LMFDB - Embedded newform 105.4.m.a.13.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,4,Mod(13,105)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(105, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("105.13");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	105.m (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:	$6.19520055060$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			13.10
Character	$\chi$	$=$	105.13
Dual form			105.4.m.a.97.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.817511 + 0.817511i) q^{2} +(2.12132 - 2.12132i) q^{3} +6.66335i q^{4} +(-8.83013 - 6.85775i) q^{5} +3.46841i q^{6} +(-4.27846 - 18.0193i) q^{7} +(-11.9875 - 11.9875i) q^{8} -9.00000i q^{9} +O(q^{10})$	\(q+(-0.817511 + 0.817511i) q^{2} +(2.12132 - 2.12132i) q^{3} +6.66335i q^{4} +(-8.83013 - 6.85775i) q^{5} +3.46841i q^{6} +(-4.27846 - 18.0193i) q^{7} +(-11.9875 - 11.9875i) q^{8} -9.00000i q^{9} +(12.8250 - 1.61244i) q^{10} -14.7693 q^{11} +(14.1351 + 14.1351i) q^{12} +(44.4120 - 44.4120i) q^{13} +(18.2287 + 11.2333i) q^{14} +(-33.2790 + 4.18405i) q^{15} -33.7070 q^{16} +(-47.4679 - 47.4679i) q^{17} +(7.35760 + 7.35760i) q^{18} +9.66755 q^{19} +(45.6956 - 58.8383i) q^{20} +(-47.3007 - 29.1487i) q^{21} +(12.0740 - 12.0740i) q^{22} +(-59.3379 - 59.3379i) q^{23} -50.8585 q^{24} +(30.9425 + 121.110i) q^{25} +72.6146i q^{26} +(-19.0919 - 19.0919i) q^{27} +(120.069 - 28.5089i) q^{28} -228.642i q^{29} +(23.7855 - 30.6265i) q^{30} -10.3652i q^{31} +(123.456 - 123.456i) q^{32} +(-31.3303 + 31.3303i) q^{33} +77.6110 q^{34} +(-85.7924 + 188.453i) q^{35} +59.9702 q^{36} +(-198.831 + 198.831i) q^{37} +(-7.90333 + 7.90333i) q^{38} -188.424i q^{39} +(23.6438 + 188.058i) q^{40} +345.832i q^{41} +(62.4982 - 14.8394i) q^{42} +(333.255 + 333.255i) q^{43} -98.4128i q^{44} +(-61.7198 + 79.4712i) q^{45} +97.0189 q^{46} +(-152.394 - 152.394i) q^{47} +(-71.5034 + 71.5034i) q^{48} +(-306.390 + 154.190i) q^{49} +(-124.304 - 73.7127i) q^{50} -201.389 q^{51} +(295.933 + 295.933i) q^{52} +(348.840 + 348.840i) q^{53} +31.2157 q^{54} +(130.415 + 101.284i) q^{55} +(-164.718 + 267.293i) q^{56} +(20.5080 - 20.5080i) q^{57} +(186.917 + 186.917i) q^{58} -593.332 q^{59} +(-27.8798 - 221.750i) q^{60} -328.164i q^{61} +(8.47370 + 8.47370i) q^{62} +(-162.174 + 38.5061i) q^{63} -67.8038i q^{64} +(-696.730 + 87.5974i) q^{65} -51.2258i q^{66} +(626.936 - 626.936i) q^{67} +(316.295 - 316.295i) q^{68} -251.750 q^{69} +(-83.9264 - 224.199i) q^{70} +360.302 q^{71} +(-107.887 + 107.887i) q^{72} +(504.894 - 504.894i) q^{73} -325.093i q^{74} +(322.551 + 191.274i) q^{75} +64.4183i q^{76} +(63.1897 + 266.132i) q^{77} +(154.039 + 154.039i) q^{78} -159.951i q^{79} +(297.638 + 231.155i) q^{80} -81.0000 q^{81} +(-282.721 - 282.721i) q^{82} +(413.196 - 413.196i) q^{83} +(194.228 - 315.181i) q^{84} +(93.6247 + 744.670i) q^{85} -544.879 q^{86} +(-485.023 - 485.023i) q^{87} +(177.046 + 177.046i) q^{88} +707.614 q^{89} +(-14.5120 - 115.425i) q^{90} +(-990.288 - 610.258i) q^{91} +(395.389 - 395.389i) q^{92} +(-21.9880 - 21.9880i) q^{93} +249.168 q^{94} +(-85.3657 - 66.2976i) q^{95} -523.777i q^{96} +(-604.783 - 604.783i) q^{97} +(124.425 - 376.529i) q^{98} +132.923i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 4 q^{7} - 168 q^{8}+O(q^{10}) $ 48 * q + 4 * q^7 - 168 * q^8	$ 48 q + 4 q^{7} - 168 q^{8} + 112 q^{11} + 168 q^{15} - 544 q^{16} - 96 q^{21} - 192 q^{22} + 400 q^{23} + 520 q^{25} + 1052 q^{28} - 48 q^{30} - 1344 q^{32} + 392 q^{35} - 1728 q^{36} - 456 q^{37} + 1068 q^{42} + 192 q^{43} - 208 q^{46} + 3528 q^{50} + 672 q^{51} - 1728 q^{53} - 48 q^{56} + 696 q^{57} + 3016 q^{58} + 840 q^{60} - 36 q^{63} - 4720 q^{65} - 4784 q^{67} + 2220 q^{70} - 3088 q^{71} - 1512 q^{72} + 2352 q^{77} + 1416 q^{78} - 3888 q^{81} - 472 q^{85} + 10832 q^{86} + 2128 q^{88} - 5664 q^{91} + 10600 q^{92} - 1368 q^{93} - 6912 q^{95} - 3888 q^{98}+O(q^{100}) $ 48 * q + 4 * q^7 - 168 * q^8 + 112 * q^11 + 168 * q^15 - 544 * q^16 - 96 * q^21 - 192 * q^22 + 400 * q^23 + 520 * q^25 + 1052 * q^28 - 48 * q^30 - 1344 * q^32 + 392 * q^35 - 1728 * q^36 - 456 * q^37 + 1068 * q^42 + 192 * q^43 - 208 * q^46 + 3528 * q^50 + 672 * q^51 - 1728 * q^53 - 48 * q^56 + 696 * q^57 + 3016 * q^58 + 840 * q^60 - 36 * q^63 - 4720 * q^65 - 4784 * q^67 + 2220 * q^70 - 3088 * q^71 - 1512 * q^72 + 2352 * q^77 + 1416 * q^78 - 3888 * q^81 - 472 * q^85 + 10832 * q^86 + 2128 * q^88 - 5664 * q^91 + 10600 * q^92 - 1368 * q^93 - 6912 * q^95 - 3888 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$22$	$31$	$71$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

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 $

$2$	−0.817511	+	0.817511i	−0.289034	+	0.289034i	−0.836698	−	0.547664i	$-0.815517\pi$
$2$	−0.817511	+	0.817511i	−0.289034	+	0.289034i	0.547664	+	0.836698i	$0.315517\pi$
$3$	2.12132	−	2.12132i	0.408248	−	0.408248i
$3$	2.12132	−	2.12132i	0.408248	−	0.408248i
$4$			6.66335i			0.832919i
$5$	−8.83013	−	6.85775i	−0.789791	−	0.613376i
$5$	−8.83013	−	6.85775i	−0.789791	−	0.613376i
$6$			3.46841i			0.235995i
$7$	−4.27846	−	18.0193i	−0.231015	−	0.972950i
$7$	−4.27846	−	18.0193i	−0.231015	−	0.972950i
$8$	−11.9875	−	11.9875i	−0.529776	−	0.529776i
$9$		−	9.00000i		−	0.333333i
$10$	12.8250	−	1.61244i	0.405563	−	0.0509899i
$11$	−14.7693			−0.404827			−0.202414	−	0.979300i	$-0.564879\pi$
$11$	−14.7693			−0.404827			−0.202414	+	0.979300i	$0.564879\pi$
$12$	14.1351	+	14.1351i	0.340038	+	0.340038i
$13$	44.4120	−	44.4120i	0.947513	−	0.947513i	−0.0511763	−	0.998690i	$-0.516297\pi$
$13$	44.4120	−	44.4120i	0.947513	−	0.947513i	0.998690	+	0.0511763i	$0.0162971\pi$
$14$	18.2287	+	11.2333i	0.347987	+	0.214444i
$15$	−33.2790	+	4.18405i	−0.572841	+	0.0720212i
$16$	−33.7070			−0.526673
$17$	−47.4679	−	47.4679i	−0.677215	−	0.677215i	0.282154	−	0.959369i	$-0.408951\pi$
$17$	−47.4679	−	47.4679i	−0.677215	−	0.677215i	−0.959369	+	0.282154i	$0.908951\pi$
$18$	7.35760	+	7.35760i	0.0963446	+	0.0963446i
$19$	9.66755			0.116731			0.0583655	−	0.998295i	$-0.481411\pi$
$19$	9.66755			0.116731			0.0583655	+	0.998295i	$0.481411\pi$
$20$	45.6956	−	58.8383i	0.510892	−	0.657832i
$21$	−47.3007	−	29.1487i	−0.491517	−	0.302894i
$22$	12.0740	−	12.0740i	0.117009	−	0.117009i
$23$	−59.3379	−	59.3379i	−0.537948	−	0.537948i	0.384978	−	0.922926i	$-0.374209\pi$
$23$	−59.3379	−	59.3379i	−0.537948	−	0.537948i	−0.922926	+	0.384978i	$0.874209\pi$
$24$	−50.8585			−0.432560
$25$	30.9425	+	121.110i	0.247540	+	0.968878i
$26$			72.6146i			0.547727i
$27$	−19.0919	−	19.0919i	−0.136083	−	0.136083i
$28$	120.069	−	28.5089i	0.810389	−	0.192417i
$29$		−	228.642i		−	1.46406i	−0.681272	−	0.732030i	$-0.738573\pi$
$29$		−	228.642i		−	1.46406i	0.681272	−	0.732030i	$-0.261427\pi$
$30$	23.7855	−	30.6265i	0.144754	−	0.186387i
$31$		−	10.3652i		−	0.0600533i	−0.999549	−	0.0300267i	$-0.990441\pi$
$31$		−	10.3652i		−	0.0600533i	0.999549	−	0.0300267i	$-0.00955922\pi$
$32$	123.456	−	123.456i	0.682002	−	0.682002i
$33$	−31.3303	+	31.3303i	−0.165270	+	0.165270i
$34$	77.6110			0.391476
$35$	−85.7924	+	188.453i	−0.414331	+	0.910126i
$36$	59.9702			0.277640
$37$	−198.831	+	198.831i	−0.883449	+	0.883449i	−0.993883	−	0.110434i	$-0.964776\pi$
$37$	−198.831	+	198.831i	−0.883449	+	0.883449i	0.110434	+	0.993883i	$0.464776\pi$
$38$	−7.90333	+	7.90333i	−0.0337392	+	0.0337392i
$39$		−	188.424i		−	0.773641i
$40$	23.6438	+	188.058i	0.0934604	+	0.743364i
$41$			345.832i			1.31731i	0.752444	+	0.658657i	$0.228875\pi$
$41$			345.832i			1.31731i	−0.752444	+	0.658657i	$0.771125\pi$
$42$	62.4982	−	14.8394i	0.229612	−	0.0545184i
$43$	333.255	+	333.255i	1.18188	+	1.18188i	0.979257	+	0.202624i	$0.0649469\pi$
$43$	333.255	+	333.255i	1.18188	+	1.18188i	0.202624	+	0.979257i	$0.435053\pi$
$44$		−	98.4128i		−	0.337188i
$45$	−61.7198	+	79.4712i	−0.204459	+	0.263264i
$46$	97.0189			0.310971
$47$	−152.394	−	152.394i	−0.472956	−	0.472956i	0.429914	−	0.902870i	$-0.358544\pi$
$47$	−152.394	−	152.394i	−0.472956	−	0.472956i	−0.902870	+	0.429914i	$0.858544\pi$
$48$	−71.5034	+	71.5034i	−0.215013	+	0.215013i
$49$	−306.390	+	154.190i	−0.893264	+	0.449532i
$50$	−124.304	−	73.7127i	−0.351586	−	0.208491i
$51$	−201.389			−0.552943
$52$	295.933	+	295.933i	0.789202	+	0.789202i
$53$	348.840	+	348.840i	0.904091	+	0.904091i	0.995787	−	0.0916963i	$-0.0292289\pi$
$53$	348.840	+	348.840i	0.904091	+	0.904091i	−0.0916963	+	0.995787i	$0.529229\pi$
$54$	31.2157			0.0786651
$55$	130.415	+	101.284i	0.319729	+	0.248311i
$56$	−164.718	+	267.293i	−0.393059	+	0.637831i
$57$	20.5080	−	20.5080i	0.0476552	−	0.0476552i
$58$	186.917	+	186.917i	0.423163	+	0.423163i
