LMFDB - Embedded newform 16.5.f.a.11.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [16,5,Mod(3,16)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(16, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("16.3");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 16 = 2^{4} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	16.f (of order $4$, degree $2$, 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:	$1.65391940934$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 4 x^{13} + 15 x^{12} - 34 x^{11} + 62 x^{10} - 312 x^{9} + 1432 x^{8} - 4960 x^{7} + \cdots + 2097152 $ x^14 - 4x^13 + 15x^12 - 34x^11 + 62x^10 - 312x^9 + 1432x^8 - 4960x^7 + 11456x^6 - 19968x^5 + 31744x^4 - 139264x^3 + 491520x^2 - 1048576*x + 2097152
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{21} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			11.2
Root			$0.153862 + 2.82424i$ of defining polynomial
Character	$\chi$	$=$	16.11
Dual form			16.5.f.a.3.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.97810 + 2.67038i) q^{2} +(-9.42589 - 9.42589i) q^{3} +(1.73818 - 15.9053i) q^{4} +(-2.84710 - 2.84710i) q^{5} +(53.2419 + 2.90058i) q^{6} -76.7794 q^{7} +(37.2967 + 52.0092i) q^{8} +96.6949i q^{9} +O(q^{10})$	\(q+(-2.97810 + 2.67038i) q^{2} +(-9.42589 - 9.42589i) q^{3} +(1.73818 - 15.9053i) q^{4} +(-2.84710 - 2.84710i) q^{5} +(53.2419 + 2.90058i) q^{6} -76.7794 q^{7} +(37.2967 + 52.0092i) q^{8} +96.6949i q^{9} +(16.0818 + 0.876123i) q^{10} +(121.488 - 121.488i) q^{11} +(-166.306 + 133.538i) q^{12} +(27.1604 - 27.1604i) q^{13} +(228.657 - 205.030i) q^{14} +53.6729i q^{15} +(-249.957 - 55.2924i) q^{16} -88.0613 q^{17} +(-258.212 - 287.967i) q^{18} +(-261.112 - 261.112i) q^{19} +(-50.2328 + 40.3352i) q^{20} +(723.714 + 723.714i) q^{21} +(-37.3847 + 686.220i) q^{22} +93.4210 q^{23} +(138.678 - 841.788i) q^{24} -608.788i q^{25} +(-8.35791 + 153.415i) q^{26} +(147.938 - 147.938i) q^{27} +(-133.456 + 1221.20i) q^{28} +(272.522 - 272.522i) q^{29} +(-143.327 - 159.843i) q^{30} +1232.20i q^{31} +(892.050 - 502.814i) q^{32} -2290.26 q^{33} +(262.256 - 235.157i) q^{34} +(218.599 + 218.599i) q^{35} +(1537.96 + 168.073i) q^{36} +(-1046.16 - 1046.16i) q^{37} +(1474.89 + 80.3506i) q^{38} -512.021 q^{39} +(41.8880 - 254.263i) q^{40} -915.267i q^{41} +(-4087.88 - 222.705i) q^{42} +(1116.82 - 1116.82i) q^{43} +(-1721.13 - 2143.47i) q^{44} +(275.300 - 275.300i) q^{45} +(-278.217 + 249.469i) q^{46} +1720.70i q^{47} +(1834.89 + 2877.25i) q^{48} +3494.07 q^{49} +(1625.69 + 1813.03i) q^{50} +(830.056 + 830.056i) q^{51} +(-384.784 - 479.203i) q^{52} +(734.019 + 734.019i) q^{53} +(-45.5242 + 835.626i) q^{54} -691.775 q^{55} +(-2863.62 - 3993.23i) q^{56} +4922.43i q^{57} +(-83.8616 + 1539.33i) q^{58} +(-1202.73 + 1202.73i) q^{59} +(853.684 + 93.2930i) q^{60} +(580.221 - 580.221i) q^{61} +(-3290.44 - 3669.61i) q^{62} -7424.17i q^{63} +(-1313.91 + 3879.54i) q^{64} -154.657 q^{65} +(6820.62 - 6115.86i) q^{66} +(-1483.97 - 1483.97i) q^{67} +(-153.066 + 1400.64i) q^{68} +(-880.576 - 880.576i) q^{69} +(-1234.75 - 67.2681i) q^{70} +5571.73 q^{71} +(-5029.02 + 3606.40i) q^{72} -6615.21i q^{73} +(5909.20 + 321.929i) q^{74} +(-5738.37 + 5738.37i) q^{75} +(-4606.93 + 3699.21i) q^{76} +(-9327.75 + 9327.75i) q^{77} +(1524.85 - 1367.29i) q^{78} -5391.66i q^{79} +(554.231 + 869.077i) q^{80} +5043.39 q^{81} +(2444.11 + 2725.76i) q^{82} +(-2554.07 - 2554.07i) q^{83} +(12768.8 - 10252.9i) q^{84} +(250.719 + 250.719i) q^{85} +(-343.673 + 6308.34i) q^{86} -5137.52 q^{87} +(10849.6 + 1787.39i) q^{88} +10962.7i q^{89} +(-84.7166 + 1555.03i) q^{90} +(-2085.35 + 2085.35i) q^{91} +(162.382 - 1485.89i) q^{92} +(11614.6 - 11614.6i) q^{93} +(-4594.92 - 5124.42i) q^{94} +1486.83i q^{95} +(-13147.8 - 3668.90i) q^{96} +4713.20 q^{97} +(-10405.7 + 9330.48i) q^{98} +(11747.2 + 11747.2i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 2 q^{2} - 2 q^{3} - 8 q^{4} - 2 q^{5} + 64 q^{6} - 4 q^{7} - 92 q^{8}+O(q^{10}) $ 14 * q - 2 * q^2 - 2 * q^3 - 8 * q^4 - 2 * q^5 + 64 * q^6 - 4 * q^7 - 92 * q^8	\( 14 q - 2 q^{2} - 2 q^{3} - 8 q^{4} - 2 q^{5} + 64 q^{6} - 4 q^{7} - 92 q^{8} - 100 q^{10} + 94 q^{11} - 332 q^{12} - 2 q^{13} + 44 q^{14} - 168 q^{16} - 4 q^{17} + 1390 q^{18} - 706 q^{19} + 1900 q^{20} - 164 q^{21} + 900 q^{22} + 1148 q^{23} - 1872 q^{24} - 3416 q^{26} - 1664 q^{27} - 3784 q^{28} + 862 q^{29} - 3740 q^{30} + 3208 q^{32} - 4 q^{33} + 7508 q^{34} + 1340 q^{35} + 11468 q^{36} - 1826 q^{37} + 3568 q^{38} + 2684 q^{39} - 5144 q^{40} - 17064 q^{42} + 1694 q^{43} - 14636 q^{44} + 1410 q^{45} - 5316 q^{46} + 6888 q^{48} + 682 q^{49} + 20070 q^{50} - 3012 q^{51} + 20452 q^{52} - 482 q^{53} + 10784 q^{54} - 11780 q^{55} - 6952 q^{56} - 20456 q^{58} - 2786 q^{59} - 29920 q^{60} - 3778 q^{61} - 11472 q^{62} + 15808 q^{64} - 2020 q^{65} + 30148 q^{66} + 7998 q^{67} + 18032 q^{68} + 9628 q^{69} + 15296 q^{70} + 19964 q^{71} - 17708 q^{72} - 23780 q^{74} + 17570 q^{75} - 23996 q^{76} - 9508 q^{77} - 8052 q^{78} + 1384 q^{80} + 1454 q^{81} + 16016 q^{82} - 17282 q^{83} + 19624 q^{84} + 9948 q^{85} - 4796 q^{86} - 49284 q^{87} + 7288 q^{88} - 5416 q^{90} - 28036 q^{91} - 14632 q^{92} + 8896 q^{93} + 432 q^{94} + 6064 q^{96} - 4 q^{97} - 12246 q^{98} + 49214 q^{99}+O(q^{100}) \) 14 * q - 2 * q^2 - 2 * q^3 - 8 * q^4 - 2 * q^5 + 64 * q^6 - 4 * q^7 - 92 * q^8 - 100 * q^10 + 94 * q^11 - 332 * q^12 - 2 * q^13 + 44 * q^14 - 168 * q^16 - 4 * q^17 + 1390 * q^18 - 706 * q^19 + 1900 * q^20 - 164 * q^21 + 900 * q^22 + 1148 * q^23 - 1872 * q^24 - 3416 * q^26 - 1664 * q^27 - 3784 * q^28 + 862 * q^29 - 3740 * q^30 + 3208 * q^32 - 4 * q^33 + 7508 * q^34 + 1340 * q^35 + 11468 * q^36 - 1826 * q^37 + 3568 * q^38 + 2684 * q^39 - 5144 * q^40 - 17064 * q^42 + 1694 * q^43 - 14636 * q^44 + 1410 * q^45 - 5316 * q^46 + 6888 * q^48 + 682 * q^49 + 20070 * q^50 - 3012 * q^51 + 20452 * q^52 - 482 * q^53 + 10784 * q^54 - 11780 * q^55 - 6952 * q^56 - 20456 * q^58 - 2786 * q^59 - 29920 * q^60 - 3778 * q^61 - 11472 * q^62 + 15808 * q^64 - 2020 * q^65 + 30148 * q^66 + 7998 * q^67 + 18032 * q^68 + 9628 * q^69 + 15296 * q^70 + 19964 * q^71 - 17708 * q^72 - 23780 * q^74 + 17570 * q^75 - 23996 * q^76 - 9508 * q^77 - 8052 * q^78 + 1384 * q^80 + 1454 * q^81 + 16016 * q^82 - 17282 * q^83 + 19624 * q^84 + 9948 * q^85 - 4796 * q^86 - 49284 * q^87 + 7288 * q^88 - 5416 * q^90 - 28036 * q^91 - 14632 * q^92 + 8896 * q^93 + 432 * q^94 + 6064 * q^96 - 4 * q^97 - 12246 * q^98 + 49214 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/16\mathbb{Z}\right)^\times$.

$n$	$5$	$15$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	−2.97810	+	2.67038i	−0.744525	+	0.667594i
$2$	−2.97810	+	2.67038i	−0.744525	+	0.667594i
$3$	−9.42589	−	9.42589i	−1.04732	−	1.04732i	−0.998823	−	0.0484980i	$-0.984557\pi$
$3$	−9.42589	−	9.42589i	−1.04732	−	1.04732i	−0.0484980	−	0.998823i	$-0.515443\pi$
$4$	1.73818	−	15.9053i	0.108636	−	0.994082i
$5$	−2.84710	−	2.84710i	−0.113884	−	0.113884i	0.647868	−	0.761752i	$-0.275661\pi$
$5$	−2.84710	−	2.84710i	−0.113884	−	0.113884i	−0.761752	+	0.647868i	$0.775661\pi$
$6$	53.2419	+	2.90058i	1.47894	+	0.0805716i
$7$	−76.7794			−1.56693			−0.783463	−	0.621439i	$-0.786549\pi$
$7$	−76.7794			−1.56693			−0.783463	+	0.621439i	$0.786549\pi$
$8$	37.2967	+	52.0092i	0.582761	+	0.812644i
$9$			96.6949i			1.19376i
$10$	16.0818	+	0.876123i	0.160818	+	0.00876123i
$11$	121.488	−	121.488i	1.00403	−	1.00403i	0.00403849	−	0.999992i	$-0.498715\pi$
$11$	121.488	−	121.488i	1.00403	−	1.00403i	0.999992	−	0.00403849i	$-0.00128549\pi$
$12$	−166.306	+	133.538i	−1.15490	+	0.927346i
$13$	27.1604	−	27.1604i	0.160712	−	0.160712i	−0.622170	−	0.782882i	$-0.713749\pi$
$13$	27.1604	−	27.1604i	0.160712	−	0.160712i	0.782882	+	0.622170i	$0.213749\pi$
$14$	228.657	−	205.030i	1.16662	−	1.04607i
$15$			53.6729i			0.238546i
$16$	−249.957	−	55.2924i	−0.976396	−	0.215986i
$17$	−88.0613			−0.304710			−0.152355	−	0.988326i	$-0.548686\pi$
$17$	−88.0613			−0.304710			−0.152355	+	0.988326i	$0.548686\pi$
$18$	−258.212	−	287.967i	−0.796950	−	0.888787i
$19$	−261.112	−	261.112i	−0.723302	−	0.723302i	0.245974	−	0.969276i	$-0.420892\pi$
$19$	−261.112	−	261.112i	−0.723302	−	0.723302i	−0.969276	+	0.245974i	$0.920892\pi$
$20$	−50.2328	+	40.3352i	−0.125582	+	0.100838i
$21$	723.714	+	723.714i	1.64107	+	1.64107i
$22$	−37.3847	+	686.220i	−0.0772412	+	1.41781i
$23$	93.4210			0.176599			0.0882996	−	0.996094i	$-0.471857\pi$
$23$	93.4210			0.176599			0.0882996	+	0.996094i	$0.471857\pi$
$24$	138.678	−	841.788i	0.240761	−	1.46144i
$25$		−	608.788i		−	0.974061i
$26$	−8.35791	+	153.415i	−0.0123638	+	0.226945i
$27$	147.938	−	147.938i	0.202933	−	0.202933i
$28$	−133.456	+	1221.20i	−0.170224	+	1.55765i
$29$	272.522	−	272.522i	0.324045	−	0.324045i	−0.526272	−	0.850316i	$-0.676410\pi$
$29$	272.522	−	272.522i	0.324045	−	0.324045i	0.850316	+	0.526272i	$0.176410\pi$
$30$	−143.327	−	159.843i	−0.159252	−	0.177604i
$31$			1232.20i			1.28220i	0.767455	+	0.641102i	$0.221523\pi$
$31$			1232.20i			1.28220i	−0.767455	+	0.641102i	$0.778477\pi$
$32$	892.050	−	502.814i	0.871143	−	0.491030i
$33$	−2290.26			−2.10308
$34$	262.256	−	235.157i	0.226865	−	0.203423i
$35$	218.599	+	218.599i	0.178448	+	0.178448i
$36$	1537.96	+	168.073i	1.18670	+	0.129686i
$37$	−1046.16	−	1046.16i	−0.764177	−	0.764177i	0.212898	−	0.977075i	$-0.431710\pi$
