LMFDB - Embedded newform 1205.2.b.c.724.33

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1205,2,Mod(724,1205)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1205, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1205.724");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1205 = 5 \cdot 241 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1205.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:	$9.62197344356$
Analytic rank:	$0$
Dimension:	$46$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			724.33
Character	$\chi$	$=$	1205.724
Dual form			1205.2.b.c.724.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.30874i q^{2} -1.88426i q^{3} +0.287190 q^{4} +(2.21635 + 0.296297i) q^{5} +2.46601 q^{6} -1.28779i q^{7} +2.99335i q^{8} -0.550432 q^{9} +O(q^{10})$	\(q+1.30874i q^{2} -1.88426i q^{3} +0.287190 q^{4} +(2.21635 + 0.296297i) q^{5} +2.46601 q^{6} -1.28779i q^{7} +2.99335i q^{8} -0.550432 q^{9} +(-0.387776 + 2.90063i) q^{10} +0.698979 q^{11} -0.541141i q^{12} -5.53802i q^{13} +1.68539 q^{14} +(0.558300 - 4.17618i) q^{15} -3.34314 q^{16} -3.43199i q^{17} -0.720375i q^{18} +3.98407 q^{19} +(0.636515 + 0.0850936i) q^{20} -2.42653 q^{21} +0.914784i q^{22} +6.27054i q^{23} +5.64024 q^{24} +(4.82442 + 1.31339i) q^{25} +7.24785 q^{26} -4.61562i q^{27} -0.369841i q^{28} -6.15912 q^{29} +(5.46555 + 0.730671i) q^{30} -0.212499 q^{31} +1.61138i q^{32} -1.31706i q^{33} +4.49160 q^{34} +(0.381568 - 2.85420i) q^{35} -0.158079 q^{36} +5.91052i q^{37} +5.21413i q^{38} -10.4351 q^{39} +(-0.886918 + 6.63430i) q^{40} -9.65382 q^{41} -3.17571i q^{42} -7.78957i q^{43} +0.200740 q^{44} +(-1.21995 - 0.163091i) q^{45} -8.20652 q^{46} -3.86035i q^{47} +6.29934i q^{48} +5.34159 q^{49} +(-1.71890 + 6.31392i) q^{50} -6.46676 q^{51} -1.59047i q^{52} +10.2480i q^{53} +6.04066 q^{54} +(1.54918 + 0.207105i) q^{55} +3.85481 q^{56} -7.50702i q^{57} -8.06070i q^{58} +9.54071 q^{59} +(0.160338 - 1.19936i) q^{60} +8.82214 q^{61} -0.278107i q^{62} +0.708842i q^{63} -8.79516 q^{64} +(1.64090 - 12.2742i) q^{65} +1.72369 q^{66} -7.38392i q^{67} -0.985635i q^{68} +11.8153 q^{69} +(3.73541 + 0.499375i) q^{70} -6.00088 q^{71} -1.64763i q^{72} -2.96121i q^{73} -7.73535 q^{74} +(2.47478 - 9.09045i) q^{75} +1.14419 q^{76} -0.900139i q^{77} -13.6568i q^{78} +6.80832 q^{79} +(-7.40957 - 0.990562i) q^{80} -10.3483 q^{81} -12.6344i q^{82} +16.1202i q^{83} -0.696877 q^{84} +(1.01689 - 7.60649i) q^{85} +10.1946 q^{86} +11.6054i q^{87} +2.09228i q^{88} -1.74849 q^{89} +(0.213445 - 1.59660i) q^{90} -7.13182 q^{91} +1.80084i q^{92} +0.400404i q^{93} +5.05221 q^{94} +(8.83010 + 1.18047i) q^{95} +3.03625 q^{96} -0.714461i q^{97} +6.99077i q^{98} -0.384741 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 46 q - 34 q^{4} - 8 q^{5} - 4 q^{6} - 34 q^{9}+O(q^{10}) $ 46 * q - 34 * q^4 - 8 * q^5 - 4 * q^6 - 34 * q^9	$ 46 q - 34 q^{4} - 8 q^{5} - 4 q^{6} - 34 q^{9} - 7 q^{10} - 64 q^{11} + 66 q^{14} + 5 q^{15} + 22 q^{16} - 2 q^{20} - 14 q^{21} + 50 q^{24} + 30 q^{25} - 60 q^{26} + 36 q^{29} + 7 q^{30} - 36 q^{31} - 12 q^{34} + 3 q^{35} - 34 q^{36} + 88 q^{39} - 30 q^{40} - 76 q^{41} + 100 q^{44} - 17 q^{45} - 12 q^{46} - 22 q^{49} - 14 q^{50} - 112 q^{51} + 26 q^{54} - 5 q^{55} - 120 q^{56} + 84 q^{59} - 33 q^{60} - 78 q^{61} - 28 q^{64} + 9 q^{65} - 2 q^{66} + 24 q^{69} + 88 q^{70} - 172 q^{71} + 16 q^{74} + 59 q^{75} - 18 q^{76} + 54 q^{79} + 63 q^{80} - 42 q^{81} - 44 q^{84} + 30 q^{85} - 80 q^{86} + 86 q^{89} + 17 q^{90} - 88 q^{91} - 4 q^{94} + q^{95} - 122 q^{96} + 148 q^{99}+O(q^{100}) $ 46 * q - 34 * q^4 - 8 * q^5 - 4 * q^6 - 34 * q^9 - 7 * q^10 - 64 * q^11 + 66 * q^14 + 5 * q^15 + 22 * q^16 - 2 * q^20 - 14 * q^21 + 50 * q^24 + 30 * q^25 - 60 * q^26 + 36 * q^29 + 7 * q^30 - 36 * q^31 - 12 * q^34 + 3 * q^35 - 34 * q^36 + 88 * q^39 - 30 * q^40 - 76 * q^41 + 100 * q^44 - 17 * q^45 - 12 * q^46 - 22 * q^49 - 14 * q^50 - 112 * q^51 + 26 * q^54 - 5 * q^55 - 120 * q^56 + 84 * q^59 - 33 * q^60 - 78 * q^61 - 28 * q^64 + 9 * q^65 - 2 * q^66 + 24 * q^69 + 88 * q^70 - 172 * q^71 + 16 * q^74 + 59 * q^75 - 18 * q^76 + 54 * q^79 + 63 * q^80 - 42 * q^81 - 44 * q^84 + 30 * q^85 - 80 * q^86 + 86 * q^89 + 17 * q^90 - 88 * q^91 - 4 * q^94 + q^95 - 122 * q^96 + 148 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1205\mathbb{Z}\right)^\times$.

$n$	$242$	$971$
$\chi(n)$	$-1$	$1$

Coefficient data

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

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

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

$2$			1.30874i			0.925421i	0.886509	+	0.462711i	$0.153123\pi$
$2$			1.30874i			0.925421i	−0.886509	+	0.462711i	$0.846877\pi$
$3$		−	1.88426i		−	1.08788i	−0.839125	−	0.543939i	$-0.816932\pi$
$3$		−	1.88426i		−	1.08788i	0.839125	−	0.543939i	$-0.183068\pi$
$4$	0.287190			0.143595
$5$	2.21635	+	0.296297i	0.991182	+	0.132508i
$5$	2.21635	+	0.296297i	0.991182	+	0.132508i
$6$	2.46601			1.00675
$7$		−	1.28779i		−	0.486739i	−0.969934	−	0.243370i	$-0.921747\pi$
$7$		−	1.28779i		−	0.486739i	0.969934	−	0.243370i	$-0.0782528\pi$
$8$			2.99335i			1.05831i
$9$	−0.550432			−0.183477
$10$	−0.387776	+	2.90063i	−0.122626	+	0.917261i
$11$	0.698979			0.210750			0.105375	−	0.994433i	$-0.466396\pi$
$11$	0.698979			0.210750			0.105375	+	0.994433i	$0.466396\pi$
$12$		−	0.541141i		−	0.156214i
$13$		−	5.53802i		−	1.53597i	−0.640468	−	0.767985i	$-0.721259\pi$
$13$		−	5.53802i		−	1.53597i	0.640468	−	0.767985i	$-0.278741\pi$
$14$	1.68539			0.450439
$15$	0.558300	−	4.17618i	0.144152	−	1.07828i
$16$	−3.34314			−0.835785
$17$		−	3.43199i		−	0.832380i	−0.909278	−	0.416190i	$-0.863365\pi$
$17$		−	3.43199i		−	0.832380i	0.909278	−	0.416190i	$-0.136635\pi$
$18$		−	0.720375i		−	0.169794i
$19$	3.98407			0.914009			0.457004	−	0.889464i	$-0.348922\pi$
$19$	3.98407			0.914009			0.457004	+	0.889464i	$0.348922\pi$
$20$	0.636515	+	0.0850936i	0.142329	+	0.0190275i
$21$	−2.42653			−0.529513
$22$			0.914784i			0.195033i
$23$			6.27054i			1.30750i	0.756712	+	0.653749i	$0.226805\pi$
$23$			6.27054i			1.30750i	−0.756712	+	0.653749i	$0.773195\pi$
$24$	5.64024			1.15131
$25$	4.82442	+	1.31339i	0.964883	+	0.262679i
$26$	7.24785			1.42142
$27$		−	4.61562i		−	0.888276i
$28$		−	0.369841i		−	0.0698935i
$29$	−6.15912			−1.14372			−0.571859	−	0.820352i	$-0.693778\pi$
$29$	−6.15912			−1.14372			−0.571859	+	0.820352i	$0.693778\pi$
$30$	5.46555	+	0.730671i	0.997868	+	0.133402i
$31$	−0.212499			−0.0381660			−0.0190830	−	0.999818i	$-0.506075\pi$
$31$	−0.212499			−0.0381660			−0.0190830	+	0.999818i	$0.506075\pi$
$32$			1.61138i			0.284854i
$33$		−	1.31706i		−	0.229270i
$34$	4.49160			0.770302
$35$	0.381568	−	2.85420i	0.0644968	−	0.482447i
$36$	−0.158079			−0.0263465
$37$			5.91052i			0.971683i	0.874047	+	0.485841i	$0.161487\pi$
$37$			5.91052i			0.971683i	−0.874047	+	0.485841i	$0.838513\pi$
$38$			5.21413i			0.845843i
$39$	−10.4351			−1.67095
$40$	−0.886918	+	6.63430i	−0.140234	+	1.04898i
$41$	−9.65382			−1.50767			−0.753837	−	0.657062i	$-0.771799\pi$
$41$	−9.65382			−1.50767			−0.753837	+	0.657062i	$0.771799\pi$
$42$		−	3.17571i		−	0.490023i
$43$		−	7.78957i		−	1.18790i	−0.804502	−	0.593949i	$-0.797568\pi$
$43$		−	7.78957i		−	1.18790i	0.804502	−	0.593949i	$-0.202432\pi$
$44$	0.200740			0.0302627
