−	19.4337i	−0.903163	−	0.903163i	−0.995708	+	0.0925456i	$0.970500\pi$
$464$	19.2668	−	33.3711i	0.894440	−	1.54922i
$465$		0			0
$466$	14.1474	+	24.5041i	0.655367	+	1.13513i
$467$	21.0969	+	21.0969i	0.976246	+	0.976246i	0.999724	−	0.0234783i	$-0.00747406\pi$
$467$	21.0969	+	21.0969i	0.976246	+	0.976246i	−0.0234783	+	0.999724i	$0.507474\pi$
$468$	−3.35625	−	1.42105i	−0.155143	−	0.0656881i
$469$		−	4.74191i		−	0.218961i
$470$		0			0
$471$	−4.07378	−	34.5386i	−0.187710	−	1.59146i
$472$	−6.82841	−	25.4840i	−0.314303	−	1.17300i
$473$	4.03437	−	4.03437i	0.185500	−	0.185500i
$474$	−28.4302	+	21.2120i	−1.30584	+	0.974299i
$475$		0			0
$476$		−	0.499339i		−	0.0228871i
$477$	−5.53867	−	3.40026i	−0.253598	−	0.155687i
$478$	−1.98734	+	7.41686i	−0.0908989	+	0.339239i
$479$	−8.43633	−	14.6121i	−0.385466	−	0.667646i	0.606368	−	0.795184i	$-0.292626\pi$
$479$	−8.43633	−	14.6121i	−0.385466	−	0.667646i	−0.991834	+	0.127538i	$0.959292\pi$
$480$		0			0
$481$	8.01327	−	20.4456i	0.365373	−	0.932239i
$482$	13.2365	+	13.2365i	0.602907	+	0.602907i
$483$	−30.2977	−	23.9047i	−1.37860	−	1.08770i
$484$	2.51794	−	1.45373i	0.114452	−	0.0660787i
$485$		0			0
$486$	21.3514	+	10.5830i	0.968517	+	0.480053i
$487$	2.56689	+	9.57978i	0.116317	+	0.434101i	0.999382	−	0.0351494i	$-0.0111907\pi$
$487$	2.56689	+	9.57978i	0.116317	+	0.434101i	−0.883065	+	0.469251i	$0.844524\pi$
$488$	−2.15848	−	8.05554i	−0.0977096	−	0.364657i
$489$	8.43501	−	19.6112i	0.381444	−	0.886848i
$490$		0			0
$491$	−24.1136	+	13.9220i	−1.08823	+	0.628291i	−0.933105	−	0.359603i	$-0.882912\pi$
$491$	−24.1136	+	13.9220i	−1.08823	+	0.628291i	−0.155127	+	0.987895i	$0.549579\pi$
$492$	−2.93095	+	3.71480i	−0.132137	+	0.167476i
$493$	−1.87343	−	1.87343i	−0.0843748	−	0.0843748i
$494$	1.08223	+	1.35577i	0.0486917	+	0.0609988i
$495$		0			0
$496$	−1.17913	−	2.04232i	−0.0529447	−	0.0917030i
$497$	4.20416	−	15.6902i	0.188583	−	0.703800i
$498$	−3.35036	−	0.487160i	−0.150133	−	0.0218302i
$499$			33.6386i			1.50587i	0.658094	+	0.752936i	$0.271363\pi$
$499$			33.6386i			1.50587i	−0.658094	+	0.752936i	$0.728637\pi$
$500$		0			0
$501$	22.6739	+	30.3896i	1.01300	+	1.35771i
$502$	7.75716	−	7.75716i	0.346219	−	0.346219i
$503$	5.57421	+	20.8032i	0.248542	+	0.927571i	0.971570	+	0.236752i	$0.0760829\pi$
$503$	5.57421	+	20.8032i	0.248542	+	0.927571i	−0.723028	+	0.690818i	$0.757250\pi$
$504$	−10.2657	+	34.5541i	−0.457273	+	1.53916i
$505$		0			0
$506$			11.0980i			0.493366i
$507$	−17.5177	+	14.1468i	−0.777987	+	0.628280i
$508$	−3.65925	−	3.65925i	−0.162353	−	0.162353i
$509$	18.7696	+	32.5098i	0.831946	+	1.44097i	0.896493	+	0.443059i	$0.146107\pi$
$509$	18.7696	+	32.5098i	0.831946	+	1.44097i	−0.0645462	+	0.997915i	$0.520560\pi$
$510$		0			0
$511$	−9.79777	+	16.9702i	−0.433428	+	0.750719i
$512$	−10.3118	−	10.3118i	−0.455722	−	0.455722i
$513$	−0.942235	−	1.33666i	−0.0416007	−	0.0590151i
$514$	37.7632	+	21.8026i	1.66566	+	0.961672i
$515$		0			0
$516$	1.73312	−	1.29309i	0.0762963	−	0.0569252i
$517$	−1.05589	−	0.282924i	−0.0464378	−	0.0124430i
$518$	42.5052	+	11.3892i	1.86757	+	0.500414i
$519$	−9.89957	−	4.25793i	−0.434543	−	0.186902i
$520$		0			0
$521$		−	9.92485i		−	0.434815i	−0.976081	−	0.217408i	$-0.930240\pi$
$521$		−	9.92485i		−	0.434815i	0.976081	−	0.217408i	$-0.0697601\pi$
$522$	−18.4630	−	34.0703i	−0.808105	−	1.49121i
$523$	3.31160	−	12.3591i	0.144806	−	0.540424i	−0.854958	−	0.518698i	$-0.826417\pi$
$523$	3.31160	−	12.3591i	0.144806	−	0.540424i	0.999764	−	0.0217263i	$-0.00691625\pi$
$524$	1.75105	−	3.03290i	0.0764949	−	0.132493i
$525$		0			0
$526$	−4.85571	+	8.41034i	−0.211719	+	0.366708i
$527$	−0.156620	+	0.0419663i	−0.00682249	+	0.00182808i
$528$	11.2992	−	4.50265i	0.491736	−	0.195953i
$529$	−0.670613	−	0.387179i	−0.0291571	−	0.0168338i
$530$		0			0
$531$	−29.8434	−	8.86623i	−1.29509	−	0.384762i
$532$	−0.354410	+	0.354410i	−0.0153656	+	0.0153656i
$533$	11.7025	+	26.7883i	0.506893	+	1.16033i
$534$	8.69840	−	20.2236i	0.376417	−	0.875159i
$535$		0			0
$536$	2.20901	−	1.27537i	0.0954148	−	0.0550878i
$537$	−37.9317	−	5.51547i	−1.63687	−	0.238010i
$538$	24.7030	+	24.7030i	1.06502	+	1.06502i
$539$	11.8090	−	20.4538i	0.508649	−	0.881006i
$540$		0			0
$541$	−35.5969			−1.53043			−0.765214	−	0.643776i	$-0.777367\pi$
$541$	−35.5969			−1.53043			−0.765214	+	0.643776i	$0.777367\pi$
$542$	5.24182	−	1.40454i	0.225156	−	0.0603303i
$543$	1.55793	−	1.97459i	0.0668573	−	0.0847377i
$544$	0.512363	−	0.295813i	0.0219674	−	0.0126829i
$545$		0			0
