LMFDB - Embedded newform 300.5.c.b.151.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [300,5,Mod(151,300)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(300, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("300.151");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	300.c (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:	$31.0109889252$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6 x^{15} + 20 x^{14} - 108 x^{13} + 492 x^{12} - 2160 x^{11} + 7360 x^{10} - 39552 x^{9} + \cdots + 4294967296 $ x^16 - 6x^15 + 20x^14 - 108x^13 + 492x^12 - 2160x^11 + 7360x^10 - 39552x^9 + 234752x^8 - 632832x^7 + 1884160x^6 - 8847360x^5 + 32243712x^4 - 113246208x^3 + 335544320x^2 - 1610612736*x + 4294967296
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{32}\cdot 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			151.4
Root			$3.79586 + 1.26152i$ of defining polynomial
Character	$\chi$	$=$	300.151
Dual form			300.5.c.b.151.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.99044 + 2.65655i) q^{2} -5.19615i q^{3} +(1.88545 - 15.8885i) q^{4} +(13.8039 + 15.5388i) q^{6} +74.3539i q^{7} +(36.5704 + 52.5224i) q^{8} -27.0000 q^{9} +O(q^{10})$	\(q+(-2.99044 + 2.65655i) q^{2} -5.19615i q^{3} +(1.88545 - 15.8885i) q^{4} +(13.8039 + 15.5388i) q^{6} +74.3539i q^{7} +(36.5704 + 52.5224i) q^{8} -27.0000 q^{9} +107.360i q^{11} +(-82.5592 - 9.79706i) q^{12} +30.7085 q^{13} +(-197.525 - 222.351i) q^{14} +(-248.890 - 59.9139i) q^{16} +292.805 q^{17} +(80.7418 - 71.7269i) q^{18} -357.767i q^{19} +386.354 q^{21} +(-285.207 - 321.053i) q^{22} -488.885i q^{23} +(272.915 - 190.025i) q^{24} +(-91.8318 + 81.5787i) q^{26} +140.296i q^{27} +(1181.37 + 140.190i) q^{28} -1035.75 q^{29} +411.471i q^{31} +(903.455 - 482.021i) q^{32} +557.858 q^{33} +(-875.616 + 777.852i) q^{34} +(-50.9070 + 428.990i) q^{36} -1506.64 q^{37} +(950.428 + 1069.88i) q^{38} -159.566i q^{39} -2003.19 q^{41} +(-1155.37 + 1026.37i) q^{42} +3279.91i q^{43} +(1705.79 + 202.421i) q^{44} +(1298.75 + 1461.98i) q^{46} +1602.96i q^{47} +(-311.322 + 1293.27i) q^{48} -3127.50 q^{49} -1521.46i q^{51} +(57.8991 - 487.912i) q^{52} +4381.56 q^{53} +(-372.704 - 419.547i) q^{54} +(-3905.25 + 2719.15i) q^{56} -1859.01 q^{57} +(3097.35 - 2751.53i) q^{58} +851.518i q^{59} -5539.08 q^{61} +(-1093.09 - 1230.48i) q^{62} -2007.55i q^{63} +(-1421.21 + 3841.53i) q^{64} +(-1668.24 + 1481.98i) q^{66} +4189.05i q^{67} +(552.068 - 4652.24i) q^{68} -2540.32 q^{69} -6302.56i q^{71} +(-987.401 - 1418.11i) q^{72} -7030.68 q^{73} +(4505.52 - 4002.48i) q^{74} +(-5684.40 - 674.551i) q^{76} -7982.62 q^{77} +(423.895 + 477.172i) q^{78} +7014.54i q^{79} +729.000 q^{81} +(5990.42 - 5321.58i) q^{82} -9127.59i q^{83} +(728.449 - 6138.59i) q^{84} +(-8713.26 - 9808.37i) q^{86} +5381.92i q^{87} +(-5638.80 + 3926.19i) q^{88} +3180.88 q^{89} +2283.29i q^{91} +(-7767.67 - 921.767i) q^{92} +2138.07 q^{93} +(-4258.35 - 4793.55i) q^{94} +(-2504.66 - 4694.49i) q^{96} -12299.4 q^{97} +(9352.59 - 8308.37i) q^{98} -2898.72i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{2} + 8 q^{4} + 18 q^{6} + 180 q^{8} - 432 q^{9}+O(q^{10}) $ 16 * q - 6 * q^2 + 8 * q^4 + 18 * q^6 + 180 * q^8 - 432 * q^9	$ 16 q - 6 q^{2} + 8 q^{4} + 18 q^{6} + 180 q^{8} - 432 q^{9} - 176 q^{13} + 78 q^{14} - 376 q^{16} + 162 q^{18} - 144 q^{21} + 788 q^{22} + 108 q^{24} + 678 q^{26} - 3368 q^{28} + 1728 q^{29} - 2016 q^{32} - 2932 q^{34} - 216 q^{36} + 1568 q^{37} + 6990 q^{38} + 1248 q^{41} - 162 q^{42} + 8088 q^{44} + 5956 q^{46} - 2088 q^{48} - 10720 q^{49} - 3128 q^{52} + 288 q^{53} - 486 q^{54} - 10236 q^{56} - 5616 q^{57} + 16164 q^{58} - 3760 q^{61} + 12714 q^{62} + 10544 q^{64} + 8100 q^{66} - 26136 q^{68} + 9792 q^{69} - 4860 q^{72} - 11040 q^{73} - 17004 q^{74} - 28344 q^{76} - 768 q^{77} + 16830 q^{78} + 11664 q^{81} + 21280 q^{82} + 15120 q^{84} + 24414 q^{86} - 52840 q^{88} - 768 q^{89} - 23736 q^{92} + 9936 q^{93} - 45156 q^{94} - 11088 q^{96} - 7248 q^{97} + 58140 q^{98}+O(q^{100}) $ 16 * q - 6 * q^2 + 8 * q^4 + 18 * q^6 + 180 * q^8 - 432 * q^9 - 176 * q^13 + 78 * q^14 - 376 * q^16 + 162 * q^18 - 144 * q^21 + 788 * q^22 + 108 * q^24 + 678 * q^26 - 3368 * q^28 + 1728 * q^29 - 2016 * q^32 - 2932 * q^34 - 216 * q^36 + 1568 * q^37 + 6990 * q^38 + 1248 * q^41 - 162 * q^42 + 8088 * q^44 + 5956 * q^46 - 2088 * q^48 - 10720 * q^49 - 3128 * q^52 + 288 * q^53 - 486 * q^54 - 10236 * q^56 - 5616 * q^57 + 16164 * q^58 - 3760 * q^61 + 12714 * q^62 + 10544 * q^64 + 8100 * q^66 - 26136 * q^68 + 9792 * q^69 - 4860 * q^72 - 11040 * q^73 - 17004 * q^74 - 28344 * q^76 - 768 * q^77 + 16830 * q^78 + 11664 * q^81 + 21280 * q^82 + 15120 * q^84 + 24414 * q^86 - 52840 * q^88 - 768 * q^89 - 23736 * q^92 + 9936 * q^93 - 45156 * q^94 - 11088 * q^96 - 7248 * q^97 + 58140 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$277$
$\chi(n)$	$1$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−2.99044	+	2.65655i	−0.747610	+	0.664138i
$2$	−2.99044	+	2.65655i	−0.747610	+	0.664138i
$3$		−	5.19615i		−	0.577350i
$3$		−	5.19615i		−	0.577350i
$4$	1.88545	−	15.8885i	0.117840	−	0.993033i
$5$		0			0
$5$		0			0
$6$	13.8039	+	15.5388i	0.383440	+	0.431633i
$7$			74.3539i			1.51743i	0.651425	+	0.758713i	$0.274171\pi$
$7$			74.3539i			1.51743i	−0.651425	+	0.758713i	$0.725829\pi$
$8$	36.5704	+	52.5224i	0.571413	+	0.820663i
$9$	−27.0000			−0.333333
$10$		0			0
$11$			107.360i			0.887271i	0.896207	+	0.443636i	$0.146312\pi$
$11$			107.360i			0.887271i	−0.896207	+	0.443636i	$0.853688\pi$
$12$	−82.5592	−	9.79706i	−0.573328	−	0.0680351i
$13$	30.7085			0.181707			0.0908535	−	0.995864i	$-0.471041\pi$
$13$	30.7085			0.181707			0.0908535	+	0.995864i	$0.471041\pi$
$14$	−197.525	−	222.351i	−1.00778	−	1.13444i
$15$		0			0
$16$	−248.890	−	59.9139i	−0.972227	−	0.234039i
$17$	292.805			1.01317			0.506583	−	0.862191i	$-0.330908\pi$
$17$	292.805			1.01317			0.506583	+	0.862191i	$0.330908\pi$
$18$	80.7418	−	71.7269i	0.249203	−	0.221379i
$19$		−	357.767i		−	0.991046i	−0.868595	−	0.495523i	$-0.834977\pi$
$19$		−	357.767i		−	0.991046i	0.868595	−	0.495523i	$-0.165023\pi$
$20$		0			0
$21$	386.354			0.876086
$22$	−285.207	−	321.053i	−0.589271	−	0.663333i
$23$		−	488.885i		−	0.924169i	−0.886836	−	0.462084i	$-0.847102\pi$
$23$		−	488.885i		−	0.924169i	0.886836	−	0.462084i	$-0.152898\pi$
$24$	272.915	−	190.025i	0.473810	−	0.329905i
$25$		0			0
$26$	−91.8318	+	81.5787i	−0.135846	+	0.120679i
$27$			140.296i			0.192450i
$28$	1181.37	+	140.190i	1.50685	+	0.178814i
$29$	−1035.75			−1.23157			−0.615785	−	0.787914i	$-0.711161\pi$
$29$	−1035.75			−1.23157			−0.615785	+	0.787914i	$0.711161\pi$
$30$		0			0
$31$			411.471i			0.428169i	0.976815	+	0.214085i	$0.0686769\pi$
$31$			411.471i			0.428169i	−0.976815	+	0.214085i	$0.931323\pi$
$32$	903.455	−	482.021i	0.882280	−	0.470724i
$33$	557.858			0.512266
$34$	−875.616	+	777.852i	−0.757453	+	0.672883i
$35$		0			0
$36$	−50.9070	+	428.990i	−0.0392801	+	0.331011i
$37$	−1506.64			−1.10054			−0.550272	−	0.834986i	$-0.685476\pi$
$37$	−1506.64			−1.10054			−0.550272	+	0.834986i	$0.685476\pi$
$38$	950.428	+	1069.88i	0.658191	+	0.740915i
$39$		−	159.566i		−	0.104909i
$40$		0			0
$41$	−2003.19			−1.19167			−0.595833	−	0.803108i	$-0.703178\pi$
$41$	−2003.19			−1.19167			−0.595833	+	0.803108i	$0.703178\pi$
$42$	−1155.37	+	1026.37i	−0.654971	+	0.581843i
$43$			3279.91i			1.77388i	0.461882	+	0.886942i	$0.347175\pi$
$43$			3279.91i			1.77388i	−0.461882	+	0.886942i	$0.652825\pi$