$45$	−1.21995	−	0.163091i	−0.181860	−	0.0243122i
$46$	−8.20652			−1.20999
$47$		−	3.86035i		−	0.563090i	−0.959548	−	0.281545i	$-0.909153\pi$
$47$		−	3.86035i		−	0.563090i	0.959548	−	0.281545i	$-0.0908469\pi$
$48$			6.29934i			0.909232i
$49$	5.34159			0.763085
$50$	−1.71890	+	6.31392i	−0.243089	+	0.892924i
$51$	−6.46676			−0.905527
$52$		−	1.59047i		−	0.220558i
$53$			10.2480i			1.40767i	0.710361	+	0.703837i	$0.248532\pi$
$53$			10.2480i			1.40767i	−0.710361	+	0.703837i	$0.751468\pi$
$54$	6.04066			0.822030
$55$	1.54918	+	0.207105i	0.208892	+	0.0279260i
$56$	3.85481			0.515120
$57$		−	7.50702i		−	0.994329i
$58$		−	8.06070i		−	1.05842i
$59$	9.54071			1.24209			0.621047	−	0.783773i	$-0.286707\pi$
$59$	9.54071			1.24209			0.621047	+	0.783773i	$0.286707\pi$
$60$	0.160338	−	1.19936i	0.0206996	−	0.154837i
$61$	8.82214			1.12956			0.564779	−	0.825242i	$-0.308961\pi$
$61$	8.82214			1.12956			0.564779	+	0.825242i	$0.308961\pi$
$62$		−	0.278107i		−	0.0353196i
$63$			0.708842i			0.0893057i
$64$	−8.79516			−1.09940
$65$	1.64090	−	12.2742i	0.203528	−	1.52243i
$66$	1.72369			0.212172
$67$		−	7.38392i		−	0.902089i	−0.892501	−	0.451045i	$-0.851052\pi$
$67$		−	7.38392i		−	0.902089i	0.892501	−	0.451045i	$-0.148948\pi$
$68$		−	0.985635i		−	0.119526i
$69$	11.8153			1.42240
$70$	3.73541	+	0.499375i	0.446467	+	0.0596867i
$71$	−6.00088			−0.712174			−0.356087	−	0.934453i	$-0.615889\pi$
$71$	−6.00088			−0.712174			−0.356087	+	0.934453i	$0.615889\pi$
$72$		−	1.64763i		−	0.194176i
$73$		−	2.96121i		−	0.346584i	−0.984870	−	0.173292i	$-0.944560\pi$
$73$		−	2.96121i		−	0.346584i	0.984870	−	0.173292i	$-0.0554404\pi$
$74$	−7.73535			−0.899216
$75$	2.47478	−	9.09045i	0.285762	−	1.04967i
$76$	1.14419			0.131247
$77$		−	0.900139i		−	0.102580i
$78$		−	13.6568i		−	1.54633i
$79$	6.80832			0.765996			0.382998	−	0.923749i	$-0.374892\pi$
$79$	6.80832			0.765996			0.382998	+	0.923749i	$0.374892\pi$
$80$	−7.40957	−	0.990562i	−0.828415	−	0.110748i
$81$	−10.3483			−1.14981
$82$		−	12.6344i		−	1.39523i
$83$			16.1202i			1.76942i	0.466144	+	0.884709i	$0.345643\pi$
$83$			16.1202i			1.76942i	−0.466144	+	0.884709i	$0.654357\pi$
$84$	−0.696877			−0.0760355
$85$	1.01689	−	7.60649i	0.110297	−	0.825040i
$86$	10.1946			1.09931
$87$			11.6054i			1.24423i
$88$			2.09228i			0.223038i
$89$	−1.74849			−0.185340			−0.0926698	−	0.995697i	$-0.529540\pi$
$89$	−1.74849			−0.185340			−0.0926698	+	0.995697i	$0.529540\pi$
$90$	0.213445	−	1.59660i	0.0224990	−	0.168297i
$91$	−7.13182			−0.747617
$92$			1.80084i			0.187750i
$93$			0.400404i			0.0415199i
$94$	5.05221			0.521096
$95$	8.83010	+	1.18047i	0.905949	+	0.121113i
$96$	3.03625			0.309886
$97$		−	0.714461i		−	0.0725425i	−0.999342	−	0.0362713i	$-0.988452\pi$
$97$		−	0.714461i		−	0.0725425i	0.999342	−	0.0362713i	$-0.0115480\pi$
$98$			6.99077i			0.706175i
$99$	−0.384741			−0.0386679
$100$	1.38553	+	0.377194i	0.138553	+	0.0377194i
$101$	−2.31355			−0.230207			−0.115104	−	0.993353i	$-0.536720\pi$
$101$	−2.31355			−0.230207			−0.115104	+	0.993353i	$0.536720\pi$
$102$		−	8.46333i		−	0.837994i
$103$		−	2.90751i		−	0.286485i	−0.989688	−	0.143243i	$-0.954247\pi$
$103$		−	2.90751i		−	0.286485i	0.989688	−	0.143243i	$-0.0457529\pi$
$104$	16.5772			1.62553
$105$	−5.37805	−	0.718974i	−0.524844	−	0.0701646i
$106$	−13.4120			−1.30269
$107$		−	14.8579i		−	1.43637i	−0.695851	−	0.718186i	$-0.744973\pi$
$107$		−	14.8579i		−	1.43637i	0.695851	−	0.718186i	$-0.255027\pi$
$108$		−	1.32556i		−	0.127552i
$109$	11.2125			1.07396			0.536980	−	0.843595i	$-0.319565\pi$
$109$	11.2125			1.07396			0.536980	+	0.843595i	$0.319565\pi$
$110$	−0.271047	+	2.02748i	−0.0258434	+	0.193313i
$111$	11.1369			1.05707
$112$			4.30527i			0.406810i
$113$			15.7753i			1.48402i	0.670390	+	0.742009i	$0.266127\pi$
$113$			15.7753i			1.48402i	−0.670390	+	0.742009i	$0.733873\pi$
$114$	9.82477			0.920174
$115$	−1.85794	+	13.8977i	−0.173254	+	1.29597i
$116$	−1.76884			−0.164233
$117$			3.04831i			0.281816i
$118$			12.4863i			1.14946i
$119$	−4.41969			−0.405152
$120$	12.5007	+	1.67118i	1.14116	+	0.152558i
$121$	−10.5114			−0.955584
$122$			11.5459i			1.04532i
$123$			18.1903i			1.64016i
$124$	−0.0610277			−0.00548045
$125$	10.3034	+	4.34040i	0.921568	+	0.388217i
$126$	−0.927693			−0.0826454
$127$			12.8024i			1.13603i	0.823018	+	0.568016i	$0.192289\pi$
$127$			12.8024i			1.13603i	−0.823018	+	0.568016i	$0.807711\pi$
$128$		−	8.28786i		−	0.732550i
$129$	−14.6776			−1.29229
$130$	16.0638	+	2.14751i	1.40889	+	0.188349i
$131$	−1.22476			−0.107008			−0.0535039	−	0.998568i	$-0.517039\pi$
$131$	−1.22476			−0.107008			−0.0535039	+	0.998568i	$0.517039\pi$
$132$		−	0.378246i		−	0.0329221i
$133$		−	5.13065i		−	0.444884i
$134$	9.66366			0.834813
$135$	1.36759	−	10.2298i	0.117704	−	0.880444i
$136$	10.2731			0.880914
$137$			2.83614i			0.242308i	0.992634	+	0.121154i	$0.0386594\pi$
$137$			2.83614i			0.242308i	−0.992634	+	0.121154i	$0.961341\pi$
$138$			15.4632i			1.31632i
$139$	−2.03279			−0.172419			−0.0862095	−	0.996277i	$-0.527475\pi$
$139$	−2.03279			−0.172419			−0.0862095	+	0.996277i	$0.527475\pi$
$140$	0.109583	−	0.819698i	0.00926144	−	0.0692771i
$141$	−7.27390			−0.612573
$142$		−	7.85362i		−	0.659061i
$143$		−	3.87096i		−	0.323706i
$144$	1.84017			0.153348
$145$	−13.6508	−	1.82493i	−1.13363	−	0.151552i
$146$	3.87547			0.320736
$147$		−	10.0649i		−	0.830143i
$148$			1.69744i			0.139529i
$149$	−21.0260			−1.72252			−0.861259	−	0.508166i	$-0.830324\pi$
$149$	−21.0260			−1.72252			−0.861259	+	0.508166i	$0.830324\pi$
$150$	11.8971	+	3.23885i	0.971392	+	0.264451i
$151$	5.32656			0.433469			0.216735	−	0.976231i	$-0.430459\pi$
$151$	5.32656			0.433469			0.216735	+	0.976231i	$0.430459\pi$
$152$			11.9257i			0.967302i
$153$			1.88908i			0.152723i
$154$	1.17805			0.0949300
$155$	−0.470973	−	0.0629628i	−0.0378294	−	0.00505729i
$156$	−2.99685			−0.239940
$157$			16.8020i			1.34094i	0.741936	+	0.670471i	$0.233908\pi$
$157$			16.8020i			1.34094i	−0.741936	+	0.670471i	$0.766092\pi$
$158$			8.91035i			0.708869i
$159$	19.3099			1.53138
$160$	−0.477446	+	3.57138i	−0.0377454	+	0.282342i
$161$	8.07514			0.636410
$162$		−	13.5433i		−	1.06406i
$163$		−	6.28719i		−	0.492450i	−0.969213	−	0.246225i	$-0.920810\pi$
$163$		−	6.28719i		−	0.492450i	0.969213	−	0.246225i	$-0.0791903\pi$
$164$	−2.77249			−0.216495
$165$	0.390240	−	2.91906i	0.0303801	−	0.227248i
$166$	−21.0972			−1.63746
$167$		−	15.4202i		−	1.19325i	−0.802519	−	0.596626i	$-0.796508\pi$
$167$		−	15.4202i		−	1.19325i	0.802519	−	0.596626i	$-0.203492\pi$
$168$		−	7.26345i		−	0.560387i
$169$	−17.6697			−1.35921
$170$	9.95495	+	1.33084i	0.763510	+	0.102071i
$171$	−2.19296			−0.167700
$172$		−	2.23709i		−	0.170577i
$173$			3.72835i			0.283461i	0.989905	+	0.141731i	$0.0452667\pi$
$173$			3.72835i			0.283461i	−0.989905	+	0.141731i	$0.954733\pi$
$174$	−15.1885			−1.15143
$175$	1.69138	−	6.21284i	0.127856	−	0.469647i
$176$	−2.33678			−0.176142
$177$		−	17.9772i		−	1.35125i
$178$		−	2.28833i		−	0.171517i
$179$	−10.9282			−0.816811			−0.408405	−	0.912801i	$-0.633915\pi$
$179$	−10.9282			−0.816811			−0.408405	+	0.912801i	$0.633915\pi$
$180$	−0.350358	−	0.0468383i	−0.0261142	−	0.00349112i
$181$	12.6140			0.937590			0.468795	−	0.883307i	$-0.344688\pi$
$181$	12.6140			0.937590			0.468795	+	0.883307i	$0.344688\pi$
$182$		−	9.33372i		−	0.691861i
