LMFDB - Embedded newform 354.7.d.a.235.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [354,7,Mod(235,354)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(354, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("354.235");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 354 = 2 \cdot 3 \cdot 59 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	354.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:	$81.4391456014$
Analytic rank:	$0$
Dimension:	$60$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			235.7
Character	$\chi$	$=$	354.235
Dual form			354.7.d.a.235.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.65685i q^{2} -15.5885 q^{3} -32.0000 q^{4} +133.407 q^{5} +88.1816i q^{6} -65.3612 q^{7} +181.019i q^{8} +243.000 q^{9} +O(q^{10})$	\(q-5.65685i q^{2} -15.5885 q^{3} -32.0000 q^{4} +133.407 q^{5} +88.1816i q^{6} -65.3612 q^{7} +181.019i q^{8} +243.000 q^{9} -754.665i q^{10} +2068.65i q^{11} +498.831 q^{12} +1207.45i q^{13} +369.739i q^{14} -2079.61 q^{15} +1024.00 q^{16} -6518.71 q^{17} -1374.62i q^{18} -10714.7 q^{19} -4269.03 q^{20} +1018.88 q^{21} +11702.1 q^{22} -16945.3i q^{23} -2821.81i q^{24} +2172.47 q^{25} +6830.38 q^{26} -3788.00 q^{27} +2091.56 q^{28} +40004.1 q^{29} +11764.1i q^{30} +34198.9i q^{31} -5792.62i q^{32} -32247.1i q^{33} +36875.4i q^{34} -8719.65 q^{35} -7776.00 q^{36} -58831.2i q^{37} +60611.4i q^{38} -18822.3i q^{39} +24149.3i q^{40} +32389.4 q^{41} -5763.66i q^{42} +44556.9i q^{43} -66196.9i q^{44} +32417.9 q^{45} -95857.2 q^{46} -161964. i q^{47} -15962.6 q^{48} -113377. q^{49} -12289.3i q^{50} +101617. q^{51} -38638.5i q^{52} +167124. q^{53} +21428.1i q^{54} +275973. i q^{55} -11831.6i q^{56} +167025. q^{57} -226297. i q^{58} +(113416. + 171223. i) q^{59} +66547.6 q^{60} -278813. i q^{61} +193458. q^{62} -15882.8 q^{63} -32768.0 q^{64} +161083. i q^{65} -182417. q^{66} -273291. i q^{67} +208599. q^{68} +264151. i q^{69} +49325.8i q^{70} -83863.8 q^{71} +43987.7i q^{72} -575773. i q^{73} -332799. q^{74} -33865.4 q^{75} +342870. q^{76} -135210. i q^{77} -106475. q^{78} +398418. q^{79} +136609. q^{80} +59049.0 q^{81} -183222. i q^{82} -847454. i q^{83} -32604.2 q^{84} -869642. q^{85} +252052. q^{86} -623602. q^{87} -374466. q^{88} +211856. i q^{89} -183384. i q^{90} -78920.5i q^{91} +542250. i q^{92} -533109. i q^{93} -916204. q^{94} -1.42941e6 q^{95} +90298.0i q^{96} +101556. i q^{97} +641357. i q^{98} +502683. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 1920 q^{4} + 408 q^{7} + 14580 q^{9}+O(q^{10}) $ 60 * q - 1920 * q^4 + 408 * q^7 + 14580 * q^9	$ 60 q - 1920 q^{4} + 408 q^{7} + 14580 q^{9} + 4536 q^{15} + 61440 q^{16} - 15840 q^{17} - 5616 q^{19} - 17472 q^{22} + 226260 q^{25} - 34048 q^{26} - 13056 q^{28} - 75392 q^{29} + 278000 q^{35} - 466560 q^{36} + 67376 q^{41} + 209856 q^{46} + 269100 q^{49} - 206064 q^{51} + 490000 q^{53} - 373248 q^{57} - 863472 q^{59} - 145152 q^{60} - 155072 q^{62} + 99144 q^{63} - 1966080 q^{64} - 404352 q^{66} + 506880 q^{68} - 2041856 q^{71} - 2146176 q^{74} + 808704 q^{75} + 179712 q^{76} + 228096 q^{78} + 670248 q^{79} + 3542940 q^{81} + 873408 q^{85} + 1832576 q^{86} - 2568024 q^{87} + 559104 q^{88} + 1049472 q^{94} - 245856 q^{95}+O(q^{100}) $ 60 * q - 1920 * q^4 + 408 * q^7 + 14580 * q^9 + 4536 * q^15 + 61440 * q^16 - 15840 * q^17 - 5616 * q^19 - 17472 * q^22 + 226260 * q^25 - 34048 * q^26 - 13056 * q^28 - 75392 * q^29 + 278000 * q^35 - 466560 * q^36 + 67376 * q^41 + 209856 * q^46 + 269100 * q^49 - 206064 * q^51 + 490000 * q^53 - 373248 * q^57 - 863472 * q^59 - 145152 * q^60 - 155072 * q^62 + 99144 * q^63 - 1966080 * q^64 - 404352 * q^66 + 506880 * q^68 - 2041856 * q^71 - 2146176 * q^74 + 808704 * q^75 + 179712 * q^76 + 228096 * q^78 + 670248 * q^79 + 3542940 * q^81 + 873408 * q^85 + 1832576 * q^86 - 2568024 * q^87 + 559104 * q^88 + 1049472 * q^94 - 245856 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/354\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$-1$	$1$

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 $

$2$		−	5.65685i		−	0.707107i
$2$		−	5.65685i		−	0.707107i
$3$	−15.5885			−0.577350
$3$	−15.5885			−0.577350
$4$	−32.0000			−0.500000
$5$	133.407			1.06726			0.533629	−	0.845719i	$-0.320828\pi$
$5$	133.407			1.06726			0.533629	+	0.845719i	$0.320828\pi$
$6$			88.1816i			0.408248i
$7$	−65.3612			−0.190557			−0.0952787	−	0.995451i	$-0.530374\pi$
$7$	−65.3612			−0.190557			−0.0952787	+	0.995451i	$0.530374\pi$
$8$			181.019i			0.353553i
$9$	243.000			0.333333
$10$		−	754.665i		−	0.754665i
$11$			2068.65i			1.55421i	0.629371	+	0.777105i	$0.283313\pi$
$11$			2068.65i			1.55421i	−0.629371	+	0.777105i	$0.716687\pi$
$12$	498.831			0.288675
$13$			1207.45i			0.549591i	0.961503	+	0.274796i	$0.0886102\pi$
$13$			1207.45i			0.549591i	−0.961503	+	0.274796i	$0.911390\pi$
$14$			369.739i			0.134744i
$15$	−2079.61			−0.616181
$16$	1024.00			0.250000
$17$	−6518.71			−1.32683			−0.663414	−	0.748253i	$-0.730893\pi$
$17$	−6518.71			−1.32683			−0.663414	+	0.748253i	$0.730893\pi$
$18$		−	1374.62i		−	0.235702i
$19$	−10714.7			−1.56213			−0.781067	−	0.624447i	$-0.785324\pi$
$19$	−10714.7			−1.56213			−0.781067	+	0.624447i	$0.785324\pi$
$20$	−4269.03			−0.533629
$21$	1018.88			0.110018
$22$	11702.1			1.09899
$23$		−	16945.3i		−	1.39273i	−0.717689	−	0.696364i	$-0.754800\pi$
$23$		−	16945.3i		−	1.39273i	0.717689	−	0.696364i	$-0.245200\pi$
$24$		−	2821.81i		−	0.204124i
$25$	2172.47			0.139038
$26$	6830.38			0.388620
$27$	−3788.00			−0.192450
$28$	2091.56			0.0952787
$29$	40004.1			1.64025			0.820126	−	0.572183i	$-0.193903\pi$
$29$	40004.1			1.64025			0.820126	+	0.572183i	$0.193903\pi$
$30$			11764.1i			0.435706i
$31$			34198.9i			1.14796i	0.818869	+	0.573981i	$0.194602\pi$
$31$			34198.9i			1.14796i	−0.818869	+	0.573981i	$0.805398\pi$
$32$		−	5792.62i		−	0.176777i
$33$		−	32247.1i		−	0.897324i
$34$			36875.4i			0.938209i
$35$	−8719.65			−0.203374
$36$	−7776.00			−0.166667
$37$		−	58831.2i		−	1.16145i	−0.814098	−	0.580727i	$-0.802768\pi$
$37$		−	58831.2i		−	1.16145i	0.814098	−	0.580727i	$-0.197232\pi$
$38$			60611.4i			1.10460i
$39$		−	18822.3i		−	0.317307i
$40$			24149.3i			0.377332i
$41$	32389.4			0.469950			0.234975	−	0.972001i	$-0.424499\pi$
$41$	32389.4			0.469950			0.234975	+	0.972001i	$0.424499\pi$
$42$		−	5763.66i		−	0.0777948i
$43$			44556.9i			0.560415i	0.959939	+	0.280208i	$0.0904033\pi$
$43$			44556.9i			0.560415i	−0.959939	+	0.280208i	$0.909597\pi$
$44$		−	66196.9i		−	0.777105i
$45$	32417.9			0.355752
$46$	−95857.2			−0.984807
$47$		−	161964.i		−	1.56000i	−0.625782	−	0.779998i	$-0.715220\pi$
$47$		−	161964.i		−	1.56000i	0.625782	−	0.779998i	$-0.284780\pi$
$48$	−15962.6			−0.144338
$49$	−113377.			−0.963688
$50$		−	12289.3i		−	0.0983146i
$51$	101617.			0.766044
$52$		−	38638.5i		−	0.274796i
$53$	167124.			1.12256			0.561281	−	0.827626i	$-0.310309\pi$
$53$	167124.			1.12256			0.561281	+	0.827626i	$0.310309\pi$
