LMFDB - Embedded newform 345.3.d.a.229.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [345,3,Mod(229,345)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(345, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("345.229");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 345 = 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	345.d (of order $2$, degree $1$, 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:	$9.40056912043$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			229.18
Character	$\chi$	$=$	345.229
Dual form			345.3.d.a.229.32

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.17949i q^{2} -1.73205i q^{3} +2.60880 q^{4} +(3.95152 + 3.06357i) q^{5} -2.04294 q^{6} -0.208857 q^{7} -7.79502i q^{8} -3.00000 q^{9} +O(q^{10})$	\(q-1.17949i q^{2} -1.73205i q^{3} +2.60880 q^{4} +(3.95152 + 3.06357i) q^{5} -2.04294 q^{6} -0.208857 q^{7} -7.79502i q^{8} -3.00000 q^{9} +(3.61345 - 4.66079i) q^{10} +0.522038i q^{11} -4.51857i q^{12} -8.12234i q^{13} +0.246345i q^{14} +(5.30626 - 6.84424i) q^{15} +1.24104 q^{16} +20.2606 q^{17} +3.53847i q^{18} -0.425132i q^{19} +(10.3087 + 7.99224i) q^{20} +0.361751i q^{21} +0.615740 q^{22} +(14.5738 - 17.7934i) q^{23} -13.5014 q^{24} +(6.22908 + 24.2115i) q^{25} -9.58023 q^{26} +5.19615i q^{27} -0.544867 q^{28} +13.9955 q^{29} +(-8.07272 - 6.25869i) q^{30} -8.33003 q^{31} -32.6439i q^{32} +0.904197 q^{33} -23.8972i q^{34} +(-0.825305 - 0.639849i) q^{35} -7.82640 q^{36} +1.55889 q^{37} -0.501439 q^{38} -14.0683 q^{39} +(23.8806 - 30.8022i) q^{40} -15.9010 q^{41} +0.426683 q^{42} -35.2346 q^{43} +1.36189i q^{44} +(-11.8546 - 9.19071i) q^{45} +(-20.9872 - 17.1896i) q^{46} -10.1673i q^{47} -2.14955i q^{48} -48.9564 q^{49} +(28.5573 - 7.34714i) q^{50} -35.0923i q^{51} -21.1896i q^{52} +8.25037 q^{53} +6.12882 q^{54} +(-1.59930 + 2.06285i) q^{55} +1.62805i q^{56} -0.736350 q^{57} -16.5076i q^{58} -1.84529 q^{59} +(13.8430 - 17.8553i) q^{60} +21.1358i q^{61} +9.82520i q^{62} +0.626572 q^{63} -33.5390 q^{64} +(24.8834 - 32.0956i) q^{65} -1.06649i q^{66} -78.5872 q^{67} +52.8558 q^{68} +(-30.8191 - 25.2425i) q^{69} +(-0.754696 + 0.973439i) q^{70} +60.4503 q^{71} +23.3851i q^{72} +39.6674i q^{73} -1.83870i q^{74} +(41.9356 - 10.7891i) q^{75} -1.10908i q^{76} -0.109032i q^{77} +16.5934i q^{78} +123.690i q^{79} +(4.90401 + 3.80202i) q^{80} +9.00000 q^{81} +18.7550i q^{82} +39.2464 q^{83} +0.943737i q^{84} +(80.0601 + 62.0697i) q^{85} +41.5589i q^{86} -24.2409i q^{87} +4.06930 q^{88} +164.237i q^{89} +(-10.8404 + 13.9824i) q^{90} +1.69641i q^{91} +(38.0200 - 46.4195i) q^{92} +14.4280i q^{93} -11.9922 q^{94} +(1.30242 - 1.67992i) q^{95} -56.5409 q^{96} -64.5399 q^{97} +57.7436i q^{98} -1.56611i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 92 q^{4} + 12 q^{6} - 144 q^{9}+O(q^{10}) $ 48 * q - 92 * q^4 + 12 * q^6 - 144 * q^9	$ 48 q - 92 q^{4} + 12 q^{6} - 144 q^{9} + 148 q^{16} - 12 q^{24} - 64 q^{25} + 136 q^{26} + 76 q^{29} - 68 q^{31} - 108 q^{35} + 276 q^{36} + 48 q^{39} + 20 q^{41} + 344 q^{46} + 412 q^{49} - 352 q^{50} - 36 q^{54} - 184 q^{55} - 396 q^{59} - 684 q^{64} - 144 q^{69} + 600 q^{70} + 156 q^{71} - 120 q^{75} + 432 q^{81} - 76 q^{85} + 112 q^{95} + 516 q^{96}+O(q^{100}) $ 48 * q - 92 * q^4 + 12 * q^6 - 144 * q^9 + 148 * q^16 - 12 * q^24 - 64 * q^25 + 136 * q^26 + 76 * q^29 - 68 * q^31 - 108 * q^35 + 276 * q^36 + 48 * q^39 + 20 * q^41 + 344 * q^46 + 412 * q^49 - 352 * q^50 - 36 * q^54 - 184 * q^55 - 396 * q^59 - 684 * q^64 - 144 * q^69 + 600 * q^70 + 156 * q^71 - 120 * q^75 + 432 * q^81 - 76 * q^85 + 112 * q^95 + 516 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/345\mathbb{Z}\right)^\times$.

$n$	$116$	$166$	$277$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$		−	1.17949i		−	0.589746i	−0.955537	−	0.294873i	$-0.904723\pi$
$2$		−	1.17949i		−	0.589746i	0.955537	−	0.294873i	$-0.0952773\pi$
$3$		−	1.73205i		−	0.577350i
$3$		−	1.73205i		−	0.577350i
$4$	2.60880			0.652200
$5$	3.95152	+	3.06357i	0.790305	+	0.612714i
$5$	3.95152	+	3.06357i	0.790305	+	0.612714i
$6$	−2.04294			−0.340490
$7$	−0.208857			−0.0298368			−0.0149184	−	0.999889i	$-0.504749\pi$
$7$	−0.208857			−0.0298368			−0.0149184	+	0.999889i	$0.504749\pi$
$8$		−	7.79502i		−	0.974378i
$9$	−3.00000			−0.333333
$10$	3.61345	−	4.66079i	0.361345	−	0.466079i
$11$			0.522038i			0.0474580i	0.999718	+	0.0237290i	$0.00755389\pi$
$11$			0.522038i			0.0474580i	−0.999718	+	0.0237290i	$0.992446\pi$
$12$		−	4.51857i		−	0.376548i
$13$		−	8.12234i		−	0.624795i	−0.949951	−	0.312398i	$-0.898868\pi$
$13$		−	8.12234i		−	0.624795i	0.949951	−	0.312398i	$-0.101132\pi$
$14$			0.246345i			0.0175961i
$15$	5.30626	−	6.84424i	0.353751	−	0.456283i
$16$	1.24104			0.0775651
$17$	20.2606			1.19180			0.595899	−	0.803059i	$-0.296796\pi$
$17$	20.2606			1.19180			0.595899	+	0.803059i	$0.296796\pi$
$18$			3.53847i			0.196582i
$19$		−	0.425132i		−	0.0223753i	−0.999937	−	0.0111877i	$-0.996439\pi$
$19$		−	0.425132i		−	0.0223753i	0.999937	−	0.0111877i	$-0.00356122\pi$
$20$	10.3087	+	7.99224i	0.515437	+	0.399612i
$21$			0.361751i			0.0172263i
$22$	0.615740			0.0279882
$23$	14.5738	−	17.7934i	0.633641	−	0.773627i
$23$	14.5738	−	17.7934i	0.633641	−	0.773627i
$24$	−13.5014			−0.562557
$25$	6.22908	+	24.2115i	0.249163	+	0.968462i
$26$	−9.58023			−0.368470
$27$			5.19615i			0.192450i
$28$	−0.544867			−0.0194595
$29$	13.9955			0.482604			0.241302	−	0.970450i	$-0.422426\pi$
$29$	13.9955			0.482604			0.241302	+	0.970450i	$0.422426\pi$
$30$	−8.07272	−	6.25869i	−0.269091	−	0.208623i
$31$	−8.33003			−0.268711			−0.134355	−	0.990933i	$-0.542896\pi$
$31$	−8.33003			−0.268711			−0.134355	+	0.990933i	$0.542896\pi$
$32$		−	32.6439i		−	1.02012i
$33$	0.904197			0.0273999
$34$		−	23.8972i		−	0.702858i
$35$	−0.825305	−	0.639849i	−0.0235801	−	0.0182814i
$36$	−7.82640			−0.217400
$37$	1.55889			0.0421322			0.0210661	−	0.999778i	$-0.493294\pi$
$37$	1.55889			0.0421322			0.0210661	+	0.999778i	$0.493294\pi$
$38$	−0.501439			−0.0131958
$39$	−14.0683			−0.360726
$40$	23.8806	−	30.8022i	0.597015	−	0.770055i
$41$	−15.9010			−0.387828			−0.193914	−	0.981018i	$-0.562118\pi$
$41$	−15.9010			−0.387828			−0.193914	+	0.981018i	$0.562118\pi$
$42$	0.426683			0.0101591
$43$	−35.2346			−0.819409			−0.409704	−	0.912218i	$-0.634368\pi$
$43$	−35.2346			−0.819409			−0.409704	+	0.912218i	$0.634368\pi$
$44$			1.36189i			0.0309521i
$45$	−11.8546	−	9.19071i	−0.263435	−	0.204238i
$46$	−20.9872	−	17.1896i	−0.456243	−	0.373687i
$47$		−	10.1673i		−	0.216325i	−0.994133	−	0.108163i	$-0.965503\pi$
$47$		−	10.1673i		−	0.216325i	0.994133	−	0.108163i	$-0.0344967\pi$
$48$		−	2.14955i		−	0.0447822i
$49$	−48.9564			−0.999110
$50$	28.5573	−	7.34714i	0.571146	−	0.146943i
$51$		−	35.0923i		−	0.688085i
$52$		−	21.1896i		−	0.407492i
$53$	8.25037			0.155667			0.0778336	−	0.996966i	$-0.475200\pi$
$53$	8.25037			0.155667			0.0778336	+	0.996966i	$0.475200\pi$
$54$	6.12882			0.113497
$55$	−1.59930	+	2.06285i	−0.0290782	+	0.0375063i
$56$			1.62805i			0.0290723i
$57$	−0.736350			−0.0129184
$58$		−	16.5076i		−	0.284614i
$59$	−1.84529			−0.0312761			−0.0156380	−	0.999878i	$-0.504978\pi$
$59$	−1.84529			−0.0312761			−0.0156380	+	0.999878i	$0.504978\pi$
$60$	13.8430	−	17.8553i	0.230716	−	0.297588i