$59$	−593.332			−1.30924			−0.654621	−	0.755957i	$-0.727172\pi$
$59$	−593.332			−1.30924			−0.654621	+	0.755957i	$0.727172\pi$
$60$	−27.8798	−	221.750i	−0.0599878	−	0.477130i
$61$		−	328.164i		−	0.688805i	−0.938822	−	0.344403i	$-0.888081\pi$
$61$		−	328.164i		−	0.688805i	0.938822	−	0.344403i	$-0.111919\pi$
$62$	8.47370	+	8.47370i	0.0173574	+	0.0173574i
$63$	−162.174	+	38.5061i	−0.324317	+	0.0770050i
$64$		−	67.8038i		−	0.132429i
$65$	−696.730	+	87.5974i	−1.32952	+	0.167156i
$66$		−	51.2258i		−	0.0955373i
$67$	626.936	−	626.936i	1.14317	−	1.14317i	0.155303	−	0.987867i	$-0.450364\pi$
$67$	626.936	−	626.936i	1.14317	−	1.14317i	0.987867	−	0.155303i	$-0.0496355\pi$
$68$	316.295	−	316.295i	0.564065	−	0.564065i
$69$	−251.750			−0.439233
$70$	−83.9264	−	224.199i	−0.143302	−	0.382813i
$71$	360.302			0.602253			0.301126	−	0.953584i	$-0.402637\pi$
$71$	360.302			0.602253			0.301126	+	0.953584i	$0.402637\pi$
$72$	−107.887	+	107.887i	−0.176592	+	0.176592i
$73$	504.894	−	504.894i	0.809499	−	0.809499i	−0.175059	−	0.984558i	$-0.556012\pi$
$73$	504.894	−	504.894i	0.809499	−	0.809499i	0.984558	+	0.175059i	$0.0560116\pi$
$74$		−	325.093i		−	0.510693i
$75$	322.551	+	191.274i	0.496600	+	0.294485i
$76$			64.4183i			0.0972274i
$77$	63.1897	+	266.132i	0.0935212	+	0.393877i
$78$	154.039	+	154.039i	0.223609	+	0.223609i
$79$		−	159.951i		−	0.227797i	−0.993492	−	0.113898i	$-0.963666\pi$
$79$		−	159.951i		−	0.227797i	0.993492	−	0.113898i	$-0.0363338\pi$
$80$	297.638	+	231.155i	0.415961	+	0.323048i
$81$	−81.0000			−0.111111
$82$	−282.721	−	282.721i	−0.380748	−	0.380748i
$83$	413.196	−	413.196i	0.546436	−	0.546436i	−0.378972	−	0.925408i	$-0.623722\pi$
$83$	413.196	−	413.196i	0.546436	−	0.546436i	0.925408	+	0.378972i	$0.123722\pi$
$84$	194.228	−	315.181i	0.252286	−	0.409394i
$85$	93.6247	+	744.670i	0.119471	+	0.950245i
$86$	−544.879			−0.683207
$87$	−485.023	−	485.023i	−0.597700	−	0.597700i
$88$	177.046	+	177.046i	0.214468	+	0.214468i
$89$	707.614			0.842774			0.421387	−	0.906881i	$-0.361543\pi$
$89$	707.614			0.842774			0.421387	+	0.906881i	$0.361543\pi$
$90$	−14.5120	−	115.425i	−0.0169966	−	0.135188i
$91$	−990.288	−	610.258i	−1.14077	−	0.702993i
$92$	395.389	−	395.389i	0.448067	−	0.448067i
$93$	−21.9880	−	21.9880i	−0.0245167	−	0.0245167i
$94$	249.168			0.273401
$95$	−85.3657	−	66.2976i	−0.0921930	−	0.0715999i
$96$		−	523.777i		−	0.556852i
$97$	−604.783	−	604.783i	−0.633056	−	0.633056i	0.315777	−	0.948833i	$-0.397735\pi$
$97$	−604.783	−	604.783i	−0.633056	−	0.633056i	−0.948833	+	0.315777i	$0.897735\pi$
$98$	124.425	−	376.529i	0.128253	−	0.388114i
$99$			132.923i			0.134942i
$100$	−806.997	+	206.181i	−0.806997	+	0.206181i
$101$		−	537.727i		−	0.529760i	−0.964281	−	0.264880i	$-0.914668\pi$
$101$		−	537.727i		−	0.529760i	0.964281	−	0.264880i	$-0.0853324\pi$
$102$	164.638	−	164.638i	0.159819	−	0.159819i
$103$	−1098.85	+	1098.85i	−1.05119	+	1.05119i	−0.0525739	+	0.998617i	$0.516743\pi$
$103$	−1098.85	+	1098.85i	−1.05119	+	1.05119i	−0.998617	+	0.0525739i	$0.983257\pi$
$104$	−1064.77			−1.00394
$105$	217.777	+	581.763i	0.202408	+	0.540707i
$106$	−570.361			−0.522626
$107$	−367.542	+	367.542i	−0.332072	+	0.332072i	−0.853373	−	0.521301i	$-0.825447\pi$
$107$	−367.542	+	367.542i	−0.332072	+	0.332072i	0.521301	+	0.853373i	$0.325447\pi$
$108$	127.216	−	127.216i	0.113346	−	0.113346i
$109$		−	1282.11i		−	1.12664i	−0.826238	−	0.563321i	$-0.809523\pi$
$109$		−	1282.11i		−	1.12664i	0.826238	−	0.563321i	$-0.190477\pi$
$110$	−189.416	+	23.8146i	−0.164183	+	0.0206421i
$111$			843.569i			0.721333i
$112$	144.214	+	607.377i	0.121669	+	0.512426i
$113$	−374.746	−	374.746i	−0.311975	−	0.311975i	0.533700	−	0.845674i	$-0.320801\pi$
$113$	−374.746	−	374.746i	−0.311975	−	0.311975i	−0.845674	+	0.533700i	$0.820801\pi$
$114$			33.5310i			0.0275479i
$115$	117.037	+	930.887i	0.0949022	+	0.754832i
$116$	1523.52			1.21944
$117$	−399.708	−	399.708i	−0.315838	−	0.315838i
$118$	485.056	−	485.056i	0.378415	−	0.378415i
$119$	−652.248	+	1058.43i	−0.502449	+	0.815343i
$120$	449.087	+	348.775i	0.341632	+	0.265322i
$121$	−1112.87			−0.836115
$122$	268.278	+	268.278i	0.199088	+	0.199088i
$123$	733.620	+	733.620i	0.537791	+	0.537791i
$124$	69.0672			0.0500195
$125$	557.314	−	1281.61i	0.398782	−	0.917046i
$126$	101.100	−	164.058i	0.0714815	−	0.115996i
$127$	1516.59	−	1516.59i	1.05965	−	1.05965i	0.0615448	−	0.998104i	$-0.480397\pi$
$127$	1516.59	−	1516.59i	1.05965	−	1.05965i	0.998104	−	0.0615448i	$-0.0196027\pi$
$128$	1043.07	+	1043.07i	0.720278	+	0.720278i
$129$	1413.88			0.965001
$130$	497.973	−	641.197i	0.335963	−	0.432590i
$131$			800.044i			0.533589i	0.963753	+	0.266795i	$0.0859645\pi$
$131$			800.044i			0.533589i	−0.963753	+	0.266795i	$0.914035\pi$
$132$	−208.765	−	208.765i	−0.137657	−	0.137657i
$133$	−41.3622	−	174.202i	−0.0269666	−	0.113573i
$134$			1025.05i			0.660830i
$135$	37.6565	+	299.511i	0.0240071	+	0.190947i
$136$			1138.04i			0.717544i
$137$	1459.07	−	1459.07i	0.909902	−	0.909902i	−0.0863617	−	0.996264i	$-0.527524\pi$
$137$	1459.07	−	1459.07i	0.909902	−	0.909902i	0.996264	+	0.0863617i	$0.0275241\pi$
$138$	205.808	−	205.808i	0.126953	−	0.126953i
$139$	348.479			0.212645			0.106322	−	0.994332i	$-0.466092\pi$
$139$	348.479			0.212645			0.106322	+	0.994332i	$0.466092\pi$
$140$	−1255.73	−	571.665i	−0.758061	−	0.345104i
$141$	−646.553			−0.386167
$142$	−294.551	+	294.551i	−0.174071	+	0.174071i
$143$	−655.932	+	655.932i	−0.383579	+	0.383579i
$144$			303.363i			0.175558i
$145$	−1567.97	+	2018.94i	−0.898019	+	1.15630i
$146$			825.514i			0.467945i
$147$	−322.865	+	977.036i	−0.181153	+	0.548194i
$148$	−1324.88	−	1324.88i	−0.735841	−	0.735841i
$149$		−	31.0610i		−	0.0170780i	−0.999964	−	0.00853899i	$-0.997282\pi$
$149$		−	31.0610i		−	0.0170780i	0.999964	−	0.00853899i	$-0.00271808\pi$
$150$	−420.058	+	107.321i	−0.228650	+	0.0584182i
$151$	3045.48			1.64131			0.820655	−	0.571424i	$-0.193609\pi$
$151$	3045.48			1.64131			0.820655	+	0.571424i	$0.193609\pi$
$152$	−115.889	−	115.889i	−0.0618412	−	0.0618412i
$153$	−427.211	+	427.211i	−0.225738	+	0.225738i
$154$	−269.224	−	165.907i	−0.140875	−	0.0868129i
$155$	−71.0823	+	91.5265i	−0.0368353	+	0.0474296i
$156$	1255.54			0.644380
$157$	−988.660	−	988.660i	−0.502571	−	0.502571i	0.409665	−	0.912236i	$-0.365646\pi$
$157$	−988.660	−	988.660i	−0.502571	−	0.502571i	−0.912236	+	0.409665i	$0.865646\pi$
$158$	130.762	+	130.762i	0.0658409	+	0.0658409i
$159$	1480.00			0.738187
$160$	−1936.76	+	243.501i	−0.956963	+	0.120315i
$161$	−815.352	+	1323.10i	−0.399123	+	0.647671i
$162$	66.2184	−	66.2184i	0.0321149	−	0.0321149i
$163$	−689.230	−	689.230i	−0.331194	−	0.331194i	0.521846	−	0.853040i	$-0.325244\pi$
$163$	−689.230	−	689.230i	−0.331194	−	0.331194i	−0.853040	+	0.521846i	$0.825244\pi$
$164$	−2304.40			−1.09721
$165$	491.507	−	61.7953i	0.231901	−	0.0291561i
$166$			675.585i			0.315877i
$167$	1701.15	+	1701.15i	0.788257	+	0.788257i	0.981208	−	0.192952i	$-0.0618060\pi$
$167$	1701.15	+	1701.15i	0.788257	+	0.788257i	−0.192952	+	0.981208i	$0.561806\pi$
$168$	217.596	+	916.433i	0.0999279	+	0.420859i
$169$		−	1747.85i		−	0.795563i
$170$	−685.316	−	532.237i	−0.309184	−	0.240122i
$171$		−	87.0079i		−	0.0389103i
$172$	−2220.59	+	2220.59i	−0.984411	+	0.984411i
$173$	948.066	−	948.066i	0.416648	−	0.416648i	−0.467399	−	0.884047i	$-0.654809\pi$
$173$	948.066	−	948.066i	0.416648	−	0.416648i	0.884047	+	0.467399i	$0.154809\pi$
$174$	793.023			0.345511
$175$	2049.92	−	1075.72i	0.885484	−	0.464669i
$176$	497.828			0.213211
$177$	−1258.65	+	1258.65i	−0.534496	+	0.534496i
$178$	−578.482	+	578.482i	−0.243590	+	0.243590i
$179$			2382.56i			0.994864i	0.867503	+	0.497432i	$0.165724\pi$
$179$			2382.56i			0.994864i	−0.867503	+	0.497432i	$0.834276\pi$
$180$	−529.544	−	411.260i	−0.219277	−	0.170297i
$181$		−	854.972i		−	0.351103i	−0.984470	−	0.175551i	$-0.943829\pi$
$181$		−	854.972i		−	0.351103i	0.984470	−	0.175551i	$-0.0561708\pi$
$182$	1308.46	−	310.679i	0.532911	−	0.126533i
$183$	−696.141	−	696.141i	−0.281204	−	0.281204i
$184$			1422.62i			0.569984i
$185$	3119.24	−	392.170i	1.23963	−	0.155854i
$186$	35.9509			0.0141723
$187$	701.065	+	701.065i	0.274155	+	0.274155i
$188$	1015.45	−	1015.45i	0.393934	−	0.393934i
$189$	−262.338	+	425.706i	−0.100965	+	0.163839i
$190$	123.986	−	15.5884i	0.0473417	−	0.00595210i
$191$	3254.66			1.23298			0.616489	−	0.787364i	$-0.288555\pi$
$191$	3254.66			1.23298			0.616489	+	0.787364i	$0.288555\pi$
$192$	−143.834	−	143.834i	−0.0540641	−	0.0540641i
$193$	−668.389	−	668.389i	−0.249283	−	0.249283i	0.571393	−	0.820677i	$-0.306403\pi$
$193$	−668.389	−	668.389i	−0.249283	−	0.249283i	−0.820677	+	0.571393i	$0.806403\pi$
