LMFDB - Embedded newform 300.5.c.b.151.2

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			151.2
Root			$1.95664 - 3.48878i$ of defining polynomial
Character	$\chi$	$=$	300.151
Dual form			300.5.c.b.151.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.99969 + 0.0498899i) q^{2} +5.19615i q^{3} +(15.9950 - 0.399088i) q^{4} +(-0.259236 - 20.7830i) q^{6} +35.2842i q^{7} +(-63.9552 + 2.39422i) q^{8} -27.0000 q^{9} +O(q^{10})$	\(q+(-3.99969 + 0.0498899i) q^{2} +5.19615i q^{3} +(15.9950 - 0.399088i) q^{4} +(-0.259236 - 20.7830i) q^{6} +35.2842i q^{7} +(-63.9552 + 2.39422i) q^{8} -27.0000 q^{9} +3.95158i q^{11} +(2.07372 + 83.1126i) q^{12} -41.0572 q^{13} +(-1.76033 - 141.126i) q^{14} +(255.681 - 12.7668i) q^{16} -186.761 q^{17} +(107.992 - 1.34703i) q^{18} -580.932i q^{19} -183.342 q^{21} +(-0.197144 - 15.8051i) q^{22} +472.336i q^{23} +(-12.4407 - 332.321i) q^{24} +(164.216 - 2.04834i) q^{26} -140.296i q^{27} +(14.0815 + 564.372i) q^{28} -979.409 q^{29} +33.2865i q^{31} +(-1022.01 + 63.8193i) q^{32} -20.5330 q^{33} +(746.987 - 9.31750i) q^{34} +(-431.866 + 10.7754i) q^{36} +623.253 q^{37} +(28.9826 + 2323.55i) q^{38} -213.340i q^{39} +154.478 q^{41} +(733.312 - 9.14693i) q^{42} +2675.32i q^{43} +(1.57703 + 63.2057i) q^{44} +(-23.5648 - 1889.20i) q^{46} -2925.06i q^{47} +(66.3385 + 1328.56i) q^{48} +1156.02 q^{49} -970.440i q^{51} +(-656.711 + 16.3855i) q^{52} -3782.10 q^{53} +(6.99936 + 561.141i) q^{54} +(-84.4782 - 2256.61i) q^{56} +3018.61 q^{57} +(3917.33 - 48.8626i) q^{58} -3487.58i q^{59} -488.539 q^{61} +(-1.66066 - 133.135i) q^{62} -952.674i q^{63} +(4084.54 - 306.245i) q^{64} +(82.1257 - 1.02439i) q^{66} -7491.56i q^{67} +(-2987.25 + 74.5342i) q^{68} -2454.33 q^{69} -4620.06i q^{71} +(1726.79 - 64.6439i) q^{72} +6959.14 q^{73} +(-2492.82 + 31.0940i) q^{74} +(-231.843 - 9292.01i) q^{76} -139.429 q^{77} +(10.6435 + 853.292i) q^{78} -6756.51i q^{79} +729.000 q^{81} +(-617.865 + 7.70690i) q^{82} -4862.15i q^{83} +(-2932.56 + 73.1697i) q^{84} +(-133.471 - 10700.4i) q^{86} -5089.16i q^{87} +(-9.46096 - 252.724i) q^{88} +513.707 q^{89} -1448.67i q^{91} +(188.504 + 7555.03i) q^{92} -172.962 q^{93} +(145.931 + 11699.3i) q^{94} +(-331.615 - 5310.52i) q^{96} -12119.3 q^{97} +(-4623.73 + 57.6739i) q^{98} -106.693i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−3.99969	+	0.0498899i	−0.999922	+	0.0124725i
$2$	−3.99969	+	0.0498899i	−0.999922	+	0.0124725i
$3$			5.19615i			0.577350i
$3$			5.19615i			0.577350i
$4$	15.9950	−	0.399088i	0.999689	−	0.0249430i
$5$		0			0
$5$		0			0
$6$	−0.259236	−	20.7830i	−0.00720099	−	0.577305i
$7$			35.2842i			0.720086i	0.932936	+	0.360043i	$0.117238\pi$
$7$			35.2842i			0.720086i	−0.932936	+	0.360043i	$0.882762\pi$
$8$	−63.9552	+	2.39422i	−0.999300	+	0.0374097i