$44$	1705.79	+	202.421i	0.881089	+	0.104556i
$45$		0			0
$46$	1298.75	+	1461.98i	0.613776	+	0.690918i
$47$			1602.96i			0.725650i	0.931857	+	0.362825i	$0.118188\pi$
$47$			1602.96i			0.725650i	−0.931857	+	0.362825i	$0.881812\pi$
$48$	−311.322	+	1293.27i	−0.135122	+	0.561316i
$49$	−3127.50			−1.30258
$50$		0			0
$51$		−	1521.46i		−	0.584952i
$52$	57.8991	−	487.912i	0.0214124	−	0.180441i
$53$	4381.56			1.55983			0.779915	−	0.625885i	$-0.215262\pi$
$53$	4381.56			1.55983			0.779915	+	0.625885i	$0.215262\pi$
$54$	−372.704	−	419.547i	−0.127813	−	0.143878i
$55$		0			0
$56$	−3905.25	+	2719.15i	−1.24530	+	0.867076i
$57$	−1859.01			−0.572180
$58$	3097.35	−	2751.53i	0.920734	−	0.817933i
$59$			851.518i			0.244619i	0.992492	+	0.122309i	$0.0390300\pi$
$59$			851.518i			0.244619i	−0.992492	+	0.122309i	$0.960970\pi$
$60$		0			0
$61$	−5539.08			−1.48860			−0.744300	−	0.667845i	$-0.767217\pi$
$61$	−5539.08			−1.48860			−0.744300	+	0.667845i	$0.767217\pi$
$62$	−1093.09	−	1230.48i	−0.284364	−	0.320104i
$63$		−	2007.55i		−	0.505809i
$64$	−1421.21	+	3841.53i	−0.346975	+	0.937874i
$65$		0			0
$66$	−1668.24	+	1481.98i	−0.382975	+	0.340216i
$67$			4189.05i			0.933181i	0.884473	+	0.466590i	$0.154518\pi$
$67$			4189.05i			0.933181i	−0.884473	+	0.466590i	$0.845482\pi$
$68$	552.068	−	4652.24i	0.119392	−	1.00611i
$69$	−2540.32			−0.533569
$70$		0			0
$71$		−	6302.56i		−	1.25026i	−0.780521	−	0.625130i	$-0.785046\pi$
$71$		−	6302.56i		−	1.25026i	0.780521	−	0.625130i	$-0.214954\pi$
$72$	−987.401	−	1418.11i	−0.190471	−	0.273554i
$73$	−7030.68			−1.31933			−0.659663	−	0.751562i	$-0.729301\pi$
$73$	−7030.68			−1.31933			−0.659663	+	0.751562i	$0.729301\pi$
$74$	4505.52	−	4002.48i	0.822777	−	0.730913i
$75$		0			0
$76$	−5684.40	−	674.551i	−0.984140	−	0.116785i
$77$	−7982.62			−1.34637
$78$	423.895	+	477.172i	0.0696738	+	0.0784306i
$79$			7014.54i			1.12395i	0.827156	+	0.561973i	$0.189957\pi$
$79$			7014.54i			1.12395i	−0.827156	+	0.561973i	$0.810043\pi$
$80$		0			0
$81$	729.000			0.111111
$82$	5990.42	−	5321.58i	0.890901	−	0.791431i
$83$		−	9127.59i		−	1.32495i	−0.749083	−	0.662476i	$-0.769506\pi$
$83$		−	9127.59i		−	1.32495i	0.749083	−	0.662476i	$-0.230494\pi$
$84$	728.449	−	6138.59i	0.103238	−	0.869982i
$85$		0			0
$86$	−8713.26	−	9808.37i	−1.17810	−	1.32617i
$87$			5381.92i			0.711048i
$88$	−5638.80	+	3926.19i	−0.728151	+	0.506998i
$89$	3180.88			0.401575			0.200788	−	0.979635i	$-0.435650\pi$
$89$	3180.88			0.401575			0.200788	+	0.979635i	$0.435650\pi$
$90$		0			0
$91$			2283.29i			0.275727i
$92$	−7767.67	−	921.767i	−0.917730	−	0.108904i
$93$	2138.07			0.247204
$94$	−4258.35	−	4793.55i	−0.481932	−	0.542503i
$95$		0			0
$96$	−2504.66	−	4694.49i	−0.271773	−	0.509385i
$97$	−12299.4			−1.30720			−0.653600	−	0.756840i	$-0.726742\pi$
$97$	−12299.4			−1.30720			−0.653600	+	0.756840i	$0.726742\pi$
$98$	9352.59	−	8308.37i	0.973822	−	0.865094i
$99$		−	2898.72i		−	0.295757i
$100$		0			0
$101$	8454.27			0.828769			0.414385	−	0.910102i	$-0.363997\pi$
$101$	8454.27			0.828769			0.414385	+	0.910102i	$0.363997\pi$
$102$	4041.84	+	4549.83i	0.388489	+	0.437316i
$103$			12655.1i			1.19287i	0.802662	+	0.596435i	$0.203416\pi$
$103$			12655.1i			1.19287i	−0.802662	+	0.596435i	$0.796584\pi$
$104$	1123.02	+	1612.88i	0.103830	+	0.149120i
$105$		0			0
$106$	−13102.8	+	11639.9i	−1.16614	+	1.03594i
$107$			6961.91i			0.608080i	0.952659	+	0.304040i	$0.0983357\pi$
$107$			6961.91i			0.608080i	−0.952659	+	0.304040i	$0.901664\pi$
$108$	2229.10	+	264.521i	0.191109	+	0.0226784i
$109$	−10686.8			−0.899489			−0.449744	−	0.893157i	$-0.648485\pi$
$109$	−10686.8			−0.899489			−0.449744	+	0.893157i	$0.648485\pi$
$110$		0			0
$111$			7828.75i			0.635399i
$112$	4454.83	−	18505.9i	0.355136	−	1.47528i
$113$	−18780.7			−1.47080			−0.735402	−	0.677632i	$-0.763006\pi$
$113$	−18780.7			−1.47080			−0.735402	+	0.677632i	$0.763006\pi$
$114$	5559.27	−	4938.57i	0.427768	−	0.380007i
$115$		0			0
$116$	−1952.85	+	16456.5i	−0.145129	+	1.22299i
$117$	−829.129			−0.0605690
$118$	−2262.10	−	2546.41i	−0.162461	−	0.182879i
$119$			21771.2i			1.53740i
$120$		0			0
$121$	3114.87			0.212750
$122$	16564.3	−	14714.9i	1.11289	−	0.988637i
$123$			10408.9i			0.688009i
$124$	6537.66	+	775.806i	0.425186	+	0.0504556i
$125$		0			0
$126$	5333.18	+	6003.47i	0.335927	+	0.378147i
$127$		−	4370.53i		−	0.270974i	−0.990779	−	0.135487i	$-0.956740\pi$
$127$		−	4370.53i		−	0.270974i	0.990779	−	0.135487i	$-0.0432598\pi$
$128$	−5955.19	−	15263.4i	−0.363476	−	0.931604i
$129$	17042.9			1.02415
$130$		0			0
$131$		−	20280.0i		−	1.18175i	−0.806763	−	0.590875i	$-0.798783\pi$
$131$		−	20280.0i		−	1.18175i	0.806763	−	0.590875i	$-0.201217\pi$
$132$	1051.81	−	8863.54i	0.0603656	−	0.508697i
$133$	26601.4			1.50384
$134$	−11128.4	−	12527.1i	−0.619761	−	0.697655i
$135$		0			0
$136$	10708.0	+	15378.8i	0.578936	+	0.831468i
$137$	−25989.4			−1.38470			−0.692349	−	0.721563i	$-0.743424\pi$
$137$	−25989.4			−1.38470			−0.692349	+	0.721563i	$0.743424\pi$
$138$	7596.68	−	6748.50i	0.398901	−	0.354364i
$139$			21049.3i			1.08945i	0.838614	+	0.544726i	$0.183366\pi$
$139$			21049.3i			1.08945i	−0.838614	+	0.544726i	$0.816634\pi$
$140$		0			0
$141$	8329.22			0.418954
$142$	16743.1	+	18847.4i	0.830346	+	0.934707i
$143$			3296.86i			0.161223i
$144$	6720.04	+	1617.67i	0.324076	+	0.0780128i
$145$		0			0
$146$	21024.8	−	18677.4i	0.986340	−	0.876214i
$147$			16251.0i			0.752046i
$148$	−2840.69	+	23938.3i	−0.129688	+	1.09288i
$149$	−19502.4			−0.878447			−0.439223	−	0.898378i	$-0.644746\pi$
$149$	−19502.4			−0.878447			−0.439223	+	0.898378i	$0.644746\pi$
$150$		0			0
$151$		−	33284.1i		−	1.45977i	−0.683572	−	0.729883i	$-0.739574\pi$
$151$		−	33284.1i		−	1.45977i	0.683572	−	0.729883i	$-0.260426\pi$
$152$	18790.8	−	13083.7i	0.813314	−	0.566296i
$153$	−7905.74			−0.337722
$154$	23871.5	−	21206.3i	1.00656	−	0.894175i
$155$		0			0
$156$	−2535.27	−	300.853i	−0.104178	−	0.0123625i
$157$	10857.6			0.440487			0.220243	−	0.975445i	$-0.429315\pi$
$157$	10857.6			0.440487			0.220243	+	0.975445i	$0.429315\pi$
$158$	−18634.5	−	20976.6i	−0.746455	−	0.840272i
$159$		−	22767.3i		−	0.900568i
$160$		0			0
$161$	36350.5			1.40236
$162$	−2180.03	+	1936.63i	−0.0830677	+	0.0737932i
$163$			28923.6i			1.08862i	0.838883	+	0.544311i	$0.183209\pi$
$163$			28923.6i			1.08862i	−0.838883	+	0.544311i	$0.816791\pi$
$164$	−3776.91	+	31827.7i	−0.140426	+	1.18336i
$165$		0			0
$166$	24247.9	+	27295.5i	0.879951	+	0.990546i
$167$			31156.8i			1.11717i	0.829447	+	0.558585i	$0.188656\pi$
$167$			31156.8i			1.11717i	−0.829447	+	0.558585i	$0.811344\pi$
$168$	14129.1	+	20292.3i	0.500607	+	0.718972i
$169$	−27618.0			−0.966983
$170$		0			0
$171$			9659.72i			0.330349i
$172$	52112.9	+	6184.09i	1.76152	+	0.209035i
$173$	−11118.3			−0.371489			−0.185744	−	0.982598i	$-0.559470\pi$
$173$	−11118.3			−0.371489			−0.185744	+	0.982598i	$0.559470\pi$
$174$	−14297.4	−	16094.3i	−0.472234	−	0.531586i
$175$		0			0
$176$	6432.34	−	26720.8i	0.207656	−	0.862629i
$177$	4424.62			0.141231
$178$	−9512.22	+	8450.18i	−0.300222	+	0.266702i
$179$			8347.18i			0.260515i	0.991480	+	0.130258i	$0.0415805\pi$
$179$			8347.18i			0.260515i	−0.991480	+	0.130258i	$0.958420\pi$
$180$		0			0
$181$	54703.3			1.66977			0.834885	−	0.550425i	$-0.185534\pi$
$181$	54703.3			1.66977			0.834885	+	0.550425i	$0.185534\pi$
$182$	−6065.69	−	6828.05i	−0.183121	−	0.206136i
$183$			28781.9i			0.859444i