$194$	988.834			0.365949
$195$	−1292.17	+	1663.81i	−0.474533	+	0.611015i
$196$	−1027.42	−	2041.58i	−0.374424	−	0.744016i
$197$	−747.576	+	747.576i	−0.270368	+	0.270368i	−0.829248	−	0.558880i	$-0.811231\pi$
$197$	−747.576	+	747.576i	−0.270368	+	0.270368i	0.558880	+	0.829248i	$0.311231\pi$
$198$	−108.666	−	108.666i	−0.0390029	−	0.0390029i
$199$	−374.066			−0.133250			−0.0666252	−	0.997778i	$-0.521223\pi$
$199$	−374.066			−0.133250			−0.0666252	+	0.997778i	$0.521223\pi$
$200$	1080.88	−	1822.72i	0.382147	−	0.644428i
$201$		−	2659.86i		−	0.933395i
$202$	439.598	+	439.598i	0.153119	+	0.153119i
$203$	−4119.97	+	978.235i	−1.42446	+	0.338220i
$204$		−	1341.93i		−	0.460557i
$205$	2371.63	−	3053.74i	0.808008	−	1.04040i
$206$		−	1796.64i		−	0.607660i
$207$	−534.041	+	534.041i	−0.179316	+	0.179316i
$208$	−1497.00	+	1497.00i	−0.499029	+	0.499029i
$209$	−142.783			−0.0472559
$210$	−653.633	−	297.563i	−0.214785	−	0.0977800i
$211$	−885.548			−0.288927			−0.144464	−	0.989510i	$-0.546146\pi$
$211$	−885.548			−0.288927			−0.144464	+	0.989510i	$0.546146\pi$
$212$	−2324.44	+	2324.44i	−0.753034	+	0.753034i
$213$	764.315	−	764.315i	0.245869	−	0.245869i
$214$		−	600.940i		−	0.191960i
$215$	−657.305	−	5228.06i	−0.208502	−	1.65838i
$216$			457.726i			0.144187i
$217$	−186.774	+	44.3473i	−0.0584289	+	0.0138732i
$218$	1048.14	+	1048.14i	0.325638	+	0.325638i
$219$		−	2142.09i		−	0.660953i
$220$	−674.890	+	868.998i	−0.206823	+	0.266308i
$221$	−4216.29			−1.28334
$222$	−689.627	−	689.627i	−0.208490	−	0.208490i
$223$	2498.01	−	2498.01i	0.750130	−	0.750130i	−0.224373	−	0.974503i	$-0.572034\pi$
$223$	2498.01	−	2498.01i	0.750130	−	0.750130i	0.974503	+	0.224373i	$0.0720335\pi$
$224$	−2752.78	−	1696.38i	−0.821107	−	0.506001i
$225$	1089.99	−	278.482i	0.322959	−	0.0825133i
$226$	612.718			0.180342
$227$	656.134	+	656.134i	0.191847	+	0.191847i	0.796494	−	0.604647i	$-0.206686\pi$
$227$	656.134	+	656.134i	0.191847	+	0.191847i	−0.604647	+	0.796494i	$0.706686\pi$
$228$	136.652	+	136.652i	0.0396929	+	0.0396929i
$229$	3183.72			0.918717			0.459359	−	0.888251i	$-0.348079\pi$
$229$	3183.72			0.918717			0.459359	+	0.888251i	$0.348079\pi$
$230$	−856.689	−	665.331i	−0.245602	−	0.190742i
$231$	698.596	+	430.505i	0.198979	+	0.122620i
$232$	−2740.83	+	2740.83i	−0.775623	+	0.775623i
$233$	−2487.87	−	2487.87i	−0.699511	−	0.699511i	0.264794	−	0.964305i	$-0.414696\pi$
$233$	−2487.87	−	2487.87i	−0.699511	−	0.699511i	−0.964305	+	0.264794i	$0.914696\pi$
$234$	653.532			0.182576
$235$	300.579	+	2390.74i	0.0834367	+	0.663637i
$236$		−	3953.58i		−	1.09049i
$237$	−339.308	−	339.308i	−0.0929975	−	0.0929975i
$238$	−332.056	−	1398.50i	−0.0904369	−	0.380887i
$239$			4478.70i			1.21215i	0.795409	+	0.606073i	$0.207256\pi$
$239$			4478.70i			1.21215i	−0.795409	+	0.606073i	$0.792744\pi$
$240$	1121.74	−	141.032i	0.301699	−	0.0379316i
$241$		−	5232.93i		−	1.39868i	−0.714788	−	0.699341i	$-0.753477\pi$
$241$		−	5232.93i		−	1.39868i	0.714788	−	0.699341i	$-0.246523\pi$
$242$	909.783	−	909.783i	0.241666	−	0.241666i
$243$	−171.827	+	171.827i	−0.0453609	+	0.0453609i
$244$	2186.67			0.573719
$245$	3762.85	+	739.629i	0.981224	+	0.192870i
$246$	−1199.48			−0.310880
$247$	429.355	−	429.355i	0.110604	−	0.110604i
$248$	−124.253	+	124.253i	−0.0318148	+	0.0318148i
$249$		−	1753.04i		−	0.446163i
$250$	592.121	+	1503.34i	0.149796	+	0.380319i
$251$			6395.52i			1.60829i	0.594431	+	0.804147i	$0.297377\pi$
$251$			6395.52i			1.60829i	−0.594431	+	0.804147i	$0.702623\pi$
$252$	−256.580	−	1080.62i	−0.0641389	−	0.270130i
$253$	876.377	+	876.377i	0.217776	+	0.217776i
$254$			2479.66i			0.612549i
$255$	1778.29	+	1381.08i	0.436710	+	0.339162i
$256$	−1163.02			−0.283940
$257$	1398.90	+	1398.90i	0.339538	+	0.339538i	0.856193	−	0.516655i	$-0.172823\pi$
$257$	1398.90	+	1398.90i	0.339538	+	0.339538i	−0.516655	+	0.856193i	$0.672823\pi$
$258$	−1155.86	+	1155.86i	−0.278918	+	0.278918i
$259$	4433.48	+	2732.10i	1.06364	+	0.655462i
$260$	−583.692	−	4642.56i	−0.139227	−	1.10738i
$261$	−2057.78			−0.488020
$262$	−654.045	−	654.045i	−0.154225	−	0.154225i
$263$	−5638.88	−	5638.88i	−1.32209	−	1.32209i	−0.912086	−	0.409999i	$-0.865529\pi$
$263$	−5638.88	−	5638.88i	−1.32209	−	1.32209i	−0.409999	−	0.912086i	$-0.634471\pi$
$264$	751.142			0.175112
$265$	−688.045	−	5472.56i	−0.159495	−	1.26859i
$266$	176.226	+	108.598i	0.0406208	+	0.0250323i
$267$	1501.08	−	1501.08i	0.344061	−	0.344061i
$268$	4177.49	+	4177.49i	0.952168	+	0.952168i
$269$	−3672.74			−0.832458			−0.416229	−	0.909260i	$-0.636648\pi$
$269$	−3672.74			−0.832458			−0.416229	+	0.909260i	$0.636648\pi$
$270$	−275.638	−	214.069i	−0.0621290	−	0.0482513i
$271$			7503.82i			1.68201i	0.541028	+	0.841005i	$0.318035\pi$
$271$			7503.82i			1.68201i	−0.541028	+	0.841005i	$0.681965\pi$
$272$	1600.00	+	1600.00i	0.356670	+	0.356670i
$273$	−3395.27	+	806.165i	−0.752714	+	0.178723i
$274$			2385.61i			0.525985i
$275$	−456.998	−	1788.70i	−0.100211	−	0.392228i
$276$		−	1677.50i		−	0.365845i
$277$	−1260.40	+	1260.40i	−0.273393	+	0.273393i	−0.830465	−	0.557071i	$-0.811925\pi$
$277$	−1260.40	+	1260.40i	−0.273393	+	0.273393i	0.557071	+	0.830465i	$0.311925\pi$
$278$	−284.886	+	284.886i	−0.0614616	+	0.0614616i
$279$	−93.2872			−0.0200178
$280$	3287.51	−	1230.64i	0.701665	−	0.262661i
$281$	2828.67			0.600514			0.300257	−	0.953858i	$-0.402928\pi$
$281$	2828.67			0.600514			0.300257	+	0.953858i	$0.402928\pi$
$282$	528.564	−	528.564i	0.111615	−	0.111615i
$283$	−5085.43	+	5085.43i	−1.06819	+	1.06819i	−0.0706903	+	0.997498i	$0.522520\pi$
$283$	−5085.43	+	5085.43i	−1.06819	+	1.06819i	−0.997498	+	0.0706903i	$0.977480\pi$
$284$			2400.82i			0.501628i
$285$	−321.727	+	40.4495i	−0.0668682	+	0.00840710i
$286$		−	1072.46i		−	0.221735i
$287$	6231.64	−	1479.63i	1.28168	−	0.304319i
$288$	−1111.10	−	1111.10i	−0.227334	−	0.227334i
$289$		−	406.603i		−	0.0827606i
$290$	−368.672	−	2932.34i	−0.0746523	−	0.593768i
$291$	−2565.88			−0.516888
$292$	3364.29	+	3364.29i	0.674247	+	0.674247i
$293$	1231.62	−	1231.62i	0.245570	−	0.245570i	−0.573580	−	0.819150i	$-0.694446\pi$
$293$	1231.62	−	1231.62i	0.245570	−	0.245570i	0.819150	+	0.573580i	$0.194446\pi$
$294$	−534.792	−	1062.68i	−0.106087	−	0.210806i
$295$	5239.20	+	4068.92i	1.03403	+	0.803057i
$296$	4766.96			0.936060
$297$	281.973	+	281.973i	0.0550900	+	0.0550900i
$298$	25.3927	+	25.3927i	0.00493611	+	0.00493611i
$299$	−5270.63			−1.01943
$300$	−1274.52	+	2149.27i	−0.245282	+	0.413628i
$301$	4579.20	−	7430.83i	0.876879	−	1.42294i
$302$	−2489.72	+	2489.72i	−0.474394	+	0.474394i
$303$	−1140.69	−	1140.69i	−0.216274	−	0.216274i
$304$	−325.864			−0.0614790
$305$	−2250.47	+	2897.73i	−0.422497	+	0.544012i
$306$		−	698.499i		−	0.130492i
$307$	−4940.14	−	4940.14i	−0.918400	−	0.918400i	0.0785128	−	0.996913i	$-0.474983\pi$
$307$	−4940.14	−	4940.14i	−0.918400	−	0.918400i	−0.996913	+	0.0785128i	$0.974983\pi$
$308$	−1773.33	+	421.055i	−0.328067	+	0.0778956i
$309$			4662.02i			0.858294i
$310$	−16.7134	−	132.934i	−0.00306211	−	0.0243554i
$311$			8018.73i			1.46206i	0.682345	+	0.731030i	$0.260960\pi$
$311$			8018.73i			1.46206i	−0.682345	+	0.731030i	$0.739040\pi$
$312$	−2258.73	+	2258.73i	−0.409856	+	0.409856i
$313$	−6369.51	+	6369.51i	−1.15024	+	1.15024i	−0.163740	+	0.986504i	$0.552356\pi$
$313$	−6369.51	+	6369.51i	−1.15024	+	1.15024i	−0.986504	+	0.163740i	$0.947644\pi$
$314$	1616.48			0.290520
$315$	1696.08	+	772.132i	0.303375	+	0.138110i
$316$	1065.81			0.189736
$317$	5288.99	−	5288.99i	0.937095	−	0.937095i	−0.0610403	−	0.998135i	$-0.519442\pi$
$317$	5288.99	−	5288.99i	0.937095	−	0.937095i	0.998135	+	0.0610403i	$0.0194418\pi$
$318$	−1209.92	+	1209.92i	−0.213361	+	0.213361i
$319$			3376.87i			0.592691i
$320$	−464.982	+	598.717i	−0.0812290	+	0.104592i
$321$			1559.35i			0.271135i
$322$	−415.091	−	1748.21i	−0.0718389	−	0.302559i
$323$	−458.898	−	458.898i	−0.0790519	−	0.0790519i
$324$		−	539.731i		−	0.0925465i
$325$	6752.94	+	4004.51i	1.15257	+	0.683477i
$326$	1126.91			0.191453
$327$	−2719.77	−	2719.77i	−0.459950	−	0.459950i
$328$	4145.64	−	4145.64i	0.697880	−	0.697880i
$329$	−2094.02	+	3398.04i	−0.350903	+	0.569423i
$330$	−351.294	+	452.331i	−0.0586003	+	0.0754545i
$331$	1802.71			0.299353			0.149677	−	0.988735i	$-0.452177\pi$
$331$	1802.71			0.299353			0.149677	+	0.988735i	$0.452177\pi$
$332$	2753.27	+	2753.27i	0.455137	+	0.455137i
$333$	1789.48	+	1789.48i	0.294483	+	0.294483i
$334$	−2781.42			−0.455666
$335$	−9835.30	+	1236.56i	−1.60406	+	0.201672i
$336$	1594.37	+	982.517i	0.258868	+	0.159526i
$337$	1593.51	−	1593.51i	0.257578	−	0.257578i	−0.566490	−	0.824068i	$-0.691699\pi$
$337$	1593.51	−	1593.51i	0.257578	−	0.257578i	0.824068	+	0.566490i	$0.191699\pi$