$54$			21428.1i			0.136083i
$55$			275973.i			1.65874i
$56$		−	11831.6i		−	0.0673722i
$57$	167025.			0.901899
$58$		−	226297.i		−	1.15983i
$59$	113416.	+	171223.i	0.552228	+	0.833693i
$59$	113416.	+	171223.i	0.552228	+	0.833693i
$60$	66547.6			0.308091
$61$		−	278813.i		−	1.22835i	−0.789169	−	0.614176i	$-0.789488\pi$
$61$		−	278813.i		−	1.22835i	0.789169	−	0.614176i	$-0.210512\pi$
$62$	193458.			0.811732
$63$	−15882.8			−0.0635192
$64$	−32768.0			−0.125000
$65$			161083.i			0.586555i
$66$	−182417.			−0.634504
$67$		−	273291.i		−	0.908659i	−0.890834	−	0.454329i	$-0.849879\pi$
$67$		−	273291.i		−	0.908659i	0.890834	−	0.454329i	$-0.150121\pi$
$68$	208599.			0.663414
$69$			264151.i			0.804092i
$70$			49325.8i			0.143807i
$71$	−83863.8			−0.234315			−0.117157	−	0.993113i	$-0.537378\pi$
$71$	−83863.8			−0.234315			−0.117157	+	0.993113i	$0.537378\pi$
$72$			43987.7i			0.117851i
$73$		−	575773.i		−	1.48007i	−0.672567	−	0.740036i	$-0.734808\pi$
$73$		−	575773.i		−	1.48007i	0.672567	−	0.740036i	$-0.265192\pi$
$74$	−332799.			−0.821272
$75$	−33865.4			−0.0802736
$76$	342870.			0.781067
$77$		−	135210.i		−	0.296166i
$78$	−106475.			−0.224370
$79$	398418.			0.808085			0.404043	−	0.914740i	$-0.367605\pi$
$79$	398418.			0.808085			0.404043	+	0.914740i	$0.367605\pi$
$80$	136609.			0.266814
$81$	59049.0			0.111111
$82$		−	183222.i		−	0.332305i
$83$		−	847454.i		−	1.48211i	−0.671442	−	0.741057i	$-0.734325\pi$
$83$		−	847454.i		−	1.48211i	0.671442	−	0.741057i	$-0.265675\pi$
$84$	−32604.2			−0.0550092
$85$	−869642.			−1.41607
$86$	252052.			0.396273
$87$	−623602.			−0.947000
$88$	−374466.			−0.549496
$89$			211856.i			0.300518i	0.988647	+	0.150259i	$0.0480108\pi$
$89$			211856.i			0.300518i	−0.988647	+	0.150259i	$0.951989\pi$
$90$		−	183384.i		−	0.251555i
$91$		−	78920.5i		−	0.104729i
$92$			542250.i			0.696364i
$93$		−	533109.i		−	0.662776i
$94$	−916204.			−1.10308
$95$	−1.42941e6			−1.66720
$96$			90298.0i			0.102062i
$97$			101556.i			0.111274i	0.998451	+	0.0556368i	$0.0177189\pi$
$97$			101556.i			0.111274i	−0.998451	+	0.0556368i	$0.982281\pi$
$98$			641357.i			0.681430i
$99$			502683.i			0.518070i
$100$	−69519.0			−0.0695190
$101$		−	240388.i		−	0.233318i	−0.993172	−	0.116659i	$-0.962782\pi$
$101$		−	240388.i		−	0.233318i	0.993172	−	0.116659i	$-0.0372185\pi$
$102$		−	574830.i		−	0.541675i
$103$		−	951974.i		−	0.871191i	−0.900142	−	0.435596i	$-0.856538\pi$
$103$		−	951974.i		−	0.871191i	0.900142	−	0.435596i	$-0.143462\pi$
$104$	−218572.			−0.194310
$105$	135926.			0.117418
$106$		−	945393.i		−	0.793771i
$107$	−1.04972e6			−0.856883			−0.428441	−	0.903570i	$-0.640937\pi$
$107$	−1.04972e6			−0.856883			−0.428441	+	0.903570i	$0.640937\pi$
$108$	121216.			0.0962250
$109$		−	884215.i		−	0.682776i	−0.939922	−	0.341388i	$-0.889103\pi$
$109$		−	884215.i		−	0.682776i	0.939922	−	0.341388i	$-0.110897\pi$
$110$	1.56114e6			1.17291
$111$			917087.i			0.670566i
$112$	−66929.9			−0.0476394
$113$		−	135170.i		−	0.0936798i	−0.998902	−	0.0468399i	$-0.985085\pi$
$113$		−	135170.i		−	0.0936798i	0.998902	−	0.0468399i	$-0.0149151\pi$
$114$		−	944838.i		−	0.637739i
$115$		−	2.26063e6i		−	1.48640i
$116$	−1.28013e6			−0.820126
$117$			293411.i			0.183197i
$118$	968584.	−	641578.i	0.589510	−	0.390484i
$119$	426070.			0.252837
$120$		−	376450.i		−	0.217853i
$121$	−2.50777e6			−1.41557
$122$	−1.57720e6			−0.868576
$123$	−504901.			−0.271326
$124$		−	1.09437e6i		−	0.573981i
$125$	−1.79466e6			−0.918868
$126$			89846.5i			0.0449148i
$127$	−3.60298e6			−1.75894			−0.879469	−	0.475955i	$-0.842102\pi$
$127$	−3.60298e6			−1.75894			−0.879469	+	0.475955i	$0.842102\pi$
$128$			185364.i			0.0883883i
$129$		−	694574.i		−	0.323556i
$130$	911222.			0.414757
$131$		−	2.16293e6i		−	0.962117i	−0.876688	−	0.481059i	$-0.840252\pi$
$131$		−	2.16293e6i		−	0.962117i	0.876688	−	0.481059i	$-0.159748\pi$
$132$			1.03191e6i			0.448662i
$133$	700324.			0.297676
$134$	−1.54597e6			−0.642519
$135$	−505346.			−0.205394
$136$		−	1.18001e6i		−	0.469105i
$137$	4.91246e6			1.91046			0.955229	−	0.295866i	$-0.0956082\pi$
$137$	4.91246e6			1.91046			0.955229	+	0.295866i	$0.0956082\pi$
$138$	1.49427e6			0.568579
$139$	−4.92793e6			−1.83493			−0.917466	−	0.397815i	$-0.869769\pi$
$139$	−4.92793e6			−1.83493			−0.917466	+	0.397815i	$0.869769\pi$
$140$	279029.			0.101687
$141$			2.52476e6i			0.900664i
$142$			474405.i			0.165685i
$143$	−2.49780e6			−0.854180
$144$	248832.			0.0833333
$145$	5.33683e6			1.75057
$146$	−3.25707e6			−1.04657
$147$	1.76737e6			0.556385
$148$			1.88260e6i			0.580727i
$149$		−	1.61868e6i		−	0.489330i	−0.969608	−	0.244665i	$-0.921322\pi$
$149$		−	1.61868e6i		−	0.489330i	0.969608	−	0.244665i	$-0.0786780\pi$
$150$			191572.i			0.0567620i
$151$			6.10499e6i			1.77319i	0.462551	+	0.886593i	$0.346934\pi$
$151$			6.10499e6i			1.77319i	−0.462551	+	0.886593i	$0.653066\pi$
$152$		−	1.93956e6i		−	0.552298i
$153$	−1.58405e6			−0.442276
$154$	−764862.			−0.209421
$155$			4.56238e6i			1.22517i
$156$			602314.i			0.158653i
$157$			2.66985e6i			0.689903i	0.938621	+	0.344951i	$0.112105\pi$
$157$			2.66985e6i			0.689903i	−0.938621	+	0.344951i	$0.887895\pi$
$158$		−	2.25379e6i		−	0.571403i
$159$	−2.60520e6			−0.648111
$160$		−	772777.i		−	0.188666i
$161$			1.10757e6i			0.265395i
$162$		−	334032.i		−	0.0785674i
$163$	5.95721e6			1.37556			0.687781	−	0.725918i	$-0.258585\pi$
$163$	5.95721e6			1.37556			0.687781	+	0.725918i	$0.258585\pi$
$164$	−1.03646e6			−0.234975
$165$		−	4.30200e6i		−	0.957675i
$166$	−4.79392e6			−1.04801
$167$	−1.66030e6			−0.356482			−0.178241	−	0.983987i	$-0.557041\pi$
$167$	−1.66030e6			−0.356482			−0.178241	+	0.983987i	$0.557041\pi$
$168$			184437.i			0.0388974i
$169$	3.36887e6			0.697949
$170$			4.91944e6i			1.00131i
$171$	−2.60367e6			−0.520711
$172$		−	1.42582e6i		−	0.280208i
$173$		−	4.77599e6i		−	0.922411i	−0.887293	−	0.461206i	$-0.847417\pi$
$173$		−	4.77599e6i		−	0.922411i	0.887293	−	0.461206i	$-0.152583\pi$
$174$			3.52763e6i			0.669630i
$175$	−141995.			−0.0264947
$176$			2.11830e6i			0.388553i
$177$	−1.76798e6	−	2.66910e6i	−0.318829	−	0.481333i
$178$	1.19844e6			0.212499
$179$			2.17479e6i			0.379192i	0.981862	+	0.189596i	$0.0607178\pi$
$179$			2.17479e6i			0.379192i	−0.981862	+	0.189596i	$0.939282\pi$
$180$	−1.03737e6			−0.177876
$181$	−8.23021e6			−1.38795			−0.693977	−	0.719997i	$-0.744143\pi$
$181$	−8.23021e6			−1.38795			−0.693977	+	0.719997i	$0.744143\pi$
$182$	−446442.			−0.0740544
$183$			4.34626e6i			0.709189i
$184$	3.06743e6			0.492404
$185$		−	7.84850e6i		−	1.23957i
$186$	−3.01572e6			−0.468654
$187$		−	1.34849e7i		−	2.06217i
$188$			5.18283e6i			0.779998i
$189$	247588.			0.0366728
$190$			8.08599e6i			1.17889i
$191$			1.81298e6i			0.260192i	0.991501	+	0.130096i	$0.0415285\pi$
$191$			1.81298e6i			0.260192i	−0.991501	+	0.130096i	$0.958472\pi$
$192$	510803.			0.0721688
$193$	−5.75396e6			−0.800378			−0.400189	−	0.916433i	$-0.631055\pi$