$9$	−27.0000			−0.333333
$10$		0			0
$11$			3.95158i			0.0326577i	0.999867	+	0.0163289i	$0.00519787\pi$
$11$			3.95158i			0.0326577i	−0.999867	+	0.0163289i	$0.994802\pi$
$12$	2.07372	+	83.1126i	0.0144009	+	0.577171i
$13$	−41.0572			−0.242942			−0.121471	−	0.992595i	$-0.538761\pi$
$13$	−41.0572			−0.242942			−0.121471	+	0.992595i	$0.538761\pi$
$14$	−1.76033	−	141.126i	−0.00898126	−	0.720030i
$15$		0			0
$16$	255.681	−	12.7668i	0.998756	−	0.0498705i
$17$	−186.761			−0.646233			−0.323116	−	0.946359i	$-0.604731\pi$
$17$	−186.761			−0.646233			−0.323116	+	0.946359i	$0.604731\pi$
$18$	107.992	−	1.34703i	0.333307	−	0.00415749i
$19$		−	580.932i		−	1.60923i	−0.593798	−	0.804614i	$-0.702372\pi$
$19$		−	580.932i		−	1.60923i	0.593798	−	0.804614i	$-0.297628\pi$
$20$		0			0
$21$	−183.342			−0.415742
$22$	−0.197144	−	15.8051i	−0.000407323	−	0.0326552i
$23$			472.336i			0.892885i	0.894812	+	0.446443i	$0.147309\pi$
$23$			472.336i			0.892885i	−0.894812	+	0.446443i	$0.852691\pi$
$24$	−12.4407	−	332.321i	−0.0215985	−	0.576946i
$25$		0			0
$26$	164.216	−	2.04834i	0.242923	−	0.00303009i
$27$		−	140.296i		−	0.192450i
$28$	14.0815	+	564.372i	0.0179611	+	0.719862i
$29$	−979.409			−1.16458			−0.582288	−	0.812982i	$-0.697843\pi$
$29$	−979.409			−1.16458			−0.582288	+	0.812982i	$0.697843\pi$
$30$		0			0
$31$			33.2865i			0.0346373i	0.999850	+	0.0173187i	$0.00551298\pi$
$31$			33.2865i			0.0346373i	−0.999850	+	0.0173187i	$0.994487\pi$
$32$	−1022.01	+	63.8193i	−0.998056	+	0.0623236i
$33$	−20.5330			−0.0188549
$34$	746.987	−	9.31750i	0.646183	−	0.00806012i
$35$		0			0
$36$	−431.866	+	10.7754i	−0.333230	+	0.00831434i
$37$	623.253			0.455262			0.227631	−	0.973748i	$-0.426902\pi$
$37$	623.253			0.455262			0.227631	+	0.973748i	$0.426902\pi$
$38$	28.9826	+	2323.55i	0.0200711	+	1.60910i
$39$		−	213.340i		−	0.140263i
$40$		0			0
$41$	154.478			0.0918966			0.0459483	−	0.998944i	$-0.485369\pi$
$41$	154.478			0.0918966			0.0459483	+	0.998944i	$0.485369\pi$
$42$	733.312	−	9.14693i	0.415710	−	0.00518533i
$43$			2675.32i			1.44690i	0.690377	+	0.723450i	$0.257445\pi$
$43$			2675.32i			1.44690i	−0.690377	+	0.723450i	$0.742555\pi$
$44$	1.57703	+	63.2057i	0.000814582	+	0.0326476i
$45$		0			0
$46$	−23.5648	−	1889.20i	−0.0111365	−	0.892816i
$47$		−	2925.06i		−	1.32416i	−0.749434	−	0.662079i	$-0.769674\pi$
$47$		−	2925.06i		−	1.32416i	0.749434	−	0.662079i	$-0.230326\pi$
$48$	66.3385	+	1328.56i	0.0287927	+	0.576632i
$49$	1156.02			0.481476
$50$		0			0
$51$		−	970.440i		−	0.373103i
$52$	−656.711	+	16.3855i	−0.242867	+	0.00605971i
$53$	−3782.10			−1.34642			−0.673212	−	0.739450i	$-0.735086\pi$
$53$	−3782.10			−1.34642			−0.673212	+	0.739450i	$0.735086\pi$
$54$	6.99936	+	561.141i	0.00240033	+	0.192435i
$55$		0			0
$56$	−84.4782	−	2256.61i	−0.0269382	−	0.719582i