$183$		−	16.6232i		−	1.22882i
$184$	−18.7699			−1.38373
$185$	−1.75127	+	13.0998i	−0.128756	+	0.963114i
$186$	−0.524026			−0.0384234
$187$		−	2.39889i		−	0.175424i
$188$		−	1.10866i		−	0.0808571i
$189$	−5.94396			−0.432359
$190$	−1.54493	+	11.5563i	−0.112081	+	0.838384i
$191$	14.4657			1.04670			0.523349	−	0.852118i	$-0.324682\pi$
$191$	14.4657			1.04670			0.523349	+	0.852118i	$0.324682\pi$
$192$			16.5724i			1.19601i
$193$			8.80554i			0.633837i	0.948453	+	0.316918i	$0.102648\pi$
$193$			8.80554i			0.633837i	−0.948453	+	0.316918i	$0.897352\pi$
$194$	0.935046			0.0671324
$195$	−23.1278	−	3.09188i	−1.65621	−	0.221414i
$196$	1.53405			0.109575
$197$			20.3391i			1.44910i	0.689220	+	0.724552i	$0.257953\pi$
$197$			20.3391i			1.44910i	−0.689220	+	0.724552i	$0.742047\pi$
$198$		−	0.503527i		−	0.0357841i
$199$	−18.6435			−1.32160			−0.660800	−	0.750562i	$-0.729783\pi$
$199$	−18.6435			−1.32160			−0.660800	+	0.750562i	$0.729783\pi$
$200$	−3.93144	+	14.4411i	−0.277995	+	1.02114i
$201$	−13.9132			−0.981363
$202$		−	3.02785i		−	0.213039i
$203$			7.93166i			0.556693i
$204$	−1.85719			−0.130029
$205$	−21.3962	−	2.86040i	−1.49438	−	0.199779i
$206$	3.80518			0.265120
$207$		−	3.45151i		−	0.239896i
$208$			18.5144i			1.28374i
$209$	2.78478			0.192627
$210$	0.940952	−	7.03848i	0.0649319	−	0.485702i
$211$	−9.60455			−0.661205			−0.330602	−	0.943770i	$-0.607252\pi$
$211$	−9.60455			−0.661205			−0.330602	+	0.943770i	$0.607252\pi$
$212$			2.94314i			0.202135i
$213$			11.3072i			0.774758i
$214$	19.4452			1.32925
$215$	2.30802	−	17.2644i	0.157406	−	1.17742i
$216$	13.8161			0.940070
$217$			0.273655i			0.0185769i
$218$			14.6743i			0.993866i
$219$	−5.57970			−0.377041
$220$	0.444910	+	0.0594786i	0.0299958	+	0.00401005i
$221$	−19.0064			−1.27851
$222$			14.5754i			0.978237i
$223$			21.8910i			1.46593i	0.680265	+	0.732967i	$0.261865\pi$
$223$			21.8910i			1.46593i	−0.680265	+	0.732967i	$0.738135\pi$
$224$	2.07512			0.138650
$225$	−2.65552	−	0.722935i	−0.177034	−	0.0481957i
$226$	−20.6459			−1.37334
$227$		−	25.5764i		−	1.69757i	−0.528742	−	0.848783i	$-0.677336\pi$
$227$		−	25.5764i		−	1.69757i	0.528742	−	0.848783i	$-0.322664\pi$
$228$		−	2.15595i		−	0.142781i
$229$	−17.6417			−1.16580			−0.582899	−	0.812544i	$-0.698082\pi$
$229$	−17.6417			−1.16580			−0.582899	+	0.812544i	$0.698082\pi$
$230$	−18.1885	−	2.43157i	−1.19932	−	0.160333i
$231$	−1.69609			−0.111595
$232$		−	18.4364i		−	1.21041i
$233$			9.74499i			0.638416i	0.947685	+	0.319208i	$0.103417\pi$
$233$			9.74499i			0.638416i	−0.947685	+	0.319208i	$0.896583\pi$
$234$	−3.98945			−0.260799
$235$	1.14381	−	8.55589i	0.0746139	−	0.558125i
$236$	2.74000			0.178359
$237$		−	12.8286i		−	0.833310i
$238$		−	5.78424i		−	0.374936i
$239$	29.1323			1.88441			0.942205	−	0.335037i	$-0.108749\pi$
$239$	29.1323			1.88441			0.942205	+	0.335037i	$0.108749\pi$
$240$	−1.86647	+	13.9616i	−0.120480	+	0.901214i
$241$	1.00000			0.0644157
$241$	1.00000			0.0644157
$242$		−	13.7568i		−	0.884318i
$243$			5.65206i			0.362580i
$244$	2.53363			0.162199
$245$	11.8388	+	1.58270i	0.756356	+	0.101115i
$246$	−23.8064			−1.51784
$247$		−	22.0639i		−	1.40389i
$248$		−	0.636084i		−	0.0403913i
$249$	30.3746			1.92491
$250$	−5.68047	+	13.4846i	−0.359265	+	0.852839i
$251$	17.9810			1.13495			0.567474	−	0.823391i	$-0.307921\pi$
$251$	17.9810			1.13495			0.567474	+	0.823391i	$0.307921\pi$
$252$			0.203573i			0.0128239i
$253$			4.38297i			0.275555i
$254$	−16.7551			−1.05131
$255$	−14.3326	−	1.91608i	−0.897542	−	0.119990i
$256$	−6.74365			−0.421478
$257$			20.0744i			1.25221i	0.779739	+	0.626105i	$0.215352\pi$
$257$			20.0744i			1.25221i	−0.779739	+	0.626105i	$0.784648\pi$
$258$		−	19.2092i		−	1.19591i
$259$	7.61151			0.472956
$260$	0.471250	−	3.52503i	0.0292257	−	0.218613i
$261$	3.39018			0.209847
$262$		−	1.60290i		−	0.0990273i
$263$		−	15.6319i		−	0.963906i	−0.876197	−	0.481953i	$-0.839928\pi$
$263$		−	15.6319i		−	0.963906i	0.876197	−	0.481953i	$-0.160072\pi$
$264$	3.94241			0.242638
$265$	−3.03646	+	22.7132i	−0.186528	+	1.39526i
$266$	6.71471			0.411705
$267$			3.29461i			0.201627i
$268$		−	2.12059i		−	0.129536i
$269$	−22.2853			−1.35876			−0.679379	−	0.733787i	$-0.737751\pi$
$269$	−22.2853			−1.35876			−0.679379	+	0.733787i	$0.737751\pi$
$270$	13.3882	+	1.78983i	0.814781	+	0.108925i
$271$	−19.6867			−1.19588			−0.597939	−	0.801541i	$-0.704014\pi$
$271$	−19.6867			−1.19588			−0.597939	+	0.801541i	$0.704014\pi$
$272$			11.4736i			0.695691i
$273$			13.4382i			0.813316i
$274$	−3.71178			−0.224237
$275$	3.37216	+	0.918035i	0.203349	+	0.0553596i
$276$	3.39325			0.204249
$277$			19.8218i			1.19097i	0.803365	+	0.595487i	$0.203041\pi$
$277$			19.8218i			1.19097i	−0.803365	+	0.595487i	$0.796959\pi$
$278$		−	2.66040i		−	0.159560i
$279$	0.116966			0.00700260
$280$	8.54360	+	1.14217i	0.510578	+	0.0682575i
$281$	−25.1818			−1.50222			−0.751111	−	0.660176i	$-0.770482\pi$
$281$	−25.1818			−1.50222			−0.751111	+	0.660176i	$0.770482\pi$
$282$		−	9.51967i		−	0.566888i
$283$			1.69555i			0.100790i	0.998729	+	0.0503950i	$0.0160480\pi$
$283$			1.69555i			0.100790i	−0.998729	+	0.0503950i	$0.983952\pi$
$284$	−1.72340			−0.102265
$285$	2.22431	−	16.6382i	0.131757	−	0.985561i
$286$	5.06609			0.299564
$287$			12.4321i			0.733844i
$288$		−	0.886955i		−	0.0522643i
$289$	5.22144			0.307144
$290$	2.38836	−	17.8653i	0.140249	−	1.04909i
$291$	−1.34623			−0.0789174
$292$		−	0.850433i		−	0.0497678i
$293$			21.2874i			1.24362i	0.783167	+	0.621811i	$0.213603\pi$
$293$			21.2874i			1.24362i	−0.783167	+	0.621811i	$0.786397\pi$
$294$	13.1724			0.768232
$295$	21.1456	+	2.82688i	1.23114	+	0.164587i
$296$	−17.6922			−1.02834
$297$		−	3.22622i		−	0.187204i
$298$		−	27.5177i		−	1.59405i
$299$	34.7264			2.00828
$300$	0.710732	−	2.61069i	0.0410341	−	0.150728i
$301$	−10.0313			−0.578197
$302$			6.97110i			0.401142i
$303$			4.35933i			0.250437i
$304$	−13.3193			−0.763915
$305$	19.5529	+	2.61397i	1.11960	+	0.149675i
$306$	−2.47232			−0.141333
$307$			17.5022i			0.998901i	0.866342	+	0.499450i	$0.166465\pi$
$307$			17.5022i			0.998901i	−0.866342	+	0.499450i	$0.833535\pi$
$308$		−	0.258511i		−	0.0147300i
$309$	−5.47850			−0.311661
$310$	0.0824022	−	0.616382i	0.00468013	−	0.0350082i
$311$	−27.1108			−1.53732			−0.768658	−	0.639661i	$-0.779075\pi$
$311$	−27.1108			−1.53732			−0.768658	+	0.639661i	$0.779075\pi$
$312$		−	31.2358i		−	1.76838i
$313$		−	5.43613i		−	0.307268i	−0.988128	−	0.153634i	$-0.950902\pi$
$313$		−	5.43613i		−	0.307268i	0.988128	−	0.153634i	$-0.0490977\pi$
$314$	−21.9894			−1.24094
$315$	−0.210028	+	1.57104i	−0.0118337	+	0.0885182i
$316$	1.95528			0.109993
$317$		−	1.24021i		−	0.0696573i	−0.999393	−	0.0348287i	$-0.988911\pi$
$317$		−	1.24021i		−	0.0696573i	0.999393	−	0.0348287i	$-0.0110886\pi$
$318$			25.2718i			1.41717i
$319$	−4.30509			−0.241039
$320$	−19.4932	−	2.60598i	−1.08970	−	0.145679i
$321$	−27.9962			−1.56260
$322$			10.5683i			0.588948i
$323$		−	13.6733i		−	0.760802i
$324$	−2.97194			−0.165108
$325$	7.27360	−	26.7177i	0.403467	−	1.48203i
$326$	8.22831			0.455724
$327$		−	21.1272i		−	1.16834i
$328$		−	28.8972i		−	1.59558i
$329$	−4.97133			−0.274078
$330$	3.82030	+	0.510724i	0.210301	+	0.0281144i
$331$	−13.6324			−0.749307			−0.374654	−	0.927165i	$-0.622238\pi$
$331$	−13.6324			−0.749307			−0.374654	+	0.927165i	$0.622238\pi$
