LMFDB - Embedded newform 201.4.d.b.200.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [201,4,Mod(200,201)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(201, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("201.200");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 201 = 3 \cdot 67 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	201.d (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:	$11.8593839112$
Analytic rank:	$0$
Dimension:	$64$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			200.8
Character	$\chi$	$=$	201.200
Dual form			201.4.d.b.200.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.88518 q^{2} +(4.71863 + 2.17590i) q^{3} +15.8650 q^{4} -9.70204 q^{5} +(-23.0513 - 10.6297i) q^{6} -27.9776i q^{7} -38.4219 q^{8} +(17.5309 + 20.5346i) q^{9} +O(q^{10})$	\(q-4.88518 q^{2} +(4.71863 + 2.17590i) q^{3} +15.8650 q^{4} -9.70204 q^{5} +(-23.0513 - 10.6297i) q^{6} -27.9776i q^{7} -38.4219 q^{8} +(17.5309 + 20.5346i) q^{9} +47.3962 q^{10} -35.0170 q^{11} +(74.8609 + 34.5207i) q^{12} +61.3422i q^{13} +136.676i q^{14} +(-45.7803 - 21.1107i) q^{15} +60.7779 q^{16} -8.03644i q^{17} +(-85.6415 - 100.315i) q^{18} +86.7493 q^{19} -153.923 q^{20} +(60.8767 - 132.016i) q^{21} +171.064 q^{22} +2.37084i q^{23} +(-181.298 - 83.6023i) q^{24} -30.8704 q^{25} -299.668i q^{26} +(38.0404 + 135.040i) q^{27} -443.865i q^{28} +152.108i q^{29} +(223.645 + 103.130i) q^{30} +150.096i q^{31} +10.4640 q^{32} +(-165.232 - 76.1936i) q^{33} +39.2595i q^{34} +271.440i q^{35} +(278.127 + 325.781i) q^{36} -344.278 q^{37} -423.786 q^{38} +(-133.475 + 289.451i) q^{39} +372.771 q^{40} -123.510 q^{41} +(-297.394 + 644.922i) q^{42} +151.039i q^{43} -555.544 q^{44} +(-170.085 - 199.227i) q^{45} -11.5820i q^{46} +405.781i q^{47} +(286.788 + 132.247i) q^{48} -439.748 q^{49} +150.807 q^{50} +(17.4865 - 37.9210i) q^{51} +973.193i q^{52} +128.291 q^{53} +(-185.834 - 659.697i) q^{54} +339.736 q^{55} +1074.95i q^{56} +(409.337 + 188.758i) q^{57} -743.077i q^{58} +679.460i q^{59} +(-726.304 - 334.921i) q^{60} +412.746i q^{61} -733.246i q^{62} +(574.509 - 490.472i) q^{63} -537.342 q^{64} -595.145i q^{65} +(807.188 + 372.219i) q^{66} +(-478.262 - 268.381i) q^{67} -127.498i q^{68} +(-5.15873 + 11.1871i) q^{69} -1326.03i q^{70} -921.473i q^{71} +(-673.569 - 788.977i) q^{72} -772.508 q^{73} +1681.86 q^{74} +(-145.666 - 67.1710i) q^{75} +1376.28 q^{76} +979.692i q^{77} +(652.048 - 1414.02i) q^{78} +1257.39i q^{79} -589.670 q^{80} +(-114.337 + 719.978i) q^{81} +603.366 q^{82} -792.698i q^{83} +(965.808 - 2094.43i) q^{84} +77.9699i q^{85} -737.855i q^{86} +(-330.974 + 717.743i) q^{87} +1345.42 q^{88} -810.039i q^{89} +(830.897 + 973.261i) q^{90} +1716.21 q^{91} +37.6134i q^{92} +(-326.594 + 708.247i) q^{93} -1982.31i q^{94} -841.645 q^{95} +(49.3758 + 22.7687i) q^{96} -672.231i q^{97} +2148.25 q^{98} +(-613.878 - 719.058i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 268 q^{4} - 46 q^{6} + 22 q^{9}+O(q^{10}) $ 64 * q + 268 * q^4 - 46 * q^6 + 22 * q^9	$ 64 q + 268 q^{4} - 46 q^{6} + 22 q^{9} - 36 q^{10} + 20 q^{15} + 556 q^{16} + 128 q^{19} + 96 q^{22} - 904 q^{24} + 2080 q^{25} - 236 q^{33} - 1574 q^{36} + 1004 q^{37} - 176 q^{39} - 648 q^{40} - 1220 q^{49} + 2188 q^{54} - 1344 q^{55} + 550 q^{60} + 4336 q^{64} - 3512 q^{67} + 3968 q^{73} - 3316 q^{76} - 1170 q^{81} + 4020 q^{82} - 9270 q^{84} + 2436 q^{88} + 746 q^{90} - 3408 q^{91} - 1412 q^{93} - 7032 q^{96}+O(q^{100}) $ 64 * q + 268 * q^4 - 46 * q^6 + 22 * q^9 - 36 * q^10 + 20 * q^15 + 556 * q^16 + 128 * q^19 + 96 * q^22 - 904 * q^24 + 2080 * q^25 - 236 * q^33 - 1574 * q^36 + 1004 * q^37 - 176 * q^39 - 648 * q^40 - 1220 * q^49 + 2188 * q^54 - 1344 * q^55 + 550 * q^60 + 4336 * q^64 - 3512 * q^67 + 3968 * q^73 - 3316 * q^76 - 1170 * q^81 + 4020 * q^82 - 9270 * q^84 + 2436 * q^88 + 746 * q^90 - 3408 * q^91 - 1412 * q^93 - 7032 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/201\mathbb{Z}\right)^\times$.

$n$	$68$	$136$
$\chi(n)$	$-1$	$-1$

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 $

$2$	−4.88518			−1.72717			−0.863586	−	0.504202i	$-0.831787\pi$
$2$	−4.88518			−1.72717			−0.863586	+	0.504202i	$0.831787\pi$
$3$	4.71863	+	2.17590i	0.908100	+	0.418753i
$3$	4.71863	+	2.17590i	0.908100	+	0.418753i
$4$	15.8650			1.98312
$5$	−9.70204			−0.867777			−0.433888	−	0.900967i	$-0.642859\pi$
$5$	−9.70204			−0.867777			−0.433888	+	0.900967i	$0.642859\pi$
$6$	−23.0513	−	10.6297i	−1.56845	−	0.723259i
$7$		−	27.9776i		−	1.51065i	−0.655350	−	0.755325i	$-0.727479\pi$
$7$		−	27.9776i		−	1.51065i	0.655350	−	0.755325i	$-0.272521\pi$
$8$	−38.4219			−1.69802
$9$	17.5309	+	20.5346i	0.649292	+	0.760539i
$10$	47.3962			1.49880
$11$	−35.0170			−0.959819			−0.479910	−	0.877318i	$-0.659331\pi$
$11$	−35.0170			−0.959819			−0.479910	+	0.877318i	$0.659331\pi$
$12$	74.8609	+	34.5207i	1.80087	+	0.830439i
$13$			61.3422i			1.30871i	0.756186	+	0.654356i	$0.227060\pi$
$13$			61.3422i			1.30871i	−0.756186	+	0.654356i	$0.772940\pi$
$14$			136.676i			2.60915i
$15$	−45.7803	−	21.1107i	−0.788028	−	0.363384i
$16$	60.7779			0.949655
$17$		−	8.03644i		−	0.114654i	−0.998355	−	0.0573272i	$-0.981742\pi$
$17$		−	8.03644i		−	0.114654i	0.998355	−	0.0573272i	$-0.0182578\pi$
$18$	−85.6415	−	100.315i	−1.12144	−	1.31358i
$19$	86.7493			1.04746			0.523728	−	0.851886i	$-0.324541\pi$
$19$	86.7493			1.04746			0.523728	+	0.851886i	$0.324541\pi$
$20$	−153.923			−1.72091
$21$	60.8767	−	132.016i	0.632590	−	1.37182i
$22$	171.064			1.65777
$23$			2.37084i			0.0214937i	0.999942	+	0.0107469i	$0.00342090\pi$
$23$			2.37084i			0.0214937i	−0.999942	+	0.0107469i	$0.996579\pi$
$24$	−181.298	−	83.6023i	−1.54197	−	0.711052i
$25$	−30.8704			−0.246963
$26$		−	299.668i		−	2.26037i
$27$	38.0404	+	135.040i	0.271144	+	0.962539i
$28$		−	443.865i		−	2.99581i
$29$			152.108i			0.973994i	0.873404	+	0.486997i	$0.161908\pi$
$29$			152.108i			0.973994i	−0.873404	+	0.486997i	$0.838092\pi$
$30$	223.645	+	103.130i	1.36106	+	0.627627i
$31$			150.096i			0.869614i	0.900524	+	0.434807i	$0.143183\pi$
$31$			150.096i			0.869614i	−0.900524	+	0.434807i	$0.856817\pi$
$32$	10.4640			0.0578061
$33$	−165.232	−	76.1936i	−0.871612	−	0.401927i
$34$			39.2595i			0.198028i
$35$			271.440i			1.31091i
$36$	278.127	+	325.781i	1.28763	+	1.50824i
$37$	−344.278			−1.52970			−0.764850	−	0.644208i	$-0.777187\pi$
$37$	−344.278			−1.52970			−0.764850	+	0.644208i	$0.777187\pi$
$38$	−423.786			−1.80914
$39$	−133.475	+	289.451i	−0.548028	+	1.18844i
$40$	372.771			1.47351
$41$	−123.510			−0.470462			−0.235231	−	0.971939i	$-0.575585\pi$
$41$	−123.510			−0.470462			−0.235231	+	0.971939i	$0.575585\pi$
$42$	−297.394	+	644.922i	−1.09259	+	2.36937i
$43$			151.039i			0.535658i	0.963466	+	0.267829i	$0.0863062\pi$
$43$			151.039i			0.535658i	−0.963466	+	0.267829i	$0.913694\pi$
$44$	−555.544			−1.90344
$45$	−170.085	−	199.227i	−0.563440	−	0.659979i
$46$		−	11.5820i		−	0.0371233i
$47$			405.781i			1.25934i	0.776861	+	0.629672i	$0.216811\pi$
$47$			405.781i			1.25934i	−0.776861	+	0.629672i	$0.783189\pi$
$48$	286.788	+	132.247i	0.862381	+	0.397671i
$49$	−439.748			−1.28206
$50$	150.807			0.426548
$51$	17.4865	−	37.9210i	0.0480119	−	0.104118i
$52$			973.193i			2.59534i
$53$	128.291			0.332494			0.166247	−	0.986084i	$-0.446835\pi$
$53$	128.291			0.332494			0.166247	+	0.986084i	$0.446835\pi$
$54$	−185.834	−	659.697i	−0.468312	−	1.66247i
$55$	339.736			0.832909
$56$			1074.95i			2.56512i
