LMFDB - Embedded newform 1205.2.b.c.724.12

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			724.12
Character	$\chi$	$=$	1205.724
Dual form			1205.2.b.c.724.35

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.49203i q^{2} -3.12646i q^{3} -0.226139 q^{4} +(0.643201 - 2.14156i) q^{5} -4.66475 q^{6} +4.66024i q^{7} -2.64665i q^{8} -6.77474 q^{9} +O(q^{10})$	\(q-1.49203i q^{2} -3.12646i q^{3} -0.226139 q^{4} +(0.643201 - 2.14156i) q^{5} -4.66475 q^{6} +4.66024i q^{7} -2.64665i q^{8} -6.77474 q^{9} +(-3.19527 - 0.959673i) q^{10} -5.92431 q^{11} +0.707014i q^{12} +4.29102i q^{13} +6.95319 q^{14} +(-6.69551 - 2.01094i) q^{15} -4.40114 q^{16} -5.72527i q^{17} +10.1081i q^{18} +1.23168 q^{19} +(-0.145453 + 0.484291i) q^{20} +14.5700 q^{21} +8.83922i q^{22} +3.63376i q^{23} -8.27462 q^{24} +(-4.17258 - 2.75491i) q^{25} +6.40231 q^{26} +11.8016i q^{27} -1.05386i q^{28} -1.81182 q^{29} +(-3.00038 + 9.98986i) q^{30} -1.11419 q^{31} +1.27332i q^{32} +18.5221i q^{33} -8.54225 q^{34} +(9.98019 + 2.99747i) q^{35} +1.53203 q^{36} -7.32690i q^{37} -1.83770i q^{38} +13.4157 q^{39} +(-5.66796 - 1.70233i) q^{40} -6.45271 q^{41} -21.7389i q^{42} +4.57155i q^{43} +1.33972 q^{44} +(-4.35752 + 14.5085i) q^{45} +5.42167 q^{46} -7.71296i q^{47} +13.7600i q^{48} -14.7178 q^{49} +(-4.11040 + 6.22560i) q^{50} -17.8998 q^{51} -0.970368i q^{52} -10.1745i q^{53} +17.6082 q^{54} +(-3.81052 + 12.6873i) q^{55} +12.3340 q^{56} -3.85081i q^{57} +2.70329i q^{58} +5.66965 q^{59} +(1.51412 + 0.454752i) q^{60} +4.76640 q^{61} +1.66239i q^{62} -31.5719i q^{63} -6.90245 q^{64} +(9.18949 + 2.75999i) q^{65} +27.6354 q^{66} -14.0103i q^{67} +1.29471i q^{68} +11.3608 q^{69} +(4.47230 - 14.8907i) q^{70} -3.96855 q^{71} +17.9303i q^{72} -8.92040i q^{73} -10.9319 q^{74} +(-8.61312 + 13.0454i) q^{75} -0.278532 q^{76} -27.6087i q^{77} -20.0166i q^{78} -1.77420 q^{79} +(-2.83082 + 9.42532i) q^{80} +16.5729 q^{81} +9.62761i q^{82} +9.93218i q^{83} -3.29485 q^{84} +(-12.2610 - 3.68250i) q^{85} +6.82087 q^{86} +5.66459i q^{87} +15.6795i q^{88} +7.03898 q^{89} +(21.6471 + 6.50153i) q^{90} -19.9972 q^{91} -0.821736i q^{92} +3.48346i q^{93} -11.5079 q^{94} +(0.792221 - 2.63773i) q^{95} +3.98098 q^{96} +5.03884i q^{97} +21.9594i q^{98} +40.1356 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	1.49203i		−	1.05502i	−0.849548	−	0.527511i	$-0.823126\pi$
$2$		−	1.49203i		−	1.05502i	0.849548	−	0.527511i	$-0.176874\pi$
$3$		−	3.12646i		−	1.80506i	−0.430626	−	0.902531i	$-0.641707\pi$
$3$		−	3.12646i		−	1.80506i	0.430626	−	0.902531i	$-0.358293\pi$
$4$	−0.226139			−0.113070
$5$	0.643201	−	2.14156i	0.287648	−	0.957736i
$5$	0.643201	−	2.14156i	0.287648	−	0.957736i
$6$	−4.66475			−1.90438
$7$			4.66024i			1.76140i	0.473670	+	0.880702i	$0.342929\pi$
$7$			4.66024i			1.76140i	−0.473670	+	0.880702i	$0.657071\pi$
$8$		−	2.64665i		−	0.935730i
$9$	−6.77474			−2.25825
$10$	−3.19527	−	0.959673i	−1.01043	−	0.303475i
$11$	−5.92431			−1.78625			−0.893123	−	0.449812i	$-0.851491\pi$
$11$	−5.92431			−1.78625			−0.893123	+	0.449812i	$0.851491\pi$
$12$			0.707014i			0.204097i
$13$			4.29102i			1.19012i	0.803683	+	0.595058i	$0.202871\pi$
$13$			4.29102i			1.19012i	−0.803683	+	0.595058i	$0.797129\pi$
$14$	6.95319			1.85832
$15$	−6.69551	−	2.01094i	−1.72877	−	0.519223i
$16$	−4.40114			−1.10028
$17$		−	5.72527i		−	1.38858i	−0.719694	−	0.694291i	$-0.755718\pi$
$17$		−	5.72527i		−	1.38858i	0.719694	−	0.694291i	$-0.244282\pi$
$18$			10.1081i			2.38250i
$19$	1.23168			0.282568			0.141284	−	0.989969i	$-0.454877\pi$
$19$	1.23168			0.282568			0.141284	+	0.989969i	$0.454877\pi$
$20$	−0.145453	+	0.484291i	−0.0325243	+	0.108291i
$21$	14.5700			3.17944
$22$			8.83922i			1.88453i
$23$			3.63376i			0.757692i	0.925460	+	0.378846i	$0.123679\pi$
$23$			3.63376i			0.757692i	−0.925460	+	0.378846i	$0.876321\pi$
$24$	−8.27462			−1.68905
$25$	−4.17258	−	2.75491i	−0.834517	−	0.550983i
$26$	6.40231			1.25560
$27$			11.8016i			2.27121i
$28$		−	1.05386i		−	0.199161i
$29$	−1.81182			−0.336447			−0.168224	−	0.985749i	$-0.553803\pi$
$29$	−1.81182			−0.336447			−0.168224	+	0.985749i	$0.553803\pi$
$30$	−3.00038	+	9.98986i	−0.547791	+	1.82389i
$31$	−1.11419			−0.200114			−0.100057	−	0.994982i	$-0.531902\pi$
$31$	−1.11419			−0.200114			−0.100057	+	0.994982i	$0.531902\pi$
$32$			1.27332i			0.225093i
$33$			18.5221i			3.22428i
$34$	−8.54225			−1.46498
$35$	9.98019	+	2.99747i	1.68696	+	0.506665i
$36$	1.53203			0.255339
$37$		−	7.32690i		−	1.20454i	−0.798294	−	0.602268i	$-0.794264\pi$
$37$		−	7.32690i		−	1.20454i	0.798294	−	0.602268i	$-0.205736\pi$
$38$		−	1.83770i		−	0.298115i
$39$	13.4157			2.14823
$40$	−5.66796	−	1.70233i	−0.896183	−	0.269161i
$41$	−6.45271			−1.00774			−0.503872	−	0.863778i	$-0.668092\pi$
$41$	−6.45271			−1.00774			−0.503872	+	0.863778i	$0.668092\pi$
$42$		−	21.7389i		−	3.35438i
$43$			4.57155i			0.697155i	0.937280	+	0.348578i	$0.113335\pi$
$43$			4.57155i			0.697155i	−0.937280	+	0.348578i	$0.886665\pi$
$44$	1.33972			0.201970
$45$	−4.35752	+	14.5085i	−0.649581	+	2.16280i
$46$	5.42167			0.799381
$47$		−	7.71296i		−	1.12505i	−0.826780	−	0.562525i	$-0.809830\pi$
$47$		−	7.71296i		−	1.12505i	0.826780	−	0.562525i	$-0.190170\pi$
$48$			13.7600i			1.98608i
$49$	−14.7178			−2.10255
$50$	−4.11040	+	6.22560i	−0.581298	+	0.880433i
$51$	−17.8998			−2.50648
$52$		−	0.970368i		−	0.134566i
$53$		−	10.1745i		−	1.39758i	−0.715329	−	0.698788i	$-0.753723\pi$
$53$		−	10.1745i		−	1.39758i	0.715329	−	0.698788i	$-0.246277\pi$
$54$	17.6082			2.39618
$55$	−3.81052	+	12.6873i	−0.513811	+	1.71075i
$56$	12.3340			1.64820
$57$		−	3.85081i		−	0.510052i
$58$			2.70329i			0.354959i
$59$	5.66965			0.738126			0.369063	−	0.929404i	$-0.379679\pi$
$59$	5.66965			0.738126			0.369063	+	0.929404i	$0.379679\pi$
$60$	1.51412	+	0.454752i	0.195471	+	0.0587083i
$61$	4.76640			0.610275			0.305138	−	0.952308i	$-0.401298\pi$
$61$	4.76640			0.610275			0.305138	+	0.952308i	$0.401298\pi$
$62$			1.66239i			0.211124i
$63$		−	31.5719i		−	3.97768i
$64$	−6.90245			−0.862807
$65$	9.18949	+	2.75999i	1.13982	+	0.342335i
$66$	27.6354			3.40169
$67$		−	14.0103i		−	1.71163i	−0.517283	−	0.855814i	$-0.673057\pi$
$67$		−	14.0103i		−	1.71163i	0.517283	−	0.855814i	$-0.326943\pi$
$68$			1.29471i			0.157006i
$69$	11.3608			1.36768
$70$	4.47230	−	14.8907i	0.534543	−	1.77978i
$71$	−3.96855			−0.470980			−0.235490	−	0.971877i	$-0.575669\pi$
$71$	−3.96855			−0.470980			−0.235490	+	0.971877i	$0.575669\pi$
$72$			17.9303i			2.11311i
$73$		−	8.92040i		−	1.04405i	−0.852929	−	0.522027i	$-0.825176\pi$
$73$		−	8.92040i		−	1.04405i	0.852929	−	0.522027i	$-0.174824\pi$
$74$	−10.9319			−1.27081
$75$	−8.61312	+	13.0454i	−0.994557	+	1.50635i
$76$	−0.278532			−0.0319498
$77$		−	27.6087i		−	3.14630i
$78$		−	20.0166i		−	2.26643i