$193$	−5.75396e6			−0.800378			−0.400189	+	0.916433i	$0.631055\pi$
$194$	574490.			0.0786823
$195$		−	2.51103e6i		−	0.338648i
$196$	3.62806e6			0.481844
$197$	−7.56351e6			−0.989293			−0.494646	−	0.869094i	$-0.664702\pi$
$197$	−7.56351e6			−0.989293			−0.494646	+	0.869094i	$0.664702\pi$
$198$	2.84360e6			0.366331
$199$	1.32128e7			1.67662			0.838310	−	0.545194i	$-0.183544\pi$
$199$	1.32128e7			1.67662			0.838310	+	0.545194i	$0.183544\pi$
$200$			393259.i			0.0491573i
$201$			4.26018e6i			0.524614i
$202$	−1.35984e6			−0.164981
$203$	−2.61472e6			−0.312562
$204$	−3.25173e6			−0.383022
$205$	4.32098e6			0.501558
$206$	−5.38518e6			−0.616025
$207$		−	4.11771e6i		−	0.464243i
$208$			1.23643e6i			0.137398i
$209$		−	2.21650e7i		−	2.42788i
$210$		−	768913.i		−	0.0830270i
$211$			6.64381e6i			0.707245i	0.935388	+	0.353623i	$0.115050\pi$
$211$			6.64381e6i			0.707245i	−0.935388	+	0.353623i	$0.884950\pi$
$212$	−5.34795e6			−0.561281
$213$	1.30731e6			0.135282
$214$			5.93810e6i			0.605908i
$215$			5.94421e6i			0.598107i
$216$		−	685700.i		−	0.0680414i
$217$		−	2.23528e6i		−	0.218753i
$218$	−5.00187e6			−0.482795
$219$			8.97542e6i			0.854520i
$220$		−	8.83114e6i		−	0.829371i
$221$		−	7.87103e6i		−	0.729213i
$222$	5.18783e6			0.474162
$223$	−4.75680e6			−0.428944			−0.214472	−	0.976730i	$-0.568803\pi$
$223$	−4.75680e6			−0.428944			−0.214472	+	0.976730i	$0.568803\pi$
$224$			378613.i			0.0336861i
$225$	527910.			0.0463460
$226$	−764638.			−0.0662416
$227$			5.46231e6i			0.466981i	0.972359	+	0.233490i	$0.0750147\pi$
$227$			5.46231e6i			0.466981i	−0.972359	+	0.233490i	$0.924985\pi$
$228$	−5.34481e6			−0.450949
$229$		−	1.69163e7i		−	1.40863i	−0.709885	−	0.704317i	$-0.751253\pi$
$229$		−	1.69163e7i		−	1.40863i	0.709885	−	0.704317i	$-0.248747\pi$
$230$	−1.27880e7			−1.05104
$231$			2.10771e6i			0.170992i
$232$			7.24151e6i			0.579916i
$233$		−	1.16889e7i		−	0.924074i	−0.886861	−	0.462037i	$-0.847119\pi$
$233$		−	1.16889e7i		−	0.924074i	0.886861	−	0.462037i	$-0.152881\pi$
$234$	1.65978e6			0.129540
$235$		−	2.16071e7i		−	1.66492i
$236$	−3.62931e6	−	5.47914e6i	−0.276114	−	0.416847i
$237$	−6.21072e6			−0.466548
$238$		−	2.41022e6i		−	0.178783i
$239$	−1.60548e7			−1.17601			−0.588007	−	0.808856i	$-0.700087\pi$
$239$	−1.60548e7			−1.17601			−0.588007	+	0.808856i	$0.700087\pi$
$240$	−2.12952e6			−0.154045
$241$	2.11790e7			1.51305			0.756526	−	0.653964i	$-0.226895\pi$
$241$	2.11790e7			1.51305			0.756526	+	0.653964i	$0.226895\pi$
$242$			1.41861e7i			1.00096i
$243$	−920483.			−0.0641500
$244$			8.92200e6i			0.614176i
$245$	−1.51253e7			−1.02850
$246$			2.85615e6i			0.191856i
$247$		−	1.29375e7i		−	0.858535i
$248$	−6.19067e6			−0.405866
$249$			1.32105e7i			0.855699i
$250$			1.01522e7i			0.649738i
$251$	1.52170e6			0.0962293			0.0481146	−	0.998842i	$-0.484679\pi$
$251$	1.52170e6			0.0962293			0.0481146	+	0.998842i	$0.484679\pi$
$252$	508249.			0.0317596
$253$	3.50540e7			2.16459
$254$			2.03815e7i			1.24376i
$255$	1.35564e7			0.817566
$256$	1.04858e6			0.0625000
$257$	364151.			0.0214527			0.0107263	−	0.999942i	$-0.496586\pi$
$257$	364151.			0.0214527			0.0107263	+	0.999942i	$0.496586\pi$
$258$	−3.92910e6			−0.228789
$259$			3.84528e6i			0.221324i
$260$		−	5.15465e6i		−	0.293278i
$261$	9.72099e6			0.546750
$262$	−1.22354e7			−0.680320
$263$	1.73924e7			0.956078			0.478039	−	0.878339i	$-0.341348\pi$
$263$	1.73924e7			0.956078			0.478039	+	0.878339i	$0.341348\pi$
$264$	5.83735e6			0.317252
$265$	2.22955e7			1.19806
$266$		−	3.96163e6i		−	0.210489i
$267$		−	3.30251e6i		−	0.173504i
$268$			8.74531e6i			0.454329i
$269$		−	4.05072e6i		−	0.208102i	−0.994572	−	0.104051i	$-0.966820\pi$
$269$		−	4.05072e6i		−	0.208102i	0.994572	−	0.104051i	$-0.0331804\pi$
$270$			2.85867e6i			0.145235i
$271$	1.72933e7			0.868901			0.434451	−	0.900696i	$-0.356943\pi$
$271$	1.72933e7			0.868901			0.434451	+	0.900696i	$0.356943\pi$
$272$	−6.67515e6			−0.331707
$273$			1.23025e6i			0.0604652i
$274$		−	2.77891e7i		−	1.35090i
$275$			4.49408e6i			0.216094i
$276$		−	8.45285e6i		−	0.402046i
$277$	−2.02752e7			−0.953952			−0.476976	−	0.878916i	$-0.658267\pi$
$277$	−2.02752e7			−0.953952			−0.476976	+	0.878916i	$0.658267\pi$
$278$			2.78766e7i			1.29749i
$279$			8.31034e6i			0.382654i
$280$		−	1.57843e6i		−	0.0719035i
$281$	1.26122e7			0.568425			0.284213	−	0.958761i	$-0.408268\pi$
$281$	1.26122e7			0.568425			0.284213	+	0.958761i	$0.408268\pi$
$282$	1.42822e7			0.636866
$283$		−	3.26479e7i		−	1.44044i	−0.693745	−	0.720220i	$-0.744041\pi$
$283$		−	3.26479e7i		−	1.44044i	0.693745	−	0.720220i	$-0.255959\pi$
$284$	2.68364e6			0.117157
$285$	2.22824e7			0.962558
$286$			1.41297e7i			0.603997i
$287$	−2.11701e6			−0.0895525
$288$		−	1.40761e6i		−	0.0589256i
$289$	1.83560e7			0.760472
$290$		−	3.01897e7i		−	1.23784i
$291$		−	1.58311e6i		−	0.0642438i
$292$			1.84247e7i			0.740036i
$293$	2.75208e7			1.09410			0.547052	−	0.837099i	$-0.315750\pi$
$293$	2.75208e7			1.09410			0.547052	+	0.837099i	$0.315750\pi$
$294$		−	9.99776e6i		−	0.393424i
$295$	1.51305e7	+	2.28424e7i	0.589369	+	0.889765i
$296$	1.06496e7			0.410636
$297$		−	7.83605e6i		−	0.299108i
$298$	−9.15663e6			−0.346009
$299$	2.04607e7			0.765431
$300$	1.08369e6			0.0401368
$301$		−	2.91230e6i		−	0.106791i
$302$	3.45350e7			1.25383
$303$			3.74728e6i			0.134706i
$304$	−1.09718e7			−0.390534
$305$		−	3.71956e7i		−	1.31097i
$306$			8.96071e6i			0.312736i
$307$	−5.00872e7			−1.73106			−0.865530	−	0.500858i	$-0.833018\pi$
$307$	−5.00872e7			−1.73106			−0.865530	+	0.500858i	$0.833018\pi$
$308$			4.32671e6i			0.148083i
$309$			1.48398e7i			0.502982i
$310$	2.58087e7			0.866326
$311$	−4.39457e7			−1.46095			−0.730476	−	0.682939i	$-0.760702\pi$
$311$	−4.39457e7			−1.46095			−0.730476	+	0.682939i	$0.760702\pi$
$312$	3.40720e6			0.112185
$313$		−	2.27217e7i		−	0.740984i	−0.928836	−	0.370492i	$-0.879189\pi$
$313$		−	2.27217e7i		−	0.740984i	0.928836	−	0.370492i	$-0.120811\pi$
$314$	1.51030e7			0.487835
$315$	−2.11888e6			−0.0677913
$316$	−1.27494e7			−0.404043
$317$	−3.19284e7			−1.00230			−0.501151	−	0.865360i	$-0.667090\pi$
$317$	−3.19284e7			−1.00230			−0.501151	+	0.865360i	$0.667090\pi$
$318$			1.47372e7i			0.458284i
$319$			8.27546e7i			2.54930i
$320$	−4.37149e6			−0.133407
$321$	1.63635e7			0.494722
$322$	6.26534e6			0.187662
$323$	6.98458e7			2.07268
$324$	−1.88957e6			−0.0555556
$325$			2.62315e6i			0.0764140i
$326$		−	3.36991e7i		−	0.972669i
$327$			1.37835e7i			0.394201i
$328$			5.86312e6i			0.166153i
$329$			1.05861e7i			0.297269i
$330$	−2.43358e7			−0.677179
$331$	4.83498e7			1.33325			0.666623	−	0.745395i	$-0.267739\pi$
$331$	4.83498e7			1.33325			0.666623	+	0.745395i	$0.267739\pi$
$332$			2.71185e7i			0.741057i
$333$		−	1.42960e7i		−	0.387151i
$334$			9.39209e6i			0.252071i
$335$		−	3.64590e7i		−	0.969773i
$336$	1.04333e6			0.0275046
$337$			6.89179e7i			1.80070i	0.435163	+	0.900352i	$0.356691\pi$
$337$			6.89179e7i			1.80070i	−0.435163	+	0.900352i	$0.643309\pi$
