LMFDB - Embedded newform 195.4.b.c.181.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [195,4,Mod(181,195)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(195, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("195.181");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 195 = 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	195.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$11.5053724511$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			181.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	195.181
Dual form			195.4.b.c.181.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +3.00000 q^{3} +7.00000 q^{4} +5.00000i q^{5} -3.00000i q^{6} -16.0000i q^{7} -15.0000i q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +3.00000 q^{3} +7.00000 q^{4} +5.00000i q^{5} -3.00000i q^{6} -16.0000i q^{7} -15.0000i q^{8} +9.00000 q^{9} +5.00000 q^{10} -60.0000i q^{11} +21.0000 q^{12} +(-39.0000 + 26.0000i) q^{13} -16.0000 q^{14} +15.0000i q^{15} +41.0000 q^{16} +116.000 q^{17} -9.00000i q^{18} +4.00000i q^{19} +35.0000i q^{20} -48.0000i q^{21} -60.0000 q^{22} +142.000 q^{23} -45.0000i q^{24} -25.0000 q^{25} +(26.0000 + 39.0000i) q^{26} +27.0000 q^{27} -112.000i q^{28} -220.000 q^{29} +15.0000 q^{30} +290.000i q^{31} -161.000i q^{32} -180.000i q^{33} -116.000i q^{34} +80.0000 q^{35} +63.0000 q^{36} +44.0000i q^{37} +4.00000 q^{38} +(-117.000 + 78.0000i) q^{39} +75.0000 q^{40} -370.000i q^{41} -48.0000 q^{42} +212.000 q^{43} -420.000i q^{44} +45.0000i q^{45} -142.000i q^{46} -176.000i q^{47} +123.000 q^{48} +87.0000 q^{49} +25.0000i q^{50} +348.000 q^{51} +(-273.000 + 182.000i) q^{52} -378.000 q^{53} -27.0000i q^{54} +300.000 q^{55} -240.000 q^{56} +12.0000i q^{57} +220.000i q^{58} +804.000i q^{59} +105.000i q^{60} -578.000 q^{61} +290.000 q^{62} -144.000i q^{63} +167.000 q^{64} +(-130.000 - 195.000i) q^{65} -180.000 q^{66} +294.000i q^{67} +812.000 q^{68} +426.000 q^{69} -80.0000i q^{70} -140.000i q^{71} -135.000i q^{72} +662.000i q^{73} +44.0000 q^{74} -75.0000 q^{75} +28.0000i q^{76} -960.000 q^{77} +(78.0000 + 117.000i) q^{78} -1400.00 q^{79} +205.000i q^{80} +81.0000 q^{81} -370.000 q^{82} +792.000i q^{83} -336.000i q^{84} +580.000i q^{85} -212.000i q^{86} -660.000 q^{87} -900.000 q^{88} +294.000i q^{89} +45.0000 q^{90} +(416.000 + 624.000i) q^{91} +994.000 q^{92} +870.000i q^{93} -176.000 q^{94} -20.0000 q^{95} -483.000i q^{96} -286.000i q^{97} -87.0000i q^{98} -540.000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 6 q^{3} + 14 q^{4} + 18 q^{9}+O(q^{10}) $ 2 * q + 6 * q^3 + 14 * q^4 + 18 * q^9	$ 2 q + 6 q^{3} + 14 q^{4} + 18 q^{9} + 10 q^{10} + 42 q^{12} - 78 q^{13} - 32 q^{14} + 82 q^{16} + 232 q^{17} - 120 q^{22} + 284 q^{23} - 50 q^{25} + 52 q^{26} + 54 q^{27} - 440 q^{29} + 30 q^{30} + 160 q^{35} + 126 q^{36} + 8 q^{38} - 234 q^{39} + 150 q^{40} - 96 q^{42} + 424 q^{43} + 246 q^{48} + 174 q^{49} + 696 q^{51} - 546 q^{52} - 756 q^{53} + 600 q^{55} - 480 q^{56} - 1156 q^{61} + 580 q^{62} + 334 q^{64} - 260 q^{65} - 360 q^{66} + 1624 q^{68} + 852 q^{69} + 88 q^{74} - 150 q^{75} - 1920 q^{77} + 156 q^{78} - 2800 q^{79} + 162 q^{81} - 740 q^{82} - 1320 q^{87} - 1800 q^{88} + 90 q^{90} + 832 q^{91} + 1988 q^{92} - 352 q^{94} - 40 q^{95}+O(q^{100}) $ 2 * q + 6 * q^3 + 14 * q^4 + 18 * q^9 + 10 * q^10 + 42 * q^12 - 78 * q^13 - 32 * q^14 + 82 * q^16 + 232 * q^17 - 120 * q^22 + 284 * q^23 - 50 * q^25 + 52 * q^26 + 54 * q^27 - 440 * q^29 + 30 * q^30 + 160 * q^35 + 126 * q^36 + 8 * q^38 - 234 * q^39 + 150 * q^40 - 96 * q^42 + 424 * q^43 + 246 * q^48 + 174 * q^49 + 696 * q^51 - 546 * q^52 - 756 * q^53 + 600 * q^55 - 480 * q^56 - 1156 * q^61 + 580 * q^62 + 334 * q^64 - 260 * q^65 - 360 * q^66 + 1624 * q^68 + 852 * q^69 + 88 * q^74 - 150 * q^75 - 1920 * q^77 + 156 * q^78 - 2800 * q^79 + 162 * q^81 - 740 * q^82 - 1320 * q^87 - 1800 * q^88 + 90 * q^90 + 832 * q^91 + 1988 * q^92 - 352 * q^94 - 40 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/195\mathbb{Z}\right)^\times$.

$n$	$106$	$131$	$157$
$\chi(n)$	$-1$	$1$	$1$

Coefficient data

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

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

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

$2$		−	1.00000i		−	0.353553i	−0.984251	−	0.176777i	$-0.943433\pi$
$2$		−	1.00000i		−	0.353553i	0.984251	−	0.176777i	$-0.0565670\pi$
$3$	3.00000			0.577350
$3$	3.00000			0.577350
$4$	7.00000			0.875000
$5$			5.00000i			0.447214i
$5$			5.00000i			0.447214i
$6$		−	3.00000i		−	0.204124i
$7$		−	16.0000i		−	0.863919i	−0.901893	−	0.431959i	$-0.857822\pi$
$7$		−	16.0000i		−	0.863919i	0.901893	−	0.431959i	$-0.142178\pi$
$8$		−	15.0000i		−	0.662913i
$9$	9.00000			0.333333
$10$	5.00000			0.158114
$11$		−	60.0000i		−	1.64461i	−0.569049	−	0.822304i	$-0.692689\pi$
$11$		−	60.0000i		−	1.64461i	0.569049	−	0.822304i	$-0.307311\pi$
$12$	21.0000			0.505181
$13$	−39.0000	+	26.0000i	−0.832050	+	0.554700i
$13$	−39.0000	+	26.0000i	−0.832050	+	0.554700i
$14$	−16.0000			−0.305441
$15$			15.0000i			0.258199i
$16$	41.0000			0.640625
$17$	116.000			1.65495			0.827474	−	0.561503i	$-0.189777\pi$
$17$	116.000			1.65495			0.827474	+	0.561503i	$0.189777\pi$
$18$		−	9.00000i		−	0.117851i
$19$			4.00000i			0.0482980i	0.999708	+	0.0241490i	$0.00768762\pi$
$19$			4.00000i			0.0482980i	−0.999708	+	0.0241490i	$0.992312\pi$
$20$			35.0000i			0.391312i
$21$		−	48.0000i		−	0.498784i
$22$	−60.0000			−0.581456
$23$	142.000			1.28735			0.643675	−	0.765299i	$-0.277409\pi$
$23$	142.000			1.28735			0.643675	+	0.765299i	$0.277409\pi$
$24$		−	45.0000i		−	0.382733i
$25$	−25.0000			−0.200000
$26$	26.0000	+	39.0000i	0.196116	+	0.294174i
$27$	27.0000			0.192450
$28$		−	112.000i		−	0.755929i
$29$	−220.000			−1.40872			−0.704362	−	0.709841i	$-0.748767\pi$
$29$	−220.000			−1.40872			−0.704362	+	0.709841i	$0.748767\pi$
$30$	15.0000			0.0912871
$31$			290.000i			1.68018i	0.542448	+	0.840089i	$0.317498\pi$
$31$			290.000i			1.68018i	−0.542448	+	0.840089i	$0.682502\pi$
$32$		−	161.000i		−	0.889408i
$33$		−	180.000i		−	0.949514i
$34$		−	116.000i		−	0.585113i
$35$	80.0000			0.386356
$36$	63.0000			0.291667
$37$			44.0000i			0.195501i	0.995211	+	0.0977507i	$0.0311648\pi$
$37$			44.0000i			0.195501i	−0.995211	+	0.0977507i	$0.968835\pi$
$38$	4.00000			0.0170759
$39$	−117.000	+	78.0000i	−0.480384	+	0.320256i
$40$	75.0000			0.296464
$41$		−	370.000i		−	1.40937i	−0.709519	−	0.704686i	$-0.751088\pi$
$41$		−	370.000i		−	1.40937i	0.709519	−	0.704686i	$-0.248912\pi$
$42$	−48.0000			−0.176347
$43$	212.000			0.751853			0.375927	−	0.926649i	$-0.377324\pi$
$43$	212.000			0.751853			0.375927	+	0.926649i	$0.377324\pi$
$44$		−	420.000i		−	1.43903i
$45$			45.0000i			0.149071i
$46$		−	142.000i		−	0.455147i
$47$		−	176.000i		−	0.546218i	−0.961983	−	0.273109i	$-0.911948\pi$
$47$		−	176.000i		−	0.546218i	0.961983	−	0.273109i	$-0.0880519\pi$