$61$			21.1358i			0.346488i	0.984879	+	0.173244i	$0.0554249\pi$
$61$			21.1358i			0.346488i	−0.984879	+	0.173244i	$0.944575\pi$
$62$			9.82520i			0.158471i
$63$	0.626572			0.00994559
$64$	−33.5390			−0.524047
$65$	24.8834	−	32.0956i	0.382821	−	0.493779i
$66$		−	1.06649i		−	0.0161590i
$67$	−78.5872			−1.17294			−0.586472	−	0.809970i	$-0.699483\pi$
$67$	−78.5872			−1.17294			−0.586472	+	0.809970i	$0.699483\pi$
$68$	52.8558			0.777291
$69$	−30.8191	−	25.2425i	−0.446654	−	0.365833i
$70$	−0.754696	+	0.973439i	−0.0107814	+	0.0139063i
$71$	60.4503			0.851413			0.425706	−	0.904861i	$-0.360026\pi$
$71$	60.4503			0.851413			0.425706	+	0.904861i	$0.360026\pi$
$72$			23.3851i			0.324793i
$73$			39.6674i			0.543389i	0.962384	+	0.271695i	$0.0875840\pi$
$73$			39.6674i			0.543389i	−0.962384	+	0.271695i	$0.912416\pi$
$74$		−	1.83870i		−	0.0248473i
$75$	41.9356	−	10.7891i	0.559142	−	0.143854i
$76$		−	1.10908i		−	0.0145932i
$77$		−	0.109032i		−	0.00141599i
$78$			16.5934i			0.212736i
$79$			123.690i			1.56570i	0.622212	+	0.782849i	$0.286234\pi$
$79$			123.690i			1.56570i	−0.622212	+	0.782849i	$0.713766\pi$
$80$	4.90401	+	3.80202i	0.0613001	+	0.0475252i
$81$	9.00000			0.111111
$82$			18.7550i			0.228720i
$83$	39.2464			0.472849			0.236424	−	0.971650i	$-0.424024\pi$
$83$	39.2464			0.472849			0.236424	+	0.971650i	$0.424024\pi$
$84$			0.943737i			0.0112350i
$85$	80.0601	+	62.0697i	0.941884	+	0.730231i
$86$			41.5589i			0.483243i
$87$		−	24.2409i		−	0.278632i
$88$	4.06930			0.0462420
$89$			164.237i			1.84536i	0.385566	+	0.922680i	$0.374006\pi$
$89$			164.237i			1.84536i	−0.385566	+	0.922680i	$0.625994\pi$
$90$	−10.8404	+	13.9824i	−0.120448	+	0.155360i
$91$			1.69641i			0.0186419i
$92$	38.0200	−	46.4195i	0.413261	−	0.504560i
$93$			14.4280i			0.155140i
$94$	−11.9922			−0.127577
$95$	1.30242	−	1.67992i	0.0137097	−	0.0176833i
$96$	−56.5409			−0.588967
$97$	−64.5399			−0.665360			−0.332680	−	0.943040i	$-0.607953\pi$
$97$	−64.5399			−0.665360			−0.332680	+	0.943040i	$0.607953\pi$
$98$			57.7436i			0.589221i
$99$		−	1.56611i		−	0.0158193i
$100$	16.2504	+	63.1631i	0.162504	+	0.631631i
$101$	163.402			1.61785			0.808923	−	0.587915i	$-0.200051\pi$
$101$	163.402			1.61785			0.808923	+	0.587915i	$0.200051\pi$
$102$	−41.3911			−0.405795
$103$	−96.3936			−0.935860			−0.467930	−	0.883766i	$-0.655000\pi$
$103$	−96.3936			−0.935860			−0.467930	+	0.883766i	$0.655000\pi$
$104$	−63.3138			−0.608787
$105$	−1.10825	+	1.42947i	−0.0105548	+	0.0136140i
$106$		−	9.73123i		−	0.0918041i
$107$	−105.825			−0.989021			−0.494510	−	0.869172i	$-0.664653\pi$
$107$	−105.825			−0.989021			−0.494510	+	0.869172i	$0.664653\pi$
$108$			13.5557i			0.125516i
$109$			52.6842i			0.483342i	0.970358	+	0.241671i	$0.0776954\pi$
$109$			52.6842i			0.483342i	−0.970358	+	0.241671i	$0.922305\pi$
$110$	2.43311	+	1.88636i	0.0221192	+	0.0171487i
$111$		−	2.70008i		−	0.0243250i
$112$	−0.259201			−0.00231429
$113$	−136.139			−1.20477			−0.602385	−	0.798206i	$-0.705783\pi$
$113$	−136.139			−1.20477			−0.602385	+	0.798206i	$0.705783\pi$
$114$			0.868518i			0.00761858i
$115$	112.100	−	25.6634i	0.974782	−	0.223160i
$116$	36.5115			0.314754
$117$			24.3670i			0.208265i
$118$			2.17650i			0.0184449i
$119$	−4.23157			−0.0355594
$120$	−53.3510	−	41.3624i	−0.444592	−	0.344687i
$121$	120.727			0.997748
$122$	24.9294			0.204340
$123$			27.5413i			0.223913i
$124$	−21.7314			−0.175253
$125$	−49.5594	+	114.756i	−0.396475	+	0.918045i
$126$		−	0.739036i		−	0.00586537i
$127$		−	28.4440i		−	0.223969i	−0.993710	−	0.111984i	$-0.964279\pi$
$127$		−	28.4440i		−	0.223969i	0.993710	−	0.111984i	$-0.0357207\pi$
$128$		−	91.0166i		−	0.711067i
$129$			61.0281i			0.473086i
$130$	−37.8565	−	29.3497i	−0.291204	−	0.225767i
$131$	126.193			0.963303			0.481652	−	0.876363i	$-0.340037\pi$
$131$	126.193			0.963303			0.481652	+	0.876363i	$0.340037\pi$
$132$	2.35887			0.0178702
$133$			0.0887918i			0.000667608i
$134$			92.6929i			0.691738i
$135$	−15.9188	+	20.5327i	−0.117917	+	0.152094i
$136$		−	157.932i		−	1.16126i
$137$	89.1598			0.650801			0.325401	−	0.945576i	$-0.394501\pi$
$137$	89.1598			0.650801			0.325401	+	0.945576i	$0.394501\pi$
$138$	−29.7733	+	36.3509i	−0.215748	+	0.263412i
$139$	−222.534			−1.60096			−0.800482	−	0.599357i	$-0.795423\pi$
$139$	−222.534			−1.60096			−0.800482	+	0.599357i	$0.795423\pi$
$140$	−2.15305	−	1.66924i	−0.0153790	−	0.0119231i
$141$	−17.6102			−0.124895
$142$		−	71.3006i		−	0.502117i
$143$	4.24017			0.0296516
$144$	−3.72313			−0.0258550
$145$	55.3036	+	42.8762i	0.381404	+	0.295698i
$146$	46.7874			0.320461
$147$			84.7949i			0.576836i
$148$	4.06683			0.0274786
$149$			169.344i			1.13654i	0.822842	+	0.568270i	$0.192387\pi$
$149$			169.344i			1.13654i	−0.822842	+	0.568270i	$0.807613\pi$
$150$	−12.7256	−	49.4627i	−0.0848375	−	0.329751i
$151$	−5.33089			−0.0353039			−0.0176520	−	0.999844i	$-0.505619\pi$
$151$	−5.33089			−0.0353039			−0.0176520	+	0.999844i	$0.505619\pi$
$152$	−3.31391			−0.0218020
$153$	−60.7817			−0.397266
$154$	−0.128602			−0.000835076
$155$	−32.9163	−	25.5196i	−0.212363	−	0.164643i
$156$	−36.7014			−0.235265
$157$	23.8548			0.151941			0.0759706	−	0.997110i	$-0.475794\pi$
$157$	23.8548			0.151941			0.0759706	+	0.997110i	$0.475794\pi$
$158$	145.891			0.923363
$159$		−	14.2901i		−	0.0898746i
$160$	100.007	−	128.993i	0.625043	−	0.806207i
$161$	−3.04383	+	3.71629i	−0.0189058	+	0.0230825i
$162$		−	10.6154i		−	0.0655273i
$163$		−	78.7914i		−	0.483383i	−0.970353	−	0.241692i	$-0.922298\pi$
$163$		−	78.7914i		−	0.483383i	0.970353	−	0.241692i	$-0.0777022\pi$
$164$	−41.4824			−0.252942
$165$	3.57296	+	2.77007i	0.0216543	+	0.0167883i
$166$		−	46.2908i		−	0.278860i
$167$			88.3990i			0.529335i	0.964340	+	0.264668i	$0.0852622\pi$
$167$			88.3990i			0.529335i	−0.964340	+	0.264668i	$0.914738\pi$
$168$	2.81986			0.0167849
$169$	103.028			0.609631
$170$	73.2106	−	94.4302i	0.430651	−	0.555472i
$171$			1.27539i			0.00745845i
$172$	−91.9200			−0.534419
$173$			153.550i			0.887574i	0.896132	+	0.443787i	$0.146365\pi$
$173$			153.550i			0.887574i	−0.896132	+	0.443787i	$0.853635\pi$
$174$	−28.5920			−0.164322
$175$	−1.30099	−	5.05676i	−0.00743422	−	0.0288958i
$176$			0.647871i			0.00368109i
$177$			3.19614i			0.0180573i
$178$	193.716			1.08829
$179$	−240.045			−1.34104			−0.670518	−	0.741894i	$-0.733928\pi$
$179$	−240.045			−1.34104			−0.670518	+	0.741894i	$0.733928\pi$
$180$	−30.9262	−	23.9767i	−0.171812	−	0.133204i
$181$		−	50.7211i		−	0.280227i	−0.990135	−	0.140114i	$-0.955253\pi$
$181$		−	50.7211i		−	0.280227i	0.990135	−	0.140114i	$-0.0447468\pi$
$182$	2.00090			0.0109940
$183$	36.6082			0.200045
$184$	−138.700	−	113.603i	−0.753805	−	0.617406i
$185$	6.15999	+	4.77577i	0.0332972	+	0.0258150i
$186$	17.0177			0.0914932
$187$			10.5768i			0.0565604i
$188$		−	26.5244i		−	0.141087i
$189$		−	1.08525i		−	0.00574209i
$190$	−1.98145	−	1.53619i	−0.0104287	−	0.00808523i
$191$		−	257.636i		−	1.34888i	−0.738330	−	0.674440i	$-0.764385\pi$
$191$		−	257.636i		−	1.34888i	0.738330	−	0.674440i	$-0.235615\pi$
$192$			58.0913i			0.302559i
$193$			215.416i			1.11614i	0.829793	+	0.558072i	$0.188459\pi$
$193$			215.416i			1.11614i	−0.829793	+	0.558072i	$0.811541\pi$
$194$			76.1243i			0.392393i
