LMFDB - Embedded newform 605.3.d.b.604.37

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [605,3,Mod(604,605)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(605, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("605.604"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	605.d (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [40,0,0,68] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$16.4850559938$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			604.37
Character	$\chi$	$=$	605.604
Dual form			605.3.d.b.604.38

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+3.55203 q^{2} +1.52519i q^{3} +8.61693 q^{4} +(4.52233 - 2.13273i) q^{5} +5.41753i q^{6} -1.09026 q^{7} +16.3995 q^{8} +6.67379 q^{9} +(16.0635 - 7.57554i) q^{10} +13.1425i q^{12} +0.874050 q^{13} -3.87264 q^{14} +(3.25282 + 6.89741i) q^{15} +23.7838 q^{16} -23.3553 q^{17} +23.7055 q^{18} -25.3361i q^{19} +(38.9686 - 18.3776i) q^{20} -1.66285i q^{21} +33.3562i q^{23} +25.0123i q^{24} +(15.9029 - 19.2898i) q^{25} +3.10466 q^{26} +23.9055i q^{27} -9.39469 q^{28} +16.8499i q^{29} +(11.5541 + 24.4998i) q^{30} -6.40321 q^{31} +18.8828 q^{32} -82.9587 q^{34} +(-4.93051 + 2.32523i) q^{35} +57.5076 q^{36} -65.5809i q^{37} -89.9946i q^{38} +1.33309i q^{39} +(74.1638 - 34.9757i) q^{40} +38.7022i q^{41} -5.90651i q^{42} +15.0656 q^{43} +(30.1811 - 14.2334i) q^{45} +118.482i q^{46} +59.2957i q^{47} +36.2748i q^{48} -47.8113 q^{49} +(56.4876 - 68.5181i) q^{50} -35.6213i q^{51} +7.53163 q^{52} +23.6638i q^{53} +84.9132i q^{54} -17.8797 q^{56} +38.6424 q^{57} +59.8515i q^{58} +38.0356 q^{59} +(28.0294 + 59.4345i) q^{60} -34.0882i q^{61} -22.7444 q^{62} -7.27617 q^{63} -28.0629 q^{64} +(3.95274 - 1.86412i) q^{65} -43.7033i q^{67} -201.251 q^{68} -50.8746 q^{69} +(-17.5133 + 8.25931i) q^{70} +36.2338 q^{71} +109.447 q^{72} -84.0533 q^{73} -232.946i q^{74} +(29.4207 + 24.2549i) q^{75} -218.319i q^{76} +4.73519i q^{78} +30.3428i q^{79} +(107.558 - 50.7244i) q^{80} +23.6037 q^{81} +137.471i q^{82} -136.109 q^{83} -14.3287i q^{84} +(-105.620 + 49.8106i) q^{85} +53.5134 q^{86} -25.6994 q^{87} -8.46901 q^{89} +(107.204 - 50.5576i) q^{90} -0.952942 q^{91} +287.428i q^{92} -9.76612i q^{93} +210.620i q^{94} +(-54.0351 - 114.578i) q^{95} +28.7998i q^{96} +66.6404i q^{97} -169.827 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 68 q^{4} - 8 q^{5} - 24 q^{9} - 12 q^{14} + 64 q^{15} + 212 q^{16} - 48 q^{20} + 32 q^{25} - 288 q^{26} - 212 q^{31} - 112 q^{34} + 288 q^{36} + 196 q^{45} - 472 q^{49} + 144 q^{56} + 256 q^{59}+ \cdots + 1032 q^{91}+O(q^{100}) $ 40 * q + 68 * q^4 - 8 * q^5 - 24 * q^9 - 12 * q^14 + 64 * q^15 + 212 * q^16 - 48 * q^20 + 32 * q^25 - 288 * q^26 - 212 * q^31 - 112 * q^34 + 288 * q^36 + 196 * q^45 - 472 * q^49 + 144 * q^56 + 256 * q^59 + 124 * q^60 + 756 * q^64 - 744 * q^69 + 400 * q^70 + 300 * q^71 + 624 * q^75 - 728 * q^80 - 1024 * q^81 - 1508 * q^86 - 812 * q^89 + 1032 * q^91

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$-1$	$-1$

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 $

$2$	3.55203			1.77602			0.888008	−	0.459828i	$-0.152089\pi$
$2$	3.55203			1.77602			0.888008	+	0.459828i	$0.152089\pi$
$3$			1.52519i			0.508397i	0.967152	+	0.254198i	$0.0818116\pi$
$3$			1.52519i			0.508397i	−0.967152	+	0.254198i	$0.918188\pi$
$4$	8.61693			2.15423
$5$	4.52233	−	2.13273i	0.904466	−	0.426547i
$5$	4.52233	−	2.13273i	0.904466	−	0.426547i
$6$			5.41753i			0.902921i
$7$	−1.09026			−0.155751			−0.0778757	−	0.996963i	$-0.524814\pi$
$7$	−1.09026			−0.155751			−0.0778757	+	0.996963i	$0.524814\pi$
$8$	16.3995			2.04994
$9$	6.67379			0.741533
$10$	16.0635	−	7.57554i	1.60635	−	0.757554i
$11$		0			0
$11$		0			0
$12$			13.1425i			1.09521i
$13$	0.874050			0.0672347			0.0336173	−	0.999435i	$-0.489297\pi$
$13$	0.874050			0.0672347			0.0336173	+	0.999435i	$0.489297\pi$
$14$	−3.87264			−0.276617
$15$	3.25282	+	6.89741i	0.216855	+	0.459827i
$16$	23.7838			1.48649
$17$	−23.3553			−1.37384			−0.686920	−	0.726733i	$-0.741038\pi$
$17$	−23.3553			−1.37384			−0.686920	+	0.726733i	$0.741038\pi$
$18$	23.7055			1.31697
$19$		−	25.3361i		−	1.33348i	−0.745291	−	0.666739i	$-0.767690\pi$
$19$		−	25.3361i		−	1.33348i	0.745291	−	0.666739i	$-0.232310\pi$
$20$	38.9686	−	18.3776i	1.94843	−	0.918881i
$21$		−	1.66285i		−	0.0791835i
$22$		0			0
$23$			33.3562i			1.45027i	0.688606	+	0.725135i	$0.258223\pi$
$23$			33.3562i			1.45027i	−0.688606	+	0.725135i	$0.741777\pi$
$24$			25.0123i			1.04218i
$25$	15.9029	−	19.2898i	0.636116	−	0.771594i
$26$	3.10466			0.119410
$27$			23.9055i			0.885390i
$28$	−9.39469			−0.335525
$29$			16.8499i			0.581032i	0.956870	+	0.290516i	$0.0938270\pi$
$29$			16.8499i			0.581032i	−0.956870	+	0.290516i	$0.906173\pi$
$30$	11.5541	+	24.4998i	0.385138	+	0.816661i
$31$	−6.40321			−0.206555			−0.103278	−	0.994653i	$-0.532933\pi$
$31$	−6.40321			−0.206555			−0.103278	+	0.994653i	$0.532933\pi$
$32$	18.8828			0.590087
$33$		0			0
$34$	−82.9587			−2.43996
$35$	−4.93051	+	2.32523i	−0.140872	+	0.0664353i
$36$	57.5076			1.59743
$37$		−	65.5809i		−	1.77246i	−0.463248	−	0.886229i	$-0.653316\pi$
$37$		−	65.5809i		−	1.77246i	0.463248	−	0.886229i	$-0.346684\pi$
$38$		−	89.9946i		−	2.36828i
$39$			1.33309i			0.0341819i
$40$	74.1638	−	34.9757i	1.85410	−	0.874393i
$41$			38.7022i			0.943955i	0.881611	+	0.471978i	$0.156460\pi$
$41$			38.7022i			0.943955i	−0.881611	+	0.471978i	$0.843540\pi$
$42$		−	5.90651i		−	0.140631i
$43$	15.0656			0.350362			0.175181	−	0.984536i	$-0.443949\pi$
$43$	15.0656			0.350362			0.175181	+	0.984536i	$0.443949\pi$
$44$		0			0
$45$	30.1811	−	14.2334i	0.670691	−	0.316298i
$46$			118.482i			2.57570i
$47$			59.2957i			1.26161i	0.775941	+	0.630805i	$0.217275\pi$
$47$			59.2957i			1.26161i	−0.775941	+	0.630805i	$0.782725\pi$
$48$			36.2748i			0.755725i
$49$	−47.8113			−0.975741
$50$	56.4876	−	68.5181i	1.12975	−	1.37036i
$51$		−	35.6213i		−	0.698456i
$52$	7.53163			0.144839
$53$			23.6638i			0.446486i	0.974763	+	0.223243i	$0.0716644\pi$
$53$			23.6638i			0.446486i	−0.974763	+	0.223243i	$0.928336\pi$
$54$			84.9132i			1.57247i
$55$		0			0
$56$	−17.8797			−0.319280
$57$	38.6424			0.677936
$58$			59.8515i			1.03192i
$59$	38.0356			0.644672			0.322336	−	0.946625i	$-0.395532\pi$
$59$	38.0356			0.644672			0.322336	+	0.946625i	$0.395532\pi$
$60$	28.0294	+	59.4345i	0.467156	+	0.990575i
$61$		−	34.0882i		−	0.558823i	−0.960171	−	0.279411i	$-0.909861\pi$
$61$		−	34.0882i		−	0.558823i	0.960171	−	0.279411i	$-0.0901394\pi$
$62$	−22.7444			−0.366846
$63$	−7.27617			−0.115495
$64$	−28.0629			−0.438482
$65$	3.95274	−	1.86412i	0.0608114	−	0.0286787i
$66$		0			0
$67$		−	43.7033i		−	0.652288i	−0.945320	−	0.326144i	$-0.894250\pi$
$67$		−	43.7033i		−	0.652288i	0.945320	−	0.326144i	$-0.105750\pi$
