LMFDB - Embedded newform 1205.2.b.c.724.1

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			724.1
Character	$\chi$	$=$	1205.724
Dual form			1205.2.b.c.724.46

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.68673i q^{2} -2.58072i q^{3} -5.21850 q^{4} +(1.90521 + 1.17055i) q^{5} -6.93370 q^{6} +1.24945i q^{7} +8.64724i q^{8} -3.66013 q^{9} +O(q^{10})$	\(q-2.68673i q^{2} -2.58072i q^{3} -5.21850 q^{4} +(1.90521 + 1.17055i) q^{5} -6.93370 q^{6} +1.24945i q^{7} +8.64724i q^{8} -3.66013 q^{9} +(3.14494 - 5.11877i) q^{10} -5.71181 q^{11} +13.4675i q^{12} +3.28322i q^{13} +3.35693 q^{14} +(3.02086 - 4.91681i) q^{15} +12.7958 q^{16} +5.29090i q^{17} +9.83378i q^{18} -6.14996 q^{19} +(-9.94233 - 6.10851i) q^{20} +3.22448 q^{21} +15.3461i q^{22} -2.22338i q^{23} +22.3161 q^{24} +(2.25963 + 4.46027i) q^{25} +8.82111 q^{26} +1.70362i q^{27} -6.52026i q^{28} +5.09304 q^{29} +(-13.2101 - 8.11623i) q^{30} -4.50984 q^{31} -17.0842i q^{32} +14.7406i q^{33} +14.2152 q^{34} +(-1.46254 + 2.38046i) q^{35} +19.1004 q^{36} -4.88794i q^{37} +16.5233i q^{38} +8.47308 q^{39} +(-10.1220 + 16.4748i) q^{40} -4.77605 q^{41} -8.66331i q^{42} -2.72100i q^{43} +29.8071 q^{44} +(-6.97331 - 4.28436i) q^{45} -5.97362 q^{46} -2.52165i q^{47} -33.0223i q^{48} +5.43887 q^{49} +(11.9835 - 6.07102i) q^{50} +13.6544 q^{51} -17.1335i q^{52} +7.67961i q^{53} +4.57716 q^{54} +(-10.8822 - 6.68594i) q^{55} -10.8043 q^{56} +15.8714i q^{57} -13.6836i q^{58} +8.39323 q^{59} +(-15.7644 + 25.6584i) q^{60} -12.2037 q^{61} +12.1167i q^{62} -4.57315i q^{63} -20.3092 q^{64} +(-3.84316 + 6.25521i) q^{65} +39.6039 q^{66} +15.2352i q^{67} -27.6106i q^{68} -5.73793 q^{69} +(6.39565 + 3.92945i) q^{70} -6.27039 q^{71} -31.6500i q^{72} +5.27275i q^{73} -13.1325 q^{74} +(11.5107 - 5.83149i) q^{75} +32.0936 q^{76} -7.13662i q^{77} -22.7648i q^{78} -9.38460 q^{79} +(24.3786 + 14.9781i) q^{80} -6.58383 q^{81} +12.8319i q^{82} +2.13252i q^{83} -16.8270 q^{84} +(-6.19326 + 10.0803i) q^{85} -7.31059 q^{86} -13.1437i q^{87} -49.3913i q^{88} -8.11125 q^{89} +(-11.5109 + 18.7354i) q^{90} -4.10222 q^{91} +11.6027i q^{92} +11.6386i q^{93} -6.77498 q^{94} +(-11.7170 - 7.19883i) q^{95} -44.0897 q^{96} -10.0464i q^{97} -14.6128i q^{98} +20.9060 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	2.68673i		−	1.89980i	−0.312550	−	0.949901i	$-0.601183\pi$
$2$		−	2.68673i		−	1.89980i	0.312550	−	0.949901i	$-0.398817\pi$
$3$		−	2.58072i		−	1.48998i	−0.667075	−	0.744991i	$-0.732454\pi$
$3$		−	2.58072i		−	1.48998i	0.667075	−	0.744991i	$-0.267546\pi$
$4$	−5.21850			−2.60925
$5$	1.90521	+	1.17055i	0.852035	+	0.523485i
$5$	1.90521	+	1.17055i	0.852035	+	0.523485i
$6$	−6.93370			−2.83067
$7$			1.24945i			0.472248i	0.971723	+	0.236124i	$0.0758771\pi$
$7$			1.24945i			0.472248i	−0.971723	+	0.236124i	$0.924123\pi$
$8$			8.64724i			3.05726i
$9$	−3.66013			−1.22004
$10$	3.14494	−	5.11877i	0.994518	−	1.61870i
$11$	−5.71181			−1.72217			−0.861087	−	0.508457i	$-0.830216\pi$
$11$	−5.71181			−1.72217			−0.861087	+	0.508457i	$0.830216\pi$
$12$			13.4675i			3.88774i
$13$			3.28322i			0.910601i	0.890338	+	0.455300i	$0.150468\pi$
$13$			3.28322i			0.910601i	−0.890338	+	0.455300i	$0.849532\pi$
$14$	3.35693			0.897178
$15$	3.02086	−	4.91681i	0.779983	−	1.26952i
$16$	12.7958			3.19894
$17$			5.29090i			1.28323i	0.767026	+	0.641616i	$0.221736\pi$
$17$			5.29090i			1.28323i	−0.767026	+	0.641616i	$0.778264\pi$
$18$			9.83378i			2.31784i
$19$	−6.14996			−1.41090			−0.705449	−	0.708760i	$-0.749255\pi$
$19$	−6.14996			−1.41090			−0.705449	+	0.708760i	$0.749255\pi$
$20$	−9.94233	−	6.10851i	−2.22317	−	1.36590i
$21$	3.22448			0.703640
$22$			15.3461i			3.27179i
$23$		−	2.22338i		−	0.463607i	−0.972763	−	0.231804i	$-0.925537\pi$
$23$		−	2.22338i		−	0.463607i	0.972763	−	0.231804i	$-0.0744627\pi$
$24$	22.3161			4.55526
$25$	2.25963	+	4.46027i	0.451927	+	0.892055i
$26$	8.82111			1.72996
$27$			1.70362i			0.327862i
$28$		−	6.52026i		−	1.23221i
$29$	5.09304			0.945753			0.472877	−	0.881129i	$-0.343216\pi$
$29$	5.09304			0.945753			0.472877	+	0.881129i	$0.343216\pi$
$30$	−13.2101	−	8.11623i	−2.41183	−	1.48181i
$31$	−4.50984			−0.809991			−0.404996	−	0.914319i	$-0.632727\pi$
$31$	−4.50984			−0.809991			−0.404996	+	0.914319i	$0.632727\pi$
$32$		−	17.0842i		−	3.02010i
$33$			14.7406i			2.56601i
$34$	14.2152			2.43789
$35$	−1.46254	+	2.38046i	−0.247215	+	0.402372i
$36$	19.1004			3.18340
$37$		−	4.88794i		−	0.803572i	−0.915734	−	0.401786i	$-0.868390\pi$
$37$		−	4.88794i		−	0.803572i	0.915734	−	0.401786i	$-0.131610\pi$
$38$			16.5233i			2.68043i
$39$	8.47308			1.35678
$40$	−10.1220	+	16.4748i	−1.60043	+	2.60489i
$41$	−4.77605			−0.745894			−0.372947	−	0.927853i	$-0.621653\pi$
$41$	−4.77605			−0.745894			−0.372947	+	0.927853i	$0.621653\pi$
$42$		−	8.66331i		−	1.33678i
$43$		−	2.72100i		−	0.414949i	−0.978240	−	0.207474i	$-0.933476\pi$
$43$		−	2.72100i		−	0.414949i	0.978240	−	0.207474i	$-0.0665244\pi$
$44$	29.8071			4.49359
$45$	−6.97331	−	4.28436i	−1.03952	−	0.638675i
$46$	−5.97362			−0.880762
$47$		−	2.52165i		−	0.367820i	−0.982943	−	0.183910i	$-0.941124\pi$
$47$		−	2.52165i		−	0.367820i	0.982943	−	0.183910i	$-0.0588755\pi$
$48$		−	33.0223i		−	4.76636i
$49$	5.43887			0.776982
$50$	11.9835	−	6.07102i	1.69473	−	0.858572i
$51$	13.6544			1.91199
$52$		−	17.1335i		−	2.37599i
$53$			7.67961i			1.05488i	0.849594	+	0.527438i	$0.176847\pi$
$53$			7.67961i			1.05488i	−0.849594	+	0.527438i	$0.823153\pi$
$54$	4.57716			0.622873
$55$	−10.8822	−	6.68594i	−1.46735	−	0.901532i
$56$	−10.8043			−1.44378
$57$			15.8714i			2.10221i
$58$		−	13.6836i		−	1.79675i
$59$	8.39323			1.09271			0.546353	−	0.837555i	$-0.316016\pi$
$59$	8.39323			1.09271			0.546353	+	0.837555i	$0.316016\pi$
$60$	−15.7644	+	25.6584i	−2.03517	+	3.31249i
$61$	−12.2037			−1.56252			−0.781260	−	0.624205i	$-0.785423\pi$
$61$	−12.2037			−1.56252			−0.781260	+	0.624205i	$0.785423\pi$
$62$			12.1167i			1.53882i
$63$		−	4.57315i		−	0.576163i
$64$	−20.3092			−2.53865
$65$	−3.84316	+	6.25521i	−0.476686	+	0.775864i
$66$	39.6039			4.87491
$67$			15.2352i			1.86128i	0.365934	+	0.930641i	$0.380750\pi$
$67$			15.2352i			1.86128i	−0.365934	+	0.930641i	$0.619250\pi$
$68$		−	27.6106i		−	3.34828i
$69$	−5.73793			−0.690766
$70$	6.39565	+	3.92945i	0.764427	+	0.469659i
$71$	−6.27039			−0.744159			−0.372079	−	0.928201i	$-0.621355\pi$
$71$	−6.27039			−0.744159			−0.372079	+	0.928201i	$0.621355\pi$
$72$		−	31.6500i		−	3.72999i
$73$			5.27275i			0.617129i	0.951203	+	0.308564i	$0.0998485\pi$
$73$			5.27275i			0.617129i	−0.951203	+	0.308564i	$0.900151\pi$
$74$	−13.1325			−1.52663
$75$	11.5107	−	5.83149i	1.32915	−	0.673363i
$76$	32.0936			3.68139
$77$		−	7.13662i		−	0.813293i