$195$	−55.5912	−	43.0992i	−0.285083	−	0.221022i
$196$	−127.717			−0.651620
$197$			97.0776i			0.492780i	0.969171	+	0.246390i	$0.0792444\pi$
$197$			97.0776i			0.492780i	−0.969171	+	0.246390i	$0.920756\pi$
$198$	−1.84722			−0.00932939
$199$			14.2579i			0.0716475i	0.999358	+	0.0358238i	$0.0114055\pi$
$199$			14.2579i			0.0716475i	−0.999358	+	0.0358238i	$0.988595\pi$
$200$	188.729	−	48.5558i	0.943647	−	0.242779i
$201$			136.117i			0.677199i
$202$		−	192.732i		−	0.954118i
$203$	−2.92307			−0.0143993
$204$		−	91.5489i		−	0.448769i
$205$	−62.8330	−	48.7137i	−0.306503	−	0.237628i
$206$			113.695i			0.551919i
$207$	−43.7213	+	53.3803i	−0.211214	+	0.257876i
$208$		−	10.0802i		−	0.0484623i
$209$	0.221935			0.00106189
$210$	1.68605	+	1.30717i	0.00802879	+	0.00622463i
$211$	13.7073			0.0649635			0.0324817	−	0.999472i	$-0.489659\pi$
$211$	13.7073			0.0649635			0.0324817	+	0.999472i	$0.489659\pi$
$212$	21.5236			0.101526
$213$		−	104.703i		−	0.491563i
$214$			124.820i			0.583271i
$215$	−139.230	−	107.944i	−0.647583	−	0.502063i
$216$	40.5041			0.187519
$217$	1.73979			0.00801745
$218$	62.1406			0.285049
$219$	68.7060			0.313726
$220$	−4.17226	+	5.38156i	−0.0189648	+	0.0244616i
$221$		−	164.563i		−	0.744630i
$222$	−3.18472			−0.0143456
$223$		−	130.649i		−	0.585869i	−0.956132	−	0.292935i	$-0.905368\pi$
$223$		−	130.649i		−	0.585869i	0.956132	−	0.292935i	$-0.0946318\pi$
$224$			6.81791i			0.0304371i
$225$	−18.6872	−	72.6346i	−0.0830544	−	0.322821i
$226$			160.575i			0.710508i
$227$	194.376			0.856281			0.428141	−	0.903712i	$-0.359169\pi$
$227$	194.376			0.856281			0.428141	+	0.903712i	$0.359169\pi$
$228$	−1.92099			−0.00842539
$229$		−	82.1787i		−	0.358859i	−0.983771	−	0.179430i	$-0.942575\pi$
$229$		−	82.1787i		−	0.358859i	0.983771	−	0.179430i	$-0.0574252\pi$
$230$	−30.2698	−	132.221i	−0.131608	−	0.574873i
$231$	−0.188848			−0.000817524
$232$		−	109.095i		−	0.470239i
$233$		−	247.242i		−	1.06113i	−0.847646	−	0.530563i	$-0.821981\pi$
$233$		−	247.242i		−	1.06113i	0.847646	−	0.530563i	$-0.178019\pi$
$234$	28.7407			0.122823
$235$	31.1482	−	40.1762i	0.132545	−	0.170963i
$236$	−4.81399			−0.0203983
$237$	214.238			0.903956
$238$			4.99110i			0.0209710i
$239$	−128.680			−0.538410			−0.269205	−	0.963083i	$-0.586761\pi$
$239$	−128.680			−0.538410			−0.269205	+	0.963083i	$0.586761\pi$
$240$	6.58529	−	8.49399i	0.0274387	−	0.0353916i
$241$			197.531i			0.819629i	0.912169	+	0.409815i	$0.134407\pi$
$241$			197.531i			0.819629i	−0.912169	+	0.409815i	$0.865593\pi$
$242$		−	142.397i		−	0.588417i
$243$		−	15.5885i		−	0.0641500i
$244$			55.1390i			0.225979i
$245$	−193.452	−	149.981i	−0.789601	−	0.612169i
$246$	32.4847			0.132052
$247$	−3.45306			−0.0139800
$248$			64.9328i			0.261826i
$249$		−	67.9768i		−	0.272999i
$250$	135.353	+	58.4549i	0.541413	+	0.233820i
$251$		−	394.154i		−	1.57034i	−0.619283	−	0.785168i	$-0.712577\pi$
$251$		−	394.154i		−	1.57034i	0.619283	−	0.785168i	$-0.287423\pi$
$252$	1.63460			0.00648651
$253$	9.28885	+	7.60806i	0.0367148	+	0.0300714i
$254$	−33.5495			−0.132085
$255$	107.508	−	138.668i	0.421599	−	0.543797i
$256$	−241.509			−0.943396
$257$			173.054i			0.673360i	0.941619	+	0.336680i	$0.109304\pi$
$257$			173.054i			0.673360i	−0.941619	+	0.336680i	$0.890696\pi$
$258$	71.9821			0.279000
$259$	−0.325586			−0.00125709
$260$	64.9157	−	83.7311i	0.249676	−	0.322043i
$261$	−41.9866			−0.160868
$262$		−	148.843i		−	0.568104i
$263$	−19.8567			−0.0755006			−0.0377503	−	0.999287i	$-0.512019\pi$
$263$	−19.8567			−0.0755006			−0.0377503	+	0.999287i	$0.512019\pi$
$264$		−	7.04823i		−	0.0266979i
$265$	32.6015	+	25.2756i	0.123025	+	0.0953795i
$266$	0.104729			0.000393719
$267$	284.467			1.06542
$268$	−205.018			−0.764994
$269$	−459.161			−1.70692			−0.853460	−	0.521158i	$-0.825500\pi$
$269$	−459.161			−1.70692			−0.853460	+	0.521158i	$0.825500\pi$
$270$	24.2182	+	18.7761i	0.0896969	+	0.0695410i
$271$	2.08801			0.00770485			0.00385242	−	0.999993i	$-0.498774\pi$
$271$	2.08801			0.00770485			0.00385242	+	0.999993i	$0.498774\pi$
$272$	25.1442			0.0924420
$273$	2.93827			0.0107629
$274$		−	105.163i		−	0.383807i
$275$	−12.6394	+	3.25182i	−0.0459613	+	0.0118248i
$276$	−80.4009	−	65.8526i	−0.291308	−	0.238596i
$277$		−	183.981i		−	0.664191i	−0.943246	−	0.332096i	$-0.892244\pi$
$277$		−	183.981i		−	0.664191i	0.943246	−	0.332096i	$-0.107756\pi$
$278$			262.477i			0.944162i
$279$	24.9901			0.0895702
$280$	−4.98764	+	6.43327i	−0.0178130	+	0.0229760i
$281$		−	198.613i		−	0.706808i	−0.935471	−	0.353404i	$-0.885024\pi$
$281$		−	198.613i		−	0.706808i	0.935471	−	0.353404i	$-0.114976\pi$
$282$			20.7711i			0.0736565i
$283$	501.210			1.77106			0.885530	−	0.464581i	$-0.153795\pi$
$283$	501.210			1.77106			0.885530	+	0.464581i	$0.153795\pi$
$284$	157.703			0.555292
$285$	−2.90970	−	2.25586i	−0.0102095	−	0.00791529i
$286$		−	5.00125i		−	0.0174869i
$287$	3.32103			0.0115715
$288$			97.9317i			0.340040i
$289$	121.491			0.420383
$290$	50.5722	−	65.2301i	0.174387	−	0.224931i
$291$			111.786i			0.384146i
$292$			103.484i			0.354398i
$293$	−375.766			−1.28248			−0.641239	−	0.767341i	$-0.721579\pi$
$293$	−375.766			−1.28248			−0.641239	+	0.767341i	$0.721579\pi$
$294$	100.015			0.340187
$295$	−7.29171	−	5.65317i	−0.0247176	−	0.0191633i
$296$		−	12.1516i		−	0.0410526i
$297$	−2.71259			−0.00913330
$298$	199.740			0.670269
$299$	−144.524	−	118.373i	−0.483358	−	0.395896i
$300$	109.402	−	28.1466i	0.364672	−	0.0938218i
$301$	7.35900			0.0244485
$302$			6.28774i			0.0208203i
$303$		−	283.021i		−	0.934064i
$304$		−	0.527606i		−	0.00173555i
$305$	−64.7509	+	83.5184i	−0.212298	+	0.273831i
$306$			71.6915i			0.234286i
$307$		−	160.627i		−	0.523214i	−0.965175	−	0.261607i	$-0.915748\pi$
$307$		−	160.627i		−	0.523214i	0.965175	−	0.261607i	$-0.0842524\pi$
$308$		−	0.284441i		−	0.000923511i
$309$			166.959i			0.540319i
$310$	−30.1002	+	38.8245i	−0.0970974	+	0.125240i
$311$	−62.6731			−0.201521			−0.100761	−	0.994911i	$-0.532128\pi$
$311$	−62.6731			−0.201521			−0.100761	+	0.994911i	$0.532128\pi$
$312$			109.663i			0.351483i
$313$	147.913			0.472566			0.236283	−	0.971684i	$-0.424071\pi$
$313$	147.913			0.472566			0.236283	+	0.971684i	$0.424071\pi$
$314$		−	28.1365i		−	0.0896066i
$315$	2.47591	+	1.91955i	0.00786004	+	0.00609380i
$316$			322.683i			1.02115i
$317$			472.762i			1.49136i	0.666302	+	0.745682i	$0.267876\pi$
$317$			472.762i			1.49136i	−0.666302	+	0.745682i	$0.732124\pi$
$318$	−16.8550			−0.0530031
$319$			7.30620i			0.0229034i
$320$	−132.530	−	102.749i	−0.414157	−	0.321091i
$321$			183.295i			0.571011i
$322$	4.38333	+	3.59018i	0.0136128	+	0.0111496i
$323$		−	8.61341i		−	0.0266669i
$324$	23.4792			0.0724667
$325$	196.654	−	50.5947i	0.605090	−	0.155676i
$326$	−92.9338			−0.285073
$327$	91.2518			0.279057
$328$			123.948i			0.377891i
$329$			2.12351i			0.00645444i
$330$	3.26727	−	4.21427i	0.00990083	−	0.0127705i
$331$	−162.437			−0.490746			−0.245373	−	0.969429i	$-0.578910\pi$
$331$	−162.437			−0.490746			−0.245373	+	0.969429i	$0.578910\pi$
$332$	102.386			0.308392
$333$	−4.67667			−0.0140441
$334$	104.266			0.312173
$335$	−310.539	−	240.757i	−0.926982	−	0.718679i
$336$			0.448949i			0.00133616i
$337$	−452.722			−1.34339			−0.671694	−	0.740829i	$-0.734433\pi$
$337$	−452.722			−1.34339			−0.671694	+	0.740829i	$0.734433\pi$