$79$	−1.77420			−0.199614			−0.0998068	−	0.995007i	$-0.531822\pi$
$79$	−1.77420			−0.199614			−0.0998068	+	0.995007i	$0.531822\pi$
$80$	−2.83082	+	9.42532i	−0.316495	+	1.05378i
$81$	16.5729			1.84143
$82$			9.62761i			1.06319i
$83$			9.93218i			1.09020i	0.838372	+	0.545099i	$0.183508\pi$
$83$			9.93218i			1.09020i	−0.838372	+	0.545099i	$0.816492\pi$
$84$	−3.29485			−0.359498
$85$	−12.2610	−	3.68250i	−1.32990	−	0.399423i
$86$	6.82087			0.735514
$87$			5.66459i			0.607308i
$88$			15.6795i			1.67144i
$89$	7.03898			0.746131			0.373065	−	0.927805i	$-0.378307\pi$
$89$	7.03898			0.746131			0.373065	+	0.927805i	$0.378307\pi$
$90$	21.6471	+	6.50153i	2.28180	+	0.685322i
$91$	−19.9972			−2.09627
$92$		−	0.821736i		−	0.0856719i
$93$			3.48346i			0.361217i
$94$	−11.5079			−1.18695
$95$	0.792221	−	2.63773i	0.0812802	−	0.270625i
$96$	3.98098			0.406307
$97$			5.03884i			0.511617i	0.966727	+	0.255808i	$0.0823416\pi$
$97$			5.03884i			0.511617i	−0.966727	+	0.255808i	$0.917658\pi$
$98$			21.9594i			2.21823i
$99$	40.1356			4.03378
$100$	0.943584	+	0.622993i	0.0943584	+	0.0622993i
$101$	−8.87959			−0.883552			−0.441776	−	0.897125i	$-0.645651\pi$
$101$	−8.87959			−0.883552			−0.441776	+	0.897125i	$0.645651\pi$
$102$			26.7070i			2.64438i
$103$		−	3.12126i		−	0.307547i	−0.988106	−	0.153774i	$-0.950857\pi$
$103$		−	3.12126i		−	0.307547i	0.988106	−	0.153774i	$-0.0491427\pi$
$104$	11.3568			1.11363
$105$	9.37147	−	31.2027i	0.914562	−	3.04507i
$106$	−15.1806			−1.47447
$107$		−	2.37926i		−	0.230012i	−0.993365	−	0.115006i	$-0.963311\pi$
$107$		−	2.37926i		−	0.230012i	0.993365	−	0.115006i	$-0.0366887\pi$
$108$		−	2.66879i		−	0.256805i
$109$	10.9286			1.04677			0.523386	−	0.852096i	$-0.324669\pi$
$109$	10.9286			1.04677			0.523386	+	0.852096i	$0.324669\pi$
$110$	18.9297	+	5.68540i	1.80488	+	0.542081i
$111$	−22.9072			−2.17426
$112$		−	20.5104i		−	1.93805i
$113$		−	12.3477i		−	1.16157i	−0.814055	−	0.580787i	$-0.802745\pi$
$113$		−	12.3477i		−	1.16157i	0.814055	−	0.580787i	$-0.197255\pi$
$114$	−5.74550			−0.538116
$115$	7.78193	+	2.33724i	0.725669	+	0.217949i
$116$	0.409724			0.0380419
$117$		−	29.0706i		−	2.68757i
$118$		−	8.45926i		−	0.778738i
$119$	26.6811			2.44585
$120$	−5.32225	+	17.7206i	−0.485853	+	1.61766i
$121$	24.0974			2.19068
$122$		−	7.11159i		−	0.643853i
$123$			20.1741i			1.81904i
$124$	0.251961			0.0226268
$125$	−8.58363	+	7.16389i	−0.767743	+	0.640758i
$126$	−47.1061			−4.19654
$127$		−	8.83493i		−	0.783974i	−0.919971	−	0.391987i	$-0.871788\pi$
$127$		−	8.83493i		−	0.783974i	0.919971	−	0.391987i	$-0.128212\pi$
$128$			12.8453i			1.13537i
$129$	14.2928			1.25841
$130$	4.11798	−	13.7110i	0.361170	−	1.20253i
$131$	10.6930			0.934252			0.467126	−	0.884191i	$-0.345289\pi$
$131$	10.6930			0.934252			0.467126	+	0.884191i	$0.345289\pi$
$132$		−	4.18857i		−	0.364568i
$133$			5.73994i			0.497716i
$134$	−20.9037			−1.80580
$135$	25.2738	+	7.59078i	2.17522	+	0.653310i
$136$	−15.1528			−1.29934
$137$		−	6.53145i		−	0.558020i	−0.960288	−	0.279010i	$-0.909994\pi$
$137$		−	6.53145i		−	0.558020i	0.960288	−	0.279010i	$-0.0900062\pi$
$138$		−	16.9506i		−	1.44293i
$139$	9.68333			0.821329			0.410664	−	0.911787i	$-0.365297\pi$
$139$	9.68333			0.821329			0.410664	+	0.911787i	$0.365297\pi$
$140$	−2.25691	−	0.677845i	−0.190744	−	0.0572884i
$141$	−24.1142			−2.03079
$142$			5.92117i			0.496893i
$143$		−	25.4213i		−	2.12584i
$144$	29.8166			2.48471
$145$	−1.16537	+	3.88014i	−0.0967786	+	0.322228i
$146$	−13.3095			−1.10150
$147$			46.0147i			3.79522i
$148$			1.65690i			0.136196i
$149$	−14.7898			−1.21163			−0.605814	−	0.795606i	$-0.707153\pi$
$149$	−14.7898			−1.21163			−0.605814	+	0.795606i	$0.707153\pi$
$150$	19.4641	+	12.8510i	1.58924	+	1.04928i
$151$	−1.21804			−0.0991228			−0.0495614	−	0.998771i	$-0.515782\pi$
$151$	−1.21804			−0.0991228			−0.0495614	+	0.998771i	$0.515782\pi$
$152$		−	3.25983i		−	0.264407i
$153$			38.7872i			3.13576i
$154$	−41.1929			−3.31942
$155$	−0.716646	+	2.38610i	−0.0575624	+	0.191656i
$156$	−3.03381			−0.242899
$157$			9.48425i			0.756926i	0.925616	+	0.378463i	$0.123547\pi$
$157$			9.48425i			0.756926i	−0.925616	+	0.378463i	$0.876453\pi$
$158$			2.64716i			0.210597i
$159$	−31.8101			−2.52271
$160$	2.72689	+	0.819001i	0.215580	+	0.0647477i
$161$	−16.9342			−1.33460
$162$		−	24.7271i		−	1.94275i
$163$		−	2.02231i		−	0.158400i	−0.996859	−	0.0791999i	$-0.974763\pi$
$163$		−	2.02231i		−	0.158400i	0.996859	−	0.0791999i	$-0.0252365\pi$
$164$	1.45921			0.113945
$165$	39.6662	+	11.9134i	3.08801	+	0.927460i
$166$	14.8191			1.15018
$167$		−	12.0440i		−	0.931992i	−0.884787	−	0.465996i	$-0.845696\pi$
$167$		−	12.0440i		−	0.931992i	0.884787	−	0.465996i	$-0.154304\pi$
$168$		−	38.5617i		−	2.97510i
$169$	−5.41287			−0.416375
$170$	−5.49439	+	18.2938i	−0.421400	+	1.40307i
$171$	−8.34434			−0.638107
$172$		−	1.03381i		−	0.0788270i
$173$		−	10.6055i		−	0.806322i	−0.915129	−	0.403161i	$-0.867911\pi$
$173$		−	10.6055i		−	0.806322i	0.915129	−	0.403161i	$-0.132089\pi$
$174$	8.45171			0.640723
$175$	12.8386	−	19.4452i	0.970503	−	1.46992i
$176$	26.0737			1.96538
$177$		−	17.7259i		−	1.33236i
$178$		−	10.5023i		−	0.787184i
$179$	15.6670			1.17101			0.585505	−	0.810669i	$-0.300896\pi$
$179$	15.6670			1.17101			0.585505	+	0.810669i	$0.300896\pi$
$180$	0.985406	−	3.28094i	0.0734478	−	0.244547i
$181$	6.00433			0.446298			0.223149	−	0.974784i	$-0.428366\pi$
$181$	6.00433			0.446298			0.223149	+	0.974784i	$0.428366\pi$
$182$			29.8363i			2.21161i
$183$		−	14.9020i		−	1.10158i
$184$	9.61728			0.708995
$185$	−15.6910	−	4.71267i	−1.15363	−	0.346483i
$186$	5.19740			0.381092
$187$			33.9183i			2.48035i
$188$			1.74420i			0.127209i
$189$	−54.9981			−4.00052
$190$	−3.93556	−	1.18201i	−0.285515	−	0.0857523i
$191$	−14.5050			−1.04954			−0.524772	−	0.851243i	$-0.675849\pi$
$191$	−14.5050			−1.04954			−0.524772	+	0.851243i	$0.675849\pi$
$192$			21.5802i			1.55742i
$193$		−	3.41996i		−	0.246174i	−0.992396	−	0.123087i	$-0.960721\pi$
$193$		−	3.41996i		−	0.246174i	0.992396	−	0.123087i	$-0.0392795\pi$
$194$	7.51808			0.539767
$195$	8.62900	−	28.7306i	0.617935	−	2.05744i
$196$	3.32827			0.237734
$197$			20.5076i			1.46111i	0.682855	+	0.730554i	$0.260738\pi$
$197$			20.5076i			1.46111i	−0.682855	+	0.730554i	$0.739262\pi$
$198$		−	59.8834i		−	4.25573i
$199$	2.77785			0.196917			0.0984583	−	0.995141i	$-0.468609\pi$
$199$	2.77785			0.196917			0.0984583	+	0.995141i	$0.468609\pi$
$200$	−7.29128	+	11.0433i	−0.515571	+	0.780883i
$201$	−43.8026			−3.08959
$202$			13.2486i			0.932166i
$203$		−	8.44353i		−	0.592620i
$204$	4.04785			0.283406
$205$	−4.15039	+	13.8189i	−0.289876	+	0.965153i
$206$	−4.65700			−0.324469
$207$		−	24.6178i		−	1.71105i
$208$		−	18.8854i		−	1.30947i
$209$	−7.29688			−0.504735
