LMFDB - Embedded newform 1205.2.b.c.724.10

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			724.10
Character	$\chi$	$=$	1205.724
Dual form			1205.2.b.c.724.37

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.83307i q^{2} +2.40621i q^{3} -1.36013 q^{4} +(-1.46796 + 1.68674i) q^{5} +4.41073 q^{6} -0.302396i q^{7} -1.17293i q^{8} -2.78983 q^{9} +O(q^{10})$	\(q-1.83307i q^{2} +2.40621i q^{3} -1.36013 q^{4} +(-1.46796 + 1.68674i) q^{5} +4.41073 q^{6} -0.302396i q^{7} -1.17293i q^{8} -2.78983 q^{9} +(3.09191 + 2.69086i) q^{10} -5.09885 q^{11} -3.27275i q^{12} -4.63318i q^{13} -0.554311 q^{14} +(-4.05865 - 3.53220i) q^{15} -4.87031 q^{16} -1.03451i q^{17} +5.11394i q^{18} +8.55559 q^{19} +(1.99661 - 2.29419i) q^{20} +0.727627 q^{21} +9.34653i q^{22} -1.34508i q^{23} +2.82231 q^{24} +(-0.690213 - 4.95213i) q^{25} -8.49293 q^{26} +0.505718i q^{27} +0.411297i q^{28} -10.3038 q^{29} +(-6.47476 + 7.43978i) q^{30} +0.459299 q^{31} +6.58174i q^{32} -12.2689i q^{33} -1.89632 q^{34} +(0.510064 + 0.443904i) q^{35} +3.79452 q^{36} -1.55014i q^{37} -15.6830i q^{38} +11.1484 q^{39} +(1.97843 + 1.72181i) q^{40} +5.44165 q^{41} -1.33379i q^{42} -5.45885i q^{43} +6.93509 q^{44} +(4.09534 - 4.70573i) q^{45} -2.46562 q^{46} -10.3833i q^{47} -11.7190i q^{48} +6.90856 q^{49} +(-9.07758 + 1.26521i) q^{50} +2.48924 q^{51} +6.30172i q^{52} -4.20240i q^{53} +0.927014 q^{54} +(7.48489 - 8.60046i) q^{55} -0.354689 q^{56} +20.5865i q^{57} +18.8875i q^{58} +5.01849 q^{59} +(5.52029 + 4.80425i) q^{60} -6.46168 q^{61} -0.841924i q^{62} +0.843632i q^{63} +2.32413 q^{64} +(7.81500 + 6.80131i) q^{65} -22.4897 q^{66} -14.8239i q^{67} +1.40707i q^{68} +3.23654 q^{69} +(0.813704 - 0.934981i) q^{70} -6.08615 q^{71} +3.27227i q^{72} -13.8254i q^{73} -2.84152 q^{74} +(11.9158 - 1.66080i) q^{75} -11.6367 q^{76} +1.54187i q^{77} -20.4357i q^{78} -2.63720 q^{79} +(7.14940 - 8.21497i) q^{80} -9.58634 q^{81} -9.97491i q^{82} +2.13404i q^{83} -0.989665 q^{84} +(1.74495 + 1.51862i) q^{85} -10.0064 q^{86} -24.7930i q^{87} +5.98059i q^{88} +2.74947 q^{89} +(-8.62590 - 7.50703i) q^{90} -1.40106 q^{91} +1.82948i q^{92} +1.10517i q^{93} -19.0333 q^{94} +(-12.5592 + 14.4311i) q^{95} -15.8370 q^{96} +10.5373i q^{97} -12.6638i q^{98} +14.2249 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	1.83307i		−	1.29617i	−0.761567	−	0.648086i	$-0.775570\pi$
$2$		−	1.83307i		−	1.29617i	0.761567	−	0.648086i	$-0.224430\pi$
$3$			2.40621i			1.38922i	0.719385	+	0.694612i	$0.244424\pi$
$3$			2.40621i			1.38922i	−0.719385	+	0.694612i	$0.755576\pi$
$4$	−1.36013			−0.680064
$5$	−1.46796	+	1.68674i	−0.656490	+	0.754335i
$5$	−1.46796	+	1.68674i	−0.656490	+	0.754335i
$6$	4.41073			1.80067
$7$		−	0.302396i		−	0.114295i	−0.998366	−	0.0571474i	$-0.981799\pi$
$7$		−	0.302396i		−	0.114295i	0.998366	−	0.0571474i	$-0.0182005\pi$
$8$		−	1.17293i		−	0.414693i
$9$	−2.78983			−0.929943
$10$	3.09191	+	2.69086i	0.977748	+	0.850924i
$11$	−5.09885			−1.53736			−0.768681	−	0.639633i	$-0.779086\pi$
$11$	−5.09885			−1.53736			−0.768681	+	0.639633i	$0.779086\pi$
$12$		−	3.27275i		−	0.944761i
$13$		−	4.63318i		−	1.28501i	−0.766280	−	0.642507i	$-0.777894\pi$
$13$		−	4.63318i		−	1.28501i	0.766280	−	0.642507i	$-0.222106\pi$
$14$	−0.554311			−0.148146
$15$	−4.05865	−	3.53220i	−1.04794	−	0.912011i
$16$	−4.87031			−1.21758
$17$		−	1.03451i		−	0.250906i	−0.992100	−	0.125453i	$-0.959962\pi$
$17$		−	1.03451i		−	0.250906i	0.992100	−	0.125453i	$-0.0400384\pi$
$18$			5.11394i			1.20537i
$19$	8.55559			1.96279			0.981394	−	0.192006i	$-0.0614995\pi$
$19$	8.55559			1.96279			0.981394	+	0.192006i	$0.0614995\pi$
$20$	1.99661	−	2.29419i	0.446455	−	0.512996i
$21$	0.727627			0.158781
$22$			9.34653i			1.99269i
$23$		−	1.34508i		−	0.280469i	−0.990118	−	0.140234i	$-0.955214\pi$
$23$		−	1.34508i		−	0.280469i	0.990118	−	0.140234i	$-0.0447856\pi$
$24$	2.82231			0.576101
$25$	−0.690213	−	4.95213i	−0.138043	−	0.990426i
$26$	−8.49293			−1.66560
$27$			0.505718i			0.0973255i
$28$			0.411297i			0.0777278i
$29$	−10.3038			−1.91336			−0.956681	−	0.291138i	$-0.905966\pi$
$29$	−10.3038			−1.91336			−0.956681	+	0.291138i	$0.905966\pi$
$30$	−6.47476	+	7.43978i	−1.18212	+	1.35831i
$31$	0.459299			0.0824925			0.0412462	−	0.999149i	$-0.486867\pi$
$31$	0.459299			0.0824925			0.0412462	+	0.999149i	$0.486867\pi$
$32$			6.58174i			1.16350i
$33$		−	12.2689i		−	2.13574i
$34$	−1.89632			−0.325217
$35$	0.510064	+	0.443904i	0.0862166	+	0.0750334i
$36$	3.79452			0.632420
$37$		−	1.55014i		−	0.254842i	−0.991849	−	0.127421i	$-0.959330\pi$
$37$		−	1.55014i		−	0.254842i	0.991849	−	0.127421i	$-0.0406700\pi$
$38$		−	15.6830i		−	2.54411i
$39$	11.1484			1.78517
$40$	1.97843	+	1.72181i	0.312817	+	0.272242i
$41$	5.44165			0.849844			0.424922	−	0.905230i	$-0.360302\pi$
$41$	5.44165			0.849844			0.424922	+	0.905230i	$0.360302\pi$
$42$		−	1.33379i		−	0.205808i
$43$		−	5.45885i		−	0.832467i	−0.909258	−	0.416234i	$-0.863350\pi$
$43$		−	5.45885i		−	0.832467i	0.909258	−	0.416234i	$-0.136650\pi$
$44$	6.93509			1.04550
$45$	4.09534	−	4.70573i	0.610498	−	0.701488i
$46$	−2.46562			−0.363536
$47$		−	10.3833i		−	1.51456i	−0.653090	−	0.757280i	$-0.726528\pi$
$47$		−	10.3833i		−	1.51456i	0.653090	−	0.757280i	$-0.273472\pi$
$48$		−	11.7190i		−	1.69149i
$49$	6.90856			0.986937
$50$	−9.07758	+	1.26521i	−1.28376	+	0.178927i
$51$	2.48924			0.348564
$52$			6.30172i			0.873891i
$53$		−	4.20240i		−	0.577244i	−0.957443	−	0.288622i	$-0.906803\pi$
$53$		−	4.20240i		−	0.577244i	0.957443	−	0.288622i	$-0.0931971\pi$
$54$	0.927014			0.126151
$55$	7.48489	−	8.60046i	1.00926	−	1.15969i
$56$	−0.354689			−0.0473973
$57$			20.5865i			2.72675i
$58$			18.8875i			2.48005i
$59$	5.01849			0.653352			0.326676	−	0.945136i	$-0.394071\pi$
$59$	5.01849			0.653352			0.326676	+	0.945136i	$0.394071\pi$
$60$	5.52029	+	4.80425i	0.712666	+	0.620226i
$61$	−6.46168			−0.827333			−0.413667	−	0.910428i	$-0.635752\pi$
$61$	−6.46168			−0.827333			−0.413667	+	0.910428i	$0.635752\pi$
$62$		−	0.841924i		−	0.106924i
$63$			0.843632i			0.106288i
$64$	2.32413			0.290516
$65$	7.81500	+	6.80131i	0.969331	+	0.843598i
$66$	−22.4897			−2.76829
$67$		−	14.8239i		−	1.81103i	−0.424311	−	0.905516i	$-0.639484\pi$
$67$		−	14.8239i		−	1.81103i	0.424311	−	0.905516i	$-0.360516\pi$
$68$			1.40707i			0.170632i
$69$	3.23654			0.389634
$70$	0.813704	−	0.934981i	0.0972562	−	0.111752i
$71$	−6.08615			−0.722293			−0.361147	−	0.932509i	$-0.617615\pi$
$71$	−6.08615			−0.722293			−0.361147	+	0.932509i	$0.617615\pi$
$72$			3.27227i			0.385640i
$73$		−	13.8254i		−	1.61814i	−0.587712	−	0.809070i	$-0.699971\pi$
$73$		−	13.8254i		−	1.61814i	0.587712	−	0.809070i	$-0.300029\pi$
$74$	−2.84152			−0.330320
$75$	11.9158	−	1.66080i	1.37592	−	0.191772i
$76$	−11.6367			−1.33482
$77$			1.54187i			0.175713i