$338$		−	121.520i		−	0.359527i
$339$			235.800i			0.695574i
$340$	208.861	+	161.927i	0.614297	+	0.476257i
$341$		−	4.34859i		−	0.0127525i
$342$	1.50432			0.00439859
$343$	20.4589			0.0596470
$344$			274.654i			0.798414i
$345$	−44.4503	−	194.163i	−0.128842	−	0.562791i
$346$	181.111			0.523443
$347$			511.505i			1.47408i	0.675850	+	0.737039i	$0.263777\pi$
$347$			511.505i			1.47408i	−0.675850	+	0.737039i	$0.736223\pi$
$348$		−	63.2398i		−	0.181724i
$349$	449.014			1.28657			0.643287	−	0.765625i	$-0.277570\pi$
$349$	449.014			1.28657			0.643287	+	0.765625i	$0.277570\pi$
$350$	−5.96440	+	1.53450i	−0.0170411	+	0.00438430i
$351$	42.2049			0.120242
$352$	17.0414			0.0484130
$353$		−	428.631i		−	1.21425i	−0.794605	−	0.607127i	$-0.792322\pi$
$353$		−	428.631i		−	1.21425i	0.794605	−	0.607127i	$-0.207678\pi$
$354$	3.76981			0.0106492
$355$	238.871	+	185.194i	0.672876	+	0.521673i
$356$			428.462i			1.20354i
$357$			7.32929i			0.0205302i
$358$			283.131i			0.790870i
$359$		−	578.029i		−	1.61011i	−0.593201	−	0.805054i	$-0.702136\pi$
$359$		−	578.029i		−	1.61011i	0.593201	−	0.805054i	$-0.297864\pi$
$360$	−71.6418	+	92.4066i	−0.199005	+	0.256685i
$361$	360.819			0.999499
$362$	−59.8251			−0.165263
$363$		−	209.106i		−	0.576050i
$364$			4.42559i			0.0121582i
$365$	−121.524	+	156.747i	−0.332942	+	0.429443i
$366$		−	43.1791i		−	0.117976i
$367$	264.958			0.721955			0.360978	−	0.932575i	$-0.382443\pi$
$367$	264.958			0.721955			0.360978	+	0.932575i	$0.382443\pi$
$368$	18.0866	−	22.0824i	0.0491485	−	0.0600065i
$369$	47.7029			0.129276
$370$	5.63298	−	7.26566i	0.0152243	−	0.0196369i
$371$	−1.72315			−0.00464461
$372$			37.6399i			0.101182i
$373$	−614.635			−1.64781			−0.823907	−	0.566724i	$-0.808210\pi$
$373$	−614.635			−1.64781			−0.823907	+	0.566724i	$0.808210\pi$
$374$	12.4752			0.0333562
$375$	198.763	+	85.8394i	0.530034	+	0.228905i
$376$	−79.2542			−0.210782
$377$		−	113.676i		−	0.301529i
$378$	−1.28005			−0.00338637
$379$			658.857i			1.73841i	0.494452	+	0.869205i	$0.335369\pi$
$379$			658.857i			1.73841i	−0.494452	+	0.869205i	$0.664631\pi$
$380$	3.39776	−	4.38257i	0.00894146	−	0.0115331i
$381$	−49.2665			−0.129308
$382$	−303.879			−0.795496
$383$	−758.205			−1.97965			−0.989824	−	0.142295i	$-0.954552\pi$
$383$	−758.205			−1.97965			−0.989824	+	0.142295i	$0.954552\pi$
$384$	−157.645			−0.410535
$385$	0.334026	−	0.430841i	0.000867599	−	0.00111907i
$386$	254.081			0.658241
$387$	105.704			0.273136
$388$	−168.372			−0.433948
$389$		−	303.736i		−	0.780812i	−0.920643	−	0.390406i	$-0.872335\pi$
$389$		−	303.736i		−	0.780812i	0.920643	−	0.390406i	$-0.127665\pi$
$390$	−50.8352	+	65.5694i	−0.130347	+	0.168127i
$391$	295.272	−	360.505i	0.755173	−	0.922007i
$392$			381.616i			0.973510i
$393$		−	218.572i		−	0.556163i
$394$	114.502			0.290615
$395$	−378.933	+	488.764i	−0.959325	+	1.23738i
$396$		−	4.08568i		−	0.0103174i
$397$		−	288.785i		−	0.727417i	−0.931513	−	0.363709i	$-0.881510\pi$
$397$		−	288.785i		−	0.727417i	0.931513	−	0.363709i	$-0.118490\pi$
$398$	16.8170			0.0422538
$399$	0.153792			0.000385444
$400$	7.73055	+	30.0475i	0.0193264	+	0.0751188i
$401$		−	50.4122i		−	0.125716i	−0.998022	−	0.0628581i	$-0.979978\pi$
$401$		−	50.4122i		−	0.125716i	0.998022	−	0.0628581i	$-0.0200216\pi$
$402$	160.549			0.399375
$403$			67.6593i			0.167889i
$404$	426.284			1.05516
$405$	35.5637	+	27.5721i	0.0878116	+	0.0680793i
$406$			3.44773i			0.00849195i
$407$			0.813800i			0.00199951i
$408$	−273.546			−0.670455
$409$	9.51037			0.0232527			0.0116264	−	0.999932i	$-0.496299\pi$
$409$	9.51037			0.0232527			0.0116264	+	0.999932i	$0.496299\pi$
$410$	−57.4574	+	74.1110i	−0.140140	+	0.180759i
$411$		−	154.429i		−	0.375740i
$412$	−251.472			−0.610368
$413$	0.385402			0.000933177
$414$	62.9615	+	51.5688i	0.152081	+	0.124562i
$415$	155.083	+	120.234i	0.373695	+	0.289721i
$416$	−265.145			−0.637367
$417$			385.440i			0.924317i
$418$		−	0.261770i		−	0.000626245i
$419$		−	295.089i		−	0.704270i	−0.935949	−	0.352135i	$-0.885456\pi$
$419$		−	295.089i		−	0.704270i	0.935949	−	0.352135i	$-0.114544\pi$
$420$	−2.89121	+	3.72920i	−0.00688382	+	0.00887905i
$421$			359.179i			0.853156i	0.904451	+	0.426578i	$0.140281\pi$
$421$			359.179i			0.853156i	−0.904451	+	0.426578i	$0.859719\pi$
$422$		−	16.1676i		−	0.0383119i
$423$			30.5018i			0.0721084i
$424$		−	64.3118i		−	0.151679i
$425$	126.205	+	490.540i	0.296952	+	1.15421i
$426$	−123.496			−0.289897
$427$		−	4.41436i		−	0.0103381i
$428$	−276.077			−0.645040
$429$		−	7.34419i		−	0.0171193i
$430$	−127.319	+	164.221i	−0.296090	+	0.381909i
$431$			205.344i			0.476436i	0.971212	+	0.238218i	$0.0765632\pi$
$431$			205.344i			0.476436i	−0.971212	+	0.238218i	$0.923437\pi$
$432$			6.44864i			0.0149274i
$433$	108.786			0.251237			0.125619	−	0.992079i	$-0.459908\pi$
$433$	108.786			0.251237			0.125619	+	0.992079i	$0.459908\pi$
$434$		−	2.05206i		−	0.00472826i
$435$	74.2638	−	95.7887i	0.170721	−	0.220204i
$436$			137.443i			0.315236i
$437$	−7.56455	−	6.19576i	−0.0173102	−	0.0141779i
$438$		−	81.0381i		−	0.185018i
$439$	−21.9847			−0.0500791			−0.0250395	−	0.999686i	$-0.507971\pi$
$439$	−21.9847			−0.0500791			−0.0250395	+	0.999686i	$0.507971\pi$
$440$	16.0799	+	12.4666i	0.0365453	+	0.0283332i
$441$	146.869			0.333037
$442$	−194.101			−0.439142
$443$			30.3510i			0.0685123i	0.999413	+	0.0342562i	$0.0109062\pi$
$443$			30.3510i			0.0685123i	−0.999413	+	0.0342562i	$0.989094\pi$
$444$		−	7.04396i		−	0.0158648i
$445$	−503.152	+	648.987i	−1.13068	+	1.45840i
$446$	−154.099			−0.345514
$447$	293.313			0.656181
$448$	7.00487			0.0156359
$449$	461.260			1.02730			0.513652	−	0.857998i	$-0.328292\pi$
$449$	461.260			1.02730			0.513652	+	0.857998i	$0.328292\pi$
$450$	−85.6719	+	22.0414i	−0.190382	+	0.0489809i
$451$		−	8.30091i		−	0.0184056i
$452$	−355.159			−0.785751
$453$			9.23337i			0.0203827i
$454$		−	229.265i		−	0.504988i
$455$	−5.19707	+	6.70340i	−0.0114221	+	0.0147328i
$456$			5.73986i			0.0125874i
$457$	−391.966			−0.857694			−0.428847	−	0.903377i	$-0.641080\pi$
$457$	−391.966			−0.857694			−0.428847	+	0.903377i	$0.641080\pi$
$458$	−96.9291			−0.211636
$459$			105.277i			0.229362i
$460$	292.446	−	66.9507i	0.635753	−	0.145545i
$461$	−358.590			−0.777853			−0.388927	−	0.921269i	$-0.627154\pi$
$461$	−358.590			−0.777853			−0.388927	+	0.921269i	$0.627154\pi$
$462$			0.222745i			0.000482131i
$463$			397.755i			0.859083i	0.903047	+	0.429542i	$0.141325\pi$
$463$			397.755i			0.859083i	−0.903047	+	0.429542i	$0.858675\pi$
$464$	17.3690			0.0374332
$465$	−44.2013	+	57.0127i	−0.0950566	+	0.122608i
$466$	−291.620			−0.625794
$467$	656.225			1.40519			0.702597	−	0.711588i	$-0.252024\pi$
$467$	656.225			1.40519			0.702597	+	0.711588i	$0.252024\pi$
$468$			63.5687i			0.135831i
$469$	16.4135			0.0349968
$470$	−47.3875	−	36.7390i	−0.100825	−	0.0781681i
$471$		−	41.3177i		−	0.0877233i
$472$			14.3841i			0.0304747i
$473$		−	18.3938i		−	0.0388875i
$474$		−	252.691i		−	0.533104i
$475$	10.2931	−	2.64818i	0.0216697	−	0.00557511i
$476$	−11.0393			−0.0231918
$477$	−24.7511			−0.0518891
$478$			151.777i			0.317525i
$479$		−	454.865i		−	0.949613i	−0.880090	−	0.474807i	$-0.842518\pi$
$479$		−	454.865i		−	0.949613i	0.880090	−	0.474807i	$-0.157482\pi$
