LMFDB - Embedded newform 105.3.c.a.71.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,3,Mod(71,105)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(105, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("105.71");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	105.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.86104277578$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 46x^{14} + 823x^{12} + 7252x^{10} + 32831x^{8} + 71486x^{6} + 60809x^{4} + 15680x^{2} + 576 $ x^16 + 46x^14 + 823x^12 + 7252x^10 + 32831x^8 + 71486x^6 + 60809x^4 + 15680*x^2 + 576
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{10}\cdot 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			71.13
Root			$2.60953i$ of defining polynomial
Character	$\chi$	$=$	105.71
Dual form			105.3.c.a.71.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.60953i q^{2} +(2.93192 - 0.635503i) q^{3} -2.80964 q^{4} +2.23607i q^{5} +(1.65836 + 7.65092i) q^{6} -2.64575 q^{7} +3.10627i q^{8} +(8.19227 - 3.72648i) q^{9} +O(q^{10})$	\(q+2.60953i q^{2} +(2.93192 - 0.635503i) q^{3} -2.80964 q^{4} +2.23607i q^{5} +(1.65836 + 7.65092i) q^{6} -2.64575 q^{7} +3.10627i q^{8} +(8.19227 - 3.72648i) q^{9} -5.83508 q^{10} +7.66806i q^{11} +(-8.23764 + 1.78553i) q^{12} +12.2825 q^{13} -6.90416i q^{14} +(1.42103 + 6.55597i) q^{15} -19.3445 q^{16} -28.0003i q^{17} +(9.72436 + 21.3780i) q^{18} -22.7197 q^{19} -6.28255i q^{20} +(-7.75712 + 1.68138i) q^{21} -20.0100 q^{22} -18.7912i q^{23} +(1.97405 + 9.10734i) q^{24} -5.00000 q^{25} +32.0517i q^{26} +(21.6509 - 16.1319i) q^{27} +7.43361 q^{28} -13.5398i q^{29} +(-17.1080 + 3.70821i) q^{30} +59.4153 q^{31} -38.0549i q^{32} +(4.87307 + 22.4821i) q^{33} +73.0675 q^{34} -5.91608i q^{35} +(-23.0174 + 10.4701i) q^{36} -28.7214 q^{37} -59.2878i q^{38} +(36.0114 - 7.80559i) q^{39} -6.94584 q^{40} +11.5277i q^{41} +(-4.38761 - 20.2424i) q^{42} -4.45594 q^{43} -21.5445i q^{44} +(8.33267 + 18.3185i) q^{45} +49.0362 q^{46} -6.20599i q^{47} +(-56.7164 + 12.2935i) q^{48} +7.00000 q^{49} -13.0476i q^{50} +(-17.7942 - 82.0944i) q^{51} -34.5095 q^{52} -38.3577i q^{53} +(42.0968 + 56.4986i) q^{54} -17.1463 q^{55} -8.21843i q^{56} +(-66.6124 + 14.4384i) q^{57} +35.3325 q^{58} +106.375i q^{59} +(-3.99258 - 18.4199i) q^{60} -55.5951 q^{61} +155.046i q^{62} +(-21.6747 + 9.85934i) q^{63} +21.9274 q^{64} +27.4646i q^{65} +(-58.6677 + 12.7164i) q^{66} -87.8140 q^{67} +78.6707i q^{68} +(-11.9419 - 55.0942i) q^{69} +15.4382 q^{70} +29.0934i q^{71} +(11.5755 + 25.4475i) q^{72} +0.585358 q^{73} -74.9494i q^{74} +(-14.6596 + 3.17751i) q^{75} +63.8343 q^{76} -20.2878i q^{77} +(20.3689 + 93.9728i) q^{78} +7.71590 q^{79} -43.2556i q^{80} +(53.2267 - 61.0567i) q^{81} -30.0819 q^{82} -62.0031i q^{83} +(21.7947 - 4.72408i) q^{84} +62.6105 q^{85} -11.6279i q^{86} +(-8.60458 - 39.6976i) q^{87} -23.8191 q^{88} +150.739i q^{89} +(-47.8026 + 21.7443i) q^{90} -32.4966 q^{91} +52.7965i q^{92} +(174.201 - 37.7586i) q^{93} +16.1947 q^{94} -50.8029i q^{95} +(-24.1840 - 111.574i) q^{96} -36.3478 q^{97} +18.2667i q^{98} +(28.5749 + 62.8188i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{3} - 28 q^{4} - 28 q^{6} + 22 q^{9}+O(q^{10}) $ 16 * q + 8 * q^3 - 28 * q^4 - 28 * q^6 + 22 * q^9	$ 16 q + 8 q^{3} - 28 q^{4} - 28 q^{6} + 22 q^{9} - 20 q^{10} + 12 q^{12} + 10 q^{15} + 92 q^{16} - 52 q^{18} - 16 q^{19} - 14 q^{21} + 16 q^{22} + 128 q^{24} - 80 q^{25} - 148 q^{27} + 112 q^{28} + 80 q^{30} - 72 q^{31} - 4 q^{33} - 176 q^{34} - 76 q^{36} - 40 q^{37} + 90 q^{39} - 60 q^{40} + 280 q^{43} + 40 q^{45} + 72 q^{46} - 172 q^{48} + 112 q^{49} + 38 q^{51} - 88 q^{52} + 208 q^{54} + 80 q^{55} - 36 q^{57} - 24 q^{58} - 80 q^{60} - 56 q^{61} - 56 q^{63} - 44 q^{64} - 260 q^{66} - 120 q^{67} + 60 q^{69} + 376 q^{72} - 208 q^{73} - 40 q^{75} + 144 q^{76} - 228 q^{78} - 204 q^{79} + 458 q^{81} - 384 q^{82} - 84 q^{84} + 100 q^{85} - 324 q^{87} + 168 q^{88} - 160 q^{90} - 28 q^{91} + 108 q^{93} + 984 q^{94} + 40 q^{96} + 728 q^{97} - 166 q^{99}+O(q^{100}) $ 16 * q + 8 * q^3 - 28 * q^4 - 28 * q^6 + 22 * q^9 - 20 * q^10 + 12 * q^12 + 10 * q^15 + 92 * q^16 - 52 * q^18 - 16 * q^19 - 14 * q^21 + 16 * q^22 + 128 * q^24 - 80 * q^25 - 148 * q^27 + 112 * q^28 + 80 * q^30 - 72 * q^31 - 4 * q^33 - 176 * q^34 - 76 * q^36 - 40 * q^37 + 90 * q^39 - 60 * q^40 + 280 * q^43 + 40 * q^45 + 72 * q^46 - 172 * q^48 + 112 * q^49 + 38 * q^51 - 88 * q^52 + 208 * q^54 + 80 * q^55 - 36 * q^57 - 24 * q^58 - 80 * q^60 - 56 * q^61 - 56 * q^63 - 44 * q^64 - 260 * q^66 - 120 * q^67 + 60 * q^69 + 376 * q^72 - 208 * q^73 - 40 * q^75 + 144 * q^76 - 228 * q^78 - 204 * q^79 + 458 * q^81 - 384 * q^82 - 84 * q^84 + 100 * q^85 - 324 * q^87 + 168 * q^88 - 160 * q^90 - 28 * q^91 + 108 * q^93 + 984 * q^94 + 40 * q^96 + 728 * q^97 - 166 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$1$	$1$	$-1$

Coefficient data

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

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

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

$2$			2.60953i			1.30476i	0.757890	+	0.652382i	$0.226230\pi$
$2$			2.60953i			1.30476i	−0.757890	+	0.652382i	$0.773770\pi$
$3$	2.93192	−	0.635503i	0.977306	−	0.211834i
$3$	2.93192	−	0.635503i	0.977306	−	0.211834i
$4$	−2.80964			−0.702410
$5$			2.23607i			0.447214i
$5$			2.23607i			0.447214i
$6$	1.65836	+	7.65092i	0.276394	+	1.27515i
$7$	−2.64575			−0.377964
$7$	−2.64575			−0.377964
$8$			3.10627i			0.388284i
$9$	8.19227	−	3.72648i	0.910253	−	0.414053i
$10$	−5.83508			−0.583508
$11$			7.66806i			0.697096i	0.937291	+	0.348548i	$0.113325\pi$
$11$			7.66806i			0.697096i	−0.937291	+	0.348548i	$0.886675\pi$
$12$	−8.23764	+	1.78553i	−0.686470	+	0.148795i
$13$	12.2825			0.944811			0.472406	−	0.881381i	$-0.343386\pi$
$13$	12.2825			0.944811			0.472406	+	0.881381i	$0.343386\pi$
$14$		−	6.90416i		−	0.493155i
$15$	1.42103	+	6.55597i	0.0947351	+	0.437064i
$16$	−19.3445			−1.20903
$17$		−	28.0003i		−	1.64707i	−0.567262	−	0.823537i	$-0.691997\pi$
$17$		−	28.0003i		−	1.64707i	0.567262	−	0.823537i	$-0.308003\pi$
$18$	9.72436	+	21.3780i	0.540242	+	1.18767i
$19$	−22.7197			−1.19578			−0.597888	−	0.801580i	$-0.703993\pi$
$19$	−22.7197			−1.19578			−0.597888	+	0.801580i	$0.703993\pi$
$20$		−	6.28255i		−	0.314127i
$21$	−7.75712	+	1.68138i	−0.369387	+	0.0800658i
$22$	−20.0100			−0.909546
$23$		−	18.7912i		−	0.817008i	−0.912756	−	0.408504i	$-0.866051\pi$
$23$		−	18.7912i		−	0.817008i	0.912756	−	0.408504i	$-0.133949\pi$
$24$	1.97405	+	9.10734i	0.0822519	+	0.379472i
$25$	−5.00000			−0.200000
$26$			32.0517i			1.23276i
$27$	21.6509	−	16.1319i	0.801884	−	0.597479i
$28$	7.43361			0.265486
$29$		−	13.5398i		−	0.466890i	−0.972370	−	0.233445i	$-0.925000\pi$
$29$		−	13.5398i		−	0.466890i	0.972370	−	0.233445i	$-0.0749999\pi$
$30$	−17.1080	+	3.70821i	−0.570266	+	0.123607i
$31$	59.4153			1.91662			0.958311	−	0.285727i	$-0.0922350\pi$
$31$	59.4153			1.91662			0.958311	+	0.285727i	$0.0922350\pi$
$32$		−	38.0549i		−	1.18922i
$33$	4.87307	+	22.4821i	0.147669	+	0.681276i
$34$	73.0675			2.14904
$35$		−	5.91608i		−	0.169031i
$36$	−23.0174	+	10.4701i	−0.639371	+	0.290835i
$37$	−28.7214			−0.776255			−0.388127	−	0.921606i	$-0.626878\pi$
$37$	−28.7214			−0.776255			−0.388127	+	0.921606i	$0.626878\pi$
$38$		−	59.2878i		−	1.56020i
$39$	36.0114	−	7.80559i	0.923369	−	0.200143i
$40$	−6.94584			−0.173646
$41$			11.5277i			0.281164i	0.990069	+	0.140582i	$0.0448973\pi$
$41$			11.5277i			0.281164i	−0.990069	+	0.140582i	$0.955103\pi$
$42$	−4.38761	−	20.2424i	−0.104467	−	0.481963i
$43$	−4.45594			−0.103627			−0.0518133	−	0.998657i	$-0.516500\pi$
$43$	−4.45594			−0.103627			−0.0518133	+	0.998657i	$0.516500\pi$
$44$		−	21.5445i		−	0.489648i