$37$	−1046.16	−	1046.16i	−0.764177	−	0.764177i	−0.977075	+	0.212898i	$0.931710\pi$
$38$	1474.89	+	80.3506i	1.02139	+	0.0556445i
$39$	−512.021			−0.336635
$40$	41.8880	−	254.263i	0.0261800	−	0.158914i
$41$		−	915.267i		−	0.544478i	−0.962230	−	0.272239i	$-0.912236\pi$
$41$		−	915.267i		−	0.544478i	0.962230	−	0.272239i	$-0.0877641\pi$
$42$	−4087.88	−	222.705i	−2.31739	−	0.126250i
$43$	1116.82	−	1116.82i	0.604013	−	0.604013i	−0.337362	−	0.941375i	$-0.609535\pi$
$43$	1116.82	−	1116.82i	0.604013	−	0.604013i	0.941375	+	0.337362i	$0.109535\pi$
$44$	−1721.13	−	2143.47i	−0.889014	−	1.10716i
$45$	275.300	−	275.300i	0.135951	−	0.135951i
$46$	−278.217	+	249.469i	−0.131483	+	0.117897i
$47$			1720.70i			0.778949i	0.921037	+	0.389475i	$0.127343\pi$
$47$			1720.70i			0.778949i	−0.921037	+	0.389475i	$0.872657\pi$
$48$	1834.89	+	2877.25i	0.796394	+	1.24881i
$49$	3494.07			1.45526
$50$	1625.69	+	1813.03i	0.650277	+	0.725213i
$51$	830.056	+	830.056i	0.319130	+	0.319130i
$52$	−384.784	−	479.203i	−0.142302	−	0.177220i
$53$	734.019	+	734.019i	0.261310	+	0.261310i	0.825586	−	0.564276i	$-0.190845\pi$
$53$	734.019	+	734.019i	0.261310	+	0.261310i	−0.564276	+	0.825586i	$0.690845\pi$
$54$	−45.5242	+	835.626i	−0.0156119	+	0.286566i
$55$	−691.775			−0.228686
$56$	−2863.62	−	3993.23i	−0.913143	−	1.27335i
$57$			4922.43i			1.51506i
$58$	−83.8616	+	1539.33i	−0.0249291	+	0.457590i
$59$	−1202.73	+	1202.73i	−0.345512	+	0.345512i	−0.858435	−	0.512923i	$-0.828563\pi$
$59$	−1202.73	+	1202.73i	−0.345512	+	0.345512i	0.512923	+	0.858435i	$0.328563\pi$
$60$	853.684	+	93.2930i	0.237135	+	0.0259147i
$61$	580.221	−	580.221i	0.155932	−	0.155932i	−0.624830	−	0.780761i	$-0.714832\pi$
$61$	580.221	−	580.221i	0.155932	−	0.155932i	0.780761	+	0.624830i	$0.214832\pi$
$62$	−3290.44	−	3669.61i	−0.855993	−	0.954634i
$63$		−	7424.17i		−	1.87054i
$64$	−1313.91	+	3879.54i	−0.320779	+	0.947154i
$65$	−154.657			−0.0366051
$66$	6820.62	−	6115.86i	1.56580	−	1.40401i
$67$	−1483.97	−	1483.97i	−0.330580	−	0.330580i	0.522227	−	0.852807i	$-0.325101\pi$
$67$	−1483.97	−	1483.97i	−0.330580	−	0.330580i	−0.852807	+	0.522227i	$0.825101\pi$
$68$	−153.066	+	1400.64i	−0.0331025	+	0.302907i
$69$	−880.576	−	880.576i	−0.184956	−	0.184956i
$70$	−1234.75	−	67.2681i	−0.251990	−	0.0137282i
$71$	5571.73			1.10528			0.552641	−	0.833419i	$-0.313620\pi$
$71$	5571.73			1.10528			0.552641	+	0.833419i	$0.313620\pi$
$72$	−5029.02	+	3606.40i	−0.970105	+	0.695679i
$73$		−	6615.21i		−	1.24136i	−0.784064	−	0.620681i	$-0.786856\pi$
$73$		−	6615.21i		−	1.24136i	0.784064	−	0.620681i	$-0.213144\pi$
$74$	5909.20	+	321.929i	1.07911	+	0.0587890i
$75$	−5738.37	+	5738.37i	−1.02015	+	1.02015i
$76$	−4606.93	+	3699.21i	−0.797598	+	0.640445i
$77$	−9327.75	+	9327.75i	−1.57324	+	1.57324i
$78$	1524.85	−	1367.29i	0.250633	−	0.224735i
$79$		−	5391.66i		−	0.863910i	−0.901895	−	0.431955i	$-0.857824\pi$
$79$		−	5391.66i		−	0.863910i	0.901895	−	0.431955i	$-0.142176\pi$
$80$	554.231	+	869.077i	0.0865986	+	0.135793i
$81$	5043.39			0.768692
$82$	2444.11	+	2725.76i	0.363490	+	0.405378i
$83$	−2554.07	−	2554.07i	−0.370747	−	0.370747i	0.497002	−	0.867749i	$-0.334434\pi$
$83$	−2554.07	−	2554.07i	−0.370747	−	0.370747i	−0.867749	+	0.497002i	$0.834434\pi$
$84$	12768.8	−	10252.9i	1.80964	−	1.45308i
$85$	250.719	+	250.719i	0.0347017	+	0.0347017i
$86$	−343.673	+	6308.34i	−0.0464674	+	0.852939i
$87$	−5137.52			−0.678758
$88$	10849.6	+	1787.39i	1.40103	+	0.230809i
$89$			10962.7i			1.38400i	0.721898	+	0.691999i	$0.243270\pi$
$89$			10962.7i			1.38400i	−0.721898	+	0.691999i	$0.756730\pi$
$90$	−84.7166	+	1555.03i	−0.0104588	+	0.191979i
$91$	−2085.35	+	2085.35i	−0.251824	+	0.251824i
$92$	162.382	−	1485.89i	0.0191850	−	0.175554i
$93$	11614.6	−	11614.6i	1.34288	−	1.34288i
$94$	−4594.92	−	5124.42i	−0.520022	−	0.579948i
$95$			1486.83i			0.164745i
$96$	−13147.8	−	3668.90i	−1.42663	−	0.398101i
$97$	4713.20			0.500925			0.250462	−	0.968126i	$-0.419417\pi$
$97$	4713.20			0.500925			0.250462	+	0.968126i	$0.419417\pi$
$98$	−10405.7	+	9330.48i	−1.08347	+	0.971520i
$99$	11747.2	+	11747.2i	1.19858	+	1.19858i
$100$	−9682.96	−	1058.18i	−0.968296	−	0.105818i
$101$	−11381.0	−	11381.0i	−1.11568	−	1.11568i	−0.992369	−	0.123307i	$-0.960650\pi$
$101$	−11381.0	−	11381.0i	−1.11568	−	1.11568i	−0.123307	−	0.992369i	$-0.539350\pi$
$102$	−4688.56	−	255.429i	−0.450649	−	0.0245510i
$103$	175.758			0.0165668			0.00828342	−	0.999966i	$-0.497363\pi$
$103$	175.758			0.0165668			0.00828342	+	0.999966i	$0.497363\pi$
$104$	2425.58	+	399.597i	0.224258	+	0.0369450i
$105$		−	4120.97i		−	0.373784i
$106$	−4146.09	−	225.876i	−0.369000	−	0.0201028i
$107$	15151.8	−	15151.8i	1.32342	−	1.32342i	0.412432	−	0.910988i	$-0.364679\pi$
$107$	15151.8	−	15151.8i	1.32342	−	1.32342i	0.910988	−	0.412432i	$-0.135321\pi$
$108$	−2095.86	−	2610.14i	−0.179686	−	0.223778i
$109$	−2349.51	+	2349.51i	−0.197754	+	0.197754i	−0.799036	−	0.601283i	$-0.794657\pi$
$109$	−2349.51	+	2349.51i	−0.197754	+	0.197754i	0.601283	+	0.799036i	$0.294657\pi$
$110$	2060.18	−	1847.30i	0.170263	−	0.152669i
$111$			19721.9i			1.60068i
$112$	19191.6	+	4245.32i	1.52994	+	0.338434i
$113$	−8526.30			−0.667734			−0.333867	−	0.942620i	$-0.608354\pi$
$113$	−8526.30			−0.667734			−0.333867	+	0.942620i	$0.608354\pi$
$114$	−13144.7	−	14659.5i	−1.01145	−	1.12800i
$115$	−265.979	−	265.979i	−0.0201118	−	0.0201118i
$116$	−3860.85	−	4808.23i	−0.286924	−	0.357330i
$117$	2626.27	+	2626.27i	0.191852	+	0.191852i
$118$	370.108	−	6793.57i	0.0265806	−	0.487904i
$119$	6761.29			0.477459
$120$	−2791.49	+	2001.82i	−0.193853	+	0.139015i
$121$		−	14877.5i		−	1.01615i
$122$	−178.548	+	3277.37i	−0.0119960	+	0.220194i
$123$	−8627.21	+	8627.21i	−0.570243	+	0.570243i
$124$	19598.5	+	2141.78i	1.27462	+	0.139294i
$125$	−3512.72	+	3512.72i	−0.224814	+	0.224814i
$126$	19825.3	+	22109.9i	1.24876	+	1.39266i
$127$			2844.31i			0.176347i	0.996105	+	0.0881737i	$0.0281031\pi$
$127$			2844.31i			0.176347i	−0.996105	+	0.0881737i	$0.971897\pi$
$128$	−6446.87	−	15062.3i	−0.393486	−	0.919331i
$129$	−21054.1			−1.26519
$130$	460.583	−	412.991i	0.0272534	−	0.0244373i
$131$	−6989.87	−	6989.87i	−0.407311	−	0.407311i	0.473489	−	0.880800i	$-0.342994\pi$
$131$	−6989.87	−	6989.87i	−0.407311	−	0.407311i	−0.880800	+	0.473489i	$0.842994\pi$
$132$	−3980.87	+	36427.3i	−0.228471	+	2.09064i
$133$	20048.0	+	20048.0i	1.13336	+	1.13336i
$134$	8382.19	+	456.655i	0.466818	+	0.0254319i
$135$	−842.390			−0.0462217
$136$	−3284.40	−	4580.00i	−0.177573	−	0.247621i
$137$			3669.69i			0.195519i	0.995210	+	0.0977594i	$0.0311676\pi$
$137$			3669.69i			0.195519i	−0.995210	+	0.0977594i	$0.968832\pi$
$138$	4973.92	+	270.975i	0.261180	+	0.0142289i
$139$	4401.33	−	4401.33i	0.227800	−	0.227800i	−0.583973	−	0.811773i	$-0.698503\pi$
$139$	4401.33	−	4401.33i	0.227800	−	0.227800i	0.811773	+	0.583973i	$0.198503\pi$
$140$	3856.84	−	3096.91i	0.196778	−	0.158006i
$141$	16219.1	−	16219.1i	0.815810	−	0.815810i
$142$	−16593.2	+	14878.6i	−0.822911	+	0.737880i
$143$		−	6599.30i		−	0.322720i
$144$	5346.49	−	24169.6i	0.257836	−	1.16559i
$145$	−1551.79			−0.0738071
$146$	17665.1	+	19700.8i	0.828725	+	0.924225i
$147$	−32934.7	−	32934.7i	−1.52412	−	1.52412i
$148$	−18457.9	+	14821.1i	−0.842671	+	0.676637i
$149$	15737.5	+	15737.5i	0.708863	+	0.708863i	0.966296	−	0.257433i	$-0.0828766\pi$
$149$	15737.5	+	15737.5i	0.708863	+	0.708863i	−0.257433	+	0.966296i	$0.582877\pi$
$150$	1765.84	−	32413.1i	0.0784817	−	1.44058i
$151$	−41972.2			−1.84080			−0.920402	−	0.390974i	$-0.872138\pi$
$151$	−41972.2			−1.84080			−0.920402	+	0.390974i	$0.872138\pi$
$152$	3841.61	−	23318.9i	0.166275	−	1.00930i
$153$		−	8515.08i		−	0.363752i
$154$	2870.38	−	52687.6i	0.121031	−	2.22160i
$155$	3508.19	−	3508.19i	0.146023	−	0.146023i
$156$	−889.982	+	8143.85i	−0.0365706	+	0.334642i
$157$	−24735.4	+	24735.4i	−1.00351	+	1.00351i	−0.00351271	+	0.999994i	$0.501118\pi$
$157$	−24735.4	+	24735.4i	−1.00351	+	1.00351i	−0.999994	+	0.00351271i	$0.998882\pi$
$158$	14397.8	+	16056.9i	0.576741	+	0.643203i
$159$		−	13837.6i		−	0.547350i
$160$	−3971.32	−	1108.19i	−0.155130	−	0.0432888i
$161$	−7172.80			−0.276718
$162$	−15019.7	+	13467.7i	−0.572310	+	0.513174i
$163$	24429.8	+	24429.8i	0.919483	+	0.919483i	0.996992	−	0.0775084i	$-0.0246965\pi$
$163$	24429.8	+	24429.8i	0.919483	+	0.919483i	−0.0775084	+	0.996992i	$0.524696\pi$
$164$	−14557.6	−	1590.90i	−0.541255	−	0.0591499i
$165$	6520.60	+	6520.60i	0.239508	+	0.239508i
$166$	14426.6	+	785.951i	0.523539	+	0.0285220i
$167$	52178.2			1.87093			0.935463	−	0.353425i	$-0.114983\pi$
$167$	52178.2			1.87093			0.935463	+	0.353425i	$0.114983\pi$
$168$	−10647.6	+	64631.9i	−0.377255	+	2.28996i
$169$			27085.6i			0.948343i
$170$	−1416.18	−	77.1525i	−0.0490029	−	0.00266964i
$171$	25248.2	−	25248.2i	0.863452	−	0.863452i
$172$	−15822.1	−	19704.6i	−0.534821	−	0.666056i
$173$	26316.2	−	26316.2i	0.879289	−	0.879289i	−0.114172	−	0.993461i	$-0.536422\pi$
$173$	26316.2	−	26316.2i	0.879289	−	0.879289i	0.993461	+	0.114172i	$0.0364216\pi$
$174$	15300.1	−	13719.1i	0.505353	−	0.453135i
$175$			46742.4i			1.52628i
$176$	−37084.1	+	23649.4i	−1.19719	+	0.763475i
$177$	22673.5			0.723723
$178$	−29274.4	−	32647.9i	−0.923949	−	1.03042i
$179$	4815.78	+	4815.78i	0.150301	+	0.150301i	0.778252	−	0.627952i	$-0.216106\pi$
$179$	4815.78	+	4815.78i	0.150301	+	0.150301i	−0.627952	+	0.778252i	$0.716106\pi$