$57$	3018.61			0.929089
$58$	3917.33	−	48.8626i	1.16449	−	0.0145252i
$59$		−	3487.58i		−	1.00189i	−0.865479	−	0.500945i	$-0.832986\pi$
$59$		−	3487.58i		−	1.00189i	0.865479	−	0.500945i	$-0.167014\pi$
$60$		0			0
$61$	−488.539			−0.131292			−0.0656462	−	0.997843i	$-0.520911\pi$
$61$	−488.539			−0.131292			−0.0656462	+	0.997843i	$0.520911\pi$
$62$	−1.66066	−	133.135i	−0.000432013	−	0.0346346i
$63$		−	952.674i		−	0.240029i
$64$	4084.54	−	306.245i	0.997201	−	0.0747670i
$65$		0			0
$66$	82.1257	−	1.02439i	0.0188535	−	0.000235168i
$67$		−	7491.56i		−	1.66887i	−0.551107	−	0.834435i	$-0.685794\pi$
$67$		−	7491.56i		−	1.66887i	0.551107	−	0.834435i	$-0.314206\pi$
$68$	−2987.25	+	74.5342i	−0.646032	+	0.0161190i
$69$	−2454.33			−0.515507
$70$		0			0
$71$		−	4620.06i		−	0.916496i	−0.888824	−	0.458248i	$-0.848477\pi$
$71$		−	4620.06i		−	0.916496i	0.888824	−	0.458248i	$-0.151523\pi$
$72$	1726.79	−	64.6439i	0.333100	−	0.0124699i
$73$	6959.14			1.30590			0.652950	−	0.757401i	$-0.273531\pi$
$73$	6959.14			1.30590			0.652950	+	0.757401i	$0.273531\pi$
$74$	−2492.82	+	31.0940i	−0.455226	+	0.00567824i
$75$		0			0
$76$	−231.843	−	9292.01i	−0.0401390	−	1.60873i
$77$	−139.429			−0.0235164
$78$	10.6435	+	853.292i	0.00174942	+	0.140252i
$79$		−	6756.51i		−	1.08260i	−0.840829	−	0.541300i	$-0.817932\pi$
$79$		−	6756.51i		−	1.08260i	0.840829	−	0.541300i	$-0.182068\pi$
$80$		0			0
$81$	729.000			0.111111
$82$	−617.865	+	7.70690i	−0.0918895	+	0.00114618i
$83$		−	4862.15i		−	0.705785i	−0.935664	−	0.352893i	$-0.885198\pi$
$83$		−	4862.15i		−	0.705785i	0.935664	−	0.352893i	$-0.114802\pi$
$84$	−2932.56	+	73.1697i	−0.415613	+	0.0103699i
$85$		0			0
$86$	−133.471	−	10700.4i	−0.0180464	−	1.44679i
$87$		−	5089.16i		−	0.672369i
$88$	−9.46096	−	252.724i	−0.00122171	−	0.0326349i
$89$	513.707			0.0648538			0.0324269	−	0.999474i	$-0.489676\pi$
$89$	513.707			0.0648538			0.0324269	+	0.999474i	$0.489676\pi$
$90$		0			0
$91$		−	1448.67i		−	0.174939i
$92$	188.504	+	7555.03i	0.0222712	+	0.892607i
$93$	−172.962			−0.0199979
$94$	145.931	+	11699.3i	0.0165155	+	1.32405i
$95$		0			0
$96$	−331.615	−	5310.52i	−0.0359825	−	0.576228i
$97$	−12119.3			−1.28805			−0.644026	−	0.765004i	$-0.722737\pi$
$97$	−12119.3			−1.28805			−0.644026	+	0.765004i	$0.722737\pi$
$98$	−4623.73	+	57.6739i	−0.481438	+	0.00600519i
$99$		−	106.693i		−	0.0108859i
$100$		0			0
$101$	−7191.20			−0.704951			−0.352475	−	0.935821i	$-0.614660\pi$
$101$	−7191.20			−0.704951			−0.352475	+	0.935821i	$0.614660\pi$
$102$	48.4152	+	3881.46i	0.00465351	+	0.373074i
$103$		−	10189.6i		−	0.960470i	−0.877140	−	0.480235i	$-0.840551\pi$
$103$		−	10189.6i		−	0.960470i	0.877140	−	0.480235i	$-0.159449\pi$
$104$	2625.82	−	98.3000i	0.242772	−	0.00908839i
$105$		0			0
$106$	15127.2	−	188.689i	1.34632	−	0.0167932i