$68$	−201.251			−2.95957
$69$	−50.8746			−0.737313
$70$	−17.5133	+	8.25931i	−0.250191	+	0.117990i
$71$	36.2338			0.510335			0.255168	−	0.966897i	$-0.417869\pi$
$71$	36.2338			0.510335			0.255168	+	0.966897i	$0.417869\pi$
$72$	109.447			1.52009
$73$	−84.0533			−1.15142			−0.575708	−	0.817656i	$-0.695273\pi$
$73$	−84.0533			−1.15142			−0.575708	+	0.817656i	$0.695273\pi$
$74$		−	232.946i		−	3.14791i
$75$	29.4207	+	24.2549i	0.392276	+	0.323399i
$76$		−	218.319i		−	2.87262i
$77$		0			0
$78$			4.73519i			0.0607076i
$79$			30.3428i			0.384086i	0.981387	+	0.192043i	$0.0615113\pi$
$79$			30.3428i			0.384086i	−0.981387	+	0.192043i	$0.938489\pi$
$80$	107.558	−	50.7244i	1.34448	−	0.634056i
$81$	23.6037			0.291403
$82$			137.471i			1.67648i
$83$	−136.109			−1.63987			−0.819936	−	0.572456i	$-0.805991\pi$
$83$	−136.109			−1.63987			−0.819936	+	0.572456i	$0.805991\pi$
$84$		−	14.3287i		−	0.170580i
$85$	−105.620	+	49.8106i	−1.24259	+	0.586007i
$86$	53.5134			0.622249
$87$	−25.6994			−0.295395
$88$		0			0
$89$	−8.46901			−0.0951574			−0.0475787	−	0.998867i	$-0.515150\pi$
$89$	−8.46901			−0.0951574			−0.0475787	+	0.998867i	$0.515150\pi$
$90$	107.204	−	50.5576i	1.19116	−	0.561751i
$91$	−0.952942			−0.0104719
$92$			287.428i			3.12422i
$93$		−	9.76612i		−	0.105012i
$94$			210.620i			2.24064i
$95$	−54.0351	−	114.578i	−0.568791	−	1.20608i
$96$			28.7998i			0.299998i
$97$			66.6404i			0.687015i	0.939150	+	0.343507i	$0.111615\pi$
$97$			66.6404i			0.687015i	−0.939150	+	0.343507i	$0.888385\pi$
$98$	−169.827			−1.73293
$99$		0			0
$100$	137.034	−	166.219i	1.37034	−	1.66219i
$101$		−	79.9985i		−	0.792064i	−0.918237	−	0.396032i	$-0.870387\pi$
$101$		−	79.9985i		−	0.792064i	0.918237	−	0.396032i	$-0.129613\pi$
$102$		−	126.528i		−	1.24047i
$103$		−	111.512i		−	1.08264i	−0.840815	−	0.541322i	$-0.817924\pi$
$103$		−	111.512i		−	1.08264i	0.840815	−	0.541322i	$-0.182076\pi$
$104$	14.3340			0.137827
$105$	−3.54642	−	7.51997i	−0.0337755	−	0.0716188i
$106$			84.0545i			0.792967i
$107$	−21.0075			−0.196332			−0.0981659	−	0.995170i	$-0.531298\pi$
$107$	−21.0075			−0.196332			−0.0981659	+	0.995170i	$0.531298\pi$
$108$			205.992i			1.90734i
$109$		−	118.493i		−	1.08710i	−0.839378	−	0.543548i	$-0.817081\pi$
$109$		−	118.493i		−	1.08710i	0.839378	−	0.543548i	$-0.182919\pi$
$110$		0			0
$111$	100.023			0.901112
$112$	−25.9305			−0.231522
$113$			106.589i			0.943264i	0.881795	+	0.471632i	$0.156335\pi$
$113$			106.589i			0.943264i	−0.881795	+	0.471632i	$0.843665\pi$
$114$	137.259			1.20403
$115$	71.1399	+	150.848i	0.618608	+	1.31172i
$116$			145.195i			1.25168i
$117$	5.83323			0.0498567
$118$	135.104			1.14495
$119$	25.4633			0.213978
$120$	53.3447	+	113.114i	0.444539	+	0.942617i
$121$		0			0
$122$		−	121.082i		−	0.992479i
$123$	−59.0282			−0.479904
$124$	−55.1761			−0.444968
$125$	30.7780	−	121.152i	0.246224	−	0.969213i
$126$	−25.8452			−0.205121
$127$	128.264			1.00995			0.504975	−	0.863134i	$-0.331502\pi$
$127$	128.264			1.00995			0.504975	+	0.863134i	$0.331502\pi$
$128$	−175.211			−1.36884
$129$			22.9779i			0.178123i
$130$	14.0403	−	6.62140i	0.108002	−	0.0509339i
$131$			15.3029i			0.116816i	0.998293	+	0.0584079i	$0.0186024\pi$
$131$			15.3029i			0.116816i	−0.998293	+	0.0584079i	$0.981398\pi$
$132$		0			0
$133$			27.6229i			0.207691i
$134$		−	155.236i		−	1.15847i
$135$	50.9841	+	108.109i	0.377660	+	0.800804i
$136$	−383.015			−2.81628
$137$			27.4757i			0.200553i	0.994960	+	0.100276i	$0.0319727\pi$
$137$			27.4757i			0.200553i	−0.994960	+	0.100276i	$0.968027\pi$
$138$	−180.708			−1.30948
$139$		−	56.2422i		−	0.404621i	−0.979321	−	0.202310i	$-0.935155\pi$
$139$		−	56.2422i		−	0.404621i	0.979321	−	0.202310i	$-0.0648449\pi$
$140$	−42.4859	+	20.0364i	−0.303471	+	0.143117i
$141$	−90.4373			−0.641399
$142$	128.704			0.906363
$143$		0			0
$144$	158.728			1.10228
$145$	35.9364	+	76.2009i	0.247837	+	0.525524i
$146$	−298.560			−2.04493
$147$		−	72.9214i		−	0.496064i
$148$		−	565.106i		−	3.81829i
$149$		−	237.208i		−	1.59200i	−0.605298	−	0.795999i	$-0.706946\pi$
$149$		−	237.208i		−	1.59200i	0.605298	−	0.795999i	$-0.293054\pi$
$150$	104.503	+	86.1543i	0.696688	+	0.574362i
$151$			47.0334i			0.311479i	0.987798	+	0.155740i	$0.0497761\pi$
$151$			47.0334i			0.311479i	−0.987798	+	0.155740i	$0.950224\pi$
$152$		−	415.499i		−	2.73354i
$153$	−155.868			−1.01875
$154$		0			0
$155$	−28.9574	+	13.6564i	−0.186822	+	0.0881055i
$156$			11.4872i			0.0736357i
$157$		−	145.968i		−	0.929731i	−0.885381	−	0.464865i	$-0.846103\pi$
$157$		−	145.968i		−	0.929731i	0.885381	−	0.464865i	$-0.153897\pi$
$158$			107.779i			0.682142i
$159$	−36.0918			−0.226992
$160$	85.3941	−	40.2719i	0.533713	−	0.251700i
$161$		−	36.3670i		−	0.225882i
$162$	83.8410			0.517537
$163$			80.5446i			0.494139i	0.968998	+	0.247069i	$0.0794676\pi$
$163$			80.5446i			0.494139i	−0.968998	+	0.247069i	$0.920532\pi$
$164$			333.494i			2.03350i
$165$		0			0
$166$	−483.465			−2.91244
$167$	112.120			0.671380			0.335690	−	0.941972i	$-0.391031\pi$
$167$	112.120			0.671380			0.335690	+	0.941972i	$0.391031\pi$
$168$		−	27.2700i		−	0.162321i
$169$	−168.236			−0.995480
$170$	−375.166	+	176.929i	−2.20686	+	1.04076i
$171$		−	169.088i		−	0.988818i
$172$	129.819			0.754762
$173$	−189.060			−1.09283			−0.546416	−	0.837514i	$-0.684008\pi$
$173$	−189.060			−1.09283			−0.546416	+	0.837514i	$0.684008\pi$
$174$	−91.2849			−0.524626
$175$	−17.3383	+	21.0309i	−0.0990759	+	0.120177i
$176$		0			0
$177$			58.0116i			0.327749i
$178$	−30.0822			−0.169001
$179$	228.881			1.27867			0.639333	−	0.768930i	$-0.279211\pi$
$179$	228.881			1.27867			0.639333	+	0.768930i	$0.279211\pi$
$180$	260.068	−	122.648i	1.44482	−	0.681380i
$181$	−12.4445			−0.0687543			−0.0343772	−	0.999409i	$-0.510945\pi$
$181$	−12.4445			−0.0687543			−0.0343772	+	0.999409i	$0.510945\pi$
$182$	−3.38488			−0.0185982
$183$	51.9910			0.284104
$184$			547.025i			2.97296i
$185$	−139.867	−	296.578i	−0.756036	−	1.60313i
$186$		−	34.6896i		−	0.186503i
$187$		0			0
$188$			510.947i			2.71780i
$189$		−	26.0632i		−	0.137901i
$190$	−191.934	−	406.985i	−1.01018	−	2.14203i
$191$	−0.933635			−0.00488814			−0.00244407	−	0.999997i	$-0.500778\pi$
$191$	−0.933635			−0.00488814			−0.00244407	+	0.999997i	$0.500778\pi$
$192$		−	42.8012i		−	0.222923i
$193$	−41.6135			−0.215614			−0.107807	−	0.994172i	$-0.534383\pi$
$193$	−41.6135			−0.215614			−0.107807	+	0.994172i	$0.534383\pi$
$194$			236.709i			1.22015i
$195$	2.84313	+	6.02869i	0.0145802	+	0.0309163i
$196$	−411.987			−2.10197
$197$	85.8608			0.435842			0.217921	−	0.975966i	$-0.430073\pi$
$197$	85.8608			0.435842			0.217921	+	0.975966i	$0.430073\pi$
$198$		0			0
$199$	78.5577			0.394763			0.197381	−	0.980327i	$-0.436756\pi$
