LMFDB - Embedded newform 177.4.d.c.176.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,4,Mod(176,177)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(177, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("177.176");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	177.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:	$10.4433380710$
Analytic rank:	$0$
Dimension:	$52$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			176.14
Character	$\chi$	$=$	177.176
Dual form			177.4.d.c.176.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.37014 q^{2} +(1.51919 + 4.96911i) q^{3} +3.35783 q^{4} +10.3951i q^{5} +(-5.11987 - 16.7466i) q^{6} -22.3857 q^{7} +15.6447 q^{8} +(-22.3841 + 15.0980i) q^{9} +O(q^{10})$	\(q-3.37014 q^{2} +(1.51919 + 4.96911i) q^{3} +3.35783 q^{4} +10.3951i q^{5} +(-5.11987 - 16.7466i) q^{6} -22.3857 q^{7} +15.6447 q^{8} +(-22.3841 + 15.0980i) q^{9} -35.0329i q^{10} -29.3191 q^{11} +(5.10117 + 16.6854i) q^{12} +2.60330i q^{13} +75.4429 q^{14} +(-51.6543 + 15.7921i) q^{15} -79.5876 q^{16} +37.1200i q^{17} +(75.4377 - 50.8824i) q^{18} +116.745 q^{19} +34.9049i q^{20} +(-34.0081 - 111.237i) q^{21} +98.8095 q^{22} -70.3128 q^{23} +(23.7673 + 77.7405i) q^{24} +16.9423 q^{25} -8.77349i q^{26} +(-109.029 - 88.2926i) q^{27} -75.1674 q^{28} +82.7478i q^{29} +(174.082 - 53.2214i) q^{30} -269.641i q^{31} +143.063 q^{32} +(-44.5412 - 145.690i) q^{33} -125.099i q^{34} -232.701i q^{35} +(-75.1622 + 50.6966i) q^{36} -248.510i q^{37} -393.446 q^{38} +(-12.9361 + 3.95490i) q^{39} +162.628i q^{40} -129.586i q^{41} +(114.612 + 374.884i) q^{42} -161.471i q^{43} -98.4487 q^{44} +(-156.945 - 232.685i) q^{45} +236.964 q^{46} -349.870 q^{47} +(-120.908 - 395.480i) q^{48} +158.120 q^{49} -57.0980 q^{50} +(-184.453 + 56.3922i) q^{51} +8.74145i q^{52} -264.779i q^{53} +(367.444 + 297.558i) q^{54} -304.775i q^{55} -350.219 q^{56} +(177.357 + 580.117i) q^{57} -278.872i q^{58} +(404.169 + 205.003i) q^{59} +(-173.447 + 53.0271i) q^{60} +623.548i q^{61} +908.727i q^{62} +(501.085 - 337.980i) q^{63} +154.558 q^{64} -27.0615 q^{65} +(150.110 + 490.995i) q^{66} -11.5921i q^{67} +124.643i q^{68} +(-106.818 - 349.392i) q^{69} +784.235i q^{70} -97.1804i q^{71} +(-350.194 + 236.205i) q^{72} +562.273i q^{73} +837.513i q^{74} +(25.7386 + 84.1883i) q^{75} +392.009 q^{76} +656.329 q^{77} +(43.5964 - 13.3286i) q^{78} -599.822 q^{79} -827.320i q^{80} +(273.100 - 675.912i) q^{81} +436.722i q^{82} -499.474 q^{83} +(-114.193 - 373.515i) q^{84} -385.865 q^{85} +544.180i q^{86} +(-411.183 + 125.709i) q^{87} -458.690 q^{88} -530.960 q^{89} +(528.927 + 784.180i) q^{90} -58.2768i q^{91} -236.099 q^{92} +(1339.88 - 409.635i) q^{93} +1179.11 q^{94} +1213.57i q^{95} +(217.340 + 710.898i) q^{96} +1527.88i q^{97} -532.886 q^{98} +(656.283 - 442.661i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q - 8 q^{3} + 268 q^{4} - 16 q^{7} - 4 q^{9}+O(q^{10}) $ 52 * q - 8 * q^3 + 268 * q^4 - 16 * q^7 - 4 * q^9	$ 52 q - 8 q^{3} + 268 q^{4} - 16 q^{7} - 4 q^{9} + 28 q^{12} + 114 q^{15} + 484 q^{16} - 184 q^{19} - 758 q^{21} - 60 q^{22} + 36 q^{25} + 742 q^{27} - 4 q^{28} - 888 q^{36} + 1402 q^{45} - 660 q^{46} - 488 q^{48} - 924 q^{49} - 1772 q^{51} - 630 q^{57} - 1880 q^{60} - 212 q^{63} + 7648 q^{64} + 1316 q^{66} - 1556 q^{75} - 5680 q^{76} + 3224 q^{78} - 1504 q^{79} - 276 q^{81} + 1228 q^{84} - 848 q^{85} + 3598 q^{87} + 5760 q^{88} + 888 q^{94}+O(q^{100}) $ 52 * q - 8 * q^3 + 268 * q^4 - 16 * q^7 - 4 * q^9 + 28 * q^12 + 114 * q^15 + 484 * q^16 - 184 * q^19 - 758 * q^21 - 60 * q^22 + 36 * q^25 + 742 * q^27 - 4 * q^28 - 888 * q^36 + 1402 * q^45 - 660 * q^46 - 488 * q^48 - 924 * q^49 - 1772 * q^51 - 630 * q^57 - 1880 * q^60 - 212 * q^63 + 7648 * q^64 + 1316 * q^66 - 1556 * q^75 - 5680 * q^76 + 3224 * q^78 - 1504 * q^79 - 276 * q^81 + 1228 * q^84 - 848 * q^85 + 3598 * q^87 + 5760 * q^88 + 888 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/177\mathbb{Z}\right)^\times$.

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

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 $

$2$	−3.37014			−1.19152			−0.595762	−	0.803161i	$-0.703150\pi$
$2$	−3.37014			−1.19152			−0.595762	+	0.803161i	$0.703150\pi$
$3$	1.51919	+	4.96911i	0.292368	+	0.956306i
$3$	1.51919	+	4.96911i	0.292368	+	0.956306i
$4$	3.35783			0.419729
$5$			10.3951i			0.929764i	0.885373	+	0.464882i	$0.153903\pi$
$5$			10.3951i			0.929764i	−0.885373	+	0.464882i	$0.846097\pi$
$6$	−5.11987	−	16.7466i	−0.348363	−	1.13946i
$7$	−22.3857			−1.20871			−0.604357	−	0.796713i	$-0.706570\pi$
$7$	−22.3857			−1.20871			−0.604357	+	0.796713i	$0.706570\pi$
$8$	15.6447			0.691407
$9$	−22.3841	+	15.0980i	−0.829042	+	0.559186i
$10$		−	35.0329i		−	1.10784i
$11$	−29.3191			−0.803641			−0.401820	−	0.915719i	$-0.631622\pi$
$11$	−29.3191			−0.803641			−0.401820	+	0.915719i	$0.631622\pi$
$12$	5.10117	+	16.6854i	0.122715	+	0.401389i
$13$			2.60330i			0.0555405i	0.999614	+	0.0277702i	$0.00884068\pi$
$13$			2.60330i			0.0555405i	−0.999614	+	0.0277702i	$0.991159\pi$
$14$	75.4429			1.44021
$15$	−51.6543	+	15.7921i	−0.889139	+	0.271833i
$16$	−79.5876			−1.24356
$17$			37.1200i			0.529584i	0.964306	+	0.264792i	$0.0853032\pi$
$17$			37.1200i			0.529584i	−0.964306	+	0.264792i	$0.914697\pi$
$18$	75.4377	−	50.8824i	0.987824	−	0.666283i
$19$	116.745			1.40964			0.704818	−	0.709389i	$-0.251029\pi$
$19$	116.745			1.40964			0.704818	+	0.709389i	$0.251029\pi$
$20$			34.9049i			0.390249i
$21$	−34.0081	−	111.237i	−0.353389	−	1.15590i
$22$	98.8095			0.957557
$23$	−70.3128			−0.637445			−0.318723	−	0.947848i	$-0.603254\pi$
$23$	−70.3128			−0.637445			−0.318723	+	0.947848i	$0.603254\pi$
$24$	23.7673	+	77.7405i	0.202145	+	0.661196i
$25$	16.9423			0.135539
$26$		−	8.77349i		−	0.0661778i
$27$	−109.029	−	88.2926i	−0.777138	−	0.629330i
$28$	−75.1674			−0.507333
$29$			82.7478i			0.529858i	0.964268	+	0.264929i	$0.0853485\pi$
$29$			82.7478i			0.529858i	−0.964268	+	0.264929i	$0.914651\pi$
$30$	174.082	−	53.2214i	1.05943	−	0.323895i
$31$		−	269.641i		−	1.56222i	−0.624392	−	0.781112i	$-0.714653\pi$
$31$		−	269.641i		−	1.56222i	0.624392	−	0.781112i	$-0.285347\pi$
$32$	143.063			0.790321
$33$	−44.5412	−	145.690i	−0.234959	−	0.768526i
$34$		−	125.099i		−	0.631011i
$35$		−	232.701i		−	1.12382i
$36$	−75.1622	+	50.6966i	−0.347973	+	0.234706i
$37$		−	248.510i		−	1.10418i	−0.833783	−	0.552092i	$-0.813830\pi$
$37$		−	248.510i		−	1.10418i	0.833783	−	0.552092i	$-0.186170\pi$
$38$	−393.446			−1.67961
$39$	−12.9361	+	3.95490i	−0.0531137	+	0.0162382i
$40$			162.628i			0.642845i
$41$		−	129.586i		−	0.493608i	−0.969065	−	0.246804i	$-0.920620\pi$
$41$		−	129.586i		−	0.493608i	0.969065	−	0.246804i	$-0.0793803\pi$
$42$	114.612	+	374.884i	0.421071	+	1.37728i
$43$		−	161.471i		−	0.572654i	−0.958132	−	0.286327i	$-0.907566\pi$
$43$		−	161.471i		−	0.572654i	0.958132	−	0.286327i	$-0.0924343\pi$
$44$	−98.4487			−0.337311
$45$	−156.945	−	232.685i	−0.519911	−	0.770814i
$46$	236.964			0.759531
$47$	−349.870			−1.08583			−0.542913	−	0.839789i	$-0.682678\pi$
$47$	−349.870			−1.08583			−0.542913	+	0.839789i	$0.682678\pi$
$48$	−120.908	−	395.480i	−0.363576	−	1.18922i
$49$	158.120			0.460991
$50$	−57.0980			−0.161497
$51$	−184.453	+	56.3922i	−0.506444	+	0.154833i
$52$			8.74145i			0.0233119i
$53$		−	264.779i		−	0.686230i	−0.939293	−	0.343115i	$-0.888518\pi$
$53$		−	264.779i		−	0.686230i	0.939293	−	0.343115i	$-0.111482\pi$
$54$	367.444	+	297.558i	0.925978	+	0.749862i
$55$		−	304.775i		−	0.747196i
$56$	−350.219			−0.835713
