LMFDB - Embedded newform 273.2.n.c.8.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(8,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 1]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("273.8");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.n (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			8.2
Character	$\chi$	$=$	273.8
Dual form			273.2.n.c.239.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.76503 + 1.76503i) q^{2} +(-0.743367 + 1.56442i) q^{3} -4.23065i q^{4} +(-0.269592 + 0.269592i) q^{5} +(-1.44918 - 4.07331i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(3.93715 + 3.93715i) q^{8} +(-1.89481 - 2.32587i) q^{9} +O(q^{10})$	\(q+(-1.76503 + 1.76503i) q^{2} +(-0.743367 + 1.56442i) q^{3} -4.23065i q^{4} +(-0.269592 + 0.269592i) q^{5} +(-1.44918 - 4.07331i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(3.93715 + 3.93715i) q^{8} +(-1.89481 - 2.32587i) q^{9} -0.951676i q^{10} +(-4.05888 - 4.05888i) q^{11} +(6.61850 + 3.14492i) q^{12} +(1.60663 - 3.22781i) q^{13} -2.49613i q^{14} +(-0.221349 - 0.622161i) q^{15} -5.43707 q^{16} +1.75630 q^{17} +(7.44963 + 0.760836i) q^{18} +(-2.02770 - 2.02770i) q^{19} +(1.14055 + 1.14055i) q^{20} +(-0.580571 - 1.63185i) q^{21} +14.3281 q^{22} -1.70703 q^{23} +(-9.08610 + 3.23260i) q^{24} +4.85464i q^{25} +(2.86141 + 8.53292i) q^{26} +(5.04718 - 1.23530i) q^{27} +(2.99152 + 2.99152i) q^{28} +3.90375i q^{29} +(1.48882 + 0.707444i) q^{30} +(-2.13090 - 2.13090i) q^{31} +(1.72227 - 1.72227i) q^{32} +(9.36702 - 3.33255i) q^{33} +(-3.09991 + 3.09991i) q^{34} -0.381261i q^{35} +(-9.83995 + 8.01628i) q^{36} +(-2.60226 + 2.60226i) q^{37} +7.15791 q^{38} +(3.85532 + 4.91289i) q^{39} -2.12285 q^{40} +(5.68886 - 5.68886i) q^{41} +(3.90499 + 1.85554i) q^{42} -10.3355i q^{43} +(-17.1717 + 17.1717i) q^{44} +(1.13786 + 0.116211i) q^{45} +(3.01296 - 3.01296i) q^{46} +(-7.30097 - 7.30097i) q^{47} +(4.04174 - 8.50585i) q^{48} -1.00000i q^{49} +(-8.56857 - 8.56857i) q^{50} +(-1.30557 + 2.74759i) q^{51} +(-13.6557 - 6.79710i) q^{52} -6.27401i q^{53} +(-6.72807 + 11.0888i) q^{54} +2.18849 q^{55} -5.56797 q^{56} +(4.67951 - 1.66485i) q^{57} +(-6.89022 - 6.89022i) q^{58} +(-7.32307 - 7.32307i) q^{59} +(-2.63214 + 0.936451i) q^{60} -4.57058 q^{61} +7.52219 q^{62} +(2.98448 + 0.304807i) q^{63} -4.79441i q^{64} +(0.437056 + 1.30333i) q^{65} +(-10.6510 + 22.4151i) q^{66} +(9.02876 + 9.02876i) q^{67} -7.43027i q^{68} +(1.26895 - 2.67052i) q^{69} +(0.672937 + 0.672937i) q^{70} +(0.688691 - 0.688691i) q^{71} +(1.69716 - 16.6175i) q^{72} +(-7.93286 + 7.93286i) q^{73} -9.18611i q^{74} +(-7.59469 - 3.60878i) q^{75} +(-8.57850 + 8.57850i) q^{76} +5.74012 q^{77} +(-15.4761 - 1.86664i) q^{78} -3.01315 q^{79} +(1.46579 - 1.46579i) q^{80} +(-1.81938 + 8.81419i) q^{81} +20.0820i q^{82} +(-8.09006 + 8.09006i) q^{83} +(-6.90378 + 2.45619i) q^{84} +(-0.473485 + 0.473485i) q^{85} +(18.2424 + 18.2424i) q^{86} +(-6.10709 - 2.90192i) q^{87} -31.9608i q^{88} +(-3.81154 - 3.81154i) q^{89} +(-2.21348 + 1.80325i) q^{90} +(1.14634 + 3.41846i) q^{91} +7.22186i q^{92} +(4.91766 - 1.74958i) q^{93} +25.7728 q^{94} +1.09331 q^{95} +(1.41408 + 3.97464i) q^{96} +(-7.04914 - 7.04914i) q^{97} +(1.76503 + 1.76503i) q^{98} +(-1.74963 + 17.1312i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 8 q^{3} + 4 q^{6}+O(q^{10}) $ 48 * q + 8 * q^3 + 4 * q^6	$ 48 q + 8 q^{3} + 4 q^{6} + 8 q^{13} - 16 q^{15} - 72 q^{16} - 12 q^{18} + 40 q^{19} + 16 q^{22} + 8 q^{24} - 16 q^{27} + 44 q^{33} - 32 q^{34} - 8 q^{37} - 4 q^{39} - 48 q^{40} - 8 q^{42} + 44 q^{45} - 32 q^{46} + 80 q^{48} - 72 q^{52} + 44 q^{54} - 80 q^{55} - 52 q^{57} + 16 q^{58} + 44 q^{60} - 64 q^{61} + 24 q^{63} - 152 q^{66} + 56 q^{67} + 16 q^{70} + 16 q^{72} + 32 q^{73} + 104 q^{76} - 44 q^{78} + 8 q^{79} + 12 q^{84} - 96 q^{85} - 72 q^{87} - 8 q^{91} - 8 q^{93} + 160 q^{94} + 8 q^{96} - 32 q^{97} - 12 q^{99}+O(q^{100}) $ 48 * q + 8 * q^3 + 4 * q^6 + 8 * q^13 - 16 * q^15 - 72 * q^16 - 12 * q^18 + 40 * q^19 + 16 * q^22 + 8 * q^24 - 16 * q^27 + 44 * q^33 - 32 * q^34 - 8 * q^37 - 4 * q^39 - 48 * q^40 - 8 * q^42 + 44 * q^45 - 32 * q^46 + 80 * q^48 - 72 * q^52 + 44 * q^54 - 80 * q^55 - 52 * q^57 + 16 * q^58 + 44 * q^60 - 64 * q^61 + 24 * q^63 - 152 * q^66 + 56 * q^67 + 16 * q^70 + 16 * q^72 + 32 * q^73 + 104 * q^76 - 44 * q^78 + 8 * q^79 + 12 * q^84 - 96 * q^85 - 72 * q^87 - 8 * q^91 - 8 * q^93 + 160 * q^94 + 8 * q^96 - 32 * q^97 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.76503	+	1.76503i	−1.24806	+	1.24806i	−0.291489	+	0.956574i	$0.594151\pi$
$2$	−1.76503	+	1.76503i	−1.24806	+	1.24806i	−0.956574	+	0.291489i	$0.905849\pi$
$3$	−0.743367	+	1.56442i	−0.429183	+	0.903218i
$3$	−0.743367	+	1.56442i	−0.429183	+	0.903218i
$4$		−	4.23065i		−	2.11532i
$5$	−0.269592	+	0.269592i	−0.120565	+	0.120565i	−0.764815	−	0.644250i	$-0.777170\pi$
$5$	−0.269592	+	0.269592i	−0.120565	+	0.120565i	0.644250	+	0.764815i	$0.277170\pi$
$6$	−1.44918	−	4.07331i	−0.591625	−	1.66292i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$8$	3.93715	+	3.93715i	1.39199	+	1.39199i
$9$	−1.89481	−	2.32587i	−0.631604	−	0.775291i
$10$		−	0.951676i		−	0.300946i
$11$	−4.05888	−	4.05888i	−1.22380	−	1.22380i	−0.966271	−	0.257527i	$-0.917092\pi$
$11$	−4.05888	−	4.05888i	−1.22380	−	1.22380i	−0.257527	−	0.966271i	$-0.582908\pi$
$12$	6.61850	+	3.14492i	1.91060	+	0.907860i
$13$	1.60663	−	3.22781i	0.445600	−	0.895232i
$13$	1.60663	−	3.22781i	0.445600	−	0.895232i
$14$		−	2.49613i		−	0.667118i
$15$	−0.221349	−	0.622161i	−0.0571522	−	0.160641i
$16$	−5.43707			−1.35927
$17$	1.75630			0.425965			0.212982	−	0.977056i	$-0.431682\pi$
$17$	1.75630			0.425965			0.212982	+	0.977056i	$0.431682\pi$
$18$	7.44963	+	0.760836i	1.75589	+	0.179331i
$19$	−2.02770	−	2.02770i	−0.465187	−	0.465187i	0.435164	−	0.900351i	$-0.356690\pi$
$19$	−2.02770	−	2.02770i	−0.465187	−	0.465187i	−0.900351	+	0.435164i	$0.856690\pi$
$20$	1.14055	+	1.14055i	0.255035	+	0.255035i
$21$	−0.580571	−	1.63185i	−0.126691	−	0.356099i
$22$	14.3281			3.05475
$23$	−1.70703			−0.355941			−0.177971	−	0.984036i	$-0.556953\pi$
$23$	−1.70703			−0.355941			−0.177971	+	0.984036i	$0.556953\pi$
$24$	−9.08610	+	3.23260i	−1.85469	+	0.659853i
$25$			4.85464i			0.970928i
$26$	2.86141	+	8.53292i	0.561169	+	1.67344i
$27$	5.04718	−	1.23530i	0.971330	−	0.237734i
$28$	2.99152	+	2.99152i	0.565344	+	0.565344i
$29$			3.90375i			0.724908i	0.932002	+	0.362454i	$0.118061\pi$
$29$			3.90375i			0.724908i	−0.932002	+	0.362454i	$0.881939\pi$
$30$	1.48882	+	0.707444i	0.271820	+	0.129161i
$31$	−2.13090	−	2.13090i	−0.382721	−	0.382721i	0.489361	−	0.872081i	$-0.337230\pi$
$31$	−2.13090	−	2.13090i	−0.382721	−	0.382721i	−0.872081	+	0.489361i	$0.837230\pi$
$32$	1.72227	−	1.72227i	0.304458	−	0.304458i
$33$	9.36702	−	3.33255i	1.63059	−	0.580123i
$34$	−3.09991	+	3.09991i	−0.531631	+	0.531631i
$35$		−	0.381261i		−	0.0644449i
$36$	−9.83995	+	8.01628i	−1.63999	+	1.33605i
$37$	−2.60226	+	2.60226i	−0.427808	+	0.427808i	−0.887881	−	0.460073i	$-0.847823\pi$
$37$	−2.60226	+	2.60226i	−0.427808	+	0.427808i	0.460073	+	0.887881i	$0.347823\pi$
$38$	7.15791			1.16117
$39$	3.85532	+	4.91289i	0.617345	+	0.786692i
$40$	−2.12285			−0.335652
$41$	5.68886	−	5.68886i	0.888451	−	0.888451i	−0.105923	−	0.994374i	$-0.533780\pi$
$41$	5.68886	−	5.68886i	0.888451	−	0.888451i	0.994374	+	0.105923i	$0.0337798\pi$
$42$	3.90499	+	1.85554i	0.602552	+	0.286316i
$43$		−	10.3355i		−	1.57614i	−0.615582	−	0.788072i	$-0.711079\pi$
$43$		−	10.3355i		−	1.57614i	0.615582	−	0.788072i	$-0.288921\pi$
$44$	−17.1717	+	17.1717i	−2.58873	+	2.58873i
$45$	1.13786	+	0.116211i	0.169623	+	0.0173237i
$46$	3.01296	−	3.01296i	0.444237	−	0.444237i
$47$	−7.30097	−	7.30097i	−1.06496	−	1.06496i	−0.997738	−	0.0672174i	$-0.978588\pi$
$47$	−7.30097	−	7.30097i	−1.06496	−	1.06496i	−0.0672174	−	0.997738i	$-0.521412\pi$
$48$	4.04174	−	8.50585i	0.583374	−	1.22771i
$49$		−	1.00000i		−	0.142857i
$50$	−8.56857	−	8.56857i	−1.21178	−	1.21178i
$51$	−1.30557	+	2.74759i	−0.182817	+	0.384739i
$52$	−13.6557	−	6.79710i	−1.89370	−	0.942588i
$53$		−	6.27401i		−	0.861802i	−0.902399	−	0.430901i	$-0.858196\pi$
$53$		−	6.27401i		−	0.861802i	0.902399	−	0.430901i	$-0.141804\pi$
$54$	−6.72807	+	11.0888i	−0.915575	+	1.50899i
$55$	2.18849			0.295095
$56$	−5.56797			−0.744051
$57$	4.67951	−	1.66485i	0.619816	−	0.220515i
$58$	−6.89022	−	6.89022i	−0.904730	−	0.904730i
$59$	−7.32307	−	7.32307i	−0.953383	−	0.953383i	0.0455780	−	0.998961i	$-0.485487\pi$
$59$	−7.32307	−	7.32307i	−0.953383	−	0.953383i	−0.998961	+	0.0455780i	$0.985487\pi$
$60$	−2.63214	+	0.936451i	−0.339808	+	0.120895i
$61$	−4.57058			−0.585203			−0.292602	−	0.956234i	$-0.594521\pi$