$338$	1428.89	+	1428.89i	0.229945	+	0.229945i
$339$	−1589.91			−0.254726
$340$	−4962.00	+	623.854i	−0.791477	+	0.0995096i
$341$			153.087i			0.0243112i
$342$	71.1300	+	71.1300i	0.0112464	+	0.0112464i
$343$	4089.26	+	4861.23i	0.643730	+	0.765253i
$344$		−	7989.75i		−	1.25226i
$345$	2222.98	+	1726.44i	0.346902	+	0.269415i
$346$			1550.11i			0.240851i
$347$	−6330.40	+	6330.40i	−0.979349	+	0.979349i	−0.999791	−	0.0204425i	$-0.993492\pi$
$347$	−6330.40	+	6330.40i	−0.979349	+	0.979349i	0.0204425	+	0.999791i	$0.493492\pi$
$348$	3231.88	−	3231.88i	0.497836	−	0.497836i
$349$	8093.46			1.24136			0.620678	−	0.784066i	$-0.286857\pi$
$349$	8093.46			1.24136			0.620678	+	0.784066i	$0.286857\pi$
$350$	−796.420	+	2555.25i	−0.121630	+	0.390240i
$351$	−1695.82			−0.257880
$352$	−1823.35	+	1823.35i	−0.276093	+	0.276093i
$353$	7660.45	−	7660.45i	1.15503	−	1.15503i	0.169496	−	0.985531i	$-0.445786\pi$
$353$	7660.45	−	7660.45i	1.15503	−	1.15503i	0.985531	−	0.169496i	$-0.0542140\pi$
$354$		−	2057.92i		−	0.308975i
$355$	−3181.51	−	2470.86i	−0.475654	−	0.369407i
$356$			4715.08i			0.701963i
$357$	861.635	+	3628.89i	0.127738	+	0.537986i
$358$	−1947.77	−	1947.77i	−0.287549	−	0.287549i
$359$		−	9220.97i		−	1.35561i	−0.735241	−	0.677806i	$-0.762931\pi$
$359$		−	9220.97i		−	1.35561i	0.735241	−	0.677806i	$-0.237069\pi$
$360$	1692.52	−	212.794i	0.247788	−	0.0311535i
$361$	−6765.54			−0.986374
$362$	698.950	+	698.950i	0.101481	+	0.101481i
$363$	−2360.75	+	2360.75i	−0.341342	+	0.341342i
$364$	4066.36	−	6598.63i	0.585536	−	0.950171i
$365$	−7920.73	+	995.844i	−1.13586	+	0.142808i
$366$	1138.21			0.162555
$367$	526.288	+	526.288i	0.0748556	+	0.0748556i	0.743543	−	0.668688i	$-0.233144\pi$
$367$	526.288	+	526.288i	0.0748556	+	0.0748556i	−0.668688	+	0.743543i	$0.733144\pi$
$368$	2000.11	+	2000.11i	0.283323	+	0.283323i
$369$	3112.49			0.439104
$370$	−2229.41	+	2870.62i	−0.313247	+	0.403341i
$371$	4793.35	−	7778.34i	0.670777	−	1.08849i
$372$	146.514	−	146.514i	0.0204204	−	0.0204204i
$373$	−4597.71	−	4597.71i	−0.638232	−	0.638232i	0.311887	−	0.950119i	$-0.399039\pi$
$373$	−4597.71	−	4597.71i	−0.638232	−	0.638232i	−0.950119	+	0.311887i	$0.899039\pi$
$374$	−1146.26			−0.158480
$375$	−1536.46	−	3900.95i	−0.211581	−	0.537184i
$376$			3653.63i			0.501122i
$377$	−10154.4	−	10154.4i	−1.38722	−	1.38722i
$378$	−133.555	−	562.484i	−0.0181728	−	0.0765372i
$379$			1413.40i			0.191560i	0.995403	+	0.0957801i	$0.0305346\pi$
$379$			1413.40i			0.191560i	−0.995403	+	0.0957801i	$0.969465\pi$
$380$	441.764	−	568.822i	0.0596369	−	0.0767893i
$381$		−	6434.34i		−	0.865200i
$382$	−2660.72	+	2660.72i	−0.356372	+	0.356372i
$383$	7656.55	−	7656.55i	1.02149	−	1.02149i	0.0217275	−	0.999764i	$-0.493083\pi$
$383$	7656.55	−	7656.55i	1.02149	−	1.02149i	0.999764	−	0.0217275i	$-0.00691661\pi$
$384$	4425.39			0.588105
$385$	1267.09	−	2783.32i	0.167732	−	0.368444i
$386$	1092.83			0.144103
$387$	2999.29	−	2999.29i	0.393960	−	0.393960i
$388$	4029.88	−	4029.88i	0.527284	−	0.527284i
$389$			7675.96i			1.00048i	0.865887	+	0.500240i	$0.166755\pi$
$389$			7675.96i			1.00048i	−0.865887	+	0.500240i	$0.833245\pi$
$390$	−303.823	−	2416.54i	−0.0394479	−	0.313760i
$391$			5633.29i			0.728613i
$392$	5521.17	+	1824.49i	0.711381	+	0.235078i
$393$	1697.15	+	1697.15i	0.217837	+	0.217837i
$394$		−	1222.30i		−	0.156291i
$395$	−1096.91	+	1412.39i	−0.139725	+	0.179912i
$396$	−885.715			−0.112396
$397$	−644.145	−	644.145i	−0.0814325	−	0.0814325i	0.665217	−	0.746650i	$-0.268339\pi$
$397$	−644.145	−	644.145i	−0.0814325	−	0.0814325i	−0.746650	+	0.665217i	$0.768339\pi$
$398$	305.803	−	305.803i	0.0385139	−	0.0385139i
$399$	−457.281	−	281.796i	−0.0573752	−	0.0353571i
$400$	−1042.98	−	4082.25i	−0.130372	−	0.510281i
$401$	−8668.80			−1.07955			−0.539775	−	0.841809i	$-0.681491\pi$
$401$	−8668.80			−1.07955			−0.539775	+	0.841809i	$0.681491\pi$
$402$	2174.47	+	2174.47i	0.269783	+	0.269783i
$403$	−460.341	−	460.341i	−0.0569013	−	0.0569013i
$404$	3583.06			0.441247
$405$	715.241	+	555.478i	0.0877546	+	0.0681529i
$406$	2568.40	−	4167.84i	0.313959	−	0.509473i
$407$	2936.59	−	2936.59i	0.357644	−	0.357644i
$408$	2414.14	+	2414.14i	0.292936	+	0.292936i
$409$	−12334.1			−1.49116			−0.745578	−	0.666418i	$-0.767827\pi$
$409$	−12334.1			−1.49116			−0.745578	+	0.666418i	$0.767827\pi$
$410$	557.634	+	4435.30i	0.0671697	+	0.534253i
$411$		−	6190.30i		−	0.742932i
$412$	−7322.01	−	7322.01i	−0.875557	−	0.875557i
$413$	2538.55	+	10691.4i	0.302455	+	1.27383i
$414$		−	873.170i		−	0.103657i
$415$	−6482.18	+	814.981i	−0.766741	+	0.0963996i
$416$		−	10965.8i		−	1.29241i
$417$	739.237	−	739.237i	0.0868119	−	0.0868119i
$418$	116.726	−	116.726i	0.0136585	−	0.0136585i
$419$	6518.23			0.759992			0.379996	−	0.924988i	$-0.375925\pi$
$419$	6518.23			0.759992			0.379996	+	0.924988i	$0.375925\pi$
$420$	−3876.49	+	1451.12i	−0.450365	+	0.168589i
$421$	−14408.4			−1.66799			−0.833995	−	0.551771i	$-0.813952\pi$
$421$	−14408.4			−1.66799			−0.833995	+	0.551771i	$0.813952\pi$
$422$	723.945	−	723.945i	0.0835097	−	0.0835097i
$423$	−1371.55	+	1371.55i	−0.157652	+	0.157652i
$424$		−	8363.40i		−	0.957930i
$425$	4280.05	−	7217.59i	0.488501	−	0.823776i
$426$			1249.67i			0.142129i
$427$	−5913.29	+	1404.04i	−0.670173	+	0.159124i
$428$	−2449.06	−	2449.06i	−0.276589	−	0.276589i
$429$			2782.89i			0.313191i
$430$	4811.35	+	3736.64i	0.539591	+	0.419063i
$431$	−612.236			−0.0684231			−0.0342116	−	0.999415i	$-0.510892\pi$
$431$	−612.236			−0.0684231			−0.0342116	+	0.999415i	$0.510892\pi$
$432$	643.531	+	643.531i	0.0716711	+	0.0716711i
$433$	6442.70	−	6442.70i	0.715049	−	0.715049i	−0.252538	−	0.967587i	$-0.581265\pi$
$433$	6442.70	−	6442.70i	0.715049	−	0.715049i	0.967587	+	0.252538i	$0.0812652\pi$
$434$	116.436	−	188.944i	0.0128781	−	0.0208978i
$435$	956.650	+	7608.98i	0.105443	+	0.838673i
$436$	8543.16			0.938402
$437$	−573.652	−	573.652i	−0.0627952	−	0.0627952i
$438$	1751.18	+	1751.18i	0.191038	+	0.191038i
$439$	−3263.94			−0.354850			−0.177425	−	0.984134i	$-0.556777\pi$
$439$	−3263.94			−0.354850			−0.177425	+	0.984134i	$0.556777\pi$
$440$	−349.202	−	2777.47i	−0.0378353	−	0.300934i
$441$	1387.71	+	2757.51i	0.149844	+	0.297755i
$442$	3446.86	−	3446.86i	0.370929	−	0.370929i
$443$	5424.12	+	5424.12i	0.581733	+	0.581733i	0.935379	−	0.353646i	$-0.115058\pi$
$443$	5424.12	+	5424.12i	0.581733	+	0.581733i	−0.353646	+	0.935379i	$0.615058\pi$
$444$	−5620.99			−0.600812
$445$	−6248.32	−	4852.64i	−0.665616	−	0.516937i
$446$			4084.30i			0.433626i
$447$	−65.8904	−	65.8904i	−0.00697205	−	0.00697205i
$448$	−1221.78	+	290.096i	−0.128847	+	0.0305932i
$449$			99.0663i			0.0104125i	0.999986	+	0.00520626i	$0.00165721\pi$
$449$			99.0663i			0.0104125i	−0.999986	+	0.00520626i	$0.998343\pi$
$450$	−663.415	+	1118.74i	−0.0694970	+	0.117195i
$451$		−	5107.68i		−	0.533284i
$452$	2497.06	−	2497.06i	0.259850	−	0.259850i
$453$	6460.44	−	6460.44i	0.670062	−	0.670062i
$454$	−1072.79			−0.110900
$455$	4559.38	+	12179.8i	0.469773	+	1.25494i
$456$	−491.677			−0.0504931
$457$	12842.3	−	12842.3i	1.31453	−	1.31453i	0.396485	−	0.918041i	$-0.370230\pi$
$457$	12842.3	−	12842.3i	1.31453	−	1.31453i	0.918041	−	0.396485i	$-0.129770\pi$
$458$	−2602.73	+	2602.73i	−0.265540	+	0.265540i
$459$			1812.50i			0.184314i
$460$	−6202.82	+	779.859i	−0.628713	+	0.0790459i
$461$			19398.1i			1.95978i	0.199529	+	0.979892i	$0.436059\pi$
$461$			19398.1i			1.95978i	−0.199529	+	0.979892i	$0.563941\pi$
$462$	−923.052	+	219.168i	−0.0929530	+	0.0220706i
$463$	4788.35	+	4788.35i	0.480633	+	0.480633i	0.905334	−	0.424700i	$-0.139621\pi$
$463$	4788.35	+	4788.35i	0.480633	+	0.480633i	−0.424700	+	0.905334i	$0.639621\pi$
$464$			7706.84i			0.771080i
$465$	43.3687	+	344.945i	0.00432511	+	0.0344010i
$466$	4067.73			0.404365
$467$	220.031	+	220.031i	0.0218026	+	0.0218026i	0.717924	−	0.696121i	$-0.245092\pi$
$467$	220.031	+	220.031i	0.0218026	+	0.0218026i	−0.696121	+	0.717924i	$0.745092\pi$
$468$	2663.39	−	2663.39i	0.263067	−	0.263067i
$469$	−13979.3	−	8614.62i	−1.37634	−	0.848158i
$470$	−2200.18	−	1708.73i	−0.215930	−	0.167698i
$471$	−4194.53			−0.410347
$472$	7112.54	+	7112.54i	0.693604	+	0.693604i
$473$	−4921.93	−	4921.93i	−0.478457	−	0.478457i
$474$	554.776			0.0537589
$475$	299.138	+	1170.83i	0.0288956	+	0.113098i
$476$	−7052.67	−	4346.16i	−0.679114	−	0.418499i
$477$	3139.56	−	3139.56i	0.301364	−	0.301364i
$478$	−3661.39	−	3661.39i	−0.350351	−	0.350351i
$479$	1128.47			0.107643			0.0538217	−	0.998551i	$-0.482860\pi$
$479$	1128.47			0.107643			0.0538217	+	0.998551i	$0.482860\pi$
$480$	−3591.94	+	4625.02i	−0.341560	+	0.439797i
$481$			17661.0i			1.67416i