$48$	123.000			0.369865
$49$	87.0000			0.253644
$50$			25.0000i			0.0707107i
$51$	348.000			0.955485
$52$	−273.000	+	182.000i	−0.728044	+	0.485363i
$53$	−378.000			−0.979666			−0.489833	−	0.871816i	$-0.662942\pi$
$53$	−378.000			−0.979666			−0.489833	+	0.871816i	$0.662942\pi$
$54$		−	27.0000i		−	0.0680414i
$55$	300.000			0.735491
$56$	−240.000			−0.572703
$57$			12.0000i			0.0278849i
$58$			220.000i			0.498059i
$59$			804.000i			1.77410i	0.461674	+	0.887050i	$0.347249\pi$
$59$			804.000i			1.77410i	−0.461674	+	0.887050i	$0.652751\pi$
$60$			105.000i			0.225924i
$61$	−578.000			−1.21320			−0.606601	−	0.795006i	$-0.707467\pi$
$61$	−578.000			−1.21320			−0.606601	+	0.795006i	$0.707467\pi$
$62$	290.000			0.594033
$63$		−	144.000i		−	0.287973i
$64$	167.000			0.326172
$65$	−130.000	−	195.000i	−0.248069	−	0.372104i
$66$	−180.000			−0.335704
$67$			294.000i			0.536087i	0.963407	+	0.268043i	$0.0863771\pi$
$67$			294.000i			0.536087i	−0.963407	+	0.268043i	$0.913623\pi$
$68$	812.000			1.44808
$69$	426.000			0.743252
$70$		−	80.0000i		−	0.136598i
$71$		−	140.000i		−	0.234013i	−0.993131	−	0.117007i	$-0.962670\pi$
$71$		−	140.000i		−	0.234013i	0.993131	−	0.117007i	$-0.0373299\pi$
$72$		−	135.000i		−	0.220971i
$73$			662.000i			1.06139i	0.847564	+	0.530693i	$0.178068\pi$
$73$			662.000i			1.06139i	−0.847564	+	0.530693i	$0.821932\pi$
$74$	44.0000			0.0691202
$75$	−75.0000			−0.115470
$76$			28.0000i			0.0422608i
$77$	−960.000			−1.42081
$78$	78.0000	+	117.000i	0.113228	+	0.169842i
$79$	−1400.00			−1.99383			−0.996913	−	0.0785100i	$-0.974984\pi$
$79$	−1400.00			−1.99383			−0.996913	+	0.0785100i	$0.974984\pi$
$80$			205.000i			0.286496i
$81$	81.0000			0.111111
$82$	−370.000			−0.498289
$83$			792.000i			1.04739i	0.851906	+	0.523695i	$0.175447\pi$
$83$			792.000i			1.04739i	−0.851906	+	0.523695i	$0.824553\pi$
$84$		−	336.000i		−	0.436436i
$85$			580.000i			0.740116i
$86$		−	212.000i		−	0.265820i
$87$	−660.000			−0.813327
$88$	−900.000			−1.09023
$89$			294.000i			0.350157i	0.984555	+	0.175078i	$0.0560179\pi$
$89$			294.000i			0.350157i	−0.984555	+	0.175078i	$0.943982\pi$
$90$	45.0000			0.0527046
$91$	416.000	+	624.000i	0.479216	+	0.718824i
$92$	994.000			1.12643
$93$			870.000i			0.970052i
$94$	−176.000			−0.193117
$95$	−20.0000			−0.0215995
$96$		−	483.000i		−	0.513500i
$97$		−	286.000i		−	0.299370i	−0.988734	−	0.149685i	$-0.952174\pi$
$97$		−	286.000i		−	0.299370i	0.988734	−	0.149685i	$-0.0478260\pi$
$98$		−	87.0000i		−	0.0896768i
$99$		−	540.000i		−	0.548202i
$100$	−175.000			−0.175000
$101$	−488.000			−0.480770			−0.240385	−	0.970678i	$-0.577274\pi$
$101$	−488.000			−0.480770			−0.240385	+	0.970678i	$0.577274\pi$
$102$		−	348.000i		−	0.337815i
$103$	1612.00			1.54209			0.771044	−	0.636782i	$-0.219735\pi$
$103$	1612.00			1.54209			0.771044	+	0.636782i	$0.219735\pi$
$104$	390.000	+	585.000i	0.367718	+	0.551577i
$105$	240.000			0.223063
$106$			378.000i			0.346364i
$107$	176.000			0.159015			0.0795073	−	0.996834i	$-0.474665\pi$
$107$	176.000			0.159015			0.0795073	+	0.996834i	$0.474665\pi$
$108$	189.000			0.168394
$109$			1934.00i			1.69948i	0.527200	+	0.849741i	$0.323242\pi$
$109$			1934.00i			1.69948i	−0.527200	+	0.849741i	$0.676758\pi$
$110$		−	300.000i		−	0.260035i
$111$			132.000i			0.112873i
$112$		−	656.000i		−	0.553448i
$113$	1852.00			1.54178			0.770892	−	0.636966i	$-0.219811\pi$
$113$	1852.00			1.54178			0.770892	+	0.636966i	$0.219811\pi$
$114$	12.0000			0.00985880
$115$			710.000i			0.575720i
$116$	−1540.00			−1.23263
$117$	−351.000	+	234.000i	−0.277350	+	0.184900i
$118$	804.000			0.627239
$119$		−	1856.00i		−	1.42974i
$120$	225.000			0.171163
$121$	−2269.00			−1.70473
$122$			578.000i			0.428932i
$123$		−	1110.00i		−	0.813702i
$124$			2030.00i			1.47016i
$125$		−	125.000i		−	0.0894427i
$126$	−144.000			−0.101814
$127$	−2064.00			−1.44213			−0.721065	−	0.692868i	$-0.756347\pi$
$127$	−2064.00			−1.44213			−0.721065	+	0.692868i	$0.756347\pi$
$128$		−	1455.00i		−	1.00473i
$129$	636.000			0.434083
$130$	−195.000	+	130.000i	−0.131559	+	0.0877058i
$131$	−978.000			−0.652277			−0.326138	−	0.945322i	$-0.605748\pi$
$131$	−978.000			−0.652277			−0.326138	+	0.945322i	$0.605748\pi$
$132$		−	1260.00i		−	0.830825i
$133$	64.0000			0.0417256
$134$	294.000			0.189535
$135$			135.000i			0.0860663i
$136$		−	1740.00i		−	1.09709i
$137$		−	786.000i		−	0.490164i	−0.969502	−	0.245082i	$-0.921185\pi$
$137$		−	786.000i		−	0.490164i	0.969502	−	0.245082i	$-0.0788149\pi$
$138$		−	426.000i		−	0.262779i
$139$	280.000			0.170858			0.0854291	−	0.996344i	$-0.472774\pi$
$139$	280.000			0.170858			0.0854291	+	0.996344i	$0.472774\pi$
$140$	560.000			0.338062
$141$		−	528.000i		−	0.315359i
$142$	−140.000			−0.0827362
$143$	1560.00	+	2340.00i	0.912264	+	1.36840i
$144$	369.000			0.213542
$145$		−	1100.00i		−	0.630000i
$146$	662.000			0.375257
$147$	261.000			0.146442
$148$			308.000i			0.171064i
$149$		−	586.000i		−	0.322195i	−0.986939	−	0.161097i	$-0.948497\pi$
$149$		−	586.000i		−	0.322195i	0.986939	−	0.161097i	$-0.0515033\pi$
$150$			75.0000i			0.0408248i
$151$		−	2270.00i		−	1.22338i	−0.791099	−	0.611689i	$-0.790491\pi$
$151$		−	2270.00i		−	1.22338i	0.791099	−	0.611689i	$-0.209509\pi$
$152$	60.0000			0.0320174
$153$	1044.00			0.551650
$154$			960.000i			0.502331i
$155$	−1450.00			−0.751399
$156$	−819.000	+	546.000i	−0.420336	+	0.280224i
$157$	266.000			0.135217			0.0676086	−	0.997712i	$-0.478463\pi$
$157$	266.000			0.135217			0.0676086	+	0.997712i	$0.478463\pi$
$158$			1400.00i			0.704924i
$159$	−1134.00			−0.565610
$160$	805.000			0.397755
$161$		−	2272.00i		−	1.11217i
$162$		−	81.0000i		−	0.0392837i
$163$			2142.00i			1.02929i	0.857403	+	0.514645i	$0.172076\pi$
$163$			2142.00i			1.02929i	−0.857403	+	0.514645i	$0.827924\pi$
$164$		−	2590.00i		−	1.23320i
$165$	900.000			0.424636
$166$	792.000			0.370308
$167$			1904.00i			0.882251i	0.897445	+	0.441126i	$0.145421\pi$
$167$			1904.00i			0.882251i	−0.897445	+	0.441126i	$0.854579\pi$
$168$	−720.000			−0.330650
$169$	845.000	−	2028.00i	0.384615	−	0.923077i
$170$	580.000			0.261670
$171$			36.0000i			0.0160993i
$172$	1484.00			0.657872
$173$	2782.00			1.22261			0.611305	−	0.791395i	$-0.290645\pi$
$173$	2782.00			1.22261			0.611305	+	0.791395i	$0.290645\pi$
$174$			660.000i			0.287554i
$175$			400.000i			0.172784i
$176$		−	2460.00i		−	1.05358i
$177$			2412.00i			1.02428i
$178$	294.000			0.123799
$179$	−1530.00			−0.638869			−0.319435	−	0.947608i	$-0.603493\pi$
$179$	−1530.00			−0.638869			−0.319435	+	0.947608i	$0.603493\pi$
$180$			315.000i			0.130437i
$181$	−1458.00			−0.598742			−0.299371	−	0.954137i	$-0.596777\pi$
$181$	−1458.00			−0.598742			−0.299371	+	0.954137i	$0.596777\pi$
$182$	624.000	−	416.000i	0.254143	−	0.169428i
$183$	−1734.00			−0.700442
$184$		−	2130.00i		−	0.853400i
$185$	−220.000			−0.0874309
$186$	870.000			0.342965
$187$		−	6960.00i		−	2.72174i