$210$	−46.5551	−	13.9825i	−3.21261	−	0.964882i
$211$	22.9148			1.57752			0.788760	−	0.614701i	$-0.210723\pi$
$211$	22.9148			1.57752			0.788760	+	0.614701i	$0.210723\pi$
$212$			2.30085i			0.158023i
$213$			12.4075i			0.850147i
$214$	−3.54991			−0.242667
$215$	9.79027	+	2.94043i	0.667691	+	0.200536i
$216$	31.2345			2.12524
$217$		−	5.19237i		−	0.352481i
$218$		−	16.3058i		−	1.10437i
$219$	−27.8893			−1.88458
$220$	0.861708	−	2.86909i	0.0580963	−	0.193434i
$221$	24.5673			1.65257
$222$			34.1782i			2.29389i
$223$		−	7.52468i		−	0.503890i	−0.967742	−	0.251945i	$-0.918930\pi$
$223$		−	7.52468i		−	0.503890i	0.967742	−	0.251945i	$-0.0810701\pi$
$224$	−5.93397			−0.396480
$225$	28.2682	+	18.6638i	1.88454	+	1.24425i
$226$	−18.4231			−1.22549
$227$			0.950254i			0.0630706i	0.999503	+	0.0315353i	$0.0100397\pi$
$227$			0.950254i			0.0630706i	−0.999503	+	0.0315353i	$0.989960\pi$
$228$			0.870818i			0.0576713i
$229$	−14.6545			−0.968396			−0.484198	−	0.874958i	$-0.660889\pi$
$229$	−14.6545			−0.968396			−0.484198	+	0.874958i	$0.660889\pi$
$230$	3.48722	−	11.6108i	0.229941	−	0.765596i
$231$	−86.3174			−5.67927
$232$			4.79526i			0.314824i
$233$			19.1614i			1.25530i	0.778495	+	0.627651i	$0.215984\pi$
$233$			19.1614i			1.25530i	−0.778495	+	0.627651i	$0.784016\pi$
$234$	−43.3740			−2.83545
$235$	−16.5178	−	4.96099i	−1.07750	−	0.323619i
$236$	−1.28213			−0.0834595
$237$			5.54697i			0.360315i
$238$		−	39.8089i		−	2.58043i
$239$	3.88636			0.251388			0.125694	−	0.992069i	$-0.459884\pi$
$239$	3.88636			0.251388			0.125694	+	0.992069i	$0.459884\pi$
$240$	29.4679	+	8.85044i	1.90214	+	0.571293i
$241$	1.00000			0.0644157
$241$	1.00000			0.0644157
$242$		−	35.9540i		−	2.31121i
$243$		−	16.4097i		−	1.05268i
$244$	−1.07787			−0.0690035
$245$	−9.46653	+	31.5191i	−0.604794	+	2.01368i
$246$	30.1003			1.91913
$247$			5.28518i			0.336288i
$248$			2.94885i			0.187252i
$249$	31.0525			1.96787
$250$	10.6887	+	12.8070i	0.676013	+	0.809985i
$251$	−13.8452			−0.873904			−0.436952	−	0.899485i	$-0.643942\pi$
$251$	−13.8452			−0.873904			−0.436952	+	0.899485i	$0.643942\pi$
$252$			7.13964i			0.449755i
$253$		−	21.5275i		−	1.35342i
$254$	−13.1819			−0.827109
$255$	−11.5132	+	38.3336i	−0.720984	+	2.40054i
$256$	5.36056			0.335035
$257$			6.17221i			0.385012i	0.981296	+	0.192506i	$0.0616615\pi$
$257$			6.17221i			0.385012i	−0.981296	+	0.192506i	$0.938338\pi$
$258$		−	21.3252i		−	1.32765i
$259$	34.1451			2.12167
$260$	−2.07810	−	0.624142i	−0.128878	−	0.0387076i
$261$	12.2746			0.759781
$262$		−	15.9542i		−	0.985656i
$263$		−	14.8523i		−	0.915835i	−0.888995	−	0.457917i	$-0.848596\pi$
$263$		−	14.8523i		−	0.915835i	0.888995	−	0.457917i	$-0.151404\pi$
$264$	49.0214			3.01706
$265$	−21.7893	−	6.54425i	−1.33851	−	0.402010i
$266$	8.56414			0.525101
$267$		−	22.0071i		−	1.34681i
$268$			3.16827i			0.193533i
$269$	−24.7594			−1.50960			−0.754802	−	0.655952i	$-0.772267\pi$
$269$	−24.7594			−1.50960			−0.754802	+	0.655952i	$0.772267\pi$
$270$	11.3256	−	37.7091i	0.689256	−	2.29490i
$271$	21.9399			1.33275			0.666376	−	0.745616i	$-0.267845\pi$
$271$	21.9399			1.33275			0.666376	+	0.745616i	$0.267845\pi$
$272$			25.1977i			1.52784i
$273$			62.5204i			3.78390i
$274$	−9.74509			−0.588723
$275$	24.7197	+	16.3210i	1.49065	+	0.984190i
$276$	−2.56912			−0.154643
$277$			17.9537i			1.07873i	0.842071	+	0.539367i	$0.181336\pi$
$277$			17.9537i			1.07873i	−0.842071	+	0.539367i	$0.818664\pi$
$278$		−	14.4478i		−	0.866519i
$279$	7.54832			0.451906
$280$	7.93325	−	26.4140i	0.474102	−	1.57854i
$281$	14.9520			0.891960			0.445980	−	0.895043i	$-0.352855\pi$
$281$	14.9520			0.891960			0.445980	+	0.895043i	$0.352855\pi$
$282$			35.9791i			2.14252i
$283$			16.8819i			1.00352i	0.865006	+	0.501761i	$0.167314\pi$
$283$			16.8819i			1.00352i	−0.865006	+	0.501761i	$0.832686\pi$
$284$	0.897443			0.0532534
$285$	−8.24675	−	2.47685i	−0.488495	−	0.146716i
$286$	−37.9293			−2.24281
$287$		−	30.0712i		−	1.77505i
$288$		−	8.62641i		−	0.508316i
$289$	−15.7787			−0.928160
$290$	5.78926	+	1.73876i	0.339957	+	0.102103i
$291$	15.7537			0.923500
$292$			2.01725i			0.118051i
$293$			16.3651i			0.956061i	0.878343	+	0.478030i	$0.158649\pi$
$293$			16.3651i			0.956061i	−0.878343	+	0.478030i	$0.841351\pi$
$294$	68.6550			4.00404
$295$	3.64673	−	12.1419i	0.212321	−	0.706930i
$296$	−19.3917			−1.12712
$297$		−	69.9161i		−	4.05694i
$298$			22.0668i			1.27829i
$299$	−15.5926			−0.901741
$300$	1.94776	−	2.95008i	0.112454	−	0.170323i
$301$	−21.3045			−1.22797
$302$			1.81735i			0.104577i
$303$			27.7617i			1.59487i
$304$	−5.42081			−0.310905
$305$	3.06576	−	10.2076i	0.175545	−	0.584483i
$306$	57.8715			3.30829
$307$			19.0297i			1.08608i	0.839706	+	0.543041i	$0.182727\pi$
$307$			19.0297i			1.08608i	−0.839706	+	0.543041i	$0.817273\pi$
$308$			6.24340i			0.355751i
$309$	−9.75850			−0.555142
$310$	3.56012	+	1.06925i	0.202201	+	0.0607295i
$311$	−16.3005			−0.924318			−0.462159	−	0.886797i	$-0.652925\pi$
$311$	−16.3005			−0.924318			−0.462159	+	0.886797i	$0.652925\pi$
$312$		−	35.5066i		−	2.01017i
$313$		−	1.71271i		−	0.0968084i	−0.998828	−	0.0484042i	$-0.984586\pi$
$313$		−	1.71271i		−	0.0968084i	0.998828	−	0.0484042i	$-0.0154136\pi$
$314$	14.1507			0.798573
$315$	−67.6132	−	20.3071i	−3.80957	−	1.14417i
$316$	0.401217			0.0225702
$317$			9.33229i			0.524154i	0.965047	+	0.262077i	$0.0844074\pi$
$317$			9.33229i			0.524154i	−0.965047	+	0.262077i	$0.915593\pi$
$318$			47.4615i			2.66151i
$319$	10.7338			0.600978
$320$	−4.43967	+	14.7820i	−0.248185	+	0.826341i
$321$	−7.43865			−0.415185
$322$			25.2663i			1.40803i
$323$		−	7.05172i		−	0.392368i
$324$	−3.74777			−0.208209
$325$	11.8214	−	17.9046i	0.655733	−	0.993171i
$326$	−3.01734			−0.167115
$327$		−	34.1678i		−	1.88949i
$328$			17.0780i			0.942977i
$329$	35.9442			1.98167
$330$	17.7752	−	59.1830i	0.978490	−	3.25792i
$331$	12.2007			0.670613			0.335306	−	0.942109i	$-0.391160\pi$
$331$	12.2007			0.670613			0.335306	+	0.942109i	$0.391160\pi$
$332$		−	2.24605i		−	0.123268i
$333$			49.6378i			2.72014i
$334$	−17.9699			−0.983271
$335$	−30.0039	−	9.01143i	−1.63929	−	0.492347i
$336$	−64.1248			−3.49829
$337$			1.32894i			0.0723920i	0.999345	+	0.0361960i	$0.0115241\pi$
$337$			1.32894i			0.0723920i	−0.999345	+	0.0361960i	$0.988476\pi$
$338$			8.07614i			0.439284i
$339$	−38.6046			−2.09671
$340$	2.77270	+	0.832757i	0.150371	+	0.0451626i
$341$	6.60078			0.357452
$342$			12.4500i			0.673217i
$343$		−	35.9669i		−	1.94203i
$344$	12.0993			0.652350
$345$	7.30729	−	24.3299i	0.393411	−	1.30988i
$346$	−15.8237			−0.850687
$347$		−	2.21075i		−	0.118679i	−0.998238	−	0.0593396i	$-0.981101\pi$
$347$		−	2.21075i		−	0.118679i	0.998238	−	0.0593396i	$-0.0188995\pi$
$348$		−	1.28099i		−	0.0686680i