$57$	177.357	+	580.117i	0.412132	+	1.34804i
$58$		−	278.872i		−	0.631339i
$59$	404.169	+	205.003i	0.891836	+	0.452358i
$59$	404.169	+	205.003i	0.891836	+	0.452358i
$60$	−173.447	+	53.0271i	−0.373197	+	0.114096i
$61$			623.548i			1.30881i	0.756146	+	0.654403i	$0.227080\pi$
$61$			623.548i			1.30881i	−0.756146	+	0.654403i	$0.772920\pi$
$62$			908.727i			1.86143i
$63$	501.085	−	337.980i	1.00208	−	0.675896i
$64$	154.558			0.301871
$65$	−27.0615			−0.0516395
$66$	150.110	+	490.995i	0.279959	+	0.915718i
$67$		−	11.5921i		−	0.0211373i	−0.999944	−	0.0105687i	$-0.996636\pi$
$67$		−	11.5921i		−	0.0211373i	0.999944	−	0.0105687i	$-0.00336417\pi$
$68$			124.643i			0.222282i
$69$	−106.818	−	349.392i	−0.186368	−	0.609593i
$70$			784.235i			1.33906i
$71$		−	97.1804i		−	0.162439i	−0.996696	−	0.0812196i	$-0.974118\pi$
$71$		−	97.1804i		−	0.162439i	0.996696	−	0.0812196i	$-0.0258815\pi$
$72$	−350.194	+	236.205i	−0.573205	+	0.386625i
$73$			562.273i			0.901495i	0.892652	+	0.450747i	$0.148843\pi$
$73$			562.273i			0.901495i	−0.892652	+	0.450747i	$0.851157\pi$
$74$			837.513i			1.31566i
$75$	25.7386	+	84.1883i	0.0396271	+	0.129616i
$76$	392.009			0.591665
$77$	656.329			0.971372
$78$	43.5964	−	13.3286i	0.0632862	−	0.0193482i
$79$	−599.822			−0.854244			−0.427122	−	0.904194i	$-0.640472\pi$
$79$	−599.822			−0.854244			−0.427122	+	0.904194i	$0.640472\pi$
$80$		−	827.320i		−	1.15621i
$81$	273.100	−	675.912i	0.374623	−	0.927177i
$82$			436.722i			0.588145i
$83$	−499.474			−0.660534			−0.330267	−	0.943887i	$-0.607139\pi$
$83$	−499.474			−0.660534			−0.330267	+	0.943887i	$0.607139\pi$
$84$	−114.193	−	373.515i	−0.148328	−	0.485165i
$85$	−385.865			−0.492388
$86$			544.180i			0.682331i
$87$	−411.183	+	125.709i	−0.506707	+	0.154913i
$88$	−458.690			−0.555643
$89$	−530.960			−0.632378			−0.316189	−	0.948696i	$-0.602403\pi$
$89$	−530.960			−0.632378			−0.316189	+	0.948696i	$0.602403\pi$
$90$	528.927	+	784.180i	0.619486	+	0.918443i
$91$		−	58.2768i		−	0.0671326i
$92$	−236.099			−0.267554
$93$	1339.88	−	409.635i	1.49396	−	0.456743i
$94$	1179.11			1.29379
$95$			1213.57i			1.31063i
$96$	217.340	+	710.898i	0.231064	+	0.755788i
$97$			1527.88i			1.59930i	0.600464	+	0.799652i	$0.294983\pi$
$97$			1527.88i			1.59930i	−0.600464	+	0.799652i	$0.705017\pi$
$98$	−532.886			−0.549282
$99$	656.283	−	442.661i	0.666252	−	0.449384i
$100$	56.8895			0.0568895
$101$	−257.690			−0.253872			−0.126936	−	0.991911i	$-0.540514\pi$
$101$	−257.690			−0.253872			−0.126936	+	0.991911i	$0.540514\pi$
$102$	621.633	−	190.049i	0.603440	−	0.184487i
$103$			1232.61i			1.17916i	0.807712	+	0.589578i	$0.200706\pi$
$103$			1232.61i			1.17916i	−0.807712	+	0.589578i	$0.799294\pi$
$104$			40.7280i			0.0384011i
$105$	1156.32	−	353.517i	1.07472	−	0.328568i
$106$			892.342i			0.817660i
$107$		−	1418.59i		−	1.28168i	−0.767673	−	0.640842i	$-0.778586\pi$
$107$		−	1418.59i		−	1.28168i	0.767673	−	0.640842i	$-0.221414\pi$
$108$	−366.102	−	296.472i	−0.326187	−	0.264148i
$109$		−	2213.07i		−	1.94471i	−0.233498	−	0.972357i	$-0.575017\pi$
$109$		−	2213.07i		−	1.94471i	0.233498	−	0.972357i	$-0.424983\pi$
$110$			1027.13i			0.890302i
$111$	1234.87	−	377.533i	1.05594	−	0.322828i
$112$	1781.63			1.50310
$113$	−2305.55			−1.91936			−0.959682	−	0.281088i	$-0.909305\pi$
$113$	−2305.55			−1.91936			−0.959682	+	0.281088i	$0.909305\pi$
$114$	−597.717	−	1955.08i	−0.491065	−	1.60622i
$115$		−	730.907i		−	0.592674i
$116$			277.853i			0.222397i
$117$	−39.3047	−	58.2727i	−0.0310574	−	0.0460454i
$118$	−1362.11	−	690.889i	−1.06264	−	0.538996i
$119$		−	830.957i		−	0.640115i
$120$	−808.119	+	247.063i	−0.614757	+	0.187947i
$121$	−471.389			−0.354162
$122$		−	2101.44i		−	1.55947i
$123$	643.927	−	196.865i	0.472040	−	0.144315i
$124$		−	905.408i		−	0.655710i
$125$			1475.50i			1.05578i
$126$	−1688.73	+	1139.04i	−1.19400	+	0.805346i
$127$	−587.658			−0.410600			−0.205300	−	0.978699i	$-0.565817\pi$
$127$	−587.658			−0.410600			−0.205300	+	0.978699i	$0.565817\pi$
$128$	−1665.39			−1.15001
$129$	802.368	−	245.305i	0.547632	−	0.167425i
$130$	91.2011			0.0615297
$131$	830.179			0.553688			0.276844	−	0.960915i	$-0.410711\pi$
$131$	830.179			0.553688			0.276844	+	0.960915i	$0.410711\pi$
$132$	−149.562	−	489.203i	−0.0986189	−	0.322573i
$133$	−2613.41			−1.70385
$134$			39.0670i			0.0251856i
$135$	917.809	−	1133.37i	0.585129	−	0.722555i
$136$			580.733i			0.366158i
$137$			513.844i			0.320443i	0.987081	+	0.160221i	$0.0512208\pi$
$137$			513.844i			0.320443i	−0.987081	+	0.160221i	$0.948779\pi$
$138$	359.992	+	1177.50i	0.222062	+	0.726344i
$139$	−1894.55			−1.15607			−0.578033	−	0.816013i	$-0.696180\pi$
$139$	−1894.55			−1.15607			−0.578033	+	0.816013i	$0.696180\pi$
$140$		−	781.372i		−	0.471700i
$141$	−531.518	−	1738.54i	−0.317460	−	1.03838i
$142$			327.511i			0.193550i
$143$		−	76.3265i		−	0.0446346i
$144$	1781.50	−	1201.62i	1.03096	−	0.695379i
$145$	−860.170			−0.492643
$146$		−	1894.94i		−	1.07415i
$147$	240.214	+	785.715i	0.134779	+	0.440848i
$148$		−	834.455i		−	0.463458i
$149$	−2830.23			−1.55612			−0.778058	−	0.628193i	$-0.783795\pi$
$149$	−2830.23			−1.55612			−0.778058	+	0.628193i	$0.783795\pi$
$150$	−86.7425	−	283.726i	−0.0472166	−	0.154441i
$151$		−	2008.00i		−	1.08218i	−0.840965	−	0.541089i	$-0.818012\pi$
$151$		−	2008.00i		−	1.08218i	0.840965	−	0.541089i	$-0.181988\pi$
$152$	1826.44			0.974631
$153$	−560.438	−	830.899i	−0.296136	−	0.439047i
$154$	−2211.92			−1.15741
$155$	2802.94			1.45250
$156$	−43.4373	+	13.2799i	−0.0222934	+	0.00681566i
$157$		−	1331.26i		−	0.676726i	−0.941016	−	0.338363i	$-0.890127\pi$
$157$		−	1331.26i		−	0.676726i	0.941016	−	0.338363i	$-0.109873\pi$
$158$	2021.48			1.01785
$159$	1315.72	−	402.249i	0.656246	−	0.200631i
$160$			1487.15i			0.734812i
$161$	1574.00			0.770489
$162$	−920.384	+	2277.92i	−0.446372	+	1.10475i
$163$	462.931			0.222451			0.111226	−	0.993795i	$-0.464522\pi$
$163$	462.931			0.222451			0.111226	+	0.993795i	$0.464522\pi$
$164$		−	435.127i		−	0.207181i
$165$	1514.46	−	463.009i	0.714548	−	0.218456i
$166$	1683.30			0.787042
$167$			3421.98i			1.58563i	0.609460	+	0.792817i	$0.291386\pi$
$167$			3421.98i			1.58563i	−0.609460	+	0.792817i	$0.708614\pi$
$168$	−532.048	−	1740.28i	−0.244335	−	0.799198i
$169$	2190.22			0.996915
$170$	1300.42			0.586692
$171$	−2613.23	+	1762.61i	−1.16865	+	0.788248i
$172$		−	542.193i		−	0.240359i
$173$	−1531.18			−0.672910			−0.336455	−	0.941699i	$-0.609228\pi$
$173$	−1531.18			−0.672910			−0.336455	+	0.941699i	$0.609228\pi$
$174$	1385.74	−	423.658i	0.603753	−	0.184583i
$175$	−379.266			−0.163828
$176$	2333.44			0.999373
$177$	−404.675	+	2319.80i	−0.171849	+	0.985123i
$178$	1789.41			0.753494
$179$	2200.21			0.918723			0.459362	−	0.888249i	$-0.348078\pi$
$179$	2200.21			0.918723			0.459362	+	0.888249i	$0.348078\pi$
$180$	−526.995	−	781.317i	−0.218222	−	0.323533i
$181$	−2254.70			−0.925913			−0.462956	−	0.886381i	$-0.653211\pi$
$181$	−2254.70			−0.925913			−0.462956	+	0.886381i	$0.653211\pi$
$182$			196.401i			0.0799901i
$183$	−3098.48	+	947.285i	−1.25162	+	0.382652i
$184$	−1100.03			−0.440734
$185$	2583.28			1.02663
$186$	−4515.56	+	1380.53i	−1.78009	+	0.544221i
$187$		−	1088.33i		−	0.425595i
$188$	−1174.80			−0.455752
$189$	2440.70	+	1976.49i	0.939338	+	0.760681i
$190$		−	4089.90i		−	1.56164i
$191$	2228.16			0.844104			0.422052	−	0.906572i	$-0.361310\pi$
$191$	2228.16			0.844104			0.422052	+	0.906572i	$0.361310\pi$
$192$	234.802	+	768.015i	0.0882572	+	0.288681i
$193$	2575.61			0.960603			0.480301	−	0.877104i	$-0.340527\pi$