$188$		−	1232.00i		−	0.477941i
$189$		−	432.000i		−	0.166261i
$190$			20.0000i			0.00763659i
$191$	292.000			0.110620			0.0553099	−	0.998469i	$-0.482385\pi$
$191$	292.000			0.110620			0.0553099	+	0.998469i	$0.482385\pi$
$192$	501.000			0.188315
$193$		−	418.000i		−	0.155898i	−0.996957	−	0.0779490i	$-0.975163\pi$
$193$		−	418.000i		−	0.155898i	0.996957	−	0.0779490i	$-0.0248371\pi$
$194$	−286.000			−0.105843
$195$	−390.000	−	585.000i	−0.143223	−	0.214834i
$196$	609.000			0.221939
$197$			3614.00i			1.30704i	0.756909	+	0.653520i	$0.226708\pi$
$197$			3614.00i			1.30704i	−0.756909	+	0.653520i	$0.773292\pi$
$198$	−540.000			−0.193819
$199$	2880.00			1.02592			0.512959	−	0.858413i	$-0.328549\pi$
$199$	2880.00			1.02592			0.512959	+	0.858413i	$0.328549\pi$
$200$			375.000i			0.132583i
$201$			882.000i			0.309510i
$202$			488.000i			0.169978i
$203$			3520.00i			1.21702i
$204$	2436.00			0.836050
$205$	1850.00			0.630291
$206$		−	1612.00i		−	0.545210i
$207$	1278.00			0.429117
$208$	−1599.00	+	1066.00i	−0.533032	+	0.355355i
$209$	240.000			0.0794313
$210$		−	240.000i		−	0.0788646i
$211$	−768.000			−0.250575			−0.125287	−	0.992120i	$-0.539985\pi$
$211$	−768.000			−0.250575			−0.125287	+	0.992120i	$0.539985\pi$
$212$	−2646.00			−0.857208
$213$		−	420.000i		−	0.135108i
$214$		−	176.000i		−	0.0562202i
$215$			1060.00i			0.336239i
$216$		−	405.000i		−	0.127578i
$217$	4640.00			1.45154
$218$	1934.00			0.600858
$219$			1986.00i			0.612792i
$220$	2100.00			0.643554
$221$	−4524.00	+	3016.00i	−1.37700	+	0.918001i
$222$	132.000			0.0399066
$223$			2452.00i			0.736314i	0.929764	+	0.368157i	$0.120011\pi$
$223$			2452.00i			0.736314i	−0.929764	+	0.368157i	$0.879989\pi$
$224$	−2576.00			−0.768376
$225$	−225.000			−0.0666667
$226$		−	1852.00i		−	0.545103i
$227$		−	3336.00i		−	0.975410i	−0.873008	−	0.487705i	$-0.837834\pi$
$227$		−	3336.00i		−	0.975410i	0.873008	−	0.487705i	$-0.162166\pi$
$228$			84.0000i			0.0243993i
$229$		−	3926.00i		−	1.13291i	−0.824091	−	0.566457i	$-0.808314\pi$
$229$		−	3926.00i		−	1.13291i	0.824091	−	0.566457i	$-0.191686\pi$
$230$	710.000			0.203548
$231$	−2880.00			−0.820303
$232$			3300.00i			0.933860i
$233$	−1528.00			−0.429625			−0.214812	−	0.976655i	$-0.568914\pi$
$233$	−1528.00			−0.429625			−0.214812	+	0.976655i	$0.568914\pi$
$234$	234.000	+	351.000i	0.0653720	+	0.0980581i
$235$	880.000			0.244276
$236$			5628.00i			1.55234i
$237$	−4200.00			−1.15114
$238$	−1856.00			−0.505490
$239$		−	5336.00i		−	1.44417i	−0.691803	−	0.722086i	$-0.743183\pi$
$239$		−	5336.00i		−	1.44417i	0.691803	−	0.722086i	$-0.256817\pi$
$240$			615.000i			0.165409i
$241$			1860.00i			0.497150i	0.968613	+	0.248575i	$0.0799622\pi$
$241$			1860.00i			0.497150i	−0.968613	+	0.248575i	$0.920038\pi$
$242$			2269.00i			0.602714i
$243$	243.000			0.0641500
$244$	−4046.00			−1.06155
$245$			435.000i			0.113433i
$246$	−1110.00			−0.287687
$247$	−104.000	−	156.000i	−0.0267909	−	0.0401864i
$248$	4350.00			1.11381
$249$			2376.00i			0.604710i
$250$	−125.000			−0.0316228
$251$	4722.00			1.18745			0.593725	−	0.804668i	$-0.297657\pi$
$251$	4722.00			1.18745			0.593725	+	0.804668i	$0.297657\pi$
$252$		−	1008.00i		−	0.251976i
$253$		−	8520.00i		−	2.11719i
$254$			2064.00i			0.509870i
$255$			1740.00i			0.427306i
$256$	−119.000			−0.0290527
$257$	−4284.00			−1.03980			−0.519900	−	0.854227i	$-0.674031\pi$
$257$	−4284.00			−1.03980			−0.519900	+	0.854227i	$0.674031\pi$
$258$		−	636.000i		−	0.153471i
$259$	704.000			0.168897
$260$	−910.000	−	1365.00i	−0.217061	−	0.325591i
$261$	−1980.00			−0.469574
$262$			978.000i			0.230615i
$263$	−198.000			−0.0464228			−0.0232114	−	0.999731i	$-0.507389\pi$
$263$	−198.000			−0.0464228			−0.0232114	+	0.999731i	$0.507389\pi$
$264$	−2700.00			−0.629445
$265$		−	1890.00i		−	0.438120i
$266$		−	64.0000i		−	0.0147522i
$267$			882.000i			0.202163i
$268$			2058.00i			0.469076i
$269$	−5840.00			−1.32368			−0.661842	−	0.749643i	$-0.730225\pi$
$269$	−5840.00			−1.32368			−0.661842	+	0.749643i	$0.730225\pi$
$270$	135.000			0.0304290
$271$			4790.00i			1.07370i	0.843679	+	0.536848i	$0.180385\pi$
$271$			4790.00i			1.07370i	−0.843679	+	0.536848i	$0.819615\pi$
$272$	4756.00			1.06020
$273$	1248.00	+	1872.00i	0.276675	+	0.415013i
$274$	−786.000			−0.173299
$275$			1500.00i			0.328921i
$276$	2982.00			0.650345
$277$	946.000			0.205197			0.102599	−	0.994723i	$-0.467284\pi$
$277$	946.000			0.205197			0.102599	+	0.994723i	$0.467284\pi$
$278$		−	280.000i		−	0.0604075i
$279$			2610.00i			0.560060i
$280$		−	1200.00i		−	0.256120i
$281$			4530.00i			0.961698i	0.876803	+	0.480849i	$0.159671\pi$
$281$			4530.00i			0.961698i	−0.876803	+	0.480849i	$0.840329\pi$
$282$	−528.000			−0.111496
$283$	2612.00			0.548648			0.274324	−	0.961637i	$-0.411546\pi$
$283$	2612.00			0.548648			0.274324	+	0.961637i	$0.411546\pi$
$284$		−	980.000i		−	0.204762i
$285$	−60.0000			−0.0124705
$286$	2340.00	−	1560.00i	0.483801	−	0.322534i
$287$	−5920.00			−1.21758
$288$		−	1449.00i		−	0.296469i
$289$	8543.00			1.73886
$290$	−1100.00			−0.222739
$291$		−	858.000i		−	0.172841i
$292$			4634.00i			0.928713i
$293$			4422.00i			0.881693i	0.897583	+	0.440846i	$0.145322\pi$
$293$			4422.00i			0.881693i	−0.897583	+	0.440846i	$0.854678\pi$
$294$		−	261.000i		−	0.0517749i
$295$	−4020.00			−0.793402
$296$	660.000			0.129600
$297$		−	1620.00i		−	0.316505i
$298$	−586.000			−0.113913
$299$	−5538.00	+	3692.00i	−1.07114	+	0.714093i
$300$	−525.000			−0.101036
$301$		−	3392.00i		−	0.649540i
$302$	−2270.00			−0.432529
$303$	−1464.00			−0.277573
$304$			164.000i			0.0309409i
$305$		−	2890.00i		−	0.542560i
$306$		−	1044.00i		−	0.195038i
$307$		−	8306.00i		−	1.54413i	−0.635542	−	0.772066i	$-0.719224\pi$
$307$		−	8306.00i		−	1.54413i	0.635542	−	0.772066i	$-0.280776\pi$
$308$	−6720.00			−1.24321
$309$	4836.00			0.890325
$310$			1450.00i			0.265660i
$311$	2812.00			0.512713			0.256357	−	0.966582i	$-0.417478\pi$
$311$	2812.00			0.512713			0.256357	+	0.966582i	$0.417478\pi$
$312$	1170.00	+	1755.00i	0.212302	+	0.318453i
$313$	−1978.00			−0.357199			−0.178599	−	0.983922i	$-0.557157\pi$
$313$	−1978.00			−0.357199			−0.178599	+	0.983922i	$0.557157\pi$
$314$		−	266.000i		−	0.0478065i
$315$	720.000			0.128785
$316$	−9800.00			−1.74460
$317$		−	7666.00i		−	1.35825i	−0.734022	−	0.679125i	$-0.762359\pi$
$317$		−	7666.00i		−	1.35825i	0.734022	−	0.679125i	$-0.237641\pi$
$318$			1134.00i			0.199973i
$319$			13200.0i			2.31680i
$320$			835.000i			0.145868i
$321$	528.000			0.0918071
$322$	−2272.00			−0.393210
$323$			464.000i			0.0799308i
$324$	567.000			0.0972222
$325$	975.000	−	650.000i	0.166410	−	0.110940i
$326$	2142.00			0.363909
$327$			5802.00i			0.981197i
$328$	−5550.00			−0.934291
$329$	−2816.00			−0.471888
$330$		−	900.000i		−	0.150131i
$331$		−	160.000i		−	0.0265692i	−0.999912	−	0.0132846i	$-0.995771\pi$
$331$		−	160.000i		−	0.0265692i	0.999912	−	0.0132846i	$-0.00422874\pi$