$546$	−32.0855	−	31.7234i	−1.37313	−	1.35764i
$547$	−17.8066	+	17.8066i	−0.761357	+	0.761357i	−0.976568	−	0.215211i	$-0.930956\pi$
$547$	−17.8066	+	17.8066i	−0.761357	+	0.761357i	0.215211	+	0.976568i	$0.430956\pi$
$548$	−0.730490	−	0.195734i	−0.0312050	−	0.00836135i
$549$	−9.43356	−	2.80263i	−0.402614	−	0.119614i
$550$		0			0
$551$			2.65936i			0.113293i
$552$	2.98713	−	20.5435i	0.127141	−	0.874389i
$553$	−61.1580	+	16.3872i	−2.60070	+	0.696856i
$554$	0.744234			0.0316195
$555$		0			0
$556$	−2.62946	−	4.55436i	−0.111514	−	0.193148i
$557$	3.29990	−	12.3154i	0.139821	−	0.521820i	−0.860110	−	0.510108i	$-0.829605\pi$
$557$	3.29990	−	12.3154i	0.139821	−	0.521820i	0.999931	−	0.0117118i	$-0.00372807\pi$
$558$	−2.37073	−	0.0639952i	−0.100361	−	0.00270913i
$559$	−1.99722	−	13.2087i	−0.0844734	−	0.558670i
$560$		0			0
$561$	−0.0979615	−	0.830545i	−0.00413594	−	0.0350657i
$562$	−9.47317	−	2.53833i	−0.399602	−	0.107073i
$563$	−1.31304	−	4.90034i	−0.0553381	−	0.206525i	0.932721	−	0.360598i	$-0.117427\pi$
$563$	−1.31304	−	4.90034i	−0.0553381	−	0.206525i	−0.988059	+	0.154073i	$0.950761\pi$
$564$	−0.380585	−	0.163694i	−0.0160255	−	0.00689277i
$565$		0			0
$566$	−15.6868	−	9.05677i	−0.659365	−	0.380684i
$567$	28.4112	+	31.6565i	1.19316	+	1.32945i
$568$	8.43997	−	2.26148i	0.354133	−	0.0948897i
$569$	−2.83450	−	4.90950i	−0.118829	−	0.205817i	0.800475	−	0.599366i	$-0.204581\pi$
$569$	−2.83450	−	4.90950i	−0.118829	−	0.205817i	−0.919304	+	0.393549i	$0.871247\pi$
$570$		0			0
$571$	−17.6465			−0.738481			−0.369240	−	0.929334i	$-0.620382\pi$
$571$	−17.6465			−0.738481			−0.369240	+	0.929334i	$0.620382\pi$
$572$	−0.208595	+	1.85916i	−0.00872181	+	0.0777352i
$573$	11.4288	−	4.55429i	0.477446	−	0.190258i
$574$	−50.7307	+	29.2894i	−2.11746	+	1.22252i
$575$		0			0
$576$	−18.1955	+	4.35282i	−0.758145	+	0.181367i
$577$	12.7836	−	12.7836i	0.532188	−	0.532188i	−0.389035	−	0.921223i	$-0.627192\pi$
$577$	12.7836	−	12.7836i	0.532188	−	0.532188i	0.921223	+	0.389035i	$0.127192\pi$
$578$	6.68731	+	24.9574i	0.278155	+	1.03809i
$579$	19.2086	+	25.7451i	0.798283	+	1.06993i
$580$		0			0
$581$	−5.23354	−	3.02159i	−0.217124	−	0.125357i
$582$	−8.39020	+	10.6341i	−0.347785	+	0.440797i
$583$	−0.863420	+	3.22233i	−0.0357592	+	0.133455i
$584$	−10.5407			−0.436179
$585$		0			0
$586$	−19.6372			−0.811205
$587$	−1.55743	+	5.81240i	−0.0642819	+	0.239903i	−0.990590	−	0.136864i	$-0.956298\pi$
$587$	−1.55743	+	5.81240i	−0.0642819	+	0.239903i	0.926308	+	0.376767i	$0.122964\pi$
$588$	5.54445	−	7.02726i	0.228649	−	0.289799i
$589$	0.140949	+	0.0813769i	0.00580770	+	0.00335307i
$590$		0			0
$591$	−9.13780	−	12.2473i	−0.375879	−	0.503787i
$592$	7.18876	+	26.8288i	0.295456	+	1.10266i
$593$	−16.4055	+	16.4055i	−0.673691	+	0.673691i	−0.958565	−	0.284874i	$-0.908048\pi$
$593$	−16.4055	+	16.4055i	−0.673691	+	0.673691i	0.284874	+	0.958565i	$0.408048\pi$
$594$	2.08609	−	12.0528i	0.0855933	−	0.494534i
$595$		0			0
$596$	−5.31643	+	3.06944i	−0.217769	+	0.125729i
$597$	−13.6425	+	5.43641i	−0.558349	+	0.222497i
$598$	20.9147	+	15.4207i	0.855267	+	0.630598i
$599$	−26.4602			−1.08114			−0.540568	−	0.841301i	$-0.681790\pi$
$599$	−26.4602			−1.08114			−0.540568	+	0.841301i	$0.681790\pi$
$600$		0			0
$601$	11.1821	+	19.3680i	0.456127	+	0.790036i	0.998752	−	0.0499395i	$-0.0159029\pi$
$601$	11.1821	+	19.3680i	0.456127	+	0.790036i	−0.542625	+	0.839975i	$0.682570\pi$
$602$	25.8573	−	6.92844i	1.05386	−	0.282382i
$603$	0.0812207	−	3.00885i	0.00330756	−	0.122530i
$604$	−0.336129	−	0.194064i	−0.0136769	−	0.00789636i
$605$		0			0
$606$	26.4911	+	11.3942i	1.07613	+	0.462856i
$607$	−0.479507	−	1.78954i	−0.0194626	−	0.0726354i	0.955512	−	0.294954i	$-0.0953042\pi$
$607$	−0.479507	−	1.78954i	−0.0194626	−	0.0726354i	−0.974974	+	0.222318i	$0.928638\pi$
$608$	−0.573610	−	0.153698i	−0.0232630	−	0.00623329i
$609$	−8.10232	−	68.6937i	−0.328322	−	2.78361i
$610$		0			0
$611$	−2.00034	+	1.59675i	−0.0809251	+	0.0645976i
$612$	0.00855280	−	0.316842i	0.000345726	−	0.0128076i
$613$	−6.50251	+	24.2677i	−0.262634	+	0.980162i	0.701049	+	0.713113i	$0.252715\pi$
$613$	−6.50251	+	24.2677i	−0.262634	+	0.980162i	−0.963683	+	0.267049i	$0.913951\pi$
$614$	10.0003	+	17.3211i	0.403581	+	0.699023i
$615$		0			0
$616$	18.5028			0.745499
$617$	−18.6076	+	4.98588i	−0.749113	+	0.200724i	−0.613124	−	0.789986i	$-0.710088\pi$
$617$	−18.6076	+	4.98588i	−0.749113	+	0.200724i	−0.135988	+	0.990710i	$0.543421\pi$
$618$	4.74810	−	32.6542i	0.190996	−	1.31354i