$57$	409.337	+	188.758i	0.951194	+	0.438625i
$58$		−	743.077i		−	1.68226i
$59$			679.460i			1.49929i	0.661840	+	0.749645i	$0.269776\pi$
$59$			679.460i			1.49929i	−0.661840	+	0.749645i	$0.730224\pi$
$60$	−726.304	−	334.921i	−1.56276	−	0.720636i
$61$			412.746i			0.866339i	0.901312	+	0.433170i	$0.142605\pi$
$61$			412.746i			0.866339i	−0.901312	+	0.433170i	$0.857395\pi$
$62$		−	733.246i		−	1.50197i
$63$	574.509	−	490.472i	1.14891	−	0.980853i
$64$	−537.342			−1.04950
$65$		−	595.145i		−	1.13567i
$66$	807.188	+	372.219i	1.50542	+	0.694197i
$67$	−478.262	−	268.381i	−0.872075	−	0.489372i
$67$	−478.262	−	268.381i	−0.872075	−	0.489372i
$68$		−	127.498i		−	0.227374i
$69$	−5.15873	+	11.1871i	−0.00900056	+	0.0195184i
$70$		−	1326.03i		−	2.26416i
$71$		−	921.473i		−	1.54026i	−0.637885	−	0.770132i	$-0.720190\pi$
$71$		−	921.473i		−	1.54026i	0.637885	−	0.770132i	$-0.279810\pi$
$72$	−673.569	−	788.977i	−1.10251	−	1.29141i
$73$	−772.508			−1.23857			−0.619283	−	0.785168i	$-0.712576\pi$
$73$	−772.508			−1.23857			−0.619283	+	0.785168i	$0.712576\pi$
$74$	1681.86			2.64206
$75$	−145.666	−	67.1710i	−0.224267	−	0.103417i
$76$	1376.28			2.07723
$77$			979.692i			1.44995i
$78$	652.048	−	1414.02i	0.946538	−	2.05264i
$79$			1257.39i			1.79072i	0.445343	+	0.895360i	$0.353082\pi$
$79$			1257.39i			1.79072i	−0.445343	+	0.895360i	$0.646918\pi$
$80$	−589.670			−0.824088
$81$	−114.337	+	719.978i	−0.156841	+	0.987624i
$82$	603.366			0.812569
$83$		−	792.698i		−	1.04831i	−0.851622	−	0.524156i	$-0.824381\pi$
$83$		−	792.698i		−	1.04831i	0.851622	−	0.524156i	$-0.175619\pi$
$84$	965.808	−	2094.43i	1.25450	−	2.72049i
$85$			77.9699i			0.0994944i
$86$		−	737.855i		−	0.925174i
$87$	−330.974	+	717.743i	−0.407863	+	0.884484i
$88$	1345.42			1.62979
$89$		−	810.039i		−	0.964764i	−0.875961	−	0.482382i	$-0.839772\pi$
$89$		−	810.039i		−	0.964764i	0.875961	−	0.482382i	$-0.160228\pi$
$90$	830.897	+	973.261i	0.973158	+	1.13990i
$91$	1716.21			1.97701
$92$			37.6134i			0.0426247i
$93$	−326.594	+	708.247i	−0.364153	+	0.789696i
$94$		−	1982.31i		−	2.17510i
$95$	−841.645			−0.908958
$96$	49.3758	+	22.7687i	0.0524937	+	0.0242065i
$97$		−	672.231i		−	0.703656i	−0.936065	−	0.351828i	$-0.885560\pi$
$97$		−	672.231i		−	0.703656i	0.936065	−	0.351828i	$-0.114440\pi$
$98$	2148.25			2.21435
$99$	−613.878	−	719.058i	−0.623202	−	0.729980i
$100$	−489.758			−0.489758
$101$	−970.416			−0.956039			−0.478020	−	0.878349i	$-0.658645\pi$
$101$	−970.416			−0.956039			−0.478020	+	0.878349i	$0.658645\pi$
$102$	−85.4249	+	185.251i	−0.0829247	+	0.179829i
$103$	312.154			0.298616			0.149308	−	0.988791i	$-0.452295\pi$
$103$	312.154			0.298616			0.149308	+	0.988791i	$0.452295\pi$
$104$		−	2356.88i		−	2.22222i
$105$	−590.628	+	1280.83i	−0.548947	+	1.19044i
$106$	−626.726			−0.574274
$107$			749.832i			0.677467i	0.940882	+	0.338734i	$0.109999\pi$
$107$			749.832i			0.677467i	−0.940882	+	0.338734i	$0.890001\pi$
$108$	603.510	+	2142.42i	0.537711	+	1.90883i
$109$			1161.88i			1.02099i	0.859881	+	0.510495i	$0.170538\pi$
$109$			1161.88i			1.02099i	−0.859881	+	0.510495i	$0.829462\pi$
$110$	−1659.67			−1.43858
$111$	−1624.52	−	749.116i	−1.38912	−	0.640567i
$112$		−	1700.42i		−	1.43460i
$113$	349.681			0.291108			0.145554	−	0.989350i	$-0.453504\pi$
$113$	349.681			0.291108			0.145554	+	0.989350i	$0.453504\pi$
$114$	−1999.69	−	922.118i	−1.64288	−	0.757581i
$115$		−	23.0020i		−	0.0186517i
$116$			2413.20i			1.93155i
$117$	−1259.64	+	1075.38i	−0.995328	+	0.849736i
$118$		−	3319.28i		−	2.58953i
$119$	−224.841			−0.173203
$120$	1758.97	+	811.113i	1.33809	+	0.617035i
$121$	−104.813			−0.0787475
$122$		−	2016.34i		−	1.49632i
$123$	−582.795	−	268.745i	−0.427227	−	0.197007i
$124$			2381.27i			1.72455i
$125$	1512.26			1.08209
$126$	−2806.58	+	2396.05i	−1.98436	+	1.69410i
$127$	2237.44			1.56331			0.781655	−	0.623711i	$-0.214376\pi$
$127$	2237.44			1.56331			0.781655	+	0.623711i	$0.214376\pi$
$128$	2541.30			1.75485
$129$	−328.647	+	712.699i	−0.224308	+	0.486431i
$130$			2907.39i			1.96150i
$131$			313.481i			0.209076i	0.994521	+	0.104538i	$0.0333364\pi$
$131$			313.481i			0.209076i	−0.994521	+	0.104538i	$0.966664\pi$
$132$	−2621.40	−	1208.81i	−1.72851	−	0.797071i
$133$		−	2427.04i		−	1.58234i
$134$	2336.40	+	1311.09i	1.50622	+	0.845229i
$135$	−369.069	−	1310.17i	−0.235292	−	0.835269i
$136$			308.775i			0.194686i
$137$	1580.88			0.985869			0.492935	−	0.870066i	$-0.335924\pi$
$137$	1580.88			0.985869			0.492935	+	0.870066i	$0.335924\pi$
$138$	25.2013	−	54.6511i	0.0155455	−	0.0337117i
$139$		−	1895.23i		−	1.15649i	−0.815864	−	0.578244i	$-0.803738\pi$
$139$		−	1895.23i		−	1.15649i	0.815864	−	0.578244i	$-0.196262\pi$
$140$			4306.40i			2.59969i
$141$	−882.940	+	1914.73i	−0.527354	+	1.14361i
$142$			4501.56i			2.66030i
$143$		−	2148.02i		−	1.25613i
$144$	1065.49	+	1248.05i	0.616603	+	0.722250i
$145$		−	1475.76i		−	0.845210i
$146$	3773.84			2.13922
$147$	−2075.01	−	956.850i	−1.16424	−	0.536869i
$148$	−5461.96			−3.03358
$149$			3218.29i			1.76948i	0.466083	+	0.884741i	$0.345665\pi$
$149$			3218.29i			1.76948i	−0.466083	+	0.884741i	$0.654335\pi$
$150$	711.604	+	328.143i	0.387348	+	0.178618i
$151$	−973.828			−0.524828			−0.262414	−	0.964955i	$-0.584519\pi$
$151$	−973.828			−0.524828			−0.262414	+	0.964955i	$0.584519\pi$
$152$	−3333.07			−1.77860
$153$	165.025	−	140.886i	0.0871992	−	0.0744441i
$154$		−	4785.97i		−	2.50431i
$155$		−	1456.24i		−	0.754631i
$156$	−2117.58	+	4592.14i	−1.08681	+	2.35683i
$157$	3907.80			1.98647			0.993236	−	0.116111i	$-0.0370429\pi$
$157$	3907.80			1.98647			0.993236	+	0.116111i	$0.0370429\pi$
$158$		−	6142.55i		−	3.09288i
$159$	605.359	+	279.150i	0.301937	+	0.139233i
$160$	−101.522			−0.0501628
$161$	66.3306			0.0324695
$162$	558.556	−	3517.22i	0.270891	−	1.70580i
$163$	3998.20			1.92125			0.960624	−	0.277853i	$-0.0896228\pi$
$163$	3998.20			1.92125			0.960624	+	0.277853i	$0.0896228\pi$
$164$	−1959.48			−0.932985
$165$	1603.09	+	739.233i	0.756365	+	0.348783i
$166$			3872.47i			1.81062i
$167$		−	899.439i		−	0.416771i	−0.978047	−	0.208385i	$-0.933179\pi$
$167$		−	899.439i		−	0.416771i	0.978047	−	0.208385i	$-0.0668208\pi$
$168$	−2339.00	+	5072.30i	−1.07415	+	2.32939i
$169$	−1565.87			−0.712729
$170$		−	380.897i		−	0.171844i
$171$	1520.79	+	1781.36i	0.680104	+	0.796631i
$172$			2396.24i			1.06228i
$173$		−	1119.61i		−	0.492036i	−0.969265	−	0.246018i	$-0.920878\pi$
$173$		−	1119.61i		−	0.492036i	0.969265	−	0.246018i	$-0.0791222\pi$
$174$	1616.87	−	3506.30i	0.704450	−	1.52766i
$175$			863.680i			0.373075i
$176$	−2128.26			−0.911497
$177$	−1478.44	+	3206.12i	−0.627833	+	1.36151i
$178$			3957.19i			1.66631i
$179$	−2123.70			−0.886774			−0.443387	−	0.896330i	$-0.646223\pi$
$179$	−2123.70			−0.886774			−0.443387	+	0.896330i	$0.646223\pi$
$180$	−2698.40	−	3160.74i	−1.11737	−	1.30882i
$181$	−1841.54			−0.756246			−0.378123	−	0.925755i	$-0.623430\pi$
$181$	−1841.54			−0.756246			−0.378123	+	0.925755i	$0.623430\pi$
$182$	−8384.00			−3.41463
$183$	−898.096	+	1947.59i	−0.362782	+	0.786723i
$184$		−	91.0923i		−	0.0364968i
$185$	3340.20			1.32744
$186$	1595.47	−	3459.91i	0.628956	−	1.36394i
$187$			281.412i			0.110047i
$188$			6437.70i			2.49743i
$189$	3778.11	−	1064.28i	1.45406	−	0.409603i
$190$	4111.59			1.56993
$191$	−2963.78			−1.12278			−0.561391	−	0.827550i	$-0.689734\pi$
$191$	−2963.78			−1.12278			−0.561391	+	0.827550i	$0.689734\pi$
$192$	−2535.52	−	1169.20i	−0.953047	−	0.439480i
$193$	−4624.37			−1.72471			−0.862355	−	0.506304i	$-0.831011\pi$