$332$			5544.00i			0.916465i
$333$			396.000i			0.0651672i
$334$	1904.00			0.311923
$335$	−1470.00			−0.239745
$336$		−	1968.00i		−	0.319533i
$337$	6786.00			1.09690			0.548452	−	0.836182i	$-0.315217\pi$
$337$	6786.00			1.09690			0.548452	+	0.836182i	$0.315217\pi$
$338$	−2028.00	−	845.000i	−0.326357	−	0.135982i
$339$	5556.00			0.890149
$340$			4060.00i			0.647601i
$341$	17400.0			2.76323
$342$	36.0000			0.00569198
$343$		−	6880.00i		−	1.08305i
$344$		−	3180.00i		−	0.498413i
$345$			2130.00i			0.332392i
$346$		−	2782.00i		−	0.432258i
$347$	16.0000			0.00247529			0.00123764	−	0.999999i	$-0.499606\pi$
$347$	16.0000			0.00247529			0.00123764	+	0.999999i	$0.499606\pi$
$348$	−4620.00			−0.711661
$349$		−	2986.00i		−	0.457985i	−0.973428	−	0.228993i	$-0.926457\pi$
$349$		−	2986.00i		−	0.457985i	0.973428	−	0.228993i	$-0.0735432\pi$
$350$	400.000			0.0610883
$351$	−1053.00	+	702.000i	−0.160128	+	0.106752i
$352$	−9660.00			−1.46273
$353$		−	678.000i		−	0.102227i	−0.998693	−	0.0511137i	$-0.983723\pi$
$353$		−	678.000i		−	0.102227i	0.998693	−	0.0511137i	$-0.0162771\pi$
$354$	2412.00			0.362137
$355$	700.000			0.104654
$356$			2058.00i			0.306387i
$357$		−	5568.00i		−	0.825462i
$358$			1530.00i			0.225874i
$359$		−	5416.00i		−	0.796227i	−0.917336	−	0.398114i	$-0.869665\pi$
$359$		−	5416.00i		−	0.796227i	0.917336	−	0.398114i	$-0.130335\pi$
$360$	675.000			0.0988212
$361$	6843.00			0.997667
$362$			1458.00i			0.211687i
$363$	−6807.00			−0.984228
$364$	2912.00	+	4368.00i	0.419314	+	0.628971i
$365$	−3310.00			−0.474667
$366$			1734.00i			0.247644i
$367$	−7464.00			−1.06163			−0.530814	−	0.847488i	$-0.678114\pi$
$367$	−7464.00			−1.06163			−0.530814	+	0.847488i	$0.678114\pi$
$368$	5822.00			0.824709
$369$		−	3330.00i		−	0.469791i
$370$			220.000i			0.0309115i
$371$			6048.00i			0.846352i
$372$			6090.00i			0.848795i
$373$	8542.00			1.18576			0.592879	−	0.805291i	$-0.297991\pi$
$373$	8542.00			1.18576			0.592879	+	0.805291i	$0.297991\pi$
$374$	−6960.00			−0.962281
$375$		−	375.000i		−	0.0516398i
$376$	−2640.00			−0.362095
$377$	8580.00	−	5720.00i	1.17213	−	0.781419i
$378$	−432.000			−0.0587822
$379$			10224.0i			1.38568i	0.721093	+	0.692839i	$0.243640\pi$
$379$			10224.0i			1.38568i	−0.721093	+	0.692839i	$0.756360\pi$
$380$	−140.000			−0.0188996
$381$	−6192.00			−0.832614
$382$		−	292.000i		−	0.0391100i
$383$			6032.00i			0.804754i	0.915474	+	0.402377i	$0.131816\pi$
$383$			6032.00i			0.804754i	−0.915474	+	0.402377i	$0.868184\pi$
$384$		−	4365.00i		−	0.580079i
$385$		−	4800.00i		−	0.635404i
$386$	−418.000			−0.0551182
$387$	1908.00			0.250618
$388$		−	2002.00i		−	0.261949i
$389$	3820.00			0.497896			0.248948	−	0.968517i	$-0.419915\pi$
$389$	3820.00			0.497896			0.248948	+	0.968517i	$0.419915\pi$
$390$	−585.000	+	390.000i	−0.0759555	+	0.0506370i
$391$	16472.0			2.13050
$392$		−	1305.00i		−	0.168144i
$393$	−2934.00			−0.376592
$394$	3614.00			0.462108
$395$		−	7000.00i		−	0.891666i
$396$		−	3780.00i		−	0.479677i
$397$		−	11156.0i		−	1.41034i	−0.709040	−	0.705168i	$-0.750871\pi$
$397$		−	11156.0i		−	1.41034i	0.709040	−	0.705168i	$-0.249129\pi$
$398$		−	2880.00i		−	0.362717i
$399$	192.000			0.0240903
$400$	−1025.00			−0.128125
$401$			1030.00i			0.128269i	0.997941	+	0.0641343i	$0.0204286\pi$
$401$			1030.00i			0.128269i	−0.997941	+	0.0641343i	$0.979571\pi$
$402$	882.000			0.109428
$403$	−7540.00	−	11310.0i	−0.931995	−	1.39799i
$404$	−3416.00			−0.420674
$405$			405.000i			0.0496904i
$406$	3520.00			0.430282
$407$	2640.00			0.321523
$408$		−	5220.00i		−	0.633403i
$409$		−	16296.0i		−	1.97014i	−0.172168	−	0.985068i	$-0.555077\pi$
$409$		−	16296.0i		−	1.97014i	0.172168	−	0.985068i	$-0.444923\pi$
$410$		−	1850.00i		−	0.222841i
$411$		−	2358.00i		−	0.282997i
$412$	11284.0			1.34933
$413$	12864.0			1.53268
$414$		−	1278.00i		−	0.151716i
$415$	−3960.00			−0.468407
$416$	4186.00	+	6279.00i	0.493355	+	0.740032i
$417$	840.000			0.0986450
$418$		−	240.000i		−	0.0280832i
$419$	30.0000			0.00349784			0.00174892	−	0.999998i	$-0.499443\pi$
$419$	30.0000			0.00349784			0.00174892	+	0.999998i	$0.499443\pi$
$420$	1680.00			0.195180
$421$		−	11990.0i		−	1.38802i	−0.719965	−	0.694011i	$-0.755842\pi$
$421$		−	11990.0i		−	1.38802i	0.719965	−	0.694011i	$-0.244158\pi$
$422$			768.000i			0.0885916i
$423$		−	1584.00i		−	0.182073i
$424$			5670.00i			0.649433i
$425$	−2900.00			−0.330990
$426$	−420.000			−0.0477678
$427$			9248.00i			1.04811i
$428$	1232.00			0.139138
$429$	4680.00	+	7020.00i	0.526696	+	0.790044i
$430$	1060.00			0.118878
$431$			1260.00i			0.140817i	0.997518	+	0.0704084i	$0.0224303\pi$
$431$			1260.00i			0.140817i	−0.997518	+	0.0704084i	$0.977570\pi$
$432$	1107.00			0.123288
$433$	−1678.00			−0.186234			−0.0931172	−	0.995655i	$-0.529683\pi$
$433$	−1678.00			−0.186234			−0.0931172	+	0.995655i	$0.529683\pi$
$434$		−	4640.00i		−	0.513196i
$435$		−	3300.00i		−	0.363731i
$436$			13538.0i			1.48705i
$437$			568.000i			0.0621765i
$438$	1986.00			0.216655
$439$	7360.00			0.800168			0.400084	−	0.916479i	$-0.368981\pi$
$439$	7360.00			0.800168			0.400084	+	0.916479i	$0.368981\pi$
$440$		−	4500.00i		−	0.487566i
$441$	783.000			0.0845481
$442$	3016.00	+	4524.00i	0.324562	+	0.486843i
$443$	−8628.00			−0.925347			−0.462673	−	0.886529i	$-0.653110\pi$
$443$	−8628.00			−0.925347			−0.462673	+	0.886529i	$0.653110\pi$
$444$			924.000i			0.0987637i
$445$	−1470.00			−0.156595
$446$	2452.00			0.260326
$447$		−	1758.00i		−	0.186019i
$448$		−	2672.00i		−	0.281786i
$449$		−	11586.0i		−	1.21777i	−0.793260	−	0.608883i	$-0.791618\pi$
$449$		−	11586.0i		−	1.21777i	0.793260	−	0.608883i	$-0.208382\pi$
$450$			225.000i			0.0235702i
$451$	−22200.0			−2.31787
$452$	12964.0			1.34906
$453$		−	6810.00i		−	0.706317i
$454$	−3336.00			−0.344860
$455$	−3120.00	+	2080.00i	−0.321468	+	0.214312i
$456$	180.000			0.0184852
$457$			12994.0i			1.33005i	0.746820	+	0.665026i	$0.231580\pi$
$457$			12994.0i			1.33005i	−0.746820	+	0.665026i	$0.768420\pi$
$458$	−3926.00			−0.400546
$459$	3132.00			0.318495
$460$			4970.00i			0.503755i
$461$			1330.00i			0.134369i	0.997741	+	0.0671847i	$0.0214017\pi$
$461$			1330.00i			0.134369i	−0.997741	+	0.0671847i	$0.978598\pi$
$462$			2880.00i			0.290021i
$463$		−	14348.0i		−	1.44019i	−0.693875	−	0.720095i	$-0.744098\pi$
$463$		−	14348.0i		−	1.44019i	0.693875	−	0.720095i	$-0.255902\pi$
$464$	−9020.00			−0.902463
$465$	−4350.00			−0.433820
$466$			1528.00i			0.151895i
$467$	−2484.00			−0.246137			−0.123068	−	0.992398i	$-0.539273\pi$
$467$	−2484.00			−0.246137			−0.123068	+	0.992398i	$0.539273\pi$
$468$	−2457.00	+	1638.00i	−0.242681	+	0.161788i
$469$	4704.00			0.463135
$470$		−	880.000i		−	0.0863646i
$471$	798.000			0.0780677
$472$	12060.0			1.17607
$473$		−	12720.0i		−	1.23650i
$474$			4200.00i			0.406988i
$475$		−	100.000i		−	0.00965961i
$476$		−	12992.0i		−	1.25102i
$477$	−3402.00			−0.326555
$478$	−5336.00			−0.510592