$107$		−	21648.8i		−	1.89089i	−0.325777	−	0.945446i	$-0.605626\pi$
$107$		−	21648.8i		−	1.89089i	0.325777	−	0.945446i	$-0.394374\pi$
$108$	−55.9905	−	2244.04i	−0.00480028	−	0.192390i
$109$	10655.6			0.896859			0.448430	−	0.893818i	$-0.351983\pi$
$109$	10655.6			0.896859			0.448430	+	0.893818i	$0.351983\pi$
$110$		0			0
$111$			3238.52i			0.262845i
$112$	450.468	+	9021.52i	0.0359111	+	0.719190i
$113$	−9876.07			−0.773441			−0.386721	−	0.922197i	$-0.626392\pi$
$113$	−9876.07			−0.773441			−0.386721	+	0.922197i	$0.626392\pi$
$114$	−12073.5	+	150.598i	−0.929017	+	0.0115880i
$115$		0			0
$116$	−15665.7	+	390.871i	−1.16421	+	0.0290480i
$117$	1108.55			0.0809807
$118$	173.995	+	13949.2i	0.0124961	+	1.00181i
$119$		−	6589.73i		−	0.465343i
$120$		0			0
$121$	14625.4			0.998933
$122$	1954.00	−	24.3732i	0.131282	−	0.00163754i
$123$			802.692i			0.0530565i
$124$	13.2842	+	532.418i	0.000863959	+	0.0346265i
$125$		0			0
$126$	47.5288	+	3810.40i	0.00299375	+	0.240010i
$127$		−	19972.7i		−	1.23831i	−0.785269	−	0.619155i	$-0.787475\pi$
$127$		−	19972.7i		−	1.23831i	0.785269	−	0.619155i	$-0.212525\pi$
$128$	−16321.6	+	1428.66i	−0.996191	+	0.0871987i
$129$	−13901.4			−0.835368
$130$		0			0
$131$			30733.6i			1.79090i	0.445164	+	0.895449i	$0.353145\pi$
$131$			30733.6i			1.79090i	−0.445164	+	0.895449i	$0.646855\pi$
$132$	−328.426	+	8.19449i	−0.0188491	+	0.000470299i
$133$	20497.7			1.15878
$134$	373.753	+	29963.9i	0.0208149	+	1.66874i
$135$		0			0
$136$	11944.4	−	447.147i	0.645780	−	0.0241754i
$137$	7177.05			0.382388			0.191194	−	0.981552i	$-0.438764\pi$
$137$	7177.05			0.382388			0.191194	+	0.981552i	$0.438764\pi$
$138$	9816.56	−	122.446i	0.515467	−	0.00642965i
$139$		−	4628.80i		−	0.239574i	−0.992800	−	0.119787i	$-0.961779\pi$
$139$		−	4628.80i		−	0.239574i	0.992800	−	0.119787i	$-0.0382211\pi$
$140$		0			0
$141$	15199.1			0.764503
$142$	230.494	+	18478.8i	0.0114310	+	0.916425i
$143$		−	162.241i		−	0.00793394i
$144$	−6903.40	+	344.705i	−0.332919	+	0.0166235i
$145$		0			0
$146$	−27834.4	+	347.191i	−1.30580	+	0.0162878i
$147$			6006.87i			0.277980i
$148$	9968.95	−	248.733i	0.455120	−	0.0113556i
$149$	35128.8			1.58231			0.791154	−	0.611617i	$-0.209481\pi$
$149$	35128.8			1.58231			0.791154	+	0.611617i	$0.209481\pi$
$150$		0			0
$151$			41309.8i			1.81176i	0.423539	+	0.905878i	$0.360788\pi$
$151$			41309.8i			1.81176i	−0.423539	+	0.905878i	$0.639212\pi$
$152$	1390.88	+	37153.6i	0.0602007	+	1.60810i
$153$	5042.55			0.215411
$154$	557.671	−	6.95608i	0.0235146	−	0.000293307i
$155$		0			0
$156$	−85.1413	−	3412.37i	−0.00349857	−	0.140219i
$157$	−3581.96			−0.145319			−0.0726594	−	0.997357i	$-0.523149\pi$
$157$	−3581.96			−0.145319			−0.0726594	+	0.997357i	$0.523149\pi$
$158$	337.082	+	27023.9i	0.0135027	+	1.08252i
$159$		−	19652.4i		−	0.777358i