$338$		−	1.90572e7i		−	0.493525i
$339$			2.10710e6i			0.0540860i
$340$	2.78285e7			0.708033
$341$	−7.07458e7			−1.78417
$342$			1.47286e7i			0.368199i
$343$	1.51001e7			0.374195
$344$	−8.06567e6			−0.198137
$345$			3.52397e7i			0.858173i
$346$	−2.70171e7			−0.652243
$347$			7.67058e7i			1.83586i	0.396742	+	0.917930i	$0.370141\pi$
$347$			7.67058e7i			1.83586i	−0.396742	+	0.917930i	$0.629859\pi$
$348$	1.99553e7			0.473500
$349$		−	5.32376e7i		−	1.25240i	−0.779663	−	0.626199i	$-0.784610\pi$
$349$		−	5.32376e7i		−	1.25240i	0.779663	−	0.626199i	$-0.215390\pi$
$350$			803245.i			0.0187346i
$351$		−	4.57382e6i		−	0.105769i
$352$	1.19829e7			0.274748
$353$			1.06374e7i			0.241830i	0.992663	+	0.120915i	$0.0385828\pi$
$353$			1.06374e7i			0.241830i	−0.992663	+	0.120915i	$0.961417\pi$
$354$	−1.50987e7	+	1.00012e7i	−0.340354	+	0.225446i
$355$	−1.11880e7			−0.250074
$356$		−	6.77940e6i		−	0.150259i
$357$	−6.64178e6			−0.145975
$358$	1.23025e7			0.268129
$359$	−2.67558e7			−0.578275			−0.289138	−	0.957288i	$-0.593369\pi$
$359$	−2.67558e7			−0.578275			−0.289138	+	0.957288i	$0.593369\pi$
$360$			5.86827e6i			0.125777i
$361$	6.77584e7			1.44026
$362$			4.65571e7i			0.981432i
$363$	3.90922e7			0.817279
$364$			2.52546e6i			0.0523644i
$365$		−	7.68123e7i		−	1.57962i
$366$	2.45861e7			0.501473
$367$		−	6.82169e7i		−	1.38005i	−0.723787	−	0.690023i	$-0.757600\pi$
$367$		−	6.82169e7i		−	1.38005i	0.723787	−	0.690023i	$-0.242400\pi$
$368$		−	1.73520e7i		−	0.348182i
$369$	7.87063e6			0.156650
$370$	−4.43978e7			−0.876509
$371$	−1.09234e7			−0.213912
$372$			1.70595e7i			0.331388i
$373$	3.59496e7			0.692736			0.346368	−	0.938099i	$-0.387415\pi$
$373$	3.59496e7			0.692736			0.346368	+	0.938099i	$0.387415\pi$
$374$	−7.62824e7			−1.45817
$375$	2.79760e7			0.530509
$376$	2.93185e7			0.551542
$377$			4.83030e7i			0.901468i
$378$		−	1.40057e6i		−	0.0259316i
$379$	−4.40724e7			−0.809560			−0.404780	−	0.914414i	$-0.632652\pi$
$379$	−4.40724e7			−0.809560			−0.404780	+	0.914414i	$0.632652\pi$
$380$	4.57413e7			0.833599
$381$	5.61649e7			1.01552
$382$	1.02558e7			0.183983
$383$	−9.74455e7			−1.73446			−0.867232	−	0.497904i	$-0.834103\pi$
$383$	−9.74455e7			−1.73446			−0.867232	+	0.497904i	$0.834103\pi$
$384$		−	2.88954e6i		−	0.0510310i
$385$		−	1.80379e7i		−	0.316086i
$386$			3.25493e7i			0.565952i
$387$			1.08273e7i			0.186805i
$388$		−	3.24981e6i		−	0.0556368i
$389$	−3.93694e7			−0.668822			−0.334411	−	0.942427i	$-0.608537\pi$
$389$	−3.93694e7			−0.668822			−0.334411	+	0.942427i	$0.608537\pi$
$390$	−1.42045e7			−0.239460
$391$			1.10462e8i			1.84791i
$392$		−	2.05234e7i		−	0.340715i
$393$			3.37167e7i			0.555479i
$394$			4.27857e7i			0.699536i
$395$	5.31518e7			0.862435
$396$		−	1.60859e7i		−	0.259035i
$397$		−	5.00081e7i		−	0.799225i	−0.916684	−	0.399613i	$-0.869145\pi$
$397$		−	5.00081e7i		−	0.799225i	0.916684	−	0.399613i	$-0.130855\pi$
$398$		−	7.47427e7i		−	1.18555i
$399$	−1.09170e7			−0.171863
$400$	2.22461e6			0.0347595
$401$		−	4.15781e6i		−	0.0644810i	−0.999480	−	0.0322405i	$-0.989736\pi$
$401$		−	4.15781e6i		−	0.0644810i	0.999480	−	0.0322405i	$-0.0102642\pi$
$402$	2.40992e7			0.370958
$403$	−4.12936e7			−0.630910
$404$			7.69242e6i			0.116659i
$405$	7.87756e6			0.118584
$406$			1.47911e7i			0.221015i
$407$	1.21701e8			1.80514
$408$			1.83946e7i			0.270838i
$409$			7.61604e7i			1.11316i	0.830793	+	0.556582i	$0.187887\pi$
$409$			7.61604e7i			1.11316i	−0.830793	+	0.556582i	$0.812113\pi$
$410$		−	2.44432e7i		−	0.354655i
$411$	−7.65777e7			−1.10300
$412$			3.04632e7i			0.435596i
$413$	−7.41300e6	−	1.11913e7i	−0.105231	−	0.158866i
$414$	−2.32933e7			−0.328269
$415$		−	1.13056e8i		−	1.58180i
$416$	6.99431e6			0.0971549
$417$	7.68188e7			1.05940
$418$	−1.25384e8			−1.71677
$419$		−	6.43469e7i		−	0.874753i	−0.899279	−	0.437376i	$-0.855908\pi$
$419$		−	6.43469e7i		−	0.874753i	0.899279	−	0.437376i	$-0.144092\pi$
$420$	−4.34963e6			−0.0587090
$421$		−	3.72453e7i		−	0.499143i	−0.968356	−	0.249571i	$-0.919710\pi$
$421$		−	3.72453e7i		−	0.499143i	0.968356	−	0.249571i	$-0.0802898\pi$
$422$	3.75831e7			0.500098
$423$		−	3.93571e7i		−	0.519999i
$424$			3.02526e7i			0.396885i
$425$	−1.41617e7			−0.184479
$426$		−	7.39525e6i		−	0.0956586i
$427$			1.82235e7i			0.234072i
$428$	3.35910e7			0.428441
$429$	3.89369e7			0.493161
$430$	3.36256e7			0.422926
$431$			4.03456e7i			0.503923i	0.967737	+	0.251962i	$0.0810756\pi$
$431$			4.03456e7i			0.503923i	−0.967737	+	0.251962i	$0.918924\pi$
$432$	−3.87891e6			−0.0481125
$433$	1.54297e8			1.90062			0.950308	−	0.311310i	$-0.100768\pi$
$433$	1.54297e8			1.90062			0.950308	+	0.311310i	$0.100768\pi$
$434$	−1.26447e7			−0.154682
$435$	−8.31930e7			−1.01069
$436$			2.82949e7i			0.341388i
$437$			1.81564e8i			2.17563i
$438$	5.07726e7			0.604237
$439$	5.21139e7			0.615971			0.307985	−	0.951391i	$-0.400345\pi$
$439$	5.21139e7			0.615971			0.307985	+	0.951391i	$0.400345\pi$
$440$	−4.99565e7			−0.586454
$441$	−2.75506e7			−0.321229
$442$	−4.45252e7			−0.515632
$443$		−	7.91573e7i		−	0.910500i	−0.890364	−	0.455250i	$-0.849550\pi$
$443$		−	7.91573e7i		−	0.910500i	0.890364	−	0.455250i	$-0.150450\pi$
$444$		−	2.93468e7i		−	0.335283i
$445$			2.82631e7i			0.320730i
$446$			2.69085e7i			0.303309i
$447$			2.52327e7i			0.282515i
$448$	2.14176e6			0.0238197
$449$	−7.83448e7			−0.865508			−0.432754	−	0.901512i	$-0.642458\pi$
$449$	−7.83448e7			−0.865508			−0.432754	+	0.901512i	$0.642458\pi$
$450$		−	2.98631e6i		−	0.0327715i
$451$			6.70025e7i			0.730401i
$452$			4.32545e6i			0.0468399i
$453$		−	9.51674e7i		−	1.02375i
$454$	3.08995e7			0.330205
$455$		−	1.05286e7i		−	0.111772i
$456$			3.02348e7i			0.318869i
$457$		−	7.61931e7i		−	0.798301i	−0.916885	−	0.399151i	$-0.869305\pi$
$457$		−	7.61931e7i		−	0.798301i	0.916885	−	0.399151i	$-0.130695\pi$
$458$	−9.56929e7			−0.996055
$459$	2.46928e7			0.255348
$460$			7.23401e7i			0.743199i
$461$	−2.58922e7			−0.264281			−0.132140	−	0.991231i	$-0.542185\pi$
$461$	−2.58922e7			−0.264281			−0.132140	+	0.991231i	$0.542185\pi$
$462$	1.19230e7			0.120909
$463$			1.22437e8i			1.23359i	0.787125	+	0.616793i	$0.211568\pi$
$463$			1.22437e8i			1.23359i	−0.787125	+	0.616793i	$0.788432\pi$
$464$	4.09642e7			0.410063
$465$		−	7.11205e7i		−	0.707353i
$466$	−6.61225e7			−0.653419
$467$			9.29818e7i			0.912950i	0.889736	+	0.456475i	$0.150888\pi$
$467$			9.29818e7i			0.912950i	−0.889736	+	0.456475i	$0.849112\pi$
$468$		−	9.38915e6i		−	0.0915986i
$469$			1.78626e7i			0.173152i
$470$	−1.22228e8			−1.17727
$471$		−	4.16188e7i		−	0.398316i
$472$	−3.09947e7	+	2.05305e7i	−0.294755	+	0.195242i
$473$	−9.21729e7			−0.871003
$474$			3.51331e7i			0.329899i
$475$	−2.32773e7			−0.217196
$476$	−1.36343e7			−0.126418
$477$	4.06110e7			0.374187
$478$			9.08199e7i			0.831567i
$479$	1.94751e7			0.177204			0.0886020	−	0.996067i	$-0.471760\pi$
$479$	1.94751e7			0.177204			0.0886020	+	0.996067i	$0.471760\pi$