$193$	−4624.37			−1.72471			−0.862355	+	0.506304i	$0.831011\pi$
$194$			3283.97i			1.21534i
$195$	1294.98	−	2808.27i	0.475566	−	1.03130i
$196$	−6976.60			−2.54249
$197$	2955.20			1.06878			0.534390	−	0.845238i	$-0.320542\pi$
$197$	2955.20			1.06878			0.534390	+	0.845238i	$0.320542\pi$
$198$	2998.90	+	3512.73i	1.07638	+	1.26080i
$199$	1306.15			0.465278			0.232639	−	0.972563i	$-0.425264\pi$
$199$	1306.15			0.465278			0.232639	+	0.972563i	$0.425264\pi$
$200$	1186.10			0.419349
$201$	−1672.77	−	2307.04i	−0.587006	−	0.809583i
$202$	4740.66			1.65124
$203$	4255.64			1.47136
$204$	277.424	−	601.616i	0.0952134	−	0.206478i
$205$	1198.29			0.408256
$206$	−1524.93			−0.515761
$207$	−48.6843	+	41.5630i	−0.0163468	+	0.0139557i
$208$			3728.25i			1.24283i
$209$	−3037.70			−1.00537
$210$	2885.32	−	6257.06i	0.948125	−	2.05609i
$211$	−3298.10			−1.07607			−0.538034	−	0.842923i	$-0.680833\pi$
$211$	−3298.10			−1.07607			−0.538034	+	0.842923i	$0.680833\pi$
$212$	2035.34			0.659376
$213$	2005.04	−	4348.09i	0.644990	−	1.39871i
$214$		−	3663.07i		−	1.17010i
$215$		−	1465.39i		−	0.464832i
$216$	−1461.58	−	5188.51i	−0.460408	−	1.63441i
$217$	4199.33			1.31368
$218$		−	5675.99i		−	1.76342i
$219$	−3645.18	−	1680.90i	−1.12474	−	0.518653i
$220$	5389.91			1.65176
$221$	492.973			0.150050
$222$	7936.06	+	3659.57i	2.39925	+	1.10637i
$223$	−1239.35			−0.372165			−0.186082	−	0.982534i	$-0.559579\pi$
$223$	−1239.35			−0.372165			−0.186082	+	0.982534i	$0.559579\pi$
$224$		−	292.759i		−	0.0873248i
$225$	−541.185	−	633.910i	−0.160351	−	0.187825i
$226$	−1708.25			−0.502793
$227$		−	3485.61i		−	1.01916i	−0.860425	−	0.509578i	$-0.829802\pi$
$227$		−	3485.61i		−	1.01916i	0.860425	−	0.509578i	$-0.170198\pi$
$228$	6494.13	+	2994.65i	1.88634	+	0.869848i
$229$		−	5341.10i		−	1.54126i	−0.637280	−	0.770632i	$-0.719941\pi$
$229$		−	5341.10i		−	1.54126i	0.637280	−	0.770632i	$-0.280059\pi$
$230$			112.369i			0.0322148i
$231$	−2131.72	+	4622.80i	−0.607172	+	1.31670i
$232$		−	5844.29i		−	1.65386i
$233$	−4504.76			−1.26660			−0.633298	−	0.773908i	$-0.718299\pi$
$233$	−4504.76			−1.26660			−0.633298	+	0.773908i	$0.718299\pi$
$234$	6153.55	−	5253.44i	1.71910	−	1.46764i
$235$		−	3936.90i		−	1.09283i
$236$			10779.6i			2.97328i
$237$	−2735.95	+	5933.13i	−0.749870	+	1.62615i
$238$	1098.39			0.299151
$239$	1004.02			0.271734			0.135867	−	0.990727i	$-0.456618\pi$
$239$	1004.02			0.271734			0.135867	+	0.990727i	$0.456618\pi$
$240$	−2782.43	−	1283.07i	−0.748355	−	0.345090i
$241$	−100.705			−0.0269169			−0.0134585	−	0.999909i	$-0.504284\pi$
$241$	−100.705			−0.0269169			−0.0134585	+	0.999909i	$0.504284\pi$
$242$	512.030			0.136010
$243$	−2106.12	+	3148.52i	−0.555998	+	0.831184i
$244$			6548.21i			1.71806i
$245$	4266.46			1.11255
$246$	2847.06	+	1312.87i	0.737894	+	0.340266i
$247$			5321.39i			1.37082i
$248$		−	5766.97i		−	1.47662i
$249$	1724.84	−	3740.45i	0.438984	−	0.951973i
$250$	−7387.67			−1.86895
$251$	556.626			0.139976			0.0699879	−	0.997548i	$-0.477704\pi$
$251$	556.626			0.139976			0.0699879	+	0.997548i	$0.477704\pi$
$252$	9114.57	−	7781.34i	2.27843	−	1.94515i
$253$		−	83.0198i		−	0.0206301i
$254$	−10930.3			−2.70011
$255$	−169.655	+	367.911i	−0.0416636	+	0.0903509i
$256$	−8115.97			−1.98144
$257$		−	5884.46i		−	1.42826i	−0.700013	−	0.714130i	$-0.746823\pi$
$257$		−	5884.46i		−	1.42826i	0.700013	−	0.714130i	$-0.253177\pi$
$258$	1605.50	−	3481.66i	0.387419	−	0.840150i
$259$			9632.08i			2.31084i
$260$		−	9441.96i		−	2.25218i
$261$	−3123.48	+	2666.59i	−0.740761	+	0.632406i
$262$		−	1531.41i		−	0.361110i
$263$			5888.39i			1.38058i	0.723531	+	0.690292i	$0.242518\pi$
$263$			5888.39i			1.38058i	−0.723531	+	0.690292i	$0.757482\pi$
$264$	6348.52	+	2927.50i	1.48002	+	0.682482i
$265$	−1244.69			−0.288530
$266$			11856.5i			2.73297i
$267$	1762.57	−	3822.27i	0.403998	−	0.876102i
$268$	−7587.62	−	4257.85i	−1.72943	−	0.970485i
$269$			4083.28i			0.925509i	0.886486	+	0.462754i	$0.153139\pi$
$269$			4083.28i			0.925509i	−0.886486	+	0.462754i	$0.846861\pi$
$270$	1802.97	+	6400.41i	0.406390	+	1.44265i
$271$			5526.09i			1.23869i	0.785117	+	0.619347i	$0.212603\pi$
$271$			5526.09i			1.23869i	−0.785117	+	0.619347i	$0.787397\pi$
$272$		−	488.438i		−	0.108882i
$273$	8098.15	+	3734.31i	1.79532	+	0.827878i
$274$	−7722.91			−1.70277
$275$	1080.99			0.237040
$276$	−81.8432	+	177.484i	−0.0178492	+	0.0387075i
$277$	691.577			0.150010			0.0750051	−	0.997183i	$-0.476103\pi$
$277$	691.577			0.150010			0.0750051	+	0.997183i	$0.476103\pi$
$278$			9258.56i			1.99745i
$279$	−3082.15	+	2631.31i	−0.661375	+	0.564633i
$280$		−	10429.2i		−	2.22595i
$281$	803.393			0.170557			0.0852783	−	0.996357i	$-0.472822\pi$
$281$	803.393			0.170557			0.0852783	+	0.996357i	$0.472822\pi$
$282$	4313.32	−	9353.79i	0.910831	−	1.97521i
$283$	−901.886			−0.189440			−0.0947201	−	0.995504i	$-0.530196\pi$
$283$	−901.886			−0.189440			−0.0947201	+	0.995504i	$0.530196\pi$
$284$		−	14619.2i		−	3.05453i
$285$	−3971.41	−	1831.34i	−0.825424	−	0.380629i
$286$			10493.5i			2.16955i
$287$			3455.51i			0.710704i
$288$	183.443	+	214.874i	0.0375330	+	0.0439638i
$289$	4848.42			0.986854
$290$			7209.37i			1.45982i
$291$	1462.71	−	3172.01i	0.294658	−	0.638991i
$292$	−12255.8			−2.45623
$293$		−	3295.55i		−	0.657093i	−0.944488	−	0.328546i	$-0.893441\pi$
$293$		−	3295.55i		−	0.657093i	0.944488	−	0.328546i	$-0.106559\pi$
$294$	10136.8	+	4674.39i	2.01085	+	0.927265i
$295$		−	6592.15i		−	1.30105i
$296$	13227.8			2.59747
$297$	−1332.06	−	4728.71i	−0.260249	−	0.923863i
$298$		−	15721.9i		−	3.05620i
$299$	−145.433			−0.0281291
$300$	−2310.99	−	1065.67i	−0.444750	−	0.205088i
$301$	4225.73			0.809192
$302$	4757.32			0.906467
$303$	−4579.03	−	2111.53i	−0.868180	−	0.400344i
$304$	5272.44			0.994721
$305$		−	4004.48i		−	0.751789i
$306$	−806.176	+	688.253i	−0.150608	+	0.128578i
$307$	1881.18			0.349722			0.174861	−	0.984593i	$-0.444052\pi$
$307$	1881.18			0.349722			0.174861	+	0.984593i	$0.444052\pi$
$308$			15542.8i			2.87543i
$309$	1472.94	+	679.217i	0.271173	+	0.125046i
$310$			7113.98i			1.30338i
$311$	−8261.68			−1.50636			−0.753178	−	0.657816i	$-0.771480\pi$
$311$	−8261.68			−1.50636			−0.753178	+	0.657816i	$0.771480\pi$
$312$	5128.35	−	11121.2i	0.930563	−	2.01800i
$313$			2702.35i			0.488006i	0.969774	+	0.244003i	$0.0784607\pi$
$313$			2702.35i			0.488006i	−0.969774	+	0.244003i	$0.921539\pi$
$314$	−19090.3			−3.43098
$315$	−5573.91	+	4758.58i	−0.996997	+	0.851162i
$316$			19948.4i			3.55122i
$317$			5655.72i			1.00207i	0.865426	+	0.501036i	$0.167048\pi$
$317$			5655.72i			1.00207i	−0.865426	+	0.501036i	$0.832952\pi$
$318$	−2957.29	−	1363.70i	−0.521498	−	0.240479i
$319$		−	5326.38i		−	0.934858i
$320$	5213.31			0.910728
$321$	−1631.56	+	3538.18i	−0.283692	+	0.615208i
$322$	−324.037			−0.0560804
$323$		−	697.156i		−	0.120095i
$324$	−1813.95	+	11422.4i	−0.311034	+	1.95858i
$325$		−	1893.66i		−	0.323204i
$326$	−19531.9			−3.31832
$327$	−2528.14	+	5482.47i	−0.427542	+	0.927161i
$328$	4745.47			0.798856
$329$	11352.8			1.90243
$330$	−7831.37	−	3611.29i	−1.30637	−	0.602409i
$331$		−	3701.55i		−	0.614670i	−0.951601	−	0.307335i	$-0.900563\pi$
$331$		−	3701.55i		−	0.614670i	0.951601	−	0.307335i	$-0.0994372\pi$
$332$		−	12576.1i		−	2.07893i
$333$	−6035.49	−	7069.59i	−0.993222	−	1.16340i
$334$			4393.92i			0.719834i
$335$	4640.12	+	2603.84i	0.756767	+	0.424666i
$336$	3699.96	−	8023.66i	0.600742	−	1.30276i