$480$	−223.423	−	173.217i	−0.465464	−	0.360869i
$481$		−	12.6618i		−	0.0263240i
$482$	232.986			0.483373
$483$	6.43680	+	5.27208i	0.0133267	+	0.0109153i
$484$	314.954			0.650731
$485$	−255.031	−	197.723i	−0.525837	−	0.407675i
$486$	−18.3864			−0.0378322
$487$		−	643.412i		−	1.32118i	−0.750749	−	0.660588i	$-0.770307\pi$
$487$		−	643.412i		−	1.32118i	0.750749	−	0.660588i	$-0.229693\pi$
$488$	164.754			0.337610
$489$	−136.471			−0.279081
$490$	−176.902	+	228.175i	−0.361024	+	0.465664i
$491$	206.492			0.420553			0.210277	−	0.977642i	$-0.432564\pi$
$491$	206.492			0.420553			0.210277	+	0.977642i	$0.432564\pi$
$492$			71.8497i			0.146036i
$493$	283.557			0.575167
$494$			4.07286i			0.00824465i
$495$	4.79790	−	6.18854i	0.00969273	−	0.0125021i
$496$	−10.3379			−0.0208426
$497$	−12.6255			−0.0254034
$498$	−80.1781			−0.161000
$499$	−608.547			−1.21953			−0.609766	−	0.792581i	$-0.708737\pi$
$499$	−608.547			−1.21953			−0.609766	+	0.792581i	$0.708737\pi$
$500$	−129.291	+	299.375i	−0.258581	+	0.598749i
$501$	153.112			0.305612
$502$	−464.901			−0.926098
$503$	146.961			0.292169			0.146084	−	0.989272i	$-0.453333\pi$
$503$	146.961			0.292169			0.146084	+	0.989272i	$0.453333\pi$
$504$		−	4.88414i		−	0.00969076i
$505$	645.689	+	500.595i	1.27859	+	0.991277i
$506$	8.97364	−	10.9561i	0.0177345	−	0.0216524i
$507$		−	178.449i		−	0.351971i
$508$		−	74.2048i		−	0.146073i
$509$	792.044			1.55608			0.778039	−	0.628215i	$-0.216214\pi$
$509$	792.044			1.55608			0.778039	+	0.628215i	$0.216214\pi$
$510$	−163.558	−	126.805i	−0.320702	−	0.248636i
$511$		−	8.28483i		−	0.0162130i
$512$		−	79.2082i		−	0.154704i
$513$	2.20905			0.00430614
$514$	204.115			0.397111
$515$	−380.902	−	295.308i	−0.739615	−	0.573415i
$516$			159.210i			0.308547i
$517$	5.30771			0.0102664
$518$			0.384025i			0.000741362i
$519$	265.957			0.512441
$520$	−250.186	−	193.966i	−0.481127	−	0.373012i
$521$		−	571.054i		−	1.09607i	−0.836454	−	0.548037i	$-0.815375\pi$
$521$		−	571.054i		−	1.09607i	0.836454	−	0.548037i	$-0.184625\pi$
$522$			49.5228i			0.0948712i
$523$	860.301			1.64494			0.822468	−	0.568812i	$-0.192597\pi$
$523$	860.301			1.64494			0.822468	+	0.568812i	$0.192597\pi$
$524$	329.212			0.628267
$525$	−8.75856	+	2.25338i	−0.0166830	+	0.00429215i
$526$			23.4208i			0.0445262i
$527$	−168.771			−0.320249
$528$	1.12215			0.00212528
$529$	−104.212	−	518.634i	−0.196997	−	0.980404i
$530$	29.8123	−	38.4532i	0.0562497	−	0.0725532i
$531$	5.53587			0.0104254
$532$			0.231640i			0.000435414i
$533$			129.153i			0.242313i
$534$		−	335.526i		−	0.628326i
$535$	−418.171	−	324.203i	−0.781628	−	0.605987i
$536$			612.589i			1.14289i
$537$			415.771i			0.774247i
$538$			541.577i			1.00665i
$539$		−	25.5571i		−	0.0474158i
$540$	−41.5289	+	53.5658i	−0.0769054	+	0.0991959i
$541$	−21.4413			−0.0396328			−0.0198164	−	0.999804i	$-0.506308\pi$
$541$	−21.4413			−0.0396328			−0.0198164	+	0.999804i	$0.506308\pi$
$542$		−	2.46279i		−	0.00454390i
$543$	−87.8516			−0.161789
$544$		−	661.384i		−	1.21578i
$545$	−161.402	+	208.183i	−0.296150	+	0.381987i
$546$		−	3.46566i		−	0.00634736i
$547$		−	817.677i		−	1.49484i	−0.664352	−	0.747420i	$-0.731292\pi$
$547$		−	817.677i		−	1.49484i	0.664352	−	0.747420i	$-0.268708\pi$
$548$	232.600			0.424453
$549$		−	63.4073i		−	0.115496i
$550$	3.83549	+	14.9080i	0.00697362	+	0.0271055i
$551$		−	5.94994i		−	0.0107984i
$552$	−196.766	+	240.236i	−0.356460	+	0.435209i
$553$		−	25.8336i		−	0.0467153i
$554$	−217.004			−0.391704
$555$	8.27187	−	10.6694i	0.0149043	−	0.0192242i
$556$	−580.547			−1.04415
$557$	−572.628			−1.02806			−0.514029	−	0.857773i	$-0.671848\pi$
$557$	−572.628			−1.02806			−0.514029	+	0.857773i	$0.671848\pi$
$558$		−	29.4756i		−	0.0528236i
$559$			286.187i			0.511963i
$560$	−1.02424	−	0.794079i	−0.00182900	−	0.00141800i
$561$	18.3195			0.0326552
$562$	−234.262			−0.416837
$563$	662.325			1.17642			0.588211	−	0.808708i	$-0.299833\pi$
$563$	662.325			1.17642			0.588211	+	0.808708i	$0.299833\pi$
$564$	−45.9416			−0.0814568
$565$	−537.956	−	417.071i	−0.952135	−	0.738179i
$566$		−	591.173i		−	1.04448i
$567$	−1.87972			−0.00331520
$568$		−	471.212i		−	0.829598i
$569$			415.048i			0.729435i	0.931118	+	0.364717i	$0.118834\pi$
$569$			415.048i			0.729435i	−0.931118	+	0.364717i	$0.881166\pi$
$570$	−2.66077	+	3.43197i	−0.00466801	+	0.00602100i
$571$		−	839.295i		−	1.46987i	−0.678138	−	0.734934i	$-0.737213\pi$
$571$		−	839.295i		−	1.46987i	0.678138	−	0.734934i	$-0.262787\pi$
$572$	11.0618			0.0193387
$573$	−446.239			−0.778776
$574$		−	3.91713i		−	0.00682426i
$575$	521.587	+	242.016i	0.907108	+	0.420898i
$576$	100.617			0.174682
$577$		−	519.223i		−	0.899867i	−0.893062	−	0.449933i	$-0.851448\pi$
$577$		−	519.223i		−	0.899867i	0.893062	−	0.449933i	$-0.148552\pi$
$578$		−	143.297i		−	0.247919i
$579$	373.111			0.644406
$580$	144.276	+	111.856i	0.248752	+	0.192854i
$581$	−8.19691			−0.0141083
$582$	131.851			0.226548
$583$			4.30701i			0.00738766i
$584$	309.208			0.529466
$585$	−74.6501	+	96.2868i	−0.127607	+	0.164593i
$586$			443.213i			0.756336i
$587$		−	517.320i		−	0.881295i	−0.897680	−	0.440647i	$-0.854749\pi$
$587$		−	517.320i		−	0.881295i	0.897680	−	0.440647i	$-0.145251\pi$
$588$			221.213i			0.376213i
$589$			3.54136i			0.00601249i
$590$	−6.66787	+	8.60050i	−0.0113015	+	0.0145771i
$591$	168.143			0.284507
$592$	1.93465			0.00326799
$593$			90.6834i			0.152923i	0.997073	+	0.0764615i	$0.0243622\pi$
$593$			90.6834i			0.152923i	−0.997073	+	0.0764615i	$0.975638\pi$
$594$			3.19948i			0.00538632i
$595$	−16.7211	−	12.9637i	−0.0281028	−	0.0217877i
$596$			441.786i			0.741251i
$597$	24.6953			0.0413657
$598$	−139.620	+	170.465i	−0.233478	+	0.285059i
$599$	409.353			0.683394			0.341697	−	0.939810i	$-0.388998\pi$
$599$	409.353			0.683394			0.341697	+	0.939810i	$0.388998\pi$
$600$	−84.1011	−	326.889i	−0.140168	−	0.544815i
$601$	294.779			0.490481			0.245240	−	0.969462i	$-0.421133\pi$
$601$	294.779			0.490481			0.245240	+	0.969462i	$0.421133\pi$
$602$		−	8.67988i		−	0.0144184i
$603$	235.762			0.390981
$604$	−13.9072			−0.0230252
$605$	477.057	+	369.857i	0.788525	+	0.611334i
$606$	−333.821			−0.550860
$607$		−	922.211i		−	1.51929i	−0.650336	−	0.759647i	$-0.725372\pi$
$607$		−	922.211i		−	1.51929i	0.650336	−	0.759647i	$-0.274628\pi$
$608$	−13.8779			−0.0228256
$609$			5.06290i			0.00831346i
$610$	98.5093	+	76.3731i	0.161491	+	0.125202i
$611$	−82.5821			−0.135159
$612$	−158.567			−0.259097
$613$	793.760			1.29488			0.647439	−	0.762117i	$-0.275840\pi$
$613$	793.760			1.29488			0.647439	+	0.762117i	$0.275840\pi$
$614$	−189.458			−0.308563
$615$	−84.3746	+	108.830i	−0.137195	+	0.176959i
$616$	−0.849903			−0.00137971
$617$	397.232			0.643812			0.321906	−	0.946772i	$-0.395676\pi$
$617$	397.232			0.643812			0.321906	+	0.946772i	$0.395676\pi$
$618$	196.926			0.318651
$619$		−	635.112i		−	1.02603i	−0.858380	−	0.513015i	$-0.828529\pi$
$619$		−	635.112i		−	1.02603i	0.858380	−	0.513015i	$-0.171471\pi$
$620$	−85.8721	−	66.5756i	−0.138503	−	0.107380i
$621$	92.4573	+	75.7274i	0.148885	+	0.121944i
$622$			73.9224i			0.118846i
$623$		−	34.3021i		−	0.0550596i
$624$	−17.4594			−0.0279797
$625$	−547.397	+	301.631i	−0.875836	+	0.482610i
$626$		−	174.462i		−	0.278694i
$627$		−	0.384403i		−	0.000613082i