$619$			14.2527i			0.572865i	0.958100	+	0.286433i	$0.0924695\pi$
$619$			14.2527i			0.572865i	−0.958100	+	0.286433i	$0.907531\pi$
$620$		0			0
$621$	−18.8152	−	15.6870i	−0.755027	−	0.629498i
$622$	17.0372	+	4.56511i	0.683130	+	0.183044i
$623$	27.7863	−	27.7863i	1.11324	−	1.11324i
$624$	7.21482	−	27.5505i	0.288824	−	1.10290i
$625$		0			0
$626$	15.6740	−	9.04939i	0.626459	−	0.361686i
$627$	−0.519959	+	0.659017i	−0.0207651	+	0.0263186i
$628$	−6.53517	+	1.75109i	−0.260782	+	0.0698762i
$629$	1.90971			0.0761453
$630$		0			0
$631$	−19.3413	+	33.5002i	−0.769966	+	1.33362i	0.167615	+	0.985853i	$0.446394\pi$
$631$	−19.3413	+	33.5002i	−0.769966	+	1.33362i	−0.937581	+	0.347768i	$0.886940\pi$
$632$	−24.0829	−	24.0829i	−0.957965	−	0.957965i
$633$	−17.1754	−	2.49739i	−0.682660	−	0.0992625i
$634$	−6.94612	+	4.01034i	−0.275866	+	0.159271i
$635$		0			0
$636$	−0.499558	+	1.16146i	−0.0198088	+	0.0460549i
$637$	−22.1376	−	50.6752i	−0.877123	−	2.00782i
$638$	−14.0651	+	14.0651i	−0.556842	+	0.556842i
$639$	2.93638	−	9.88375i	0.116161	−	0.390995i
$640$		0			0
$641$	16.6960	+	9.63941i	0.659450	+	0.380734i	0.792068	−	0.610433i	$-0.209005\pi$
$641$	16.6960	+	9.63941i	0.659450	+	0.380734i	−0.132617	+	0.991167i	$0.542338\pi$
$642$	−8.48413	+	3.38086i	−0.334842	+	0.133432i
$643$	25.3451	−	6.79119i	0.999511	−	0.267818i	0.278271	−	0.960503i	$-0.410239\pi$
$643$	25.3451	−	6.79119i	0.999511	−	0.267818i	0.721241	+	0.692684i	$0.243572\pi$
$644$	−3.75389	+	6.50193i	−0.147924	+	0.256212i
$645$		0			0
$646$	−0.0754298	+	0.130648i	−0.00296775	+	0.00514029i
$647$	5.34525	−	19.9488i	0.210144	−	0.784267i	−0.777676	−	0.628665i	$-0.783602\pi$
$647$	5.34525	−	19.9488i	0.210144	−	0.784267i	0.987820	−	0.155602i	$-0.0497317\pi$
$648$	−7.10570	+	21.7495i	−0.279138	+	0.854402i
$649$			15.9803i			0.627283i
$650$		0			0
$651$	−3.88876	−	1.67260i	−0.152413	−	0.0655546i
$652$	−4.01157	−	1.07490i	−0.157105	−	0.0420962i
$653$	4.89904	+	1.31270i	0.191714	+	0.0513697i	0.353399	−	0.935473i	$-0.385026\pi$
$653$	4.89904	+	1.31270i	0.191714	+	0.0513697i	−0.161684	+	0.986843i	$0.551693\pi$
$654$	−6.54359	+	4.88221i	−0.255874	+	0.190910i
$655$		0			0
$656$	−32.0207	−	18.4871i	−1.25020	−	0.721801i
$657$	−6.50758	+	10.6002i	−0.253885	+	0.413552i
$658$	−3.62666	−	3.62666i	−0.141382	−	0.141382i
$659$	−0.324643	+	0.562298i	−0.0126463	+	0.0219040i	−0.872279	−	0.489008i	$-0.837359\pi$
$659$	−0.324643	+	0.562298i	−0.0126463	+	0.0219040i	0.859633	+	0.510912i	$0.170692\pi$
$660$		0			0
$661$	6.78399	+	11.7502i	0.263867	+	0.457031i	0.967266	−	0.253764i	$-0.0816687\pi$
$661$	6.78399	+	11.7502i	0.263867	+	0.457031i	−0.703399	+	0.710795i	$0.748335\pi$
$662$	5.30921	+	5.30921i	0.206348	+	0.206348i
$663$	−1.70132	−	0.969430i	−0.0660740	−	0.0376496i
$664$		−	3.25072i		−	0.126152i
$665$		0			0
$666$	26.7755	+	7.95477i	1.03753	+	0.308241i
$667$	10.3101	+	38.4779i	0.399210	+	1.48987i
$668$	5.21576	−	5.21576i	0.201804	−	0.201804i
$669$	−4.40220	−	5.90023i	−0.170199	−	0.228116i
$670$		0			0
$671$			5.05142i			0.195008i
$672$	15.2851	+	2.22254i	0.589637	+	0.0857363i
$673$	9.24375	−	34.4981i	0.356320	−	1.32981i	−0.522495	−	0.852643i	$-0.674999\pi$
$673$	9.24375	−	34.4981i	0.356320	−	1.32981i	0.878815	−	0.477163i	$-0.158335\pi$
$674$	8.17906	+	14.1665i	0.315046	+	0.545675i
$675$		0			0
$676$	3.21383	+	2.97641i	0.123609	+	0.114477i
$677$	−20.3740	−	20.3740i	−0.783036	−	0.783036i	0.197306	−	0.980342i	$-0.436781\pi$
$677$	−20.3740	−	20.3740i	−0.783036	−	0.783036i	−0.980342	+	0.197306i	$0.936781\pi$
$678$	26.6594	−	33.7892i	1.02385	−	1.29767i
$679$	−20.9389	+	12.0891i	−0.803562	+	0.463937i
$680$		0			0
$681$	12.0572	−	28.0327i	0.462033	−	1.07422i
$682$	0.315070	+	1.17586i	0.0120646	+	0.0450259i
$683$	10.4105	+	38.8525i	0.398347	+	1.48665i	0.816004	+	0.578046i	$0.196185\pi$
$683$	10.4105	+	38.8525i	0.398347	+	1.48665i	−0.417657	+	0.908605i	$0.637149\pi$
$684$	−0.230952	+	0.218811i	−0.00883067	+	0.00836645i
$685$		0			0
$686$	52.1674	−	30.1189i	1.99176	−	1.14994i
$687$	−3.01316	−	2.37736i	−0.114959	−	0.0907019i
$688$	11.9477	+	11.9477i	0.455500	+	0.455500i
$689$	4.87292	+	6.10459i	0.185644	+	0.232566i
$690$		0			0
$691$	−15.7859	−	27.3420i	−0.600525	−	1.04014i	−0.992742	−	0.120267i	$-0.961625\pi$
$691$	−15.7859	−	27.3420i	−0.600525	−	1.04014i	0.392216	−	0.919873i	$-0.371709\pi$
$692$	−0.542599	+	2.02501i	−0.0206265	+	0.0769792i
$693$	11.4232	−	18.6072i	0.433930	−	0.706827i
$694$		−	21.0359i		−	0.798511i
$695$		0			0