$61$	−4.57058			−0.585203			−0.292602	+	0.956234i	$0.594521\pi$
$62$	7.52219			0.955319
$63$	2.98448	+	0.304807i	0.376009	+	0.0384021i
$64$		−	4.79441i		−	0.599301i
$65$	0.437056	+	1.30333i	0.0542101	+	0.161658i
$66$	−10.6510	+	22.4151i	−1.31105	+	2.75911i
$67$	9.02876	+	9.02876i	1.10304	+	1.10304i	0.994042	+	0.108996i	$0.0347636\pi$
$67$	9.02876	+	9.02876i	1.10304	+	1.10304i	0.108996	+	0.994042i	$0.465236\pi$
$68$		−	7.43027i		−	0.901053i
$69$	1.26895	−	2.67052i	0.152764	−	0.321492i
$70$	0.672937	+	0.672937i	0.0804313	+	0.0804313i
$71$	0.688691	−	0.688691i	0.0817326	−	0.0817326i	−0.665059	−	0.746791i	$-0.731593\pi$
$71$	0.688691	−	0.688691i	0.0817326	−	0.0817326i	0.746791	+	0.665059i	$0.231593\pi$
$72$	1.69716	−	16.6175i	0.200012	−	1.95839i
$73$	−7.93286	+	7.93286i	−0.928471	+	0.928471i	−0.997607	−	0.0691362i	$-0.977976\pi$
$73$	−7.93286	+	7.93286i	−0.928471	+	0.928471i	0.0691362	+	0.997607i	$0.477976\pi$
$74$		−	9.18611i		−	1.06786i
$75$	−7.59469	−	3.60878i	−0.876959	−	0.416706i
$76$	−8.57850	+	8.57850i	−0.984021	+	0.984021i
$77$	5.74012			0.654148
$78$	−15.4761	−	1.86664i	−1.75233	−	0.211355i
$79$	−3.01315			−0.339006			−0.169503	−	0.985530i	$-0.554216\pi$
$79$	−3.01315			−0.339006			−0.169503	+	0.985530i	$0.554216\pi$
$80$	1.46579	−	1.46579i	0.163881	−	0.163881i
$81$	−1.81938	+	8.81419i	−0.202153	+	0.979354i
$82$			20.0820i			2.21769i
$83$	−8.09006	+	8.09006i	−0.887999	+	0.887999i	−0.994331	−	0.106331i	$-0.966090\pi$
$83$	−8.09006	+	8.09006i	−0.887999	+	0.887999i	0.106331	+	0.994331i	$0.466090\pi$
$84$	−6.90378	+	2.45619i	−0.753264	+	0.267992i
$85$	−0.473485	+	0.473485i	−0.0513566	+	0.0513566i
$86$	18.2424	+	18.2424i	1.96713	+	1.96713i
$87$	−6.10709	−	2.90192i	−0.654749	−	0.311118i
$88$		−	31.9608i		−	3.40704i
$89$	−3.81154	−	3.81154i	−0.404022	−	0.404022i	0.475626	−	0.879648i	$-0.342222\pi$
$89$	−3.81154	−	3.81154i	−0.404022	−	0.404022i	−0.879648	+	0.475626i	$0.842222\pi$
$90$	−2.21348	+	1.80325i	−0.233321	+	0.190079i
$91$	1.14634	+	3.41846i	0.120169	+	0.358352i
$92$			7.22186i			0.752931i
$93$	4.91766	−	1.74958i	0.509937	−	0.181423i
$94$	25.7728			2.65826
$95$	1.09331			0.112171
$96$	1.41408	+	3.97464i	0.144324	+	0.405660i
$97$	−7.04914	−	7.04914i	−0.715732	−	0.715732i	0.251996	−	0.967728i	$-0.418913\pi$
$97$	−7.04914	−	7.04914i	−0.715732	−	0.715732i	−0.967728	+	0.251996i	$0.918913\pi$
$98$	1.76503	+	1.76503i	0.178295	+	0.178295i
$99$	−1.74963	+	17.1312i	−0.175844	+	1.72176i
$100$	20.5383			2.05383
$101$	10.4598			1.04079			0.520395	−	0.853925i	$-0.325785\pi$
$101$	10.4598			1.04079			0.520395	+	0.853925i	$0.325785\pi$
$102$	−2.54519	−	7.15394i	−0.252011	−	0.708345i
$103$		−	8.20744i		−	0.808704i	−0.914604	−	0.404352i	$-0.867497\pi$
$103$		−	8.20744i		−	0.808704i	0.914604	−	0.404352i	$-0.132503\pi$
$104$	19.0339	−	6.38280i	1.86643	−	0.625885i
$105$	0.596452	+	0.283417i	0.0582078	+	0.0276587i
$106$	11.0738	+	11.0738i	1.07558	+	1.07558i
$107$		−	5.57222i		−	0.538687i	−0.963044	−	0.269343i	$-0.913193\pi$
$107$		−	5.57222i		−	0.538687i	0.963044	−	0.269343i	$-0.0868066\pi$
$108$	−5.22612	−	21.3528i	−0.502884	−	2.05468i
$109$	−10.3243	−	10.3243i	−0.988885	−	0.988885i	0.0110544	−	0.999939i	$-0.496481\pi$
$109$	−10.3243	−	10.3243i	−0.988885	−	0.988885i	−0.999939	+	0.0110544i	$0.996481\pi$
$110$	−3.86274	+	3.86274i	−0.368298	+	0.368298i
$111$	−2.13659	−	6.00545i	−0.202796	−	0.570012i
$112$	3.84459	−	3.84459i	0.363279	−	0.363279i
$113$		−	3.71234i		−	0.349227i	−0.984637	−	0.174614i	$-0.944132\pi$
$113$		−	3.71234i		−	0.349227i	0.984637	−	0.174614i	$-0.0558677\pi$
$114$	−5.32095	+	11.1980i	−0.498353	+	1.04879i
$115$	0.460203	−	0.460203i	0.0429142	−	0.0429142i
$116$	16.5154			1.53341
$117$	−10.5517	+	2.37926i	−0.975508	+	0.219962i
$118$	25.8508			2.37976
$119$	−1.24189	+	1.24189i	−0.113844	+	0.113844i
$120$	1.57806	−	3.32103i	0.144056	−	0.303167i
$121$			21.9490i			1.99536i
$122$	8.06720	−	8.06720i	0.730370	−	0.730370i
$123$	4.67085	+	13.1287i	0.421157	+	1.18377i
$124$	−9.01507	+	9.01507i	−0.809577	+	0.809577i
$125$	−2.65674	−	2.65674i	−0.237626	−	0.237626i
$126$	−5.80567	+	4.72969i	−0.517211	+	0.421354i
$127$			7.14748i			0.634237i	0.948386	+	0.317118i	$0.102715\pi$
$127$			7.14748i			0.634237i	−0.948386	+	0.317118i	$0.897285\pi$
$128$	11.9068	+	11.9068i	1.05242	+	1.05242i
$129$	16.1690	+	7.68305i	1.42360	+	0.676455i
$130$	−3.07183	−	1.52900i	−0.269417	−	0.134102i
$131$		−	7.39582i		−	0.646175i	−0.946369	−	0.323088i	$-0.895279\pi$
$131$		−	7.39582i		−	0.646175i	0.946369	−	0.323088i	$-0.104721\pi$
$132$	−14.0988	−	39.6285i	−1.22715	−	3.44922i
$133$	2.86761			0.248653
$134$	−31.8720			−2.75332
$135$	−1.02765	+	1.69371i	−0.0884463	+	0.145771i
$136$	6.91481	+	6.91481i	0.592940	+	0.592940i
$137$	13.5545	+	13.5545i	1.15804	+	1.15804i	0.984896	+	0.173147i	$0.0553935\pi$
$137$	13.5545	+	13.5545i	1.15804	+	1.15804i	0.173147	+	0.984896i	$0.444607\pi$
$138$	2.47380	+	6.95327i	0.210584	+	0.591902i
$139$	−11.8893			−1.00844			−0.504220	−	0.863575i	$-0.668220\pi$
$139$	−11.8893			−1.00844			−0.504220	+	0.863575i	$0.668220\pi$
$140$	−1.61298			−0.136322
$141$	16.8491	−	5.99447i	1.41895	−	0.504826i
$142$			2.43112i			0.204015i
$143$	−19.6224	+	6.58014i	−1.64091	+	0.550259i
$144$	10.3022	+	12.6459i	0.858518	+	1.05383i
$145$	−1.05242	−	1.05242i	−0.0873988	−	0.0873988i
$146$		−	28.0034i		−	2.31758i
$147$	1.56442	+	0.743367i	0.129031	+	0.0613119i
$148$	11.0092	+	11.0092i	0.904952	+	0.904952i
$149$	6.82354	−	6.82354i	0.559006	−	0.559006i	−0.370018	−	0.929025i	$-0.620649\pi$
$149$	6.82354	−	6.82354i	0.559006	−	0.559006i	0.929025	+	0.370018i	$0.120649\pi$
$150$	19.7744	−	7.03524i	1.61458	−	0.574425i
$151$	−13.6451	+	13.6451i	−1.11042	+	1.11042i	−0.117325	+	0.993094i	$0.537432\pi$
$151$	−13.6451	+	13.6451i	−1.11042	+	1.11042i	−0.993094	+	0.117325i	$0.962568\pi$
$152$		−	15.9668i		−	1.29507i
$153$	−3.32785	−	4.08493i	−0.269041	−	0.330247i
$154$	−10.1315	+	10.1315i	−0.816417	+	0.816417i
$155$	1.14895			0.0922857
$156$	20.7847	−	16.3105i	1.66411	−	1.30588i
$157$	10.3361			0.824911			0.412456	−	0.910978i	$-0.364671\pi$
$157$	10.3361			0.824911			0.412456	+	0.910978i	$0.364671\pi$
$158$	5.31829	−	5.31829i	0.423100	−	0.423100i
$159$	9.81518	+	4.66389i	0.778395	+	0.369871i
$160$			0.928624i			0.0734142i
$161$	1.20706	−	1.20706i	0.0951293	−	0.0951293i
$162$	−12.3460	−	18.7685i	−0.969996	−	1.47460i
$163$	6.20512	−	6.20512i	0.486022	−	0.486022i	−0.421026	−	0.907048i	$-0.638330\pi$
$163$	6.20512	−	6.20512i	0.486022	−	0.486022i	0.907048	+	0.421026i	$0.138330\pi$
$164$	−24.0676	−	24.0676i	−1.87936	−	1.87936i
$165$	−1.62685	+	3.42371i	−0.126650	+	0.266535i
$166$		−	28.5584i		−	2.21656i
$167$	7.30880	+	7.30880i	0.565572	+	0.565572i	0.930885	−	0.365313i	$-0.119038\pi$
$167$	7.30880	+	7.30880i	0.565572	+	0.565572i	−0.365313	+	0.930885i	$0.619038\pi$
$168$	4.13904	−	8.71064i	0.319334	−	0.672040i
$169$	−7.83746	−	10.3718i	−0.602881	−	0.797831i
$170$		−	1.67143i		−	0.128193i
$171$	−0.874066	+	8.55830i	−0.0668415	+	0.654470i
$172$	−43.7257			−3.33406
$173$	4.11028			0.312499			0.156250	−	0.987718i	$-0.450060\pi$
$173$	4.11028			0.312499			0.156250	+	0.987718i	$0.450060\pi$
$174$	15.9012	−	5.65723i	1.20546	−	0.428873i
$175$	−3.43275	−	3.43275i	−0.259491	−	0.259491i
$176$	22.0684	+	22.0684i	1.66347	+	1.66347i
$177$	16.9001	−	6.01262i	1.27029	−	0.451936i
$178$	13.4549			1.00849
$179$	5.92322			0.442722			0.221361	−	0.975192i	$-0.428950\pi$
$179$	5.92322			0.442722			0.221361	+	0.975192i	$0.428950\pi$
$180$	0.491648	−	4.81390i	0.0366453	−	0.358807i
$181$			4.75831i			0.353683i	0.984239	+	0.176841i	$0.0565879\pi$
$181$			4.75831i			0.353683i	−0.984239	+	0.176841i	$0.943412\pi$
$182$	−8.05701	−	4.01036i	−0.597225	−	0.297268i
$183$	3.39762	−	7.15031i	0.251159	−	0.528566i
$184$	−6.72085	−	6.72085i	−0.495468	−	0.495468i
$185$		−	1.40310i		−	0.103158i
$186$	−5.59174	+	11.7679i	−0.410007	+	0.862861i
$187$	−7.12860	−	7.12860i	−0.521295	−	0.521295i
$188$	−30.8878	+	30.8878i	−2.25272	+	2.25272i
$189$	−2.69541	+	4.44239i	−0.196062	+	0.323136i
$190$	−1.92972	+	1.92972i	−0.139996	+	0.139996i
$191$			18.8457i			1.36363i	0.731525	+	0.681815i	$0.238809\pi$
$191$			18.8457i			1.36363i	−0.731525	+	0.681815i	$0.761191\pi$
$192$	7.50047	+	3.56401i	0.541300	+	0.257210i
$193$	10.5452	−	10.5452i	0.759063	−	0.759063i	−0.217089	−	0.976152i	$-0.569656\pi$
$193$	10.5452	−	10.5452i	0.759063	−	0.759063i	0.976152	+	0.217089i	$0.0696562\pi$
$194$	24.8839			1.78656
$195$	−2.36384	−	0.285113i	−0.169278	−	0.0204174i
$196$	−4.23065			−0.302189
$197$	−15.7410	+	15.7410i	−1.12150	+	1.12150i	−0.129982	+	0.991516i	$0.541492\pi$