$184$	25677.4	−	17878.7i	0.758431	−	0.528082i
$185$		0			0
$186$	−6393.75	+	5679.88i	−0.184812	+	0.164178i
$187$			31435.5i			0.898953i
$188$	25468.7	+	3022.29i	0.720594	+	0.0855108i
$189$	−10431.6			−0.292029
$190$		0			0
$191$			170.614i			0.00467678i	0.999997	+	0.00233839i	$0.000744333\pi$
$191$			170.614i			0.00467678i	−0.999997	+	0.00233839i	$0.999256\pi$
$192$	19961.2	+	7384.83i	0.541482	+	0.200326i
$193$	−38429.3			−1.03169			−0.515843	−	0.856683i	$-0.672521\pi$
$193$	−38429.3			−1.03169			−0.515843	+	0.856683i	$0.672521\pi$
$194$	36780.7	−	32674.1i	0.977276	−	0.868162i
$195$		0			0
$196$	−5896.73	+	49691.3i	−0.153497	+	1.29351i
$197$	47014.6			1.21143			0.605717	−	0.795680i	$-0.292886\pi$
$197$	47014.6			1.21143			0.605717	+	0.795680i	$0.292886\pi$
$198$	7700.59	+	8668.43i	0.196424	+	0.221111i
$199$		−	49175.8i		−	1.24178i	−0.783897	−	0.620891i	$-0.786771\pi$
$199$		−	49175.8i		−	1.24178i	0.783897	−	0.620891i	$-0.213229\pi$
$200$		0			0
$201$	21766.9			0.538772
$202$	−25282.0	+	22459.2i	−0.619596	+	0.550417i
$203$		−	77012.1i		−	1.86882i
$204$	−24173.7	−	2868.63i	−0.580876	−	0.0689309i
$205$		0			0
$206$	−33619.1	−	37844.4i	−0.792230	−	0.891800i
$207$			13199.9i			0.308056i
$208$	−7643.04	−	1839.86i	−0.176660	−	0.0425264i
$209$	38409.8			0.879326
$210$		0			0
$211$		−	4500.34i		−	0.101084i	−0.998722	−	0.0505418i	$-0.983905\pi$
$211$		−	4500.34i		−	0.101084i	0.998722	−	0.0505418i	$-0.0160948\pi$
$212$	8261.20	−	69616.6i	0.183811	−	1.54896i
$213$	−32749.1			−0.721838
$214$	−18494.7	−	20819.2i	−0.403849	−	0.454607i
$215$		0			0
$216$	−7368.69	+	5130.69i	−0.157937	+	0.109968i
$217$	−30594.4			−0.649715
$218$	31958.3	−	28390.1i	0.672466	−	0.597385i
$219$			36532.5i			0.761713i
$220$		0			0
$221$	8991.60			0.184099
$222$	−20797.5	−	23411.4i	−0.421993	−	0.475030i
$223$		−	480.278i		−	0.00965790i	−0.999988	−	0.00482895i	$-0.998463\pi$
$223$		−	480.278i		−	0.00965790i	0.999988	−	0.00482895i	$-0.00153711\pi$
$224$	35840.2	+	67175.4i	0.714289	+	1.33880i
$225$		0			0
$226$	56162.5	−	49891.9i	1.09959	−	0.976817i
$227$		−	38994.8i		−	0.756754i	−0.925652	−	0.378377i	$-0.876482\pi$
$227$		−	38994.8i		−	0.756754i	0.925652	−	0.378377i	$-0.123518\pi$
$228$	−3505.07	+	29537.0i	−0.0674259	+	0.568194i
$229$	27569.4			0.525723			0.262861	−	0.964834i	$-0.415334\pi$
$229$	27569.4			0.525723			0.262861	+	0.964834i	$0.415334\pi$
$230$		0			0
$231$			41478.9i			0.777326i
$232$	−37877.8	−	54400.1i	−0.703735	−	1.01070i
$233$	−42015.1			−0.773915			−0.386957	−	0.922098i	$-0.626474\pi$
$233$	−42015.1			−0.773915			−0.386957	+	0.922098i	$0.626474\pi$
$234$	2479.46	−	2202.63i	0.0452820	−	0.0402262i
$235$		0			0
$236$	13529.4	+	1605.49i	0.242914	+	0.0288260i
$237$	36448.6			0.648910
$238$	−57836.3	−	65105.4i	−1.02105	−	1.14938i
$239$			93158.6i			1.63090i	0.578828	+	0.815450i	$0.303510\pi$
$239$			93158.6i			1.63090i	−0.578828	+	0.815450i	$0.696490\pi$
$240$		0			0
$241$	−108882.			−1.87466			−0.937328	−	0.348447i	$-0.886709\pi$
$241$	−108882.			−1.87466			−0.937328	+	0.348447i	$0.886709\pi$
$242$	−9314.82	+	8274.81i	−0.159054	+	0.141295i
$243$		−	3788.00i		−	0.0641500i
$244$	−10443.6	+	88007.8i	−0.175417	+	1.47823i
$245$		0			0
$246$	−27651.8	−	31127.1i	−0.456933	−	0.514362i
$247$		−	10986.5i		−	0.180080i
$248$	−21611.4	+	15047.7i	−0.351383	+	0.244661i
$249$	−47428.3			−0.764961
$250$		0			0
$251$		−	31606.9i		−	0.501689i	−0.968027	−	0.250845i	$-0.919292\pi$
$251$		−	31606.9i		−	0.501689i	0.968027	−	0.250845i	$-0.0807083\pi$
$252$	−31897.1	−	3785.13i	−0.502284	−	0.0596047i
$253$	52486.6			0.819989
$254$	11610.6	+	13069.8i	0.179964	+	0.202582i
$255$		0			0
$256$	58356.7	+	29823.9i	0.890452	+	0.455077i
$257$	20019.5			0.303101			0.151550	−	0.988450i	$-0.451573\pi$
$257$	20019.5			0.303101			0.151550	+	0.988450i	$0.451573\pi$
$258$	−50965.8	+	45275.4i	−0.765666	+	0.680179i
$259$		−	112025.i		−	1.66999i
$260$		0			0
$261$	27965.3			0.410523
$262$	53875.0	+	60646.2i	0.784846	+	0.883488i
$263$		−	62700.2i		−	0.906478i	−0.891389	−	0.453239i	$-0.850268\pi$
$263$		−	62700.2i		−	0.906478i	0.891389	−	0.453239i	$-0.149732\pi$
$264$	20401.1	+	29300.1i	0.292715	+	0.420398i
$265$		0			0
$266$	−79549.8	+	70668.0i	−1.12428	+	0.998757i
$267$		−	16528.3i		−	0.231850i
$268$	66557.8	+	7898.22i	0.926679	+	0.109966i
$269$	33804.6			0.467166			0.233583	−	0.972337i	$-0.424955\pi$
$269$	33804.6			0.467166			0.233583	+	0.972337i	$0.424955\pi$
$270$		0			0
$271$		−	56181.7i		−	0.764991i	−0.923957	−	0.382496i	$-0.875065\pi$
$271$		−	56181.7i		−	0.764991i	0.923957	−	0.382496i	$-0.124935\pi$
$272$	−72876.3	−	17543.1i	−0.985028	−	0.237120i
$273$	11864.3			0.159191
$274$	77719.7	−	69042.2i	1.03521	−	0.919631i
$275$		0			0
$276$	−4789.64	+	40362.0i	−0.0628760	+	0.529852i
$277$	−121560.			−1.58428			−0.792141	−	0.610338i	$-0.791034\pi$
$277$	−121560.			−1.58428			−0.792141	+	0.610338i	$0.791034\pi$
$278$	−55918.6	−	62946.7i	−0.723547	−	0.814485i
$279$		−	11109.7i		−	0.142723i
$280$		0			0
$281$	−51790.9			−0.655905			−0.327952	−	0.944694i	$-0.606359\pi$
$281$	−51790.9			−0.655905			−0.327952	+	0.944694i	$0.606359\pi$
$282$	−24908.0	+	22127.0i	−0.313214	+	0.278243i
$283$			126660.i			1.58149i	0.612149	+	0.790743i	$0.290305\pi$
$283$			126660.i			1.58149i	−0.612149	+	0.790743i	$0.709695\pi$
$284$	−100138.	−	11883.1i	−1.24155	−	0.147331i
$285$		0			0
$286$	−8758.28	−	9859.05i	−0.107075	−	0.120532i
$287$		−	148945.i		−	1.80826i
$288$	−24393.3	+	13014.6i	−0.294093	+	0.156908i
$289$	2213.80			0.0265059
$290$		0			0
$291$			63909.8i			0.754712i
$292$	−13256.0	+	111707.i	−0.155470	+	1.31013i
$293$	5958.17			0.0694029			0.0347014	−	0.999398i	$-0.488952\pi$
$293$	5958.17			0.0694029			0.0347014	+	0.999398i	$0.488952\pi$
$294$	−43171.5	−	48597.5i	−0.499462	−	0.562237i
$295$		0			0
$296$	−55098.6	−	79132.6i	−0.628864	−	0.903175i
$297$	−15062.2			−0.170755
$298$	58320.7	−	51809.2i	0.656735	−	0.583410i
$299$		−	15012.9i		−	0.167928i
$300$		0			0
$301$	−243874.			−2.69174
$302$	88421.1	+	99534.1i	0.969487	+	1.09134i
$303$		−	43929.7i		−	0.478490i
$304$	−21435.2	+	89044.8i	−0.231943	+	0.963522i
$305$		0			0
$306$	23641.6	−	21002.0i	0.252484	−	0.224294i
$307$		−	78071.0i		−	0.828348i	−0.910198	−	0.414174i	$-0.864070\pi$
$307$		−	78071.0i		−	0.828348i	0.910198	−	0.414174i	$-0.135930\pi$
$308$	−15050.8	+	126832.i	−0.158656	+	1.33699i
$309$	65758.1			0.688703
$310$		0			0
$311$			36755.5i			0.380016i	0.981783	+	0.190008i	$0.0608514\pi$
$311$			36755.5i			0.380016i	−0.981783	+	0.190008i	$0.939149\pi$
$312$	8380.79	−	5835.39i	0.0860946	−	0.0599461i
$313$	169020.			1.72524			0.862619	−	0.505854i	$-0.168823\pi$
$313$	169020.			1.72524			0.862619	+	0.505854i	$0.168823\pi$
$314$	−32468.8	+	28843.7i	−0.329312	+	0.292544i
$315$		0			0
$316$	111451.	+	13225.5i	1.11611	+	0.132446i
$317$	129820.			1.29188			0.645939	−	0.763389i	$-0.276466\pi$
$317$	129820.			1.29188			0.645939	+	0.763389i	$0.276466\pi$
$318$	60482.5	+	68084.1i	0.598102	+	0.673274i
$319$		−	111198.i		−	1.09274i
$320$		0			0
$321$	36175.1			0.351075
$322$	−108704.	+	96567.1i	−1.04842	+	0.931360i
$323$		−	104756.i		−	1.00409i
$324$	1374.49	−	11582.7i	0.0130934	−	0.110337i
$325$		0			0
$326$	−76837.1	−	86494.3i	−0.722996	−	0.813865i
$327$			55530.4i			0.519320i
$328$	−73257.5	−	105212.i	−0.680933	−	0.977956i
$329$	−119186.			−1.10112
$330$		0			0
$331$			58912.8i			0.537717i	0.963180	+	0.268858i	$0.0866463\pi$
$331$			58912.8i			0.537717i	−0.963180	+	0.268858i	$0.913354\pi$