$479$			2424.00i			0.231222i	0.993295	+	0.115611i	$0.0368826\pi$
$479$			2424.00i			0.231222i	−0.993295	+	0.115611i	$0.963117\pi$
$480$	2415.00			0.229644
$481$	−1144.00	−	1716.00i	−0.108445	−	0.162667i
$482$	1860.00			0.175769
$483$		−	6816.00i		−	0.642109i
$484$	−15883.0			−1.49164
$485$	1430.00			0.133882
$486$		−	243.000i		−	0.0226805i
$487$			10584.0i			0.984819i	0.870364	+	0.492409i	$0.163884\pi$
$487$			10584.0i			0.984819i	−0.870364	+	0.492409i	$0.836116\pi$
$488$			8670.00i			0.804247i
$489$			6426.00i			0.594261i
$490$	435.000			0.0401047
$491$	1622.00			0.149083			0.0745416	−	0.997218i	$-0.476251\pi$
$491$	1622.00			0.149083			0.0745416	+	0.997218i	$0.476251\pi$
$492$		−	7770.00i		−	0.711989i
$493$	−25520.0			−2.33137
$494$	−156.000	+	104.000i	−0.0142080	+	0.00947203i
$495$	2700.00			0.245164
$496$			11890.0i			1.07636i
$497$	−2240.00			−0.202168
$498$	2376.00			0.213797
$499$			17884.0i			1.60440i	0.597052	+	0.802202i	$0.296338\pi$
$499$			17884.0i			1.60440i	−0.597052	+	0.802202i	$0.703662\pi$
$500$		−	875.000i		−	0.0782624i
$501$			5712.00i			0.509368i
$502$		−	4722.00i		−	0.419827i
$503$	11282.0			1.00008			0.500039	−	0.866003i	$-0.333319\pi$
$503$	11282.0			1.00008			0.500039	+	0.866003i	$0.333319\pi$
$504$	−2160.00			−0.190901
$505$		−	2440.00i		−	0.215007i
$506$	−8520.00			−0.748538
$507$	2535.00	−	6084.00i	0.222058	−	0.532939i
$508$	−14448.0			−1.26186
$509$			8754.00i			0.762307i	0.924512	+	0.381153i	$0.124473\pi$
$509$			8754.00i			0.762307i	−0.924512	+	0.381153i	$0.875527\pi$
$510$	1740.00			0.151075
$511$	10592.0			0.916952
$512$		−	11521.0i		−	0.994455i
$513$			108.000i			0.00929496i
$514$			4284.00i			0.367625i
$515$			8060.00i			0.689643i
$516$	4452.00			0.379822
$517$	−10560.0			−0.898314
$518$		−	704.000i		−	0.0597143i
$519$	8346.00			0.705874
$520$	−2925.00	+	1950.00i	−0.246673	+	0.164448i
$521$	4642.00			0.390345			0.195172	−	0.980769i	$-0.437473\pi$
$521$	4642.00			0.390345			0.195172	+	0.980769i	$0.437473\pi$
$522$			1980.00i			0.166020i
$523$	−6028.00			−0.503989			−0.251994	−	0.967729i	$-0.581086\pi$
$523$	−6028.00			−0.503989			−0.251994	+	0.967729i	$0.581086\pi$
$524$	−6846.00			−0.570742
$525$			1200.00i			0.0997567i
$526$			198.000i			0.0164129i
$527$			33640.0i			2.78061i
$528$		−	7380.00i		−	0.608283i
$529$	7997.00			0.657270
$530$	−1890.00			−0.154899
$531$			7236.00i			0.591367i
$532$	448.000			0.0365099
$533$	9620.00	+	14430.0i	0.781779	+	1.17267i
$534$	882.000			0.0714754
$535$			880.000i			0.0711135i
$536$	4410.00			0.355379
$537$	−4590.00			−0.368851
$538$			5840.00i			0.467993i
$539$		−	5220.00i		−	0.417145i
$540$			945.000i			0.0753080i
$541$			2630.00i			0.209007i	0.994525	+	0.104503i	$0.0333253\pi$
$541$			2630.00i			0.209007i	−0.994525	+	0.104503i	$0.966675\pi$
$542$	4790.00			0.379609
$543$	−4374.00			−0.345684
$544$		−	18676.0i		−	1.47192i
$545$	−9670.00			−0.760032
$546$	1872.00	−	1248.00i	0.146729	−	0.0978195i
$547$	6236.00			0.487444			0.243722	−	0.969845i	$-0.421631\pi$
$547$	6236.00			0.487444			0.243722	+	0.969845i	$0.421631\pi$
$548$		−	5502.00i		−	0.428894i
$549$	−5202.00			−0.404401
$550$	1500.00			0.116291
$551$		−	880.000i		−	0.0680386i
$552$		−	6390.00i		−	0.492711i
$553$			22400.0i			1.72250i
$554$		−	946.000i		−	0.0725482i
$555$	−660.000			−0.0504783
$556$	1960.00			0.149501
$557$		−	16026.0i		−	1.21911i	−0.792744	−	0.609554i	$-0.791348\pi$
$557$		−	16026.0i		−	1.21911i	0.792744	−	0.609554i	$-0.208652\pi$
$558$	2610.00			0.198011
$559$	−8268.00	+	5512.00i	−0.625580	+	0.417053i
$560$	3280.00			0.247509
$561$		−	20880.0i		−	1.57140i
$562$	4530.00			0.340012
$563$	−7068.00			−0.529095			−0.264548	−	0.964373i	$-0.585223\pi$
$563$	−7068.00			−0.529095			−0.264548	+	0.964373i	$0.585223\pi$
$564$		−	3696.00i		−	0.275939i
$565$			9260.00i			0.689506i
$566$		−	2612.00i		−	0.193976i
$567$		−	1296.00i		−	0.0959910i
$568$	−2100.00			−0.155130
$569$	−5970.00			−0.439851			−0.219926	−	0.975517i	$-0.570581\pi$
$569$	−5970.00			−0.439851			−0.219926	+	0.975517i	$0.570581\pi$
$570$			60.0000i			0.00440899i
$571$	−3568.00			−0.261499			−0.130750	−	0.991415i	$-0.541738\pi$
$571$	−3568.00			−0.261499			−0.130750	+	0.991415i	$0.541738\pi$
$572$	10920.0	+	16380.0i	0.798231	+	1.19735i
$573$	876.000			0.0638664
$574$			5920.00i			0.430481i
$575$	−3550.00			−0.257470
$576$	1503.00			0.108724
$577$			8954.00i			0.646031i	0.946394	+	0.323016i	$0.104697\pi$
$577$			8954.00i			0.646031i	−0.946394	+	0.323016i	$0.895303\pi$
$578$		−	8543.00i		−	0.614778i
$579$		−	1254.00i		−	0.0900077i
$580$		−	7700.00i		−	0.551250i
$581$	12672.0			0.904859
$582$	−858.000			−0.0611087
$583$			22680.0i			1.61117i
$584$	9930.00			0.703607
$585$	−1170.00	−	1755.00i	−0.0826898	−	0.124035i
$586$	4422.00			0.311725
$587$		−	16876.0i		−	1.18662i	−0.804973	−	0.593311i	$-0.797820\pi$
$587$		−	16876.0i		−	1.18662i	0.804973	−	0.593311i	$-0.202180\pi$
$588$	1827.00			0.128136
$589$	−1160.00			−0.0811494
$590$			4020.00i			0.280510i
$591$			10842.0i			0.754620i
$592$			1804.00i			0.125243i
$593$		−	19778.0i		−	1.36962i	−0.728721	−	0.684810i	$-0.759885\pi$
$593$		−	19778.0i		−	1.36962i	0.728721	−	0.684810i	$-0.240115\pi$
$594$	−1620.00			−0.111901
$595$	9280.00			0.639400
$596$		−	4102.00i		−	0.281920i
$597$	8640.00			0.592314
$598$	3692.00	+	5538.00i	0.252470	+	0.378705i
$599$	−16880.0			−1.15142			−0.575708	−	0.817655i	$-0.695273\pi$
$599$	−16880.0			−1.15142			−0.575708	+	0.817655i	$0.695273\pi$
$600$			1125.00i			0.0765466i
$601$	−4918.00			−0.333793			−0.166896	−	0.985974i	$-0.553375\pi$
$601$	−4918.00			−0.333793			−0.166896	+	0.985974i	$0.553375\pi$
$602$	−3392.00			−0.229647
$603$			2646.00i			0.178696i
$604$		−	15890.0i		−	1.07046i
$605$		−	11345.0i		−	0.762380i
$606$			1464.00i			0.0981369i
$607$	−27944.0			−1.86855			−0.934277	−	0.356549i	$-0.883953\pi$
$607$	−27944.0			−1.86855			−0.934277	+	0.356549i	$0.883953\pi$
$608$	644.000			0.0429567
$609$			10560.0i			0.702648i
$610$	−2890.00			−0.191824
$611$	4576.00	+	6864.00i	0.302987	+	0.454481i
$612$	7308.00			0.482693
$613$		−	2668.00i		−	0.175790i	−0.996130	−	0.0878952i	$-0.971986\pi$
$613$		−	2668.00i		−	0.175790i	0.996130	−	0.0878952i	$-0.0280141\pi$
$614$	−8306.00			−0.545933
$615$	5550.00			0.363899
$616$			14400.0i			0.941871i
$617$			2134.00i			0.139241i	0.997574	+	0.0696204i	$0.0221788\pi$
$617$			2134.00i			0.139241i	−0.997574	+	0.0696204i	$0.977821\pi$
$618$		−	4836.00i		−	0.314777i
$619$			10744.0i			0.697638i	0.937190	+	0.348819i	$0.113417\pi$
$619$			10744.0i			0.697638i	−0.937190	+	0.348819i	$0.886583\pi$
$620$	−10150.0			−0.657474
$621$	3834.00			0.247751
$622$		−	2812.00i		−	0.181272i
$623$	4704.00			0.302507
$624$	−4797.00	+	3198.00i	−0.307746	+	0.205164i
$625$	625.000			0.0400000
$626$			1978.00i			0.126289i
$627$	720.000			0.0458597
$628$	1862.00			0.118315
$629$			5104.00i			0.323545i
$630$		−	720.000i		−	0.0455325i