$480$			1.20464e7i			0.108926i
$481$	7.10358e7			0.638325
$482$		−	1.19806e8i		−	1.06989i
$483$		−	1.72653e7i		−	0.153226i
$484$	8.02485e7			0.707785
$485$			1.35484e7i			0.118758i
$486$			5.20704e6i			0.0453609i
$487$	−4.57133e7			−0.395782			−0.197891	−	0.980224i	$-0.563409\pi$
$487$	−4.57133e7			−0.395782			−0.197891	+	0.980224i	$0.563409\pi$
$488$	5.04705e7			0.434288
$489$	−9.28637e7			−0.794181
$490$			8.55616e7i			0.727261i
$491$	−2.07304e8			−1.75131			−0.875656	−	0.482936i	$-0.839570\pi$
$491$	−2.07304e8			−1.75131			−0.875656	+	0.482936i	$0.839570\pi$
$492$	1.61568e7			0.135663
$493$	−2.60775e8			−2.17633
$494$	−7.31853e7			−0.607076
$495$			6.70615e7i			0.552914i
$496$			3.50197e7i			0.286990i
$497$	5.48144e6			0.0446504
$498$	7.47298e7			0.605070
$499$	1.49194e8			1.20074			0.600370	−	0.799722i	$-0.295020\pi$
$499$	1.49194e8			1.20074			0.600370	+	0.799722i	$0.295020\pi$
$500$	5.74292e7			0.459434
$501$	2.58816e7			0.205815
$502$		−	8.60802e6i		−	0.0680444i
$503$		−	1.91874e8i		−	1.50769i	−0.657050	−	0.753847i	$-0.728196\pi$
$503$		−	1.91874e8i		−	1.50769i	0.657050	−	0.753847i	$-0.271804\pi$
$504$		−	2.87509e6i		−	0.0224574i
$505$		−	3.20695e7i		−	0.249011i
$506$		−	1.98295e8i		−	1.53060i
$507$	−5.25155e7			−0.402961
$508$	1.15295e8			0.879469
$509$		−	8.38680e7i		−	0.635979i	−0.948094	−	0.317990i	$-0.896992\pi$
$509$		−	8.38680e7i		−	0.635979i	0.948094	−	0.317990i	$-0.103008\pi$
$510$		−	7.66864e7i		−	0.578107i
$511$			3.76332e7i			0.282039i
$512$		−	5.93164e6i		−	0.0441942i
$513$	4.05871e7			0.300633
$514$		−	2.05995e6i		−	0.0151693i
$515$		−	1.27000e8i		−	0.929785i
$516$			2.22264e7i			0.161778i
$517$	3.35046e8			2.42456
$518$	2.17522e7			0.156500
$519$			7.44502e7i			0.532555i
$520$	−2.91591e7			−0.207379
$521$	−2.94735e7			−0.208410			−0.104205	−	0.994556i	$-0.533230\pi$
$521$	−2.94735e7			−0.208410			−0.104205	+	0.994556i	$0.533230\pi$
$522$		−	5.49902e7i		−	0.386611i
$523$	−7.60711e7			−0.531759			−0.265879	−	0.964006i	$-0.585662\pi$
$523$	−7.60711e7			−0.531759			−0.265879	+	0.964006i	$0.585662\pi$
$524$			6.92137e7i			0.481059i
$525$	2.21348e6			0.0152967
$526$		−	9.83865e7i		−	0.676049i
$527$		−	2.22933e8i		−	1.52315i
$528$		−	3.30211e7i		−	0.224331i
$529$	−1.39108e8			−0.939691
$530$		−	1.26122e8i		−	0.847157i
$531$	2.75601e7	+	4.16072e7i	0.184076	+	0.277898i
$532$	−2.24104e7			−0.148838
$533$			3.91087e7i			0.258281i
$534$	−1.86818e7			−0.122686
$535$	−1.40040e8			−0.914514
$536$	4.94709e7			0.321259
$537$		−	3.39017e7i		−	0.218927i
$538$	−2.29143e7			−0.147150
$539$		−	2.34538e8i		−	1.49777i
$540$	1.61711e7			0.102697
$541$		−	1.38266e8i		−	0.873218i	−0.899651	−	0.436609i	$-0.856179\pi$
$541$		−	1.38266e8i		−	0.873218i	0.899651	−	0.436609i	$-0.143821\pi$
$542$		−	9.78258e7i		−	0.614406i
$543$	1.28296e8			0.801336
$544$			3.77604e7i			0.234552i
$545$		−	1.17961e8i		−	0.728698i
$546$	6.95934e6			0.0427553
$547$	−1.66533e8			−1.01751			−0.508755	−	0.860912i	$-0.669894\pi$
$547$	−1.66533e8			−1.01751			−0.508755	+	0.860912i	$0.669894\pi$
$548$	−1.57199e8			−0.955229
$549$		−	6.77515e7i		−	0.409451i
$550$	2.54224e7			0.152802
$551$	−4.28631e8			−2.56229
$552$	−4.78165e7			−0.284289
$553$	−2.60411e7			−0.153987
$554$			1.14694e8i			0.674546i
$555$			1.22346e8i			0.715666i
$556$	1.57694e8			0.917466
$557$	−6.62640e7			−0.383453			−0.191726	−	0.981448i	$-0.561409\pi$
$557$	−6.62640e7			−0.383453			−0.191726	+	0.981448i	$0.561409\pi$
$558$	4.70104e7			0.270577
$559$	−5.38004e7			−0.307999
$560$	−8.92892e6			−0.0508435
$561$			2.10209e8i			1.19059i
$562$		−	7.13456e7i		−	0.401937i
$563$		−	2.16374e8i		−	1.21250i	−0.795275	−	0.606249i	$-0.792674\pi$
$563$		−	2.16374e8i		−	1.21250i	0.795275	−	0.606249i	$-0.207326\pi$
$564$		−	8.07924e7i		−	0.450332i
$565$		−	1.80327e7i		−	0.0999804i
$566$	−1.84684e8			−1.01855
$567$	−3.85951e6			−0.0211731
$568$		−	1.51810e7i		−	0.0828427i
$569$		−	2.55628e8i		−	1.38762i	−0.720157	−	0.693812i	$-0.755930\pi$
$569$		−	2.55628e8i		−	1.38762i	0.720157	−	0.693812i	$-0.244070\pi$
$570$		−	1.26048e8i		−	0.680631i
$571$		−	7.88000e6i		−	0.0423270i	−0.999776	−	0.0211635i	$-0.993263\pi$
$571$		−	7.88000e6i		−	0.0423270i	0.999776	−	0.0211635i	$-0.00673706\pi$
$572$	7.99296e7			0.427090
$573$		−	2.82616e7i		−	0.150222i
$574$			1.19756e7i			0.0633232i
$575$		−	3.68132e7i		−	0.193642i
$576$	−7.96262e6			−0.0416667
$577$	−2.01312e8			−1.04795			−0.523976	−	0.851733i	$-0.675552\pi$
$577$	−2.01312e8			−1.04795			−0.523976	+	0.851733i	$0.675552\pi$
$578$		−	1.03837e8i		−	0.537735i
$579$	8.96954e7			0.462098
$580$	−1.70779e8			−0.875285
$581$			5.53906e7i			0.282428i
$582$	−8.95541e6			−0.0454273
$583$			3.45721e8i			1.74470i
$584$	1.04226e8			0.523285
$585$			3.91431e7i			0.195518i
$586$		−	1.55681e8i		−	0.773648i
$587$			3.54900e8i			1.75465i	0.479894	+	0.877327i	$0.340675\pi$
$587$			3.54900e8i			1.75465i	−0.479894	+	0.877327i	$0.659325\pi$
$588$	−5.65559e7			−0.278193
$589$		−	3.66431e8i		−	1.79327i
$590$	1.29216e8	−	8.55910e7i	0.629159	−	0.416747i
$591$	1.17903e8			0.571168
$592$		−	6.02431e7i		−	0.290364i
$593$	3.80000e7			0.182230			0.0911150	−	0.995840i	$-0.470957\pi$
$593$	3.80000e7			0.182230			0.0911150	+	0.995840i	$0.470957\pi$
$594$	−4.43274e7			−0.211501
$595$	5.68408e7			0.269842
$596$			5.17977e7i			0.244665i
$597$	−2.05967e8			−0.967997
$598$		−	1.15743e8i		−	0.541242i
$599$	1.57774e8			0.734098			0.367049	−	0.930202i	$-0.380368\pi$
$599$	1.57774e8			0.734098			0.367049	+	0.930202i	$0.380368\pi$
$600$		−	6.13029e6i		−	0.0283810i
$601$			2.76737e8i			1.27481i	0.770530	+	0.637403i	$0.219991\pi$
$601$			2.76737e8i			1.27481i	−0.770530	+	0.637403i	$0.780009\pi$
$602$	−1.64744e7			−0.0755129
$603$		−	6.64097e7i		−	0.302886i
$604$		−	1.95360e8i		−	0.886593i
$605$	−3.34554e8			−1.51078
$606$	2.11978e7			0.0952518
$607$	9.63814e7			0.430950			0.215475	−	0.976509i	$-0.430870\pi$
$607$	9.63814e7			0.430950			0.215475	+	0.976509i	$0.430870\pi$
$608$			6.20660e7i			0.276149i
$609$	4.07594e7			0.180458
$610$	−2.10410e8			−0.926994
$611$	1.95563e8			0.857361
$612$	5.06895e7			0.221138
$613$			1.82328e8i			0.791537i	0.918350	+	0.395768i	$0.129522\pi$
$613$			1.82328e8i			0.791537i	−0.918350	+	0.395768i	$0.870478\pi$
$614$			2.83336e8i			1.22404i
$615$	−6.73575e7			−0.289575
$616$	2.44756e7			0.104711
$617$	1.77817e8			0.757040			0.378520	−	0.925593i	$-0.376433\pi$
$617$	1.77817e8			0.757040			0.378520	+	0.925593i	$0.376433\pi$
$618$	8.39466e7			0.355662
$619$	2.92620e8			1.23377			0.616883	−	0.787055i	$-0.288395\pi$
$619$	2.92620e8			1.23377			0.616883	+	0.787055i	$0.288395\pi$
$620$		−	1.45996e8i		−	0.612585i
$621$			6.41888e7i			0.268031i
$622$			2.48595e8i			1.03305i
$623$		−	1.38472e7i		−	0.0572660i
$624$		−	1.92741e7i		−	0.0793267i
$625$	−2.73366e8			−1.11971
$626$	−1.28534e8			−0.523955
$627$			3.45517e8i			1.40174i
$628$		−	8.54352e7i		−	0.344951i
$629$			3.83503e8i			1.54105i