$78$		−	22.7648i		−	2.57761i
$79$	−9.38460			−1.05585			−0.527925	−	0.849291i	$-0.677030\pi$
$79$	−9.38460			−1.05585			−0.527925	+	0.849291i	$0.677030\pi$
$80$	24.3786	+	14.9781i	2.72561	+	1.67460i
$81$	−6.58383			−0.731536
$82$			12.8319i			1.41705i
$83$			2.13252i			0.234074i	0.993128	+	0.117037i	$0.0373397\pi$
$83$			2.13252i			0.234074i	−0.993128	+	0.117037i	$0.962660\pi$
$84$	−16.8270			−1.83597
$85$	−6.19326	+	10.0803i	−0.671753	+	1.09336i
$86$	−7.31059			−0.788321
$87$		−	13.1437i		−	1.40915i
$88$		−	49.3913i		−	5.26514i
$89$	−8.11125			−0.859791			−0.429895	−	0.902879i	$-0.641450\pi$
$89$	−8.11125			−0.859791			−0.429895	+	0.902879i	$0.641450\pi$
$90$	−11.5109	+	18.7354i	−1.21336	+	1.97488i
$91$	−4.10222			−0.430029
$92$			11.6027i			1.20967i
$93$			11.6386i			1.20687i
$94$	−6.77498			−0.698786
$95$	−11.7170	−	7.19883i	−1.20213	−	0.738584i
$96$	−44.0897			−4.49989
$97$		−	10.0464i		−	1.02006i	−0.860156	−	0.510031i	$-0.829634\pi$
$97$		−	10.0464i		−	1.02006i	0.860156	−	0.510031i	$-0.170366\pi$
$98$		−	14.6128i		−	1.47611i
$99$	20.9060			2.10113
$100$	−11.7919	−	23.2760i	−1.17919	−	2.32760i
$101$	−16.4859			−1.64041			−0.820207	−	0.572067i	$-0.806142\pi$
$101$	−16.4859			−1.64041			−0.820207	+	0.572067i	$0.806142\pi$
$102$		−	36.6855i		−	3.63241i
$103$		−	8.12695i		−	0.800772i	−0.916347	−	0.400386i	$-0.868876\pi$
$103$		−	8.12695i		−	0.800772i	0.916347	−	0.400386i	$-0.131124\pi$
$104$	−28.3908			−2.78394
$105$	6.14331	+	3.77441i	0.599526	+	0.368345i
$106$	20.6330			2.00406
$107$			15.5719i			1.50539i	0.658368	+	0.752697i	$0.271247\pi$
$107$			15.5719i			1.50539i	−0.658368	+	0.752697i	$0.728753\pi$
$108$		−	8.89035i		−	0.855474i
$109$	17.5584			1.68179			0.840893	−	0.541202i	$-0.182030\pi$
$109$	17.5584			1.68179			0.840893	+	0.541202i	$0.182030\pi$
$110$	−17.9633	+	29.2374i	−1.71273	+	2.78768i
$111$	−12.6144			−1.19731
$112$			15.9877i			1.51069i
$113$			4.82918i			0.454291i	0.973861	+	0.227146i	$0.0729393\pi$
$113$			4.82918i			0.454291i	−0.973861	+	0.227146i	$0.927061\pi$
$114$	42.6420			3.99379
$115$	2.60258	−	4.23601i	0.242691	−	0.395010i
$116$	−26.5780			−2.46771
$117$		−	12.0170i		−	1.11097i
$118$		−	22.5503i		−	2.07592i
$119$	−6.61072			−0.606004
$120$	42.5169	+	26.1221i	3.88124	+	2.38461i
$121$	21.6247			1.96588
$122$			32.7880i			2.96848i
$123$			12.3257i			1.11137i
$124$	23.5346			2.11347
$125$	−0.915891	+	11.1428i	−0.0819198	+	0.996639i
$126$	−12.2868			−1.09460
$127$			12.2103i			1.08349i	0.840542	+	0.541746i	$0.182237\pi$
$127$			12.2103i			1.08349i	−0.840542	+	0.541746i	$0.817763\pi$
$128$			20.3967i			1.80283i
$129$	−7.02215			−0.618266
$130$	16.8060	+	10.3255i	1.47399	+	0.905609i
$131$	−10.1109			−0.883392			−0.441696	−	0.897165i	$-0.645623\pi$
$131$	−10.1109			−0.883392			−0.441696	+	0.897165i	$0.645623\pi$
$132$		−	76.9238i		−	6.69536i
$133$		−	7.68407i		−	0.666294i
$134$	40.9330			3.53607
$135$	−1.99417	+	3.24575i	−0.171631	+	0.279350i
$136$	−45.7517			−3.92318
$137$		−	13.2155i		−	1.12908i	−0.825406	−	0.564539i	$-0.809054\pi$
$137$		−	13.2155i		−	1.12908i	0.825406	−	0.564539i	$-0.190946\pi$
$138$			15.4163i			1.31232i
$139$	−15.9583			−1.35357			−0.676784	−	0.736182i	$-0.736627\pi$
$139$	−15.9583			−1.35357			−0.676784	+	0.736182i	$0.736627\pi$
$140$	7.63228	−	12.4224i	0.645045	−	1.04989i
$141$	−6.50768			−0.548045
$142$			16.8468i			1.41375i
$143$		−	18.7531i		−	1.56821i
$144$	−46.8342			−3.90285
$145$	9.70330	+	5.96165i	0.805815	+	0.495088i
$146$	14.1664			1.17242
$147$		−	14.0362i		−	1.15769i
$148$			25.5077i			2.09672i
$149$	−4.94740			−0.405307			−0.202653	−	0.979251i	$-0.564956\pi$
$149$	−4.94740			−0.405307			−0.202653	+	0.979251i	$0.564956\pi$
$150$	−15.6676	−	30.9262i	−1.27926	−	2.52511i
$151$	−9.19121			−0.747970			−0.373985	−	0.927435i	$-0.622009\pi$
$151$	−9.19121			−0.747970			−0.373985	+	0.927435i	$0.622009\pi$
$152$		−	53.1802i		−	4.31348i
$153$		−	19.3654i		−	1.56560i
$154$	−19.1741			−1.54510
$155$	−8.59218	−	5.27898i	−0.690141	−	0.424018i
$156$	−44.2168			−3.54017
$157$			7.17472i			0.572605i	0.958139	+	0.286302i	$0.0924262\pi$
$157$			7.17472i			0.572605i	−0.958139	+	0.286302i	$0.907574\pi$
$158$			25.2138i			2.00591i
$159$	19.8190			1.57174
$160$	19.9979	−	32.5490i	1.58098	−	2.57323i
$161$	2.77801			0.218937
$162$			17.6889i			1.38977i
$163$		−	14.9501i		−	1.17098i	−0.810680	−	0.585490i	$-0.800902\pi$
$163$		−	14.9501i		−	1.17098i	0.810680	−	0.585490i	$-0.199098\pi$
$164$	24.9238			1.94622
$165$	−17.2546	+	28.0839i	−1.34327	+	2.18633i
$166$	5.72950			0.444695
$167$			4.27656i			0.330930i	0.986216	+	0.165465i	$0.0529125\pi$
$167$			4.27656i			0.330930i	−0.986216	+	0.165465i	$0.947088\pi$
$168$			27.8829i			2.15121i
$169$	2.22048			0.170807
$170$	27.0829	+	16.6396i	2.07717	+	1.27620i
$171$	22.5097			1.72136
$172$			14.1996i			1.08271i
$173$			8.86646i			0.674105i	0.941486	+	0.337052i	$0.109430\pi$
$173$			8.86646i			0.674105i	−0.941486	+	0.337052i	$0.890570\pi$
$174$	−35.3136			−2.67712
$175$	−5.57289	+	2.82330i	−0.421271	+	0.213421i
$176$	−73.0869			−5.50913
$177$		−	21.6606i		−	1.62811i
$178$			21.7927i			1.63343i
$179$	−19.6157			−1.46615			−0.733075	−	0.680148i	$-0.761916\pi$
$179$	−19.6157			−1.46615			−0.733075	+	0.680148i	$0.761916\pi$
$180$	36.3903	+	22.3579i	2.71237	+	1.66646i
$181$	15.9326			1.18426			0.592132	−	0.805841i	$-0.298286\pi$
$181$	15.9326			1.18426			0.592132	+	0.805841i	$0.298286\pi$
$182$			11.0215i			0.816971i
$183$			31.4943i			2.32813i
$184$	19.2261			1.41737
$185$	5.72156	−	9.31253i	0.420658	−	0.684671i
$186$	31.2699			2.29282
$187$		−	30.2206i		−	2.20995i
$188$			13.1592i			0.959735i
$189$	−2.12859			−0.154832
$190$	−19.3413	+	31.4803i	−1.40316	+	2.28382i
$191$	−13.9904			−1.01231			−0.506157	−	0.862442i	$-0.668934\pi$
$191$	−13.9904			−1.01231			−0.506157	+	0.862442i	$0.668934\pi$
$192$			52.4124i			3.78254i
$193$		−	5.85035i		−	0.421117i	−0.977581	−	0.210559i	$-0.932472\pi$
$193$		−	5.85035i		−	0.421117i	0.977581	−	0.210559i	$-0.0675283\pi$
$194$	−26.9920			−1.93792
$195$	16.1430	+	9.91814i	1.15602	+	0.710253i
$196$	−28.3828			−2.02734
$197$			0.760772i			0.0542028i	0.999633	+	0.0271014i	$0.00862770\pi$
$197$			0.760772i			0.0542028i	−0.999633	+	0.0271014i	$0.991372\pi$
$198$		−	56.1686i		−	3.99173i
$199$	13.2393			0.938511			0.469255	−	0.883063i	$-0.344522\pi$
$199$	13.2393			0.938511			0.469255	+	0.883063i	$0.344522\pi$
$200$	−38.5691	+	19.5396i	−2.72724	+	1.38166i
$201$	39.3180			2.77328
$202$			44.2932i			3.11646i
$203$			6.36350i			0.446630i
$204$	−71.2553			−4.98887
$205$	−9.09937	−	5.59060i	−0.635528	−	0.390464i
$206$	−21.8349			−1.52131
$207$			8.13787i			0.565621i
$208$			42.0113i			2.91296i
$209$	35.1274			2.42981
