LMFDB - Embedded newform 354.7.d.a.235.10

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			235.10
Character	$\chi$	$=$	354.235
Dual form			354.7.d.a.235.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+5.65685i q^{2} -15.5885 q^{3} -32.0000 q^{4} +204.428 q^{5} -88.1816i q^{6} +398.882 q^{7} -181.019i q^{8} +243.000 q^{9} +O(q^{10})$	\(q+5.65685i q^{2} -15.5885 q^{3} -32.0000 q^{4} +204.428 q^{5} -88.1816i q^{6} +398.882 q^{7} -181.019i q^{8} +243.000 q^{9} +1156.42i q^{10} +2025.05i q^{11} +498.831 q^{12} +680.048i q^{13} +2256.42i q^{14} -3186.71 q^{15} +1024.00 q^{16} -8516.96 q^{17} +1374.62i q^{18} +4313.17 q^{19} -6541.68 q^{20} -6217.96 q^{21} -11455.4 q^{22} +914.403i q^{23} +2821.81i q^{24} +26165.6 q^{25} -3846.93 q^{26} -3788.00 q^{27} -12764.2 q^{28} -46927.6 q^{29} -18026.8i q^{30} -9206.71i q^{31} +5792.62i q^{32} -31567.5i q^{33} -48179.2i q^{34} +81542.5 q^{35} -7776.00 q^{36} +77456.2i q^{37} +24399.0i q^{38} -10600.9i q^{39} -37005.3i q^{40} +55541.8 q^{41} -35174.1i q^{42} +152533. i q^{43} -64801.7i q^{44} +49675.9 q^{45} -5172.65 q^{46} +92076.9i q^{47} -15962.6 q^{48} +41457.9 q^{49} +148015. i q^{50} +132766. q^{51} -21761.5i q^{52} +119072. q^{53} -21428.1i q^{54} +413977. i q^{55} -72205.4i q^{56} -67235.6 q^{57} -265462. i q^{58} +(100959. - 178852. i) q^{59} +101975. q^{60} -144544. i q^{61} +52081.0 q^{62} +96928.3 q^{63} -32768.0 q^{64} +139020. i q^{65} +178572. q^{66} -341523. i q^{67} +272543. q^{68} -14254.1i q^{69} +461274. i q^{70} -141603. q^{71} -43987.7i q^{72} -91491.8i q^{73} -438158. q^{74} -407882. q^{75} -138021. q^{76} +807757. i q^{77} +59967.7 q^{78} -305900. q^{79} +209334. q^{80} +59049.0 q^{81} +314192. i q^{82} -469089. i q^{83} +198975. q^{84} -1.74110e6 q^{85} -862857. q^{86} +731528. q^{87} +366574. q^{88} -380058. i q^{89} +281009. i q^{90} +271259. i q^{91} -29260.9i q^{92} +143518. i q^{93} -520865. q^{94} +881730. q^{95} -90298.0i q^{96} +391044. i q^{97} +234521. i q^{98} +492088. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	204.428			1.63542			0.817710	−	0.575630i	$-0.195243\pi$
$5$	204.428			1.63542			0.817710	+	0.575630i	$0.195243\pi$
$6$		−	88.1816i		−	0.408248i
$7$	398.882			1.16292			0.581461	−	0.813575i	$-0.302481\pi$
$7$	398.882			1.16292			0.581461	+	0.813575i	$0.302481\pi$
$8$		−	181.019i		−	0.353553i
$9$	243.000			0.333333
$10$			1156.42i			1.15642i
$11$			2025.05i			1.52145i	0.649073	+	0.760726i	$0.275157\pi$
$11$			2025.05i			1.52145i	−0.649073	+	0.760726i	$0.724843\pi$
$12$	498.831			0.288675
$13$			680.048i			0.309535i	0.987951	+	0.154767i	$0.0494628\pi$
$13$			680.048i			0.309535i	−0.987951	+	0.154767i	$0.950537\pi$
$14$			2256.42i			0.822310i
$15$	−3186.71			−0.944211
$16$	1024.00			0.250000
$17$	−8516.96			−1.73356			−0.866778	−	0.498693i	$-0.833813\pi$
$17$	−8516.96			−1.73356			−0.866778	+	0.498693i	$0.833813\pi$
$18$			1374.62i			0.235702i
$19$	4313.17			0.628833			0.314417	−	0.949285i	$-0.398191\pi$
$19$	4313.17			0.628833			0.314417	+	0.949285i	$0.398191\pi$
$20$	−6541.68			−0.817710
$21$	−6217.96			−0.671413
$22$	−11455.4			−1.07583
$23$			914.403i			0.0751544i	0.999294	+	0.0375772i	$0.0119640\pi$
$23$			914.403i			0.0751544i	−0.999294	+	0.0375772i	$0.988036\pi$
$24$			2821.81i			0.204124i
$25$	26165.6			1.67460
$26$	−3846.93			−0.218874
$27$	−3788.00			−0.192450
$28$	−12764.2			−0.581461
$29$	−46927.6			−1.92413			−0.962064	−	0.272824i	$-0.912042\pi$
$29$	−46927.6			−1.92413			−0.962064	+	0.272824i	$0.912042\pi$
$30$		−	18026.8i		−	0.667658i
$31$		−	9206.71i		−	0.309043i	−0.987989	−	0.154522i	$-0.950616\pi$
$31$		−	9206.71i		−	0.309043i	0.987989	−	0.154522i	$-0.0493836\pi$
$32$			5792.62i			0.176777i
$33$		−	31567.5i		−	0.878411i
$34$		−	48179.2i		−	1.22581i
$35$	81542.5			1.90187
$36$	−7776.00			−0.166667
$37$			77456.2i			1.52915i	0.644533	+	0.764576i	$0.277052\pi$
$37$			77456.2i			1.52915i	−0.644533	+	0.764576i	$0.722948\pi$
$38$			24399.0i			0.444652i
$39$		−	10600.9i		−	0.178710i
$40$		−	37005.3i		−	0.578209i
$41$	55541.8			0.805877			0.402938	−	0.915227i	$-0.367989\pi$
$41$	55541.8			0.805877			0.402938	+	0.915227i	$0.367989\pi$
$42$		−	35174.1i		−	0.474761i
$43$			152533.i			1.91849i	0.282584	+	0.959243i	$0.408808\pi$
$43$			152533.i			1.91849i	−0.282584	+	0.959243i	$0.591192\pi$
$44$		−	64801.7i		−	0.760726i
$45$	49675.9			0.545140
$46$	−5172.65			−0.0531422
$47$			92076.9i			0.886864i	0.896308	+	0.443432i	$0.146239\pi$
$47$			92076.9i			0.886864i	−0.896308	+	0.443432i	$0.853761\pi$
$48$	−15962.6			−0.144338
$49$	41457.9			0.352386
$50$			148015.i			1.18412i
$51$	132766.			1.00087
$52$		−	21761.5i		−	0.154767i
$53$	119072.			0.799804			0.399902	−	0.916558i	$-0.369044\pi$
$53$	119072.			0.799804			0.399902	+	0.916558i	$0.369044\pi$
$54$		−	21428.1i		−	0.136083i
$55$			413977.i			2.48821i
$56$		−	72205.4i		−	0.411155i
$57$	−67235.6			−0.363057
$58$		−	265462.i		−	1.36056i
$59$	100959.	−	178852.i	0.491572	−	0.870837i
$59$	100959.	−	178852.i	0.491572	−	0.870837i
$60$	101975.			0.472105
$61$		−	144544.i		−	0.636811i	−0.947955	−	0.318406i	$-0.896853\pi$
$61$		−	144544.i		−	0.636811i	0.947955	−	0.318406i	$-0.103147\pi$
$62$	52081.0			0.218527
$63$	96928.3			0.387640
$64$	−32768.0			−0.125000
$65$			139020.i			0.506219i
$66$	178572.			0.621130
$67$		−	341523.i		−	1.13552i	−0.823193	−	0.567762i	$-0.807809\pi$
$67$		−	341523.i		−	1.13552i	0.823193	−	0.567762i	$-0.192191\pi$
$68$	272543.			0.866778
$69$		−	14254.1i		−	0.0433904i
$70$			461274.i			1.34482i
$71$	−141603.			−0.395637			−0.197818	−	0.980239i	$-0.563386\pi$
$71$	−141603.			−0.395637			−0.197818	+	0.980239i	$0.563386\pi$
$72$		−	43987.7i		−	0.117851i
$73$		−	91491.8i		−	0.235187i	−0.993062	−	0.117594i	$-0.962482\pi$
$73$		−	91491.8i		−	0.235187i	0.993062	−	0.117594i	$-0.0375180\pi$
$74$	−438158.			−1.08127
$75$	−407882.			−0.966831
$76$	−138021.			−0.314417
$77$			807757.i			1.76933i
$78$	59967.7			0.126367
$79$	−305900.			−0.620438			−0.310219	−	0.950665i	$-0.600402\pi$
$79$	−305900.			−0.620438			−0.310219	+	0.950665i	$0.600402\pi$
$80$	209334.			0.408855
$81$	59049.0			0.111111
$82$			314192.i			0.569841i
$83$		−	469089.i		−	0.820392i	−0.911997	−	0.410196i	$-0.865460\pi$
$83$		−	469089.i		−	0.820392i	0.911997	−	0.410196i	$-0.134540\pi$
$84$	198975.			0.335706
$85$	−1.74110e6			−2.83509
$86$	−862857.			−1.35657
$87$	731528.			1.11090
$88$	366574.			0.537915
$89$		−	380058.i		−	0.539113i	−0.962985	−	0.269556i	$-0.913123\pi$