$199$	78.5577			0.394763			0.197381	+	0.980327i	$0.436756\pi$
$200$	260.799	−	316.343i	1.30400	−	1.58172i
$201$	66.6559			0.331621
$202$		−	284.157i		−	1.40672i
$203$		−	18.3708i		−	0.0904966i
$204$		−	306.946i		−	1.50464i
$205$	82.5414	+	175.024i	0.402641	+	0.853775i
$206$		−	396.096i		−	1.92279i
$207$			222.613i			1.07542i
$208$	20.7882			0.0999433
$209$		0			0
$210$	−12.5970	−	26.7112i	−0.0599858	−	0.127196i
$211$			134.083i			0.635464i	0.948181	+	0.317732i	$0.102921\pi$
$211$			134.083i			0.635464i	−0.948181	+	0.317732i	$0.897079\pi$
$212$			203.909i			0.961835i
$213$			55.2634i			0.259453i
$214$	−74.6193			−0.348688
$215$	68.1315	−	32.1309i	0.316891	−	0.149446i
$216$			392.038i			1.81499i
$217$	6.98117			0.0321713
$218$		−	420.893i		−	1.93070i
$219$		−	128.197i		−	0.585376i
$220$		0			0
$221$	−20.4137			−0.0923697
$222$	355.286			1.60039
$223$			200.724i			0.900109i	0.893001	+	0.450055i	$0.148596\pi$
$223$			200.724i			0.900109i	−0.893001	+	0.450055i	$0.851404\pi$
$224$	−20.5871			−0.0919068
$225$	106.133	−	128.736i	0.471701	−	0.572162i
$226$			378.607i			1.67525i
$227$	7.44700			0.0328062			0.0164031	−	0.999865i	$-0.494778\pi$
$227$	7.44700			0.0328062			0.0164031	+	0.999865i	$0.494778\pi$
$228$	332.978			1.46043
$229$	185.776			0.811249			0.405625	−	0.914040i	$-0.367054\pi$
$229$	185.776			0.811249			0.405625	+	0.914040i	$0.367054\pi$
$230$	252.691	+	535.816i	1.09866	+	2.32964i
$231$		0			0
$232$			276.330i			1.19108i
$233$	−94.8094			−0.406907			−0.203454	−	0.979085i	$-0.565217\pi$
$233$	−94.8094			−0.406907			−0.203454	+	0.979085i	$0.565217\pi$
$234$	20.7198			0.0885463
$235$	126.462	+	268.155i	0.538136	+	1.14108i
$236$	327.750			1.38877
$237$	−46.2785			−0.195268
$238$	90.4466			0.380028
$239$			395.405i			1.65441i	0.561899	+	0.827206i	$0.310071\pi$
$239$			395.405i			1.65441i	−0.561899	+	0.827206i	$0.689929\pi$
$240$	77.3644	+	164.046i	0.322352	+	0.683527i
$241$			26.3347i			0.109273i	0.998506	+	0.0546364i	$0.0174000\pi$
$241$			26.3347i			0.109273i	−0.998506	+	0.0546364i	$0.982600\pi$
$242$		0			0
$243$			251.150i			1.03354i
$244$		−	293.736i		−	1.20383i
$245$	−216.219	+	101.969i	−0.882525	+	0.416199i
$246$	−209.670			−0.852317
$247$		−	22.1450i		−	0.0896559i
$248$	−105.009			−0.423425
$249$		−	207.593i		−	0.833705i
$250$	109.324	−	430.334i	0.437298	−	1.72134i
$251$	374.579			1.49235			0.746173	−	0.665752i	$-0.231889\pi$
$251$	374.579			1.49235			0.746173	+	0.665752i	$0.231889\pi$
$252$	−62.6983			−0.248803
$253$		0			0
$254$	455.597			1.79369
$255$	−75.9706	−	161.091i	−0.297924	−	0.631729i
$256$	−510.105			−1.99260
$257$		−	255.512i		−	0.994211i	−0.867690	−	0.497105i	$-0.834396\pi$
$257$		−	255.512i		−	0.994211i	0.867690	−	0.497105i	$-0.165604\pi$
$258$			81.6182i			0.316349i
$259$			71.5003i			0.276063i
$260$	34.0605	−	16.0630i	0.131002	−	0.0617806i
$261$			112.453i			0.430854i
$262$			54.3562i			0.207467i
$263$	288.916			1.09854			0.549270	−	0.835645i	$-0.314906\pi$
$263$	288.916			1.09854			0.549270	+	0.835645i	$0.314906\pi$
$264$		0			0
$265$	50.4685	+	107.015i	0.190447	+	0.403831i
$266$			98.1175i			0.368863i
$267$		−	12.9168i		−	0.0483777i
$268$		−	376.589i		−	1.40518i
$269$	216.614			0.805258			0.402629	−	0.915363i	$-0.368097\pi$
$269$	216.614			0.805258			0.402629	+	0.915363i	$0.368097\pi$
$270$	181.097	+	384.005i	0.670730	+	1.42224i
$271$			52.7139i			0.194516i	0.995259	+	0.0972581i	$0.0310072\pi$
$271$			52.7139i			0.194516i	−0.995259	+	0.0972581i	$0.968993\pi$
$272$	−555.477			−2.04219
$273$		−	1.45342i		−	0.00532388i
$274$			97.5947i			0.356185i
$275$		0			0
$276$	−438.383			−1.58834
$277$	164.025			0.592149			0.296074	−	0.955165i	$-0.404322\pi$
$277$	164.025			0.592149			0.296074	+	0.955165i	$0.404322\pi$
$278$		−	199.774i		−	0.718612i
$279$	−42.7337			−0.153168
$280$	−80.8579	+	38.1326i	−0.288778	+	0.136188i
$281$			511.263i			1.81944i	0.415219	+	0.909721i	$0.363705\pi$
$281$			511.263i			1.81944i	−0.415219	+	0.909721i	$0.636295\pi$
$282$	−321.236			−1.13913
$283$	178.463			0.630610			0.315305	−	0.948990i	$-0.397893\pi$
$283$	178.463			0.630610			0.315305	+	0.948990i	$0.397893\pi$
$284$	312.224			1.09938
$285$	174.753	−	82.4138i	0.613170	−	0.289171i
$286$		0			0
$287$		−	42.1954i		−	0.147022i
$288$	126.020			0.437569
$289$	256.469			0.887437
$290$	127.647	+	270.668i	0.440163	+	0.933338i
$291$	−101.639			−0.349276
$292$	−724.282			−2.48042
$293$	−56.9530			−0.194379			−0.0971893	−	0.995266i	$-0.530985\pi$
$293$	−56.9530			−0.194379			−0.0971893	+	0.995266i	$0.530985\pi$
$294$		−	259.019i		−	0.881017i
$295$	172.010	−	81.1198i	0.583083	−	0.274983i
$296$		−	1075.49i		−	3.63342i
$297$		0			0
$298$		−	842.569i		−	2.82741i
$299$			29.1550i			0.0975084i
$300$	253.516	+	209.003i	0.845053	+	0.696677i
$301$	−16.4254			−0.0545694
$302$			167.064i			0.553192i
$303$	122.013			0.402683
$304$		−	602.588i		−	1.98220i
$305$	−72.7011	−	154.158i	−0.238364	−	0.505436i
$306$	−553.649			−1.80931
$307$	−427.615			−1.39288			−0.696442	−	0.717613i	$-0.745234\pi$
$307$	−427.615			−1.39288			−0.696442	+	0.717613i	$0.745234\pi$
$308$		0			0
$309$	170.078			0.550413
$310$	−102.858	+	48.5078i	−0.331799	+	0.156477i
$311$	−99.7274			−0.320667			−0.160333	−	0.987063i	$-0.551257\pi$
$311$	−99.7274			−0.320667			−0.160333	+	0.987063i	$0.551257\pi$
$312$			21.8620i			0.0700707i
$313$			52.7279i			0.168460i	0.996446	+	0.0842298i	$0.0268430\pi$
$313$			52.7279i			0.168460i	−0.996446	+	0.0842298i	$0.973157\pi$
$314$		−	518.482i		−	1.65122i
$315$	−32.9052	+	15.5181i	−0.104461	+	0.0492639i
$316$			261.462i			0.827410i
$317$			325.041i			1.02536i	0.858578	+	0.512682i	$0.171348\pi$
$317$			325.041i			1.02536i	−0.858578	+	0.512682i	$0.828652\pi$
$318$	−128.199			−0.403142
$319$		0			0
$320$	−126.909	+	59.8506i	−0.396592	+	0.187033i
$321$		−	32.0404i		−	0.0998145i
$322$		−	129.177i		−	0.401170i
$323$			591.731i			1.83199i
$324$	203.391			0.627751
$325$	13.8999	−	16.8603i	0.0427690	−	0.0518778i
$326$			286.097i			0.877599i
$327$	180.725			0.552676
$328$			634.695i			1.93505i
$329$		−	64.6477i		−	0.196498i
$330$		0			0
$331$	343.048			1.03640			0.518199	−	0.855260i	$-0.326603\pi$
$331$	343.048			1.03640			0.518199	+	0.855260i	$0.326603\pi$
$332$	−1172.84			−3.53266
$333$		−	437.674i		−	1.31434i
$334$	398.256			1.19238
$335$	−93.2076	−	197.641i	−0.278232	−	0.589972i
$336$		−	39.5489i		−	0.117705i
$337$	625.633			1.85648			0.928239	−	0.371985i	$-0.121323\pi$
$337$	625.633			1.85648			0.928239	+	0.371985i	$0.121323\pi$
$338$	−597.580			−1.76799
$339$	−162.568			−0.479553
$340$	−910.122	+	429.214i	−2.67683	+	1.26240i
$341$		0			0
$342$		−	600.605i		−	1.75616i
$343$	105.550			0.307725
$344$	247.068			0.718220
$345$	−230.072	+	108.502i	−0.666874	+	0.314498i