$210$	10.1408	−	16.5054i	0.699783	−	1.13898i
$211$	10.5091			0.723480			0.361740	−	0.932279i	$-0.382183\pi$
$211$	10.5091			0.723480			0.361740	+	0.932279i	$0.382183\pi$
$212$		−	40.0761i		−	2.75244i
$213$			16.1821i			1.10878i
$214$	41.8375			2.85995
$215$	3.18506	−	5.18407i	0.217219	−	0.353551i
$216$	−14.7316			−1.00236
$217$		−	5.63482i		−	0.382516i
$218$		−	47.1745i		−	3.19506i
$219$	13.6075			0.919510
$220$	56.7887	+	34.8906i	3.82869	+	2.35232i
$221$	−17.3712			−1.16851
$222$			33.8915i			2.27465i
$223$			11.7804i			0.788876i	0.918923	+	0.394438i	$0.129061\pi$
$223$			11.7804i			0.788876i	−0.918923	+	0.394438i	$0.870939\pi$
$224$	21.3459			1.42623
$225$	−8.27056	−	16.3252i	−0.551371	−	1.08835i
$226$	12.9747			0.863063
$227$		−	9.33932i		−	0.619873i	−0.950757	−	0.309936i	$-0.899692\pi$
$227$		−	9.33932i		−	0.619873i	0.950757	−	0.309936i	$-0.100308\pi$
$228$		−	82.8247i		−	5.48520i
$229$	16.5911			1.09637			0.548186	−	0.836357i	$-0.315319\pi$
$229$	16.5911			1.09637			0.548186	+	0.836357i	$0.315319\pi$
$230$	−11.3810	−	6.99241i	−0.750440	−	0.461066i
$231$	−18.4176			−1.21179
$232$			44.0407i			2.89141i
$233$		−	2.57802i		−	0.168892i	−0.996428	−	0.0844460i	$-0.973088\pi$
$233$		−	2.57802i		−	0.168892i	0.996428	−	0.0844460i	$-0.0269120\pi$
$234$	−32.2864			−2.11063
$235$	2.95171	−	4.80427i	0.192548	−	0.313396i
$236$	−43.8001			−2.85114
$237$			24.2190i			1.57320i
$238$			17.7612i			1.15129i
$239$	26.0214			1.68318			0.841592	−	0.540113i	$-0.181619\pi$
$239$	26.0214			1.68318			0.841592	+	0.540113i	$0.181619\pi$
$240$	38.6542	−	62.9144i	2.49512	−	4.06111i
$241$	1.00000			0.0644157
$241$	1.00000			0.0644157
$242$		−	58.0998i		−	3.73479i
$243$			22.1019i			1.41784i
$244$	63.6849			4.07701
$245$	10.3622	+	6.36646i	0.662016	+	0.406738i
$246$	33.1157			2.11138
$247$		−	20.1917i		−	1.28477i
$248$		−	38.9977i		−	2.47635i
$249$	5.50344			0.348767
$250$	29.9376	+	2.46075i	1.89342	+	0.155631i
$251$	27.0049			1.70453			0.852267	−	0.523107i	$-0.175227\pi$
$251$	27.0049			1.70453			0.852267	+	0.523107i	$0.175227\pi$
$252$			23.8650i			1.50335i
$253$			12.6995i			0.798413i
$254$	32.8059			2.05842
$255$	26.0144	+	15.9831i	1.62908	+	1.00090i
$256$	14.1821			0.886381
$257$		−	27.5253i		−	1.71698i	−0.512830	−	0.858490i	$-0.671403\pi$
$257$		−	27.5253i		−	1.71698i	0.512830	−	0.858490i	$-0.328597\pi$
$258$			18.8666i			1.17458i
$259$	6.10723			0.379485
$260$	20.0556	−	32.6428i	1.24379	−	2.02442i
$261$	−18.6412			−1.15386
$262$			27.1652i			1.67827i
$263$		−	7.57437i		−	0.467056i	−0.972350	−	0.233528i	$-0.924973\pi$
$263$		−	7.57437i		−	0.467056i	0.972350	−	0.233528i	$-0.0750270\pi$
$264$	−127.465			−7.84495
$265$	−8.98935	+	14.6313i	−0.552212	+	0.898791i
$266$	−20.6450			−1.26583
$267$			20.9329i			1.28107i
$268$		−	79.5052i		−	4.85655i
$269$	8.18678			0.499157			0.249578	−	0.968355i	$-0.419708\pi$
$269$	8.18678			0.499157			0.249578	+	0.968355i	$0.419708\pi$
$270$	8.72045	+	5.35779i	0.530710	+	0.326065i
$271$	−3.63408			−0.220755			−0.110377	−	0.993890i	$-0.535206\pi$
$271$	−3.63408			−0.220755			−0.110377	+	0.993890i	$0.535206\pi$
$272$			67.7012i			4.10499i
$273$			10.5867i			0.640735i
$274$	−35.5065			−2.14503
$275$	−12.9066	−	25.4762i	−0.778297	−	1.53627i
$276$	29.9434			1.80238
$277$		−	2.42885i		−	0.145935i	−0.997334	−	0.0729677i	$-0.976753\pi$
$277$		−	2.42885i		−	0.145935i	0.997334	−	0.0729677i	$-0.0232470\pi$
$278$			42.8757i			2.57151i
$279$	16.5066			0.988225
$280$	−20.5844	−	12.6469i	−1.23015	−	0.755799i
$281$	−16.3717			−0.976655			−0.488328	−	0.872660i	$-0.662393\pi$
$281$	−16.3717			−0.976655			−0.488328	+	0.872660i	$0.662393\pi$
$282$			17.4844i			1.04118i
$283$		−	6.08266i		−	0.361576i	−0.983522	−	0.180788i	$-0.942135\pi$
$283$		−	6.08266i		−	0.361576i	0.983522	−	0.180788i	$-0.0578648\pi$
$284$	32.7221			1.94170
$285$	−18.5782	+	30.2382i	−1.10048	+	1.79116i
$286$	−50.3845			−2.97930
$287$		−	5.96744i		−	0.352247i
$288$			62.5306i			3.68465i
$289$	−10.9937			−0.646686
$290$	16.0173	−	26.0701i	0.940569	−	1.53089i
$291$	−25.9271			−1.51987
$292$		−	27.5159i		−	1.61024i
$293$		−	10.4470i		−	0.610322i	−0.952301	−	0.305161i	$-0.901290\pi$
$293$		−	10.4470i		−	0.610322i	0.952301	−	0.305161i	$-0.0987102\pi$
$294$	−37.7115			−2.19938
$295$	15.9908	+	9.82468i	0.931023	+	0.572015i
$296$	42.2671			2.45673
$297$		−	9.73075i		−	0.564635i
$298$			13.2923i			0.770003i
$299$	7.29985			0.422161
$300$	−60.0688	+	30.4317i	−3.46807	+	1.75697i
$301$	3.39976			0.195959
$302$			24.6943i			1.42100i
$303$			42.5457i			2.44418i
$304$	−78.6935			−4.51338
$305$	−23.2505	−	14.2850i	−1.33132	−	0.817956i
$306$	−52.0296			−2.97433
$307$			17.7832i			1.01494i	0.861669	+	0.507470i	$0.169419\pi$
$307$			17.7832i			1.01494i	−0.861669	+	0.507470i	$0.830581\pi$
$308$			37.2425i			2.12209i
$309$	−20.9734			−1.19314
$310$	−14.1832	+	23.0849i	−0.805551	+	1.31113i
$311$	−5.30634			−0.300895			−0.150447	−	0.988618i	$-0.548071\pi$
$311$	−5.30634			−0.300895			−0.150447	+	0.988618i	$0.548071\pi$
$312$			73.2687i			4.14802i
$313$			25.9853i			1.46878i	0.678729	+	0.734389i	$0.262531\pi$
$313$			25.9853i			1.46878i	−0.678729	+	0.734389i	$0.737469\pi$
$314$	19.2765			1.08784
$315$	5.35310	−	8.71281i	0.301613	−	0.490911i
$316$	48.9735			2.75498
$317$			0.511802i			0.0287457i	0.999897	+	0.0143728i	$0.00457517\pi$
$317$			0.511802i			0.0287457i	−0.999897	+	0.0143728i	$0.995425\pi$
$318$		−	53.2481i		−	2.98601i
$319$	−29.0904			−1.62875
$320$	−38.6932	−	23.7729i	−2.16302	−	1.32894i
$321$	40.1868			2.24301
$322$		−	7.46374i		−	0.415938i
$323$		−	32.5389i		−	1.81051i
$324$	34.3577			1.90876
$325$	−14.6441	+	7.41887i	−0.812306	+	0.411525i
$326$	−40.1668			−2.22463
$327$		−	45.3133i		−	2.50583i
$328$		−	41.2997i		−	2.28039i
$329$	3.15067			0.173702
$330$	75.4538	+	46.3583i	4.15359	+	2.55194i
$331$	−4.37953			−0.240721			−0.120360	−	0.992730i	$-0.538405\pi$
$331$	−4.37953			−0.240721			−0.120360	+	0.992730i	$0.538405\pi$
$332$		−	11.1286i		−	0.610759i
$333$			17.8905i			0.980393i
$334$	11.4899			0.628702
$335$	−17.8336	+	29.0263i	−0.974353	+	1.58588i
$336$	41.2597			2.25090
$337$		−	9.09028i		−	0.495179i	−0.968865	−	0.247589i	$-0.920362\pi$
$337$		−	9.09028i		−	0.495179i	0.968865	−	0.247589i	$-0.0796384\pi$
$338$		−	5.96584i		−	0.324499i
$339$	12.4628			0.676885
$340$	32.3195	−	52.6039i	1.75277	−	2.85285i
$341$	25.7593			1.39495
$342$		−	60.4774i		−	3.27024i
$343$			15.5418i			0.839176i
$344$	23.5291			1.26861
$345$	−10.9320	−	6.71653i	−0.588557	−	0.361606i
$346$	23.8218			1.28067
$347$			0.771121i			0.0413959i	0.999786	+	0.0206980i	$0.00658884\pi$
$347$			0.771121i			0.0413959i	−0.999786	+	0.0206980i	$0.993411\pi$
$348$			68.5905i			3.67684i