$45$	8.33267	+	18.3185i	0.185170	+	0.407077i
$46$	49.0362			1.06600
$47$		−	6.20599i		−	0.132042i	−0.997818	−	0.0660211i	$-0.978970\pi$
$47$		−	6.20599i		−	0.132042i	0.997818	−	0.0660211i	$-0.0210305\pi$
$48$	−56.7164	+	12.2935i	−1.18159	+	0.256114i
$49$	7.00000			0.142857
$50$		−	13.0476i		−	0.260953i
$51$	−17.7942	−	82.0944i	−0.348907	−	1.60970i
$52$	−34.5095			−0.663645
$53$		−	38.3577i		−	0.723730i	−0.932231	−	0.361865i	$-0.882140\pi$
$53$		−	38.3577i		−	0.723730i	0.932231	−	0.361865i	$-0.117860\pi$
$54$	42.0968	+	56.4986i	0.779570	+	1.04627i
$55$	−17.1463			−0.311751
$56$		−	8.21843i		−	0.146758i
$57$	−66.6124	+	14.4384i	−1.16864	+	0.253306i
$58$	35.3325			0.609181
$59$			106.375i			1.80297i	0.432810	+	0.901485i	$0.357522\pi$
$59$			106.375i			1.80297i	−0.432810	+	0.901485i	$0.642478\pi$
$60$	−3.99258	−	18.4199i	−0.0665429	−	0.306999i
$61$	−55.5951			−0.911395			−0.455698	−	0.890135i	$-0.650610\pi$
$61$	−55.5951			−0.911395			−0.455698	+	0.890135i	$0.650610\pi$
$62$			155.046i			2.50074i
$63$	−21.6747	+	9.85934i	−0.344043	+	0.156497i
$64$	21.9274			0.342616
$65$			27.4646i			0.422532i
$66$	−58.6677	+	12.7164i	−0.888905	+	0.192673i
$67$	−87.8140			−1.31066			−0.655329	−	0.755344i	$-0.727470\pi$
$67$	−87.8140			−1.31066			−0.655329	+	0.755344i	$0.727470\pi$
$68$			78.6707i			1.15692i
$69$	−11.9419	−	55.0942i	−0.173070	−	0.798467i
$70$	15.4382			0.220545
$71$			29.0934i			0.409766i	0.978786	+	0.204883i	$0.0656814\pi$
$71$			29.0934i			0.409766i	−0.978786	+	0.204883i	$0.934319\pi$
$72$	11.5755	+	25.4475i	0.160770	+	0.353437i
$73$	0.585358			0.00801860			0.00400930	−	0.999992i	$-0.498724\pi$
$73$	0.585358			0.00801860			0.00400930	+	0.999992i	$0.498724\pi$
$74$		−	74.9494i		−	1.01283i
$75$	−14.6596	+	3.17751i	−0.195461	+	0.0423668i
$76$	63.8343			0.839925
$77$		−	20.2878i		−	0.263478i
$78$	20.3689	+	93.9728i	0.261140	+	1.20478i
$79$	7.71590			0.0976697			0.0488348	−	0.998807i	$-0.484449\pi$
$79$	7.71590			0.0976697			0.0488348	+	0.998807i	$0.484449\pi$
$80$		−	43.2556i		−	0.540695i
$81$	53.2267	−	61.0567i	0.657119	−	0.753786i
$82$	−30.0819			−0.366853
$83$		−	62.0031i		−	0.747026i	−0.927625	−	0.373513i	$-0.878153\pi$
$83$		−	62.0031i		−	0.747026i	0.927625	−	0.373513i	$-0.121847\pi$
$84$	21.7947	−	4.72408i	0.259461	−	0.0562390i
$85$	62.6105			0.736594
$86$		−	11.6279i		−	0.135208i
$87$	−8.60458	−	39.6976i	−0.0989033	−	0.456294i
$88$	−23.8191			−0.270672
$89$			150.739i			1.69370i	0.531835	+	0.846848i	$0.321503\pi$
$89$			150.739i			1.69370i	−0.531835	+	0.846848i	$0.678497\pi$
$90$	−47.8026	+	21.7443i	−0.531140	+	0.241604i
$91$	−32.4966			−0.357105
$92$			52.7965i			0.573875i
$93$	174.201	−	37.7586i	1.87313	−	0.406006i
$94$	16.1947			0.172284
$95$		−	50.8029i		−	0.534767i
$96$	−24.1840	−	111.574i	−0.251916	−	1.16223i
$97$	−36.3478			−0.374719			−0.187360	−	0.982291i	$-0.559993\pi$
$97$	−36.3478			−0.374719			−0.187360	+	0.982291i	$0.559993\pi$
$98$			18.2667i			0.186395i
$99$	28.5749	+	62.8188i	0.288635	+	0.634534i
$100$	14.0482			0.140482
$101$		−	89.3548i		−	0.884701i	−0.896842	−	0.442351i	$-0.854145\pi$
$101$		−	89.3548i		−	0.884701i	0.896842	−	0.442351i	$-0.145855\pi$
$102$	214.228	−	46.4346i	2.10027	−	0.455241i
$103$	90.8104			0.881654			0.440827	−	0.897592i	$-0.354685\pi$
$103$	90.8104			0.881654			0.440827	+	0.897592i	$0.354685\pi$
$104$			38.1530i			0.366855i
$105$	−3.75968	−	17.3455i	−0.0358065	−	0.165195i
$106$	100.095			0.944297
$107$			166.020i			1.55159i	0.630988	+	0.775793i	$0.282650\pi$
$107$			166.020i			1.55159i	−0.630988	+	0.775793i	$0.717350\pi$
$108$	−60.8312	+	45.3250i	−0.563252	+	0.419676i
$109$	−198.692			−1.82287			−0.911433	−	0.411449i	$-0.865023\pi$
$109$	−198.692			−1.82287			−0.911433	+	0.411449i	$0.865023\pi$
$110$		−	44.7438i		−	0.406761i
$111$	−84.2088	+	18.2525i	−0.758638	+	0.164437i
$112$	51.1807			0.456970
$113$		−	28.0198i		−	0.247963i	−0.992285	−	0.123981i	$-0.960434\pi$
$113$		−	28.0198i		−	0.247963i	0.992285	−	0.123981i	$-0.0395663\pi$
$114$	−37.6775	−	173.827i	−0.330505	−	1.52480i
$115$	42.0184			0.365377
$116$			38.0420i			0.327948i
$117$	100.622	−	45.7707i	0.860017	−	0.391202i
$118$	−277.589			−2.35245
$119$			74.0817i			0.622536i
$120$	−20.3646	+	4.41410i	−0.169705	+	0.0367842i
$121$	62.2009			0.514057
$122$		−	145.077i		−	1.18916i
$123$	7.32589	+	33.7983i	0.0595601	+	0.274783i
$124$	−166.936			−1.34626
$125$		−	11.1803i		−	0.0894427i
$126$	−25.7282	−	56.5608i	−0.204192	−	0.448895i
$127$	−90.0147			−0.708777			−0.354388	−	0.935098i	$-0.615311\pi$
$127$	−90.0147			−0.708777			−0.354388	+	0.935098i	$0.615311\pi$
$128$		−	94.9993i		−	0.742182i
$129$	−13.0645	+	2.83176i	−0.101275	+	0.0219517i
$130$	−71.6697			−0.551305
$131$			170.091i			1.29841i	0.760615	+	0.649203i	$0.224897\pi$
$131$			170.091i			1.29841i	−0.760615	+	0.649203i	$0.775103\pi$
$132$	−13.6916	−	63.1667i	−0.103724	−	0.478535i
$133$	60.1107			0.451961
$134$		−	229.153i		−	1.71010i
$135$	36.0721	+	48.4128i	0.267201	+	0.358614i
$136$	86.9765			0.639533
$137$			1.90559i			0.0139094i	0.999976	+	0.00695470i	$0.00221377\pi$
$137$			1.90559i			0.0139094i	−0.999976	+	0.00695470i	$0.997786\pi$
$138$	143.770	−	31.1626i	1.04181	−	0.225816i
$139$	21.2901			0.153167			0.0765833	−	0.997063i	$-0.475599\pi$
$139$	21.2901			0.153167			0.0765833	+	0.997063i	$0.475599\pi$
$140$			16.6221i			0.118729i
$141$	−3.94392	−	18.1954i	−0.0279711	−	0.129046i
$142$	−75.9201			−0.534648
$143$			94.1832i			0.658624i
$144$	−158.475	+	72.0868i	−1.10052	+	0.500603i
$145$	30.2759			0.208800
$146$			1.52751i			0.0104624i
$147$	20.5234	−	4.44852i	0.139615	−	0.0302620i
$148$	80.6969			0.545249
$149$		−	234.799i		−	1.57583i	−0.615781	−	0.787917i	$-0.711159\pi$
$149$		−	234.799i		−	1.57583i	0.615781	−	0.787917i	$-0.288841\pi$
$150$	−8.29181	−	38.2546i	−0.0552787	−	0.255031i
$151$	−40.8547			−0.270561			−0.135280	−	0.990807i	$-0.543193\pi$
$151$	−40.8547			−0.270561			−0.135280	+	0.990807i	$0.543193\pi$
$152$		−	70.5737i		−	0.464301i
$153$	−104.342	−	229.386i	−0.681977	−	1.49925i
$154$	52.9415			0.343776
$155$			132.857i			0.857140i
$156$	−101.179	+	21.9309i	−0.648584	+	0.140583i
$157$	232.269			1.47942			0.739711	−	0.672924i	$-0.234962\pi$
$157$	232.269			1.47942			0.739711	+	0.672924i	$0.234962\pi$
$158$			20.1349i			0.127436i
$159$	−24.3764	−	112.462i	−0.153311	−	0.707305i
$160$	85.0933			0.531833
$161$			49.7168i			0.308800i
$162$	159.329	+	138.897i	0.983514	+	0.857386i
$163$	−12.6645			−0.0776964			−0.0388482	−	0.999245i	$-0.512369\pi$
$163$	−12.6645			−0.0776964			−0.0388482	+	0.999245i	$0.512369\pi$
$164$		−	32.3888i		−	0.197492i
$165$	−50.2715	+	10.8965i	−0.304676	+	0.0660395i
$166$	161.799			0.974693
$167$			56.1313i			0.336116i	0.985777	+	0.168058i	$0.0537495\pi$
$167$			56.1313i			0.336116i	−0.985777	+	0.168058i	$0.946250\pi$
$168$	−5.22283	−	24.0958i	−0.0310883	−	0.143427i
$169$	−18.1391			−0.107332
$170$			163.384i			0.961082i
$171$	−186.126	+	84.6646i	−1.08846	+	0.495115i
$172$	12.5196			0.0727884
$173$			128.913i			0.745164i	0.927999	+	0.372582i	$0.121528\pi$
$173$			128.913i			0.745164i	−0.927999	+	0.372582i	$0.878472\pi$
$174$	103.592	−	22.4539i	0.595357	−	0.129045i
$175$	13.2288			0.0755929
$176$		−	148.335i		−	0.842810i
$177$	67.6017	+	311.883i	0.381931	+	1.76205i
$178$	−393.358			−2.20987
$179$			326.323i			1.82303i	0.411263	+	0.911517i	$0.365088\pi$
$179$			326.323i			1.82303i	−0.411263	+	0.911517i	$0.634912\pi$
$180$	−23.4118	−	51.4684i	−0.130066	−	0.285935i
$181$	89.6235			0.495158			0.247579	−	0.968868i	$-0.420365\pi$
$181$	89.6235			0.495158			0.247579	+	0.968868i	$0.420365\pi$
$182$		−	84.8007i		−	0.465938i
$183$	−163.000	+	35.3308i	−0.890712	+	0.193065i
$184$	58.3706			0.317232
$185$		−	64.2230i		−	0.347152i