$193$	2575.61			0.960603			0.480301	+	0.877104i	$0.340527\pi$
$194$		−	5149.16i		−	1.90561i
$195$	−41.1115	−	134.472i	−0.0150977	−	0.0493832i
$196$	530.940			0.193491
$197$			4723.13i			1.70817i	0.520136	+	0.854083i	$0.325881\pi$
$197$			4723.13i			1.70817i	−0.520136	+	0.854083i	$0.674119\pi$
$198$	−2211.77	+	1491.83i	−0.793855	+	0.535452i
$199$	425.662			0.151630			0.0758151	−	0.997122i	$-0.475844\pi$
$199$	425.662			0.151630			0.0758151	+	0.997122i	$0.475844\pi$
$200$	265.058			0.0937123
$201$	57.6025	−	17.6106i	0.0202138	−	0.00617987i
$202$	868.450			0.302495
$203$		−	1852.37i		−	0.640447i
$204$	−619.363	+	189.355i	−0.212569	+	0.0649879i
$205$	1347.06			0.458939
$206$		−	4154.08i		−	1.40499i
$207$	1573.89	−	1061.58i	0.528469	−	0.356450i
$208$		−	207.191i		−	0.0690677i
$209$	−3422.85			−1.13284
$210$	−3896.95	+	1191.40i	−1.28055	+	0.391497i
$211$		−	436.103i		−	0.142287i	−0.997466	−	0.0711435i	$-0.977335\pi$
$211$		−	436.103i		−	0.142287i	0.997466	−	0.0711435i	$-0.0226648\pi$
$212$		−	889.084i		−	0.288031i
$213$	482.900	−	147.635i	0.155342	−	0.0474920i
$214$			4780.84i			1.52716i
$215$	1678.50			0.532433
$216$	−1705.74	−	1381.32i	−0.537318	−	0.435123i
$217$			6036.10i			1.88828i
$218$			7458.36i			2.31717i
$219$	−2794.00	+	854.198i	−0.862105	+	0.263568i
$220$		−	1023.38i		−	0.313620i
$221$	−96.6345			−0.0294133
$222$	−4161.70	+	1272.34i	−1.25817	+	0.384657i
$223$	−3186.19			−0.956785			−0.478392	−	0.878146i	$-0.658780\pi$
$223$	−3186.19			−0.956785			−0.478392	+	0.878146i	$0.658780\pi$
$224$	−3202.57			−0.955272
$225$	−379.240	+	255.796i	−0.112367	+	0.0757913i
$226$	7770.03			2.28697
$227$	−2499.16			−0.730727			−0.365364	−	0.930865i	$-0.619055\pi$
$227$	−2499.16			−0.730727			−0.365364	+	0.930865i	$0.619055\pi$
$228$	595.535	+	1947.94i	0.172984	+	0.565813i
$229$			1010.52i			0.291602i	0.989314	+	0.145801i	$0.0465759\pi$
$229$			1010.52i			0.291602i	−0.989314	+	0.145801i	$0.953424\pi$
$230$			2463.26i			0.706185i
$231$	997.087	+	3261.37i	0.283998	+	0.928929i
$232$			1294.57i			0.366347i
$233$	−5588.38			−1.57128			−0.785638	−	0.618687i	$-0.787665\pi$
$233$	−5588.38			−1.57128			−0.785638	+	0.618687i	$0.787665\pi$
$234$	132.462	+	196.387i	0.0370057	+	0.0548642i
$235$		−	3636.93i		−	1.00956i
$236$	1357.13	+	688.366i	0.374330	+	0.189868i
$237$	−911.242	−	2980.58i	−0.249753	−	0.816918i
$238$			2800.44i			0.762713i
$239$		−	6666.77i		−	1.80434i	−0.431379	−	0.902171i	$-0.641973\pi$
$239$		−	6666.77i		−	1.80434i	0.431379	−	0.902171i	$-0.358027\pi$
$240$	4111.04	−	1256.85i	1.10569	−	0.338040i
$241$	−3807.75			−1.01775			−0.508877	−	0.860839i	$-0.669939\pi$
$241$	−3807.75			−1.01775			−0.508877	+	0.860839i	$0.669939\pi$
$242$	1588.65			0.421992
$243$	3773.57	+	330.227i	0.996193	+	0.0871772i
$244$			2093.77i			0.549344i
$245$			1643.67i			0.428613i
$246$	−2170.12	+	663.462i	−0.562447	+	0.171955i
$247$			303.922i			0.0782918i
$248$		−	4218.46i		−	1.08013i
$249$	−758.794	−	2481.94i	−0.193119	−	0.631673i
$250$		−	4972.64i		−	1.25799i
$251$		−	2293.16i		−	0.576666i	−0.957530	−	0.288333i	$-0.906899\pi$
$251$		−	2293.16i		−	0.576666i	0.957530	−	0.288333i	$-0.0931009\pi$
$252$	1682.56	−	1134.88i	0.420600	−	0.283693i
$253$	2061.51			0.512277
$254$	1980.49			0.489240
$255$	−586.201	−	1917.41i	−0.143958	−	0.470873i
$256$	4376.12			1.06839
$257$			4853.05i			1.17792i	0.808163	+	0.588959i	$0.200462\pi$
$257$			4853.05i			1.17792i	−0.808163	+	0.588959i	$0.799538\pi$
$258$	−2704.09	+	826.711i	−0.652517	+	0.199491i
$259$			5563.07i			1.33464i
$260$	−90.8681			−0.0216746
$261$	−1249.33	−	1852.24i	−0.296289	−	0.439275i
$262$	−2797.82			−0.659732
$263$		−	1427.79i		−	0.334759i	−0.985893	−	0.167379i	$-0.946470\pi$
$263$		−	1427.79i		−	0.334759i	0.985893	−	0.167379i	$-0.0535305\pi$
$264$	−696.836	−	2279.28i	−0.162452	−	0.531364i
$265$	2752.40			0.638032
$266$	8807.56			2.03017
$267$	−806.628	−	2638.40i	−0.184887	−	0.604747i
$268$		−	38.9243i		−	0.00887195i
$269$	−1987.25			−0.450426			−0.225213	−	0.974310i	$-0.572308\pi$
$269$	−1987.25			−0.450426			−0.225213	+	0.974310i	$0.572308\pi$
$270$	−3093.14	+	3819.61i	−0.697195	+	0.860941i
$271$	6430.82			1.44149			0.720746	−	0.693199i	$-0.243799\pi$
$271$	6430.82			1.44149			0.720746	+	0.693199i	$0.243799\pi$
$272$		−	2954.29i		−	0.658567i
$273$	289.584	−	88.5333i	0.0641993	−	0.0196274i
$274$		−	1731.73i		−	0.381815i
$275$	−496.734			−0.108924
$276$	−358.678	−	1173.20i	−0.0782242	−	0.255864i
$277$	2442.33			0.529766			0.264883	−	0.964281i	$-0.414667\pi$
$277$	2442.33			0.529766			0.264883	+	0.964281i	$0.414667\pi$
$278$	6384.88			1.37748
$279$	4071.04	+	6035.68i	0.873573	+	1.29515i
$280$		−	3640.55i		−	0.777016i
$281$		−	8202.30i		−	1.74131i	−0.491894	−	0.870655i	$-0.663695\pi$
$281$		−	8202.30i		−	1.74131i	0.491894	−	0.870655i	$-0.336305\pi$
$282$	1791.29	+	5859.13i	0.378261	+	1.23726i
$283$		−	4649.58i		−	0.976639i	−0.872665	−	0.488320i	$-0.837610\pi$
$283$		−	4649.58i		−	0.976639i	0.872665	−	0.488320i	$-0.162390\pi$
$284$		−	326.315i		−	0.0681805i
$285$	−6030.37	+	1843.64i	−1.25336	+	0.383185i
$286$			257.231i			0.0531832i
$287$			2900.87i			0.596631i
$288$	−3202.35	+	2159.97i	−0.655209	+	0.441936i
$289$	3535.11			0.719541
$290$	2898.89			0.586996
$291$	−7592.20	+	2321.13i	−1.52942	+	0.467585i
$292$			1888.02i			0.378384i
$293$		−	3469.71i		−	0.691817i	−0.938268	−	0.345909i	$-0.887571\pi$
$293$		−	3469.71i		−	0.691817i	0.938268	−	0.345909i	$-0.112429\pi$
$294$	−809.553	−	2647.97i	−0.160592	−	0.525281i
$295$	−2131.02	+	4201.37i	−0.420587	+	0.829197i
$296$		−	3887.88i		−	0.763440i
$297$	3196.65	+	2588.66i	0.624540	+	0.505756i
$298$	9538.26			1.85415
$299$		−	183.046i		−	0.0354040i
$300$	86.4258	+	282.690i	0.0166326	+	0.0544038i
$301$			3614.64i			0.692175i
$302$			6767.24i			1.28944i
$303$	−391.479	−	1280.49i	−0.0742240	−	0.242780i
$304$	−9291.43			−1.75296
$305$	−6481.83			−1.21688
$306$	1888.75	+	2800.25i	0.352853	+	0.523135i
$307$	307.080			0.0570879			0.0285439	−	0.999593i	$-0.490913\pi$
$307$	307.080			0.0570879			0.0285439	+	0.999593i	$0.490913\pi$
$308$	2203.84			0.407713
$309$	−6125.00	+	1872.57i	−1.12763	+	0.344747i
$310$	−9446.29			−1.73069
$311$		−	3479.56i		−	0.634430i	−0.948354	−	0.317215i	$-0.897252\pi$
$311$		−	3479.56i		−	0.634430i	0.948354	−	0.317215i	$-0.102748\pi$
$312$	−202.382	+	61.8734i	−0.0367232	+	0.0112272i
$313$			7489.91i			1.35257i	0.736640	+	0.676285i	$0.236411\pi$
$313$			7489.91i			1.35257i	−0.736640	+	0.676285i	$0.763589\pi$
$314$			4486.52i			0.806335i
$315$	3513.33	+	5208.82i	0.628424	+	0.931694i
$316$	−2014.10			−0.358551
$317$			1313.10i			0.232654i	0.993211	+	0.116327i	$0.0371120\pi$
$317$			1313.10i			0.232654i	−0.993211	+	0.116327i	$0.962888\pi$
$318$	−4434.15	+	1355.63i	−0.781933	+	0.239057i
$319$		−	2426.09i		−	0.425816i
$320$			1606.64i			0.280669i
$321$	7049.12	−	2155.10i	1.22568	−	0.374723i
$322$	−5304.60			−0.918056
$323$			4333.56i			0.746520i
$324$	917.023	−	2269.60i	0.157240	−	0.389163i
$325$			44.1060i			0.00752788i
$326$	−1560.14			−0.265056
$327$	10997.0	−	3362.07i	1.85974	−	0.568571i
$328$		−	2027.34i		−	0.341284i
$329$	7832.09			1.31245
$330$	−5103.94	+	1560.41i	−0.851401	+	0.260296i
$331$	−9986.34			−1.65830			−0.829152	−	0.559023i	$-0.811176\pi$
$331$	−9986.34			−1.65830			−0.829152	+	0.559023i	$0.811176\pi$
$332$	−1677.15			−0.277245
$333$	3752.01	+	5562.68i	0.617444	+	0.915415i
$334$		−	11532.6i		−	1.88932i
$335$	120.501			0.0196527
$336$	2706.62	+	8853.09i	0.439459	+	1.43743i