$346$	−671.547			−1.94089
$347$	477.091			1.37490			0.687452	−	0.726230i	$-0.258729\pi$
$347$	477.091			1.37490			0.687452	+	0.726230i	$0.258729\pi$
$348$	−221.450			−0.636349
$349$			183.885i			0.526891i	0.964674	+	0.263445i	$0.0848589\pi$
$349$			183.885i			0.526891i	−0.964674	+	0.263445i	$0.915141\pi$
$350$	−61.5862	+	74.7026i	−0.175960	+	0.213436i
$351$			20.8946i			0.0595289i
$352$		0			0
$353$		−	289.312i		−	0.819580i	−0.912180	−	0.409790i	$-0.865602\pi$
$353$		−	289.312i		−	0.819580i	0.912180	−	0.409790i	$-0.134398\pi$
$354$			206.059i			0.582087i
$355$	163.861	−	77.2770i	0.461581	−	0.217682i
$356$	−72.9769			−0.204991
$357$			38.8364i			0.108786i
$358$	812.993			2.27093
$359$		−	335.331i		−	0.934069i	−0.884239	−	0.467034i	$-0.845322\pi$
$359$		−	335.331i		−	0.934069i	0.884239	−	0.467034i	$-0.154678\pi$
$360$	494.954	−	233.421i	1.37487	−	0.648391i
$361$	−280.917			−0.778164
$362$	−44.2034			−0.122109
$363$		0			0
$364$	−8.21144			−0.0225589
$365$	−380.117	+	179.263i	−1.04142	+	0.491132i
$366$	184.674			0.504573
$367$			237.840i			0.648066i	0.946046	+	0.324033i	$0.105039\pi$
$367$			237.840i			0.648066i	−0.946046	+	0.324033i	$0.894961\pi$
$368$			793.337i			2.15581i
$369$			258.290i			0.699974i
$370$	−496.811	−	1053.46i	−1.34273	−	2.84718i
$371$		−	25.7997i		−	0.0695409i
$372$		−	84.1540i		−	0.226220i
$373$	240.258			0.644124			0.322062	−	0.946719i	$-0.395624\pi$
$373$	240.258			0.644124			0.322062	+	0.946719i	$0.395624\pi$
$374$		0			0
$375$	184.779	+	46.9423i	0.492745	+	0.125180i
$376$			972.419i			2.58622i
$377$			14.7277i			0.0390655i
$378$		−	92.5774i		−	0.244914i
$379$	−262.256			−0.691968			−0.345984	−	0.938240i	$-0.612455\pi$
$379$	−262.256			−0.691968			−0.345984	+	0.938240i	$0.612455\pi$
$380$	−465.617	−	987.311i	−1.22531	−	2.59819i
$381$			195.627i			0.513455i
$382$	−3.31630			−0.00868141
$383$		−	342.668i		−	0.894693i	−0.894361	−	0.447347i	$-0.852369\pi$
$383$		−	342.668i		−	0.894693i	0.894361	−	0.447347i	$-0.147631\pi$
$384$		−	267.231i		−	0.695913i
$385$		0			0
$386$	−147.813			−0.382934
$387$	100.545			0.259805
$388$			574.236i			1.47999i
$389$	−632.428			−1.62578			−0.812889	−	0.582418i	$-0.802107\pi$
$389$	−632.428			−1.62578			−0.812889	+	0.582418i	$0.802107\pi$
$390$	10.0989	+	21.4141i	0.0258946	+	0.0549079i
$391$		−	779.044i		−	1.99244i
$392$	−784.081			−2.00021
$393$	−23.3398			−0.0593887
$394$	304.980			0.774062
$395$	64.7131	+	137.220i	0.163831	+	0.347392i
$396$		0			0
$397$		−	335.656i		−	0.845482i	−0.906251	−	0.422741i	$-0.861068\pi$
$397$		−	335.656i		−	0.845482i	0.906251	−	0.422741i	$-0.138932\pi$
$398$	279.040			0.701105
$399$	−42.1302			−0.105589
$400$	378.231	−	458.785i	0.945577	−	1.14696i
$401$	700.382			1.74659			0.873294	−	0.487193i	$-0.161979\pi$
$401$	700.382			1.74659			0.873294	+	0.487193i	$0.161979\pi$
$402$	236.764			0.588965
$403$	−5.59673			−0.0138877
$404$		−	689.341i		−	1.70629i
$405$	106.744	−	50.3404i	0.263564	−	0.124297i
$406$		−	65.2537i		−	0.160723i
$407$		0			0
$408$		−	584.170i		−	1.43179i
$409$		−	18.3049i		−	0.0447552i	−0.999750	−	0.0223776i	$-0.992876\pi$
$409$		−	18.3049i		−	0.0447552i	0.999750	−	0.0223776i	$-0.00712361\pi$
$410$	293.190	+	621.690i	0.715097	+	1.51632i
$411$	−41.9057			−0.101960
$412$		−	960.895i		−	2.33227i
$413$	−41.4687			−0.100409
$414$			790.727i			1.90997i
$415$	−615.531	+	290.285i	−1.48321	+	0.699482i
$416$	16.5045			0.0396743
$417$	85.7801			0.205708
$418$		0			0
$419$	−420.944			−1.00464			−0.502320	−	0.864682i	$-0.667520\pi$
$419$	−420.944			−1.00464			−0.502320	+	0.864682i	$0.667520\pi$
$420$	−30.5593	−	64.7991i	−0.0727602	−	0.154284i
$421$	466.728			1.10862			0.554309	−	0.832311i	$-0.312983\pi$
$421$	466.728			1.10862			0.554309	+	0.832311i	$0.312983\pi$
$422$			476.267i			1.12859i
$423$			395.727i			0.935526i
$424$			388.074i			0.915268i
$425$	−371.417	+	450.520i	−0.873921	+	1.06005i
$426$			196.298i			0.460792i
$427$			37.1650i			0.0870375i
$428$	−181.020			−0.422944
$429$		0			0
$430$	242.005	−	114.130i	0.562803	−	0.265418i
$431$		−	238.824i		−	0.554117i	−0.960853	−	0.277059i	$-0.910640\pi$
$431$		−	238.824i		−	0.554117i	0.960853	−	0.277059i	$-0.0893596\pi$
$432$			568.563i			1.31612i
$433$			95.9207i			0.221526i	0.993847	+	0.110763i	$0.0353294\pi$
$433$			95.9207i			0.221526i	−0.993847	+	0.110763i	$0.964671\pi$
$434$	24.7973			0.0571367
$435$	−116.221	+	54.8099i	−0.267175	+	0.126000i
$436$		−	1021.05i		−	2.34186i
$437$	845.116			1.93390
$438$		−	455.361i		−	1.03964i
$439$			749.426i			1.70712i	0.520994	+	0.853560i	$0.325561\pi$
$439$			749.426i			1.70712i	−0.520994	+	0.853560i	$0.674439\pi$
$440$		0			0
$441$	−319.083			−0.723544
$442$	−72.5101			−0.164050
$443$		−	46.3408i		−	0.104607i	−0.998631	−	0.0523034i	$-0.983344\pi$
$443$		−	46.3408i		−	0.104607i	0.998631	−	0.0523034i	$-0.0166563\pi$
$444$	861.895			1.94120
$445$	−38.2996	+	18.0621i	−0.0860666	+	0.0405891i
$446$			712.980i			1.59861i
$447$	361.787			0.809367
$448$	30.5958			0.0682943
$449$	48.5549			0.108140			0.0540700	−	0.998537i	$-0.482781\pi$
$449$	48.5549			0.108140			0.0540700	+	0.998537i	$0.482781\pi$
$450$	376.987	−	457.276i	0.837748	−	1.01617i
$451$		0			0
$452$			918.469i			2.03201i
$453$	−71.7349			−0.158355
$454$	26.4520			0.0582643
$455$	−4.30952	+	2.03237i	−0.00947147	+	0.00446675i
$456$	633.715			1.38973
$457$	415.513			0.909218			0.454609	−	0.890691i	$-0.349779\pi$
$457$	415.513			0.909218			0.454609	+	0.890691i	$0.349779\pi$
$458$	659.883			1.44079
$459$		−	558.320i		−	1.21638i
$460$	613.008	+	1299.84i	1.33263	+	2.82575i
$461$		−	704.025i		−	1.52717i	−0.645707	−	0.763585i	$-0.723437\pi$
$461$		−	704.025i		−	1.52717i	0.645707	−	0.763585i	$-0.276563\pi$
$462$		0			0
$463$			506.506i			1.09397i	0.837144	+	0.546983i	$0.184224\pi$
$463$			506.506i			1.09397i	−0.837144	+	0.546983i	$0.815776\pi$
$464$			400.755i			0.863696i
$465$	−20.8285	−	44.1656i	−0.0447926	−	0.0949798i
$466$	−336.766			−0.722674
$467$		−	359.350i		−	0.769487i	−0.923024	−	0.384743i	$-0.874290\pi$
$467$		−	359.350i		−	0.769487i	0.923024	−	0.384743i	$-0.125710\pi$
$468$	50.2646			0.107403
$469$			47.6480i			0.101595i
$470$	449.197	+	952.494i	0.955738	+	2.02658i
$471$	222.629			0.472672
$472$	623.765			1.32154
$473$		0			0
$474$	−164.383			−0.346799
$475$	−488.729	−	402.917i	−1.02890	−	0.848246i
$476$	219.416			0.460957
$477$			157.927i			0.331084i
$478$			1404.49i			2.93826i
$479$			538.500i			1.12422i	0.827064	+	0.562108i	$0.190010\pi$
$479$			538.500i			1.12422i	−0.827064	+	0.562108i	$0.809990\pi$
$480$	61.4224	+	130.242i	0.127963	+	0.271338i
$481$		−	57.3210i		−	0.119171i
$482$			93.5418i			0.194070i
$483$	55.4665			0.114838
$484$		0			0
$485$	142.126	+	301.370i	0.293044	+	0.621381i
$486$			892.092i			1.83558i