$628$	62.2323			0.0990960
$629$	31.5840			0.0502130
$630$	2.26409	−	2.92032i	0.00359379	−	0.00463543i
$631$			879.720i			1.39417i	0.716989	+	0.697084i	$0.245520\pi$
$631$			879.720i			1.39417i	−0.716989	+	0.697084i	$0.754480\pi$
$632$	964.167			1.52558
$633$		−	23.7417i		−	0.0375067i
$634$	557.619			0.879526
$635$	87.1403	−	112.397i	0.137229	−	0.177004i
$636$		−	37.2799i		−	0.0586162i
$637$			397.640i			0.624239i
$638$	8.61759			0.0135072
$639$	−181.351			−0.283804
$640$	278.836	−	359.654i	0.435681	−	0.561960i
$641$			595.999i			0.929795i	0.885365	+	0.464898i	$0.153909\pi$
$641$			595.999i			0.929795i	−0.885365	+	0.464898i	$0.846091\pi$
$642$	216.194			0.336751
$643$	721.166			1.12156			0.560782	−	0.827963i	$-0.310501\pi$
$643$	721.166			1.12156			0.560782	+	0.827963i	$0.310501\pi$
$644$	−7.94076	+	9.69505i	−0.0123304	+	0.0150544i
$645$	−186.964	+	241.154i	−0.289866	+	0.373882i
$646$	−10.1594			−0.0157267
$647$		−	292.141i		−	0.451531i	−0.974182	−	0.225765i	$-0.927512\pi$
$647$		−	292.141i		−	0.451531i	0.974182	−	0.225765i	$-0.0724883\pi$
$648$		−	70.1552i		−	0.108264i
$649$		−	0.963312i		−	0.00148430i
$650$	−59.6760	−	231.952i	−0.0918092	−	0.356849i
$651$		−	3.01340i		−	0.00462888i
$652$		−	205.551i		−	0.315262i
$653$		−	84.0976i		−	0.128787i	−0.997925	−	0.0643933i	$-0.979489\pi$
$653$		−	84.0976i		−	0.128787i	0.997925	−	0.0643933i	$-0.0205112\pi$
$654$		−	107.631i		−	0.164573i
$655$	498.654	+	386.600i	0.761303	+	0.590229i
$656$	−19.7338			−0.0300820
$657$		−	119.002i		−	0.181130i
$658$	2.50466			0.00380648
$659$		−	322.032i		−	0.488667i	−0.969691	−	0.244334i	$-0.921431\pi$
$659$		−	322.032i		−	0.488667i	0.969691	−	0.244334i	$-0.0785692\pi$
$660$	9.32113	+	7.22656i	0.0141229	+	0.0109493i
$661$		−	1159.19i		−	1.75370i	−0.480767	−	0.876849i	$-0.659642\pi$
$661$		−	1159.19i		−	1.75370i	0.480767	−	0.876849i	$-0.340358\pi$
$662$			191.593i			0.289415i
$663$	−285.032			−0.429912
$664$		−	305.927i		−	0.460733i
$665$	−0.272020	+	0.350863i	−0.000409053	+	0.000527614i
$666$			5.51609i			0.00828242i
$667$	203.967	−	249.028i	0.305798	−	0.373355i
$668$			230.615i			0.345232i
$669$	−226.290			−0.338252
$670$	−283.971	+	366.278i	−0.423838	+	0.546684i
$671$	−11.0337			−0.0164436
$672$	11.8090			0.0175729
$673$			473.707i			0.703873i	0.936024	+	0.351937i	$0.114477\pi$
$673$			473.707i			0.703873i	−0.936024	+	0.351937i	$0.885523\pi$
$674$			533.981i			0.792257i
$675$	−125.807	+	32.3672i	−0.186381	+	0.0479515i
$676$	268.778			0.397601
$677$	184.139			0.271992			0.135996	−	0.990709i	$-0.456577\pi$
$677$	184.139			0.271992			0.135996	+	0.990709i	$0.456577\pi$
$678$	278.124			0.410212
$679$	13.4796			0.0198522
$680$	483.834	−	624.070i	0.711521	−	0.917750i
$681$		−	336.669i		−	0.494374i
$682$	−5.12913			−0.00752072
$683$		−	517.805i		−	0.758134i	−0.925369	−	0.379067i	$-0.876245\pi$
$683$		−	517.805i		−	0.758134i	0.925369	−	0.379067i	$-0.123755\pi$
$684$			3.32725i			0.00486440i
$685$	352.317	+	273.147i	0.514331	+	0.398755i
$686$		−	24.1311i		−	0.0351765i
$687$	−142.338			−0.207187
$688$	−43.7276			−0.0635575
$689$		−	67.0123i		−	0.0972602i
$690$	−229.013	+	52.4288i	−0.331903	+	0.0759837i
$691$	−279.174			−0.404014			−0.202007	−	0.979384i	$-0.564746\pi$
$691$	−279.174			−0.404014			−0.202007	+	0.979384i	$0.564746\pi$
$692$			400.582i			0.578876i
$693$			0.327095i			0.000471998i
$694$	603.316			0.869331
$695$	−879.349	−	681.749i	−1.26525	−	0.980933i
$696$	−188.959			−0.271492
$697$	−322.163			−0.462213
$698$		−	529.608i		−	0.758751i
$699$	−428.236			−0.612641
$700$	−3.39402	−	13.1921i	−0.00484860	−	0.0188458i
$701$			965.713i			1.37762i	0.724941	+	0.688811i	$0.241867\pi$
$701$			965.713i			1.37762i	−0.724941	+	0.688811i	$0.758133\pi$
$702$		−	49.7803i		−	0.0709121i
$703$		−	0.662734i		−	0.000942722i
$704$		−	17.5086i		−	0.0248702i
$705$	−69.5873	−	53.9502i	−0.0987054	−	0.0765251i
$706$	−505.567			−0.716101
$707$	−34.1278			−0.0482713
$708$			8.33808i			0.0117769i
$709$		−	899.712i		−	1.26899i	−0.772928	−	0.634493i	$-0.781209\pi$
$709$		−	899.712i		−	1.26899i	0.772928	−	0.634493i	$-0.218791\pi$
$710$	218.434	−	281.746i	0.307654	−	0.396825i
$711$		−	371.070i		−	0.521899i
$712$	1280.23			1.79808
$713$	−121.400	+	148.220i	−0.170266	+	0.207882i
$714$	8.64483			0.0121076
$715$	16.7551	+	12.9901i	0.0234338	+	0.0181679i
$716$	−626.230			−0.874623
$717$			222.880i			0.310851i
$718$	−681.780			−0.949555
$719$	−391.654			−0.544721			−0.272360	−	0.962195i	$-0.587804\pi$
$719$	−391.654			−0.544721			−0.272360	+	0.962195i	$0.587804\pi$
$720$	−14.7120	−	11.4061i	−0.0204334	−	0.0158417i
$721$	20.1325			0.0279230
$722$		−	425.583i		−	0.589450i
$723$	342.133			0.473213
$724$		−	132.321i		−	0.182764i
$725$	87.1792	+	338.853i	0.120247	+	0.467383i
$726$	−246.639			−0.339723
$727$	−763.786			−1.05060			−0.525300	−	0.850917i	$-0.676047\pi$
$727$	−763.786			−1.05060			−0.525300	+	0.850917i	$0.676047\pi$
$728$	13.2236			0.0181642
$729$	−27.0000			−0.0370370
$730$	184.881	+	143.336i	0.253262	+	0.196351i
$731$	−713.873			−0.976570
$732$	95.5035			0.130469
$733$	−1146.79			−1.56451			−0.782256	−	0.622956i	$-0.785931\pi$
$733$	−1146.79			−1.56451			−0.782256	+	0.622956i	$0.785931\pi$
$734$		−	312.515i		−	0.425770i
$735$	−259.775	+	335.069i	−0.353436	+	0.455876i
$736$	−580.846	−	475.744i	−0.789193	−	0.646391i
$737$		−	41.0255i		−	0.0556656i
$738$		−	56.2651i		−	0.0762400i
$739$	244.822			0.331288			0.165644	−	0.986186i	$-0.447030\pi$
$739$	244.822			0.331288			0.165644	+	0.986186i	$0.447030\pi$
$740$	16.0702	+	12.4590i	0.0217165	+	0.0168365i
$741$			5.98088i			0.00807136i
$742$			2.03244i			0.00273914i
$743$	673.089			0.905907			0.452954	−	0.891534i	$-0.350370\pi$
$743$	673.089			0.905907			0.452954	+	0.891534i	$0.350370\pi$
$744$	112.467			0.151165
$745$	−518.798	+	669.168i	−0.696373	+	0.898212i
$746$			724.957i			0.971792i
$747$	−117.739			−0.157616
$748$			27.5927i			0.0368887i
$749$	22.1024			0.0295092
$750$	101.247	−	234.439i	0.134996	−	0.312585i
$751$		−	1192.42i		−	1.58778i	−0.608061	−	0.793890i	$-0.708053\pi$
$751$		−	1192.42i		−	1.58778i	0.608061	−	0.793890i	$-0.291947\pi$
$752$		−	12.6180i		−	0.0167793i
$753$	−682.695			−0.906634
$754$	−134.080			−0.177825
$755$	−21.0651	−	16.3316i	−0.0279008	−	0.0216312i
$756$		−	2.83121i		−	0.00374499i
$757$	−1124.62			−1.48563			−0.742813	−	0.669499i	$-0.766509\pi$
$757$	−1124.62			−1.48563			−0.742813	+	0.669499i	$0.766509\pi$
$758$	777.117			1.02522
$759$	13.1775	−	16.0888i	0.0173617	−	0.0211973i
$760$	−13.0950	−	10.1524i	−0.0172303	−	0.0133584i
$761$	685.544			0.900846			0.450423	−	0.892815i	$-0.351273\pi$
$761$	685.544			0.900846			0.450423	+	0.892815i	$0.351273\pi$
$762$			58.1094i			0.0762591i
$763$		−	11.0035i		−	0.0144213i
$764$		−	672.121i		−	0.879739i
$765$	−240.180	−	186.209i	−0.313961	−	0.243410i
$766$			894.297i			1.16749i
$767$			14.9881i			0.0195412i
$768$			418.306i			0.544670i
$769$			635.177i			0.825978i	0.910736	+	0.412989i	$0.135515\pi$
$769$			635.177i			0.825978i	−0.910736	+	0.412989i	$0.864485\pi$
$770$	−0.508173	−	0.393980i	−0.000659965	−	0.000511663i
$771$	299.737			0.388765
$772$			561.977i			0.727949i
$773$	−461.524			−0.597056			−0.298528	−	0.954401i	$-0.596496\pi$