$186$	98.5321	+	454.582i	0.529742	+	2.44399i
$187$	214.708			1.14817
$188$			17.4366i			0.0927479i
$189$	−57.2828	+	42.6811i	−0.303084	+	0.225826i
$190$	132.572			0.697745
$191$			190.367i			0.996687i	0.866980	+	0.498344i	$0.166058\pi$
$191$			190.367i			0.996687i	−0.866980	+	0.498344i	$0.833942\pi$
$192$	64.2893	−	13.9349i	0.334840	−	0.0725777i
$193$	282.311			1.46275			0.731374	−	0.681976i	$-0.238879\pi$
$193$	282.311			1.46275			0.731374	+	0.681976i	$0.238879\pi$
$194$		−	94.8506i		−	0.488921i
$195$	17.4538	+	80.5239i	0.0895068	+	0.412943i
$196$	−19.6675			−0.100344
$197$		−	360.744i		−	1.83119i	−0.402104	−	0.915594i	$-0.631721\pi$
$197$		−	360.744i		−	1.83119i	0.402104	−	0.915594i	$-0.368279\pi$
$198$	−163.928	+	74.5670i	−0.827917	+	0.376601i
$199$	202.528			1.01773			0.508864	−	0.860847i	$-0.330066\pi$
$199$	202.528			1.01773			0.508864	+	0.860847i	$0.330066\pi$
$200$		−	15.5314i		−	0.0776569i
$201$	−257.463	+	55.8060i	−1.28091	+	0.277642i
$202$	233.174			1.15433
$203$			35.8230i			0.176468i
$204$	49.9954	+	230.656i	0.245076	+	1.13067i
$205$	−25.7768			−0.125740
$206$			236.972i			1.15035i
$207$	−70.0250	−	153.943i	−0.338285	−	0.743684i
$208$	−237.599			−1.14230
$209$		−	174.216i		−	0.833570i
$210$	45.2635	−	9.81100i	0.215540	−	0.0467191i
$211$	−368.946			−1.74856			−0.874279	−	0.485424i	$-0.838665\pi$
$211$	−368.946			−1.74856			−0.874279	+	0.485424i	$0.838665\pi$
$212$			107.771i			0.508355i
$213$	18.4889	+	85.2994i	0.0868025	+	0.400467i
$214$	−433.233			−2.02445
$215$		−	9.96379i		−	0.0463432i
$216$	50.1102	+	67.2536i	0.231992	+	0.311359i
$217$	−157.198			−0.724415
$218$		−	518.493i		−	2.37841i
$219$	1.71622	−	0.371997i	0.00783663	−	0.00169861i
$220$	48.1750			0.218977
$221$		−	343.914i		−	1.55617i
$222$	−47.6305	−	219.745i	−0.214552	−	0.989844i
$223$	143.161			0.641975			0.320988	−	0.947083i	$-0.395985\pi$
$223$	143.161			0.641975			0.320988	+	0.947083i	$0.395985\pi$
$224$			100.684i			0.449481i
$225$	−40.9614	+	18.6324i	−0.182051	+	0.0828107i
$226$	73.1184			0.323533
$227$		−	149.110i		−	0.656870i	−0.944527	−	0.328435i	$-0.893479\pi$
$227$		−	149.110i		−	0.656870i	0.944527	−	0.328435i	$-0.106521\pi$
$228$	187.157	−	40.5669i	0.820863	−	0.177925i
$229$	−245.184			−1.07067			−0.535337	−	0.844639i	$-0.679815\pi$
$229$	−245.184			−1.07067			−0.535337	+	0.844639i	$0.679815\pi$
$230$			109.648i			0.476731i
$231$	−12.8929	−	59.4821i	−0.0558136	−	0.257498i
$232$	42.0584			0.181286
$233$			226.865i			0.973671i	0.873494	+	0.486836i	$0.161849\pi$
$233$			226.865i			0.973671i	−0.873494	+	0.486836i	$0.838151\pi$
$234$	119.440	+	262.576i	0.510427	+	1.12212i
$235$	13.8770			0.0590511
$236$		−	298.876i		−	1.26643i
$237$	22.6224	−	4.90348i	0.0954531	−	0.0206898i
$238$	−193.318			−0.812262
$239$			34.6432i			0.144950i	0.997370	+	0.0724752i	$0.0230898\pi$
$239$			34.6432i			0.144950i	−0.997370	+	0.0724752i	$0.976910\pi$
$240$	−27.4890	−	126.822i	−0.114538	−	0.528424i
$241$	−44.5519			−0.184863			−0.0924314	−	0.995719i	$-0.529464\pi$
$241$	−44.5519			−0.184863			−0.0924314	+	0.995719i	$0.529464\pi$
$242$			162.315i			0.670723i
$243$	117.255	−	212.839i	0.482529	−	0.875880i
$244$	156.202			0.640173
$245$			15.6525i			0.0638877i
$246$	−88.1977	+	19.1171i	−0.358527	+	0.0777119i
$247$	−279.056			−1.12978
$248$			184.560i			0.744194i
$249$	−39.4031	−	181.788i	−0.158246	−	0.730072i
$250$	29.1754			0.116702
$251$		−	399.865i		−	1.59309i	−0.604582	−	0.796543i	$-0.706660\pi$
$251$		−	399.865i		−	1.59309i	0.604582	−	0.796543i	$-0.293340\pi$
$252$	60.8982	−	27.7012i	0.241659	−	0.109925i
$253$	144.092			0.569533
$254$		−	234.896i		−	0.924787i
$255$	183.569	−	39.7891i	0.719877	−	0.156036i
$256$	335.613			1.31099
$257$		−	403.137i		−	1.56862i	−0.620366	−	0.784312i	$-0.713016\pi$
$257$		−	403.137i		−	1.56862i	0.620366	−	0.784312i	$-0.286984\pi$
$258$	−7.38957	−	34.0921i	−0.0286417	−	0.132140i
$259$	75.9897			0.293397
$260$		−	77.1657i		−	0.296791i
$261$	−50.4558	−	110.922i	−0.193317	−	0.424988i
$262$	−443.858			−1.69411
$263$			256.235i			0.974278i	0.873325	+	0.487139i	$0.161959\pi$
$263$			256.235i			0.974278i	−0.873325	+	0.487139i	$0.838041\pi$
$264$	−69.8356	+	15.1371i	−0.264529	+	0.0573375i
$265$	85.7704			0.323662
$266$			156.861i			0.589702i
$267$	95.7950	+	441.954i	0.358783	+	1.65526i
$268$	246.726			0.920619
$269$		−	25.1063i		−	0.0933321i	−0.998911	−	0.0466661i	$-0.985140\pi$
$269$		−	25.1063i		−	0.0933321i	0.998911	−	0.0466661i	$-0.0148597\pi$
$270$	−126.335	+	94.1312i	−0.467906	+	0.348634i
$271$	254.970			0.940850			0.470425	−	0.882440i	$-0.344101\pi$
$271$	254.970			0.940850			0.470425	+	0.882440i	$0.344101\pi$
$272$			541.651i			1.99136i
$273$	−95.2772	+	20.6516i	−0.349001	+	0.0756470i
$274$	−4.97269			−0.0181485
$275$		−	38.3403i		−	0.139419i
$276$	33.5523	+	154.795i	0.121566	+	0.560851i
$277$	269.497			0.972912			0.486456	−	0.873705i	$-0.338289\pi$
$277$	269.497			0.972912			0.486456	+	0.873705i	$0.338289\pi$
$278$			55.5572i			0.199846i
$279$	486.746	−	221.410i	1.74461	−	0.793584i
$280$	18.3770			0.0656320
$281$		−	218.995i		−	0.779342i	−0.920954	−	0.389671i	$-0.872589\pi$
$281$		−	218.995i		−	0.779342i	0.920954	−	0.389671i	$-0.127411\pi$
$282$	47.4815	−	10.2918i	0.168374	−	0.0364957i
$283$	−201.024			−0.710333			−0.355166	−	0.934803i	$-0.615576\pi$
$283$	−201.024			−0.710333			−0.355166	+	0.934803i	$0.615576\pi$
$284$		−	81.7420i		−	0.287824i
$285$	−32.2853	−	148.950i	−0.113282	−	0.522631i
$286$	−245.774			−0.859349
$287$		−	30.4995i		−	0.106270i
$288$	−141.811	−	311.756i	−0.492399	−	1.08249i
$289$	−495.015			−1.71285
$290$			79.0059i			0.272434i
$291$	−106.569	+	23.0991i	−0.366215	+	0.0793784i
$292$	−1.64465			−0.00563235
$293$			9.05359i			0.0308996i	0.999881	+	0.0154498i	$0.00491803\pi$
$293$			9.05359i			0.0308996i	−0.999881	+	0.0154498i	$0.995082\pi$
$294$	11.6085	+	53.5565i	0.0394848	+	0.182165i
$295$	−237.862			−0.806313
$296$		−	89.2166i		−	0.301407i
$297$	123.701	+	166.020i	0.416501	+	0.558990i
$298$	612.716			2.05609
$299$		−	230.804i		−	0.771919i
$300$	41.1882	−	8.92767i	0.137294	−	0.0297589i
$301$	11.7893			0.0391672
$302$		−	106.611i		−	0.353018i
$303$	−56.7852	−	261.981i	−0.187410	−	0.864623i
$304$	439.501			1.44573
$305$		−	124.314i		−	0.407588i
$306$	598.589	−	272.285i	1.95617	−	0.889819i
$307$	−483.874			−1.57614			−0.788069	−	0.615587i	$-0.788919\pi$
$307$	−483.874			−1.57614			−0.788069	+	0.615587i	$0.788919\pi$
$308$			57.0014i			0.185069i
$309$	266.248	−	57.7102i	0.861645	−	0.186764i
$310$	−346.693			−1.11837
$311$		−	448.237i		−	1.44128i	−0.693311	−	0.720638i	$-0.743849\pi$
$311$		−	448.237i		−	1.44128i	0.693311	−	0.720638i	$-0.256151\pi$
$312$	24.2463	+	111.861i	0.0777125	+	0.358530i
$313$	283.174			0.904711			0.452355	−	0.891838i	$-0.350584\pi$
$313$	283.174			0.904711			0.452355	+	0.891838i	$0.350584\pi$
$314$			606.114i			1.93030i
$315$	−22.0462	−	48.4661i	−0.0699878	−	0.153861i
$316$	−21.6789			−0.0686042
$317$			361.224i			1.13951i	0.821815	+	0.569754i	$0.192962\pi$
$317$			361.224i			1.13951i	−0.821815	+	0.569754i	$0.807038\pi$
$318$	293.472	−	63.6109i	0.922867	−	0.200034i
$319$	103.824			0.325467
$320$			49.0312i			0.153222i
$321$	105.506	+	486.756i	0.328679	+	1.51637i
$322$	−129.737			−0.402911
$323$			636.158i			1.96953i
$324$	−149.548	+	171.547i	−0.461568	+	0.529467i
$325$	−61.4127			−0.188962
$326$		−	33.0484i		−	0.101376i
$327$	−582.549	+	126.269i	−1.78150	+	0.386145i
$328$	−35.8083			−0.109172
$329$			16.4195i			0.0499073i
$330$	−28.4348	−	131.185i	−0.0861660	−	0.397530i
$331$	208.057			0.628572			0.314286	−	0.949328i	$-0.398235\pi$
$331$	208.057			0.628572			0.314286	+	0.949328i	$0.398235\pi$
$332$			174.207i			0.524719i
