LMFDB - Embedded newform 121.4.c.b.27.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [121,4,Mod(3,121)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("121.3"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(121, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([8])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 121 = 11^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	121.c (of order $5$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,-3,-3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$7.13923111069$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.29283765625.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 10x^{6} - 19x^{5} + 109x^{4} + 171x^{3} + 810x^{2} + 729x + 6561 $ x^8 - x^7 + 10x^6 - 19x^5 + 109x^4 + 171x^3 + 810x^2 + 729x + 6561
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 11)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			27.2
Root			$-2.05602 + 1.49379i$ of defining polynomial
Character	$\chi$	$=$	121.27
Dual form			121.4.c.b.9.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.285330 + 0.878155i) q^{2} +(1.24700 + 0.906001i) q^{3} +(5.78239 - 4.20115i) q^{4} +(2.69633 - 8.29844i) q^{5} +(-0.439802 + 1.35357i) q^{6} +(0.627082 - 0.455601i) q^{7} +(11.3152 + 8.22096i) q^{8} +(-7.60928 - 23.4190i) q^{9} +8.05666 q^{10} +11.0169 q^{12} +(-19.9632 - 61.4404i) q^{13} +(0.579014 + 0.420678i) q^{14} +(10.8807 - 7.90531i) q^{15} +(13.6787 - 42.0987i) q^{16} +(-21.6699 + 66.6930i) q^{17} +(18.3943 - 13.3643i) q^{18} +(104.861 + 76.1863i) q^{19} +(-19.2718 - 59.3125i) q^{20} +1.19475 q^{21} +103.308 q^{23} +(6.66187 + 20.5031i) q^{24} +(39.5332 + 28.7225i) q^{25} +(48.2581 - 35.0616i) q^{26} +(24.5893 - 75.6779i) q^{27} +(1.71198 - 5.26893i) q^{28} +(-55.6258 + 40.4145i) q^{29} +(10.0467 + 7.29935i) q^{30} +(1.76980 + 5.44688i) q^{31} +152.763 q^{32} -64.7499 q^{34} +(-2.08996 - 6.43225i) q^{35} +(-142.386 - 103.450i) q^{36} +(-139.388 + 101.272i) q^{37} +(-36.9833 + 113.823i) q^{38} +(30.7709 - 94.7031i) q^{39} +(98.7306 - 71.7320i) q^{40} +(-171.044 - 124.271i) q^{41} +(0.340898 + 1.04917i) q^{42} -300.793 q^{43} -214.858 q^{45} +(29.4768 + 90.7203i) q^{46} +(154.537 + 112.277i) q^{47} +(55.1989 - 40.1043i) q^{48} +(-105.807 + 325.641i) q^{49} +(-13.9428 + 42.9117i) q^{50} +(-87.4464 + 63.5335i) q^{51} +(-373.556 - 271.404i) q^{52} +(198.266 + 610.201i) q^{53} +73.4730 q^{54} +10.8410 q^{56} +(61.7378 + 190.009i) q^{57} +(-51.3620 - 37.3166i) q^{58} +(-42.0710 + 30.5663i) q^{59} +(29.7052 - 91.4232i) q^{60} +(152.276 - 468.657i) q^{61} +(-4.27823 + 3.10832i) q^{62} +(-15.4413 - 11.2188i) q^{63} +(-65.8417 - 202.640i) q^{64} -563.687 q^{65} -320.988 q^{67} +(154.884 + 476.684i) q^{68} +(128.825 + 93.5970i) q^{69} +(5.05219 - 3.67063i) q^{70} +(-56.4304 + 173.675i) q^{71} +(106.426 - 327.545i) q^{72} +(-168.213 + 122.214i) q^{73} +(-128.704 - 93.5088i) q^{74} +(23.2754 + 71.6342i) q^{75} +926.421 q^{76} +91.9439 q^{78} +(-201.747 - 620.913i) q^{79} +(-312.471 - 227.024i) q^{80} +(-438.649 + 318.697i) q^{81} +(60.3252 - 185.662i) q^{82} +(-371.554 + 1143.52i) q^{83} +(6.90850 - 5.01932i) q^{84} +(495.019 + 359.652i) q^{85} +(-85.8253 - 264.143i) q^{86} -105.981 q^{87} +716.942 q^{89} +(-61.3054 - 188.679i) q^{90} +(-40.5109 - 29.4329i) q^{91} +(597.366 - 434.012i) q^{92} +(-2.72794 + 8.39572i) q^{93} +(-54.5031 + 167.743i) q^{94} +(914.969 - 664.764i) q^{95} +(190.496 + 138.403i) q^{96} +(-194.177 - 597.614i) q^{97} -316.153 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 3 q^{2} - 3 q^{3} - 17 q^{4} + 18 q^{5} + 14 q^{6} - 10 q^{7} + 113 q^{8} + 31 q^{9} - 40 q^{10} + 190 q^{12} - 40 q^{13} + 64 q^{14} + 119 q^{15} + 343 q^{16} + 201 q^{17} - 53 q^{18} + 302 q^{19}+ \cdots - 2740 q^{98}+O(q^{100}) $ 8 * q - 3 * q^2 - 3 * q^3 - 17 * q^4 + 18 * q^5 + 14 * q^6 - 10 * q^7 + 113 * q^8 + 31 * q^9 - 40 * q^10 + 190 * q^12 - 40 * q^13 + 64 * q^14 + 119 * q^15 + 343 * q^16 + 201 * q^17 - 53 * q^18 + 302 * q^19 - 88 * q^20 - 334 * q^21 - 12 * q^23 - 348 * q^24 + 214 * q^25 + 340 * q^26 + 72 * q^27 - 18 * q^28 + 164 * q^29 - 306 * q^30 + 324 * q^31 - 324 * q^32 - 298 * q^34 + 593 * q^35 - 125 * q^36 - 174 * q^37 - 327 * q^38 + 125 * q^39 - 282 * q^40 + 121 * q^41 - 590 * q^42 + 650 * q^43 + 452 * q^45 - 54 * q^46 + 12 * q^47 - 991 * q^48 - 1130 * q^49 - 1163 * q^50 - 194 * q^51 - 1600 * q^52 + 682 * q^53 + 3100 * q^54 - 1560 * q^56 + 333 * q^57 - 2348 * q^58 - 854 * q^59 - 502 * q^60 - 630 * q^61 + 2114 * q^62 - 67 * q^63 - 1289 * q^64 - 1790 * q^65 + 86 * q^67 + 575 * q^68 + 1198 * q^69 + 166 * q^70 - 1772 * q^71 - 104 * q^72 - 2425 * q^73 - 1274 * q^74 + 975 * q^75 + 242 * q^76 - 1340 * q^78 + 116 * q^79 + 1794 * q^80 - 26 * q^81 + 2708 * q^82 + 1738 * q^83 + 174 * q^84 + 1662 * q^85 - 784 * q^86 - 2310 * q^87 + 3782 * q^89 - 2658 * q^90 - 55 * q^91 + 5900 * q^92 + 2743 * q^93 + 1458 * q^94 + 487 * q^95 + 2383 * q^96 + 3116 * q^97 - 2740 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/121\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{2}{5}\right)$

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 $

$2$	0.285330	+	0.878155i	0.100879	+	0.310475i	0.988741	−	0.149635i	$-0.0478099\pi$
$2$	0.285330	+	0.878155i	0.100879	+	0.310475i	−0.887862	+	0.460110i	$0.847810\pi$
$3$	1.24700	+	0.906001i	0.239986	+	0.174360i	0.701277	−	0.712889i	$-0.252614\pi$
$3$	1.24700	+	0.906001i	0.239986	+	0.174360i	−0.461291	+	0.887249i	$0.652614\pi$
$4$	5.78239	−	4.20115i	0.722799	−	0.525144i
$5$	2.69633	−	8.29844i	0.241167	−	0.742235i	−0.755076	−	0.655637i	$-0.772400\pi$
$5$	2.69633	−	8.29844i	0.241167	−	0.742235i	0.996243	−	0.0865984i	$-0.0275997\pi$
$6$	−0.439802	+	1.35357i	−0.0299248	+	0.0920989i
$7$	0.627082	−	0.455601i	0.0338592	−	0.0246002i	−0.570727	−	0.821140i	$-0.693339\pi$
$7$	0.627082	−	0.455601i	0.0338592	−	0.0246002i	0.604586	+	0.796540i	$0.293339\pi$
$8$	11.3152	+	8.22096i	0.500065	+	0.363319i
$9$	−7.60928	−	23.4190i	−0.281825	−	0.867369i
$10$	8.05666			0.254774
$11$		0			0
$11$		0			0
$12$	11.0169			0.265026
$13$	−19.9632	−	61.4404i	−0.425907	−	1.31081i	−0.902123	−	0.431480i	$-0.857992\pi$
$13$	−19.9632	−	61.4404i	−0.425907	−	1.31081i	0.476215	−	0.879329i	$-0.342008\pi$
$14$	0.579014	+	0.420678i	0.0110534	+	0.00803079i
$15$	10.8807	−	7.90531i	0.187293	−	0.136076i
$16$	13.6787	−	42.0987i	0.213730	−	0.657792i
$17$	−21.6699	+	66.6930i	−0.309160	+	0.951496i	0.668932	+	0.743323i	$0.266752\pi$
$17$	−21.6699	+	66.6930i	−0.309160	+	0.951496i	−0.978092	+	0.208173i	$0.933248\pi$
$18$	18.3943	−	13.3643i	0.240866	−	0.174999i
$19$	104.861	+	76.1863i	1.26615	+	0.919913i	0.999042	−	0.0437534i	$-0.0139316\pi$
$19$	104.861	+	76.1863i	1.26615	+	0.919913i	0.267109	+	0.963666i	$0.413932\pi$
$20$	−19.2718	−	59.3125i	−0.215465	−	0.663134i
$21$	1.19475			0.0124150
$22$		0			0
$23$	103.308			0.936572			0.468286	−	0.883577i	$-0.344872\pi$
$23$	103.308			0.936572			0.468286	+	0.883577i	$0.344872\pi$
$24$	6.66187	+	20.5031i	0.0566604	+	0.174383i
$25$	39.5332	+	28.7225i	0.316265	+	0.229780i
$26$	48.2581	−	35.0616i	0.364008	−	0.264467i
$27$	24.5893	−	75.6779i	0.175267	−	0.539416i
$28$	1.71198	−	5.26893i	0.0115548	−	0.0355620i
$29$	−55.6258	+	40.4145i	−0.356188	+	0.258786i	−0.751460	−	0.659778i	$-0.770650\pi$
$29$	−55.6258	+	40.4145i	−0.356188	+	0.258786i	0.395272	+	0.918564i	$0.370650\pi$
$30$	10.0467	+	7.29935i	0.0611422	+	0.0444224i
$31$	1.76980	+	5.44688i	0.0102537	+	0.0315577i	0.956052	−	0.293196i	$-0.0947187\pi$
$31$	1.76980	+	5.44688i	0.0102537	+	0.0315577i	−0.945799	+	0.324753i	$0.894719\pi$
$32$	152.763			0.843903
$33$		0			0
$34$	−64.7499			−0.326604
$35$	−2.08996	−	6.43225i	−0.0100934	−	0.0310642i
$36$	−142.386	−	103.450i	−0.659197	−	0.478934i
$37$	−139.388	+	101.272i	−0.619332	+	0.449971i	−0.852688	−	0.522420i	$-0.825029\pi$
$37$	−139.388	+	101.272i	−0.619332	+	0.449971i	0.233356	+	0.972391i	$0.425029\pi$
$38$	−36.9833	+	113.823i	−0.157881	+	0.485908i
$39$	30.7709	−	94.7031i	0.126341	−	0.388837i
$40$	98.7306	−	71.7320i	0.390267	−	0.283546i
$41$	−171.044	−	124.271i	−0.651528	−	0.473363i	0.212263	−	0.977213i	$-0.431917\pi$
$41$	−171.044	−	124.271i	−0.651528	−	0.473363i	−0.863791	+	0.503850i	$0.831917\pi$
$42$	0.340898	+	1.04917i	0.00125242	+	0.00385455i
$43$	−300.793			−1.06676			−0.533378	−	0.845877i	$-0.679078\pi$
$43$	−300.793			−1.06676			−0.533378	+	0.845877i	$0.679078\pi$
$44$		0			0
$45$	−214.858			−0.711758
$46$	29.4768	+	90.7203i	0.0944808	+	0.290782i
$47$	154.537	+	112.277i	0.479606	+	0.348454i	0.801173	−	0.598433i	$-0.204210\pi$
$47$	154.537	+	112.277i	0.479606	+	0.348454i	−0.321567	+	0.946887i	$0.604210\pi$
$48$	55.1989	−	40.1043i	0.165985	−	0.120595i
$49$	−105.807	+	325.641i	−0.308476	+	0.949391i
$50$	−13.9428	+	42.9117i	−0.0394363	+	0.121373i
$51$	−87.4464	+	63.5335i	−0.240097	+	0.174441i
$52$	−373.556	−	271.404i	−0.996209	−	0.723788i