$197$	−15.7410	+	15.7410i	−1.12150	+	1.12150i	−0.991516	+	0.129982i	$0.958508\pi$
$198$	−27.1490	−	33.3253i	−1.92939	−	2.36832i
$199$			3.50580i			0.248520i	0.992250	+	0.124260i	$0.0396556\pi$
$199$			3.50580i			0.248520i	−0.992250	+	0.124260i	$0.960344\pi$
$200$	−19.1134	+	19.1134i	−1.35152	+	1.35152i
$201$	−20.8364	+	7.41308i	−1.46969	+	0.522878i
$202$	−18.4619	+	18.4619i	−1.29897	+	1.29897i
$203$	−2.76037	−	2.76037i	−0.193740	−	0.193740i
$204$	11.6241	+	5.52342i	0.813847	+	0.386717i
$205$			3.06735i			0.214233i
$206$	14.4864	+	14.4864i	1.00931	+	1.00931i
$207$	3.23451	+	3.97035i	0.224814	+	0.275958i
$208$	−8.73538	+	17.5498i	−0.605689	+	1.21686i
$209$			16.4604i			1.13859i
$210$	−1.55299	+	0.552516i	−0.107167	+	0.0381272i
$211$	−14.6559			−1.00896			−0.504478	−	0.863425i	$-0.668315\pi$
$211$	−14.6559			−1.00896			−0.504478	+	0.863425i	$0.668315\pi$
$212$	−26.5431			−1.82299
$213$	0.565451	+	1.58935i	0.0387441	+	0.108901i
$214$	9.83512	+	9.83512i	0.672315	+	0.672315i
$215$	2.78637	+	2.78637i	0.190029	+	0.190029i
$216$	24.7351	+	15.0079i	1.68301	+	1.02116i
$217$	3.01354			0.204573
$218$	36.4452			2.46838
$219$	−6.51329	−	18.3073i	−0.440127	−	1.23710i
$220$		−	9.25871i		−	0.624222i
$221$	2.82173	−	5.66899i	0.189810	−	0.381337i
$222$	14.3709	+	6.82865i	0.964513	+	0.458309i
$223$	7.65928	+	7.65928i	0.512903	+	0.512903i	0.915415	−	0.402512i	$-0.131863\pi$
$223$	7.65928	+	7.65928i	0.512903	+	0.512903i	−0.402512	+	0.915415i	$0.631863\pi$
$224$			2.43566i			0.162740i
$225$	11.2913	−	9.19863i	0.752752	−	0.613242i
$226$	6.55238	+	6.55238i	0.435858	+	0.435858i
$227$	3.42189	−	3.42189i	0.227119	−	0.227119i	−0.584369	−	0.811488i	$-0.698658\pi$
$227$	3.42189	−	3.42189i	0.227119	−	0.227119i	0.811488	+	0.584369i	$0.198658\pi$
$228$	−7.04339	−	19.7973i	−0.466460	−	1.31111i
$229$	20.7362	−	20.7362i	1.37029	−	1.37029i	0.510282	−	0.860007i	$-0.329541\pi$
$229$	20.7362	−	20.7362i	1.37029	−	1.37029i	0.860007	−	0.510282i	$-0.170459\pi$
$230$			1.62454i			0.107119i
$231$	−4.26702	+	8.97995i	−0.280749	+	0.590838i
$232$	−15.3696	+	15.3696i	−1.00907	+	1.00907i
$233$	−18.1540			−1.18931			−0.594655	−	0.803981i	$-0.702711\pi$
$233$	−18.1540			−1.18931			−0.594655	+	0.803981i	$0.702711\pi$
$234$	14.4247	−	22.8236i	0.942969	−	1.49202i
$235$	3.93657			0.256794
$236$	−30.9813	+	30.9813i	−2.01671	+	2.01671i
$237$	2.23987	−	4.71382i	0.145495	−	0.306196i
$238$		−	4.38394i		−	0.284169i
$239$	−18.1101	+	18.1101i	−1.17145	+	1.17145i	−0.189583	+	0.981865i	$0.560714\pi$
$239$	−18.1101	+	18.1101i	−1.17145	+	1.17145i	−0.981865	+	0.189583i	$0.939286\pi$
$240$	1.20349	+	3.38273i	0.0776850	+	0.218355i
$241$	−7.49827	+	7.49827i	−0.483006	+	0.483006i	−0.906090	−	0.423084i	$-0.860947\pi$
$241$	−7.49827	+	7.49827i	−0.483006	+	0.483006i	0.423084	+	0.906090i	$0.360947\pi$
$242$	−38.7406	−	38.7406i	−2.49034	−	2.49034i
$243$	−12.4366	−	9.39844i	−0.797809	−	0.602910i
$244$			19.3365i			1.23789i
$245$	0.269592	+	0.269592i	0.0172236	+	0.0172236i
$246$	−31.4167	−	14.9283i	−2.00305	−	0.951793i
$247$	−9.80282	+	3.28726i	−0.623738	+	0.209163i
$248$		−	16.7793i		−	1.06549i
$249$	−6.64236	−	18.6701i	−0.420942	−	1.18317i
$250$	9.37843			0.593144
$251$	16.3065			1.02926			0.514628	−	0.857413i	$-0.327930\pi$
$251$	16.3065			1.02926			0.514628	+	0.857413i	$0.327930\pi$
$252$	1.28953	−	12.6263i	0.0812327	−	0.795379i
$253$	6.92864	+	6.92864i	0.435600	+	0.435600i
$254$	−12.6155	−	12.6155i	−0.791567	−	0.791567i
$255$	−0.388755	−	1.09270i	−0.0243448	−	0.0684276i
$256$	−32.4429			−2.02768
$257$	1.24745			0.0778138			0.0389069	−	0.999243i	$-0.487612\pi$
$257$	1.24745			0.0778138			0.0389069	+	0.999243i	$0.487612\pi$
$258$	−42.0995	+	14.9780i	−2.62100	+	0.932487i
$259$		−	3.68015i		−	0.228673i
$260$	5.51392	−	1.84903i	0.341959	−	0.114672i
$261$	9.07962	−	7.39687i	0.562015	−	0.457854i
$262$	13.0538	+	13.0538i	0.806468	+	0.806468i
$263$			17.6212i			1.08657i	0.839548	+	0.543286i	$0.182820\pi$
$263$			17.6212i			1.08657i	−0.839548	+	0.543286i	$0.817180\pi$
$264$	50.0001	+	23.7586i	3.07729	+	1.46224i
$265$	1.69143	+	1.69143i	0.103903	+	0.103903i
$266$	−5.06141	+	5.06141i	−0.310335	+	0.310335i
$267$	8.79621	−	3.12947i	0.538319	−	0.191520i
$268$	38.1975	−	38.1975i	2.33328	−	2.33328i
$269$		−	29.2228i		−	1.78175i	−0.454252	−	0.890873i	$-0.650094\pi$
$269$		−	29.2228i		−	1.78175i	0.454252	−	0.890873i	$-0.349906\pi$
$270$	−1.17561	−	4.80328i	−0.0715452	−	0.292318i
$271$	20.2783	−	20.2783i	1.23182	−	1.23182i	0.268552	−	0.963265i	$-0.413455\pi$
$271$	20.2783	−	20.2783i	1.23182	−	1.23182i	0.963265	−	0.268552i	$-0.0865450\pi$
$272$	−9.54911			−0.579000
$273$	−6.20006	−	0.747815i	−0.375245	−	0.0452598i
$274$	−47.8483			−2.89062
$275$	19.7044	−	19.7044i	1.18822	−	1.18822i
$276$	−11.2980	−	5.36849i	−0.680060	−	0.323145i
$277$			4.65036i			0.279413i	0.990193	+	0.139707i	$0.0446159\pi$
$277$			4.65036i			0.279413i	−0.990193	+	0.139707i	$0.955384\pi$
$278$	20.9850	−	20.9850i	1.25860	−	1.25860i
$279$	−0.918549	+	8.99385i	−0.0549921	+	0.538448i
$280$	1.50108	−	1.50108i	0.0897069	−	0.0897069i
$281$	3.81023	+	3.81023i	0.227299	+	0.227299i	0.811563	−	0.584264i	$-0.198617\pi$
$281$	3.81023	+	3.81023i	0.227299	+	0.227299i	−0.584264	+	0.811563i	$0.698617\pi$
$282$	−19.1587	+	40.3195i	−1.14088	+	2.40099i
$283$			9.01610i			0.535951i	0.963426	+	0.267976i	$0.0863547\pi$
$283$			9.01610i			0.535951i	−0.963426	+	0.267976i	$0.913645\pi$
$284$	−2.91361	−	2.91361i	−0.172891	−	0.172891i
$285$	−0.812729	+	1.71039i	−0.0481419	+	0.101315i
$286$	23.0200	−	46.2482i	1.36120	−	2.73471i
$287$			8.04527i			0.474897i
$288$	−7.26918	−	0.742407i	−0.428341	−	0.0437468i
$289$	−13.9154			−0.818554
$290$	3.71510			0.218158
$291$	16.2679	−	5.78771i	0.953642	−	0.339282i
$292$	33.5611	+	33.5611i	1.96402	+	1.96402i
$293$	−0.300420	−	0.300420i	−0.0175507	−	0.0175507i	0.698277	−	0.715828i	$-0.253950\pi$
$293$	−0.300420	−	0.300420i	−0.0175507	−	0.0175507i	−0.715828	+	0.698277i	$0.753950\pi$
$294$	−4.07331	+	1.44918i	−0.237560	+	0.0845179i
$295$	3.94849			0.229890
$296$	−20.4909			−1.19101
$297$	−25.4998	−	15.4720i	−1.47965	−	0.897774i
$298$			24.0875i			1.39535i
$299$	−2.74258	+	5.50997i	−0.158607	+	0.318650i
$300$	−15.2675	+	32.1304i	−0.881467	+	1.85505i
$301$	7.30828	+	7.30828i	0.421242	+	0.421242i
$302$		−	48.1678i		−	2.77174i
$303$	−7.77548	+	16.3635i	−0.446690	+	0.940061i
$304$	11.0248	+	11.0248i	0.632314	+	0.632314i
$305$	1.23219	−	1.23219i	0.0705552	−	0.0705552i
$306$	13.0838	+	1.33626i	0.747949	+	0.0763886i
$307$	0.484765	−	0.484765i	0.0276670	−	0.0276670i	−0.693138	−	0.720805i	$-0.743772\pi$
$307$	0.484765	−	0.484765i	0.0276670	−	0.0276670i	0.720805	+	0.693138i	$0.243772\pi$
$308$		−	24.2844i		−	1.38373i
$309$	12.8399	+	6.10114i	0.730435	+	0.347082i
$310$	−2.02792	+	2.02792i	−0.115178	+	0.115178i
$311$	−28.0477			−1.59044			−0.795220	−	0.606321i	$-0.792645\pi$
$311$	−28.0477			−1.59044			−0.795220	+	0.606321i	$0.792645\pi$
$312$	−4.16381	+	34.5218i	−0.235730	+	1.95441i
$313$	−2.39012			−0.135098			−0.0675489	−	0.997716i	$-0.521518\pi$
$313$	−2.39012			−0.135098			−0.0675489	+	0.997716i	$0.521518\pi$
$314$	−18.2435	+	18.2435i	−1.02954	+	1.02954i
$315$	−0.886765	+	0.722418i	−0.0499636	+	0.0407037i
$316$			12.7476i			0.717106i
$317$	−3.43887	+	3.43887i	−0.193146	+	0.193146i	−0.797054	−	0.603908i	$-0.793609\pi$
$317$	−3.43887	+	3.43887i	−0.193146	+	0.193146i	0.603908	+	0.797054i	$0.293609\pi$
$318$	−25.5560	+	9.09217i	−1.43311	+	0.509864i
$319$	15.8448	−	15.8448i	0.887140	−	0.887140i
$320$	1.29254	+	1.29254i	0.0722550	+	0.0722550i
$321$	8.71728	+	4.14220i	0.486551	+	0.231195i
$322$			4.26097i			0.237455i
$323$	−3.56125	−	3.56125i	−0.198153	−	0.198153i
$324$	37.2897	+	7.69714i	2.07165	+	0.427619i
$325$	15.6698	+	7.79963i	0.869206	+	0.432646i
$326$			21.9044i			1.21317i
$327$	23.8262	−	8.47675i	1.31759	−	0.468765i
$328$	44.7958			2.47344
$329$	10.3251			0.569243
$330$	−3.17151	−	8.91437i	−0.174586	−	0.490720i
$331$	3.06285	+	3.06285i	0.168349	+	0.168349i	0.786253	−	0.617904i	$-0.212018\pi$
$331$	3.06285	+	3.06285i	0.168349	+	0.168349i	−0.617904	+	0.786253i	$0.712018\pi$
$332$	34.2262	+	34.2262i	1.87841	+	1.87841i
$333$	10.9833	+	1.12173i	0.601881	+	0.0614706i
$334$	−25.8005			−1.41174
$335$	−4.86817			−0.265976
$336$	3.15661	+	8.87248i	0.172207	+	0.484034i
$337$			4.12553i			0.224732i	0.993667	+	0.112366i	$0.0358429\pi$
$337$			4.12553i			0.224732i	−0.993667	+	0.112366i	$0.964157\pi$
$338$	32.1398	+	4.47319i	1.74818	+	0.243310i
$339$	5.80765	+	2.75963i	0.315428	+	0.149882i
$340$	2.00315	+	2.00315i	0.108636	+	0.108636i
$341$			17.2981i			0.936745i
$342$	−13.5629	−	16.6484i	−0.733397	−	0.900242i