$349$	−30.0795			−1.61012			−0.805060	−	0.593194i	$-0.797867\pi$
$349$	−30.0795			−1.61012			−0.805060	+	0.593194i	$0.797867\pi$
$350$	7.58544	+	14.9728i	0.405459	+	0.800332i
$351$	−5.59336			−0.298551
$352$			97.5819i			5.20113i
$353$		−	27.7365i		−	1.47627i	−0.674655	−	0.738133i	$-0.735707\pi$
$353$		−	27.7365i		−	1.47627i	0.674655	−	0.738133i	$-0.264293\pi$
$354$	−58.1961			−3.09309
$355$	−11.9464	−	7.33979i	−0.634049	−	0.389556i
$356$	42.3286			2.24341
$357$			17.0604i			0.902934i
$358$			52.7022i			2.78540i
$359$	−6.19082			−0.326739			−0.163370	−	0.986565i	$-0.552236\pi$
$359$	−6.19082			−0.326739			−0.163370	+	0.986565i	$0.552236\pi$
$360$	37.0479	−	60.2999i	1.95260	−	3.17808i
$361$	18.8221			0.990635
$362$		−	42.8067i		−	2.24987i
$363$		−	55.8075i		−	2.92913i
$364$	21.4074			1.12205
$365$	−6.17201	+	10.0457i	−0.323058	+	0.525815i
$366$	84.6166			4.42298
$367$		−	14.6701i		−	0.765772i	−0.923796	−	0.382886i	$-0.874930\pi$
$367$		−	14.6701i		−	0.765772i	0.923796	−	0.382886i	$-0.125070\pi$
$368$		−	28.4499i		−	1.48305i
$369$	17.4810			0.910024
$370$	−25.0202	−	15.3723i	−1.30074	−	0.799167i
$371$	−9.59529			−0.498163
$372$		−	60.7363i		−	3.14903i
$373$			7.45878i			0.386201i	0.981179	+	0.193100i	$0.0618543\pi$
$373$			7.45878i			0.386201i	−0.981179	+	0.193100i	$0.938146\pi$
$374$	−81.1946			−4.19847
$375$	28.7564	+	2.36366i	1.48497	+	0.122059i
$376$	21.8053			1.12452
$377$			16.7216i			0.861204i
$378$			5.71894i			0.294150i
$379$	32.3225			1.66030			0.830148	−	0.557543i	$-0.188256\pi$
$379$	32.3225			1.66030			0.830148	+	0.557543i	$0.188256\pi$
$380$	61.1450	+	37.5671i	3.13667	+	1.92715i
$381$	31.5115			1.61438
$382$			37.5885i			1.92320i
$383$		−	4.30576i		−	0.220014i	−0.993931	−	0.110007i	$-0.964913\pi$
$383$		−	4.30576i		−	0.220014i	0.993931	−	0.110007i	$-0.0350874\pi$
$384$	52.6383			2.68619
$385$	8.35375	−	13.5967i	0.425747	−	0.692954i
$386$	−15.7183			−0.800040
$387$			9.95923i			0.506256i
$388$			52.4274i			2.66160i
$389$	−16.1415			−0.818404			−0.409202	−	0.912444i	$-0.634193\pi$
$389$	−16.1415			−0.818404			−0.409202	+	0.912444i	$0.634193\pi$
$390$	26.6473	−	43.3718i	1.34934	−	2.19621i
$391$	11.7637			0.594916
$392$			47.0312i			2.37544i
$393$			26.0934i			1.31624i
$394$	2.04399			0.102975
$395$	−17.8796	−	10.9851i	−0.899621	−	0.552721i
$396$	−109.098			−5.48237
$397$		−	31.3345i		−	1.57263i	−0.617825	−	0.786316i	$-0.711986\pi$
$397$		−	31.3345i		−	1.57263i	0.617825	−	0.786316i	$-0.288014\pi$
$398$		−	35.5704i		−	1.78299i
$399$	−19.8305			−0.992765
$400$	28.9138	+	57.0726i	1.44569	+	2.85363i
$401$	−27.1821			−1.35741			−0.678705	−	0.734411i	$-0.737458\pi$
$401$	−27.1821			−1.35741			−0.678705	+	0.734411i	$0.737458\pi$
$402$		−	105.637i		−	5.26868i
$403$		−	14.8068i		−	0.737578i
$404$	86.0320			4.28025
$405$	−12.5436	−	7.70668i	−0.623294	−	0.382948i
$406$	17.0970			0.848509
$407$			27.9189i			1.38389i
$408$			118.072i			5.84546i
$409$	−36.8301			−1.82113			−0.910566	−	0.413363i	$-0.864354\pi$
$409$	−36.8301			−1.82113			−0.910566	+	0.413363i	$0.864354\pi$
$410$	−15.0204	+	24.4475i	−0.741805	+	1.20738i
$411$	−34.1056			−1.68230
$412$			42.4105i			2.08942i
$413$			10.4869i			0.516028i
$414$	21.8642			1.07457
$415$	−2.49622	+	4.06289i	−0.122534	+	0.199440i
$416$	56.0913			2.75010
$417$			41.1840i			2.01679i
$418$		−	94.3778i		−	4.61617i
$419$	13.5764			0.663249			0.331624	−	0.943411i	$-0.392403\pi$
$419$	13.5764			0.663249			0.331624	+	0.943411i	$0.392403\pi$
$420$	−32.0589	−	19.6968i	−1.56431	−	0.961105i
$421$	−12.1607			−0.592678			−0.296339	−	0.955083i	$-0.595766\pi$
$421$	−12.1607			−0.592678			−0.296339	+	0.955083i	$0.595766\pi$
$422$		−	28.2352i		−	1.37447i
$423$			9.22957i			0.448757i
$424$	−66.4074			−3.22503
$425$	−23.5989	+	11.9555i	−1.14471	+	0.579927i
$426$	43.4770			2.10647
$427$		−	15.2479i		−	0.737897i
$428$		−	81.2620i		−	3.92795i
$429$	−48.3966			−2.33661
$430$	−13.9282	−	8.55739i	−0.671677	−	0.412674i
$431$	−15.1822			−0.731301			−0.365650	−	0.930752i	$-0.619153\pi$
$431$	−15.1822			−0.731301			−0.365650	+	0.930752i	$0.619153\pi$
$432$			21.7991i			1.04881i
$433$			28.7849i			1.38331i	0.722226	+	0.691657i	$0.243119\pi$
$433$			28.7849i			1.38331i	−0.722226	+	0.691657i	$0.756881\pi$
$434$	−15.1392			−0.726706
$435$	15.3854	−	25.0415i	0.737671	−	1.20065i
$436$	−91.6283			−4.38820
$437$			13.6737i			0.654103i
$438$		−	36.5597i		−	1.74689i
$439$	−39.1528			−1.86866			−0.934331	−	0.356406i	$-0.884002\pi$
$439$	−39.1528			−1.86866			−0.934331	+	0.356406i	$0.884002\pi$
$440$	57.8149	−	94.1008i	2.75622	−	4.48608i
$441$	−19.9070			−0.947953
$442$			46.6716i			2.21994i
$443$			26.4163i			1.25508i	0.778586	+	0.627538i	$0.215937\pi$
$443$			26.4163i			1.25508i	−0.778586	+	0.627538i	$0.784063\pi$
$444$	65.8283			3.12407
$445$	−15.4536	−	9.49460i	−0.732572	−	0.450087i
$446$	31.6508			1.49871
$447$			12.7679i			0.603899i
$448$		−	25.3753i		−	1.19887i
$449$	9.28281			0.438083			0.219041	−	0.975716i	$-0.429707\pi$
$449$	9.28281			0.438083			0.219041	+	0.975716i	$0.429707\pi$
$450$	−43.8614	+	22.2207i	−2.06764	+	1.04750i
$451$	27.2799			1.28456
$452$		−	25.2011i		−	1.18536i
$453$			23.7200i			1.11446i
$454$	−25.0922			−1.17764
$455$	−7.81557	−	4.80184i	−0.366400	−	0.225114i
$456$	−137.243			−6.42701
$457$			8.44046i			0.394828i	0.980320	+	0.197414i	$0.0632544\pi$
$457$			8.44046i			0.394828i	−0.980320	+	0.197414i	$0.936746\pi$
$458$		−	44.5758i		−	2.08289i
$459$	−9.01369			−0.420723
$460$	−13.5815	+	22.1056i	−0.633243	+	1.03068i
$461$	−2.99442			−0.139464			−0.0697319	−	0.997566i	$-0.522214\pi$
$461$	−2.99442			−0.139464			−0.0697319	+	0.997566i	$0.522214\pi$
$462$			49.4832i			2.30216i
$463$		−	10.3910i		−	0.482910i	−0.970412	−	0.241455i	$-0.922375\pi$
$463$		−	10.3910i		−	0.482910i	0.970412	−	0.241455i	$-0.0776245\pi$
$464$	65.1693			3.02541
$465$	−13.6236	+	22.1740i	−0.631779	+	1.02830i
$466$	−6.92645			−0.320861
$467$			23.5923i			1.09172i	0.837876	+	0.545861i	$0.183797\pi$
$467$			23.5923i			1.09172i	−0.837876	+	0.545861i	$0.816203\pi$
$468$			62.7108i			2.89881i
$469$	−19.0357			−0.878986
$470$	−12.9077	−	7.93044i	−0.595390	−	0.365804i
$471$	18.5160			0.853170
$472$			72.5782i			3.34068i
$473$			15.5418i			0.714614i
$474$	65.0700			2.98876
$475$	−13.8967	−	27.4305i	−0.637623	−	1.25860i
$476$	34.4981			1.58122
$477$		−	28.1084i		−	1.28700i
$478$		−	69.9124i		−	3.19772i
$479$	5.49906			0.251259			0.125629	−	0.992077i	$-0.459905\pi$
$479$	5.49906			0.251259			0.125629	+	0.992077i	$0.459905\pi$
$480$	−84.0001	−	51.6091i	−3.83406	−	2.35562i
$481$	16.0482			0.731733
$482$		−	2.68673i		−	0.122377i
$483$		−	7.16926i		−	0.326213i
$484$	−112.849			−5.12949
$485$	11.7598	−	19.1406i	0.533987	−	0.869128i