$89$		−	380058.i		−	0.539113i	0.962985	−	0.269556i	$-0.0868771\pi$
$90$			281009.i			0.385472i
$91$			271259.i			0.359964i
$92$		−	29260.9i		−	0.0375772i
$93$			143518.i			0.178426i
$94$	−520865.			−0.627108
$95$	881730.			1.02841
$96$		−	90298.0i		−	0.102062i
$97$			391044.i			0.428461i	0.976783	+	0.214230i	$0.0687243\pi$
$97$			391044.i			0.428461i	−0.976783	+	0.214230i	$0.931276\pi$
$98$			234521.i			0.249175i
$99$			492088.i			0.507151i
$100$	−837300.			−0.837300
$101$			905154.i			0.878534i	0.898357	+	0.439267i	$0.144762\pi$
$101$			905154.i			0.878534i	−0.898357	+	0.439267i	$0.855238\pi$
$102$			751040.i			0.707722i
$103$			1.39001e6i			1.27206i	0.771666	+	0.636028i	$0.219424\pi$
$103$			1.39001e6i			1.27206i	−0.771666	+	0.636028i	$0.780576\pi$
$104$	123102.			0.109437
$105$	−1.27112e6			−1.09804
$106$			673575.i			0.565547i
$107$	−1.09783e6			−0.896155			−0.448078	−	0.893995i	$-0.647891\pi$
$107$	−1.09783e6			−0.896155			−0.448078	+	0.893995i	$0.647891\pi$
$108$	121216.			0.0962250
$109$			1.59103e6i			1.22857i	0.789085	+	0.614284i	$0.210555\pi$
$109$			1.59103e6i			1.22857i	−0.789085	+	0.614284i	$0.789445\pi$
$110$	−2.34181e6			−1.75943
$111$		−	1.20742e6i		−	0.882857i
$112$	408455.			0.290730
$113$		−	203685.i		−	0.141164i	−0.997506	−	0.0705819i	$-0.977514\pi$
$113$		−	203685.i		−	0.141164i	0.997506	−	0.0705819i	$-0.0224856\pi$
$114$		−	380342.i		−	0.256720i
$115$			186929.i			0.122909i
$116$	1.50168e6			0.962064
$117$			165252.i			0.103178i
$118$	1.01174e6	+	571108.i	0.615775	+	0.347594i
$119$	−3.39726e6			−2.01599
$120$			576856.i			0.333829i
$121$	−2.32928e6			−1.31482
$122$	817664.			0.450293
$123$	−865811.			−0.465273
$124$			294615.i			0.154522i
$125$	2.15480e6			1.10326
$126$			548309.i			0.274103i
$127$	−1.54986e6			−0.756625			−0.378313	−	0.925678i	$-0.623496\pi$
$127$	−1.54986e6			−0.756625			−0.378313	+	0.925678i	$0.623496\pi$
$128$		−	185364.i		−	0.0883883i
$129$		−	2.37775e6i		−	1.10764i
$130$	−786419.			−0.357951
$131$		−	3.37247e6i		−	1.50015i	−0.661354	−	0.750074i	$-0.730018\pi$
$131$		−	3.37247e6i		−	1.50015i	0.661354	−	0.750074i	$-0.269982\pi$
$132$			1.01016e6i			0.439205i
$133$	1.72045e6			0.731284
$134$	1.93195e6			0.802936
$135$	−774371.			−0.314737
$136$			1.54174e6i			0.612905i
$137$	1.46167e6			0.568443			0.284222	−	0.958759i	$-0.408265\pi$
$137$	1.46167e6			0.568443			0.284222	+	0.958759i	$0.408265\pi$
$138$	80633.6			0.0306816
$139$	2.97189e6			1.10659			0.553296	−	0.832985i	$-0.313370\pi$
$139$	2.97189e6			1.10659			0.553296	+	0.832985i	$0.313370\pi$
$140$	−2.60936e6			−0.950933
$141$		−	1.43534e6i		−	0.512031i
$142$		−	801026.i		−	0.279757i
$143$	−1.37713e6			−0.470942
$144$	248832.			0.0833333
$145$	−9.59329e6			−3.14676
$146$	517556.			0.166303
$147$	−646264.			−0.203450
$148$		−	2.47860e6i		−	0.764576i
$149$			3.85233e6i			1.16457i	0.812985	+	0.582284i	$0.197841\pi$
$149$			3.85233e6i			1.16457i	−0.812985	+	0.582284i	$0.802159\pi$
$150$		−	2.30733e6i		−	0.683653i
$151$			4.89354e6i			1.42132i	0.703535	+	0.710661i	$0.251604\pi$
$151$			4.89354e6i			1.42132i	−0.703535	+	0.710661i	$0.748396\pi$
$152$		−	780767.i		−	0.222326i
$153$	−2.06962e6			−0.577852
$154$	−4.56937e6			−1.25110
$155$		−	1.88211e6i		−	0.505416i
$156$			339229.i			0.0893549i
$157$			4.37601e6i			1.13078i	0.824823	+	0.565392i	$0.191275\pi$
$157$			4.37601e6i			1.13078i	−0.824823	+	0.565392i	$0.808725\pi$
$158$		−	1.73043e6i		−	0.438716i
$159$	−1.85616e6			−0.461767
$160$			1.18417e6i			0.289104i
$161$			364739.i			0.0873986i
$162$			334032.i			0.0785674i
$163$	−1.06176e6			−0.245168			−0.122584	−	0.992458i	$-0.539118\pi$
$163$	−1.06176e6			−0.245168			−0.122584	+	0.992458i	$0.539118\pi$
$164$	−1.77734e6			−0.402938
$165$		−	6.45326e6i		−	1.43657i
$166$	2.65357e6			0.580105
$167$	−426252.			−0.0915201			−0.0457601	−	0.998952i	$-0.514571\pi$
$167$	−426252.			−0.0915201			−0.0457601	+	0.998952i	$0.514571\pi$
$168$			1.12557e6i			0.237380i
$169$	4.36434e6			0.904188
$170$		−	9.84916e6i		−	2.00471i
$171$	1.04810e6			0.209611
$172$		−	4.88106e6i		−	0.959243i
$173$			1.66223e6i			0.321036i	0.987033	+	0.160518i	$0.0513165\pi$
$173$			1.66223e6i			0.321036i	−0.987033	+	0.160518i	$0.948684\pi$
$174$			4.13815e6i			0.785522i
$175$	1.04370e7			1.94743
$176$			2.07365e6i			0.380363i
$177$	−1.57379e6	+	2.78802e6i	−0.283809	+	0.502778i
$178$	2.14993e6			0.381210
$179$			175153.i			0.0305392i	0.999883	+	0.0152696i	$0.00486065\pi$
$179$			175153.i			0.0305392i	−0.999883	+	0.0152696i	$0.995139\pi$
$180$	−1.58963e6			−0.272570
$181$	9.27899e6			1.56482			0.782411	−	0.622762i	$-0.213990\pi$
$181$	9.27899e6			1.56482			0.782411	+	0.622762i	$0.213990\pi$
$182$	−1.53447e6			−0.254533
$183$			2.25322e6i			0.367663i
$184$	165525.			0.0265711
$185$			1.58342e7i			2.50081i
$186$	−811863.			−0.126166
$187$		−	1.72473e7i		−	2.63752i
$188$		−	2.94646e6i		−	0.443432i
$189$	−1.51096e6			−0.223804
$190$			4.98782e6i			0.727194i
$191$			759534.i			0.109005i	0.998514	+	0.0545026i	$0.0173573\pi$
$191$			759534.i			0.109005i	−0.998514	+	0.0545026i	$0.982643\pi$
$192$	510803.			0.0721688
$193$	2.83700e6			0.394628			0.197314	−	0.980340i	$-0.436778\pi$
$193$	2.83700e6			0.394628			0.197314	+	0.980340i	$0.436778\pi$
$194$	−2.21208e6			−0.302967
$195$		−	2.16711e6i		−	0.292266i
$196$	−1.32665e6			−0.176193
$197$	−8.50845e6			−1.11289			−0.556445	−	0.830885i	$-0.687835\pi$
$197$	−8.50845e6			−1.11289			−0.556445	+	0.830885i	$0.687835\pi$
$198$	−2.78367e6			−0.358610
$199$	−8.47794e6			−1.07580			−0.537899	−	0.843009i	$-0.680782\pi$
$199$	−8.47794e6			−1.07580			−0.537899	+	0.843009i	$0.680782\pi$
$200$		−	4.73649e6i		−	0.592061i
$201$			5.32382e6i			0.655595i
$202$	−5.12032e6			−0.621217
$203$	−1.87186e7			−2.23761
$204$	−4.24852e6			−0.500435
$205$	1.13543e7			1.31795
$206$	−7.86308e6			−0.899479
$207$			222200.i			0.0250515i
$208$			696369.i			0.0773837i
$209$			8.73439e6i			0.956740i
$210$		−	7.19055e6i		−	0.776433i
$211$		−	2.46757e6i		−	0.262677i	−0.991338	−	0.131338i	$-0.958073\pi$
$211$		−	2.46757e6i		−	0.262677i	0.991338	−	0.131338i	$-0.0419274\pi$
$212$	−3.81032e6			−0.399902
$213$	2.20737e6			0.228421
$214$		−	6.21026e6i		−	0.633677i
$215$			3.11820e7i			3.13753i
$216$			685700.i			0.0680414i
$217$		−	3.67239e6i		−	0.359393i
$218$	−9.00023e6			−0.868729
$219$			1.42622e6i			0.135785i
$220$		−	1.32473e7i		−	1.24411i
$221$		−	5.79194e6i		−	0.536596i
$222$	6.83021e6			0.624274