$343$	0.707107	+	0.707107i	0.0381802	+	0.0381802i
$344$	40.6923	−	40.6923i	2.19398	−	2.19398i
$345$	0.377851	+	1.06205i	0.0203428	+	0.0571789i
$346$	−7.25476	+	7.25476i	−0.390019	+	0.390019i
$347$		−	2.27964i		−	0.122378i	−0.998126	−	0.0611888i	$-0.980511\pi$
$347$		−	2.27964i		−	0.122378i	0.998126	−	0.0611888i	$-0.0194892\pi$
$348$	−12.2770	+	25.8370i	−0.658115	+	1.38501i
$349$	16.3992	−	16.3992i	0.877831	−	0.877831i	−0.115479	−	0.993310i	$-0.536840\pi$
$349$	16.3992	−	16.3992i	0.877831	−	0.877831i	0.993310	+	0.115479i	$0.0368404\pi$
$350$	12.1178			0.647723
$351$	4.12166	−	18.2760i	0.219998	−	0.975500i
$352$	−13.9810			−0.745190
$353$	−1.79555	+	1.79555i	−0.0955677	+	0.0955677i	−0.753274	−	0.657707i	$-0.771527\pi$
$353$	−1.79555	+	1.79555i	−0.0955677	+	0.0955677i	0.657707	+	0.753274i	$0.271527\pi$
$354$	−19.2167	+	40.4416i	−1.02135	+	2.14944i
$355$			0.371332i			0.0197083i
$356$	−16.1253	+	16.1253i	−0.854637	+	0.854637i
$357$	−1.01966	−	2.86602i	−0.0539659	−	0.151686i
$358$	−10.4546	+	10.4546i	−0.552545	+	0.552545i
$359$	13.0141	+	13.0141i	0.686860	+	0.686860i	0.961537	−	0.274677i	$-0.0885709\pi$
$359$	13.0141	+	13.0141i	0.686860	+	0.686860i	−0.274677	+	0.961537i	$0.588571\pi$
$360$	4.02240	+	4.93748i	0.211999	+	0.260228i
$361$		−	10.7768i		−	0.567201i
$362$	−8.39855	−	8.39855i	−0.441418	−	0.441418i
$363$	−34.3374	−	16.3161i	−1.80225	−	0.856376i
$364$	14.4623	−	4.84976i	0.758031	−	0.254197i
$365$		−	4.27728i		−	0.223883i
$366$	6.62359	+	18.6174i	0.346221	+	0.973146i
$367$	19.3739			1.01131			0.505655	−	0.862736i	$-0.331251\pi$
$367$	19.3739			1.01131			0.505655	+	0.862736i	$0.331251\pi$
$368$	9.28126			0.483819
$369$	−24.0109	−	2.45225i	−1.24996	−	0.127659i
$370$	2.47650	+	2.47650i	0.128747	+	0.128747i
$371$	4.43640	+	4.43640i	0.230326	+	0.230326i
$372$	−7.40184	−	20.8049i	−0.383768	−	1.07868i
$373$	−22.9594			−1.18879			−0.594396	−	0.804173i	$-0.702609\pi$
$373$	−22.9594			−1.18879			−0.594396	+	0.804173i	$0.702609\pi$
$374$	25.1644			1.30122
$375$	6.13118	−	2.18132i	0.316613	−	0.112643i
$376$		−	57.4900i		−	2.96482i
$377$	12.6005	+	6.27189i	0.648961	+	0.323019i
$378$	−3.08347	−	12.5984i	−0.158597	−	0.647992i
$379$	−10.9408	−	10.9408i	−0.561990	−	0.561990i	0.367882	−	0.929872i	$-0.380083\pi$
$379$	−10.9408	−	10.9408i	−0.561990	−	0.561990i	−0.929872	+	0.367882i	$0.880083\pi$
$380$		−	4.62540i		−	0.237278i
$381$	−11.1817	−	5.31320i	−0.572854	−	0.272204i
$382$	−33.2633	−	33.2633i	−1.70190	−	1.70190i
$383$	12.6569	−	12.6569i	0.646739	−	0.646739i	−0.305465	−	0.952203i	$-0.598812\pi$
$383$	12.6569	−	12.6569i	0.646739	−	0.646739i	0.952203	+	0.305465i	$0.0988118\pi$
$384$	−27.4784	+	9.77612i	−1.40225	+	0.498885i
$385$	−1.54749	+	1.54749i	−0.0788675	+	0.0788675i
$386$			37.2253i			1.89472i
$387$	−24.0390	+	19.5838i	−1.22197	+	0.995499i
$388$	−29.8224	+	29.8224i	−1.51400	+	1.51400i
$389$	15.1292			0.767083			0.383541	−	0.923524i	$-0.374704\pi$
$389$	15.1292			0.767083			0.383541	+	0.923524i	$0.374704\pi$
$390$	4.67548	−	3.66902i	0.236752	−	0.185788i
$391$	−2.99806			−0.151618
$392$	3.93715	−	3.93715i	0.198856	−	0.198856i
$393$	11.5702	+	5.49780i	0.583637	+	0.277328i
$394$		−	55.5665i		−	2.79940i
$395$	0.812322	−	0.812322i	0.0408723	−	0.0408723i
$396$	72.4762	+	7.40206i	3.64207	+	0.371967i
$397$	−8.90187	+	8.90187i	−0.446772	+	0.446772i	−0.894280	−	0.447508i	$-0.852312\pi$
$397$	−8.90187	+	8.90187i	−0.446772	+	0.446772i	0.447508	+	0.894280i	$0.352312\pi$
$398$	−6.18784	−	6.18784i	−0.310168	−	0.310168i
$399$	−2.13168	+	4.48614i	−0.106718	+	0.224588i
$400$		−	26.3950i		−	1.31975i
$401$	5.94465	+	5.94465i	0.296862	+	0.296862i	0.839783	−	0.542922i	$-0.182682\pi$
$401$	5.94465	+	5.94465i	0.296862	+	0.296862i	−0.542922	+	0.839783i	$0.682682\pi$
$402$	23.6926	−	49.8612i	1.18168	−	2.48685i
$403$	−10.3017	+	3.45455i	−0.513164	+	0.172083i
$404$		−	44.2518i		−	2.20161i
$405$	−1.88575	−	2.86673i	−0.0937035	−	0.142449i
$406$	9.74424			0.483599
$407$	21.1245			1.04710
$408$	−15.9579	+	5.67742i	−0.790034	+	0.281074i
$409$	−22.1038	−	22.1038i	−1.09296	−	1.09296i	−0.995211	−	0.0977516i	$-0.968835\pi$
$409$	−22.1038	−	22.1038i	−1.09296	−	1.09296i	−0.0977516	−	0.995211i	$-0.531165\pi$
$410$	−5.41395	−	5.41395i	−0.267376	−	0.267376i
$411$	−31.2810	+	11.1290i	−1.54298	+	0.548952i
$412$	−34.7228			−1.71067
$413$	10.3564			0.509605
$414$	−12.7168	−	1.29877i	−0.624995	−	0.0638312i
$415$		−	4.36204i		−	0.214124i
$416$	−2.79210	−	8.32623i	−0.136894	−	0.408227i
$417$	8.83813	−	18.5999i	0.432805	−	0.910840i
$418$	−29.0531	−	29.0531i	−1.42103	−	1.42103i
$419$		−	30.2695i		−	1.47876i	−0.673288	−	0.739381i	$-0.735118\pi$
$419$		−	30.2695i		−	1.47876i	0.673288	−	0.739381i	$-0.264882\pi$
$420$	1.19904	−	2.52338i	0.0585070	−	0.123128i
$421$	15.0958	+	15.0958i	0.735723	+	0.735723i	0.971747	−	0.236024i	$-0.0758444\pi$
$421$	15.0958	+	15.0958i	0.735723	+	0.735723i	−0.236024	+	0.971747i	$0.575844\pi$
$422$	25.8681	−	25.8681i	1.25924	−	1.25924i
$423$	−3.14717	+	30.8151i	−0.153021	+	1.49828i
$424$	24.7017	−	24.7017i	1.19962	−	1.19962i
$425$			8.52619i			0.413581i
$426$	−3.80329	−	1.80721i	−0.184270	−	0.0875598i
$427$	3.23189	−	3.23189i	0.156402	−	0.156402i
$428$	−23.5741			−1.13950
$429$	4.29255	−	35.5891i	0.207246	−	1.71826i
$430$	−9.83602			−0.474335
$431$	2.37562	−	2.37562i	0.114430	−	0.114430i	−0.647573	−	0.762003i	$-0.724216\pi$
$431$	2.37562	−	2.37562i	0.114430	−	0.114430i	0.762003	+	0.647573i	$0.224216\pi$
$432$	−27.4419	+	6.71642i	−1.32030	+	0.323144i
$433$		−	1.70459i		−	0.0819172i	−0.999161	−	0.0409586i	$-0.986959\pi$
$433$		−	1.70459i		−	0.0819172i	0.999161	−	0.0409586i	$-0.0130412\pi$
$434$	−5.31899	+	5.31899i	−0.255320	+	0.255320i
$435$	2.42876	−	0.864092i	0.116450	−	0.0414300i
$436$	−43.6783	+	43.6783i	−2.09181	+	2.09181i
$437$	3.46136	+	3.46136i	0.165579	+	0.165579i
$438$	43.8091	+	20.8168i	2.09328	+	0.994666i
$439$			15.1158i			0.721439i	0.932674	+	0.360720i	$0.117469\pi$
$439$			15.1158i			0.721439i	−0.932674	+	0.360720i	$0.882531\pi$
$440$	8.61640	+	8.61640i	0.410771	+	0.410771i
$441$	−2.32587	+	1.89481i	−0.110756	+	0.0902291i
$442$	5.02549	+	14.9863i	0.239038	+	0.712828i
$443$		−	14.7952i		−	0.702943i	−0.936199	−	0.351471i	$-0.885681\pi$
$443$		−	14.7952i		−	0.702943i	0.936199	−	0.351471i	$-0.114319\pi$
$444$	−25.4069	+	9.03914i	−1.20576	+	0.428979i
$445$	2.05512			0.0974221
$446$	−27.0377			−1.28027
$447$	5.60248	+	15.7473i	0.264988	+	0.744820i
$448$	3.39016	+	3.39016i	0.160170	+	0.160170i
$449$	−11.6459	−	11.6459i	−0.549602	−	0.549602i	0.376724	−	0.926326i	$-0.377051\pi$
$449$	−11.6459	−	11.6459i	−0.549602	−	0.549602i	−0.926326	+	0.376724i	$0.877051\pi$
$450$	−3.69359	+	36.1653i	−0.174117	+	1.70485i
$451$	−46.1808			−2.17457
$452$	−15.7056			−0.738728
$453$	−11.2033	−	31.4899i	−0.526377	−	1.47952i
$454$			12.0795i			0.566917i
$455$	−1.23064	−	0.612547i	−0.0576932	−	0.0287167i
$456$	24.9787	+	11.8692i	1.16973	+	0.555824i
$457$	1.43617	+	1.43617i	0.0671811	+	0.0671811i	0.739899	−	0.672718i	$-0.234873\pi$
$457$	1.43617	+	1.43617i	0.0671811	+	0.0671811i	−0.672718	+	0.739899i	$0.734873\pi$
$458$			73.2001i			3.42041i
$459$	8.86435	−	2.16956i	0.413753	−	0.101266i
$460$	−1.94696	−	1.94696i	−0.0907774	−	0.0907774i
$461$	19.3054	−	19.3054i	0.899140	−	0.899140i	−0.0962196	−	0.995360i	$-0.530675\pi$
$461$	19.3054	−	19.3054i	0.899140	−	0.899140i	0.995360	+	0.0962196i	$0.0306751\pi$
$462$	−8.31846	−	23.3813i	−0.387010	−	1.08779i
$463$	10.6682	−	10.6682i	0.495793	−	0.495793i	−0.414333	−	0.910125i	$-0.635985\pi$
$463$	10.6682	−	10.6682i	0.495793	−	0.495793i	0.910125	+	0.414333i	$0.135985\pi$
$464$		−	21.2249i		−	0.985343i
$465$	−0.854090	+	1.79744i	−0.0396075	+	0.0833541i
$466$	32.0423	−	32.0423i	1.48433	−	1.48433i
$467$	25.8237			1.19498			0.597490	−	0.801876i	$-0.296165\pi$
$467$	25.8237			1.19498			0.597490	+	0.801876i	$0.296165\pi$
$468$	10.0658	+	44.6407i	0.465291	+	2.06351i
$469$	−12.7686			−0.589599
$470$	−6.94816	+	6.94816i	−0.320495	+	0.320495i
$471$	−7.68352	+	16.1700i	−0.354038	+	0.745074i
$472$		−	57.6641i		−	2.65420i
$473$	−41.9504	+	41.9504i	−1.92888	+	1.92888i
$474$	4.36659	+	12.2735i	0.200564	+	0.563739i
$475$	9.84378	−	9.84378i	0.451663	−	0.451663i
$476$	5.25400	+	5.25400i	0.240817	+	0.240817i
$477$	−14.5926	+	11.8881i	−0.668147	+	0.544317i
$478$		−	63.9298i		−	2.92408i
$479$	4.84679	+	4.84679i	0.221456	+	0.221456i	0.809111	−	0.587656i	$-0.199949\pi$
$479$	4.84679	+	4.84679i	0.221456	+	0.221456i	−0.587656	+	0.809111i	$0.699949\pi$
$480$	−1.45276	−	0.690309i	−0.0663090	−	0.0315081i
$481$	4.21870	+	12.5804i	0.192356	+	0.573619i
$482$		−	26.4693i		−	1.20564i
$483$	0.991055	+	2.78563i	0.0450946	+	0.126750i