$78$		−	20.4357i		−	2.31389i
$79$	−2.63720			−0.296708			−0.148354	−	0.988934i	$-0.547398\pi$
$79$	−2.63720			−0.296708			−0.148354	+	0.988934i	$0.547398\pi$
$80$	7.14940	−	8.21497i	0.799327	−	0.918461i
$81$	−9.58634			−1.06515
$82$		−	9.97491i		−	1.10154i
$83$			2.13404i			0.234242i	0.993118	+	0.117121i	$0.0373665\pi$
$83$			2.13404i			0.234242i	−0.993118	+	0.117121i	$0.962633\pi$
$84$	−0.989665			−0.107981
$85$	1.74495	+	1.51862i	0.189267	+	0.164717i
$86$	−10.0064			−1.07902
$87$		−	24.7930i		−	2.65809i
$88$			5.98059i			0.637533i
$89$	2.74947			0.291443			0.145722	−	0.989326i	$-0.453450\pi$
$89$	2.74947			0.291443			0.145722	+	0.989326i	$0.453450\pi$
$90$	−8.62590	−	7.50703i	−0.909250	−	0.791310i
$91$	−1.40106			−0.146871
$92$			1.82948i			0.190737i
$93$			1.10517i			0.114600i
$94$	−19.0333			−1.96313
$95$	−12.5592	+	14.4311i	−1.28855	+	1.48060i
$96$	−15.8370			−1.61636
$97$			10.5373i			1.06990i	0.844884	+	0.534950i	$0.179669\pi$
$97$			10.5373i			1.06990i	−0.844884	+	0.534950i	$0.820331\pi$
$98$		−	12.6638i		−	1.27924i
$99$	14.2249			1.42966
$100$	0.938778	+	6.73553i	0.0938778	+	0.673553i
$101$	−6.99997			−0.696523			−0.348262	−	0.937397i	$-0.613228\pi$
$101$	−6.99997			−0.696523			−0.348262	+	0.937397i	$0.613228\pi$
$102$		−	4.56295i		−	0.451799i
$103$		−	0.931512i		−	0.0917846i	−0.998946	−	0.0458923i	$-0.985387\pi$
$103$		−	0.931512i		−	0.0917846i	0.998946	−	0.0458923i	$-0.0146131\pi$
$104$	−5.43439			−0.532886
$105$	−1.06812	+	1.22732i	−0.104238	+	0.119774i
$106$	−7.70327			−0.748208
$107$			9.32032i			0.901029i	0.892769	+	0.450515i	$0.148759\pi$
$107$			9.32032i			0.901029i	−0.892769	+	0.450515i	$0.851241\pi$
$108$		−	0.687841i		−	0.0661875i
$109$	−6.86942			−0.657971			−0.328986	−	0.944335i	$-0.606707\pi$
$109$	−6.86942			−0.657971			−0.328986	+	0.944335i	$0.606707\pi$
$110$	−15.7652	−	13.7203i	−1.50315	−	1.30818i
$111$	3.72997			0.354033
$112$			1.47276i			0.139163i
$113$		−	3.92833i		−	0.369546i	−0.982781	−	0.184773i	$-0.940845\pi$
$113$		−	3.92833i		−	0.369546i	0.982781	−	0.184773i	$-0.0591550\pi$
$114$	37.7364			3.53434
$115$	2.26881	+	1.97452i	0.211567	+	0.184125i
$116$	14.0144			1.30121
$117$			12.9258i			1.19499i
$118$		−	9.19922i		−	0.846857i
$119$	−0.312832			−0.0286772
$120$	−4.14302	+	4.76051i	−0.378204	+	0.434573i
$121$	14.9983			1.36348
$122$			11.8447i			1.07237i
$123$			13.0937i			1.18062i
$124$	−0.624705			−0.0561001
$125$	9.36618	+	6.10529i	0.837737	+	0.546074i
$126$	1.54643			0.137767
$127$			19.0590i			1.69121i	0.533810	+	0.845604i	$0.320760\pi$
$127$			19.0590i			1.69121i	−0.533810	+	0.845604i	$0.679240\pi$
$128$			8.90319i			0.786938i
$129$	13.1351			1.15648
$130$	12.4672	−	14.3254i	1.09345	−	1.25642i
$131$	11.9830			1.04696			0.523481	−	0.852038i	$-0.324633\pi$
$131$	11.9830			1.04696			0.523481	+	0.852038i	$0.324633\pi$
$132$			16.6872i			1.45244i
$133$		−	2.58717i		−	0.224337i
$134$	−27.1733			−2.34741
$135$	−0.853017	−	0.742372i	−0.0734160	−	0.0638932i
$136$	−1.21341			−0.104049
$137$		−	11.4620i		−	0.979266i	−0.871929	−	0.489633i	$-0.837131\pi$
$137$		−	11.4620i		−	0.979266i	0.871929	−	0.489633i	$-0.162869\pi$
$138$		−	5.93279i		−	0.505033i
$139$	−16.6366			−1.41110			−0.705551	−	0.708660i	$-0.749300\pi$
$139$	−16.6366			−1.41110			−0.705551	+	0.708660i	$0.749300\pi$
$140$	−0.693752	−	0.603765i	−0.0586328	−	0.0510275i
$141$	24.9844			2.10406
$142$			11.1563i			0.936217i
$143$			23.6239i			1.97553i
$144$	13.5873			1.13228
$145$	15.1255	−	17.3798i	1.25610	−	1.44332i
$146$	−25.3429			−2.09739
$147$			16.6234i			1.37108i
$148$			2.10839i			0.173309i
$149$	−16.2343			−1.32997			−0.664983	−	0.746858i	$-0.731561\pi$
$149$	−16.2343			−1.32997			−0.664983	+	0.746858i	$0.731561\pi$
$150$	−3.04435	−	21.8425i	−0.248570	−	1.78343i
$151$	−7.40916			−0.602949			−0.301474	−	0.953474i	$-0.597479\pi$
$151$	−7.40916			−0.602949			−0.301474	+	0.953474i	$0.597479\pi$
$152$		−	10.0351i		−	0.813954i
$153$			2.88611i			0.233328i
$154$	2.82635			0.227754
$155$	−0.674230	+	0.774719i	−0.0541554	+	0.0622270i
$156$	−15.1632			−1.21403
$157$			16.4755i			1.31489i	0.753503	+	0.657444i	$0.228362\pi$
$157$			16.4755i			1.31489i	−0.753503	+	0.657444i	$0.771638\pi$
$158$			4.83416i			0.384585i
$159$	10.1118			0.801921
$160$	−11.1017	−	9.66169i	−0.877667	−	0.763824i
$161$	−0.406747			−0.0320561
$162$			17.5724i			1.38062i
$163$		−	21.5566i		−	1.68845i	−0.535991	−	0.844224i	$-0.680062\pi$
$163$		−	21.5566i		−	1.68845i	0.535991	−	0.844224i	$-0.319938\pi$
$164$	−7.40134			−0.577948
$165$	20.6945	+	18.0102i	1.61106	+	1.40209i
$166$	3.91184			0.303618
$167$		−	2.83253i		−	0.219188i	−0.993976	−	0.109594i	$-0.965045\pi$
$167$		−	2.83253i		−	0.219188i	0.993976	−	0.109594i	$-0.0349550\pi$
$168$		−	0.853454i		−	0.0658454i
$169$	−8.46640			−0.651261
$170$	2.78372	−	3.19861i	0.213502	−	0.245323i
$171$	−23.8686			−1.82528
$172$			7.42473i			0.566131i
$173$			22.2673i			1.69296i	0.532424	+	0.846478i	$0.321281\pi$
$173$			22.2673i			1.69296i	−0.532424	+	0.846478i	$0.678719\pi$
$174$	−45.4472			−3.44534
$175$	−1.49750	+	0.208718i	−0.113201	+	0.0157776i
$176$	24.8330			1.87186
$177$			12.0755i			0.907652i
$178$		−	5.03996i		−	0.377761i
$179$	−1.82748			−0.136592			−0.0682962	−	0.997665i	$-0.521756\pi$
$179$	−1.82748			−0.136592			−0.0682962	+	0.997665i	$0.521756\pi$
$180$	−5.57019	+	6.40039i	−0.415177	+	0.477057i
$181$	12.5134			0.930114			0.465057	−	0.885281i	$-0.346034\pi$
$181$	12.5134			0.930114			0.465057	+	0.885281i	$0.346034\pi$
$182$			2.56823i			0.190370i
$183$		−	15.5481i		−	1.14935i
$184$	−1.57768			−0.116308
$185$	2.61470	+	2.27554i	0.192236	+	0.167301i
$186$	2.02584			0.148542
$187$			5.27481i			0.385733i
$188$			14.1226i			1.03000i
$189$	0.152927			0.0111238
$190$	26.4531	+	23.0219i	1.91911	+	1.67018i
$191$	3.47735			0.251612			0.125806	−	0.992055i	$-0.459848\pi$
$191$	3.47735			0.251612			0.125806	+	0.992055i	$0.459848\pi$
$192$			5.59234i			0.403592i
$193$			4.00614i			0.288368i	0.989551	+	0.144184i	$0.0460557\pi$
$193$			4.00614i			0.288368i	−0.989551	+	0.144184i	$0.953944\pi$
$194$	19.3155			1.38677
$195$	−16.3653	+	18.8045i	−1.17195	+	1.34662i
$196$	−9.39652			−0.671180
$197$		−	5.14600i		−	0.366638i	−0.983054	−	0.183319i	$-0.941316\pi$
$197$		−	5.14600i		−	0.366638i	0.983054	−	0.183319i	$-0.0586841\pi$
$198$		−	26.0752i		−	1.85308i
$199$	−10.3802			−0.735835			−0.367917	−	0.929858i	$-0.619929\pi$
$199$	−10.3802			−0.735835			−0.367917	+	0.929858i	$0.619929\pi$
$200$	−5.80849	+	0.809571i	−0.410723	+	0.0572453i
$201$	35.6695			2.51593
$202$			12.8314i			0.902815i
$203$			3.11582i			0.218687i
$204$	−3.38569			−0.237046
$205$	−7.98811	+	9.17868i	−0.557914	+	0.641067i
$206$	−1.70752			−0.118969
$207$			3.75254i			0.260820i
$208$			22.5650i			1.56460i