$180$	−3900.21	−	4857.25i	−0.120377	−	0.149915i
$181$	−23924.9	−	23924.9i	−0.730286	−	0.730286i	0.240391	−	0.970676i	$-0.422724\pi$
$181$	−23924.9	−	23924.9i	−0.730286	−	0.730286i	−0.970676	+	0.240391i	$0.922724\pi$
$182$	641.715	−	11779.1i	0.0193731	−	0.355606i
$183$	−10938.2			−0.326621
$184$	3484.29	+	4858.75i	0.102915	+	0.143512i
$185$			5957.04i			0.174055i
$186$	−3574.09	+	65604.7i	−0.103309	+	1.89631i
$187$	−10698.4	+	10698.4i	−0.305939	+	0.305939i
$188$	27368.2	+	2990.88i	0.774339	+	0.0846219i
$189$	−11358.6	+	11358.6i	−0.317981	+	0.317981i
$190$	−3970.38	−	4427.92i	−0.109983	−	0.122657i
$191$		−	45079.4i		−	1.23569i	−0.786298	−	0.617847i	$-0.788005\pi$
$191$		−	45079.4i		−	1.23569i	0.786298	−	0.617847i	$-0.211995\pi$
$192$	48952.9	−	24183.3i	1.32793	−	0.656015i
$193$	50286.0			1.34999			0.674997	−	0.737820i	$-0.264145\pi$
$193$	50286.0			1.34999			0.674997	+	0.737820i	$0.264145\pi$
$194$	−14036.4	+	12586.0i	−0.372951	+	0.334415i
$195$	1457.78	+	1457.78i	0.0383373	+	0.0383373i
$196$	6073.31	−	55574.2i	0.158093	−	1.44664i
$197$	−25662.2	−	25662.2i	−0.661243	−	0.661243i	0.294430	−	0.955673i	$-0.404870\pi$
$197$	−25662.2	−	25662.2i	−0.661243	−	0.661243i	−0.955673	+	0.294430i	$0.904870\pi$
$198$	−66354.0	−	3614.91i	−1.69253	−	0.0922077i
$199$	−44599.1			−1.12621			−0.563106	−	0.826385i	$-0.690394\pi$
$199$	−44599.1			−1.12621			−0.563106	+	0.826385i	$0.690394\pi$
$200$	31662.6	−	22705.8i	0.791564	−	0.567645i
$201$			27975.5i			0.692447i
$202$	64285.4	+	3502.21i	1.57547	+	0.0858302i
$203$	−20924.0	+	20924.0i	−0.507754	+	0.507754i
$204$	14645.1	−	11759.5i	0.351910	−	0.282572i
$205$	−2605.86	+	2605.86i	−0.0620073	+	0.0620073i
$206$	−523.424	+	469.339i	−0.0123344	+	0.0110599i
$207$			9033.33i			0.210818i
$208$	−8290.70	+	5287.17i	−0.191630	+	0.122207i
$209$	−63443.8			−1.45244
$210$	11004.6	+	12272.7i	0.249536	+	0.278292i
$211$	25828.5	+	25828.5i	0.580143	+	0.580143i	0.934942	−	0.354800i	$-0.115451\pi$
$211$	25828.5	+	25828.5i	0.580143	+	0.580143i	−0.354800	+	0.934942i	$0.615451\pi$
$212$	12950.6	−	10398.9i	0.288151	−	0.231375i
$213$	−52518.5	−	52518.5i	−1.15759	−	1.15759i
$214$	−4662.59	+	85584.8i	−0.101812	+	1.86883i
$215$	−6359.40			−0.137575
$216$	13211.8	+	2176.54i	0.283174	+	0.0466508i
$217$		−	94607.4i		−	2.00912i
$218$	723.003	−	13271.2i	0.0152134	−	0.279252i
$219$	−62354.3	+	62354.3i	−1.30010	+	1.30010i
$220$	−1202.43	+	11002.9i	−0.0248435	+	0.227333i
$221$	−2391.78	+	2391.78i	−0.0489707	+	0.0489707i
$222$	−52665.0	−	58734.0i	−1.06860	−	1.19175i
$223$		−	72650.0i		−	1.46092i	−0.682957	−	0.730459i	$-0.739306\pi$
$223$		−	72650.0i		−	1.46092i	0.682957	−	0.730459i	$-0.260694\pi$
$224$	−68491.1	+	38605.8i	−1.36502	+	0.769407i
$225$	58866.7			1.16280
$226$	25392.2	−	22768.4i	0.497145	−	0.445776i
$227$	18858.2	+	18858.2i	0.365972	+	0.365972i	0.866006	−	0.500034i	$-0.166679\pi$
$227$	18858.2	+	18858.2i	0.365972	+	0.365972i	−0.500034	+	0.866006i	$0.666679\pi$
$228$	78292.8	+	8556.05i	1.50609	+	0.164590i
$229$	41675.9	+	41675.9i	0.794721	+	0.794721i	0.982258	−	0.187537i	$-0.0600504\pi$
$229$	41675.9	+	41675.9i	0.794721	+	0.794721i	−0.187537	+	0.982258i	$0.560050\pi$
$230$	1502.38	+	81.8483i	0.0284003	+	0.00154723i
$231$	175845.			3.29538
$232$	24337.8	+	4009.48i	0.452174	+	0.0744923i
$233$			2767.61i			0.0509792i	0.999675	+	0.0254896i	$0.00811447\pi$
$233$			2767.61i			0.0509792i	−0.999675	+	0.0254896i	$0.991886\pi$
$234$	−14834.4	−	808.167i	−0.270918	−	0.0147594i
$235$	4899.00	−	4899.00i	0.0887099	−	0.0887099i
$236$	17039.2	+	21220.3i	0.305932	+	0.381002i
$237$	−50821.2	+	50821.2i	−0.904791	+	0.904791i
$238$	−20135.8	+	18055.2i	−0.355480	+	0.318749i
$239$			49981.8i			0.875016i	0.899215	+	0.437508i	$0.144139\pi$
$239$			49981.8i			0.875016i	−0.899215	+	0.437508i	$0.855861\pi$
$240$	2967.71	−	13416.0i	0.0515227	−	0.232916i
$241$	−44076.0			−0.758872			−0.379436	−	0.925218i	$-0.623882\pi$
$241$	−44076.0			−0.758872			−0.379436	+	0.925218i	$0.623882\pi$
$242$	39728.6	+	44306.7i	0.678378	+	0.756552i
$243$	−59521.4	−	59521.4i	−1.00800	−	1.00800i
$244$	−8220.07	−	10237.1i	−0.138069	−	0.171948i
$245$	−9947.97	−	9947.97i	−0.165730	−	0.165730i
$246$	2654.80	−	48730.6i	0.0438695	−	0.805252i
$247$	−14183.8			−0.232487
$248$	−64085.7	+	45957.0i	−1.04198	+	0.747219i
$249$			48148.8i			0.776582i
$250$	1080.95	−	19841.5i	0.0172952	−	0.317464i
$251$	−31786.2	+	31786.2i	−0.504534	+	0.504534i	−0.912844	−	0.408309i	$-0.866119\pi$
$251$	−31786.2	+	31786.2i	−0.504534	+	0.504534i	0.408309	+	0.912844i	$0.366119\pi$
$252$	−118084.	−	12904.5i	−1.85947	−	0.203208i
$253$	11349.5	−	11349.5i	0.177311	−	0.177311i
$254$	−7595.38	−	8470.64i	−0.117729	−	0.131295i
$255$		−	4726.51i		−	0.0726876i
$256$	59421.5	+	27641.5i	0.906700	+	0.421776i
$257$	70865.6			1.07292			0.536462	−	0.843924i	$-0.319760\pi$
$257$	70865.6			1.07292			0.536462	+	0.843924i	$0.319760\pi$
$258$	62701.1	−	56222.3i	0.941968	−	0.844635i
$259$	80323.4	+	80323.4i	1.19741	+	1.19741i
$260$	−268.820	+	2459.86i	−0.00397663	+	0.0363885i
$261$	26351.5	+	26351.5i	0.386833	+	0.386833i
$262$	39482.1	+	2150.95i	0.575172	+	0.0313349i
$263$	−113289.			−1.63786			−0.818929	−	0.573894i	$-0.805432\pi$
$263$	−113289.			−1.63786			−0.818929	+	0.573894i	$0.805432\pi$
$264$	−85419.1	−	119115.i	−1.22560	−	1.70906i
$265$		−	4179.65i		−	0.0595180i
$266$	−113241.	−	6169.27i	−1.60044	−	0.0871908i
$267$	103333.	−	103333.i	1.44949	−	1.44949i
$268$	−26182.5	+	21023.6i	−0.364536	+	0.292711i
$269$	70652.7	−	70652.7i	0.976393	−	0.976393i	−0.0233352	−	0.999728i	$-0.507428\pi$
$269$	70652.7	−	70652.7i	0.976393	−	0.976393i	0.999728	+	0.0233352i	$0.00742850\pi$
$270$	2508.72	−	2249.50i	0.0344132	−	0.0308573i
$271$		−	110180.i		−	1.50025i	−0.661294	−	0.750126i	$-0.729993\pi$
$271$		−	110180.i		−	1.50025i	0.661294	−	0.750126i	$-0.270007\pi$
$272$	22011.6	+	4869.12i	0.297518	+	0.0658132i
$273$	39312.7			0.527481
$274$	−9799.47	−	10928.7i	−0.130527	−	0.145569i
$275$	−73960.2	−	73960.2i	−0.977987	−	0.977987i
$276$	−15536.4	+	12475.2i	−0.203954	+	0.163769i
$277$	34611.0	+	34611.0i	0.451081	+	0.451081i	0.895713	−	0.444632i	$-0.146666\pi$
$277$	34611.0	+	34611.0i	0.451081	+	0.451081i	−0.444632	+	0.895713i	$0.646666\pi$
$278$	−1354.40	+	24860.8i	−0.0175249	+	0.321681i
$279$	−119147.			−1.53065
$280$	−3216.13	+	19522.1i	−0.0410221	+	0.249007i
$281$			147980.i			1.87408i	0.349216	+	0.937042i	$0.386448\pi$
$281$			147980.i			1.87408i	−0.349216	+	0.937042i	$0.613552\pi$
$282$	−4991.02	+	91613.4i	−0.0627612	+	1.15202i
$283$	39761.2	−	39761.2i	0.496463	−	0.496463i	−0.413872	−	0.910335i	$-0.635824\pi$
$283$	39761.2	−	39761.2i	0.496463	−	0.496463i	0.910335	+	0.413872i	$0.135824\pi$
$284$	9684.65	−	88620.1i	0.120073	−	1.09874i
$285$	14014.7	−	14014.7i	0.172541	−	0.172541i
$286$	17622.6	+	19653.4i	0.215446	+	0.240273i
$287$			70273.6i			0.853156i
$288$	48619.6	+	86256.7i	0.586173	+	1.03994i
$289$	−75766.2			−0.907152
$290$	4621.40	−	4143.87i	0.0549512	−	0.0492732i
$291$	−44426.1	−	44426.1i	−0.524629	−	0.524629i
$292$	−105217.	−	11498.4i	−1.23401	−	0.134856i
$293$	−708.909	−	708.909i	−0.00825763	−	0.00825763i	0.702966	−	0.711224i	$-0.251859\pi$
$293$	−708.909	−	708.909i	−0.00825763	−	0.00825763i	−0.711224	+	0.702966i	$0.751859\pi$
$294$	186031.	+	10134.8i	2.15224	+	0.117252i
$295$	6848.56			0.0786965
$296$	15391.6	−	93428.1i	0.175671	−	1.06634i
$297$		−	35945.3i		−	0.407502i
$298$	−88892.8	−	4842.81i	−1.00100	−	0.0545337i
$299$	2537.35	−	2537.35i	0.0283816	−	0.0283816i
$300$	81296.2	+	101245.i	0.903292	+	1.12494i
$301$	−85748.8	+	85748.8i	−0.946444	+	0.946444i
$302$	124997.	−	112081.i	1.37052	−	1.22891i
$303$			214552.i			2.33694i
$304$	50829.4	+	79704.5i	0.550007	+	0.862453i
$305$	−3303.90			−0.0355162
$306$	22738.5	+	25358.8i	0.242839	+	0.270823i
$307$	−20597.1	−	20597.1i	−0.218539	−	0.218539i	0.589344	−	0.807883i	$-0.299386\pi$
$307$	−20597.1	−	20597.1i	−0.218539	−	0.218539i	−0.807883	+	0.589344i	$0.799386\pi$
$308$	132147.	+	164574.i	1.39302	+	1.73484i
$309$	−1656.67	−	1656.67i	−0.0173508	−	0.0173508i
$310$	−1079.56	+	19816.0i	−0.0112337	+	0.206201i
$311$	82310.6			0.851011			0.425505	−	0.904956i	$-0.360096\pi$
$311$	82310.6			0.851011			0.425505	+	0.904956i	$0.360096\pi$
$312$	−19096.7	−	26629.8i	−0.196177	−	0.273564i
$313$		−	120415.i		−	1.22911i	−0.788872	−	0.614557i	$-0.789335\pi$
$313$		−	120415.i		−	1.22911i	0.788872	−	0.614557i	$-0.210665\pi$
$314$	7611.70	−	139718.i	0.0772009	−	1.41707i
$315$	−21137.4	+	21137.4i	−0.213025	+	0.213025i
$316$	−85756.0	−	9371.65i	−0.858797	−	0.0938517i
$317$	14795.3	−	14795.3i	0.147233	−	0.147233i	−0.629648	−	0.776881i	$-0.716801\pi$
$317$	14795.3	−	14795.3i	0.147233	−	0.147233i	0.776881	+	0.629648i	$0.216801\pi$
$318$	36951.5	+	41209.7i	0.365408	+	0.407516i
$319$		−	66216.1i		−	0.650702i
$320$	14786.3	−	7304.61i	0.144397	−	0.0713340i
$321$	−285639.			−2.77209
$322$	21361.3	−	19154.1i	0.206023	−	0.184735i
$323$	22993.9	+	22993.9i	0.220398	+	0.220398i
$324$	8766.29	−	80216.6i	0.0835076	−	0.764142i
$325$	−16534.9	−	16534.9i	−0.156543	−	0.156543i
$326$	−137991.	−	7517.63i	−1.29842	−	0.0707369i
$327$	44292.5			0.414224
$328$	47602.3	−	34136.4i	0.442467	−	0.317300i
$329$		−	132114.i		−	1.22056i
$330$	−36831.5	−	2006.55i	−0.338214	−	0.0184256i
$331$	82868.2	−	82868.2i	0.756366	−	0.756366i	−0.219293	−	0.975659i	$-0.570375\pi$