$332$	−145024.	−	17209.6i	−1.31572	−	0.156133i
$333$	40679.4			0.366848
$334$	−82769.6	−	93172.4i	−0.741956	−	0.835208i
$335$		0			0
$336$	−96159.7	−	23148.0i	−0.851755	−	0.205038i
$337$	−46849.1			−0.412517			−0.206258	−	0.978498i	$-0.566129\pi$
$337$	−46849.1			−0.412517			−0.206258	+	0.978498i	$0.566129\pi$
$338$	82589.9	−	73368.7i	0.722925	−	0.642210i
$339$			97587.3i			0.849169i
$340$		0			0
$341$	−44175.4			−0.379902
$342$	−25661.6	−	28886.8i	−0.219397	−	0.246972i
$343$		−	54017.9i		−	0.459145i
$344$	−172269.	+	119948.i	−1.45576	+	1.01362i
$345$		0			0
$346$	33248.6	−	29536.3i	0.277729	−	0.246720i
$347$			170481.i			1.41585i	0.706290	+	0.707923i	$0.250368\pi$
$347$			170481.i			1.41585i	−0.706290	+	0.707923i	$0.749632\pi$
$348$	85510.7	+	10147.3i	0.706093	+	0.0837901i
$349$	93820.0			0.770273			0.385136	−	0.922860i	$-0.374154\pi$
$349$	93820.0			0.770273			0.385136	+	0.922860i	$0.374154\pi$
$350$		0			0
$351$			4308.28i			0.0349695i
$352$	51749.7	+	96994.8i	0.417660	+	0.782822i
$353$	150254.			1.20581			0.602903	−	0.797814i	$-0.294011\pi$
$353$	150254.			1.20581			0.602903	+	0.797814i	$0.294011\pi$
$354$	−13231.5	+	11754.2i	−0.105585	+	0.0937968i
$355$		0			0
$356$	5997.37	−	50539.5i	0.0473218	−	0.398778i
$357$	113126.			0.887621
$358$	−22174.7	−	24961.7i	−0.173018	−	0.194764i
$359$		−	6723.72i		−	0.0521700i	−0.999660	−	0.0260850i	$-0.991696\pi$
$359$		−	6723.72i		−	0.0521700i	0.999660	−	0.0260850i	$-0.00830406\pi$
$360$		0			0
$361$	2323.47			0.0178288
$362$	−163587.	+	145322.i	−1.24834	+	1.10896i
$363$		−	16185.3i		−	0.122831i
$364$	36278.2	+	4305.03i	0.273806	+	0.0324917i
$365$		0			0
$366$	−76460.7	−	86070.6i	−0.570790	−	0.642529i
$367$		−	119927.i		−	0.890401i	−0.895431	−	0.445200i	$-0.853132\pi$
$367$		−	119927.i		−	0.890401i	0.895431	−	0.445200i	$-0.146868\pi$
$368$	−29291.0	+	121679.i	−0.216291	+	0.898502i
$369$	54086.1			0.397222
$370$		0			0
$371$			325786.i			2.36693i
$372$	4031.20	−	33970.7i	0.0291306	−	0.245481i
$373$	49886.2			0.358561			0.179280	−	0.983798i	$-0.442623\pi$
$373$	49886.2			0.358561			0.179280	+	0.983798i	$0.442623\pi$
$374$	−83510.1	−	94005.9i	−0.597029	−	0.672066i
$375$		0			0
$376$	−84191.4	+	58620.9i	−0.595514	+	0.414645i
$377$	−31806.3			−0.223785
$378$	31194.9	−	27712.0i	0.218324	−	0.193948i
$379$			42377.4i			0.295023i	0.989060	+	0.147512i	$0.0471264\pi$
$379$			42377.4i			0.295023i	−0.989060	+	0.147512i	$0.952874\pi$
$380$		0			0
$381$	−22710.0			−0.156447
$382$	−453.244	−	510.209i	−0.00310603	−	0.00349641i
$383$			249132.i			1.69837i	0.528098	+	0.849184i	$0.322905\pi$
$383$			249132.i			1.69837i	−0.528098	+	0.849184i	$0.677095\pi$
$384$	−79310.9	+	30944.1i	−0.537862	+	0.209853i
$385$		0			0
$386$	114920.	−	102089.i	0.771299	−	0.685183i
$387$		−	88557.6i		−	0.591294i
$388$	−23189.9	+	195420.i	−0.154041	+	1.29809i
$389$	187712.			1.24049			0.620244	−	0.784409i	$-0.287034\pi$
$389$	187712.			1.24049			0.620244	+	0.784409i	$0.287034\pi$
$390$		0			0
$391$		−	143148.i		−	0.936337i
$392$	−114374.	−	164264.i	−0.744311	−	1.06898i
$393$	−105378.			−0.682284
$394$	−140594.	+	124897.i	−0.905680	+	0.804560i
$395$		0			0
$396$	−46056.3	−	5465.37i	−0.293696	−	0.0348521i
$397$	239081.			1.51693			0.758463	−	0.651716i	$-0.225951\pi$
$397$	239081.			1.51693			0.758463	+	0.651716i	$0.225951\pi$
$398$	130638.	+	147057.i	0.824715	+	0.928368i
$399$		−	138225.i		−	0.868241i
$400$		0			0
$401$	226859.			1.41080			0.705402	−	0.708807i	$-0.250766\pi$
$401$	226859.			1.41080			0.705402	+	0.708807i	$0.250766\pi$
$402$	−65092.7	+	57825.0i	−0.402791	+	0.357819i
$403$			12635.6i			0.0778014i
$404$	15940.1	−	134326.i	0.0976624	−	0.822995i
$405$		0			0
$406$	204587.	+	230300.i	1.24115	+	1.39715i
$407$		−	161753.i		−	0.976480i
$408$	79910.8	−	55640.4i	0.480048	−	0.334249i
$409$	−165859.			−0.991497			−0.495748	−	0.868466i	$-0.665106\pi$
$409$	−165859.			−0.991497			−0.495748	+	0.868466i	$0.665106\pi$
$410$		0			0
$411$			135045.i			0.799456i
$412$	201072.	+	23860.6i	1.18456	+	0.140568i
$413$	−63313.7			−0.371191
$414$	−35066.3	−	39473.5i	−0.204592	−	0.230306i
$415$		0			0
$416$	27743.7	−	14802.1i	0.160317	−	0.0855338i
$417$	109375.			0.628996
$418$	−114862.	+	102038.i	−0.657393	+	0.583994i
$419$		−	154230.i		−	0.878498i	−0.898365	−	0.439249i	$-0.855245\pi$
$419$		−	154230.i		−	0.878498i	0.898365	−	0.439249i	$-0.144755\pi$
$420$		0			0
$421$	−247852.			−1.39839			−0.699196	−	0.714930i	$-0.746459\pi$
$421$	−247852.			−1.39839			−0.699196	+	0.714930i	$0.746459\pi$
$422$	11955.4	+	13458.0i	0.0671335	+	0.0755711i
$423$		−	43279.9i		−	0.241883i
$424$	160236.	+	230130.i	0.891306	+	1.28009i
$425$		0			0
$426$	97934.1	−	86999.7i	0.539653	−	0.479400i
$427$		−	411852.i		−	2.25884i
$428$	110614.	+	13126.3i	0.603843	+	0.0716564i
$429$	17131.0			0.0930824
$430$		0			0
$431$			132150.i			0.711396i	0.934601	+	0.355698i	$0.115757\pi$
$431$			132150.i			0.711396i	−0.934601	+	0.355698i	$0.884243\pi$
$432$	8405.68	−	34918.3i	0.0450407	−	0.187105i
$433$	341105.			1.81933			0.909666	−	0.415341i	$-0.136338\pi$
$433$	341105.			1.81933			0.909666	+	0.415341i	$0.136338\pi$
$434$	91490.8	−	81275.8i	0.485733	−	0.431501i
$435$		0			0
$436$	−20149.4	+	169798.i	−0.105996	+	0.893222i
$437$	−174907.			−0.915893
$438$	−97050.6	−	109248.i	−0.505883	−	0.569464i
$439$			1536.95i			0.00797498i	0.999992	+	0.00398749i	$0.00126926\pi$
$439$			1536.95i			0.00797498i	−0.999992	+	0.00398749i	$0.998731\pi$
$440$		0			0
$441$	84442.4			0.434194
$442$	−26888.8	+	23886.7i	−0.137634	+	0.122267i
$443$		−	259829.i		−	1.32398i	−0.749513	−	0.661989i	$-0.769712\pi$
$443$		−	259829.i		−	1.32398i	0.749513	−	0.661989i	$-0.230288\pi$
$444$	124387.	+	14760.7i	0.630972	+	0.0748756i
$445$		0			0
$446$	1275.88	+	1436.24i	0.00641418	+	0.00722034i
$447$			101337.i			0.507171i
$448$	−285633.	−	105673.i	−1.42315	−	0.526510i
$449$	123490.			0.612547			0.306274	−	0.951944i	$-0.400918\pi$
$449$	123490.			0.612547			0.306274	+	0.951944i	$0.400918\pi$
$450$		0			0
$451$		−	215062.i		−	1.05733i
$452$	−35409.9	+	298397.i	−0.173320	+	1.46056i
$453$	−172949.			−0.842796
$454$	103592.	+	116611.i	0.502589	+	0.565756i
$455$		0			0
$456$	−67984.9	−	97639.9i	−0.326951	−	0.469567i
$457$	−24937.6			−0.119405			−0.0597024	−	0.998216i	$-0.519015\pi$
$457$	−24937.6			−0.119405			−0.0597024	+	0.998216i	$0.519015\pi$
$458$	−82444.7	+	73239.7i	−0.393036	+	0.349153i
$459$			41079.4i			0.194984i
$460$		0			0
$461$	−142842.			−0.672130			−0.336065	−	0.941839i	$-0.609096\pi$
$461$	−142842.			−0.672130			−0.336065	+	0.941839i	$0.609096\pi$
$462$	−110191.	−	124040.i	−0.516252	−	0.581137i
$463$		−	58133.2i		−	0.271183i	−0.990765	−	0.135591i	$-0.956707\pi$
$463$		−	58133.2i		−	0.271183i	0.990765	−	0.135591i	$-0.0432935\pi$
$464$	257788.	+	62055.8i	1.19737	+	0.288235i
$465$		0			0
$466$	125643.	−	111615.i	0.578586	−	0.513986i
$467$			305454.i			1.40059i	0.713852	+	0.700296i	$0.246949\pi$
$467$			305454.i			1.40059i	−0.713852	+	0.700296i	$0.753051\pi$
$468$	−1563.28	+	13173.6i	−0.00713747	+	0.0601470i
$469$	−311472.			−1.41603
$470$		0			0
$471$		−	56417.5i		−	0.254315i
$472$	−44723.8	+	31140.4i	−0.200750	+	0.139778i
$473$	−352131.			−1.57392
$474$	−108997.	+	96827.7i	−0.485131	+	0.430966i
$475$		0			0
$476$	345912.	+	41048.4i	1.52669	+	0.181168i
$477$	−118302.			−0.519943
$478$	−247481.	−	278585.i	−1.08314	−	1.21928i
$479$		−	214385.i		−	0.934378i	−0.884157	−	0.467189i	$-0.845267\pi$