$209$	−43.6237			−3.01751
$210$	2.24976	+	1.95794i	0.155248	+	0.135111i
$211$	−12.4398			−0.856394			−0.428197	−	0.903685i	$-0.640851\pi$
$211$	−12.4398			−0.856394			−0.428197	+	0.903685i	$0.640851\pi$
$212$			5.71580i			0.392563i
$213$		−	14.6445i		−	1.00343i
$214$	17.0847			1.16789
$215$	9.20769	+	8.01335i	0.627959	+	0.546506i
$216$	0.593171			0.0403602
$217$		−	0.138890i		−	0.00942846i
$218$			12.5921i			0.852844i
$219$	33.2668			2.24796
$220$	−10.1804	+	11.6977i	−0.686362	+	0.788660i
$221$	−4.79308			−0.322417
$222$		−	6.83727i		−	0.458888i
$223$			2.52846i			0.169318i	0.996410	+	0.0846591i	$0.0269801\pi$
$223$			2.52846i			0.169318i	−0.996410	+	0.0846591i	$0.973020\pi$
$224$	1.99029			0.132982
$225$	1.92558	+	13.8156i	0.128372	+	0.921040i
$226$	−7.20088			−0.478996
$227$		−	11.2535i		−	0.746922i	−0.927646	−	0.373461i	$-0.878171\pi$
$227$		−	11.2535i		−	0.746922i	0.927646	−	0.373461i	$-0.121829\pi$
$228$		−	28.0003i		−	1.85436i
$229$	−21.9401			−1.44985			−0.724923	−	0.688830i	$-0.758125\pi$
$229$	−21.9401			−1.44985			−0.724923	+	0.688830i	$0.758125\pi$
$230$	3.61942	−	4.15887i	0.238658	−	0.274228i
$231$	−3.71006			−0.244104
$232$			12.0856i			0.793457i
$233$			1.43595i			0.0940720i	0.998893	+	0.0470360i	$0.0149776\pi$
$233$			1.43595i			0.0940720i	−0.998893	+	0.0470360i	$0.985022\pi$
$234$	23.6938			1.54891
$235$	17.5140	+	15.2422i	1.14249	+	0.994294i
$236$	−6.82579			−0.444321
$237$		−	6.34564i		−	0.412194i
$238$			0.573441i			0.0371706i
$239$	27.7962			1.79799			0.898994	−	0.437961i	$-0.144299\pi$
$239$	27.7962			1.79799			0.898994	+	0.437961i	$0.144299\pi$
$240$	19.7669	+	17.2029i	1.27595	+	1.11044i
$241$	1.00000			0.0644157
$241$	1.00000			0.0644157
$242$		−	27.4928i		−	1.76731i
$243$		−	21.5496i		−	1.38241i
$244$	8.78870			0.562639
$245$	−10.1415	+	11.6530i	−0.647914	+	0.744481i
$246$	24.0017			1.53029
$247$		−	39.6396i		−	2.52221i
$248$		−	0.538724i		−	0.0342090i
$249$	−5.13495			−0.325414
$250$	11.1914	−	17.1688i	0.707806	−	1.08585i
$251$	−8.17551			−0.516034			−0.258017	−	0.966140i	$-0.583069\pi$
$251$	−8.17551			−0.516034			−0.258017	+	0.966140i	$0.583069\pi$
$252$		−	1.14745i		−	0.0722824i
$253$			6.85837i			0.431182i
$254$	34.9363			2.19210
$255$	−3.65410	+	4.19872i	−0.228829	+	0.262934i
$256$	20.9684			1.31052
$257$			2.28257i			0.142383i	0.997463	+	0.0711913i	$0.0226801\pi$
$257$			2.28257i			0.142383i	−0.997463	+	0.0711913i	$0.977320\pi$
$258$		−	24.0775i		−	1.49900i
$259$	−0.468757			−0.0291272
$260$	−10.6294	−	9.25064i	−0.659207	−	0.573701i
$261$	28.7457			1.77932
$262$		−	21.9657i		−	1.35704i
$263$		−	6.59117i		−	0.406429i	−0.979134	−	0.203214i	$-0.934861\pi$
$263$		−	6.59117i		−	0.406429i	0.979134	−	0.203214i	$-0.0651388\pi$
$264$	−14.3905			−0.885676
$265$	7.08837	+	6.16894i	0.435435	+	0.378955i
$266$	−4.74246			−0.290779
$267$			6.61580i			0.404880i
$268$			20.1625i			1.23162i
$269$	−17.1330			−1.04462			−0.522310	−	0.852756i	$-0.674929\pi$
$269$	−17.1330			−1.04462			−0.522310	+	0.852756i	$0.674929\pi$
$270$	−1.36082	+	1.56364i	−0.0828166	+	0.0951599i
$271$	9.21261			0.559626			0.279813	−	0.960055i	$-0.409728\pi$
$271$	9.21261			0.559626			0.279813	+	0.960055i	$0.409728\pi$
$272$			5.03838i			0.305497i
$273$		−	3.37123i		−	0.204036i
$274$	−21.0106			−1.26930
$275$	3.51930	+	25.2502i	0.212221	+	1.52264i
$276$	−4.40211			−0.264976
$277$		−	21.1695i		−	1.27195i	−0.771708	−	0.635977i	$-0.780597\pi$
$277$		−	21.1695i		−	1.27195i	0.771708	−	0.635977i	$-0.219403\pi$
$278$			30.4960i			1.82903i
$279$	−1.28136			−0.0767132
$280$	0.520667	−	0.598269i	0.0311158	−	0.0357534i
$281$	−28.2982			−1.68813			−0.844066	−	0.536240i	$-0.819844\pi$
$281$	−28.2982			−1.68813			−0.844066	+	0.536240i	$0.819844\pi$
$282$		−	45.7980i		−	2.72723i
$283$		−	26.7052i		−	1.58746i	−0.608270	−	0.793730i	$-0.708136\pi$
$283$		−	26.7052i		−	1.58746i	0.608270	−	0.793730i	$-0.291864\pi$
$284$	8.27794			0.491206
$285$	−34.7242	−	30.2201i	−2.05688	−	1.79008i
$286$	43.3042			2.56063
$287$		−	1.64553i		−	0.0971328i
$288$		−	18.3619i		−	1.08199i
$289$	15.9298			0.937046
$290$	−31.8583	−	27.7260i	−1.87079	−	1.62813i
$291$	−25.3549			−1.48633
$292$			18.8043i			1.10044i
$293$			20.6913i			1.20880i	0.796682	+	0.604399i	$0.206587\pi$
$293$			20.6913i			1.20880i	−0.796682	+	0.604399i	$0.793413\pi$
$294$	30.4718			1.77715
$295$	−7.36692	+	8.46491i	−0.428919	+	0.492846i
$296$	−1.81821			−0.105681
$297$		−	2.57858i		−	0.149624i
$298$			29.7585i			1.72387i
$299$	−6.23201			−0.360406
$300$	−16.2071	+	2.25889i	−0.935716	+	0.130417i
$301$	−1.65073			−0.0951467
$302$			13.5815i			0.781526i
$303$		−	16.8434i		−	0.967627i
$304$	−41.6684			−2.38984
$305$	9.48545	−	10.8992i	0.543136	−	0.624086i
$306$	5.29042			0.302433
$307$			20.2769i			1.15727i	0.815588	+	0.578633i	$0.196414\pi$
$307$			20.2769i			1.15727i	−0.815588	+	0.578633i	$0.803586\pi$
$308$		−	2.09714i		−	0.119496i
$309$	2.24141			0.127509
$310$	1.42011	+	1.23591i	0.0806569	+	0.0701948i
$311$	12.3238			0.698820			0.349410	−	0.936970i	$-0.386382\pi$
$311$	12.3238			0.698820			0.349410	+	0.936970i	$0.386382\pi$
$312$		−	13.0763i		−	0.740298i
$313$		−	10.5428i		−	0.595912i	−0.954580	−	0.297956i	$-0.903695\pi$
$313$		−	10.5428i		−	0.595912i	0.954580	−	0.297956i	$-0.0963048\pi$
$314$	30.2007			1.70432
$315$	−1.42299	−	1.23841i	−0.0801765	−	0.0697767i
$316$	3.58693			0.201780
$317$			20.9718i			1.17790i	0.808171	+	0.588948i	$0.200458\pi$
$317$			20.9718i			1.17790i	−0.808171	+	0.588948i	$0.799542\pi$
$318$		−	18.5357i		−	1.03943i
$319$	52.5374			2.94153
$320$	−3.41172	+	3.92022i	−0.190721	+	0.219147i
$321$	−22.4266			−1.25173
$322$			0.745593i			0.0415503i
$323$		−	8.85085i		−	0.492474i
$324$	13.0386			0.724369
$325$	−22.9441	+	3.19789i	−1.27271	+	0.177387i
$326$	−39.5147			−2.18852
$327$		−	16.5292i		−	0.914069i
$328$		−	6.38267i		−	0.352424i
$329$	−3.13987			−0.173107
$330$	33.0138	−	37.9343i	1.81735	−	2.08822i
$331$	−19.2909			−1.06033			−0.530163	−	0.847896i	$-0.677869\pi$
$331$	−19.2909			−1.06033			−0.530163	+	0.847896i	$0.677869\pi$
$332$		−	2.90257i		−	0.159299i
$333$			4.32464i			0.236989i
$334$	−5.19221			−0.284105
$335$	25.0042	+	21.7609i	1.36613	+	1.18892i
$336$	−3.54377			−0.193328
$337$		−	27.5023i		−	1.49815i	−0.662487	−	0.749074i	$-0.730499\pi$
$337$		−	27.5023i		−	1.49815i	0.662487	−	0.749074i	$-0.269501\pi$
$338$			15.5195i			0.844147i
$339$	9.45237			0.513382
$340$	−2.37336	−	2.06551i	−0.128714	−	0.112018i
$341$	−2.34190			−0.126821
$342$			43.7527i			2.36588i
$343$		−	4.20589i		−	0.227097i
$344$	−6.40284			−0.345218
$345$	−4.75110	+	5.45922i	−0.255791	+	0.293914i
$346$	40.8175			2.19436
$347$		−	23.2293i		−	1.24701i	−0.781819	−	0.623506i	$-0.785708\pi$
$347$		−	23.2293i		−	1.24701i	0.781819	−	0.623506i	$-0.214292\pi$