$331$	82868.2	−	82868.2i	0.756366	−	0.756366i	0.975659	+	0.219293i	$0.0703752\pi$
$332$	−45062.8	+	36183.9i	−0.408829	+	0.328276i
$333$	101158.	−	101158.i	0.912247	−	0.912247i
$334$	−155392.	+	139336.i	−1.39295	+	1.24902i
$335$			8450.04i			0.0752955i
$336$	−140882.	−	220914.i	−1.24789	−	1.95679i
$337$	78854.4			0.694331			0.347165	−	0.937804i	$-0.387144\pi$
$337$	78854.4			0.694331			0.347165	+	0.937804i	$0.387144\pi$
$338$	−72328.8	−	80663.8i	−0.633108	−	0.706066i
$339$	80368.0	+	80368.0i	0.699332	+	0.699332i
$340$	4423.56	−	3551.98i	0.0382661	−	0.0307264i
$341$	149697.	+	149697.i	1.28737	+	1.28737i
$342$	−7769.49	+	142614.i	−0.0664264	+	1.21930i
$343$	−83925.2			−0.713352
$344$	99738.7	+	16431.2i	0.842843	+	0.138852i
$345$			5014.18i			0.0421271i
$346$	−8098.15	+	148647.i	−0.0676447	+	1.24166i
$347$	−59543.0	+	59543.0i	−0.494506	+	0.494506i	−0.909723	−	0.415216i	$-0.863706\pi$
$347$	−59543.0	+	59543.0i	−0.494506	+	0.494506i	0.415216	+	0.909723i	$0.363706\pi$
$348$	−8929.91	+	81713.8i	−0.0737375	+	0.674741i
$349$	−756.172	+	756.172i	−0.00620826	+	0.00620826i	−0.710204	−	0.703996i	$-0.751397\pi$
$349$	−756.172	+	756.172i	−0.00620826	+	0.00620826i	0.703996	+	0.710204i	$0.251397\pi$
$350$	−124820.	−	139203.i	−1.01894	−	1.13635i
$351$		−	8036.11i		−	0.0652276i
$352$	47287.4	−	169459.i	0.381645	−	1.36766i
$353$	23723.5			0.190384			0.0951918	−	0.995459i	$-0.469654\pi$
$353$	23723.5			0.190384			0.0951918	+	0.995459i	$0.469654\pi$
$354$	−67524.1	+	60546.9i	−0.538830	+	0.483154i
$355$	−15863.3	−	15863.3i	−0.125874	−	0.125874i
$356$	174364.	+	19055.0i	1.37581	+	0.150352i
$357$	−63731.2	−	63731.2i	−0.500053	−	0.500053i
$358$	−27201.8	−	1481.93i	−0.212242	−	0.0115628i
$359$	146064.			1.13333			0.566663	−	0.823950i	$-0.308234\pi$
$359$	146064.			1.13333			0.566663	+	0.823950i	$0.308234\pi$
$360$	24585.9	+	4050.35i	0.189706	+	0.0312527i
$361$			6038.12i			0.0463327i
$362$	135139.	+	7362.28i	1.03125	+	0.0561817i
$363$	−140234.	+	140234.i	−1.06424	+	1.06424i
$364$	29543.5	+	36792.9i	0.222976	+	0.277691i
$365$	−18834.2	+	18834.2i	−0.141371	+	0.141371i
$366$	32575.1	−	29209.1i	0.243177	−	0.218050i
$367$			151129.i			1.12206i	0.827797	+	0.561028i	$0.189594\pi$
$367$			151129.i			1.12206i	−0.827797	+	0.561028i	$0.810406\pi$
$368$	−23351.3	−	5165.47i	−0.172431	−	0.0381430i
$369$	88501.7			0.649978
$370$	−15907.5	−	17740.7i	−0.116198	−	0.129588i
$371$	−56357.5	−	56357.5i	−0.409453	−	0.409453i
$372$	−164545.	−	204922.i	−1.18905	−	1.48082i
$373$	26207.7	+	26207.7i	0.188370	+	0.188370i	0.794991	−	0.606621i	$-0.207476\pi$
$373$	26207.7	+	26207.7i	0.188370	+	0.188370i	−0.606621	+	0.794991i	$0.707476\pi$
$374$	3292.15	−	60429.5i	0.0235362	−	0.432022i
$375$	66221.0			0.470905
$376$	−89492.2	+	64176.4i	−0.633008	+	0.453941i
$377$		−	14803.6i		−	0.104156i
$378$	3495.32	−	64158.8i	0.0244626	−	0.449027i
$379$	110424.	−	110424.i	0.768752	−	0.768752i	−0.209135	−	0.977887i	$-0.567065\pi$
$379$	110424.	−	110424.i	0.768752	−	0.768752i	0.977887	+	0.209135i	$0.0670647\pi$
$380$	23648.4	+	2584.36i	0.163770	+	0.0178973i
$381$	26810.1	−	26810.1i	0.184692	−	0.184692i
$382$	120379.	+	134251.i	0.824942	+	0.920006i
$383$		−	10514.9i		−	0.0716819i	−0.999358	−	0.0358409i	$-0.988589\pi$
$383$		−	10514.9i		−	0.0716819i	0.999358	−	0.0358409i	$-0.0114110\pi$
$384$	−81208.2	+	202743.i	−0.550728	+	1.37494i
$385$	53114.1			0.358334
$386$	−149757.	+	134282.i	−1.00511	+	0.901249i
$387$	107991.	+	107991.i	0.721049	+	0.721049i
$388$	8192.37	−	74964.9i	0.0544185	−	0.497960i
$389$	−166762.	−	166762.i	−1.10204	−	1.10204i	−0.994164	−	0.107877i	$-0.965595\pi$
$389$	−166762.	−	166762.i	−1.10204	−	1.10204i	−0.107877	−	0.994164i	$-0.534405\pi$
$390$	−8234.21	−	448.593i	−0.0541368	−	0.00294933i
$391$	−8226.78			−0.0538116
$392$	130317.	+	181724.i	0.848066	+	1.18260i
$393$			131772.i			0.853172i
$394$	144952.	+	7896.89i	0.933755	+	0.0508702i
$395$	−15350.6	+	15350.6i	−0.0983855	+	0.0983855i
$396$	207262.	−	166425.i	1.32169	−	1.06127i
$397$	−192542.	+	192542.i	−1.22164	+	1.22164i	−0.254594	+	0.967048i	$0.581942\pi$
$397$	−192542.	+	192542.i	−1.22164	+	1.22164i	−0.967048	+	0.254594i	$0.918058\pi$
$398$	132821.	−	119096.i	0.838494	−	0.751853i
$399$		−	377941.i		−	2.37399i
$400$	−33661.4	+	152171.i	−0.210384	+	0.951070i
$401$	91157.6			0.566897			0.283448	−	0.958987i	$-0.408522\pi$
$401$	91157.6			0.566897			0.283448	+	0.958987i	$0.408522\pi$
$402$	−74705.2	−	83314.0i	−0.462273	−	0.515544i
$403$	33467.0	+	33467.0i	0.206066	+	0.206066i
$404$	−200801.	+	161236.i	−1.23027	+	0.987870i
$405$	−14359.0	−	14359.0i	−0.0875417	−	0.0875417i
$406$	6438.84	−	118189.i	0.0390621	−	0.717010i
$407$	−254191.			−1.53451
$408$	−12212.2	+	74128.9i	−0.0733624	+	0.445315i
$409$			107774.i			0.644272i	0.946693	+	0.322136i	$0.104401\pi$
$409$			107774.i			0.644272i	−0.946693	+	0.322136i	$0.895599\pi$
$410$	801.887	−	14719.1i	0.00477029	−	0.0875618i
$411$	34590.1	−	34590.1i	0.204771	−	0.204771i
$412$	305.497	−	2795.48i	0.00179975	−	0.0164688i
$413$	92344.5	−	92344.5i	0.541391	−	0.541391i
$414$	−24122.4	−	26902.2i	−0.140741	−	0.156959i
$415$			14543.4i			0.0844442i
$416$	10571.8	−	37885.0i	0.0610888	−	0.218918i
$417$	−82972.9			−0.477160
$418$	188942.	−	169419.i	1.08137	−	0.969637i
$419$	−118524.	−	118524.i	−0.675115	−	0.675115i	0.283776	−	0.958891i	$-0.408413\pi$
$419$	−118524.	−	118524.i	−0.675115	−	0.675115i	−0.958891	+	0.283776i	$0.908413\pi$
$420$	−65545.3	−	7162.97i	−0.371572	−	0.0406064i
$421$	−226616.	−	226616.i	−1.27858	−	1.27858i	−0.941464	−	0.337113i	$-0.890549\pi$
$421$	−226616.	−	226616.i	−1.27858	−	1.27858i	−0.337113	−	0.941464i	$-0.609451\pi$
$422$	−145892.	−	7948.08i	−0.819231	−	0.0446310i
$423$	−166383.			−0.929882
$424$	−10799.2	+	65552.2i	−0.0600706	+	0.364633i
$425$			53610.7i			0.296807i
$426$	296650.	+	16161.2i	1.63465	+	0.0890544i
$427$	−44549.0	+	44549.0i	−0.244333	+	0.244333i
$428$	−214658.	−	267331.i	−1.17182	−	1.45936i
$429$	−62204.3	+	62204.3i	−0.337991	+	0.337991i
$430$	18938.9	−	16982.0i	0.102428	−	0.0918442i
$431$			5397.51i			0.0290562i	0.999894	+	0.0145281i	$0.00462460\pi$
$431$			5397.51i			0.0290562i	−0.999894	+	0.0145281i	$0.995375\pi$
$432$	−45158.1	+	28798.4i	−0.241974	+	0.154312i
$433$	163835.			0.873840			0.436920	−	0.899500i	$-0.356069\pi$
$433$	163835.			0.873840			0.436920	+	0.899500i	$0.356069\pi$
$434$	252638.	+	281751.i	1.34128	+	1.49584i
$435$	14627.0	+	14627.0i	0.0772997	+	0.0772997i
$436$	33285.9	+	41453.6i	0.175100	+	0.218067i
$437$	−24393.4	−	24393.4i	−0.127735	−	0.127735i
$438$	19187.9	−	352207.i	0.100018	−	1.83590i
$439$	158472.			0.822289			0.411144	−	0.911570i	$-0.365129\pi$
$439$	158472.			0.822289			0.411144	+	0.911570i	$0.365129\pi$
$440$	−25800.9	−	35978.7i	−0.133269	−	0.185840i
$441$			337859.i			1.73723i
$442$	736.008	−	13509.9i	0.00376737	−	0.0691524i
$443$	−137929.	+	137929.i	−0.702826	+	0.702826i	−0.965016	−	0.262190i	$-0.915555\pi$
$443$	−137929.	+	137929.i	−0.702826	+	0.702826i	0.262190	+	0.965016i	$0.415555\pi$
$444$	313684.	+	34280.2i	1.59120	+	0.173891i
$445$	31211.8	−	31211.8i	0.157615	−	0.157615i
$446$	194003.	+	216359.i	0.975300	+	1.08769i
$447$		−	296680.i		−	1.48482i
$448$	100881.	−	297869.i	0.502638	−	1.48412i
$449$	327336.			1.62368			0.811841	−	0.583879i	$-0.198466\pi$
$449$	327336.			1.62368			0.811841	+	0.583879i	$0.198466\pi$
$450$	−175311.	+	157196.i	−0.865733	+	0.776278i
$451$	−111194.	−	111194.i	−0.546672	−	0.546672i
$452$	−14820.2	+	135613.i	−0.0725400	+	0.663782i
$453$	395625.	+	395625.i	1.92791	+	1.92791i
$454$	−106520.	−	5803.13i	−0.516797	−	0.0281547i
$455$	11874.4			0.0573575
$456$	−256012.	+	183590.i	−1.23120	+	0.882918i
$457$		−	154510.i		−	0.739817i	−0.929068	−	0.369909i	$-0.879389\pi$
$457$		−	154510.i		−	0.739817i	0.929068	−	0.369909i	$-0.120611\pi$
$458$	−235406.	−	12824.7i	−1.12224	−	0.0611388i
$459$	−13027.6	+	13027.6i	−0.0618358	+	0.0618358i
$460$	−4692.80	+	3768.16i	−0.0221777	+	0.0178079i
$461$	19296.3	−	19296.3i	0.0907971	−	0.0907971i	−0.660249	−	0.751046i	$-0.729549\pi$
$461$	19296.3	−	19296.3i	0.0907971	−	0.0907971i	0.751046	+	0.660249i	$0.229549\pi$
$462$	−523683.	+	469571.i	−2.45349	+	2.19997i
$463$		−	26503.6i		−	0.123635i	−0.998087	−	0.0618176i	$-0.980310\pi$
$463$		−	26503.6i		−	0.123635i	0.998087	−	0.0618176i	$-0.0196897\pi$
$464$	−83187.2	+	53050.5i	−0.386385	+	0.246407i
$465$	−66135.7			−0.305865
$466$	−7390.56	−	8242.22i	−0.0340334	−	0.0379553i
$467$	111797.	+	111797.i	0.512622	+	0.512622i	0.915329	−	0.402707i	$-0.131931\pi$
$467$	111797.	+	111797.i	0.512622	+	0.512622i	−0.402707	+	0.915329i	$0.631931\pi$
$468$	46336.5	−	37206.7i	0.211559	−	0.169875i
$469$	113939.	+	113939.i	0.517994	+	0.517994i
$470$	−1507.54	+	27671.9i	−0.00682455	+	0.125269i
$471$	466307.			2.10199
$472$	−107411.	−	17695.1i	−0.482129	−	0.0794272i
$473$		−	271360.i		−	1.21290i
$474$	15638.9	−	287063.i	0.0696066	−	1.27767i
$475$	−158962.	+	158962.i	−0.704541	+	0.704541i
$476$	11752.3	−	107540.i	0.0518692	−	0.474633i
$477$	−70975.8	+	70975.8i	−0.311942	+	0.311942i
$478$	−133470.	−	148851.i	−0.584155	−	0.651471i
$479$			225380.i			0.982301i	0.871075	+	0.491150i	$0.163423\pi$
$479$			225380.i			0.982301i	−0.871075	+	0.491150i	$0.836577\pi$
$480$	26987.5	+	47879.0i	0.117133	+	0.207808i
$481$	−56828.1			−0.245625
$482$	131263.	−	117700.i	0.564999	−	0.506618i
$483$	67610.1	+	67610.1i	0.289813	+	0.289813i