$486$	59.3818			2.69361
$487$		−	9.89752i		−	0.448499i	−0.974532	−	0.224250i	$-0.928007\pi$
$487$		−	9.89752i		−	0.448499i	0.974532	−	0.224250i	$-0.0719931\pi$
$488$		−	105.528i		−	4.77703i
$489$	−38.5820			−1.74474
$490$	17.1050	−	27.8404i	0.772723	−	1.25770i
$491$	−22.6134			−1.02053			−0.510265	−	0.860017i	$-0.670453\pi$
$491$	−22.6134			−1.02053			−0.510265	+	0.860017i	$0.670453\pi$
$492$		−	64.3215i		−	2.89984i
$493$			26.9468i			1.21362i
$494$	−54.2495			−2.44080
$495$	39.8302	+	24.4714i	1.79024	+	1.09991i
$496$	−57.7068			−2.59111
$497$		−	7.83454i		−	0.351427i
$498$		−	14.7863i		−	0.662588i
$499$	25.9120			1.15998			0.579990	−	0.814624i	$-0.303056\pi$
$499$	25.9120			1.15998			0.579990	+	0.814624i	$0.303056\pi$
$500$	4.77958	−	58.1485i	0.213749	−	2.60048i
$501$	11.0366			0.493080
$502$		−	72.5548i		−	3.23828i
$503$		−	1.28878i		−	0.0574637i	−0.999587	−	0.0287319i	$-0.990853\pi$
$503$		−	1.28878i		−	0.0574637i	0.999587	−	0.0287319i	$-0.00914689\pi$
$504$	39.5451			1.76148
$505$	−31.4092	−	19.2976i	−1.39769	−	0.858732i
$506$	34.1202			1.51683
$507$		−	5.73046i		−	0.254499i
$508$		−	63.7197i		−	2.82710i
$509$	−8.97659			−0.397880			−0.198940	−	0.980012i	$-0.563750\pi$
$509$	−8.97659			−0.397880			−0.198940	+	0.980012i	$0.563750\pi$
$510$	42.9422	−	69.8936i	1.90151	−	3.09494i
$511$	−6.58804			−0.291438
$512$			2.69004i			0.118884i
$513$		−	10.4772i		−	0.462580i
$514$	−73.9530			−3.26192
$515$	9.51299	−	15.4835i	0.419192	−	0.682286i
$516$	36.6451			1.61321
$517$			14.4032i			0.633451i
$518$		−	16.4085i		−	0.720947i
$519$	22.8819			1.00440
$520$	−54.0903	−	33.2327i	−2.37202	−	1.45735i
$521$	−8.94427			−0.391856			−0.195928	−	0.980618i	$-0.562772\pi$
$521$	−8.94427			−0.391856			−0.195928	+	0.980618i	$0.562772\pi$
$522$			50.0838i			2.19211i
$523$			29.1659i			1.27534i	0.770311	+	0.637669i	$0.220101\pi$
$523$			29.1659i			1.27534i	−0.770311	+	0.637669i	$0.779899\pi$
$524$	52.7636			2.30499
$525$	7.28616	+	14.3821i	0.317994	+	0.627686i
$526$	−20.3503			−0.887313
$527$		−	23.8611i		−	1.03941i
$528$			188.617i			8.20851i
$529$	18.0566			0.785068
$530$	39.3102	+	24.1519i	1.70753	+	1.04909i
$531$	−30.7203			−1.33315
$532$			40.0994i			1.73853i
$533$		−	15.6808i		−	0.679212i
$534$	56.2410			2.43378
$535$	−18.2277	+	29.6677i	−0.788051	+	1.28265i
$536$	−131.743			−5.69042
$537$			50.6228i			2.18454i
$538$		−	21.9956i		−	0.948300i
$539$	−31.0658			−1.33810
$540$	10.4066	−	16.9380i	0.447828	−	0.728894i
$541$	33.3854			1.43535			0.717676	−	0.696378i	$-0.245206\pi$
$541$	33.3854			1.43535			0.717676	+	0.696378i	$0.245206\pi$
$542$			9.76379i			0.419391i
$543$		−	41.1177i		−	1.76453i
$544$	90.3911			3.87549
$545$	33.4523	+	20.5529i	1.43294	+	0.880390i
$546$	28.4435			1.21727
$547$		−	2.45635i		−	0.105026i	−0.998620	−	0.0525129i	$-0.983277\pi$
$547$		−	2.45635i		−	0.105026i	0.998620	−	0.0525129i	$-0.0167231\pi$
$548$			68.9652i			2.94605i
$549$	44.6671			1.90634
$550$	−68.4477	+	34.6765i	−2.91862	+	1.47861i
$551$	−31.3220			−1.33436
$552$		−	49.6173i		−	2.11185i
$553$		−	11.7256i		−	0.498623i
$554$	−6.52565			−0.277248
$555$	−24.0331	−	14.7658i	−1.02015	−	0.626772i
$556$	83.2785			3.53180
$557$		−	24.1979i		−	1.02530i	−0.858598	−	0.512649i	$-0.828664\pi$
$557$		−	24.1979i		−	1.02530i	0.858598	−	0.512649i	$-0.171336\pi$
$558$		−	44.3488i		−	1.87743i
$559$	8.93364			0.377853
$560$	−18.7143	+	30.4598i	−0.790825	+	1.28716i
$561$	−77.9911			−3.29279
$562$			43.9864i			1.85545i
$563$		−	16.2348i		−	0.684214i	−0.939661	−	0.342107i	$-0.888859\pi$
$563$		−	16.2348i		−	0.684214i	0.939661	−	0.342107i	$-0.111141\pi$
$564$	33.9603			1.42999
$565$	−5.65279	+	9.20059i	−0.237815	+	0.387072i
$566$	−16.3424			−0.686924
$567$		−	8.22616i		−	0.345466i
$568$		−	54.2216i		−	2.27509i
$569$	−21.7141			−0.910303			−0.455152	−	0.890414i	$-0.650415\pi$
$569$	−21.7141			−0.910303			−0.455152	+	0.890414i	$0.650415\pi$
$570$	81.2419	+	49.9145i	3.40285	+	2.09069i
$571$	−12.1684			−0.509232			−0.254616	−	0.967042i	$-0.581949\pi$
$571$	−12.1684			−0.509232			−0.254616	+	0.967042i	$0.581949\pi$
$572$			97.8631i			4.09186i
$573$			36.1055i			1.50833i
$574$	−16.0329			−0.669199
$575$	9.91690	−	5.02403i	0.413563	−	0.209517i
$576$	74.3343			3.09726
$577$		−	37.8843i		−	1.57714i	−0.614942	−	0.788572i	$-0.710821\pi$
$577$		−	37.8843i		−	1.57714i	0.614942	−	0.788572i	$-0.289179\pi$
$578$			29.5370i			1.22858i
$579$	−15.0981			−0.627457
$580$	−50.6367	−	31.1109i	−2.10257	−	1.29181i
$581$	−2.66448			−0.110541
$582$			69.6590i			2.88746i
$583$		−	43.8644i		−	1.81668i
$584$	−45.5947			−1.88672
$585$	14.0665	−	22.8949i	0.581578	−	0.946588i
$586$	−28.0683			−1.15949
$587$			1.81908i			0.0750813i	0.999295	+	0.0375406i	$0.0119524\pi$
$587$			1.81908i			0.0750813i	−0.999295	+	0.0375406i	$0.988048\pi$
$588$			73.2481i			3.02070i
$589$	27.7354			1.14282
$590$	26.3962	−	42.9630i	1.08672	−	1.76876i
$591$	1.96334			0.0807612
$592$		−	62.5449i		−	2.57058i
$593$		−	43.3283i		−	1.77928i	−0.456663	−	0.889640i	$-0.650955\pi$
$593$		−	43.3283i		−	1.77928i	0.456663	−	0.889640i	$-0.349045\pi$
$594$	−26.1439			−1.07270
$595$	−12.5948	−	7.73817i	−0.516336	−	0.317234i
$596$	25.8180			1.05755
$597$		−	34.1670i		−	1.39836i
$598$		−	19.6127i		−	0.802023i
$599$	17.5241			0.716017			0.358008	−	0.933718i	$-0.383456\pi$
$599$	17.5241			0.716017			0.358008	+	0.933718i	$0.383456\pi$
$600$	50.4263	+	99.5361i	2.05865	+	4.06354i
$601$	25.6494			1.04626			0.523129	−	0.852253i	$-0.324764\pi$
$601$	25.6494			1.04626			0.523129	+	0.852253i	$0.324764\pi$
$602$		−	9.13421i		−	0.372283i
$603$		−	55.7630i		−	2.27085i
$604$	47.9644			1.95164
$605$	41.1996	+	25.3128i	1.67500	+	1.02911i
$606$	114.309			4.64347
$607$			7.39927i			0.300327i	0.988661	+	0.150163i	$0.0479800\pi$
$607$			7.39927i			0.300327i	−0.988661	+	0.150163i	$0.952020\pi$
$608$			105.068i			4.26105i
$609$	16.4224			0.665470
$610$	−38.3799	+	62.4679i	−1.55396	+	2.52925i
$611$	8.27912			0.334937
$612$			101.058i			4.08505i
$613$			22.5538i			0.910938i	0.890252	+	0.455469i	$0.150528\pi$
$613$			22.5538i			0.910938i	−0.890252	+	0.455469i	$0.849472\pi$
$614$	47.7786			1.92819
$615$	−14.4278	+	23.4830i	−0.581785	+	0.946924i
$616$	61.7120			2.48645
$617$			27.0999i			1.09100i	0.838111	+	0.545500i	$0.183660\pi$
$617$			27.0999i			1.09100i	−0.838111	+	0.545500i	$0.816340\pi$
$618$			56.3498i			2.26672i
$619$	23.3911			0.940168			0.470084	−	0.882622i	$-0.344224\pi$
$619$	23.3911			0.940168			0.470084	+	0.882622i	$0.344224\pi$
$620$	44.8383	+	27.5484i	1.80075	+	1.10637i
$621$	3.78780			0.151999
$622$			14.2567i			0.571641i
$623$		−	10.1346i		−	0.406034i
$624$	108.419			4.34025
$625$	−14.7881	+	20.1572i	−0.591524	+	0.806287i
$626$	69.8155			2.79039