$696$	29.8217	−	22.2501i	1.13039	−	0.843389i
$697$	−1.79761	+	1.79761i	−0.0680893	+	0.0680893i
$698$	2.80142	+	10.4551i	0.106035	+	0.395730i
$699$	3.75522	+	31.8378i	0.142036	+	1.20422i
$700$		0			0
$701$		−	35.6849i		−	1.34780i	−0.738822	−	0.673901i	$-0.764618\pi$
$701$		−	35.6849i		−	1.34780i	0.738822	−	0.673901i	$-0.235382\pi$
$702$	−19.8156	−	20.6788i	−0.747892	−	0.780471i
$703$	−1.35544	−	1.35544i	−0.0511213	−	0.0511213i
$704$	4.80163	+	8.31667i	0.180968	+	0.313446i
$705$		0			0
$706$	22.7606	−	39.4224i	0.856605	−	1.48368i
$707$	36.3977	+	36.3977i	1.36888	+	1.36888i
$708$	−0.871485	+	5.99349i	−0.0327524	+	0.225249i
$709$	−9.62223	−	5.55540i	−0.361371	−	0.208637i	0.308311	−	0.951286i	$-0.400236\pi$
$709$	−9.62223	−	5.55540i	−0.361371	−	0.208637i	−0.669682	+	0.742648i	$0.733570\pi$
$710$		0			0
$711$	−39.0868	+	9.35055i	−1.46587	+	0.350673i
$712$	20.4176	+	5.47087i	0.765181	+	0.205030i
$713$	2.35486	+	0.630982i	0.0881901	+	0.0236305i
$714$	1.55037	−	3.60457i	0.0580211	−	0.134898i
$715$		0			0
$716$			7.45681i			0.278674i
$717$	−5.38879	+	6.82997i	−0.201248	+	0.255070i
$718$	3.46420	−	12.9286i	0.129283	−	0.482490i
$719$	−6.00581	+	10.4024i	−0.223979	+	0.387943i	−0.956013	−	0.293325i	$-0.905238\pi$
$719$	−6.00581	+	10.4024i	−0.223979	+	0.387943i	0.732034	+	0.681269i	$0.238571\pi$
$720$		0			0
$721$	29.4498	−	51.0086i	1.09677	−	1.89966i
$722$	−27.9095	+	7.47833i	−1.03868	+	0.278315i
$723$	7.85128	+	19.7025i	0.291992	+	0.732743i
$724$	−0.423749	−	0.244652i	−0.0157485	−	0.00909240i
$725$		0			0
$726$	22.6898	−	2.67623i	0.842099	−	0.0993243i
$727$	−24.8496	+	24.8496i	−0.921620	+	0.921620i	−0.997144	−	0.0755236i	$-0.975937\pi$
$727$	−24.8496	+	24.8496i	−0.921620	+	0.921620i	0.0755236	+	0.997144i	$0.475937\pi$
$728$	25.7097	−	34.8695i	0.952864	−	1.29235i
$729$	17.4853	+	20.5734i	0.647604	+	0.761977i
$730$		0			0
$731$	1.00610	−	0.580870i	0.0372118	−	0.0214843i
$732$	−0.275478	+	1.89456i	−0.0101820	+	0.0700248i
$733$	−34.2228	−	34.2228i	−1.26405	−	1.26405i	−0.949113	−	0.314936i	$-0.898017\pi$
$733$	−34.2228	−	34.2228i	−1.26405	−	1.26405i	−0.314936	−	0.949113i	$-0.601983\pi$
$734$	−10.1866	+	17.6437i	−0.375995	+	0.651242i
$735$		0			0
$736$	−8.89535			−0.327887
$737$	−1.49236	+	0.399877i	−0.0549718	+	0.0147296i
$738$	−32.6915	+	17.7159i	−1.20339	+	0.652130i
$739$	22.2251	−	12.8316i	0.817562	−	0.472020i	−0.0320128	−	0.999487i	$-0.510192\pi$
$739$	22.2251	−	12.8316i	0.817562	−	0.472020i	0.849575	+	0.527468i	$0.176858\pi$
$740$		0			0
$741$	0.519469	+	1.89559i	0.0190832	+	0.0696364i
$742$	−11.0678	+	11.0678i	−0.406310	+	0.406310i
$743$	33.7228	+	9.03600i	1.23717	+	0.331499i	0.817367	−	0.576117i	$-0.195433\pi$
$743$	33.7228	+	9.03600i	1.23717	+	0.331499i	0.419803	+	0.907615i	$0.362099\pi$
$744$	−0.266733	−	2.26143i	−0.00977889	−	0.0829082i
$745$		0			0
$746$		−	1.41327i		−	0.0517434i
$747$	−3.26905	−	2.00691i	−0.119608	−	0.0734289i
$748$	−0.157150	+	0.0421083i	−0.00574598	+	0.00153963i
$749$	−16.3020			−0.595663
$750$		0			0
$751$	18.4173	+	31.8998i	0.672058	+	1.16404i	0.977320	+	0.211770i	$0.0679228\pi$
$751$	18.4173	+	31.8998i	0.672058	+	1.16404i	−0.305262	+	0.952269i	$0.598744\pi$
$752$	0.837871	−	3.12698i	0.0305540	−	0.114029i
$753$	11.5465	−	4.60118i	0.420777	−	0.167676i
$754$	6.96295	+	46.0499i	0.253576	+	1.67704i
$755$		0			0
$756$	5.29904	−	6.35573i	0.192724	−	0.231156i
$757$	2.36847	+	0.634630i	0.0860835	+	0.0230660i	0.301604	−	0.953433i	$-0.402478\pi$
$757$	2.36847	+	0.634630i	0.0860835	+	0.0230660i	−0.215520	+	0.976499i	$0.569145\pi$
$758$	−9.12872	−	34.0688i	−0.331570	−	1.23744i
$759$	−4.96825	+	11.5510i	−0.180336	+	0.419276i
$760$		0			0
$761$	32.3914	+	18.7012i	1.17419	+	0.677918i	0.954663	−	0.297688i	$-0.0962156\pi$
$761$	32.3914	+	18.7012i	1.17419	+	0.677918i	0.219526	+	0.975607i	$0.429549\pi$
$762$	−15.0536	−	37.7764i	−0.545334	−	1.36850i
$763$	−14.0763	+	3.77174i	−0.509597	+	0.136546i
$764$	−1.19669	−	2.07273i	−0.0432948	−	0.0749888i
$765$		0			0
$766$	−22.9777			−0.830217
$767$	30.1158	+	22.2047i	1.08742	+	0.801765i
$768$	5.04618	+	12.6632i	0.182088	+	0.456944i
$769$	−39.6657	+	22.9010i	−1.43038	+	0.825832i	−0.997150	−	0.0754505i	$-0.975961\pi$
$769$	−39.6657	+	22.9010i	−1.43038	+	0.825832i	−0.433233	+	0.901282i	$0.642627\pi$
$770$		0			0
$771$	29.5445	+	39.5982i	1.06402	+	1.42609i
$772$	4.41862	−	4.41862i	0.159030	−	0.159030i
$773$	−12.5182	−	46.7186i	−0.450249	−	1.68035i	−0.701692	−	0.712481i	$-0.747572\pi$