$487$		−	661.194i		−	1.35769i	−0.734282	−	0.678844i	$-0.762481\pi$
$487$		−	661.194i		−	1.35769i	0.734282	−	0.678844i	$-0.237519\pi$
$488$		−	559.029i		−	1.14555i
$489$	−122.846			−0.251219
$490$	−768.015	+	362.197i	−1.56738	+	0.739177i
$491$			67.7982i			0.138082i	0.997614	+	0.0690410i	$0.0219939\pi$
$491$			67.7982i			0.138082i	−0.997614	+	0.0690410i	$0.978006\pi$
$492$	−508.642			−1.03382
$493$		−	393.535i		−	0.798245i
$494$		−	78.6598i		−	0.159230i
$495$		0			0
$496$	−152.293			−0.307042
$497$	−39.5043			−0.0794854
$498$		−	737.376i		−	1.48067i
$499$	386.074			0.773696			0.386848	−	0.922144i	$-0.373564\pi$
$499$	386.074			0.773696			0.386848	+	0.922144i	$0.373564\pi$
$500$	265.212	−	1043.96i	0.530424	−	2.08791i
$501$			171.005i			0.341328i
$502$	1330.52			2.65043
$503$	−259.269			−0.515446			−0.257723	−	0.966219i	$-0.582972\pi$
$503$	−259.269			−0.515446			−0.257723	+	0.966219i	$0.582972\pi$
$504$	−119.325			−0.236757
$505$	−170.615	−	361.779i	−0.337852	−	0.716395i
$506$		0			0
$507$		−	256.592i		−	0.506099i
$508$	1105.24			2.17567
$509$	−807.667			−1.58677			−0.793386	−	0.608719i	$-0.791684\pi$
$509$	−807.667			−1.58677			−0.793386	+	0.608719i	$0.791684\pi$
$510$	−269.850	−	572.200i	−0.529118	−	1.12196i
$511$	91.6400			0.179335
$512$	−1111.06			−2.17004
$513$	605.672			1.18065
$514$		−	907.587i		−	1.76573i
$515$	−237.826	−	504.296i	−0.461799	−	0.979215i
$516$			197.999i			0.383719i
$517$		0			0
$518$			253.971i			0.490292i
$519$		−	288.353i		−	0.555593i
$520$	64.8229	−	30.5706i	0.124660	−	0.0587895i
$521$	312.048			0.598940			0.299470	−	0.954106i	$-0.403190\pi$
$521$	312.048			0.598940			0.299470	+	0.954106i	$0.403190\pi$
$522$			399.437i			0.765204i
$523$	73.6569			0.140835			0.0704177	−	0.997518i	$-0.477567\pi$
$523$	73.6569			0.140835			0.0704177	+	0.997518i	$0.477567\pi$
$524$			131.864i			0.251648i
$525$	−32.0762	−	26.4442i	−0.0610975	−	0.0503699i
$526$	1026.24			1.95103
$527$	149.549			0.283774
$528$		0			0
$529$	−583.638			−1.10328
$530$	179.266	+	380.122i	0.338237	+	0.717211i
$531$	253.842			0.478045
$532$			238.025i			0.447415i
$533$			33.8276i			0.0634665i
$534$		−	45.8811i		−	0.0859196i
$535$	−95.0028	+	44.8034i	−0.177575	+	0.0837447i
$536$		−	716.712i		−	1.33715i
$537$			349.087i			0.650069i
$538$	769.421			1.43015
$539$		0			0
$540$	439.327	+	931.564i	0.813568	+	1.72512i
$541$			41.4191i			0.0765603i	0.999267	+	0.0382802i	$0.0121879\pi$
$541$			41.4191i			0.0765603i	−0.999267	+	0.0382802i	$0.987812\pi$
$542$			187.241i			0.345464i
$543$		−	18.9803i		−	0.0349545i
$544$	−441.012			−0.810685
$545$	−252.715	−	535.866i	−0.463697	−	0.983241i
$546$		−	5.16259i		−	0.00945529i
$547$	644.686			1.17859			0.589293	−	0.807920i	$-0.299407\pi$
$547$	644.686			1.17859			0.589293	+	0.807920i	$0.299407\pi$
$548$			236.756i			0.432037i
$549$		−	227.498i		−	0.414386i
$550$		0			0
$551$	426.911			0.774794
$552$	−834.317			−1.51144
$553$		−	33.0815i		−	0.0598219i
$554$	582.623			1.05167
$555$	452.339	−	213.323i	0.815025	−	0.384366i
$556$		−	484.636i		−	0.871647i
$557$	−448.656			−0.805487			−0.402743	−	0.915313i	$-0.631943\pi$
$557$	−448.656			−0.805487			−0.402743	+	0.915313i	$0.631943\pi$
$558$	−151.792			−0.272028
$559$	13.1681			0.0235565
$560$	−117.266	+	55.3028i	−0.209404	+	0.0987551i
$561$		0			0
$562$			1816.02i			3.23136i
$563$	534.562			0.949489			0.474744	−	0.880124i	$-0.342540\pi$
$563$	534.562			0.949489			0.474744	+	0.880124i	$0.342540\pi$
$564$	−779.292			−1.38172
$565$	227.326	+	482.030i	0.402346	+	0.853150i
$566$	633.905			1.11997
$567$	−25.7341			−0.0453865
$568$	594.216			1.04615
$569$			441.511i			0.775941i	0.921672	+	0.387971i	$0.126824\pi$
$569$			441.511i			0.775941i	−0.921672	+	0.387971i	$0.873176\pi$
$570$	620.730	−	292.737i	1.08900	−	0.513573i
$571$			935.409i			1.63819i	0.573655	+	0.819097i	$0.305525\pi$
$571$			935.409i			1.63819i	−0.573655	+	0.819097i	$0.694475\pi$
$572$		0			0
$573$		−	1.42397i		−	0.00248511i
$574$		−	149.879i		−	0.261114i
$575$	643.436	+	530.461i	1.11902	+	0.922540i
$576$	−187.286			−0.325149
$577$		−	565.796i		−	0.980583i	−0.871559	−	0.490291i	$-0.836890\pi$
$577$		−	565.796i		−	0.980583i	0.871559	−	0.490291i	$-0.163110\pi$
$578$	910.987			1.57610
$579$		−	63.4686i		−	0.109618i
$580$	309.662	+	656.618i	0.533899	+	1.13210i
$581$	148.395			0.255412
$582$	−361.026			−0.620320
$583$		0			0
$584$	−1378.43			−2.36033
$585$	26.3798	−	12.4407i	0.0450937	−	0.0212662i
$586$	−202.299			−0.345220
$587$		−	979.469i		−	1.66860i	−0.551309	−	0.834301i	$-0.685872\pi$
$587$		−	979.469i		−	1.66860i	0.551309	−	0.834301i	$-0.314128\pi$
$588$		−	628.359i		−	1.06864i
$589$			162.232i			0.275437i
$590$	610.983	−	288.140i	1.03557	−	0.488373i
$591$			130.954i			0.221580i
$592$		−	1559.76i		−	2.63473i
$593$	1106.21			1.86544			0.932720	−	0.360600i	$-0.117428\pi$
$593$	1106.21			1.86544			0.932720	+	0.360600i	$0.117428\pi$
$594$		0			0
$595$	115.154	−	54.3065i	0.193535	−	0.0912714i
$596$		−	2044.00i		−	3.42953i
$597$			119.816i			0.200696i
$598$			103.560i			0.173177i
$599$	−570.796			−0.952915			−0.476458	−	0.879197i	$-0.658079\pi$
$599$	−570.796			−0.952915			−0.476458	+	0.879197i	$0.658079\pi$
$600$	482.484	+	397.769i	0.804140	+	0.662948i
$601$		−	167.567i		−	0.278814i	−0.990235	−	0.139407i	$-0.955480\pi$
$601$		−	167.567i		−	0.278814i	0.990235	−	0.139407i	$-0.0445196\pi$
$602$	−58.3435			−0.0969162
$603$		−	291.667i		−	0.483693i
$604$			405.283i			0.670999i
$605$		0			0
$606$	433.394			0.715171
$607$	843.183			1.38910			0.694549	−	0.719445i	$-0.255604\pi$
$607$	843.183			1.38910			0.694549	+	0.719445i	$0.255604\pi$
$608$		−	478.415i		−	0.786868i
$609$	28.0190			0.0460082
$610$	−258.236	−	547.574i	−0.423338	−	0.897663i
$611$			51.8274i			0.0848240i
$612$	−1343.11			−2.19462
$613$	−334.544			−0.545749			−0.272875	−	0.962050i	$-0.587974\pi$
$613$	−334.544			−0.545749			−0.272875	+	0.962050i	$0.587974\pi$
$614$	−1518.90			−2.47378
$615$	−266.945	+	125.891i	−0.434056	+	0.204701i
$616$		0			0
$617$		−	916.072i		−	1.48472i	−0.670001	−	0.742360i	$-0.733706\pi$
$617$		−	916.072i		−	1.48472i	0.670001	−	0.742360i	$-0.266294\pi$
$618$	604.121			0.977543
$619$	−696.083			−1.12453			−0.562264	−	0.826958i	$-0.690070\pi$
$619$	−696.083			−1.12453			−0.562264	+	0.826958i	$0.690070\pi$
$620$	−249.524	+	117.676i	−0.402458	+	0.189800i
$621$	−797.398			−1.28405
$622$	−354.235			−0.569509
$623$	9.23342			0.0148209
$624$			31.7060i			0.0508109i
$625$	−119.196	−	613.529i	−0.190713	−	0.981646i
$626$			187.291i			0.299187i
$627$		0			0
$628$		−	1257.79i		−	2.00286i
$629$			1531.66i			2.43507i
$630$	−116.880	+	55.1209i	−0.185524	+	0.0874935i
$631$	−439.420			−0.696386			−0.348193	−	0.937423i	$-0.613205\pi$