$349$	−17.8704			−0.956580			−0.478290	−	0.878202i	$-0.658743\pi$
$349$	−17.8704			−0.956580			−0.478290	+	0.878202i	$0.658743\pi$
$350$	−29.0128	−	19.1554i	−1.55080	−	1.02390i
$351$	−50.6407			−2.70300
$352$		−	7.54354i		−	0.402072i
$353$		−	9.10115i		−	0.484405i	−0.970226	−	0.242203i	$-0.922130\pi$
$353$		−	9.10115i		−	0.484405i	0.970226	−	0.242203i	$-0.0778699\pi$
$354$	−26.4475			−1.40567
$355$	−2.55257	+	8.49889i	−0.135477	+	0.451074i
$356$	−1.59179			−0.0843647
$357$		−	83.4174i		−	4.41492i
$358$		−	23.3756i		−	1.23544i
$359$	23.0382			1.21591			0.607956	−	0.793971i	$-0.291990\pi$
$359$	23.0382			1.21591			0.607956	+	0.793971i	$0.291990\pi$
$360$	38.3989	+	11.5328i	2.02380	+	0.607833i
$361$	−17.4830			−0.920155
$362$		−	8.95861i		−	0.470854i
$363$		−	75.3396i		−	3.95430i
$364$	4.52214			0.237025
$365$	−19.1036	−	5.73762i	−0.999928	−	0.300320i
$366$	−22.2341			−1.16219
$367$			32.4970i			1.69633i	0.529734	+	0.848164i	$0.322292\pi$
$367$			32.4970i			1.69633i	−0.529734	+	0.848164i	$0.677708\pi$
$368$		−	15.9927i		−	0.833677i
$369$	43.7154			2.27573
$370$	−7.03143	+	23.4114i	−0.365546	+	1.21710i
$371$	47.4156			2.46170
$372$		−	0.787745i		−	0.0408427i
$373$		−	35.2363i		−	1.82447i	−0.409671	−	0.912234i	$-0.634356\pi$
$373$		−	35.2363i		−	1.82447i	0.409671	−	0.912234i	$-0.365644\pi$
$374$	50.6069			2.61682
$375$	22.3976	+	26.8364i	1.15661	+	1.38582i
$376$	−20.4135			−1.05274
$377$		−	7.77458i		−	0.400411i
$378$			82.0585i			4.22063i
$379$	5.18922			0.266553			0.133276	−	0.991079i	$-0.457450\pi$
$379$	5.18922			0.266553			0.133276	+	0.991079i	$0.457450\pi$
$380$	−0.179152	+	0.596493i	−0.00919031	+	0.0305995i
$381$	−27.6221			−1.41512
$382$			21.6418i			1.10729i
$383$			5.72356i			0.292460i	0.989251	+	0.146230i	$0.0467140\pi$
$383$			5.72356i			0.292460i	−0.989251	+	0.146230i	$0.953286\pi$
$384$	40.1602			2.04942
$385$	−59.1257	−	17.7579i	−3.01333	−	0.905029i
$386$	−5.10267			−0.259719
$387$		−	30.9711i		−	1.57435i
$388$		−	1.13948i		−	0.0578483i
$389$	−24.8562			−1.26026			−0.630130	−	0.776490i	$-0.716998\pi$
$389$	−24.8562			−1.26026			−0.630130	+	0.776490i	$0.716998\pi$
$390$	−42.8667	−	12.8747i	−2.17064	−	0.651935i
$391$	20.8043			1.05212
$392$			38.9529i			1.96742i
$393$		−	33.4312i		−	1.68638i
$394$	30.5979			1.54150
$395$	−1.14117	+	3.79957i	−0.0574185	+	0.191177i
$396$	−9.07623			−0.456098
$397$		−	34.8213i		−	1.74763i	−0.486259	−	0.873815i	$-0.661639\pi$
$397$		−	34.8213i		−	1.74763i	0.486259	−	0.873815i	$-0.338361\pi$
$398$		−	4.14462i		−	0.207751i
$399$	17.9457			0.898408
$400$	18.3641	+	12.1248i	0.918206	+	0.606238i
$401$	−32.1370			−1.60484			−0.802422	−	0.596757i	$-0.796456\pi$
$401$	−32.1370			−1.60484			−0.802422	+	0.596757i	$0.796456\pi$
$402$			65.3545i			3.25959i
$403$		−	4.78100i		−	0.238158i
$404$	2.00802			0.0999028
$405$	10.6597	−	35.4918i	0.529684	−	1.76360i
$406$	−12.5980			−0.625227
$407$			43.4068i			2.15160i
$408$			47.3745i			2.34539i
$409$	30.4791			1.50709			0.753547	−	0.657395i	$-0.228341\pi$
$409$	30.4791			1.50709			0.753547	+	0.657395i	$0.228341\pi$
$410$	20.6181	+	6.19249i	1.01826	+	0.305825i
$411$	−20.4203			−1.00726
$412$			0.705839i			0.0347742i
$413$			26.4219i			1.30014i
$414$	−36.7304			−1.80520
$415$	21.2704	+	6.38839i	1.04412	+	0.313594i
$416$	−5.46384			−0.267887
$417$		−	30.2745i		−	1.48255i
$418$			10.8871i			0.532507i
$419$	14.0542			0.686592			0.343296	−	0.939227i	$-0.388457\pi$
$419$	14.0542			0.686592			0.343296	+	0.939227i	$0.388457\pi$
$420$	−2.11926	+	7.05614i	−0.103409	+	0.344304i
$421$	7.96690			0.388283			0.194141	−	0.980974i	$-0.437808\pi$
$421$	7.96690			0.388283			0.194141	+	0.980974i	$0.437808\pi$
$422$		−	34.1895i		−	1.66432i
$423$			52.2533i			2.54064i
$424$	−26.9283			−1.30775
$425$	−15.7726	+	23.8892i	−0.765085	+	1.15880i
$426$	18.5123			0.896923
$427$			22.2126i			1.07494i
$428$			0.538043i			0.0260073i
$429$	−79.4787			−3.83727
$430$	4.38720	−	14.6073i	0.211569	−	0.704428i
$431$	−39.6560			−1.91016			−0.955080	−	0.296348i	$-0.904231\pi$
$431$	−39.6560			−1.91016			−0.955080	+	0.296348i	$0.904231\pi$
$432$		−	51.9403i		−	2.49898i
$433$		−	3.27667i		−	0.157467i	−0.996896	−	0.0787333i	$-0.974912\pi$
$433$		−	3.27667i		−	0.157467i	0.996896	−	0.0787333i	$-0.0250875\pi$
$434$	−7.74715			−0.371875
$435$	12.1311	+	3.64347i	0.581641	+	0.174691i
$436$	−2.47139			−0.118358
$437$			4.47565i			0.214099i
$438$			41.6115i			1.98827i
$439$	14.5064			0.692355			0.346177	−	0.938169i	$-0.387480\pi$
$439$	14.5064			0.692355			0.346177	+	0.938169i	$0.387480\pi$
$440$	33.5787	+	10.0851i	1.60080	+	0.480788i
$441$	99.7094			4.74807
$442$		−	36.6550i		−	1.74350i
$443$			19.5267i			0.927742i	0.885903	+	0.463871i	$0.153540\pi$
$443$			19.5267i			0.927742i	−0.885903	+	0.463871i	$0.846460\pi$
$444$	5.18022			0.245842
$445$	4.52749	−	15.0744i	0.214623	−	0.714596i
$446$	−11.2270			−0.531614
$447$			46.2397i			2.18706i
$448$		−	32.1671i		−	1.51975i
$449$	2.85475			0.134724			0.0673621	−	0.997729i	$-0.478542\pi$
$449$	2.85475			0.134724			0.0673621	+	0.997729i	$0.478542\pi$
$450$	27.8469	−	42.1768i	1.31271	−	1.98823i
$451$	38.2279			1.80008
$452$			2.79230i			0.131339i
$453$			3.80815i			0.178923i
$454$	1.41780			0.0665408
$455$	−12.8622	+	42.8252i	−0.602990	+	2.00768i
$456$	−10.1917			−0.477271
$457$		−	11.7309i		−	0.548749i	−0.961623	−	0.274375i	$-0.911529\pi$
$457$		−	11.7309i		−	0.548749i	0.961623	−	0.274375i	$-0.0884708\pi$
$458$			21.8649i			1.02168i
$459$	67.5671			3.15376
$460$	−1.75980	−	0.528542i	−0.0820510	−	0.0246434i
$461$	1.41285			0.0658028			0.0329014	−	0.999459i	$-0.489525\pi$
$461$	1.41285			0.0658028			0.0329014	+	0.999459i	$0.489525\pi$
$462$			128.788i			5.99175i
$463$			30.3025i			1.40827i	0.710064	+	0.704137i	$0.248666\pi$
$463$			30.3025i			1.40827i	−0.710064	+	0.704137i	$0.751334\pi$
$464$	7.97409			0.370188
$465$	7.46004	+	2.24056i	0.345951	+	0.103904i
$466$	28.5892			1.32437
$467$			10.2416i			0.473927i	0.971519	+	0.236963i	$0.0761522\pi$
$467$			10.2416i			0.473927i	−0.971519	+	0.236963i	$0.923848\pi$
$468$			6.57399i			0.303883i
$469$	65.2913			3.01487
$470$	−7.40192	+	24.6450i	−0.341425	+	1.13679i
$471$	29.6521			1.36630
$472$		−	15.0056i		−	0.690687i
$473$		−	27.0833i		−	1.24529i
$474$	8.27623			0.380140
$475$	−5.13930	−	3.39318i	−0.235807	−	0.155690i
$476$	−6.03364			−0.276552
$477$			68.9296i			3.15607i
$478$		−	5.79855i		−	0.265219i
$479$	16.8364			0.769275			0.384638	−	0.923068i	$-0.374326\pi$
$479$	16.8364			0.769275			0.384638	+	0.923068i	$0.374326\pi$
$480$	2.56057	−	8.52552i	0.116874	−	0.389135i
$481$	31.4399			1.43354
$482$		−	1.49203i		−	0.0679599i
$483$			52.9441i			2.40904i
$484$	−5.44937			−0.247699
$485$	10.7910	+	3.24099i	0.489994	+	0.147166i
$486$	−24.4836			−1.11060