$53$	198.266	+	610.201i	0.513848	+	1.58146i	0.785368	+	0.619030i	$0.212474\pi$
$53$	198.266	+	610.201i	0.513848	+	1.58146i	−0.271519	+	0.962433i	$0.587526\pi$
$54$	73.4730			0.185156
$55$		0			0
$56$	10.8410			0.0258695
$57$	61.7378	+	190.009i	0.143463	+	0.441532i
$58$	−51.3620	−	37.3166i	−0.116279	−	0.0844813i
$59$	−42.0710	+	30.5663i	−0.0928334	+	0.0674474i	−0.633234	−	0.773961i	$-0.718273\pi$
$59$	−42.0710	+	30.5663i	−0.0928334	+	0.0674474i	0.540400	+	0.841408i	$0.318273\pi$
$60$	29.7052	−	91.4232i	0.0639154	−	0.196711i
$61$	152.276	−	468.657i	0.319621	−	0.983694i	−0.654189	−	0.756331i	$-0.726990\pi$
$61$	152.276	−	468.657i	0.319621	−	0.983694i	0.973810	−	0.227362i	$-0.0730102\pi$
$62$	−4.27823	+	3.10832i	−0.00876348	+	0.00636704i
$63$	−15.4413	−	11.2188i	−0.0308798	−	0.0224355i
$64$	−65.8417	−	202.640i	−0.128597	−	0.395781i
$65$	−563.687			−1.07564
$66$		0			0
$67$	−320.988			−0.585298			−0.292649	−	0.956220i	$-0.594537\pi$
$67$	−320.988			−0.585298			−0.292649	+	0.956220i	$0.594537\pi$
$68$	154.884	+	476.684i	0.276212	+	0.850094i
$69$	128.825	+	93.5970i	0.224764	+	0.163301i
$70$	5.05219	−	3.67063i	0.00862645	−	0.00626749i
$71$	−56.4304	+	173.675i	−0.0943248	+	0.290302i	−0.987077	−	0.160246i	$-0.948771\pi$
$71$	−56.4304	+	173.675i	−0.0943248	+	0.290302i	0.892752	+	0.450548i	$0.148771\pi$
$72$	106.426	−	327.545i	0.174200	−	0.536133i
$73$	−168.213	+	122.214i	−0.269696	+	0.195946i	−0.714411	−	0.699727i	$-0.753305\pi$
$73$	−168.213	+	122.214i	−0.269696	+	0.195946i	0.444714	+	0.895672i	$0.353305\pi$
$74$	−128.704	−	93.5088i	−0.202183	−	0.146894i
$75$	23.2754	+	71.6342i	0.0358348	+	0.110288i
$76$	926.421			1.39826
$77$		0			0
$78$	91.9439			0.133469
$79$	−201.747	−	620.913i	−0.287320	−	0.884281i	−0.985694	−	0.168547i	$-0.946092\pi$
$79$	−201.747	−	620.913i	−0.287320	−	0.884281i	0.698373	−	0.715734i	$-0.253908\pi$
$80$	−312.471	−	227.024i	−0.436692	−	0.317275i
$81$	−438.649	+	318.697i	−0.601714	+	0.437171i
$82$	60.3252	−	185.662i	0.0812415	−	0.250036i
$83$	−371.554	+	1143.52i	−0.491365	+	1.51227i	0.331181	+	0.943567i	$0.392553\pi$
$83$	−371.554	+	1143.52i	−0.491365	+	1.51227i	−0.822546	+	0.568699i	$0.807447\pi$
$84$	6.90850	−	5.01932i	0.00897357	−	0.00651968i
$85$	495.019	+	359.652i	0.631675	+	0.458939i
$86$	−85.8253	−	264.143i	−0.107614	−	0.331201i
$87$	−105.981			−0.130602
$88$		0			0
$89$	716.942			0.853885			0.426942	−	0.904279i	$-0.359591\pi$
$89$	716.942			0.853885			0.426942	+	0.904279i	$0.359591\pi$
$90$	−61.3054	−	188.679i	−0.0718017	−	0.220983i
$91$	−40.5109	−	29.4329i	−0.0466670	−	0.0339056i
$92$	597.366	−	434.012i	0.676954	−	0.491836i
$93$	−2.72794	+	8.39572i	−0.00304165	+	0.00936124i
$94$	−54.5031	+	167.743i	−0.0598039	+	0.184057i
$95$	914.969	−	664.764i	0.988145	−	0.717930i
$96$	190.496	+	138.403i	0.202525	+	0.147143i
$97$	−194.177	−	597.614i	−0.203254	−	0.625552i	−0.999781	−	0.0209481i	$-0.993332\pi$
$97$	−194.177	−	597.614i	−0.203254	−	0.625552i	0.796526	−	0.604604i	$-0.206668\pi$
$98$	−316.153			−0.325881
$99$		0			0
$100$	349.264			0.349264
$101$	−157.355	−	484.288i	−0.155024	−	0.477114i	0.843140	−	0.537695i	$-0.180705\pi$
$101$	−157.355	−	484.288i	−0.155024	−	0.477114i	−0.998163	+	0.0605810i	$0.980705\pi$
$102$	−80.7434	−	58.6635i	−0.0783803	−	0.0569466i
$103$	141.519	−	102.820i	0.135381	−	0.0983604i	−0.518033	−	0.855360i	$-0.673336\pi$
$103$	141.519	−	102.820i	0.135381	−	0.0983604i	0.653415	+	0.757000i	$0.273336\pi$
$104$	279.212	−	859.327i	0.263260	−	0.810230i
$105$	3.22143	−	9.91455i	0.00299409	−	0.00921487i
$106$	−479.280	+	348.217i	−0.439168	+	0.319074i
$107$	1431.42	+	1039.99i	1.29327	+	0.939619i	0.999866	−	0.0163681i	$-0.00521035\pi$
$107$	1431.42	+	1039.99i	1.29327	+	0.939619i	0.293409	+	0.955987i	$0.405210\pi$
$108$	−175.750	−	540.903i	−0.156588	−	0.481930i
$109$	823.593			0.723724			0.361862	−	0.932232i	$-0.382141\pi$
$109$	823.593			0.723724			0.361862	+	0.932232i	$0.382141\pi$
$110$		0			0
$111$	−265.570			−0.227088
$112$	−10.6026	−	32.6314i	−0.00894508	−	0.0275301i
$113$	880.947	+	640.045i	0.733385	+	0.532836i	0.890633	−	0.454724i	$-0.150262\pi$
$113$	880.947	+	640.045i	0.733385	+	0.532836i	−0.157247	+	0.987559i	$0.550262\pi$
$114$	−149.242	+	108.431i	−0.122612	+	0.0890830i
$115$	278.552	−	857.294i	0.225870	−	0.695157i
$116$	−151.863	+	467.385i	−0.121553	+	0.374100i
$117$	−1286.96	+	935.035i	−1.01692	+	0.738838i
$118$	−38.8461	−	28.2234i	−0.0303057	−	0.0220184i
$119$	16.7967	+	51.6948i	0.0129391	+	0.0398223i
$120$	188.107			0.143098
$121$		0			0
$122$	455.002			0.337655
$123$	−100.703	−	309.933i	−0.0738221	−	0.227201i
$124$	33.1169	+	24.0608i	0.0239837	+	0.0174252i
$125$	1227.33	−	891.708i	0.878207	−	0.638054i
$126$	5.44597	−	16.7610i	0.00385052	−	0.0118507i
$127$	387.895	−	1193.82i	0.271024	−	0.834127i	−0.719220	−	0.694783i	$-0.755501\pi$
$127$	387.895	−	1193.82i	0.271024	−	0.834127i	0.990244	−	0.139344i	$-0.0444994\pi$
$128$	1147.86	−	833.973i	0.792640	−	0.575886i
$129$	−375.090	−	272.519i	−0.256007	−	0.186000i
$130$	−160.837	−	495.005i	−0.108510	−	0.333960i
$131$	−1401.18			−0.934519			−0.467259	−	0.884120i	$-0.654759\pi$
$131$	−1401.18			−0.934519			−0.467259	+	0.884120i	$0.654759\pi$
$132$		0			0
$133$	100.467			0.0655009
$134$	−91.5876	−	281.878i	−0.0590445	−	0.181720i
$135$	−561.708	−	408.105i	−0.358105	−	0.260178i
$136$	−793.480	+	576.497i	−0.500296	+	0.363487i
$137$	−126.491	+	389.300i	−0.0788822	+	0.242775i	−0.982719	−	0.185102i	$-0.940738\pi$
$137$	−126.491	+	389.300i	−0.0788822	+	0.242775i	0.903837	+	0.427877i	$0.140738\pi$
$138$	−45.4350	+	139.835i	−0.0280267	+	0.0862573i
$139$	481.672	−	349.955i	0.293920	−	0.213545i	−0.431046	−	0.902330i	$-0.641855\pi$
$139$	481.672	−	349.955i	0.293920	−	0.213545i	0.724966	+	0.688784i	$0.241855\pi$
$140$	−39.1079	−	28.4135i	−0.0236087	−	0.0171527i
$141$	90.9842	+	280.021i	0.0543422	+	0.167248i
$142$	−168.615			−0.0996468
$143$		0			0
$144$	−1089.99			−0.630783
$145$	185.392	+	570.578i	0.106179	+	0.326786i
$146$	−155.319	−	112.846i	−0.0880430	−	0.0639670i
$147$	−426.973	+	310.214i	−0.239566	+	0.174055i
$148$	−380.541	+	1171.18i	−0.211353	+	0.650478i
$149$	−670.593	+	2063.87i	−0.368705	+	1.13476i	0.578923	+	0.815383i	$0.303473\pi$
$149$	−670.593	+	2063.87i	−0.368705	+	1.13476i	−0.947628	+	0.319376i	$0.896527\pi$
$150$	−56.2648	+	40.8788i	−0.0306267	+	0.0222516i
$151$	−1455.23	−	1057.28i	−0.784269	−	0.569805i	0.121988	−	0.992532i	$-0.461073\pi$
$151$	−1455.23	−	1057.28i	−0.784269	−	0.569805i	−0.906257	+	0.422727i	$0.861073\pi$
$152$	560.202	+	1724.13i	0.298937	+	0.920033i
$153$	1726.77			0.912427
$154$		0			0
$155$	49.9726			0.0258961
$156$	−219.933	−	676.884i	−0.112876	−	0.347398i
$157$	63.4380	+	46.0904i	0.0322478	+	0.0234294i	0.603792	−	0.797142i	$-0.293656\pi$
$157$	63.4380	+	46.0904i	0.0322478	+	0.0234294i	−0.571545	+	0.820571i	$0.693656\pi$
$158$	487.694	−	354.330i	0.245562	−	0.178411i
$159$	−305.604	+	940.552i	−0.152427	+	0.469123i
$160$	411.899	−	1267.69i	0.203522	−	0.626375i
$161$	64.7824	−	47.0672i	0.0317116	−	0.0230398i
$162$	−405.026	−	294.268i	−0.196431	−	0.142715i
$163$	101.615	+	312.739i	0.0488289	+	0.150280i	0.972498	−	0.232911i	$-0.0748251\pi$
$163$	101.615	+	312.739i	0.0488289	+	0.150280i	−0.923669	+	0.383191i	$0.874825\pi$
$164$	−1511.13			−0.719508
$165$		0			0
$166$	−1110.21			−0.519089
$167$	1088.90	+	3351.28i	0.504560	+	1.55287i	0.801510	+	0.597982i	$0.204030\pi$
$167$	1088.90	+	3351.28i	0.504560	+	1.55287i	−0.296950	+	0.954893i	$0.595970\pi$
$168$	13.5188	+	9.82198i	0.00620832	+	0.00451061i
$169$	−1598.99	+	1161.73i	−0.727804	+	0.528781i
$170$	−174.587	+	537.323i	−0.0787659	+	0.242417i
$171$	986.284	−	3035.47i	0.441070	−	1.35747i
$172$	−1739.30	+	1263.68i	−0.771050	+	0.560201i
$173$	−2190.19	−	1591.27i	−0.962526	−	0.699316i	−0.00878983	−	0.999961i	$-0.502798\pi$
$173$	−2190.19	−	1591.27i	−0.962526	−	0.699316i	−0.953736	+	0.300645i	$0.902798\pi$
$174$	−30.2396	−	93.0680i	−0.0131751	−	0.0405487i
$175$	37.8766			0.0163611
$176$		0			0
$177$	−80.1558			−0.0340389
$178$	204.565	+	629.587i	0.0861394	+	0.265110i
$179$	−1191.82	−	865.907i	−0.497658	−	0.361570i	0.310464	−	0.950585i	$-0.399516\pi$
$179$	−1191.82	−	865.907i	−0.497658	−	0.361570i	−0.808122	+	0.589016i	$0.799516\pi$
$180$	−1242.39	+	902.651i	−0.514458	+	0.373776i
$181$	−152.074	+	468.035i	−0.0624505	+	0.192203i	−0.977414	−	0.211334i	$-0.932219\pi$
$181$	−152.074	+	468.035i	−0.0624505	+	0.192203i	0.914963	+	0.403537i	$0.132219\pi$
$182$	14.2877	−	43.9730i	0.00581908	−	0.0179093i
$183$	614.492	−	446.454i	0.248222	−	0.180343i
$184$	1168.95	+	849.289i	0.468347	+	0.340274i
$185$	464.559	+	1429.77i	0.184622	+	0.568208i
$186$	−8.15111			−0.00321327
$187$		0			0
$188$	1365.29			0.529647
$189$	−19.0595	−	58.6591i	−0.00733532	−	0.0225758i
$190$	844.834	+	613.808i	0.322583	+	0.234370i
$191$	1046.81	−	760.549i	0.396566	−	0.288122i	−0.371575	−	0.928403i	$-0.621182\pi$