$482$	4277.98	+	4277.98i	0.404266	+	0.404266i
$483$	1077.10	+	4536.35i	0.101469	+	0.427352i
$484$		−	7415.44i		−	0.696416i
$485$	1192.86	+	9487.77i	0.111681	+	0.888284i
$486$		−	280.941i		−	0.0262217i
$487$	4726.44	−	4726.44i	0.439786	−	0.439786i	−0.452154	−	0.891940i	$-0.649344\pi$
$487$	4726.44	−	4726.44i	0.439786	−	0.439786i	0.891940	+	0.452154i	$0.149344\pi$
$488$	−3933.85	+	3933.85i	−0.364912	+	0.364912i
$489$	−2924.15			−0.270419
$490$	−3680.83	+	2471.52i	−0.339353	+	0.227861i
$491$	6370.72			0.585553			0.292776	−	0.956181i	$-0.405421\pi$
$491$	6370.72			0.585553			0.292776	+	0.956181i	$0.405421\pi$
$492$	−4888.37	+	4888.37i	−0.447936	+	0.447936i
$493$	−10853.1	+	10853.1i	−0.991483	+	0.991483i
$494$			702.005i			0.0639367i
$495$	911.555	−	1173.73i	0.0827704	−	0.106576i
$496$			349.382i			0.0316284i
$497$	−1541.54	−	6492.38i	−0.139129	−	0.585962i
$498$	1433.13	+	1433.13i	0.128956	+	0.128956i
$499$			2380.86i			0.213591i	0.994281	+	0.106795i	$0.0340590\pi$
$499$			2380.86i			0.213591i	−0.994281	+	0.106795i	$0.965941\pi$
$500$	8539.82	+	3713.58i	0.763825	+	0.332153i
$501$	7217.36			0.643609
$502$	−5228.41	−	5228.41i	−0.464851	−	0.464851i
$503$	2333.04	−	2333.04i	0.206810	−	0.206810i	−0.596100	−	0.802910i	$-0.703284\pi$
$503$	2333.04	−	2333.04i	0.206810	−	0.206810i	0.802910	+	0.596100i	$0.203284\pi$
$504$	2405.64	+	1482.46i	0.212610	+	0.131020i
$505$	−3687.60	+	4748.20i	−0.324942	+	0.418400i
$506$	−1432.90			−0.125889
$507$	−3707.75	−	3707.75i	−0.324787	−	0.324787i
$508$	10105.6	+	10105.6i	0.882602	+	0.882602i
$509$	−3188.18			−0.277630			−0.138815	−	0.990318i	$-0.544329\pi$
$509$	−3188.18			−0.277630			−0.138815	+	0.990318i	$0.544329\pi$
$510$	−2582.82	+	324.729i	−0.224253	+	0.0281946i
$511$	−11258.0	−	6937.67i	−0.974609	−	0.600596i
$512$	−7393.81	+	7393.81i	−0.638210	+	0.638210i
$513$	−184.572	−	184.572i	−0.0158851	−	0.0158851i
$514$	−2287.24			−0.196276
$515$	17238.6	−	2167.35i	1.47500	−	0.185446i
$516$			9421.18i			0.803768i
$517$	2250.75	+	2250.75i	0.191466	+	0.191466i
$518$	−5857.95	+	1390.90i	−0.496879	+	0.117978i
$519$		−	4022.30i		−	0.340192i
$520$	9402.09	+	7301.95i	0.792902	+	0.615792i
$521$		−	8558.46i		−	0.719679i	−0.933014	−	0.359840i	$-0.882831\pi$
$521$		−	8558.46i		−	0.719679i	0.933014	−	0.359840i	$-0.117169\pi$
$522$	1682.26	−	1682.26i	0.141054	−	0.141054i
$523$	2006.95	−	2006.95i	0.167797	−	0.167797i	−0.618214	−	0.786010i	$-0.712143\pi$
$523$	2006.95	−	2006.95i	0.167797	−	0.167797i	0.786010	+	0.618214i	$0.212143\pi$
$524$	−5330.97			−0.444436
$525$	2066.59	−	6630.50i	0.171797	−	0.551198i
$526$	9219.70			0.764255
$527$	−492.016	+	492.016i	−0.0406690	+	0.0406690i
$528$	1056.05	−	1056.05i	0.0870432	−	0.0870432i
$529$		−	5125.02i		−	0.421223i
$530$	5036.36	+	3911.39i	0.412765	+	0.320566i
$531$			5339.99i			0.436414i
$532$	1160.77	−	275.611i	0.0945974	−	0.0224610i
$533$	15359.1	+	15359.1i	1.24817	+	1.24817i
$534$			2454.29i			0.198891i
$535$	5765.96	−	724.933i	0.465952	−	0.0585824i
$536$	−15030.7			−1.21125
$537$	5054.17	+	5054.17i	0.406152	+	0.406152i
$538$	3002.51	−	3002.51i	0.240608	−	0.240608i
$539$	4525.15	−	2277.27i	0.361618	−	0.181983i
$540$	−1995.75	+	250.918i	−0.159043	+	0.0199959i
$541$	−10856.3			−0.862751			−0.431376	−	0.902172i	$-0.641972\pi$
$541$	−10856.3			−0.862751			−0.431376	+	0.902172i	$0.641972\pi$
$542$	−6134.46	−	6134.46i	−0.486158	−	0.486158i
$543$	−1813.67	−	1813.67i	−0.143337	−	0.143337i
$544$	−11720.3			−0.923723
$545$	−8792.40	+	11321.2i	−0.691055	+	0.889812i
$546$	2116.62	−	3434.72i	0.165903	−	0.269217i
$547$	−7493.50	+	7493.50i	−0.585738	+	0.585738i	−0.936474	−	0.350736i	$-0.885931\pi$
$547$	−7493.50	+	7493.50i	−0.585738	+	0.585738i	0.350736	+	0.936474i	$0.385931\pi$
$548$	9722.28	+	9722.28i	0.757875	+	0.757875i
$549$	−2953.48			−0.229602
$550$	1835.88	+	1088.68i	0.142332	+	0.0844029i
$551$		−	2210.41i		−	0.170901i
$552$	3017.84	+	3017.84i	0.232695	+	0.232695i
$553$	−2882.21	+	684.345i	−0.221635	+	0.0526244i
$554$		−	2060.78i		−	0.158040i
$555$	5784.98	−	7448.82i	0.442448	−	0.569702i
$556$			2322.04i			0.177116i
$557$	13484.3	−	13484.3i	1.02576	−	1.02576i	0.0261023	−	0.999659i	$-0.491690\pi$
$557$	13484.3	−	13484.3i	1.02576	−	1.02576i	0.999659	−	0.0261023i	$-0.00830957\pi$
$558$	76.2633	−	76.2633i	0.00578581	−	0.00578581i
$559$	29601.0			2.23970
$560$	2891.81	−	6352.21i	0.218217	−	0.479339i
$561$	2974.37			0.223847
$562$	−2312.47	+	2312.47i	−0.173569	+	0.173569i
$563$	−7873.75	+	7873.75i	−0.589412	+	0.589412i	−0.937472	−	0.348060i	$-0.886841\pi$
$563$	−7873.75	+	7873.75i	−0.589412	+	0.589412i	0.348060	+	0.937472i	$0.386841\pi$
$564$		−	4308.21i		−	0.321646i
$565$	739.142	+	5878.97i	0.0550370	+	0.437752i
$566$		−	8314.79i		−	0.617485i
$567$	346.555	+	1459.56i	0.0256683	+	0.108106i
$568$	−4319.10	−	4319.10i	−0.319059	−	0.319059i
$569$		−	20344.8i		−	1.49895i	−0.662035	−	0.749473i	$-0.730307\pi$
$569$		−	20344.8i		−	1.49895i	0.662035	−	0.749473i	$-0.269693\pi$
$570$	229.947	−	296.083i	0.0168972	−	0.0217571i
$571$	−2325.78			−0.170457			−0.0852283	−	0.996361i	$-0.527162\pi$
$571$	−2325.78			−0.170457			−0.0852283	+	0.996361i	$0.527162\pi$
$572$	−4370.71	−	4370.71i	−0.319490	−	0.319490i
$573$	6904.17	−	6904.17i	0.503361	−	0.503361i
$574$	−3884.83	+	6304.05i	−0.282490	+	0.458408i
$575$	5350.34	−	9022.46i	0.388043	−	0.654370i
$576$	−610.234			−0.0441431
$577$	6172.12	+	6172.12i	0.445318	+	0.445318i	0.893795	−	0.448476i	$-0.148033\pi$
$577$	6172.12	+	6172.12i	0.445318	+	0.445318i	−0.448476	+	0.893795i	$0.648033\pi$
$578$	332.403	+	332.403i	0.0239206	+	0.0239206i
$579$	−2835.74			−0.203539
$580$	−13452.9	−	10447.9i	−0.963105	−	0.747977i
$581$	−9213.35	−	5677.66i	−0.657890	−	0.405420i
$582$	2097.63	−	2097.63i	0.149398	−	0.149398i
$583$	−5152.10	−	5152.10i	−0.366001	−	0.366001i
$584$	−12104.8			−0.857706
$585$	788.376	+	6270.57i	0.0557186	+	0.443173i
$586$			2013.72i			0.141956i
$587$	−9950.92	−	9950.92i	−0.699690	−	0.699690i	0.264653	−	0.964344i	$-0.414743\pi$
$587$	−9950.92	−	9950.92i	−0.699690	−	0.699690i	−0.964344	+	0.264653i	$0.914743\pi$
$588$	−6510.33	−	2151.36i	−0.456601	−	0.150885i
$589$		−	100.206i		−	0.00701008i
$590$	−7609.50	+	956.715i	−0.530980	+	0.0667582i
$591$			3171.70i			0.220755i
$592$	6702.01	−	6702.01i	0.465288	−	0.465288i
$593$	4807.05	−	4807.05i	0.332887	−	0.332887i	−0.520795	−	0.853682i	$-0.674364\pi$
$593$	4807.05	−	4807.05i	0.332887	−	0.332887i	0.853682	+	0.520795i	$0.174364\pi$
$594$	−461.032			−0.0318458
$595$	13017.9	−	4873.09i	0.896942	−	0.335760i
$596$	206.971			0.0142246
$597$	−793.514	+	793.514i	−0.0543993	+	0.0543993i
$598$	4308.80	−	4308.80i	0.294649	−	0.294649i
$599$		−	11132.6i		−	0.759378i	−0.925114	−	0.379689i	$-0.876031\pi$
$599$		−	11132.6i		−	0.759378i	0.925114	−	0.379689i	$-0.123969\pi$
$600$	−1573.69	−	6159.45i	−0.107076	−	0.419098i
$601$			9545.42i			0.647864i	0.946080	+	0.323932i	$0.105005\pi$
$601$			9545.42i			0.647864i	−0.946080	+	0.323932i	$0.894995\pi$
$602$	2331.24	+	9818.33i	0.157831	+	0.664726i
$603$	−5642.42	−	5642.42i	−0.381057	−	0.381057i
$604$			20293.1i			1.36708i
$605$	9826.78	+	7631.78i	0.660356	+	0.512853i
$606$	1865.05			0.125021
$607$	11697.0	+	11697.0i	0.782150	+	0.782150i	0.980193	−	0.198043i	$-0.0634585\pi$
$607$	11697.0	+	11697.0i	0.782150	+	0.782150i	−0.198043	+	0.980193i	$0.563459\pi$
$608$	1193.51	−	1193.51i	0.0796107	−	0.0796107i
$609$	−6664.62	+	10814.9i	−0.443455	+	0.719610i
$610$	−529.146	−	4208.71i	−0.0351221	−	0.279354i
$611$	−13536.2			−0.896265
$612$	−2846.66	−	2846.66i	−0.188022	−	0.188022i
$613$	7209.51	+	7209.51i	0.475023	+	0.475023i	0.903536	−	0.428512i	$-0.140962\pi$
$613$	7209.51	+	7209.51i	0.475023	+	0.475023i	−0.428512	+	0.903536i	$0.640962\pi$
$614$	8077.25			0.530898
$615$	−1446.98	−	11508.9i	−0.0948744	−	0.754610i
$616$	2432.76	−	3947.72i	0.159121	−	0.258212i
$617$	−18273.4	+	18273.4i	−1.19231	+	1.19231i	−0.215899	+	0.976416i	$0.569268\pi$
$617$	−18273.4	+	18273.4i	−1.19231	+	1.19231i	−0.976416	+	0.215899i	$0.930732\pi$
$618$	−3811.25	−	3811.25i	−0.248076	−	0.248076i
$619$	184.644			0.0119894			0.00599472	−	0.999982i	$-0.498092\pi$
$619$	184.644			0.0119894			0.00599472	+	0.999982i	$0.498092\pi$
$620$	−609.873	−	473.646i	−0.0395050	−	0.0306808i
$621$			2265.75i			0.146411i
$622$	−6555.40	−	6555.40i	−0.422585	−	0.422585i
$623$	−3027.50	−	12750.7i	−0.194694	−	0.819977i
$624$			6351.22i			0.407456i
$625$	−13710.1	+	7494.87i	−0.877448	+	0.479672i
$626$		−	10414.3i		−	0.664918i
$627$	−302.887	+	302.887i	−0.0192921	+	0.0192921i
$628$	6587.79	−	6587.79i	0.418601	−	0.418601i
$629$	18876.2			1.19657
$630$	−2017.79	+	755.338i	−0.127604	+	0.0477673i