$332$			4.62956i			0.254080i
$333$		−	3.25334i		−	0.178282i
$334$	20.1811			1.10426
$335$	2.18783	−	16.3654i	0.119534	−	0.894135i
$336$	8.11224			0.442559
$337$			9.45300i			0.514938i	0.966287	+	0.257469i	$0.0828885\pi$
$337$			9.45300i			0.514938i	−0.966287	+	0.257469i	$0.917112\pi$
$338$		−	23.1251i		−	1.25784i
$339$	29.7248			1.61443
$340$	0.292040	−	2.18451i	0.0158381	−	0.118472i
$341$	−0.148532			−0.00804348
$342$		−	2.87002i		−	0.155193i
$343$		−	15.8934i		−	0.858163i
$344$	23.3169			1.25716
$345$	26.1869	+	3.50084i	1.40985	+	0.188479i
$346$	−4.87945			−0.262321
$347$			25.8641i			1.38846i	0.719754	+	0.694230i	$0.244255\pi$
$347$			25.8641i			1.38846i	−0.719754	+	0.694230i	$0.755745\pi$
$348$			3.33295i			0.178665i
$349$	−10.7675			−0.576372			−0.288186	−	0.957575i	$-0.593052\pi$
$349$	−10.7675			−0.576372			−0.288186	+	0.957575i	$0.593052\pi$
$350$	8.13102	+	2.21358i	0.434621	+	0.118321i
$351$	−25.5614			−1.36437
$352$			1.12632i			0.0600330i
$353$		−	29.7801i		−	1.58504i	−0.609848	−	0.792518i	$-0.708770\pi$
$353$		−	29.7801i		−	1.58504i	0.609848	−	0.792518i	$-0.291230\pi$
$354$	23.5275			1.25047
$355$	−13.3001	−	1.77804i	−0.705894	−	0.0943686i
$356$	−0.502150			−0.0266139
$357$			8.32784i			0.440756i
$358$		−	14.3022i		−	0.755894i
$359$	−9.88958			−0.521952			−0.260976	−	0.965345i	$-0.584044\pi$
$359$	−9.88958			−0.521952			−0.260976	+	0.965345i	$0.584044\pi$
$360$	0.488189	−	3.65174i	0.0257298	−	0.192463i
$361$	−3.12718			−0.164588
$362$			16.5085i			0.867666i
$363$			19.8063i			1.03956i
$364$	−2.04819			−0.107354
$365$	0.877398	−	6.56309i	0.0459251	−	0.343528i
$366$	21.7555			1.13718
$367$		−	24.3156i		−	1.26926i	−0.772815	−	0.634631i	$-0.781152\pi$
$367$		−	24.3156i		−	1.26926i	0.772815	−	0.634631i	$-0.218848\pi$
$368$		−	20.9633i		−	1.09279i
$369$	5.31378			0.276624
$370$	−17.1442	−	2.29196i	−0.891287	−	0.119153i
$371$	13.1973			0.685171
$372$			0.114992i			0.00596206i
$373$		−	6.98503i		−	0.361671i	−0.983513	−	0.180836i	$-0.942120\pi$
$373$		−	6.98503i		−	0.361671i	0.983513	−	0.180836i	$-0.0578802\pi$
$374$	3.13953			0.162341
$375$	8.17844	−	19.4144i	0.422333	−	1.00255i
$376$	11.5554			0.595923
$377$			34.1093i			1.75672i
$378$		−	7.77911i		−	0.400114i
$379$	−24.8142			−1.27462			−0.637309	−	0.770608i	$-0.719953\pi$
$379$	−24.8142			−1.27462			−0.637309	+	0.770608i	$0.719953\pi$
$380$	2.53592	+	0.339019i	0.130090	+	0.0173913i
$381$	24.1231			1.23586
$382$			18.9318i			0.968637i
$383$		−	7.88965i		−	0.403142i	−0.979474	−	0.201571i	$-0.935395\pi$
$383$		−	7.88965i		−	0.403142i	0.979474	−	0.201571i	$-0.0646047\pi$
$384$	−15.6165			−0.796924
$385$	0.266708	−	1.99502i	0.0135927	−	0.101676i
$386$	−11.5242			−0.586566
$387$			4.28763i			0.217953i
$388$		−	0.205186i		−	0.0104168i
$389$	18.8488			0.955670			0.477835	−	0.878450i	$-0.341422\pi$
$389$	18.8488			0.955670			0.477835	+	0.878450i	$0.341422\pi$
$390$	4.04647	−	30.2683i	0.204901	−	1.53270i
$391$	21.5204			1.08833
$392$			15.9892i			0.807578i
$393$			2.30776i			0.116411i
$394$	−26.6187			−1.34103
$395$	15.0896	+	2.01728i	0.759241	+	0.101501i
$396$	−0.110494			−0.00555252
$397$		−	0.758306i		−	0.0380583i	−0.999819	−	0.0190292i	$-0.993942\pi$
$397$		−	0.758306i		−	0.0380583i	0.999819	−	0.0190292i	$-0.00605753\pi$
$398$		−	24.3995i		−	1.22304i
$399$	−9.66748			−0.483979
$400$	−16.1287	−	4.39086i	−0.806435	−	0.219543i
$401$	−34.8303			−1.73934			−0.869672	−	0.493629i	$-0.835670\pi$
$401$	−34.8303			−1.73934			−0.869672	+	0.493629i	$0.835670\pi$
$402$		−	18.2088i		−	0.908174i
$403$			1.17682i			0.0586218i
$404$	−0.664431			−0.0330567
$405$	−22.9355	−	3.06617i	−1.13967	−	0.152359i
$406$	−10.3805			−0.515176
$407$			4.13132i			0.204782i
$408$		−	19.3572i		−	0.958326i
$409$	−17.3471			−0.857760			−0.428880	−	0.903361i	$-0.641092\pi$
$409$	−17.3471			−0.857760			−0.428880	+	0.903361i	$0.641092\pi$
$410$	3.74352	−	28.0022i	0.184879	−	1.38293i
$411$	5.34402			0.263601
$412$		−	0.835008i		−	0.0411379i
$413$		−	12.2864i		−	0.604576i
$414$	4.51714			0.222005
$415$	−4.77635	+	35.7279i	−0.234462	+	1.75381i
$416$	8.92384			0.437527
$417$			3.83031i			0.187571i
$418$			3.64456i			0.178261i
$419$	22.5895			1.10357			0.551786	−	0.833986i	$-0.313947\pi$
$419$	22.5895			1.10357			0.551786	+	0.833986i	$0.313947\pi$
$420$	−1.54452	−	0.206482i	−0.0753650	−	0.0100753i
$421$	−27.8005			−1.35491			−0.677457	−	0.735563i	$-0.736918\pi$
$421$	−27.8005			−1.35491			−0.677457	+	0.735563i	$0.736918\pi$
$422$		−	12.5699i		−	0.611893i
$423$			2.12486i			0.103314i
$424$	−30.6759			−1.48975
$425$	4.50756	−	16.5574i	0.218649	−	0.803150i
$426$	−14.7982			−0.716977
$427$		−	11.3611i		−	0.549801i
$428$		−	4.26706i		−	0.206256i
$429$	−7.29389			−0.352152
$430$	22.5947	+	3.02061i	1.08961	+	0.145667i
$431$	−17.6040			−0.847957			−0.423978	−	0.905672i	$-0.639367\pi$
$431$	−17.6040			−0.847957			−0.423978	+	0.905672i	$0.639367\pi$
$432$			15.4307i			0.742408i
$433$		−	7.38130i		−	0.354723i	−0.984146	−	0.177361i	$-0.943244\pi$
$433$		−	7.38130i		−	0.354723i	0.984146	−	0.177361i	$-0.0567561\pi$
$434$	−0.358144			−0.0171915
$435$	−3.43863	+	25.7216i	−0.164870	+	1.23325i
$436$	3.22012			0.154216
$437$			24.9823i			1.19506i
$438$		−	7.30239i		−	0.348922i
$439$	−2.17048			−0.103591			−0.0517956	−	0.998658i	$-0.516494\pi$
$439$	−2.17048			−0.103591			−0.0517956	+	0.998658i	$0.516494\pi$
$440$	−0.619937	+	4.63724i	−0.0295543	+	0.221072i
$441$	−2.94019			−0.140009
$442$		−	24.8745i		−	1.18316i
$443$			12.7026i			0.603518i	0.953384	+	0.301759i	$0.0975738\pi$
$443$			12.7026i			0.603518i	−0.953384	+	0.301759i	$0.902426\pi$
$444$	3.19842			0.151790
$445$	−3.87527	−	0.518072i	−0.183705	−	0.0245590i
$446$	−28.6498			−1.35661
$447$			39.6185i			1.87389i
$448$			11.3263i			0.535119i
$449$	4.30823			0.203318			0.101659	−	0.994819i	$-0.467585\pi$
$449$	4.30823			0.203318			0.101659	+	0.994819i	$0.467585\pi$
$450$	0.946136	−	3.47539i	0.0446013	−	0.163831i
$451$	−6.74781			−0.317742
$452$			4.53052i			0.213098i
$453$		−	10.0366i		−	0.471561i
$454$	33.4730			1.57096
$455$	−15.8066	−	2.11313i	−0.741025	−	0.0990652i
$456$	22.4711			1.05231
$457$			3.68356i			0.172310i	0.996282	+	0.0861548i	$0.0274580\pi$
$457$			3.68356i			0.172310i	−0.996282	+	0.0861548i	$0.972542\pi$
$458$		−	23.0885i		−	1.07886i
$459$	−15.8408			−0.739384
$460$	−0.533582	+	3.99129i	−0.0248784	+	0.186095i
$461$	37.3221			1.73826			0.869131	−	0.494582i	$-0.164679\pi$
$461$	37.3221			1.73826			0.869131	+	0.494582i	$0.164679\pi$
$462$		−	2.21975i		−	0.103272i
$463$		−	12.4345i		−	0.577880i	−0.957347	−	0.288940i	$-0.906697\pi$
$463$		−	12.4345i		−	0.577880i	0.957347	−	0.288940i	$-0.0933027\pi$
$464$	20.5908			0.955903
$465$	−0.118638	+	0.887435i	−0.00550172	+	0.0411538i
$466$	−12.7537			−0.590804
$467$		−	3.71254i		−	0.171796i	−0.996304	−	0.0858980i	$-0.972624\pi$
$467$		−	3.71254i		−	0.171796i	0.996304	−	0.0858980i	$-0.0273759\pi$
$468$			0.875444i			0.0404674i
$469$	−9.50895			−0.439082
$470$	11.1975	+	1.49695i	0.516501	+	0.0690493i
$471$	31.6592			1.45878
$472$			28.5586i			1.31452i
$473$		−	5.44475i		−	0.250350i
$474$	16.7894			0.771163
$475$	19.2208	+	5.23266i	0.881912	+	0.240091i
$476$	−1.26929			−0.0581779
$477$		−	5.64085i		−	0.258277i
$478$			38.1267i			1.74387i