$223$	9.64444e6			0.869686			0.434843	−	0.900506i	$-0.356804\pi$
$223$	9.64444e6			0.869686			0.434843	+	0.900506i	$0.356804\pi$
$224$			2.31057e6i			0.205577i
$225$	6.35825e6			0.558200
$226$	1.15222e6			0.0998179
$227$		−	8.51796e6i		−	0.728212i	−0.931357	−	0.364106i	$-0.881375\pi$
$227$		−	8.51796e6i		−	0.728212i	0.931357	−	0.364106i	$-0.118625\pi$
$228$	2.15154e6			0.181529
$229$			1.83916e7i			1.53149i	0.643145	+	0.765744i	$0.277629\pi$
$229$			1.83916e7i			1.53149i	−0.643145	+	0.765744i	$0.722371\pi$
$230$	−1.05743e6			−0.0869098
$231$		−	1.25917e7i		−	1.02152i
$232$			8.49480e6i			0.680282i
$233$		−	1.56541e7i		−	1.23754i	−0.785572	−	0.618770i	$-0.787631\pi$
$233$		−	1.56541e7i		−	1.23754i	0.785572	−	0.618770i	$-0.212369\pi$
$234$	−934804.			−0.0729580
$235$			1.88231e7i			1.45040i
$236$	−3.23068e6	+	5.72325e6i	−0.245786	+	0.435418i
$237$	4.76851e6			0.358210
$238$		−	1.92178e7i		−	1.42552i
$239$	−2.19586e7			−1.60846			−0.804231	−	0.594317i	$-0.797422\pi$
$239$	−2.19586e7			−1.60846			−0.804231	+	0.594317i	$0.797422\pi$
$240$	−3.26319e6			−0.236053
$241$	−6.24100e6			−0.445865			−0.222932	−	0.974834i	$-0.571563\pi$
$241$	−6.24100e6			−0.445865			−0.222932	+	0.974834i	$0.571563\pi$
$242$		−	1.31764e7i		−	0.929716i
$243$	−920483.			−0.0641500
$244$			4.62541e6i			0.318406i
$245$	8.47513e6			0.576299
$246$		−	4.89777e6i		−	0.328998i
$247$			2.93316e6i			0.194646i
$248$	−1.66659e6			−0.109263
$249$			7.31238e6i			0.473654i
$250$			1.21894e7i			0.780120i
$251$	1.52136e7			0.962078			0.481039	−	0.876699i	$-0.340260\pi$
$251$	1.52136e7			0.962078			0.481039	+	0.876699i	$0.340260\pi$
$252$	−3.10171e6			−0.193820
$253$	−1.85172e6			−0.114344
$254$		−	8.76732e6i		−	0.535015i
$255$	2.71411e7			1.63684
$256$	1.04858e6			0.0625000
$257$	−1.73765e7			−1.02368			−0.511839	−	0.859081i	$-0.671036\pi$
$257$	−1.73765e7			−1.02368			−0.511839	+	0.859081i	$0.671036\pi$
$258$	1.34506e7			0.783218
$259$			3.08959e7i			1.77828i
$260$		−	4.44866e6i		−	0.253110i
$261$	−1.14034e7			−0.641376
$262$	1.90776e7			1.06076
$263$	−6.82481e6			−0.375166			−0.187583	−	0.982249i	$-0.560065\pi$
$263$	−6.82481e6			−0.375166			−0.187583	+	0.982249i	$0.560065\pi$
$264$	−5.71432e6			−0.310565
$265$	2.43417e7			1.30802
$266$			9.73231e6i			0.517096i
$267$			5.92452e6i			0.311257i
$268$			1.09288e7i			0.567762i
$269$			1.56964e7i			0.806384i	0.915115	+	0.403192i	$0.132099\pi$
$269$			1.56964e7i			0.806384i	−0.915115	+	0.403192i	$0.867901\pi$
$270$		−	4.38050e6i		−	0.222553i
$271$	−2.61601e7			−1.31441			−0.657206	−	0.753711i	$-0.728262\pi$
$271$	−2.61601e7			−1.31441			−0.657206	+	0.753711i	$0.728262\pi$
$272$	−8.72137e6			−0.433389
$273$		−	4.22851e6i		−	0.207826i
$274$			8.26845e6i			0.401950i
$275$			5.29868e7i			2.54783i
$276$			456132.i			0.0216952i
$277$	1.52181e7			0.716011			0.358006	−	0.933719i	$-0.383457\pi$
$277$	1.52181e7			0.716011			0.358006	+	0.933719i	$0.383457\pi$
$278$			1.68115e7i			0.782479i
$279$		−	2.23723e6i		−	0.103014i
$280$		−	1.47608e7i		−	0.672411i
$281$	1.63993e7			0.739106			0.369553	−	0.929210i	$-0.379511\pi$
$281$	1.63993e7			0.739106			0.369553	+	0.929210i	$0.379511\pi$
$282$	8.11949e6			0.362061
$283$		−	2.49926e7i		−	1.10269i	−0.834278	−	0.551344i	$-0.814115\pi$
$283$		−	2.49926e7i		−	1.10269i	0.834278	−	0.551344i	$-0.185885\pi$
$284$	4.53129e6			0.197818
$285$	−1.37448e7			−0.593751
$286$		−	7.79024e6i		−	0.333006i
$287$	2.21546e7			0.937171
$288$			1.40761e6i			0.0589256i
$289$	4.84011e7			2.00522
$290$		−	5.42678e7i		−	2.22509i
$291$		−	6.09578e6i		−	0.247372i
$292$			2.92774e6i			0.117594i
$293$	3.08653e7			1.22707			0.613533	−	0.789669i	$-0.289748\pi$
$293$	3.08653e7			1.22707			0.613533	+	0.789669i	$0.289748\pi$
$294$		−	3.65582e6i		−	0.143861i
$295$	2.06387e7	−	3.65622e7i	0.803928	−	1.42418i
$296$	1.40211e7			0.540637
$297$		−	7.67089e6i		−	0.292804i
$298$	−2.17921e7			−0.823475
$299$	−621838.			−0.0232629
$300$	1.30522e7			0.483416
$301$			6.08427e7i			2.23105i
$302$	−2.76820e7			−1.00503
$303$		−	1.41100e7i		−	0.507222i
$304$	4.41668e6			0.157208
$305$		−	2.95488e7i		−	1.04145i
$306$		−	1.17076e7i		−	0.408603i
$307$	5.09255e7			1.76003			0.880014	−	0.474947i	$-0.157533\pi$
$307$	5.09255e7			1.76003			0.880014	+	0.474947i	$0.157533\pi$
$308$		−	2.58482e7i		−	0.884665i
$309$		−	2.16681e7i		−	0.734422i
$310$	1.06468e7			0.357383
$311$	2.62923e6			0.0874072			0.0437036	−	0.999045i	$-0.486084\pi$
$311$	2.62923e6			0.0874072			0.0437036	+	0.999045i	$0.486084\pi$
$312$	−1.91897e6			−0.0631835
$313$			3.60777e7i			1.17654i	0.808665	+	0.588269i	$0.200190\pi$
$313$			3.60777e7i			1.17654i	−0.808665	+	0.588269i	$0.799810\pi$
$314$	−2.47545e7			−0.799584
$315$	1.98148e7			0.633955
$316$	9.78881e6			0.310219
$317$	2.67309e7			0.839143			0.419572	−	0.907722i	$-0.362180\pi$
$317$	2.67309e7			0.839143			0.419572	+	0.907722i	$0.362180\pi$
$318$		−	1.05000e7i		−	0.326519i
$319$		−	9.50308e7i		−	2.92747i
$320$	−6.69868e6			−0.204428
$321$	1.71135e7			0.517395
$322$	−2.06328e6			−0.0618002
$323$	−3.67351e7			−1.09012
$324$	−1.88957e6			−0.0555556
$325$			1.77939e7i			0.518347i
$326$		−	6.00623e6i		−	0.173360i
$327$		−	2.48017e7i		−	0.709314i
$328$		−	1.00541e7i		−	0.284920i
$329$			3.67278e7i			1.03135i
$330$	3.65051e7			1.01581
$331$	−4.95838e7			−1.36727			−0.683637	−	0.729822i	$-0.739603\pi$
$331$	−4.95838e7			−1.36727			−0.683637	+	0.729822i	$0.739603\pi$
$332$			1.50109e7i			0.410196i
$333$			1.88219e7i			0.509718i
$334$		−	2.41124e6i		−	0.0647145i
$335$		−	6.98168e7i		−	1.85706i
$336$	−6.36719e6			−0.167853
$337$			4.59065e7i			1.19946i	0.800204	+	0.599728i	$0.204724\pi$
$337$			4.59065e7i			1.19946i	−0.800204	+	0.599728i	$0.795276\pi$
$338$			2.46885e7i			0.639358i
$339$			3.17513e6i			0.0815010i
$340$	5.57153e7			1.41755
$341$	1.86441e7			0.470195
$342$			5.92895e6i			0.148217i
$343$	−3.03913e7			−0.753124
$344$	2.76114e7			0.678287
$345$		−	2.91394e6i		−	0.0709616i
$346$	−9.40301e6			−0.227007
$347$		−	2.81905e7i		−	0.674707i	−0.941378	−	0.337353i	$-0.890468\pi$
$347$		−	2.81905e7i		−	0.674707i	0.941378	−	0.337353i	$-0.109532\pi$
$348$	−2.34089e7			−0.555448
$349$		−	5.16680e7i		−	1.21547i	−0.794138	−	0.607737i	$-0.792077\pi$
$349$		−	5.16680e7i		−	1.21547i	0.794138	−	0.607737i	$-0.207923\pi$
$350$			5.90406e7i			1.37704i
$351$		−	2.57602e6i		−	0.0595700i
$352$	−1.17304e7			−0.268957
$353$		−	1.18599e7i		−	0.269622i	−0.990871	−	0.134811i	$-0.956957\pi$