$773$	−12.5182	−	46.7186i	−0.450249	−	1.68035i	0.251443	−	0.967872i	$-0.419095\pi$
$774$	16.5257	−	3.95336i	0.594004	−	0.142101i
$775$		0			0
$776$	−11.2634	−	6.50291i	−0.404331	−	0.233441i
$777$	39.1418	+	30.8825i	1.40420	+	1.10791i
$778$	−1.25317	+	4.67691i	−0.0449284	+	0.167675i
$779$	2.55174			0.0914257
$780$		0			0
$781$	−5.29248			−0.189380
$782$	−0.584870	+	2.18276i	−0.0209149	+	0.0780555i
$783$	−3.96450	−	43.7265i	−0.141680	−	1.56266i
$784$	60.5733	+	34.9720i	2.16333	+	1.24900i
$785$		0			0
$786$	22.0570	−	16.4569i	0.786746	−	0.586997i
$787$	−9.86610	−	36.8208i	−0.351688	−	1.31252i	−0.884601	−	0.466349i	$-0.845569\pi$
$787$	−9.86610	−	36.8208i	−0.351688	−	1.31252i	0.532913	−	0.846170i	$-0.321097\pi$
$788$	−2.10200	+	2.10200i	−0.0748806	+	0.0748806i
$789$	−8.81900	+	6.57992i	−0.313965	+	0.234251i
$790$		0			0
$791$	66.5322	−	38.4124i	2.36561	−	1.36579i
$792$	11.7405	+	0.316921i	0.417179	+	0.0112613i
$793$	9.51967	+	7.01896i	0.338053	+	0.249250i
$794$	4.12669			0.146451
$795$		0			0
$796$	1.42848	+	2.47420i	0.0506311	+	0.0876956i
$797$	11.4219	−	3.06050i	0.404586	−	0.108408i	−0.0507866	−	0.998710i	$-0.516173\pi$
$797$	11.4219	−	3.06050i	0.404586	−	0.108408i	0.455372	+	0.890301i	$0.349506\pi$
$798$	−3.65877	+	1.45799i	−0.129519	+	0.0516123i
$799$	−0.192762	−	0.111291i	−0.00681945	−	0.00393721i
$800$		0			0
$801$	18.1070	−	17.1551i	0.639779	−	0.606147i
$802$	7.09844	+	26.4917i	0.250655	+	0.935456i
$803$	6.16705	+	1.65245i	0.217630	+	0.0583139i
$804$	−0.581523	+	0.0685897i	−0.0205087	+	0.00241897i
$805$		0			0
$806$	2.65375	+	1.04009i	0.0934745	+	0.0366356i
$807$	14.6527	+	36.7703i	0.515799	+	1.29438i
$808$	−7.16637	+	26.7452i	−0.252112	+	0.940895i
$809$	−24.8889	−	43.1089i	−0.875048	−	1.51563i	−0.856711	−	0.515796i	$-0.827496\pi$
$809$	−24.8889	−	43.1089i	−0.875048	−	1.51563i	−0.0183367	−	0.999832i	$-0.505837\pi$
$810$		0			0
$811$	−25.7526			−0.904295			−0.452147	−	0.891943i	$-0.649342\pi$
$811$	−25.7526			−0.904295			−0.452147	+	0.891943i	$0.649342\pi$
$812$	−12.9978	+	3.48274i	−0.456132	+	0.122220i
$813$	6.08459	+	0.884731i	0.213396	+	0.0310289i
$814$		−	14.3375i		−	0.502531i
$815$		0			0
$816$	2.45964	−	0.290110i	0.0861046	−	0.0101559i
$817$	−1.12637	−	0.301809i	−0.0394065	−	0.0105589i
$818$	−9.74979	+	9.74979i	−0.340894	+	0.340894i
$819$	−19.1937	−	47.3822i	−0.670681	−	1.65567i
$820$		0			0
$821$	2.25764	−	1.30345i	0.0787922	−	0.0454907i	−0.460086	−	0.887874i	$-0.652182\pi$
$821$	2.25764	−	1.30345i	0.0787922	−	0.0454907i	0.538878	+	0.842384i	$0.318848\pi$
$822$	−4.66546	−	3.68101i	−0.162727	−	0.128390i
$823$	−31.8920	+	8.54545i	−1.11169	+	0.297875i	−0.767515	−	0.641031i	$-0.778507\pi$
$823$	−31.8920	+	8.54545i	−1.11169	+	0.297875i	−0.344172	+	0.938907i	$0.611840\pi$
$824$	31.6830			1.10373
$825$		0			0
$826$	−37.4891	+	64.9330i	−1.30441	+	2.25931i
$827$	−24.3594	−	24.3594i	−0.847058	−	0.847058i	0.142707	−	0.989765i	$-0.454419\pi$
$827$	−24.3594	−	24.3594i	−0.847058	−	0.847058i	−0.989765	+	0.142707i	$0.954419\pi$
$828$	−2.49330	+	4.06132i	−0.0866480	+	0.141141i
$829$	32.5322	−	18.7825i	1.12989	−	0.652342i	0.185983	−	0.982553i	$-0.440453\pi$
$829$	32.5322	−	18.7825i	1.12989	−	0.652342i	0.943907	+	0.330211i	$0.107120\pi$
$830$		0			0
$831$	0.774616	+	0.333172i	0.0268711	+	0.0115576i
$832$	22.3451	+	2.50710i	0.774677	+	0.0869179i
$833$	3.40053	−	3.40053i	0.117821	−	0.117821i
$834$	−4.84068	−	41.0406i	−0.167619	−	1.42112i
$835$		0			0
$836$	0.141426	+	0.0816522i	0.00489131	+	0.00282400i
$837$	−2.43886	−	1.12791i	−0.0842994	−	0.0389864i
$838$	45.8779	−	12.2929i	1.58483	−	0.424653i
$839$	11.9784	−	20.7472i	0.413539	−	0.716271i	−0.581735	−	0.813379i	$-0.697626\pi$
$839$	11.9784	−	20.7472i	0.413539	−	0.716271i	0.995274	+	0.0971075i	$0.0309591\pi$
$840$		0			0
$841$	−21.1986	+	36.7170i	−0.730986	+	1.26610i
$842$	12.7312	−	47.5133i	0.438745	−	1.63742i
$843$	−8.72356	−	6.88281i	−0.300455	−	0.237057i
$844$			3.37643i			0.116221i
$845$		0			0
$846$	−2.23908	−	2.36332i	−0.0769812	−	0.0812525i
$847$	39.3918	+	10.5550i	1.35352	+	0.362674i
$848$	−9.54284	−	2.55700i	−0.327702	−	0.0878076i
$849$	−12.2727	−	16.4490i	−0.421199	−	0.564529i
$850$		0			0
$851$	−24.8665	−	14.3567i	−0.852414	−	0.492142i
$852$	−1.98497	−	0.288625i	−0.0680039	−	0.00988812i
$853$	−39.8147	−	39.8147i	−1.36323	−	1.36323i	−0.869767	−	0.493462i	$-0.835731\pi$
$853$	−39.8147	−	39.8147i	−1.36323	−	1.36323i	−0.493462	−	0.869767i	$-0.664269\pi$
$854$	−11.8504	+	20.5255i	−0.405512	+	0.702367i