$479$		−	214385.i		−	0.934378i	0.884157	−	0.467189i	$-0.154733\pi$
$480$		0			0
$481$	−46266.7			−0.199976
$482$	325605.	−	289251.i	1.40151	−	1.24503i
$483$		−	188883.i		−	0.809652i
$484$	5872.91	−	49490.6i	0.0250705	−	0.211267i
$485$		0			0
$486$	10063.0	+	11327.8i	0.0426045	+	0.0479592i
$487$		−	132928.i		−	0.560480i	−0.959930	−	0.280240i	$-0.909586\pi$
$487$		−	132928.i		−	0.560480i	0.959930	−	0.280240i	$-0.0904140\pi$
$488$	−202566.	−	290926.i	−0.850605	−	1.22164i
$489$	150292.			0.628517
$490$		0			0
$491$		−	203534.i		−	0.844256i	−0.906536	−	0.422128i	$-0.861283\pi$
$491$		−	203534.i		−	0.844256i	0.906536	−	0.422128i	$-0.138717\pi$
$492$	165382.	+	19625.4i	0.683215	+	0.0810752i
$493$	−303273.			−1.24779
$494$	29186.2	+	32854.4i	0.119598	+	0.134629i
$495$		0			0
$496$	24652.8	−	102411.i	0.100208	−	0.416278i
$497$	468620.			1.89718
$498$	141832.	−	125996.i	0.571892	−	0.508040i
$499$			282205.i			1.13335i	0.823942	+	0.566674i	$0.191770\pi$
$499$			282205.i			1.13335i	−0.823942	+	0.566674i	$0.808230\pi$
$500$		0			0
$501$	161895.			0.644999
$502$	83965.5	+	94518.6i	0.333191	+	0.375068i
$503$			307654.i			1.21598i	0.793944	+	0.607991i	$0.208024\pi$
$503$			307654.i			1.21598i	−0.793944	+	0.607991i	$0.791976\pi$
$504$	105442.	−	73417.1i	0.415098	−	0.289025i
$505$		0			0
$506$	−156958.	+	139434.i	−0.613031	+	0.544586i
$507$			143507.i			0.558288i
$508$	−69441.3	−	8240.40i	−0.269086	−	0.0319316i
$509$	164324.			0.634256			0.317128	−	0.948383i	$-0.397282\pi$
$509$	164324.			0.634256			0.317128	+	0.948383i	$0.397282\pi$
$510$		0			0
$511$		−	522759.i		−	2.00198i
$512$	−253741.	+	65840.9i	−0.967945	+	0.251163i
$513$	50193.4			0.190727
$514$	−59867.1	+	53182.9i	−0.226601	+	0.201301i
$515$		0			0
$516$	32133.5	−	270787.i	0.120686	−	1.01702i
$517$	−172094.			−0.643848
$518$	297600.	+	335003.i	1.10911	+	1.24850i
$519$			57772.3i			0.214479i
$520$		0			0
$521$	317062.			1.16807			0.584034	−	0.811729i	$-0.301473\pi$
$521$	317062.			1.16807			0.584034	+	0.811729i	$0.301473\pi$
$522$	−83628.4	+	74291.2i	−0.306911	+	0.272644i
$523$		−	55332.3i		−	0.202290i	−0.994872	−	0.101145i	$-0.967749\pi$
$523$		−	55332.3i		−	0.202290i	0.994872	−	0.101145i	$-0.0322507\pi$
$524$	−322220.	−	38236.9i	−1.17352	−	0.139258i
$525$		0			0
$526$	166566.	+	187501.i	0.602027	+	0.677692i
$527$			120481.i			0.433807i
$528$	−138845.	−	33423.4i	−0.498039	−	0.119890i
$529$	40832.1			0.145912
$530$		0			0
$531$		−	22991.0i		−	0.0815396i
$532$	50155.5	−	422657.i	0.177213	−	1.49336i
$533$	−61514.9			−0.216534
$534$	43908.4	+	49427.0i	0.153980	+	0.173333i
$535$		0			0
$536$	−220019.	+	153195.i	−0.765827	+	0.533231i
$537$	43373.2			0.150409
$538$	−101091.	+	89803.7i	−0.349258	+	0.310263i
$539$		−	335768.i		−	1.15574i
$540$		0			0
$541$	−86217.1			−0.294577			−0.147289	−	0.989094i	$-0.547055\pi$
$541$	−86217.1			−0.294577			−0.147289	+	0.989094i	$0.547055\pi$
$542$	149250.	+	168008.i	0.508060	+	0.571915i
$543$		−	284247.i		−	0.964042i
$544$	264536.	−	141138.i	0.893897	−	0.476922i
$545$		0			0
$546$	−35479.6	+	31518.3i	−0.119013	+	0.105725i
$547$			288324.i			0.963620i	0.876276	+	0.481810i	$0.160020\pi$
$547$			288324.i			0.963620i	−0.876276	+	0.481810i	$0.839980\pi$
$548$	−49001.6	+	412933.i	−0.163173	+	1.37505i
$549$	149555.			0.496200
$550$		0			0
$551$			370558.i			1.22054i
$552$	−92900.6	−	133424.i	−0.304888	−	0.437880i
$553$	−521558.			−1.70550
$554$	363519.	−	322932.i	1.18442	−	1.05218i
$555$		0			0
$556$	334442.	+	39687.3i	1.08186	+	0.128381i
$557$	465454.			1.50026			0.750129	−	0.661291i	$-0.229991\pi$
$557$	465454.			1.50026			0.750129	+	0.661291i	$0.229991\pi$
$558$	29513.5	+	33222.9i	0.0947879	+	0.106701i
$559$			100721.i			0.322327i
$560$		0			0
$561$	163344.			0.519011
$562$	154877.	−	137585.i	0.490361	−	0.435611i
$563$			276410.i			0.872040i	0.899937	+	0.436020i	$0.143612\pi$
$563$			276410.i			0.872040i	−0.899937	+	0.436020i	$0.856388\pi$
$564$	15704.3	−	132339.i	0.0493697	−	0.416035i
$565$		0			0
$566$	−336478.	−	378768.i	−1.05033	−	1.18233i
$567$			54204.0i			0.168603i
$568$	331026.	−	230487.i	1.02604	−	0.714414i
$569$	−178268.			−0.550615			−0.275307	−	0.961356i	$-0.588780\pi$
$569$	−178268.			−0.550615			−0.275307	+	0.961356i	$0.588780\pi$
$570$		0			0
$571$			430413.i			1.32012i	0.751213	+	0.660060i	$0.229469\pi$
$571$			430413.i			1.32012i	−0.751213	+	0.660060i	$0.770531\pi$
$572$	52382.2	+	6216.04i	0.160100	+	0.0189986i
$573$	886.534			0.00270014
$574$	395680.	+	445411.i	1.20094	+	1.35188i
$575$		0			0
$576$	38372.7	−	103721.i	0.115658	−	0.312625i
$577$	−349598.			−1.05007			−0.525034	−	0.851081i	$-0.675947\pi$
$577$	−349598.			−1.05007			−0.525034	+	0.851081i	$0.675947\pi$
$578$	−6620.22	+	5881.07i	−0.0198160	+	0.0176036i
$579$			199684.i			0.595645i
$580$		0			0
$581$	678672.			2.01052
$582$	−169780.	−	191118.i	−0.501234	−	0.564230i
$583$			470404.i			1.38399i
$584$	−257115.	−	369269.i	−0.753879	−	1.08272i
$585$		0			0
$586$	−17817.5	+	15828.2i	−0.0518862	+	0.0460931i
$587$			401716.i			1.16585i	0.812525	+	0.582926i	$0.198092\pi$
$587$			401716.i			1.16585i	−0.812525	+	0.582926i	$0.801908\pi$
$588$	258204.	+	30640.3i	0.746806	+	0.0886213i
$589$	147211.			0.424335
$590$		0			0
$591$		−	244295.i		−	0.699422i
$592$	374989.	+	90268.8i	1.06998	+	0.257569i
$593$	83500.7			0.237455			0.118727	−	0.992927i	$-0.462119\pi$
$593$	83500.7			0.237455			0.118727	+	0.992927i	$0.462119\pi$
$594$	45042.5	−	40013.5i	0.127658	−	0.113405i
$595$		0			0
$596$	−36770.7	+	309864.i	−0.103516	+	0.872326i
$597$	−255525.			−0.716943
$598$	39882.6	+	44895.2i	0.111527	+	0.125545i
$599$			655204.i			1.82609i	0.407855	+	0.913047i	$0.366277\pi$
$599$			655204.i			1.82609i	−0.407855	+	0.913047i	$0.633723\pi$
$600$		0			0
$601$	350508.			0.970396			0.485198	−	0.874404i	$-0.338747\pi$
$601$	350508.			0.970396			0.485198	+	0.874404i	$0.338747\pi$
$602$	729290.	−	647864.i	2.01237	−	1.78769i
$603$		−	113104.i		−	0.311060i
$604$	−528836.	−	62755.4i	−1.44960	−	0.172019i
$605$		0			0
$606$	116702.	+	131369.i	0.317784	+	0.357724i
$607$		−	14709.5i		−	0.0399228i	−0.999801	−	0.0199614i	$-0.993646\pi$
$607$		−	14709.5i		−	0.0399228i	0.999801	−	0.0199614i	$-0.00635434\pi$
$608$	−172452.	−	323227.i	−0.466509	−	0.874380i
$609$	−400166.			−1.07896
$610$		0			0
$611$			49224.5i			0.131856i
$612$	−14905.8	+	125610.i	−0.0397973	+	0.335369i
$613$	440819.			1.17311			0.586556	−	0.809909i	$-0.300483\pi$
$613$	440819.			1.17311			0.586556	+	0.809909i	$0.300483\pi$
$614$	207400.	+	233467.i	0.550138	+	0.619281i
$615$		0			0
$616$	−291928.	−	419267.i	−0.769332	−	1.10491i
$617$	−670222.			−1.76055			−0.880275	−	0.474465i	$-0.842642\pi$
$617$	−670222.			−1.76055			−0.880275	+	0.474465i	$0.842642\pi$
$618$	−196646.	+	174690.i	−0.514881	+	0.457394i
$619$			273459.i			0.713692i	0.934163	+	0.356846i	$0.116148\pi$
$619$			273459.i			0.713692i	−0.934163	+	0.356846i	$0.883852\pi$
$620$		0			0
$621$	68588.7			0.177856
$622$	−97643.1	−	109915.i	−0.252383	−	0.284104i
$623$			236511.i			0.609361i
$624$	−9560.21	+	39714.4i	−0.0245526	+	0.101995i
$625$		0			0
$626$	−505443.	+	449010.i	−1.28980	+	1.14580i
$627$		−	199583.i		−	0.507679i
$628$	20471.3	−	172510.i	0.0519071	−	0.437417i
$629$	−441153.			−1.11503
$630$		0			0
$631$		−	322420.i		−	0.809774i	−0.914367	−	0.404887i	$-0.867311\pi$
$631$		−	322420.i		−	0.809774i	0.914367	−	0.404887i	$-0.132689\pi$
$632$	−368421.	+	256525.i	−0.922380	+	0.642236i