$337$		−	3454.99i		−	0.558473i	−0.960222	−	0.279236i	$-0.909919\pi$
$337$		−	3454.99i		−	0.558473i	0.960222	−	0.279236i	$-0.0900813\pi$
$338$	−7381.35			−1.18785
$339$	−3502.56	−	11456.5i	−0.561160	−	1.83550i
$340$	−1295.67			−0.206669
$341$			7905.63i			1.25547i
$342$	8806.95	−	5940.25i	1.39247	−	0.939216i
$343$	4138.67			0.651508
$344$		−	2526.17i		−	0.395937i
$345$	3631.96	−	1110.38i	0.566777	−	0.173279i
$346$	5160.29			0.801789
$347$	−3191.72			−0.493776			−0.246888	−	0.969044i	$-0.579408\pi$
$347$	−3191.72			−0.493776			−0.246888	+	0.969044i	$0.579408\pi$
$348$	−1380.68	+	422.111i	−0.212679	+	0.0650216i
$349$			285.854i			0.0438435i	0.999760	+	0.0219218i	$0.00697848\pi$
$349$			285.854i			0.0438435i	−0.999760	+	0.0219218i	$0.993022\pi$
$350$	1278.18			0.195204
$351$	229.852	−	283.837i	0.0349533	−	0.0431626i
$352$	−4194.49			−0.635134
$353$	1417.10			0.213668			0.106834	−	0.994277i	$-0.465929\pi$
$353$	1417.10			0.213668			0.106834	+	0.994277i	$0.465929\pi$
$354$	1363.81	−	7818.05i	0.204762	−	1.17380i
$355$	1010.20			0.151030
$356$	−1782.88			−0.265428
$357$	4129.12	−	1262.38i	0.612146	−	0.187149i
$358$	−7415.01			−1.09468
$359$		−	1416.48i		−	0.208242i	−0.994565	−	0.104121i	$-0.966797\pi$
$359$		−	1416.48i		−	0.208242i	0.994565	−	0.104121i	$-0.0332029\pi$
$360$	−2455.37	−	3640.30i	−0.359470	−	0.532946i
$361$	6770.32			0.987071
$362$	7598.64			1.10325
$363$	−716.128	−	2342.38i	−0.103545	−	0.338687i
$364$		−	195.684i		−	0.0281775i
$365$	−5844.88			−0.838178
$366$	10442.3	−	3192.48i	1.49133	−	0.455939i
$367$		−	12370.0i		−	1.75943i	−0.475503	−	0.879714i	$-0.657734\pi$
$367$		−	12370.0i		−	1.75943i	0.475503	−	0.879714i	$-0.342266\pi$
$368$	5596.03			0.792699
$369$	1956.49	+	2900.67i	0.276018	+	0.409222i
$370$	−8706.02			−1.22325
$371$			5927.27i			0.829456i
$372$	4499.08	−	1375.48i	0.627060	−	0.191708i
$373$	7175.24			0.996031			0.498016	−	0.867168i	$-0.334062\pi$
$373$	7175.24			0.996031			0.498016	+	0.867168i	$0.334062\pi$
$374$			3667.81i			0.507106i
$375$	−7331.93	+	2241.56i	−1.00965	+	0.308677i
$376$	−5473.63			−0.750747
$377$	−215.418			−0.0294286
$378$	−8225.50	−	6661.05i	−1.11924	−	0.906369i
$379$	−7996.12			−1.08373			−0.541864	−	0.840466i	$-0.682281\pi$
$379$	−7996.12			−1.08373			−0.541864	+	0.840466i	$0.682281\pi$
$380$			4074.97i			0.550109i
$381$	−892.762	−	2920.14i	−0.120046	−	0.392660i
$382$	−7509.20			−1.00577
$383$			4584.32i			0.611613i	0.952094	+	0.305807i	$0.0989261\pi$
$383$			4584.32i			0.611613i	−0.952094	+	0.305807i	$0.901074\pi$
$384$	−2530.03	−	8275.50i	−0.336225	−	1.09976i
$385$			6822.59i			0.903147i
$386$	−8680.15			−1.14458
$387$	2437.89	+	3614.39i	0.320220	+	0.474754i
$388$			5130.36i			0.671274i
$389$		−	10782.3i		−	1.40536i	−0.711504	−	0.702682i	$-0.751986\pi$
$389$		−	10782.3i		−	1.40536i	0.711504	−	0.702682i	$-0.248014\pi$
$390$	138.551	+	453.188i	0.0179893	+	0.0588413i
$391$		−	2610.01i		−	0.337580i
$392$	2473.75			0.318732
$393$	1261.20	+	4125.25i	0.161880	+	0.529495i
$394$		−	15917.6i		−	2.03532i
$395$		−	6235.20i		−	0.794245i
$396$	2203.69	−	1486.38i	0.279645	−	0.188620i
$397$			14023.6i			1.77285i	0.462869	+	0.886426i	$0.346820\pi$
$397$			14023.6i			1.77285i	−0.462869	+	0.886426i	$0.653180\pi$
$398$	−1434.54			−0.180671
$399$	−3970.26	−	12986.3i	−0.498149	−	1.62940i
$400$	−1348.40			−0.168550
$401$	11372.8			1.41629			0.708143	−	0.706069i	$-0.249533\pi$
$401$	11372.8			1.41629			0.708143	+	0.706069i	$0.249533\pi$
$402$	−194.128	+	59.3501i	−0.0240852	+	0.00736346i
$403$	701.956			0.0867666
$404$	−865.279			−0.106558
$405$	7026.16	+	2838.89i	0.862056	+	0.348311i
$406$			6242.74i			0.763108i
$407$			7286.10i			0.887367i
$408$	−2885.73	+	882.242i	−0.350159	+	0.107053i
$409$			12028.5i			1.45421i	0.686527	+	0.727104i	$0.259134\pi$
$409$			12028.5i			1.45421i	−0.686527	+	0.727104i	$0.740866\pi$
$410$	−4539.76			−0.546836
$411$	−2553.35	+	780.625i	−0.306441	+	0.0936871i
$412$			4138.91i			0.494926i
$413$	−9047.61	−	4589.14i	−1.07798	−	0.546772i
$414$	−5304.23	+	3577.69i	−0.629683	+	0.424719i
$415$		−	5192.07i		−	0.614141i
$416$			372.437i			0.0438948i
$417$	−2878.17	−	9414.21i	−0.337996	−	1.10555i
$418$	11535.5			1.34981
$419$	6467.36			0.754060			0.377030	−	0.926201i	$-0.376945\pi$
$419$	6467.36			0.754060			0.377030	+	0.926201i	$0.376945\pi$
$420$	3882.72	−	1187.05i	0.451089	−	0.137910i
$421$			11696.5i			1.35404i	0.735964	+	0.677021i	$0.236729\pi$
$421$			11696.5i			1.35404i	−0.735964	+	0.677021i	$0.763271\pi$
$422$			1469.73i			0.169538i
$423$	7831.54	−	5282.34i	0.900195	−	0.607178i
$424$		−	4142.40i		−	0.474464i
$425$			628.899i			0.0717790i
$426$	−1627.44	+	497.551i	−0.185093	+	0.0565878i
$427$		−	13958.6i		−	1.58197i
$428$		−	4763.38i		−	0.537960i
$429$	379.275	−	115.954i	0.0426843	−	0.0130497i
$430$	−5656.79			−0.634407
$431$	−15276.2			−1.70726			−0.853630	−	0.520880i	$-0.825604\pi$
$431$	−15276.2			−1.70726			−0.853630	+	0.520880i	$0.825604\pi$
$432$	8677.39	+	7027.00i	0.966415	+	0.782608i
$433$	8311.84			0.922497			0.461249	−	0.887271i	$-0.347402\pi$
$433$	8311.84			0.922497			0.461249	+	0.887271i	$0.347402\pi$
$434$		−	20342.5i		−	2.24993i
$435$	−1306.76	−	4274.28i	−0.144033	−	0.471118i
$436$		−	7431.12i		−	0.816253i
$437$	−8208.65			−0.898565
$438$	9416.17	−	2878.77i	1.02722	−	0.314047i
$439$	−11860.1			−1.28941			−0.644705	−	0.764431i	$-0.723020\pi$
$439$	−11860.1			−1.28941			−0.644705	+	0.764431i	$0.723020\pi$
$440$		−	4768.12i		−	0.516617i
$441$	−3539.38	+	2387.30i	−0.382181	+	0.257779i
$442$	325.672			0.0350467
$443$	−4519.87			−0.484753			−0.242376	−	0.970182i	$-0.577927\pi$
$443$	−4519.87			−0.484753			−0.242376	+	0.970182i	$0.577927\pi$
$444$	4146.50	−	1267.69i	0.443208	−	0.135500i
$445$		−	5519.37i		−	0.587963i
$446$	10737.9			1.14003
$447$	−4299.64	−	14063.7i	−0.454958	−	1.48812i
$448$	−3459.89			−0.364876
$449$			7370.48i			0.774687i	0.921935	+	0.387344i	$0.126607\pi$
$449$			7370.48i			0.774687i	−0.921935	+	0.387344i	$0.873393\pi$
$450$	1278.09	−	862.066i	0.133888	−	0.0903071i
$451$			3799.34i			0.396683i
$452$	−7741.66			−0.805613
$453$	9977.99	−	3050.53i	1.03489	−	0.316394i
$454$	8422.52			0.870679
$455$	605.792			0.0624175
$456$	2774.70	+	9075.79i	0.284951	+	0.932046i
$457$			8543.74i			0.874528i	0.899333	+	0.437264i	$0.144052\pi$
$457$			8543.74i			0.874528i	−0.899333	+	0.437264i	$0.855948\pi$
$458$		−	3405.58i		−	0.347451i
$459$	3277.42	−	4047.17i	0.333283	−	0.411559i
$460$		−	2454.26i		−	0.248762i
$461$		−	2030.35i		−	0.205125i	−0.994727	−	0.102563i	$-0.967296\pi$
$461$		−	2030.35i		−	0.205125i	0.994727	−	0.102563i	$-0.0327042\pi$
$462$	−3360.32	−	10991.3i	−0.338390	−	1.10684i
$463$		−	6633.07i		−	0.665799i	−0.942962	−	0.332899i	$-0.891973\pi$
$463$		−	6633.07i		−	0.665799i	0.942962	−	0.332899i	$-0.108027\pi$
$464$		−	6585.70i		−	0.658909i
$465$	4258.18	+	13928.1i	0.424664	+	1.38903i
$466$	18833.6			1.87221
$467$	477.556			0.0473204			0.0236602	−	0.999720i	$-0.492468\pi$
$467$	477.556			0.0473204			0.0236602	+	0.999720i	$0.492468\pi$
$468$	−131.979	−	195.670i	−0.0130357	−	0.0193266i
$469$			259.497i			0.0255490i
$470$			12256.9i			1.20292i
$471$	6615.17	−	2022.43i	0.647157	−	0.197853i
$472$	6323.12	+	3207.22i	0.616622	+	0.312764i
$473$			4734.19i			0.460208i
$474$	3071.01	+	10045.0i	0.297587	+	0.973378i
$475$	1977.93			0.191060
$476$		−	2790.21i		−	0.268675i
$477$	3997.64	+	5926.85i	0.383730	+	0.568914i
$478$			22467.9i			2.14992i
$479$			4268.57i			0.407173i	0.979057	+	0.203587i	$0.0652599\pi$
$479$			4268.57i			0.407173i	−0.979057	+	0.203587i	$0.934740\pi$