$773$	−461.524			−0.597056			−0.298528	+	0.954401i	$0.596496\pi$
$774$		−	124.677i		−	0.161081i
$775$	−51.8884	−	201.683i	−0.0669528	−	0.260236i
$776$			503.090i			0.648312i
$777$			0.563931i			0.000725780i
$778$	−358.254			−0.460480
$779$			6.76000i			0.00867779i
$780$	−145.026	−	112.437i	−0.185931	−	0.144150i
$781$			31.5574i			0.0404064i
$782$	−425.212	−	348.271i	−0.543750	−	0.445360i
$783$			72.7228i			0.0928772i
$784$	−60.7569			−0.0774961
$785$	94.2627	+	73.0807i	0.120080	+	0.0930965i
$786$	−257.804			−0.327995
$787$	−1038.33			−1.31936			−0.659679	−	0.751547i	$-0.729308\pi$
$787$	−1038.33			−1.31936			−0.659679	+	0.751547i	$0.729308\pi$
$788$			253.256i			0.321391i
$789$			34.3928i			0.0435903i
$790$	576.493	+	446.949i	0.729738	+	0.565758i
$791$	28.4336			0.0359464
$792$	−12.2079			−0.0154140
$793$	171.672			0.216484
$794$	−340.619			−0.428991
$795$	43.7786	−	56.4675i	0.0550674	−	0.0710283i
$796$			37.1959i			0.0467285i
$797$	204.188			0.256195			0.128098	−	0.991762i	$-0.459113\pi$
$797$	204.188			0.256195			0.128098	+	0.991762i	$0.459113\pi$
$798$		−	0.181396i		−	0.000227314i
$799$		−	205.995i		−	0.257816i
$800$	790.359	−	203.341i	0.987948	−	0.254177i
$801$		−	492.711i		−	0.615120i
$802$	−59.4608			−0.0741406
$803$	−20.7079			−0.0257882
$804$			355.102i			0.441669i
$805$	−23.4129	+	5.35999i	−0.0290843	+	0.00665837i
$806$	79.8036			0.0990119
$807$			795.291i			0.985491i
$808$		−	1273.73i		−	1.57639i
$809$	1116.40			1.37997			0.689986	−	0.723822i	$-0.257617\pi$
$809$	1116.40			1.37997			0.689986	+	0.723822i	$0.257617\pi$
$810$	32.5211	−	41.9471i	0.0401495	−	0.0517865i
$811$	984.368			1.21377			0.606885	−	0.794789i	$-0.292419\pi$
$811$	984.368			1.21377			0.606885	+	0.794789i	$0.292419\pi$
$812$	−7.62570			−0.00939125
$813$		−	3.61655i		−	0.00444840i
$814$	0.959870			0.00117920
$815$	241.383	−	311.346i	0.296176	−	0.382020i
$816$		−	43.5511i		−	0.0533714i
$817$			14.9793i			0.0183346i
$818$		−	11.2174i		−	0.0137132i
$819$		−	5.08923i		−	0.00621396i
$820$	−163.919	−	127.084i	−0.199901	−	0.154981i
$821$	652.577			0.794856			0.397428	−	0.917633i	$-0.369903\pi$
$821$	652.577			0.794856			0.397428	+	0.917633i	$0.369903\pi$
$822$	−182.148			−0.221591
$823$			579.859i			0.704568i	0.935893	+	0.352284i	$0.114595\pi$
$823$			579.859i			0.704568i	−0.935893	+	0.352284i	$0.885405\pi$
$824$			751.390i			0.911881i
$825$	5.63231	+	21.8920i	0.00682704	+	0.0265358i
$826$		−	0.454579i		−	0.000550337i
$827$	−836.184			−1.01111			−0.505553	−	0.862796i	$-0.668711\pi$
$827$	−836.184			−1.01111			−0.505553	+	0.862796i	$0.668711\pi$
$828$	−114.060	+	139.258i	−0.137754	+	0.168187i
$829$	116.259			0.140240			0.0701201	−	0.997539i	$-0.477662\pi$
$829$	116.259			0.140240			0.0701201	+	0.997539i	$0.477662\pi$
$830$	141.815	−	182.919i	0.170862	−	0.220385i
$831$	−318.664			−0.383471
$832$			272.415i			0.327422i
$833$	−991.884			−1.19074
$834$	454.623			0.545112
$835$	−270.816	+	349.311i	−0.324331	+	0.418336i
$836$	0.578984			0.000692565
$837$		−	43.2841i		−	0.0517134i
$838$	−348.055			−0.415340
$839$			1479.66i			1.76360i	0.471620	+	0.881802i	$0.343669\pi$
$839$			1479.66i			1.76360i	−0.471620	+	0.881802i	$0.656331\pi$
$840$	11.1427	+	8.63884i	0.0132652	+	0.0102843i
$841$	−645.125			−0.767093
$842$	423.648			0.503145
$843$	−344.008			−0.408076
$844$	35.7596			0.0423692
$845$	407.116	+	315.632i	0.481794	+	0.373529i
$846$	35.9767			0.0425256
$847$	−25.2148			−0.0297696
$848$	10.2391			0.0120744
$849$		−	868.122i		−	1.02252i
$850$	578.587	−	148.857i	0.680691	−	0.175126i
$851$	22.7189	−	27.7380i	0.0266967	−	0.0325946i
$852$		−	273.149i		−	0.320598i
$853$			741.608i			0.869412i	0.900572	+	0.434706i	$0.143148\pi$
$853$			741.608i			0.869412i	−0.900572	+	0.434706i	$0.856852\pi$
$854$	−5.20670			−0.00609683
$855$	−3.90726	+	5.03975i	−0.00456990	+	0.00589445i
$856$			824.910i			0.963680i
$857$			627.459i			0.732158i	0.930584	+	0.366079i	$0.119300\pi$
$857$			627.459i			0.732158i	−0.930584	+	0.366079i	$0.880700\pi$
$858$	−8.66241			−0.0100961
$859$	−777.480			−0.905099			−0.452549	−	0.891739i	$-0.649485\pi$
$859$	−777.480			−0.905099			−0.452549	+	0.891739i	$0.649485\pi$
$860$	−363.224	−	281.603i	−0.422354	−	0.327446i
$861$		−	5.75220i		−	0.00668083i
$862$	242.201			0.280976
$863$			1341.61i			1.55459i	0.629139	+	0.777293i	$0.283408\pi$
$863$			1341.61i			1.55459i	−0.629139	+	0.777293i	$0.716592\pi$
$864$	169.623			0.196322
$865$	−470.412	+	606.758i	−0.543829	+	0.701454i
$866$		−	128.312i		−	0.148166i
$867$		−	210.428i		−	0.242708i
$868$	4.53876			0.00522898
$869$	−64.5710			−0.0743049
$870$	−112.982	−	87.5935i	−0.129864	−	0.100682i
$871$			638.312i			0.732849i
$872$	410.675			0.470957
$873$	193.620			0.221787
$874$	−7.30785	+	8.92232i	−0.00836138	+	0.0102086i
$875$	10.3508	−	23.9676i	0.0118295	−	0.0273915i
$876$	179.240			0.204612
$877$			1221.50i			1.39282i	0.717644	+	0.696410i	$0.245221\pi$
$877$			1221.50i			1.39282i	−0.717644	+	0.696410i	$0.754779\pi$
$878$			25.9308i			0.0295339i
$879$			650.846i			0.740439i
$880$	−1.98480	+	2.56008i	−0.00225545	+	0.00290918i
$881$			1374.31i			1.55994i	0.625815	+	0.779972i	$0.284767\pi$
$881$			1374.31i			1.55994i	−0.625815	+	0.779972i	$0.715233\pi$
$882$		−	173.231i		−	0.196407i
$883$			498.742i			0.564826i	0.959293	+	0.282413i	$0.0911349\pi$
$883$			498.742i			0.564826i	−0.959293	+	0.282413i	$0.908865\pi$
$884$		−	429.313i		−	0.485648i
$885$	−9.79159	+	12.6296i	−0.0110639	+	0.0142707i
$886$	35.7987			0.0404048
$887$			1147.74i			1.29395i	0.762509	+	0.646977i	$0.223967\pi$
$887$			1147.74i			1.29395i	−0.762509	+	0.646977i	$0.776033\pi$
$888$	−21.0472			−0.0237018
$889$			5.94075i			0.00668250i
$890$	765.474	+	593.463i	0.860083	+	0.666813i
$891$			4.69834i			0.00527311i
$892$		−	340.837i		−	0.382104i
$893$	−4.32243			−0.00484035
$894$		−	345.960i		−	0.386980i
$895$	−948.545	−	735.396i	−1.05983	−	0.821671i
$896$			19.0095i			0.0212159i
$897$	−205.028	+	250.323i	−0.228571	+	0.279067i
$898$		−	544.052i		−	0.605848i
$899$	−116.583			−0.129681
$900$	−48.7513	−	189.489i	−0.0541681	−	0.210544i
$901$	167.157			0.185524
$902$	−9.79085			−0.0108546
$903$		−	12.7462i		−	0.0141153i
$904$			1061.21i			1.17390i
$905$	155.388	−	200.426i	0.171699	−	0.221465i
$906$	10.8907			0.0120206
$907$	526.591			0.580586			0.290293	−	0.956938i	$-0.406247\pi$
$907$	526.591			0.580586			0.290293	+	0.956938i	$0.406247\pi$
$908$	507.088			0.558467
$909$	−490.207			−0.539282
$910$	7.90661	+	6.12990i	0.00868858	+	0.00673615i
$911$			639.968i			0.702489i	0.936284	+	0.351245i	$0.114241\pi$
$911$			639.968i			0.702489i	−0.936284	+	0.351245i	$0.885759\pi$
$912$	−0.913841			−0.00100202
$913$			20.4881i			0.0224405i
$914$			462.321i			0.505821i
$915$	144.658	+	112.152i	0.158096	+	0.122570i
$916$		−	214.388i		−	0.234048i
$917$	−26.3563			−0.0287418
$918$	124.173			0.135265
$919$			1047.59i			1.13992i	0.821672	+	0.569960i	$0.193041\pi$
$919$			1047.59i			1.13992i	−0.821672	+	0.569960i	$0.806959\pi$
$920$	−200.047	−	873.821i	−0.217442	−	0.949806i
$921$	−278.214			−0.302078
$922$			422.954i			0.458735i
$923$		−	490.998i		−	0.531959i
$924$	−0.492667			−0.000533189
$925$	9.71045	+	37.7431i	0.0104978	+	0.0408034i
$926$	469.149			0.506640
$927$	289.181			0.311953