$631$	15220.0			0.960219			0.480109	−	0.877209i	$-0.340597\pi$
$631$	15220.0			0.960219			0.480109	+	0.877209i	$0.340597\pi$
$632$	−1917.41	+	1917.41i	−0.120681	+	0.120681i
$633$	−1878.53	+	1878.53i	−0.117954	+	0.117954i
$634$			8647.61i			0.541704i
$635$	−23792.1	+	2991.29i	−1.48686	+	0.186938i
$636$			9861.77i			0.614850i
$637$	−6759.51	+	20455.2i	−0.420442	+	1.27232i
$638$	−2760.63	−	2760.63i	−0.171308	−	0.171308i
$639$		−	3242.72i		−	0.200751i
$640$	−2057.34	−	16363.6i	−0.127068	−	1.01067i
$641$	29730.9			1.83198			0.915991	−	0.401200i	$-0.131407\pi$
$641$	29730.9			1.83198			0.915991	+	0.401200i	$0.131407\pi$
$642$	−1274.79	−	1274.79i	−0.0783673	−	0.0783673i
$643$	13026.2	−	13026.2i	0.798919	−	0.798919i	−0.184006	−	0.982925i	$-0.558907\pi$
$643$	13026.2	−	13026.2i	0.798919	−	0.798919i	0.982925	+	0.184006i	$0.0589067\pi$
$644$	−8816.29	−	5432.98i	−0.539458	−	0.332437i
$645$	−12484.7	−	9696.04i	−0.762150	−	0.591909i
$646$	750.308			0.0456973
$647$	4979.22	+	4979.22i	0.302555	+	0.302555i	0.842013	−	0.539458i	$-0.181371\pi$
$647$	4979.22	+	4979.22i	0.302555	+	0.302555i	−0.539458	+	0.842013i	$0.681371\pi$
$648$	970.984	+	970.984i	0.0588640	+	0.0588640i
$649$	8763.08			0.530017
$650$	−8794.34	+	2246.88i	−0.530680	+	0.135584i
$651$	−302.133	+	490.283i	−0.0181898	+	0.0295172i
$652$	4592.58	−	4592.58i	0.275858	−	0.275858i
$653$	−3117.65	−	3117.65i	−0.186835	−	0.186835i	0.607492	−	0.794326i	$-0.292176\pi$
$653$	−3117.65	−	3117.65i	−0.186835	−	0.186835i	−0.794326	+	0.607492i	$0.792176\pi$
$654$	4446.88			0.265882
$655$	5486.50	−	7064.49i	0.327291	−	0.421424i
$656$		−	11657.0i		−	0.693793i
$657$	−4544.05	−	4544.05i	−0.269833	−	0.269833i
$658$	−1066.05	−	4489.82i	−0.0631597	−	0.266005i
$659$		−	7826.23i		−	0.462620i	−0.972880	−	0.231310i	$-0.925699\pi$
$659$		−	7826.23i		−	0.462620i	0.972880	−	0.231310i	$-0.0743012\pi$
$660$	411.764	+	3275.08i	0.0242847	+	0.193155i
$661$		−	13109.2i		−	0.771390i	−0.922626	−	0.385695i	$-0.873962\pi$
$661$		−	13109.2i		−	0.771390i	0.922626	−	0.385695i	$-0.126038\pi$
$662$	−1473.74	+	1473.74i	−0.0865232	+	0.0865232i
$663$	−8944.09	+	8944.09i	−0.523921	+	0.523921i
$664$	−9906.35			−0.578977
$665$	−829.402	+	1821.88i	−0.0483652	+	0.106240i
$666$	−2925.84			−0.170231
$667$	−13567.1	+	13567.1i	−0.787589	+	0.787589i
$668$	−11335.4	+	11335.4i	−0.656554	+	0.656554i
$669$		−	10598.1i		−	0.612478i
$670$	7029.57	−	9051.36i	0.405337	−	0.521917i
$671$			4846.74i			0.278847i
$672$	−9438.10	+	2240.96i	−0.541789	+	0.128641i
$673$	5641.63	+	5641.63i	0.323133	+	0.323133i	0.849968	−	0.526835i	$-0.176621\pi$
$673$	5641.63	+	5641.63i	0.323133	+	0.323133i	−0.526835	+	0.849968i	$0.676621\pi$
$674$			2605.42i			0.148898i
$675$	1721.46	−	2902.96i	0.0981616	−	0.165533i
$676$	11646.5			0.662639
$677$	−8644.87	−	8644.87i	−0.490767	−	0.490767i	0.417781	−	0.908548i	$-0.362808\pi$
$677$	−8644.87	−	8644.87i	−0.490767	−	0.490767i	−0.908548	+	0.417781i	$0.862808\pi$
$678$	1299.77	−	1299.77i	0.0736245	−	0.0736245i
$679$	−8310.23	+	13485.3i	−0.469687	+	0.762178i
$680$	7804.38	−	10049.0i	0.440124	−	0.566710i
$681$	2783.74			0.156642
$682$	−125.150	−	125.150i	−0.00702676	−	0.00702676i
$683$	−19131.7	−	19131.7i	−1.07182	−	1.07182i	−0.997213	−	0.0746058i	$-0.976230\pi$
$683$	−19131.7	−	19131.7i	−1.07182	−	1.07182i	−0.0746058	−	0.997213i	$-0.523770\pi$
$684$	579.764			0.0324091
$685$	−22889.7	+	2877.84i	−1.27674	+	0.160520i
$686$	−7317.13	−	631.091i	−0.407244	−	0.0351241i
$687$	6753.69	−	6753.69i	0.375065	−	0.375065i
$688$	−11233.0	−	11233.0i	−0.622464	−	0.622464i
$689$	30985.3			1.71328
$690$	−3228.69	+	405.932i	−0.178137	+	0.0223965i
$691$		−	27861.8i		−	1.53388i	−0.641717	−	0.766941i	$-0.721778\pi$
$691$		−	27861.8i		−	1.53388i	0.641717	−	0.766941i	$-0.278222\pi$
$692$	6317.30	+	6317.30i	0.347034	+	0.347034i
$693$	2395.18	−	568.707i	0.131292	−	0.0311737i
$694$		−	10350.4i		−	0.566130i
$695$	−3077.12	−	2389.79i	−0.167945	−	0.130431i
$696$			11628.4i			0.633294i
$697$	16415.9	−	16415.9i	0.892104	−	0.892104i
$698$	−6616.50	+	6616.50i	−0.358794	+	0.358794i
$699$	−10555.2			−0.571148
$700$	7167.93	+	13659.4i	0.387032	+	0.737537i
$701$	17660.6			0.951543			0.475771	−	0.879569i	$-0.342169\pi$
$701$	17660.6			0.951543			0.475771	+	0.879569i	$0.342169\pi$
$702$	1386.35	−	1386.35i	0.0745362	−	0.0745362i
$703$	−1922.21	+	1922.21i	−0.103126	+	0.103126i
$704$			1001.41i			0.0536110i
$705$	5709.15	+	4433.90i	0.304991	+	0.236866i
$706$			12525.0i			0.667684i
$707$	−9689.45	+	2300.64i	−0.515430	+	0.122383i
$708$	−8386.81	−	8386.81i	−0.445192	−	0.445192i
$709$			17146.6i			0.908257i	0.890936	+	0.454128i	$0.150049\pi$
$709$			17146.6i			0.908257i	−0.890936	+	0.454128i	$0.849951\pi$
$710$	4620.88	−	580.966i	0.244251	−	0.0307088i
$711$	−1439.56			−0.0759322
$712$	−8482.49	−	8482.49i	−0.446481	−	0.446481i
$713$	−615.052	+	615.052i	−0.0323056	+	0.0323056i
$714$	−3671.05	−	2262.26i	−0.192417	−	0.118576i
$715$	10290.2	−	1293.75i	0.538226	−	0.0676692i
$716$	−15875.8			−0.828641
$717$	9500.76	+	9500.76i	0.494857	+	0.494857i
$718$	7538.25	+	7538.25i	0.391818	+	0.391818i
$719$	15734.5			0.816131			0.408065	−	0.912953i	$-0.366204\pi$
$719$	15734.5			0.816131			0.408065	+	0.912953i	$0.366204\pi$
$720$	2080.39	−	2678.74i	0.107683	−	0.138654i
$721$	24501.8	+	15099.1i	1.26560	+	0.779915i
$722$	5530.90	−	5530.90i	0.285095	−	0.285095i
$723$	−11100.7	−	11100.7i	−0.571010	−	0.571010i
$724$	5696.98			0.292440
$725$	27690.8	−	7074.75i	1.41850	−	0.362413i
$726$		−	3859.88i		−	0.197319i
$727$	20491.2	+	20491.2i	1.04536	+	1.04536i	0.998921	+	0.0464385i	$0.0147871\pi$
$727$	20491.2	+	20491.2i	1.04536	+	1.04536i	0.0464385	+	0.998921i	$0.485213\pi$
$728$	4555.59	+	19186.5i	0.231925	+	0.976783i
$729$			729.000i			0.0370370i
$730$	5661.17	−	7289.40i	0.287026	−	0.369579i
$731$		−	31637.8i		−	1.60077i
$732$	4638.63	−	4638.63i	0.234220	−	0.234220i
$733$	10904.3	−	10904.3i	0.549467	−	0.549467i	−0.376820	−	0.926287i	$-0.622982\pi$
$733$	10904.3	−	10904.3i	0.549467	−	0.549467i	0.926287	+	0.376820i	$0.122982\pi$
$734$	−860.493			−0.0432716
$735$	9551.21	−	6413.23i	0.479322	−	0.321844i
$736$	−14651.2			−0.733764
$737$	−9259.38	+	9259.38i	−0.462786	+	0.462786i
$738$	−2544.49	+	2544.49i	−0.126916	+	0.126916i
$739$			25680.3i			1.27830i	0.769082	+	0.639150i	$0.220714\pi$
$739$			25680.3i			1.27830i	−0.769082	+	0.639150i	$0.779286\pi$
$740$	2613.17	+	20784.6i	0.129814	+	1.03251i
$741$		−	1821.60i		−	0.0903079i
$742$	2440.26	+	10277.5i	0.120734	+	0.508489i
$743$	−11399.1	−	11399.1i	−0.562842	−	0.562842i	0.367272	−	0.930114i	$-0.380292\pi$
$743$	−11399.1	−	11399.1i	−0.562842	−	0.562842i	−0.930114	+	0.367272i	$0.880292\pi$
$744$			527.160i			0.0259767i
$745$	−213.009	+	274.273i	−0.0104752	+	0.0134880i
$746$	7517.37			0.368942
$747$	−3718.77	−	3718.77i	−0.182145	−	0.182145i
$748$	−4671.44	+	4671.44i	−0.228349	+	0.228349i
$749$	8195.36	+	5050.34i	0.399803	+	0.246375i
$750$	4445.15	+	1932.99i	0.216418	+	0.0941105i
$751$	13266.2			0.644594			0.322297	−	0.946639i	$-0.395545\pi$
$751$	13266.2			0.644594			0.322297	+	0.946639i	$0.395545\pi$
$752$	5136.75	+	5136.75i	0.249093	+	0.249093i
$753$	13566.9	+	13566.9i	0.656583	+	0.656583i
$754$	16602.7			0.801905
$755$	−26892.0	−	20885.2i	−1.29629	−	1.00674i
$756$	−2836.63	−	1748.05i	−0.136465	−	0.0840953i
$757$	3819.82	−	3819.82i	0.183400	−	0.183400i	−0.609436	−	0.792835i	$-0.708604\pi$
$757$	3819.82	−	3819.82i	0.183400	−	0.183400i	0.792835	+	0.609436i	$0.208604\pi$
$758$	−1155.47	−	1155.47i	−0.0553674	−	0.0553674i
$759$	3718.15			0.177814
$760$	228.578	+	1818.06i	0.0109097	+	0.0867735i
$761$			24380.2i			1.16134i	0.814138	+	0.580672i	$0.197210\pi$
$761$			24380.2i			1.16134i	−0.814138	+	0.580672i	$0.802790\pi$
$762$	5260.14	+	5260.14i	0.250072	+	0.250072i
$763$	−23102.7	+	5485.46i	−1.09617	+	0.260271i
$764$			21686.9i			1.02697i
$765$	6702.03	−	842.622i	0.316748	−	0.0398236i
$766$			12518.6i			0.590491i
$767$	−26351.1	+	26351.1i	−1.24052	+	1.24052i
$768$	−2467.14	+	2467.14i	−0.115918	+	0.115918i
$769$	−27754.8			−1.30151			−0.650756	−	0.759287i	$-0.725548\pi$
$769$	−27754.8			−1.30151			−0.650756	+	0.759287i	$0.725548\pi$
$770$	1239.53	+	3311.25i	0.0580125	+	0.154973i
$771$	5935.05			0.277232
$772$	4453.71	−	4453.71i	0.207633	−	0.207633i
$773$	−27683.0	+	27683.0i	−1.28808	+	1.28808i	−0.352132	+	0.935951i	$0.614543\pi$
$773$	−27683.0	+	27683.0i	−1.28808	+	1.28808i	−0.935951	+	0.352132i	$0.885457\pi$
$774$			4903.91i			0.227736i
$775$	1255.33	−	320.726i	0.0581843	−	0.0148656i
$776$			14499.6i			0.670755i
$777$	15200.5	−	3609.17i	0.701821	−	0.166639i
$778$	−6275.19	−	6275.19i	−0.289173	−	0.289173i