$480$	−7389.84	+	2259.26i	−0.702705	+	0.214835i
$481$	646.947			0.0613269
$482$	12832.7			1.21268
$483$	2391.20	+	7821.39i	0.225266	+	0.736823i
$484$	−1582.85			−0.148652
$485$	−15882.4			−1.48698
$486$	−12717.5	−	1112.91i	−1.18699	−	0.103874i
$487$	−8039.94			−0.748100			−0.374050	−	0.927409i	$-0.622031\pi$
$487$	−8039.94			−0.748100			−0.374050	+	0.927409i	$0.622031\pi$
$488$			9755.25i			0.904917i
$489$	703.279	+	2300.36i	0.0650376	+	0.212732i
$490$		−	5539.39i		−	0.510702i
$491$			13575.7i			1.24778i	0.781511	+	0.623892i	$0.214449\pi$
$491$			13575.7i			1.24778i	−0.781511	+	0.623892i	$0.785551\pi$
$492$	2162.20	−	661.040i	0.198129	−	0.0605731i
$493$	−3071.60			−0.280604
$494$		−	1024.26i		−	0.0932865i
$495$	4601.49	+	6822.12i	0.417822	+	0.619457i
$496$			21460.1i			1.94271i
$497$			2175.45i			0.196343i
$498$	2557.24	+	8364.48i	0.230106	+	0.752653i
$499$	2461.10			0.220789			0.110395	−	0.993888i	$-0.464788\pi$
$499$	2461.10			0.220789			0.110395	+	0.993888i	$0.464788\pi$
$500$			4954.49i			0.443143i
$501$	−17004.2	+	5198.63i	−1.51635	+	0.463588i
$502$			7728.27i			0.687111i
$503$	−10940.9			−0.969841			−0.484920	−	0.874558i	$-0.661151\pi$
$503$	−10940.9			−0.969841			−0.484920	+	0.874558i	$0.661151\pi$
$504$	7839.35	−	5287.61i	0.692842	−	0.467319i
$505$		−	2678.71i		−	0.236041i
$506$	−6947.57			−0.610390
$507$	3327.36	+	10883.5i	0.291466	+	0.953356i
$508$	−1973.26			−0.172341
$509$	6598.10			0.574569			0.287284	−	0.957845i	$-0.407248\pi$
$509$	6598.10			0.574569			0.287284	+	0.957845i	$0.407248\pi$
$510$	1975.58	+	6461.93i	0.171530	+	0.561057i
$511$		−	12586.9i		−	1.08965i
$512$	−1425.04			−0.123005
$513$	−12728.6	−	10307.7i	−1.09548	−	0.887126i
$514$		−	16355.5i		−	1.40352i
$515$	−12813.1			−1.09634
$516$	2694.22	−	823.692i	0.229857	−	0.0702733i
$517$	10257.9			0.872613
$518$		−	18748.3i		−	1.59026i
$519$	−2326.15	−	7608.61i	−0.196737	−	0.643508i
$520$	−423.371			−0.0357039
$521$			14069.4i			1.18310i	0.806270	+	0.591548i	$0.201483\pi$
$521$			14069.4i			1.18310i	−0.806270	+	0.591548i	$0.798517\pi$
$522$	4210.41	+	6242.30i	0.353036	+	0.523406i
$523$	8391.38			0.701586			0.350793	−	0.936453i	$-0.385912\pi$
$523$	8391.38			0.701586			0.350793	+	0.936453i	$0.385912\pi$
$524$	2787.60			0.232399
$525$	−576.176	−	1884.62i	−0.0478979	−	0.156669i
$526$			4811.87i			0.398873i
$527$	10009.1			0.827328
$528$	3544.93	+	11595.1i	0.292184	+	0.955706i
$529$	−7223.11			−0.593664
$530$	−9275.97			−0.760231
$531$	−12142.1	+	1513.33i	−0.992322	+	0.123678i
$532$	−8775.40			−0.715154
$533$	337.351			0.0274152
$534$	2718.45	+	8891.77i	0.220297	+	0.720571i
$535$	14746.3			1.19166
$536$		−	181.356i		−	0.0146145i
$537$	3342.53	+	10933.1i	0.268605	+	0.878581i
$538$	6697.29			0.536693
$539$	−4635.94			−0.370471
$540$	3081.85	−	3805.66i	0.245596	−	0.303277i
$541$		−	22826.0i		−	1.81398i	−0.421150	−	0.906991i	$-0.638373\pi$
$541$		−	22826.0i		−	1.81398i	0.421150	−	0.906991i	$-0.361627\pi$
$542$	−21672.7			−1.71757
$543$	−3425.30	−	11203.8i	−0.270707	−	0.885456i
$544$			5310.51i			0.418541i
$545$	23005.1			1.80813
$546$	−975.937	+	298.369i	−0.0764950	+	0.0233865i
$547$	−12977.5			−1.01440			−0.507201	−	0.861828i	$-0.669320\pi$
$547$	−12977.5			−1.01440			−0.507201	+	0.861828i	$0.669320\pi$
$548$			1725.40i			0.134499i
$549$	−9414.33	−	13957.6i	−0.731865	−	1.08505i
$550$	1674.06			0.129786
$551$			9660.37i			0.746907i
$552$	−1671.15	−	5466.15i	−0.128856	−	0.421476i
$553$	13427.4			1.03254
$554$	−8230.97			−0.631228
$555$	3924.49	+	12836.6i	0.300153	+	0.981773i
$556$	−6361.57			−0.485235
$557$			22118.7i			1.68258i	0.540582	+	0.841291i	$0.318204\pi$
$557$			22118.7i			1.68258i	−0.540582	+	0.841291i	$0.681796\pi$
$558$	−13720.0	−	20341.1i	−1.04088	−	1.54320i
$559$	420.358			0.0318055
$560$			18520.1i			1.39753i
$561$	5408.01	−	1653.37i	0.406999	−	0.124430i
$562$			27642.9i			2.07481i
$563$	1124.63			0.0841877			0.0420939	−	0.999114i	$-0.486597\pi$
$563$	1124.63			0.0841877			0.0420939	+	0.999114i	$0.486597\pi$
$564$	−1784.75	−	5837.74i	−0.133247	−	0.435839i
$565$		−	23966.4i		−	1.78456i
$566$			15669.7i			1.16369i
$567$	−6113.53	+	15130.8i	−0.452812	+	1.12069i
$568$		−	1520.36i		−	0.112312i
$569$	−5453.65			−0.401808			−0.200904	−	0.979611i	$-0.564388\pi$
$569$	−5453.65			−0.401808			−0.200904	+	0.979611i	$0.564388\pi$
$570$	20323.2	−	6213.32i	1.49341	−	0.456574i
$571$			1714.66i			0.125668i	0.998024	+	0.0628340i	$0.0200139\pi$
$571$			1714.66i			0.125668i	−0.998024	+	0.0628340i	$0.979986\pi$
$572$		−	256.292i		−	0.0187344i
$573$	3384.99	+	11072.0i	0.246789	+	0.807222i
$574$		−	9776.33i		−	0.710900i
$575$	−1191.26			−0.0863984
$576$	−3459.65	+	2333.52i	−0.250264	+	0.168802i
$577$	6334.02			0.456999			0.228500	−	0.973544i	$-0.426618\pi$
$577$	6334.02			0.456999			0.228500	+	0.973544i	$0.426618\pi$
$578$	−11913.8			−0.857351
$579$	3912.83	+	12798.5i	0.280849	+	0.918630i
$580$	−2888.31			−0.206777
$581$	11181.1			0.798397
$582$	25586.7	−	7822.53i	1.82235	−	0.557138i
$583$			7763.09i			0.551482i
$584$			8796.63i			0.623300i
$585$	605.749	−	408.575i	0.0428114	−	0.0288761i
$586$			11693.4i			0.824316i
$587$	−303.276			−0.0213246			−0.0106623	−	0.999943i	$-0.503394\pi$
$587$	−303.276			−0.0213246			−0.0106623	+	0.999943i	$0.503394\pi$
$588$	806.597	+	2638.30i	0.0565706	+	0.185037i
$589$		−	31479.1i		−	2.20216i
$590$	7181.85	−	14159.2i	0.501139	−	0.988008i
$591$	−23469.7	+	7175.31i	−1.63353	+	0.499413i
$592$			19778.3i			1.37311i
$593$			607.929i			0.0420989i	0.999778	+	0.0210495i	$0.00670075\pi$
$593$			607.929i			0.0420989i	−0.999778	+	0.0210495i	$0.993299\pi$
$594$	−10773.1	−	8724.15i	−0.744154	−	0.602620i
$595$	8637.87			0.595156
$596$	−9503.43			−0.653147
$597$	646.661	+	2115.16i	0.0443318	+	0.145005i
$598$			616.889i			0.0421847i
$599$		−	24611.8i		−	1.67882i	−0.543499	−	0.839410i	$-0.682901\pi$
$599$		−	24611.8i		−	1.67882i	0.543499	−	0.839410i	$-0.317099\pi$
$600$	402.673	+	1317.11i	0.0273984	+	0.0896176i
$601$			11034.3i			0.748915i	0.927244	+	0.374458i	$0.122171\pi$
$601$			11034.3i			0.748915i	−0.927244	+	0.374458i	$0.877829\pi$
$602$		−	12181.9i		−	0.824743i
$603$	175.018	+	259.479i	0.0118197	+	0.0175237i
$604$		−	6742.53i		−	0.454222i
$605$		−	4900.13i		−	0.329287i
$606$	1319.34	+	4315.43i	0.0884397	+	0.289278i
$607$	−25937.9			−1.73441			−0.867204	−	0.497953i	$-0.834085\pi$
$607$	−25937.9			−1.73441			−0.867204	+	0.497953i	$0.834085\pi$
$608$	16701.9			1.11406
$609$	9204.63	−	2814.09i	0.612464	−	0.187246i
$610$	21844.7			1.44994
$611$		−	910.817i		−	0.0603072i
$612$	−1881.86	−	2790.02i	−0.124297	−	0.184281i
$613$			25833.1i			1.70211i	0.525081	+	0.851053i	$0.324035\pi$
$613$			25833.1i			1.70211i	−0.525081	+	0.851053i	$0.675965\pi$
$614$	−1034.90			−0.0680216
$615$	2046.43	+	6693.67i	0.134179	+	0.438886i
$616$	10268.1			0.671613
$617$		−	2140.04i		−	0.139635i	−0.997560	−	0.0698174i	$-0.977758\pi$
$617$		−	2140.04i		−	0.139635i	0.997560	−	0.0698174i	$-0.0222417\pi$
$618$	20642.1	−	6310.82i	1.34360	−	0.410774i
$619$	24476.2			1.58931			0.794655	−	0.607061i	$-0.207652\pi$
$619$	24476.2			1.58931			0.794655	+	0.607061i	$0.207652\pi$
$620$	9411.79			0.609656
$621$	7666.17	+	6208.10i	0.495383	+	0.401164i
$622$			11726.6i			0.755938i
$623$	11885.9			0.764365
$624$	1029.55	−	314.761i	0.0660499	−	0.0201932i
$625$	−13220.2			−0.846091
$626$		−	25242.0i		−	1.61162i
$627$	−5199.95	−	17008.5i	−0.331206	−	1.08334i
$628$		−	4470.14i		−	0.284041i
$629$	9224.69			0.584757