$191$	1046.81	−	760.549i	0.396566	−	0.288122i	0.768141	+	0.640281i	$0.221182\pi$
$192$	101.487	−	312.346i	0.0381469	−	0.117404i
$193$	161.968	−	498.485i	0.0604077	−	0.185916i	−0.916299	−	0.400495i	$-0.868838\pi$
$193$	161.968	−	498.485i	0.0604077	−	0.185916i	0.976707	+	0.214580i	$0.0688381\pi$
$194$	469.394	−	341.034i	0.173714	−	0.126211i
$195$	−702.920	−	510.701i	−0.258139	−	0.187549i
$196$	756.249	+	2327.50i	0.275601	+	0.848213i
$197$	1177.35			0.425801			0.212900	−	0.977074i	$-0.431709\pi$
$197$	1177.35			0.425801			0.212900	+	0.977074i	$0.431709\pi$
$198$		0			0
$199$	−3054.83			−1.08820			−0.544098	−	0.839022i	$-0.683128\pi$
$199$	−3054.83			−1.08820			−0.544098	+	0.839022i	$0.683128\pi$
$200$	211.198	+	650.002i	0.0746699	+	0.229810i
$201$	−400.274	−	290.816i	−0.140463	−	0.102053i
$202$	380.382	−	276.364i	0.132493	−	0.0962619i
$203$	−16.4690	+	50.6864i	−0.00569408	+	0.0175246i
$204$	−238.735	+	734.751i	−0.0819353	+	0.252171i
$205$	−1492.45	+	1084.33i	−0.508474	+	0.369428i
$206$	130.671	+	94.9382i	0.0441956	+	0.0321100i
$207$	−786.098	−	2419.36i	−0.263950	−	0.812353i
$208$	−2859.63			−0.953269
$209$		0			0
$210$	9.62569			0.00316303
$211$	−526.763	−	1621.21i	−0.171867	−	0.528951i	0.827610	−	0.561304i	$-0.189700\pi$
$211$	−526.763	−	1621.21i	−0.171867	−	0.528951i	−0.999477	+	0.0323524i	$0.989700\pi$
$212$	3710.00	+	2695.47i	1.20191	+	0.873235i
$213$	−227.719	+	165.447i	−0.0732536	+	0.0532219i
$214$	−504.843	+	1553.75i	−0.161263	+	0.496317i
$215$	−811.037	+	2496.11i	−0.257266	+	0.791784i
$216$	900.377	−	654.162i	0.283625	−	0.206065i
$217$	3.59142	+	2.60932i	0.00112351	+	0.000816276i
$218$	234.996	+	723.243i	0.0730088	+	0.224698i
$219$	−320.488			−0.0988884
$220$		0			0
$221$	4530.25			1.37890
$222$	−75.7750	−	233.212i	−0.0229085	−	0.0705051i
$223$	−3723.52	−	2705.29i	−1.11814	−	0.812376i	−0.134214	−	0.990952i	$-0.542851\pi$
$223$	−3723.52	−	2705.29i	−1.11814	−	0.812376i	−0.983926	+	0.178576i	$0.942851\pi$
$224$	95.7948	−	69.5990i	0.0285739	−	0.0207602i
$225$	371.833	−	1144.38i	0.110173	−	0.339077i
$226$	−310.699	+	956.233i	−0.0914486	+	0.281450i
$227$	2659.61	−	1932.32i	0.777640	−	0.564989i	−0.126630	−	0.991950i	$-0.540416\pi$
$227$	2659.61	−	1932.32i	0.777640	−	0.564989i	0.904270	+	0.426961i	$0.140416\pi$
$228$	1155.25	+	839.338i	0.335563	+	0.243801i
$229$	−911.905	−	2806.56i	−0.263146	−	0.809880i	−0.992115	−	0.125333i	$-0.960000\pi$
$229$	−911.905	−	2806.56i	−0.263146	−	0.809880i	0.728969	−	0.684547i	$-0.240000\pi$
$230$	832.316			0.238614
$231$		0			0
$232$	−961.663			−0.272139
$233$	−872.263	−	2684.55i	−0.245253	−	0.754810i	−0.995595	−	0.0937604i	$-0.970111\pi$
$233$	−872.263	−	2684.55i	−0.245253	−	0.754810i	0.750342	−	0.661050i	$-0.229889\pi$
$234$	−1188.32	−	863.362i	−0.331977	−	0.241195i
$235$	1348.41	−	979.676i	0.374300	−	0.271945i
$236$	−114.857	+	353.493i	−0.0316803	+	0.0975019i
$237$	310.969	−	957.064i	0.0852304	−	0.262312i
$238$	−40.6035	+	29.5002i	−0.0110585	+	0.00803450i
$239$	1667.52	+	1211.52i	0.451309	+	0.327895i	0.790112	−	0.612962i	$-0.210022\pi$
$239$	1667.52	+	1211.52i	0.451309	+	0.327895i	−0.338804	+	0.940857i	$0.610022\pi$
$240$	−183.969	−	566.199i	−0.0494798	−	0.152283i
$241$	3089.45			0.825763			0.412881	−	0.910785i	$-0.364522\pi$
$241$	3089.45			0.825763			0.412881	+	0.910785i	$0.364522\pi$
$242$		0			0
$243$	−2984.19			−0.787803
$244$	−1088.38	−	3349.69i	−0.285559	−	0.878860i
$245$	2417.02	+	1756.07i	0.630277	+	0.457923i
$246$	243.436	−	176.866i	0.0630930	−	0.0458398i
$247$	2587.55	−	7963.66i	0.666566	−	2.05148i
$248$	−24.7530	+	76.1819i	−0.00633797	+	0.0195063i
$249$	−1499.36	+	1089.35i	−0.381600	+	0.277248i
$250$	1133.25	+	823.356i	0.286693	+	0.208295i
$251$	−1245.08	−	3831.95i	−0.313102	−	0.963629i	−0.976529	−	0.215387i	$-0.930899\pi$
$251$	−1245.08	−	3831.95i	−0.313102	−	0.963629i	0.663427	−	0.748241i	$-0.269101\pi$
$252$	−136.420			−0.0341017
$253$		0			0
$254$	1159.03			0.286316
$255$	291.445	+	896.976i	0.0715726	+	0.220278i
$256$	−319.130	−	231.861i	−0.0779125	−	0.0566068i
$257$	3557.63	−	2584.77i	0.863498	−	0.627368i	−0.0653367	−	0.997863i	$-0.520812\pi$
$257$	3557.63	−	2584.77i	0.863498	−	0.627368i	0.928834	+	0.370496i	$0.120812\pi$
$258$	132.289	−	407.145i	0.0319224	−	0.0982471i
$259$	−41.2684	+	127.011i	−0.00990074	+	0.0304714i
$260$	−3259.46	+	2368.14i	−0.777474	+	0.564868i
$261$	1369.74	+	995.173i	0.324846	+	0.236014i
$262$	−399.800	−	1230.46i	−0.0942737	−	0.290145i
$263$	914.661			0.214450			0.107225	−	0.994235i	$-0.465803\pi$
$263$	914.661			0.214450			0.107225	+	0.994235i	$0.465803\pi$
$264$		0			0
$265$	5598.31			1.29774
$266$	28.6663	+	88.2259i	0.00660769	+	0.0203364i
$267$	894.030	+	649.551i	0.204920	+	0.148883i
$268$	−1856.08	+	1348.52i	−0.423053	+	0.307366i
$269$	−546.582	+	1682.21i	−0.123887	+	0.381286i	−0.993697	−	0.112102i	$-0.964242\pi$
$269$	−546.582	+	1682.21i	−0.123887	+	0.381286i	0.869809	+	0.493388i	$0.164242\pi$
$270$	198.107	−	609.712i	0.0446534	−	0.137429i
$271$	3251.07	−	2362.04i	0.728739	−	0.529460i	−0.160425	−	0.987048i	$-0.551287\pi$
$271$	3251.07	−	2362.04i	0.728739	−	0.529460i	0.889164	+	0.457588i	$0.151287\pi$
$272$	2511.27	+	1824.55i	0.559810	+	0.406726i
$273$	−23.8510	−	73.4059i	−0.00528765	−	0.0162737i
$274$	−377.957			−0.0833330
$275$		0			0
$276$	1138.13			0.248216
$277$	2053.67	+	6320.53i	0.445461	+	1.37099i	0.881977	+	0.471293i	$0.156212\pi$
$277$	2053.67	+	6320.53i	0.445461	+	1.37099i	−0.436516	+	0.899697i	$0.643788\pi$
$278$	444.751	+	323.130i	0.0959510	+	0.0697125i
$279$	114.093	−	82.8937i	0.0244824	−	0.0177875i
$280$	29.2310	−	89.9636i	0.00623887	−	0.0192013i
$281$	−1354.44	+	4168.53i	−0.287541	+	0.884960i	0.698085	+	0.716015i	$0.254036\pi$
$281$	−1354.44	+	4168.53i	−0.287541	+	0.884960i	−0.985626	+	0.168945i	$0.945964\pi$
$282$	−219.941	+	159.797i	−0.0464443	+	0.0337438i
$283$	3021.57	+	2195.30i	0.634677	+	0.461120i	0.858017	−	0.513620i	$-0.171696\pi$
$283$	3021.57	+	2195.30i	0.634677	+	0.461120i	−0.223340	+	0.974741i	$0.571696\pi$
$284$	403.332	+	1241.33i	0.0842724	+	0.259364i
$285$	1743.25			0.362319
$286$		0			0
$287$	−163.877			−0.0337050
$288$	−1162.42	−	3577.55i	−0.237833	−	0.731975i
$289$	−3.67677	−	2.67133i	−0.000748376	−	0.000543727i
$290$	−448.159	+	325.606i	−0.0907475	+	0.0659319i
$291$	299.300	−	921.151i	0.0602931	−	0.185563i
$292$	−459.234	+	1413.38i	−0.0920364	+	0.283259i
$293$	−1808.29	+	1313.80i	−0.360551	+	0.261956i	−0.753282	−	0.657698i	$-0.771530\pi$
$293$	−1808.29	+	1313.80i	−0.360551	+	0.261956i	0.392731	+	0.919653i	$0.371530\pi$
$294$	−394.244	−	286.435i	−0.0782068	−	0.0568206i
$295$	140.216	+	431.540i	0.0276735	+	0.0851703i
$296$	−2409.75			−0.473190
$297$		0			0
$298$	−2003.74			−0.389509
$299$	−2062.35	−	6347.27i	−0.398893	−	1.22767i
$300$	435.534	+	316.434i	0.0838185	+	0.0608977i
$301$	−188.622	+	137.042i	−0.0361195	+	0.0262424i
$302$	513.240	−	1579.59i	0.0977934	−	0.300977i
$303$	242.544	−	746.473i	0.0459860	−	0.141530i
$304$	4641.71	−	3372.40i	0.875726	−	0.636252i
$305$	−3478.53	−	2527.30i	−0.653050	−	0.474469i
$306$	492.700	+	1516.38i	0.0920451	+	0.283286i
$307$	−1022.51			−0.190090			−0.0950451	−	0.995473i	$-0.530300\pi$
$307$	−1022.51			−0.190090			−0.0950451	+	0.995473i	$0.530300\pi$
$308$		0			0
$309$	269.629			0.0496398
$310$	14.2587	+	43.8837i	0.00261238	+	0.00804009i
$311$	−4303.47	−	3126.66i	−0.784655	−	0.570085i	0.121718	−	0.992565i	$-0.461160\pi$
$311$	−4303.47	−	3126.66i	−0.784655	−	0.570085i	−0.906372	+	0.422480i	$0.861160\pi$
$312$	1126.73	−	818.617i	0.204450	−	0.148542i
$313$	−2161.10	+	6651.18i	−0.390264	+	1.20111i	0.542326	+	0.840168i	$0.317544\pi$
$313$	−2161.10	+	6651.18i	−0.390264	+	1.20111i	−0.932589	+	0.360939i	$0.882456\pi$
$314$	−22.3738	+	68.8594i	−0.00402110	+	0.0123757i
$315$	−134.733	+	97.8896i	−0.0240996	+	0.0175094i
$316$	−3775.13	−	2742.79i	−0.672050	−	0.488273i
$317$	1333.31	+	4103.50i	0.236233	+	0.727052i	0.996955	+	0.0779740i	$0.0248451\pi$
$317$	1333.31	+	4103.50i	0.236233	+	0.727052i	−0.760722	+	0.649078i	$0.775155\pi$
$318$	−913.149			−0.161028
$319$		0			0
$320$	−1859.13			−0.324776
$321$	842.755	+	2593.73i	0.146536	+	0.450991i
$322$	59.8167	+	43.4593i	0.0103523	+	0.00752141i
$323$	−7353.43	+	5342.58i	−1.26674	+	0.920338i
$324$	−1197.55	+	3685.67i	−0.205340	+	0.631973i
$325$	975.516	−	3002.33i	0.166498	−	0.512429i
$326$	−245.640	+	178.468i	−0.0417323	+	0.0303203i
$327$	1027.02	+	746.176i	0.173684	+	0.126189i
$328$	−913.772	−	2812.30i	−0.153825	−	0.473425i
$329$	148.061			0.0248111
$330$		0			0
$331$	−3886.73			−0.645420			−0.322710	−	0.946498i	$-0.604594\pi$
$331$	−3886.73			−0.645420			−0.322710	+	0.946498i	$0.604594\pi$
$332$	2655.65	+	8173.26i	0.439000	+	1.35110i
$333$	3432.32	+	2493.72i	0.564834	+	0.410376i
$334$	−2632.25	+	1912.44i	−0.431229	+	0.313306i
$335$	−865.489	+	2663.70i	−0.141154	+	0.434429i
$336$	16.3426	−	50.2974i	0.00265346	−	0.00816651i
$337$	−7363.75	+	5350.08i	−1.19029	+	0.864800i	−0.993295	−	0.115604i	$-0.963120\pi$