$779$			3343.34i			0.153771i
$780$	−11086.6	−	8610.16i	−0.508926	−	0.395247i
$781$	−5321.39			−0.243808
$782$	−4605.28	−	4605.28i	−0.210594	−	0.210594i
$783$	−4365.21	+	4365.21i	−0.199233	+	0.199233i
$784$	10327.5	−	5197.28i	0.470458	−	0.236756i
$785$	1950.01	+	15510.0i	0.0886611	+	0.705191i
$786$	−2774.88			−0.125924
$787$	−9758.66	−	9758.66i	−0.442006	−	0.442006i	0.450680	−	0.892686i	$-0.351182\pi$
$787$	−9758.66	−	9758.66i	−0.442006	−	0.442006i	−0.892686	+	0.450680i	$0.851182\pi$
$788$	−4981.36	−	4981.36i	−0.225195	−	0.225195i
$789$	−23923.8			−1.07948
$790$	−257.912	−	2051.38i	−0.0116153	−	0.0923858i
$791$	−5149.32	+	8355.99i	−0.231465	+	0.375607i
$792$	1593.41	−	1593.41i	0.0714892	−	0.0714892i
$793$	−14574.4	−	14574.4i	−0.652652	−	0.652652i
$794$	1053.19			0.0470735
$795$	−13068.6	−	10149.5i	−0.583013	−	0.452786i
$796$		−	2492.53i		−	0.110987i
$797$	−17761.8	−	17761.8i	−0.789404	−	0.789404i	0.191993	−	0.981396i	$-0.438505\pi$
$797$	−17761.8	−	17761.8i	−0.789404	−	0.789404i	−0.981396	+	0.191993i	$0.938505\pi$
$798$	604.204	−	143.461i	0.0268028	−	0.00636399i
$799$			14467.6i			0.640586i
$800$	18771.7	+	11131.6i	0.829599	+	0.491954i
$801$		−	6368.52i		−	0.280925i
$802$	7086.85	−	7086.85i	0.312026	−	0.312026i
$803$	−7456.92	+	7456.92i	−0.327707	+	0.327707i
$804$	17723.6			0.777442
$805$	16273.2	−	6091.68i	0.712490	−	0.266713i
$806$	752.668			0.0328928
$807$	−7791.07	+	7791.07i	−0.339849	+	0.339849i
$808$	−6445.97	+	6445.97i	−0.280654	+	0.280654i
$809$		−	2040.73i		−	0.0886875i	−0.999016	−	0.0443438i	$-0.985880\pi$
$809$		−	2040.73i		−	0.0886875i	0.999016	−	0.0443438i	$-0.0141197\pi$
$810$	−1038.83	+	130.608i	−0.0450625	+	0.00566555i
$811$			24472.9i			1.05963i	0.848113	+	0.529816i	$0.177739\pi$
$811$			24472.9i			1.05963i	−0.848113	+	0.529816i	$0.822261\pi$
$812$	−6518.32	−	27452.8i	−0.281710	−	1.18646i
$813$	15918.0	+	15918.0i	0.686678	+	0.686678i
$814$			4801.39i			0.206743i
$815$	1359.42	+	10812.6i	0.0584277	+	0.464721i
$816$	6788.23			0.291220
$817$	3221.76	+	3221.76i	0.137962	+	0.137962i
$818$	10083.3	−	10083.3i	0.430995	−	0.430995i
$819$	−5492.32	+	8912.59i	−0.234331	+	0.380258i
$820$	20348.1	+	15803.0i	0.866571	+	0.673005i
$821$	−9725.25			−0.413415			−0.206707	−	0.978403i	$-0.566275\pi$
$821$	−9725.25			−0.413415			−0.206707	+	0.978403i	$0.566275\pi$
$822$	5060.64	+	5060.64i	0.214733	+	0.214733i
$823$	−14721.0	−	14721.0i	−0.623499	−	0.623499i	0.322925	−	0.946425i	$-0.395334\pi$
$823$	−14721.0	−	14721.0i	−0.623499	−	0.623499i	−0.946425	+	0.322925i	$0.895334\pi$
$824$	26344.8			1.11379
$825$	−4763.85	−	2824.97i	−0.201037	−	0.119216i
$826$	−10815.7	−	6665.07i	−0.455599	−	0.280760i
$827$	9337.33	−	9337.33i	0.392613	−	0.392613i	−0.483005	−	0.875618i	$-0.660455\pi$
$827$	9337.33	−	9337.33i	0.392613	−	0.392613i	0.875618	+	0.483005i	$0.160455\pi$
$828$	−3558.51	−	3558.51i	−0.149356	−	0.149356i
$829$	−25472.7			−1.06720			−0.533598	−	0.845738i	$-0.679160\pi$
$829$	−25472.7			−1.06720			−0.533598	+	0.845738i	$0.679160\pi$
$830$	4633.00	−	5965.51i	0.193751	−	0.249477i
$831$			5347.41i			0.223225i
$832$	−3011.30	−	3011.30i	−0.125479	−	0.125479i
$833$	21862.7	+	7224.61i	0.909361	+	0.300502i
$834$			1208.67i			0.0501832i
$835$	−3355.31	−	26687.4i	−0.139060	−	1.10606i
$836$		−	951.410i		−	0.0393603i
$837$	−197.892	+	197.892i	−0.00817222	+	0.00817222i
$838$	−5328.73	+	5328.73i	−0.219663	+	0.219663i
$839$	31192.8			1.28354			0.641772	−	0.766895i	$-0.278199\pi$
$839$	31192.8			1.28354			0.641772	+	0.766895i	$0.278199\pi$
$840$	4363.27	−	9584.45i	0.179223	−	0.393684i
$841$	−27888.1			−1.14347
$842$	11779.1	−	11779.1i	0.482106	−	0.482106i
$843$	6000.52	−	6000.52i	0.245159	−	0.245159i
$844$		−	5900.71i		−	0.240653i
$845$	−11986.3	+	15433.8i	−0.487979	+	0.628328i
$846$		−	2242.51i		−	0.0911336i
$847$	4761.36	+	20053.1i	0.193155	+	0.813498i
$848$	−11758.4	−	11758.4i	−0.476160	−	0.476160i
$849$			21575.6i			0.872172i
$850$	2401.48	+	9399.45i	0.0969059	+	0.379292i
$851$	23596.4			0.950500
$852$	5092.90	+	5092.90i	0.204789	+	0.204789i
$853$	−15133.9	+	15133.9i	−0.607473	+	0.607473i	−0.942285	−	0.334812i	$-0.891327\pi$
$853$	−15133.9	+	15133.9i	−0.607473	+	0.607473i	0.334812	+	0.942285i	$0.391327\pi$
$854$	3686.36	−	5981.99i	0.147710	−	0.239695i
$855$	−596.679	+	768.291i	−0.0238666	+	0.0307310i
$856$	8811.79			0.351847
$857$	11491.9	+	11491.9i	0.458058	+	0.458058i	0.898018	−	0.439959i	$-0.145007\pi$
$857$	11491.9	+	11491.9i	0.458058	+	0.458058i	−0.439959	+	0.898018i	$0.645007\pi$
$858$	−2275.04	−	2275.04i	−0.0905228	−	0.0905228i
$859$	−3828.21			−0.152057			−0.0760284	−	0.997106i	$-0.524224\pi$
$859$	−3828.21			−0.152057			−0.0760284	+	0.997106i	$0.524224\pi$
$860$	34836.4	−	4379.85i	1.38129	−	0.173665i
$861$	10080.5	−	16358.1i	0.399006	−	0.647481i
$862$	500.510	−	500.510i	0.0197766	−	0.0197766i
$863$	9185.24	+	9185.24i	0.362305	+	0.362305i	0.864661	−	0.502356i	$-0.167533\pi$
$863$	9185.24	+	9185.24i	0.362305	+	0.362305i	−0.502356	+	0.864661i	$0.667533\pi$
$864$	−4714.00			−0.185617
$865$	−14873.2	+	1869.95i	−0.584627	+	0.0735030i
$866$			10534.0i			0.413347i
$867$	−862.535	−	862.535i	−0.0337869	−	0.0337869i
$868$	−295.501	−	1244.54i	−0.0115553	−	0.0486665i
$869$			2362.36i			0.0922182i
$870$	−7002.50	−	5438.36i	−0.272882	−	0.211928i
$871$		−	55687.0i		−	2.16634i
$872$	−15369.3	+	15369.3i	−0.596868	+	0.596868i
$873$	−5443.05	+	5443.05i	−0.211019	+	0.211019i
$874$	937.934			0.0362999
$875$	−25478.2	−	4559.09i	−0.984365	−	0.176143i
$876$	14273.5			0.550520
$877$	10764.3	−	10764.3i	0.414464	−	0.414464i	−0.468826	−	0.883291i	$-0.655323\pi$
$877$	10764.3	−	10764.3i	0.414464	−	0.414464i	0.883291	+	0.468826i	$0.155323\pi$
$878$	2668.31	−	2668.31i	0.102564	−	0.102564i
$879$		−	5225.31i		−	0.200507i
$880$	−4395.89	−	3413.98i	−0.168392	−	0.130779i
$881$		−	25673.9i		−	0.981813i	−0.871212	−	0.490906i	$-0.836666\pi$
$881$		−	25673.9i		−	0.981813i	0.871212	−	0.490906i	$-0.163334\pi$
$882$	−3388.76	−	1119.83i	−0.129371	−	0.0427512i
$883$	14714.4	+	14714.4i	0.560791	+	0.560791i	0.929532	−	0.368741i	$-0.120211\pi$
$883$	14714.4	+	14714.4i	0.560791	+	0.560791i	−0.368741	+	0.929532i	$0.620211\pi$
$884$		−	28094.6i		−	1.06892i
$885$	19745.5	−	2482.53i	0.749987	−	0.0942931i
$886$	−8868.56			−0.336281
$887$	−14049.3	−	14049.3i	−0.531827	−	0.531827i	0.389289	−	0.921116i	$-0.372721\pi$
$887$	−14049.3	−	14049.3i	−0.531827	−	0.531827i	−0.921116	+	0.389289i	$0.872721\pi$
$888$	10112.2	−	10112.2i	0.382145	−	0.382145i
$889$	−33816.5	−	20839.2i	−1.27578	−	0.786191i
$890$	9075.16	−	1140.99i	0.341798	−	0.0429730i
$891$	1196.31			0.0449808
$892$	16645.1	+	16645.1i	0.624797	+	0.624797i
$893$	−1473.28	−	1473.28i	−0.0552086	−	0.0552086i
$894$	107.732			0.00403032
$895$	16339.0	−	21038.3i	0.610226	−	0.785735i
$896$	14332.7	−	23258.2i	0.534400	−	0.867190i
$897$	−11180.7	+	11180.7i	−0.416179	+	0.416179i
$898$	−80.9878	−	80.9878i	−0.00300957	−	0.00300957i
$899$	−2369.93			−0.0879216
$900$	1855.63	+	7262.97i	0.0687269	+	0.268999i
$901$		−	33117.3i		−	1.22453i
$902$	4175.58	+	4175.58i	0.154137	+	0.154137i
$903$	−6049.23	−	25477.1i	−0.222930	−	0.938898i
$904$			8984.50i			0.330553i
$905$	−5863.19	+	7549.52i	−0.215358	+	0.277298i
$906$			10563.0i			0.387341i
$907$	−16365.8	+	16365.8i	−0.599135	+	0.599135i	−0.940083	−	0.340947i	$-0.889252\pi$
$907$	−16365.8	+	16365.8i	−0.599135	+	0.599135i	0.340947	+	0.940083i	$0.389252\pi$
$908$	−4372.05	+	4372.05i	−0.159793	+	0.159793i
$909$	−4839.54			−0.176587
$910$	−13684.5	−	6229.79i	−0.498501	−	0.226940i
$911$	−17223.9			−0.626404			−0.313202	−	0.949687i	$-0.601402\pi$
$911$	−17223.9			−0.626404			−0.313202	+	0.949687i	$0.601402\pi$
$912$	−691.263	+	691.263i	−0.0250987	+	0.0250987i
$913$	−6102.61	+	6102.61i	−0.221212	+	0.221212i
$914$			20997.5i			0.759885i
$915$	1373.06	+	10921.0i	0.0496086	+	0.394576i
$916$			21214.3i			0.765217i
$917$	14416.2	−	3422.96i	0.519156	−	0.123267i
$918$	−1481.74	−	1481.74i	−0.0532731	−	0.0532731i
$919$		−	1241.19i		−	0.0445518i	−0.999752	−	0.0222759i	$-0.992909\pi$
$919$		−	1241.19i		−	0.0445518i	0.999752	−	0.0222759i	$-0.00709123\pi$
$920$	9755.99	−	12561.9i	0.349614	−	0.450168i
$921$	−20959.3			−0.749871
$922$	−15858.2	−	15858.2i	−0.566444	−	0.566444i
$923$	16001.7	−	16001.7i	0.570642	−	0.570642i
$924$	−2868.60	+	4654.99i	−0.102132	+	0.165734i
$925$	−30232.7	−	17928.0i	−1.07464	−	0.637265i
$926$	−7829.05			−0.277839
$927$	9889.63	+	9889.63i	0.350397	+	0.350397i
$928$	−28227.1	−	28227.1i	−0.998492	−	0.998492i
$929$	−8853.24			−0.312665			−0.156332	−	0.987705i	$-0.549967\pi$
$929$	−8853.24			−0.312665			−0.156332	+	0.987705i	$0.549967\pi$