$630$	−11840.4	−	17554.4i	−0.748782	−	1.11014i
$631$	24399.6			1.53936			0.769678	−	0.638432i	$-0.220417\pi$
$631$	24399.6			1.53936			0.769678	+	0.638432i	$0.220417\pi$
$632$	−9384.07			−0.590630
$633$	2167.04	−	662.521i	0.136070	−	0.0416001i
$634$		−	4425.34i		−	0.277212i
$635$		−	6108.75i		−	0.381761i
$636$	4417.96	−	1350.68i	0.275445	−	0.0842108i
$637$			411.634i			0.0256036i
$638$			8176.27i			0.507369i
$639$	1467.23	+	2175.30i	0.0908337	+	0.134669i
$640$		−	17311.8i		−	1.06924i
$641$		−	30992.3i		−	1.90971i	−0.297075	−	0.954854i	$-0.596011\pi$
$641$		−	30992.3i		−	1.90971i	0.297075	−	0.954854i	$-0.403989\pi$
$642$	−23756.5	+	7262.99i	−1.46043	+	0.446491i
$643$	−12100.0			−0.742111			−0.371056	−	0.928611i	$-0.621004\pi$
$643$	−12100.0			−0.742111			−0.371056	+	0.928611i	$0.621004\pi$
$644$	5285.23			0.323397
$645$	2549.96	+	8340.68i	0.155666	+	0.509169i
$646$		−	14604.7i		−	0.889496i
$647$		−	7277.03i		−	0.442179i	−0.975254	−	0.221089i	$-0.929039\pi$
$647$		−	7277.03i		−	0.442179i	0.975254	−	0.221089i	$-0.0709612\pi$
$648$	4272.58	−	10574.5i	0.259017	−	0.641057i
$649$	−11849.9	−	6010.51i	−0.716716	−	0.363534i
$650$		−	148.643i		−	0.00896965i
$651$	−29994.1	+	9169.96i	−1.80578	+	0.552072i
$652$	1554.45			0.0933693
$653$		−	22976.1i		−	1.37691i	−0.725277	−	0.688457i	$-0.758288\pi$
$653$		−	22976.1i		−	1.37691i	0.725277	−	0.688457i	$-0.241712\pi$
$654$	−37061.4	+	11330.6i	−2.21593	+	0.677466i
$655$			8629.78i			0.514799i
$656$			10313.4i			0.613829i
$657$	−8489.21	−	12586.0i	−0.504103	−	0.747377i
$658$	−26395.2			−1.56382
$659$	28281.7			1.67177			0.835886	−	0.548904i	$-0.184955\pi$
$659$	28281.7			1.67177			0.835886	+	0.548904i	$0.184955\pi$
$660$	5085.30	−	1554.71i	0.299917	−	0.0916923i
$661$	−4139.77			−0.243598			−0.121799	−	0.992555i	$-0.538866\pi$
$661$	−4139.77			−0.243598			−0.121799	+	0.992555i	$0.538866\pi$
$662$	33655.3			1.97591
$663$	−146.806	−	480.188i	−0.00859950	−	0.0281281i
$664$	−7814.14			−0.456698
$665$		−	27166.6i		−	1.58418i
$666$	−12644.8	−	18747.0i	−0.735699	−	1.09074i
$667$		−	5818.23i		−	0.337755i
$668$			11490.4i			0.665537i
$669$	−4840.41	−	15832.5i	−0.279733	−	0.914979i
$670$	−406.105			−0.0234167
$671$		−	18281.9i		−	1.05181i
$672$	−4865.31	−	15913.9i	−0.279291	−	0.913532i
$673$			20873.4i			1.19556i	0.801662	+	0.597778i	$0.203950\pi$
$673$			20873.4i			1.19556i	−0.801662	+	0.597778i	$0.796050\pi$
$674$			11643.8i			0.665433i
$675$	−1847.21	−	1495.88i	−0.105332	−	0.0852986i
$676$	7354.40			0.418434
$677$			16752.5i			0.951035i	0.879706	+	0.475518i	$0.157739\pi$
$677$			16752.5i			0.951035i	−0.879706	+	0.475518i	$0.842261\pi$
$678$	11804.1	+	38610.2i	0.668635	+	2.18704i
$679$		−	34202.6i		−	1.93310i
$680$	−6036.76			−0.340440
$681$	−3796.69	−	12418.6i	−0.213641	−	0.698799i
$682$		−	26643.1i		−	1.49592i
$683$	2366.97			0.132605			0.0663027	−	0.997800i	$-0.478880\pi$
$683$	2366.97			0.132605			0.0663027	+	0.997800i	$0.478880\pi$
$684$	−8774.79	+	5918.56i	−0.490515	+	0.330851i
$685$	−5341.45			−0.297936
$686$	−13947.9			−0.776288
$687$	−5021.37	+	1535.16i	−0.278861	+	0.0852549i
$688$			12851.1i			0.712127i
$689$	689.300			0.0381135
$690$	−12240.2	+	3742.15i	−0.675329	+	0.206466i
$691$		−	1808.80i		−	0.0995804i	−0.998760	−	0.0497902i	$-0.984145\pi$
$691$		−	1808.80i		−	0.0995804i	0.998760	−	0.0497902i	$-0.0158553\pi$
$692$	−5141.45			−0.282440
$693$	−14691.4	+	9909.27i	−0.805309	+	0.543178i
$694$	10756.5			0.588346
$695$		−	19693.9i		−	1.07487i
$696$	−6432.86	+	1966.69i	−0.350340	+	0.107108i
$697$	4810.22			0.261406
$698$		−	963.366i		−	0.0522406i
$699$	−8489.80	−	27769.3i	−0.459390	−	1.50262i
$700$	−1273.51			−0.0687632
$701$	−28316.6			−1.52568			−0.762841	−	0.646587i	$-0.776196\pi$
$701$	−28316.6			−1.52568			−0.762841	+	0.646587i	$0.776196\pi$
$702$	−774.634	+	956.568i	−0.0416477	+	0.0514293i
$703$		−	29012.2i		−	1.55650i
$704$	−4531.50			−0.242596
$705$	18072.3	−	5525.17i	0.965449	−	0.295163i
$706$	−4775.83			−0.254590
$707$	5768.57			0.306859
$708$	−1358.83	+	7789.50i	−0.0721300	+	0.413485i
$709$	−12039.6			−0.637737			−0.318869	−	0.947799i	$-0.603303\pi$
$709$	−12039.6			−0.637737			−0.318869	+	0.947799i	$0.603303\pi$
$710$	−3404.51			−0.179956
$711$	13426.5	−	9056.12i	0.708204	−	0.477681i
$712$	−8306.74			−0.437231
$713$			18959.2i			0.995831i
$714$	−13915.7	+	4254.39i	−0.729387	+	0.222992i
$715$	793.420			0.0414996
$716$	7387.94			0.385615
$717$	33127.9	−	10128.1i	1.72550	−	0.527531i
$718$			4773.73i			0.248125i
$719$	19566.3			1.01488			0.507442	−	0.861686i	$-0.330591\pi$
$719$	19566.3			1.01488			0.507442	+	0.861686i	$0.330591\pi$
$720$	12490.9	+	18518.8i	0.646539	+	0.958551i
$721$		−	27592.9i		−	1.42526i
$722$	−22816.9			−1.17612
$723$	−5784.69	−	18921.1i	−0.297559	−	0.973285i
$724$	−7570.89			−0.388632
$725$			1401.94i			0.0718162i
$726$	2413.45	+	7894.16i	0.123377	+	0.403553i
$727$	−12878.8			−0.657014			−0.328507	−	0.944502i	$-0.606545\pi$
$727$	−12878.8			−0.657014			−0.328507	+	0.944502i	$0.606545\pi$
$728$		−	911.725i		−	0.0464159i
$729$	4091.83	+	19253.0i	0.207886	+	0.978153i
$730$	19698.0			0.998709
$731$	5993.81			0.303268
$732$	−10404.2	+	3180.83i	−0.525340	+	0.160610i
$733$	−31693.2			−1.59702			−0.798509	−	0.601983i	$-0.794377\pi$
$733$	−31693.2			−1.59702			−0.798509	+	0.601983i	$0.794377\pi$
$734$			41688.7i			2.09640i
$735$	−8167.57	+	2497.04i	−0.409885	+	0.125312i
$736$	−10059.2			−0.503786
$737$			339.870i			0.0169868i
$738$	−6593.64	−	9775.65i	−0.328882	−	0.487597i
$739$			22257.6i			1.10793i	0.832541	+	0.553963i	$0.186885\pi$
$739$			22257.6i			1.10793i	−0.832541	+	0.553963i	$0.813115\pi$
$740$	8674.23			0.430907
$741$	−1510.22	+	461.714i	−0.0748709	+	0.0228900i
$742$		−	19975.7i		−	0.988317i
$743$			18899.0i			0.933158i	0.884480	+	0.466579i	$0.154514\pi$
$743$			18899.0i			0.933158i	−0.884480	+	0.466579i	$0.845486\pi$
$744$	20962.0	−	6408.63i	1.03294	−	0.315795i
$745$		−	29420.4i		−	1.44682i
$746$	−24181.5			−1.18680
$747$	11180.3	−	7541.06i	0.547611	−	0.369361i
$748$		−	3654.41i		−	0.178635i
$749$			31756.1i			1.54919i
$750$	24709.6	−	7554.38i	1.20302	−	0.367796i
$751$			11556.3i			0.561514i	0.959779	+	0.280757i	$0.0905855\pi$
$751$			11556.3i			0.561514i	−0.959779	+	0.280757i	$0.909415\pi$
$752$	27845.3			1.35028
$753$	11395.0	−	3483.74i	0.551469	−	0.168598i
$754$	725.987			0.0350648
$755$	20873.3			1.00617
$756$	8195.46	+	6636.73i	0.394267	+	0.319280i
$757$	−3877.16			−0.186153			−0.0930766	−	0.995659i	$-0.529670\pi$
$757$	−3877.16			−0.186153			−0.0930766	+	0.995659i	$0.529670\pi$
$758$	26948.0			1.29129
$759$	3131.82	+	10243.9i	0.149773	+	0.489893i
$760$			18986.0i			0.906177i
$761$		−	12811.7i		−	0.610280i	−0.952307	−	0.305140i	$-0.901297\pi$
$761$		−	12811.7i		−	0.610280i	0.952307	−	0.305140i	$-0.0987033\pi$
$762$	3008.73	+	9841.27i	0.143038	+	0.467863i
$763$			49541.2i			2.35060i
$764$	7481.78			0.354295
$765$	8637.26	−	5825.80i	0.408210	−	0.275336i
$766$		−	15449.8i		−	0.728752i
$767$	−533.685	+	1052.17i	−0.0251242	+	0.0495330i
$768$	6648.15	+	21745.5i	0.312363	+	1.02171i
$769$			26411.6i			1.23853i	0.785183	+	0.619264i	$0.212569\pi$
$769$			26411.6i			1.23853i	−0.785183	+	0.619264i	$0.787431\pi$
$770$		−	22993.1i		−	1.07612i
$771$	−24115.4	+	7372.69i	−1.12645	+	0.344385i
$772$	8648.46			0.403193
$773$	−3435.09			−0.159834			−0.0799170	−	0.996802i	$-0.525466\pi$
$773$	−3435.09			−0.159834			−0.0799170	+	0.996802i	$0.525466\pi$
$774$	−8216.04	−	12181.0i	−0.381550	−	0.565681i
$775$		−	4568.34i		−	0.211742i