$631$			3310.00i			0.208826i	0.994534	+	0.104413i	$0.0332963\pi$
$631$			3310.00i			0.208826i	−0.994534	+	0.104413i	$0.966704\pi$
$632$			21000.0i			1.32173i
$633$	−2304.00			−0.144669
$634$	−7666.00			−0.480214
$635$		−	10320.0i		−	0.644940i
$636$	−7938.00			−0.494909
$637$	−3393.00	+	2262.00i	−0.211045	+	0.140697i
$638$	13200.0			0.819111
$639$		−	1260.00i		−	0.0780044i
$640$	7275.00			0.449328
$641$	−30618.0			−1.88664			−0.943322	−	0.331880i	$-0.892317\pi$
$641$	−30618.0			−1.88664			−0.943322	+	0.331880i	$0.892317\pi$
$642$		−	528.000i		−	0.0324587i
$643$		−	13138.0i		−	0.805773i	−0.915250	−	0.402887i	$-0.868007\pi$
$643$		−	13138.0i		−	0.805773i	0.915250	−	0.402887i	$-0.131993\pi$
$644$		−	15904.0i		−	0.973145i
$645$			3180.00i			0.194128i
$646$	464.000			0.0282598
$647$	−9794.00			−0.595119			−0.297559	−	0.954703i	$-0.596173\pi$
$647$	−9794.00			−0.595119			−0.297559	+	0.954703i	$0.596173\pi$
$648$		−	1215.00i		−	0.0736570i
$649$	48240.0			2.91770
$650$	−650.000	−	975.000i	−0.0392232	−	0.0588348i
$651$	13920.0			0.838046
$652$			14994.0i			0.900629i
$653$	−12098.0			−0.725010			−0.362505	−	0.931982i	$-0.618078\pi$
$653$	−12098.0			−0.725010			−0.362505	+	0.931982i	$0.618078\pi$
$654$	5802.00			0.346905
$655$		−	4890.00i		−	0.291707i
$656$		−	15170.0i		−	0.902880i
$657$			5958.00i			0.353796i
$658$			2816.00i			0.166838i
$659$	−8310.00			−0.491216			−0.245608	−	0.969369i	$-0.578988\pi$
$659$	−8310.00			−0.491216			−0.245608	+	0.969369i	$0.578988\pi$
$660$	6300.00			0.371556
$661$			4930.00i			0.290098i	0.989424	+	0.145049i	$0.0463340\pi$
$661$			4930.00i			0.290098i	−0.989424	+	0.145049i	$0.953666\pi$
$662$	−160.000			−0.00939362
$663$	−13572.0	+	9048.00i	−0.795012	+	0.530008i
$664$	11880.0			0.694327
$665$			320.000i			0.0186603i
$666$	396.000			0.0230401
$667$	−31240.0			−1.81352
$668$			13328.0i			0.771970i
$669$			7356.00i			0.425111i
$670$			1470.00i			0.0847628i
$671$			34680.0i			1.99524i
$672$	−7728.00			−0.443622
$673$	18982.0			1.08722			0.543612	−	0.839336i	$-0.317056\pi$
$673$	18982.0			1.08722			0.543612	+	0.839336i	$0.317056\pi$
$674$		−	6786.00i		−	0.387814i
$675$	−675.000			−0.0384900
$676$	5915.00	−	14196.0i	0.336538	−	0.807692i
$677$	−21894.0			−1.24292			−0.621458	−	0.783447i	$-0.713460\pi$
$677$	−21894.0			−1.24292			−0.621458	+	0.783447i	$0.713460\pi$
$678$		−	5556.00i		−	0.314715i
$679$	−4576.00			−0.258631
$680$	8700.00			0.490632
$681$		−	10008.0i		−	0.563153i
$682$		−	17400.0i		−	0.976951i
$683$			52.0000i			0.00291321i	0.999999	+	0.00145661i	$0.000463652\pi$
$683$			52.0000i			0.00291321i	−0.999999	+	0.00145661i	$0.999536\pi$
$684$			252.000i			0.0140869i
$685$	3930.00			0.219208
$686$	−6880.00			−0.382915
$687$		−	11778.0i		−	0.654088i
$688$	8692.00			0.481656
$689$	14742.0	−	9828.00i	0.815131	−	0.543421i
$690$	2130.00			0.117518
$691$			8440.00i			0.464649i	0.972638	+	0.232325i	$0.0746332\pi$
$691$			8440.00i			0.464649i	−0.972638	+	0.232325i	$0.925367\pi$
$692$	19474.0			1.06978
$693$	−8640.00			−0.473602
$694$		−	16.0000i		−	0.000875147i
$695$			1400.00i			0.0764101i
$696$			9900.00i			0.539165i
$697$		−	42920.0i		−	2.33244i
$698$	−2986.00			−0.161922
$699$	−4584.00			−0.248044
$700$			2800.00i			0.151186i
$701$	−3108.00			−0.167457			−0.0837286	−	0.996489i	$-0.526683\pi$
$701$	−3108.00			−0.167457			−0.0837286	+	0.996489i	$0.526683\pi$
$702$	702.000	+	1053.00i	0.0377426	+	0.0566139i
$703$	−176.000			−0.00944234
$704$		−	10020.0i		−	0.536425i
$705$	2640.00			0.141033
$706$	−678.000			−0.0361429
$707$			7808.00i			0.415347i
$708$			16884.0i			0.896242i
$709$		−	10246.0i		−	0.542731i	−0.962476	−	0.271366i	$-0.912525\pi$
$709$		−	10246.0i		−	0.542731i	0.962476	−	0.271366i	$-0.0874753\pi$
$710$		−	700.000i		−	0.0370007i
$711$	−12600.0			−0.664609
$712$	4410.00			0.232123
$713$			41180.0i			2.16298i
$714$	−5568.00			−0.291845
$715$	−11700.0	+	7800.00i	−0.611965	+	0.407977i
$716$	−10710.0			−0.559010
$717$		−	16008.0i		−	0.833793i
$718$	−5416.00			−0.281509
$719$	30840.0			1.59964			0.799818	−	0.600243i	$-0.204929\pi$
$719$	30840.0			1.59964			0.799818	+	0.600243i	$0.204929\pi$
$720$			1845.00i			0.0954987i
$721$		−	25792.0i		−	1.33224i
$722$		−	6843.00i		−	0.352729i
$723$			5580.00i			0.287030i
$724$	−10206.0			−0.523899
$725$	5500.00			0.281745
$726$			6807.00i			0.347977i
$727$	3836.00			0.195694			0.0978469	−	0.995201i	$-0.468804\pi$
$727$	3836.00			0.195694			0.0978469	+	0.995201i	$0.468804\pi$
$728$	9360.00	−	6240.00i	0.476517	−	0.317678i
$729$	729.000			0.0370370
$730$			3310.00i			0.167820i
$731$	24592.0			1.24428
$732$	−12138.0			−0.612887
$733$		−	10728.0i		−	0.540584i	−0.962778	−	0.270292i	$-0.912880\pi$
$733$		−	10728.0i		−	0.540584i	0.962778	−	0.270292i	$-0.0871202\pi$
$734$			7464.00i			0.375342i
$735$			1305.00i			0.0654907i
$736$		−	22862.0i		−	1.14498i
$737$	17640.0			0.881652
$738$	−3330.00			−0.166096
$739$			11544.0i			0.574632i	0.957836	+	0.287316i	$0.0927630\pi$
$739$			11544.0i			0.574632i	−0.957836	+	0.287316i	$0.907237\pi$
$740$	−1540.00			−0.0765021
$741$	−312.000	−	468.000i	−0.0154678	−	0.0232016i
$742$	6048.00			0.299231
$743$			7232.00i			0.357088i	0.983932	+	0.178544i	$0.0571387\pi$
$743$			7232.00i			0.357088i	−0.983932	+	0.178544i	$0.942861\pi$
$744$	13050.0			0.643059
$745$	2930.00			0.144090
$746$		−	8542.00i		−	0.419229i
$747$			7128.00i			0.349130i
$748$		−	48720.0i		−	2.38152i
$749$		−	2816.00i		−	0.137376i
$750$	−375.000			−0.0182574
$751$	−17648.0			−0.857503			−0.428751	−	0.903422i	$-0.641046\pi$
$751$	−17648.0			−0.857503			−0.428751	+	0.903422i	$0.641046\pi$
$752$		−	7216.00i		−	0.349921i
$753$	14166.0			0.685575
$754$	−5720.00	−	8580.00i	−0.276273	−	0.414410i
$755$	11350.0			0.547111
$756$		−	3024.00i		−	0.145479i
$757$	5666.00			0.272040			0.136020	−	0.990706i	$-0.456569\pi$
$757$	5666.00			0.272040			0.136020	+	0.990706i	$0.456569\pi$
$758$	10224.0			0.489911
$759$		−	25560.0i		−	1.22236i
$760$			300.000i			0.0143186i
$761$		−	7390.00i		−	0.352020i	−0.984388	−	0.176010i	$-0.943681\pi$
$761$		−	7390.00i		−	0.352020i	0.984388	−	0.176010i	$-0.0563191\pi$
$762$			6192.00i			0.294373i
$763$	30944.0			1.46821
$764$	2044.00			0.0967923
$765$			5220.00i			0.246705i
$766$	6032.00			0.284524
$767$	−20904.0	−	31356.0i	−0.984093	−	1.47614i
$768$	−357.000			−0.0167736
$769$		−	7576.00i		−	0.355263i	−0.984097	−	0.177632i	$-0.943156\pi$
$769$		−	7576.00i		−	0.355263i	0.984097	−	0.177632i	$-0.0568436\pi$
$770$	−4800.00			−0.224649
$771$	−12852.0			−0.600329
$772$		−	2926.00i		−	0.136411i
$773$			15042.0i			0.699901i	0.936768	+	0.349950i	$0.113802\pi$
$773$			15042.0i			0.699901i	−0.936768	+	0.349950i	$0.886198\pi$
$774$		−	1908.00i		−	0.0886068i
$775$		−	7250.00i		−	0.336036i
$776$	−4290.00			−0.198456
$777$	2112.00			0.0975130
$778$		−	3820.00i		−	0.176033i
$779$	1480.00			0.0680700
$780$	−2730.00	−	4095.00i	−0.125320	−	0.187980i