$631$	−439.420			−0.696386			−0.348193	+	0.937423i	$0.613205\pi$
$632$			497.606i			0.787351i
$633$	−204.502			−0.323068
$634$			1154.55i			1.82106i
$635$	580.050	−	273.552i	0.913465	−	0.430791i
$636$	−311.000			−0.488994
$637$	−41.7895			−0.0656036
$638$		0			0
$639$	241.817			0.378430
$640$	−792.363	+	373.679i	−1.23807	+	0.583873i
$641$	−755.940			−1.17931			−0.589657	−	0.807654i	$-0.700737\pi$
$641$	−755.940			−1.17931			−0.589657	+	0.807654i	$0.700737\pi$
$642$		−	113.809i		−	0.177272i
$643$		−	117.348i		−	0.182500i	−0.995828	−	0.0912502i	$-0.970914\pi$
$643$		−	117.348i		−	0.182500i	0.995828	−	0.0912502i	$-0.0290863\pi$
$644$		−	313.372i		−	0.486602i
$645$	49.0057	+	103.913i	0.0759778	+	0.161106i
$646$			2101.85i			3.25364i
$647$			1048.81i			1.62103i	0.585719	+	0.810514i	$0.300812\pi$
$647$			1048.81i			1.62103i	−0.585719	+	0.810514i	$0.699188\pi$
$648$	387.088			0.597358
$649$		0			0
$650$	49.3730	−	59.8883i	0.0759585	−	0.0921358i
$651$			10.6476i			0.0163558i
$652$			694.048i			1.06449i
$653$		−	394.291i		−	0.603814i	−0.953337	−	0.301907i	$-0.902377\pi$
$653$		−	394.291i		−	0.603814i	0.953337	−	0.301907i	$-0.0976232\pi$
$654$	641.941			0.981562
$655$	32.6369	+	69.2045i	0.0498274	+	0.105656i
$656$			920.483i			1.40318i
$657$	−560.955			−0.853812
$658$		−	229.631i		−	0.348983i
$659$			894.004i			1.35661i	0.734782	+	0.678303i	$0.237285\pi$
$659$			894.004i			1.35661i	−0.734782	+	0.678303i	$0.762715\pi$
$660$		0			0
$661$	−1104.87			−1.67152			−0.835759	−	0.549097i	$-0.814972\pi$
$661$	−1104.87			−1.67152			−0.835759	+	0.549097i	$0.814972\pi$
$662$	1218.52			1.84066
$663$		−	31.1348i		−	0.0469604i
$664$	−2232.12			−3.36163
$665$	58.9123	+	124.920i	0.0885900	+	0.187849i
$666$		−	1554.63i		−	2.33428i
$667$	−562.050			−0.842654
$668$	966.134			1.44631
$669$	−306.143			−0.457613
$670$	−331.076	−	702.026i	−0.494144	−	1.04780i
$671$		0			0
$672$		−	31.3993i		−	0.0467251i
$673$	−1043.74			−1.55087			−0.775436	−	0.631426i	$-0.782470\pi$
$673$	−1043.74			−1.55087			−0.775436	+	0.631426i	$0.782470\pi$
$674$	2222.27			3.29713
$675$	461.134	+	380.167i	0.683161	+	0.563210i
$676$	−1449.68			−2.14449
$677$	197.164			0.291231			0.145616	−	0.989341i	$-0.453484\pi$
$677$	197.164			0.291231			0.145616	+	0.989341i	$0.453484\pi$
$678$	−577.448			−0.851693
$679$		−	72.6554i		−	0.107004i
$680$	−1732.12	+	816.868i	−2.54723	+	1.20128i
$681$			11.3581i			0.0166786i
$682$		0			0
$683$		−	779.498i		−	1.14129i	−0.821198	−	0.570643i	$-0.806694\pi$
$683$		−	779.498i		−	1.14129i	0.821198	−	0.570643i	$-0.193306\pi$
$684$		−	1457.02i		−	2.13014i
$685$	58.5984	+	124.254i	0.0855451	+	0.181393i
$686$	374.915			0.546524
$687$			283.344i			0.412437i
$688$	358.316			0.520809
$689$			20.6833i			0.0300193i
$690$	−817.222	+	385.402i	−1.18438	+	0.558554i
$691$	−742.935			−1.07516			−0.537580	−	0.843213i	$-0.680661\pi$
$691$	−742.935			−1.07516			−0.537580	+	0.843213i	$0.680661\pi$
$692$	−1629.12			−2.35422
$693$		0			0
$694$	1694.64			2.44185
$695$	−119.950	−	254.346i	−0.172590	−	0.365965i
$696$	−421.456			−0.605541
$697$		−	903.900i		−	1.29684i
$698$			653.165i			0.935766i
$699$		−	144.602i		−	0.206870i
$700$	−149.403	+	181.222i	−0.213433	+	0.258889i
$701$		−	966.332i		−	1.37850i	−0.724521	−	0.689252i	$-0.757939\pi$
$701$		−	966.332i		−	1.37850i	0.724521	−	0.689252i	$-0.242061\pi$
$702$			74.2184i			0.105724i
$703$	−1661.56			−2.36353
$704$		0			0
$705$	−408.987	+	192.879i	−0.580123	+	0.273587i
$706$		−	1027.64i		−	1.45559i
$707$			87.2191i			0.123365i
$708$			499.882i			0.706048i
$709$	−355.431			−0.501313			−0.250657	−	0.968076i	$-0.580647\pi$
$709$	−355.431			−0.501313			−0.250657	+	0.968076i	$0.580647\pi$
$710$	582.040	−	274.491i	0.819775	−	0.386606i
$711$			202.501i			0.284812i
$712$	−138.887			−0.195067
$713$		−	213.587i		−	0.299561i
$714$			137.948i			0.193205i
$715$		0			0
$716$	1972.25			2.75454
$717$	−603.067			−0.841098
$718$		−	1191.11i		−	1.65892i
$719$	249.411			0.346886			0.173443	−	0.984844i	$-0.444511\pi$
$719$	249.411			0.346886			0.173443	+	0.984844i	$0.444511\pi$
$720$	717.820	−	338.525i	0.996972	−	0.470173i
$721$			121.578i			0.168623i
$722$	−997.826			−1.38203
$723$	−40.1655			−0.0555539
$724$	−107.234			−0.148113
$725$	325.033	+	267.963i	0.448321	+	0.369604i
$726$		0			0
$727$			883.791i			1.21567i	0.794064	+	0.607834i	$0.207961\pi$
$727$			883.791i			1.21567i	−0.794064	+	0.607834i	$0.792039\pi$
$728$	−15.6278			−0.0214667
$729$	−170.618			−0.234044
$730$	−1350.19	+	636.749i	−1.84957	+	0.872259i
$731$	−351.861			−0.481342
$732$	448.003			0.612026
$733$	−946.218			−1.29088			−0.645442	−	0.763809i	$-0.723327\pi$
$733$	−946.218			−1.29088			−0.645442	+	0.763809i	$0.723327\pi$
$734$			844.816i			1.15098i
$735$	−155.522	−	329.774i	−0.211594	−	0.448673i
$736$			629.858i			0.855785i
$737$		0			0
$738$			917.455i			1.24316i
$739$		−	474.204i		−	0.641683i	−0.947133	−	0.320841i	$-0.896034\pi$
$739$		−	474.204i		−	0.641683i	0.947133	−	0.320841i	$-0.103966\pi$
$740$	−1205.22	−	2555.60i	−1.62868	−	3.45351i
$741$	33.7754			0.0455808
$742$		−	91.6412i		−	0.123506i
$743$	−240.887			−0.324208			−0.162104	−	0.986774i	$-0.551828\pi$
$743$	−240.887			−0.324208			−0.162104	+	0.986774i	$0.551828\pi$
$744$		−	160.159i		−	0.215268i
$745$	−505.901	−	1072.73i	−0.679062	−	1.43991i
$746$	853.404			1.14397
$747$	−908.365			−1.21602
$748$		0			0
$749$	22.9036			0.0305790
$750$	656.342	+	166.741i	0.875123	+	0.222321i
$751$	386.499			0.514646			0.257323	−	0.966325i	$-0.417160\pi$
$751$	386.499			0.514646			0.257323	+	0.966325i	$0.417160\pi$
$752$			1410.28i			1.87537i
$753$			571.304i			0.758704i
$754$			52.3132i			0.0693810i
$755$	100.310	+	212.700i	0.132860	+	0.281722i
$756$		−	224.585i		−	0.297070i
$757$			778.941i			1.02898i	0.857495	+	0.514492i	$0.172020\pi$
$757$			778.941i			1.02898i	−0.857495	+	0.514492i	$0.827980\pi$
$758$	−931.541			−1.22895
$759$		0			0
$760$	−886.148	−	1879.02i	−1.16598	−	2.47240i
$761$			301.633i			0.396364i	0.980165	+	0.198182i	$0.0635037\pi$
$761$			301.633i			0.396364i	−0.980165	+	0.198182i	$0.936496\pi$
$762$			694.872i			0.911905i
$763$			129.189i			0.169317i
$764$	−8.04506			−0.0105302
$765$	−704.888	+	332.426i	−0.921422	+	0.434543i
$766$		−	1217.17i		−	1.58899i
$767$	33.2451			0.0433443
$768$		−	778.007i		−	1.01303i
$769$		−	1335.43i		−	1.73658i	−0.496054	−	0.868292i	$-0.665218\pi$
$769$		−	1335.43i		−	1.73658i	0.496054	−	0.868292i	$-0.334782\pi$
$770$		0			0
$771$	389.705			0.505453
$772$	−358.581			−0.464483
$773$			429.840i			0.556067i	0.960571	+	0.278034i	$0.0896826\pi$
$773$			429.840i			0.556067i	−0.960571	+	0.278034i	$0.910317\pi$
$774$	357.138			0.461418
$775$	−101.830	+	123.517i	−0.131393	+	0.159377i
$776$			1092.87i			1.40834i