$633$	−23384.5			−0.0583606
$634$	−388218.	+	344873.i	−0.965821	+	0.857986i
$635$		0			0
$636$	−361738.	−	42926.4i	−0.894294	−	0.106123i
$637$	−96040.7			−0.236688
$638$	295404.	+	332531.i	0.725729	+	0.816941i
$639$			170169.i			0.416753i
$640$		0			0
$641$	−534654.			−1.30124			−0.650619	−	0.759404i	$-0.725490\pi$
$641$	−534654.			−1.30124			−0.650619	+	0.759404i	$0.725490\pi$
$642$	−108180.	+	96101.2i	−0.262467	+	0.233163i
$643$		−	83676.6i		−	0.202387i	−0.994867	−	0.101193i	$-0.967734\pi$
$643$		−	83676.6i		−	0.202387i	0.994867	−	0.101193i	$-0.0322661\pi$
$644$	68536.9	−	577556.i	0.165254	−	1.39259i
$645$		0			0
$646$	278290.	+	313267.i	0.666857	+	0.750670i
$647$		−	226640.i		−	0.541411i	−0.962662	−	0.270706i	$-0.912743\pi$
$647$		−	226640.i		−	0.541411i	0.962662	−	0.270706i	$-0.0872570\pi$
$648$	26659.8	+	38288.9i	0.0634903	+	0.0911848i
$649$	−91418.8			−0.217043
$650$		0			0
$651$			158973.i			0.375113i
$652$	459554.	+	54533.9i	1.08104	+	0.128284i
$653$	499953.			1.17247			0.586236	−	0.810140i	$-0.300609\pi$
$653$	499953.			1.17247			0.586236	+	0.810140i	$0.300609\pi$
$654$	−147519.	−	166060.i	−0.344900	−	0.388249i
$655$		0			0
$656$	498574.	+	120019.i	1.15857	+	0.278896i
$657$	189828.			0.439775
$658$	356419.	−	316625.i	0.823208	−	0.731296i
$659$		−	15572.3i		−	0.0358576i	−0.999839	−	0.0179288i	$-0.994293\pi$
$659$		−	15572.3i		−	0.0358576i	0.999839	−	0.0179288i	$-0.00570722\pi$
$660$		0			0
$661$	17974.5			0.0411390			0.0205695	−	0.999788i	$-0.493452\pi$
$661$	17974.5			0.0411390			0.0205695	+	0.999788i	$0.493452\pi$
$662$	−156505.	−	176175.i	−0.357118	−	0.402002i
$663$		−	46721.7i		−	0.106290i
$664$	479403.	−	333800.i	1.08734	−	0.757094i
$665$		0			0
$666$	−121649.	+	108067.i	−0.274259	+	0.243638i
$667$			506363.i			1.13818i
$668$	495035.	+	58744.4i	1.10939	+	0.131648i
$669$	−2495.60			−0.00557599
$670$		0			0
$671$		−	594675.i		−	1.32079i
$672$	349054.	−	186231.i	0.772954	−	0.412395i
$673$	53880.1			0.118959			0.0594796	−	0.998230i	$-0.481056\pi$
$673$	53880.1			0.118959			0.0594796	+	0.998230i	$0.481056\pi$
$674$	140099.	−	124457.i	0.308401	−	0.273968i
$675$		0			0
$676$	−52072.2	+	438809.i	−0.113950	+	0.960245i
$677$	−694984.			−1.51634			−0.758172	−	0.652055i	$-0.773907\pi$
$677$	−694984.			−1.51634			−0.758172	+	0.652055i	$0.773907\pi$
$678$	−259246.	−	291829.i	−0.563965	−	0.634847i
$679$		−	914512.i		−	1.98358i
$680$		0			0
$681$	−202623.			−0.436912
$682$	132104.	−	117354.i	0.284019	−	0.252308i
$683$			54187.4i			0.116160i	0.998312	+	0.0580800i	$0.0184979\pi$
$683$			54187.4i			0.116160i	−0.998312	+	0.0580800i	$0.981502\pi$
$684$	153479.	+	18212.9i	0.328047	+	0.0389284i
$685$		0			0
$686$	143502.	+	161537.i	0.304936	+	0.343261i
$687$		−	143255.i		−	0.303526i
$688$	196512.	−	816337.i	0.415157	−	1.72462i
$689$	134551.			0.283432
$690$		0			0
$691$		−	138548.i		−	0.290165i	−0.989420	−	0.145083i	$-0.953655\pi$
$691$		−	138548.i		−	0.290165i	0.989420	−	0.145083i	$-0.0463448\pi$
$692$	−20962.9	+	176653.i	−0.0437764	+	0.368900i
$693$	215531.			0.448789
$694$	−452891.	−	509812.i	−0.940317	−	1.05850i
$695$		0			0
$696$	−282671.	+	196819.i	−0.583530	+	0.406301i
$697$	−586544.			−1.20736
$698$	−280563.	+	249238.i	−0.575863	+	0.511568i
$699$			218317.i			0.446820i
$700$		0			0
$701$	140668.			0.286259			0.143130	−	0.989704i	$-0.454283\pi$
$701$	140668.			0.286259			0.143130	+	0.989704i	$0.454283\pi$
$702$	−11445.2	−	12883.6i	−0.0232246	−	0.0261435i
$703$			539028.i			1.09069i
$704$	−412426.	−	152581.i	−0.832149	−	0.307861i
$705$		0			0
$706$	−449326.	+	399159.i	−0.901472	+	0.800822i
$707$			628608.i			1.25760i
$708$	8342.37	−	70300.6i	0.0166427	−	0.140247i
$709$	−381395.			−0.758723			−0.379361	−	0.925249i	$-0.623856\pi$
$709$	−381395.			−0.758723			−0.379361	+	0.925249i	$0.623856\pi$
$710$		0			0
$711$		−	189393.i		−	0.374648i
$712$	116326.	+	167068.i	0.229465	+	0.329558i
$713$	201162.			0.395701
$714$	−338298.	+	300526.i	−0.663594	+	0.589503i
$715$		0			0
$716$	132624.	+	15738.1i	0.258700	+	0.0306992i
$717$	484066.			0.941600
$718$	17861.9	+	20106.9i	0.0346481	+	0.0390028i
$719$		−	66799.3i		−	0.129215i	−0.997911	−	0.0646076i	$-0.979420\pi$
$719$		−	66799.3i		−	0.129215i	0.997911	−	0.0646076i	$-0.0205796\pi$
$720$		0			0
$721$	−940959.			−1.81009
$722$	−6948.19	+	6172.42i	−0.0133290	+	0.0118408i
$723$			565767.i			1.08233i
$724$	103140.	−	869155.i	0.196766	−	1.65814i
$725$		0			0
$726$	42997.2	+	48401.2i	0.0815768	+	0.0918297i
$727$			53183.1i			0.100625i	0.998734	+	0.0503124i	$0.0160217\pi$
$727$			53183.1i			0.100625i	−0.998734	+	0.0503124i	$0.983978\pi$
$728$	−119924.	+	83501.0i	−0.226279	+	0.157554i
$729$	−19683.0			−0.0370370
$730$		0			0
$731$			960374.i			1.79724i
$732$	457302.	+	54266.7i	0.853456	+	0.101277i
$733$	251943.			0.468915			0.234457	−	0.972126i	$-0.424669\pi$
$733$	251943.			0.468915			0.234457	+	0.972126i	$0.424669\pi$
$734$	318593.	+	358635.i	0.591349	+	0.665672i
$735$		0			0
$736$	−235653.	−	441686.i	−0.435029	−	0.815376i
$737$	−449736.			−0.827985
$738$	−161741.	+	143683.i	−0.296967	+	0.263810i
$739$			417899.i			0.765213i	0.923911	+	0.382607i	$0.124974\pi$
$739$			417899.i			0.765213i	−0.923911	+	0.382607i	$0.875026\pi$
$740$		0			0
$741$	−57087.5			−0.103969
$742$	−865468.	−	974243.i	−1.57197	−	1.76954i
$743$			95941.3i			0.173791i	0.996217	+	0.0868956i	$0.0276947\pi$
$743$			95941.3i			0.173791i	−0.996217	+	0.0868956i	$0.972305\pi$
$744$	78189.9	+	112296.i	0.141255	+	0.202871i
$745$		0			0
$746$	−149182.	+	132525.i	−0.268063	+	0.238134i
$747$			246445.i			0.441650i
$748$	499464.	+	59269.9i	0.892690	+	0.105933i
$749$	−517645.			−0.922717
$750$		0			0
$751$		−	313222.i		−	0.555358i	−0.960674	−	0.277679i	$-0.910435\pi$
$751$		−	313222.i		−	0.555358i	0.960674	−	0.277679i	$-0.0895651\pi$
$752$	96039.5	−	398961.i	0.169830	−	0.705496i
$753$	−164234.			−0.289650
$754$	95114.9	−	84495.2i	0.167304	−	0.148624i
$755$		0			0
$756$	−19668.1	+	165742.i	−0.0344128	+	0.289994i
$757$	−386817.			−0.675016			−0.337508	−	0.941323i	$-0.609584\pi$
$757$	−386817.			−0.675016			−0.337508	+	0.941323i	$0.609584\pi$
$758$	−112578.	−	126727.i	−0.195936	−	0.220562i
$759$		−	272729.i		−	0.473421i
$760$		0			0
$761$	−447721.			−0.773105			−0.386552	−	0.922267i	$-0.626334\pi$
$761$	−447721.			−0.773105			−0.386552	+	0.922267i	$0.626334\pi$
$762$	67912.7	−	60330.2i	0.116961	−	0.103902i
$763$		−	794607.i		−	1.36491i
$764$	2710.80	+	321.683i	0.00464419	+	0.000551113i
$765$		0			0
$766$	−661832.	−	745013.i	−1.12795	−	1.26972i
$767$			26148.8i			0.0444489i
$768$	154970.	−	303230.i	0.262739	−	0.514103i
$769$	351782.			0.594869			0.297434	−	0.954742i	$-0.403869\pi$
$769$	351782.			0.594869			0.297434	+	0.954742i	$0.403869\pi$
$770$		0			0
$771$		−	104024.i		−	0.174995i
$772$	−72456.3	+	610585.i	−0.121574	+	1.02450i
$773$	−550849.			−0.921878			−0.460939	−	0.887432i	$-0.652487\pi$
$773$	−550849.			−0.921878			−0.460939	+	0.887432i	$0.652487\pi$
$774$	235258.	+	264826.i	0.392701	+	0.442057i
$775$		0			0
$776$	−449796.	−	645997.i	−0.746951	−	1.07277i
$777$	−582098.			−0.964171
$778$	−561341.	+	498667.i	−0.927401	+	0.823856i
$779$			716676.i			1.18100i
$780$		0			0
$781$	676642.			1.10932
$782$	380281.	+	428076.i	0.621857	+	0.700014i
$783$		−	145312.i		−	0.237016i
$784$	778404.	+	187380.i	1.26641	+	0.304854i
$785$		0			0
$786$	315127.	−	279943.i	0.510082	−	0.453131i
$787$			414987.i			0.670015i	0.942215	+	0.335008i	$0.108739\pi$