$930$	−317.451	−	246.542i	−0.0111931	−	0.00869294i
$931$	−2962.04	+	1490.64i	−0.104272	+	0.0524743i
$932$	16577.6	−	16577.6i	0.582636	−	0.582636i
$933$	17010.3	+	17010.3i	0.596884	+	0.596884i
$934$	−359.756			−0.0126034
$935$	−1382.77	−	10998.2i	−0.0483651	−	0.384685i
$936$			9582.96i			0.334646i
$937$	1875.21	+	1875.21i	0.0653793	+	0.0653793i	0.739040	−	0.673661i	$-0.235279\pi$
$937$	1875.21	+	1875.21i	0.0653793	+	0.0653793i	−0.673661	+	0.739040i	$0.735279\pi$
$938$	18470.7	−	4385.65i	0.642954	−	0.152662i
$939$			27023.6i			0.939170i
$940$	−15930.3	+	2002.86i	−0.552756	+	0.0694960i
$941$			16210.5i			0.561581i	0.959769	+	0.280790i	$0.0905966\pi$
$941$			16210.5i			0.561581i	−0.959769	+	0.280790i	$0.909403\pi$
$942$	3429.07	−	3429.07i	0.118604	−	0.118604i
$943$	20520.9	−	20520.9i	0.708647	−	0.708647i
$944$	19999.5			0.689542
$945$	5235.87	−	1959.99i	0.180236	−	0.0674693i
$946$	8047.46			0.276581
$947$	−19179.1	+	19179.1i	−0.658116	+	0.658116i	−0.954934	−	0.296818i	$-0.904075\pi$
$947$	−19179.1	+	19179.1i	−0.658116	+	0.658116i	0.296818	+	0.954934i	$0.404075\pi$
$948$	2260.93	−	2260.93i	0.0774594	−	0.0774594i
$949$		−	44846.7i		−	1.53402i
$950$	−1201.72	−	712.621i	−0.0410409	−	0.0243374i
$951$		−	22439.3i		−	0.765135i
$952$	20506.6	−	4869.05i	0.698134	−	0.165763i
$953$	−6102.51	−	6102.51i	−0.207429	−	0.207429i	0.595745	−	0.803174i	$-0.296857\pi$
$953$	−6102.51	−	6102.51i	−0.207429	−	0.207429i	−0.803174	+	0.595745i	$0.796857\pi$
$954$			5133.25i			0.174209i
$955$	−28739.1	−	22319.6i	−0.973795	−	0.756279i
$956$	−29843.1			−1.00962
$957$	7163.43	+	7163.43i	0.241965	+	0.241965i
$958$	−922.538	+	922.538i	−0.0311126	+	0.0311126i
$959$	−32533.9	−	20048.8i	−1.09549	−	0.675088i
$960$	283.695	+	2256.45i	0.00953772	+	0.0758609i
$961$	29683.6			0.996394
$962$	−14438.0	−	14438.0i	−0.483889	−	0.483889i
$963$	3307.88	+	3307.88i	0.110691	+	0.110691i
$964$	34868.8			1.16499
$965$	1318.32	+	10485.6i	0.0439774	+	0.349786i
$966$	−4589.06	−	2827.97i	−0.152847	−	0.0941911i
$967$	358.727	−	358.727i	0.0119296	−	0.0119296i	−0.701117	−	0.713046i	$-0.747315\pi$
$967$	358.727	−	358.727i	0.0119296	−	0.0119296i	0.713046	+	0.701117i	$0.247315\pi$
$968$	13340.5	+	13340.5i	0.442953	+	0.442953i
$969$	−1946.94			−0.0645456
$970$	−8731.54	−	6781.18i	−0.289024	−	0.224465i
$971$			11751.7i			0.388394i	0.980963	+	0.194197i	$0.0622100\pi$
$971$			11751.7i			0.388394i	−0.980963	+	0.194197i	$0.937790\pi$
$972$	−1144.94	−	1144.94i	−0.0377820	−	0.0377820i
$973$	−1490.96	−	6279.35i	−0.0491242	−	0.206893i
$974$			7727.84i			0.254226i
$975$	22820.0	−	5830.31i	0.749564	−	0.191507i
$976$			11061.4i			0.362775i
$977$	−28208.4	+	28208.4i	−0.923710	+	0.923710i	−0.997289	−	0.0735789i	$-0.976558\pi$
$977$	−28208.4	+	28208.4i	−0.923710	+	0.923710i	0.0735789	+	0.997289i	$0.476558\pi$
$978$	2390.53	−	2390.53i	0.0781602	−	0.0781602i
$979$	−10450.9			−0.341178
$980$	−4928.41	+	25073.2i	−0.160645	+	0.817280i
$981$	−11539.0			−0.375548
$982$	−5208.13	+	5208.13i	−0.169245	+	0.169245i
$983$	9945.28	−	9945.28i	0.322691	−	0.322691i	−0.527108	−	0.849798i	$-0.676724\pi$
$983$	9945.28	−	9945.28i	0.322691	−	0.322691i	0.849798	+	0.527108i	$0.176724\pi$
$984$		−	17588.5i		−	0.569817i
$985$	11727.9	−	1474.50i	0.379372	−	0.0476971i
$986$		−	17745.1i		−	0.573144i
$987$	2766.25	+	11650.4i	0.0892105	+	0.375722i
$988$	2860.94	+	2860.94i	0.0921242	+	0.0921242i
$989$		−	39549.3i		−	1.27158i
$990$	214.331	+	1704.74i	0.00688071	+	0.0547276i
$991$	−16073.0			−0.515213			−0.257607	−	0.966250i	$-0.582934\pi$
$991$	−16073.0			−0.515213			−0.257607	+	0.966250i	$0.582934\pi$
$992$	−1279.65	−	1279.65i	−0.0409565	−	0.0409565i
$993$	3824.13	−	3824.13i	0.122210	−	0.122210i
$994$	6567.82	+	4047.37i	0.209576	+	0.129150i
$995$	3303.05	+	2565.25i	0.105240	+	0.0817326i
$996$	11681.1			0.371618
$997$	−11210.6	−	11210.6i	−0.356111	−	0.356111i	0.506266	−	0.862377i	$-0.331025\pi$
$997$	−11210.6	−	11210.6i	−0.356111	−	0.356111i	−0.862377	+	0.506266i	$0.831025\pi$
$998$	−1946.38	−	1946.38i	−0.0617350	−	0.0617350i
$999$	7592.12			0.240444

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.4.m.a.13.10	yes	48
5.2	odd	4	inner	105.4.m.a.97.9	yes	48
7.6	odd	2	inner	105.4.m.a.13.9	✓	48
35.27	even	4	inner	105.4.m.a.97.10	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.4.m.a.13.9	✓	48	7.6	odd	2	inner
105.4.m.a.13.10	yes	48	1.1	even	1	trivial
105.4.m.a.97.9	yes	48	5.2	odd	4	inner
105.4.m.a.97.10	yes	48	35.27	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	105.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.817511 + 0.817511i) q^{2} +(2.12132 - 2.12132i) q^{3} +6.66335i q^{4} +(-8.83013 - 6.85775i) q^{5} +3.46841i q^{6} +(-4.27846 - 18.0193i) q^{7} +(-11.9875 - 11.9875i) q^{8} -9.00000i q^{9} +O(q^{10})\)	\(q+(-0.817511 + 0.817511i) q^{2} +(2.12132 - 2.12132i) q^{3} +6.66335i q^{4} +(-8.83013 - 6.85775i) q^{5} +3.46841i q^{6} +(-4.27846 - 18.0193i) q^{7} +(-11.9875 - 11.9875i) q^{8} -9.00000i q^{9} +(12.8250 - 1.61244i) q^{10} -14.7693 q^{11} +(14.1351 + 14.1351i) q^{12} +(44.4120 - 44.4120i) q^{13} +(18.2287 + 11.2333i) q^{14} +(-33.2790 + 4.18405i) q^{15} -33.7070 q^{16} +(-47.4679 - 47.4679i) q^{17} +(7.35760 + 7.35760i) q^{18} +9.66755 q^{19} +(45.6956 - 58.8383i) q^{20} +(-47.3007 - 29.1487i) q^{21} +(12.0740 - 12.0740i) q^{22} +(-59.3379 - 59.3379i) q^{23} -50.8585 q^{24} +(30.9425 + 121.110i) q^{25} +72.6146i q^{26} +(-19.0919 - 19.0919i) q^{27} +(120.069 - 28.5089i) q^{28} -228.642i q^{29} +(23.7855 - 30.6265i) q^{30} -10.3652i q^{31} +(123.456 - 123.456i) q^{32} +(-31.3303 + 31.3303i) q^{33} +77.6110 q^{34} +(-85.7924 + 188.453i) q^{35} +59.9702 q^{36} +(-198.831 + 198.831i) q^{37} +(-7.90333 + 7.90333i) q^{38} -188.424i q^{39} +(23.6438 + 188.058i) q^{40} +345.832i q^{41} +(62.4982 - 14.8394i) q^{42} +(333.255 + 333.255i) q^{43} -98.4128i q^{44} +(-61.7198 + 79.4712i) q^{45} +97.0189 q^{46} +(-152.394 - 152.394i) q^{47} +(-71.5034 + 71.5034i) q^{48} +(-306.390 + 154.190i) q^{49} +(-124.304 - 73.7127i) q^{50} -201.389 q^{51} +(295.933 + 295.933i) q^{52} +(348.840 + 348.840i) q^{53} +31.2157 q^{54} +(130.415 + 101.284i) q^{55} +(-164.718 + 267.293i) q^{56} +(20.5080 - 20.5080i) q^{57} +(186.917 + 186.917i) q^{58} -593.332 q^{59} +(-27.8798 - 221.750i) q^{60} -328.164i q^{61} +(8.47370 + 8.47370i) q^{62} +(-162.174 + 38.5061i) q^{63} -67.8038i q^{64} +(-696.730 + 87.5974i) q^{65} -51.2258i q^{66} +(626.936 - 626.936i) q^{67} +(316.295 - 316.295i) q^{68} -251.750 q^{69} +(-83.9264 - 224.199i) q^{70} +360.302 q^{71} +(-107.887 + 107.887i) q^{72} +(504.894 - 504.894i) q^{73} -325.093i q^{74} +(322.551 + 191.274i) q^{75} +64.4183i q^{76} +(63.1897 + 266.132i) q^{77} +(154.039 + 154.039i) q^{78} -159.951i q^{79} +(297.638 + 231.155i) q^{80} -81.0000 q^{81} +(-282.721 - 282.721i) q^{82} +(413.196 - 413.196i) q^{83} +(194.228 - 315.181i) q^{84} +(93.6247 + 744.670i) q^{85} -544.879 q^{86} +(-485.023 - 485.023i) q^{87} +(177.046 + 177.046i) q^{88} +707.614 q^{89} +(-14.5120 - 115.425i) q^{90} +(-990.288 - 610.258i) q^{91} +(395.389 - 395.389i) q^{92} +(-21.9880 - 21.9880i) q^{93} +249.168 q^{94} +(-85.3657 - 66.2976i) q^{95} -523.777i q^{96} +(-604.783 - 604.783i) q^{97} +(124.425 - 376.529i) q^{98} +132.923i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 4 q^{7} - 168 q^{8}+O(q^{10}) \) 48 * q + 4 * q^7 - 168 * q^8	\( 48 q + 4 q^{7} - 168 q^{8} + 112 q^{11} + 168 q^{15} - 544 q^{16} - 96 q^{21} - 192 q^{22} + 400 q^{23} + 520 q^{25} + 1052 q^{28} - 48 q^{30} - 1344 q^{32} + 392 q^{35} - 1728 q^{36} - 456 q^{37} + 1068 q^{42} + 192 q^{43} - 208 q^{46} + 3528 q^{50} + 672 q^{51} - 1728 q^{53} - 48 q^{56} + 696 q^{57} + 3016 q^{58} + 840 q^{60} - 36 q^{63} - 4720 q^{65} - 4784 q^{67} + 2220 q^{70} - 3088 q^{71} - 1512 q^{72} + 2352 q^{77} + 1416 q^{78} - 3888 q^{81} - 472 q^{85} + 10832 q^{86} + 2128 q^{88} - 5664 q^{91} + 10600 q^{92} - 1368 q^{93} - 6912 q^{95} - 3888 q^{98}+O(q^{100}) \) 48 * q + 4 * q^7 - 168 * q^8 + 112 * q^11 + 168 * q^15 - 544 * q^16 - 96 * q^21 - 192 * q^22 + 400 * q^23 + 520 * q^25 + 1052 * q^28 - 48 * q^30 - 1344 * q^32 + 392 * q^35 - 1728 * q^36 - 456 * q^37 + 1068 * q^42 + 192 * q^43 - 208 * q^46 + 3528 * q^50 + 672 * q^51 - 1728 * q^53 - 48 * q^56 + 696 * q^57 + 3016 * q^58 + 840 * q^60 - 36 * q^63 - 4720 * q^65 - 4784 * q^67 + 2220 * q^70 - 3088 * q^71 - 1512 * q^72 + 2352 * q^77 + 1416 * q^78 - 3888 * q^81 - 472 * q^85 + 10832 * q^86 + 2128 * q^88 - 5664 * q^91 + 10600 * q^92 - 1368 * q^93 - 6912 * q^95 - 3888 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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