$627$		−	90.6541i		−	3.62038i
$628$		−	37.4413i		−	1.49407i
$629$	25.8616			1.03117
$630$	−23.4089	−	14.3823i	−0.932634	−	0.573005i
$631$	−14.0498			−0.559314			−0.279657	−	0.960100i	$-0.590221\pi$
$631$	−14.0498			−0.559314			−0.279657	+	0.960100i	$0.590221\pi$
$632$		−	81.1508i		−	3.22801i
$633$		−	27.1212i		−	1.07797i
$634$	1.37507			0.0546111
$635$	−14.2928	+	23.2632i	−0.567192	+	0.923174i
$636$	−103.425			−4.10108
$637$			17.8570i			0.707520i
$638$			78.1581i			3.09431i
$639$	22.9505			0.907906
$640$	−23.8754	+	38.8600i	−0.943756	+	1.53608i
$641$	15.4541			0.610400			0.305200	−	0.952288i	$-0.401277\pi$
$641$	15.4541			0.610400			0.305200	+	0.952288i	$0.401277\pi$
$642$		−	107.971i		−	4.26127i
$643$			41.9982i			1.65625i	0.560545	+	0.828124i	$0.310592\pi$
$643$			41.9982i			1.65625i	−0.560545	+	0.828124i	$0.689408\pi$
$644$	−14.4970			−0.571263
$645$	−13.3787	−	8.21976i	−0.526784	−	0.323653i
$646$	−87.4231			−3.43961
$647$			11.2851i			0.443664i	0.975085	+	0.221832i	$0.0712037\pi$
$647$			11.2851i			0.443664i	−0.975085	+	0.221832i	$0.928796\pi$
$648$		−	56.9319i		−	2.23650i
$649$	−47.9405			−1.88183
$650$	19.9325	+	39.3446i	0.781816	+	1.54322i
$651$	−14.5419			−0.569942
$652$			78.0170i			3.05538i
$653$			27.4812i			1.07542i	0.843129	+	0.537711i	$0.180711\pi$
$653$			27.4812i			1.07542i	−0.843129	+	0.537711i	$0.819289\pi$
$654$	−121.744			−4.76058
$655$	−19.2633	−	11.8353i	−0.752680	−	0.462442i
$656$	−61.1132			−2.38607
$657$		−	19.2990i		−	0.752924i
$658$		−	8.46500i		−	0.330000i
$659$	−40.0611			−1.56056			−0.780279	−	0.625431i	$-0.784923\pi$
$659$	−40.0611			−1.56056			−0.780279	+	0.625431i	$0.784923\pi$
$660$	90.0430	−	146.556i	3.50492	−	5.70468i
$661$	49.2805			1.91679			0.958394	−	0.285449i	$-0.0921426\pi$
$661$	49.2805			1.91679			0.958394	+	0.285449i	$0.0921426\pi$
$662$			11.7666i			0.457322i
$663$			44.8302i			1.74106i
$664$	−18.4404			−0.715627
$665$	8.99458	−	14.6398i	0.348795	−	0.567705i
$666$	48.0669			1.86255
$667$		−	11.3238i		−	0.438458i
$668$		−	22.3172i		−	0.863480i
$669$	30.4020			1.17541
$670$	77.9858	+	47.9140i	3.01285	+	1.85108i
$671$	69.7050			2.69093
$672$		−	55.0879i		−	2.12506i
$673$			4.32553i			0.166737i	0.996519	+	0.0833685i	$0.0265678\pi$
$673$			4.32553i			0.166737i	−0.996519	+	0.0833685i	$0.973432\pi$
$674$	−24.4231			−0.940742
$675$	−7.59862	+	3.84956i	−0.292471	+	0.148170i
$676$	−11.5876			−0.445677
$677$		−	38.0959i		−	1.46415i	−0.681226	−	0.732073i	$-0.738553\pi$
$677$		−	38.0959i		−	1.46415i	0.681226	−	0.732073i	$-0.261447\pi$
$678$		−	33.4841i		−	1.28595i
$679$	12.5525			0.481722
$680$	−87.1665	−	53.5546i	−3.34268	−	2.05372i
$681$	−24.1022			−0.923599
$682$		−	69.2083i		−	2.65012i
$683$			35.9542i			1.37575i	0.725830	+	0.687874i	$0.241456\pi$
$683$			35.9542i			1.37575i	−0.725830	+	0.687874i	$0.758544\pi$
$684$	−117.467			−4.49146
$685$	15.4694	−	25.1783i	0.591055	−	0.962014i
$686$	41.7564			1.59427
$687$		−	42.8171i		−	1.63357i
$688$		−	34.8173i		−	1.32740i
$689$	−25.2138			−0.960570
$690$	−18.0455	+	29.3712i	−0.686980	+	1.11814i
$691$	20.7606			0.789772			0.394886	−	0.918730i	$-0.370784\pi$
$691$	20.7606			0.789772			0.394886	+	0.918730i	$0.370784\pi$
$692$		−	46.2697i		−	1.75891i
$693$			26.1210i			0.992253i
$694$	2.07179			0.0786441
$695$	−30.4039	−	18.6800i	−1.15329	−	0.708572i
$696$	113.657			4.30815
$697$		−	25.2696i		−	0.957156i
$698$			80.8155i			3.05891i
$699$	−6.65317			−0.251646
$700$	29.0821	−	14.7334i	1.09920	−	0.556870i
$701$	3.55693			0.134343			0.0671716	−	0.997741i	$-0.478602\pi$
$701$	3.55693			0.134343			0.0671716	+	0.997741i	$0.478602\pi$
$702$			15.0278i			0.567189i
$703$			30.0606i			1.13376i
$704$	116.002			4.37199
$705$	−12.3985	−	7.61755i	−0.466954	−	0.286893i
$706$	−74.5205			−2.80462
$707$		−	20.5984i		−	0.774681i
$708$			113.036i			4.24815i
$709$	−19.1731			−0.720060			−0.360030	−	0.932941i	$-0.617234\pi$
$709$	−19.1731			−0.720060			−0.360030	+	0.932941i	$0.617234\pi$
$710$	−19.7200	+	32.0967i	−0.740079	+	1.20457i
$711$	34.3489			1.28818
$712$		−	70.1399i		−	2.62860i
$713$			10.0271i			0.375518i
$714$	45.8367			1.71540
$715$	21.9514	−	35.7286i	0.820936	−	1.33617i
$716$	102.365			3.82555
$717$		−	67.1541i		−	2.50791i
$718$			16.6330i			0.620740i
$719$	17.5165			0.653256			0.326628	−	0.945153i	$-0.394088\pi$
$719$	17.5165			0.653256			0.326628	+	0.945153i	$0.394088\pi$
$720$	−89.2289	−	54.8217i	−3.32536	−	2.04308i
$721$	10.1542			0.378163
$722$		−	50.5697i		−	1.88201i
$723$		−	2.58072i		−	0.0959781i
$724$	−83.1445			−3.09004
$725$	11.5084	+	22.7163i	0.427411	+	0.843664i
$726$	−149.939			−5.56477
$727$		−	28.7088i		−	1.06475i	−0.846508	−	0.532376i	$-0.821299\pi$
$727$		−	28.7088i		−	1.06475i	0.846508	−	0.532376i	$-0.178701\pi$
$728$		−	35.4728i		−	1.31471i
$729$	37.2874			1.38101
$730$	26.9900	+	16.5825i	0.998945	+	0.613746i
$731$	14.3966			0.532476
$732$		−	164.353i		−	6.07467i
$733$			42.4695i			1.56865i	0.620352	+	0.784323i	$0.286990\pi$
$733$			42.4695i			1.56865i	−0.620352	+	0.784323i	$0.713010\pi$
$734$	−39.4145			−1.45482
$735$	16.4301	−	26.7419i	0.606033	−	0.986391i
$736$	−37.9848			−1.40014
$737$		−	87.0208i		−	3.20545i
$738$		−	46.9666i		−	1.72887i
$739$	38.8874			1.43050			0.715249	−	0.698870i	$-0.246313\pi$
$739$	38.8874			1.43050			0.715249	+	0.698870i	$0.246313\pi$
$740$	−29.8580	+	48.5975i	−1.09760	+	1.78648i
$741$	−52.1091			−1.91428
$742$			25.7799i			0.946411i
$743$		−	1.03128i		−	0.0378339i	−0.999821	−	0.0189170i	$-0.993978\pi$
$743$		−	1.03128i		−	0.0378339i	0.999821	−	0.0189170i	$-0.00602182\pi$
$744$	−100.642			−3.68972
$745$	−9.42582	−	5.79117i	−0.345335	−	0.212172i
$746$	20.0397			0.733706
$747$		−	7.80531i		−	0.285581i
$748$			157.706i			5.76632i
$749$	−19.4563			−0.710918
$750$	6.35052	−	77.2606i	0.231888	−	2.82116i
$751$	14.0086			0.511181			0.255590	−	0.966785i	$-0.417730\pi$
$751$	14.0086			0.511181			0.255590	+	0.966785i	$0.417730\pi$
$752$		−	32.2664i		−	1.17664i
$753$		−	69.6922i		−	2.53972i
$754$	44.9262			1.63612
$755$	−17.5112	−	10.7588i	−0.637297	−	0.391551i
$756$	11.1080			0.403996
$757$			38.1157i			1.38534i	0.721255	+	0.692670i	$0.243566\pi$
$757$			38.1157i			1.38534i	−0.721255	+	0.692670i	$0.756434\pi$
$758$		−	86.8418i		−	3.15424i
$759$	32.7740			1.18962
$760$	62.2500	−	101.319i	2.25804	−	3.67524i
$761$	3.59136			0.130187			0.0650933	−	0.997879i	$-0.479266\pi$
$761$	3.59136			0.130187			0.0650933	+	0.997879i	$0.479266\pi$
$762$		−	84.6628i		−	3.06701i
$763$			21.9383i			0.794219i
$764$	73.0092			2.64138
$765$	22.6681	−	36.8951i	0.819568	−	1.33395i
$766$	−11.5684			−0.417984
$767$			27.5568i			0.995018i
$768$		−	36.6001i		−	1.32069i
$769$	39.3482			1.41893			0.709466	−	0.704740i	$-0.248936\pi$