$484$	−236631.	−	25859.7i	−1.01014	−	0.110391i
$485$	−13419.0	−	13419.0i	−0.0570473	−	0.0570473i
$486$	336205.	+	18316.2i	1.42342	+	0.0775466i
$487$	8483.58			0.0357702			0.0178851	−	0.999840i	$-0.494307\pi$
$487$	8483.58			0.0357702			0.0178851	+	0.999840i	$0.494307\pi$
$488$	51817.2	+	8536.50i	0.217588	+	0.0358460i
$489$		−	460544.i		−	1.92599i
$490$	56190.9	+	3061.23i	0.234031	+	0.0127498i
$491$	69265.0	−	69265.0i	0.287310	−	0.287310i	−0.548706	−	0.836016i	$-0.684879\pi$
$491$	69265.0	−	69265.0i	0.287310	−	0.287310i	0.836016	+	0.548706i	$0.184879\pi$
$492$	122223.	+	152214.i	0.504919	+	0.628817i
$493$	−23998.6	+	23998.6i	−0.0987399	+	0.0987399i
$494$	42240.8	−	37876.1i	0.173092	−	0.155207i
$495$		−	66891.1i		−	0.272997i
$496$	68131.3	−	307997.i	0.276938	−	1.25194i
$497$	−427794.			−1.73190
$498$	−128576.	−	143392.i	−0.518441	−	0.578185i
$499$	86869.4	+	86869.4i	0.348872	+	0.348872i	0.859689	−	0.510817i	$-0.170657\pi$
$499$	86869.4	+	86869.4i	0.348872	+	0.348872i	−0.510817	+	0.859689i	$0.670657\pi$
$500$	49765.1	+	61976.6i	0.199061	+	0.247906i
$501$	−491827.	−	491827.i	−1.95946	−	1.95946i
$502$	9781.39	−	179544.i	0.0388144	−	0.712463i
$503$	112271.			0.443745			0.221872	−	0.975076i	$-0.428783\pi$
$503$	112271.			0.443745			0.221872	+	0.975076i	$0.428783\pi$
$504$	386125.	−	276897.i	1.52008	−	1.09008i
$505$			64805.7i			0.254115i
$506$	−3492.52	+	64107.4i	−0.0136407	+	0.250384i
$507$	255306.	−	255306.i	0.993220	−	0.993220i
$508$	45239.6	+	4943.91i	0.175304	+	0.0191577i
$509$	−167589.	+	167589.i	−0.646861	+	0.646861i	−0.952233	−	0.305372i	$-0.901219\pi$
$509$	−167589.	+	167589.i	−0.646861	+	0.646861i	0.305372	+	0.952233i	$0.401219\pi$
$510$	12621.6	+	14076.0i	0.0485258	+	0.0541177i
$511$			507912.i			1.94512i
$512$	−250776.	+	76358.6i	−0.956636	+	0.291285i
$513$	−77256.9			−0.293564
$514$	−211045.	+	189238.i	−0.798820	+	0.716278i
$515$	−500.399	−	500.399i	−0.00188670	−	0.00188670i
$516$	−36595.7	+	334871.i	−0.137445	+	1.25770i
$517$	209044.	+	209044.i	0.782089	+	0.782089i
$518$	−453705.	−	24717.5i	−1.69088	−	0.0921180i
$519$	−496108.			−1.84180
$520$	−5768.18	−	8043.56i	−0.0213320	−	0.0297469i
$521$			287463.i			1.05903i	0.848302	+	0.529513i	$0.177625\pi$
$521$			287463.i			1.05903i	−0.848302	+	0.529513i	$0.822375\pi$
$522$	−148846.	−	8108.99i	−0.546254	−	0.0297595i
$523$	−203069.	+	203069.i	−0.742404	+	0.742404i	−0.973040	−	0.230636i	$-0.925919\pi$
$523$	−203069.	+	203069.i	−0.742404	+	0.742404i	0.230636	+	0.973040i	$0.425919\pi$
$524$	−123326.	+	99026.4i	−0.449149	+	0.360652i
$525$	440588.	−	440588.i	1.59851	−	1.59851i
$526$	337386.	−	302524.i	1.21943	−	1.09343i
$527$		−	108509.i		−	0.390701i
$528$	572467.	+	126634.i	2.05344	+	0.454237i
$529$	−271114.			−0.968813
$530$	11161.2	+	12447.4i	0.0397339	+	0.0443126i
$531$	−116297.	−	116297.i	−0.412459	−	0.412459i
$532$	353717.	−	284023.i	1.24978	−	1.00353i
$533$	−24859.0	−	24859.0i	−0.0875042	−	0.0875042i
$534$	−31798.0	+	583673.i	−0.111511	+	2.04685i
$535$	−86277.6			−0.301433
$536$	21833.0	−	132528.i	0.0759946	−	0.461293i
$537$		−	90786.1i		−	0.314826i
$538$	−21741.6	+	399080.i	−0.0751150	+	1.37878i
$539$	424486.	−	424486.i	1.46112	−	1.46112i
$540$	−1464.22	+	13398.5i	−0.00502134	+	0.0459481i
$541$	308972.	−	308972.i	1.05566	−	1.05566i	0.0573036	−	0.998357i	$-0.481750\pi$
$541$	308972.	−	308972.i	1.05566	−	1.05566i	0.998357	−	0.0573036i	$-0.0182503\pi$
$542$	294222.	+	328127.i	1.00156	+	1.11698i
$543$			451027.i			1.52969i
$544$	−78555.1	+	44278.5i	−0.265446	+	0.149622i
$545$	13378.6			0.0450420
$546$	−117077.	+	104980.i	−0.392723	+	0.352143i
$547$	−8623.13	−	8623.13i	−0.0288198	−	0.0288198i	0.692550	−	0.721370i	$-0.256487\pi$
$547$	−8623.13	−	8623.13i	−0.0288198	−	0.0288198i	−0.721370	+	0.692550i	$0.756487\pi$
$548$	58367.6	+	6378.57i	0.194362	+	0.0212404i
$549$	56104.4	+	56104.4i	0.186145	+	0.186145i
$550$	417763.	+	22759.4i	1.38103	+	0.0752376i
$551$	−142317.			−0.468765
$552$	12955.5	−	78640.6i	0.0425182	−	0.258089i
$553$			413968.i			1.35368i
$554$	−195499.	−	10650.6i	−0.636980	−	0.0347022i
$555$	56150.4	−	56150.4i	0.182292	−	0.182292i
$556$	−62354.2	−	77654.8i	−0.201705	−	0.251199i
$557$	−208785.	+	208785.i	−0.672961	+	0.672961i	−0.958398	−	0.285437i	$-0.907861\pi$
$557$	−208785.	+	208785.i	−0.672961	+	0.672961i	0.285437	+	0.958398i	$0.407861\pi$
$558$	354833.	−	318168.i	1.13961	−	1.02185i
$559$		−	60666.5i		−	0.194145i
$560$	−42553.5	−	66727.2i	−0.135694	−	0.212778i
$561$	201683.			0.640832
$562$	−395161.	−	440698.i	−1.25113	−	1.39530i
$563$	127891.	+	127891.i	0.403480	+	0.403480i	0.879458	−	0.475977i	$-0.157906\pi$
$563$	127891.	+	127891.i	0.403480	+	0.403480i	−0.475977	+	0.879458i	$0.657906\pi$
$564$	−229778.	−	286162.i	−0.722356	−	0.899608i
$565$	24275.2	+	24275.2i	0.0760443	+	0.0760443i
$566$	−12235.5	+	224590.i	−0.0381935	+	0.701065i
$567$	−387228.			−1.20448
$568$	207807.	+	289781.i	0.644116	+	0.898201i
$569$		−	488561.i		−	1.50902i	−0.656290	−	0.754509i	$-0.727875\pi$
$569$		−	488561.i		−	1.50902i	0.656290	−	0.754509i	$-0.272125\pi$
$570$	−4312.65	+	79161.5i	−0.0132738	+	0.243649i
$571$	−17324.2	+	17324.2i	−0.0531352	+	0.0531352i	−0.733175	−	0.680040i	$-0.761962\pi$
$571$	−17324.2	+	17324.2i	−0.0531352	+	0.0531352i	0.680040	+	0.733175i	$0.261962\pi$
$572$	−104964.	−	11470.7i	−0.320810	−	0.0350590i
$573$	−424913.	+	424913.i	−1.29417	+	1.29417i
$574$	−187657.	−	209282.i	−0.569562	−	0.635197i
$575$		−	56873.6i		−	0.172018i
$576$	−375132.	−	127049.i	−1.13068	−	0.382935i
$577$	−9362.93			−0.0281229			−0.0140615	−	0.999901i	$-0.504476\pi$
$577$	−9362.93			−0.0281229			−0.0140615	+	0.999901i	$0.504476\pi$
$578$	225639.	−	202324.i	0.675397	−	0.605609i
$579$	−473990.	−	473990.i	−1.41388	−	1.41388i
$580$	−2697.29	+	24681.8i	−0.00801810	+	0.0733702i
$581$	196100.	+	196100.i	0.580932	+	0.580932i
$582$	250940.	+	13671.0i	0.740839	+	0.0403603i
$583$	178348.			0.524725
$584$	344052.	−	246726.i	1.00878	−	0.723417i
$585$		−	14954.5i		−	0.0436978i
$586$	4004.26	+	218.149i	0.0116608	+	0.000635268i
$587$	46301.5	−	46301.5i	0.134375	−	0.134375i	−0.636720	−	0.771095i	$-0.719709\pi$
$587$	46301.5	−	46301.5i	0.134375	−	0.134375i	0.771095	+	0.636720i	$0.219709\pi$
$588$	−581083.	+	466590.i	−1.68067	+	1.34953i
$589$	321742.	−	321742.i	0.927422	−	0.927422i
$590$	−20395.7	+	18288.2i	−0.0585916	+	0.0525373i
$591$			483778.i			1.38507i
$592$	203650.	+	319340.i	0.581088	+	0.911191i
$593$	−194145.			−0.552099			−0.276049	−	0.961143i	$-0.589025\pi$
$593$	−194145.			−0.552099			−0.276049	+	0.961143i	$0.589025\pi$
$594$	95987.6	+	107049.i	0.272046	+	0.303395i
$595$	−19250.1	−	19250.1i	−0.0543749	−	0.0543749i
$596$	277664.	−	222955.i	0.781676	−	0.627660i
$597$	420387.	+	420387.i	1.17951	+	1.17951i
$598$	−780.804	+	14332.2i	−0.00218343	+	0.0400783i
$599$	474516.			1.32250			0.661252	−	0.750164i	$-0.270025\pi$
$599$	474516.			1.32250			0.661252	+	0.750164i	$0.270025\pi$
$600$	−512470.	−	84425.8i	−1.42353	−	0.234516i
$601$			87515.3i			0.242290i	0.992635	+	0.121145i	$0.0386566\pi$
$601$			87515.3i			0.242290i	−0.992635	+	0.121145i	$0.961343\pi$
$602$	26387.0	−	484350.i	0.0728110	−	1.33649i
$603$	143493.	−	143493.i	0.394634	−	0.394634i
$604$	−72955.0	+	667580.i	−0.199977	+	1.82991i
$605$	−42357.8	+	42357.8i	−0.115724	+	0.115724i
$606$	−572935.	−	638958.i	−1.56013	−	1.73991i
$607$		−	687260.i		−	1.86528i	−0.360808	−	0.932640i	$-0.617499\pi$
$607$		−	687260.i		−	1.86528i	0.360808	−	0.932640i	$-0.382501\pi$
$608$	−364216.	−	101634.i	−0.985263	−	0.274937i
$609$	394456.			1.06356
$610$	9839.34	−	8822.65i	0.0264427	−	0.0237104i
$611$	46734.8	+	46734.8i	0.125187	+	0.125187i
$612$	−135435.	−	14800.7i	−0.361600	−	0.0395166i
$613$	−220862.	−	220862.i	−0.587761	−	0.587761i	0.349263	−	0.937025i	$-0.386432\pi$
$613$	−220862.	−	220862.i	−0.587761	−	0.587761i	−0.937025	+	0.349263i	$0.886432\pi$
$614$	116342.	+	6338.23i	0.308603	+	0.0168124i
$615$	49125.1			0.129883
$616$	−833023.	−	137234.i	−2.19531	−	0.361661i
$617$			518967.i			1.36323i	0.731711	+	0.681615i	$0.238722\pi$
$617$			518967.i			1.36323i	−0.731711	+	0.681615i	$0.761278\pi$
$618$	9357.67	+	509.798i	0.0245014	+	0.00133482i
$619$	−77555.3	+	77555.3i	−0.202409	+	0.202409i	−0.801031	−	0.598622i	$-0.795715\pi$
$619$	−77555.3	+	77555.3i	−0.202409	+	0.202409i	0.598622	+	0.801031i	$0.295715\pi$
$620$	−49701.1	−	61896.8i	−0.129295	−	0.161022i
$621$	13820.5	−	13820.5i	0.0358378	−	0.0358378i
$622$	−245129.	+	219800.i	−0.633599	+	0.568130i
$623$		−	841705.i		−	2.16862i
$624$	127984.	+	28310.9i	0.328689	+	0.0727084i
$625$	−360490.			−0.922855
$626$	321554.	+	358609.i	0.820550	+	0.915107i
$627$	598015.	+	598015.i	1.52117	+	1.52117i
$628$	350430.	+	436419.i	0.888550	+	1.10658i
$629$	92126.1	+	92126.1i	0.232853	+	0.232853i
$630$	6504.48	−	119394.i	0.0163882	−	0.300816i
$631$	344653.			0.865612			0.432806	−	0.901487i	$-0.357523\pi$
$631$	344653.			0.865612			0.432806	+	0.901487i	$0.357523\pi$
$632$	280416.	−	201091.i	0.702051	−	0.503453i
$633$		−	486914.i		−	1.21519i
$634$	−4552.88	+	83571.0i	−0.0113268	+	0.207911i
$635$	8098.03	−	8098.03i	0.0200832	−	0.0200832i
$636$	−220091.	−	24052.1i	−0.544111	−	0.0594619i
$637$	94900.2	−	94900.2i	0.233877	−	0.233877i
$638$	176822.	+	197198.i	0.434405	+	0.484464i
$639$			538758.i			1.31945i
$640$	−24529.0	+	61238.8i	−0.0598853	+	0.149509i