$348$			33.7216i			1.80767i
$349$	31.5500			1.68883			0.844416	−	0.535688i	$-0.179948\pi$
$349$	31.5500			1.68883			0.844416	+	0.535688i	$0.179948\pi$
$350$	0.382593	+	2.74502i	0.0204505	+	0.146728i
$351$	2.34309			0.125065
$352$		−	33.5593i		−	1.78872i
$353$			5.60734i			0.298449i	0.988803	+	0.149224i	$0.0476776\pi$
$353$			5.60734i			0.298449i	−0.988803	+	0.149224i	$0.952322\pi$
$354$	22.1352			1.17647
$355$	8.93420	−	10.2658i	0.474178	−	0.544851i
$356$	−3.73963			−0.198200
$357$		−	0.752737i		−	0.0398391i
$358$			3.34989i			0.177047i
$359$	−23.8284			−1.25761			−0.628806	−	0.777562i	$-0.716456\pi$
$359$	−23.8284			−1.25761			−0.628806	+	0.777562i	$0.716456\pi$
$360$	−5.51948	−	4.80354i	−0.290902	−	0.253169i
$361$	54.1981			2.85253
$362$		−	22.9379i		−	1.20559i
$363$			36.0890i			1.89418i
$364$	1.90561			0.0998813
$365$	23.3199	+	20.2951i	1.22062	+	1.06229i
$366$	−28.5007			−1.48976
$367$			10.7773i			0.562568i	0.959625	+	0.281284i	$0.0907603\pi$
$367$			10.7773i			0.562568i	−0.959625	+	0.281284i	$0.909240\pi$
$368$			6.55096i			0.341492i
$369$	−15.1813			−0.790306
$370$	4.17122	−	4.79291i	0.216851	−	0.249172i
$371$	−1.27079			−0.0659760
$372$		−	1.50317i		−	0.0779356i
$373$			6.83088i			0.353689i	0.984239	+	0.176845i	$0.0565890\pi$
$373$			6.83088i			0.353689i	−0.984239	+	0.176845i	$0.943411\pi$
$374$	9.66908			0.499976
$375$	−14.6906	+	22.5370i	−0.758619	+	1.16380i
$376$	−12.1789			−0.628077
$377$			47.7393i			2.45870i
$378$		−	0.280325i		−	0.0144184i
$379$	11.4240			0.586813			0.293406	−	0.955988i	$-0.405211\pi$
$379$	11.4240			0.586813			0.293406	+	0.955988i	$0.405211\pi$
$380$	17.0821	−	19.6281i	0.876296	−	1.00690i
$381$	−45.8598			−2.34947
$382$		−	6.37421i		−	0.326133i
$383$		−	38.2543i		−	1.95470i	−0.211618	−	0.977352i	$-0.567873\pi$
$383$		−	38.2543i		−	1.95470i	0.211618	−	0.977352i	$-0.432127\pi$
$384$	−21.4229			−1.09323
$385$	−2.60074	−	2.26340i	−0.132546	−	0.115353i
$386$	7.34351			0.373775
$387$			15.2293i			0.774147i
$388$		−	14.3321i		−	0.727600i
$389$	0.100947			0.00511820			0.00255910	−	0.999997i	$-0.499185\pi$
$389$	0.100947			0.00511820			0.00255910	+	0.999997i	$0.499185\pi$
$390$	34.4699	+	29.9987i	1.74545	+	1.51905i
$391$	−1.39150			−0.0703712
$392$		−	8.10324i		−	0.409276i
$393$			28.8336i			1.45446i
$394$	−9.43296			−0.475226
$395$	3.87129	−	4.44828i	0.194786	−	0.223817i
$396$	−19.3477			−0.972258
$397$			18.7984i			0.943466i	0.881741	+	0.471733i	$0.156371\pi$
$397$			18.7984i			0.943466i	−0.881741	+	0.471733i	$0.843629\pi$
$398$			19.0276i			0.953769i
$399$	6.22528			0.311654
$400$	3.36155	+	24.1184i	0.168078	+	1.20592i
$401$	16.1807			0.808026			0.404013	−	0.914753i	$-0.367615\pi$
$401$	16.1807			0.808026			0.404013	+	0.914753i	$0.367615\pi$
$402$		−	65.3844i		−	3.26108i
$403$		−	2.12801i		−	0.106004i
$404$	9.52086			0.473680
$405$	14.0723	−	16.1697i	0.699260	−	0.803480i
$406$	5.71149			0.283457
$407$			7.90396i			0.391785i
$408$		−	2.91971i		−	0.144547i
$409$	−3.76534			−0.186184			−0.0930919	−	0.995658i	$-0.529675\pi$
$409$	−3.76534			−0.186184			−0.0930919	+	0.995658i	$0.529675\pi$
$410$	16.8251	+	14.6427i	0.830933	+	0.723152i
$411$	27.5800			1.36042
$412$			1.26698i			0.0624194i
$413$		−	1.51757i		−	0.0746748i
$414$	6.87866			0.338068
$415$	−3.59959	−	3.13268i	−0.176697	−	0.153777i
$416$	30.4944			1.49511
$417$		−	40.0312i		−	1.96034i
$418$			79.9651i			3.91122i
$419$	−13.7453			−0.671500			−0.335750	−	0.941951i	$-0.608990\pi$
$419$	−13.7453			−0.671500			−0.335750	+	0.941951i	$0.608990\pi$
$420$	1.45278	−	1.66931i	0.0708886	−	0.0814541i
$421$	16.6746			0.812669			0.406335	−	0.913724i	$-0.366807\pi$
$421$	16.6746			0.812669			0.406335	+	0.913724i	$0.366807\pi$
$422$			22.8030i			1.11003i
$423$			28.9676i			1.40845i
$424$	−4.92911			−0.239379
$425$	−5.12303	+	0.714033i	−0.248504	+	0.0346357i
$426$	−26.8444			−1.30061
$427$			1.95398i			0.0945599i
$428$		−	12.6768i		−	0.612757i
$429$	−56.8440			−2.74445
$430$	14.6890	−	16.8783i	0.708366	−	0.813943i
$431$	5.57968			0.268764			0.134382	−	0.990930i	$-0.457095\pi$
$431$	5.57968			0.268764			0.134382	+	0.990930i	$0.457095\pi$
$432$		−	2.46300i		−	0.118501i
$433$			10.9860i			0.527953i	0.964529	+	0.263977i	$0.0850342\pi$
$433$			10.9860i			0.527953i	−0.964529	+	0.263977i	$0.914966\pi$
$434$	−0.254594			−0.0122209
$435$	41.8194	+	36.3950i	2.00509	+	1.74501i
$436$	9.34329			0.447462
$437$		−	11.5080i		−	0.550501i
$438$		−	60.9801i		−	2.91374i
$439$	17.3442			0.827795			0.413897	−	0.910324i	$-0.364167\pi$
$439$	17.3442			0.827795			0.413897	+	0.910324i	$0.364167\pi$
$440$	−10.0877	−	8.77924i	−0.480913	−	0.418534i
$441$	−19.2737			−0.917794
$442$			8.78602i			0.417908i
$443$		−	23.6992i		−	1.12598i	−0.826463	−	0.562991i	$-0.809651\pi$
$443$		−	23.6992i		−	1.12598i	0.826463	−	0.562991i	$-0.190349\pi$
$444$	−5.07323			−0.240765
$445$	−4.03610	+	4.63766i	−0.191330	+	0.219846i
$446$	4.63483			0.219466
$447$		−	39.0631i		−	1.84762i
$448$		−	0.702808i		−	0.0332045i
$449$	27.2306			1.28509			0.642546	−	0.766247i	$-0.277878\pi$
$449$	27.2306			1.28509			0.642546	+	0.766247i	$0.277878\pi$
$450$	25.3249	−	3.52971i	1.19383	−	0.166392i
$451$	−27.7462			−1.30652
$452$			5.34303i			0.251315i
$453$		−	17.8280i		−	0.837631i
$454$	−20.6284			−0.968140
$455$	2.05669	−	2.36322i	0.0964190	−	0.110790i
$456$	24.1465			1.13076
$457$			23.5359i			1.10096i	0.834848	+	0.550481i	$0.185556\pi$
$457$			23.5359i			1.10096i	−0.834848	+	0.550481i	$0.814444\pi$
$458$			40.2177i			1.87925i
$459$	0.523171			0.0244195
$460$	−3.08587	−	2.68560i	−0.143879	−	0.125217i
$461$	−37.9663			−1.76827			−0.884133	−	0.467236i	$-0.845250\pi$
$461$	−37.9663			−1.76827			−0.884133	+	0.467236i	$0.845250\pi$
$462$			6.80078i			0.316401i
$463$			6.08858i			0.282960i	0.989941	+	0.141480i	$0.0451861\pi$
$463$			6.08858i			0.282960i	−0.989941	+	0.141480i	$0.954814\pi$
$464$	50.1825			2.32967
$465$	−1.86413	−	1.62234i	−0.0864472	−	0.0752340i
$466$	2.63218			0.121934
$467$		−	29.4171i		−	1.36126i	−0.732628	−	0.680630i	$-0.761706\pi$
$467$		−	29.4171i		−	1.36126i	0.732628	−	0.680630i	$-0.238294\pi$
$468$		−	17.5807i		−	0.812669i
$469$	−4.48270			−0.206992
$470$	27.9400	−	32.1043i	1.28878	−	1.48086i
$471$	−39.6434			−1.82667
$472$		−	5.88633i		−	0.270940i
$473$			27.8339i			1.27980i
$474$	−11.6320			−0.534274
$475$	−5.90518	−	42.3684i	−0.270948	−	1.94400i
$476$	0.425491			0.0195023
$477$			11.7240i			0.536804i
$478$		−	50.9523i		−	2.33050i
$479$	17.9285			0.819173			0.409587	−	0.912271i	$-0.365673\pi$
$479$	17.9285			0.819173			0.409587	+	0.912271i	$0.365673\pi$
$480$	23.2480	−	26.7130i	1.06112	−	1.21928i
$481$	−7.18211			−0.327476
$482$		−	1.83307i		−	0.0834938i
$483$		−	0.978717i		−	0.0445331i
$484$	−20.3996			−0.927253
$485$	−17.7737	−	15.4683i	−0.807063	−	0.702378i