$928$		−	456.868i		−	0.492315i
$929$	1089.35			1.17261			0.586305	−	0.810091i	$-0.300582\pi$
$929$	1089.35			1.17261			0.586305	+	0.810091i	$0.300582\pi$
$930$	67.2460	+	52.1350i	0.0723075	+	0.0560592i
$931$			20.8129i			0.0223554i
$932$		−	645.006i		−	0.692066i
$933$			108.553i			0.116348i
$934$		−	774.012i		−	0.828707i
$935$	−32.4027	+	41.7944i	−0.0346553	+	0.0446999i
$936$	189.941			0.202929
$937$	809.090			0.863490			0.431745	−	0.901996i	$-0.357898\pi$
$937$	809.090			0.863490			0.431745	+	0.901996i	$0.357898\pi$
$938$		−	19.3596i		−	0.0206392i
$939$		−	256.193i		−	0.272836i
$940$	81.2594	−	104.812i	0.0864461	−	0.111502i
$941$		−	473.922i		−	0.503636i	−0.967775	−	0.251818i	$-0.918972\pi$
$941$		−	473.922i		−	0.503636i	0.967775	−	0.251818i	$-0.0810285\pi$
$942$	−48.7338			−0.0517344
$943$	−231.737	+	282.932i	−0.245744	+	0.300034i
$944$	−2.29008			−0.00242593
$945$	3.32475	−	4.28841i	0.00351826	−	0.00453800i
$946$	−21.6953			−0.0229337
$947$		−	960.082i		−	1.01381i	−0.862001	−	0.506907i	$-0.830789\pi$
$947$		−	960.082i		−	1.01381i	0.862001	−	0.506907i	$-0.169211\pi$
$948$	558.903			0.589560
$949$	322.192			0.339507
$950$	−3.12350	−	12.1406i	−0.00328790	−	0.0127796i
$951$	818.849			0.861040
$952$			32.9852i			0.0346483i
$953$	940.170			0.986537			0.493268	−	0.869877i	$-0.335802\pi$
$953$	940.170			0.986537			0.493268	+	0.869877i	$0.335802\pi$
$954$			29.1937i			0.0306014i
$955$	789.286	−	1018.05i	0.826477	−	1.06603i
$956$	−335.700			−0.351151
$957$	12.6547			0.0132233
$958$	−536.509			−0.560030
$959$	−18.6217			−0.0194178
$960$	−177.967	+	229.549i	−0.185382	+	0.239114i
$961$	−891.611			−0.927795
$962$	−14.9345			−0.0155245
$963$	317.476			0.329674
$964$			515.318i			0.534562i
$965$	−659.941	+	851.220i	−0.683877	+	0.882093i
$966$	6.21837	−	7.59214i	0.00643723	−	0.00785936i
$967$			989.142i			1.02290i	0.859314	+	0.511449i	$0.170891\pi$
$967$			989.142i			1.02290i	−0.859314	+	0.511449i	$0.829109\pi$
$968$		−	941.073i		−	0.972183i
$969$	−14.9189			−0.0153961
$970$	−233.212	+	300.807i	−0.240425	+	0.310110i
$971$		−	1565.77i		−	1.61253i	−0.591553	−	0.806266i	$-0.701485\pi$
$971$		−	1565.77i		−	1.61253i	0.591553	−	0.806266i	$-0.298515\pi$
$972$		−	40.6672i		−	0.0418387i
$973$	46.4779			0.0477676
$974$	−758.899			−0.779157
$975$	−87.6325	−	340.615i	−0.0898795	−	0.349349i
$976$			26.2304i			0.0268754i
$977$	878.602			0.899285			0.449643	−	0.893208i	$-0.351551\pi$
$977$	878.602			0.899285			0.449643	+	0.893208i	$0.351551\pi$
$978$			160.966i			0.164587i
$979$	−85.7381			−0.0875772
$980$	−504.678	−	391.271i	−0.514978	−	0.399256i
$981$		−	158.053i		−	0.161114i
$982$		−	243.555i		−	0.248019i
$983$	−127.955			−0.130168			−0.0650838	−	0.997880i	$-0.520731\pi$
$983$	−127.955			−0.130168			−0.0650838	+	0.997880i	$0.520731\pi$
$984$	214.685			0.218176
$985$	−297.404	+	383.604i	−0.301933	+	0.389446i
$986$		−	334.453i		−	0.339202i
$987$	3.67803			0.00372647
$988$	−9.00835			−0.00911777
$989$	−513.500	+	626.944i	−0.519211	+	0.633917i
$990$	−7.29933	−	5.65908i	−0.00737306	−	0.00571625i
$991$	1504.84			1.51850			0.759251	−	0.650798i	$-0.225565\pi$
$991$	1504.84			1.51850			0.759251	+	0.650798i	$0.225565\pi$
$992$			271.925i			0.274118i
$993$			281.349i			0.283332i
$994$			14.8917i			0.0149815i
$995$	−43.6799	+	56.3402i	−0.0438994	+	0.0566234i
$996$		−	177.338i		−	0.178050i
$997$		−	1015.68i		−	1.01874i	−0.860548	−	0.509370i	$-0.829879\pi$
$997$		−	1015.68i		−	1.01874i	0.860548	−	0.509370i	$-0.170121\pi$
$998$			717.776i			0.719214i
$999$			8.10023i			0.00810834i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	345.3.d.a.229.18	yes	48
5.4	even	2	inner	345.3.d.a.229.31	yes	48
23.22	odd	2	inner	345.3.d.a.229.17	✓	48
115.114	odd	2	inner	345.3.d.a.229.32	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
345.3.d.a.229.17	✓	48	23.22	odd	2	inner
345.3.d.a.229.18	yes	48	1.1	even	1	trivial
345.3.d.a.229.31	yes	48	5.4	even	2	inner
345.3.d.a.229.32	yes	48	115.114	odd	2	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:	\( N \)	\(=\)	\( 345 = 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	345.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.17949i q^{2} -1.73205i q^{3} +2.60880 q^{4} +(3.95152 + 3.06357i) q^{5} -2.04294 q^{6} -0.208857 q^{7} -7.79502i q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q-1.17949i q^{2} -1.73205i q^{3} +2.60880 q^{4} +(3.95152 + 3.06357i) q^{5} -2.04294 q^{6} -0.208857 q^{7} -7.79502i q^{8} -3.00000 q^{9} +(3.61345 - 4.66079i) q^{10} +0.522038i q^{11} -4.51857i q^{12} -8.12234i q^{13} +0.246345i q^{14} +(5.30626 - 6.84424i) q^{15} +1.24104 q^{16} +20.2606 q^{17} +3.53847i q^{18} -0.425132i q^{19} +(10.3087 + 7.99224i) q^{20} +0.361751i q^{21} +0.615740 q^{22} +(14.5738 - 17.7934i) q^{23} -13.5014 q^{24} +(6.22908 + 24.2115i) q^{25} -9.58023 q^{26} +5.19615i q^{27} -0.544867 q^{28} +13.9955 q^{29} +(-8.07272 - 6.25869i) q^{30} -8.33003 q^{31} -32.6439i q^{32} +0.904197 q^{33} -23.8972i q^{34} +(-0.825305 - 0.639849i) q^{35} -7.82640 q^{36} +1.55889 q^{37} -0.501439 q^{38} -14.0683 q^{39} +(23.8806 - 30.8022i) q^{40} -15.9010 q^{41} +0.426683 q^{42} -35.2346 q^{43} +1.36189i q^{44} +(-11.8546 - 9.19071i) q^{45} +(-20.9872 - 17.1896i) q^{46} -10.1673i q^{47} -2.14955i q^{48} -48.9564 q^{49} +(28.5573 - 7.34714i) q^{50} -35.0923i q^{51} -21.1896i q^{52} +8.25037 q^{53} +6.12882 q^{54} +(-1.59930 + 2.06285i) q^{55} +1.62805i q^{56} -0.736350 q^{57} -16.5076i q^{58} -1.84529 q^{59} +(13.8430 - 17.8553i) q^{60} +21.1358i q^{61} +9.82520i q^{62} +0.626572 q^{63} -33.5390 q^{64} +(24.8834 - 32.0956i) q^{65} -1.06649i q^{66} -78.5872 q^{67} +52.8558 q^{68} +(-30.8191 - 25.2425i) q^{69} +(-0.754696 + 0.973439i) q^{70} +60.4503 q^{71} +23.3851i q^{72} +39.6674i q^{73} -1.83870i q^{74} +(41.9356 - 10.7891i) q^{75} -1.10908i q^{76} -0.109032i q^{77} +16.5934i q^{78} +123.690i q^{79} +(4.90401 + 3.80202i) q^{80} +9.00000 q^{81} +18.7550i q^{82} +39.2464 q^{83} +0.943737i q^{84} +(80.0601 + 62.0697i) q^{85} +41.5589i q^{86} -24.2409i q^{87} +4.06930 q^{88} +164.237i q^{89} +(-10.8404 + 13.9824i) q^{90} +1.69641i q^{91} +(38.0200 - 46.4195i) q^{92} +14.4280i q^{93} -11.9922 q^{94} +(1.30242 - 1.67992i) q^{95} -56.5409 q^{96} -64.5399 q^{97} +57.7436i q^{98} -1.56611i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 92 q^{4} + 12 q^{6} - 144 q^{9}+O(q^{10}) \) 48 * q - 92 * q^4 + 12 * q^6 - 144 * q^9	\( 48 q - 92 q^{4} + 12 q^{6} - 144 q^{9} + 148 q^{16} - 12 q^{24} - 64 q^{25} + 136 q^{26} + 76 q^{29} - 68 q^{31} - 108 q^{35} + 276 q^{36} + 48 q^{39} + 20 q^{41} + 344 q^{46} + 412 q^{49} - 352 q^{50} - 36 q^{54} - 184 q^{55} - 396 q^{59} - 684 q^{64} - 144 q^{69} + 600 q^{70} + 156 q^{71} - 120 q^{75} + 432 q^{81} - 76 q^{85} + 112 q^{95} + 516 q^{96}+O(q^{100}) \) 48 * q - 92 * q^4 + 12 * q^6 - 144 * q^9 + 148 * q^16 - 12 * q^24 - 64 * q^25 + 136 * q^26 + 76 * q^29 - 68 * q^31 - 108 * q^35 + 276 * q^36 + 48 * q^39 + 20 * q^41 + 344 * q^46 + 412 * q^49 - 352 * q^50 - 36 * q^54 - 184 * q^55 - 396 * q^59 - 684 * q^64 - 144 * q^69 + 600 * q^70 + 156 * q^71 - 120 * q^75 + 432 * q^81 - 76 * q^85 + 112 * q^95 + 516 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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