$353$		−	1.18599e7i		−	0.269622i	0.990871	−	0.134811i	$-0.0430428\pi$
$354$	−1.57714e7	−	8.90270e6i	−0.355518	−	0.200684i
$355$	−2.89475e7			−0.647033
$356$			1.21619e7i			0.269556i
$357$	5.29581e7			1.16393
$358$	−990813.			−0.0215945
$359$	1.28010e7			0.276670			0.138335	−	0.990386i	$-0.455825\pi$
$359$	1.28010e7			0.276670			0.138335	+	0.990386i	$0.455825\pi$
$360$		−	8.99230e6i		−	0.192736i
$361$	−2.84425e7			−0.604569
$362$			5.24899e7i			1.10650i
$363$	3.63099e7			0.759110
$364$		−	8.68028e6i		−	0.179982i
$365$		−	1.87035e7i		−	0.384630i
$366$	−1.27461e7			−0.259977
$367$		−	4.33479e7i		−	0.876940i	−0.898746	−	0.438470i	$-0.855521\pi$
$367$		−	4.33479e7i		−	0.876940i	0.898746	−	0.438470i	$-0.144479\pi$
$368$			936349.i			0.0187886i
$369$	1.34967e7			0.268626
$370$	−8.95716e7			−1.76834
$371$	4.74958e7			0.930109
$372$		−	4.59259e6i		−	0.0892131i
$373$	−1.10465e7			−0.212862			−0.106431	−	0.994320i	$-0.533942\pi$
$373$	−1.10465e7			−0.212862			−0.106431	+	0.994320i	$0.533942\pi$
$374$	9.75655e7			1.86501
$375$	−3.35900e7			−0.636965
$376$	1.66677e7			0.313554
$377$		−	3.19130e7i		−	0.595584i
$378$		−	8.54730e6i		−	0.158254i
$379$	8.15657e7			1.49827			0.749135	−	0.662417i	$-0.230469\pi$
$379$	8.15657e7			1.49827			0.749135	+	0.662417i	$0.230469\pi$
$380$	−2.82154e7			−0.514204
$381$	2.41599e7			0.436838
$382$	−4.29657e6			−0.0770783
$383$	−2.20692e7			−0.392817			−0.196408	−	0.980522i	$-0.562928\pi$
$383$	−2.20692e7			−0.392817			−0.196408	+	0.980522i	$0.562928\pi$
$384$			2.88954e6i			0.0510310i
$385$			1.65128e8i			2.89360i
$386$			1.60485e7i			0.279044i
$387$			3.70655e7i			0.639495i
$388$		−	1.25134e7i		−	0.214230i
$389$	9.23553e6			0.156896			0.0784482	−	0.996918i	$-0.475003\pi$
$389$	9.23553e6			0.156896			0.0784482	+	0.996918i	$0.475003\pi$
$390$	1.22591e7			0.206663
$391$		−	7.78794e6i		−	0.130284i
$392$		−	7.50467e6i		−	0.124587i
$393$			5.25716e7i			0.866111i
$394$		−	4.81311e7i		−	0.786931i
$395$	−6.25345e7			−1.01468
$396$		−	1.57468e7i		−	0.253575i
$397$			1.09982e8i			1.75771i	0.477085	+	0.878857i	$0.341693\pi$
$397$			1.09982e8i			1.75771i	−0.477085	+	0.878857i	$0.658307\pi$
$398$		−	4.79584e7i		−	0.760704i
$399$	−2.68191e7			−0.422207
$400$	2.67936e7			0.418650
$401$			6.80225e7i			1.05492i	0.849580	+	0.527460i	$0.176855\pi$
$401$			6.80225e7i			1.05492i	−0.849580	+	0.527460i	$0.823145\pi$
$402$	−3.01161e7			−0.463576
$403$	6.26100e6			0.0956596
$404$		−	2.89649e7i		−	0.439267i
$405$	1.20712e7			0.181713
$406$		−	1.05888e8i		−	1.58223i
$407$	−1.56853e8			−2.32653
$408$		−	2.40333e7i		−	0.353861i
$409$		−	9.09099e7i		−	1.32874i	−0.747402	−	0.664372i	$-0.768699\pi$
$409$		−	9.09099e7i		−	1.32874i	0.747402	−	0.664372i	$-0.231301\pi$
$410$			6.42295e7i			0.931929i
$411$	−2.27852e7			−0.328191
$412$		−	4.44803e7i		−	0.636028i
$413$	4.02706e7	−	7.13407e7i	0.571660	−	1.01271i
$414$	−1.25695e6			−0.0177141
$415$		−	9.58948e7i		−	1.34169i
$416$	−3.93926e6			−0.0547185
$417$	−4.63271e7			−0.638892
$418$	−4.94092e7			−0.676517
$419$		−	9.27084e7i		−	1.26031i	−0.776470	−	0.630155i	$-0.782991\pi$
$419$		−	9.27084e7i		−	1.26031i	0.776470	−	0.630155i	$-0.217009\pi$
$420$	4.06759e7			0.549021
$421$			1.50858e7i			0.202173i	0.994878	+	0.101086i	$0.0322318\pi$
$421$			1.50858e7i			0.202173i	−0.994878	+	0.101086i	$0.967768\pi$
$422$	1.39587e7			0.185740
$423$			2.23747e7i			0.295621i
$424$		−	2.15544e7i		−	0.282773i
$425$	−2.22852e8			−2.90302
$426$			1.24868e7i			0.161518i
$427$		−	5.76560e7i		−	0.740561i
$428$	3.51305e7			0.448078
$429$	2.14674e7			0.271899
$430$	−1.76392e8			−2.21857
$431$			1.14313e8i			1.42779i	0.700253	+	0.713895i	$0.253071\pi$
$431$			1.14313e8i			1.42779i	−0.700253	+	0.713895i	$0.746929\pi$
$432$	−3.87891e6			−0.0481125
$433$	7.58548e7			0.934371			0.467185	−	0.884159i	$-0.345268\pi$
$433$	7.58548e7			0.934371			0.467185	+	0.884159i	$0.345268\pi$
$434$	2.07742e7			0.254129
$435$	1.49545e8			1.81678
$436$		−	5.09130e7i		−	0.614284i
$437$			3.94398e6i			0.0472596i
$438$	−8.06790e6			−0.0960148
$439$	1.32962e8			1.57157			0.785786	−	0.618499i	$-0.212259\pi$
$439$	1.32962e8			1.57157			0.785786	+	0.618499i	$0.212259\pi$
$440$	7.49378e7			0.879717
$441$	1.00743e7			0.117462
$442$	3.27642e7			0.379431
$443$			5.50499e7i			0.633206i	0.948558	+	0.316603i	$0.102542\pi$
$443$			5.50499e7i			0.633206i	−0.948558	+	0.316603i	$0.897458\pi$
$444$			3.86375e7i			0.441428i
$445$		−	7.76943e7i		−	0.881676i
$446$			5.45572e7i			0.614961i
$447$		−	6.00519e7i		−	0.672364i
$448$	−1.30706e7			−0.145365
$449$	1.55723e8			1.72033			0.860167	−	0.510012i	$-0.170359\pi$
$449$	1.55723e8			1.72033			0.860167	+	0.510012i	$0.170359\pi$
$450$			3.59677e7i			0.394707i
$451$			1.12475e8i			1.22610i
$452$			6.51792e6i			0.0705819i
$453$		−	7.62827e7i		−	0.820600i
$454$	4.81848e7			0.514924
$455$			5.54528e7i			0.588693i
$456$			1.21709e7i			0.128360i
$457$		−	1.21560e8i		−	1.27362i	−0.771019	−	0.636812i	$-0.780253\pi$
$457$		−	1.21560e8i		−	1.27362i	0.771019	−	0.636812i	$-0.219747\pi$
$458$	−1.04039e8			−1.08293
$459$	3.22622e7			0.333623
$460$		−	5.98174e6i		−	0.0614545i
$461$	−1.11714e8			−1.14026			−0.570131	−	0.821554i	$-0.693107\pi$
$461$	−1.11714e8			−1.14026			−0.570131	+	0.821554i	$0.693107\pi$
$462$	7.12294e7			0.722326
$463$			5.18577e7i			0.522480i	0.965274	+	0.261240i	$0.0841315\pi$
$463$			5.18577e7i			0.522480i	−0.965274	+	0.261240i	$0.915869\pi$
$464$	−4.80538e7			−0.481032
$465$			2.93391e7i			0.291802i
$466$	8.85527e7			0.875073
$467$		−	2.51039e7i		−	0.246485i	−0.992377	−	0.123242i	$-0.960671\pi$
$467$		−	2.51039e7i		−	0.246485i	0.992377	−	0.123242i	$-0.0393293\pi$
$468$		−	5.28805e6i		−	0.0515891i
$469$		−	1.36228e8i		−	1.32052i
$470$	−1.06479e8			−1.02558
$471$		−	6.82152e7i		−	0.652858i
$472$	−3.23756e7	−	1.82755e7i	−0.307887	−	0.173797i
$473$	−3.08887e8			−2.91888
$474$			2.69748e7i			0.253293i
$475$	1.12857e8			1.05304
$476$	1.08712e8			1.00800
$477$	2.89346e7			0.266601
$478$		−	1.24217e8i		−	1.13735i
$479$	−2.28572e7			−0.207978			−0.103989	−	0.994578i	$-0.533161\pi$
$479$	−2.28572e7			−0.207978			−0.103989	+	0.994578i	$0.533161\pi$
$480$		−	1.84594e7i		−	0.166914i
$481$	−5.26739e7			−0.473326
$482$		−	3.53045e7i		−	0.315274i
$483$		−	5.68572e6i		−	0.0504596i
$484$	7.45369e7			0.657409
$485$			7.99403e7i			0.700713i
$486$		−	5.20704e6i		−	0.0453609i
$487$	9.62939e7			0.833704			0.416852	−	0.908974i	$-0.363133\pi$
$487$	9.62939e7			0.833704			0.416852	+	0.908974i	$0.363133\pi$