$776$			23903.3i			1.10577i
$777$	−27643.5	+	8451.34i	−1.27633	+	0.390206i
$778$			36338.0i			1.67452i
$779$		−	15128.5i		−	0.695806i
$780$	−138.046	−	451.534i	−0.00633695	−	0.0207276i
$781$			2849.24i			0.130543i
$782$			8796.10i			0.402235i
$783$	7306.02	−	9021.95i	0.333456	−	0.411773i
$784$	−12584.4			−0.573268
$785$	13838.5			0.629195
$786$	−4250.41	−	13902.7i	−0.192884	−	0.630906i
$787$	2711.20			0.122800			0.0614002	−	0.998113i	$-0.480443\pi$
$787$	2711.20			0.122800			0.0614002	+	0.998113i	$0.480443\pi$
$788$			15859.5i			0.716967i
$789$	7094.87	−	2169.09i	0.320132	−	0.0978726i
$790$			21013.5i			0.946362i
$791$	51611.4			2.31996
$792$	10267.4	−	6925.31i	0.460651	−	0.310707i
$793$	−1623.28			−0.0726917
$794$		−	47261.4i		−	2.11240i
$795$	4181.41	+	13677.0i	0.186540	+	0.610154i
$796$	1429.30			0.0636436
$797$	−23051.3			−1.02449			−0.512246	−	0.858839i	$-0.671186\pi$
$797$	−23051.3			−1.02449			−0.512246	+	0.858839i	$0.671186\pi$
$798$	13380.3	+	43765.8i	0.593557	+	1.94147i
$799$		−	12987.2i		−	0.575035i
$800$	2423.83			0.107119
$801$	11885.1	−	8016.44i	0.524268	−	0.353617i
$802$	−38327.9			−1.68754
$803$		−	16485.4i		−	0.724478i
$804$	193.419	−	59.1333i	0.00848430	−	0.00259387i
$805$			16361.9i			0.716373i
$806$	−2365.69			−0.103384
$807$	−3019.00	−	9874.84i	−0.131690	−	0.430745i
$808$	−4031.49			−0.175529
$809$	−39643.2			−1.72285			−0.861423	−	0.507888i	$-0.830426\pi$
$809$	−39643.2			−1.72285			−0.861423	+	0.507888i	$0.830426\pi$
$810$	−23679.1	−	9567.47i	−1.02716	−	0.415020i
$811$			23867.9i			1.03343i	0.856156	+	0.516717i	$0.172846\pi$
$811$			23867.9i			1.03343i	−0.856156	+	0.516717i	$0.827154\pi$
$812$		−	6219.94i		−	0.268814i
$813$	9769.61	+	31955.5i	0.421446	+	1.37851i
$814$		−	24555.2i		−	1.05732i
$815$			4812.21i			0.206827i
$816$	14680.2	−	4488.12i	0.629792	−	0.192544i
$817$		−	18850.9i		−	0.807233i
$818$		−	40537.7i		−	1.73272i
$819$	879.863	+	1304.48i	0.0375396	+	0.0556557i
$820$	4523.18			0.192630
$821$	−3723.73			−0.158293			−0.0791467	−	0.996863i	$-0.525220\pi$
$821$	−3723.73			−0.158293			−0.0791467	+	0.996863i	$0.525220\pi$
$822$	8605.14	−	2630.81i	0.365132	−	0.111630i
$823$			19924.4i			0.843890i	0.906621	+	0.421945i	$0.138653\pi$
$823$			19924.4i			0.843890i	−0.906621	+	0.421945i	$0.861347\pi$
$824$			19283.9i			0.815276i
$825$	−754.632	−	2468.33i	−0.0318460	−	0.104165i
$826$	30491.7	+	15466.0i	1.28443	+	0.651492i
$827$		−	12021.1i		−	0.505459i	−0.967537	−	0.252730i	$-0.918672\pi$
$827$		−	12021.1i		−	0.505459i	0.967537	−	0.252730i	$-0.0813283\pi$
$828$	5284.87	−	3564.62i	0.221814	−	0.149612i
$829$	−26391.6			−1.10569			−0.552845	−	0.833284i	$-0.686458\pi$
$829$	−26391.6			−1.10569			−0.552845	+	0.833284i	$0.686458\pi$
$830$			17498.0i			0.731764i
$831$	3710.35	+	12136.2i	0.154886	+	0.506618i
$832$			402.361i			0.0167660i
$833$			5869.41i			0.244133i
$834$	9699.82	+	31727.2i	0.402731	+	1.31729i
$835$	−35571.8			−1.47427
$836$	−11493.4			−0.475486
$837$	−23807.3	+	29398.8i	−0.983155	+	1.21406i
$838$	−21795.9			−0.898480
$839$	42586.7			1.75239			0.876195	−	0.481958i	$-0.160074\pi$
$839$	42586.7			1.75239			0.876195	+	0.481958i	$0.160074\pi$
$840$	18090.3	−	5530.68i	0.743065	−	0.227174i
$841$	17541.8			0.719250
$842$		−	39418.8i		−	1.61337i
$843$	40758.2	−	12460.8i	1.66523	−	0.509103i
$844$		−	1464.36i		−	0.0597219i
$845$			22767.5i			0.926896i
$846$	−26393.4	+	17802.2i	−1.07260	+	0.723467i
$847$	10552.4			0.428080
$848$			21073.1i			0.853366i
$849$	23104.3	−	7063.58i	0.933966	−	0.285538i
$850$		−	2119.48i		−	0.0855264i
$851$			17473.4i			0.703856i
$852$	1621.50	−	495.734i	0.0652014	−	0.0199338i
$853$	35092.1			1.40859			0.704297	−	0.709906i	$-0.251262\pi$
$853$	35092.1			1.40859			0.704297	+	0.709906i	$0.251262\pi$
$854$			47042.3i			1.88496i
$855$	−18322.5	−	27164.7i	−0.732885	−	1.08657i
$856$		−	22193.5i		−	0.886164i
$857$	−17666.5			−0.704174			−0.352087	−	0.935967i	$-0.614528\pi$
$857$	−17666.5			−0.704174			−0.352087	+	0.935967i	$0.614528\pi$
$858$	−1278.21	+	390.782i	−0.0508594	+	0.0155490i
$859$			9939.85i			0.394812i	0.980322	+	0.197406i	$0.0632517\pi$
$859$			9939.85i			0.394812i	−0.980322	+	0.197406i	$0.936748\pi$
$860$	5636.14			0.223478
$861$	−14414.8	+	4406.96i	−0.570561	+	0.174435i
$862$	51482.9			2.03424
$863$	−23853.5			−0.940885			−0.470442	−	0.882431i	$-0.655906\pi$
$863$	−23853.5			−0.940885			−0.470442	+	0.882431i	$0.655906\pi$
$864$	−15598.1	−	12631.4i	−0.614188	−	0.497373i
$865$		−	15916.7i		−	0.625648i
$866$	−28012.0			−1.09918
$867$	5370.49	+	17566.3i	0.210371	+	0.688102i
$868$			20268.2i			0.792567i
$869$	17586.3			0.686505
$870$	4403.96	+	14404.9i	0.171619	+	0.561348i
$871$	30.1778			0.00117398
$872$		−	34623.0i		−	1.34459i
$873$	−23067.9	−	34200.2i	−0.894308	−	1.32589i
$874$	27664.3			1.07066
$875$		−	33030.1i		−	1.27614i
$876$	−9381.78	+	2868.25i	−0.361850	+	0.110627i
$877$	−27678.4			−1.06571			−0.532857	−	0.846205i	$-0.678882\pi$
$877$	−27678.4			−1.06571			−0.532857	+	0.846205i	$0.678882\pi$
$878$	39970.2			1.53636
$879$	17241.4	−	5271.13i	0.661589	−	0.202265i
$880$			24256.3i			0.929181i
$881$	−29424.9			−1.12526			−0.562628	−	0.826710i	$-0.690210\pi$
$881$	−29424.9			−1.12526			−0.562628	+	0.826710i	$0.690210\pi$
$882$	11928.2	−	8045.52i	0.455378	−	0.307150i
$883$	18910.6			0.720718			0.360359	−	0.932814i	$-0.382654\pi$
$883$	18910.6			0.720718			0.360359	+	0.932814i	$0.382654\pi$
$884$	−324.483			−0.0123456
$885$	−24114.5	−	4206.63i	−0.915932	−	0.159779i
$886$	15232.6			0.577594
$887$	−30185.3			−1.14264			−0.571322	−	0.820726i	$-0.693569\pi$
$887$	−30185.3			−1.14264			−0.571322	+	0.820726i	$0.693569\pi$
$888$	19319.3	−	5906.41i	0.730082	−	0.223205i
$889$	13155.1			0.496299
$890$			18601.1i			0.700571i
$891$	−8007.05	+	19817.2i	−0.301062	+	0.745118i
$892$	−10698.7			−0.401590
$893$	−40845.5			−1.53062
$894$	14490.4	+	47396.7i	0.542093	+	1.77313i
$895$			22871.4i			0.854196i
$896$	37280.9			1.39003
$897$	909.574	−	278.080i	0.0338571	−	0.0103510i
$898$		−	24839.5i		−	0.923058i
$899$	22312.2			0.827757
$900$	−1273.42	+	858.918i	−0.0471638	+	0.0318118i
$901$	9828.59			0.363416
$902$		−	12804.3i		−	0.472657i
$903$	−17961.6	+	5491.32i	−0.661931	+	0.202370i
$904$	−36069.8			−1.32706
$905$		−	23437.7i		−	0.860880i
$906$	−33627.2	+	10280.7i	−1.23310	+	0.376991i
$907$	18102.7			0.662724			0.331362	−	0.943504i	$-0.392492\pi$
$907$	18102.7			0.662724			0.331362	+	0.943504i	$0.392492\pi$
$908$	−8391.76			−0.306707
$909$	5768.17	−	3890.61i	0.210471	−	0.141962i
$910$	−2041.60			−0.0743719
$911$			15175.8i			0.551916i	0.961170	+	0.275958i	$0.0889951\pi$
$911$			15175.8i			0.551916i	−0.961170	+	0.275958i	$0.911005\pi$
$912$	−14115.4	−	46170.2i	−0.512509	−	1.67637i
$913$	14644.1			0.530832
$914$		−	28793.6i		−	1.04202i
$915$	−9847.11	−	32208.9i	−0.355776	−	1.16371i
$916$			3393.15i			0.122394i
$917$	−18584.2			−0.669251
$918$	−11045.4	+	13639.5i	−0.397115	+	0.490383i
$919$		−	9982.42i		−	0.358313i	−0.983821	−	0.179157i	$-0.942663\pi$
$919$		−	9982.42i		−	0.358313i	0.983821	−	0.179157i	$-0.0573369\pi$
$920$		−	11434.9i		−	0.409778i
$921$	466.512	+	1525.91i	0.0166906	+	0.0545935i
$922$			6842.56i			0.244412i
$923$	252.990			0.00902195
$924$	3348.05	+	10951.1i	0.119202	+	0.389899i
$925$		−	4210.34i		−	0.149660i
$926$			22354.4i			0.793315i
$927$	−18610.0	−	27591.0i	−0.659367	−	0.977570i
$928$			11838.2i			0.418758i
$929$	44241.8			1.56246			0.781231	−	0.624242i	$-0.214592\pi$
$929$	44241.8			1.56246			0.781231	+	0.624242i	$0.214592\pi$