$337$		−	7881.21i		−	1.27394i	−0.770890	−	0.636969i	$-0.780188\pi$
$337$		−	7881.21i		−	1.27394i	0.770890	−	0.636969i	$-0.219812\pi$
$338$	7649.54			1.23101
$339$	1650.01	+	760.872i	0.264355	+	0.121902i
$340$			1236.99i			0.197310i
$341$		−	5255.90i		−	0.834672i
$342$	−7429.34	−	8702.26i	−1.17466	−	1.37592i
$343$			2706.79i			0.426102i
$344$		−	5803.22i		−	0.909560i
$345$	50.0502	−	108.538i	0.00781048	−	0.0169377i
$346$			5469.49i			0.849831i
$347$	9428.87			1.45870			0.729349	−	0.684141i	$-0.239823\pi$
$347$	9428.87			1.45870			0.729349	+	0.684141i	$0.239823\pi$
$348$	−5250.89	+	11387.0i	−0.808843	+	1.75404i
$349$	5794.73			0.888781			0.444391	−	0.895833i	$-0.353420\pi$
$349$	5794.73			0.888781			0.444391	+	0.895833i	$0.353420\pi$
$350$		−	4219.23i		−	0.644365i
$351$	−8283.68	+	2333.48i	−1.25969	+	0.354849i
$352$	−366.418			−0.0554834
$353$	−5682.33			−0.856771			−0.428385	−	0.903596i	$-0.640917\pi$
$353$	−5682.33			−0.856771			−0.428385	+	0.903596i	$0.640917\pi$
$354$	7222.45	−	15662.5i	1.08438	−	2.35156i
$355$			8940.17i			1.33661i
$356$		−	12851.3i		−	1.91325i
$357$	−1060.94	−	489.232i	−0.157285	−	0.0725291i
$358$	10374.6			1.53161
$359$			5846.99i			0.859589i	0.902927	+	0.429794i	$0.141414\pi$
$359$			5846.99i			0.859589i	−0.902927	+	0.429794i	$0.858586\pi$
$360$	6535.00	+	7654.68i	0.956735	+	1.12066i
$361$	666.436			0.0971623
$362$	8996.25			1.30617
$363$	−494.573	−	228.063i	−0.0715106	−	0.0329757i
$364$	27227.6			3.92065
$365$	7494.91			1.07480
$366$	4387.36	−	9514.35i	0.626587	−	1.35881i
$367$		−	3662.87i		−	0.520982i	−0.965476	−	0.260491i	$-0.916116\pi$
$367$		−	3662.87i		−	0.520982i	0.965476	−	0.260491i	$-0.0838844\pi$
$368$			144.095i			0.0204116i
$369$	−2165.23	−	2536.21i	−0.305467	−	0.357805i
$370$	−16317.5			−2.29272
$371$		−	3589.29i		−	0.502282i
$372$	−5181.42	+	11236.3i	−0.722161	+	1.56606i
$373$		−	59.1886i		−	0.00821627i	−0.999992	−	0.00410814i	$-0.998692\pi$
$373$		−	59.1886i		−	0.00821627i	0.999992	−	0.00410814i	$-0.00130766\pi$
$374$		−	1374.75i		−	0.190071i
$375$	7135.80	+	3290.54i	0.982642	+	0.453127i
$376$		−	15590.8i		−	2.13840i
$377$	−9330.67			−1.27468
$378$	−18456.8	+	5199.20i	−2.51141	+	0.707455i
$379$		−	4863.27i		−	0.659127i	−0.944133	−	0.329564i	$-0.893098\pi$
$379$		−	4863.27i		−	0.659127i	0.944133	−	0.329564i	$-0.106902\pi$
$380$	−13352.7			−1.80257
$381$	10557.6	+	4868.45i	1.41964	+	0.654641i
$382$	14478.6			1.93924
$383$	−23.4926			−0.00313424			−0.00156712	−	0.999999i	$-0.500499\pi$
$383$	−23.4926			−0.00313424			−0.00156712	+	0.999999i	$0.500499\pi$
$384$	11991.4	+	5529.63i	1.59358	+	0.734850i
$385$		−	9505.01i		−	1.25823i
$386$	22590.9			2.97887
$387$	−3101.53	+	2647.85i	−0.407389	+	0.347798i
$388$		−	10664.9i		−	1.39544i
$389$			489.277i			0.0637721i	0.999492	+	0.0318860i	$0.0101514\pi$
$389$			489.277i			0.0637721i	−0.999492	+	0.0318860i	$0.989849\pi$
$390$	−6326.20	+	13718.9i	−0.821384	+	1.78124i
$391$	19.0532			0.00246435
$392$	16896.0			2.17698
$393$	−682.105	+	1479.20i	−0.0875512	+	0.189862i
$394$	−14436.7			−1.84597
$395$		−	12199.2i		−	1.55395i
$396$	−9739.16	−	11407.8i	−1.23589	−	1.44764i
$397$	−4038.98			−0.510607			−0.255303	−	0.966861i	$-0.582175\pi$
$397$	−4038.98			−0.510607			−0.255303	+	0.966861i	$0.582175\pi$
$398$	−6380.76			−0.803615
$399$	5281.01	−	11452.3i	0.662609	−	1.43692i
$400$	−1876.24			−0.234530
$401$	−12372.8			−1.54082			−0.770408	−	0.637551i	$-0.779948\pi$
$401$	−12372.8			−1.54082			−0.770408	+	0.637551i	$0.779948\pi$
$402$	8171.79	+	11270.3i	1.01386	+	1.39829i
$403$	−9207.21			−1.13807
$404$	−15395.6			−1.89594
$405$	1109.30	−	6985.26i	0.136103	−	0.857037i
$406$	−20789.5			−2.54130
$407$	12055.6			1.46824
$408$	−671.866	+	1456.99i	−0.0815252	+	0.176794i
$409$		−	2101.01i		−	0.254005i	−0.991902	−	0.127003i	$-0.959464\pi$
$409$		−	2101.01i		−	0.254005i	0.991902	−	0.127003i	$-0.0405357\pi$
$410$	−5853.89			−0.705129
$411$	7459.60	+	3439.85i	0.895268	+	0.412836i
$412$	4952.32			0.592192
$413$	19009.7			2.26490
$414$	237.831	−	203.043i	0.0282338	−	0.0241039i
$415$			7690.79i			0.909702i
$416$			641.886i			0.0756516i
$417$	4123.85	−	8942.91i	0.484283	−	1.05021i
$418$	14839.7			1.73644
$419$			16317.9i			1.90258i	0.308291	+	0.951292i	$0.400243\pi$
$419$			16317.9i			1.90258i	−0.308291	+	0.951292i	$0.599757\pi$
$420$	−9370.31	+	20320.3i	−1.08863	+	2.36078i
$421$	−9515.71			−1.10159			−0.550793	−	0.834642i	$-0.685675\pi$
$421$	−9515.71			−1.10159			−0.550793	+	0.834642i	$0.685675\pi$
$422$	16111.8			1.85855
$423$	−8332.53	+	7113.69i	−0.957781	+	0.817682i
$424$	−4929.19			−0.564582
$425$			248.088i			0.0283154i
$426$	−9794.97	+	21241.2i	−1.11401	+	2.41582i
$427$	11547.7			1.30874
$428$			11896.1i			1.34350i
$429$	4673.88	−	10135.7i	0.526007	−	1.14069i
$430$			7158.70i			0.802844i
$431$			79.3409i			0.00886709i	0.999990	+	0.00443355i	$0.00141125\pi$
$431$			79.3409i			0.00886709i	−0.999990	+	0.00443355i	$0.998589\pi$
$432$	2312.02	+	8207.48i	0.257493	+	0.914080i
$433$			5591.43i			0.620571i	0.950643	+	0.310285i	$0.100425\pi$
$433$			5591.43i			0.620571i	−0.950643	+	0.310285i	$0.899575\pi$
$434$	−20514.5			−2.26896
$435$	3211.12	−	6963.57i	0.353934	−	0.767535i
$436$			18433.2i			2.02475i
$437$			205.669i			0.0225137i
$438$	17807.4	+	8211.52i	1.94262	+	0.895803i
$439$	−2523.69			−0.274371			−0.137186	−	0.990545i	$-0.543806\pi$
$439$	−2523.69			−0.274371			−0.137186	+	0.990545i	$0.543806\pi$
$440$	−13053.3			−1.41430
$441$	−7709.17	−	9030.04i	−0.832434	−	0.975061i
$442$	−2408.26			−0.259161
$443$	−17306.9			−1.85615			−0.928075	−	0.372394i	$-0.878537\pi$
$443$	−17306.9			−1.85615			−0.928075	+	0.372394i	$0.878537\pi$
$444$	−25773.0	−	11884.7i	−2.75480	−	1.27032i
$445$			7859.03i			0.837200i
$446$	6054.43			0.642792
$447$	−7002.70	+	15185.9i	−0.740976	+	1.60687i
$448$			15033.6i			1.58542i
$449$		−	17513.5i		−	1.84079i	−0.390991	−	0.920394i	$-0.627868\pi$
$449$		−	17513.5i		−	1.84079i	0.390991	−	0.920394i	$-0.372132\pi$
$450$	2643.79	+	3096.76i	0.276954	+	0.324406i
$451$	4324.93			0.451559
$452$	5547.68			0.577303
$453$	−4595.13	−	2118.96i	−0.476596	−	0.219773i
$454$			17027.8i			1.76026i
$455$	−16650.7			−1.71560
$456$	−15727.5	−	7252.44i	−1.61515	−	0.744796i
$457$	−12186.0			−1.24734			−0.623671	−	0.781687i	$-0.714360\pi$
$457$	−12186.0			−1.24734			−0.623671	+	0.781687i	$0.714360\pi$
$458$			26092.2i			2.66203i
$459$	1085.25	−	305.709i	0.110359	−	0.0310878i
$460$		−	364.927i		−	0.0369887i
$461$		−	1205.72i		−	0.121813i	−0.998143	−	0.0609067i	$-0.980601\pi$
$461$		−	1205.72i		−	0.121813i	0.998143	−	0.0609067i	$-0.0193992\pi$
$462$	10413.8	−	22583.2i	1.04869	−	2.27417i
$463$		−	17268.6i		−	1.73335i	−0.498875	−	0.866674i	$-0.666253\pi$
$463$		−	17268.6i		−	1.73335i	0.498875	−	0.866674i	$-0.333747\pi$
$464$			9244.83i			0.924958i
$465$	3168.63	−	6871.44i	0.316004	−	0.685280i
$466$	22006.6			2.18763
$467$		−	4032.73i		−	0.399599i	−0.979837	−	0.199799i	$-0.935971\pi$
$467$		−	4032.73i		−	0.399599i	0.979837	−	0.199799i	$-0.0640290\pi$
$468$	−19984.1	+	17060.9i	−1.97386	+	1.68513i
$469$	−7508.66	+	13380.7i	−0.739270	+	1.31740i
$470$			19232.5i			1.88751i
$471$	18439.4	+	8503.00i	1.80392	+	0.831841i
$472$		−	26106.1i		−	2.54583i
$473$		−	5288.94i		−	0.514135i
$474$	13365.6	−	28984.4i	1.29515	−	2.80865i
$475$	−2677.98			−0.258683
$476$	−3567.09			−0.343482
$477$	2249.06	+	2634.41i	0.215885	+	0.252875i
$478$	−4904.81			−0.469332
$479$			15129.1i			1.44314i	0.692340	+	0.721571i	$0.256580\pi$