$487$		−	19.1209i		−	0.866452i	−0.901285	−	0.433226i	$-0.857375\pi$
$487$		−	19.1209i		−	0.866452i	0.901285	−	0.433226i	$-0.142625\pi$
$488$		−	12.6150i		−	0.571053i
$489$	−6.32268			−0.285921
$490$	47.0274	+	14.1243i	2.12448	+	0.638071i
$491$	13.6920			0.617910			0.308955	−	0.951077i	$-0.400021\pi$
$491$	13.6920			0.617910			0.308955	+	0.951077i	$0.400021\pi$
$492$		−	4.56216i		−	0.205678i
$493$			10.3732i			0.467185i
$494$	7.88563			0.354791
$495$	25.8153	−	85.9530i	1.16031	−	3.86330i
$496$	4.90369			0.220182
$497$		−	18.4944i		−	0.829586i
$498$		−	46.3312i		−	2.07615i
$499$	−41.2184			−1.84519			−0.922595	−	0.385770i	$-0.873936\pi$
$499$	−41.2184			−1.84519			−0.922595	+	0.385770i	$0.873936\pi$
$500$	1.94109	−	1.62003i	0.0868084	−	0.0724501i
$501$	−37.6550			−1.68230
$502$			20.6575i			0.921988i
$503$		−	23.7713i		−	1.05991i	−0.848025	−	0.529956i	$-0.822209\pi$
$503$		−	23.7713i		−	1.05991i	0.848025	−	0.529956i	$-0.177791\pi$
$504$	−83.5596			−3.72204
$505$	−5.71136	+	19.0162i	−0.254152	+	0.846210i
$506$	−32.1196			−1.42789
$507$			16.9231i			0.751582i
$508$			1.99792i			0.0886435i
$509$	−0.527203			−0.0233679			−0.0116839	−	0.999932i	$-0.503719\pi$
$509$	−0.527203			−0.0233679			−0.0116839	+	0.999932i	$0.503719\pi$
$510$	57.1947	+	17.1780i	2.53262	+	0.760653i
$511$	41.5712			1.83900
$512$			17.6924i			0.781903i
$513$			14.5358i			0.641771i
$514$	9.20910			0.406196
$515$	−6.68438	−	2.00760i	−0.294549	−	0.0884655i
$516$	−3.23215			−0.142288
$517$			45.6939i			2.00962i
$518$		−	50.9454i		−	2.23841i
$519$	−33.1577			−1.45546
$520$	7.30472	−	24.3213i	0.320333	−	1.06656i
$521$	19.7412			0.864876			0.432438	−	0.901664i	$-0.357654\pi$
$521$	19.7412			0.864876			0.432438	+	0.901664i	$0.357654\pi$
$522$		−	18.3141i		−	0.801585i
$523$		−	22.0882i		−	0.965849i	−0.875662	−	0.482925i	$-0.839574\pi$
$523$		−	22.0882i		−	0.965849i	0.875662	−	0.482925i	$-0.160426\pi$
$524$	−2.41811			−0.105635
$525$	−60.7947	−	40.1392i	−2.65330	−	1.75182i
$526$	−22.1601			−0.966225
$527$			6.37902i			0.277874i
$528$		−	81.5183i		−	3.54763i
$529$	9.79577			0.425903
$530$	−9.76419	+	32.5102i	−0.424129	+	1.41215i
$531$	−38.4104			−1.66687
$532$		−	1.29802i		−	0.0562765i
$533$		−	27.6887i		−	1.19933i
$534$	−32.8351			−1.42091
$535$	−5.09533	−	1.53034i	−0.220290	−	0.0661625i
$536$	−37.0802			−1.60162
$537$		−	48.9823i		−	2.11374i
$538$			36.9416i			1.59267i
$539$	87.1929			3.75567
$540$	−5.71539	−	1.71657i	−0.245951	−	0.0738695i
$541$	−7.32264			−0.314825			−0.157412	−	0.987533i	$-0.550315\pi$
$541$	−7.32264			−0.314825			−0.157412	+	0.987533i	$0.550315\pi$
$542$		−	32.7348i		−	1.40608i
$543$		−	18.7723i		−	0.805596i
$544$	7.29010			0.312561
$545$	7.02930	−	23.4043i	0.301102	−	1.00253i
$546$	93.2820			3.99210
$547$		−	27.9274i		−	1.19409i	−0.802208	−	0.597045i	$-0.796342\pi$
$547$		−	27.9274i		−	1.19409i	0.802208	−	0.597045i	$-0.203658\pi$
$548$			1.47702i			0.0630950i
$549$	−32.2911			−1.37815
$550$	24.3513	−	36.8824i	1.03834	−	1.57267i
$551$	−2.23160			−0.0950692
$552$		−	30.0680i		−	1.27978i
$553$		−	8.26821i		−	0.351600i
$554$	26.7874			1.13809
$555$	−14.7340	+	49.0573i	−0.625422	+	2.08237i
$556$	−2.18978			−0.0928673
$557$			13.5066i			0.572293i	0.958186	+	0.286146i	$0.0923744\pi$
$557$			13.5066i			0.572293i	−0.958186	+	0.286146i	$0.907626\pi$
$558$		−	11.2623i		−	0.476770i
$559$	−19.6166			−0.829696
$560$	−43.9242	−	13.1923i	−1.85614	−	0.557476i
$561$	106.044			4.47718
$562$		−	22.3087i		−	0.941037i
$563$		−	4.30396i		−	0.181390i	−0.995879	−	0.0906951i	$-0.971091\pi$
$563$		−	4.30396i		−	0.181390i	0.995879	−	0.0906951i	$-0.0289089\pi$
$564$	5.45317			0.229620
$565$	−26.4434	−	7.94206i	−1.11248	−	0.334125i
$566$	25.1882			1.05874
$567$			77.2335i			3.24350i
$568$			10.5033i			0.440710i
$569$	−10.2392			−0.429248			−0.214624	−	0.976697i	$-0.568853\pi$
$569$	−10.2392			−0.429248			−0.214624	+	0.976697i	$0.568853\pi$
$570$	−3.69552	+	12.3044i	−0.154788	+	0.515373i
$571$	−25.4305			−1.06423			−0.532117	−	0.846671i	$-0.678603\pi$
$571$	−25.4305			−1.06423			−0.532117	+	0.846671i	$0.678603\pi$
$572$			5.74876i			0.240368i
$573$			45.3492i			1.89449i
$574$	−44.8670			−1.87271
$575$	10.0107	−	15.1622i	0.417475	−	0.632307i
$576$	46.7623			1.94843
$577$		−	12.6994i		−	0.528684i	−0.964429	−	0.264342i	$-0.914845\pi$
$577$		−	12.6994i		−	0.528684i	0.964429	−	0.264342i	$-0.0851548\pi$
$578$			23.5423i			0.979229i
$579$	−10.6924			−0.444360
$580$	0.263535	−	0.877450i	0.0109427	−	0.0364341i
$581$	−46.2863			−1.92028
$582$		−	23.5050i		−	0.974312i
$583$			60.2769i			2.49641i
$584$	−23.6091			−0.976953
$585$	−62.2564	−	18.6982i	−2.57399	−	0.773076i
$586$	24.4172			1.00866
$587$			37.3627i			1.54212i	0.636761	+	0.771061i	$0.280274\pi$
$587$			37.3627i			1.54212i	−0.636761	+	0.771061i	$0.719726\pi$
$588$		−	10.4057i		−	0.429124i
$589$	−1.37233			−0.0565457
$590$	−18.1160	−	5.44101i	−0.745826	−	0.224003i
$591$	64.1162			2.63739
$592$			32.2467i			1.32533i
$593$			20.9359i			0.859736i	0.902892	+	0.429868i	$0.141440\pi$
$593$			20.9359i			0.859736i	−0.902892	+	0.429868i	$0.858560\pi$
$594$	−104.317			−4.28016
$595$	17.1613	−	57.1393i	0.703546	−	2.34248i
$596$	3.34455			0.136998
$597$		−	8.68483i		−	0.355447i
$598$			23.2645i			0.951356i
$599$	40.5567			1.65710			0.828551	−	0.559914i	$-0.189166\pi$
$599$	40.5567			1.65710			0.828551	+	0.559914i	$0.189166\pi$
$600$	34.5266	+	22.7959i	1.40954	+	0.930637i
$601$	−21.1739			−0.863700			−0.431850	−	0.901946i	$-0.642139\pi$
$601$	−21.1739			−0.863700			−0.431850	+	0.901946i	$0.642139\pi$
$602$			31.7869i			1.29554i
$603$			94.9160i			3.86528i
$604$	0.275447			0.0112078
$605$	15.4995	−	51.6062i	0.630144	−	2.09809i
$606$	41.4211			1.68262
$607$		−	27.6387i		−	1.12182i	−0.827877	−	0.560910i	$-0.810451\pi$
$607$		−	27.6387i		−	1.12182i	0.827877	−	0.560910i	$-0.189549\pi$
$608$			1.56833i			0.0636041i
$609$	−26.3984			−1.06972
$610$	−15.2299	−	4.57419i	−0.616642	−	0.185203i
$611$	33.0965			1.33894
$612$		−	8.77130i		−	0.354559i
$613$		−	36.9421i		−	1.49208i	−0.665902	−	0.746039i	$-0.731953\pi$
$613$		−	36.9421i		−	1.49208i	0.665902	−	0.746039i	$-0.268047\pi$
$614$	28.3928			1.14584
$615$	43.2042	+	12.9760i	1.74216	+	0.523244i
$616$	−73.0704			−2.94409
$617$			40.1279i			1.61549i	0.589533	+	0.807744i	$0.299312\pi$
$617$			40.1279i			1.61549i	−0.589533	+	0.807744i	$0.700688\pi$
$618$			14.5599i			0.585686i
$619$	30.3391			1.21943			0.609716	−	0.792620i	$-0.291284\pi$
$619$	30.3391			1.21943			0.609716	+	0.792620i	$0.291284\pi$
$620$	0.162062	−	0.539590i	0.00650855	−	0.0216705i
$621$	−42.8841			−1.72088
$622$			24.3208i			0.975175i
$623$			32.8033i			1.31424i
$624$	−59.0444			−2.36367
$625$	9.82091	+	22.9902i	0.392836	+	0.919608i
$626$	−2.55541			−0.102135
$627$			22.8134i			0.911078i