$781$	−8400.00			−0.384860
$782$		−	16472.0i		−	0.753245i
$783$	−5940.00			−0.271109
$784$	3567.00			0.162491
$785$			1330.00i			0.0604710i
$786$			2934.00i			0.133145i
$787$		−	23686.0i		−	1.07283i	−0.843955	−	0.536413i	$-0.819779\pi$
$787$		−	23686.0i		−	1.07283i	0.843955	−	0.536413i	$-0.180221\pi$
$788$			25298.0i			1.14366i
$789$	−594.000			−0.0268022
$790$	−7000.00			−0.315252
$791$		−	29632.0i		−	1.33198i
$792$	−8100.00			−0.363410
$793$	22542.0	−	15028.0i	1.00945	−	0.672963i
$794$	−11156.0			−0.498629
$795$		−	5670.00i		−	0.252949i
$796$	20160.0			0.897679
$797$	1666.00			0.0740436			0.0370218	−	0.999314i	$-0.488213\pi$
$797$	1666.00			0.0740436			0.0370218	+	0.999314i	$0.488213\pi$
$798$		−	192.000i		−	0.00851720i
$799$		−	20416.0i		−	0.903963i
$800$			4025.00i			0.177882i
$801$			2646.00i			0.116719i
$802$	1030.00			0.0453498
$803$	39720.0			1.74556
$804$			6174.00i			0.270821i
$805$	11360.0			0.497376
$806$	−11310.0	+	7540.00i	−0.494265	+	0.329510i
$807$	−17520.0			−0.764230
$808$			7320.00i			0.318709i
$809$	−23010.0			−0.999986			−0.499993	−	0.866030i	$-0.666664\pi$
$809$	−23010.0			−0.999986			−0.499993	+	0.866030i	$0.666664\pi$
$810$	405.000			0.0175682
$811$			19220.0i			0.832189i	0.909321	+	0.416095i	$0.136601\pi$
$811$			19220.0i			0.832189i	−0.909321	+	0.416095i	$0.863399\pi$
$812$			24640.0i			1.06489i
$813$			14370.0i			0.619899i
$814$		−	2640.00i		−	0.113676i
$815$	−10710.0			−0.460313
$816$	14268.0			0.612108
$817$			848.000i			0.0363131i
$818$	−16296.0			−0.696548
$819$	3744.00	+	5616.00i	0.159739	+	0.239608i
$820$	12950.0			0.551504
$821$		−	15210.0i		−	0.646568i	−0.946302	−	0.323284i	$-0.895213\pi$
$821$		−	15210.0i		−	0.646568i	0.946302	−	0.323284i	$-0.104787\pi$
$822$	−2358.00			−0.100054
$823$	252.000			0.0106734			0.00533668	−	0.999986i	$-0.498301\pi$
$823$	252.000			0.0106734			0.00533668	+	0.999986i	$0.498301\pi$
$824$		−	24180.0i		−	1.02227i
$825$			4500.00i			0.189903i
$826$		−	12864.0i		−	0.541884i
$827$		−	27596.0i		−	1.16035i	−0.814493	−	0.580173i	$-0.802985\pi$
$827$		−	27596.0i		−	1.16035i	0.814493	−	0.580173i	$-0.197015\pi$
$828$	8946.00			0.375477
$829$	−12350.0			−0.517410			−0.258705	−	0.965956i	$-0.583296\pi$
$829$	−12350.0			−0.517410			−0.258705	+	0.965956i	$0.583296\pi$
$830$			3960.00i			0.165607i
$831$	2838.00			0.118471
$832$	−6513.00	+	4342.00i	−0.271391	+	0.180928i
$833$	10092.0			0.419768
$834$		−	840.000i		−	0.0348763i
$835$	−9520.00			−0.394555
$836$	1680.00			0.0695024
$837$			7830.00i			0.323351i
$838$		−	30.0000i		−	0.00123667i
$839$			29544.0i			1.21570i	0.794052	+	0.607850i	$0.207968\pi$
$839$			29544.0i			1.21570i	−0.794052	+	0.607850i	$0.792032\pi$
$840$		−	3600.00i		−	0.147871i
$841$	24011.0			0.984501
$842$	−11990.0			−0.490740
$843$			13590.0i			0.555237i
$844$	−5376.00			−0.219253
$845$	10140.0	+	4225.00i	0.412813	+	0.172005i
$846$	−1584.00			−0.0643724
$847$			36304.0i			1.47275i
$848$	−15498.0			−0.627598
$849$	7836.00			0.316762
$850$			2900.00i			0.117023i
$851$			6248.00i			0.251679i
$852$		−	2940.00i		−	0.118219i
$853$			33372.0i			1.33955i	0.742564	+	0.669775i	$0.233609\pi$
$853$			33372.0i			1.33955i	−0.742564	+	0.669775i	$0.766391\pi$
$854$	9248.00			0.370562
$855$	−180.000			−0.00719985
$856$		−	2640.00i		−	0.105413i
$857$	5276.00			0.210297			0.105149	−	0.994457i	$-0.466468\pi$
$857$	5276.00			0.210297			0.105149	+	0.994457i	$0.466468\pi$
$858$	7020.00	−	4680.00i	0.279323	−	0.186215i
$859$	14840.0			0.589446			0.294723	−	0.955583i	$-0.404773\pi$
$859$	14840.0			0.589446			0.294723	+	0.955583i	$0.404773\pi$
$860$			7420.00i			0.294209i
$861$	−17760.0			−0.702972
$862$	1260.00			0.0497863
$863$			792.000i			0.0312399i	0.999878	+	0.0156199i	$0.00497218\pi$
$863$			792.000i			0.0312399i	−0.999878	+	0.0156199i	$0.995028\pi$
$864$		−	4347.00i		−	0.171167i
$865$			13910.0i			0.546768i
$866$			1678.00i			0.0658438i
$867$	25629.0			1.00393
$868$	32480.0			1.27010
$869$			84000.0i			3.27906i
$870$	−3300.00			−0.128598
$871$	−7644.00	−	11466.0i	−0.297367	−	0.446051i
$872$	29010.0			1.12661
$873$		−	2574.00i		−	0.0997900i
$874$	568.000			0.0219827
$875$	−2000.00			−0.0772712
$876$			13902.0i			0.536193i
$877$			13264.0i			0.510711i	0.966847	+	0.255355i	$0.0821925\pi$
$877$			13264.0i			0.510711i	−0.966847	+	0.255355i	$0.917808\pi$
$878$		−	7360.00i		−	0.282902i
$879$			13266.0i			0.509046i
$880$	12300.0			0.471174
$881$	−27018.0			−1.03321			−0.516606	−	0.856223i	$-0.672805\pi$
$881$	−27018.0			−1.03321			−0.516606	+	0.856223i	$0.672805\pi$
$882$		−	783.000i		−	0.0298923i
$883$	−26348.0			−1.00417			−0.502084	−	0.864819i	$-0.667433\pi$
$883$	−26348.0			−1.00417			−0.502084	+	0.864819i	$0.667433\pi$
$884$	−31668.0	+	21112.0i	−1.20488	+	0.803250i
$885$	−12060.0			−0.458071
$886$			8628.00i			0.327160i
$887$	−26854.0			−1.01654			−0.508269	−	0.861198i	$-0.669714\pi$
$887$	−26854.0			−1.01654			−0.508269	+	0.861198i	$0.669714\pi$
$888$	1980.00			0.0748248
$889$			33024.0i			1.24588i
$890$			1470.00i			0.0553646i
$891$		−	4860.00i		−	0.182734i
$892$			17164.0i			0.644275i
$893$	704.000			0.0263813
$894$	−1758.00			−0.0657677
$895$		−	7650.00i		−	0.285711i
$896$	−23280.0			−0.868002
$897$	−16614.0	+	11076.0i	−0.618423	+	0.412282i
$898$	−11586.0			−0.430545
$899$		−	63800.0i		−	2.36691i
$900$	−1575.00			−0.0583333
$901$	−43848.0			−1.62130
$902$			22200.0i			0.819489i
$903$		−	10176.0i		−	0.375012i
$904$		−	27780.0i		−	1.02207i
$905$		−	7290.00i		−	0.267766i
$906$	−6810.00			−0.249721
$907$	44836.0			1.64141			0.820703	−	0.571355i	$-0.193582\pi$
$907$	44836.0			1.64141			0.820703	+	0.571355i	$0.193582\pi$
$908$		−	23352.0i		−	0.853484i
$909$	−4392.00			−0.160257
$910$	2080.00	+	3120.00i	0.0757707	+	0.113656i
$911$	−20368.0			−0.740749			−0.370374	−	0.928883i	$-0.620771\pi$
$911$	−20368.0			−0.740749			−0.370374	+	0.928883i	$0.620771\pi$
$912$			492.000i			0.0178638i
$913$	47520.0			1.72254
$914$	12994.0			0.470244
$915$		−	8670.00i		−	0.313247i
$916$		−	27482.0i		−	0.991300i
$917$			15648.0i			0.563514i
$918$		−	3132.00i		−	0.112605i
$919$	−36920.0			−1.32522			−0.662611	−	0.748964i	$-0.730552\pi$
$919$	−36920.0			−1.32522			−0.662611	+	0.748964i	$0.730552\pi$
$920$	10650.0			0.381652
$921$		−	24918.0i		−	0.891505i
$922$	1330.00			0.0475067
$923$	3640.00	+	5460.00i	0.129807	+	0.194711i
$924$	−20160.0			−0.717765
$925$		−	1100.00i		−	0.0391003i
$926$	−14348.0			−0.509184
$927$	14508.0			0.514029
$928$			35420.0i			1.25293i
$929$			16214.0i			0.572620i	0.958137	+	0.286310i	$0.0924287\pi$
$929$			16214.0i			0.572620i	−0.958137	+	0.286310i	$0.907571\pi$
$930$			4350.00i			0.153379i
$931$			348.000i			0.0122505i
$932$	−10696.0			−0.375922
$933$	8436.00			0.296015
$934$			2484.00i			0.0870224i
$935$	34800.0			1.21720
$936$	3510.00	+	5265.00i	0.122573	+	0.183859i
$937$	−17974.0			−0.626665			−0.313332	−	0.949644i	$-0.601445\pi$