$930$	−14350.7	−	46939.7i	−0.505997	−	1.65507i
$931$	18459.7			0.649829
$932$	−18764.9			−0.659510
$933$	17290.3	−	5286.10i	0.606709	−	0.185487i
$934$	−1609.43			−0.0563834
$935$	11313.2			0.395703
$936$	−614.912	−	911.662i	−0.0214733	−	0.0318361i
$937$			55172.0i			1.92358i	0.273795	+	0.961788i	$0.411721\pi$
$937$			55172.0i			1.92358i	−0.273795	+	0.961788i	$0.588279\pi$
$938$		−	874.542i		−	0.0304422i
$939$	−37218.2	+	11378.6i	−1.29347	+	0.395448i
$940$		−	12212.2i		−	0.423742i
$941$	−9582.77			−0.331976			−0.165988	−	0.986128i	$-0.553081\pi$
$941$	−9582.77			−0.331976			−0.165988	+	0.986128i	$0.553081\pi$
$942$	−22294.0	+	6815.87i	−0.771103	+	0.235746i
$943$			9111.55i			0.314648i
$944$	−32166.9	−	16315.7i	−1.10905	−	0.562533i
$945$	−20545.8	+	25371.3i	−0.707254	+	0.873363i
$946$		−	15954.9i		−	0.548349i
$947$		−	17371.2i		−	0.596080i	−0.954553	−	0.298040i	$-0.903667\pi$
$947$		−	17371.2i		−	0.596080i	0.954553	−	0.298040i	$-0.0963329\pi$
$948$	−3059.80	−	10008.3i	−0.104829	−	0.342884i
$949$	−1463.77			−0.0500695
$950$	−6665.89			−0.227653
$951$	−6524.96	+	1994.85i	−0.222488	+	0.0680204i
$952$		−	13000.1i		−	0.442580i
$953$			1947.46i			0.0661957i	0.999452	+	0.0330978i	$0.0105373\pi$
$953$			1947.46i			0.0661957i	−0.999452	+	0.0330978i	$0.989463\pi$
$954$	−13472.6	−	19974.3i	−0.457224	−	0.677874i
$955$			23161.9i			0.784818i
$956$		−	22385.9i		−	0.757334i
$957$	12055.5	−	3685.69i	0.407210	−	0.124495i
$958$		−	14385.7i		−	0.485157i
$959$		−	11502.8i		−	0.387324i
$960$	−7983.58	+	2440.79i	−0.268405	+	0.0820584i
$961$	−42915.2			−1.44054
$962$	−2180.30			−0.0730724
$963$	21417.9	+	31753.9i	0.716699	+	1.06257i
$964$	−12785.8			−0.427181
$965$			26773.6i			0.893134i
$966$	−8058.68	−	26359.2i	−0.268410	−	0.877943i
$967$			11825.1i			0.393245i	0.980479	+	0.196623i	$0.0629974\pi$
$967$			11825.1i			0.393245i	−0.980479	+	0.196623i	$0.937003\pi$
$968$	−7374.76			−0.244870
$969$	−21534.0	+	6583.49i	−0.713901	+	0.218258i
$970$	53525.9			1.77177
$971$			45906.7i			1.51722i	0.651547	+	0.758608i	$0.274120\pi$
$971$			45906.7i			1.51722i	−0.651547	+	0.758608i	$0.725880\pi$
$972$	12671.0	+	1108.85i	0.418131	+	0.0365908i
$973$	42410.7			1.39735
$974$	27095.7			0.891378
$975$	−219.168	+	67.0052i	−0.00719896	+	0.00220091i
$976$		−	49626.7i		−	1.62757i
$977$	1579.81			0.0517325			0.0258663	−	0.999665i	$-0.491766\pi$
$977$	1579.81			0.0517325			0.0258663	+	0.999665i	$0.491766\pi$
$978$	−2370.15	−	7752.52i	−0.0774938	−	0.253475i
$979$	15567.3			0.508205
$980$			5519.16i			0.179901i
$981$	33413.0	+	49537.7i	1.08746	+	1.61225i
$982$		−	45751.9i		−	1.48676i
$983$	−11769.9			−0.381894			−0.190947	−	0.981600i	$-0.561156\pi$
$983$	−11769.9			−0.381894			−0.190947	+	0.981600i	$0.561156\pi$
$984$	10074.1	−	3079.90i	0.326372	−	0.0997802i
$985$	−49097.3			−1.58819
$986$	10351.7			0.334346
$987$	11898.4	+	38918.5i	0.383719	+	1.25511i
$988$			1020.52i			0.0328613i
$989$			11353.5i			0.365035i
$990$	−15507.7	−	22991.5i	−0.497844	−	0.738098i
$991$		−	33297.2i		−	1.06733i	−0.845697	−	0.533664i	$-0.820815\pi$
$991$		−	33297.2i		−	1.06733i	0.845697	−	0.533664i	$-0.179185\pi$
$992$		−	38575.7i		−	1.23466i
$993$	−15171.1	−	49623.2i	−0.484834	−	1.58585i
$994$		−	7331.57i		−	0.233947i
$995$			4424.79i			0.140980i
$996$	−2547.90	−	8333.94i	−0.0810576	−	0.265131i
$997$	33097.6			1.05137			0.525683	−	0.850680i	$-0.323810\pi$
$997$	33097.6			1.05137			0.525683	+	0.850680i	$0.323810\pi$
$998$	−8294.25			−0.263076
$999$	−21941.6	+	27094.9i	−0.694896	+	0.858103i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.4.d.c.176.14	yes	52
3.2	odd	2	inner	177.4.d.c.176.39	yes	52
59.58	odd	2	inner	177.4.d.c.176.40	yes	52
177.176	even	2	inner	177.4.d.c.176.13	✓	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.4.d.c.176.13	✓	52	177.176	even	2	inner
177.4.d.c.176.14	yes	52	1.1	even	1	trivial
177.4.d.c.176.39	yes	52	3.2	odd	2	inner
177.4.d.c.176.40	yes	52	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:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	177.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-3.37014 q^{2} +(1.51919 + 4.96911i) q^{3} +3.35783 q^{4} +10.3951i q^{5} +(-5.11987 - 16.7466i) q^{6} -22.3857 q^{7} +15.6447 q^{8} +(-22.3841 + 15.0980i) q^{9} +O(q^{10})\)	\(q-3.37014 q^{2} +(1.51919 + 4.96911i) q^{3} +3.35783 q^{4} +10.3951i q^{5} +(-5.11987 - 16.7466i) q^{6} -22.3857 q^{7} +15.6447 q^{8} +(-22.3841 + 15.0980i) q^{9} -35.0329i q^{10} -29.3191 q^{11} +(5.10117 + 16.6854i) q^{12} +2.60330i q^{13} +75.4429 q^{14} +(-51.6543 + 15.7921i) q^{15} -79.5876 q^{16} +37.1200i q^{17} +(75.4377 - 50.8824i) q^{18} +116.745 q^{19} +34.9049i q^{20} +(-34.0081 - 111.237i) q^{21} +98.8095 q^{22} -70.3128 q^{23} +(23.7673 + 77.7405i) q^{24} +16.9423 q^{25} -8.77349i q^{26} +(-109.029 - 88.2926i) q^{27} -75.1674 q^{28} +82.7478i q^{29} +(174.082 - 53.2214i) q^{30} -269.641i q^{31} +143.063 q^{32} +(-44.5412 - 145.690i) q^{33} -125.099i q^{34} -232.701i q^{35} +(-75.1622 + 50.6966i) q^{36} -248.510i q^{37} -393.446 q^{38} +(-12.9361 + 3.95490i) q^{39} +162.628i q^{40} -129.586i q^{41} +(114.612 + 374.884i) q^{42} -161.471i q^{43} -98.4487 q^{44} +(-156.945 - 232.685i) q^{45} +236.964 q^{46} -349.870 q^{47} +(-120.908 - 395.480i) q^{48} +158.120 q^{49} -57.0980 q^{50} +(-184.453 + 56.3922i) q^{51} +8.74145i q^{52} -264.779i q^{53} +(367.444 + 297.558i) q^{54} -304.775i q^{55} -350.219 q^{56} +(177.357 + 580.117i) q^{57} -278.872i q^{58} +(404.169 + 205.003i) q^{59} +(-173.447 + 53.0271i) q^{60} +623.548i q^{61} +908.727i q^{62} +(501.085 - 337.980i) q^{63} +154.558 q^{64} -27.0615 q^{65} +(150.110 + 490.995i) q^{66} -11.5921i q^{67} +124.643i q^{68} +(-106.818 - 349.392i) q^{69} +784.235i q^{70} -97.1804i q^{71} +(-350.194 + 236.205i) q^{72} +562.273i q^{73} +837.513i q^{74} +(25.7386 + 84.1883i) q^{75} +392.009 q^{76} +656.329 q^{77} +(43.5964 - 13.3286i) q^{78} -599.822 q^{79} -827.320i q^{80} +(273.100 - 675.912i) q^{81} +436.722i q^{82} -499.474 q^{83} +(-114.193 - 373.515i) q^{84} -385.865 q^{85} +544.180i q^{86} +(-411.183 + 125.709i) q^{87} -458.690 q^{88} -530.960 q^{89} +(528.927 + 784.180i) q^{90} -58.2768i q^{91} -236.099 q^{92} +(1339.88 - 409.635i) q^{93} +1179.11 q^{94} +1213.57i q^{95} +(217.340 + 710.898i) q^{96} +1527.88i q^{97} -532.886 q^{98} +(656.283 - 442.661i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q - 8 q^{3} + 268 q^{4} - 16 q^{7} - 4 q^{9}+O(q^{10}) \) 52 * q - 8 * q^3 + 268 * q^4 - 16 * q^7 - 4 * q^9	\( 52 q - 8 q^{3} + 268 q^{4} - 16 q^{7} - 4 q^{9} + 28 q^{12} + 114 q^{15} + 484 q^{16} - 184 q^{19} - 758 q^{21} - 60 q^{22} + 36 q^{25} + 742 q^{27} - 4 q^{28} - 888 q^{36} + 1402 q^{45} - 660 q^{46} - 488 q^{48} - 924 q^{49} - 1772 q^{51} - 630 q^{57} - 1880 q^{60} - 212 q^{63} + 7648 q^{64} + 1316 q^{66} - 1556 q^{75} - 5680 q^{76} + 3224 q^{78} - 1504 q^{79} - 276 q^{81} + 1228 q^{84} - 848 q^{85} + 3598 q^{87} + 5760 q^{88} + 888 q^{94}+O(q^{100}) \) 52 * q - 8 * q^3 + 268 * q^4 - 16 * q^7 - 4 * q^9 + 28 * q^12 + 114 * q^15 + 484 * q^16 - 184 * q^19 - 758 * q^21 - 60 * q^22 + 36 * q^25 + 742 * q^27 - 4 * q^28 - 888 * q^36 + 1402 * q^45 - 660 * q^46 - 488 * q^48 - 924 * q^49 - 1772 * q^51 - 630 * q^57 - 1880 * q^60 - 212 * q^63 + 7648 * q^64 + 1316 * q^66 - 1556 * q^75 - 5680 * q^76 + 3224 * q^78 - 1504 * q^79 - 276 * q^81 + 1228 * q^84 - 848 * q^85 + 3598 * q^87 + 5760 * q^88 + 888 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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