$484$	92.8584			4.22084
$485$	3.80079			0.172585
$486$	38.5395	−	5.36246i	1.74819	−	0.243246i
$487$	23.0419	+	23.0419i	1.04413	+	1.04413i	0.998980	+	0.0451489i	$0.0143762\pi$
$487$	23.0419	+	23.0419i	1.04413	+	1.04413i	0.0451489	+	0.998980i	$0.485624\pi$
$488$	−17.9951	−	17.9951i	−0.814599	−	0.814599i
$489$	5.09472	+	14.3201i	0.230391	+	0.647576i
$490$	−0.951676			−0.0429923
$491$	−19.1483			−0.864149			−0.432075	−	0.901838i	$-0.642218\pi$
$491$	−19.1483			−0.864149			−0.432075	+	0.901838i	$0.642218\pi$
$492$	55.5428	−	19.7607i	2.50406	−	0.890882i
$493$			6.85614i			0.308785i
$494$	11.5001	−	23.1043i	0.517416	−	1.03951i
$495$	−4.14677	−	5.09014i	−0.186383	−	0.228785i
$496$	11.5858	+	11.5858i	0.520219	+	0.520219i
$497$			0.973957i			0.0436879i
$498$	44.6772	+	21.2293i	2.00203	+	0.951309i
$499$	16.6400	+	16.6400i	0.744910	+	0.744910i	0.973518	−	0.228608i	$-0.0734175\pi$
$499$	16.6400	+	16.6400i	0.744910	+	0.744910i	−0.228608	+	0.973518i	$0.573418\pi$
$500$	−11.2397	+	11.2397i	−0.502655	+	0.502655i
$501$	−16.8671	+	6.00091i	−0.753569	+	0.268101i
$502$	−28.7814	+	28.7814i	−1.28458	+	1.28458i
$503$			23.4652i			1.04626i	0.852252	+	0.523131i	$0.175236\pi$
$503$			23.4652i			1.04626i	−0.852252	+	0.523131i	$0.824764\pi$
$504$	10.5503	+	12.9504i	0.469946	+	0.576857i
$505$	−2.81989	+	2.81989i	−0.125483	+	0.125483i
$506$	−24.4585			−1.08731
$507$	22.0519	−	4.55101i	0.979361	−	0.202117i
$508$	30.2385			1.34161
$509$	−6.33626	+	6.33626i	−0.280850	+	0.280850i	−0.833448	−	0.552598i	$-0.813637\pi$
$509$	−6.33626	+	6.33626i	−0.280850	+	0.280850i	0.552598	+	0.833448i	$0.313637\pi$
$510$	2.61481	+	1.24248i	0.115786	+	0.0550181i
$511$		−	11.2188i		−	0.496289i
$512$	33.4490	−	33.4490i	1.47825	−	1.47825i
$513$	−12.7390	−	7.72936i	−0.562441	−	0.341260i
$514$	−2.20178	+	2.20178i	−0.0971166	+	0.0971166i
$515$	2.21266	+	2.21266i	0.0975017	+	0.0975017i
$516$	32.5042	−	68.4053i	1.43092	−	3.01138i
$517$			59.2675i			2.60658i
$518$	6.49556	+	6.49556i	0.285398	+	0.285398i
$519$	−3.05545	+	6.43020i	−0.134119	+	0.282255i
$520$	−3.41065	+	6.85215i	−0.149567	+	0.300487i
$521$		−	3.59741i		−	0.157605i	−0.996890	−	0.0788026i	$-0.974890\pi$
$521$		−	3.59741i		−	0.157605i	0.996890	−	0.0788026i	$-0.0251097\pi$
$522$	−2.97011	+	29.0815i	−0.129998	+	1.27286i
$523$	−45.1509			−1.97431			−0.987155	−	0.159767i	$-0.948926\pi$
$523$	−45.1509			−1.97431			−0.987155	+	0.159767i	$0.948926\pi$
$524$	−31.2891			−1.36687
$525$	7.92205	−	2.81847i	0.345747	−	0.123008i
$526$	−31.1020	−	31.1020i	−1.35611	−	1.35611i
$527$	−3.74249	−	3.74249i	−0.163026	−	0.163026i
$528$	−50.9291	+	18.1193i	−2.21641	+	0.788541i
$529$	−20.0860			−0.873306
$530$	−5.97083			−0.259356
$531$	−3.15670	+	30.9084i	−0.136989	+	1.34131i
$532$		−	12.1318i		−	0.525982i
$533$	−9.22262	−	27.5025i	−0.399476	−	1.19126i
$534$	−10.0019	+	21.0491i	−0.432827	+	0.910886i
$535$	1.50223	+	1.50223i	0.0649470	+	0.0649470i
$536$			71.0951i			3.07084i
$537$	−4.40312	+	9.26639i	−0.190009	+	0.399874i
$538$	51.5791	+	51.5791i	2.22373	+	2.22373i
$539$	−4.05888	+	4.05888i	−0.174828	+	0.174828i
$540$	7.16548	+	4.34764i	0.308353	+	0.187093i
$541$	15.4076	−	15.4076i	0.662423	−	0.662423i	−0.293528	−	0.955951i	$-0.594829\pi$
$541$	15.4076	−	15.4076i	0.662423	−	0.662423i	0.955951	+	0.293528i	$0.0948293\pi$
$542$			71.5834i			3.07477i
$543$	−7.44399	−	3.53717i	−0.319452	−	0.151795i
$544$	3.02483	−	3.02483i	0.129688	−	0.129688i
$545$	5.56668			0.238450
$546$	12.2632	−	9.62337i	0.524816	−	0.411842i
$547$	19.8934			0.850582			0.425291	−	0.905057i	$-0.360172\pi$
$547$	19.8934			0.850582			0.425291	+	0.905057i	$0.360172\pi$
$548$	57.3445	−	57.3445i	2.44963	−	2.44963i
$549$	8.66039	+	10.6306i	0.369617	+	0.453703i
$550$			69.5576i			2.96595i
$551$	7.91565	−	7.91565i	0.337218	−	0.337218i
$552$	15.5103	−	5.51817i	0.660161	−	0.234869i
$553$	2.13062	−	2.13062i	0.0906030	−	0.0906030i
$554$	−8.20802	−	8.20802i	−0.348725	−	0.348725i
$555$	2.19503	+	1.04302i	0.0931739	+	0.0442735i
$556$			50.2995i			2.13318i
$557$	−11.7259	−	11.7259i	−0.496844	−	0.496844i	0.413610	−	0.910454i	$-0.364268\pi$
$557$	−11.7259	−	11.7259i	−0.496844	−	0.496844i	−0.910454	+	0.413610i	$0.864268\pi$
$558$	−14.2531	−	17.4957i	−0.603383	−	0.740650i
$559$	−33.3609	−	16.6053i	−1.41102	−	0.702330i
$560$			2.07294i			0.0875978i
$561$	16.4513	−	5.85295i	0.694574	−	0.247112i
$562$	−13.4503			−0.567368
$563$	−19.3559			−0.815752			−0.407876	−	0.913037i	$-0.633731\pi$
$563$	−19.3559			−0.815752			−0.407876	+	0.913037i	$0.633731\pi$
$564$	−25.3605	−	71.2824i	−1.06787	−	3.00153i
$565$	1.00082	+	1.00082i	0.0421047	+	0.0421047i
$566$	−15.9137	−	15.9137i	−0.668901	−	0.668901i
$567$	−4.94608	−	7.51906i	−0.207716	−	0.315771i
$568$	5.42296			0.227542
$569$	15.8903			0.666156			0.333078	−	0.942899i	$-0.391913\pi$
$569$	15.8903			0.666156			0.333078	+	0.942899i	$0.391913\pi$
$570$	−1.58440	−	4.45338i	−0.0663632	−	0.186531i
$571$		−	0.330582i		−	0.0138344i	−0.999976	−	0.00691720i	$-0.997798\pi$
$571$		−	0.330582i		−	0.0138344i	0.999976	−	0.00691720i	$-0.00220183\pi$
$572$	27.8382	+	83.0154i	1.16397	+	3.47105i
$573$	−29.4826	−	14.0093i	−1.23165	−	0.585247i
$574$	−14.2001	−	14.2001i	−0.592701	−	0.592701i
$575$		−	8.28704i		−	0.345593i
$576$	−11.1512	+	9.08451i	−0.464633	+	0.378521i
$577$	−12.2488	−	12.2488i	−0.509926	−	0.509926i	0.404578	−	0.914504i	$-0.367418\pi$
$577$	−12.2488	−	12.2488i	−0.509926	−	0.509926i	−0.914504	+	0.404578i	$0.867418\pi$
$578$	24.5611	−	24.5611i	1.02161	−	1.02161i
$579$	8.65818	+	24.3361i	0.359822	+	1.01138i
$580$	−4.45242	+	4.45242i	−0.184877	+	0.184877i
$581$		−	11.4411i		−	0.474656i
$582$	−18.4978	+	38.9288i	−0.766760	+	1.61365i
$583$	−25.4655	+	25.4655i	−1.05467	+	1.05467i
$584$	−62.4657			−2.58485
$585$	2.20324	−	3.48610i	0.0910927	−	0.144132i
$586$	1.06050			0.0438089
$587$	19.6952	−	19.6952i	0.812906	−	0.812906i	−0.172162	−	0.985069i	$-0.555075\pi$
$587$	19.6952	−	19.6952i	0.812906	−	0.812906i	0.985069	+	0.172162i	$0.0550754\pi$
$588$	3.14492	−	6.61850i	0.129694	−	0.272942i
$589$			8.64166i			0.356074i
$590$	−6.96919	+	6.96919i	−0.286917	+	0.286917i
$591$	−12.9242	−	36.3268i	−0.531629	−	1.49429i
$592$	14.1486	−	14.1486i	0.581506	−	0.581506i
$593$	7.40412	+	7.40412i	0.304051	+	0.304051i	0.842596	−	0.538546i	$-0.181026\pi$
$593$	7.40412	+	7.40412i	0.304051	+	0.304051i	−0.538546	+	0.842596i	$0.681026\pi$
$594$	72.3163	−	17.6995i	2.96718	−	0.726219i
$595$		−	0.669608i		−	0.0274513i
$596$	−28.8680	−	28.8680i	−1.18248	−	1.18248i
$597$	−5.48454	−	2.60610i	−0.224467	−	0.106660i
$598$	−4.88453	−	14.5660i	−0.199743	−	0.595647i
$599$			1.57740i			0.0644509i	0.999481	+	0.0322255i	$0.0102595\pi$
$599$			1.57740i			0.0644509i	−0.999481	+	0.0322255i	$0.989741\pi$
$600$	−15.6931	−	44.1097i	−0.640669	−	1.80077i
$601$	10.8358			0.442001			0.221001	−	0.975274i	$-0.429068\pi$
$601$	10.8358			0.442001			0.221001	+	0.975274i	$0.429068\pi$
$602$	−25.7986			−1.05147
$603$	3.89195	−	38.1075i	0.158493	−	1.55186i
$604$	57.7274	+	57.7274i	2.34889	+	2.34889i
$605$	−5.91728	−	5.91728i	−0.240572	−	0.240572i
$606$	−15.1582	−	42.6060i	−0.615758	−	1.73075i
$607$	43.4073			1.76185			0.880925	−	0.473257i	$-0.156922\pi$
$607$	43.4073			1.76185			0.880925	+	0.473257i	$0.156922\pi$
$608$	−6.98453			−0.283260
$609$	6.37033	−	2.26640i	0.258139	−	0.0918393i
$610$			4.34971i			0.176115i
$611$	−35.2961	+	11.8361i	−1.42793	+	0.478838i
$612$	−17.2819	+	14.0790i	−0.698579	+	0.569109i
$613$	−0.0580088	−	0.0580088i	−0.00234295	−	0.00234295i	0.705934	−	0.708277i	$-0.250527\pi$
$613$	−0.0580088	−	0.0580088i	−0.00234295	−	0.00234295i	−0.708277	+	0.705934i	$0.750527\pi$
$614$			1.71125i			0.0690604i
$615$	−4.79862	−	2.28016i	−0.193499	−	0.0919451i
$616$	22.5997	+	22.5997i	0.910569	+	0.910569i
$617$	−13.5941	+	13.5941i	−0.547279	+	0.547279i	−0.925653	−	0.378374i	$-0.876483\pi$
$617$	−13.5941	+	13.5941i	−0.547279	+	0.547279i	0.378374	+	0.925653i	$0.376483\pi$
$618$	−33.4314	+	11.8941i	−1.34481	+	0.478449i
$619$	20.7842	−	20.7842i	0.835389	−	0.835389i	−0.152859	−	0.988248i	$-0.548848\pi$
$619$	20.7842	−	20.7842i	0.835389	−	0.835389i	0.988248	+	0.152859i	$0.0488480\pi$
$620$		−	4.86079i		−	0.195214i
$621$	−8.61571	+	2.10870i	−0.345737	+	0.0846193i
$622$	49.5050	−	49.5050i	1.98497	−	1.98497i
$623$	5.39033			0.215959
$624$	−20.9616	−	26.7117i	−0.839137	−	1.06932i
$625$	−22.8407			−0.913629
$626$	4.21863	−	4.21863i	0.168610	−	0.168610i
$627$	−25.7510	−	12.2361i	−1.02840	−	0.488664i
$628$		−	43.7284i		−	1.74495i
$629$	−4.57034	+	4.57034i	−0.182231	+	0.182231i
$630$	0.290077	−	2.84025i	0.0115570	−	0.113158i