$333$	−235.294	+	107.030i	−0.706588	+	0.321411i
$334$	−146.476			−0.438552
$335$		−	196.358i		−	0.586144i
$336$	150.058	−	32.5255i	0.446600	−	0.0968019i
$337$	39.0812			0.115968			0.0579840	−	0.998318i	$-0.481533\pi$
$337$	39.0812			0.115968			0.0579840	+	0.998318i	$0.481533\pi$
$338$		−	47.3346i		−	0.140043i
$339$	−17.8066	−	82.1517i	−0.0525270	−	0.242335i
$340$	−175.913			−0.517391
$341$			455.600i			1.33607i
$342$	−220.935	−	485.702i	−0.646008	−	1.42018i
$343$	−18.5203			−0.0539949
$344$		−	13.8414i		−	0.0402366i
$345$	123.194	−	26.7028i	0.357085	−	0.0773994i
$346$	−336.403			−0.972264
$347$		−	187.611i		−	0.540666i	−0.962767	−	0.270333i	$-0.912866\pi$
$347$		−	187.611i		−	0.540666i	0.962767	−	0.270333i	$-0.0871339\pi$
$348$	24.1758	+	111.536i	0.0694707	+	0.320506i
$349$	−4.35036			−0.0124652			−0.00623261	−	0.999981i	$-0.501984\pi$
$349$	−4.35036			−0.0124652			−0.00623261	+	0.999981i	$0.501984\pi$
$350$			34.5208i			0.0986309i
$351$	265.928	−	198.141i	0.757629	−	0.564505i
$352$	291.807			0.828997
$353$		−	278.393i		−	0.788650i	−0.918971	−	0.394325i	$-0.870978\pi$
$353$		−	278.393i		−	0.788650i	0.918971	−	0.394325i	$-0.129022\pi$
$354$	−813.869	+	176.409i	−2.29906	+	0.498330i
$355$	−65.0548			−0.183253
$356$		−	423.522i		−	1.18967i
$357$	47.0791	+	217.201i	0.131874	+	0.608408i
$358$	−851.549			−2.37863
$359$			226.446i			0.630768i	0.948964	+	0.315384i	$0.102133\pi$
$359$			226.446i			0.630768i	−0.948964	+	0.315384i	$0.897867\pi$
$360$	−56.9022	+	25.8835i	−0.158062	+	0.0718987i
$361$	155.186			0.429878
$362$			233.875i			0.646064i
$363$	182.368	−	39.5288i	0.502391	−	0.108895i
$364$	91.3037			0.250834
$365$			1.30890i			0.00358603i
$366$	−92.1968	−	425.354i	−0.251904	−	1.16217i
$367$	129.536			0.352958			0.176479	−	0.984304i	$-0.443529\pi$
$367$	129.536			0.352958			0.176479	+	0.984304i	$0.443529\pi$
$368$			363.506i			0.987788i
$369$	42.9578	+	94.4382i	0.116417	+	0.255930i
$370$	167.592			0.452951
$371$			101.485i			0.273544i
$372$	−489.442	+	106.088i	−1.31570	+	0.285183i
$373$	−164.171			−0.440136			−0.220068	−	0.975485i	$-0.570628\pi$
$373$	−164.171			−0.440136			−0.220068	+	0.975485i	$0.570628\pi$
$374$			560.286i			1.49809i
$375$	−7.10513	−	32.7798i	−0.0189470	−	0.0874129i
$376$	19.2775			0.0512700
$377$		−	166.303i		−	0.441123i
$378$	−111.378	−	149.481i	−0.294650	−	0.395453i
$379$	649.992			1.71502			0.857509	−	0.514469i	$-0.172011\pi$
$379$	649.992			1.71502			0.857509	+	0.514469i	$0.172011\pi$
$380$			142.738i			0.375626i
$381$	−263.915	+	57.2045i	−0.692692	+	0.150143i
$382$	−496.769			−1.30044
$383$		−	198.134i		−	0.517322i	−0.965968	−	0.258661i	$-0.916719\pi$
$383$		−	198.134i		−	0.517322i	0.965968	−	0.258661i	$-0.0832813\pi$
$384$	−60.3723	−	278.530i	−0.157220	−	0.725339i
$385$	45.3648			0.117831
$386$			736.697i			1.90854i
$387$	−36.5043	+	16.6050i	−0.0943264	+	0.0429070i
$388$	102.124			0.263207
$389$		−	315.702i		−	0.811573i	−0.913968	−	0.405787i	$-0.866998\pi$
$389$		−	315.702i		−	0.811573i	0.913968	−	0.405787i	$-0.133002\pi$
$390$	−210.130	+	45.5463i	−0.538794	+	0.116785i
$391$	−526.158			−1.34567
$392$			21.7439i			0.0554692i
$393$	108.093	+	498.693i	0.275047	+	1.26894i
$394$	941.372			2.38927
$395$			17.2533i			0.0436792i
$396$	−80.2851	−	176.498i	−0.202740	−	0.445703i
$397$	242.935			0.611927			0.305963	−	0.952043i	$-0.401021\pi$
$397$	242.935			0.611927			0.305963	+	0.952043i	$0.401021\pi$
$398$			528.502i			1.32789i
$399$	176.240	−	38.2005i	0.441704	−	0.0957407i
$400$	96.7224			0.241806
$401$			774.089i			1.93040i	0.261519	+	0.965198i	$0.415777\pi$
$401$			774.089i			1.93040i	−0.261519	+	0.965198i	$0.584223\pi$
$402$	−145.627	−	671.858i	−0.362257	−	1.67129i
$403$	729.771			1.81085
$404$			251.055i			0.621423i
$405$	136.527	+	119.018i	0.337104	+	0.293873i
$406$	−93.4811			−0.230249
$407$		−	220.237i		−	0.541124i
$408$	255.008	−	55.2738i	0.625019	−	0.135475i
$409$	−366.249			−0.895475			−0.447738	−	0.894165i	$-0.647770\pi$
$409$	−366.249			−0.895475			−0.447738	+	0.894165i	$0.647770\pi$
$410$		−	67.2652i		−	0.164061i
$411$	1.21101	+	5.58703i	0.00294649	+	0.0135937i
$412$	−255.145			−0.619283
$413$		−	281.442i		−	0.681459i
$414$	401.718	−	182.732i	0.970333	−	0.441382i
$415$	138.643			0.334080
$416$		−	467.411i		−	1.12358i
$417$	62.4209	−	13.5299i	0.149690	−	0.0324459i
$418$	454.622			1.08761
$419$			383.434i			0.915118i	0.889179	+	0.457559i	$0.151276\pi$
$419$			383.434i			0.915118i	−0.889179	+	0.457559i	$0.848724\pi$
$420$	10.5634	+	48.7345i	0.0251509	+	0.116035i
$421$	98.5093			0.233989			0.116994	−	0.993133i	$-0.462674\pi$
$421$	98.5093			0.233989			0.116994	+	0.993133i	$0.462674\pi$
$422$		−	962.774i		−	2.28146i
$423$	−23.1265	−	50.8411i	−0.0546726	−	0.120192i
$424$	119.149			0.281013
$425$			140.001i			0.329415i
$426$	−222.591	+	48.2474i	−0.522515	+	0.113257i
$427$	147.091			0.344475
$428$		−	466.456i		−	1.08985i
$429$	59.8537	+	276.137i	0.139519	+	0.643677i
$430$	26.0008			0.0604670
$431$			245.841i			0.570397i	0.958468	+	0.285199i	$0.0920596\pi$
$431$			245.841i			0.570397i	−0.958468	+	0.285199i	$0.907940\pi$
$432$	−418.825	+	312.064i	−0.969502	+	0.722371i
$433$	−278.085			−0.642228			−0.321114	−	0.947041i	$-0.604057\pi$
$433$	−278.085			−0.642228			−0.321114	+	0.947041i	$0.604057\pi$
$434$		−	410.213i		−	0.945191i
$435$	88.7665	−	19.2404i	0.204061	−	0.0442309i
$436$	558.254			1.28040
$437$			426.931i			0.976958i
$438$	0.970736	+	4.47853i	0.00221629	+	0.0102250i
$439$	60.6447			0.138143			0.0690714	−	0.997612i	$-0.477996\pi$
$439$	60.6447			0.138143			0.0690714	+	0.997612i	$0.477996\pi$
$440$		−	53.2611i		−	0.121048i
$441$	57.3459	−	26.0854i	0.130036	−	0.0591505i
$442$	897.455			2.03044
$443$		−	256.250i		−	0.578442i	−0.957262	−	0.289221i	$-0.906604\pi$
$443$		−	256.250i		−	0.578442i	0.957262	−	0.289221i	$-0.0933963\pi$
$444$	236.597	−	51.2831i	0.532875	−	0.115502i
$445$	−337.062			−0.757444
$446$			373.582i			0.837627i
$447$	−149.216	−	688.412i	−0.333816	−	1.54007i
$448$	−58.0144			−0.129497
$449$		−	289.276i		−	0.644268i	−0.946694	−	0.322134i	$-0.895600\pi$
$449$		−	289.276i		−	0.644268i	0.946694	−	0.322134i	$-0.104400\pi$
$450$	−48.6218	−	106.890i	−0.108048	−	0.237533i
$451$	−88.3952			−0.195998
$452$			78.7255i			0.174172i
$453$	−119.782	+	25.9632i	−0.264420	+	0.0573140i
$454$	389.106			0.857061
$455$		−	72.6645i		−	0.159702i
$456$	−44.8498	−	206.916i	−0.0983548	−	0.453764i
$457$	−94.8088			−0.207459			−0.103730	−	0.994606i	$-0.533078\pi$
$457$	−94.8088			−0.207459			−0.103730	+	0.994606i	$0.533078\pi$
$458$		−	639.815i		−	1.39698i
$459$	−451.699	−	606.230i	−0.984093	−	1.32076i
$460$	−118.057			−0.256645
$461$		−	296.969i		−	0.644185i	−0.946708	−	0.322093i	$-0.895614\pi$
$461$		−	296.969i		−	0.644185i	0.946708	−	0.322093i	$-0.104386\pi$
$462$	155.220	−	33.6445i	0.335974	−	0.0728235i
$463$	−141.887			−0.306452			−0.153226	−	0.988191i	$-0.548966\pi$
$463$	−141.887			−0.306452			−0.153226	+	0.988191i	$0.548966\pi$
$464$			261.921i			0.564484i
$465$	84.4307	+	389.525i	0.181571	+	0.837687i
$466$	−592.012			−1.27041
$467$			380.503i			0.814782i	0.913254	+	0.407391i	$0.133561\pi$
$467$			380.503i			0.814782i	−0.913254	+	0.407391i	$0.866439\pi$
$468$	−282.712	+	128.599i	−0.604085	+	0.274785i
$469$	232.334			0.495382
$470$			36.2125i			0.0770478i
$471$	680.994	−	147.608i	1.44585	−	0.313392i
$472$	−330.431			−0.700065
$473$		−	34.1684i		−	0.0722377i
$474$	12.7958	+	59.0338i	0.0269953	+	0.124544i
$475$	113.599			0.239155
$476$		−	208.143i		−	0.437275i
$477$	−142.939	−	314.237i	−0.299663	−	0.658777i
$478$	−90.4023			−0.189126
$479$		−	706.128i		−	1.47417i	−0.675800	−	0.737085i	$-0.736202\pi$
$479$		−	706.128i		−	1.47417i	0.675800	−	0.737085i	$-0.263798\pi$