$479$	32.8371			1.50036			0.750182	−	0.661231i	$-0.229966\pi$
$479$	32.8371			1.50036			0.750182	+	0.661231i	$0.229966\pi$
$480$	6.72940	+	0.899632i	0.307154	+	0.0410624i
$481$	32.7326			1.49248
$482$			1.30874i			0.0596116i
$483$		−	15.2157i		−	0.692337i
$484$	−3.01878			−0.137217
$485$	0.211692	−	1.58350i	0.00961246	−	0.0719028i
$486$	−7.39710			−0.335539
$487$			27.1109i			1.22851i	0.789107	+	0.614256i	$0.210544\pi$
$487$			27.1109i			1.22851i	−0.789107	+	0.614256i	$0.789456\pi$
$488$			26.4077i			1.19542i
$489$	−11.8467			−0.535726
$490$	−2.07134	+	15.4940i	−0.0935738	+	0.699948i
$491$	−6.70831			−0.302742			−0.151371	−	0.988477i	$-0.548369\pi$
$491$	−6.70831			−0.302742			−0.151371	+	0.988477i	$0.548369\pi$
$492$			5.22408i			0.235520i
$493$			21.1380i			0.952009i
$494$	28.8759			1.29919
$495$	−0.852720	−	0.113997i	−0.0383269	−	0.00512380i
$496$	0.710415			0.0318986
$497$			7.72789i			0.346643i
$498$			39.7525i			1.78135i
$499$	33.9775			1.52104			0.760520	−	0.649314i	$-0.224944\pi$
$499$	33.9775			1.52104			0.760520	+	0.649314i	$0.224944\pi$
$500$	2.95905	+	1.24652i	0.132333	+	0.0557461i
$501$	−29.0557			−1.29811
$502$			23.5325i			1.05031i
$503$		−	6.74907i		−	0.300926i	−0.988616	−	0.150463i	$-0.951924\pi$
$503$		−	6.74907i		−	0.300926i	0.988616	−	0.150463i	$-0.0480764\pi$
$504$	−2.12181			−0.0945129
$505$	−5.12765	−	0.685498i	−0.228177	−	0.0305043i
$506$	−5.73618			−0.255005
$507$			33.2942i			1.47865i
$508$			3.67674i			0.163129i
$509$	5.20927			0.230897			0.115448	−	0.993313i	$-0.463169\pi$
$509$	5.20927			0.230897			0.115448	+	0.993313i	$0.463169\pi$
$510$	2.50766	−	18.7577i	0.111041	−	0.830605i
$511$	−3.81343			−0.168696
$512$		−	25.4014i		−	1.12259i
$513$		−	18.3890i		−	0.811892i
$514$	−26.2723			−1.15882
$515$	0.861485	−	6.44406i	0.0379616	−	0.283959i
$516$	−4.21526			−0.185566
$517$		−	2.69830i		−	0.118671i
$518$			9.96152i			0.437684i
$519$	7.02518			0.308371
$520$	36.7409	+	4.91177i	1.61120	+	0.215395i
$521$	4.39792			0.192676			0.0963382	−	0.995349i	$-0.469287\pi$
$521$	4.39792			0.192676			0.0963382	+	0.995349i	$0.469287\pi$
$522$			4.43687i			0.194197i
$523$		−	28.7186i		−	1.25578i	−0.778303	−	0.627889i	$-0.783919\pi$
$523$		−	28.7186i		−	1.25578i	0.778303	−	0.627889i	$-0.216081\pi$
$524$	−0.351739			−0.0153658
$525$	−11.7066	−	3.18699i	−0.510918	−	0.139092i
$526$	20.4582			0.892019
$527$			0.729295i			0.0317686i
$528$			4.40311i			0.191621i
$529$	−16.3196			−0.709549
$530$	−29.7258	−	3.97394i	−1.29120	−	0.172617i
$531$	−5.25152			−0.227896
$532$		−	1.47347i		−	0.0638832i
$533$			53.4631i			2.31574i
$534$	−4.31180			−0.186590
$535$	4.40236	−	32.9304i	0.190331	−	1.42371i
$536$	22.1026			0.954688
$537$			20.5915i			0.888590i
$538$		−	29.1657i		−	1.25742i
$539$	3.73366			0.160820
$540$	0.392760	−	2.93791i	0.0169017	−	0.126428i
$541$	−11.5157			−0.495099			−0.247549	−	0.968875i	$-0.579625\pi$
$541$	−11.5157			−0.495099			−0.247549	+	0.968875i	$0.579625\pi$
$542$		−	25.7648i		−	1.10669i
$543$		−	23.7680i		−	1.01998i
$544$	5.53023			0.237107
$545$	24.8508	+	3.32222i	1.06449	+	0.142308i
$546$	−17.5871			−0.752660
$547$		−	1.46564i		−	0.0626662i	−0.999509	−	0.0313331i	$-0.990025\pi$
$547$		−	1.46564i		−	0.0626662i	0.999509	−	0.0313331i	$-0.00997527\pi$
$548$			0.814512i			0.0347942i
$549$	−4.85599			−0.207249
$550$	−1.20147	+	4.41330i	−0.0512309	+	0.188184i
$551$	−24.5384			−1.04537
$552$			35.3673i			1.50533i
$553$		−	8.76770i		−	0.372840i
$554$	−25.9416			−1.10215
$555$	24.6834	+	3.29984i	1.04775	+	0.140070i
$556$	−0.583798			−0.0247586
$557$		−	9.02751i		−	0.382508i	−0.981541	−	0.191254i	$-0.938745\pi$
$557$		−	9.02751i		−	0.382508i	0.981541	−	0.191254i	$-0.0612554\pi$
$558$			0.153079i			0.00648035i
$559$	−43.1388			−1.82458
$560$	−1.27564	+	9.54198i	−0.0539055	+	0.403222i
$561$	−4.52013			−0.190840
$562$		−	32.9566i		−	1.39019i
$563$		−	1.03855i		−	0.0437698i	−0.999760	−	0.0218849i	$-0.993033\pi$
$563$		−	1.03855i		−	0.0437698i	0.999760	−	0.0218849i	$-0.00696674\pi$
$564$	−2.08900			−0.0879626
$565$	−4.67418	+	34.9636i	−0.196644	+	1.47093i
$566$	−2.21904			−0.0932732
$567$			13.3265i			0.559660i
$568$		−	17.9627i		−	0.753699i
$569$	16.4700			0.690458			0.345229	−	0.938519i	$-0.387801\pi$
$569$	16.4700			0.690458			0.345229	+	0.938519i	$0.387801\pi$
$570$	21.7751	+	2.91105i	0.912060	+	0.121930i
$571$	34.2521			1.43341			0.716703	−	0.697378i	$-0.245650\pi$
$571$	34.2521			1.43341			0.716703	+	0.697378i	$0.245650\pi$
$572$		−	1.11170i		−	0.0464826i
$573$		−	27.2570i		−	1.13868i
$574$	−16.2704			−0.679115
$575$	−8.23569	+	30.2517i	−0.343452	+	1.26158i
$576$	4.84114			0.201714
$577$			3.72767i			0.155185i	0.996985	+	0.0775924i	$0.0247233\pi$
$577$			3.72767i			0.155185i	−0.996985	+	0.0775924i	$0.975277\pi$
$578$			6.83353i			0.284237i
$579$	16.5919			0.689537
$580$	−3.92037	−	0.524101i	−0.162784	−	0.0217621i
$581$	20.7594			0.861245
$582$		−	1.76187i		−	0.0730318i
$583$			7.16315i			0.296667i
$584$	8.86394			0.366792
$585$	−0.903203	+	6.75611i	−0.0373428	+	0.279331i
$586$	−27.8597			−1.15088
$587$			29.8715i			1.23293i	0.787383	+	0.616464i	$0.211435\pi$
$587$			29.8715i			1.23293i	−0.787383	+	0.616464i	$0.788565\pi$
$588$		−	2.89056i		−	0.119205i
$589$	−0.846612			−0.0348840
$590$	−3.69966	+	27.6741i	−0.152313	+	1.13932i
$591$	38.3242			1.57645
$592$		−	19.7597i		−	0.812118i
$593$		−	37.2358i		−	1.52909i	−0.644569	−	0.764546i	$-0.722963\pi$
$593$		−	37.2358i		−	1.52909i	0.644569	−	0.764546i	$-0.277037\pi$
$594$	4.22229			0.173243
$595$	−9.79558	−	1.30954i	−0.401580	−	0.0536859i
$596$	−6.03847			−0.247345
$597$			35.1291i			1.43774i
$598$			45.4479i			1.85850i
$599$	14.2870			0.583753			0.291877	−	0.956456i	$-0.405720\pi$
$599$	14.2870			0.583753			0.291877	+	0.956456i	$0.405720\pi$
$600$	27.2109	+	7.40786i	1.11088	+	0.302425i
$601$	−5.96440			−0.243293			−0.121647	−	0.992573i	$-0.538817\pi$
$601$	−5.96440			−0.243293			−0.121647	+	0.992573i	$0.538817\pi$
$602$		−	13.1285i		−	0.535076i
$603$			4.06435i			0.165513i
$604$	1.52974			0.0622441
$605$	−23.2970	−	3.11450i	−0.947158	−	0.126622i
$606$	−5.70525			−0.231760
$607$		−	2.52516i		−	0.102493i	−0.998686	−	0.0512466i	$-0.983681\pi$
$607$		−	2.52516i		−	0.102493i	0.998686	−	0.0512466i	$-0.0163194\pi$
$608$			6.41984i			0.260359i
$609$	14.9453			0.605614
$610$	−3.42102	+	25.5898i	−0.138513	+	1.03610i
$611$	−21.3787			−0.864890
$612$			0.542525i			0.0219303i
$613$			9.04094i			0.365160i	0.983191	+	0.182580i	$0.0584449\pi$
$613$			9.04094i			0.365160i	−0.983191	+	0.182580i	$0.941555\pi$
$614$	−22.9058			−0.924404
$615$	−5.38973	+	40.3161i	−0.217335	+	1.62570i
$616$	2.69443			0.108562
$617$			38.5569i			1.55224i	0.630585	+	0.776120i	$0.282815\pi$
$617$			38.5569i			1.55224i	−0.630585	+	0.776120i	$0.717185\pi$
$618$		−	7.16995i		−	0.288418i
$619$	18.0419			0.725166			0.362583	−	0.931951i	$-0.381895\pi$
$619$	18.0419			0.725166			0.362583	+	0.931951i	$0.381895\pi$
$620$	−0.135259	−	0.0180823i	−0.00543213	−	0.000726203i
$621$	28.9424			1.16142
$622$		−	35.4811i		−	1.42266i
$623$			2.25169i			0.0902121i
$624$	34.8859			1.39655
$625$	21.5500	+	12.6727i	0.862000	+	0.506909i
$626$	7.11449			0.284352
$627$		−	5.24725i		−	0.209555i
$628$			4.82536i			0.192553i
$629$	20.2848			0.808809
$630$	−2.05609	−	0.274872i	−0.0819167	−	0.0109512i