$855$		0			0
$856$	−4.38455	−	7.59426i	−0.149861	−	0.259567i
$857$	0.831990	+	0.831990i	0.0284202	+	0.0284202i	0.721174	−	0.692754i	$-0.243603\pi$
$857$	0.831990	+	0.831990i	0.0284202	+	0.0284202i	−0.692754	+	0.721174i	$0.743603\pi$
$858$	−7.27818	+	12.7730i	−0.248473	+	0.436064i
$859$		−	34.0985i		−	1.16343i	−0.813394	−	0.581713i	$-0.802383\pi$
$859$		−	34.0985i		−	1.16343i	0.813394	−	0.581713i	$-0.197617\pi$
$860$		0			0
$861$	−65.9138	+	7.77443i	−2.24634	+	0.264952i
$862$	10.3543	+	38.6429i	0.352670	+	1.31618i
$863$	12.5571	−	12.5571i	0.427447	−	0.427447i	−0.460311	−	0.887758i	$-0.652262\pi$
$863$	12.5571	−	12.5571i	0.427447	−	0.427447i	0.887758	+	0.460311i	$0.152262\pi$
$864$	9.66070	+	1.67206i	0.328664	+	0.0568846i
$865$		0			0
$866$			9.44976i			0.321116i
$867$	−4.21238	+	28.9699i	−0.143060	+	0.983870i
$868$	−0.213145	+	0.795466i	−0.00723460	+	0.0269999i
$869$	10.3147	+	17.8656i	0.349902	+	0.606047i
$870$		0			0
$871$	−1.32005	+	3.36806i	−0.0447281	+	0.114122i
$872$	−5.54299	−	5.54299i	−0.187709	−	0.187709i
$873$	−13.4933	+	7.31216i	−0.456679	+	0.247479i
$874$	1.96435	−	1.13412i	0.0664453	−	0.0383622i
$875$		0			0
$876$	2.22286	+	0.956079i	0.0751034	+	0.0323029i
$877$	−6.23858	−	23.2827i	−0.210662	−	0.786201i	−0.987649	−	0.156684i	$-0.949920\pi$
$877$	−6.23858	−	23.2827i	−0.210662	−	0.786201i	0.776987	−	0.629517i	$-0.216747\pi$
$878$	−6.34111	−	23.6654i	−0.214002	−	0.798667i
$879$	−20.4389	−	8.79101i	−0.689386	−	0.296513i
$880$		0			0
$881$	−11.7849	+	6.80400i	−0.397043	+	0.229233i	−0.685207	−	0.728348i	$-0.740288\pi$
$881$	−11.7849	+	6.80400i	−0.397043	+	0.229233i	0.288164	+	0.957581i	$0.406955\pi$
$882$	61.8423	−	33.5130i	2.08234	−	1.12844i
$883$	0.884878	+	0.884878i	0.0297785	+	0.0297785i	0.721839	−	0.692061i	$-0.243297\pi$
$883$	0.884878	+	0.884878i	0.0297785	+	0.0297785i	−0.692061	+	0.721839i	$0.743297\pi$
$884$	−0.139005	+	0.354668i	−0.00467525	+	0.0119288i
$885$		0			0
$886$	21.6406	+	37.4826i	0.727031	+	1.25925i
$887$	3.81600	−	14.2415i	0.128129	−	0.478183i	−0.871803	−	0.489857i	$-0.837049\pi$
$887$	3.81600	−	14.2415i	0.128129	−	0.478183i	0.999932	+	0.0116733i	$0.00371580\pi$
$888$	−3.85909	+	26.5402i	−0.129503	+	0.890632i
$889$		−	72.5863i		−	2.43447i
$890$		0			0
$891$	7.56696	−	11.6110i	0.253503	−	0.388983i
$892$	−1.01265	+	1.01265i	−0.0339062	+	0.0339062i
$893$	0.0578249	+	0.215805i	0.00193504	+	0.00722165i
$894$	−47.9078	+	5.65065i	−1.60228	+	0.188986i
$895$		0			0
$896$			62.8929i			2.10111i
$897$	14.8652	+	25.4131i	0.496334	+	0.848519i
$898$	−1.46589	−	1.46589i	−0.0489173	−	0.0489173i
$899$	2.18476	+	3.78412i	0.0728659	+	0.126207i
$900$		0			0
$901$	−0.339637	+	0.588268i	−0.0113149	+	0.0195980i
$902$	13.4959	+	13.4959i	0.449364	+	0.449364i
$903$	30.0145	+	4.36427i	0.998821	+	0.145234i
$904$	35.7887	+	20.6626i	1.19031	+	0.687228i
$905$		0			0
$906$	−1.82387	−	2.44452i	−0.0605941	−	0.0812137i
$907$	−20.9414	−	5.61123i	−0.695347	−	0.186318i	−0.106202	−	0.994345i	$-0.533869\pi$
$907$	−20.9414	−	5.61123i	−0.695347	−	0.186318i	−0.589146	+	0.808027i	$0.700536\pi$
$908$	−5.73423	−	1.53648i	−0.190297	−	0.0509900i
$909$	22.4717	+	23.7186i	0.745341	+	0.786697i
$910$		0			0
$911$			13.2054i			0.437516i	0.975779	+	0.218758i	$0.0702005\pi$
$911$			13.2054i			0.437516i	−0.975779	+	0.218758i	$0.929799\pi$
$912$	−1.95166	−	1.53984i	−0.0646260	−	0.0509893i
$913$	−0.509610	+	1.90189i	−0.0168656	+	0.0629434i
$914$	2.33163	−	4.03850i	0.0771235	−	0.133582i
$915$		0			0
$916$	−0.373331	+	0.646628i	−0.0123352	+	0.0213652i
$917$	47.4481	−	12.7137i	1.56688	−	0.419843i
$918$	1.04549	−	2.26063i	0.0345062	−	0.0746118i
$919$	26.4378	+	15.2639i	0.872103	+	0.503509i	0.868047	−	0.496483i	$-0.165375\pi$
$919$	26.4378	+	15.2639i	0.872103	+	0.503509i	0.00405678	+	0.999992i	$0.498709\pi$
$920$		0			0
$921$	2.65444	+	22.5051i	0.0874668	+	0.741568i
$922$	20.1979	−	20.1979i	0.665181	−	0.665181i
$923$	−7.35392	+	9.97397i	−0.242057	+	0.328297i
$924$	−3.90192	−	1.67826i	−0.128364	−	0.0552108i
$925$		0			0
$926$	−36.3854	+	21.0071i	−1.19570	+	0.690337i
$927$	19.5603	−	31.8617i	0.642444	−	1.04648i
$928$	−11.2736	−	11.2736i	−0.370073	−	0.370073i
$929$	−17.1979	+	29.7877i	−0.564246	+	0.977303i	0.432873	+	0.901455i	$0.357500\pi$
$929$	−17.1979	+	29.7877i	−0.564246	+	0.977303i	−0.997119	+	0.0758485i	$0.975833\pi$
$930$		0			0
$931$	−4.82712			−0.158202
$932$	6.02414	−	1.61416i	0.197327	−	0.0528737i
$933$	15.6891	+	12.3785i	0.513637	+	0.405255i