$631$	11.9796	−	11.9796i	0.476902	−	0.476902i	−0.427237	−	0.904140i	$-0.640513\pi$
$631$	11.9796	−	11.9796i	0.476902	−	0.476902i	0.904140	+	0.427237i	$0.140513\pi$
$632$	−11.8632	−	11.8632i	−0.471893	−	0.471893i
$633$	10.8947	−	22.9280i	0.433026	−	0.911306i
$634$		−	12.1394i		−	0.482117i
$635$	−1.92691	−	1.92691i	−0.0764670	−	0.0764670i
$636$	19.7313	−	41.5246i	0.782396	−	1.64656i
$637$	−3.22781	−	1.60663i	−0.127890	−	0.0636572i
$638$			55.9331i			2.21441i
$639$	−2.90675	−	0.296869i	−0.114989	−	0.0117439i
$640$	−6.41998			−0.253772
$641$	40.0535			1.58202			0.791010	−	0.611804i	$-0.209556\pi$
$641$	40.0535			1.58202			0.791010	+	0.611804i	$0.209556\pi$
$642$	−22.6973	+	8.07514i	−0.895793	+	0.318700i
$643$	−21.6613	−	21.6613i	−0.854238	−	0.854238i	0.136414	−	0.990652i	$-0.456442\pi$
$643$	−21.6613	−	21.6613i	−0.854238	−	0.854238i	−0.990652	+	0.136414i	$0.956442\pi$
$644$	−5.10662	−	5.10662i	−0.201229	−	0.201229i
$645$	−6.43033	+	2.28775i	−0.253194	+	0.0900801i
$646$	12.5714			0.494616
$647$	−24.1684			−0.950156			−0.475078	−	0.879944i	$-0.657580\pi$
$647$	−24.1684			−0.950156			−0.475078	+	0.879944i	$0.657580\pi$
$648$	−41.8659	+	27.5396i	−1.64465	+	1.08186i
$649$			59.4469i			2.33350i
$650$	−41.4242	+	13.8911i	−1.62479	+	0.544855i
$651$	−2.24017	+	4.71445i	−0.0877991	+	0.184774i
$652$	−26.2516	−	26.2516i	−1.02809	−	1.02809i
$653$			3.58100i			0.140136i	0.997542	+	0.0700678i	$0.0223215\pi$
$653$			3.58100i			0.140136i	−0.997542	+	0.0700678i	$0.977678\pi$
$654$	−27.0922	+	57.0156i	−1.05939	+	2.22948i
$655$	1.99386	+	1.99386i	0.0779064	+	0.0779064i
$656$	−30.9307	+	30.9307i	−1.20764	+	1.20764i
$657$	33.4821	+	3.41955i	1.30626	+	0.133410i
$658$	−18.2241	+	18.2241i	−0.710451	+	0.710451i
$659$			1.43239i			0.0557982i	0.999611	+	0.0278991i	$0.00888171\pi$
$659$			1.43239i			0.0557982i	−0.999611	+	0.0278991i	$0.991118\pi$
$660$	14.4845	+	6.88261i	0.563808	+	0.267905i
$661$	14.4991	−	14.4991i	0.563951	−	0.563951i	−0.366477	−	0.930427i	$-0.619436\pi$
$661$	14.4991	−	14.4991i	0.563951	−	0.563951i	0.930427	+	0.366477i	$0.119436\pi$
$662$	−10.8120			−0.420221
$663$	6.77109	+	8.62850i	0.262967	+	0.335103i
$664$	−63.7036			−2.47218
$665$	−0.773085	+	0.773085i	−0.0299790	+	0.0299790i
$666$	−21.3657	+	17.4059i	−0.827905	+	0.674467i
$667$		−	6.66383i		−	0.258025i
$668$	30.9209	−	30.9209i	1.19637	−	1.19637i
$669$	−17.6760	+	6.28866i	−0.683392	+	0.243134i
$670$	8.59245	−	8.59245i	0.331955	−	0.331955i
$671$	18.5514	+	18.5514i	0.716170	+	0.716170i
$672$	−3.81040	−	1.81059i	−0.146989	−	0.0698451i
$673$		−	3.88824i		−	0.149881i	−0.997188	−	0.0749404i	$-0.976123\pi$
$673$		−	3.88824i		−	0.149881i	0.997188	−	0.0749404i	$-0.0238766\pi$
$674$	−7.28168	−	7.28168i	−0.280480	−	0.280480i
$675$	5.99694	+	24.5022i	0.230823	+	0.943092i
$676$	−43.8794	+	33.1575i	−1.68767	+	1.27529i
$677$			40.9986i			1.57571i	0.615864	+	0.787853i	$0.288807\pi$
$677$			40.9986i			1.57571i	−0.615864	+	0.787853i	$0.711193\pi$
$678$	−15.1215	+	5.37984i	−0.580737	+	0.206612i
$679$	9.96899			0.382575
$680$	−3.72836			−0.142976
$681$	2.80955	+	7.89699i	0.107662	+	0.302613i
$682$	−30.5316	−	30.5316i	−1.16912	−	1.16912i
$683$	−15.5151	−	15.5151i	−0.593669	−	0.593669i	0.344951	−	0.938621i	$-0.387895\pi$
$683$	−15.5151	−	15.5151i	−0.593669	−	0.593669i	−0.938621	+	0.344951i	$0.887895\pi$
$684$	36.2071	+	3.69787i	1.38441	+	0.141391i
$685$	−7.30840			−0.279240
$686$	−2.49613			−0.0953025
$687$	17.0255	+	47.8548i	0.649564	+	1.82577i
$688$			56.1947i			2.14240i
$689$	−20.2513	−	10.0800i	−0.771513	−	0.384019i
$690$	−2.54147	−	1.20763i	−0.0967520	−	0.0459738i
$691$	−4.52650	−	4.52650i	−0.172196	−	0.172196i	0.615747	−	0.787944i	$-0.288854\pi$
$691$	−4.52650	−	4.52650i	−0.172196	−	0.172196i	−0.787944	+	0.615747i	$0.788854\pi$
$692$		−	17.3892i		−	0.661036i
$693$	−10.8764	−	13.3508i	−0.413162	−	0.507155i
$694$	4.02363	+	4.02363i	0.152735	+	0.152735i
$695$	3.20527	−	3.20527i	0.121583	−	0.121583i
$696$	−12.6193	−	35.4698i	−0.478332	−	1.34448i
$697$	9.99134	−	9.99134i	0.378449	−	0.378449i
$698$			57.8902i			2.19118i
$699$	13.4951	−	28.4005i	0.510431	−	1.07421i
$700$	−14.5227	+	14.5227i	−0.548908	+	0.548908i
$701$	3.10205			0.117163			0.0585815	−	0.998283i	$-0.481342\pi$
$701$	3.10205			0.117163			0.0585815	+	0.998283i	$0.481342\pi$
$702$	24.9828	+	39.5325i	0.942915	+	1.49206i
$703$	10.5532			0.398022
$704$	−19.4599	+	19.4599i	−0.733424	+	0.733424i
$705$	−2.92632	+	6.15845i	−0.110211	+	0.231940i
$706$		−	6.33840i		−	0.238549i
$707$	−7.39621	+	7.39621i	−0.278163	+	0.278163i
$708$	−25.4373	−	71.4982i	−0.955991	−	2.68707i
$709$	16.3082	−	16.3082i	0.612469	−	0.612469i	−0.331120	−	0.943589i	$-0.607426\pi$
$709$	16.3082	−	16.3082i	0.612469	−	0.612469i	0.943589	+	0.331120i	$0.107426\pi$
$710$	−0.655411	−	0.655411i	−0.0245971	−	0.0245971i
$711$	5.70935	+	7.00820i	0.214117	+	0.262828i
$712$		−	30.0132i		−	1.12479i
$713$	3.63752	+	3.63752i	0.136226	+	0.136226i
$714$	6.85832	+	3.25888i	0.256666	+	0.121960i
$715$	3.51610	−	7.06401i	0.131495	−	0.264179i
$716$		−	25.0590i		−	0.936500i
$717$	−14.8694	−	41.7943i	−0.555307	−	1.56084i
$718$	−45.9406			−1.71449
$719$	15.3070			0.570855			0.285427	−	0.958400i	$-0.407864\pi$
$719$	15.3070			0.570855			0.285427	+	0.958400i	$0.407864\pi$
$720$	−6.18665	−	0.631847i	−0.230563	−	0.0235476i
$721$	5.80354	+	5.80354i	0.216135	+	0.216135i
$722$	19.0214	+	19.0214i	0.707903	+	0.707903i
$723$	−6.15647	−	17.3044i	−0.228962	−	0.643558i
$724$	20.1307			0.748153
$725$	−18.9513			−0.703833
$726$	89.4049	−	31.8080i	3.31813	−	1.18051i
$727$		−	27.4133i		−	1.01670i	−0.861150	−	0.508352i	$-0.830255\pi$
$727$		−	27.4133i		−	1.01670i	0.861150	−	0.508352i	$-0.169745\pi$
$728$	−8.94569	+	17.9723i	−0.331549	+	0.666099i
$729$	23.9481	−	12.4696i	0.886965	−	0.461836i
$730$	7.54951	+	7.54951i	0.279420	+	0.279420i
$731$		−	18.1522i		−	0.671382i
$732$	−30.2504	−	14.3741i	−1.11809	−	0.531283i
$733$	20.8592	+	20.8592i	0.770453	+	0.770453i	0.978186	−	0.207733i	$-0.0666085\pi$
$733$	20.8592	+	20.8592i	0.770453	+	0.770453i	−0.207733	+	0.978186i	$0.566609\pi$
$734$	−34.1955	+	34.1955i	−1.26218	+	1.26218i
$735$	−0.622161	+	0.221349i	−0.0229488	+	0.00816459i
$736$	−2.93998	+	2.93998i	−0.108369	+	0.108369i
$737$		−	73.2933i		−	2.69979i
$738$	46.7082	−	38.0516i	1.71935	−	1.40070i
$739$	32.5075	−	32.5075i	1.19581	−	1.19581i	0.220396	−	0.975411i	$-0.429265\pi$
$739$	32.5075	−	32.5075i	1.19581	−	1.19581i	0.975411	−	0.220396i	$-0.0707349\pi$
$740$	−5.93601			−0.218212
$741$	2.14444	−	17.7793i	0.0787780	−	0.653141i
$742$	−15.6607			−0.574923
$743$	5.71046	−	5.71046i	0.209497	−	0.209497i	−0.594557	−	0.804053i	$-0.702673\pi$
$743$	5.71046	−	5.71046i	0.209497	−	0.209497i	0.804053	+	0.594557i	$0.202673\pi$
$744$	26.2499	+	12.4732i	0.962368	+	0.457290i
$745$			3.67915i			0.134794i
$746$	40.5239	−	40.5239i	1.48369	−	1.48369i
$747$	34.1456	+	3.48732i	1.24932	+	0.127594i
$748$	−30.1586	+	30.1586i	−1.10271	+	1.10271i
$749$	3.94015	+	3.94015i	0.143970	+	0.143970i
$750$	−6.97161	+	14.6718i	−0.254567	+	0.535738i
$751$		−	3.00915i		−	0.109805i	−0.998492	−	0.0549027i	$-0.982515\pi$
$751$		−	3.00915i		−	0.109805i	0.998492	−	0.0549027i	$-0.0174849\pi$
$752$	39.6959	+	39.6959i	1.44756	+	1.44756i
$753$	−12.1217	+	25.5102i	−0.441739	+	0.929642i
$754$	−33.3104	+	11.1702i	−1.21309	+	0.406796i
$755$		−	7.35721i		−	0.267756i
$756$	18.7942	+	11.4033i	0.683537	+	0.414734i
$757$	10.8803			0.395450			0.197725	−	0.980258i	$-0.436645\pi$
$757$	10.8803			0.395450			0.197725	+	0.980258i	$0.436645\pi$
$758$	38.6215			1.40280
$759$	−15.9898	+	5.68878i	−0.580394	+	0.206490i
$760$	4.30452	+	4.30452i	0.156141	+	0.156141i
$761$	−27.0121	−	27.0121i	−0.979190	−	0.979190i	0.0205982	−	0.999788i	$-0.493443\pi$
$761$	−27.0121	−	27.0121i	−0.979190	−	0.979190i	−0.999788	+	0.0205982i	$0.993443\pi$
$762$	29.1139	−	10.3580i	1.05468	−	0.375230i
$763$	14.6007			0.528581
$764$	79.7297			2.88452
$765$	1.99843	+	0.204101i	0.0722534	+	0.00737930i
$766$			44.6796i			1.61434i
$767$	−35.4029	+	11.8720i	−1.27833	+	0.428671i
$768$	24.1170	−	50.7543i	0.870246	−	1.83144i
$769$	36.0011	+	36.0011i	1.29823	+	1.29823i	0.929559	+	0.368674i	$0.120188\pi$
$769$	36.0011	+	36.0011i	1.29823	+	1.29823i	0.368674	+	0.929559i	$0.379812\pi$
$770$		−	5.46274i		−	0.196863i
$771$	−0.927313	+	1.95153i	−0.0333964	+	0.0702828i
$772$	−44.6131	−	44.6131i	−1.60566	−	1.60566i
$773$	−7.30894	+	7.30894i	−0.262884	+	0.262884i	−0.826225	−	0.563340i	$-0.809516\pi$
$773$	−7.30894	+	7.30894i	−0.262884	+	0.262884i	0.563340	+	0.826225i	$0.309516\pi$
$774$	7.86360	−	76.9954i	0.282651	−	2.76754i
$775$	10.3447	−	10.3447i	0.371594	−	0.371594i
$776$		−	55.5071i		−	1.99259i