$631$	−4.00131			−0.159290			−0.0796448	−	0.996823i	$-0.525379\pi$
$631$	−4.00131			−0.159290			−0.0796448	+	0.996823i	$0.525379\pi$
$632$			20.3797i			0.810659i
$633$			18.0975i			0.719310i
$634$	1.62312			0.0644624
$635$	−3.79332	+	28.3747i	−0.150533	+	1.12601i
$636$	5.54563			0.219899
$637$		−	29.5818i		−	1.17208i
$638$		−	5.63426i		−	0.223062i
$639$	3.30308			0.130668
$640$	2.45566	−	18.3688i	0.0970686	−	0.726090i
$641$	48.4959			1.91547			0.957736	−	0.287650i	$-0.0928741\pi$
$641$	48.4959			1.91547			0.957736	+	0.287650i	$0.0928741\pi$
$642$		−	36.6399i		−	1.44606i
$643$		−	24.8486i		−	0.979935i	−0.871741	−	0.489967i	$-0.837009\pi$
$643$		−	24.8486i		−	0.979935i	0.871741	−	0.489967i	$-0.162991\pi$
$644$	2.31910			0.0913855
$645$	−32.5306	−	4.34892i	−1.28089	−	0.171238i
$646$	17.8948			0.704063
$647$			43.2159i			1.69899i	0.527595	+	0.849496i	$0.323094\pi$
$647$			43.2159i			1.69899i	−0.527595	+	0.849496i	$0.676906\pi$
$648$		−	30.9761i		−	1.21686i
$649$	6.66875			0.261771
$650$	34.9666	+	9.51928i	1.37150	+	0.373377i
$651$	0.515636			0.0202094
$652$		−	1.80562i		−	0.0707135i
$653$		−	1.40884i		−	0.0551323i	−0.999620	−	0.0275662i	$-0.991224\pi$
$653$		−	1.40884i		−	0.0551323i	0.999620	−	0.0275662i	$-0.00877570\pi$
$654$	27.6501			1.08120
$655$	−2.71450	−	0.362892i	−0.106064	−	0.0141794i
$656$	32.2741			1.26009
$657$			1.62995i			0.0635904i
$658$		−	6.50619i		−	0.253638i
$659$	4.34247			0.169158			0.0845792	−	0.996417i	$-0.473045\pi$
$659$	4.34247			0.169158			0.0845792	+	0.996417i	$0.473045\pi$
$660$	0.112073	−	0.838326i	0.00436244	−	0.0326318i
$661$	26.3595			1.02527			0.512633	−	0.858608i	$-0.328670\pi$
$661$	26.3595			1.02527			0.512633	+	0.858608i	$0.328670\pi$
$662$		−	17.8414i		−	0.693425i
$663$			35.8130i			1.39086i
$664$	−48.2532			−1.87259
$665$	1.52020	−	11.3713i	0.0589507	−	0.440961i
$666$	4.25779			0.164986
$667$		−	38.6210i		−	1.49541i
$668$		−	4.42854i		−	0.171345i
$669$	41.2484			1.59476
$670$	21.4180	+	2.86331i	0.827451	+	0.110619i
$671$	6.16648			0.238054
$672$		−	3.91006i		−	0.150834i
$673$		−	1.88857i		−	0.0727989i	−0.999337	−	0.0363995i	$-0.988411\pi$
$673$		−	1.88857i		−	0.0727989i	0.999337	−	0.0363995i	$-0.0115889\pi$
$674$	−12.3716			−0.476534
$675$	6.06213	−	22.2677i	0.233331	−	0.857083i
$676$	−5.07456			−0.195175
$677$		−	40.6860i		−	1.56369i	−0.623473	−	0.781845i	$-0.714279\pi$
$677$		−	40.6860i		−	1.56369i	0.623473	−	0.781845i	$-0.285721\pi$
$678$			38.9021i			1.49403i
$679$	−0.920077			−0.0353093
$680$	22.7689	+	3.04390i	0.873146	+	0.116728i
$681$	−48.1926			−1.84674
$682$		−	0.194391i		−	0.00744361i
$683$		−	13.1902i		−	0.504710i	−0.967635	−	0.252355i	$-0.918795\pi$
$683$		−	13.1902i		−	0.504710i	0.967635	−	0.252355i	$-0.0812051\pi$
$684$	−0.629798			−0.0240809
$685$	−0.840339	+	6.28588i	−0.0321077	+	0.240171i
$686$	20.8004			0.794162
$687$			33.2416i			1.26825i
$688$			26.0416i			0.992828i
$689$	56.7538			2.16215
$690$	−4.58170	+	34.2719i	−0.174422	+	1.30471i
$691$	−21.4420			−0.815692			−0.407846	−	0.913051i	$-0.633720\pi$
$691$	−21.4420			−0.815692			−0.407846	+	0.913051i	$0.633720\pi$
$692$			1.07075i			0.0407037i
$693$			0.495466i			0.0188212i
$694$	−33.8495			−1.28491
$695$	−4.50538	−	0.602309i	−0.170899	−	0.0228469i
$696$	−34.7389			−1.31677
$697$			33.1318i			1.25496i
$698$		−	14.0919i		−	0.533387i
$699$	18.3621			0.694518
$700$	0.485748	−	1.78427i	0.0183595	−	0.0674390i
$701$	15.8950			0.600348			0.300174	−	0.953885i	$-0.402955\pi$
$701$	15.8950			0.600348			0.300174	+	0.953885i	$0.402955\pi$
$702$		−	33.4533i		−	1.26261i
$703$			23.5479i			0.888126i
$704$	−6.14763			−0.231698
$705$	−16.1215	−	2.15523i	−0.607171	−	0.0811708i
$706$	38.9746			1.46683
$707$			2.97937i			0.112051i
$708$		−	5.16287i		−	0.194033i
$709$	38.8392			1.45864			0.729318	−	0.684175i	$-0.239838\pi$
$709$	38.8392			1.45864			0.729318	+	0.684175i	$0.239838\pi$
$710$	2.32700	−	17.4064i	0.0873308	−	0.653249i
$711$	−3.74752			−0.140543
$712$		−	5.23384i		−	0.196146i
$713$		−	1.33248i		−	0.0499019i
$714$	−10.8990			−0.407885
$715$	1.14695	−	8.57940i	0.0428936	−	0.320851i
$716$	−3.13847			−0.117290
$717$		−	54.8927i		−	2.05001i
$718$		−	12.9429i		−	0.483025i
$719$	1.15150			0.0429436			0.0214718	−	0.999769i	$-0.493165\pi$
$719$	1.15150			0.0429436			0.0214718	+	0.999769i	$0.493165\pi$
$720$	4.07847	+	0.545237i	0.151996	+	0.0203198i
$721$	−3.74426			−0.139444
$722$		−	4.09267i		−	0.152314i
$723$		−	1.88426i		−	0.0700764i
$724$	3.62262			0.134634
$725$	−29.7141	−	8.08935i	−1.10356	−	0.300431i
$726$	−25.9213			−0.962030
$727$			2.07741i			0.0770469i	0.999258	+	0.0385234i	$0.0122654\pi$
$727$			2.07741i			0.0770469i	−0.999258	+	0.0385234i	$0.987735\pi$
$728$		−	21.3480i		−	0.791209i
$729$	−20.3950			−0.755371
$730$	8.58940	+	1.14829i	0.317908	+	0.0425001i
$731$	−26.7337			−0.988783
$732$		−	4.77402i		−	0.176453i
$733$		−	0.247310i		−	0.00913459i	−0.999990	−	0.00456729i	$-0.998546\pi$
$733$		−	0.247310i		−	0.00913459i	0.999990	−	0.00456729i	$-0.00145382\pi$
$734$	31.8228			1.17460
$735$	2.98221	−	22.3074i	0.110000	−	0.822822i
$736$	−10.1042			−0.372446
$737$		−	5.16120i		−	0.190115i
$738$			6.95437i			0.255994i
$739$	41.8038			1.53778			0.768889	−	0.639382i	$-0.220810\pi$
$739$	41.8038			1.53778			0.768889	+	0.639382i	$0.220810\pi$
$740$	−0.502947	+	3.76213i	−0.0184887	+	0.138299i
$741$	−41.5740			−1.52726
$742$			17.2719i			0.634072i
$743$		−	16.1617i		−	0.592916i	−0.955046	−	0.296458i	$-0.904195\pi$
$743$		−	16.1617i		−	0.592916i	0.955046	−	0.296458i	$-0.0958054\pi$
$744$	−1.19855			−0.0439408
$745$	−46.6010	−	6.22994i	−1.70733	−	0.228247i
$746$	9.14162			0.334698
$747$		−	8.87306i		−	0.324648i
$748$		−	0.688938i		−	0.0251901i
$749$	−19.1339			−0.699139
$750$	25.4084	+	10.7035i	0.927784	+	0.390836i
$751$	−8.92639			−0.325729			−0.162864	−	0.986648i	$-0.552073\pi$
$751$	−8.92639			−0.325729			−0.162864	+	0.986648i	$0.552073\pi$
$752$			12.9057i			0.470622i
$753$		−	33.8808i		−	1.23468i
$754$	−44.6403			−1.62570
$755$	11.8055	+	1.57824i	0.429647	+	0.0574381i
$756$	−1.70705			−0.0620847
$757$			2.30487i			0.0837720i	0.999122	+	0.0418860i	$0.0133366\pi$
$757$			2.30487i			0.0837720i	−0.999122	+	0.0418860i	$0.986663\pi$
$758$		−	32.4754i		−	1.17956i
$759$	8.25865			0.299770
$760$	−3.53355	+	26.4315i	−0.128175	+	0.958772i
$761$	−5.45934			−0.197901			−0.0989505	−	0.995092i	$-0.531549\pi$
$761$	−5.45934			−0.197901			−0.0989505	+	0.995092i	$0.531549\pi$
$762$			31.5709i			1.14369i
$763$		−	14.4393i		−	0.522739i
$764$	4.15440			0.150301
$765$	−0.559728	+	4.18686i	−0.0202370	+	0.151376i
$766$	10.3255			0.373076
$767$		−	52.8366i		−	1.90782i
$768$			12.7068i			0.458516i
$769$	−20.6287			−0.743890			−0.371945	−	0.928255i	$-0.621309\pi$
$769$	−20.6287			−0.743890			−0.371945	+	0.928255i	$0.621309\pi$
$770$	2.61097	+	0.349053i	0.0940929	+	0.0125790i
$771$	37.8254			1.36225
$772$			2.52887i			0.0910159i
$773$			36.9986i			1.33075i	0.746510	+	0.665374i	$0.231728\pi$
$773$			36.9986i			1.33075i	−0.746510	+	0.665374i	$0.768272\pi$
$774$	−5.61141			−0.201698
$775$	−1.02518	−	0.279095i	−0.0368257	−	0.0100254i
$776$	2.13863			0.0767723
$777$		−	14.3421i		−	0.514519i
$778$			24.6682i			0.884398i
$779$	−38.4615			−1.37803
$780$	−6.64207	−	0.887957i	−0.237824	−	0.0317940i