$337$	−7363.75	+	5350.08i	−1.19029	+	0.864800i	−0.196999	+	0.980404i	$0.563120\pi$
$338$	−1476.42	−	1072.68i	−0.237594	−	0.172622i
$339$	518.662	+	1596.28i	0.0830969	+	0.255746i
$340$	4373.35			0.697583
$341$		0			0
$342$	2947.03			0.465957
$343$	164.169	+	505.262i	0.0258435	+	0.0795381i
$344$	−3403.53	−	2472.81i	−0.533448	−	0.387572i
$345$	1124.06	−	816.680i	0.175413	−	0.127445i
$346$	772.452	−	2377.36i	0.120021	−	0.369387i
$347$	3137.36	−	9655.81i	0.485367	−	1.49381i	−0.346081	−	0.938204i	$-0.612488\pi$
$347$	3137.36	−	9655.81i	0.485367	−	1.49381i	0.831448	−	0.555602i	$-0.187512\pi$
$348$	−612.825	+	445.243i	−0.0943990	+	0.0685849i
$349$	−8633.94	−	6272.93i	−1.32425	−	0.962126i	−0.999869	−	0.0162011i	$-0.994843\pi$
$349$	−8633.94	−	6272.93i	−1.32425	−	0.962126i	−0.324385	−	0.945925i	$-0.605157\pi$
$350$	10.8073	+	33.2615i	0.00165050	+	0.00507972i
$351$	−5140.56			−0.781718
$352$		0			0
$353$	−9301.69			−1.40249			−0.701245	−	0.712920i	$-0.747372\pi$
$353$	−9301.69			−1.40249			−0.701245	+	0.712920i	$0.747372\pi$
$354$	−22.8709	−	70.3892i	−0.00343382	−	0.0105682i
$355$	1289.08	+	936.569i	0.192724	+	0.140022i
$356$	4145.64	−	3011.99i	0.617187	−	0.448413i
$357$	−25.8901	+	79.6814i	−0.00383823	+	0.0118128i
$358$	420.339	−	1293.67i	0.0620548	−	0.190985i
$359$	6793.64	−	4935.87i	0.998759	−	0.725641i	0.0369374	−	0.999318i	$-0.488240\pi$
$359$	6793.64	−	4935.87i	0.998759	−	0.725641i	0.961822	+	0.273677i	$0.0882398\pi$
$360$	−2431.16	−	1766.34i	−0.355926	−	0.258595i
$361$	3072.03	+	9454.73i	0.447883	+	1.37844i
$362$	−454.398			−0.0659742
$363$		0			0
$364$	−357.902			−0.0515362
$365$	560.627	+	1725.43i	0.0803961	+	0.247434i
$366$	567.389	+	412.232i	0.0810325	+	0.0588736i
$367$	7578.84	−	5506.35i	1.07796	−	0.783185i	0.100636	−	0.994923i	$-0.467912\pi$
$367$	7578.84	−	5506.35i	1.07796	−	0.783185i	0.977326	+	0.211738i	$0.0679124\pi$
$368$	1413.12	−	4349.12i	0.200173	−	0.616070i
$369$	−1608.77	+	4951.30i	−0.226963	+	0.698521i
$370$	−1123.00	+	815.911i	−0.157790	+	0.114641i
$371$	402.337	+	292.315i	0.0563027	+	0.0409063i
$372$	19.4977	+	60.0078i	0.00271750	+	0.00836360i
$373$	−2639.31			−0.366376			−0.183188	−	0.983078i	$-0.558642\pi$
$373$	−2639.31			−0.366376			−0.183188	+	0.983078i	$0.558642\pi$
$374$		0			0
$375$	2338.38			0.322008
$376$	825.582	+	2540.88i	0.113234	+	0.348500i
$377$	3593.56	+	2610.87i	0.490922	+	0.356676i
$378$	46.0736	−	33.4744i	0.00626923	−	0.00455486i
$379$	−2276.38	+	7005.98i	−0.308522	+	0.949532i	0.669818	+	0.742526i	$0.266372\pi$
$379$	−2276.38	+	7005.98i	−0.308522	+	0.949532i	−0.978339	+	0.207007i	$0.933628\pi$
$380$	2497.93	−	7687.85i	0.337214	−	1.03784i
$381$	1565.31	−	1137.26i	0.210480	−	0.152923i
$382$	966.565	+	702.250i	0.129460	+	0.0940583i
$383$	−995.151	−	3062.76i	−0.132767	−	0.408615i	0.862469	−	0.506110i	$-0.168917\pi$
$383$	−995.151	−	3062.76i	−0.132767	−	0.408615i	−0.995236	+	0.0974948i	$0.968917\pi$
$384$	2186.97			0.290634
$385$		0			0
$386$	483.962			0.0638160
$387$	2288.82	+	7044.26i	0.300639	+	0.925271i
$388$	−3633.47	−	2639.87i	−0.475417	−	0.345410i
$389$	−9892.63	+	7187.42i	−1.28940	+	0.936803i	−0.999793	−	0.0203426i	$-0.993524\pi$
$389$	−9892.63	+	7187.42i	−1.28940	+	0.936803i	−0.289606	+	0.957146i	$0.593524\pi$
$390$	247.911	−	762.991i	0.0321883	−	0.0990656i
$391$	−2238.67	+	6889.91i	−0.289551	+	0.891145i
$392$	−3874.31	+	2814.85i	−0.499189	+	0.362682i
$393$	−1747.28	−	1269.47i	−0.224271	−	0.162943i
$394$	335.933	+	1033.90i	0.0429545	+	0.132200i
$395$	−5696.59			−0.725636
$396$		0			0
$397$	8381.55			1.05959			0.529796	−	0.848125i	$-0.322269\pi$
$397$	8381.55			1.05959			0.529796	+	0.848125i	$0.322269\pi$
$398$	−871.634	−	2682.61i	−0.109777	−	0.337857i
$399$	125.283	+	91.0235i	0.0157193	+	0.0114207i
$400$	1749.94	−	1271.41i	0.218743	−	0.158926i
$401$	−1338.15	+	4118.41i	−0.166644	+	0.512876i	−0.999154	−	0.0411337i	$-0.986903\pi$
$401$	−1338.15	+	4118.41i	−0.166644	+	0.512876i	0.832510	+	0.554010i	$0.186903\pi$
$402$	141.171	−	434.481i	0.0175149	−	0.0539053i
$403$	299.328	−	217.474i	0.0369990	−	0.0268813i
$404$	−2944.46	−	2139.27i	−0.362604	−	0.263447i
$405$	1461.95	+	4499.42i	0.179370	+	0.552044i
$406$	−49.2097			−0.00601536
$407$		0			0
$408$	−1511.78			−0.183442
$409$	−3689.01	−	11353.6i	−0.445990	−	1.37262i	−0.881395	−	0.472381i	$-0.843395\pi$
$409$	−3689.01	−	11353.6i	−0.445990	−	1.37262i	0.435405	−	0.900235i	$-0.356605\pi$
$410$	−1378.05	−	1001.21i	−0.165993	−	0.120601i
$411$	−510.441	+	370.857i	−0.0612608	+	0.0445086i
$412$	386.358	−	1189.09i	0.0462002	−	0.142190i
$413$	−12.4559	+	38.3352i	−0.00148405	+	0.00456744i
$414$	1900.28	−	1380.63i	0.225588	−	0.163899i
$415$	8487.64	+	6166.63i	1.00396	+	0.729417i
$416$	−3049.64	−	9385.81i	−0.359425	−	1.10620i
$417$	917.707			0.107770
$418$		0			0
$419$	−11888.5			−1.38614			−0.693070	−	0.720870i	$-0.743743\pi$
$419$	−11888.5			−1.38614			−0.693070	+	0.720870i	$0.743743\pi$
$420$	−23.0250	−	70.8636i	−0.00267501	−	0.00823283i
$421$	6864.88	+	4987.63i	0.794712	+	0.577392i	0.909358	−	0.416014i	$-0.136573\pi$
$421$	6864.88	+	4987.63i	0.794712	+	0.577392i	−0.114646	+	0.993406i	$0.536573\pi$
$422$	1273.37	−	925.160i	0.146888	−	0.106721i
$423$	1453.51	−	4473.43i	0.167073	−	0.514198i
$424$	−2773.02	+	8534.47i	−0.317617	+	0.977525i
$425$	−2772.27	+	2014.17i	−0.316412	+	0.229887i
$426$	−210.263	−	152.765i	−0.0239138	−	0.0173744i
$427$	−118.031	−	363.263i	−0.0133769	−	0.0411698i
$428$	12646.2			1.42821
$429$		0			0
$430$	−2423.39			−0.271782
$431$	−3541.56	−	10899.8i	−0.395803	−	1.21816i	−0.928335	−	0.371746i	$-0.878759\pi$
$431$	−3541.56	−	10899.8i	−0.395803	−	1.21816i	0.532532	−	0.846410i	$-0.321241\pi$
$432$	−2849.59	−	2070.35i	−0.317364	−	0.230578i
$433$	−2668.20	+	1938.56i	−0.296133	+	0.215153i	−0.725924	−	0.687775i	$-0.758587\pi$
$433$	−2668.20	+	1938.56i	−0.296133	+	0.215153i	0.429790	+	0.902929i	$0.358587\pi$
$434$	−1.26665	+	3.89834i	−0.000140094	+	0.000431166i
$435$	−285.760	+	879.479i	−0.0314969	+	0.0969374i
$436$	4762.34	−	3460.04i	0.523107	−	0.380060i
$437$	10833.0	+	7870.64i	1.18584	+	0.861565i
$438$	−91.4448	−	281.438i	−0.00997581	−	0.0307024i
$439$	−5549.93			−0.603380			−0.301690	−	0.953406i	$-0.597551\pi$
$439$	−5549.93			−0.603380			−0.301690	+	0.953406i	$0.597551\pi$
$440$		0			0
$441$	8431.29			0.910408
$442$	1292.62	+	3978.26i	0.139103	+	0.428115i
$443$	−8802.78	−	6395.59i	−0.944092	−	0.685923i	0.00531025	−	0.999986i	$-0.498310\pi$
$443$	−8802.78	−	6395.59i	−0.944092	−	0.685923i	−0.949402	+	0.314063i	$0.898310\pi$
$444$	−1535.63	+	1115.70i	−0.164139	+	0.119254i
$445$	1933.11	−	5949.50i	0.205929	−	0.633783i
$446$	1313.24	−	4041.73i	0.139425	−	0.429106i
$447$	−2706.10	+	1966.10i	−0.286341	+	0.208039i
$448$	−133.611	−	97.0743i	−0.0140905	−	0.0102373i
$449$	−2331.75	−	7176.40i	−0.245083	−	0.754288i	−0.995623	−	0.0934627i	$-0.970206\pi$
$449$	−2331.75	−	7176.40i	−0.245083	−	0.754288i	0.750540	−	0.660825i	$-0.229794\pi$
$450$	1111.04			0.116389
$451$		0			0
$452$	7782.91			0.809906
$453$	−856.772	−	2636.87i	−0.0888624	−	0.273490i
$454$	2455.74	+	1784.20i	0.253863	+	0.184442i
$455$	−353.478	+	256.817i	−0.0364204	+	0.0264610i
$456$	−863.485	+	2657.53i	−0.0886763	+	0.272918i
$457$	1000.98	−	3080.71i	0.102459	−	0.315338i	−0.886666	−	0.462410i	$-0.846985\pi$
$457$	1000.98	−	3080.71i	0.102459	−	0.315338i	0.989126	+	0.147072i	$0.0469849\pi$
$458$	2204.40	−	1601.59i	0.224901	−	0.163400i
$459$	4514.34	+	3279.86i	0.459067	+	0.333531i
$460$	−1990.93	−	6127.45i	−0.201799	−	0.621073i
$461$	4837.43			0.488724			0.244362	−	0.969684i	$-0.421422\pi$
$461$	4837.43			0.488724			0.244362	+	0.969684i	$0.421422\pi$
$462$		0			0
$463$	14089.7			1.41427			0.707133	−	0.707081i	$-0.249988\pi$
$463$	14089.7			1.41427			0.707133	+	0.707081i	$0.249988\pi$
$464$	940.510	+	2894.59i	0.0940993	+	0.289608i
$465$	62.3160	+	45.2752i	0.00621470	+	0.00451524i
$466$	2108.57	−	1531.97i	0.209609	−	0.152290i
$467$	4494.75	−	13833.4i	0.445379	−	1.37074i	−0.436688	−	0.899613i	$-0.643849\pi$
$467$	4494.75	−	13833.4i	0.445379	−	1.37074i	0.882067	−	0.471123i	$-0.156151\pi$
$468$	−3513.51	+	10813.5i	−0.347034	+	1.06806i
$469$	−201.286	+	146.243i	−0.0198177	+	0.0143984i
$470$	1245.05	+	904.581i	0.122191	+	0.0887771i
$471$	37.3494	+	114.950i	0.00365387	+	0.0112454i
$472$	−727.326			−0.0709277
$473$		0			0
$474$	929.179			0.0900393
$475$	1957.24	+	6023.78i	0.189062	+	0.581873i
$476$	314.303	+	228.354i	0.0302648	+	0.0219887i
$477$	12781.6	−	9286.38i	1.22690	−	0.891392i
$478$	−588.112	+	1810.02i	−0.0562754	+	0.173198i
$479$	−874.540	+	2691.56i	−0.0834212	+	0.256744i	−0.984064	−	0.177817i	$-0.943096\pi$
$479$	−874.540	+	2691.56i	−0.0834212	+	0.256744i	0.900642	+	0.434561i	$0.143096\pi$
$480$	1662.17	−	1207.64i	0.158057	−	0.114835i
$481$	9004.80	+	6542.37i	0.853604	+	0.620180i
$482$	881.512	+	2713.02i	0.0833024	+	0.256379i
$483$	123.427			0.0116276
$484$		0			0