$486$	−39.5018			−1.79184
$487$			22.6663i			1.02711i	0.858057	+	0.513554i	$0.171671\pi$
$487$			22.6663i			1.02711i	−0.858057	+	0.513554i	$0.828329\pi$
$488$			7.57908i			0.343089i
$489$	51.8697			2.34563
$490$	21.3607	+	18.5899i	0.964976	+	0.839808i
$491$	14.3512			0.647661			0.323831	−	0.946115i	$-0.395029\pi$
$491$	14.3512			0.647661			0.323831	+	0.946115i	$0.395029\pi$
$492$		−	17.8092i		−	0.802899i
$493$			10.6594i			0.480073i
$494$	−72.6620			−3.26922
$495$	−20.8815	+	23.9938i	−0.938556	+	1.07844i
$496$	−2.23693			−0.100441
$497$			1.84043i			0.0825544i
$498$			9.41270i			0.421793i
$499$	16.1552			0.723206			0.361603	−	0.932332i	$-0.382230\pi$
$499$	16.1552			0.723206			0.361603	+	0.932332i	$0.382230\pi$
$500$	−12.7392	−	8.30398i	−0.569714	−	0.371365i
$501$	6.81565			0.304501
$502$			14.9862i			0.668869i
$503$			17.0723i			0.761215i	0.924737	+	0.380607i	$0.124285\pi$
$503$			17.0723i			0.761215i	−0.924737	+	0.380607i	$0.875715\pi$
$504$	0.989520			0.0440767
$505$	10.2757	−	11.8072i	0.457260	−	0.525412i
$506$	12.5718			0.558886
$507$		−	20.3719i		−	0.904748i
$508$		−	25.9226i		−	1.15013i
$509$	24.9620			1.10642			0.553211	−	0.833041i	$-0.313402\pi$
$509$	24.9620			1.10642			0.553211	+	0.833041i	$0.313402\pi$
$510$	7.69653	+	6.69820i	0.340808	+	0.296601i
$511$	−4.18074			−0.184945
$512$		−	20.6300i		−	0.911727i
$513$			4.32672i			0.191029i
$514$	4.18409			0.184552
$515$	1.57122	+	1.36742i	0.0692364	+	0.0602557i
$516$	−17.8654			−0.786482
$517$			52.9429i			2.32843i
$518$			0.859263i			0.0377538i
$519$	−53.5798			−2.35189
$520$	7.97745	−	9.16643i	0.349834	−	0.401975i
$521$	−31.2003			−1.36691			−0.683456	−	0.729992i	$-0.739524\pi$
$521$	−31.2003			−1.36691			−0.683456	+	0.729992i	$0.739524\pi$
$522$		−	52.6928i		−	2.30630i
$523$			21.0227i			0.919257i	0.888111	+	0.459628i	$0.152017\pi$
$523$			21.0227i			0.919257i	−0.888111	+	0.459628i	$0.847983\pi$
$524$	−16.2984			−0.712000
$525$	−0.502218	−	3.60330i	−0.0219186	−	0.157261i
$526$	−12.0820			−0.526802
$527$		−	0.475149i		−	0.0206978i
$528$			59.7533i			2.60043i
$529$	21.1908			0.921337
$530$	11.3081	−	12.9935i	0.491191	−	0.564399i
$531$	−14.0007			−0.607580
$532$			3.51889i			0.152563i
$533$		−	25.2122i		−	1.09206i
$534$	12.1272			0.524795
$535$	−15.7210	−	13.6818i	−0.679678	−	0.591516i
$536$	−17.3874			−0.751022
$537$		−	4.39730i		−	0.189757i
$538$			31.4060i			1.35401i
$539$	−35.2257			−1.51728
$540$	1.16021	+	1.00972i	0.0499276	+	0.0434514i
$541$	−19.9902			−0.859445			−0.429722	−	0.902961i	$-0.641389\pi$
$541$	−19.9902			−0.859445			−0.429722	+	0.902961i	$0.641389\pi$
$542$		−	16.8873i		−	0.725372i
$543$			30.1098i			1.29214i
$544$	6.80887			0.291928
$545$	10.0840	−	11.5870i	0.431951	−	0.496331i
$546$	−6.17968			−0.264466
$547$			1.94389i			0.0831148i	0.999136	+	0.0415574i	$0.0132319\pi$
$547$			1.94389i			0.0831148i	−0.999136	+	0.0415574i	$0.986768\pi$
$548$			15.5898i			0.665963i
$549$	18.0270			0.769372
$550$	46.2852	−	6.45110i	1.97361	−	0.275076i
$551$	−88.1548			−3.75552
$552$		−	3.79623i		−	0.161578i
$553$			0.797478i			0.0339122i
$554$	−38.8051			−1.64867
$555$	−5.47543	+	6.29150i	−0.232419	+	0.267059i
$556$	22.6279			0.959639
$557$		−	5.46031i		−	0.231361i	−0.993286	−	0.115680i	$-0.963095\pi$
$557$		−	5.46031i		−	0.231361i	0.993286	−	0.115680i	$-0.0369048\pi$
$558$			2.34882i			0.0994336i
$559$	−25.2919			−1.06973
$560$	−2.48417	−	2.16195i	−0.104975	−	0.0913589i
$561$	−12.6923			−0.535869
$562$			51.8725i			2.18811i
$563$		−	31.3778i		−	1.32242i	−0.750202	−	0.661208i	$-0.770044\pi$
$563$		−	31.3778i		−	1.32242i	0.750202	−	0.661208i	$-0.229956\pi$
$564$	−33.9819			−1.43090
$565$	6.62609	+	5.76661i	0.278762	+	0.242603i
$566$	−48.9524			−2.05762
$567$			2.89887i			0.121741i
$568$			7.13862i			0.299530i
$569$	35.0427			1.46907			0.734533	−	0.678573i	$-0.237401\pi$
$569$	35.0427			1.46907			0.734533	+	0.678573i	$0.237401\pi$
$570$	−55.3954	+	63.6517i	−2.32026	+	2.66608i
$571$	−1.82647			−0.0764356			−0.0382178	−	0.999269i	$-0.512168\pi$
$571$	−1.82647			−0.0764356			−0.0382178	+	0.999269i	$0.512168\pi$
$572$		−	32.1315i		−	1.34349i
$573$			8.36722i			0.349546i
$574$	−3.01637			−0.125901
$575$	−6.66102	+	0.928393i	−0.277784	+	0.0387167i
$576$	−6.48393			−0.270164
$577$		−	13.8070i		−	0.574792i	−0.957812	−	0.287396i	$-0.907210\pi$
$577$		−	13.8070i		−	0.574792i	0.957812	−	0.287396i	$-0.0927895\pi$
$578$		−	29.2003i		−	1.21457i
$579$	−9.63959			−0.400608
$580$	−20.5726	+	23.6388i	−0.854230	+	0.981547i
$581$	0.645326			0.0267726
$582$			46.4772i			1.92654i
$583$			21.4274i			0.887433i
$584$	−16.2162			−0.671031
$585$	−21.8025	−	18.9745i	−0.901422	−	0.784498i
$586$	37.9285			1.56681
$587$			11.7903i			0.486637i	0.969946	+	0.243319i	$0.0782361\pi$
$587$			11.7903i			0.486637i	−0.969946	+	0.243319i	$0.921764\pi$
$588$		−	22.6100i		−	0.932419i
$589$	3.92957			0.161915
$590$	15.5167	+	13.5040i	0.638814	+	0.555953i
$591$	12.3823			0.509342
$592$			7.54968i			0.310290i
$593$		−	1.87116i		−	0.0768392i	−0.999262	−	0.0384196i	$-0.987768\pi$
$593$		−	1.87116i		−	0.0768392i	0.999262	−	0.0384196i	$-0.0122323\pi$
$594$	−4.72671			−0.193939
$595$	0.459223	−	0.527667i	0.0188263	−	0.0216322i
$596$	22.0807			0.904462
$597$		−	24.9770i		−	1.02224i
$598$			11.4237i			0.467149i
$599$	25.0996			1.02554			0.512772	−	0.858525i	$-0.328619\pi$
$599$	25.0996			1.02554			0.512772	+	0.858525i	$0.328619\pi$
$600$	−1.94799	−	13.9764i	−0.0795265	−	0.570586i
$601$	17.2895			0.705254			0.352627	−	0.935764i	$-0.385288\pi$
$601$	17.2895			0.705254			0.352627	+	0.935764i	$0.385288\pi$
$602$			3.02590i			0.123327i
$603$			41.3562i			1.68416i
$604$	10.0774			0.410044
$605$	−22.0168	+	25.2983i	−0.895111	+	1.02852i
$606$	−30.8750			−1.25421
$607$		−	24.4282i		−	0.991510i	−0.868462	−	0.495755i	$-0.834891\pi$
$607$		−	24.4282i		−	0.991510i	0.868462	−	0.495755i	$-0.165109\pi$
$608$			56.3106i			2.28370i
$609$	−7.49730			−0.303806
$610$	−19.9789	−	17.3875i	−0.808924	−	0.703997i
$611$	−48.1078			−1.94623
$612$		−	3.92547i		−	0.158678i
$613$		−	0.229288i		−	0.00926086i	−0.999989	−	0.00463043i	$-0.998526\pi$
$613$		−	0.229288i		−	0.00926086i	0.999989	−	0.00463043i	$-0.00147392\pi$
$614$	37.1690			1.50002
$615$	−22.0858	−	19.2210i	−0.890585	−	0.775067i
$616$	1.80850			0.0728667
$617$		−	30.1386i		−	1.21333i	−0.794956	−	0.606667i	$-0.792506\pi$
$617$		−	30.1386i		−	1.21333i	0.794956	−	0.606667i	$-0.207494\pi$
$618$		−	4.10865i		−	0.165274i
$619$	24.6422			0.990455			0.495227	−	0.868763i	$-0.335085\pi$
$619$	24.6422			0.990455			0.495227	+	0.868763i	$0.335085\pi$
$620$	0.917038	−	1.05372i	0.0368291	−	0.0423183i
$621$	0.680232			0.0272968
$622$		−	22.5904i		−	0.905791i
$623$		−	0.831429i		−	0.0333105i
$624$	−54.2961			−2.17358