$777$	5.75729	+	2.73570i	0.206542	+	0.0981426i
$778$	−26.7035	+	26.7035i	−0.957367	+	0.957367i
$779$	−23.0707			−0.826592
$780$	−1.20621	+	10.0006i	−0.0431893	+	0.358078i
$781$	−5.59063			−0.200048
$782$	5.29166	−	5.29166i	0.189229	−	0.189229i
$783$	4.82231	+	19.7029i	0.172335	+	0.704125i
$784$			5.43707i			0.194181i
$785$	−2.78654	+	2.78654i	−0.0994558	+	0.0994558i
$786$	−30.1254	+	10.7179i	−1.07454	+	0.382294i
$787$	12.2014	−	12.2014i	0.434933	−	0.434933i	−0.455370	−	0.890303i	$-0.650493\pi$
$787$	12.2014	−	12.2014i	0.434933	−	0.434933i	0.890303	+	0.455370i	$0.150493\pi$
$788$	66.5945	+	66.5945i	2.37233	+	2.37233i
$789$	−27.5670	−	13.0990i	−0.981410	−	0.466338i
$790$			2.86754i			0.102023i
$791$	2.62502	+	2.62502i	0.0933349	+	0.0933349i
$792$	−74.3369	+	60.5598i	−2.64145	+	2.15190i
$793$	−7.34325	+	14.7530i	−0.260767	+	0.523893i
$794$		−	31.4241i		−	1.11520i
$795$	−3.90345	+	1.38875i	−0.138441	+	0.0492538i
$796$	14.8318			0.525699
$797$	−14.9021			−0.527858			−0.263929	−	0.964542i	$-0.585018\pi$
$797$	−14.9021			−0.527858			−0.263929	+	0.964542i	$0.585018\pi$
$798$	−4.15568	−	11.6806i	−0.147109	−	0.413490i
$799$	−12.8227	−	12.8227i	−0.453634	−	0.453634i
$800$	8.36102	+	8.36102i	0.295607	+	0.295607i
$801$	−1.64301	+	16.0873i	−0.0580528	+	0.568417i
$802$	−20.9850			−0.741005
$803$	64.3970			2.27252
$804$	31.3621	+	88.1516i	1.10606	+	3.10887i
$805$			0.650826i			0.0229386i
$806$	12.0854	−	24.2802i	0.425690	−	0.855232i
$807$	45.7167	+	21.7233i	1.60930	+	0.764695i
$808$	41.1819	+	41.1819i	1.44877	+	1.44877i
$809$		−	51.6094i		−	1.81449i	−0.420603	−	0.907245i	$-0.638181\pi$
$809$		−	51.6094i		−	1.81449i	0.420603	−	0.907245i	$-0.361819\pi$
$810$	8.38825	+	1.73146i	0.294733	+	0.0608372i
$811$	−5.33847	−	5.33847i	−0.187459	−	0.187459i	0.607138	−	0.794597i	$-0.292318\pi$
$811$	−5.33847	−	5.33847i	−0.187459	−	0.187459i	−0.794597	+	0.607138i	$0.792318\pi$
$812$	−11.6781	+	11.6781i	−0.409822	+	0.409822i
$813$	16.6495	+	46.7979i	0.583924	+	1.64127i
$814$	−37.2853	+	37.2853i	−1.30685	+	1.30685i
$815$			3.34571i			0.117195i
$816$	7.09849	−	14.9388i	0.248497	−	0.522963i
$817$	−20.9573	+	20.9573i	−0.733203	+	0.733203i
$818$	78.0276			2.72817
$819$	5.77882	−	9.14359i	0.201928	−	0.319503i
$820$	12.9769			0.453172
$821$	−10.2124	+	10.2124i	−0.356414	+	0.356414i	−0.862489	−	0.506075i	$-0.831096\pi$
$821$	−10.2124	+	10.2124i	−0.356414	+	0.356414i	0.506075	+	0.862489i	$0.331096\pi$
$822$	35.5688	−	74.8548i	1.24061	−	2.61086i
$823$		−	55.9824i		−	1.95142i	−0.219057	−	0.975712i	$-0.570298\pi$
$823$		−	55.9824i		−	1.95142i	0.219057	−	0.975712i	$-0.429702\pi$
$824$	32.3139	−	32.3139i	1.12571	−	1.12571i
$825$	16.1783	+	45.4735i	0.563257	+	1.58318i
$826$	−18.2793	+	18.2793i	−0.636019	+	0.636019i
$827$	−26.8145	−	26.8145i	−0.932431	−	0.932431i	0.0654262	−	0.997857i	$-0.479159\pi$
$827$	−26.8145	−	26.8145i	−0.932431	−	0.932431i	−0.997857	+	0.0654262i	$0.979159\pi$
$828$	16.7971	−	13.6841i	0.583740	−	0.475554i
$829$		−	15.2599i		−	0.529997i	−0.964249	−	0.264998i	$-0.914629\pi$
$829$		−	15.2599i		−	0.529997i	0.964249	−	0.264998i	$-0.0853715\pi$
$830$	7.69912	+	7.69912i	0.267240	+	0.267240i
$831$	−7.27511	−	3.45692i	−0.252371	−	0.119919i
$832$	−15.4754	−	7.70286i	−0.536514	−	0.267049i
$833$		−	1.75630i		−	0.0608521i
$834$	17.2298	+	48.4289i	0.596618	+	1.67695i
$835$	−3.94079			−0.136377
$836$	69.6382			2.40849
$837$	−13.3873	−	8.12272i	−0.462734	−	0.280762i
$838$	53.4265	+	53.4265i	1.84559	+	1.84559i
$839$	6.08423	+	6.08423i	0.210051	+	0.210051i	0.804289	−	0.594238i	$-0.202546\pi$
$839$	6.08423	+	6.08423i	0.210051	+	0.210051i	−0.594238	+	0.804289i	$0.702546\pi$
$840$	1.23247	+	3.46418i	0.0425241	+	0.119525i
$841$	13.7608			0.474509
$842$	−53.2889			−1.83646
$843$	−8.79319	+	3.12840i	−0.302854	+	0.107748i
$844$			62.0040i			2.13427i
$845$	4.90908	+	0.683241i	0.168877	+	0.0235042i
$846$	−48.8346	−	59.9443i	−1.67897	−	2.06093i
$847$	−15.5203	−	15.5203i	−0.533283	−	0.533283i
$848$			34.1122i			1.17142i
$849$	−14.1049	−	6.70227i	−0.484081	−	0.230021i
$850$	−15.0490	−	15.0490i	−0.516175	−	0.516175i
$851$	4.44214	−	4.44214i	0.152275	−	0.152275i
$852$	6.72398	−	2.39222i	0.230360	−	0.0819563i
$853$	−38.6535	+	38.6535i	−1.32347	+	1.32347i	−0.412522	+	0.910948i	$0.635352\pi$
$853$	−38.6535	+	38.6535i	−1.32347	+	1.32347i	−0.910948	+	0.412522i	$0.864648\pi$
$854$			11.4088i			0.390399i
$855$	−2.07161	−	2.54290i	−0.0708476	−	0.0869652i
$856$	21.9387	−	21.9387i	0.749848	−	0.749848i
$857$	3.32957			0.113736			0.0568680	−	0.998382i	$-0.481889\pi$
$857$	3.32957			0.113736			0.0568680	+	0.998382i	$0.481889\pi$
$858$	55.2393	+	70.3922i	1.88584	+	2.40315i
$859$	−14.3358			−0.489131			−0.244565	−	0.969633i	$-0.578645\pi$
$859$	−14.3358			−0.489131			−0.244565	+	0.969633i	$0.578645\pi$
$860$	11.7881	−	11.7881i	0.401972	−	0.401972i
$861$	−12.5862	−	5.98058i	−0.428935	−	0.203818i
$862$			8.38607i			0.285631i
$863$	14.8752	−	14.8752i	0.506356	−	0.506356i	−0.407050	−	0.913406i	$-0.633442\pi$
$863$	14.8752	−	14.8752i	0.506356	−	0.506356i	0.913406	+	0.407050i	$0.133442\pi$
$864$	6.56510	−	10.8202i	0.223349	−	0.368109i
$865$	−1.10810	+	1.10810i	−0.0376766	+	0.0376766i
$866$	3.00864	+	3.00864i	0.102238	+	0.102238i
$867$	10.3443	−	21.7695i	0.351309	−	0.739332i
$868$		−	12.7492i		−	0.432737i
$869$	12.2300	+	12.2300i	0.414874	+	0.414874i
$870$	−2.76168	+	5.81198i	−0.0936299	+	0.197044i
$871$	43.6490	−	14.6372i	1.47899	−	0.495961i
$872$		−	81.2963i		−	2.75304i
$873$	−3.03862	+	29.7522i	−0.102842	+	1.00696i
$874$	−12.2188			−0.413307
$875$	3.75719			0.127016
$876$	−77.4519	+	27.5554i	−2.61686	+	0.931011i
$877$	18.2464	+	18.2464i	0.616136	+	0.616136i	0.944538	−	0.328402i	$-0.106510\pi$
$877$	18.2464	+	18.2464i	0.616136	+	0.616136i	−0.328402	+	0.944538i	$0.606510\pi$
$878$	−26.6799	−	26.6799i	−0.900402	−	0.900402i
$879$	0.693306	−	0.246661i	0.0233846	−	0.00831966i
$880$	−11.8989			−0.401113
$881$	−15.5936			−0.525362			−0.262681	−	0.964883i	$-0.584607\pi$
$881$	−15.5936			−0.525362			−0.262681	+	0.964883i	$0.584607\pi$
$882$	0.760836	−	7.44963i	0.0256187	−	0.250842i
$883$			13.6749i			0.460199i	0.973167	+	0.230099i	$0.0739051\pi$
$883$			13.6749i			0.460199i	−0.973167	+	0.230099i	$0.926095\pi$
$884$	−23.9835	−	11.9377i	−0.806652	−	0.401509i
$885$	−2.93518	+	6.17709i	−0.0986648	+	0.207641i
$886$	26.1140	+	26.1140i	0.877317	+	0.877317i
$887$		−	36.0831i		−	1.21155i	−0.795635	−	0.605776i	$-0.792863\pi$
$887$		−	36.0831i		−	1.21155i	0.795635	−	0.605776i	$-0.207137\pi$
$888$	15.2323	−	32.0564i	0.511162	−	1.07574i
$889$	−5.05403	−	5.05403i	−0.169507	−	0.169507i
$890$	−3.62735	+	3.62735i	−0.121589	+	0.121589i
$891$	43.1603	−	28.3911i	1.44593	−	0.951137i
$892$	32.4037	−	32.4037i	1.08496	−	1.08496i
$893$			29.6084i			0.990808i
$894$	−37.6829	−	17.9058i	−1.26031	−	0.598861i
$895$	−1.59685	+	1.59685i	−0.0533770	+	0.0533770i
$896$	−16.8388			−0.562544
$897$	−6.58116	−	8.38647i	−0.219739	−	0.280016i
$898$	41.1105			1.37188
$899$	8.31849	−	8.31849i	0.277437	−	0.277437i
$900$	−38.9161	−	47.7694i	−1.29720	−	1.59231i
$901$		−	11.0190i		−	0.367097i
$902$	81.5104	−	81.5104i	2.71400	−	2.71400i
$903$	−16.8660	+	6.00048i	−0.561264	+	0.199683i
$904$	14.6160	−	14.6160i	0.486122	−	0.486122i
$905$	−1.28280	−	1.28280i	−0.0426419	−	0.0426419i
$906$	75.3546	+	35.8063i	2.50349	+	1.18959i
$907$		−	3.64992i		−	0.121194i	−0.998162	−	0.0605968i	$-0.980700\pi$
$907$		−	3.64992i		−	0.121194i	0.998162	−	0.0605968i	$-0.0193004\pi$
$908$	−14.4768	−	14.4768i	−0.480430	−	0.480430i
$909$	−19.8194	−	24.3282i	−0.657368	−	0.806916i
$910$	3.25327	−	1.09095i	0.107845	−	0.0361645i
$911$		−	6.03257i		−	0.199868i	−0.994994	−	0.0999340i	$-0.968137\pi$
$911$		−	6.03257i		−	0.199868i	0.994994	−	0.0999340i	$-0.0318632\pi$
$912$	−25.4428	+	9.05191i	−0.842495	+	0.299739i
$913$	65.6731			2.17346
$914$	−5.06975			−0.167692
$915$	1.01170	+	2.84364i	0.0334456	+	0.0940078i
$916$	−87.7277	−	87.7277i	−2.89860	−	2.89860i
$917$	5.22963	+	5.22963i	0.172698	+	0.172698i
$918$	−11.8165	+	19.4752i	−0.390003	+	0.642776i
$919$	−6.31980			−0.208471			−0.104235	−	0.994553i	$-0.533240\pi$
$919$	−6.31980			−0.208471			−0.104235	+	0.994553i	$0.533240\pi$
$920$	3.62378			0.119473
$921$	0.398017	+	1.11873i	0.0131151	+	0.0368635i
$922$			68.1490i			2.24437i
$923$	−1.11649	−	3.32944i	−0.0367496	−	0.109590i
$924$	37.9910	+	18.0522i	1.24981	+	0.593875i
$925$	−12.6330	−	12.6330i	−0.415371	−	0.415371i
$926$			37.6593i			1.23756i
$927$	−19.0895	+	15.5516i	−0.626981	+	0.510780i
$928$	6.72333	+	6.72333i	0.220704	+	0.220704i
$929$	−19.9127	+	19.9127i	−0.653315	+	0.653315i	−0.953790	−	0.300474i	$-0.902855\pi$