$630$			1.19862e7i			0.0479357i
$631$	1.58214e8			0.629733			0.314866	−	0.949136i	$-0.398040\pi$
$631$	1.58214e8			0.629733			0.314866	+	0.949136i	$0.398040\pi$
$632$			7.21213e7i			0.285701i
$633$		−	1.03567e8i		−	0.408328i
$634$			1.80614e8i			0.708735i
$635$	−4.80663e8			−1.87724
$636$	8.33663e7			0.324055
$637$		−	1.36897e8i		−	0.529635i
$638$	4.68131e8			1.80262
$639$	−2.03789e7			−0.0781049
$640$			2.47289e7i			0.0943331i
$641$	−2.41219e8			−0.915877			−0.457939	−	0.888984i	$-0.651412\pi$
$641$	−2.41219e8			−0.915877			−0.457939	+	0.888984i	$0.651412\pi$
$642$		−	9.25659e7i		−	0.349821i
$643$	4.88140e8			1.83616			0.918082	−	0.396391i	$-0.129738\pi$
$643$	4.88140e8			1.83616			0.918082	+	0.396391i	$0.129738\pi$
$644$		−	3.54421e7i		−	0.132697i
$645$		−	9.26611e7i		−	0.345317i
$646$		−	3.95108e8i		−	1.46561i
$647$	−1.87045e8			−0.690611			−0.345305	−	0.938490i	$-0.612225\pi$
$647$	−1.87045e8			−0.690611			−0.345305	+	0.938490i	$0.612225\pi$
$648$			1.06890e7i			0.0392837i
$649$	−3.54201e8	+	2.34618e8i	−1.29573	+	0.858278i
$650$	1.48388e7			0.0540329
$651$			3.48446e7i			0.126297i
$652$	−1.90631e8			−0.687781
$653$	−2.64982e8			−0.951650			−0.475825	−	0.879540i	$-0.657851\pi$
$653$	−2.64982e8			−0.951650			−0.475825	+	0.879540i	$0.657851\pi$
$654$	7.79715e7			0.278742
$655$		−	2.88550e8i		−	1.02683i
$656$	3.31668e7			0.117488
$657$		−	1.39913e8i		−	0.493357i
$658$	5.98842e7			0.210201
$659$			3.61471e8i			1.26304i	0.775359	+	0.631520i	$0.217569\pi$
$659$			3.61471e8i			1.26304i	−0.775359	+	0.631520i	$0.782431\pi$
$660$			1.37664e8i			0.478838i
$661$	1.33030e8			0.460622			0.230311	−	0.973117i	$-0.426026\pi$
$661$	1.33030e8			0.460622			0.230311	+	0.973117i	$0.426026\pi$
$662$		−	2.73508e8i		−	0.942748i
$663$			1.22697e8i			0.421011i
$664$	1.53405e8			0.524006
$665$	9.34283e7			0.317697
$666$	−8.08702e7			−0.273757
$667$		−	6.77882e8i		−	2.28442i
$668$	5.31297e7			0.178241
$669$	7.41511e7			0.247651
$670$	−2.06243e8			−0.685733
$671$	5.76767e8			1.90912
$672$		−	5.90199e6i		−	0.0194487i
$673$		−	1.42725e8i		−	0.468226i	−0.972209	−	0.234113i	$-0.924781\pi$
$673$		−	1.42725e8i		−	0.468226i	0.972209	−	0.234113i	$-0.0752186\pi$
$674$	3.89858e8			1.27329
$675$	−8.22930e6			−0.0267579
$676$	−1.07804e8			−0.348975
$677$	−5.20176e7			−0.167642			−0.0838212	−	0.996481i	$-0.526712\pi$
$677$	−5.20176e7			−0.167642			−0.0838212	+	0.996481i	$0.526712\pi$
$678$	1.19195e7			0.0382446
$679$		−	6.63785e6i		−	0.0212040i
$680$		−	1.57422e8i		−	0.500655i
$681$		−	8.51490e7i		−	0.269611i
$682$			4.00198e8i			1.26160i
$683$			1.90079e8i			0.596586i	0.954474	+	0.298293i	$0.0964172\pi$
$683$			1.90079e8i			0.596586i	−0.954474	+	0.298293i	$0.903583\pi$
$684$	8.33173e7			0.260356
$685$	6.55358e8			2.03895
$686$		−	8.54192e7i		−	0.264596i
$687$			2.63699e8i			0.813276i
$688$			4.56263e7i			0.140104i
$689$			2.01794e8i			0.616950i
$690$	1.99346e8			0.606820
$691$			1.30817e8i			0.396488i	0.980153	+	0.198244i	$0.0635238\pi$
$691$			1.30817e8i			0.396488i	−0.980153	+	0.198244i	$0.936476\pi$
$692$			1.52832e8i			0.461206i
$693$		−	3.28560e7i		−	0.0987221i
$694$	4.33913e8			1.29815
$695$	−6.57421e8			−1.95834
$696$		−	1.12884e8i		−	0.334815i
$697$	−2.11137e8			−0.623543
$698$	−3.01157e8			−0.885579
$699$			1.82212e8i			0.533514i
$700$	4.54384e6			0.0132474
$701$		−	1.27010e8i		−	0.368709i	−0.982860	−	0.184355i	$-0.940981\pi$
$701$		−	1.27010e8i		−	0.368709i	0.982860	−	0.184355i	$-0.0590195\pi$
$702$	−2.58735e7			−0.0747899
$703$			6.30357e8i			1.81435i
$704$		−	6.77856e7i		−	0.194276i
$705$			3.36821e8i			0.961241i
$706$	6.01740e7			0.170999
$707$			1.57121e7i			0.0444605i
$708$	5.65754e7	+	8.54113e7i	0.159414	+	0.240667i
$709$	4.30538e8			1.20801			0.604007	−	0.796979i	$-0.293570\pi$
$709$	4.30538e8			1.20801			0.604007	+	0.796979i	$0.293570\pi$
$710$			6.32891e7i			0.176829i
$711$	9.68155e7			0.269362
$712$	−3.83501e7			−0.106249
$713$	5.79512e8			1.59880
$714$			3.75716e7i			0.103220i
$715$	−3.33224e8			−0.911630
$716$		−	6.95934e7i		−	0.189596i
$717$	2.50270e8			0.678972
$718$			1.51354e8i			0.408902i
$719$			5.18814e8i			1.39581i	0.716192	+	0.697904i	$0.245884\pi$
$719$			5.18814e8i			1.39581i	−0.716192	+	0.697904i	$0.754116\pi$
$720$	3.31960e7			0.0889381
$721$			6.22222e7i			0.166012i
$722$		−	3.83300e8i		−	1.01842i
$723$	−3.30147e8			−0.873561
$724$	2.63367e8			0.693977
$725$	8.69076e7			0.228057
$726$		−	2.21139e8i		−	0.577904i
$727$	−3.24745e8			−0.845161			−0.422580	−	0.906325i	$-0.638876\pi$
$727$	−3.24745e8			−0.845161			−0.422580	+	0.906325i	$0.638876\pi$
$728$	1.42861e7			0.0370272
$729$	1.43489e7			0.0370370
$730$	−4.34516e8			−1.11696
$731$		−	2.90454e8i		−	0.743575i
$732$		−	1.39080e8i		−	0.354595i
$733$	−2.97637e8			−0.755744			−0.377872	−	0.925858i	$-0.623344\pi$
$733$	−2.97637e8			−0.755744			−0.377872	+	0.925858i	$0.623344\pi$
$734$	−3.85893e8			−0.975840
$735$	2.35780e8			0.593806
$736$	−9.81578e7			−0.246202
$737$	5.65344e8			1.41225
$738$		−	4.45230e7i		−	0.110768i
$739$		−	4.60932e7i		−	0.114210i	−0.998368	−	0.0571049i	$-0.981813\pi$
$739$		−	4.60932e7i		−	0.114210i	0.998368	−	0.0571049i	$-0.0181870\pi$
$740$			2.51152e8i			0.619785i
$741$			2.01675e8i			0.495676i
$742$			6.17921e7i			0.151259i
$743$	−7.40765e8			−1.80598			−0.902992	−	0.429658i	$-0.858634\pi$
$743$	−7.40765e8			−1.80598			−0.902992	+	0.429658i	$0.858634\pi$
$744$	9.65030e7			0.234327
$745$		−	2.15943e8i		−	0.522241i
$746$		−	2.03362e8i		−	0.489838i
$747$		−	2.05931e8i		−	0.494038i
$748$			4.31518e8i			1.03108i
$749$	6.86109e7			0.163285
$750$		−	1.58256e8i		−	0.375126i
$751$		−	2.34844e8i		−	0.554447i	−0.960805	−	0.277224i	$-0.910586\pi$
$751$		−	2.34844e8i		−	0.554447i	0.960805	−	0.277224i	$-0.0894143\pi$
$752$		−	1.65851e8i		−	0.389999i
$753$	−2.37209e7			−0.0555580
$754$	2.73243e8			0.637434
$755$			8.14449e8i			1.89244i
$756$	−7.92281e6			−0.0183364
$757$	−7.19405e8			−1.65839			−0.829193	−	0.558962i	$-0.811200\pi$
$757$	−7.19405e8			−1.65839			−0.829193	+	0.558962i	$0.811200\pi$
$758$			2.49311e8i			0.572445i
$759$	−5.46438e8			−1.24973
$760$		−	2.58752e8i		−	0.589444i
$761$	3.96556e8			0.899810			0.449905	−	0.893076i	$-0.351458\pi$
$761$	3.96556e8			0.899810			0.449905	+	0.893076i	$0.351458\pi$
$762$		−	3.17717e8i		−	0.718084i
$763$			5.77933e7i			0.130108i
$764$		−	5.80154e7i		−	0.130096i
$765$	−2.11323e8			−0.472022
$766$			5.51235e8i			1.22645i
$767$	−2.06744e8	+	1.36944e8i	−0.458191	+	0.303500i
$768$	−1.63457e7			−0.0360844
$769$		−	3.08058e8i		−	0.677413i	−0.940892	−	0.338707i	$-0.890011\pi$
$769$		−	3.08058e8i		−	0.677413i	0.940892	−	0.338707i	$-0.109989\pi$
$770$	−1.02038e8			−0.223506
$771$	−5.67654e6			−0.0123857
$772$	1.84127e8			0.400189
$773$			2.46884e8i			0.534508i	0.963626	+	0.267254i	$0.0861162\pi$
$773$			2.46884e8i			0.534508i	−0.963626	+	0.267254i	$0.913884\pi$
$774$	6.12487e7			0.132091
$775$			7.42961e7i			0.159610i