$777$	−109.052			−0.140349
$778$	−2246.40			−2.88741
$779$	980.561			1.25874
$780$	24.4991	+	51.9488i	0.0314091	+	0.0666010i
$781$		0			0
$782$		−	2767.19i		−	3.53861i
$783$	−402.806			−0.514440
$784$	−1137.13			−1.45043
$785$	−311.310	−	660.114i	−0.396574	−	0.840909i
$786$	−82.9036			−0.105475
$787$	−1023.44			−1.30043			−0.650213	−	0.759752i	$-0.725320\pi$
$787$	−1023.44			−1.30043			−0.650213	+	0.759752i	$0.725320\pi$
$788$	739.857			0.938904
$789$			440.652i			0.558495i
$790$	229.863	+	487.410i	0.290966	+	0.616974i
$791$		−	116.210i		−	0.146915i
$792$		0			0
$793$		−	29.7948i		−	0.0375723i
$794$		−	1192.26i		−	1.50159i
$795$	−163.219	+	76.9741i	−0.205307	+	0.0968228i
$796$	676.927			0.850410
$797$			670.862i			0.841735i	0.907122	+	0.420867i	$0.138274\pi$
$797$			670.862i			0.841735i	−0.907122	+	0.420867i	$0.861726\pi$
$798$	−149.648			−0.187529
$799$		−	1384.87i		−	1.73325i
$800$	300.291	−	364.246i	0.375363	−	0.455307i
$801$	−56.5204			−0.0705623
$802$	2487.78			3.10197
$803$		0			0
$804$	574.369			0.714390
$805$	−77.5610	−	164.463i	−0.0963491	−	0.204302i
$806$	−19.8798			−0.0246647
$807$			330.378i			0.409390i
$808$		−	1311.93i		−	1.62368i
$809$			388.465i			0.480179i	0.970751	+	0.240090i	$0.0771768\pi$
$809$			388.465i			0.480179i	−0.970751	+	0.240090i	$0.922823\pi$
$810$	379.157	−	178.811i	0.468094	−	0.220754i
$811$		−	1002.78i		−	1.23648i	−0.785991	−	0.618238i	$-0.787847\pi$
$811$		−	1002.78i		−	1.23648i	0.785991	−	0.618238i	$-0.212153\pi$
$812$		−	158.300i		−	0.194951i
$813$	−80.3987			−0.0988914
$814$		0			0
$815$	171.780	+	364.249i	0.210773	+	0.446932i
$816$		−	847.208i		−	1.03824i
$817$		−	381.703i		−	0.467200i
$818$		−	65.0196i		−	0.0794860i
$819$	−6.35974			−0.00776525
$820$	711.253	+	1508.17i	0.867382	+	1.83923i
$821$			532.528i			0.648634i	0.945948	+	0.324317i	$0.105134\pi$
$821$			532.528i			0.648634i	−0.945948	+	0.324317i	$0.894866\pi$
$822$	−148.850			−0.181083
$823$			903.186i			1.09743i	0.836009	+	0.548716i	$0.184883\pi$
$823$			903.186i			1.09743i	−0.836009	+	0.548716i	$0.815117\pi$
$824$		−	1828.75i		−	2.21935i
$825$		0			0
$826$	−147.298			−0.178327
$827$	1456.82			1.76157			0.880784	−	0.473519i	$-0.157017\pi$
$827$	1456.82			1.76157			0.880784	+	0.473519i	$0.157017\pi$
$828$			1918.24i			2.31671i
$829$	−847.158			−1.02190			−0.510952	−	0.859609i	$-0.670707\pi$
$829$	−847.158			−1.02190			−0.510952	+	0.859609i	$0.670707\pi$
$830$	−2186.39	+	1031.10i	−2.63420	+	1.24229i
$831$			250.170i			0.301047i
$832$	−24.5284			−0.0294812
$833$	1116.65			1.34051
$834$	304.694			0.365340
$835$	507.046	−	239.123i	0.607240	−	0.286375i
$836$		0			0
$837$		−	153.072i		−	0.182882i
$838$	−1495.21			−1.78426
$839$	−956.668			−1.14025			−0.570124	−	0.821559i	$-0.693105\pi$
$839$	−956.668			−1.14025			−0.570124	+	0.821559i	$0.693105\pi$
$840$	−58.1595	−	123.324i	−0.0692375	−	0.146814i
$841$	557.080			0.662402
$842$	1657.83			1.96892
$843$	−779.774			−0.924999
$844$			1155.38i			1.36894i
$845$	−760.818	+	358.803i	−0.900377	+	0.424619i
$846$			1405.64i			1.66151i
$847$		0			0
$848$			562.814i			0.663695i
$849$			272.190i			0.320600i
$850$	−1319.28	+	1600.26i	−1.55210	+	1.88266i
$851$	2187.53			2.57054
$852$			476.201i			0.558922i
$853$	−1252.45			−1.46829			−0.734144	−	0.678994i	$-0.762416\pi$
$853$	−1252.45			−1.46829			−0.734144	+	0.678994i	$0.762416\pi$
$854$			132.011i			0.154580i
$855$	−360.619	−	764.670i	−0.421777	−	0.894351i
$856$	−344.512			−0.402468
$857$	−628.293			−0.733131			−0.366565	−	0.930392i	$-0.619466\pi$
$857$	−628.293			−0.733131			−0.366565	+	0.930392i	$0.619466\pi$
$858$		0			0
$859$	196.824			0.229132			0.114566	−	0.993416i	$-0.463452\pi$
$859$	196.824			0.229132			0.114566	+	0.993416i	$0.463452\pi$
$860$	587.084	−	276.869i	0.682656	−	0.321941i
$861$	64.3560			0.0747457
$862$		−	848.312i		−	0.984121i
$863$		−	814.245i		−	0.943505i	−0.881731	−	0.471753i	$-0.843622\pi$
$863$		−	814.245i		−	0.943505i	0.881731	−	0.471753i	$-0.156378\pi$
$864$			451.403i			0.522457i
$865$	−854.991	+	403.215i	−0.988429	+	0.466144i
$866$			340.713i			0.393433i
$867$			391.164i			0.451170i
$868$	60.1563			0.0693044
$869$		0			0
$870$	−412.820	+	194.686i	−0.474506	+	0.223778i
$871$		−	38.1989i		−	0.0438564i
$872$		−	1943.23i		−	2.22848i
$873$			444.744i			0.509444i
$874$	3001.88			3.43464
$875$	−33.5560	+	132.087i	−0.0383498	+	0.150956i
$876$		−	1104.67i		−	1.26104i
$877$	575.065			0.655718			0.327859	−	0.944727i	$-0.393673\pi$
$877$	575.065			0.655718			0.327859	+	0.944727i	$0.393673\pi$
$878$			2661.98i			3.03187i
$879$		−	86.8641i		−	0.0988215i
$880$		0			0
$881$	513.793			0.583193			0.291596	−	0.956541i	$-0.405814\pi$
$881$	513.793			0.583193			0.291596	+	0.956541i	$0.405814\pi$
$882$	−1133.39			−1.28503
$883$			291.241i			0.329831i	0.986308	+	0.164915i	$0.0527351\pi$
$883$			291.241i			0.329831i	−0.986308	+	0.164915i	$0.947265\pi$
$884$	−175.903			−0.198986
$885$	123.723	+	262.347i	0.139800	+	0.296438i
$886$		−	164.604i		−	0.185783i
$887$	1163.42			1.31163			0.655816	−	0.754921i	$-0.272325\pi$
$887$	1163.42			1.31163			0.655816	+	0.754921i	$0.272325\pi$
$888$	1640.33			1.84722
$889$	−139.841			−0.157301
$890$	−136.042	+	64.1573i	−0.152856	+	0.0720868i
$891$		0			0
$892$			1729.63i			1.93905i
$893$	1502.32			1.68233
$894$	1285.08			1.43745
$895$	1035.08	−	488.142i	1.15651	−	0.545411i
$896$	191.026			0.213199
$897$	−44.4670			−0.0495730
$898$	172.468			0.192058
$899$		−	107.894i		−	0.120015i
$900$	914.538	−	1109.31i	1.01615	−	1.23257i
$901$		−	552.674i		−	0.613401i
$902$		0			0
$903$		−	25.0519i		−	0.0277429i
$904$			1748.00i			1.93363i
$905$	−56.2783	+	26.5409i	−0.0621859	+	0.0293269i
$906$	−254.804			−0.281241
$907$			234.719i			0.258786i	0.991593	+	0.129393i	$0.0413029\pi$
$907$			234.719i			0.258786i	−0.991593	+	0.129393i	$0.958697\pi$
$908$	64.1703			0.0706722
$909$		−	533.893i		−	0.587341i
$910$	−15.3075	+	7.21905i	−0.0168215	+	0.00793302i
$911$	−561.265			−0.616098			−0.308049	−	0.951371i	$-0.599676\pi$
$911$	−561.265			−0.616098			−0.308049	+	0.951371i	$0.599676\pi$
$912$	919.061			1.00774
$913$		0			0
$914$	1475.91			1.61479
$915$	235.120	−	110.883i	0.256962	−	0.121184i
$916$	1600.82			1.74762
$917$		−	16.6841i		−	0.0181942i
$918$		−	1983.17i		−	2.16032i
$919$		−	800.742i		−	0.871319i	−0.900112	−	0.435659i	$-0.856515\pi$
$919$		−	800.742i		−	0.871319i	0.900112	−	0.435659i	$-0.143485\pi$
$920$	1166.66	+	2473.83i	1.26811	+	2.68894i
$921$		−	652.195i		−	0.708137i
$922$		−	2500.72i		−	2.71228i
$923$	31.6702			0.0343122
$924$		0			0
$925$	−1265.05	−	1042.93i	−1.36762	−	1.12749i
$926$			1799.12i			1.94290i
$927$		−	744.211i		−	0.802817i
$928$			318.174i			0.342859i
$929$	−368.505			−0.396668			−0.198334	−	0.980134i	$-0.563553\pi$