$641$	−183353.			−0.446243			−0.223122	−	0.974791i	$-0.571625\pi$
$641$	−183353.			−0.446243			−0.223122	+	0.974791i	$0.571625\pi$
$642$	850662.	−	762764.i	2.06389	−	1.85063i
$643$	−541900.	−	541900.i	−1.31068	−	1.31068i	−0.920913	−	0.389768i	$-0.872555\pi$
$643$	−541900.	−	541900.i	−1.31068	−	1.31068i	−0.389768	−	0.920913i	$-0.627445\pi$
$644$	−12467.6	+	114086.i	−0.0300615	+	0.275080i
$645$	59943.0	+	59943.0i	0.144085	+	0.144085i
$646$	−129880.	−	7075.78i	−0.311228	−	0.0169555i
$647$	−358562.			−0.856555			−0.428278	−	0.903647i	$-0.640879\pi$
$647$	−358562.			−0.856555			−0.428278	+	0.903647i	$0.640879\pi$
$648$	188102.	+	262302.i	0.447963	+	0.624672i
$649$			292233.i			0.693808i
$650$	93397.0	+	5088.19i	0.221058	+	0.0120431i
$651$	−891760.	+	891760.i	−2.10419	+	2.10419i
$652$	431026.	−	346099.i	1.01393	−	0.814152i
$653$	−73642.4	+	73642.4i	−0.172704	+	0.172704i	−0.788166	−	0.615463i	$-0.788969\pi$
$653$	−73642.4	+	73642.4i	−0.172704	+	0.172704i	0.615463	+	0.788166i	$0.288969\pi$
$654$	−131908.	+	118278.i	−0.308400	+	0.276533i
$655$			39801.7i			0.0927725i
$656$	−50607.3	+	228778.i	−0.117600	+	0.531626i
$657$	639657.			1.48189
$658$	352795.	+	393449.i	0.814836	+	0.908735i
$659$	22081.7	+	22081.7i	0.0508467	+	0.0508467i	0.732073	−	0.681226i	$-0.238553\pi$
$659$	22081.7	+	22081.7i	0.0508467	+	0.0508467i	−0.681226	+	0.732073i	$0.738553\pi$
$660$	115046.	−	92378.2i	0.264109	−	0.212071i
$661$	20869.3	+	20869.3i	0.0477644	+	0.0477644i	0.730586	−	0.682821i	$-0.239247\pi$
$661$	20869.3	+	20869.3i	0.0477644	+	0.0477644i	−0.682821	+	0.730586i	$0.739247\pi$
$662$	−25500.6	+	468079.i	−0.0581881	+	1.06808i
$663$	45089.3			0.102576
$664$	37576.8	−	228094.i	0.0852283	−	0.517342i
$665$		−	114157.i		−	0.258143i
$666$	−31128.8	+	571390.i	−0.0701802	+	1.28820i
$667$	25459.3	−	25459.3i	0.0572261	−	0.0572261i
$668$	90694.9	−	829911.i	0.203250	−	1.85985i
$669$	−684791.	+	684791.i	−1.53005	+	1.53005i
$670$	−22564.8	−	25165.1i	−0.0502669	−	0.0560594i
$671$		−	140979.i		−	0.313120i
$672$	1.00948e6	+	281696.i	2.23543	+	0.623794i
$673$	379771.			0.838479			0.419239	−	0.907876i	$-0.362297\pi$
$673$	379771.			0.838479			0.419239	+	0.907876i	$0.362297\pi$
$674$	−234837.	+	210571.i	−0.516947	+	0.463531i
$675$	−90063.0	−	90063.0i	−0.197669	−	0.197669i
$676$	430805.	+	47079.6i	0.942731	+	0.103024i
$677$	−156167.	−	156167.i	−0.340731	−	0.340731i	0.515911	−	0.856642i	$-0.327454\pi$
$677$	−156167.	−	156167.i	−0.340731	−	0.340731i	−0.856642	+	0.515911i	$0.827454\pi$
$678$	−453957.	−	24731.2i	−0.987541	−	0.0538004i
$679$	−361877.			−0.784912
$680$	−3688.71	+	22390.7i	−0.00797731	+	0.0484228i
$681$		−	355511.i		−	0.766581i
$682$	−845560.	−	46065.4i	−1.81792	−	0.0990390i
$683$	164044.	−	164044.i	0.351656	−	0.351656i	−0.509070	−	0.860725i	$-0.670010\pi$
$683$	164044.	−	164044.i	0.351656	−	0.351656i	0.860725	+	0.509070i	$0.170010\pi$
$684$	−357695.	−	445466.i	−0.764540	−	0.952144i
$685$	10448.0	−	10448.0i	0.0222665	−	0.0222665i
$686$	249938.	−	224112.i	0.531109	−	0.476230i
$687$		−	785666.i		−	1.66466i
$688$	−340909.	+	217406.i	−0.720215	+	0.459298i
$689$	39872.4			0.0839912
$690$	−13389.7	−	14932.7i	−0.0281238	−	0.0313647i
$691$	−288207.	−	288207.i	−0.603599	−	0.603599i	0.337667	−	0.941266i	$-0.390362\pi$
$691$	−288207.	−	288207.i	−0.603599	−	0.603599i	−0.941266	+	0.337667i	$0.890362\pi$
$692$	−372825.	−	464310.i	−0.778562	−	0.969607i
$693$	−901945.	−	901945.i	−1.87808	−	1.87808i
$694$	18322.8	−	336327.i	0.0380429	−	0.698302i
$695$	−25062.1			−0.0518856
$696$	−191613.	−	267198.i	−0.395554	−	0.551589i
$697$			80599.7i			0.165908i
$698$	232.693	−	4271.22i	0.000477608	−	0.00876681i
$699$	26087.2	−	26087.2i	0.0533916	−	0.0533916i
$700$	743451.	+	81246.4i	1.51725	+	0.165809i
$701$	323248.	−	323248.i	0.657808	−	0.657808i	−0.297053	−	0.954861i	$-0.596004\pi$
$701$	323248.	−	323248.i	0.657808	−	0.657808i	0.954861	+	0.297053i	$0.0960038\pi$
$702$	21459.4	+	23932.3i	0.0435456	+	0.0485636i
$703$			546329.i			1.10546i
$704$	311692.	+	630941.i	0.628899	+	1.27304i
$705$	−92355.0			−0.185816
$706$	−70651.0	+	63350.7i	−0.141745	+	0.127099i
$707$	873826.	+	873826.i	1.74818	+	1.74818i
$708$	39410.6	−	360629.i	0.0786224	−	0.719440i
$709$	−580085.	−	580085.i	−1.15398	−	1.15398i	−0.985747	−	0.168235i	$-0.946193\pi$
$709$	−580085.	−	580085.i	−1.15398	−	1.15398i	−0.168235	−	0.985747i	$-0.553807\pi$
$710$	89603.4	+	4881.52i	0.177749	+	0.00968364i
$711$	521346.			1.03130
$712$	−570159.	+	408871.i	−1.12470	+	0.806540i
$713$			115113.i			0.226436i
$714$	359984.	+	19611.7i	0.706134	+	0.0384696i
$715$	−18788.9	+	18788.9i	−0.0367526	+	0.0367526i
$716$	84967.2	−	68225.8i	0.165739	−	0.133083i
$717$	471123.	−	471123.i	0.916423	−	0.916423i
$718$	−434994.	+	390046.i	−0.843789	+	0.756601i
$719$			332243.i			0.642684i	0.946963	+	0.321342i	$0.104134\pi$
$719$			332243.i			0.642684i	−0.946963	+	0.321342i	$0.895866\pi$
$720$	−84035.3	+	53591.3i	−0.162105	+	0.103378i
$721$	−13494.5			−0.0259590
$722$	−16124.1	−	17982.1i	−0.0309314	−	0.0344959i
$723$	415456.	+	415456.i	0.794783	+	0.794783i
$724$	−422118.	+	338947.i	−0.805299	+	0.646628i
$725$	−165908.	−	165908.i	−0.315639	−	0.315639i
$726$	43153.4	−	792107.i	0.0818732	−	1.50283i
$727$	362311.			0.685508			0.342754	−	0.939425i	$-0.388640\pi$
$727$	362311.			0.685508			0.342754	+	0.939425i	$0.388640\pi$
$728$	−186234.	−	30680.8i	−0.351396	−	0.0578900i
$729$			713570.i			1.34271i
$730$	5795.74	−	106384.i	0.0108758	−	0.199633i
$731$	−98348.7	+	98348.7i	−0.184049	+	0.184049i
$732$	−19012.5	+	173975.i	−0.0354828	+	0.324688i
$733$	377844.	−	377844.i	0.703242	−	0.703242i	−0.261863	−	0.965105i	$-0.584337\pi$
$733$	377844.	−	377844.i	0.703242	−	0.703242i	0.965105	+	0.261863i	$0.0843369\pi$
$734$	−403570.	−	450076.i	−0.749078	−	0.835399i
$735$			187537.i			0.347146i
$736$	83336.2	−	46973.4i	0.153843	−	0.0867155i
$737$	−360569.			−0.663825
$738$	−263567.	+	236333.i	−0.483925	+	0.433922i
$739$	467502.	+	467502.i	0.856042	+	0.856042i	0.990869	−	0.134828i	$-0.0430480\pi$
$739$	467502.	+	467502.i	0.856042	+	0.856042i	−0.134828	+	0.990869i	$0.543048\pi$
$740$	94748.5	+	10354.4i	0.173025	+	0.0189086i
$741$	133695.	+	133695.i	0.243489	+	0.243489i
$742$	318334.	+	17342.6i	0.578196	+	0.0314997i
$743$	−555820.			−1.00683			−0.503415	−	0.864045i	$-0.667923\pi$
$743$	−555820.			−1.00683			−0.503415	+	0.864045i	$0.667923\pi$
$744$	1.03725e6	+	170879.i	1.87386	+	0.308705i
$745$		−	89612.4i		−	0.161456i
$746$	−148034.	−	8064.75i	−0.266001	−	0.0144915i
$747$	246966.	−	246966.i	0.442584	−	0.442584i
$748$	151565.	+	188756.i	0.270892	+	0.337364i
$749$	−1.16335e6	+	1.16335e6i	−2.07370	+	2.07370i
$750$	−197213.	+	176835.i	−0.350601	+	0.314373i
$751$		−	308308.i		−	0.546644i	−0.961923	−	0.273322i	$-0.911878\pi$
$751$		−	308308.i		−	0.546644i	0.961923	−	0.273322i	$-0.0881224\pi$
$752$	95141.6	−	430102.i	0.168242	−	0.760563i
$753$	599226.			1.05682
$754$	39531.1	+	44086.5i	0.0695339	+	0.0775467i
$755$	119499.	+	119499.i	0.209638	+	0.209638i
$756$	160919.	+	200405.i	0.281555	+	0.350643i
$757$	34980.2	+	34980.2i	0.0610423	+	0.0610423i	0.736969	−	0.675927i	$-0.236256\pi$
$757$	34980.2	+	34980.2i	0.0610423	+	0.0610423i	−0.675927	+	0.736969i	$0.736256\pi$
$758$	−33980.3	+	623729.i	−0.0591410	+	1.08557i
$759$	−213958.			−0.371403
$760$	−77328.6	+	55453.7i	−0.133879	+	0.0960070i
$761$			545745.i			0.942368i	0.882035	+	0.471184i	$0.156173\pi$
$761$			545745.i			0.942368i	−0.882035	+	0.471184i	$0.843827\pi$
$762$	−8250.14	+	151437.i	−0.0142086	+	0.260808i
$763$	180394.	−	180394.i	0.309866	−	0.309866i
$764$	−717001.	−	78355.8i	−1.22838	−	0.134241i
$765$	−24243.3	+	24243.3i	−0.0414256	+	0.0414256i
$766$	28078.9	+	31314.6i	0.0478544	+	0.0533690i
$767$			65332.9i			0.111056i
$768$	−299555.	−	820646.i	−0.507871	−	1.39134i
$769$	510362.			0.863030			0.431515	−	0.902106i	$-0.357979\pi$
$769$	510362.			0.863030			0.431515	+	0.902106i	$0.357979\pi$
$770$	−158179.	+	141835.i	−0.266789	+	0.239222i
$771$	−667972.	−	667972.i	−1.12370	−	1.12370i
$772$	87405.8	−	799814.i	0.146658	−	1.34200i
$773$	596763.	+	596763.i	0.998718	+	0.998718i	0.999999	−	0.00128103i	$-0.000407764\pi$
$773$	596763.	+	596763.i	0.998718	+	0.998718i	−0.00128103	+	0.999999i	$0.500408\pi$
$774$	−609984.	−	33231.4i	−1.01821	−	0.0554711i
$775$	750148.			1.24895
$776$	175787.	+	245130.i	0.291919	+	0.407073i
$777$		−	1.51424e6i		−	2.50814i
$778$	941952.	+	51316.8i	1.55621	+	0.0847813i
$779$	−238987.	+	238987.i	−0.393822	+	0.393822i
$780$	25720.2	−	20652.5i	0.0422752	−	0.0339456i
$781$	676897.	−	676897.i	1.10974	−	1.10974i
$782$	24500.2	−	21968.6i	0.0400641	−	0.0359243i
$783$		−	80632.7i		−	0.131519i
$784$	−873369.	−	193196.i	−1.42091	−	0.314315i
$785$	140849.			0.228567
$786$	−351880.	−	392429.i	−0.569572	−	0.635208i
$787$	−463254.	−	463254.i	−0.747945	−	0.747945i	0.226148	−	0.974093i	$-0.427387\pi$
$787$	−463254.	−	463254.i	−0.747945	−	0.747945i	−0.974093	+	0.226148i	$0.927387\pi$
$788$	−452770.	+	363560.i	−0.729165	+	0.585495i
$789$	1.06785e6	+	1.06785e6i	1.71536	+	1.71536i
$790$	4723.76	−	86707.5i	0.00756891	−	0.138932i
$791$	654644.			1.04629
$792$	−172831.	+	1.04910e6i	−0.275532	+	1.67250i
$793$		−	31518.0i		−	0.0501202i
$794$	59249.8	−	1.08757e6i	0.0939823	−	1.72510i
$795$	−39396.9	+	39396.9i	−0.0623344	+	0.0623344i
$796$	−77521.1	+	709363.i	−0.122347	+	1.11955i