$160$		0			0
$161$	−16666.0			−0.642954
$162$	−2915.77	+	36.3697i	−0.111102	+	0.00138583i
$163$		−	14969.6i		−	0.563422i	−0.959499	−	0.281711i	$-0.909098\pi$
$163$		−	14969.6i		−	0.563422i	0.959499	−	0.281711i	$-0.0909020\pi$
$164$	2470.88	−	61.6504i	0.0918680	−	0.00229218i
$165$		0			0
$166$	242.572	+	19447.1i	0.00880289	+	0.705730i
$167$			12510.0i			0.448564i	0.974524	+	0.224282i	$0.0720037\pi$
$167$			12510.0i			0.448564i	−0.974524	+	0.224282i	$0.927996\pi$
$168$	11725.7	−	438.961i	0.415451	−	0.0155528i
$169$	−26875.3			−0.940979
$170$		0			0
$171$			15685.2i			0.536410i
$172$	1067.69	+	42791.8i	0.0360901	+	1.44645i
$173$	−51365.9			−1.71626			−0.858129	−	0.513434i	$-0.828373\pi$
$173$	−51365.9			−1.71626			−0.858129	+	0.513434i	$0.828373\pi$
$174$	253.898	+	20355.0i	0.00838610	+	0.672316i
$175$		0			0
$176$	50.4493	+	1010.35i	0.00162866	+	0.0326171i
$177$	18122.0			0.578442
$178$	−2054.67	+	25.6288i	−0.0648487	+	0.000808887i
$179$		−	29989.3i		−	0.935967i	−0.883737	−	0.467984i	$-0.844981\pi$
$179$		−	29989.3i		−	0.935967i	0.883737	−	0.467984i	$-0.155019\pi$
$180$		0			0
$181$	−47416.2			−1.44734			−0.723668	−	0.690149i	$-0.757545\pi$
$181$	−47416.2			−1.44734			−0.723668	+	0.690149i	$0.757545\pi$
$182$	72.2741	+	5794.24i	0.00218193	+	0.174926i
$183$		−	2538.52i		−	0.0758017i
$184$	−1130.88	−	30208.4i	−0.0334025	−	0.892260i
$185$		0			0
$186$	691.792	−	8.62903i	0.0199963	−	0.000249423i
$187$		−	738.003i		−	0.0211045i
$188$	−1167.36	−	46786.5i	−0.0330285	−	1.32375i
$189$	4950.24			0.138581
$190$		0			0
$191$			41028.6i			1.12466i	0.826914	+	0.562329i	$0.190095\pi$
$191$			41028.6i			1.12466i	−0.826914	+	0.562329i	$0.809905\pi$
$192$	1591.30	+	21223.9i	0.0431667	+	0.575734i
$193$	44180.6			1.18609			0.593044	−	0.805170i	$-0.297926\pi$
$193$	44180.6			1.18609			0.593044	+	0.805170i	$0.297926\pi$
$194$	48473.3	−	604.629i	1.28795	−	0.0160652i
$195$		0			0
$196$	18490.6	−	461.355i	0.481326	−	0.0120094i
$197$	−8724.29			−0.224801			−0.112400	−	0.993663i	$-0.535854\pi$
$197$	−8724.29			−0.224801			−0.112400	+	0.993663i	$0.535854\pi$
$198$	5.32289	+	426.738i	0.000135774	+	0.0108851i
$199$		−	6720.98i		−	0.169717i	−0.996393	−	0.0848587i	$-0.972956\pi$
$199$		−	6720.98i		−	0.169717i	0.996393	−	0.0848587i	$-0.0270439\pi$
$200$		0			0
$201$	38927.3			0.963522
$202$	28762.6	−	358.768i	0.704896	−	0.00879248i
$203$		−	34557.7i		−	0.838596i
$204$	−387.291	−	15522.2i	−0.00930630	−	0.372987i
$205$		0			0
$206$	508.359	+	40755.3i	0.0119794	+	0.960395i
$207$		−	12753.1i		−	0.297628i
$208$	−10497.6	+	524.171i	−0.242640	+	0.0121156i
$209$	2295.60			0.0525537
$210$		0			0
$211$			8501.81i			0.190962i	0.995431	+	0.0954808i	$0.0304389\pi$
$211$			8501.81i			0.190962i	−0.995431	+	0.0954808i	$0.969561\pi$