$488$	−2.61653e7			−0.225147
$489$	1.65512e7			0.141548
$490$			4.79426e7i			0.407505i
$491$	8.50645e7			0.718628			0.359314	−	0.933217i	$-0.383011\pi$
$491$	8.50645e7			0.718628			0.359314	+	0.933217i	$0.383011\pi$
$492$	2.77060e7			0.232637
$493$	3.99680e8			3.33559
$494$	−1.65925e7			−0.137635
$495$			1.00596e8i			0.829405i
$496$		−	9.42767e6i		−	0.0772608i
$497$	−5.64828e7			−0.460094
$498$	−4.13651e7			−0.334924
$499$	−4.59796e7			−0.370053			−0.185027	−	0.982734i	$-0.559237\pi$
$499$	−4.59796e7			−0.370053			−0.185027	+	0.982734i	$0.559237\pi$
$500$	−6.89535e7			−0.551628
$501$	6.64460e6			0.0528392
$502$			8.60610e7i			0.680292i
$503$			1.44411e8i			1.13474i	0.823463	+	0.567369i	$0.192039\pi$
$503$			1.44411e8i			1.13474i	−0.823463	+	0.567369i	$0.807961\pi$
$504$		−	1.75459e7i		−	0.137052i
$505$			1.85038e8i			1.43677i
$506$		−	1.04749e7i		−	0.0808533i
$507$	−6.80334e7			−0.522033
$508$	4.95955e7			0.378313
$509$		−	2.33004e8i		−	1.76689i	−0.468533	−	0.883446i	$-0.655217\pi$
$509$		−	2.33004e8i		−	1.76689i	0.468533	−	0.883446i	$-0.344783\pi$
$510$			1.53533e8i			1.15742i
$511$		−	3.64944e7i		−	0.273504i
$512$			5.93164e6i			0.0441942i
$513$	−1.63383e7			−0.121019
$514$		−	9.82965e7i		−	0.723850i
$515$			2.84156e8i			2.08035i
$516$			7.60881e7i			0.553819i
$517$	−1.86461e8			−1.34932
$518$	−1.74773e8			−1.25744
$519$		−	2.59117e7i		−	0.185350i
$520$	2.51654e7			0.178976
$521$	−1.80197e8			−1.27419			−0.637097	−	0.770784i	$-0.719865\pi$
$521$	−1.80197e8			−1.27419			−0.637097	+	0.770784i	$0.719865\pi$
$522$		−	6.45074e7i		−	0.453521i
$523$	−9.81429e7			−0.686047			−0.343024	−	0.939327i	$-0.611451\pi$
$523$	−9.81429e7			−0.686047			−0.343024	+	0.939327i	$0.611451\pi$
$524$			1.07919e8i			0.750074i
$525$	−1.62697e8			−1.12435
$526$		−	3.86069e7i		−	0.265282i
$527$			7.84132e7i			0.535744i
$528$		−	3.23251e7i		−	0.219603i
$529$	1.47200e8			0.994352
$530$			1.37697e8i			0.924907i
$531$	2.45330e7	−	4.34609e7i	0.163857	−	0.290279i
$532$	−5.50542e7			−0.365642
$533$			3.77711e7i			0.249447i
$534$	−3.35141e7			−0.220092
$535$	−2.24426e8			−1.46559
$536$	−6.18223e7			−0.401468
$537$		−	2.73036e6i		−	0.0176318i
$538$	−8.87920e7			−0.570200
$539$			8.39544e7i			0.536139i
$540$	2.47799e7			0.157368
$541$			2.34200e8i			1.47909i	0.673106	+	0.739546i	$0.264960\pi$
$541$			2.34200e8i			1.47909i	−0.673106	+	0.739546i	$0.735040\pi$
$542$		−	1.47984e8i		−	0.929430i
$543$	−1.44645e8			−0.903451
$544$		−	4.93355e7i		−	0.306452i
$545$			3.25251e8i			2.00923i
$546$	2.39200e7			0.146955
$547$	9.51833e7			0.581566			0.290783	−	0.956789i	$-0.406084\pi$
$547$	9.51833e7			0.581566			0.290783	+	0.956789i	$0.406084\pi$
$548$	−4.67734e7			−0.284222
$549$		−	3.51242e7i		−	0.212270i
$550$	−2.99739e8			−1.80158
$551$	−2.02406e8			−1.20996
$552$	−2.58027e6			−0.0153408
$553$	−1.22018e8			−0.721521
$554$			8.60863e7i			0.506296i
$555$		−	2.46830e8i		−	1.44384i
$556$	−9.51004e7			−0.553296
$557$	−2.02475e8			−1.17167			−0.585837	−	0.810429i	$-0.699234\pi$
$557$	−2.02475e8			−1.17167			−0.585837	+	0.810429i	$0.699234\pi$
$558$	1.26557e7			0.0728422
$559$	−1.03730e8			−0.593838
$560$	8.34995e7			0.475466
$561$			2.68859e8i			1.52278i
$562$			9.27686e7i			0.522627i
$563$			1.80880e8i			1.01360i	0.862064	+	0.506799i	$0.169171\pi$
$563$			1.80880e8i			1.01360i	−0.862064	+	0.506799i	$0.830829\pi$
$564$			4.59308e7i			0.256016i
$565$		−	4.16388e7i		−	0.230862i
$566$	1.41380e8			0.779718
$567$	2.35536e7			0.129213
$568$			2.56328e7i			0.139879i
$569$		−	1.98794e8i		−	1.07911i	−0.841949	−	0.539557i	$-0.818592\pi$
$569$		−	1.98794e8i		−	1.07911i	0.841949	−	0.539557i	$-0.181408\pi$
$570$		−	7.77524e7i		−	0.419845i
$571$		−	1.75150e8i		−	0.940810i	−0.882451	−	0.470405i	$-0.844108\pi$
$571$		−	1.75150e8i		−	0.940810i	0.882451	−	0.470405i	$-0.155892\pi$
$572$	4.40682e7			0.235471
$573$		−	1.18400e7i		−	0.0629342i
$574$			1.25326e8i			0.662680i
$575$			2.39259e7i			0.125854i
$576$	−7.96262e6			−0.0416667
$577$	5.22760e7			0.272129			0.136064	−	0.990700i	$-0.456555\pi$
$577$	5.22760e7			0.272129			0.136064	+	0.990700i	$0.456555\pi$
$578$			2.73798e8i			1.41790i
$579$	−4.42245e7			−0.227838
$580$	3.06985e8			1.57338
$581$		−	1.87111e8i		−	0.954051i
$582$	3.44829e7			0.174918
$583$			2.41128e8i			1.21686i
$584$	−1.65618e7			−0.0831513
$585$			3.37820e7i			0.168740i
$586$			1.74601e8i			0.867667i
$587$			1.63951e8i			0.810585i	0.914187	+	0.405292i	$0.132830\pi$
$587$			1.63951e8i			0.810585i	−0.914187	+	0.405292i	$0.867170\pi$
$588$	2.06805e7			0.101725
$589$		−	3.97101e7i		−	0.194337i
$590$	2.06827e8	+	1.16750e8i	1.00705	+	0.568463i
$591$	1.32634e8			0.642527
$592$			7.93151e7i			0.382288i
$593$	2.74566e8			1.31669			0.658345	−	0.752717i	$-0.271257\pi$
$593$	2.74566e8			1.31669			0.658345	+	0.752717i	$0.271257\pi$
$594$	4.33931e7			0.207043
$595$	−6.94494e8			−3.29699
$596$		−	1.23275e8i		−	0.582284i
$597$	1.32158e8			0.621112
$598$		−	3.51765e6i		−	0.0164493i
$599$	1.60782e8			0.748095			0.374048	−	0.927410i	$-0.377970\pi$
$599$	1.60782e8			0.748095			0.374048	+	0.927410i	$0.377970\pi$
$600$			7.38345e7i			0.341826i
$601$		−	1.94231e8i		−	0.894738i	−0.894349	−	0.447369i	$-0.852361\pi$
$601$		−	1.94231e8i		−	0.894738i	0.894349	−	0.447369i	$-0.147639\pi$
$602$	−3.44178e8			−1.57759
$603$		−	8.29902e7i		−	0.378508i
$604$		−	1.56593e8i		−	0.710661i
$605$	−4.76169e8			−2.15028
$606$	7.98180e7			0.358660
$607$	5.87615e7			0.262741			0.131370	−	0.991333i	$-0.458062\pi$
$607$	5.87615e7			0.262741			0.131370	+	0.991333i	$0.458062\pi$
$608$			2.49845e7i			0.111163i
$609$	2.91793e8			1.29188
$610$	1.67153e8			0.736419
$611$	−6.26167e7			−0.274515
$612$	6.62279e7			0.288926
$613$			2.83348e8i			1.23010i	0.788490	+	0.615048i	$0.210863\pi$
$613$			2.83348e8i			1.23010i	−0.788490	+	0.615048i	$0.789137\pi$
$614$			2.88078e8i			1.24453i
$615$	−1.76996e8			−0.760917
$616$	1.46220e8			0.625552
$617$	1.18290e7			0.0503608			0.0251804	−	0.999683i	$-0.491984\pi$
$617$	1.18290e7			0.0503608			0.0251804	+	0.999683i	$0.491984\pi$
$618$	1.22573e8			0.519315
$619$	−3.05788e7			−0.128929			−0.0644643	−	0.997920i	$-0.520534\pi$
$619$	−3.05788e7			−0.128929			−0.0644643	+	0.997920i	$0.520534\pi$
$620$			6.02274e7i			0.252708i
$621$		−	3.46376e6i		−	0.0144635i
$622$			1.48732e7i			0.0618062i
$623$		−	1.51598e8i		−	0.626946i
$624$		−	1.08553e7i		−	0.0446775i
$625$	3.16619e7			0.129687
$626$	−2.04086e8			−0.831938