$934$	39.4992	−	22.8049i	1.29245	−	0.746198i
$935$		0			0
$936$	16.9106	−	21.6851i	0.552741	−	0.708801i
$937$	−34.4013	+	34.4013i	−1.12384	+	1.12384i	−0.132683	+	0.991159i	$0.542359\pi$
$937$	−34.4013	+	34.4013i	−1.12384	+	1.12384i	−0.991159	+	0.132683i	$0.957641\pi$
$938$	−7.00201	−	1.87618i	−0.228624	−	0.0612595i
$939$	20.3650	−	2.40202i	0.664587	−	0.0783870i
$940$		0			0
$941$			9.30013i			0.303176i	0.988444	+	0.151588i	$0.0484386\pi$
$941$			9.30013i			0.303176i	−0.988444	+	0.151588i	$0.951561\pi$
$942$	−52.6122	−	7.65010i	−1.71420	−	0.249254i
$943$	36.9208	−	9.89289i	1.20231	−	0.322157i
$944$	−47.3253			−1.54031
$945$		0			0
$946$	−4.36099	−	7.55346i	−0.141788	−	0.245584i
$947$	−1.57191	+	5.86646i	−0.0510803	+	0.190634i	−0.986752	−	0.162239i	$-0.948129\pi$
$947$	−1.57191	+	5.86646i	−0.0510803	+	0.190634i	0.935671	+	0.352873i	$0.114795\pi$
$948$	2.89427	+	7.26306i	0.0940014	+	0.235893i
$949$	11.6833	−	9.32604i	0.379255	−	0.302736i
$950$		0			0
$951$	−9.02500	+	1.06448i	−0.292656	+	0.0345183i
$952$	3.63915	+	0.975107i	0.117946	+	0.0316034i
$953$	13.3435	+	49.7987i	0.432239	+	1.61314i	0.747589	+	0.664162i	$0.231211\pi$
$953$	13.3435	+	49.7987i	0.432239	+	1.61314i	−0.315350	+	0.948975i	$0.602122\pi$
$954$	−7.21232	+	6.83317i	−0.233507	+	0.221232i
$955$		0			0
$956$	1.46572	+	0.846233i	0.0474047	+	0.0273691i
$957$	−20.9358	+	8.34275i	−0.676759	+	0.269683i
$958$	−24.9145	+	6.67582i	−0.804951	+	0.215686i
$959$	−5.30381	−	9.18647i	−0.171269	−	0.296647i
$960$		0			0
$961$	−30.7326			−0.991374
$962$	−27.0199	−	19.9220i	−0.871155	−	0.642312i
$963$	−10.3440	−	0.279225i	−0.333331	−	0.00899790i
$964$	3.57325	−	2.06301i	0.115087	−	0.0664452i
$965$		0			0
$966$	−47.2857	+	35.2802i	−1.52139	+	1.13512i
$967$	−5.01571	+	5.01571i	−0.161294	+	0.161294i	−0.783140	−	0.621846i	$-0.786383\pi$
$967$	−5.01571	+	5.01571i	−0.161294	+	0.161294i	0.621846	+	0.783140i	$0.286383\pi$
$968$	5.67769	+	21.1894i	0.182488	+	0.681054i
$969$	−0.136997	+	0.102214i	−0.00440096	+	0.00328359i
$970$		0			0
$971$	31.8931	+	18.4135i	1.02350	+	0.590918i	0.915116	−	0.403191i	$-0.132099\pi$
$971$	31.8931	+	18.4135i	1.02350	+	0.590918i	0.108384	+	0.994109i	$0.465432\pi$
$972$	3.47122	−	3.94209i	0.111340	−	0.126443i
$973$	19.0915	−	71.2505i	0.612046	−	2.28419i
$974$	15.1613			0.485800
$975$		0			0
$976$	−14.9596			−0.478847
$977$	7.97746	−	29.7723i	0.255222	−	0.952500i	−0.712745	−	0.701423i	$-0.752549\pi$
$977$	7.97746	−	29.7723i	0.255222	−	0.952500i	0.967967	−	0.251077i	$-0.0807848\pi$
$978$	−25.6209	−	20.2146i	−0.819265	−	0.646393i
$979$	−11.0880	−	6.40166i	−0.354374	−	0.204598i
$980$		0			0
$981$	−8.99634	+	2.15215i	−0.287231	+	0.0687129i
$982$	11.0167	+	41.1150i	0.351558	+	1.31203i
$983$	−29.1862	+	29.1862i	−0.930896	+	0.930896i	−0.997762	−	0.0668661i	$-0.978700\pi$
$983$	−29.1862	+	29.1862i	−0.930896	+	0.930896i	0.0668661	+	0.997762i	$0.478700\pi$
$984$	−21.3497	−	28.6148i	−0.680604	−	0.912207i
$985$		0			0
$986$	−3.50757	+	2.02510i	−0.111704	+	0.0644923i
$987$	−2.15116	−	5.39826i	−0.0684723	−	0.171829i
$988$	0.350389	−	0.153068i	0.0111474	−	0.00486976i
$989$	−17.4673			−0.555427
$990$		0			0
$991$	15.7993	+	27.3652i	0.501882	+	0.869285i	0.999998	+	0.00217462i	$0.000692202\pi$
$991$	15.7993	+	27.3652i	0.501882	+	0.869285i	−0.498116	+	0.867111i	$0.665974\pi$
$992$	−0.942483	+	0.252537i	−0.0299239	+	0.00801807i
$993$	3.14917	+	7.90273i	0.0999359	+	0.250786i
$994$	−21.5050	−	12.4159i	−0.682096	−	0.393809i
$995$		0			0
$996$	−0.294850	+	0.685520i	−0.00934269	+	0.0217215i
$997$	−1.05988	−	3.95554i	−0.0335669	−	0.125273i	0.947109	−	0.320911i	$-0.103989\pi$
$997$	−1.05988	−	3.95554i	−0.0335669	−	0.125273i	−0.980676	+	0.195638i	$0.937322\pi$
$998$	49.6715	+	13.3094i	1.57232	+	0.421303i
$999$	24.3074	+	20.2661i	0.769052	+	0.641191i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.2.bt.m.68.18		96
3.2	odd	2	inner	975.2.bt.m.68.7		96
5.2	odd	4	inner	975.2.bt.m.107.18		96
5.3	odd	4		195.2.bl.a.107.7	yes	96
5.4	even	2		195.2.bl.a.68.7	✓	96
13.9	even	3	inner	975.2.bt.m.893.7		96
15.2	even	4	inner	975.2.bt.m.107.7		96
15.8	even	4		195.2.bl.a.107.18	yes	96
15.14	odd	2		195.2.bl.a.68.18	yes	96
39.35	odd	6	inner	975.2.bt.m.893.18		96
65.9	even	6		195.2.bl.a.113.18	yes	96
65.22	odd	12	inner	975.2.bt.m.932.7		96
65.48	odd	12		195.2.bl.a.152.18	yes	96
195.74	odd	6		195.2.bl.a.113.7	yes	96
195.113	even	12		195.2.bl.a.152.7	yes	96
195.152	even	12	inner	975.2.bt.m.932.18		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.bl.a.68.7	✓	96	5.4	even	2