$485$	−5482.83			−0.513325
$486$	−851.480	−	2620.59i	−0.0794731	−	0.244593i
$487$	15480.2	+	11247.0i	1.44040	+	1.04651i	0.987959	+	0.154714i	$0.0494455\pi$
$487$	15480.2	+	11247.0i	1.44040	+	1.04651i	0.452438	+	0.891796i	$0.350555\pi$
$488$	5575.84	−	4051.08i	0.517226	−	0.375787i
$489$	−156.628	+	482.050i	−0.0144845	+	0.0445788i
$490$	−852.453	+	2623.58i	−0.0785916	+	0.241880i
$491$	−9136.80	+	6638.27i	−0.839792	+	0.610145i	−0.922313	−	0.386445i	$-0.873703\pi$
$491$	−9136.80	+	6638.27i	−0.839792	+	0.610145i	0.0825206	+	0.996589i	$0.473703\pi$
$492$	−1884.38	−	1369.08i	−0.172672	−	0.125453i
$493$	−1489.96	−	4585.63i	−0.136115	−	0.418918i
$494$	7731.64			0.704176
$495$		0			0
$496$	253.515			0.0229499
$497$	43.7401	+	134.618i	0.00394771	+	0.0121498i
$498$	−1384.43	−	1005.85i	−0.124574	−	0.0905084i
$499$	−700.757	+	509.130i	−0.0628661	+	0.0456749i	−0.618775	−	0.785569i	$-0.712371\pi$
$499$	−700.757	+	509.130i	−0.0628661	+	0.0456749i	0.555908	+	0.831244i	$0.312371\pi$
$500$	3350.71	−	10312.4i	0.299696	−	0.922370i
$501$	−1678.41	+	5165.60i	−0.149672	+	0.460643i
$502$	3009.79	−	2186.74i	0.267597	−	0.194421i
$503$	−4840.76	−	3517.02i	−0.429103	−	0.311762i	0.352187	−	0.935930i	$-0.385438\pi$
$503$	−4840.76	−	3517.02i	−0.429103	−	0.311762i	−0.781290	+	0.624168i	$0.785438\pi$
$504$	−82.4924	−	253.886i	−0.00729068	−	0.0224384i
$505$	−4443.12			−0.391517
$506$		0			0
$507$	−3046.47			−0.266861
$508$	−2772.45	−	8532.72i	−0.242141	−	0.745233i
$509$	−8953.48	−	6505.08i	−0.779678	−	0.566469i	0.125205	−	0.992131i	$-0.460041\pi$
$509$	−8953.48	−	6505.08i	−0.779678	−	0.566469i	−0.904882	+	0.425662i	$0.860041\pi$
$510$	−704.526	+	511.868i	−0.0611705	+	0.0444430i
$511$	−49.8024	+	153.276i	−0.00431141	+	0.0132691i
$512$	3620.12	−	11141.6i	0.312477	−	0.961704i
$513$	8344.09	−	6062.34i	0.718130	−	0.521752i
$514$	3284.93	+	2386.64i	0.281891	+	0.204806i
$515$	−471.661	−	1451.62i	−0.0403570	−	0.124206i
$516$	−3313.81			−0.282718
$517$		0			0
$518$	−123.311			−0.0104594
$519$	−1289.49	−	3968.63i	−0.109060	−	0.335652i
$520$	−6378.22	−	4634.05i	−0.537892	−	0.390801i
$521$	−12056.6	+	8759.66i	−1.01384	+	0.736599i	−0.965011	−	0.262208i	$-0.915549\pi$
$521$	−12056.6	+	8759.66i	−1.01384	+	0.736599i	−0.0488298	+	0.998807i	$0.515549\pi$
$522$	−483.089	+	1486.80i	−0.0405062	+	0.124665i
$523$	460.262	−	1416.54i	0.0384815	−	0.118434i	−0.929970	−	0.367634i	$-0.880168\pi$
$523$	460.262	−	1416.54i	0.0384815	−	0.118434i	0.968452	+	0.249200i	$0.0801678\pi$
$524$	−8102.19	+	5886.59i	−0.675469	+	0.490757i
$525$	47.2322	+	34.3162i	0.00392644	+	0.00285273i
$526$	260.980	+	803.215i	0.0216336	+	0.0665814i
$527$	−401.620			−0.0331971
$528$		0			0
$529$	−1494.50			−0.122832
$530$	1597.36	+	4916.18i	0.130915	+	0.402916i
$531$	1035.96	+	752.670i	0.0846646	+	0.0615124i
$532$	580.941	−	422.079i	0.0473440	−	0.0343974i
$533$	−4220.67	+	12989.9i	−0.342997	+	1.05564i
$534$	−315.313	+	970.433i	−0.0255523	+	0.0786419i
$535$	12489.8	−	9074.39i	1.00931	−	0.733309i
$536$	−3632.04	−	2638.83i	−0.292687	−	0.212650i
$537$	−701.690	−	2159.58i	−0.0563876	−	0.173543i
$538$	−1633.19			−0.130877
$539$		0			0
$540$	−4962.53			−0.395469
$541$	−164.869	−	507.416i	−0.0131022	−	0.0403244i	0.944292	−	0.329110i	$-0.106749\pi$
$541$	−164.869	−	507.416i	−0.0131022	−	0.0403244i	−0.957394	+	0.288785i	$0.906749\pi$
$542$	3001.86	+	2180.98i	0.237899	+	0.172844i
$543$	−613.676	+	445.862i	−0.0484998	+	0.0352371i
$544$	−3310.35	+	10188.2i	−0.260901	+	0.802971i
$545$	2220.68	−	6834.54i	0.174538	−	0.537173i
$546$	57.6563	−	41.8898i	0.00451916	−	0.00328337i
$547$	−14966.2	−	10873.6i	−1.16985	−	0.849944i	−0.178857	−	0.983875i	$-0.557240\pi$
$547$	−14966.2	−	10873.6i	−1.16985	−	0.849944i	−0.990991	+	0.133931i	$0.957240\pi$
$548$	904.086	+	2782.49i	0.0704757	+	0.216902i
$549$	−12134.2			−0.943302
$550$		0			0
$551$	−8912.04			−0.689049
$552$	688.223	+	2118.13i	0.0530666	+	0.163322i
$553$	−409.401	−	297.447i	−0.0314819	−	0.0228729i
$554$	−4964.44	+	3606.88i	−0.380720	+	0.276609i
$555$	−716.063	+	2203.82i	−0.0547661	+	0.168553i
$556$	1315.00	−	4047.16i	0.100303	−	0.308701i
$557$	−12737.0	+	9253.95i	−0.968910	+	0.703954i	−0.955203	−	0.295952i	$-0.904363\pi$
$557$	−12737.0	+	9253.95i	−0.968910	+	0.703954i	−0.0137069	+	0.999906i	$0.504363\pi$
$558$	105.348	+	76.5397i	0.00799234	+	0.00580678i
$559$	6004.79	+	18480.9i	0.454339	+	1.39831i
$560$	−299.377			−0.0225911
$561$		0			0
$562$	−4047.08			−0.303765
$563$	−1864.04	−	5736.91i	−0.139538	−	0.429453i	0.856731	−	0.515764i	$-0.172492\pi$
$563$	−1864.04	−	5736.91i	−0.139538	−	0.429453i	−0.996268	+	0.0863115i	$0.972492\pi$
$564$	1702.52	+	1236.95i	0.127108	+	0.0923493i
$565$	7686.70	−	5584.72i	0.572357	−	0.415842i
$566$	−1065.67	+	3279.79i	−0.0791403	+	0.243569i
$567$	−129.870	+	399.699i	−0.00961909	+	0.0296045i
$568$	−2066.30	+	1501.25i	−0.152641	+	0.110900i
$569$	−12644.6	−	9186.84i	−0.931615	−	0.676858i	0.0147724	−	0.999891i	$-0.495298\pi$
$569$	−12644.6	−	9186.84i	−0.931615	−	0.676858i	−0.946388	+	0.323033i	$0.895298\pi$
$570$	497.400	+	1530.84i	0.0365505	+	0.112491i
$571$	7252.67			0.531550			0.265775	−	0.964035i	$-0.414372\pi$
$571$	7252.67			0.531550			0.265775	+	0.964035i	$0.414372\pi$
$572$		0			0
$573$	1994.43			0.145407
$574$	−46.7590	−	143.909i	−0.00340014	−	0.0104646i
$575$	4084.09	+	2967.26i	0.296205	+	0.215206i
$576$	−4244.61	+	3083.89i	−0.307046	+	0.223082i
$577$	4016.51	−	12361.5i	0.289791	−	0.891885i	−0.695131	−	0.718884i	$-0.744653\pi$
$577$	4016.51	−	12361.5i	0.289791	−	0.891885i	0.984922	−	0.173002i	$-0.0553466\pi$
$578$	1.29675	−	3.99098i	9.33178e−5	−	0.000287203i
$579$	653.602	−	474.870i	0.0469133	−	0.0340845i
$580$	3469.10	+	2520.45i	0.248356	+	0.180441i
$581$	287.997	+	886.363i	0.0205648	+	0.0632918i
$582$	894.313			0.0636950
$583$		0			0
$584$	−2908.08			−0.206057
$585$	4289.25	+	13201.0i	0.303143	+	0.932979i
$586$	−1669.68	−	1213.09i	−0.117703	−	0.0855160i
$587$	−8197.54	+	5955.86i	−0.576403	+	0.418782i	−0.837426	−	0.546551i	$-0.815940\pi$
$587$	−8197.54	+	5955.86i	−0.576403	+	0.418782i	0.261022	+	0.965333i	$0.415940\pi$
$588$	−1165.67	+	3587.56i	−0.0817540	+	0.251613i
$589$	−229.394	+	706.003i	−0.0160476	+	0.0493894i
$590$	−338.952	+	246.263i	−0.0236516	+	0.0171839i
$591$	1468.16	+	1066.68i	0.102186	+	0.0742426i
$592$	2356.75	+	7253.33i	0.163618	+	0.503564i
$593$	838.751			0.0580833			0.0290416	−	0.999578i	$-0.490754\pi$
$593$	838.751			0.0580833			0.0290416	+	0.999578i	$0.490754\pi$
$594$		0			0
$595$	474.276			0.0326780
$596$	4793.02	+	14751.4i	0.329412	+	1.01383i
$597$	−3809.38	−	2767.68i	−0.261152	−	0.189738i
$598$	4985.44	−	3622.14i	0.340920	−	0.247693i
$599$	−7945.56	+	24453.9i	−0.541981	+	1.66805i	0.186079	+	0.982535i	$0.440422\pi$
$599$	−7945.56	+	24453.9i	−0.541981	+	1.66805i	−0.728061	+	0.685513i	$0.759578\pi$
$600$	−325.537	+	1001.90i	−0.0221500	+	0.0681707i
$601$	−1151.62	+	836.701i	−0.0781623	+	0.0567883i	−0.626180	−	0.779678i	$-0.715383\pi$
$601$	−1151.62	+	836.701i	−0.0781623	+	0.0567883i	0.548018	+	0.836467i	$0.315383\pi$
$602$	−174.163	−	126.537i	−0.0117913	−	0.00856689i
$603$	2442.49	+	7517.21i	0.164952	+	0.507669i
$604$	−12856.5			−0.866098
$605$		0			0
$606$	724.724			0.0485807
$607$	7902.10	+	24320.2i	0.528396	+	1.62624i	0.757500	+	0.652835i	$0.226420\pi$
$607$	7902.10	+	24320.2i	0.528396	+	1.62624i	−0.229104	+	0.973402i	$0.573580\pi$
$608$	16018.9	+	11638.4i	1.06851	+	0.776318i
$609$	−66.4589	+	48.2852i	−0.00442208	+	0.00321283i
$610$	1226.83	−	3775.81i	0.0814313	−	0.250620i
$611$	3813.33	−	11736.2i	0.252489	−	0.777081i
$612$	9984.88	−	7254.44i	0.659501	−	0.479156i
$613$	−3925.34	−	2851.92i	−0.258634	−	0.187909i	0.450910	−	0.892569i	$-0.351099\pi$
$613$	−3925.34	−	2851.92i	−0.258634	−	0.187909i	−0.709545	+	0.704660i	$0.751099\pi$
$614$	−291.753	−	897.922i	−0.0191762	−	0.0590182i
$615$	−2843.49			−0.186440
$616$		0			0
$617$	3850.99			0.251272			0.125636	−	0.992076i	$-0.459903\pi$
$617$	3850.99			0.251272			0.125636	+	0.992076i	$0.459903\pi$
$618$	76.9334	+	236.777i	0.00500763	+	0.0154119i
$619$	−19487.2	−	14158.2i	−1.26536	−	0.919334i	−0.266348	−	0.963877i	$-0.585817\pi$
$619$	−19487.2	−	14158.2i	−1.26536	−	0.919334i	−0.999007	+	0.0445426i	$0.985817\pi$
$620$	288.961	−	209.943i	0.0187177	−	0.0135992i
$621$	2540.26	−	7818.12i	0.164150	−	0.505202i
$622$	1517.78	−	4671.25i	0.0978416	−	0.301125i
$623$	449.581	−	326.640i	0.0289119	−	0.0210057i
$624$	−3565.97	−	2590.83i	−0.228771	−	0.166212i
$625$	−2202.96	−	6780.02i	−0.140989	−	0.433921i
$626$	−6457.39			−0.412283
$627$		0			0
$628$	560.456			0.0356125
$629$	−3733.58	−	11490.8i	−0.236673	−	0.728406i
$630$	−124.406	−	90.3861i	−0.00786737	−	0.00571598i
$631$	2356.15	−	1711.84i	0.148648	−	0.107999i	−0.510976	−	0.859595i	$-0.670716\pi$
$631$	2356.15	−	1711.84i	0.148648	−	0.107999i	0.659624	+	0.751596i	$0.270716\pi$
$632$	2821.70	−	8684.30i	0.177597	−	0.546587i