$627$		−	1.36156e8i		−	0.552374i
$628$		−	1.40032e8i		−	0.565392i
$629$		−	6.59692e8i		−	2.65087i
$630$			1.12090e8i			0.448274i
$631$	−3.41704e8			−1.36007			−0.680037	−	0.733178i	$-0.738036\pi$
$631$	−3.41704e8			−1.36007			−0.680037	+	0.733178i	$0.738036\pi$
$632$			5.53739e7i			0.219358i
$633$			3.84656e7i			0.151656i
$634$			1.51213e8i			0.593364i
$635$	−3.16834e8			−1.23740
$636$	5.93970e7			0.230884
$637$			2.81933e7i			0.109076i
$638$	5.37575e8			2.07003
$639$	−3.44095e7			−0.131879
$640$		−	3.78935e7i		−	0.144552i
$641$	6.54504e7			0.248507			0.124253	−	0.992251i	$-0.460346\pi$
$641$	6.54504e7			0.248507			0.124253	+	0.992251i	$0.460346\pi$
$642$			9.68083e7i			0.365854i
$643$	3.38899e8			1.27479			0.637393	−	0.770539i	$-0.280013\pi$
$643$	3.38899e8			1.27479			0.637393	+	0.770539i	$0.280013\pi$
$644$		−	1.16716e7i		−	0.0436993i
$645$		−	4.86079e8i		−	1.81145i
$646$		−	2.07805e8i		−	0.770830i
$647$	5.05749e8			1.86734			0.933668	−	0.358140i	$-0.116589\pi$
$647$	5.05749e8			1.86734			0.933668	+	0.358140i	$0.116589\pi$
$648$		−	1.06890e7i		−	0.0392837i
$649$	3.62184e8	+	2.04447e8i	1.32494	+	0.747904i
$650$	−1.00657e8			−0.366527
$651$			5.72469e7i			0.207496i
$652$	3.39764e7			0.122584
$653$	−2.79642e8			−1.00430			−0.502149	−	0.864781i	$-0.667457\pi$
$653$	−2.79642e8			−1.00430			−0.502149	+	0.864781i	$0.667457\pi$
$654$	1.40300e8			0.501561
$655$		−	6.89426e8i		−	2.45337i
$656$	5.68748e7			0.201469
$657$		−	2.22325e7i		−	0.0783958i
$658$	−2.07764e8			−0.729277
$659$			2.04510e8i			0.714593i	0.933991	+	0.357297i	$0.116301\pi$
$659$			2.04510e8i			0.714593i	−0.933991	+	0.357297i	$0.883699\pi$
$660$			2.06504e8i			0.718286i
$661$	−1.11015e8			−0.384395			−0.192198	−	0.981356i	$-0.561561\pi$
$661$	−1.11015e8			−0.384395			−0.192198	+	0.981356i	$0.561561\pi$
$662$		−	2.80488e8i		−	0.966809i
$663$			9.02874e7i			0.309804i
$664$	−8.49143e7			−0.290052
$665$	3.51706e8			1.19596
$666$	−1.06472e8			−0.360425
$667$		−	4.29107e7i		−	0.144607i
$668$	1.36401e7			0.0457601
$669$	−1.50342e8			−0.502113
$670$	3.94944e8			1.31314
$671$	2.92709e8			0.968878
$672$		−	3.60182e7i		−	0.118690i
$673$		−	5.12666e8i		−	1.68186i	−0.541145	−	0.840929i	$-0.682009\pi$
$673$		−	5.12666e8i		−	1.68186i	0.541145	−	0.840929i	$-0.317991\pi$
$674$	−2.59686e8			−0.848143
$675$	−9.91153e7			−0.322277
$676$	−1.39659e8			−0.452094
$677$	5.05554e8			1.62930			0.814651	−	0.579952i	$-0.196929\pi$
$677$	5.05554e8			1.62930			0.814651	+	0.579952i	$0.196929\pi$
$678$	−1.79613e7			−0.0576299
$679$			1.55981e8i			0.498266i
$680$			3.15173e8i			1.00236i
$681$			1.32782e8i			0.420433i
$682$			1.05467e8i			0.332478i
$683$		−	5.39125e8i		−	1.69210i	−0.533100	−	0.846052i	$-0.678973\pi$
$683$		−	5.39125e8i		−	1.69210i	0.533100	−	0.846052i	$-0.321027\pi$
$684$	−3.35392e7			−0.104806
$685$	2.98805e8			0.929644
$686$		−	1.71919e8i		−	0.532539i
$687$		−	2.86697e8i		−	0.884206i
$688$			1.56194e8i			0.479621i
$689$			8.09749e7i			0.247567i
$690$	1.64837e7			0.0501774
$691$		−	6.28090e8i		−	1.90365i	−0.306639	−	0.951826i	$-0.599204\pi$
$691$		−	6.28090e8i		−	1.90365i	0.306639	−	0.951826i	$-0.400796\pi$
$692$		−	5.31915e7i		−	0.160518i
$693$			1.96285e8i			0.589776i
$694$	1.59470e8			0.477090
$695$	6.07536e8			1.80974
$696$		−	1.32421e8i		−	0.392761i
$697$	−4.73048e8			−1.39703
$698$	2.92279e8			0.859470
$699$			2.44023e8i			0.714494i
$700$	−3.33984e8			−0.973715
$701$		−	1.65974e8i		−	0.481822i	−0.970547	−	0.240911i	$-0.922554\pi$
$701$		−	1.65974e8i		−	0.481822i	0.970547	−	0.240911i	$-0.0774462\pi$
$702$	1.45722e7			0.0421223
$703$			3.34081e8i			0.961582i
$704$		−	6.63569e7i		−	0.190182i
$705$		−	2.93422e8i		−	0.837386i
$706$	6.70896e7			0.190652
$707$			3.61050e8i			1.02167i
$708$	5.03613e7	−	8.92166e7i	0.141905	−	0.251389i
$709$	−4.67614e8			−1.31205			−0.656023	−	0.754741i	$-0.727763\pi$
$709$	−4.67614e8			−1.31205			−0.656023	+	0.754741i	$0.727763\pi$
$710$		−	1.63752e8i		−	0.457521i
$711$	−7.43338e7			−0.206813
$712$	−6.87978e7			−0.190605
$713$	8.41865e6			0.0232260
$714$			2.99576e8i			0.823025i
$715$	−2.81524e8			−0.770189
$716$		−	5.60488e6i		−	0.0152696i
$717$	3.42301e8			0.928646
$718$			7.24136e7i			0.195635i
$719$		−	2.07856e8i		−	0.559212i	−0.960115	−	0.279606i	$-0.909796\pi$
$719$		−	2.07856e8i		−	0.559212i	0.960115	−	0.279606i	$-0.0902039\pi$
$720$	5.08681e7			0.136285
$721$			5.54450e8i			1.47930i
$722$		−	1.60895e8i		−	0.427495i
$723$	9.72876e7			0.257420
$724$	−2.96928e8			−0.782411
$725$	−1.22789e9			−3.22215
$726$			2.05400e8i			0.536772i
$727$	1.71302e8			0.445820			0.222910	−	0.974839i	$-0.428444\pi$
$727$	1.71302e8			0.445820			0.222910	+	0.974839i	$0.428444\pi$
$728$	4.91031e7			0.127267
$729$	1.43489e7			0.0370370
$730$	1.05803e8			0.271975
$731$		−	1.29912e9i		−	3.32580i
$732$		−	7.21030e7i		−	0.183832i
$733$	6.78464e8			1.72272			0.861361	−	0.507994i	$-0.169613\pi$
$733$	6.78464e8			1.72272			0.861361	+	0.507994i	$0.169613\pi$
$734$	2.45213e8			0.620090
$735$	−1.32114e8			−0.332727
$736$	−5.29679e6			−0.0132855
$737$	6.91603e8			1.72764
$738$			7.63487e7i			0.189947i
$739$		−	3.99984e8i		−	0.991082i	−0.868585	−	0.495541i	$-0.834970\pi$
$739$		−	3.99984e8i		−	0.991082i	0.868585	−	0.495541i	$-0.165030\pi$
$740$		−	5.06694e8i		−	1.25040i
$741$		−	4.57234e7i		−	0.112379i
$742$			2.68677e8i			0.657686i
$743$	−5.76464e8			−1.40542			−0.702709	−	0.711477i	$-0.748026\pi$
$743$	−5.76464e8			−1.40542			−0.702709	+	0.711477i	$0.748026\pi$
$744$	2.59796e7			0.0630832
$745$			7.87523e8i			1.90456i
$746$		−	6.24885e7i		−	0.150516i
$747$		−	1.13989e8i		−	0.273464i
$748$			5.51914e8i			1.31876i
$749$	−4.37904e8			−1.04216
$750$		−	1.90014e8i		−	0.450402i
$751$			5.68143e8i			1.34134i	0.741757	+	0.670668i	$0.233993\pi$
$751$			5.68143e8i			1.34134i	−0.741757	+	0.670668i	$0.766007\pi$
$752$			9.42867e7i			0.221716i
$753$	−2.37156e8			−0.555456
$754$	1.80527e8			0.421142
$755$			1.00037e9i			2.32446i
$756$	4.83508e7			0.111902
$757$	−3.43364e8			−0.791530			−0.395765	−	0.918352i	$-0.629520\pi$
$757$	−3.43364e8			−0.791530			−0.395765	+	0.918352i	$0.629520\pi$
$758$			4.61406e8i			1.05944i
$759$	2.88654e7			0.0660164
$760$		−	1.59610e8i		−	0.363597i
$761$	−3.84501e8			−0.872455			−0.436228	−	0.899836i	$-0.643686\pi$
$761$	−3.84501e8			−0.872455			−0.436228	+	0.899836i	$0.643686\pi$
$762$			1.36669e8i			0.308891i
$763$			6.34634e8i			1.42873i
$764$		−	2.43051e7i		−	0.0545026i
$765$	−4.23088e8			−0.945032