$797$	406283.	−	406283.i	0.639605	−	0.639605i	−0.310853	−	0.950458i	$-0.600615\pi$
$797$	406283.	−	406283.i	0.639605	−	0.639605i	0.950458	+	0.310853i	$0.100615\pi$
$798$	1.00924e6	+	1.12555e6i	1.58486	+	1.76749i
$799$		−	151527.i		−	0.237354i
$800$	−306107.	−	543070.i	−0.478293	−	0.848546i
$801$	−1.06003e6			−1.65217
$802$	−271476.	+	243425.i	−0.422069	+	0.378457i
$803$	−803667.	−	803667.i	−1.24636	−	1.24636i
$804$	444960.	+	48626.4i	0.688349	+	0.0752246i
$805$	20421.7	+	20421.7i	0.0315137	+	0.0315137i
$806$	−189037.	−	10298.6i	−0.290990	−	0.0158529i
$807$	−1.33193e6			−2.04519
$808$	167443.	−	1.01639e6i	0.256475	−	1.55682i
$809$		−	766553.i		−	1.17124i	−0.810587	−	0.585619i	$-0.800852\pi$
$809$		−	766553.i		−	1.17124i	0.810587	−	0.585619i	$-0.199148\pi$
$810$	81106.7	+	4418.63i	0.123619	+	0.00673468i
$811$	−418641.	+	418641.i	−0.636503	+	0.636503i	−0.949691	−	0.313188i	$-0.898603\pi$
$811$	−418641.	+	418641.i	−0.636503	+	0.636503i	0.313188	+	0.949691i	$0.398603\pi$
$812$	296434.	+	369173.i	0.449589	+	0.559909i
$813$	−1.03855e6	+	1.03855e6i	−1.57125	+	1.57125i
$814$	757006.	−	678785.i	1.14248	−	1.02443i
$815$		−	139108.i		−	0.209429i
$816$	−161583.	−	253375.i	−0.242670	−	0.380525i
$817$	−583231.			−0.873769
$818$	−287798.	−	320963.i	−0.430112	−	0.479677i
$819$	−201643.	−	201643.i	−0.300618	−	0.300618i
$820$	36917.5	+	45976.4i	0.0549041	+	0.0683766i
$821$	−23229.7	−	23229.7i	−0.0344633	−	0.0344633i	0.689665	−	0.724128i	$-0.257758\pi$
$821$	−23229.7	−	23229.7i	−0.0344633	−	0.0344633i	−0.724128	+	0.689665i	$0.757758\pi$
$822$	−10644.2	+	195382.i	−0.0157533	+	0.289161i
$823$	−41797.3			−0.0617090			−0.0308545	−	0.999524i	$-0.509823\pi$
$823$	−41797.3			−0.0617090			−0.0308545	+	0.999524i	$0.509823\pi$
$824$	6555.17	+	9141.01i	0.00965450	+	0.0134629i
$825$			1.39428e6i			2.04853i
$826$	−28416.7	+	521606.i	−0.0416498	+	0.764509i
$827$	−349889.	+	349889.i	−0.511587	+	0.511587i	−0.915013	−	0.403425i	$-0.867820\pi$
$827$	−349889.	+	349889.i	−0.511587	+	0.511587i	0.403425	+	0.915013i	$0.367820\pi$
$828$	143678.	+	15701.5i	0.209570	+	0.0229024i
$829$	213369.	−	213369.i	0.310472	−	0.310472i	−0.534621	−	0.845092i	$-0.679545\pi$
$829$	213369.	−	213369.i	0.310472	−	0.310472i	0.845092	+	0.534621i	$0.179545\pi$
$830$	−38836.4	−	43311.8i	−0.0563745	−	0.0628709i
$831$		−	652479.i		−	0.944853i
$832$	69683.4	+	141056.i	0.100666	+	0.203772i
$833$	−307692.			−0.443432
$834$	247102.	−	221569.i	0.355258	−	0.318549i
$835$	−148557.	−	148557.i	−0.213069	−	0.213069i
$836$	−110276.	+	1.00909e6i	−0.157787	+	1.44384i
$837$	182289.	+	182289.i	0.260202	+	0.260202i
$838$	669479.	+	36472.7i	0.953343	+	0.0519374i
$839$	−7789.74			−0.0110662			−0.00553311	−	0.999985i	$-0.501761\pi$
$839$	−7789.74			−0.0110662			−0.00553311	+	0.999985i	$0.501761\pi$
$840$	214328.	−	153699.i	0.303754	−	0.217827i
$841$			558745.i			0.789990i
$842$	1.28004e6	+	69735.4i	1.80550	+	0.0983624i
$843$	1.39484e6	−	1.39484e6i	1.96277	−	1.96277i
$844$	455705.	−	365916.i	0.639734	−	0.513685i
$845$	77115.5	−	77115.5i	0.108001	−	0.108001i
$846$	495505.	−	444305.i	0.692320	−	0.620784i
$847$			1.14229e6i			1.59224i
$848$	−142888.	−	224059.i	−0.198703	−	0.311581i
$849$	−749570.			−1.03991
$850$	−143161.	−	159658.i	−0.198146	−	0.220980i
$851$	−97733.2	−	97733.2i	−0.134953	−	0.134953i
$852$	−926610.	+	744037.i	−1.27649	+	1.02498i
$853$	485860.	+	485860.i	0.667749	+	0.667749i	0.957195	−	0.289445i	$-0.0934708\pi$
$853$	485860.	+	485860.i	0.667749	+	0.667749i	−0.289445	+	0.957195i	$0.593471\pi$
$854$	13708.8	−	251634.i	0.0187968	−	0.345028i
$855$	−143768.			−0.196667
$856$	1.35315e6	+	222921.i	1.84671	+	0.304232i
$857$		−	1.01914e6i		−	1.38763i	−0.720154	−	0.693814i	$-0.755929\pi$
$857$		−	1.01914e6i		−	1.38763i	0.720154	−	0.693814i	$-0.244071\pi$
$858$	19141.8	−	351359.i	0.0260021	−	0.477284i
$859$	232567.	−	232567.i	0.315182	−	0.315182i	−0.531731	−	0.846913i	$-0.678458\pi$
$859$	232567.	−	232567.i	0.315182	−	0.315182i	0.846913	+	0.531731i	$0.178458\pi$
$860$	−11053.8	+	101148.i	−0.0149456	+	0.136761i
$861$	662392.	−	662392.i	0.893529	−	0.893529i
$862$	−14413.4	−	16074.3i	−0.0193978	−	0.0216331i
$863$			739852.i			0.993398i	0.867923	+	0.496699i	$0.165455\pi$
$863$			739852.i			0.993398i	−0.867923	+	0.496699i	$0.834545\pi$
$864$	57582.9	−	206354.i	0.0771376	−	0.276430i
$865$	−149850.			−0.200274
$866$	−487919.	+	437502.i	−0.650596	+	0.583371i
$867$	714164.	+	714164.i	0.950079	+	0.950079i
$868$	−1.50476e6	−	164444.i	−1.99723	−	0.218263i
$869$	−655020.	−	655020.i	−0.867392	−	0.867392i
$870$	−82620.5	−	4501.10i	−0.109156	−	0.00594675i
$871$	−80610.5			−0.106256
$872$	−209825.	−	34567.2i	−0.275947	−	0.0454602i
$873$			455742.i			0.597986i
$874$	137785.	+	7506.44i	0.180377	+	0.00982677i
$875$	269704.	−	269704.i	0.352267	−	0.352267i
$876$	883381.	+	1.10015e6i	1.15117	+	1.43365i
$877$	−828805.	+	828805.i	−1.07759	+	1.07759i	−0.0808636	+	0.996725i	$0.525768\pi$
$877$	−828805.	+	828805.i	−1.07759	+	1.07759i	−0.996725	+	0.0808636i	$0.974232\pi$
$878$	−471947.	+	423181.i	−0.612215	+	0.548955i
$879$			13364.2i			0.0172968i
$880$	172914.	+	38249.9i	0.223288	+	0.0493930i
$881$	1.20631e6			1.55420			0.777099	−	0.629379i	$-0.216690\pi$
$881$	1.20631e6			1.55420			0.777099	+	0.629379i	$0.216690\pi$
$882$	−902210.	−	1.00618e6i	−1.15977	−	1.29341i
$883$	381765.	+	381765.i	0.489637	+	0.489637i	0.908192	−	0.418555i	$-0.137463\pi$
$883$	381765.	+	381765.i	0.489637	+	0.489637i	−0.418555	+	0.908192i	$0.637463\pi$
$884$	33884.6	+	42199.3i	0.0433609	+	0.0540008i
$885$	−64553.8	−	64553.8i	−0.0824205	−	0.0824205i
$886$	42444.1	−	779088.i	0.0540692	−	0.992474i
$887$	−1.44154e6			−1.83223			−0.916113	−	0.400919i	$-0.868691\pi$
$887$	−1.44154e6			−1.83223			−0.916113	+	0.400919i	$0.868691\pi$
$888$	−1.02572e6	+	735564.i	−1.30078	+	0.932812i
$889$		−	218384.i		−	0.276323i
$890$	−9604.63	+	176299.i	−0.0121255	+	0.222572i
$891$	612709.	−	612709.i	0.771790	−	0.771790i
$892$	−1.15552e6	−	126278.i	−1.45227	−	0.158708i
$893$	449295.	−	449295.i	0.563416	−	0.563416i
$894$	792246.	+	883542.i	0.991254	+	1.10548i
$895$		−	27422.0i		−	0.0342337i
$896$	494987.	+	1.15647e6i	0.616563	+	1.44052i
$897$	−47833.5			−0.0594494
$898$	−974840.	+	874110.i	−1.20887	+	1.08396i
$899$	335801.	+	335801.i	0.415492	+	0.415492i
$900$	102321.	−	936293.i	0.126322	−	1.15592i
$901$	−64638.6	−	64638.6i	−0.0796238	−	0.0796238i
$902$	628075.	+	34217.0i	0.771967	+	0.0420561i
$903$	1.61652e6			1.98246
$904$	−318003.	−	443446.i	−0.389129	−	0.542630i
$905$			136233.i			0.166336i
$906$	−2.23468e6	−	121744.i	−2.72244	−	0.148316i
$907$	−208093.	+	208093.i	−0.252955	+	0.252955i	−0.822181	−	0.569226i	$-0.807243\pi$
$907$	−208093.	+	208093.i	−0.252955	+	0.252955i	0.569226	+	0.822181i	$0.307243\pi$
$908$	332724.	−	267166.i	0.403564	−	0.324049i
$909$	1.10048e6	−	1.10048e6i	1.33185	−	1.33185i
$910$	−35363.3	+	31709.2i	−0.0427041	+	0.0382915i
$911$			861726.i			1.03832i	0.854676	+	0.519162i	$0.173756\pi$
$911$			861726.i			1.03832i	−0.854676	+	0.519162i	$0.826244\pi$
$912$	272173.	−	1.23040e6i	0.327232	−	1.47930i
$913$	−620577.			−0.744482
$914$	412600.	+	460147.i	0.493898	+	0.550813i
$915$	31142.2	+	31142.2i	0.0371969	+	0.0371969i
$916$	735309.	−	590429.i	0.876353	−	0.703682i
$917$	536678.	+	536678.i	0.638227	+	0.638227i
$918$	4008.92	−	73586.3i	0.00475710	−	0.0873196i
$919$	−368829.			−0.436711			−0.218355	−	0.975869i	$-0.570069\pi$
$919$	−368829.			−0.436711			−0.218355	+	0.975869i	$0.570069\pi$
$920$	3913.22	−	23753.5i	0.00462336	−	0.0280641i
$921$			388292.i			0.457761i
$922$	−5937.94	+	108995.i	−0.00698512	+	0.128216i
$923$	151330.	−	151330.i	0.177632	−	0.177632i
$924$	305649.	−	2.79686e6i	0.357996	−	3.27587i
$925$	−636889.	+	636889.i	−0.744355	+	0.744355i
$926$	70774.5	+	78930.3i	0.0825382	+	0.0920496i
$927$			16994.8i			0.0197769i
$928$	106075.	−	380131.i	0.123174	−	0.441405i
$929$	842458.			0.976151			0.488076	−	0.872801i	$-0.337699\pi$
$929$	842458.			0.976151			0.488076	+	0.872801i	$0.337699\pi$
$930$	196959.	−	176607.i	0.227724	−	0.204194i
$931$	−912344.	−	912344.i	−1.05259	−	1.05259i
$932$	44019.7	+	4810.59i	0.0506775	+	0.00553817i
$933$	−775851.	−	775851.i	−0.891282	−	0.891282i
$934$	−631484.	−	34402.7i	−0.723883	−	0.0394366i
$935$	60918.6			0.0696830
$936$	−38638.9	+	234541.i	−0.0441036	+	0.267712i
$937$		−	41186.1i		−	0.0469107i	−0.999725	−	0.0234553i	$-0.992533\pi$
$937$		−	41186.1i		−	0.0469107i	0.999725	−	0.0234553i	$-0.00746675\pi$
$938$	−643579.	−	35061.7i	−0.731470	−	0.0398499i
$939$	−1.13502e6	+	1.13502e6i	−1.28728	+	1.28728i
$940$	−69404.8	−	86435.5i	−0.0785478	−	0.0978220i
$941$	495362.	−	495362.i	0.559427	−	0.559427i	−0.369717	−	0.929144i	$-0.620546\pi$
$941$	495362.	−	495362.i	0.559427	−	0.559427i	0.929144	+	0.369717i	$0.120546\pi$
$942$	−1.38871e6	+	1.24522e6i	−1.56498	+	1.40327i
$943$		−	85505.2i		−	0.0961544i
$944$	367132.	−	234129.i	0.411982	−	0.262731i
$945$	64678.2			0.0724259
$946$	724633.	+	808137.i	0.809722	+	0.903031i
$947$	−825578.	−	825578.i	−0.920573	−	0.920573i	0.0764965	−	0.997070i	$-0.475627\pi$
$947$	−825578.	−	825578.i	−0.920573	−	0.920573i	−0.997070	+	0.0764965i	$0.975627\pi$
$948$	719991.	+	896663.i	0.801143	+	0.997729i
$949$	−179672.	−	179672.i	−0.199502	−	0.199502i
$950$	48916.5	−	897893.i	0.0542011	−	0.994895i
$951$	−278918.			−0.308401
$952$	252174.	+	351649.i	0.278244	+	0.388004i