$480$	249.486	−	54.0770i	0.519764	−	0.112660i
$481$	−352.772			−0.733414
$482$		−	116.260i		−	0.241202i
$483$	31.5952	+	145.766i	0.0654144	+	0.301792i
$484$	−174.762			−0.361079
$485$		−	81.2761i		−	0.167580i
$486$	555.409	+	305.979i	1.14282	+	0.629586i
$487$	−349.704			−0.718077			−0.359039	−	0.933323i	$-0.616895\pi$
$487$	−349.704			−0.718077			−0.359039	+	0.933323i	$0.616895\pi$
$488$		−	172.694i		−	0.353880i
$489$	−37.1313	+	8.04833i	−0.0759331	+	0.0164588i
$490$	−40.8456			−0.0833583
$491$			508.712i			1.03607i	0.855358	+	0.518037i	$0.173337\pi$
$491$			508.712i			1.03607i	−0.855358	+	0.518037i	$0.826663\pi$
$492$	−20.5831	−	94.9611i	−0.0418356	−	0.193010i
$493$	−379.118			−0.769003
$494$		−	728.205i		−	1.47410i
$495$	−140.467	+	63.8954i	−0.283772	+	0.129082i
$496$	−1149.36			−2.31725
$497$		−	76.9739i		−	0.154877i
$498$	474.381	−	102.824i	0.952573	−	0.206473i
$499$	−579.897			−1.16212			−0.581059	−	0.813861i	$-0.697362\pi$
$499$	−579.897			−1.16212			−0.581059	+	0.813861i	$0.697362\pi$
$500$			31.4127i			0.0628255i
$501$	35.6716	+	164.572i	0.0712008	+	0.328488i
$502$	1043.46			2.07860
$503$		−	487.063i		−	0.968316i	−0.874980	−	0.484158i	$-0.839126\pi$
$503$		−	487.063i		−	0.968316i	0.874980	−	0.484158i	$-0.160874\pi$
$504$	−30.6258	−	67.3276i	−0.0607655	−	0.133587i
$505$	199.803			0.395650
$506$			376.012i			0.743107i
$507$	−53.1824	+	11.5275i	−0.104896	+	0.0227366i
$508$	252.909			0.497852
$509$			290.414i			0.570559i	0.958444	+	0.285279i	$0.0920864\pi$
$509$			290.414i			0.570559i	−0.958444	+	0.285279i	$0.907914\pi$
$510$	103.831	+	479.028i	0.203590	+	0.939271i
$511$	−1.54871			−0.00303075
$512$			495.795i			0.968349i
$513$	−491.902	+	366.513i	−0.958873	+	0.714451i
$514$	1052.00			2.04669
$515$			203.058i			0.394288i
$516$	36.7064	−	7.95624i	0.0711365	−	0.0154191i
$517$	47.5879			0.0920462
$518$			198.297i			0.382814i
$519$	81.9248	+	377.963i	0.157851	+	0.728253i
$520$	−85.3126			−0.164063
$521$		−	56.8190i		−	0.109058i	−0.998512	−	0.0545288i	$-0.982634\pi$
$521$		−	56.8190i		−	0.109058i	0.998512	−	0.0545288i	$-0.0173657\pi$
$522$	289.454	−	131.666i	0.554509	−	0.252234i
$523$	−734.288			−1.40399			−0.701996	−	0.712181i	$-0.747708\pi$
$523$	−734.288			−1.40399			−0.701996	+	0.712181i	$0.747708\pi$
$524$		−	477.895i		−	0.912014i
$525$	38.7856	−	8.40691i	0.0738774	−	0.0160132i
$526$	−668.653			−1.27120
$527$		−	1663.64i		−	3.15682i
$528$	−94.2670	−	434.905i	−0.178536	−	0.823683i
$529$	175.891			0.332497
$530$			223.820i			0.422302i
$531$	396.405	+	871.455i	0.746526	+	1.64116i
$532$	−168.890			−0.317462
$533$			141.590i			0.265647i
$534$	−1153.29	+	249.980i	−2.15972	+	0.468127i
$535$	−371.231			−0.693890
$536$		−	272.775i		−	0.508908i
$537$	207.379	+	956.752i	0.386181	+	1.78166i
$538$	65.5157			0.121776
$539$			53.6764i			0.0995852i
$540$	−101.350	−	136.023i	−0.187685	−	0.251894i
$541$	−293.749			−0.542973			−0.271487	−	0.962442i	$-0.587515\pi$
$541$	−293.749			−0.542973			−0.271487	+	0.962442i	$0.587515\pi$
$542$			665.352i			1.22759i
$543$	262.769	−	56.9560i	0.483920	−	0.104891i
$544$	−1065.55			−1.95873
$545$		−	444.290i		−	0.815210i
$546$	−53.8911	−	248.629i	−0.0987016	−	0.455364i
$547$	−475.819			−0.869870			−0.434935	−	0.900462i	$-0.643229\pi$
$547$	−475.819			−0.869870			−0.434935	+	0.900462i	$0.643229\pi$
$548$		−	5.35402i		−	0.00977011i
$549$	−455.450	+	207.174i	−0.829600	+	0.377366i
$550$	100.050			0.181909
$551$			307.621i			0.558295i
$552$	171.138	−	37.0947i	0.310032	−	0.0672005i
$553$	−20.4144			−0.0369157
$554$			703.259i			1.26942i
$555$	−40.8139	−	188.297i	−0.0735386	−	0.339273i
$556$	−59.8177			−0.107586
$557$			675.834i			1.21335i	0.794951	+	0.606673i	$0.207496\pi$
$557$			675.834i			1.21335i	−0.794951	+	0.606673i	$0.792504\pi$
$558$	577.776	+	1270.18i	1.03544	+	2.27631i
$559$	−54.7303			−0.0979076
$560$			114.443i			0.204363i
$561$	629.505	−	136.447i	1.12211	−	0.243221i
$562$	571.474			1.01686
$563$			358.056i			0.635979i	0.948094	+	0.317989i	$0.103008\pi$
$563$			358.056i			0.635979i	−0.948094	+	0.317989i	$0.896992\pi$
$564$	11.0810	+	51.1227i	0.0196472	+	0.0906430i
$565$	62.6541			0.110892
$566$		−	524.579i		−	0.926817i
$567$	−140.825	+	161.541i	−0.248368	+	0.284904i
$568$	−90.3721			−0.159106
$569$			112.663i			0.198002i	0.995087	+	0.0990012i	$0.0315648\pi$
$569$			112.663i			0.198002i	−0.995087	+	0.0990012i	$0.968435\pi$
$570$	388.689	−	84.2495i	0.681910	−	0.147806i
$571$	471.212			0.825240			0.412620	−	0.910903i	$-0.364614\pi$
$571$	471.212			0.825240			0.412620	+	0.910903i	$0.364614\pi$
$572$		−	264.621i		−	0.462624i
$573$	120.979	+	558.141i	0.211132	+	0.974068i
$574$	79.5893			0.138657
$575$			93.9560i			0.163402i
$576$	179.635	−	81.7120i	0.311867	−	0.141861i
$577$	596.106			1.03311			0.516556	−	0.856253i	$-0.327214\pi$
$577$	596.106			1.03311			0.516556	+	0.856253i	$0.327214\pi$
$578$		−	1291.76i		−	2.23487i
$579$	827.711	−	179.409i	1.42955	−	0.309860i
$580$	−85.0645			−0.146663
$581$			164.045i			0.282349i
$582$	−60.2778	−	278.094i	−0.103570	−	0.477825i
$583$	294.129			0.504509
$584$			1.81828i			0.00311350i
$585$	102.346	+	224.998i	0.174951	+	0.384611i
$586$	−23.6256			−0.0403167
$587$			867.003i			1.47701i	0.674249	+	0.738504i	$0.264467\pi$
$587$			867.003i			1.47701i	−0.674249	+	0.738504i	$0.735533\pi$
$588$	−57.6634	+	12.4987i	−0.0980671	+	0.0212564i
$589$	−1349.90			−2.29185
$590$		−	620.709i		−	1.05205i
$591$	−229.254	−	1057.67i	−0.387908	−	1.78963i
$592$	555.601			0.938515
$593$		−	374.280i		−	0.631164i	−0.948898	−	0.315582i	$-0.897800\pi$
$593$		−	374.280i		−	0.631164i	0.948898	−	0.315582i	$-0.102200\pi$
$594$	−433.234	+	322.800i	−0.729351	+	0.543435i
$595$	−165.652			−0.278406
$596$			659.702i			1.10688i
$597$	593.795	−	128.707i	0.994631	−	0.215589i
$598$	602.289			1.00717
$599$			317.149i			0.529463i	0.964322	+	0.264732i	$0.0852834\pi$
$599$			317.149i			0.529463i	−0.964322	+	0.264732i	$0.914717\pi$
$600$	−9.87023	−	45.5367i	−0.0164504	−	0.0758945i
$601$	888.373			1.47816			0.739079	−	0.673619i	$-0.235261\pi$
$601$	888.373			1.47816			0.739079	+	0.673619i	$0.235261\pi$
$602$			30.7646i			0.0511039i
$603$	−719.397	+	327.237i	−1.19303	+	0.542682i
$604$	114.787			0.190045
$605$			139.085i			0.229893i
$606$	683.647	−	148.183i	1.12813	−	0.244526i
$607$	719.043			1.18459			0.592293	−	0.805723i	$-0.298223\pi$
$607$	719.043			1.18459			0.592293	+	0.805723i	$0.298223\pi$
$608$			864.597i			1.42203i
$609$	22.7656	+	105.030i	0.0373819	+	0.172463i
$610$	324.402			0.531807
$611$		−	76.2253i		−	0.124755i
$612$	293.165	+	644.492i	0.479028	+	1.05309i
$613$	−43.6631			−0.0712286			−0.0356143	−	0.999366i	$-0.511339\pi$
$613$	−43.6631			−0.0712286			−0.0356143	+	0.999366i	$0.511339\pi$
$614$		−	1262.68i		−	2.05649i
$615$	−75.5753	+	16.3812i	−0.122887	+	0.0266361i
$616$	63.0194			0.102304
$617$		−	550.507i		−	0.892232i	−0.894975	−	0.446116i	$-0.852807\pi$
$617$		−	550.507i		−	0.892232i	0.894975	−	0.446116i	$-0.147193\pi$
$618$	150.596	+	694.783i	0.243684	+	1.12424i
$619$	−47.1518			−0.0761741			−0.0380871	−	0.999274i	$-0.512126\pi$
$619$	−47.1518			−0.0761741			−0.0380871	+	0.999274i	$0.512126\pi$
$620$		−	373.280i		−	0.602064i
$621$	−303.138	−	406.846i	−0.488146	−	0.655146i
$622$	1169.69			1.88053
$623$		−	398.818i		−	0.640157i
$624$	−696.622	+	150.995i	−1.11638	+	0.241979i
$625$	25.0000			0.0400000
$626$			738.952i			1.18043i
$627$	−110.715	−	510.787i	−0.176579	−	0.814653i
$628$	−652.594			−1.03916
$629$			804.207i			1.27855i
$630$	126.474	−	57.5301i	0.200752	−	0.0913176i
$631$	1087.70			1.72378			0.861888	−	0.507098i	$-0.169282\pi$
$631$	1087.70			1.72378			0.861888	+	0.507098i	$0.169282\pi$
$632$			23.9677i			0.0379236i
$633$	−1081.72	+	234.466i	−1.70888	+	0.370404i