$781$	−4.19449			−0.150091
$782$			28.1647i			1.00717i
$783$			28.4281i			1.01594i
$784$	−17.8577			−0.637775
$785$	−4.97836	+	37.2390i	−0.177685	+	1.32912i
$786$	−3.02027			−0.107730
$787$		−	9.55601i		−	0.340635i	−0.985389	−	0.170317i	$-0.945521\pi$
$787$		−	9.55601i		−	0.340635i	0.985389	−	0.170317i	$-0.0544793\pi$
$788$			5.84121i			0.208084i
$789$	−29.4546			−1.04861
$790$	−2.64011	+	19.7484i	−0.0939308	+	0.702618i
$791$	20.3153			0.722330
$792$		−	1.15166i		−	0.0409225i
$793$		−	48.8572i		−	1.73497i
$794$	0.992428			0.0352200
$795$	42.7976	+	5.72147i	1.51787	+	0.202920i
$796$	−5.35423			−0.189776
$797$		−	31.5410i		−	1.11724i	−0.829424	−	0.558620i	$-0.811331\pi$
$797$		−	31.5410i		−	1.11724i	0.829424	−	0.558620i	$-0.188669\pi$
$798$		−	12.6523i		−	0.447885i
$799$	−13.2487			−0.468705
$800$	−2.11637	+	7.77396i	−0.0748251	+	0.274851i
$801$	0.962426			0.0340056
$802$		−	45.5840i		−	1.60963i
$803$		−	2.06983i		−	0.0730426i
$804$	−3.99574			−0.140919
$805$	17.8973	+	2.39264i	0.630799	+	0.0843294i
$806$	−1.54016			−0.0542499
$807$			41.9913i			1.47816i
$808$		−	6.92527i		−	0.243630i
$809$	−26.1016			−0.917685			−0.458842	−	0.888518i	$-0.651736\pi$
$809$	−26.1016			−0.917685			−0.458842	+	0.888518i	$0.651736\pi$
$810$	4.01283	−	30.0167i	0.140997	−	1.05468i
$811$	−34.3946			−1.20776			−0.603880	−	0.797076i	$-0.706379\pi$
$811$	−34.3946			−1.20776			−0.603880	+	0.797076i	$0.706379\pi$
$812$			2.27790i			0.0799385i
$813$			37.0948i			1.30097i
$814$	−5.40684			−0.189510
$815$	1.86287	−	13.9346i	0.0652536	−	0.488108i
$816$	21.6193			0.756826
$817$		−	31.0342i		−	1.08575i
$818$		−	22.7029i		−	0.793790i
$819$	3.92558			0.137171
$820$	−6.14480	−	0.821478i	−0.214586	−	0.0286873i
$821$	52.9922			1.84944			0.924720	−	0.380647i	$-0.124299\pi$
$821$	52.9922			1.84944			0.924720	+	0.380647i	$0.124299\pi$
$822$			6.99395i			0.243942i
$823$		−	20.4286i		−	0.712095i	−0.934468	−	0.356047i	$-0.884124\pi$
$823$		−	20.4286i		−	0.712095i	0.934468	−	0.356047i	$-0.115876\pi$
$824$	8.70318			0.303189
$825$	1.72982	−	6.35403i	0.0602244	−	0.221219i
$826$	16.0798			0.559488
$827$		−	40.8210i		−	1.41949i	−0.704461	−	0.709743i	$-0.748811\pi$
$827$		−	40.8210i		−	1.41949i	0.704461	−	0.709743i	$-0.251189\pi$
$828$		−	0.991240i		−	0.0344480i
$829$	−7.89986			−0.274374			−0.137187	−	0.990545i	$-0.543806\pi$
$829$	−7.89986			−0.274374			−0.137187	+	0.990545i	$0.543806\pi$
$830$	−46.7587	−	6.25102i	−1.62302	−	0.216976i
$831$	37.3494			1.29563
$832$			48.7078i			1.68864i
$833$		−	18.3323i		−	0.635176i
$834$	−5.01289			−0.173582
$835$	4.56896	−	34.1766i	0.158115	−	1.18273i
$836$	0.799762			0.0276604
$837$			0.980816i			0.0339019i
$838$			29.5639i			1.02127i
$839$	−45.1697			−1.55943			−0.779716	−	0.626133i	$-0.784637\pi$
$839$	−45.1697			−1.55943			−0.779716	+	0.626133i	$0.784637\pi$
$840$	2.15214	−	16.0984i	0.0742558	−	0.555446i
$841$	8.93470			0.308093
$842$		−	36.3837i		−	1.25387i
$843$			47.4491i			1.63423i
$844$	−2.75834			−0.0949458
$845$	−39.1622	−	5.23546i	−1.34722	−	0.180105i
$846$	−2.78090			−0.0956093
$847$			13.5365i			0.465121i
$848$		−	34.2606i		−	1.17651i
$849$	3.19486			0.109647
$850$	21.6693	+	5.89924i	0.743252	+	0.202342i
$851$	−37.0621			−1.27047
$852$			3.24732i			0.111252i
$853$			33.8378i			1.15859i	0.815120	+	0.579293i	$0.196671\pi$
$853$			33.8378i			1.15859i	−0.815120	+	0.579293i	$0.803329\pi$
$854$	14.8687			0.508797
$855$	−4.86037	−	0.649767i	−0.166221	−	0.0222216i
$856$	44.4750			1.52012
$857$		−	22.0350i		−	0.752701i	−0.926477	−	0.376351i	$-0.877179\pi$
$857$		−	22.0350i		−	0.752701i	0.926477	−	0.376351i	$-0.122821\pi$
$858$		−	9.54583i		−	0.325889i
$859$	43.0953			1.47039			0.735197	−	0.677853i	$-0.237090\pi$
$859$	43.0953			1.47039			0.735197	+	0.677853i	$0.237090\pi$
$860$	0.662843	−	4.95818i	0.0226027	−	0.169072i
$861$	23.4253			0.798333
$862$		−	23.0392i		−	0.784717i
$863$		−	41.5592i		−	1.41469i	−0.706867	−	0.707347i	$-0.749892\pi$
$863$		−	41.5592i		−	1.41469i	0.706867	−	0.707347i	$-0.250108\pi$
$864$	7.43751			0.253029
$865$	−1.10470	+	8.26333i	−0.0375609	+	0.280962i
$866$	9.66022			0.328268
$867$		−	9.83855i		−	0.334135i
$868$			0.0785910i			0.00266755i
$869$	4.75887			0.161434
$870$	−33.6629	−	4.50029i	−1.14128	−	0.152574i
$871$	−40.8923			−1.38558
$872$			33.5628i			1.13658i
$873$			0.393263i			0.0133099i
$874$	−32.6954			−1.10594
$875$	5.58953	−	13.2687i	0.188961	−	0.448563i
$876$	−1.60244			−0.0541413
$877$		−	41.5051i		−	1.40153i	−0.713394	−	0.700763i	$-0.752843\pi$
$877$		−	41.5051i		−	1.40153i	0.713394	−	0.700763i	$-0.247157\pi$
$878$		−	2.84060i		−	0.0958655i
$879$	40.1110			1.35291
$880$	−5.17913	−	0.692381i	−0.174588	−	0.0233402i
$881$	5.22392			0.175998			0.0879991	−	0.996121i	$-0.471953\pi$
$881$	5.22392			0.175998			0.0879991	+	0.996121i	$0.471953\pi$
$882$		−	3.84795i		−	0.129567i
$883$		−	31.9624i		−	1.07562i	−0.843066	−	0.537810i	$-0.819252\pi$
$883$		−	31.9624i		−	1.07562i	0.843066	−	0.537810i	$-0.180748\pi$
$884$	−5.45847			−0.183588
$885$	5.32658	−	39.8437i	0.179051	−	1.33933i
$886$	−16.6244			−0.558509
$887$		−	26.7513i		−	0.898222i	−0.893476	−	0.449111i	$-0.851741\pi$
$887$		−	26.7513i		−	0.898222i	0.893476	−	0.449111i	$-0.148259\pi$
$888$			33.3367i			1.11871i
$889$	16.4869			0.552952
$890$	0.678023	−	5.07173i	0.0227274	−	0.170005i
$891$	−7.23326			−0.242323
$892$			6.28690i			0.210501i
$893$		−	15.3799i		−	0.514669i
$894$	−51.8504			−1.73414
$895$	−24.2207	−	3.23798i	−0.809608	−	0.108234i
$896$	−10.6730			−0.356561
$897$		−	65.4335i		−	2.18476i
$898$			5.63837i			0.188155i
$899$	1.30881			0.0436512
$900$	−0.762639	−	0.207620i	−0.0254213	−	0.00692067i
$901$	35.1711			1.17172
$902$		−	8.83116i		−	0.294045i
$903$			18.9017i			0.629008i
$904$	−47.2210			−1.57055
$905$	27.9570	+	3.73748i	0.929323	+	0.124238i
$906$	13.1354			0.436393
$907$			23.1619i			0.769078i	0.923109	+	0.384539i	$0.125640\pi$
$907$			23.1619i			0.769078i	−0.923109	+	0.384539i	$0.874360\pi$
$908$		−	7.34530i		−	0.243762i
$909$	1.27346			0.0422378
$910$	2.76555	−	20.6868i	0.0916771	−	0.685760i
$911$	49.1366			1.62797			0.813984	−	0.580888i	$-0.197294\pi$
$911$	49.1366			1.62797			0.813984	+	0.580888i	$0.197294\pi$
$912$			25.0970i			0.831046i
$913$			11.2676i			0.372905i
$914$	−4.82083			−0.159459
$915$	4.92540	−	36.8428i	0.162829	−	1.21799i
$916$	−5.06654			−0.167403
$917$			1.57724i			0.0520849i
$918$		−	20.7315i		−	0.684241i
$919$	52.6144			1.73559			0.867794	−	0.496923i	$-0.165537\pi$
$919$	52.6144			1.73559			0.867794	+	0.496923i	$0.165537\pi$
$920$	−41.6006	−	5.56145i	−1.37153	−	0.183356i
$921$	32.9786			1.08668
$922$			48.8450i			1.60862i
$923$			33.2330i			1.09388i
$924$	−0.487102			−0.0160245
$925$	−7.76284	+	28.5148i	−0.255241	+	0.937560i
$926$	16.2736			0.534782
$927$			1.60039i			0.0525636i
$928$		−	9.92466i		−	0.325793i
$929$	−11.0619			−0.362930			−0.181465	−	0.983397i	$-0.558084\pi$
$929$	−11.0619			−0.362930			−0.181465	+	0.983397i	$0.558084\pi$
$930$	−1.16142	−	0.155267i	−0.0380846	−	0.00509141i
$931$	21.2813			0.697466
$932$			2.79867i			0.0916735i
$933$			51.0839i			1.67241i
$934$	4.85877			0.158984
$935$	0.710783	−	5.31678i	0.0232451	−	0.173877i
$936$	−9.12463			−0.298248
$937$		−	47.7232i		−	1.55905i	−0.626371	−	0.779525i	$-0.715461\pi$