$628$		−	2.14476i		−	0.0855852i
$629$	−41.9485			−1.67260
$630$	−30.2987	+	100.881i	−1.20713	+	4.01918i
$631$	−36.0636			−1.43567			−0.717835	−	0.696213i	$-0.754867\pi$
$631$	−36.0636			−1.43567			−0.717835	+	0.696213i	$0.754867\pi$
$632$			4.69569i			0.186784i
$633$		−	71.6422i		−	2.84752i
$634$	13.9240			0.552993
$635$	−18.9206	−	5.68264i	−0.750840	−	0.225509i
$636$	7.19352			0.285241
$637$		−	63.1545i		−	2.50227i
$638$		−	16.0151i		−	0.634044i
$639$	26.8859			1.06359
$640$	27.5090	+	8.26210i	1.08739	+	0.326588i
$641$	40.0078			1.58021			0.790106	−	0.612970i	$-0.210025\pi$
$641$	40.0078			1.58021			0.790106	+	0.612970i	$0.210025\pi$
$642$			11.0987i			0.438029i
$643$			23.3695i			0.921604i	0.887503	+	0.460802i	$0.152438\pi$
$643$			23.3695i			0.921604i	−0.887503	+	0.460802i	$0.847562\pi$
$644$	3.82948			0.150903
$645$	9.19313	−	30.6089i	0.361979	−	1.20522i
$646$	−10.5214			−0.413957
$647$		−	43.5626i		−	1.71262i	−0.516459	−	0.856312i	$-0.672750\pi$
$647$		−	43.5626i		−	1.71262i	0.516459	−	0.856312i	$-0.327250\pi$
$648$		−	43.8625i		−	1.72308i
$649$	−33.5888			−1.31847
$650$	−26.7142	−	17.6378i	−1.04782	−	0.691812i
$651$	−16.2337			−0.636250
$652$			0.457324i			0.0179102i
$653$		−	11.8810i		−	0.464939i	−0.972604	−	0.232469i	$-0.925319\pi$
$653$		−	11.8810i		−	0.464939i	0.972604	−	0.232469i	$-0.0746805\pi$
$654$	−50.9793			−1.99345
$655$	6.87776	−	22.8997i	0.268736	−	0.894767i
$656$	28.3993			1.10881
$657$			60.4334i			2.35773i
$658$		−	53.6297i		−	2.09070i
$659$	−22.2402			−0.866357			−0.433178	−	0.901308i	$-0.642608\pi$
$659$	−22.2402			−0.866357			−0.433178	+	0.901308i	$0.642608\pi$
$660$	−8.97008	−	2.69409i	−0.349160	−	0.104867i
$661$	20.7001			0.805140			0.402570	−	0.915389i	$-0.368117\pi$
$661$	20.7001			0.805140			0.402570	+	0.915389i	$0.368117\pi$
$662$		−	18.2038i		−	0.707511i
$663$		−	76.8085i		−	2.98300i
$664$	26.2870			1.02013
$665$	12.2924	+	3.69194i	0.476681	+	0.143167i
$666$	74.0609			2.86980
$667$		−	6.58374i		−	0.254923i
$668$			2.72362i			0.105380i
$669$	−23.5256			−0.909551
$670$	−13.4453	+	44.7666i	−0.519437	+	1.72948i
$671$	−28.2376			−1.09010
$672$			18.5523i			0.715671i
$673$			4.14046i			0.159603i	0.996811	+	0.0798016i	$0.0254287\pi$
$673$			4.14046i			0.159603i	−0.996811	+	0.0798016i	$0.974571\pi$
$674$	1.98281			0.0763751
$675$	32.5123	−	49.2430i	1.25140	−	1.89536i
$676$	1.22406			0.0470793
$677$		−	38.9911i		−	1.49855i	−0.662259	−	0.749275i	$-0.730402\pi$
$677$		−	38.9911i		−	1.49855i	0.662259	−	0.749275i	$-0.269598\pi$
$678$			57.5990i			2.21208i
$679$	−23.4822			−0.901164
$680$	−9.74628	+	32.4506i	−0.373753	+	1.24442i
$681$	2.97093			0.113846
$682$		−	9.84853i		−	0.377120i
$683$			20.2200i			0.773696i	0.922144	+	0.386848i	$0.126436\pi$
$683$			20.2200i			0.773696i	−0.922144	+	0.386848i	$0.873564\pi$
$684$	1.88698			0.0721505
$685$	−13.9875	−	4.20104i	−0.534436	−	0.160514i
$686$	−53.6635			−2.04888
$687$			45.8166i			1.74801i
$688$		−	20.1200i		−	0.767070i
$689$	43.6590			1.66328
$690$	−36.3008	−	10.9027i	−1.38195	−	0.415057i
$691$	−10.4772			−0.398570			−0.199285	−	0.979942i	$-0.563862\pi$
$691$	−10.4772			−0.398570			−0.199285	+	0.979942i	$0.563862\pi$
$692$			2.39832i			0.0911705i
$693$			187.042i			7.10512i
$694$	−3.29849			−0.125209
$695$	6.22833	−	20.7375i	0.236254	−	0.786616i
$696$	14.9922			0.568277
$697$			36.9435i			1.39934i
$698$			26.6631i			1.00921i
$699$	59.9072			2.26590
$700$	−2.90330	+	4.39733i	−0.109734	+	0.166203i
$701$	23.2337			0.877524			0.438762	−	0.898603i	$-0.355417\pi$
$701$	23.2337			0.877524			0.438762	+	0.898603i	$0.355417\pi$
$702$			75.5573i			2.85173i
$703$		−	9.02443i		−	0.340363i
$704$	40.8923			1.54118
$705$	−15.5103	+	51.6422i	−0.584152	+	1.94496i
$706$	−13.5791			−0.511058
$707$		−	41.3810i		−	1.55629i
$708$			4.00852i			0.150650i
$709$	28.6569			1.07623			0.538116	−	0.842871i	$-0.319136\pi$
$709$	28.6569			1.07623			0.538116	+	0.842871i	$0.319136\pi$
$710$	12.6806	+	3.80850i	0.475893	+	0.142931i
$711$	12.0198			0.450777
$712$		−	18.6297i		−	0.698177i
$713$		−	4.04869i		−	0.151625i
$714$	−124.461			−4.65783
$715$	−54.4414	−	16.3510i	−2.03599	−	0.611494i
$716$	−3.54293			−0.132405
$717$		−	12.1505i		−	0.453770i
$718$		−	34.3736i		−	1.28281i
$719$	5.87954			0.219270			0.109635	−	0.993972i	$-0.465032\pi$
$719$	5.87954			0.219270			0.109635	+	0.993972i	$0.465032\pi$
$720$	19.1781	−	63.8540i	0.714724	−	2.37970i
$721$	14.5458			0.541715
$722$			26.0850i			0.970783i
$723$		−	3.12646i		−	0.116274i
$724$	−1.35781			−0.0504627
$725$	7.55999	+	4.99142i	0.280771	+	0.185377i
$726$	−112.409			−4.17187
$727$		−	49.0096i		−	1.81767i	−0.417161	−	0.908833i	$-0.636975\pi$
$727$		−	49.0096i		−	1.81767i	0.417161	−	0.908833i	$-0.363025\pi$
$728$			52.9255i			1.96155i
$729$	−1.58556			−0.0587245
$730$	−8.56067	+	28.5031i	−0.316844	+	1.05495i
$731$	26.1734			0.968058
$732$			3.36991i			0.124556i
$733$		−	15.4332i		−	0.570040i	−0.958522	−	0.285020i	$-0.908000\pi$
$733$		−	15.4332i		−	0.570040i	0.958522	−	0.285020i	$-0.0920002\pi$
$734$	48.4863			1.78966
$735$	98.5433	+	29.5967i	3.63482	+	1.09169i
$736$	−4.62694			−0.170551
$737$			83.0012i			3.05739i
$738$		−	65.2245i		−	2.40095i
$739$	19.0798			0.701863			0.350931	−	0.936401i	$-0.385865\pi$
$739$	19.0798			0.701863			0.350931	+	0.936401i	$0.385865\pi$
$740$	3.54835	+	1.06572i	0.130440	+	0.0391766i
$741$	16.5239			0.607021
$742$		−	70.7453i		−	2.59714i
$743$			28.2323i			1.03574i	0.855459	+	0.517871i	$0.173275\pi$
$743$			28.2323i			1.03574i	−0.855459	+	0.517871i	$0.826725\pi$
$744$	9.21947			0.338002
$745$	−9.51283	+	31.6733i	−0.348523	+	1.16042i
$746$	−52.5735			−1.92485
$747$		−	67.2879i		−	2.46194i
$748$		−	7.67024i		−	0.280452i
$749$	11.0879			0.405143
$750$	40.0405	−	33.4178i	1.46207	−	1.22024i
$751$	10.2127			0.372667			0.186333	−	0.982487i	$-0.440340\pi$
$751$	10.2127			0.372667			0.186333	+	0.982487i	$0.440340\pi$
$752$			33.9458i			1.23788i
$753$			43.2866i			1.57745i
$754$	−11.5999			−0.422442
$755$	−0.783446	+	2.60851i	−0.0285125	+	0.0949335i
$756$	12.4372			0.452337
$757$		−	42.5055i		−	1.54489i	−0.635082	−	0.772445i	$-0.719034\pi$
$757$		−	42.5055i		−	1.54489i	0.635082	−	0.772445i	$-0.280966\pi$
$758$		−	7.74245i		−	0.281219i
$759$	−67.3049			−2.44301
$760$	−6.98113	−	2.09673i	−0.253232	−	0.0760563i
$761$	−33.2390			−1.20491			−0.602456	−	0.798152i	$-0.705811\pi$
$761$	−33.2390			−1.20491			−0.602456	+	0.798152i	$0.705811\pi$
$762$			41.2128i			1.49298i
$763$			50.9299i			1.84379i
$764$	3.28014			0.118671
$765$	83.0652	+	24.9480i	3.00323	+	0.901996i
$766$	8.53970			0.308552
$767$			24.3286i			0.878455i
$768$		−	16.7596i		−	0.604759i
$769$	−24.0517			−0.867328			−0.433664	−	0.901075i	$-0.642779\pi$
$769$	−24.0517			−0.867328			−0.433664	+	0.901075i	$0.642779\pi$