$634$	−942.625			−1.48679
$635$		−	201.279i		−	0.316975i
$636$	68.4889	+	315.977i	0.107687	+	0.496818i
$637$	85.9778			0.134973
$638$			270.932i			0.424658i
$639$	108.416	+	238.341i	0.169665	+	0.372991i
$640$	212.425			0.331914
$641$		−	400.018i		−	0.624053i	−0.950073	−	0.312027i	$-0.898992\pi$
$641$		−	400.018i		−	0.624053i	0.950073	−	0.312027i	$-0.101008\pi$
$642$	−1270.20	+	275.321i	−1.97851	+	0.428848i
$643$	208.571			0.324371			0.162186	−	0.986760i	$-0.448146\pi$
$643$	208.571			0.324371			0.162186	+	0.986760i	$0.448146\pi$
$644$		−	139.686i		−	0.216904i
$645$	−6.33202	−	29.2130i	−0.00981708	−	0.0452915i
$646$	−1660.07			−2.56977
$647$			28.1443i			0.0434998i	0.999763	+	0.0217499i	$0.00692375\pi$
$647$			28.1443i			0.0434998i	−0.999763	+	0.0217499i	$0.993076\pi$
$648$	189.659	+	165.337i	0.292683	+	0.255149i
$649$	−815.692			−1.25684
$650$		−	160.258i		−	0.246551i
$651$	−460.892	+	99.8998i	−0.707975	+	0.153456i
$652$	35.5828			0.0545748
$653$		−	437.054i		−	0.669302i	−0.942342	−	0.334651i	$-0.891382\pi$
$653$		−	437.054i		−	0.669302i	0.942342	−	0.334651i	$-0.108618\pi$
$654$	−329.504	−	1520.18i	−0.503828	−	2.32443i
$655$	−380.335			−0.580665
$656$		−	222.998i		−	0.339936i
$657$	4.79541	−	2.18133i	0.00729895	−	0.00332013i
$658$	−42.8472			−0.0651173
$659$			816.912i			1.23962i	0.784750	+	0.619812i	$0.212791\pi$
$659$			816.912i			1.23962i	−0.784750	+	0.619812i	$0.787209\pi$
$660$	141.245	−	30.6153i	0.214008	−	0.0463868i
$661$	174.728			0.264339			0.132170	−	0.991227i	$-0.457806\pi$
$661$	174.728			0.264339			0.132170	+	0.991227i	$0.457806\pi$
$662$			542.931i			0.820138i
$663$	−218.559	−	1008.33i	−0.329651	−	1.52086i
$664$	192.599			0.290058
$665$			134.412i			0.202123i
$666$	−279.297	−	614.006i	−0.419365	−	0.921931i
$667$	−254.429			−0.381453
$668$		−	157.709i		−	0.236091i
$669$	419.735	−	90.9789i	0.627406	−	0.135992i
$670$	512.402			0.764780
$671$		−	426.306i		−	0.635330i
$672$	63.9848	+	295.196i	0.0952154	+	0.439280i
$673$	−25.9191			−0.0385128			−0.0192564	−	0.999815i	$-0.506130\pi$
$673$	−25.9191			−0.0385128			−0.0192564	+	0.999815i	$0.506130\pi$
$674$			101.984i			0.151311i
$675$	−108.254	+	80.6597i	−0.160377	+	0.119496i
$676$	50.9644			0.0753912
$677$			1139.28i			1.68283i	0.540390	+	0.841415i	$0.318277\pi$
$677$			1139.28i			1.68283i	−0.540390	+	0.841415i	$0.681723\pi$
$678$	214.377	−	46.4669i	0.316190	−	0.0685353i
$679$	96.1672			0.141631
$680$			194.485i			0.286008i
$681$	−94.7595	−	437.177i	−0.139148	−	0.641963i
$682$	−1188.90			−1.74326
$683$			415.208i			0.607918i	0.952685	+	0.303959i	$0.0983085\pi$
$683$			415.208i			0.607918i	−0.952685	+	0.303959i	$0.901691\pi$
$684$	522.948	−	237.877i	0.764544	−	0.347774i
$685$	−4.26103			−0.00622048
$686$		−	48.3292i		−	0.0704507i
$687$	−718.860	+	155.815i	−1.04638	+	0.226805i
$688$	86.1979			0.125288
$689$		−	471.130i		−	0.683788i
$690$	69.6817	+	321.479i	0.100988	+	0.465912i
$691$	−232.401			−0.336325			−0.168163	−	0.985759i	$-0.553783\pi$
$691$	−232.401			−0.336325			−0.168163	+	0.985759i	$0.553783\pi$
$692$		−	362.201i		−	0.523411i
$693$	−75.6020	−	166.203i	−0.109094	−	0.239831i
$694$	489.577			0.705442
$695$			47.6062i			0.0684981i
$696$	123.312	−	26.7282i	0.177172	−	0.0384026i
$697$	322.779			0.463098
$698$		−	11.3524i		−	0.0162642i
$699$	144.174	+	665.150i	0.206257	+	0.951574i
$700$	−37.1681			−0.0530972
$701$		−	1211.45i		−	1.72818i	−0.503339	−	0.864089i	$-0.667895\pi$
$701$		−	1211.45i		−	1.72818i	0.503339	−	0.864089i	$-0.332105\pi$
$702$	517.055	+	693.946i	0.736546	+	0.988528i
$703$	652.543			0.928226
$704$			168.141i			0.238836i
$705$	40.6862	−	8.81887i	0.0577110	−	0.0125090i
$706$	726.476			1.02900
$707$			236.411i			0.334386i
$708$	−189.937	−	876.281i	−0.268272	−	1.23768i
$709$	358.245			0.505283			0.252641	−	0.967560i	$-0.418701\pi$
$709$	358.245			0.505283			0.252641	+	0.967560i	$0.418701\pi$
$710$		−	169.762i		−	0.239102i
$711$	63.2108	−	28.7532i	0.0889041	−	0.0404405i
$712$	−468.236			−0.657636
$713$		−	1116.48i		−	1.56590i
$714$	−566.794	+	122.854i	−0.793829	+	0.172065i
$715$	−210.600			−0.294546
$716$		−	916.851i		−	1.28052i
$717$	22.0158	+	101.571i	0.0307055	+	0.141661i
$718$	−590.916			−0.823003
$719$		−	526.351i		−	0.732059i	−0.930603	−	0.366030i	$-0.880717\pi$
$719$		−	526.351i		−	0.732059i	0.930603	−	0.366030i	$-0.119283\pi$
$720$	−161.191	−	354.361i	−0.223876	−	0.492169i
$721$	−240.262			−0.333234
$722$			404.962i			0.560890i
$723$	−130.623	+	28.3129i	−0.180667	+	0.0391603i
$724$	−251.810			−0.347804
$725$			67.6991i			0.0933780i
$726$	103.152	+	475.894i	0.142082	+	0.655502i
$727$	1390.10			1.91210			0.956052	−	0.293197i	$-0.0947193\pi$
$727$	1390.10			1.91210			0.956052	+	0.293197i	$0.0947193\pi$
$728$		−	100.943i		−	0.138658i
$729$	208.521	−	698.541i	0.286037	−	0.958219i
$730$	−3.41561			−0.00467892
$731$			124.768i			0.170681i
$732$	457.972	−	99.2670i	0.625645	−	0.135611i
$733$	1054.10			1.43806			0.719032	−	0.694977i	$-0.244586\pi$
$733$	1054.10			1.43806			0.719032	+	0.694977i	$0.244586\pi$
$734$			338.027i			0.460528i
$735$	9.94719	+	45.8918i	0.0135336	+	0.0624378i
$736$	−715.097			−0.971599
$737$		−	673.363i		−	0.913654i
$738$	−246.439	+	112.100i	−0.333929	+	0.151897i
$739$	603.691			0.816902			0.408451	−	0.912780i	$-0.366069\pi$
$739$	603.691			0.816902			0.408451	+	0.912780i	$0.366069\pi$
$740$			180.444i			0.243843i
$741$	−818.169	+	177.341i	−1.10414	+	0.239326i
$742$	−264.828			−0.356911
$743$		−	229.795i		−	0.309281i	−0.987971	−	0.154640i	$-0.950578\pi$
$743$		−	229.795i		−	0.309281i	0.987971	−	0.154640i	$-0.0494219\pi$
$744$	117.288	+	541.115i	0.157646	+	0.727305i
$745$	525.027			0.704735
$746$		−	428.408i		−	0.574274i
$747$	−231.054	−	507.947i	−0.309309	−	0.679982i
$748$	−603.251			−0.806486
$749$		−	439.247i		−	0.586444i
$750$	85.5399	−	18.5411i	0.114053	−	0.0247214i
$751$	184.416			0.245561			0.122781	−	0.992434i	$-0.460819\pi$
$751$	184.416			0.245561			0.122781	+	0.992434i	$0.460819\pi$
$752$			120.052i			0.159643i
$753$	−254.115	−	1172.37i	−0.337470	−	1.55693i
$754$	433.973			0.575561
$755$		−	91.3538i		−	0.120998i
$756$	160.944	−	119.919i	0.212889	−	0.158623i
$757$	1043.79			1.37885			0.689426	−	0.724356i	$-0.257863\pi$
$757$	1043.79			1.37885			0.689426	+	0.724356i	$0.257863\pi$
$758$			1696.17i			2.23770i
$759$	422.466	−	91.5708i	0.556608	−	0.120647i
$760$	157.808			0.207642
$761$		−	727.007i		−	0.955331i	−0.878542	−	0.477665i	$-0.841483\pi$
$761$		−	727.007i		−	0.955331i	0.878542	−	0.477665i	$-0.158517\pi$
$762$	−149.277	−	688.695i	−0.195901	−	0.903799i
$763$	525.690			0.688978
$764$		−	534.864i		−	0.700083i
$765$	512.922	−	233.317i	0.670487	−	0.304989i
$766$	517.037			0.674984
$767$			1306.56i			1.70347i
$768$	983.990	−	213.283i	1.28124	−	0.277712i
$769$	−123.151			−0.160144			−0.0800720	−	0.996789i	$-0.525515\pi$
$769$	−123.151			−0.160144			−0.0800720	+	0.996789i	$0.525515\pi$
$770$			118.381i			0.153741i
$771$	−256.194	−	1181.96i	−0.332288	−	1.53303i
$772$	−793.191			−1.02745
$773$			1309.20i			1.69366i	0.531864	+	0.846830i	$0.321492\pi$
$773$			1309.20i			1.69366i	−0.531864	+	0.846830i	$0.678508\pi$
$774$	−43.3312	−	95.2591i	−0.0559835	−	0.123074i
$775$	−297.076			−0.383324
$776$		−	112.906i		−	0.145498i
$777$	222.796	−	48.2917i	0.286738	−	0.0621514i
$778$	823.834			1.05891
$779$		−	261.907i		−	0.336209i
$780$	−49.0390	−	226.243i	−0.0628705	−	0.290056i
$781$	−223.090			−0.285646
$782$		−	1373.03i		−	1.75579i
$783$	−218.423	−	293.149i	−0.278957	−	0.374392i
$784$	−135.411			−0.172719
$785$			519.370i			0.661618i
$786$	−1301.35	+	282.073i	−1.65567	+	0.358871i
$787$	248.784			0.316117			0.158058	−	0.987430i	$-0.449477\pi$
$787$	248.784			0.316117			0.158058	+	0.987430i	$0.449477\pi$