$633$	811.943	−	2498.90i	0.0509824	−	0.156908i
$634$	−3223.08	+	2341.70i	−0.201900	+	0.146689i
$635$	−8860.93	−	6437.84i	−0.553756	−	0.402327i
$636$	2184.28	+	6722.53i	0.136183	+	0.419128i
$637$	22119.8			1.37585
$638$		0			0
$639$	4496.68			0.278382
$640$	−3825.65	−	11774.2i	−0.236285	−	0.727210i
$641$	−4975.97	−	3615.25i	−0.306613	−	0.222767i	0.423829	−	0.905742i	$-0.360686\pi$
$641$	−4975.97	−	3615.25i	−0.306613	−	0.222767i	−0.730442	+	0.682975i	$0.760686\pi$
$642$	−2037.24	+	1480.14i	−0.125239	+	0.0909913i
$643$	−3014.57	+	9277.89i	−0.184888	+	0.569027i	−0.999946	−	0.0103518i	$-0.996705\pi$
$643$	−3014.57	+	9277.89i	−0.184888	+	0.569027i	0.815058	+	0.579379i	$0.196705\pi$
$644$	176.861	−	544.322i	0.0108219	−	0.0333063i
$645$	−3272.85	+	2377.86i	−0.199796	+	0.145160i
$646$	−6789.77	−	4933.06i	−0.413530	−	0.300447i
$647$	−562.924	−	1732.50i	−0.0342053	−	0.105273i	0.932496	−	0.361180i	$-0.117626\pi$
$647$	−562.924	−	1732.50i	−0.0342053	−	0.105273i	−0.966701	+	0.255907i	$0.917626\pi$
$648$	−7583.40			−0.459728
$649$		0			0
$650$	2914.86			0.175892
$651$	2.11446	+	6.50765i	0.000127300	+	0.000391790i
$652$	1901.44	+	1381.48i	0.114212	+	0.0829799i
$653$	−5162.62	+	3750.87i	−0.309386	+	0.224782i	−0.731633	−	0.681699i	$-0.761241\pi$
$653$	−5162.62	+	3750.87i	−0.309386	+	0.224782i	0.422247	+	0.906481i	$0.361241\pi$
$654$	−362.218	+	1114.79i	−0.0216573	+	0.0666542i
$655$	−3778.05	+	11627.6i	−0.225375	+	0.693633i
$656$	−7571.32	+	5500.88i	−0.450625	+	0.327398i
$657$	4142.10	+	3009.41i	0.245964	+	0.178704i
$658$	42.2462	+	130.020i	0.00250293	+	0.00770323i
$659$	27285.6			1.61289			0.806445	−	0.591309i	$-0.201389\pi$
$659$	27285.6			1.61289			0.806445	+	0.591309i	$0.201389\pi$
$660$		0			0
$661$	−23925.0			−1.40783			−0.703913	−	0.710286i	$-0.748566\pi$
$661$	−23925.0			−1.40783			−0.703913	+	0.710286i	$0.748566\pi$
$662$	−1109.00	−	3413.15i	−0.0651095	−	0.200387i
$663$	5649.24	+	4104.41i	0.330917	+	0.240426i
$664$	−13605.1	+	9884.66i	−0.795149	+	0.577710i
$665$	270.893	−	833.722i	0.0157966	−	0.0486171i
$666$	−1210.53	+	3725.64i	−0.0704313	+	0.216765i
$667$	−5746.58	+	4175.14i	−0.333596	+	0.242372i
$668$	20375.7	+	14803.8i	1.18018	+	0.857450i
$669$	−2192.24	−	6747.02i	−0.126692	−	0.389918i
$670$	−2586.10			−0.149119
$671$		0			0
$672$	182.513			0.0104771
$673$	2576.19	+	7928.70i	0.147556	+	0.454129i	0.997331	−	0.0730159i	$-0.0232624\pi$
$673$	2576.19	+	7928.70i	0.147556	+	0.454129i	−0.849775	+	0.527145i	$0.823262\pi$
$674$	−6799.30	−	4939.98i	−0.388575	−	0.282316i
$675$	3145.75	−	2285.52i	0.179378	−	0.130326i
$676$	−4365.35	+	13435.2i	−0.248370	+	0.764405i
$677$	343.102	−	1055.96i	0.0194778	−	0.0599465i	−0.940845	−	0.338837i	$-0.889967\pi$
$677$	343.102	−	1055.96i	0.0194778	−	0.0599465i	0.960323	+	0.278890i	$0.0899666\pi$
$678$	−1253.79	+	910.932i	−0.0710200	+	0.0515990i
$679$	−394.038	−	286.286i	−0.0222707	−	0.0161806i
$680$	2644.54	+	8139.07i	0.149138	+	0.458999i
$681$	5067.22			0.285134
$682$		0			0
$683$	8337.88			0.467116			0.233558	−	0.972343i	$-0.424963\pi$
$683$	8337.88			0.467116			0.233558	+	0.972343i	$0.424963\pi$
$684$	−7049.39	−	21695.8i	−0.394065	−	1.21281i
$685$	2889.52	+	2099.36i	0.161172	+	0.117098i
$686$	−396.856	+	288.333i	−0.0220875	+	0.0160475i
$687$	1405.59	−	4325.97i	0.0780593	−	0.240242i
$688$	−4114.46	+	12663.0i	−0.227997	+	0.701704i
$689$	33533.0	−	24363.1i	1.85414	−	1.34711i
$690$	1037.90	+	754.079i	0.0572641	+	0.0416048i
$691$	−10312.5	−	31738.6i	−0.567736	−	1.74731i	−0.659678	−	0.751548i	$-0.729307\pi$
$691$	−10312.5	−	31738.6i	−0.567736	−	1.74731i	0.0919419	−	0.995764i	$-0.470693\pi$
$692$	−19349.7			−1.06295
$693$		0			0
$694$	9374.48			0.512753
$695$	−1605.34	−	4940.72i	−0.0876172	−	0.269658i
$696$	−1199.20	−	871.268i	−0.0653096	−	0.0474502i
$697$	11994.5	−	8714.54i	0.651830	−	0.473582i
$698$	3045.08	−	9371.80i	0.165126	−	0.508206i
$699$	1344.49	−	4137.92i	0.0727515	−	0.223906i
$700$	219.017	−	159.125i	0.0118258	−	0.00859196i
$701$	6317.50	+	4589.93i	0.340383	+	0.247303i	0.744824	−	0.667261i	$-0.232534\pi$
$701$	6317.50	+	4589.93i	0.340383	+	0.247303i	−0.404440	+	0.914564i	$0.632534\pi$
$702$	−1466.76	−	4514.22i	−0.0788592	−	0.242704i
$703$	−22332.0			−1.19810
$704$		0			0
$705$	2569.06			0.137243
$706$	−2654.05	−	8168.33i	−0.141482	−	0.435438i
$707$	−319.317	−	231.997i	−0.0169861	−	0.0123411i
$708$	−463.492	+	336.747i	−0.0246033	+	0.0178753i
$709$	8637.66	−	26584.0i	0.457537	−	1.40816i	−0.410593	−	0.911819i	$-0.634678\pi$
$709$	8637.66	−	26584.0i	0.457537	−	1.40816i	0.868130	−	0.496336i	$-0.165322\pi$
$710$	−454.641	+	1399.24i	−0.0240315	+	0.0739614i
$711$	−13006.0	+	9449.40i	−0.686023	+	0.498425i
$712$	8112.34	+	5893.96i	0.426998	+	0.310232i
$713$	182.834	+	562.705i	0.00960335	+	0.0295561i
$714$	−77.3599			−0.00405479
$715$		0			0
$716$	−10529.4			−0.549583
$717$	981.760	+	3021.55i	0.0511360	+	0.157380i
$718$	6272.89	+	4557.52i	0.326047	+	0.236887i
$719$	20211.6	−	14684.6i	1.04835	−	0.761672i	0.0764538	−	0.997073i	$-0.475640\pi$
$719$	20211.6	−	14684.6i	1.04835	−	0.761672i	0.971898	+	0.235401i	$0.0756402\pi$
$720$	−2938.98	+	9045.24i	−0.152124	+	0.468189i
$721$	41.8992	−	128.953i	0.00216423	−	0.00666081i
$722$	−7426.18	+	5395.44i	−0.382789	+	0.278113i
$723$	3852.55	+	2799.04i	0.198171	+	0.143980i
$724$	1086.94	+	3345.24i	0.0557951	+	0.171720i
$725$	−3359.87			−0.172114
$726$		0			0
$727$	31671.2			1.61571			0.807855	−	0.589381i	$-0.200628\pi$
$727$	31671.2			1.61571			0.807855	+	0.589381i	$0.200628\pi$
$728$	−216.422	−	666.077i	−0.0110180	−	0.0339100i
$729$	8122.23	+	5901.14i	0.412652	+	0.299809i
$730$	−1355.23	+	984.636i	−0.0687116	+	0.0499219i
$731$	6518.15	−	20060.8i	0.329798	−	1.01501i
$732$	1677.61	−	5163.15i	0.0847079	−	0.260704i
$733$	9572.11	−	6954.55i	0.482338	−	0.350439i	−0.319892	−	0.947454i	$-0.603647\pi$
$733$	9572.11	−	6954.55i	0.482338	−	0.350439i	0.802230	+	0.597015i	$0.203647\pi$
$734$	6997.90	+	5084.27i	0.351903	+	0.255673i
$735$	1423.03	+	4379.65i	0.0714142	+	0.219790i
$736$	15781.6			0.790377
$737$		0			0
$738$	−4807.04			−0.239769
$739$	−1715.09	−	5278.50i	−0.0853728	−	0.262750i	0.899253	−	0.437430i	$-0.144111\pi$
$739$	−1715.09	−	5278.50i	−0.0853728	−	0.262750i	−0.984625	+	0.174679i	$0.944111\pi$
$740$	8692.93	+	6315.79i	0.431836	+	0.313747i
$741$	10441.8	−	7586.39i	0.517663	−	0.376104i
$742$	−141.899	+	436.721i	−0.00702060	+	0.0216072i
$743$	−11526.3	+	35474.2i	−0.569121	+	1.75158i	0.0862546	+	0.996273i	$0.472510\pi$
$743$	−11526.3	+	35474.2i	−0.569121	+	1.75158i	−0.655376	+	0.755303i	$0.727490\pi$
$744$	−99.8880	+	72.5729i	−0.00492214	+	0.00357614i
$745$	15318.8	+	11129.8i	0.753338	+	0.547332i
$746$	−753.073	−	2317.72i	−0.0369598	−	0.113750i
$747$	29607.4			1.45017
$748$		0			0
$749$	1371.43			0.0669041
$750$	667.209	+	2053.46i	0.0324840	+	0.0999755i
$751$	4206.30	+	3056.05i	0.204381	+	0.148491i	0.685268	−	0.728291i	$-0.259685\pi$
$751$	4206.30	+	3056.05i	0.204381	+	0.148491i	−0.480887	+	0.876783i	$0.659685\pi$
$752$	6840.59	−	4969.98i	0.331716	−	0.241006i
$753$	1919.14	−	5906.50i	0.0928782	−	0.285850i
$754$	−1267.40	+	3900.66i	−0.0612149	+	0.188400i
$755$	−12697.6	+	9225.32i	−0.612069	+	0.444694i
$756$	−356.646	−	259.118i	−0.0171575	−	0.0124657i
$757$	48.8436	+	150.325i	0.00234512	+	0.00721752i	0.952222	−	0.305406i	$-0.0987922\pi$
$757$	48.8436	+	150.325i	0.00234512	+	0.00721752i	−0.949877	+	0.312624i	$0.898792\pi$
$758$	−6801.86			−0.325929
$759$		0			0
$760$	15818.0			0.754974
$761$	−2056.12	−	6328.10i	−0.0979428	−	0.301437i	0.890067	−	0.455830i	$-0.150658\pi$
$761$	−2056.12	−	6328.10i	−0.0979428	−	0.301437i	−0.988009	+	0.154394i	$0.950658\pi$
$762$	1445.32	+	1050.09i	0.0687119	+	0.0499221i
$763$	516.460	−	375.230i	0.0245047	−	0.0178037i
$764$	2857.86	−	8795.58i	0.135332	−	0.416509i
$765$	4655.95	−	14329.5i	0.220047	−	0.677235i
$766$	2405.63	−	1747.79i	0.113471	−	0.0824417i
$767$	2717.88	+	1974.66i	0.127949	+	0.0929605i
$768$	−187.889	−	578.264i	−0.00882796	−	0.0271697i
$769$	−5519.26			−0.258816			−0.129408	−	0.991591i	$-0.541308\pi$
$769$	−5519.26			−0.258816			−0.129408	+	0.991591i	$0.541308\pi$
$770$		0			0
$771$	6778.18			0.316615
$772$	−1157.65	−	3562.89i	−0.0539700	−	0.166102i
$773$	−24977.9	−	18147.5i	−1.16222	−	0.844400i	−0.172160	−	0.985069i	$-0.555075\pi$
$773$	−24977.9	−	18147.5i	−1.16222	−	0.844400i	−0.990057	+	0.140669i	$0.955075\pi$
$774$	−5532.89	+	4019.88i	−0.256945	+	0.186682i
$775$	−86.4825	+	266.166i	−0.00400844	+	0.0123367i
$776$	2715.82	−	8358.43i	0.125634	−	0.386663i
$777$	−166.534	+	120.994i	−0.00768903	+	0.00558640i
$778$	−9134.33	−	6636.48i	−0.420928	−	0.305822i
$779$	−8468.22	−	26062.5i	−0.389481	−	1.19870i
$780$	−6210.09			−0.285073
$781$		0			0
$782$	−6689.17			−0.305888
$783$	1690.69	+	5203.41i	0.0771652	+	0.237490i
$784$	12261.8	+	8908.69i	0.558571	+	0.405826i
$785$	553.528	−	402.162i	0.0251672	−	0.0182850i
$786$	616.244	−	1896.60i	0.0279652	−	0.0860682i