$929$	−368.505			−0.396668			−0.198334	+	0.980134i	$0.563553\pi$
$930$	−73.9836	−	156.878i	−0.0795523	−	0.168686i
$931$			1211.35i			1.30113i
$932$	−816.966			−0.876573
$933$		−	152.103i		−	0.163026i
$934$		−	1276.42i		−	1.36662i
$935$		0			0
$936$	95.6620			0.102203
$937$	−35.1307			−0.0374927			−0.0187464	−	0.999824i	$-0.505968\pi$
$937$	−35.1307			−0.0374927			−0.0187464	+	0.999824i	$0.505968\pi$
$938$			169.247i			0.180434i
$939$	−80.4200			−0.0856443
$940$	1089.71	+	2310.67i	1.15927	+	2.45816i
$941$			943.737i			1.00291i	0.865184	+	0.501454i	$0.167201\pi$
$941$			943.737i			1.00291i	−0.865184	+	0.501454i	$0.832799\pi$
$942$	790.784			0.839473
$943$	−1290.96			−1.36899
$944$	904.631			0.958295
$945$	−55.5859	−	117.866i	−0.0588211	−	0.124726i
$946$		0			0
$947$		−	337.731i		−	0.356633i	−0.983973	−	0.178316i	$-0.942935\pi$
$947$		−	337.731i		−	0.356633i	0.983973	−	0.178316i	$-0.0570650\pi$
$948$	−398.779			−0.420653
$949$	−73.4669			−0.0774150
$950$	−1735.98	−	1431.17i	−1.82735	−	1.50650i
$951$	−495.749			−0.521292
$952$	417.585			0.438640
$953$	−1053.77			−1.10574			−0.552872	−	0.833266i	$-0.686468\pi$
$953$	−1053.77			−1.10574			−0.552872	+	0.833266i	$0.686468\pi$
$954$			560.962i			0.588011i
$955$	−4.22220	+	1.99119i	−0.00442115	+	0.00208502i
$956$			3407.17i			3.56399i
$957$		0			0
$958$			1912.77i			1.99663i
$959$		−	29.9557i		−	0.0312364i
$960$	−91.2836	−	193.561i	−0.0950871	−	0.201626i
$961$	−919.999			−0.957335
$962$		−	203.606i		−	0.211649i
$963$	−140.200			−0.145586
$964$			226.925i			0.235399i
$965$	−188.190	+	88.7506i	−0.195016	+	0.0919695i
$966$	197.019			0.203953
$967$	200.406			0.207246			0.103623	−	0.994617i	$-0.466957\pi$
$967$	200.406			0.207246			0.103623	+	0.994617i	$0.466957\pi$
$968$		0			0
$969$	−902.503			−0.931376
$970$	504.837	+	1070.48i	0.520451	+	1.10358i
$971$	−312.778			−0.322119			−0.161060	−	0.986945i	$-0.551491\pi$
$971$	−312.778			−0.322119			−0.161060	+	0.986945i	$0.551491\pi$
$972$			2164.14i			2.22648i
$973$			61.3187i			0.0630202i
$974$		−	2348.58i		−	2.41128i
$975$	25.7152	+	21.2000i	0.0263745	+	0.0217436i
$976$		−	810.746i		−	0.830682i
$977$		−	491.515i		−	0.503086i	−0.967846	−	0.251543i	$-0.919062\pi$
$977$		−	491.515i		−	0.503086i	0.967846	−	0.251543i	$-0.0809380\pi$
$978$	−436.353			−0.446168
$979$		0			0
$980$	−1863.14	+	878.658i	−1.90116	+	0.896590i
$981$		−	790.801i		−	0.806117i
$982$			240.821i			0.245236i
$983$		−	869.168i		−	0.884199i	−0.896966	−	0.442100i	$-0.854234\pi$
$983$		−	869.168i		−	0.884199i	0.896966	−	0.442100i	$-0.145766\pi$
$984$	−968.031			−0.983772
$985$	388.291	−	183.118i	0.394204	−	0.185907i
$986$		−	1397.85i		−	1.41770i
$987$	98.6001			0.0998988
$988$		−	190.822i		−	0.193140i
$989$			502.531i			0.508120i
$990$		0			0
$991$	−901.175			−0.909360			−0.454680	−	0.890655i	$-0.650246\pi$
$991$	−901.175			−0.909360			−0.454680	+	0.890655i	$0.650246\pi$
$992$	−120.910			−0.121886
$993$			523.213i			0.526901i
$994$	−140.320			−0.141167
$995$	355.264	−	167.543i	0.357049	−	0.168385i
$996$		−	1788.81i		−	1.79600i
$997$	1273.41			1.27724			0.638621	−	0.769521i	$-0.279505\pi$
$997$	1273.41			1.27724			0.638621	+	0.769521i	$0.279505\pi$
$998$	1371.35			1.37410
$999$	1567.75			1.56932

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.3.d.b.604.37		40
5.4	even	2	inner	605.3.d.b.604.4		40
11.3	even	5		55.3.h.a.24.10	yes	40
11.7	odd	10		55.3.h.a.39.1	yes	40
11.10	odd	2	inner	605.3.d.b.604.3		40
55.3	odd	20		275.3.x.j.101.1		40
55.7	even	20		275.3.x.j.226.10		40
55.14	even	10		55.3.h.a.24.1	✓	40
55.18	even	20		275.3.x.j.226.1		40
55.29	odd	10		55.3.h.a.39.10	yes	40
55.47	odd	20		275.3.x.j.101.10		40
55.54	odd	2	inner	605.3.d.b.604.38		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.3.h.a.24.1	✓	40	55.14	even	10
55.3.h.a.24.10	yes	40	11.3	even	5
55.3.h.a.39.1	yes	40	11.7	odd	10
55.3.h.a.39.10	yes	40	55.29	odd	10
275.3.x.j.101.1		40	55.3	odd	20
275.3.x.j.101.10		40	55.47	odd	20
275.3.x.j.226.1		40	55.18	even	20
275.3.x.j.226.10		40	55.7	even	20
605.3.d.b.604.3		40	11.10	odd	2	inner
605.3.d.b.604.4		40	5.4	even	2	inner
605.3.d.b.604.37		40	1.1	even	1	trivial
605.3.d.b.604.38		40	55.54	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	605.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+3.55203 q^{2} +1.52519i q^{3} +8.61693 q^{4} +(4.52233 - 2.13273i) q^{5} +5.41753i q^{6} -1.09026 q^{7} +16.3995 q^{8} +6.67379 q^{9} +(16.0635 - 7.57554i) q^{10} +13.1425i q^{12} +0.874050 q^{13} -3.87264 q^{14} +(3.25282 + 6.89741i) q^{15} +23.7838 q^{16} -23.3553 q^{17} +23.7055 q^{18} -25.3361i q^{19} +(38.9686 - 18.3776i) q^{20} -1.66285i q^{21} +33.3562i q^{23} +25.0123i q^{24} +(15.9029 - 19.2898i) q^{25} +3.10466 q^{26} +23.9055i q^{27} -9.39469 q^{28} +16.8499i q^{29} +(11.5541 + 24.4998i) q^{30} -6.40321 q^{31} +18.8828 q^{32} -82.9587 q^{34} +(-4.93051 + 2.32523i) q^{35} +57.5076 q^{36} -65.5809i q^{37} -89.9946i q^{38} +1.33309i q^{39} +(74.1638 - 34.9757i) q^{40} +38.7022i q^{41} -5.90651i q^{42} +15.0656 q^{43} +(30.1811 - 14.2334i) q^{45} +118.482i q^{46} +59.2957i q^{47} +36.2748i q^{48} -47.8113 q^{49} +(56.4876 - 68.5181i) q^{50} -35.6213i q^{51} +7.53163 q^{52} +23.6638i q^{53} +84.9132i q^{54} -17.8797 q^{56} +38.6424 q^{57} +59.8515i q^{58} +38.0356 q^{59} +(28.0294 + 59.4345i) q^{60} -34.0882i q^{61} -22.7444 q^{62} -7.27617 q^{63} -28.0629 q^{64} +(3.95274 - 1.86412i) q^{65} -43.7033i q^{67} -201.251 q^{68} -50.8746 q^{69} +(-17.5133 + 8.25931i) q^{70} +36.2338 q^{71} +109.447 q^{72} -84.0533 q^{73} -232.946i q^{74} +(29.4207 + 24.2549i) q^{75} -218.319i q^{76} +4.73519i q^{78} +30.3428i q^{79} +(107.558 - 50.7244i) q^{80} +23.6037 q^{81} +137.471i q^{82} -136.109 q^{83} -14.3287i q^{84} +(-105.620 + 49.8106i) q^{85} +53.5134 q^{86} -25.6994 q^{87} -8.46901 q^{89} +(107.204 - 50.5576i) q^{90} -0.952942 q^{91} +287.428i q^{92} -9.76612i q^{93} +210.620i q^{94} +(-54.0351 - 114.578i) q^{95} +28.7998i q^{96} +66.6404i q^{97} -169.827 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 68 q^{4} - 8 q^{5} - 24 q^{9} - 12 q^{14} + 64 q^{15} + 212 q^{16} - 48 q^{20} + 32 q^{25} - 288 q^{26} - 212 q^{31} - 112 q^{34} + 288 q^{36} + 196 q^{45} - 472 q^{49} + 144 q^{56} + 256 q^{59}+ \cdots + 1032 q^{91}+O(q^{100}) \) 40 * q + 68 * q^4 - 8 * q^5 - 24 * q^9 - 12 * q^14 + 64 * q^15 + 212 * q^16 - 48 * q^20 + 32 * q^25 - 288 * q^26 - 212 * q^31 - 112 * q^34 + 288 * q^36 + 196 * q^45 - 472 * q^49 + 144 * q^56 + 256 * q^59 + 124 * q^60 + 756 * q^64 - 744 * q^69 + 400 * q^70 + 300 * q^71 + 624 * q^75 - 728 * q^80 - 1024 * q^81 - 1508 * q^86 - 812 * q^89 + 1032 * q^91

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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