$769$	39.3482			1.41893			0.709466	+	0.704740i	$0.248936\pi$
$770$	−36.5307	−	22.4443i	−1.31648	−	0.808835i
$771$	−71.0352			−2.55827
$772$			30.5301i			1.09880i
$773$		−	25.6925i		−	0.924094i	−0.886856	−	0.462047i	$-0.847115\pi$
$773$		−	25.6925i		−	0.924094i	0.886856	−	0.462047i	$-0.152885\pi$
$774$	26.7577			0.961786
$775$	−10.1906	−	20.1151i	−0.366057	−	0.722557i
$776$	86.8740			3.11859
$777$		−	15.7611i		−	0.565425i
$778$			43.3677i			1.55481i
$779$	29.3726			1.05238
$780$	−84.2421	−	51.7578i	−3.01635	−	1.85323i
$781$	35.8153			1.28157
$782$		−	31.6059i		−	1.13022i
$783$			8.67660i			0.310077i
$784$	69.5945			2.48552
$785$	−8.39835	+	13.6693i	−0.299750	+	0.487879i
$786$	70.1058			2.50059
$787$			3.98083i			0.141901i	0.997480	+	0.0709506i	$0.0226033\pi$
$787$			3.98083i			0.141901i	−0.997480	+	0.0709506i	$0.977397\pi$
$788$		−	3.97009i		−	0.141429i
$789$	−19.5473			−0.695904
$790$	−29.5140	+	48.0376i	−1.05006	+	1.70910i
$791$	−6.03382			−0.214538
$792$			180.779i			6.42370i
$793$		−	40.0673i		−	1.42283i
$794$	−84.1871			−2.98769
$795$	37.7592	+	23.1990i	1.33918	+	0.822785i
$796$	−69.0894			−2.44881
$797$			39.8549i			1.41173i	0.708345	+	0.705866i	$0.249442\pi$
$797$			39.8549i			1.41173i	−0.708345	+	0.705866i	$0.750558\pi$
$798$			53.2791i			1.88606i
$799$	13.3418			0.471999
$800$	76.2004	−	38.6042i	2.69409	−	1.36486i
$801$	29.6882			1.04898
$802$			73.0309i			2.57881i
$803$		−	30.1169i		−	1.06280i
$804$	−205.181			−7.23617
$805$	5.29268	+	3.25179i	0.186542	+	0.114610i
$806$	−39.7818			−1.40125
$807$		−	21.1278i		−	0.743734i
$808$		−	142.558i		−	5.01517i
$809$	−14.3004			−0.502774			−0.251387	−	0.967887i	$-0.580887\pi$
$809$	−14.3004			−0.502774			−0.251387	+	0.967887i	$0.580887\pi$
$810$	−20.7058	+	33.7011i	−0.727526	+	1.18414i
$811$	52.5174			1.84414			0.922068	−	0.387028i	$-0.126498\pi$
$811$	52.5174			1.84414			0.922068	+	0.387028i	$0.126498\pi$
$812$		−	33.2079i		−	1.16537i
$813$			9.37857i			0.328921i
$814$	75.0106			2.62912
$815$	17.4998	−	28.4830i	0.612991	−	0.997716i
$816$	174.718			6.11635
$817$			16.7341i			0.585451i
$818$			98.9525i			3.45979i
$819$	15.0147			0.524655
$820$	47.4851	+	29.1746i	1.65825	+	1.01882i
$821$	−18.4325			−0.643300			−0.321650	−	0.946859i	$-0.604237\pi$
$821$	−18.4325			−0.643300			−0.321650	+	0.946859i	$0.604237\pi$
$822$			91.6324i			3.19605i
$823$			38.9994i			1.35944i	0.733474	+	0.679718i	$0.237898\pi$
$823$			38.9994i			1.35944i	−0.733474	+	0.679718i	$0.762102\pi$
$824$	70.2757			2.44817
$825$	−65.7471	+	33.3084i	−2.28902	+	1.15965i
$826$	28.1755			0.980351
$827$			18.2963i			0.636226i	0.948053	+	0.318113i	$0.103049\pi$
$827$			18.2963i			0.636226i	−0.948053	+	0.318113i	$0.896951\pi$
$828$		−	42.4675i		−	1.47585i
$829$	−2.36565			−0.0821624			−0.0410812	−	0.999156i	$-0.513080\pi$
$829$	−2.36565			−0.0821624			−0.0410812	+	0.999156i	$0.513080\pi$
$830$	10.9159	+	6.70665i	0.378896	+	0.232791i
$831$	−6.26818			−0.217441
$832$		−	66.6795i		−	2.31169i
$833$			28.7766i			0.997049i
$834$	110.650			3.83150
$835$	−5.00592	+	8.14773i	−0.173237	+	0.281964i
$836$	−183.312			−6.33999
$837$		−	7.68306i		−	0.265565i
$838$		−	36.4760i		−	1.26004i
$839$	19.8535			0.685420			0.342710	−	0.939441i	$-0.388655\pi$
$839$	19.8535			0.685420			0.342710	+	0.939441i	$0.388655\pi$
$840$	−32.6383	+	53.1227i	−1.12613	+	1.83291i
$841$	−3.06096			−0.105550
$842$			32.6726i			1.12597i
$843$			42.2509i			1.45520i
$844$	−54.8420			−1.88774
$845$	4.23049	+	2.59918i	0.145533	+	0.0894146i
$846$	24.7973			0.852550
$847$			27.0190i			0.928385i
$848$			98.2665i			3.37448i
$849$	−15.6977			−0.538742
$850$	32.1212	+	63.4038i	1.10175	+	2.17473i
$851$	−10.8677			−0.372542
$852$		−	84.4466i		−	2.89309i
$853$		−	17.5358i		−	0.600415i	−0.953874	−	0.300208i	$-0.902944\pi$
$853$		−	17.5358i		−	0.600415i	0.953874	−	0.300208i	$-0.0970560\pi$
$854$	−40.9669			−1.40186
$855$	42.8856	+	26.3487i	1.46666	+	0.901105i
$856$	−134.654			−4.60238
$857$		−	42.6899i		−	1.45826i	−0.684375	−	0.729130i	$-0.739925\pi$
$857$		−	42.6899i		−	1.45826i	0.684375	−	0.729130i	$-0.260075\pi$
$858$			130.028i			4.43910i
$859$	19.1579			0.653659			0.326830	−	0.945083i	$-0.394020\pi$
$859$	19.1579			0.653659			0.326830	+	0.945083i	$0.394020\pi$
$860$	−16.6213	+	27.0531i	−0.566780	+	0.922503i
$861$	−15.4003			−0.524841
$862$			40.7904i			1.38933i
$863$		−	12.8156i		−	0.436248i	−0.975921	−	0.218124i	$-0.930006\pi$
$863$		−	12.8156i		−	0.436248i	0.975921	−	0.218124i	$-0.0699936\pi$
$864$	29.1051			0.990175
$865$	−10.3786	+	16.8925i	−0.352884	+	0.574361i
$866$	77.3372			2.62803
$867$			28.3716i			0.963550i
$868$			29.4053i			0.998082i
$869$	53.6030			1.81836
$870$	−67.2797	−	41.3363i	−2.28100	−	1.40143i
$871$	−50.0206			−1.69488
$872$			151.831i			5.14166i
$873$			36.7713i			1.24452i
$874$	36.7376			1.24267
$875$	−13.9223	−	1.14436i	−0.470660	−	0.0386864i
$876$	−71.0108			−2.39923
$877$			29.6224i			1.00028i	0.865945	+	0.500139i	$0.166718\pi$
$877$			29.6224i			1.00028i	−0.865945	+	0.500139i	$0.833282\pi$
$878$			105.193i			3.55009i
$879$	−26.9609			−0.909368
$880$	−139.246	−	85.5517i	−4.69397	−	2.88395i
$881$	27.5400			0.927845			0.463922	−	0.885876i	$-0.346442\pi$
$881$	27.5400			0.927845			0.463922	+	0.885876i	$0.346442\pi$
$882$			53.4847i			1.80092i
$883$		−	9.69519i		−	0.326269i	−0.986604	−	0.163134i	$-0.947840\pi$
$883$		−	9.69519i		−	0.326269i	0.986604	−	0.163134i	$-0.0521604\pi$
$884$	90.6516			3.04894
$885$	25.3548	−	41.2679i	0.852291	−	1.38721i
$886$	70.9733			2.38440
$887$			6.60583i			0.221802i	0.993831	+	0.110901i	$0.0353737\pi$
$887$			6.60583i			0.221802i	−0.993831	+	0.110901i	$0.964626\pi$
$888$		−	109.080i		−	3.66048i
$889$	−15.2562			−0.511677
$890$	−25.5094	+	41.5196i	−0.855077	+	1.39174i
$891$	37.6055			1.25983
$892$		−	61.4762i		−	2.05838i
$893$			15.5080i			0.518957i
$894$	34.3038			1.14729
$895$	−37.3721	−	22.9612i	−1.24921	−	0.767507i
$896$	−25.4847			−0.851384
$897$		−	18.8389i		−	0.629012i
$898$		−	24.9404i		−	0.832271i
$899$	−22.9688			−0.766052
$900$	43.1600	+	85.1931i	1.43867	+	2.83977i
$901$	−40.6321			−1.35365
$902$		−	73.2936i		−	2.44041i
$903$		−	8.77383i		−	0.291975i
$904$	−41.7591			−1.38889
$905$	30.3550	+	18.6499i	1.00903	+	0.619944i
$906$	63.7291			2.11726
$907$			18.6330i			0.618700i	0.950948	+	0.309350i	$0.100112\pi$
$907$			18.6330i			0.618700i	−0.950948	+	0.309350i	$0.899888\pi$
$908$			48.7373i			1.61740i
$909$	60.3408			2.00138
$910$	−12.9012	+	20.9983i	−0.427672	+	0.696087i
$911$	−10.4778			−0.347146			−0.173573	−	0.984821i	$-0.555531\pi$
$911$	−10.4778			−0.347146			−0.173573	+	0.984821i	$0.555531\pi$
$912$			203.086i			6.72485i
$913$		−	12.1805i		−	0.403117i
$914$	22.6772			0.750096