$766$		−	1.24842e8i		−	0.277763i
$767$	1.21628e8	+	6.86567e7i	0.269554	+	0.152159i
$768$	−1.63457e7			−0.0360844
$769$		−	3.14432e7i		−	0.0691430i	−0.999402	−	0.0345715i	$-0.988993\pi$
$769$		−	3.14432e7i		−	0.0691430i	0.999402	−	0.0345715i	$-0.0110066\pi$
$770$	−9.34104e8			−2.04608
$771$	2.70873e8			0.591021
$772$	−9.07840e7			−0.197314
$773$		−	7.48626e8i		−	1.62079i	−0.585884	−	0.810395i	$-0.699253\pi$
$773$		−	7.48626e8i		−	1.62079i	0.585884	−	0.810395i	$-0.300747\pi$
$774$	−2.09674e8			−0.452191
$775$		−	2.40899e8i		−	0.517524i
$776$	7.07866e7			0.151484
$777$		−	4.81619e8i		−	1.02669i
$778$			5.22441e7i			0.110943i
$779$	2.39561e8			0.506762
$780$			6.93477e7i			0.146133i
$781$		−	2.86753e8i		−	0.601943i
$782$	4.40552e7			0.0921250
$783$	1.77761e8			0.370299
$784$	4.24529e7			0.0880965
$785$			8.94577e8i			1.84931i
$786$	−2.97390e8			−0.612433
$787$	3.68274e8			0.755523			0.377761	−	0.925903i	$-0.376694\pi$
$787$	3.68274e8			0.755523			0.377761	+	0.925903i	$0.376694\pi$
$788$	2.72270e8			0.556445
$789$	1.06388e8			0.216602
$790$		−	3.53748e8i		−	0.717486i
$791$		−	8.12463e7i		−	0.164163i
$792$	8.90774e7			0.179305
$793$	9.82968e7			0.197115
$794$	−6.22150e8			−1.24289
$795$	−3.79449e8			−0.755183
$796$	2.71294e8			0.537899
$797$		−	3.75512e8i		−	0.741736i	−0.928686	−	0.370868i	$-0.879060\pi$
$797$		−	3.75512e8i		−	0.741736i	0.928686	−	0.370868i	$-0.120940\pi$
$798$		−	1.51712e8i		−	0.298545i
$799$		−	7.84216e8i		−	1.53743i
$800$			1.51568e8i			0.296030i
$801$		−	9.23541e7i		−	0.179704i
$802$	−3.84793e8			−0.745941
$803$	1.85276e8			0.357826
$804$		−	1.70362e8i		−	0.327797i
$805$			7.45627e7i			0.142934i
$806$			3.54176e7i			0.0676416i
$807$		−	2.44682e8i		−	0.465566i
$808$	1.63850e8			0.310609
$809$			1.66798e8i			0.315025i	0.987517	+	0.157513i	$0.0503475\pi$
$809$			1.66798e8i			0.315025i	−0.987517	+	0.157513i	$0.949652\pi$
$810$			6.82853e7i			0.128491i
$811$			2.19278e8i			0.411087i	0.978648	+	0.205543i	$0.0658962\pi$
$811$			2.19278e8i			0.411087i	−0.978648	+	0.205543i	$0.934104\pi$
$812$	5.98994e8			1.11880
$813$	4.07796e8			0.758876
$814$		−	8.87294e8i		−	1.64511i
$815$	−2.17053e8			−0.400953
$816$	1.35953e8			0.250217
$817$			6.57900e8i			1.20641i
$818$	5.14264e8			0.939564
$819$			6.59159e7i			0.119988i
$820$	−3.63337e8			−0.658974
$821$			5.94376e8i			1.07407i	0.843561	+	0.537034i	$0.180455\pi$
$821$			5.94376e8i			1.07407i	−0.843561	+	0.537034i	$0.819545\pi$
$822$		−	1.28892e8i		−	0.232066i
$823$			6.74510e7i			0.121001i	0.998168	+	0.0605005i	$0.0192697\pi$
$823$			6.74510e7i			0.121001i	−0.998168	+	0.0605005i	$0.980730\pi$
$824$	2.51619e8			0.449740
$825$		−	8.25983e8i		−	1.47099i
$826$	4.03564e8	+	2.27805e8i	0.716097	+	0.404225i
$827$	−1.49662e8			−0.264603			−0.132302	−	0.991210i	$-0.542237\pi$
$827$	−1.49662e8			−0.264603			−0.132302	+	0.991210i	$0.542237\pi$
$828$		−	7.11040e6i		−	0.0125257i
$829$	8.27526e8			1.45251			0.726253	−	0.687427i	$-0.241260\pi$
$829$	8.27526e8			1.45251			0.726253	+	0.687427i	$0.241260\pi$
$830$	5.42463e8			0.948715
$831$	−2.37226e8			−0.413389
$832$		−	2.22838e7i		−	0.0386918i
$833$	−3.53095e8			−0.610881
$834$		−	2.62066e8i		−	0.451765i
$835$	−8.71376e7			−0.149674
$836$		−	2.79501e8i		−	0.478370i
$837$			3.48750e7i			0.0594754i
$838$	5.24438e8			0.891173
$839$		−	6.83408e8i		−	1.15716i	−0.815625	−	0.578581i	$-0.803607\pi$
$839$		−	6.83408e8i		−	1.15716i	0.815625	−	0.578581i	$-0.196393\pi$
$840$			2.30098e8i			0.388217i
$841$	1.60737e9			2.70227
$842$	−8.53382e7			−0.142958
$843$	−2.55640e8			−0.426723
$844$			7.89621e7i			0.131338i
$845$	8.92192e8			1.47873
$846$	−1.26570e8			−0.209036
$847$	−9.29108e8			−1.52903
$848$	1.21930e8			0.199951
$849$			3.89596e8i			0.636637i
$850$		−	1.26064e9i		−	2.05274i
$851$	−7.08262e7			−0.114923
$852$	−7.06358e7			−0.114211
$853$	5.40185e8			0.870352			0.435176	−	0.900345i	$-0.356686\pi$
$853$	5.40185e8			0.870352			0.435176	+	0.900345i	$0.356686\pi$
$854$	3.26152e8			0.523656
$855$	2.14261e8			0.342802
$856$			1.98728e8i			0.316839i
$857$		−	5.44477e8i		−	0.865042i	−0.901624	−	0.432521i	$-0.857624\pi$
$857$		−	5.44477e8i		−	0.865042i	0.901624	−	0.432521i	$-0.142376\pi$
$858$			1.21438e8i			0.192261i
$859$		−	1.73704e8i		−	0.274050i	−0.990568	−	0.137025i	$-0.956246\pi$
$859$		−	1.73704e8i		−	0.274050i	0.990568	−	0.137025i	$-0.0437541\pi$
$860$		−	9.97822e8i		−	1.56877i
$861$	−3.45357e8			−0.541076
$862$	−6.46653e8			−1.00960
$863$		−	1.00705e9i		−	1.56681i	−0.621511	−	0.783405i	$-0.713481\pi$
$863$		−	1.00705e9i		−	1.56681i	0.621511	−	0.783405i	$-0.286519\pi$
$864$		−	2.19424e7i		−	0.0340207i
$865$			3.39806e8i			0.525029i
$866$			4.29099e8i			0.660700i
$867$	−7.54499e8			−1.15771
$868$			1.17517e8i			0.179697i
$869$		−	6.19464e8i		−	0.943968i
$870$			8.45952e8i			1.28466i
$871$	2.32252e8			0.351484
$872$	2.88007e8			0.434364
$873$			9.50238e7i			0.142820i
$874$	−2.23105e7			−0.0334176
$875$	8.59510e8			1.28300
$876$		−	4.56389e7i		−	0.0678927i
$877$	3.76391e7			0.0558007			0.0279004	−	0.999611i	$-0.491118\pi$
$877$	3.76391e7			0.0558007			0.0279004	+	0.999611i	$0.491118\pi$
$878$			7.52147e8i			1.11127i
$879$	−4.81143e8			−0.708447
$880$			4.23912e8i			0.622054i
$881$			1.13400e9i			1.65838i	0.558964	+	0.829192i	$0.311199\pi$
$881$			1.13400e9i			1.65838i	−0.558964	+	0.829192i	$0.688801\pi$
$882$			5.69886e7i			0.0830582i
$883$	1.20859e9			1.75548			0.877740	−	0.479137i	$-0.159050\pi$
$883$	1.20859e9			1.75548			0.877740	+	0.479137i	$0.159050\pi$
$884$			1.85342e8i			0.268298i
$885$	−3.21726e8	+	5.69948e8i	−0.464148	+	0.822253i
$886$	−3.11409e8			−0.447745
$887$		−	7.65652e8i		−	1.09714i	−0.836106	−	0.548568i	$-0.815173\pi$
$887$		−	7.65652e8i		−	1.09714i	0.836106	−	0.548568i	$-0.184827\pi$
$888$	−2.18567e8			−0.312137
$889$	−6.18210e8			−0.879895
$890$	4.39505e8			0.623439
$891$			1.19577e8i			0.169050i
$892$	−3.08622e8			−0.434843
$893$			3.97143e8i			0.557690i
$894$	3.39705e8			0.475433
$895$			3.58060e7i			0.0499444i
$896$		−	7.39383e7i		−	0.102789i
$897$	9.69349e6			0.0134308
$898$			8.80901e8i			1.21646i
$899$			4.32048e8i			0.594639i
$900$	−2.03464e8			−0.279100
$901$	−1.01414e9			−1.38651
$902$	−6.36256e8			−0.866986
$903$		−	9.48443e8i		−	1.28810i
$904$	−3.68709e7			−0.0499090
$905$	1.89688e9			2.55914
$906$	4.31520e8			0.580252
$907$	1.40007e9			1.87642			0.938208	−	0.346072i	$-0.112485\pi$
$907$	1.40007e9			1.87642			0.938208	+	0.346072i	$0.112485\pi$