$787$	7723.49	−	23770.5i	0.349825	−	1.07665i	−0.609124	−	0.793075i	$-0.708479\pi$
$787$	7723.49	−	23770.5i	0.349825	−	1.07665i	0.958949	−	0.283577i	$-0.0915212\pi$
$788$	6807.90	−	4946.23i	0.307768	−	0.223607i
$789$	1140.59	+	828.684i	0.0514650	+	0.0373915i
$790$	−1625.41	−	5002.49i	−0.0732017	−	0.225292i
$791$	844.031			0.0379397
$792$		0			0
$793$	−31834.4			−1.42556
$794$	2391.51	+	7360.30i	0.106891	+	0.328976i
$795$	6981.11	+	5072.07i	0.311439	+	0.226274i
$796$	−17664.2	+	12833.8i	−0.786547	+	0.571460i
$797$	−6326.64	+	19471.4i	−0.281181	+	0.865385i	0.706337	+	0.707876i	$0.250346\pi$
$797$	−6326.64	+	19471.4i	−0.281181	+	0.865385i	−0.987517	+	0.157509i	$0.949654\pi$
$798$	−44.1858	+	135.990i	−0.00196010	+	0.00603256i
$799$	−10836.9	+	7873.48i	−0.479828	+	0.348615i
$800$	6039.20	+	4387.74i	0.266898	+	0.193912i
$801$	−5455.42	−	16790.0i	−0.240646	−	0.740633i
$802$	−3998.41			−0.176046
$803$		0			0
$804$	−3536.30			−0.155119
$805$	−215.910	−	664.502i	−0.00945319	−	0.0290939i
$806$	276.384	+	200.804i	0.0120784	+	0.00877548i
$807$	−2205.67	+	1602.51i	−0.0962122	+	0.0699023i
$808$	2200.82	−	6773.42i	0.0958224	−	0.294911i
$809$	−4534.69	+	13956.3i	−0.197072	+	0.606524i	0.802874	+	0.596148i	$0.203303\pi$
$809$	−4534.69	+	13956.3i	−0.197072	+	0.606524i	−0.999946	+	0.0103763i	$0.996697\pi$
$810$	−3534.05	+	2567.64i	−0.153301	+	0.111380i
$811$	3821.98	+	2776.83i	0.165484	+	0.120232i	0.667445	−	0.744659i	$-0.267388\pi$
$811$	3821.98	+	2776.83i	0.165484	+	0.120232i	−0.501961	+	0.864890i	$0.667388\pi$
$812$	117.711	+	362.278i	0.00508725	+	0.0156570i
$813$	6194.10			0.267204
$814$		0			0
$815$	2869.23			0.123319
$816$	1478.53	+	4550.43i	0.0634299	+	0.195217i
$817$	−31541.6	−	22916.3i	−1.35067	−	0.981323i
$818$	8917.65	−	6479.05i	0.381171	−	0.276937i
$819$	−381.029	+	1172.69i	−0.0162567	+	0.0500329i
$820$	−4074.50	+	12540.0i	−0.173521	+	0.534044i
$821$	36342.4	−	26404.3i	1.54489	−	1.12243i	0.597721	−	0.801704i	$-0.296073\pi$
$821$	36342.4	−	26404.3i	1.54489	−	1.12243i	0.947172	−	0.320726i	$-0.103927\pi$
$822$	−471.314	−	342.430i	−0.0199987	−	0.0145299i
$823$	12223.9	+	37621.4i	0.517740	+	1.59344i	0.778241	+	0.627966i	$0.216112\pi$
$823$	12223.9	+	37621.4i	0.517740	+	1.59344i	−0.260501	+	0.965474i	$0.583888\pi$
$824$	2446.59			0.103436
$825$		0			0
$826$	−37.2183			−0.00156778
$827$	−4870.94	−	14991.2i	−0.204811	−	0.630345i	−0.999721	−	0.0236169i	$-0.992482\pi$
$827$	−4870.94	−	14991.2i	−0.204811	−	0.630345i	0.794910	−	0.606728i	$-0.207518\pi$
$828$	−14709.6	−	10687.2i	−0.617385	−	0.448557i
$829$	−18268.1	+	13272.6i	−0.765354	+	0.556062i	−0.900548	−	0.434757i	$-0.856834\pi$
$829$	−18268.1	+	13272.6i	−0.765354	+	0.556062i	0.135194	+	0.990819i	$0.456834\pi$
$830$	−2993.48	+	9212.99i	−0.125187	+	0.385286i
$831$	−3165.48	+	9742.35i	−0.132141	+	0.406689i
$832$	−11135.9	+	8090.69i	−0.464023	+	0.337132i
$833$	−19425.2	−	14113.2i	−0.807973	−	0.587027i
$834$	261.849	+	805.889i	0.0108718	+	0.0334600i
$835$	30746.4			1.27428
$836$		0			0
$837$	455.727			0.0188199
$838$	−3392.16	−	10440.0i	−0.139833	−	0.430362i
$839$	18969.6	+	13782.2i	0.780575	+	0.567121i	0.905152	−	0.425089i	$-0.139757\pi$
$839$	18969.6	+	13782.2i	0.780575	+	0.567121i	−0.124576	+	0.992210i	$0.539757\pi$
$840$	117.958	−	85.7017i	0.00484517	−	0.00352023i
$841$	−6075.72	+	18699.1i	−0.249117	+	0.766704i
$842$	−2421.15	+	7451.55i	−0.0990956	+	0.304985i
$843$	−5465.68	+	3971.05i	−0.223307	+	0.162242i
$844$	−9856.91	−	7161.46i	−0.402001	−	0.292071i
$845$	5329.17	+	16401.5i	0.216957	+	0.667726i
$846$	4343.10			0.176500
$847$		0			0
$848$	28400.7			1.15010
$849$	1778.97	+	5475.09i	0.0719128	+	0.221325i
$850$	−2559.77	−	1859.78i	−0.103293	−	0.0750471i
$851$	−14399.9	+	10462.1i	−0.580049	+	0.421431i
$852$	−621.689	+	1913.36i	−0.0249985	+	0.0769374i
$853$	4634.27	−	14262.8i	0.186019	−	0.572508i	−0.813945	−	0.580941i	$-0.802685\pi$
$853$	4634.27	−	14262.8i	0.186019	−	0.572508i	0.999964	+	0.00843365i	$0.00268455\pi$
$854$	285.323	−	207.300i	0.0114327	−	0.00830638i
$855$	−22530.3	−	16369.2i	−0.901194	−	0.654756i
$856$	7647.07	+	23535.3i	0.305341	+	0.939742i
$857$	−46121.7			−1.83838			−0.919188	−	0.393819i	$-0.871154\pi$
$857$	−46121.7			−1.83838			−0.919188	+	0.393819i	$0.871154\pi$
$858$		0			0
$859$	−17398.7			−0.691080			−0.345540	−	0.938404i	$-0.612304\pi$
$859$	−17398.7			−0.691080			−0.345540	+	0.938404i	$0.612304\pi$
$860$	5796.83	+	17840.8i	0.229849	+	0.707403i
$861$	−204.355	−	148.473i	−0.00808874	−	0.00587681i
$862$	8561.21	−	6220.08i	0.338278	−	0.245774i
$863$	−3433.71	+	10567.9i	−0.135440	+	0.416842i	−0.995658	−	0.0930845i	$-0.970327\pi$
$863$	−3433.71	+	10567.9i	−0.135440	+	0.416842i	0.860218	+	0.509926i	$0.170327\pi$
$864$	3756.32	−	11560.8i	0.147908	−	0.455215i
$865$	−19110.5	+	13884.6i	−0.751186	+	0.545769i
$866$	−2463.68	−	1789.97i	−0.0966735	−	0.0702374i
$867$	−2.16472	−	6.66231i	−8.47954e−5	−	0.000260974i
$868$	31.7291			0.00124073
$869$		0			0
$870$	−853.855			−0.0332740
$871$	6407.96	+	19721.7i	0.249283	+	0.767213i
$872$	9319.11	+	6770.73i	0.361909	+	0.262942i
$873$	−12518.0	+	9094.82i	−0.485302	+	0.352592i
$874$	−3820.66	+	11758.8i	−0.147867	+	0.455088i
$875$	363.373	−	1118.35i	0.0140391	−	0.0432081i
$876$	−1853.19	+	1346.42i	−0.0714765	+	0.0519307i
$877$	1291.69	+	938.471i	0.0497348	+	0.0361345i	0.612375	−	0.790567i	$-0.290214\pi$
$877$	1291.69	+	938.471i	0.0497348	+	0.0361345i	−0.562640	+	0.826702i	$0.690214\pi$
$878$	−1583.56	−	4873.70i	−0.0608686	−	0.187334i
$879$	−3445.25			−0.132202
$880$		0			0
$881$	4924.45			0.188319			0.0941594	−	0.995557i	$-0.469984\pi$
$881$	4924.45			0.188319			0.0941594	+	0.995557i	$0.469984\pi$
$882$	2405.70	+	7403.98i	0.0918414	+	0.282659i
$883$	17451.5	+	12679.2i	0.665105	+	0.483227i	0.868383	−	0.495894i	$-0.165159\pi$
$883$	17451.5	+	12679.2i	0.665105	+	0.483227i	−0.203278	+	0.979121i	$0.565159\pi$
$884$	26195.7	−	19032.3i	0.996670	−	0.724123i
$885$	−216.126	+	665.168i	−0.00820904	+	0.0252648i
$886$	3104.63	−	9555.06i	0.117722	−	0.362312i
$887$	17898.6	−	13004.1i	0.677539	−	0.492261i	−0.195001	−	0.980803i	$-0.562471\pi$
$887$	17898.6	−	13004.1i	0.677539	−	0.492261i	0.872540	+	0.488542i	$0.162471\pi$
$888$	−3004.97	−	2183.24i	−0.113559	−	0.0825053i
$889$	−300.663	−	925.346i	−0.0113430	−	0.0349101i
$890$	5776.16			0.217548
$891$		0			0
$892$	−32896.2			−1.23481
$893$	7650.93	+	23547.2i	0.286706	+	0.882391i
$894$	−2498.67	−	1815.39i	−0.0934766	−	0.0679148i
$895$	−10399.2	+	7555.47i	−0.388388	+	0.282181i
$896$	339.846	−	1045.94i	0.0126713	−	0.0389981i
$897$	3178.87	−	9783.57i	0.118327	−	0.364174i
$898$	5636.68	−	4095.28i	0.209464	−	0.152184i
$899$	−318.580	−	231.462i	−0.0118189	−	0.00858696i
$900$	−2657.65	−	8179.40i	−0.0984314	−	0.302941i
$901$	−44992.5			−1.66362
$902$		0			0
$903$	−359.372			−0.0132438
$904$	4706.29	+	14484.5i	0.173151	+	0.532905i
$905$	3473.92	+	2523.95i	0.127599	+	0.0927060i
$906$	2071.12	−	1504.76i	0.0759474	−	0.0551791i
$907$	−629.720	+	1938.08i	−0.0230535	+	0.0709514i	−0.961921	−	0.273326i	$-0.911876\pi$
$907$	−629.720	+	1938.08i	−0.0230535	+	0.0709514i	0.938868	+	0.344278i	$0.111876\pi$
$908$	7260.93	−	22346.8i	0.265377	−	0.816747i
$909$	−10144.2	+	7370.17i	−0.370144	+	0.268925i
$910$	−326.383	−	237.131i	−0.0118895	−	0.00863826i
$911$	13436.6	+	41353.5i	0.488665	+	1.50396i	0.826602	+	0.562787i	$0.190271\pi$
$911$	13436.6	+	41353.5i	0.488665	+	1.50396i	−0.337938	+	0.941169i	$0.609729\pi$
$912$	8843.64			0.321099
$913$		0			0
$914$	2990.95			0.108241
$915$	−2048.00	−	6303.11i	−0.0739945	−	0.227732i
$916$	−17063.8	−	12397.6i	−0.615505	−	0.447191i
$917$	−878.656	+	638.381i	−0.0316421	+	0.0229893i
$918$	−1592.15	+	4900.14i	−0.0572428	+	0.176175i
$919$	2977.93	−	9165.13i	0.106891	−	0.328977i	−0.883279	−	0.468849i	$-0.844669\pi$
$919$	2977.93	−	9165.13i	0.106891	−	0.328977i	0.990170	+	0.139872i	$0.0446690\pi$
$920$	10199.6	−	7410.47i	0.365513	−	0.265561i
$921$	−1275.07	−	926.395i	−0.0456190	−	0.0331441i
$922$	1380.26	+	4248.02i	0.0493022	+	0.151736i
$923$	11797.2			0.420704
$924$		0			0
$925$	−8419.24			−0.299268
$926$	4020.22	+	12373.0i	0.142670	+	0.439094i
$927$	−3484.79	−	2531.85i	−0.123469	−	0.0897052i
$928$	−8497.56	+	6173.84i	−0.300588	+	0.218390i
$929$	1942.40	−	5978.10i	0.0685987	−	0.211125i	−0.910881	−	0.412670i	$-0.864596\pi$
$929$	1942.40	−	5978.10i	0.0685987	−	0.211125i	0.979479	+	0.201545i	$0.0645962\pi$
$930$	−21.9781	+	67.6415i	−0.000774934	+	0.00238500i
$931$	−35904.5	+	26086.1i	−1.26393	+	0.918302i
$932$	−16322.0	−	11858.6i	−0.573653	−	0.416783i
$933$	−2533.69	−	7797.90i	−0.0889061	−	0.273625i
$934$	13430.4			0.470509
$935$		0			0
$936$	−22249.1			−0.776961
$937$	−7606.06	−	23409.0i	−0.265186	−	0.816158i	−0.991651	−	0.128954i	$-0.958838\pi$
$937$	−7606.06	−	23409.0i	−0.265186	−	0.816158i	0.726465	−	0.687204i	$-0.241162\pi$
$938$	−185.857	−	135.033i	−0.00646955	−	0.00470040i
$939$	−8720.87	+	6336.08i	−0.303083	+	0.220203i