$479$			15129.1i			1.44314i	−0.692340	+	0.721571i	$0.743420\pi$
$480$	−479.046	−	220.903i	−0.0455528	−	0.0210058i
$481$		−	21118.8i		−	2.00194i
$482$	491.962			0.0464901
$483$	312.989	+	144.329i	0.0294855	+	0.0135967i
$484$	−1662.86			−0.156166
$485$			6522.01i			0.610617i
$486$	10288.8	−	15381.1i	0.960303	−	1.43560i
$487$		−	10248.6i		−	0.953610i	−0.879009	−	0.476805i	$-0.841795\pi$
$487$		−	10248.6i		−	0.953610i	0.879009	−	0.476805i	$-0.158205\pi$
$488$		−	15858.5i		−	1.47106i
$489$	18866.0	+	8699.71i	1.74468	+	0.804528i
$490$	−20842.4			−1.92156
$491$			5499.47i			0.505474i	0.967535	+	0.252737i	$0.0813307\pi$
$491$			5499.47i			0.505474i	−0.967535	+	0.252737i	$0.918669\pi$
$492$	−9246.04	−	4263.64i	−0.847243	−	0.390690i
$493$	1222.41			0.111673
$494$		−	25996.0i		−	2.36764i
$495$	5955.87	+	6976.33i	0.540801	+	0.633460i
$496$			9122.51i			0.825833i
$497$	−25780.6			−2.32680
$498$	−8426.14	+	18272.8i	−0.758201	+	1.64422i
$499$			8856.62i			0.794542i	0.917701	+	0.397271i	$0.130043\pi$
$499$			8856.62i			0.794542i	−0.917701	+	0.397271i	$0.869957\pi$
$500$	23992.0			2.14591
$501$	1957.09	−	4244.12i	0.174524	−	0.378469i
$502$	−2719.22			−0.241762
$503$	1891.95			0.167709			0.0838547	−	0.996478i	$-0.473277\pi$
$503$	1891.95			0.167709			0.0838547	+	0.996478i	$0.473277\pi$
$504$	−22073.7	+	18844.9i	−1.95087	+	1.66551i
$505$	9415.01			0.829629
$506$			405.566i			0.0356317i
$507$	−7388.74	−	3407.18i	−0.647230	−	0.298458i
$508$	35496.9			3.10024
$509$		−	1386.34i		−	0.120724i	−0.998177	−	0.0603621i	$-0.980774\pi$
$509$		−	1386.34i		−	0.120724i	0.998177	−	0.0603621i	$-0.0192255\pi$
$510$	828.796	−	1797.31i	0.0719602	−	0.156052i
$511$			21613.0i			1.87104i
$512$	19317.6			1.66743
$513$	3299.98	+	11714.7i	0.284011	+	1.00822i
$514$			28746.7i			2.46685i
$515$	−3028.53			−0.259132
$516$	−5213.99	+	11307.0i	−0.444831	+	0.964653i
$517$		−	14209.2i		−	1.20874i
$518$		−	47054.4i		−	3.99122i
$519$	2436.16	−	5283.01i	0.206042	−	0.446818i
$520$			22866.6i			1.92840i
$521$	13262.4			1.11523			0.557616	−	0.830099i	$-0.311716\pi$
$521$	13262.4			1.11523			0.557616	+	0.830099i	$0.311716\pi$
$522$	15258.8	−	13026.8i	1.27942	−	1.09227i
$523$	−732.293			−0.0612255			−0.0306128	−	0.999531i	$-0.509746\pi$
$523$	−732.293			−0.0612255			−0.0306128	+	0.999531i	$0.509746\pi$
$524$			4973.37i			0.414623i
$525$	−1879.29	+	4075.39i	−0.156226	+	0.338789i
$526$		−	28765.8i		−	2.38450i
$527$	1206.24			0.0997050
$528$	−10042.4	−	4630.88i	−0.827730	−	0.381692i
$529$	12161.4			0.999538
$530$	6080.52			0.498341
$531$	−13952.4	+	11911.5i	−1.14027	+	0.973477i
$532$		−	38505.0i		−	3.13797i
$533$		−	7576.35i		−	0.615700i
$534$	−8610.46	+	18672.5i	−0.697774	+	1.51318i
$535$		−	7274.90i		−	0.587891i
$536$	18375.7	+	10311.7i	1.48080	+	0.830965i
$537$	−10020.9	−	4620.96i	−0.805279	−	0.371339i
$538$		−	19947.6i		−	1.59851i
$539$	15398.6			1.23055
$540$	−5855.28	−	20785.8i	−0.466613	−	1.65644i
$541$			9591.97i			0.762275i	0.924518	+	0.381138i	$0.124468\pi$
$541$			9591.97i			0.762275i	−0.924518	+	0.381138i	$0.875532\pi$
$542$		−	26996.0i		−	2.13944i
$543$	−8689.54	−	4007.02i	−0.686747	−	0.316681i
$544$		−	84.0935i		−	0.00662772i
$545$		−	11272.6i		−	0.885991i
$546$	−39560.9	−	18242.8i	−3.10083	−	1.42989i
$547$		−	10371.2i		−	0.810675i	−0.914167	−	0.405337i	$-0.867154\pi$
$547$		−	10371.2i		−	0.810675i	0.914167	−	0.405337i	$-0.132846\pi$
$548$	25080.7			1.95510
$549$	−8475.56	+	7235.80i	−0.658885	+	0.562507i
$550$	−5280.82			−0.409409
$551$			13195.3i			1.02022i
$552$	198.208	−	429.831i	0.0152832	−	0.0331428i
$553$	35178.7			2.70515
$554$	−3378.48			−0.259094
$555$	15761.1	+	7267.95i	1.20545	+	0.555869i
$556$		−	30067.9i		−	2.29346i
$557$			20703.4i			1.57492i	0.616364	+	0.787462i	$0.288605\pi$
$557$			20703.4i			1.57492i	−0.616364	+	0.787462i	$0.711395\pi$
$558$	15056.9	−	12854.4i	1.14231	−	0.975218i
$559$	−9265.09			−0.701023
$560$			16497.6i			1.24491i
$561$	−612.325	+	1327.88i	−0.0460827	+	0.0999341i
$562$	−3924.72			−0.294581
$563$	−6960.81			−0.521071			−0.260536	−	0.965464i	$-0.583899\pi$
$563$	−6960.81			−0.521071			−0.260536	+	0.965464i	$0.583899\pi$
$564$	−14007.8	+	30377.1i	−1.04581	+	2.26792i
$565$	−3392.62			−0.252617
$566$	4405.88			0.327196
$567$	20143.3	+	3198.87i	1.49195	+	0.236931i
$568$			35404.7i			2.61540i
$569$			5209.32i			0.383807i	0.981414	+	0.191903i	$0.0614660\pi$
$569$			5209.32i			0.383807i	−0.981414	+	0.191903i	$0.938534\pi$
$570$	19401.0	+	8946.42i	1.42565	+	0.657411i
$571$	9555.27			0.700308			0.350154	−	0.936692i	$-0.386129\pi$
$571$	9555.27			0.700308			0.350154	+	0.936692i	$0.386129\pi$
$572$		−	34078.3i		−	2.49106i
$573$	−13985.0	−	6448.90i	−1.01960	−	0.470169i
$574$		−	16880.8i		−	1.22751i
$575$		−	73.1889i		−	0.00530815i
$576$	−9420.07	−	11034.1i	−0.681429	−	0.798183i
$577$			9607.43i			0.693176i	0.938018	+	0.346588i	$0.112660\pi$
$577$			9607.43i			0.693176i	−0.938018	+	0.346588i	$0.887340\pi$
$578$	−23685.4			−1.70447
$579$	−21820.7	−	10062.2i	−1.56621	−	0.722228i
$580$		−	23413.0i		−	1.67616i
$581$	−22177.8			−1.58363
$582$	−7145.60	+	15495.8i	−0.508926	+	1.10365i
$583$	−4492.37			−0.319134
$584$	29681.2			2.10311
$585$	12221.0	−	10433.4i	0.863723	−	0.737382i
$586$			16099.4i			1.13491i
$587$	−932.348			−0.0655573			−0.0327786	−	0.999463i	$-0.510436\pi$
$587$	−932.348			−0.0655573			−0.0327786	+	0.999463i	$0.510436\pi$
$588$	−32920.0	−	15180.4i	−2.30884	−	1.06468i
$589$			13020.7i			0.910881i
$590$			32203.8i			2.24714i
$591$	13944.5	+	6430.24i	0.970559	+	0.447555i
$592$	−20924.5			−1.45269
$593$	19202.9			1.32979			0.664897	−	0.746935i	$-0.268475\pi$
$593$	19202.9			1.32979			0.664897	+	0.746935i	$0.268475\pi$
$594$	6507.35	+	23100.6i	0.449494	+	1.59567i
$595$	2181.41			0.150301
$596$			51058.2i			3.50910i
$597$	6163.22	+	2842.05i	0.422519	+	0.194837i
$598$	710.466			0.0485838
$599$	−12374.0			−0.844057			−0.422028	−	0.906583i	$-0.638682\pi$
$599$	−12374.0			−0.844057			−0.422028	+	0.906583i	$0.638682\pi$
$600$	5596.75	+	2580.84i	0.380811	+	0.175604i
$601$	19952.9			1.35424			0.677119	−	0.735873i	$-0.263228\pi$
$601$	19952.9			1.35424			0.677119	+	0.735873i	$0.263228\pi$
$602$	−20643.4			−1.39761
$603$	−2873.28	−	14525.9i	−0.194045	−	0.980993i
$604$	−15449.8			−1.04080
$605$	1016.90			0.0683352
$606$	22369.4	+	10315.2i	1.49950	+	0.691464i
$607$	9460.80			0.632623			0.316311	−	0.948655i	$-0.397556\pi$
$607$	9460.80			0.632623			0.316311	+	0.948655i	$0.397556\pi$
$608$	907.746			0.0605493
$609$	20080.8	+	9259.86i	1.33615	+	0.616139i
$610$			19562.6i			1.29847i
$611$	−24891.5			−1.64812
$612$	2618.12	−	2235.15i	0.172927	−	0.147632i
$613$	9572.24			0.630700			0.315350	−	0.948975i	$-0.397878\pi$
$613$	9572.24			0.630700			0.315350	+	0.948975i	$0.397878\pi$
$614$	−9189.92			−0.604031
$615$	5654.31	+	2607.38i	0.370738	+	0.170959i
$616$		−	37641.6i		−	2.46205i
$617$		−	5808.53i		−	0.378999i	−0.981881	−	0.189500i	$-0.939313\pi$
$617$		−	5808.53i		−	0.378999i	0.981881	−	0.189500i	$-0.0606866\pi$
$618$	−7195.57	−	3318.10i	−0.468363	−	0.215977i
$619$	7016.00			0.455568			0.227784	−	0.973712i	$-0.426852\pi$
$619$	7016.00			0.455568			0.227784	+	0.973712i	$0.426852\pi$
$620$		−	23103.2i		−	1.49653i
$621$	−320.160	+	90.1879i	−0.0206885	+	0.00582788i
$622$	40359.8			2.60174
$623$	−22663.0			−1.45742
$624$	−8112.32	+	17592.2i	−0.520437	+	1.12861i
$625$	−10813.2			−0.692046
$626$		−	13201.5i		−	0.842871i
$627$	−14333.8	−	6609.74i	−0.912974	−	0.421001i