$770$	−26.4953	+	88.2171i	−0.954825	+	3.17912i
$771$	19.2972			0.694971
$772$			0.773387i			0.0278348i
$773$			19.5958i			0.704813i	0.935847	+	0.352407i	$0.114637\pi$
$773$			19.5958i			0.704813i	−0.935847	+	0.352407i	$0.885363\pi$
$774$	−46.2096			−1.66097
$775$	4.64903	+	3.06949i	0.166998	+	0.110259i
$776$	13.3360			0.478735
$777$		−	106.753i		−	3.82975i
$778$			37.0861i			1.32960i
$779$	−7.94770			−0.284756
$780$	−1.95135	+	6.49710i	−0.0698696	+	0.232634i
$781$	23.5109			0.841286
$782$		−	31.0405i		−	1.11001i
$783$		−	21.3824i		−	0.764143i
$784$	64.7752			2.31340
$785$	20.3111	+	6.10029i	0.724935	+	0.217729i
$786$	−49.8802			−1.77917
$787$			14.4340i			0.514515i	0.966343	+	0.257257i	$0.0828189\pi$
$787$			14.4340i			0.514515i	−0.966343	+	0.257257i	$0.917181\pi$
$788$		−	4.63757i		−	0.165207i
$789$	−46.4352			−1.65314
$790$	5.66905	+	1.70266i	0.201696	+	0.0605778i
$791$	57.5432			2.04600
$792$		−	106.225i		−	3.77453i
$793$			20.4527i			0.726298i
$794$	−51.9542			−1.84379
$795$	−20.4603	+	68.1234i	−0.725653	+	2.41609i
$796$	−0.628181			−0.0222653
$797$		−	36.2235i		−	1.28310i	−0.767081	−	0.641551i	$-0.778291\pi$
$797$		−	36.2235i		−	1.28310i	0.767081	−	0.641551i	$-0.221709\pi$
$798$		−	26.7754i		−	0.947839i
$799$	−44.1588			−1.56223
$800$	3.50789	−	5.31303i	0.124022	−	0.187844i
$801$	−47.6873			−1.68495
$802$			47.9492i			1.69314i
$803$			52.8472i			1.86494i
$804$	9.90547			0.349339
$805$	−10.8921	+	36.2657i	−0.383896	+	1.27820i
$806$	−7.13337			−0.251262
$807$			77.4091i			2.72493i
$808$			23.5011i			0.826766i
$809$	33.5485			1.17950			0.589751	−	0.807585i	$-0.299226\pi$
$809$	33.5485			1.17950			0.589751	+	0.807585i	$0.299226\pi$
$810$	−52.9547	−	15.9045i	−1.86064	−	0.558828i
$811$	−41.8458			−1.46941			−0.734703	−	0.678389i	$-0.762678\pi$
$811$	−41.8458			−1.46941			−0.734703	+	0.678389i	$0.762678\pi$
$812$			1.90941i			0.0670072i
$813$		−	68.5940i		−	2.40570i
$814$	64.7641			2.26998
$815$	−4.33091	−	1.30075i	−0.151705	−	0.0455634i
$816$	78.7796			2.75784
$817$			5.63071i			0.196994i
$818$		−	45.4755i		−	1.59002i
$819$	135.476			4.73390
$820$	0.938566	−	3.12499i	0.0327761	−	0.109129i
$821$	−29.6138			−1.03353			−0.516765	−	0.856127i	$-0.672864\pi$
$821$	−29.6138			−1.03353			−0.516765	+	0.856127i	$0.672864\pi$
$822$			30.4676i			1.06268i
$823$		−	5.60965i		−	0.195540i	−0.995209	−	0.0977701i	$-0.968829\pi$
$823$		−	5.60965i		−	0.195540i	0.995209	−	0.0977701i	$-0.0311710\pi$
$824$	−8.26088			−0.287781
$825$	51.0268	−	77.2850i	1.77652	−	2.69072i
$826$	39.4222			1.37167
$827$			13.9106i			0.483720i	0.970311	+	0.241860i	$0.0777575\pi$
$827$			13.9106i			0.483720i	−0.970311	+	0.241860i	$0.922242\pi$
$828$			5.56704i			0.193468i
$829$	−22.9062			−0.795567			−0.397783	−	0.917479i	$-0.630220\pi$
$829$	−22.9062			−0.795567			−0.397783	+	0.917479i	$0.630220\pi$
$830$	9.53164	−	31.7360i	0.330848	−	1.10157i
$831$	56.1315			1.94718
$832$		−	29.6186i		−	1.02684i
$833$			84.2635i			2.91956i
$834$	−45.1703			−1.56412
$835$	−25.7930	−	7.74671i	−0.892602	−	0.268086i
$836$	1.65011			0.0570702
$837$		−	13.1491i		−	0.454500i
$838$		−	20.9692i		−	0.724369i
$839$	5.57070			0.192322			0.0961609	−	0.995366i	$-0.469344\pi$
$839$	5.57070			0.192322			0.0961609	+	0.995366i	$0.469344\pi$
$840$	−82.5824	−	24.8030i	−2.84936	−	0.855783i
$841$	−25.7173			−0.886803
$842$		−	11.8868i		−	0.409647i
$843$		−	46.7467i		−	1.61004i
$844$	−5.18193			−0.178369
$845$	−3.48157	+	11.5920i	−0.119770	+	0.398777i
$846$	77.9632			2.68043
$847$			112.300i			3.85867i
$848$			44.7794i			1.53773i
$849$	52.7804			1.81142
$850$	35.6432	+	23.5331i	1.22255	+	0.807180i
$851$	26.6242			0.912667
$852$		−	2.80582i		−	0.0961257i
$853$		−	35.8612i		−	1.22786i	−0.789359	−	0.613931i	$-0.789587\pi$
$853$		−	35.8612i		−	1.22786i	0.789359	−	0.613931i	$-0.210413\pi$
$854$	33.1417			1.13409
$855$	−5.36709	+	17.8699i	−0.183551	+	0.611138i
$856$	−6.29705			−0.215229
$857$		−	0.654119i		−	0.0223443i	−0.999938	−	0.0111721i	$-0.996444\pi$
$857$		−	0.654119i		−	0.0223443i	0.999938	−	0.0111721i	$-0.00355628\pi$
$858$			118.584i			4.04840i
$859$	−2.58305			−0.0881324			−0.0440662	−	0.999029i	$-0.514031\pi$
$859$	−2.58305			−0.0881324			−0.0440662	+	0.999029i	$0.514031\pi$
$860$	−2.21396	−	0.664946i	−0.0754955	−	0.0226745i
$861$	−94.0163			−3.20407
$862$			59.1677i			2.01526i
$863$		−	52.4627i		−	1.78585i	−0.450206	−	0.892925i	$-0.648649\pi$
$863$		−	52.4627i		−	1.78585i	0.450206	−	0.892925i	$-0.351351\pi$
$864$	−15.0272			−0.511234
$865$	−22.7124	−	6.82148i	−0.772244	−	0.231937i
$866$	−4.88887			−0.166130
$867$			49.3315i			1.67539i
$868$			1.17420i			0.0398549i
$869$	10.5109			0.356559
$870$	5.43615	−	18.0999i	0.184303	−	0.613643i
$871$	60.1184			2.03704
$872$		−	28.9242i		−	0.979496i
$873$		−	34.1368i		−	1.15536i
$874$	6.67778			0.225879
$875$	−33.3854	−	40.0018i	−1.12863	−	1.35231i
$876$	6.30685			0.213089
$877$			19.1481i			0.646586i	0.946299	+	0.323293i	$0.104790\pi$
$877$			19.1481i			0.646586i	−0.946299	+	0.323293i	$0.895210\pi$
$878$		−	21.6440i		−	0.730449i
$879$	51.1649			1.72575
$880$	16.7706	−	55.8385i	0.565338	−	1.88231i
$881$	−38.6243			−1.30129			−0.650643	−	0.759384i	$-0.725501\pi$
$881$	−38.6243			−1.30129			−0.650643	+	0.759384i	$0.725501\pi$
$882$		−	148.769i		−	5.00931i
$883$		−	40.7541i		−	1.37149i	−0.727844	−	0.685743i	$-0.759477\pi$
$883$		−	40.7541i		−	1.37149i	0.727844	−	0.685743i	$-0.240523\pi$
$884$	−5.55562			−0.186856
$885$	−37.9612	−	11.4013i	−1.27605	−	0.383252i
$886$	29.1344			0.978788
$887$		−	44.2838i		−	1.48690i	−0.668789	−	0.743452i	$-0.733187\pi$
$887$		−	44.2838i		−	1.48690i	0.668789	−	0.743452i	$-0.266813\pi$
$888$			60.6274i			2.03452i
$889$	41.1729			1.38089
$890$	−22.4914	−	6.75512i	−0.753914	−	0.226432i
$891$	−98.1827			−3.28925
$892$			1.70162i			0.0569745i
$893$		−	9.49993i		−	0.317903i
$894$	68.9908			2.30740
$895$	10.0771	−	33.5520i	0.336839	−	1.12152i
$896$	−59.8620			−1.99985
$897$			48.7495i			1.62770i
$898$		−	4.25936i		−	0.142137i
$899$	2.01871			0.0673277
$900$	−6.39253	−	4.22062i	−0.213084	−	0.140687i
$901$	−58.2518			−1.94065
$902$		−	57.0369i		−	1.89912i
$903$			66.6077i			2.21657i
$904$	−32.6800			−1.08692
$905$	3.86199	−	12.8587i	0.128377	−	0.427436i
$906$	5.68186			0.188767
$907$		−	0.773290i		−	0.0256767i	−0.999918	−	0.0128383i	$-0.995913\pi$
$907$		−	0.773290i		−	0.0256767i	0.999918	−	0.0128383i	$-0.00408668\pi$
$908$		−	0.214889i		−	0.00713136i
$909$	60.1569			1.99528
$910$	63.8963	+	19.1908i	2.11814	+	0.636167i
$911$	39.1307			1.29646			0.648228	−	0.761446i	$-0.275510\pi$
$911$	39.1307			1.29646			0.648228	+	0.761446i	$0.275510\pi$
$912$			16.9479i			0.561202i
$913$		−	58.8413i		−	1.94736i
$914$	−17.5028			−0.578942