$776$	−1.83837e7			−0.0393412
$777$		−	5.99419e7i		−	0.127781i
$778$			2.22707e8i			0.472928i
$779$	−3.47042e8			−0.734125
$780$			8.03530e7i			0.169324i
$781$		−	1.73485e8i		−	0.364174i
$782$	6.24865e8			1.30667
$783$	−1.51535e8			−0.315667
$784$	−1.16098e8			−0.240922
$785$			3.56177e8i			0.736304i
$786$	1.90730e8			0.392783
$787$	−1.23647e8			−0.253664			−0.126832	−	0.991924i	$-0.540481\pi$
$787$	−1.23647e8			−0.253664			−0.126832	+	0.991924i	$0.540481\pi$
$788$	2.42032e8			0.494646
$789$	−2.71121e8			−0.551992
$790$		−	3.00672e8i		−	0.609834i
$791$			8.83489e6i			0.0178514i
$792$	−9.09953e7			−0.183165
$793$	3.36653e8			0.675092
$794$	−2.82889e8			−0.565138
$795$	−3.47552e8			−0.691701
$796$	−4.22809e8			−0.838310
$797$		−	4.91414e8i		−	0.970673i	−0.874327	−	0.485336i	$-0.838697\pi$
$797$		−	4.91414e8i		−	0.970673i	0.874327	−	0.485336i	$-0.161303\pi$
$798$			6.17557e7i			0.121526i
$799$			1.05579e9i			2.06985i
$800$		−	1.25843e7i		−	0.0245787i
$801$			5.14811e7i			0.100173i
$802$	−2.35201e7			−0.0455949
$803$	1.19108e9			2.30034
$804$		−	1.36326e8i		−	0.262307i
$805$			1.47757e8i			0.283244i
$806$			2.33592e8i			0.446121i
$807$			6.31445e7i			0.120147i
$808$	4.35149e7			0.0824905
$809$		−	6.33379e8i		−	1.19624i	−0.801407	−	0.598119i	$-0.795915\pi$
$809$		−	6.33379e8i		−	1.19624i	0.801407	−	0.598119i	$-0.204085\pi$
$810$		−	4.45622e7i		−	0.0838516i
$811$		−	6.67664e8i		−	1.25169i	−0.779949	−	0.625843i	$-0.784755\pi$
$811$		−	6.67664e8i		−	1.25169i	0.779949	−	0.625843i	$-0.215245\pi$
$812$	8.36709e7			0.156281
$813$	−2.69576e8			−0.501660
$814$		−	6.88446e8i		−	1.27643i
$815$	7.94735e8			1.46808
$816$	1.04055e8			0.191511
$817$		−	4.77413e8i		−	0.875444i
$818$	4.30828e8			0.787126
$819$		−	1.91777e7i		−	0.0349096i
$820$	−1.38271e8			−0.250779
$821$			7.14211e8i			1.29062i	0.763922	+	0.645308i	$0.223271\pi$
$821$			7.14211e8i			1.29062i	−0.763922	+	0.645308i	$0.776729\pi$
$822$			4.33189e8i			0.779942i
$823$			1.32578e7i			0.0237833i	0.999929	+	0.0118916i	$0.00378532\pi$
$823$			1.32578e7i			0.0237833i	−0.999929	+	0.0118916i	$0.996215\pi$
$824$	1.72326e8			0.308013
$825$		−	7.00558e7i		−	0.124762i
$826$	−6.33078e7	+	4.19343e7i	−0.112336	+	0.0744096i
$827$	9.31231e8			1.64642			0.823211	−	0.567736i	$-0.192181\pi$
$827$	9.31231e8			1.64642			0.823211	+	0.567736i	$0.192181\pi$
$828$			1.31767e8i			0.232121i
$829$	−7.97142e7			−0.139917			−0.0699587	−	0.997550i	$-0.522287\pi$
$829$	−7.97142e7			−0.139917			−0.0699587	+	0.997550i	$0.522287\pi$
$830$	−6.39543e8			−1.11850
$831$	3.16060e8			0.550765
$832$		−	3.95658e7i		−	0.0686989i
$833$	7.39071e8			1.27865
$834$		−	4.34553e8i		−	0.749108i
$835$	−2.21496e8			−0.380458
$836$			7.09279e8i			1.21394i
$837$		−	1.29545e8i		−	0.220925i
$838$	−3.64001e8			−0.618544
$839$			1.70805e8i			0.289211i	0.989489	+	0.144605i	$0.0461913\pi$
$839$			1.70805e8i			0.289211i	−0.989489	+	0.144605i	$0.953809\pi$
$840$			2.46052e7i			0.0415135i
$841$	1.00550e9			1.69042
$842$	−2.10691e8			−0.352947
$843$	−1.96605e8			−0.328181
$844$		−	2.12602e8i		−	0.353623i
$845$	4.49431e8			0.744891
$846$	−2.22638e8			−0.367695
$847$	1.63911e8			0.269747
$848$	1.71134e8			0.280640
$849$			5.08930e8i			0.831639i
$850$			8.01105e7i			0.130447i
$851$	−9.96913e8			−1.61759
$852$	−4.18338e7			−0.0676408
$853$	1.45118e8			0.233816			0.116908	−	0.993143i	$-0.462702\pi$
$853$	1.45118e8			0.233816			0.116908	+	0.993143i	$0.462702\pi$
$854$	1.03088e8			0.165514
$855$	−3.47348e8			−0.555733
$856$		−	1.90019e8i		−	0.302954i
$857$			3.59211e7i			0.0570700i	0.999593	+	0.0285350i	$0.00908420\pi$
$857$			3.59211e7i			0.0570700i	−0.999593	+	0.0285350i	$0.990916\pi$
$858$		−	2.20260e8i		−	0.348718i
$859$		−	5.53225e8i		−	0.872816i	−0.899749	−	0.436408i	$-0.856250\pi$
$859$		−	5.53225e8i		−	0.872816i	0.899749	−	0.436408i	$-0.143750\pi$
$860$		−	1.90215e8i		−	0.299054i
$861$	3.30010e7			0.0517032
$862$	2.28229e8			0.356327
$863$		−	1.10907e9i		−	1.72554i	−0.505595	−	0.862771i	$-0.668727\pi$
$863$		−	1.10907e9i		−	1.72554i	0.505595	−	0.862771i	$-0.331273\pi$
$864$			2.19424e7i			0.0340207i
$865$		−	6.37151e8i		−	0.984450i
$866$		−	8.72837e8i		−	1.34394i
$867$	−2.86141e8			−0.439059
$868$			7.15291e7i			0.109376i
$869$			8.24188e8i			1.25593i
$870$			4.70611e8i			0.714667i
$871$	3.29986e8			0.499391
$872$	1.60060e8			0.241398
$873$			2.46782e7i			0.0370912i
$874$	1.02708e9			1.53840
$875$	1.17301e8			0.175097
$876$		−	2.87213e8i		−	0.427260i
$877$	1.10349e9			1.63595			0.817975	−	0.575253i	$-0.195096\pi$
$877$	1.10349e9			1.63595			0.817975	+	0.575253i	$0.195096\pi$
$878$		−	2.94801e8i		−	0.435557i
$879$	−4.29007e8			−0.631681
$880$			2.82597e8i			0.414685i
$881$			6.75315e8i			0.987595i	0.869577	+	0.493797i	$0.164392\pi$
$881$			6.75315e8i			0.987595i	−0.869577	+	0.493797i	$0.835608\pi$
$882$			1.55850e8i			0.227143i
$883$	5.89454e8			0.856186			0.428093	−	0.903735i	$-0.359186\pi$
$883$	5.89454e8			0.856186			0.428093	+	0.903735i	$0.359186\pi$
$884$			2.51873e8i			0.364607i
$885$	−2.35861e8	−	3.56078e8i	−0.340272	−	0.513706i
$886$	−4.47781e8			−0.643820
$887$			1.22480e9i			1.75507i	0.479513	+	0.877535i	$0.340813\pi$
$887$			1.22480e9i			1.75507i	−0.479513	+	0.877535i	$0.659187\pi$
$888$	−1.66010e8			−0.237081
$889$	2.35495e8			0.335179
$890$	1.59880e8			0.226791
$891$			1.22152e8i			0.172690i
$892$	1.52218e8			0.214472
$893$			1.73539e9i			2.43692i
$894$	1.42738e8			0.199768
$895$			2.90133e8i			0.404695i
$896$		−	1.21156e7i		−	0.0168431i
$897$	−3.18950e8			−0.441922
$898$			4.43185e8i			0.612007i
$899$			1.36810e9i			1.88295i
$900$	−1.68931e7			−0.0231730
$901$	−1.08943e9			−1.48945
$902$	3.79024e8			0.516472
$903$			4.53982e7i			0.0616560i
$904$	2.44684e7			0.0331208
$905$	−1.09797e9			−1.48130
$906$	−5.38348e8			−0.723900
$907$	−4.53152e8			−0.607327			−0.303663	−	0.952779i	$-0.598210\pi$
$907$	−4.53152e8			−0.607327			−0.303663	+	0.952779i	$0.598210\pi$
$908$		−	1.74794e8i		−	0.233490i
$909$		−	5.84143e7i		−	0.0777727i
$910$	−5.95585e7			−0.0790351
$911$	−5.82186e8			−0.770029			−0.385014	−	0.922911i	$-0.625804\pi$
$911$	−5.82186e8			−0.770029			−0.385014	+	0.922911i	$0.625804\pi$
$912$	1.71034e8			0.225475
$913$	1.75309e9			2.30352
$914$	−4.31013e8			−0.564484
$915$			5.79822e8i			0.756887i
$916$			5.41321e8i			0.704317i
$917$			1.41372e8i			0.183339i
$918$		−	1.39684e8i		−	0.180558i
$919$		−	7.33309e8i		−	0.944801i	−0.881384	−	0.472401i	$-0.843388\pi$
$919$		−	7.33309e8i		−	0.944801i	0.881384	−	0.472401i	$-0.156612\pi$
$920$	4.09217e8			0.525521
$921$	7.80783e8			0.999428
$922$			1.46468e8i			0.186875i
$923$		−	1.01262e8i		−	0.128777i
$924$		−	6.74467e7i		−	0.0854959i
$925$		−	1.27809e8i		−	0.161486i
$926$	6.92608e8			0.872277
$927$		−	2.31330e8i		−	0.290397i
$928$		−	2.31728e8i		−	0.289958i
$929$			3.98801e8i			0.497404i	0.968580	+	0.248702i	$0.0800039\pi$
$929$			3.98801e8i			0.497404i	−0.968580	+	0.248702i	$0.919996\pi$