$628$	61997.1			3.93942
$629$			2766.77i			0.175387i
$630$	27229.5	−	23246.5i	1.72199	−	1.47010i
$631$			3685.52i			0.232517i	0.993219	+	0.116259i	$0.0370901\pi$
$631$			3685.52i			0.232517i	−0.993219	+	0.116259i	$0.962910\pi$
$632$		−	48311.1i		−	3.04068i
$633$	−15562.5	−	7176.34i	−0.977177	−	0.450607i
$634$		−	27629.2i		−	1.73075i
$635$	−21707.7			−1.35660
$636$	9604.01	+	4428.70i	0.598779	+	0.276116i
$637$		−	26975.1i		−	1.67785i
$638$			26020.3i			1.61466i
$639$	18922.0	−	16154.2i	1.17143	−	1.00008i
$640$	−24655.8			−1.52282
$641$	21969.1			1.35371			0.676853	−	0.736118i	$-0.263343\pi$
$641$	21969.1			1.35371			0.676853	+	0.736118i	$0.263343\pi$
$642$	7970.48	−	17284.6i	0.489984	−	1.06257i
$643$	3755.43			0.230326			0.115163	−	0.993347i	$-0.463261\pi$
$643$	3755.43			0.230326			0.115163	+	0.993347i	$0.463261\pi$
$644$	1052.33			0.0643910
$645$	3188.55	−	6914.63i	0.194650	−	0.422114i
$646$			3405.73i			0.207425i
$647$	−7932.06			−0.481981			−0.240990	−	0.970528i	$-0.577472\pi$
$647$	−7932.06			−0.481981			−0.240990	+	0.970528i	$0.577472\pi$
$648$	4393.03	−	27662.9i	0.266319	−	1.67701i
$649$		−	23792.6i		−	1.43905i
$650$			9250.86i			0.558228i
$651$	19815.1	+	9137.34i	1.19295	+	0.550108i
$652$	63431.4			3.81007
$653$	7112.60			0.426244			0.213122	−	0.977026i	$-0.431637\pi$
$653$	7112.60			0.426244			0.213122	+	0.977026i	$0.431637\pi$
$654$	12350.4	−	26782.9i	0.738439	−	1.60137i
$655$		−	3041.40i		−	0.181431i
$656$	−7506.65			−0.446777
$657$	−13542.7	−	15863.1i	−0.804190	−	0.941978i
$658$	−55460.4			−3.28582
$659$		−	25655.9i		−	1.51656i	−0.651929	−	0.758280i	$-0.726040\pi$
$659$		−	25655.9i		−	1.51656i	0.651929	−	0.758280i	$-0.273960\pi$
$660$	25433.0	+	11727.9i	1.49996	+	0.691680i
$661$			1512.37i			0.0889932i	0.999010	+	0.0444966i	$0.0141684\pi$
$661$			1512.37i			0.0889932i	−0.999010	+	0.0444966i	$0.985832\pi$
$662$			18082.7i			1.06164i
$663$	2326.16	+	1072.66i	0.136260	+	0.0628337i
$664$			30457.0i			1.78006i
$665$			23547.2i			1.37312i
$666$	29484.5	+	34536.2i	1.71546	+	2.00939i
$667$	−360.626			−0.0209347
$668$		−	14269.6i		−	0.826507i
$669$	−5848.01	−	2696.70i	−0.337963	−	0.155845i
$670$	−22667.8	−	12720.2i	−1.30707	−	0.733471i
$671$		−	14453.1i		−	0.831529i
$672$	637.015	−	1381.42i	0.0365675	−	0.0792997i
$673$		−	3570.29i		−	0.204494i	−0.994759	−	0.102247i	$-0.967397\pi$
$673$		−	3570.29i		−	0.204494i	0.994759	−	0.102247i	$-0.0326032\pi$
$674$			38501.1i			2.20031i
$675$	−1174.32	−	4168.75i	−0.0669625	−	0.237712i
$676$	−24842.4			−1.41343
$677$	−7551.23			−0.428682			−0.214341	−	0.976759i	$-0.568760\pi$
$677$	−7551.23			−0.428682			−0.214341	+	0.976759i	$0.568760\pi$
$678$	−8060.61	−	3717.00i	−0.456587	−	0.210546i
$679$	−18807.4			−1.06298
$680$		−	2995.75i		−	0.168944i
$681$	7584.36	−	16447.3i	0.426774	−	0.925495i
$682$			25676.0i			1.44162i
$683$	23659.5			1.32548			0.662742	−	0.748848i	$-0.269393\pi$
$683$	23659.5			1.32548			0.662742	+	0.748848i	$0.269393\pi$
$684$	24127.3	+	28261.2i	1.34873	+	1.57982i
$685$	−15337.8			−0.855515
$686$		−	13223.1i		−	0.735951i
$687$	11621.7	−	25202.6i	0.645409	−	1.39962i
$688$			9179.86i			0.508690i
$689$			7869.67i			0.435139i
$690$	−244.504	+	530.228i	−0.0134900	+	0.0292542i
$691$	−7381.42			−0.406371			−0.203186	−	0.979140i	$-0.565129\pi$
$691$	−7381.42			−0.406371			−0.203186	+	0.979140i	$0.565129\pi$
$692$		−	17762.6i		−	0.975768i
$693$	−20117.5	+	17174.9i	−1.10275	+	0.941441i
$694$	−46061.8			−2.51942
$695$			18387.6i			1.00357i
$696$	12716.6	−	27577.0i	0.692561	−	1.50187i
$697$			992.577i			0.0539405i
$698$	−28308.3			−1.53508
$699$	−21256.3	−	9801.93i	−1.15020	−	0.530391i
$700$			13702.3i			0.739854i
$701$	−1836.11			−0.0989284			−0.0494642	−	0.998776i	$-0.515751\pi$
$701$	−1836.11			−0.0989284			−0.0494642	+	0.998776i	$0.515751\pi$
$702$	40467.3	−	11399.5i	2.17570	−	0.612885i
$703$	−29865.8			−1.60229
$704$	18816.1			1.00733
$705$	8566.32	−	18576.8i	0.457626	−	0.992399i
$706$	27759.2			1.47979
$707$			27149.9i			1.44424i
$708$	−23455.4	+	50865.0i	−1.24507	+	2.70003i
$709$	20475.0			1.08456			0.542282	−	0.840196i	$-0.317560\pi$
$709$	20475.0			1.08456			0.542282	+	0.840196i	$0.317560\pi$
$710$		−	43674.3i		−	2.30855i
$711$	−25819.9	+	22043.1i	−1.36191	+	1.16270i
$712$			31123.2i			1.63819i
$713$	−355.854			−0.0186912
$714$	5182.88	+	2389.99i	0.271659	+	0.125270i
$715$			20840.2i			1.09004i
$716$	−33692.4			−1.75858
$717$	4737.58	+	2184.65i	0.246762	+	0.113790i
$718$		−	28563.6i		−	1.48466i
$719$		−	20645.8i		−	1.07088i	−0.844575	−	0.535438i	$-0.820147\pi$
$719$		−	20645.8i		−	1.07088i	0.844575	−	0.535438i	$-0.179853\pi$
$720$	−10337.4	−	12108.6i	−0.535074	−	0.626752i
$721$		−	8733.33i		−	0.451104i
$722$	−3255.66			−0.167816
$723$	−475.189	−	219.124i	−0.0244432	−	0.0112715i
$724$	−29216.0			−1.49973
$725$		−	4695.65i		−	0.240541i
$726$	2416.08	+	1114.13i	0.123511	+	0.0569548i
$727$			2101.86i			0.107227i	0.998562	+	0.0536133i	$0.0170738\pi$
$727$			2101.86i			0.107227i	−0.998562	+	0.0536133i	$0.982926\pi$
$728$	−65940.0			−3.35700
$729$	−16788.9	+	10274.0i	−0.852962	+	0.521973i
$730$	−36614.0			−1.85636
$731$	1213.82			0.0614155
$732$	−14248.3	+	30898.6i	−0.719442	+	1.56017i
$733$			13146.4i			0.662448i	0.943552	+	0.331224i	$0.107462\pi$
$733$			13146.4i			0.662448i	−0.943552	+	0.331224i	$0.892538\pi$
$734$			17893.8i			0.899825i
$735$	20131.8	+	9283.40i	1.01030	+	0.465882i
$736$			24.8086i			0.00124247i
$737$	16747.3	+	9397.87i	0.837034	+	0.469708i
$738$	10577.5	+	12389.9i	0.527594	+	0.617991i
$739$			31272.0i			1.55664i	0.627866	+	0.778321i	$0.283928\pi$
$739$			31272.0i			1.55664i	−0.627866	+	0.778321i	$0.716072\pi$
$740$	52992.2			2.63248
$741$	−11578.8	+	25109.7i	−0.574034	+	1.24484i
$742$			17534.3i			0.867527i
$743$			29480.8i			1.45565i	0.685764	+	0.727824i	$0.259468\pi$
$743$			29480.8i			1.45565i	−0.685764	+	0.727824i	$0.740532\pi$
$744$	12548.4	−	27212.2i	0.618341	−	1.34092i
$745$		−	31224.0i		−	1.53552i
$746$			289.147i			0.0141909i
$747$	16277.7	−	13896.7i	0.797283	−	0.680661i
$748$			4464.59i			0.218238i
$749$	20978.5			1.02342
$750$	−34859.6	−	16074.9i	−1.69719	−	0.782628i
$751$	−16547.1			−0.804010			−0.402005	−	0.915637i	$-0.631687\pi$
$751$	−16547.1			−0.804010			−0.402005	+	0.915637i	$0.631687\pi$
$752$			24662.5i			1.19594i
$753$	2626.51	+	1211.17i	0.127112	+	0.0586153i
$754$	45582.0			2.20159
$755$	9448.12			0.455433
$756$	59939.7	−	16884.8i	2.88358	−	0.812294i
$757$			13666.1i			0.656144i	0.944653	+	0.328072i	$0.106399\pi$
$757$			13666.1i			0.656144i	−0.944653	+	0.328072i	$0.893601\pi$
$758$			23757.9i			1.13843i
$759$	180.643	−	391.739i	0.00863890	−	0.0187342i
$760$	32337.6			1.54343
$761$			1348.37i			0.0642293i	0.999484	+	0.0321146i	$0.0102242\pi$
$761$			1348.37i			0.0642293i	−0.999484	+	0.0321146i	$0.989776\pi$
$762$	−51575.9	−	23783.3i	−2.45197	−	1.13068i
$763$	32506.6			1.54236
$764$	−47020.3			−2.22662
$765$	−1601.08	+	1366.88i	−0.0756694	+	0.0646009i
$766$	114.765			0.00541337
$767$	−41679.6			−1.96214
$768$	−38296.2	−	17659.6i	−1.79934	−	0.829733i
$769$			17914.9i			0.840089i	0.907504	+	0.420044i	$0.137985\pi$
$769$			17914.9i			0.840089i	−0.907504	+	0.420044i	$0.862015\pi$
$770$			46433.7i			2.17319i
$771$	12804.0	−	27766.6i	0.598088	−	1.29700i
$772$	−73365.5			−3.42031
$773$		−	37699.4i		−	1.75414i	−0.480361	−	0.877071i	$-0.659494\pi$
$773$		−	37699.4i		−	1.75414i	0.480361	−	0.877071i	$-0.340506\pi$
$774$	15151.5	−	12935.2i	0.703631	−	0.600707i