$787$			414987.i			0.670015i	−0.942215	+	0.335008i	$0.891261\pi$
$788$	88643.4	−	746992.i	0.142756	−	1.20299i
$789$	−325800.			−0.523355
$790$		0			0
$791$		−	1.39642e6i		−	2.23183i
$792$	152248.	−	106007.i	0.242717	−	0.168999i
$793$	−170097.			−0.270489
$794$	−714957.	+	635132.i	−1.13407	+	1.00745i
$795$		0			0
$796$	−781331.	−	92718.3i	−1.23313	−	0.146332i
$797$	−47477.2			−0.0747426			−0.0373713	−	0.999301i	$-0.511898\pi$
$797$	−47477.2			−0.0747426			−0.0373713	+	0.999301i	$0.511898\pi$
$798$	367202.	+	413353.i	0.576632	+	0.649106i
$799$			469355.i			0.735204i
$800$		0			0
$801$	−85883.7			−0.133858
$802$	−678407.	+	602662.i	−1.05473	+	0.936969i
$803$		−	754813.i		−	1.17060i
$804$	41040.4	−	345844.i	0.0634891	−	0.535018i
$805$		0			0
$806$	−33567.3	−	37786.1i	−0.0516709	−	0.0581651i
$807$		−	175654.i		−	0.269718i
$808$	309176.	+	444039.i	0.473569	+	0.680140i
$809$	191528.			0.292640			0.146320	−	0.989237i	$-0.453257\pi$
$809$	191528.			0.292640			0.146320	+	0.989237i	$0.453257\pi$
$810$		0			0
$811$			502064.i			0.763339i	0.924299	+	0.381670i	$0.124651\pi$
$811$			502064.i			0.763339i	−0.924299	+	0.381670i	$0.875349\pi$
$812$	−1.22361e6	−	145202.i	−1.85580	−	0.220222i
$813$	−291929.			−0.441668
$814$	429705.	+	483712.i	0.648518	+	0.730026i
$815$		0			0
$816$	−91156.5	+	378676.i	−0.136901	+	0.568706i
$817$	1.17345e6			1.75800
$818$	495990.	−	440612.i	0.741253	−	0.658491i
$819$		−	61648.9i		−	0.0919089i
$820$		0			0
$821$	−184973.			−0.274424			−0.137212	−	0.990542i	$-0.543814\pi$
$821$	−184973.			−0.274424			−0.137212	+	0.990542i	$0.543814\pi$
$822$	−358754.	−	403843.i	−0.530949	−	0.597681i
$823$		−	728359.i		−	1.07534i	−0.843155	−	0.537670i	$-0.819305\pi$
$823$		−	728359.i		−	1.07534i	0.843155	−	0.537670i	$-0.180695\pi$
$824$	−664679.	+	462804.i	−0.978944	+	0.681620i
$825$		0			0
$826$	189336.	−	168196.i	0.277506	−	0.246522i
$827$		−	692660.i		−	1.01277i	−0.862309	−	0.506383i	$-0.830982\pi$
$827$		−	692660.i		−	1.01277i	0.862309	−	0.506383i	$-0.169018\pi$
$828$	209727.	+	24887.7i	0.305910	+	0.0363015i
$829$	501976.			0.730422			0.365211	−	0.930925i	$-0.380997\pi$
$829$	501976.			0.730422			0.365211	+	0.930925i	$0.380997\pi$
$830$		0			0
$831$			631646.i			0.914686i
$832$	−43643.2	+	117968.i	−0.0630479	+	0.170418i
$833$	−915747.			−1.31973
$834$	−327080.	+	290562.i	−0.470243	+	0.417740i
$835$		0			0
$836$	72419.7	−	610276.i	0.103620	−	0.873200i
$837$	−57727.8			−0.0824012
$838$	409720.	+	461215.i	0.583444	+	0.656774i
$839$			275008.i			0.390680i	0.980736	+	0.195340i	$0.0625810\pi$
$839$			275008.i			0.390680i	−0.980736	+	0.195340i	$0.937419\pi$
$840$		0			0
$841$	365499.			0.516766
$842$	741187.	−	658433.i	1.04545	−	0.928726i
$843$			269113.i			0.378687i
$844$	−71503.8	−	8485.15i	−0.100379	−	0.0119117i
$845$		0			0
$846$	114975.	+	129426.i	0.160644	+	0.180834i
$847$			231602.i			0.322832i
$848$	−1.09053e6	−	262516.i	−1.51651	−	0.365060i
$849$	658142.			0.913071
$850$		0			0
$851$			736576.i			1.01709i
$852$	−61746.6	+	520334.i	−0.0850616	+	0.716809i
$853$	−203129.			−0.279174			−0.139587	−	0.990210i	$-0.544577\pi$
$853$	−203129.			−0.279174			−0.139587	+	0.990210i	$0.544577\pi$
$854$	1.09411e6	+	1.23162e6i	1.50018	+	1.68873i
$855$		0			0
$856$	−365656.	+	254600.i	−0.499029	+	0.347465i
$857$	219558.			0.298943			0.149471	−	0.988766i	$-0.452243\pi$
$857$	219558.			0.298943			0.149471	+	0.988766i	$0.452243\pi$
$858$	−51229.1	+	45509.3i	−0.0695893	+	0.0618196i
$859$		−	306354.i		−	0.415180i	−0.978216	−	0.207590i	$-0.933438\pi$
$859$		−	306354.i		−	0.415180i	0.978216	−	0.207590i	$-0.0665621\pi$
$860$		0			0
$861$	−773941.			−1.04400
$862$	−351063.	−	395185.i	−0.472466	−	0.531847i
$863$			590022.i			0.792221i	0.918203	+	0.396111i	$0.129640\pi$
$863$			590022.i			0.792221i	−0.918203	+	0.396111i	$0.870360\pi$
$864$	67625.7	+	126751.i	0.0905909	+	0.169795i
$865$		0			0
$866$	−1.02005e6	+	906163.i	−1.36015	+	1.20829i
$867$		−	11503.2i		−	0.0153032i
$868$	−57684.2	+	486101.i	−0.0765627	+	0.645189i
$869$	−753080.			−0.997244
$870$		0			0
$871$			128639.i			0.169565i
$872$	−390822.	−	561298.i	−0.513979	−	0.738177i
$873$	332085.			0.435733
$874$	523049.	−	464651.i	0.684731	−	0.608280i
$875$		0			0
$876$	580447.	+	68880.0i	0.756406	+	0.0897605i
$877$	54310.2			0.0706127			0.0353063	−	0.999377i	$-0.488759\pi$
$877$	54310.2			0.0706127			0.0353063	+	0.999377i	$0.488759\pi$
$878$	−4082.98	−	4596.15i	−0.00529649	−	0.00596218i
$879$		−	30959.5i		−	0.0400698i
$880$		0			0
$881$	−395072.			−0.509008			−0.254504	−	0.967072i	$-0.581912\pi$
$881$	−395072.			−0.509008			−0.254504	+	0.967072i	$0.581912\pi$
$882$	−252520.	+	224326.i	−0.324607	+	0.288365i
$883$		−	1.22117e6i		−	1.56623i	−0.621878	−	0.783114i	$-0.713630\pi$
$883$		−	1.22117e6i		−	1.56623i	0.621878	−	0.783114i	$-0.286370\pi$
$884$	16953.2	−	142863.i	0.0216943	−	0.182817i
$885$		0			0
$886$	690251.	+	777004.i	0.879305	+	0.989819i
$887$		−	668218.i		−	0.849319i	−0.905353	−	0.424660i	$-0.860394\pi$
$887$		−	668218.i		−	0.849319i	0.905353	−	0.424660i	$-0.139606\pi$
$888$	−411185.	+	286300.i	−0.521448	+	0.363075i
$889$	324966.			0.411182
$890$		0			0
$891$			78265.3i			0.0985857i
$892$	−7630.90	−	905.537i	−0.00959061	−	0.00113809i
$893$	573487.			0.719152
$894$	−269208.	−	303043.i	−0.336832	−	0.379166i
$895$		0			0
$896$	1.13489e6	−	442792.i	1.41364	−	0.551548i
$897$	−78009.4			−0.0969532
$898$	−369290.	+	328058.i	−0.457946	+	0.406816i
$899$		−	426181.i		−	0.527321i
$900$		0			0
$901$	1.28294e6			1.58037
$902$	571324.	+	643130.i	0.702214	+	0.790471i
$903$			1.26721e6i			1.55407i
$904$	−686817.	−	986407.i	−0.840435	−	1.20703i
$905$		0			0
$906$	517195.	−	459449.i	0.630083	−	0.559734i
$907$			426441.i			0.518375i	0.965827	+	0.259188i	$0.0834548\pi$
$907$			426441.i			0.518375i	−0.965827	+	0.259188i	$0.916545\pi$
$908$	−619569.	−	73522.5i	−0.751481	−	0.0891761i
$909$	−228265.			−0.276256
$910$		0			0
$911$		−	1.05132e6i		−	1.26677i	−0.773839	−	0.633383i	$-0.781666\pi$
$911$		−	1.05132e6i		−	1.26677i	0.773839	−	0.633383i	$-0.218334\pi$
$912$	462690.	+	111381.i	0.556289	+	0.133912i
$913$	979936.			1.17559
$914$	74574.3	−	66248.0i	0.0892682	−	0.0793013i
$915$		0			0
$916$	51980.7	−	438038.i	0.0619514	−	0.522060i
$917$	1.50790e6			1.79322
$918$	−109130.	−	122845.i	−0.129496	−	0.145772i
$919$		−	1.00986e6i		−	1.19572i	−0.801600	−	0.597861i	$-0.796018\pi$
$919$		−	1.00986e6i		−	1.19572i	0.801600	−	0.597861i	$-0.203982\pi$
$920$		0			0
$921$	−405669.			−0.478247
$922$	427160.	−	379467.i	0.502491	−	0.446388i
$923$		−	193542.i		−	0.227181i
$924$	659038.	+	78206.2i	0.771910	+	0.0916004i
$925$		0			0
$926$	154434.	+	173844.i	0.180103	+	0.202739i
$927$		−	341689.i		−	0.397623i
$928$	−935754.	+	499254.i	−1.08659	+	0.579730i
$929$	516568.			0.598544			0.299272	−	0.954168i	$-0.403256\pi$
$929$	516568.			0.598544			0.299272	+	0.954168i	$0.403256\pi$
$930$		0			0
$931$			1.11892e6i			1.29092i
$932$	−79217.1	+	667557.i	−0.0911984	+	0.768522i
$933$	190987.			0.219402
$934$	−811455.	−	913441.i	−0.930187	−	1.04710i
$935$		0			0
$936$	−30321.6	−	43547.9i	−0.0346099	−	0.0497067i
$937$	1.03317e6			1.17678			0.588388	−	0.808579i	$-0.299763\pi$
$937$	1.03317e6			1.17678			0.588388	+	0.808579i	$0.299763\pi$
$938$	931438.	−	827442.i	1.05864	−	0.940442i
$939$		−	878253.i		−	0.996067i
$940$		0			0
$941$	−755128.			−0.852789			−0.426394	−	0.904537i	$-0.640216\pi$
$941$	−755128.			−0.852789			−0.426394	+	0.904537i	$0.640216\pi$