$930$	−4.02318e8			−0.500174
$931$	1.21480e9			1.50541
$932$			3.74045e8i			0.462037i
$933$	6.85046e8			0.843480
$934$	5.25984e8			0.645553
$935$		−	1.79899e9i		−	2.20087i
$936$	−5.31130e7			−0.0647700
$937$		−	1.44101e9i		−	1.75166i	−0.482623	−	0.875828i	$-0.660316\pi$
$937$		−	1.44101e9i		−	1.75166i	0.482623	−	0.875828i	$-0.339684\pi$
$938$	1.01046e8			0.122437
$939$			3.54197e8i			0.427807i
$940$			6.91427e8i			0.832459i
$941$		−	1.54394e9i		−	1.85295i	−0.376361	−	0.926473i	$-0.622825\pi$
$941$		−	1.54394e9i		−	1.85295i	0.376361	−	0.926473i	$-0.377175\pi$
$942$	−2.35432e8			−0.281652
$943$		−	5.48850e8i		−	0.654513i
$944$	1.16138e8	+	1.75332e8i	0.138057	+	0.208423i
$945$	3.30300e7			0.0391393
$946$			5.21409e8i			0.615892i
$947$	3.30815e8			0.389525			0.194762	−	0.980850i	$-0.437606\pi$
$947$	3.30815e8			0.389525			0.194762	+	0.980850i	$0.437606\pi$
$948$	1.98743e8			0.233274
$949$	6.95219e8			0.813435
$950$			1.31676e8i			0.153581i
$951$	4.97714e8			0.578680
$952$			7.71270e7i			0.0893914i
$953$	4.17591e8			0.482472			0.241236	−	0.970466i	$-0.422447\pi$
$953$	4.17591e8			0.482472			0.241236	+	0.970466i	$0.422447\pi$
$954$		−	2.29731e8i		−	0.264590i
$955$			2.41865e8i			0.277691i
$956$	5.13755e8			0.588007
$957$		−	1.29002e9i		−	1.47184i
$958$		−	1.10168e8i		−	0.125302i
$959$	−3.21085e8			−0.364052
$960$	6.81447e7			0.0770227
$961$	−2.82064e8			−0.317817
$962$		−	4.01839e8i		−	0.451364i
$963$	−2.55082e8			−0.285628
$964$	−6.77727e8			−0.756526
$965$	−7.67619e8			−0.854209
$966$	−9.76670e7			−0.108347
$967$			6.94177e8i			0.767699i	0.923396	+	0.383849i	$0.125402\pi$
$967$			6.94177e8i			0.767699i	−0.923396	+	0.383849i	$0.874598\pi$
$968$		−	4.53954e8i		−	0.500479i
$969$	−1.08879e9			−1.19666
$970$	7.66411e7			0.0839743
$971$	1.52362e9			1.66425			0.832124	−	0.554589i	$-0.187125\pi$
$971$	1.52362e9			1.66425			0.832124	+	0.554589i	$0.187125\pi$
$972$	2.94555e7			0.0320750
$973$	3.22095e8			0.349660
$974$			2.58594e8i			0.279860i
$975$		−	4.08909e7i		−	0.0441177i
$976$		−	2.85504e8i		−	0.307088i
$977$		−	1.10382e9i		−	1.18362i	−0.806077	−	0.591811i	$-0.798413\pi$
$977$		−	1.10382e9i		−	1.18362i	0.806077	−	0.591811i	$-0.201587\pi$
$978$			5.25317e8i			0.561571i
$979$	−4.38257e8			−0.467069
$980$	4.84009e8			0.514251
$981$		−	2.14864e8i		−	0.227592i
$982$			1.17269e9i			1.23836i
$983$			1.48454e9i			1.56290i	0.623968	+	0.781450i	$0.285519\pi$
$983$			1.48454e9i			1.56290i	−0.623968	+	0.781450i	$0.714481\pi$
$984$		−	9.13969e7i		−	0.0959282i
$985$	−1.00903e9			−1.05583
$986$			1.47517e9i			1.53890i
$987$		−	1.65021e8i		−	0.171628i
$988$			4.13999e8i			0.429268i
$989$	7.55032e8			0.780506
$990$	3.79357e8			0.390969
$991$			1.13778e8i			0.116906i	0.998290	+	0.0584530i	$0.0186168\pi$
$991$			1.13778e8i			0.116906i	−0.998290	+	0.0584530i	$0.981383\pi$
$992$	1.98101e8			0.202933
$993$	−7.53698e8			−0.769750
$994$		−	3.10077e7i		−	0.0315726i
$995$	1.76268e9			1.78939
$996$		−	4.22736e8i		−	0.427849i
$997$	1.80373e9			1.82006			0.910030	−	0.414542i	$-0.136058\pi$
$997$	1.80373e9			1.82006			0.910030	+	0.414542i	$0.136058\pi$
$998$		−	8.43967e8i		−	0.849052i
$999$			2.22852e8i			0.223522i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.7.d.a.235.7	✓	60
59.58	odd	2	inner	354.7.d.a.235.8	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.7.d.a.235.7	✓	60	1.1	even	1	trivial
354.7.d.a.235.8	yes	60	59.58	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:	\( N \)	\(=\)	\( 354 = 2 \cdot 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	354.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-5.65685i q^{2} -15.5885 q^{3} -32.0000 q^{4} +133.407 q^{5} +88.1816i q^{6} -65.3612 q^{7} +181.019i q^{8} +243.000 q^{9} +O(q^{10})\)	\(q-5.65685i q^{2} -15.5885 q^{3} -32.0000 q^{4} +133.407 q^{5} +88.1816i q^{6} -65.3612 q^{7} +181.019i q^{8} +243.000 q^{9} -754.665i q^{10} +2068.65i q^{11} +498.831 q^{12} +1207.45i q^{13} +369.739i q^{14} -2079.61 q^{15} +1024.00 q^{16} -6518.71 q^{17} -1374.62i q^{18} -10714.7 q^{19} -4269.03 q^{20} +1018.88 q^{21} +11702.1 q^{22} -16945.3i q^{23} -2821.81i q^{24} +2172.47 q^{25} +6830.38 q^{26} -3788.00 q^{27} +2091.56 q^{28} +40004.1 q^{29} +11764.1i q^{30} +34198.9i q^{31} -5792.62i q^{32} -32247.1i q^{33} +36875.4i q^{34} -8719.65 q^{35} -7776.00 q^{36} -58831.2i q^{37} +60611.4i q^{38} -18822.3i q^{39} +24149.3i q^{40} +32389.4 q^{41} -5763.66i q^{42} +44556.9i q^{43} -66196.9i q^{44} +32417.9 q^{45} -95857.2 q^{46} -161964. i q^{47} -15962.6 q^{48} -113377. q^{49} -12289.3i q^{50} +101617. q^{51} -38638.5i q^{52} +167124. q^{53} +21428.1i q^{54} +275973. i q^{55} -11831.6i q^{56} +167025. q^{57} -226297. i q^{58} +(113416. + 171223. i) q^{59} +66547.6 q^{60} -278813. i q^{61} +193458. q^{62} -15882.8 q^{63} -32768.0 q^{64} +161083. i q^{65} -182417. q^{66} -273291. i q^{67} +208599. q^{68} +264151. i q^{69} +49325.8i q^{70} -83863.8 q^{71} +43987.7i q^{72} -575773. i q^{73} -332799. q^{74} -33865.4 q^{75} +342870. q^{76} -135210. i q^{77} -106475. q^{78} +398418. q^{79} +136609. q^{80} +59049.0 q^{81} -183222. i q^{82} -847454. i q^{83} -32604.2 q^{84} -869642. q^{85} +252052. q^{86} -623602. q^{87} -374466. q^{88} +211856. i q^{89} -183384. i q^{90} -78920.5i q^{91} +542250. i q^{92} -533109. i q^{93} -916204. q^{94} -1.42941e6 q^{95} +90298.0i q^{96} +101556. i q^{97} +641357. i q^{98} +502683. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 1920 q^{4} + 408 q^{7} + 14580 q^{9}+O(q^{10}) \) 60 * q - 1920 * q^4 + 408 * q^7 + 14580 * q^9	\( 60 q - 1920 q^{4} + 408 q^{7} + 14580 q^{9} + 4536 q^{15} + 61440 q^{16} - 15840 q^{17} - 5616 q^{19} - 17472 q^{22} + 226260 q^{25} - 34048 q^{26} - 13056 q^{28} - 75392 q^{29} + 278000 q^{35} - 466560 q^{36} + 67376 q^{41} + 209856 q^{46} + 269100 q^{49} - 206064 q^{51} + 490000 q^{53} - 373248 q^{57} - 863472 q^{59} - 145152 q^{60} - 155072 q^{62} + 99144 q^{63} - 1966080 q^{64} - 404352 q^{66} + 506880 q^{68} - 2041856 q^{71} - 2146176 q^{74} + 808704 q^{75} + 179712 q^{76} + 228096 q^{78} + 670248 q^{79} + 3542940 q^{81} + 873408 q^{85} + 1832576 q^{86} - 2568024 q^{87} + 559104 q^{88} + 1049472 q^{94} - 245856 q^{95}+O(q^{100}) \) 60 * q - 1920 * q^4 + 408 * q^7 + 14580 * q^9 + 4536 * q^15 + 61440 * q^16 - 15840 * q^17 - 5616 * q^19 - 17472 * q^22 + 226260 * q^25 - 34048 * q^26 - 13056 * q^28 - 75392 * q^29 + 278000 * q^35 - 466560 * q^36 + 67376 * q^41 + 209856 * q^46 + 269100 * q^49 - 206064 * q^51 + 490000 * q^53 - 373248 * q^57 - 863472 * q^59 - 145152 * q^60 - 155072 * q^62 + 99144 * q^63 - 1966080 * q^64 - 404352 * q^66 + 506880 * q^68 - 2041856 * q^71 - 2146176 * q^74 + 808704 * q^75 + 179712 * q^76 + 228096 * q^78 + 670248 * q^79 + 3542940 * q^81 + 873408 * q^85 + 1832576 * q^86 - 2568024 * q^87 + 559104 * q^88 + 1049472 * q^94 - 245856 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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