$775$		−	4633.52i		−	0.214762i
$776$			25828.4i			1.19482i
$777$	−20958.5	+	45450.2i	−0.967673	+	2.09848i
$778$		−	2390.21i		−	0.110145i
$779$	−10714.4			−0.492788
$780$	20544.8	−	44553.1i	0.943105	−	2.04520i
$781$			32267.2i			1.47837i
$782$	−93.0781			−0.00425635
$783$	−20540.8	+	5786.27i	−0.937507	+	0.264092i
$784$	−26727.0			−1.21752
$785$	−37913.6			−1.72382
$786$	3332.20	−	7226.16i	0.151216	−	0.327924i
$787$			24349.1i			1.10286i	0.834221	+	0.551430i	$0.185918\pi$
$787$			24349.1i			1.10286i	−0.834221	+	0.551430i	$0.814082\pi$
$788$	46884.3			2.11952
$789$	−12812.6	+	27785.1i	−0.578124	+	1.25371i
$790$			59595.3i			2.68393i
$791$		−	9783.24i		−	0.439762i
$792$	23586.3	+	27627.6i	1.05821	+	1.23952i
$793$	−25318.7			−1.13379
$794$	19731.2			0.881905
$795$	−5873.21	−	2708.32i	−0.262014	−	0.120823i
$796$	20722.0			0.922703
$797$		−	5937.63i		−	0.263892i	−0.991257	−	0.131946i	$-0.957878\pi$
$797$		−	5937.63i		−	0.263892i	0.991257	−	0.131946i	$-0.0421225\pi$
$798$	−25798.7	+	55946.5i	−1.14444	+	2.48181i
$799$	3261.03			0.144389
$800$	−323.028			−0.0142760
$801$	16633.8	−	14200.7i	0.733741	−	0.626413i
$802$	60443.3			2.66126
$803$	27050.9			1.18880
$804$	−26538.5	−	36601.2i	−1.16410	−	1.60550i
$805$	−643.543			−0.0281763
$806$	44978.9			1.96565
$807$	−8884.83	+	19267.5i	−0.387560	+	0.840455i
$808$	37285.2			1.62338
$809$	12425.8			0.540009			0.270005	−	0.962859i	$-0.412975\pi$
$809$	12425.8			0.540009			0.270005	+	0.962859i	$0.412975\pi$
$810$	−5419.13	+	34124.2i	−0.235073	+	1.48025i
$811$			21544.8i			0.932846i	0.884562	+	0.466423i	$0.154458\pi$
$811$			21544.8i			0.932846i	−0.884562	+	0.466423i	$0.845542\pi$
$812$	67515.6			2.91790
$813$	−12024.3	+	26075.6i	−0.518707	+	1.12486i
$814$	−58893.6			−2.53590
$815$	−38790.7			−1.66721
$816$	1062.79	−	2304.76i	0.0455947	−	0.0988758i
$817$			13102.6i			0.561078i
$818$			10263.8i			0.438711i
$819$	30086.7	+	35241.6i	1.28365	+	1.50359i
$820$	19010.9			0.809622
$821$		−	12268.4i		−	0.521522i	−0.965403	−	0.260761i	$-0.916026\pi$
$821$		−	12268.4i		−	0.521522i	0.965403	−	0.260761i	$-0.0839735\pi$
$822$	−36441.5	−	16804.3i	−1.54628	−	0.713038i
$823$	−23905.5			−1.01251			−0.506255	−	0.862384i	$-0.668970\pi$
$823$	−23905.5			−1.01251			−0.506255	+	0.862384i	$0.668970\pi$
$824$	−11993.5			−0.507057
$825$	5100.77	+	2352.12i	0.215256	+	0.0992612i
$826$	−92865.7			−3.91188
$827$			14635.8i			0.615400i	0.951483	+	0.307700i	$0.0995593\pi$
$827$			14635.8i			0.615400i	−0.951483	+	0.307700i	$0.900441\pi$
$828$	−772.375	+	659.396i	−0.0324177	+	0.0276758i
$829$	34826.2			1.45906			0.729531	−	0.683948i	$-0.239738\pi$
$829$	34826.2			1.45906			0.729531	+	0.683948i	$0.239738\pi$
$830$		−	37570.9i		−	1.57121i
$831$	3263.29	+	1504.81i	0.136224	+	0.0628173i
$832$		−	32961.7i		−	1.37349i
$833$			3534.01i			0.146994i
$834$	−20145.8	+	43687.7i	−0.836439	+	1.81389i
$835$			8726.39i			0.361664i
$836$	−48193.0			−1.99377
$837$	−20269.0	+	5709.71i	−0.837037	+	0.235790i
$838$		−	79716.0i		−	3.28609i
$839$			14059.6i			0.578536i	0.957248	+	0.289268i	$0.0934118\pi$
$839$			14059.6i			0.578536i	−0.957248	+	0.289268i	$0.906588\pi$
$840$	22693.0	−	49211.7i	0.932124	−	2.02139i
$841$	1252.01			0.0513352
$842$	46486.0			1.90263
$843$	3790.91	+	1748.11i	0.154882	+	0.0714211i
$844$	−52324.2			−2.13397
$845$	15192.1			0.618490
$846$	40705.9	−	34751.6i	1.65425	−	1.41228i
$847$			2932.42i			0.118960i
$848$	7797.27			0.315754
$849$	−4255.66	−	1962.42i	−0.172031	−	0.0793287i
$850$		−	1211.96i		−	0.0489055i
$851$		−	816.229i		−	0.0328789i
$852$	31809.9	−	68982.3i	1.27910	−	2.77382i
$853$	11826.0			0.474694			0.237347	−	0.971425i	$-0.423722\pi$
$853$	11826.0			0.474694			0.237347	+	0.971425i	$0.423722\pi$
$854$	−56412.4			−2.26041
$855$	−14754.8	−	17282.8i	−0.590179	−	0.691298i
$856$		−	28810.0i		−	1.15036i
$857$	−1829.02			−0.0729033			−0.0364517	−	0.999335i	$-0.511605\pi$
$857$	−1829.02			−0.0729033			−0.0364517	+	0.999335i	$0.511605\pi$
$858$	−22832.8	+	49514.7i	−0.908505	+	1.97017i
$859$	−27224.1			−1.08134			−0.540672	−	0.841234i	$-0.681830\pi$
$859$	−27224.1			−1.08134			−0.540672	+	0.841234i	$0.681830\pi$
$860$		−	23248.4i		−	0.921819i
$861$	−7518.85	+	16305.2i	−0.297609	+	0.645390i
$862$		−	387.595i		−	0.0153150i
$863$		−	331.409i		−	0.0130722i	−0.999979	−	0.00653609i	$-0.997919\pi$
$863$		−	331.409i		−	0.0130722i	0.999979	−	0.00653609i	$-0.00208052\pi$
$864$	398.055	+	1413.07i	0.0156737	+	0.0556406i
$865$			10862.5i			0.426977i
$866$		−	27315.1i		−	1.07183i
$867$	22877.9	+	10549.7i	0.896163	+	0.413248i
$868$	66622.3			2.60519
$869$		−	44029.8i		−	1.71877i
$870$	−15686.9	+	34018.3i	−0.611305	+	1.32567i
$871$	16463.1	−	29337.7i	0.640447	−	1.14130i
$872$		−	44641.6i		−	1.73366i
$873$	13804.0	−	11784.8i	0.535159	−	0.456878i
$874$		−	1004.73i		−	0.0388850i
$875$		−	42309.5i		−	1.63465i
$876$	−57830.7	−	26667.5i	−2.23050	−	1.02855i
$877$	−49380.6			−1.90133			−0.950663	−	0.310225i	$-0.899596\pi$
$877$	−49380.6			−1.90133			−0.950663	+	0.310225i	$0.899596\pi$
$878$	12328.7			0.473887
$879$	7170.81	−	15550.5i	0.275160	−	0.596706i
$880$	20648.4			0.790976
$881$			23956.7i			0.916142i	0.888916	+	0.458071i	$0.151459\pi$
$881$			23956.7i			0.916142i	−0.888916	+	0.458071i	$0.848541\pi$
$882$	37660.7	+	44113.4i	1.43776	+	1.68410i
$883$		−	21441.0i		−	0.817154i	−0.912724	−	0.408577i	$-0.866025\pi$
$883$		−	21441.0i		−	0.817154i	0.912724	−	0.408577i	$-0.133975\pi$
$884$	7821.01			0.297567
$885$	14343.9	−	31105.9i	0.544819	−	1.18148i
$886$	84547.2			3.20589
$887$			22190.8i			0.840015i	0.907521	+	0.420007i	$0.137972\pi$
$887$			22190.8i			0.840015i	−0.907521	+	0.420007i	$0.862028\pi$
$888$	62417.0	+	28782.4i	2.35876	+	1.08770i
$889$		−	62598.2i		−	2.36162i
$890$		−	38392.8i		−	1.44599i
$891$	4003.73	−	25211.4i	0.150539	−	0.947940i
$892$	−19662.2			−0.738048
$893$			35201.2i			1.31911i
$894$	34209.4	−	74186.0i	1.27979	−	2.77534i
$895$	20604.2			0.769522
$896$		−	71099.6i		−	2.65097i
$897$	−686.243	−	316.448i	−0.0255440	−	0.0117791i
$898$			85556.7i			3.17936i
$899$	−22830.9			−0.846999
$900$	−8585.89	−	10057.0i	−0.317996	−	0.372480i
$901$		−	1031.01i		−	0.0381218i
$902$	−21128.1			−0.779919
$903$	19939.6	+	9194.78i	0.734827	+	0.338852i
$904$	−13435.4			−0.494308
$905$	17866.7			0.656253
$906$	22448.0	+	10351.5i	0.823163	+	0.379586i
$907$	−6600.85			−0.241651			−0.120826	−	0.992674i	$-0.538554\pi$
$907$	−6600.85			−0.241651			−0.120826	+	0.992674i	$0.538554\pi$
$908$		−	55299.2i		−	2.02111i
$909$	−17012.2	−	19927.1i	−0.620748	−	0.727106i
$910$	81341.9			2.96314
$911$			24339.7i			0.885191i	0.896721	+	0.442596i	$0.145942\pi$
$911$			24339.7i			0.885191i	−0.896721	+	0.442596i	$0.854058\pi$
$912$	24878.7	+	11472.3i	0.903306	+	0.416542i
$913$			27757.9i			1.00619i
$914$	59530.6			2.15437
$915$	8713.36	−	18895.6i	0.314814	−	0.682700i
$916$		−	84736.4i		−	3.05652i
$917$	8770.46			0.315841
$918$	−5301.62	+	1493.45i	−0.190609	+	0.0536940i
$919$			9187.27i			0.329772i	0.986313	+	0.164886i	$0.0527256\pi$
$919$			9187.27i			0.329772i	−0.986313	+	0.164886i	$0.947274\pi$
$920$			883.781i			0.0316711i
$921$	8876.60	+	4093.27i	0.317583	+	0.146447i
$922$			5890.16i			0.210393i
$923$	56525.2			2.01576
$924$	−33819.6	+	73340.6i	−1.20410	+	2.61118i
$925$	10628.0			0.377780
$926$			84360.2i			2.99379i
$927$	5472.33	+	6409.95i	0.193889	+	0.227109i
$928$			1591.67i			0.0563028i
$929$	33087.6			1.16853			0.584267	−	0.811561i	$-0.301382\pi$