$915$	−36.8656	+	60.0032i	−1.21874	+	1.98365i
$916$	−86.5807			−2.86071
$917$		−	12.6330i		−	0.417180i
$918$			24.2173i			0.799291i
$919$	−33.4620			−1.10381			−0.551905	−	0.833907i	$-0.686099\pi$
$919$	−33.4620			−1.10381			−0.551905	+	0.833907i	$0.686099\pi$
$920$	36.6297	+	22.5051i	1.20765	+	0.741971i
$921$	45.8935			1.51224
$922$			8.04518i			0.264954i
$923$		−	20.5871i		−	0.677631i
$924$	96.1125			3.16187
$925$	21.8015	−	11.0449i	0.716830	−	0.363156i
$926$	−27.9177			−0.917433
$927$			29.7457i			0.976978i
$928$		−	87.0107i		−	2.85627i
$929$	−38.0410			−1.24809			−0.624043	−	0.781390i	$-0.714511\pi$
$929$	−38.0410			−1.24809			−0.624043	+	0.781390i	$0.714511\pi$
$930$	59.5756	+	36.6029i	1.95356	+	1.20026i
$931$	−33.4489			−1.09624
$932$			13.4534i			0.440681i
$933$			13.6942i			0.448328i
$934$	63.3861			2.07406
$935$	35.3747	−	57.5766i	1.15688	−	1.88296i
$936$	103.914			3.39653
$937$			27.2333i			0.889673i	0.895612	+	0.444836i	$0.146738\pi$
$937$			27.2333i			0.889673i	−0.895612	+	0.444836i	$0.853262\pi$
$938$			51.1437i			1.66990i
$939$	67.0609			2.18845
$940$	−15.4035	+	25.0711i	−0.502407	+	0.817728i
$941$	−39.6482			−1.29249			−0.646247	−	0.763129i	$-0.723662\pi$
$941$	−39.6482			−1.29249			−0.646247	+	0.763129i	$0.723662\pi$
$942$		−	49.7473i		−	1.62086i
$943$			10.6190i			0.345802i
$944$	107.398			3.49550
$945$	−4.05540	−	2.49162i	−0.131922	−	0.0810522i
$946$	41.7567			1.35763
$947$		−	3.86951i		−	0.125742i	−0.998022	−	0.0628711i	$-0.979974\pi$
$947$		−	3.86951i		−	0.125742i	0.998022	−	0.0628711i	$-0.0200257\pi$
$948$		−	126.387i		−	4.10486i
$949$	−17.3116			−0.561958
$950$	−73.6984	+	37.3366i	−2.39109	+	1.21136i
$951$	1.32082			0.0428305
$952$		−	57.1645i		−	1.85271i
$953$		−	20.5864i		−	0.666859i	−0.942775	−	0.333430i	$-0.891794\pi$
$953$		−	20.5864i		−	0.666859i	0.942775	−	0.333430i	$-0.108206\pi$
$954$	−75.5196			−2.44504
$955$	−26.6547	−	16.3765i	−0.862526	−	0.529931i
$956$	−135.793			−4.39185
$957$			75.0744i			2.42681i
$958$		−	14.7745i		−	0.477342i
$959$	16.5121			0.533204
$960$	−61.3512	+	99.8565i	−1.98010	+	3.22285i
$961$	−10.6613			−0.343914
$962$		−	43.1170i		−	1.39015i
$963$		−	56.9952i		−	1.83665i
$964$	−5.21850			−0.168077
$965$	6.84811	−	11.1461i	0.220449	−	0.358807i
$966$	−19.2619			−0.619740
$967$		−	52.3145i		−	1.68232i	−0.540785	−	0.841161i	$-0.681873\pi$
$967$		−	52.3145i		−	1.68232i	0.540785	−	0.841161i	$-0.318127\pi$
$968$			186.994i			6.01022i
$969$	−83.9738			−2.69763
$970$	−51.4255	−	31.5955i	−1.65117	−	1.01447i
$971$	29.3275			0.941165			0.470582	−	0.882356i	$-0.344044\pi$
$971$	29.3275			0.941165			0.470582	+	0.882356i	$0.344044\pi$
$972$		−	115.339i		−	3.69949i
$973$		−	19.9391i		−	0.639219i
$974$	−26.5919			−0.852061
$975$	19.1461	+	37.7922i	0.613165	+	1.21032i
$976$	−156.155			−4.99841
$977$		−	43.0111i		−	1.37605i	−0.725688	−	0.688024i	$-0.758478\pi$
$977$		−	43.0111i		−	1.37605i	0.725688	−	0.688024i	$-0.241522\pi$
$978$			103.659i			3.31466i
$979$	46.3299			1.48071
$980$	−54.0751	−	33.2234i	−1.72737	−	1.06128i
$981$	−64.2659			−2.05185
$982$			60.7561i			1.93880i
$983$		−	47.7953i		−	1.52443i	−0.647322	−	0.762216i	$-0.724111\pi$
$983$		−	47.7953i		−	1.52443i	0.647322	−	0.762216i	$-0.275889\pi$
$984$	−106.583			−3.39774
$985$	−0.890521	+	1.44943i	−0.0283743	+	0.0461827i
$986$	72.3986			2.30564
$987$		−	8.13102i		−	0.258813i
$988$			105.370i			3.35228i
$989$	−6.04983			−0.192373
$990$	65.7481	−	107.013i	2.08961	−	3.40109i
$991$	−8.79367			−0.279340			−0.139670	−	0.990198i	$-0.544604\pi$
$991$	−8.79367			−0.279340			−0.139670	+	0.990198i	$0.544604\pi$
$992$			77.0472i			2.44625i
$993$			11.3023i			0.358669i
$994$	−21.0493			−0.667642
$995$	25.2237	+	15.4973i	0.799644	+	0.491296i
$996$	−28.7197			−0.910020
$997$			25.3984i			0.804375i	0.915557	+	0.402188i	$0.131750\pi$
$997$			25.3984i			0.804375i	−0.915557	+	0.402188i	$0.868250\pi$
$998$		−	69.6185i		−	2.20373i
$999$	8.32719			0.263461

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1205.2.b.c.724.1	✓	46
5.2	odd	4		6025.2.a.p.1.46		46
5.3	odd	4		6025.2.a.p.1.1		46
5.4	even	2	inner	1205.2.b.c.724.46	yes	46

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1205.2.b.c.724.1	✓	46	1.1	even	1	trivial
1205.2.b.c.724.46	yes	46	5.4	even	2	inner
6025.2.a.p.1.1		46	5.3	odd	4
6025.2.a.p.1.46		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)

\(f(q)\)	\(=\)	\(q-2.68673i q^{2} -2.58072i q^{3} -5.21850 q^{4} +(1.90521 + 1.17055i) q^{5} -6.93370 q^{6} +1.24945i q^{7} +8.64724i q^{8} -3.66013 q^{9} +O(q^{10})\)	\(q-2.68673i q^{2} -2.58072i q^{3} -5.21850 q^{4} +(1.90521 + 1.17055i) q^{5} -6.93370 q^{6} +1.24945i q^{7} +8.64724i q^{8} -3.66013 q^{9} +(3.14494 - 5.11877i) q^{10} -5.71181 q^{11} +13.4675i q^{12} +3.28322i q^{13} +3.35693 q^{14} +(3.02086 - 4.91681i) q^{15} +12.7958 q^{16} +5.29090i q^{17} +9.83378i q^{18} -6.14996 q^{19} +(-9.94233 - 6.10851i) q^{20} +3.22448 q^{21} +15.3461i q^{22} -2.22338i q^{23} +22.3161 q^{24} +(2.25963 + 4.46027i) q^{25} +8.82111 q^{26} +1.70362i q^{27} -6.52026i q^{28} +5.09304 q^{29} +(-13.2101 - 8.11623i) q^{30} -4.50984 q^{31} -17.0842i q^{32} +14.7406i q^{33} +14.2152 q^{34} +(-1.46254 + 2.38046i) q^{35} +19.1004 q^{36} -4.88794i q^{37} +16.5233i q^{38} +8.47308 q^{39} +(-10.1220 + 16.4748i) q^{40} -4.77605 q^{41} -8.66331i q^{42} -2.72100i q^{43} +29.8071 q^{44} +(-6.97331 - 4.28436i) q^{45} -5.97362 q^{46} -2.52165i q^{47} -33.0223i q^{48} +5.43887 q^{49} +(11.9835 - 6.07102i) q^{50} +13.6544 q^{51} -17.1335i q^{52} +7.67961i q^{53} +4.57716 q^{54} +(-10.8822 - 6.68594i) q^{55} -10.8043 q^{56} +15.8714i q^{57} -13.6836i q^{58} +8.39323 q^{59} +(-15.7644 + 25.6584i) q^{60} -12.2037 q^{61} +12.1167i q^{62} -4.57315i q^{63} -20.3092 q^{64} +(-3.84316 + 6.25521i) q^{65} +39.6039 q^{66} +15.2352i q^{67} -27.6106i q^{68} -5.73793 q^{69} +(6.39565 + 3.92945i) q^{70} -6.27039 q^{71} -31.6500i q^{72} +5.27275i q^{73} -13.1325 q^{74} +(11.5107 - 5.83149i) q^{75} +32.0936 q^{76} -7.13662i q^{77} -22.7648i q^{78} -9.38460 q^{79} +(24.3786 + 14.9781i) q^{80} -6.58383 q^{81} +12.8319i q^{82} +2.13252i q^{83} -16.8270 q^{84} +(-6.19326 + 10.0803i) q^{85} -7.31059 q^{86} -13.1437i q^{87} -49.3913i q^{88} -8.11125 q^{89} +(-11.5109 + 18.7354i) q^{90} -4.10222 q^{91} +11.6027i q^{92} +11.6386i q^{93} -6.77498 q^{94} +(-11.7170 - 7.19883i) q^{95} -44.0897 q^{96} -10.0464i q^{97} -14.6128i q^{98} +20.9060 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 46 q - 34 q^{4} - 8 q^{5} - 4 q^{6} - 34 q^{9}+O(q^{10}) \) 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

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Database

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