$788$			1013.56i			1.28625i
$789$	162.838	+	751.260i	0.206385	+	0.952167i
$790$	−45.0229			−0.0569911
$791$			74.1334i			0.0937211i
$792$	−195.133	+	88.7614i	−0.246379	+	0.112072i
$793$	−682.849			−0.861096
$794$			633.946i			0.798421i
$795$	251.472	−	54.5073i	0.316316	−	0.0685626i
$796$	−569.030			−0.714862
$797$		−	563.084i		−	0.706504i	−0.935528	−	0.353252i	$-0.885076\pi$
$797$		−	563.084i		−	0.706504i	0.935528	−	0.353252i	$-0.114924\pi$
$798$	99.6854	+	459.903i	0.124919	+	0.576319i
$799$	−173.769			−0.217483
$800$			190.274i			0.237843i
$801$	561.726	+	1234.89i	0.701281	+	1.54169i
$802$	−2020.01			−2.51871
$803$			4.48856i			0.00558974i
$804$	723.380	−	156.795i	0.899726	−	0.195019i
$805$	−111.170			−0.138100
$806$			1904.36i			2.36273i
$807$	−15.9551	−	73.6097i	−0.0197709	−	0.0912140i
$808$	277.561			0.343516
$809$			1377.11i			1.70224i	0.524972	+	0.851120i	$0.324076\pi$
$809$			1377.11i			1.70224i	−0.524972	+	0.851120i	$0.675924\pi$
$810$	−310.582	+	356.271i	−0.383435	+	0.439841i
$811$	549.880			0.678028			0.339014	−	0.940781i	$-0.389907\pi$
$811$	549.880			0.678028			0.339014	+	0.940781i	$0.389907\pi$
$812$		−	100.650i		−	0.123953i
$813$	747.552	−	162.034i	0.919498	−	0.199304i
$814$	574.716			0.706039
$815$		−	28.3187i		−	0.0347469i
$816$	344.220	+	1588.07i	0.421839	+	1.94617i
$817$	101.238			0.123914
$818$		−	955.738i		−	1.16838i
$819$	−266.221	+	121.098i	−0.325056	+	0.147861i
$820$	72.4235			0.0883213
$821$			1321.45i			1.60956i	0.593572	+	0.804781i	$0.297717\pi$
$821$			1321.45i			1.60956i	−0.593572	+	0.804781i	$0.702283\pi$
$822$	−14.5795	+	3.16016i	−0.0177366	+	0.00384447i
$823$	−1302.61			−1.58276			−0.791379	−	0.611326i	$-0.790637\pi$
$823$	−1302.61			−1.58276			−0.791379	+	0.611326i	$0.790637\pi$
$824$			282.082i			0.342332i
$825$	−24.3653	−	112.411i	−0.0295338	−	0.136255i
$826$	734.432			0.889143
$827$		−	902.596i		−	1.09141i	−0.837977	−	0.545705i	$-0.816262\pi$
$827$		−	902.596i		−	1.09141i	0.837977	−	0.545705i	$-0.183738\pi$
$828$	196.745	+	432.524i	0.237615	+	0.522371i
$829$	390.435			0.470971			0.235485	−	0.971878i	$-0.424332\pi$
$829$	390.435			0.470971			0.235485	+	0.971878i	$0.424332\pi$
$830$			361.794i			0.435896i
$831$	790.141	−	171.266i	0.950832	−	0.206096i
$832$	269.324			0.323707
$833$		−	196.002i		−	0.235296i
$834$	35.3068	+	162.889i	0.0423343	+	0.195311i
$835$	−125.513			−0.150316
$836$			489.485i			0.585508i
$837$	1286.39	−	958.484i	1.53691	−	1.14514i
$838$	−1000.58			−1.19401
$839$			307.783i			0.366846i	0.983034	+	0.183423i	$0.0587177\pi$
$839$			307.783i			0.366846i	−0.983034	+	0.183423i	$0.941282\pi$
$840$	53.8797	−	11.6786i	0.0641426	−	0.0139031i
$841$	657.674			0.782014
$842$			257.063i			0.305300i
$843$	−139.172	−	642.076i	−0.165091	−	0.761656i
$844$	1036.61			1.22821
$845$		−	40.5603i		−	0.0480004i
$846$	132.671	−	60.3493i	0.156822	−	0.0713348i
$847$	−164.568			−0.194295
$848$			742.009i			0.875011i
$849$	−589.386	+	127.751i	−0.694212	+	0.150473i
$850$	−365.337			−0.429809
$851$			539.710i			0.634206i
$852$	−51.9473	−	239.661i	−0.0609710	−	0.281292i
$853$	−1575.68			−1.84723			−0.923613	−	0.383327i	$-0.874778\pi$
$853$	−1575.68			−1.84723			−0.923613	+	0.383327i	$0.874778\pi$
$854$			383.838i			0.449459i
$855$	−189.316	−	416.191i	−0.221422	−	0.486773i
$856$	−515.703			−0.602456
$857$			650.869i			0.759474i	0.925095	+	0.379737i	$0.123985\pi$
$857$			650.869i			0.759474i	−0.925095	+	0.379737i	$0.876015\pi$
$858$	−720.589	+	156.190i	−0.839847	+	0.182040i
$859$	−0.781280			−0.000909522			−0.000454761	−	1.00000i	$-0.500145\pi$
$859$	−0.781280			−0.000909522			−0.000454761		1.00000i	$0.500145\pi$
$860$			27.9947i			0.0325520i
$861$	−19.3825	−	89.4219i	−0.0225116	−	0.103858i
$862$	−641.530			−0.744234
$863$		−	188.050i		−	0.217903i	−0.994047	−	0.108952i	$-0.965251\pi$
$863$		−	188.050i		−	0.217903i	0.994047	−	0.108952i	$-0.0347493\pi$
$864$	−613.899	−	823.922i	−0.710532	−	0.953613i
$865$	−288.259			−0.333248
$866$		−	725.670i		−	0.837956i
$867$	−1451.34	+	314.583i	−1.67398	+	0.362841i
$868$	441.670			0.508837
$869$			59.1660i			0.0680851i
$870$	50.2085	+	231.639i	0.0577109	+	0.266252i
$871$	−1078.58			−1.23832
$872$		−	617.193i		−	0.707790i
$873$	−297.771	+	135.449i	−0.341089	+	0.155154i
$874$	−1114.09			−1.27470
$875$			29.5804i			0.0338062i
$876$	−4.82197	+	1.04518i	−0.00550453	+	0.00119312i
$877$	−775.353			−0.884096			−0.442048	−	0.896991i	$-0.645748\pi$
$877$	−775.353			−0.884096			−0.442048	+	0.896991i	$0.645748\pi$
$878$			158.254i			0.180244i
$879$	5.75358	+	26.5444i	0.00654560	+	0.0301984i
$880$	331.686			0.376916
$881$			453.608i			0.514879i	0.966294	+	0.257439i	$0.0828788\pi$
$881$			453.608i			0.514879i	−0.966294	+	0.257439i	$0.917121\pi$
$882$	68.0705	+	149.646i	0.0771775	+	0.169666i
$883$	226.736			0.256780			0.128390	−	0.991724i	$-0.459019\pi$
$883$	226.736			0.256780			0.128390	+	0.991724i	$0.459019\pi$
$884$			966.276i			1.09307i
$885$	−697.392	+	151.162i	−0.788014	+	0.170805i
$886$	668.691			0.754731
$887$			132.055i			0.148878i	0.997226	+	0.0744390i	$0.0237166\pi$
$887$			132.055i			0.148878i	−0.997226	+	0.0744390i	$0.976283\pi$
$888$	−56.6974	−	261.576i	−0.0638484	−	0.294567i
$889$	238.156			0.267892
$890$		−	879.574i		−	0.988286i
$891$	468.186	+	408.145i	0.525462	+	0.458075i
$892$	−402.230			−0.450930
$893$			140.998i			0.157893i
$894$	1796.43	−	389.382i	2.00943	−	0.435551i
$895$	−729.681			−0.815285
$896$			251.345i			0.280519i
$897$	−146.676	−	676.697i	−0.163519	−	0.754400i
$898$	754.875			0.840618
$899$		−	804.472i		−	0.894852i
$900$	115.087	−	52.3504i	0.127874	−	0.0581671i
$901$	−1074.02			−1.19204
$902$		−	230.670i		−	0.255732i
$903$	34.5653	−	7.49214i	0.0382783	−	0.00829695i
$904$	87.0371			0.0962800
$905$			200.404i			0.221441i
$906$	−67.7518	−	312.576i	−0.0747813	−	0.345006i
$907$	−1450.44			−1.59917			−0.799583	−	0.600556i	$-0.794946\pi$
$907$	−1450.44			−1.59917			−0.799583	+	0.600556i	$0.794946\pi$
$908$			418.944i			0.461392i
$909$	−332.979	−	732.019i	−0.366314	−	0.805302i
$910$	189.620			0.208374
$911$		−	128.872i		−	0.141462i	−0.997495	−	0.0707312i	$-0.977467\pi$
$911$		−	128.872i		−	0.141462i	0.997495	−	0.0707312i	$-0.0225332\pi$
$912$	1288.58	−	279.304i	1.41292	−	0.306255i
$913$	475.444			0.520749
$914$		−	247.406i		−	0.270685i
$915$	−79.0021	−	364.480i	−0.0863411	−	0.398338i
$916$	688.880			0.752052
$917$		−	450.019i		−	0.490751i
$918$	1581.98	−	1178.72i	1.72328	−	1.28401i
$919$	487.154			0.530091			0.265046	−	0.964236i	$-0.414613\pi$
$919$	487.154			0.530091			0.265046	+	0.964236i	$0.414613\pi$
$920$			130.521i			0.141870i
$921$	−1418.68	+	307.503i	−1.54037	+	0.333880i
$922$	774.950			0.840510
$923$			357.341i			0.387152i
$924$	36.2245	+	167.123i	0.0392040	+	0.180869i
$925$	143.607			0.155251
$926$		−	370.259i		−	0.399847i
$927$	743.943	−	338.403i	0.802528	−	0.365052i
$928$	−515.256			−0.555233
$929$		−	1131.14i		−	1.21759i	−0.793327	−	0.608796i	$-0.791653\pi$
$929$		−	1131.14i		−	1.21759i	0.793327	−	0.608796i	$-0.208347\pi$
$930$	−1016.48	+	220.324i	−1.09298	+	0.236908i
$931$	−159.038			−0.170825
$932$		−	637.410i		−	0.683917i
$933$	−284.856	−	1314.19i	−0.305312	−	1.40857i
$934$	−992.934			−1.06310
$935$			480.101i			0.513477i
$936$	142.176	+	312.559i	0.151898	+	0.333931i
$937$	−1096.74			−1.17048			−0.585239	−	0.810861i	$-0.698999\pi$
$937$	−1096.74			−1.17048			−0.585239	+	0.810861i	$0.698999\pi$
$938$			606.283i			0.646357i
$939$	830.244	−	179.958i	0.884179	−	0.191649i
$940$	−38.9894			−0.0414781
$941$			269.673i			0.286581i	0.989681	+	0.143291i	$0.0457683\pi$
$941$			269.673i			0.286581i	−0.989681	+	0.143291i	$0.954232\pi$
$942$	385.187	+	1777.07i	0.408903	+	1.88649i
$943$	216.620			0.229713