$937$	−17974.0			−0.626665			−0.313332	+	0.949644i	$0.601445\pi$
$938$		−	4704.00i		−	0.163743i
$939$	−5934.00			−0.206229
$940$	6160.00			0.213742
$941$			13450.0i			0.465948i	0.972483	+	0.232974i	$0.0748458\pi$
$941$			13450.0i			0.465948i	−0.972483	+	0.232974i	$0.925154\pi$
$942$		−	798.000i		−	0.0276011i
$943$		−	52540.0i		−	1.81436i
$944$			32964.0i			1.13653i
$945$	2160.00			0.0743543
$946$	−12720.0			−0.437170
$947$			10584.0i			0.363182i	0.983374	+	0.181591i	$0.0581248\pi$
$947$			10584.0i			0.363182i	−0.983374	+	0.181591i	$0.941875\pi$
$948$	−29400.0			−1.00724
$949$	−17212.0	−	25818.0i	−0.588751	−	0.883127i
$950$	−100.000			−0.00341519
$951$		−	22998.0i		−	0.784186i
$952$	−27840.0			−0.947794
$953$	−5208.00			−0.177024			−0.0885119	−	0.996075i	$-0.528211\pi$
$953$	−5208.00			−0.177024			−0.0885119	+	0.996075i	$0.528211\pi$
$954$			3402.00i			0.115455i
$955$			1460.00i			0.0494707i
$956$		−	37352.0i		−	1.26365i
$957$			39600.0i			1.33760i
$958$	2424.00			0.0817494
$959$	−12576.0			−0.423462
$960$			2505.00i			0.0842172i
$961$	−54309.0			−1.82300
$962$	−1716.00	+	1144.00i	−0.0575115	+	0.0383410i
$963$	1584.00			0.0530049
$964$			13020.0i			0.435006i
$965$	2090.00			0.0697197
$966$	−6816.00			−0.227020
$967$			42464.0i			1.41215i	0.708136	+	0.706076i	$0.249536\pi$
$967$			42464.0i			1.41215i	−0.708136	+	0.706076i	$0.750464\pi$
$968$			34035.0i			1.13009i
$969$			1392.00i			0.0461481i
$970$		−	1430.00i		−	0.0473346i
$971$	2622.00			0.0866570			0.0433285	−	0.999061i	$-0.486204\pi$
$971$	2622.00			0.0866570			0.0433285	+	0.999061i	$0.486204\pi$
$972$	1701.00			0.0561313
$973$		−	4480.00i		−	0.147608i
$974$	10584.0			0.348186
$975$	2925.00	−	1950.00i	0.0960769	−	0.0640513i
$976$	−23698.0			−0.777207
$977$		−	21406.0i		−	0.700961i	−0.936570	−	0.350480i	$-0.886018\pi$
$977$		−	21406.0i		−	0.700961i	0.936570	−	0.350480i	$-0.113982\pi$
$978$	6426.00			0.210103
$979$	17640.0			0.575870
$980$			3045.00i			0.0992540i
$981$			17406.0i			0.566494i
$982$		−	1622.00i		−	0.0527089i
$983$		−	368.000i		−	0.0119404i	−0.999982	−	0.00597018i	$-0.998100\pi$
$983$		−	368.000i		−	0.0119404i	0.999982	−	0.00597018i	$-0.00190038\pi$
$984$	−16650.0			−0.539413
$985$	−18070.0			−0.584526
$986$			25520.0i			0.824262i
$987$	−8448.00			−0.272445
$988$	−728.000	−	1092.00i	−0.0234421	−	0.0351631i
$989$	30104.0			0.967898
$990$		−	2700.00i		−	0.0866784i
$991$	33352.0			1.06908			0.534541	−	0.845142i	$-0.320484\pi$
$991$	33352.0			1.06908			0.534541	+	0.845142i	$0.320484\pi$
$992$	46690.0			1.49436
$993$		−	480.000i		−	0.0153397i
$994$			2240.00i			0.0714773i
$995$			14400.0i			0.458805i
$996$			16632.0i			0.529122i
$997$	3666.00			0.116453			0.0582264	−	0.998303i	$-0.481455\pi$
$997$	3666.00			0.116453			0.0582264	+	0.998303i	$0.481455\pi$
$998$	17884.0			0.567243
$999$			1188.00i			0.0376243i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	195.4.b.c.181.1	✓	2
3.2	odd	2		585.4.b.c.181.2		2
13.12	even	2	inner	195.4.b.c.181.2	yes	2
39.38	odd	2		585.4.b.c.181.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.4.b.c.181.1	✓	2	1.1	even	1	trivial
195.4.b.c.181.2	yes	2	13.12	even	2	inner
585.4.b.c.181.1		2	39.38	odd	2
585.4.b.c.181.2		2	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 195 = 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	195.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +3.00000 q^{3} +7.00000 q^{4} +5.00000i q^{5} -3.00000i q^{6} -16.0000i q^{7} -15.0000i q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +3.00000 q^{3} +7.00000 q^{4} +5.00000i q^{5} -3.00000i q^{6} -16.0000i q^{7} -15.0000i q^{8} +9.00000 q^{9} +5.00000 q^{10} -60.0000i q^{11} +21.0000 q^{12} +(-39.0000 + 26.0000i) q^{13} -16.0000 q^{14} +15.0000i q^{15} +41.0000 q^{16} +116.000 q^{17} -9.00000i q^{18} +4.00000i q^{19} +35.0000i q^{20} -48.0000i q^{21} -60.0000 q^{22} +142.000 q^{23} -45.0000i q^{24} -25.0000 q^{25} +(26.0000 + 39.0000i) q^{26} +27.0000 q^{27} -112.000i q^{28} -220.000 q^{29} +15.0000 q^{30} +290.000i q^{31} -161.000i q^{32} -180.000i q^{33} -116.000i q^{34} +80.0000 q^{35} +63.0000 q^{36} +44.0000i q^{37} +4.00000 q^{38} +(-117.000 + 78.0000i) q^{39} +75.0000 q^{40} -370.000i q^{41} -48.0000 q^{42} +212.000 q^{43} -420.000i q^{44} +45.0000i q^{45} -142.000i q^{46} -176.000i q^{47} +123.000 q^{48} +87.0000 q^{49} +25.0000i q^{50} +348.000 q^{51} +(-273.000 + 182.000i) q^{52} -378.000 q^{53} -27.0000i q^{54} +300.000 q^{55} -240.000 q^{56} +12.0000i q^{57} +220.000i q^{58} +804.000i q^{59} +105.000i q^{60} -578.000 q^{61} +290.000 q^{62} -144.000i q^{63} +167.000 q^{64} +(-130.000 - 195.000i) q^{65} -180.000 q^{66} +294.000i q^{67} +812.000 q^{68} +426.000 q^{69} -80.0000i q^{70} -140.000i q^{71} -135.000i q^{72} +662.000i q^{73} +44.0000 q^{74} -75.0000 q^{75} +28.0000i q^{76} -960.000 q^{77} +(78.0000 + 117.000i) q^{78} -1400.00 q^{79} +205.000i q^{80} +81.0000 q^{81} -370.000 q^{82} +792.000i q^{83} -336.000i q^{84} +580.000i q^{85} -212.000i q^{86} -660.000 q^{87} -900.000 q^{88} +294.000i q^{89} +45.0000 q^{90} +(416.000 + 624.000i) q^{91} +994.000 q^{92} +870.000i q^{93} -176.000 q^{94} -20.0000 q^{95} -483.000i q^{96} -286.000i q^{97} -87.0000i q^{98} -540.000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 6 q^{3} + 14 q^{4} + 18 q^{9}+O(q^{10}) \) 2 * q + 6 * q^3 + 14 * q^4 + 18 * q^9	\( 2 q + 6 q^{3} + 14 q^{4} + 18 q^{9} + 10 q^{10} + 42 q^{12} - 78 q^{13} - 32 q^{14} + 82 q^{16} + 232 q^{17} - 120 q^{22} + 284 q^{23} - 50 q^{25} + 52 q^{26} + 54 q^{27} - 440 q^{29} + 30 q^{30} + 160 q^{35} + 126 q^{36} + 8 q^{38} - 234 q^{39} + 150 q^{40} - 96 q^{42} + 424 q^{43} + 246 q^{48} + 174 q^{49} + 696 q^{51} - 546 q^{52} - 756 q^{53} + 600 q^{55} - 480 q^{56} - 1156 q^{61} + 580 q^{62} + 334 q^{64} - 260 q^{65} - 360 q^{66} + 1624 q^{68} + 852 q^{69} + 88 q^{74} - 150 q^{75} - 1920 q^{77} + 156 q^{78} - 2800 q^{79} + 162 q^{81} - 740 q^{82} - 1320 q^{87} - 1800 q^{88} + 90 q^{90} + 832 q^{91} + 1988 q^{92} - 352 q^{94} - 40 q^{95}+O(q^{100}) \) 2 * q + 6 * q^3 + 14 * q^4 + 18 * q^9 + 10 * q^10 + 42 * q^12 - 78 * q^13 - 32 * q^14 + 82 * q^16 + 232 * q^17 - 120 * q^22 + 284 * q^23 - 50 * q^25 + 52 * q^26 + 54 * q^27 - 440 * q^29 + 30 * q^30 + 160 * q^35 + 126 * q^36 + 8 * q^38 - 234 * q^39 + 150 * q^40 - 96 * q^42 + 424 * q^43 + 246 * q^48 + 174 * q^49 + 696 * q^51 - 546 * q^52 - 756 * q^53 + 600 * q^55 - 480 * q^56 - 1156 * q^61 + 580 * q^62 + 334 * q^64 - 260 * q^65 - 360 * q^66 + 1624 * q^68 + 852 * q^69 + 88 * q^74 - 150 * q^75 - 1920 * q^77 + 156 * q^78 - 2800 * q^79 + 162 * q^81 - 740 * q^82 - 1320 * q^87 - 1800 * q^88 + 90 * q^90 + 832 * q^91 + 1988 * q^92 - 352 * q^94 - 40 * q^95

Introduction

L-functions

Modular forms

Varieties

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Database

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