195.2.bl.a.68.18	yes	96	15.14	odd	2
195.2.bl.a.107.7	yes	96	5.3	odd	4
195.2.bl.a.107.18	yes	96	15.8	even	4
195.2.bl.a.113.7	yes	96	195.74	odd	6
195.2.bl.a.113.18	yes	96	65.9	even	6
195.2.bl.a.152.7	yes	96	195.113	even	12
195.2.bl.a.152.18	yes	96	65.48	odd	12
975.2.bt.m.68.7		96	3.2	odd	2	inner
975.2.bt.m.68.18		96	1.1	even	1	trivial
975.2.bt.m.107.7		96	15.2	even	4	inner
975.2.bt.m.107.18		96	5.2	odd	4	inner
975.2.bt.m.893.7		96	13.9	even	3	inner
975.2.bt.m.893.18		96	39.35	odd	6	inner
975.2.bt.m.932.7		96	65.22	odd	12	inner
975.2.bt.m.932.18		96	195.152	even	12	inner

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:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	975.bt (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.395659 - 1.47662i) q^{2} +(1.07285 - 1.35978i) q^{3} +(-0.291809 - 0.168476i) q^{4} +(-1.58339 - 2.12220i) q^{6} +(-1.22324 - 4.56520i) q^{7} +(1.79769 - 1.79769i) q^{8} +(-0.697981 - 2.91767i) q^{9} +O(q^{10})\)	\(q+(0.395659 - 1.47662i) q^{2} +(1.07285 - 1.35978i) q^{3} +(-0.291809 - 0.168476i) q^{4} +(-1.58339 - 2.12220i) q^{6} +(-1.22324 - 4.56520i) q^{7} +(1.79769 - 1.79769i) q^{8} +(-0.697981 - 2.91767i) q^{9} +(-1.33359 + 0.769949i) q^{11} +(-0.542158 + 0.216045i) q^{12} +(-0.402017 + 3.58307i) q^{13} -7.22505 q^{14} +(-2.28018 - 3.94939i) q^{16} +(-0.302869 + 0.0811535i) q^{17} +(-4.58446 - 0.123752i) q^{18} +(0.272564 + 0.157365i) q^{19} +(-7.52000 - 3.23444i) q^{21} +(0.609275 + 2.27384i) q^{22} +(4.55377 + 1.22018i) q^{23} +(-0.515801 - 4.37311i) q^{24} +(5.13177 + 2.01130i) q^{26} +(-4.71621 - 2.18113i) q^{27} +(-0.412174 + 1.53825i) q^{28} +(4.22484 + 7.31764i) q^{29} +0.517123 q^{31} +(-1.82255 + 0.488351i) q^{32} +(-0.383787 + 2.63943i) q^{33} +0.479331i q^{34} +(-0.287881 + 0.968998i) q^{36} +(-5.88304 - 1.57635i) q^{37} +(0.340210 - 0.340210i) q^{38} +(4.44087 + 4.39075i) q^{39} +(7.02151 - 4.05387i) q^{41} +(-7.75140 + 9.82445i) q^{42} +(-3.57884 + 0.958947i) q^{43} +0.518872 q^{44} +(3.60348 - 6.24141i) q^{46} +(0.501957 + 0.501957i) q^{47} +(-7.81659 - 1.13657i) q^{48} +(-13.2825 + 7.66868i) q^{49} +(-0.214583 + 0.498899i) q^{51} +(0.720974 - 0.977843i) q^{52} +(1.53186 - 1.53186i) q^{53} +(-5.08672 + 6.10107i) q^{54} +(-10.4058 - 6.00780i) q^{56} +(0.506401 - 0.201797i) q^{57} +(12.4770 - 3.34319i) q^{58} +(5.18876 - 8.98720i) q^{59} +(1.64018 - 2.84087i) q^{61} +(0.204604 - 0.763594i) q^{62} +(-12.4660 + 6.75544i) q^{63} -6.23630i q^{64} +(3.74558 + 1.61102i) q^{66} +(0.969129 + 0.259677i) q^{67} +(0.102052 + 0.0273448i) q^{68} +(6.54469 - 4.88303i) q^{69} +(2.97645 + 1.71845i) q^{71} +(-6.49982 - 3.99032i) q^{72} +(-2.93175 - 2.93175i) q^{73} +(-4.65535 + 8.06331i) q^{74} +(-0.0530244 - 0.0918409i) q^{76} +(5.14627 + 5.14627i) q^{77} +(8.24054 - 4.82023i) q^{78} -13.3966i q^{79} +(-8.02565 + 4.07296i) q^{81} +(-3.20790 - 11.9720i) q^{82} +(0.904137 - 0.904137i) q^{83} +(1.64948 + 2.21078i) q^{84} +5.66400i q^{86} +(14.4830 + 2.10590i) q^{87} +(-1.01325 + 3.78151i) q^{88} +(4.15720 + 7.20048i) q^{89} +(16.8492 - 2.54767i) q^{91} +(-1.12326 - 1.12326i) q^{92} +(0.554796 - 0.703171i) q^{93} +(0.939803 - 0.542595i) q^{94} +(-1.29128 + 3.00219i) q^{96} +(-1.32405 - 4.94142i) q^{97} +(6.06836 + 22.6474i) q^{98} +(3.17728 + 3.35357i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 2 q^{3} - 4 q^{6} + 4 q^{7}+O(q^{10}) \) 96 * q + 2 * q^3 - 4 * q^6 + 4 * q^7	\( 96 q + 2 q^{3} - 4 q^{6} + 4 q^{7} + 28 q^{12} + 24 q^{13} + 16 q^{16} - 16 q^{18} - 8 q^{21} + 12 q^{22} + 32 q^{27} + 44 q^{28} + 16 q^{31} + 46 q^{33} - 36 q^{36} - 20 q^{37} - 8 q^{42} + 16 q^{43} - 64 q^{48} + 48 q^{51} + 76 q^{52} - 68 q^{57} + 20 q^{58} + 18 q^{63} + 32 q^{66} + 52 q^{67} - 6 q^{72} - 64 q^{73} - 104 q^{76} - 144 q^{78} + 52 q^{82} - 14 q^{87} - 84 q^{88} + 64 q^{91} - 32 q^{93} - 240 q^{96} - 48 q^{97}+O(q^{100}) \) 96 * q + 2 * q^3 - 4 * q^6 + 4 * q^7 + 28 * q^12 + 24 * q^13 + 16 * q^16 - 16 * q^18 - 8 * q^21 + 12 * q^22 + 32 * q^27 + 44 * q^28 + 16 * q^31 + 46 * q^33 - 36 * q^36 - 20 * q^37 - 8 * q^42 + 16 * q^43 - 64 * q^48 + 48 * q^51 + 76 * q^52 - 68 * q^57 + 20 * q^58 + 18 * q^63 + 32 * q^66 + 52 * q^67 - 6 * q^72 - 64 * q^73 - 104 * q^76 - 144 * q^78 + 52 * q^82 - 14 * q^87 - 84 * q^88 + 64 * q^91 - 32 * q^93 - 240 * q^96 - 48 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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