$908$			2.72575e8i			0.364106i
$909$			2.19952e8i			0.292845i
$910$	−3.13688e8			−0.416269
$911$	1.15368e8			0.152591			0.0762956	−	0.997085i	$-0.475691\pi$
$911$	1.15368e8			0.152591			0.0762956	+	0.997085i	$0.475691\pi$
$912$	−6.88493e7			−0.0907643
$913$	9.49931e8			1.24819
$914$	6.87646e8			0.900589
$915$			4.60620e8i			0.601284i
$916$		−	5.88532e8i		−	0.765744i
$917$		−	1.34522e9i		−	1.74455i
$918$			1.82503e8i			0.235907i
$919$		−	9.44662e8i		−	1.21711i	−0.793512	−	0.608555i	$-0.791749\pi$
$919$		−	9.44662e8i		−	1.21711i	0.793512	−	0.608555i	$-0.208251\pi$
$920$	3.38378e7			0.0434549
$921$	−7.93849e8			−1.01615
$922$		−	6.31949e8i		−	0.806287i
$923$		−	9.62966e7i		−	0.122463i
$924$			4.02934e8i			0.510761i
$925$			2.02669e9i			2.56072i
$926$	−2.93351e8			−0.369449
$927$			3.37772e8i			0.424019i
$928$		−	2.71833e8i		−	0.340141i
$929$			1.47960e9i			1.84543i	0.385484	+	0.922714i	$0.374034\pi$
$929$			1.47960e9i			1.84543i	−0.385484	+	0.922714i	$0.625966\pi$
$930$	−1.65967e8			−0.206335
$931$	1.78815e8			0.221592
$932$			5.00930e8i			0.618770i
$933$	−4.09856e7			−0.0504645
$934$	1.42009e8			0.174291
$935$		−	3.52583e9i		−	4.31346i
$936$	2.99137e7			0.0364790
$937$		−	3.41361e8i		−	0.414949i	−0.978240	−	0.207474i	$-0.933476\pi$
$937$		−	3.41361e8i		−	0.414949i	0.978240	−	0.207474i	$-0.0665244\pi$
$938$	7.70619e8			0.933752
$939$		−	5.62396e8i		−	0.679275i
$940$		−	6.02338e8i		−	0.725198i
$941$			1.46361e8i			0.175653i	0.996136	+	0.0878265i	$0.0279921\pi$
$941$			1.46361e8i			0.175653i	−0.996136	+	0.0878265i	$0.972008\pi$
$942$	3.85884e8			0.461640
$943$			5.07876e7i			0.0605652i
$944$	1.03382e8	−	1.83144e8i	0.122893	−	0.217709i
$945$	−3.08883e8			−0.366014
$946$		−	1.74733e9i		−	2.06396i
$947$	6.55562e7			0.0771904			0.0385952	−	0.999255i	$-0.487712\pi$
$947$	6.55562e7			0.0771904			0.0385952	+	0.999255i	$0.487712\pi$
$948$	−1.52592e8			−0.179105
$949$	6.22188e7			0.0727986
$950$			6.38414e8i			0.744615i
$951$	−4.16694e8			−0.484480
$952$			6.14970e8i			0.712760i
$953$	4.52797e8			0.523149			0.261574	−	0.965183i	$-0.415758\pi$
$953$	4.52797e8			0.523149			0.261574	+	0.965183i	$0.415758\pi$
$954$			1.63679e8i			0.188516i
$955$			1.55270e8i			0.178269i
$956$	7.02675e8			0.804231
$957$			1.48138e9i			1.69018i
$958$		−	1.29300e8i		−	0.147062i
$959$	5.83033e8			0.661055
$960$	1.04422e8			0.118026
$961$	8.02740e8			0.904492
$962$		−	2.97968e8i		−	0.334692i
$963$	−2.66772e8			−0.298718
$964$	1.99712e8			0.222932
$965$	5.79961e8			0.645382
$966$	3.21633e7			0.0356803
$967$			1.70922e9i			1.89024i	0.326718	+	0.945122i	$0.394057\pi$
$967$			1.70922e9i			1.89024i	−0.326718	+	0.945122i	$0.605943\pi$
$968$			4.21645e8i			0.464858i
$969$	5.72643e8			0.629380
$970$	−4.52210e8			−0.495479
$971$	−2.89468e8			−0.316186			−0.158093	−	0.987424i	$-0.550535\pi$
$971$	−2.89468e8			−0.316186			−0.158093	+	0.987424i	$0.550535\pi$
$972$	2.94555e7			0.0320750
$973$	1.18543e9			1.28688
$974$			5.44721e8i			0.589518i
$975$		−	2.77379e8i		−	0.299268i
$976$		−	1.48013e8i		−	0.159203i
$977$			3.42276e8i			0.367022i	0.983018	+	0.183511i	$0.0587463\pi$
$977$			3.42276e8i			0.367022i	−0.983018	+	0.183511i	$0.941254\pi$
$978$			9.36279e7i			0.100089i
$979$	7.69637e8			0.820235
$980$	−2.71204e8			−0.288150
$981$			3.86621e8i			0.409523i
$982$			4.81198e8i			0.508147i
$983$		−	9.92022e8i		−	1.04439i	−0.852828	−	0.522193i	$-0.825114\pi$
$983$		−	9.92022e8i		−	1.04439i	0.852828	−	0.522193i	$-0.174886\pi$
$984$			1.56729e8i			0.164499i
$985$	−1.73936e9			−1.82004
$986$			2.26093e9i			2.35862i
$987$		−	5.72530e8i		−	0.595452i
$988$		−	9.38611e7i		−	0.0973228i
$989$	−1.39477e8			−0.144183
$990$	−5.69059e8			−0.586478
$991$		−	7.51899e8i		−	0.772572i	−0.922379	−	0.386286i	$-0.873758\pi$
$991$		−	7.51899e8i		−	0.772572i	0.922379	−	0.386286i	$-0.126242\pi$
$992$	5.33310e7			0.0546317
$993$	7.72935e8			0.789396
$994$		−	3.19515e8i		−	0.325336i
$995$	−1.73312e9			−1.75938
$996$		−	2.33996e8i		−	0.236827i
$997$	−9.21677e8			−0.930022			−0.465011	−	0.885305i	$-0.653950\pi$
$997$	−9.21677e8			−0.930022			−0.465011	+	0.885305i	$0.653950\pi$
$998$		−	2.60100e8i		−	0.261667i
$999$		−	2.93404e8i		−	0.294286i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.7.d.a.235.10	yes	60
59.58	odd	2	inner	354.7.d.a.235.9	✓	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.7.d.a.235.9	✓	60	59.58	odd	2	inner
354.7.d.a.235.10	yes	60	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+5.65685i q^{2} -15.5885 q^{3} -32.0000 q^{4} +204.428 q^{5} -88.1816i q^{6} +398.882 q^{7} -181.019i q^{8} +243.000 q^{9} +O(q^{10})\)	\(q+5.65685i q^{2} -15.5885 q^{3} -32.0000 q^{4} +204.428 q^{5} -88.1816i q^{6} +398.882 q^{7} -181.019i q^{8} +243.000 q^{9} +1156.42i q^{10} +2025.05i q^{11} +498.831 q^{12} +680.048i q^{13} +2256.42i q^{14} -3186.71 q^{15} +1024.00 q^{16} -8516.96 q^{17} +1374.62i q^{18} +4313.17 q^{19} -6541.68 q^{20} -6217.96 q^{21} -11455.4 q^{22} +914.403i q^{23} +2821.81i q^{24} +26165.6 q^{25} -3846.93 q^{26} -3788.00 q^{27} -12764.2 q^{28} -46927.6 q^{29} -18026.8i q^{30} -9206.71i q^{31} +5792.62i q^{32} -31567.5i q^{33} -48179.2i q^{34} +81542.5 q^{35} -7776.00 q^{36} +77456.2i q^{37} +24399.0i q^{38} -10600.9i q^{39} -37005.3i q^{40} +55541.8 q^{41} -35174.1i q^{42} +152533. i q^{43} -64801.7i q^{44} +49675.9 q^{45} -5172.65 q^{46} +92076.9i q^{47} -15962.6 q^{48} +41457.9 q^{49} +148015. i q^{50} +132766. q^{51} -21761.5i q^{52} +119072. q^{53} -21428.1i q^{54} +413977. i q^{55} -72205.4i q^{56} -67235.6 q^{57} -265462. i q^{58} +(100959. - 178852. i) q^{59} +101975. q^{60} -144544. i q^{61} +52081.0 q^{62} +96928.3 q^{63} -32768.0 q^{64} +139020. i q^{65} +178572. q^{66} -341523. i q^{67} +272543. q^{68} -14254.1i q^{69} +461274. i q^{70} -141603. q^{71} -43987.7i q^{72} -91491.8i q^{73} -438158. q^{74} -407882. q^{75} -138021. q^{76} +807757. i q^{77} +59967.7 q^{78} -305900. q^{79} +209334. q^{80} +59049.0 q^{81} +314192. i q^{82} -469089. i q^{83} +198975. q^{84} -1.74110e6 q^{85} -862857. q^{86} +731528. q^{87} +366574. q^{88} -380058. i q^{89} +281009. i q^{90} +271259. i q^{91} -29260.9i q^{92} +143518. i q^{93} -520865. q^{94} +881730. q^{95} -90298.0i q^{96} +391044. i q^{97} +234521. i q^{98} +492088. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 1920 q^{4} + 408 q^{7} + 14580 q^{9}+O(q^{10}) \) 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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