$915$	−31.9135	−	9.58496i	−1.05503	−	0.316869i
$916$	3.31395			0.109496
$917$			49.8319i			1.64560i
$918$		−	100.812i		−	3.32729i
$919$	−24.2527			−0.800023			−0.400011	−	0.916510i	$-0.630994\pi$
$919$	−24.2527			−0.800023			−0.400011	+	0.916510i	$0.630994\pi$
$920$	6.18585	−	20.5960i	0.203941	−	0.679030i
$921$	59.4955			1.96044
$922$		−	2.10800i		−	0.0694233i
$923$		−	17.0291i		−	0.560520i
$924$	19.5197			0.642152
$925$	−20.1850	+	30.5721i	−0.663678	+	1.00520i
$926$	45.2120			1.48576
$927$			21.1457i			0.694517i
$928$		−	2.30703i		−	0.0757320i
$929$	−4.12264			−0.135260			−0.0676298	−	0.997710i	$-0.521544\pi$
$929$	−4.12264			−0.135260			−0.0676298	+	0.997710i	$0.521544\pi$
$930$	3.34298	−	11.1306i	0.109621	−	0.364986i
$931$	−18.1277			−0.594112
$932$		−	4.33313i		−	0.141936i
$933$			50.9629i			1.66845i
$934$	15.2808			0.500003
$935$	72.6381	+	21.8163i	2.37552	+	0.713469i
$936$	−76.9394			−2.51484
$937$		−	8.27592i		−	0.270362i	−0.990821	−	0.135181i	$-0.956838\pi$
$937$		−	8.27592i		−	0.270362i	0.990821	−	0.135181i	$-0.0431617\pi$
$938$		−	97.4162i		−	3.18075i
$939$	−5.35473			−0.174745
$940$	3.73532	+	1.12187i	0.121833	+	0.0365914i
$941$	11.2610			0.367100			0.183550	−	0.983010i	$-0.441241\pi$
$941$	11.2610			0.367100			0.183550	+	0.983010i	$0.441241\pi$
$942$		−	44.2417i		−	1.44147i
$943$		−	23.4476i		−	0.763560i
$944$	−24.9529			−0.812148
$945$	−35.3748	+	117.782i	−1.15074	+	3.83144i
$946$	−40.4090			−1.31381
$947$			28.2529i			0.918096i	0.888411	+	0.459048i	$0.151809\pi$
$947$			28.2529i			0.918096i	−0.888411	+	0.459048i	$0.848191\pi$
$948$		−	1.25439i		−	0.0407406i
$949$	38.2776			1.24254
$950$	−5.06271	+	7.66797i	−0.164256	+	0.248782i
$951$	29.1770			0.946130
$952$		−	70.6155i		−	2.28866i
$953$		−	39.0186i		−	1.26394i	−0.774995	−	0.631968i	$-0.782248\pi$
$953$		−	39.0186i		−	1.26394i	0.774995	−	0.631968i	$-0.217752\pi$
$954$	102.845			3.32972
$955$	−9.32963	+	31.0633i	−0.301900	+	1.00519i
$956$	−0.878858			−0.0284243
$957$		−	33.5588i		−	1.08480i
$958$		−	25.1203i		−	0.811602i
$959$	30.4381			0.982899
$960$	46.2154	+	13.8804i	1.49160	+	0.447989i
$961$	−29.7586			−0.959955
$962$		−	46.9091i		−	1.51241i
$963$			16.1188i			0.519423i
$964$	−0.226139			−0.00728345
$965$	−7.32407	−	2.19972i	−0.235770	−	0.0708116i
$966$	78.9939			2.54159
$967$			39.9098i			1.28341i	0.766950	+	0.641707i	$0.221773\pi$
$967$			39.9098i			1.28341i	−0.766950	+	0.641707i	$0.778227\pi$
$968$		−	63.7773i		−	2.04988i
$969$	−22.0469			−0.708249
$970$	4.83564	−	16.1004i	0.155263	−	0.516954i
$971$	50.1082			1.60805			0.804024	−	0.594597i	$-0.202688\pi$
$971$	50.1082			1.60805			0.804024	+	0.594597i	$0.202688\pi$
$972$			3.71087i			0.119026i
$973$			45.1266i			1.44669i
$974$	−28.5289			−0.914126
$975$	−55.9781	−	36.9591i	−1.79273	−	1.18364i
$976$	−20.9776			−0.671477
$977$		−	42.4558i		−	1.35828i	−0.734008	−	0.679141i	$-0.762352\pi$
$977$		−	42.4558i		−	1.35828i	0.734008	−	0.679141i	$-0.237648\pi$
$978$			9.43359i			0.301653i
$979$	−41.7011			−1.33277
$980$	2.14075	−	7.12771i	0.0683838	−	0.227686i
$981$	−74.0385			−2.36387
$982$		−	20.4288i		−	0.651908i
$983$		−	18.7770i		−	0.598895i	−0.954113	−	0.299447i	$-0.903198\pi$
$983$		−	18.7770i		−	0.598895i	0.954113	−	0.299447i	$-0.0968023\pi$
$984$	53.3938			1.70213
$985$	43.9184	+	13.1905i	1.39936	+	0.420285i
$986$	15.4771			0.492890
$987$		−	112.378i		−	3.57703i
$988$		−	1.19519i		−	0.0380239i
$989$	−16.6119			−0.528229
$990$	−128.244	−	38.5171i	−4.07586	−	1.22415i
$991$	−7.86345			−0.249791			−0.124895	−	0.992170i	$-0.539860\pi$
$991$	−7.86345			−0.249791			−0.124895	+	0.992170i	$0.539860\pi$
$992$		−	1.41872i		−	0.0450443i
$993$		−	38.1451i		−	1.21050i
$994$	−27.5941			−0.875230
$995$	1.78672	−	5.94894i	0.0566428	−	0.188594i
$996$	−7.02219			−0.222507
$997$			4.32111i			0.136851i	0.997656	+	0.0684255i	$0.0217975\pi$
$997$			4.32111i			0.136851i	−0.997656	+	0.0684255i	$0.978202\pi$
$998$			61.4989i			1.94671i
$999$	86.4688			2.73575

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1205.2.b.c.724.12	✓	46
5.2	odd	4		6025.2.a.p.1.35		46
5.3	odd	4		6025.2.a.p.1.12		46
5.4	even	2	inner	1205.2.b.c.724.35	yes	46

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1205.2.b.c.724.12	✓	46	1.1	even	1	trivial
1205.2.b.c.724.35	yes	46	5.4	even	2	inner
6025.2.a.p.1.12		46	5.3	odd	4
6025.2.a.p.1.35		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)

\(f(q)\)	\(=\)	\(q-1.49203i q^{2} -3.12646i q^{3} -0.226139 q^{4} +(0.643201 - 2.14156i) q^{5} -4.66475 q^{6} +4.66024i q^{7} -2.64665i q^{8} -6.77474 q^{9} +O(q^{10})\)	\(q-1.49203i q^{2} -3.12646i q^{3} -0.226139 q^{4} +(0.643201 - 2.14156i) q^{5} -4.66475 q^{6} +4.66024i q^{7} -2.64665i q^{8} -6.77474 q^{9} +(-3.19527 - 0.959673i) q^{10} -5.92431 q^{11} +0.707014i q^{12} +4.29102i q^{13} +6.95319 q^{14} +(-6.69551 - 2.01094i) q^{15} -4.40114 q^{16} -5.72527i q^{17} +10.1081i q^{18} +1.23168 q^{19} +(-0.145453 + 0.484291i) q^{20} +14.5700 q^{21} +8.83922i q^{22} +3.63376i q^{23} -8.27462 q^{24} +(-4.17258 - 2.75491i) q^{25} +6.40231 q^{26} +11.8016i q^{27} -1.05386i q^{28} -1.81182 q^{29} +(-3.00038 + 9.98986i) q^{30} -1.11419 q^{31} +1.27332i q^{32} +18.5221i q^{33} -8.54225 q^{34} +(9.98019 + 2.99747i) q^{35} +1.53203 q^{36} -7.32690i q^{37} -1.83770i q^{38} +13.4157 q^{39} +(-5.66796 - 1.70233i) q^{40} -6.45271 q^{41} -21.7389i q^{42} +4.57155i q^{43} +1.33972 q^{44} +(-4.35752 + 14.5085i) q^{45} +5.42167 q^{46} -7.71296i q^{47} +13.7600i q^{48} -14.7178 q^{49} +(-4.11040 + 6.22560i) q^{50} -17.8998 q^{51} -0.970368i q^{52} -10.1745i q^{53} +17.6082 q^{54} +(-3.81052 + 12.6873i) q^{55} +12.3340 q^{56} -3.85081i q^{57} +2.70329i q^{58} +5.66965 q^{59} +(1.51412 + 0.454752i) q^{60} +4.76640 q^{61} +1.66239i q^{62} -31.5719i q^{63} -6.90245 q^{64} +(9.18949 + 2.75999i) q^{65} +27.6354 q^{66} -14.0103i q^{67} +1.29471i q^{68} +11.3608 q^{69} +(4.47230 - 14.8907i) q^{70} -3.96855 q^{71} +17.9303i q^{72} -8.92040i q^{73} -10.9319 q^{74} +(-8.61312 + 13.0454i) q^{75} -0.278532 q^{76} -27.6087i q^{77} -20.0166i q^{78} -1.77420 q^{79} +(-2.83082 + 9.42532i) q^{80} +16.5729 q^{81} +9.62761i q^{82} +9.93218i q^{83} -3.29485 q^{84} +(-12.2610 - 3.68250i) q^{85} +6.82087 q^{86} +5.66459i q^{87} +15.6795i q^{88} +7.03898 q^{89} +(21.6471 + 6.50153i) q^{90} -19.9972 q^{91} -0.821736i q^{92} +3.48346i q^{93} -11.5079 q^{94} +(0.792221 - 2.63773i) q^{95} +3.98098 q^{96} +5.03884i q^{97} +21.9594i q^{98} +40.1356 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 46 q - 34 q^{4} - 8 q^{5} - 4 q^{6} - 34 q^{9}+O(q^{10}) \) 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

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Representations

Groups

Database

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