$940$	3681.26	−	11329.7i	0.127733	−	0.393123i
$941$	−6072.49	+	18689.2i	−0.210369	+	0.647450i	0.789081	+	0.614289i	$0.210557\pi$
$941$	−6072.49	+	18689.2i	−0.210369	+	0.647450i	−0.999450	+	0.0331604i	$0.989443\pi$
$942$	−90.2869	+	65.5972i	−0.00312283	+	0.00226887i
$943$	−17670.2	−	12838.2i	−0.610203	−	0.443339i
$944$	711.327	+	2189.24i	0.0245251	+	0.0754806i
$945$	−538.170			−0.0185256
$946$		0			0
$947$	3025.82			0.103829			0.0519144	−	0.998652i	$-0.483468\pi$
$947$	3025.82			0.103829			0.0519144	+	0.998652i	$0.483468\pi$
$948$	−2222.63	−	6840.55i	−0.0761473	−	0.234357i
$949$	10866.9	+	7895.29i	0.371713	+	0.270065i
$950$	−4731.35	+	3437.53i	−0.161585	+	0.117398i
$951$	−2055.14	+	6325.06i	−0.0700761	+	0.215672i
$952$	−234.924	+	723.021i	−0.00799782	+	0.0246148i
$953$	−9471.44	+	6881.40i	−0.321941	+	0.233904i	−0.737003	−	0.675889i	$-0.763760\pi$
$953$	−9471.44	+	6881.40i	−0.321941	+	0.233904i	0.415062	+	0.909793i	$0.363760\pi$
$954$	11801.9	+	8574.55i	0.400523	+	0.290997i
$955$	−3488.84	−	10737.5i	−0.118216	−	0.363831i
$956$	14732.0			0.498398
$957$		0			0
$958$	−2613.14			−0.0881281
$959$	98.0452	+	301.752i	0.00330140	+	0.0101607i
$960$	−2318.34	−	1684.37i	−0.0779417	−	0.0566280i
$961$	24074.9	−	17491.4i	0.808126	−	0.587138i
$962$	−3175.88	+	9774.35i	−0.106439	+	0.327586i
$963$	13463.3	−	41435.9i	0.450519	−	1.38655i
$964$	17864.4	−	12979.2i	0.596860	−	0.433645i
$965$	−3699.93	−	2688.16i	−0.123425	−	0.0896734i
$966$	35.2174	+	108.388i	0.00117298	+	0.00361007i
$967$	−12352.3			−0.410779			−0.205390	−	0.978680i	$-0.565846\pi$
$967$	−12352.3			−0.410779			−0.205390	+	0.978680i	$0.565846\pi$
$968$		0			0
$969$	−14010.1			−0.464469
$970$	−1564.42	−	4814.78i	−0.0517839	−	0.159374i
$971$	13679.4	+	9938.68i	0.452104	+	0.328473i	0.790426	−	0.612557i	$-0.209859\pi$
$971$	13679.4	+	9938.68i	0.452104	+	0.328473i	−0.338322	+	0.941031i	$0.609859\pi$
$972$	−17255.8	+	12537.1i	−0.569423	+	0.413710i
$973$	142.608	−	438.901i	0.00469865	−	0.0144610i
$974$	−5459.66	+	16803.1i	−0.179609	+	0.552778i
$975$	3936.59	−	2860.10i	0.129304	−	0.0939450i
$976$	−17646.9	−	12821.2i	−0.578753	−	0.420489i
$977$	7631.70	+	23487.9i	0.249907	+	0.769136i	0.994790	+	0.101941i	$0.0325053\pi$
$977$	7631.70	+	23487.9i	0.249907	+	0.769136i	−0.744883	+	0.667195i	$0.767495\pi$
$978$	−468.005			−0.0153018
$979$		0			0
$980$	21353.7			0.696039
$981$	−6266.95	−	19287.7i	−0.203964	−	0.627736i
$982$	−8436.44	−	6129.43i	−0.274152	−	0.199183i
$983$	24862.2	−	18063.4i	0.806694	−	0.586097i	−0.106176	−	0.994347i	$-0.533861\pi$
$983$	24862.2	−	18063.4i	0.806694	−	0.586097i	0.912870	+	0.408250i	$0.133861\pi$
$984$	1408.47	−	4334.83i	0.0456305	−	0.140436i
$985$	3174.52	−	9770.17i	0.102689	−	0.316044i
$986$	3601.77	−	2616.84i	0.116332	−	0.0845204i
$987$	184.632	+	134.143i	0.00595432	+	0.00432607i
$988$	−18494.3	−	56919.7i	−0.595529	−	1.83285i
$989$	−31074.3			−0.999094
$990$		0			0
$991$	40862.5			1.30983			0.654915	−	0.755703i	$-0.272705\pi$
$991$	40862.5			1.30983			0.654915	+	0.755703i	$0.272705\pi$
$992$	270.360	+	832.081i	0.00865315	+	0.0266317i
$993$	−4846.76	−	3521.38i	−0.154892	−	0.112535i
$994$	−105.735	+	76.8212i	−0.00337396	+	0.00245133i
$995$	−8236.81	+	25350.3i	−0.262437	+	0.807697i
$996$	−4093.37	+	12598.1i	−0.130224	+	0.400790i
$997$	46954.3	−	34114.3i	1.49153	−	1.08366i	0.517927	−	0.855425i	$-0.326704\pi$
$997$	46954.3	−	34114.3i	1.49153	−	1.08366i	0.973606	−	0.228237i	$-0.0732960\pi$
$998$	−647.042	−	470.104i	−0.0205228	−	0.0149107i
$999$	4236.57	+	13038.8i	0.134173	+	0.412943i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	121.4.c.b.27.2		8
11.2	odd	10		121.4.c.h.9.1		8
11.3	even	5		121.4.a.f.1.3		4
11.4	even	5		121.4.c.i.3.1		8
11.5	even	5		121.4.c.i.81.1		8
11.6	odd	10		11.4.c.a.4.2	yes	8
11.7	odd	10		11.4.c.a.3.2	✓	8
11.8	odd	10		121.4.a.g.1.2		4
11.9	even	5	inner	121.4.c.b.9.2		8
11.10	odd	2		121.4.c.h.27.1		8
33.8	even	10		1089.4.a.y.1.3		4
33.14	odd	10		1089.4.a.bh.1.2		4
33.17	even	10		99.4.f.c.37.1		8
33.29	even	10		99.4.f.c.91.1		8
44.3	odd	10		1936.4.a.bl.1.4		4
44.7	even	10		176.4.m.c.113.2		8
44.19	even	10		1936.4.a.bk.1.4		4
44.39	even	10		176.4.m.c.81.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
11.4.c.a.3.2	✓	8	11.7	odd	10
11.4.c.a.4.2	yes	8	11.6	odd	10
99.4.f.c.37.1		8	33.17	even	10
99.4.f.c.91.1		8	33.29	even	10
121.4.a.f.1.3		4	11.3	even	5
121.4.a.g.1.2		4	11.8	odd	10
121.4.c.b.9.2		8	11.9	even	5	inner
121.4.c.b.27.2		8	1.1	even	1	trivial
121.4.c.h.9.1		8	11.2	odd	10
121.4.c.h.27.1		8	11.10	odd	2
121.4.c.i.3.1		8	11.4	even	5
121.4.c.i.81.1		8	11.5	even	5
176.4.m.c.81.2		8	44.39	even	10
176.4.m.c.113.2		8	44.7	even	10
1089.4.a.y.1.3		4	33.8	even	10
1089.4.a.bh.1.2		4	33.14	odd	10
1936.4.a.bk.1.4		4	44.19	even	10
1936.4.a.bl.1.4		4	44.3	odd	10

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 121 = 11^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	121.c (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.285330 + 0.878155i) q^{2} +(1.24700 + 0.906001i) q^{3} +(5.78239 - 4.20115i) q^{4} +(2.69633 - 8.29844i) q^{5} +(-0.439802 + 1.35357i) q^{6} +(0.627082 - 0.455601i) q^{7} +(11.3152 + 8.22096i) q^{8} +(-7.60928 - 23.4190i) q^{9} +8.05666 q^{10} +11.0169 q^{12} +(-19.9632 - 61.4404i) q^{13} +(0.579014 + 0.420678i) q^{14} +(10.8807 - 7.90531i) q^{15} +(13.6787 - 42.0987i) q^{16} +(-21.6699 + 66.6930i) q^{17} +(18.3943 - 13.3643i) q^{18} +(104.861 + 76.1863i) q^{19} +(-19.2718 - 59.3125i) q^{20} +1.19475 q^{21} +103.308 q^{23} +(6.66187 + 20.5031i) q^{24} +(39.5332 + 28.7225i) q^{25} +(48.2581 - 35.0616i) q^{26} +(24.5893 - 75.6779i) q^{27} +(1.71198 - 5.26893i) q^{28} +(-55.6258 + 40.4145i) q^{29} +(10.0467 + 7.29935i) q^{30} +(1.76980 + 5.44688i) q^{31} +152.763 q^{32} -64.7499 q^{34} +(-2.08996 - 6.43225i) q^{35} +(-142.386 - 103.450i) q^{36} +(-139.388 + 101.272i) q^{37} +(-36.9833 + 113.823i) q^{38} +(30.7709 - 94.7031i) q^{39} +(98.7306 - 71.7320i) q^{40} +(-171.044 - 124.271i) q^{41} +(0.340898 + 1.04917i) q^{42} -300.793 q^{43} -214.858 q^{45} +(29.4768 + 90.7203i) q^{46} +(154.537 + 112.277i) q^{47} +(55.1989 - 40.1043i) q^{48} +(-105.807 + 325.641i) q^{49} +(-13.9428 + 42.9117i) q^{50} +(-87.4464 + 63.5335i) q^{51} +(-373.556 - 271.404i) q^{52} +(198.266 + 610.201i) q^{53} +73.4730 q^{54} +10.8410 q^{56} +(61.7378 + 190.009i) q^{57} +(-51.3620 - 37.3166i) q^{58} +(-42.0710 + 30.5663i) q^{59} +(29.7052 - 91.4232i) q^{60} +(152.276 - 468.657i) q^{61} +(-4.27823 + 3.10832i) q^{62} +(-15.4413 - 11.2188i) q^{63} +(-65.8417 - 202.640i) q^{64} -563.687 q^{65} -320.988 q^{67} +(154.884 + 476.684i) q^{68} +(128.825 + 93.5970i) q^{69} +(5.05219 - 3.67063i) q^{70} +(-56.4304 + 173.675i) q^{71} +(106.426 - 327.545i) q^{72} +(-168.213 + 122.214i) q^{73} +(-128.704 - 93.5088i) q^{74} +(23.2754 + 71.6342i) q^{75} +926.421 q^{76} +91.9439 q^{78} +(-201.747 - 620.913i) q^{79} +(-312.471 - 227.024i) q^{80} +(-438.649 + 318.697i) q^{81} +(60.3252 - 185.662i) q^{82} +(-371.554 + 1143.52i) q^{83} +(6.90850 - 5.01932i) q^{84} +(495.019 + 359.652i) q^{85} +(-85.8253 - 264.143i) q^{86} -105.981 q^{87} +716.942 q^{89} +(-61.3054 - 188.679i) q^{90} +(-40.5109 - 29.4329i) q^{91} +(597.366 - 434.012i) q^{92} +(-2.72794 + 8.39572i) q^{93} +(-54.5031 + 167.743i) q^{94} +(914.969 - 664.764i) q^{95} +(190.496 + 138.403i) q^{96} +(-194.177 - 597.614i) q^{97} -316.153 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 3 q^{2} - 3 q^{3} - 17 q^{4} + 18 q^{5} + 14 q^{6} - 10 q^{7} + 113 q^{8} + 31 q^{9} - 40 q^{10} + 190 q^{12} - 40 q^{13} + 64 q^{14} + 119 q^{15} + 343 q^{16} + 201 q^{17} - 53 q^{18} + 302 q^{19}+ \cdots - 2740 q^{98}+O(q^{100}) \) 8 * q - 3 * q^2 - 3 * q^3 - 17 * q^4 + 18 * q^5 + 14 * q^6 - 10 * q^7 + 113 * q^8 + 31 * q^9 - 40 * q^10 + 190 * q^12 - 40 * q^13 + 64 * q^14 + 119 * q^15 + 343 * q^16 + 201 * q^17 - 53 * q^18 + 302 * q^19 - 88 * q^20 - 334 * q^21 - 12 * q^23 - 348 * q^24 + 214 * q^25 + 340 * q^26 + 72 * q^27 - 18 * q^28 + 164 * q^29 - 306 * q^30 + 324 * q^31 - 324 * q^32 - 298 * q^34 + 593 * q^35 - 125 * q^36 - 174 * q^37 - 327 * q^38 + 125 * q^39 - 282 * q^40 + 121 * q^41 - 590 * q^42 + 650 * q^43 + 452 * q^45 - 54 * q^46 + 12 * q^47 - 991 * q^48 - 1130 * q^49 - 1163 * q^50 - 194 * q^51 - 1600 * q^52 + 682 * q^53 + 3100 * q^54 - 1560 * q^56 + 333 * q^57 - 2348 * q^58 - 854 * q^59 - 502 * q^60 - 630 * q^61 + 2114 * q^62 - 67 * q^63 - 1289 * q^64 - 1790 * q^65 + 86 * q^67 + 575 * q^68 + 1198 * q^69 + 166 * q^70 - 1772 * q^71 - 104 * q^72 - 2425 * q^73 - 1274 * q^74 + 975 * q^75 + 242 * q^76 - 1340 * q^78 + 116 * q^79 + 1794 * q^80 - 26 * q^81 + 2708 * q^82 + 1738 * q^83 + 174 * q^84 + 1662 * q^85 - 784 * q^86 - 2310 * q^87 + 3782 * q^89 - 2658 * q^90 - 55 * q^91 + 5900 * q^92 + 2743 * q^93 + 1458 * q^94 + 487 * q^95 + 2383 * q^96 + 3116 * q^97 - 2740 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more