$942$	149876.	+	168713.i	0.168900	+	0.190128i
$943$			979331.i			1.10130i
$944$	51017.7	−	211935.i	0.0572502	−	0.237825i
$945$		0			0
$946$	1.05302e6	−	935454.i	1.17667	−	1.04530i
$947$		−	521546.i		−	0.581558i	−0.956790	−	0.290779i	$-0.906086\pi$
$947$		−	521546.i		−	0.581558i	0.956790	−	0.290779i	$-0.0939144\pi$
$948$	68721.9	−	579115.i	0.0764678	−	0.644389i
$949$	−215902.			−0.239731
$950$		0			0
$951$		−	674562.i		−	0.745867i
$952$	−1.14348e6	+	796181.i	−1.26169	+	0.878492i
$953$	−278502.			−0.306650			−0.153325	−	0.988176i	$-0.548998\pi$
$953$	−278502.			−0.306650			−0.153325	+	0.988176i	$0.548998\pi$
$954$	353775.	−	314276.i	0.388715	−	0.345314i
$955$		0			0
$956$	1.48015e6	+	175645.i	1.61954	+	0.192186i
$957$	−577802.			−0.630892
$958$	569524.	+	641104.i	0.620557	+	0.698550i
$959$		−	1.93241e6i		−	2.10118i
$960$		0			0
$961$	754213.			0.816671
$962$	138358.	−	122910.i	0.149504	−	0.132812i
$963$		−	187972.i		−	0.202693i
$964$	−205291.	+	1.72997e6i	−0.220910	+	1.86160i
$965$		0			0
$966$	501777.	+	564843.i	0.537721	+	0.605303i
$967$		−	1.53687e6i		−	1.64356i	−0.569806	−	0.821779i	$-0.692982\pi$
$967$		−	1.53687e6i		−	1.64356i	0.569806	−	0.821779i	$-0.307018\pi$
$968$	113912.	+	163600.i	0.121568	+	0.174596i
$969$	−544329.			−0.579714
$970$		0			0
$971$		−	889418.i		−	0.943338i	−0.881776	−	0.471669i	$-0.843652\pi$
$971$		−	889418.i		−	0.943338i	0.881776	−	0.471669i	$-0.156348\pi$
$972$	−60185.6	−	7142.06i	−0.0637031	−	0.00755946i
$973$	−1.56510e6			−1.65316
$974$	353132.	+	397514.i	0.372236	+	0.419020i
$975$		0			0
$976$	1.37862e6	+	331868.i	1.44726	+	0.348390i
$977$	998756.			1.04633			0.523167	−	0.852230i	$-0.324750\pi$
$977$	998756.			1.04633			0.523167	+	0.852230i	$0.324750\pi$
$978$	−449438.	+	399258.i	−0.469885	+	0.417422i
$979$			341499.i			0.356306i
$980$		0			0
$981$	288544.			0.299830
$982$	540699.	+	608656.i	0.560703	+	0.631174i
$983$		−	1.34511e6i		−	1.39204i	−0.718024	−	0.696019i	$-0.754953\pi$
$983$		−	1.34511e6i		−	1.39204i	0.718024	−	0.696019i	$-0.245047\pi$
$984$	−546700.	+	380657.i	−0.564623	+	0.393137i
$985$		0			0
$986$	906919.	−	805661.i	0.932857	−	0.828702i
$987$			619310.i			0.635732i
$988$	−174559.	−	20714.4i	−0.178825	−	0.0212207i
$989$	1.60350e6			1.63937
$990$		0			0
$991$			1.25414e6i			1.27702i	0.769613	+	0.638510i	$0.220449\pi$
$991$			1.25414e6i			1.27702i	−0.769613	+	0.638510i	$0.779551\pi$
$992$	198338.	+	371745.i	0.201550	+	0.377766i
$993$	306120.			0.310451
$994$	−1.40138e6	+	1.24491e6i	−1.41835	+	1.25999i
$995$		0			0
$996$	−89423.5	+	753566.i	−0.0901432	+	0.759631i
$997$	552753.			0.556085			0.278042	−	0.960569i	$-0.410314\pi$
$997$	552753.			0.556085			0.278042	+	0.960569i	$0.410314\pi$
$998$	−749692.	−	843915.i	−0.752699	−	0.847301i
$999$		−	211376.i		−	0.211800i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.5.c.b.151.4	yes	16
4.3	odd	2	inner	300.5.c.b.151.3	✓	16
5.2	odd	4		300.5.f.c.199.9		32
5.3	odd	4		300.5.f.c.199.24		32
5.4	even	2		300.5.c.c.151.13	yes	16
20.3	even	4		300.5.f.c.199.10		32
20.7	even	4		300.5.f.c.199.23		32
20.19	odd	2		300.5.c.c.151.14	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.5.c.b.151.3	✓	16	4.3	odd	2	inner
300.5.c.b.151.4	yes	16	1.1	even	1	trivial
300.5.c.c.151.13	yes	16	5.4	even	2
300.5.c.c.151.14	yes	16	20.19	odd	2
300.5.f.c.199.9		32	5.2	odd	4
300.5.f.c.199.10		32	20.3	even	4
300.5.f.c.199.23		32	20.7	even	4
300.5.f.c.199.24		32	5.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	300.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.99044 + 2.65655i) q^{2} -5.19615i q^{3} +(1.88545 - 15.8885i) q^{4} +(13.8039 + 15.5388i) q^{6} +74.3539i q^{7} +(36.5704 + 52.5224i) q^{8} -27.0000 q^{9} +O(q^{10})\)	\(q+(-2.99044 + 2.65655i) q^{2} -5.19615i q^{3} +(1.88545 - 15.8885i) q^{4} +(13.8039 + 15.5388i) q^{6} +74.3539i q^{7} +(36.5704 + 52.5224i) q^{8} -27.0000 q^{9} +107.360i q^{11} +(-82.5592 - 9.79706i) q^{12} +30.7085 q^{13} +(-197.525 - 222.351i) q^{14} +(-248.890 - 59.9139i) q^{16} +292.805 q^{17} +(80.7418 - 71.7269i) q^{18} -357.767i q^{19} +386.354 q^{21} +(-285.207 - 321.053i) q^{22} -488.885i q^{23} +(272.915 - 190.025i) q^{24} +(-91.8318 + 81.5787i) q^{26} +140.296i q^{27} +(1181.37 + 140.190i) q^{28} -1035.75 q^{29} +411.471i q^{31} +(903.455 - 482.021i) q^{32} +557.858 q^{33} +(-875.616 + 777.852i) q^{34} +(-50.9070 + 428.990i) q^{36} -1506.64 q^{37} +(950.428 + 1069.88i) q^{38} -159.566i q^{39} -2003.19 q^{41} +(-1155.37 + 1026.37i) q^{42} +3279.91i q^{43} +(1705.79 + 202.421i) q^{44} +(1298.75 + 1461.98i) q^{46} +1602.96i q^{47} +(-311.322 + 1293.27i) q^{48} -3127.50 q^{49} -1521.46i q^{51} +(57.8991 - 487.912i) q^{52} +4381.56 q^{53} +(-372.704 - 419.547i) q^{54} +(-3905.25 + 2719.15i) q^{56} -1859.01 q^{57} +(3097.35 - 2751.53i) q^{58} +851.518i q^{59} -5539.08 q^{61} +(-1093.09 - 1230.48i) q^{62} -2007.55i q^{63} +(-1421.21 + 3841.53i) q^{64} +(-1668.24 + 1481.98i) q^{66} +4189.05i q^{67} +(552.068 - 4652.24i) q^{68} -2540.32 q^{69} -6302.56i q^{71} +(-987.401 - 1418.11i) q^{72} -7030.68 q^{73} +(4505.52 - 4002.48i) q^{74} +(-5684.40 - 674.551i) q^{76} -7982.62 q^{77} +(423.895 + 477.172i) q^{78} +7014.54i q^{79} +729.000 q^{81} +(5990.42 - 5321.58i) q^{82} -9127.59i q^{83} +(728.449 - 6138.59i) q^{84} +(-8713.26 - 9808.37i) q^{86} +5381.92i q^{87} +(-5638.80 + 3926.19i) q^{88} +3180.88 q^{89} +2283.29i q^{91} +(-7767.67 - 921.767i) q^{92} +2138.07 q^{93} +(-4258.35 - 4793.55i) q^{94} +(-2504.66 - 4694.49i) q^{96} -12299.4 q^{97} +(9352.59 - 8308.37i) q^{98} -2898.72i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{2} + 8 q^{4} + 18 q^{6} + 180 q^{8} - 432 q^{9}+O(q^{10}) \) 16 * q - 6 * q^2 + 8 * q^4 + 18 * q^6 + 180 * q^8 - 432 * q^9	\( 16 q - 6 q^{2} + 8 q^{4} + 18 q^{6} + 180 q^{8} - 432 q^{9} - 176 q^{13} + 78 q^{14} - 376 q^{16} + 162 q^{18} - 144 q^{21} + 788 q^{22} + 108 q^{24} + 678 q^{26} - 3368 q^{28} + 1728 q^{29} - 2016 q^{32} - 2932 q^{34} - 216 q^{36} + 1568 q^{37} + 6990 q^{38} + 1248 q^{41} - 162 q^{42} + 8088 q^{44} + 5956 q^{46} - 2088 q^{48} - 10720 q^{49} - 3128 q^{52} + 288 q^{53} - 486 q^{54} - 10236 q^{56} - 5616 q^{57} + 16164 q^{58} - 3760 q^{61} + 12714 q^{62} + 10544 q^{64} + 8100 q^{66} - 26136 q^{68} + 9792 q^{69} - 4860 q^{72} - 11040 q^{73} - 17004 q^{74} - 28344 q^{76} - 768 q^{77} + 16830 q^{78} + 11664 q^{81} + 21280 q^{82} + 15120 q^{84} + 24414 q^{86} - 52840 q^{88} - 768 q^{89} - 23736 q^{92} + 9936 q^{93} - 45156 q^{94} - 11088 q^{96} - 7248 q^{97} + 58140 q^{98}+O(q^{100}) \) 16 * q - 6 * q^2 + 8 * q^4 + 18 * q^6 + 180 * q^8 - 432 * q^9 - 176 * q^13 + 78 * q^14 - 376 * q^16 + 162 * q^18 - 144 * q^21 + 788 * q^22 + 108 * q^24 + 678 * q^26 - 3368 * q^28 + 1728 * q^29 - 2016 * q^32 - 2932 * q^34 - 216 * q^36 + 1568 * q^37 + 6990 * q^38 + 1248 * q^41 - 162 * q^42 + 8088 * q^44 + 5956 * q^46 - 2088 * q^48 - 10720 * q^49 - 3128 * q^52 + 288 * q^53 - 486 * q^54 - 10236 * q^56 - 5616 * q^57 + 16164 * q^58 - 3760 * q^61 + 12714 * q^62 + 10544 * q^64 + 8100 * q^66 - 26136 * q^68 + 9792 * q^69 - 4860 * q^72 - 11040 * q^73 - 17004 * q^74 - 28344 * q^76 - 768 * q^77 + 16830 * q^78 + 11664 * q^81 + 21280 * q^82 + 15120 * q^84 + 24414 * q^86 - 52840 * q^88 - 768 * q^89 - 23736 * q^92 + 9936 * q^93 - 45156 * q^94 - 11088 * q^96 - 7248 * q^97 + 58140 * q^98

Introduction

L-functions

Modular forms

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