$625$	−24.0472	+	6.83605i	−0.961888	+	0.273442i
$626$	−19.3256			−0.772405
$627$		−	104.968i		−	4.19200i
$628$		−	22.4088i		−	0.894207i
$629$	−1.60364			−0.0639413
$630$	−2.27009	+	2.60844i	−0.0904427	+	0.103923i
$631$	−12.0079			−0.478027			−0.239014	−	0.971016i	$-0.576824\pi$
$631$	−12.0079			−0.478027			−0.239014	+	0.971016i	$0.576824\pi$
$632$			3.09325i			0.123043i
$633$		−	29.9328i		−	1.18972i
$634$	38.4427			1.52676
$635$	−32.1476	−	27.9777i	−1.27574	−	1.11026i
$636$	−13.7534			−0.545357
$637$		−	32.0086i		−	1.26823i
$638$		−	96.3044i		−	3.81273i
$639$	16.9793			0.671691
$640$	−15.0174	−	13.0695i	−0.593615	−	0.516617i
$641$	−21.7431			−0.858799			−0.429400	−	0.903115i	$-0.641275\pi$
$641$	−21.7431			−0.858799			−0.429400	+	0.903115i	$0.641275\pi$
$642$			41.1094i			1.62246i
$643$			28.4439i			1.12172i	0.827911	+	0.560860i	$0.189529\pi$
$643$			28.4439i			1.12172i	−0.827911	+	0.560860i	$0.810471\pi$
$644$	0.553227			0.0218002
$645$	−19.2818	+	22.1556i	−0.759219	+	0.872376i
$646$	−16.2242			−0.638332
$647$		−	10.8334i		−	0.425903i	−0.977063	−	0.212952i	$-0.931692\pi$
$647$		−	10.8334i		−	0.425903i	0.977063	−	0.212952i	$-0.0683076\pi$
$648$			11.2441i			0.441710i
$649$	−25.5885			−1.00444
$650$	5.86193	+	42.0581i	0.229924	+	1.64965i
$651$	0.334198			0.0130982
$652$			29.3198i			1.14825i
$653$			29.1679i			1.14143i	0.821149	+	0.570714i	$0.193333\pi$
$653$			29.1679i			1.14143i	−0.821149	+	0.570714i	$0.806667\pi$
$654$	−30.2992			−1.18479
$655$	−17.5905	+	20.2123i	−0.687319	+	0.789759i
$656$	−26.5025			−1.03475
$657$			38.5705i			1.50478i
$658$			5.75558i			0.224376i
$659$	−3.98489			−0.155229			−0.0776147	−	0.996983i	$-0.524730\pi$
$659$	−3.98489			−0.155229			−0.0776147	+	0.996983i	$0.524730\pi$
$660$	−28.1471	−	24.4961i	−1.09563	−	0.953511i
$661$	10.7056			0.416399			0.208200	−	0.978086i	$-0.433240\pi$
$661$	10.7056			0.416399			0.208200	+	0.978086i	$0.433240\pi$
$662$			35.3615i			1.37437i
$663$		−	11.5331i		−	0.447910i
$664$	2.50308			0.0971384
$665$	4.36390	+	3.79786i	0.169225	+	0.147275i
$666$	7.92734			0.307178
$667$			13.8594i			0.536638i
$668$			3.85260i			0.149062i
$669$	−6.08400			−0.235221
$670$	39.8891	−	45.8343i	1.54105	−	1.77073i
$671$	32.9471			1.27191
$672$			4.78905i			0.184741i
$673$		−	9.82304i		−	0.378650i	−0.981914	−	0.189325i	$-0.939370\pi$
$673$		−	9.82304i		−	0.378650i	0.981914	−	0.189325i	$-0.0606300\pi$
$674$	−50.4136			−1.94186
$675$	2.50438	−	0.349053i	0.0963937	−	0.0134351i
$676$	11.5154			0.442899
$677$			26.9422i			1.03547i	0.855540	+	0.517737i	$0.173225\pi$
$677$			26.9422i			1.03547i	−0.855540	+	0.517737i	$0.826775\pi$
$678$		−	17.3268i		−	0.665432i
$679$	3.18643			0.122284
$680$	1.78123	−	2.04671i	0.0683069	−	0.0784876i
$681$	27.0783			1.03764
$682$			4.29285i			0.164382i
$683$		−	44.7069i		−	1.71066i	−0.518082	−	0.855331i	$-0.673354\pi$
$683$		−	44.7069i		−	1.71066i	0.518082	−	0.855331i	$-0.326646\pi$
$684$	32.4644			1.24131
$685$	19.3335	+	16.8257i	0.738694	+	0.642878i
$686$	−7.70967			−0.294356
$687$		−	52.7925i		−	2.01416i
$688$			26.5863i			1.01359i
$689$	−19.4705			−0.741767
$690$	10.0071	+	8.70907i	0.380964	+	0.331549i
$691$	38.1949			1.45300			0.726502	−	0.687164i	$-0.241145\pi$
$691$	38.1949			1.45300			0.726502	+	0.687164i	$0.241145\pi$
$692$		−	30.2864i		−	1.15132i
$693$		−	4.30155i		−	0.163403i
$694$	−42.5807			−1.61634
$695$	24.4218	−	28.0618i	0.926373	−	1.06444i
$696$	−29.0804			−1.10229
$697$		−	5.62945i		−	0.213231i
$698$		−	57.8332i		−	2.18902i
$699$	−3.45519			−0.130687
$700$	2.03680	−	0.283883i	0.0769836	−	0.0107298i
$701$	20.1487			0.761008			0.380504	−	0.924779i	$-0.375751\pi$
$701$	20.1487			0.761008			0.380504	+	0.924779i	$0.375751\pi$
$702$		−	4.29503i		−	0.162105i
$703$		−	13.2624i		−	0.500201i
$704$	−11.8504			−0.446629
$705$	−36.6759	+	42.1423i	−1.38130	+	1.58717i
$706$	10.2786			0.386841
$707$			2.11676i			0.0796091i
$708$		−	16.4242i		−	0.617261i
$709$	−29.3168			−1.10102			−0.550508	−	0.834830i	$-0.685566\pi$
$709$	−29.3168			−1.10102			−0.550508	+	0.834830i	$0.685566\pi$
$710$	−18.8178	−	16.3770i	−0.706221	−	0.614617i
$711$	7.35733			0.275921
$712$		−	3.22493i		−	0.120859i
$713$		−	0.617794i		−	0.0231366i
$714$	−1.37982			−0.0516383
$715$	−39.8475	−	34.6789i	−1.49021	−	1.29692i
$716$	2.48561			0.0928916
$717$			66.8834i			2.49781i
$718$			43.6789i			1.63008i
$719$	−3.26007			−0.121580			−0.0607900	−	0.998151i	$-0.519362\pi$
$719$	−3.26007			−0.121580			−0.0607900	+	0.998151i	$0.519362\pi$
$720$	−19.9456	+	22.9183i	−0.743328	+	0.854116i
$721$	−0.281685			−0.0104905
$722$		−	99.3487i		−	3.69738i
$723$			2.40621i			0.0894878i
$724$	−17.0198			−0.632536
$725$	7.11180	+	51.0256i	0.264126	+	1.89504i
$726$	66.1534			2.45518
$727$		−	20.1773i		−	0.748336i	−0.927361	−	0.374168i	$-0.877928\pi$
$727$		−	20.1773i		−	0.748336i	0.927361	−	0.374168i	$-0.122072\pi$
$728$			1.64334i			0.0609061i
$729$	23.0937			0.855321
$730$	37.2022	−	42.7469i	1.37691	−	1.58213i
$731$	−5.64724			−0.208871
$732$			21.1474i			0.781632i
$733$			13.8239i			0.510599i	0.966862	+	0.255299i	$0.0821740\pi$
$733$			13.8239i			0.510599i	−0.966862	+	0.255299i	$0.917826\pi$
$734$	19.7554			0.729185
$735$	−28.0394	−	24.4024i	−1.03425	−	0.900097i
$736$	8.85297			0.326325
$737$			75.5851i			2.78421i
$738$			27.8283i			1.02437i
$739$	−7.81411			−0.287447			−0.143723	−	0.989618i	$-0.545908\pi$
$739$	−7.81411			−0.287447			−0.143723	+	0.989618i	$0.545908\pi$
$740$	−3.55632	−	3.09503i	−0.130733	−	0.113776i
$741$	95.3811			3.50391
$742$			2.32944i			0.0855163i
$743$			34.4155i			1.26258i	0.775546	+	0.631291i	$0.217475\pi$
$743$			34.4155i			1.26258i	−0.775546	+	0.631291i	$0.782525\pi$
$744$	1.29628			0.0475240
$745$	23.8312	−	27.3831i	0.873109	−	1.00324i
$746$	12.5214			0.458442
$747$		−	5.95362i		−	0.217831i
$748$		−	7.17442i		−	0.262323i
$749$	2.81842			0.102983
$750$	41.3117	+	26.9288i	1.50849	+	0.983301i
$751$	−32.6623			−1.19187			−0.595933	−	0.803034i	$-0.703218\pi$
$751$	−32.6623			−1.19187			−0.595933	+	0.803034i	$0.703218\pi$
$752$			50.5699i			1.84409i
$753$		−	19.6720i		−	0.716886i
$754$	87.5092			3.18690
$755$	10.8763	−	12.4974i	0.395830	−	0.454826i
$756$	−0.208000			−0.00756489
$757$			17.6525i			0.641590i	0.947149	+	0.320795i	$0.103950\pi$
$757$			17.6525i			0.641590i	−0.947149	+	0.320795i	$0.896050\pi$
$758$		−	20.9410i		−	0.760611i
$759$	−16.5026			−0.599008
$760$	16.9266	+	14.7311i	0.613994	+	0.534352i
$761$	−40.8281			−1.48002			−0.740008	−	0.672598i	$-0.765178\pi$
$761$	−40.8281			−1.48002			−0.740008	+	0.672598i	$0.765178\pi$
$762$			84.0639i			3.04532i
$763$			2.07728i			0.0752027i
$764$	−4.72964			−0.171112
$765$	−4.86812	−	4.23667i	−0.176007	−	0.153177i
$766$	−70.1227			−2.53363
$767$		−	23.2516i		−	0.839566i
$768$			50.4542i			1.82061i