$944$		−	2057.77i		−	2.17985i
$945$	−95.4379	−	128.088i	−0.100992	−	0.135543i
$946$	89.1635			0.0942532
$947$			717.018i			0.757146i	0.925571	+	0.378573i	$0.123585\pi$
$947$			717.018i			0.757146i	−0.925571	+	0.378573i	$0.876415\pi$
$948$	−63.5608	+	13.7770i	−0.0670473	+	0.0145327i
$949$	7.18969			0.00757606
$950$			296.439i			0.312041i
$951$	229.559	+	1059.08i	0.241387	+	1.11365i
$952$	−230.118			−0.241721
$953$			794.422i			0.833601i	0.908998	+	0.416800i	$0.136849\pi$
$953$			794.422i			0.833601i	−0.908998	+	0.416800i	$0.863151\pi$
$954$	820.009	−	373.004i	0.859549	−	0.390989i
$955$	−425.674			−0.445732
$956$		−	97.3348i		−	0.101815i
$957$	304.403	−	65.9804i	0.318081	−	0.0689451i
$958$	1842.66			1.92345
$959$		−	5.04171i		−	0.00525726i
$960$	31.1594	+	143.755i	0.0324577	+	0.149745i
$961$	2569.18			2.67344
$962$		−	920.569i		−	0.956932i
$963$	618.669	+	1360.08i	0.642439	+	1.41233i
$964$	125.175			0.129850
$965$			631.266i			0.654161i
$966$	−380.380	+	82.4485i	−0.393768	+	0.0853504i
$967$	339.659			0.351250			0.175625	−	0.984457i	$-0.443805\pi$
$967$	339.659			0.351250			0.175625	+	0.984457i	$0.443805\pi$
$968$			193.213i			0.199600i
$969$	404.280	+	1865.16i	0.417214	+	1.92483i
$970$	212.092			0.218652
$971$		−	173.113i		−	0.178283i	−0.996019	−	0.0891417i	$-0.971588\pi$
$971$		−	173.113i		−	0.178283i	0.996019	−	0.0891417i	$-0.0284124\pi$
$972$	−329.443	+	598.001i	−0.338933	+	0.615227i
$973$	−56.3284			−0.0578915
$974$		−	912.562i		−	0.936922i
$975$	−180.057	+	39.0279i	−0.184674	+	0.0400287i
$976$	1075.46			1.10190
$977$		−	696.372i		−	0.712765i	−0.934340	−	0.356383i	$-0.884010\pi$
$977$		−	696.372i		−	0.712765i	0.934340	−	0.356383i	$-0.115990\pi$
$978$	−21.0024	−	96.8952i	−0.0214748	−	0.0990749i
$979$	−1155.87			−1.18067
$980$		−	43.9778i		−	0.0448754i
$981$	−1627.74	+	740.423i	−1.65927	+	0.754764i
$982$	−1327.50			−1.35183
$983$		−	717.101i		−	0.729503i	−0.931105	−	0.364752i	$-0.881154\pi$
$983$		−	717.101i		−	0.729503i	0.931105	−	0.364752i	$-0.118846\pi$
$984$	−104.987	+	22.7562i	−0.106694	+	0.0231263i
$985$	806.648			0.818932
$986$		−	989.320i		−	1.00337i
$987$	10.4346	+	48.1406i	0.0105721	+	0.0487747i
$988$	784.047			0.793570
$989$			83.7325i			0.0846638i
$990$	−166.737	−	366.553i	−0.168421	−	0.370256i
$991$	−1178.90			−1.18961			−0.594803	−	0.803871i	$-0.702770\pi$
$991$	−1178.90			−1.18961			−0.594803	+	0.803871i	$0.702770\pi$
$992$		−	2261.04i		−	2.27928i
$993$	610.006	−	132.221i	0.614306	−	0.133153i
$994$	200.866			0.202078
$995$			452.866i			0.455142i
$996$	110.709	+	510.759i	0.111153	+	0.512810i
$997$	−328.077			−0.329064			−0.164532	−	0.986372i	$-0.552611\pi$
$997$	−328.077			−0.329064			−0.164532	+	0.986372i	$0.552611\pi$
$998$		−	1513.26i		−	1.51629i
$999$	−621.844	+	463.332i	−0.622466	+	0.463796i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.3.c.a.71.13	yes	16
3.2	odd	2	inner	105.3.c.a.71.4	✓	16
4.3	odd	2		1680.3.l.a.1121.2		16
5.2	odd	4		525.3.f.b.449.8		32
5.3	odd	4		525.3.f.b.449.26		32
5.4	even	2		525.3.c.b.176.4		16
12.11	even	2		1680.3.l.a.1121.1		16
15.2	even	4		525.3.f.b.449.25		32
15.8	even	4		525.3.f.b.449.7		32
15.14	odd	2		525.3.c.b.176.13		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.c.a.71.4	✓	16	3.2	odd	2	inner
105.3.c.a.71.13	yes	16	1.1	even	1	trivial
525.3.c.b.176.4		16	5.4	even	2
525.3.c.b.176.13		16	15.14	odd	2
525.3.f.b.449.7		32	15.8	even	4
525.3.f.b.449.8		32	5.2	odd	4
525.3.f.b.449.25		32	15.2	even	4
525.3.f.b.449.26		32	5.3	odd	4
1680.3.l.a.1121.1		16	12.11	even	2
1680.3.l.a.1121.2		16	4.3	odd	2

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:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	105.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.60953i q^{2} +(2.93192 - 0.635503i) q^{3} -2.80964 q^{4} +2.23607i q^{5} +(1.65836 + 7.65092i) q^{6} -2.64575 q^{7} +3.10627i q^{8} +(8.19227 - 3.72648i) q^{9} +O(q^{10})\)	\(q+2.60953i q^{2} +(2.93192 - 0.635503i) q^{3} -2.80964 q^{4} +2.23607i q^{5} +(1.65836 + 7.65092i) q^{6} -2.64575 q^{7} +3.10627i q^{8} +(8.19227 - 3.72648i) q^{9} -5.83508 q^{10} +7.66806i q^{11} +(-8.23764 + 1.78553i) q^{12} +12.2825 q^{13} -6.90416i q^{14} +(1.42103 + 6.55597i) q^{15} -19.3445 q^{16} -28.0003i q^{17} +(9.72436 + 21.3780i) q^{18} -22.7197 q^{19} -6.28255i q^{20} +(-7.75712 + 1.68138i) q^{21} -20.0100 q^{22} -18.7912i q^{23} +(1.97405 + 9.10734i) q^{24} -5.00000 q^{25} +32.0517i q^{26} +(21.6509 - 16.1319i) q^{27} +7.43361 q^{28} -13.5398i q^{29} +(-17.1080 + 3.70821i) q^{30} +59.4153 q^{31} -38.0549i q^{32} +(4.87307 + 22.4821i) q^{33} +73.0675 q^{34} -5.91608i q^{35} +(-23.0174 + 10.4701i) q^{36} -28.7214 q^{37} -59.2878i q^{38} +(36.0114 - 7.80559i) q^{39} -6.94584 q^{40} +11.5277i q^{41} +(-4.38761 - 20.2424i) q^{42} -4.45594 q^{43} -21.5445i q^{44} +(8.33267 + 18.3185i) q^{45} +49.0362 q^{46} -6.20599i q^{47} +(-56.7164 + 12.2935i) q^{48} +7.00000 q^{49} -13.0476i q^{50} +(-17.7942 - 82.0944i) q^{51} -34.5095 q^{52} -38.3577i q^{53} +(42.0968 + 56.4986i) q^{54} -17.1463 q^{55} -8.21843i q^{56} +(-66.6124 + 14.4384i) q^{57} +35.3325 q^{58} +106.375i q^{59} +(-3.99258 - 18.4199i) q^{60} -55.5951 q^{61} +155.046i q^{62} +(-21.6747 + 9.85934i) q^{63} +21.9274 q^{64} +27.4646i q^{65} +(-58.6677 + 12.7164i) q^{66} -87.8140 q^{67} +78.6707i q^{68} +(-11.9419 - 55.0942i) q^{69} +15.4382 q^{70} +29.0934i q^{71} +(11.5755 + 25.4475i) q^{72} +0.585358 q^{73} -74.9494i q^{74} +(-14.6596 + 3.17751i) q^{75} +63.8343 q^{76} -20.2878i q^{77} +(20.3689 + 93.9728i) q^{78} +7.71590 q^{79} -43.2556i q^{80} +(53.2267 - 61.0567i) q^{81} -30.0819 q^{82} -62.0031i q^{83} +(21.7947 - 4.72408i) q^{84} +62.6105 q^{85} -11.6279i q^{86} +(-8.60458 - 39.6976i) q^{87} -23.8191 q^{88} +150.739i q^{89} +(-47.8026 + 21.7443i) q^{90} -32.4966 q^{91} +52.7965i q^{92} +(174.201 - 37.7586i) q^{93} +16.1947 q^{94} -50.8029i q^{95} +(-24.1840 - 111.574i) q^{96} -36.3478 q^{97} +18.2667i q^{98} +(28.5749 + 62.8188i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{3} - 28 q^{4} - 28 q^{6} + 22 q^{9}+O(q^{10}) \) 16 * q + 8 * q^3 - 28 * q^4 - 28 * q^6 + 22 * q^9	\( 16 q + 8 q^{3} - 28 q^{4} - 28 q^{6} + 22 q^{9} - 20 q^{10} + 12 q^{12} + 10 q^{15} + 92 q^{16} - 52 q^{18} - 16 q^{19} - 14 q^{21} + 16 q^{22} + 128 q^{24} - 80 q^{25} - 148 q^{27} + 112 q^{28} + 80 q^{30} - 72 q^{31} - 4 q^{33} - 176 q^{34} - 76 q^{36} - 40 q^{37} + 90 q^{39} - 60 q^{40} + 280 q^{43} + 40 q^{45} + 72 q^{46} - 172 q^{48} + 112 q^{49} + 38 q^{51} - 88 q^{52} + 208 q^{54} + 80 q^{55} - 36 q^{57} - 24 q^{58} - 80 q^{60} - 56 q^{61} - 56 q^{63} - 44 q^{64} - 260 q^{66} - 120 q^{67} + 60 q^{69} + 376 q^{72} - 208 q^{73} - 40 q^{75} + 144 q^{76} - 228 q^{78} - 204 q^{79} + 458 q^{81} - 384 q^{82} - 84 q^{84} + 100 q^{85} - 324 q^{87} + 168 q^{88} - 160 q^{90} - 28 q^{91} + 108 q^{93} + 984 q^{94} + 40 q^{96} + 728 q^{97} - 166 q^{99}+O(q^{100}) \) 16 * q + 8 * q^3 - 28 * q^4 - 28 * q^6 + 22 * q^9 - 20 * q^10 + 12 * q^12 + 10 * q^15 + 92 * q^16 - 52 * q^18 - 16 * q^19 - 14 * q^21 + 16 * q^22 + 128 * q^24 - 80 * q^25 - 148 * q^27 + 112 * q^28 + 80 * q^30 - 72 * q^31 - 4 * q^33 - 176 * q^34 - 76 * q^36 - 40 * q^37 + 90 * q^39 - 60 * q^40 + 280 * q^43 + 40 * q^45 + 72 * q^46 - 172 * q^48 + 112 * q^49 + 38 * q^51 - 88 * q^52 + 208 * q^54 + 80 * q^55 - 36 * q^57 - 24 * q^58 - 80 * q^60 - 56 * q^61 - 56 * q^63 - 44 * q^64 - 260 * q^66 - 120 * q^67 + 60 * q^69 + 376 * q^72 - 208 * q^73 - 40 * q^75 + 144 * q^76 - 228 * q^78 - 204 * q^79 + 458 * q^81 - 384 * q^82 - 84 * q^84 + 100 * q^85 - 324 * q^87 + 168 * q^88 - 160 * q^90 - 28 * q^91 + 108 * q^93 + 984 * q^94 + 40 * q^96 + 728 * q^97 - 166 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more