$937$		−	47.7232i		−	1.55905i	0.626371	−	0.779525i	$-0.284539\pi$
$938$		−	12.4448i		−	0.406336i
$939$	−10.2431			−0.334270
$940$	0.328491	−	2.45717i	0.0107142	−	0.0801441i
$941$	−7.26848			−0.236946			−0.118473	−	0.992957i	$-0.537800\pi$
$941$	−7.26848			−0.236946			−0.118473	+	0.992957i	$0.537800\pi$
$942$			41.4338i			1.34999i
$943$		−	60.5346i		−	1.97128i
$944$	−31.8959			−1.03812
$945$	−13.1739	−	1.76117i	−0.428547	−	0.0572910i
$946$	7.12577			0.231679
$947$			42.4508i			1.37947i	0.724063	+	0.689734i	$0.242272\pi$
$947$			42.4508i			1.37947i	−0.724063	+	0.689734i	$0.757728\pi$
$948$		−	3.68426i		−	0.119659i
$949$	−16.3993			−0.532343
$950$	−6.84821	+	25.1551i	−0.222185	+	0.816140i
$951$	−2.33688			−0.0757787
$952$		−	13.2297i		−	0.428776i
$953$		−	31.8336i		−	1.03119i	−0.856832	−	0.515596i	$-0.827571\pi$
$953$		−	31.8336i		−	1.03119i	0.856832	−	0.515596i	$-0.172429\pi$
$954$	7.38242			0.239015
$955$	32.0610	+	4.28613i	1.03747	+	0.138696i
$956$	8.36651			0.270592
$957$			8.11190i			0.262221i
$958$			42.9753i			1.38847i
$959$	3.65236			0.117941
$960$	−4.91034	+	36.7302i	−0.158480	+	1.18546i
$961$	−30.9548			−0.998543
$962$			42.8385i			1.38117i
$963$			8.17830i			0.263542i
$964$	0.287190			0.00924978
$965$	−2.60905	+	19.5162i	−0.0839884	+	0.628248i
$966$	19.9134			0.640703
$967$		−	1.98161i		−	0.0637242i	−0.999492	−	0.0318621i	$-0.989856\pi$
$967$		−	1.98161i		−	0.0637242i	0.999492	−	0.0318621i	$-0.0101437\pi$
$968$		−	31.4643i		−	1.01130i
$969$	−25.7640			−0.827660
$970$	2.07239	+	0.277051i	0.0665404	+	0.00889557i
$971$	−24.3073			−0.780057			−0.390029	−	0.920803i	$-0.627535\pi$
$971$	−24.3073			−0.780057			−0.390029	+	0.920803i	$0.627535\pi$
$972$			1.62322i			0.0520647i
$973$			2.61781i			0.0839232i
$974$	−35.4812			−1.13689
$975$	−50.3431	−	13.7054i	−1.61227	−	0.438923i
$976$	−29.4936			−0.944068
$977$			22.5696i			0.722064i	0.932553	+	0.361032i	$0.117576\pi$
$977$			22.5696i			0.722064i	−0.932553	+	0.361032i	$0.882424\pi$
$978$		−	15.5043i		−	0.495772i
$979$	−1.22216			−0.0390603
$980$	3.40000	+	0.454535i	0.108609	+	0.0145196i
$981$	−6.17171			−0.197048
$982$		−	8.77946i		−	0.280164i
$983$		−	27.4009i		−	0.873953i	−0.899473	−	0.436976i	$-0.856049\pi$
$983$		−	27.4009i		−	0.873953i	0.899473	−	0.436976i	$-0.143951\pi$
$984$	−54.4499			−1.73580
$985$	−6.02642	+	45.0786i	−0.192018	+	1.43633i
$986$	−27.6643			−0.881009
$987$			9.36727i			0.298164i
$988$		−	6.33653i		−	0.201592i
$989$	48.8448			1.55317
$990$	0.149193	−	1.11599i	0.00474167	−	0.0354685i
$991$	−39.0711			−1.24114			−0.620568	−	0.784153i	$-0.713098\pi$
$991$	−39.0711			−1.24114			−0.620568	+	0.784153i	$0.713098\pi$
$992$		−	0.342416i		−	0.0108717i
$993$			25.6871i			0.815154i
$994$	−10.1138			−0.320791
$995$	−41.3205	−	5.52400i	−1.30995	−	0.175123i
$996$	8.72329			0.276408
$997$		−	55.0824i		−	1.74448i	−0.489080	−	0.872239i	$-0.662667\pi$
$997$		−	55.0824i		−	1.74448i	0.489080	−	0.872239i	$-0.337333\pi$
$998$			44.4678i			1.40760i
$999$	27.2807			0.863123

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1205.2.b.c.724.33	yes	46
5.2	odd	4		6025.2.a.p.1.14		46
5.3	odd	4		6025.2.a.p.1.33		46
5.4	even	2	inner	1205.2.b.c.724.14	✓	46

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1205.2.b.c.724.14	✓	46	5.4	even	2	inner
1205.2.b.c.724.33	yes	46	1.1	even	1	trivial
6025.2.a.p.1.14		46	5.2	odd	4
6025.2.a.p.1.33		46	5.3	odd	4

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:	\( N \)	\(=\)	\( 1205 = 5 \cdot 241 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1205.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.30874i q^{2} -1.88426i q^{3} +0.287190 q^{4} +(2.21635 + 0.296297i) q^{5} +2.46601 q^{6} -1.28779i q^{7} +2.99335i q^{8} -0.550432 q^{9} +O(q^{10})\)	\(q+1.30874i q^{2} -1.88426i q^{3} +0.287190 q^{4} +(2.21635 + 0.296297i) q^{5} +2.46601 q^{6} -1.28779i q^{7} +2.99335i q^{8} -0.550432 q^{9} +(-0.387776 + 2.90063i) q^{10} +0.698979 q^{11} -0.541141i q^{12} -5.53802i q^{13} +1.68539 q^{14} +(0.558300 - 4.17618i) q^{15} -3.34314 q^{16} -3.43199i q^{17} -0.720375i q^{18} +3.98407 q^{19} +(0.636515 + 0.0850936i) q^{20} -2.42653 q^{21} +0.914784i q^{22} +6.27054i q^{23} +5.64024 q^{24} +(4.82442 + 1.31339i) q^{25} +7.24785 q^{26} -4.61562i q^{27} -0.369841i q^{28} -6.15912 q^{29} +(5.46555 + 0.730671i) q^{30} -0.212499 q^{31} +1.61138i q^{32} -1.31706i q^{33} +4.49160 q^{34} +(0.381568 - 2.85420i) q^{35} -0.158079 q^{36} +5.91052i q^{37} +5.21413i q^{38} -10.4351 q^{39} +(-0.886918 + 6.63430i) q^{40} -9.65382 q^{41} -3.17571i q^{42} -7.78957i q^{43} +0.200740 q^{44} +(-1.21995 - 0.163091i) q^{45} -8.20652 q^{46} -3.86035i q^{47} +6.29934i q^{48} +5.34159 q^{49} +(-1.71890 + 6.31392i) q^{50} -6.46676 q^{51} -1.59047i q^{52} +10.2480i q^{53} +6.04066 q^{54} +(1.54918 + 0.207105i) q^{55} +3.85481 q^{56} -7.50702i q^{57} -8.06070i q^{58} +9.54071 q^{59} +(0.160338 - 1.19936i) q^{60} +8.82214 q^{61} -0.278107i q^{62} +0.708842i q^{63} -8.79516 q^{64} +(1.64090 - 12.2742i) q^{65} +1.72369 q^{66} -7.38392i q^{67} -0.985635i q^{68} +11.8153 q^{69} +(3.73541 + 0.499375i) q^{70} -6.00088 q^{71} -1.64763i q^{72} -2.96121i q^{73} -7.73535 q^{74} +(2.47478 - 9.09045i) q^{75} +1.14419 q^{76} -0.900139i q^{77} -13.6568i q^{78} +6.80832 q^{79} +(-7.40957 - 0.990562i) q^{80} -10.3483 q^{81} -12.6344i q^{82} +16.1202i q^{83} -0.696877 q^{84} +(1.01689 - 7.60649i) q^{85} +10.1946 q^{86} +11.6054i q^{87} +2.09228i q^{88} -1.74849 q^{89} +(0.213445 - 1.59660i) q^{90} -7.13182 q^{91} +1.80084i q^{92} +0.400404i q^{93} +5.05221 q^{94} +(8.83010 + 1.18047i) q^{95} +3.03625 q^{96} -0.714461i q^{97} +6.99077i q^{98} -0.384741 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 46 q - 34 q^{4} - 8 q^{5} - 4 q^{6} - 34 q^{9}+O(q^{10}) \) 46 * q - 34 * q^4 - 8 * q^5 - 4 * q^6 - 34 * q^9	\( 46 q - 34 q^{4} - 8 q^{5} - 4 q^{6} - 34 q^{9} - 7 q^{10} - 64 q^{11} + 66 q^{14} + 5 q^{15} + 22 q^{16} - 2 q^{20} - 14 q^{21} + 50 q^{24} + 30 q^{25} - 60 q^{26} + 36 q^{29} + 7 q^{30} - 36 q^{31} - 12 q^{34} + 3 q^{35} - 34 q^{36} + 88 q^{39} - 30 q^{40} - 76 q^{41} + 100 q^{44} - 17 q^{45} - 12 q^{46} - 22 q^{49} - 14 q^{50} - 112 q^{51} + 26 q^{54} - 5 q^{55} - 120 q^{56} + 84 q^{59} - 33 q^{60} - 78 q^{61} - 28 q^{64} + 9 q^{65} - 2 q^{66} + 24 q^{69} + 88 q^{70} - 172 q^{71} + 16 q^{74} + 59 q^{75} - 18 q^{76} + 54 q^{79} + 63 q^{80} - 42 q^{81} - 44 q^{84} + 30 q^{85} - 80 q^{86} + 86 q^{89} + 17 q^{90} - 88 q^{91} - 4 q^{94} + q^{95} - 122 q^{96} + 148 q^{99}+O(q^{100}) \) 46 * q - 34 * q^4 - 8 * q^5 - 4 * q^6 - 34 * q^9 - 7 * q^10 - 64 * q^11 + 66 * q^14 + 5 * q^15 + 22 * q^16 - 2 * q^20 - 14 * q^21 + 50 * q^24 + 30 * q^25 - 60 * q^26 + 36 * q^29 + 7 * q^30 - 36 * q^31 - 12 * q^34 + 3 * q^35 - 34 * q^36 + 88 * q^39 - 30 * q^40 - 76 * q^41 + 100 * q^44 - 17 * q^45 - 12 * q^46 - 22 * q^49 - 14 * q^50 - 112 * q^51 + 26 * q^54 - 5 * q^55 - 120 * q^56 + 84 * q^59 - 33 * q^60 - 78 * q^61 - 28 * q^64 + 9 * q^65 - 2 * q^66 + 24 * q^69 + 88 * q^70 - 172 * q^71 + 16 * q^74 + 59 * q^75 - 18 * q^76 + 54 * q^79 + 63 * q^80 - 42 * q^81 - 44 * q^84 + 30 * q^85 - 80 * q^86 + 86 * q^89 + 17 * q^90 - 88 * q^91 - 4 * q^94 + q^95 - 122 * q^96 + 148 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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