$953$		−	1.06311e6i		−	1.17055i	−0.810834	−	0.585276i	$-0.800986\pi$
$953$		−	1.06311e6i		−	1.17055i	0.810834	−	0.585276i	$-0.199014\pi$
$954$	21841.0	−	400905.i	0.0239980	−	0.440499i
$955$	−128345.	+	128345.i	−0.140726	+	0.140726i
$956$	794975.	+	86877.1i	0.869837	+	0.0950582i
$957$	−624145.	+	624145.i	−0.681494	+	0.681494i
$958$	−601850.	−	671205.i	−0.655778	−	0.731348i
$959$		−	281757.i		−	0.306364i
$960$	−208226.	−	70521.5i	−0.225940	−	0.0765208i
$961$	−594793.			−0.644050
$962$	169240.	−	151752.i	0.182874	−	0.163978i
$963$	1.46511e6	+	1.46511e6i	1.57985	+	1.57985i
$964$	−76611.9	+	701043.i	−0.0824408	+	0.754381i
$965$	−143169.	−	143169.i	−0.153743	−	0.153743i
$966$	−381894.	−	20805.3i	−0.409250	−	0.0222956i
$967$	1.03910e6			1.11123			0.555615	−	0.831440i	$-0.312483\pi$
$967$	1.03910e6			1.11123			0.555615	+	0.831440i	$0.312483\pi$
$968$	773767.	−	554882.i	0.825771	−	0.592175i
$969$		−	433476.i		−	0.461655i
$970$	75796.7	+	4129.34i	0.0805577	+	0.00438872i
$971$	624932.	−	624932.i	0.662818	−	0.662818i	−0.293225	−	0.956043i	$-0.594729\pi$
$971$	624932.	−	624932.i	0.662818	−	0.662818i	0.956043	+	0.293225i	$0.0947285\pi$
$972$	−1.05016e6	+	843247.i	−1.11154	+	0.892529i
$973$	−337931.	+	337931.i	−0.356946	+	0.356946i
$974$	−25265.0	+	22654.4i	−0.0266318	+	0.0238800i
$975$			311712.i			0.327903i
$976$	−177112.	+	112949.i	−0.185930	+	0.118572i
$977$	1.37121e6			1.43653			0.718264	−	0.695771i	$-0.244937\pi$
$977$	1.37121e6			1.43653			0.718264	+	0.695771i	$0.244937\pi$
$978$	1.22983e6	+	1.37155e6i	1.28578	+	1.43395i
$979$	1.33183e6	+	1.33183e6i	1.38958	+	1.38958i
$980$	−175517.	+	140934.i	−0.182754	+	0.146745i
$981$	−227186.	−	227186.i	−0.236071	−	0.236071i
$982$	−21314.5	+	391242.i	−0.0221031	+	0.405716i
$983$	838159.			0.867400			0.433700	−	0.901057i	$-0.357208\pi$
$983$	838159.			0.867400			0.433700	+	0.901057i	$0.357208\pi$
$984$	−770461.	−	126928.i	−0.795720	−	0.131089i
$985$			146126.i			0.150610i
$986$	7384.97	−	135556.i	0.00759617	−	0.139432i
$987$	−1.24529e6	+	1.24529e6i	−1.27831	+	1.27831i
$988$	−24653.9	+	225598.i	−0.0252564	+	0.231111i
$989$	104335.	−	104335.i	0.106668	−	0.106668i
$990$	178625.	+	199209.i	0.182251	+	0.203253i
$991$		−	817540.i		−	0.832457i	−0.909260	−	0.416228i	$-0.863352\pi$
$991$		−	817540.i		−	0.832457i	0.909260	−	0.416228i	$-0.136648\pi$
$992$	619567.	+	1.09918e6i	0.629601	+	1.11698i
$993$	−1.56221e6			−1.58432
$994$	1.27401e6	−	1.14237e6i	1.28944	−	1.15620i
$995$	126978.	+	126978.i	0.128258	+	0.128258i
$996$	765822.	+	83691.1i	0.771986	+	0.0843647i
$997$	−243046.	−	243046.i	−0.244511	−	0.244511i	0.574203	−	0.818713i	$-0.305312\pi$
$997$	−243046.	−	243046.i	−0.244511	−	0.244511i	−0.818713	+	0.574203i	$0.805312\pi$
$998$	−490680.	−	26731.9i	−0.492649	−	0.0268391i
$999$	−309534.			−0.310154

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	16.5.f.a.11.2	yes	14
3.2	odd	2		144.5.m.a.91.6		14
4.3	odd	2		64.5.f.a.15.7		14
8.3	odd	2		128.5.f.a.31.1		14
8.5	even	2		128.5.f.b.31.7		14
12.11	even	2		576.5.m.a.271.4		14
16.3	odd	4	inner	16.5.f.a.3.2	✓	14
16.5	even	4		128.5.f.a.95.1		14
16.11	odd	4		128.5.f.b.95.7		14
16.13	even	4		64.5.f.a.47.7		14
48.29	odd	4		576.5.m.a.559.4		14
48.35	even	4		144.5.m.a.19.6		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.5.f.a.3.2	✓	14	16.3	odd	4	inner
16.5.f.a.11.2	yes	14	1.1	even	1	trivial
64.5.f.a.15.7		14	4.3	odd	2
64.5.f.a.47.7		14	16.13	even	4
128.5.f.a.31.1		14	8.3	odd	2
128.5.f.a.95.1		14	16.5	even	4
128.5.f.b.31.7		14	8.5	even	2
128.5.f.b.95.7		14	16.11	odd	4
144.5.m.a.19.6		14	48.35	even	4
144.5.m.a.91.6		14	3.2	odd	2
576.5.m.a.271.4		14	12.11	even	2
576.5.m.a.559.4		14	48.29	odd	4

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:	\( N \)	\(=\)	\( 16 = 2^{4} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	16.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.97810 + 2.67038i) q^{2} +(-9.42589 - 9.42589i) q^{3} +(1.73818 - 15.9053i) q^{4} +(-2.84710 - 2.84710i) q^{5} +(53.2419 + 2.90058i) q^{6} -76.7794 q^{7} +(37.2967 + 52.0092i) q^{8} +96.6949i q^{9} +O(q^{10})\)	\(q+(-2.97810 + 2.67038i) q^{2} +(-9.42589 - 9.42589i) q^{3} +(1.73818 - 15.9053i) q^{4} +(-2.84710 - 2.84710i) q^{5} +(53.2419 + 2.90058i) q^{6} -76.7794 q^{7} +(37.2967 + 52.0092i) q^{8} +96.6949i q^{9} +(16.0818 + 0.876123i) q^{10} +(121.488 - 121.488i) q^{11} +(-166.306 + 133.538i) q^{12} +(27.1604 - 27.1604i) q^{13} +(228.657 - 205.030i) q^{14} +53.6729i q^{15} +(-249.957 - 55.2924i) q^{16} -88.0613 q^{17} +(-258.212 - 287.967i) q^{18} +(-261.112 - 261.112i) q^{19} +(-50.2328 + 40.3352i) q^{20} +(723.714 + 723.714i) q^{21} +(-37.3847 + 686.220i) q^{22} +93.4210 q^{23} +(138.678 - 841.788i) q^{24} -608.788i q^{25} +(-8.35791 + 153.415i) q^{26} +(147.938 - 147.938i) q^{27} +(-133.456 + 1221.20i) q^{28} +(272.522 - 272.522i) q^{29} +(-143.327 - 159.843i) q^{30} +1232.20i q^{31} +(892.050 - 502.814i) q^{32} -2290.26 q^{33} +(262.256 - 235.157i) q^{34} +(218.599 + 218.599i) q^{35} +(1537.96 + 168.073i) q^{36} +(-1046.16 - 1046.16i) q^{37} +(1474.89 + 80.3506i) q^{38} -512.021 q^{39} +(41.8880 - 254.263i) q^{40} -915.267i q^{41} +(-4087.88 - 222.705i) q^{42} +(1116.82 - 1116.82i) q^{43} +(-1721.13 - 2143.47i) q^{44} +(275.300 - 275.300i) q^{45} +(-278.217 + 249.469i) q^{46} +1720.70i q^{47} +(1834.89 + 2877.25i) q^{48} +3494.07 q^{49} +(1625.69 + 1813.03i) q^{50} +(830.056 + 830.056i) q^{51} +(-384.784 - 479.203i) q^{52} +(734.019 + 734.019i) q^{53} +(-45.5242 + 835.626i) q^{54} -691.775 q^{55} +(-2863.62 - 3993.23i) q^{56} +4922.43i q^{57} +(-83.8616 + 1539.33i) q^{58} +(-1202.73 + 1202.73i) q^{59} +(853.684 + 93.2930i) q^{60} +(580.221 - 580.221i) q^{61} +(-3290.44 - 3669.61i) q^{62} -7424.17i q^{63} +(-1313.91 + 3879.54i) q^{64} -154.657 q^{65} +(6820.62 - 6115.86i) q^{66} +(-1483.97 - 1483.97i) q^{67} +(-153.066 + 1400.64i) q^{68} +(-880.576 - 880.576i) q^{69} +(-1234.75 - 67.2681i) q^{70} +5571.73 q^{71} +(-5029.02 + 3606.40i) q^{72} -6615.21i q^{73} +(5909.20 + 321.929i) q^{74} +(-5738.37 + 5738.37i) q^{75} +(-4606.93 + 3699.21i) q^{76} +(-9327.75 + 9327.75i) q^{77} +(1524.85 - 1367.29i) q^{78} -5391.66i q^{79} +(554.231 + 869.077i) q^{80} +5043.39 q^{81} +(2444.11 + 2725.76i) q^{82} +(-2554.07 - 2554.07i) q^{83} +(12768.8 - 10252.9i) q^{84} +(250.719 + 250.719i) q^{85} +(-343.673 + 6308.34i) q^{86} -5137.52 q^{87} +(10849.6 + 1787.39i) q^{88} +10962.7i q^{89} +(-84.7166 + 1555.03i) q^{90} +(-2085.35 + 2085.35i) q^{91} +(162.382 - 1485.89i) q^{92} +(11614.6 - 11614.6i) q^{93} +(-4594.92 - 5124.42i) q^{94} +1486.83i q^{95} +(-13147.8 - 3668.90i) q^{96} +4713.20 q^{97} +(-10405.7 + 9330.48i) q^{98} +(11747.2 + 11747.2i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 2 q^{2} - 2 q^{3} - 8 q^{4} - 2 q^{5} + 64 q^{6} - 4 q^{7} - 92 q^{8}+O(q^{10}) \) 14 * q - 2 * q^2 - 2 * q^3 - 8 * q^4 - 2 * q^5 + 64 * q^6 - 4 * q^7 - 92 * q^8	\( 14 q - 2 q^{2} - 2 q^{3} - 8 q^{4} - 2 q^{5} + 64 q^{6} - 4 q^{7} - 92 q^{8} - 100 q^{10} + 94 q^{11} - 332 q^{12} - 2 q^{13} + 44 q^{14} - 168 q^{16} - 4 q^{17} + 1390 q^{18} - 706 q^{19} + 1900 q^{20} - 164 q^{21} + 900 q^{22} + 1148 q^{23} - 1872 q^{24} - 3416 q^{26} - 1664 q^{27} - 3784 q^{28} + 862 q^{29} - 3740 q^{30} + 3208 q^{32} - 4 q^{33} + 7508 q^{34} + 1340 q^{35} + 11468 q^{36} - 1826 q^{37} + 3568 q^{38} + 2684 q^{39} - 5144 q^{40} - 17064 q^{42} + 1694 q^{43} - 14636 q^{44} + 1410 q^{45} - 5316 q^{46} + 6888 q^{48} + 682 q^{49} + 20070 q^{50} - 3012 q^{51} + 20452 q^{52} - 482 q^{53} + 10784 q^{54} - 11780 q^{55} - 6952 q^{56} - 20456 q^{58} - 2786 q^{59} - 29920 q^{60} - 3778 q^{61} - 11472 q^{62} + 15808 q^{64} - 2020 q^{65} + 30148 q^{66} + 7998 q^{67} + 18032 q^{68} + 9628 q^{69} + 15296 q^{70} + 19964 q^{71} - 17708 q^{72} - 23780 q^{74} + 17570 q^{75} - 23996 q^{76} - 9508 q^{77} - 8052 q^{78} + 1384 q^{80} + 1454 q^{81} + 16016 q^{82} - 17282 q^{83} + 19624 q^{84} + 9948 q^{85} - 4796 q^{86} - 49284 q^{87} + 7288 q^{88} - 5416 q^{90} - 28036 q^{91} - 14632 q^{92} + 8896 q^{93} + 432 q^{94} + 6064 q^{96} - 4 q^{97} - 12246 q^{98} + 49214 q^{99}+O(q^{100}) \) 14 * q - 2 * q^2 - 2 * q^3 - 8 * q^4 - 2 * q^5 + 64 * q^6 - 4 * q^7 - 92 * q^8 - 100 * q^10 + 94 * q^11 - 332 * q^12 - 2 * q^13 + 44 * q^14 - 168 * q^16 - 4 * q^17 + 1390 * q^18 - 706 * q^19 + 1900 * q^20 - 164 * q^21 + 900 * q^22 + 1148 * q^23 - 1872 * q^24 - 3416 * q^26 - 1664 * q^27 - 3784 * q^28 + 862 * q^29 - 3740 * q^30 + 3208 * q^32 - 4 * q^33 + 7508 * q^34 + 1340 * q^35 + 11468 * q^36 - 1826 * q^37 + 3568 * q^38 + 2684 * q^39 - 5144 * q^40 - 17064 * q^42 + 1694 * q^43 - 14636 * q^44 + 1410 * q^45 - 5316 * q^46 + 6888 * q^48 + 682 * q^49 + 20070 * q^50 - 3012 * q^51 + 20452 * q^52 - 482 * q^53 + 10784 * q^54 - 11780 * q^55 - 6952 * q^56 - 20456 * q^58 - 2786 * q^59 - 29920 * q^60 - 3778 * q^61 - 11472 * q^62 + 15808 * q^64 - 2020 * q^65 + 30148 * q^66 + 7998 * q^67 + 18032 * q^68 + 9628 * q^69 + 15296 * q^70 + 19964 * q^71 - 17708 * q^72 - 23780 * q^74 + 17570 * q^75 - 23996 * q^76 - 9508 * q^77 - 8052 * q^78 + 1384 * q^80 + 1454 * q^81 + 16016 * q^82 - 17282 * q^83 + 19624 * q^84 + 9948 * q^85 - 4796 * q^86 - 49284 * q^87 + 7288 * q^88 - 5416 * q^90 - 28036 * q^91 - 14632 * q^92 + 8896 * q^93 + 432 * q^94 + 6064 * q^96 - 4 * q^97 - 12246 * q^98 + 49214 * q^99

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