$769$	12.1935			0.439709			0.219854	−	0.975533i	$-0.429442\pi$
$769$	12.1935			0.439709			0.219854	+	0.975533i	$0.429442\pi$
$770$	−4.14896	+	4.76733i	−0.149518	+	0.171803i
$771$	−5.49232			−0.197801
$772$		−	5.44886i		−	0.196109i
$773$			37.8215i			1.36035i	0.733052	+	0.680173i	$0.238095\pi$
$773$			37.8215i			1.36035i	−0.733052	+	0.680173i	$0.761905\pi$
$774$	27.9162			1.00343
$775$	−0.317014	−	2.27451i	−0.0113875	−	0.0817027i
$776$	12.3595			0.443680
$777$		−	1.12793i		−	0.0404641i
$778$		−	0.185042i		−	0.00663407i
$779$	46.5566			1.66806
$780$	22.2590	−	25.5765i	0.796999	−	0.915786i
$781$	31.0324			1.11043
$782$			2.55071i			0.0912132i
$783$		−	5.21080i		−	0.186219i
$784$	−33.6468			−1.20167
$785$	−27.7900	−	24.1853i	−0.991866	−	0.863210i
$786$	52.8539			1.88524
$787$			13.9696i			0.497964i	0.968508	+	0.248982i	$0.0800960\pi$
$787$			13.9696i			0.497964i	−0.968508	+	0.248982i	$0.919904\pi$
$788$			6.99922i			0.249337i
$789$	15.8597			0.564620
$790$	−8.15399	−	7.09633i	−0.290106	−	0.252476i
$791$	−1.18791			−0.0422372
$792$		−	16.6848i		−	0.592869i
$793$			29.9381i			1.06313i
$794$	34.4587			1.22289
$795$	−14.8437	+	17.0561i	−0.526453	+	0.604917i
$796$	14.1184			0.500415
$797$		−	12.1732i		−	0.431198i	−0.976482	−	0.215599i	$-0.930830\pi$
$797$		−	12.1732i		−	0.431198i	0.976482	−	0.215599i	$-0.0691705\pi$
$798$		−	11.4113i		−	0.403957i
$799$	−10.7416			−0.380012
$800$	32.5936	−	4.54280i	1.15236	−	0.160612i
$801$	−7.67055			−0.271026
$802$		−	29.6603i		−	1.04734i
$803$			70.4937i			2.48767i
$804$	−48.5150			−1.71099
$805$	0.597086	−	0.686078i	0.0210445	−	0.0241811i
$806$	−3.90079			−0.137399
$807$		−	41.2256i		−	1.45121i
$808$			8.21047i			0.288843i
$809$	25.0091			0.879271			0.439636	−	0.898176i	$-0.355108\pi$
$809$	25.0091			0.879271			0.439636	+	0.898176i	$0.355108\pi$
$810$	−29.6401	−	25.7955i	−1.04145	−	0.906361i
$811$	39.0119			1.36989			0.684947	−	0.728593i	$-0.259826\pi$
$811$	39.0119			1.36989			0.684947	+	0.728593i	$0.259826\pi$
$812$		−	4.23791i		−	0.148721i
$813$			22.1674i			0.777446i
$814$	14.4885			0.507821
$815$	36.3606	+	31.6442i	1.27365	+	1.10845i
$816$	−12.1234			−0.424404
$817$		−	46.7037i		−	1.63396i
$818$			6.90210i			0.241326i
$819$	3.90870			0.136581
$820$	10.8648	−	12.4842i	0.379417	−	0.435966i
$821$	−18.5556			−0.647595			−0.323797	−	0.946126i	$-0.604960\pi$
$821$	−18.5556			−0.647595			−0.323797	+	0.946126i	$0.604960\pi$
$822$		−	50.5559i		−	1.76334i
$823$		−	50.5534i		−	1.76218i	−0.472949	−	0.881090i	$-0.656810\pi$
$823$		−	50.5534i		−	1.76218i	0.472949	−	0.881090i	$-0.343190\pi$
$824$	−1.09260			−0.0380624
$825$	−60.7571	+	8.46815i	−2.11529	+	0.294823i
$826$	−2.78180			−0.0967914
$827$		−	14.1845i		−	0.493242i	−0.969112	−	0.246621i	$-0.920680\pi$
$827$		−	14.1845i		−	0.493242i	0.969112	−	0.246621i	$-0.0793203\pi$
$828$		−	5.10394i		−	0.177374i
$829$	56.2077			1.95217			0.976087	−	0.217381i	$-0.0697513\pi$
$829$	56.2077			1.95217			0.976087	+	0.217381i	$0.0697513\pi$
$830$	−5.74241	+	6.59828i	−0.199322	+	0.229030i
$831$	50.9382			1.76703
$832$		−	10.7681i		−	0.373318i
$833$		−	7.14697i		−	0.247628i
$834$	−73.3798			−2.54093
$835$	4.77776	+	4.15803i	0.165341	+	0.143895i
$836$	59.3338			2.05210
$837$			0.232276i			0.00802862i
$838$			25.1960i			0.870380i
$839$	9.83492			0.339539			0.169770	−	0.985484i	$-0.445698\pi$
$839$	9.83492			0.339539			0.169770	+	0.985484i	$0.445698\pi$
$840$	1.43956	+	1.25283i	0.0496695	+	0.0432268i
$841$	77.1677			2.66095
$842$		−	30.5656i		−	1.05336i
$843$		−	68.0914i		−	2.34519i
$844$	16.9198			0.582402
$845$	12.4283	−	14.2806i	0.427546	−	0.491269i
$846$	53.0996			1.82560
$847$		−	4.53542i		−	0.155839i
$848$			20.4670i			0.702839i
$849$	64.2583			2.20534
$850$	1.30887	+	9.39085i	0.0448938	+	0.322103i
$851$	−2.08507			−0.0714753
$852$			19.9184i			0.682394i
$853$			34.2541i			1.17284i	0.810008	+	0.586419i	$0.199463\pi$
$853$			34.2541i			1.17284i	−0.810008	+	0.586419i	$0.800537\pi$
$854$	3.58178			0.122566
$855$	35.0381	−	40.2603i	1.19828	−	1.37687i
$856$	10.9321			0.373650
$857$		−	45.4343i		−	1.55201i	−0.630729	−	0.776004i	$-0.717244\pi$
$857$		−	45.4343i		−	1.55201i	0.630729	−	0.776004i	$-0.282756\pi$
$858$			104.199i			3.55729i
$859$	−8.81001			−0.300594			−0.150297	−	0.988641i	$-0.548023\pi$
$859$	−8.81001			−0.300594			−0.150297	+	0.988641i	$0.548023\pi$
$860$	−12.5236	−	10.8992i	−0.427052	−	0.371659i
$861$	3.95949			0.134939
$862$		−	10.2279i		−	0.348364i
$863$			26.7733i			0.911374i	0.890140	+	0.455687i	$0.150606\pi$
$863$			26.7733i			0.911374i	−0.890140	+	0.455687i	$0.849394\pi$
$864$	−3.32850			−0.113238
$865$	−37.5593	−	32.6875i	−1.27706	−	1.11141i
$866$	20.1380			0.684319
$867$			38.3304i			1.30177i
$868$			0.188908i			0.00641196i
$869$	13.4467			0.456148
$870$	66.7144	−	76.6578i	2.26183	−	2.59894i
$871$	−68.6821			−2.32720
$872$			8.05734i			0.272856i
$873$		−	29.3972i		−	0.994945i
$874$	−21.0948			−0.713544
$875$	1.84622	−	2.83229i	0.0624135	−	0.0957490i
$876$	−45.2470			−1.52876
$877$		−	28.5732i		−	0.964850i	−0.875937	−	0.482425i	$-0.839756\pi$
$877$		−	28.5732i		−	0.964850i	0.875937	−	0.482425i	$-0.160244\pi$
$878$		−	31.7931i		−	1.07296i
$879$	−49.7875			−1.67929
$880$	−36.4537	+	41.8869i	−1.22885	+	1.41201i
$881$	13.4524			0.453224			0.226612	−	0.973985i	$-0.427235\pi$
$881$	13.4524			0.453224			0.226612	+	0.973985i	$0.427235\pi$
$882$			35.3299i			1.18962i
$883$			2.30504i			0.0775706i	0.999248	+	0.0387853i	$0.0123488\pi$
$883$			2.30504i			0.0775706i	−0.999248	+	0.0387853i	$0.987651\pi$
$884$	6.51919			0.219264
$885$	−20.3683	−	17.7263i	−0.684674	−	0.595864i
$886$	−43.4421			−1.45947
$887$		−	7.50871i		−	0.252118i	−0.992023	−	0.126059i	$-0.959767\pi$
$887$		−	7.50871i		−	0.252118i	0.992023	−	0.126059i	$-0.0402328\pi$
$888$		−	4.37498i		−	0.146815i
$889$	5.76335			0.193296
$890$	8.50112	+	7.39844i	0.284958	+	0.247996i
$891$	48.8793			1.63752
$892$		−	3.43903i		−	0.115147i
$893$		−	88.8353i		−	2.97276i
$894$	−71.6052			−2.39484
$895$	2.68266	−	3.08250i	0.0896715	−	0.103036i
$896$	2.69229			0.0899430
$897$		−	14.9955i		−	0.500685i
$898$		−	49.9155i		−	1.66570i
$899$	−4.73251			−0.157838
$900$	−2.61903	−	18.7910i	−0.0873010	−	0.626366i
$901$	−4.34743			−0.144834
$902$			50.8606i			1.69347i
$903$		−	3.97201i		−	0.132180i
$904$	−4.60765			−0.153248
$905$	−18.3691	+	21.1069i	−0.610610	+	0.701617i
$906$	−32.6798			−1.08571
$907$		−	27.9423i		−	0.927810i	−0.885885	−	0.463905i	$-0.846448\pi$
$907$		−	27.9423i		−	0.927810i	0.885885	−	0.463905i	$-0.153552\pi$
$908$			15.3062i			0.507954i
$909$	19.5287			0.647727
$910$	−4.33194	−	3.77004i	−0.143602	−	0.124976i
$911$	21.0515			0.697468			0.348734	−	0.937222i	$-0.386612\pi$
$911$	21.0515			0.697468			0.348734	+	0.937222i	$0.386612\pi$
$912$		−	100.263i		−	3.32003i