$929$	−19.9127	+	19.9127i	−0.653315	+	0.653315i	0.300474	+	0.953790i	$0.402855\pi$
$930$	−1.66503	−	4.68001i	−0.0545985	−	0.153464i
$931$	−2.02770	+	2.02770i	−0.0664553	+	0.0664553i
$932$			76.8032i			2.51577i
$933$	20.8497	−	43.8784i	0.682590	−	1.43651i
$934$	−45.5796	+	45.5796i	−1.49141	+	1.49141i
$935$	3.84363			0.125700
$936$	−50.9113	−	32.1763i	−1.66409	−	1.05171i
$937$	6.70690			0.219105			0.109552	−	0.993981i	$-0.465058\pi$
$937$	6.70690			0.219105			0.109552	+	0.993981i	$0.465058\pi$
$938$	22.5369	−	22.5369i	0.735856	−	0.735856i
$939$	1.77674	−	3.73915i	0.0579816	−	0.122023i
$940$		−	16.6542i		−	0.543201i
$941$	0.887100	−	0.887100i	0.0289186	−	0.0289186i	−0.692500	−	0.721418i	$-0.743491\pi$
$941$	0.887100	−	0.887100i	0.0289186	−	0.0289186i	0.721418	+	0.692500i	$0.243491\pi$
$942$	−14.9789	−	42.1021i	−0.488038	−	1.37176i
$943$	−9.71108	+	9.71108i	−0.316236	+	0.316236i
$944$	39.8160	+	39.8160i	1.29590	+	1.29590i
$945$	−0.470973	−	1.92429i	−0.0153207	−	0.0625973i
$946$		−	148.087i		−	4.81473i
$947$	8.60266	+	8.60266i	0.279549	+	0.279549i	0.832929	−	0.553380i	$-0.186662\pi$
$947$	8.60266	+	8.60266i	0.279549	+	0.279549i	−0.553380	+	0.832929i	$0.686662\pi$
$948$	−19.9425	−	9.47611i	−0.647703	−	0.307770i
$949$	12.8605	+	38.3509i	0.417470	+	1.24492i
$950$			34.7491i			1.12741i
$951$	−2.82349	−	7.93616i	−0.0915579	−	0.257348i
$952$	−9.77902			−0.316940
$953$	−18.3979			−0.595967			−0.297983	−	0.954571i	$-0.596314\pi$
$953$	−18.3979			−0.595967			−0.297983	+	0.954571i	$0.596314\pi$
$954$	4.77350	−	46.7390i	0.154548	−	1.51323i
$955$	−5.08067	−	5.08067i	−0.164407	−	0.164407i
$956$	76.6176	+	76.6176i	2.47799	+	2.47799i
$957$	13.0094	+	36.5665i	0.420535	+	1.18203i
$958$	−17.1094			−0.552781
$959$	−19.1690			−0.619000
$960$	−2.98290	+	1.06124i	−0.0962726	+	0.0342514i
$961$		−	21.9185i		−	0.707050i
$962$	−29.6510	−	14.7587i	−0.955986	−	0.475840i
$963$	−12.9603	+	10.5583i	−0.417639	+	0.340237i
$964$	31.7225	+	31.7225i	1.02171	+	1.02171i
$965$			5.68583i			0.183033i
$966$	−6.66595	−	3.16747i	−0.214473	−	0.101912i
$967$	28.4595	+	28.4595i	0.915195	+	0.915195i	0.996675	−	0.0814799i	$-0.0259646\pi$
$967$	28.4595	+	28.4595i	0.915195	+	0.915195i	−0.0814799	+	0.996675i	$0.525965\pi$
$968$	−86.4165	+	86.4165i	−2.77753	+	2.77753i
$969$	8.21861	−	2.92397i	0.264020	−	0.0939316i
$970$	−6.70850	+	6.70850i	−0.215397	+	0.215397i
$971$		−	39.0065i		−	1.25178i	−0.779912	−	0.625889i	$-0.784736\pi$
$971$		−	39.0065i		−	1.25178i	0.779912	−	0.625889i	$-0.215264\pi$
$972$	−39.7615	+	52.6149i	−1.27535	+	1.68762i
$973$	8.40702	−	8.40702i	0.269517	−	0.269517i
$974$	−81.3393			−2.60628
$975$	−23.8503	+	18.7162i	−0.763821	+	0.599398i
$976$	24.8506			0.795447
$977$	12.4122	−	12.4122i	0.397102	−	0.397102i	−0.480108	−	0.877209i	$-0.659403\pi$
$977$	12.4122	−	12.4122i	0.397102	−	0.397102i	0.877209	+	0.480108i	$0.159403\pi$
$978$	−34.2677	−	16.2830i	−1.09576	−	0.520673i
$979$			30.9411i			0.988883i
$980$	1.14055	−	1.14055i	0.0364335	−	0.0364335i
$981$	−4.45040	+	43.5754i	−0.142090	+	1.39126i
$982$	33.7972	−	33.7972i	1.07851	−	1.07851i
$983$	10.5488	+	10.5488i	0.336456	+	0.336456i	0.855032	−	0.518576i	$-0.173538\pi$
$983$	10.5488	+	10.5488i	0.336456	+	0.336456i	−0.518576	+	0.855032i	$0.673538\pi$
$984$	−33.2997	+	70.0794i	−1.06156	+	2.23405i
$985$		−	8.48730i		−	0.270428i
$986$	−12.1013	−	12.1013i	−0.385383	−	0.385383i
$987$	−7.67536	+	16.1528i	−0.244309	+	0.514150i
$988$	13.9072	+	41.4722i	0.442448	+	1.31941i
$989$			17.6430i			0.561015i
$990$	16.3034	+	1.66508i	0.518156	+	0.0529197i
$991$	−5.45515			−0.173289			−0.0866443	−	0.996239i	$-0.527614\pi$
$991$	−5.45515			−0.173289			−0.0866443	+	0.996239i	$0.527614\pi$
$992$	−7.33998			−0.233045
$993$	−7.06840	+	2.51476i	−0.224309	+	0.0798034i
$994$	−1.71906	−	1.71906i	−0.0545253	−	0.0545253i
$995$	−0.945137	−	0.945137i	−0.0299629	−	0.0299629i
$996$	−78.9867	+	28.1015i	−2.50279	+	0.890429i
$997$	5.27601			0.167093			0.0835465	−	0.996504i	$-0.473375\pi$
$997$	5.27601			0.167093			0.0835465	+	0.996504i	$0.473375\pi$
$998$	−58.7402			−1.85939
$999$	−9.91948	+	16.3486i	−0.313839	+	0.517248i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.n.c.8.2	✓	48
3.2	odd	2	inner	273.2.n.c.8.23	yes	48
13.5	odd	4	inner	273.2.n.c.239.23	yes	48
39.5	even	4	inner	273.2.n.c.239.2	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.n.c.8.2	✓	48	1.1	even	1	trivial
273.2.n.c.8.23	yes	48	3.2	odd	2	inner
273.2.n.c.239.2	yes	48	39.5	even	4	inner
273.2.n.c.239.23	yes	48	13.5	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.n (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.76503 + 1.76503i) q^{2} +(-0.743367 + 1.56442i) q^{3} -4.23065i q^{4} +(-0.269592 + 0.269592i) q^{5} +(-1.44918 - 4.07331i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(3.93715 + 3.93715i) q^{8} +(-1.89481 - 2.32587i) q^{9} +O(q^{10})\)	\(q+(-1.76503 + 1.76503i) q^{2} +(-0.743367 + 1.56442i) q^{3} -4.23065i q^{4} +(-0.269592 + 0.269592i) q^{5} +(-1.44918 - 4.07331i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(3.93715 + 3.93715i) q^{8} +(-1.89481 - 2.32587i) q^{9} -0.951676i q^{10} +(-4.05888 - 4.05888i) q^{11} +(6.61850 + 3.14492i) q^{12} +(1.60663 - 3.22781i) q^{13} -2.49613i q^{14} +(-0.221349 - 0.622161i) q^{15} -5.43707 q^{16} +1.75630 q^{17} +(7.44963 + 0.760836i) q^{18} +(-2.02770 - 2.02770i) q^{19} +(1.14055 + 1.14055i) q^{20} +(-0.580571 - 1.63185i) q^{21} +14.3281 q^{22} -1.70703 q^{23} +(-9.08610 + 3.23260i) q^{24} +4.85464i q^{25} +(2.86141 + 8.53292i) q^{26} +(5.04718 - 1.23530i) q^{27} +(2.99152 + 2.99152i) q^{28} +3.90375i q^{29} +(1.48882 + 0.707444i) q^{30} +(-2.13090 - 2.13090i) q^{31} +(1.72227 - 1.72227i) q^{32} +(9.36702 - 3.33255i) q^{33} +(-3.09991 + 3.09991i) q^{34} -0.381261i q^{35} +(-9.83995 + 8.01628i) q^{36} +(-2.60226 + 2.60226i) q^{37} +7.15791 q^{38} +(3.85532 + 4.91289i) q^{39} -2.12285 q^{40} +(5.68886 - 5.68886i) q^{41} +(3.90499 + 1.85554i) q^{42} -10.3355i q^{43} +(-17.1717 + 17.1717i) q^{44} +(1.13786 + 0.116211i) q^{45} +(3.01296 - 3.01296i) q^{46} +(-7.30097 - 7.30097i) q^{47} +(4.04174 - 8.50585i) q^{48} -1.00000i q^{49} +(-8.56857 - 8.56857i) q^{50} +(-1.30557 + 2.74759i) q^{51} +(-13.6557 - 6.79710i) q^{52} -6.27401i q^{53} +(-6.72807 + 11.0888i) q^{54} +2.18849 q^{55} -5.56797 q^{56} +(4.67951 - 1.66485i) q^{57} +(-6.89022 - 6.89022i) q^{58} +(-7.32307 - 7.32307i) q^{59} +(-2.63214 + 0.936451i) q^{60} -4.57058 q^{61} +7.52219 q^{62} +(2.98448 + 0.304807i) q^{63} -4.79441i q^{64} +(0.437056 + 1.30333i) q^{65} +(-10.6510 + 22.4151i) q^{66} +(9.02876 + 9.02876i) q^{67} -7.43027i q^{68} +(1.26895 - 2.67052i) q^{69} +(0.672937 + 0.672937i) q^{70} +(0.688691 - 0.688691i) q^{71} +(1.69716 - 16.6175i) q^{72} +(-7.93286 + 7.93286i) q^{73} -9.18611i q^{74} +(-7.59469 - 3.60878i) q^{75} +(-8.57850 + 8.57850i) q^{76} +5.74012 q^{77} +(-15.4761 - 1.86664i) q^{78} -3.01315 q^{79} +(1.46579 - 1.46579i) q^{80} +(-1.81938 + 8.81419i) q^{81} +20.0820i q^{82} +(-8.09006 + 8.09006i) q^{83} +(-6.90378 + 2.45619i) q^{84} +(-0.473485 + 0.473485i) q^{85} +(18.2424 + 18.2424i) q^{86} +(-6.10709 - 2.90192i) q^{87} -31.9608i q^{88} +(-3.81154 - 3.81154i) q^{89} +(-2.21348 + 1.80325i) q^{90} +(1.14634 + 3.41846i) q^{91} +7.22186i q^{92} +(4.91766 - 1.74958i) q^{93} +25.7728 q^{94} +1.09331 q^{95} +(1.41408 + 3.97464i) q^{96} +(-7.04914 - 7.04914i) q^{97} +(1.76503 + 1.76503i) q^{98} +(-1.74963 + 17.1312i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 8 q^{3} + 4 q^{6}+O(q^{10}) \) 48 * q + 8 * q^3 + 4 * q^6	\( 48 q + 8 q^{3} + 4 q^{6} + 8 q^{13} - 16 q^{15} - 72 q^{16} - 12 q^{18} + 40 q^{19} + 16 q^{22} + 8 q^{24} - 16 q^{27} + 44 q^{33} - 32 q^{34} - 8 q^{37} - 4 q^{39} - 48 q^{40} - 8 q^{42} + 44 q^{45} - 32 q^{46} + 80 q^{48} - 72 q^{52} + 44 q^{54} - 80 q^{55} - 52 q^{57} + 16 q^{58} + 44 q^{60} - 64 q^{61} + 24 q^{63} - 152 q^{66} + 56 q^{67} + 16 q^{70} + 16 q^{72} + 32 q^{73} + 104 q^{76} - 44 q^{78} + 8 q^{79} + 12 q^{84} - 96 q^{85} - 72 q^{87} - 8 q^{91} - 8 q^{93} + 160 q^{94} + 8 q^{96} - 32 q^{97} - 12 q^{99}+O(q^{100}) \) 48 * q + 8 * q^3 + 4 * q^6 + 8 * q^13 - 16 * q^15 - 72 * q^16 - 12 * q^18 + 40 * q^19 + 16 * q^22 + 8 * q^24 - 16 * q^27 + 44 * q^33 - 32 * q^34 - 8 * q^37 - 4 * q^39 - 48 * q^40 - 8 * q^42 + 44 * q^45 - 32 * q^46 + 80 * q^48 - 72 * q^52 + 44 * q^54 - 80 * q^55 - 52 * q^57 + 16 * q^58 + 44 * q^60 - 64 * q^61 + 24 * q^63 - 152 * q^66 + 56 * q^67 + 16 * q^70 + 16 * q^72 + 32 * q^73 + 104 * q^76 - 44 * q^78 + 8 * q^79 + 12 * q^84 - 96 * q^85 - 72 * q^87 - 8 * q^91 - 8 * q^93 + 160 * q^94 + 8 * q^96 - 32 * q^97 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more