$929$	33087.6			1.16853			0.584267	+	0.811561i	$0.301382\pi$
$930$	−15479.3	+	33568.2i	−0.545793	+	1.18360i
$931$	−38147.8			−1.34291
$932$	−71468.0			−2.51181
$933$	−38983.8	−	17976.6i	−1.36792	−	0.630792i
$934$			19700.6i			0.690176i
$935$		−	2730.27i		−	0.0954966i
$936$	48397.6	−	41318.2i	1.69009	−	1.44287i
$937$			22288.5i			0.777090i	0.921430	+	0.388545i	$0.127022\pi$
$937$			22288.5i			0.777090i	−0.921430	+	0.388545i	$0.872978\pi$
$938$	36681.1	−	65366.9i	1.27685	−	2.27538i
$939$	−5880.06	+	12751.4i	−0.204354	+	0.443159i
$940$		−	62458.9i		−	2.16722i
$941$	−16941.5			−0.586906			−0.293453	−	0.955974i	$-0.594804\pi$
$941$	−16941.5			−0.586906			−0.293453	+	0.955974i	$0.594804\pi$
$942$	−90080.0	−	41538.7i	−3.11567	−	1.43673i
$943$		−	292.822i		−	0.0101120i
$944$			41296.2i			1.42381i
$945$	−36655.4	+	10325.7i	−1.26180	+	0.355444i
$946$			25837.4i			0.887999i
$947$			28678.0i			0.984064i	0.870577	+	0.492032i	$0.163746\pi$
$947$			28678.0i			0.984064i	−0.870577	+	0.492032i	$0.836254\pi$
$948$	−43405.8	+	94129.0i	−1.48708	+	3.22486i
$949$		−	47387.4i		−	1.62093i
$950$	13082.4			0.446790
$951$	−12306.3	+	26687.2i	−0.419621	+	0.909982i
$952$	8638.80			0.294102
$953$		−	35200.5i		−	1.19649i	−0.801312	−	0.598246i	$-0.795864\pi$
$953$		−	35200.5i		−	1.19649i	0.801312	−	0.598246i	$-0.204136\pi$
$954$	−10987.1	−	12869.5i	−0.372871	−	0.436758i
$955$	28754.7			0.974325
$956$	15928.7			0.538883
$957$	11589.7	−	25133.2i	0.391475	−	0.848945i
$958$		−	73908.3i		−	2.49255i
$959$		−	44229.4i		−	1.48930i
$960$	24599.7	+	11343.7i	0.827032	+	0.381370i
$961$	7262.22			0.243772
$962$			103169.i			3.45769i
$963$	−15397.5	+	13145.2i	−0.515241	+	0.439874i
$964$	−1597.68			−0.0533795
$965$	44865.8			1.49666
$966$	−1529.01	−	705.074i	−0.0509266	−	0.0234838i
$967$	2946.49			0.0979863			0.0489931	−	0.998799i	$-0.484399\pi$
$967$	2946.49			0.0979863			0.0489931	+	0.998799i	$0.484399\pi$
$968$	4027.11			0.133715
$969$	1516.94	−	3289.62i	0.0502903	−	0.109059i
$970$		−	31861.2i		−	1.05464i
$971$		−	25998.0i		−	0.859232i	−0.903012	−	0.429616i	$-0.858649\pi$
$971$		−	25998.0i		−	0.859232i	0.903012	−	0.429616i	$-0.141351\pi$
$972$	−33413.5	+	49951.2i	−1.10261	+	1.64834i
$973$	−53024.2			−1.74705
$974$			50066.2i			1.64705i
$975$	4120.42	−	8935.46i	0.135343	−	0.293501i
$976$			25085.8i			0.822723i
$977$			24525.0i			0.803097i	0.915838	+	0.401548i	$0.131528\pi$
$977$			24525.0i			0.803097i	−0.915838	+	0.401548i	$0.868472\pi$
$978$	−92163.9	−	42499.6i	−3.01337	−	1.38956i
$979$			28365.1i			0.925998i
$980$	67687.3			2.20632
$981$	−23858.7	+	20368.8i	−0.776503	+	0.662920i
$982$		−	26865.9i		−	0.873040i
$983$	14349.3			0.465587			0.232793	−	0.972526i	$-0.425213\pi$
$983$	14349.3			0.465587			0.232793	+	0.972526i	$0.425213\pi$
$984$	22392.1	+	10325.7i	0.725441	+	0.334523i
$985$	−28671.5			−0.927462
$986$	−5971.70			−0.192878
$987$	53569.5	+	24702.6i	1.72760	+	0.796648i
$988$			84423.8i			2.71850i
$989$	−358.091			−0.0115133
$990$	−29095.5	−	34080.6i	−0.934056	−	1.09409i
$991$		−	43233.5i		−	1.38583i	−0.721019	−	0.692915i	$-0.756326\pi$
$991$		−	43233.5i		−	1.38583i	0.721019	−	0.692915i	$-0.243674\pi$
$992$			1570.61i			0.0502690i
$993$	8054.23	−	17466.2i	0.257395	−	0.558182i
$994$	125943.			4.01878
$995$	−12672.3			−0.403757
$996$	27364.5	−	59342.2i	0.870560	−	1.88788i
$997$	−18562.1			−0.589637			−0.294819	−	0.955553i	$-0.595259\pi$
$997$	−18562.1			−0.589637			−0.294819	+	0.955553i	$0.595259\pi$
$998$		−	43266.2i		−	1.37231i
$999$	−13096.5	−	46491.4i	−0.414768	−	1.47240i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.4.d.b.200.8	yes	64
3.2	odd	2	inner	201.4.d.b.200.58	yes	64
67.66	odd	2	inner	201.4.d.b.200.57	yes	64
201.200	even	2	inner	201.4.d.b.200.7	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.4.d.b.200.7	✓	64	201.200	even	2	inner
201.4.d.b.200.8	yes	64	1.1	even	1	trivial
201.4.d.b.200.57	yes	64	67.66	odd	2	inner
201.4.d.b.200.58	yes	64	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 201 = 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	201.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-4.88518 q^{2} +(4.71863 + 2.17590i) q^{3} +15.8650 q^{4} -9.70204 q^{5} +(-23.0513 - 10.6297i) q^{6} -27.9776i q^{7} -38.4219 q^{8} +(17.5309 + 20.5346i) q^{9} +O(q^{10})\)	\(q-4.88518 q^{2} +(4.71863 + 2.17590i) q^{3} +15.8650 q^{4} -9.70204 q^{5} +(-23.0513 - 10.6297i) q^{6} -27.9776i q^{7} -38.4219 q^{8} +(17.5309 + 20.5346i) q^{9} +47.3962 q^{10} -35.0170 q^{11} +(74.8609 + 34.5207i) q^{12} +61.3422i q^{13} +136.676i q^{14} +(-45.7803 - 21.1107i) q^{15} +60.7779 q^{16} -8.03644i q^{17} +(-85.6415 - 100.315i) q^{18} +86.7493 q^{19} -153.923 q^{20} +(60.8767 - 132.016i) q^{21} +171.064 q^{22} +2.37084i q^{23} +(-181.298 - 83.6023i) q^{24} -30.8704 q^{25} -299.668i q^{26} +(38.0404 + 135.040i) q^{27} -443.865i q^{28} +152.108i q^{29} +(223.645 + 103.130i) q^{30} +150.096i q^{31} +10.4640 q^{32} +(-165.232 - 76.1936i) q^{33} +39.2595i q^{34} +271.440i q^{35} +(278.127 + 325.781i) q^{36} -344.278 q^{37} -423.786 q^{38} +(-133.475 + 289.451i) q^{39} +372.771 q^{40} -123.510 q^{41} +(-297.394 + 644.922i) q^{42} +151.039i q^{43} -555.544 q^{44} +(-170.085 - 199.227i) q^{45} -11.5820i q^{46} +405.781i q^{47} +(286.788 + 132.247i) q^{48} -439.748 q^{49} +150.807 q^{50} +(17.4865 - 37.9210i) q^{51} +973.193i q^{52} +128.291 q^{53} +(-185.834 - 659.697i) q^{54} +339.736 q^{55} +1074.95i q^{56} +(409.337 + 188.758i) q^{57} -743.077i q^{58} +679.460i q^{59} +(-726.304 - 334.921i) q^{60} +412.746i q^{61} -733.246i q^{62} +(574.509 - 490.472i) q^{63} -537.342 q^{64} -595.145i q^{65} +(807.188 + 372.219i) q^{66} +(-478.262 - 268.381i) q^{67} -127.498i q^{68} +(-5.15873 + 11.1871i) q^{69} -1326.03i q^{70} -921.473i q^{71} +(-673.569 - 788.977i) q^{72} -772.508 q^{73} +1681.86 q^{74} +(-145.666 - 67.1710i) q^{75} +1376.28 q^{76} +979.692i q^{77} +(652.048 - 1414.02i) q^{78} +1257.39i q^{79} -589.670 q^{80} +(-114.337 + 719.978i) q^{81} +603.366 q^{82} -792.698i q^{83} +(965.808 - 2094.43i) q^{84} +77.9699i q^{85} -737.855i q^{86} +(-330.974 + 717.743i) q^{87} +1345.42 q^{88} -810.039i q^{89} +(830.897 + 973.261i) q^{90} +1716.21 q^{91} +37.6134i q^{92} +(-326.594 + 708.247i) q^{93} -1982.31i q^{94} -841.645 q^{95} +(49.3758 + 22.7687i) q^{96} -672.231i q^{97} +2148.25 q^{98} +(-613.878 - 719.058i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 268 q^{4} - 46 q^{6} + 22 q^{9}+O(q^{10}) \) 64 * q + 268 * q^4 - 46 * q^6 + 22 * q^9	\( 64 q + 268 q^{4} - 46 q^{6} + 22 q^{9} - 36 q^{10} + 20 q^{15} + 556 q^{16} + 128 q^{19} + 96 q^{22} - 904 q^{24} + 2080 q^{25} - 236 q^{33} - 1574 q^{36} + 1004 q^{37} - 176 q^{39} - 648 q^{40} - 1220 q^{49} + 2188 q^{54} - 1344 q^{55} + 550 q^{60} + 4336 q^{64} - 3512 q^{67} + 3968 q^{73} - 3316 q^{76} - 1170 q^{81} + 4020 q^{82} - 9270 q^{84} + 2436 q^{88} + 746 q^{90} - 3408 q^{91} - 1412 q^{93} - 7032 q^{96}+O(q^{100}) \) 64 * q + 268 * q^4 - 46 * q^6 + 22 * q^9 - 36 * q^10 + 20 * q^15 + 556 * q^16 + 128 * q^19 + 96 * q^22 - 904 * q^24 + 2080 * q^25 - 236 * q^33 - 1574 * q^36 + 1004 * q^37 - 176 * q^39 - 648 * q^40 - 1220 * q^49 + 2188 * q^54 - 1344 * q^55 + 550 * q^60 + 4336 * q^64 - 3512 * q^67 + 3968 * q^73 - 3316 * q^76 - 1170 * q^81 + 4020 * q^82 - 9270 * q^84 + 2436 * q^88 + 746 * q^90 - 3408 * q^91 - 1412 * q^93 - 7032 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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