$913$		−	10.8812i		−	0.360114i
$914$	43.1428			1.42704
$915$	26.2257	+	22.8240i	0.866995	+	0.754537i
$916$	29.8414			0.985987
$917$		−	3.62361i		−	0.119662i
$918$		−	0.959006i		−	0.0316519i
$919$	−5.21572			−0.172051			−0.0860253	−	0.996293i	$-0.527417\pi$
$919$	−5.21572			−0.172051			−0.0860253	+	0.996293i	$0.527417\pi$
$920$	2.31597	−	2.66115i	0.0763552	−	0.0877355i
$921$	−48.7905			−1.60770
$922$			69.5946i			2.29198i
$923$			28.1983i			0.928157i
$924$	5.04615			0.166006
$925$	−7.67652	+	1.06993i	−0.252402	+	0.0351791i
$926$	11.1608			0.366765
$927$			2.59876i			0.0853544i
$928$		−	67.8167i		−	2.22619i
$929$	51.1232			1.67730			0.838649	−	0.544672i	$-0.183346\pi$
$929$	51.1232			1.67730			0.838649	+	0.544672i	$0.183346\pi$
$930$	−2.97385	+	3.41708i	−0.0975163	+	0.112050i
$931$	59.1068			1.93715
$932$		−	1.95307i		−	0.0639750i
$933$			29.6536i			0.970817i
$934$	−53.9234			−1.76443
$935$	−8.89726	−	7.74319i	−0.290972	−	0.253229i
$936$	15.1610			0.495553
$937$			23.5517i			0.769400i	0.923042	+	0.384700i	$0.125695\pi$
$937$			23.5517i			0.769400i	−0.923042	+	0.384700i	$0.874305\pi$
$938$			8.21708i			0.268297i
$939$	25.3680			0.827855
$940$	−23.8212	−	20.7314i	−0.776963	−	0.676183i
$941$	45.4674			1.48219			0.741097	−	0.671398i	$-0.234306\pi$
$941$	45.4674			1.48219			0.741097	+	0.671398i	$0.234306\pi$
$942$			72.6690i			2.36768i
$943$		−	7.31947i		−	0.238355i
$944$	−24.4416			−0.795506
$945$	−0.224490	+	0.257949i	−0.00730266	+	0.00839107i
$946$	51.0213			1.65885
$947$			22.5514i			0.732821i	0.930453	+	0.366411i	$0.119413\pi$
$947$			22.5514i			0.732821i	−0.930453	+	0.366411i	$0.880587\pi$
$948$			8.63088i			0.280318i
$949$	−64.0556			−2.07933
$950$	−77.6641	+	10.8246i	−2.51975	+	0.351196i
$951$	−50.4626			−1.63636
$952$			0.366929i			0.0118922i
$953$		−	0.231111i		−	0.00748642i	−0.999993	−	0.00374321i	$-0.998808\pi$
$953$		−	0.231111i		−	0.00748642i	0.999993	−	0.00374321i	$-0.00119150\pi$
$954$	21.4908			0.695790
$955$	−5.10459	+	5.86540i	−0.165181	+	0.189800i
$956$	−37.8064			−1.22275
$957$			126.416i			4.08644i
$958$		−	32.8641i		−	1.06179i
$959$	−3.46606			−0.111925
$960$	−9.43285	−	8.20931i	−0.304444	−	0.264954i
$961$	−30.7890			−0.993195
$962$			13.1653i			0.424465i
$963$		−	26.0021i		−	0.837905i
$964$	−1.36013			−0.0438068
$965$	−6.75733	−	5.88083i	−0.217526	−	0.189311i
$966$	−1.79405			−0.0577227
$967$		−	3.83002i		−	0.123165i	−0.998102	−	0.0615825i	$-0.980385\pi$
$967$		−	3.83002i		−	0.123165i	0.998102	−	0.0615825i	$-0.0196147\pi$
$968$		−	17.5919i		−	0.565425i
$969$	21.2970			0.684157
$970$	−28.3543	+	32.5804i	−0.910403	+	1.04609i
$971$	−37.2292			−1.19474			−0.597371	−	0.801965i	$-0.703788\pi$
$971$	−37.2292			−1.19474			−0.597371	+	0.801965i	$0.703788\pi$
$972$			29.3102i			0.940124i
$973$			5.03085i			0.161282i
$974$	41.5488			1.33131
$975$	−7.69477	−	55.2083i	−0.246430	−	1.76808i
$976$	31.4704			1.00734
$977$		−	3.50188i		−	0.112035i	−0.998430	−	0.0560175i	$-0.982160\pi$
$977$		−	3.50188i		−	0.112035i	0.998430	−	0.0560175i	$-0.0178402\pi$
$978$		−	95.0806i		−	3.04034i
$979$	−14.0191			−0.448054
$980$	13.7937	−	15.8495i	0.440623	−	0.506294i
$981$	19.1645			0.611875
$982$		−	26.3067i		−	0.839481i
$983$		−	52.1048i		−	1.66188i	−0.556358	−	0.830942i	$-0.687802\pi$
$983$		−	52.1048i		−	1.66188i	0.556358	−	0.830942i	$-0.312198\pi$
$984$	15.3580			0.489596
$985$	8.67999	+	7.55410i	0.276568	+	0.240694i
$986$	19.5393			0.622258
$987$		−	7.55517i		−	0.240484i
$988$			53.9149i			1.71526i
$989$	−7.34260			−0.233481
$990$	43.9822	+	38.2772i	1.39785	+	1.21653i
$991$	55.2696			1.75570			0.877848	−	0.478939i	$-0.158978\pi$
$991$	55.2696			1.75570			0.877848	+	0.478939i	$0.158978\pi$
$992$			3.02298i			0.0959798i
$993$		−	46.4180i		−	1.47303i
$994$	3.37362			0.107005
$995$	15.2377	−	17.5088i	0.483068	−	0.555066i
$996$	6.98419			0.221302
$997$			4.93251i			0.156214i	0.996945	+	0.0781071i	$0.0248876\pi$
$997$			4.93251i			0.156214i	−0.996945	+	0.0781071i	$0.975112\pi$
$998$		−	29.6135i		−	0.937399i
$999$	0.783936			0.0248026

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1205.2.b.c.724.10	✓	46
5.2	odd	4		6025.2.a.p.1.37		46
5.3	odd	4		6025.2.a.p.1.10		46
5.4	even	2	inner	1205.2.b.c.724.37	yes	46

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1205.2.b.c.724.10	✓	46	1.1	even	1	trivial
1205.2.b.c.724.37	yes	46	5.4	even	2	inner
6025.2.a.p.1.10		46	5.3	odd	4
6025.2.a.p.1.37		46	5.2	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)

\(f(q)\)	\(=\)	\(q-1.83307i q^{2} +2.40621i q^{3} -1.36013 q^{4} +(-1.46796 + 1.68674i) q^{5} +4.41073 q^{6} -0.302396i q^{7} -1.17293i q^{8} -2.78983 q^{9} +O(q^{10})\)	\(q-1.83307i q^{2} +2.40621i q^{3} -1.36013 q^{4} +(-1.46796 + 1.68674i) q^{5} +4.41073 q^{6} -0.302396i q^{7} -1.17293i q^{8} -2.78983 q^{9} +(3.09191 + 2.69086i) q^{10} -5.09885 q^{11} -3.27275i q^{12} -4.63318i q^{13} -0.554311 q^{14} +(-4.05865 - 3.53220i) q^{15} -4.87031 q^{16} -1.03451i q^{17} +5.11394i q^{18} +8.55559 q^{19} +(1.99661 - 2.29419i) q^{20} +0.727627 q^{21} +9.34653i q^{22} -1.34508i q^{23} +2.82231 q^{24} +(-0.690213 - 4.95213i) q^{25} -8.49293 q^{26} +0.505718i q^{27} +0.411297i q^{28} -10.3038 q^{29} +(-6.47476 + 7.43978i) q^{30} +0.459299 q^{31} +6.58174i q^{32} -12.2689i q^{33} -1.89632 q^{34} +(0.510064 + 0.443904i) q^{35} +3.79452 q^{36} -1.55014i q^{37} -15.6830i q^{38} +11.1484 q^{39} +(1.97843 + 1.72181i) q^{40} +5.44165 q^{41} -1.33379i q^{42} -5.45885i q^{43} +6.93509 q^{44} +(4.09534 - 4.70573i) q^{45} -2.46562 q^{46} -10.3833i q^{47} -11.7190i q^{48} +6.90856 q^{49} +(-9.07758 + 1.26521i) q^{50} +2.48924 q^{51} +6.30172i q^{52} -4.20240i q^{53} +0.927014 q^{54} +(7.48489 - 8.60046i) q^{55} -0.354689 q^{56} +20.5865i q^{57} +18.8875i q^{58} +5.01849 q^{59} +(5.52029 + 4.80425i) q^{60} -6.46168 q^{61} -0.841924i q^{62} +0.843632i q^{63} +2.32413 q^{64} +(7.81500 + 6.80131i) q^{65} -22.4897 q^{66} -14.8239i q^{67} +1.40707i q^{68} +3.23654 q^{69} +(0.813704 - 0.934981i) q^{70} -6.08615 q^{71} +3.27227i q^{72} -13.8254i q^{73} -2.84152 q^{74} +(11.9158 - 1.66080i) q^{75} -11.6367 q^{76} +1.54187i q^{77} -20.4357i q^{78} -2.63720 q^{79} +(7.14940 - 8.21497i) q^{80} -9.58634 q^{81} -9.97491i q^{82} +2.13404i q^{83} -0.989665 q^{84} +(1.74495 + 1.51862i) q^{85} -10.0064 q^{86} -24.7930i q^{87} +5.98059i q^{88} +2.74947 q^{89} +(-8.62590 - 7.50703i) q^{90} -1.40106 q^{91} +1.82948i q^{92} +1.10517i q^{93} -19.0333 q^{94} +(-12.5592 + 14.4311i) q^{95} -15.8370 q^{96} +10.5373i q^{97} -12.6638i q^{98} +14.2249 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 46 q - 34 q^{4} - 8 q^{5} - 4 q^{6} - 34 q^{9}+O(q^{10}) \) 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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