$212$	−60494.8	+	1509.39i	−1.34600	+	0.0335839i
$213$	24006.5			0.529139
$214$	1080.06	+	86588.6i	0.0235841	+	1.89075i
$215$		0			0
$216$	335.900	+	8972.67i	0.00719949	+	0.192315i
$217$	−1174.49			−0.0249419
$218$	−42619.0	+	531.606i	−0.896790	+	0.0111861i
$219$			36160.7i			0.753961i
$220$		0			0
$221$	7667.90			0.156997
$222$	−161.569	−	12953.1i	−0.00327833	−	0.262825i
$223$		−	28886.8i		−	0.580883i	−0.956893	−	0.290442i	$-0.906198\pi$
$223$		−	28886.8i		−	0.580883i	0.956893	−	0.290442i	$-0.0938022\pi$
$224$	−2251.82	−	36060.8i	−0.0448784	−	0.718687i
$225$		0			0
$226$	39501.2	−	492.716i	0.773381	−	0.00964672i
$227$		−	17662.3i		−	0.342764i	−0.985205	−	0.171382i	$-0.945177\pi$
$227$		−	17662.3i		−	0.342764i	0.985205	−	0.171382i	$-0.0548233\pi$
$228$	48282.7	−	1204.69i	0.928800	−	0.0231743i
$229$	−99665.8			−1.90053			−0.950266	−	0.311439i	$-0.899189\pi$
$229$	−99665.8			−1.90053			−0.950266	+	0.311439i	$0.899189\pi$
$230$		0			0
$231$		−	724.492i		−	0.0135772i
$232$	62638.3	−	2344.92i	1.16376	−	0.0435664i
$233$	−72559.0			−1.33653			−0.668266	−	0.743922i	$-0.732963\pi$
$233$	−72559.0			−1.33653			−0.668266	+	0.743922i	$0.732963\pi$
$234$	−4433.84	+	55.3052i	−0.0809744	+	0.00101003i
$235$		0			0
$236$	−1391.85	−	55783.9i	−0.0249902	−	1.00158i
$237$	35107.9			0.625040
$238$	328.761	+	26356.9i	0.00580399	+	0.465307i
$239$			70208.6i			1.22912i	0.788870	+	0.614560i	$0.210666\pi$
$239$			70208.6i			1.22912i	−0.788870	+	0.614560i	$0.789334\pi$
$240$		0			0
$241$	−51440.5			−0.885668			−0.442834	−	0.896604i	$-0.646027\pi$
$241$	−51440.5			−0.885668			−0.442834	+	0.896604i	$0.646027\pi$
$242$	−58497.0	+	729.659i	−0.998856	+	0.0124592i
$243$			3788.00i			0.0641500i
$244$	−7814.19	+	194.970i	−0.131252	+	0.00327483i
$245$		0			0
$246$	−40.0462	−	3210.52i	−0.000661746	−	0.0530524i
$247$			23851.4i			0.390950i
$248$	−79.6951	−	2128.84i	−0.00129577	−	0.0346131i
$249$	25264.5			0.407485
$250$		0			0
$251$		−	72429.1i		−	1.14965i	−0.818276	−	0.574825i	$-0.805070\pi$
$251$		−	72429.1i		−	1.14965i	0.818276	−	0.574825i	$-0.194930\pi$
$252$	−380.201	−	15238.0i	−0.00598704	−	0.239954i
$253$	−1866.48			−0.0291596
$254$	996.436	+	79884.6i	0.0154448	+	1.23821i
$255$		0			0
$256$	65210.0	−	6528.49i	0.995026	−	0.0996169i
$257$	−77711.9			−1.17658			−0.588290	−	0.808650i	$-0.700199\pi$
$257$	−77711.9			−1.17658			−0.588290	+	0.808650i	$0.700199\pi$
$258$	55601.1	−	693.538i	0.835303	−	0.0104191i
$259$			21991.0i			0.327828i
$260$		0			0
$261$	26444.0			0.388192
$262$	−1533.30	−	122925.i	−0.0223369	−	1.79076i
$263$		−	2716.70i		−	0.0392763i	−0.999807	−	0.0196382i	$-0.993749\pi$
$263$		−	2716.70i		−	0.0392763i	0.999807	−	0.0196382i	$-0.00625142\pi$
$264$	1313.19	−	49.1606i	0.0188417	−	0.000705357i
$265$		0			0
$266$	−81984.5	+	1022.63i	−1.15869	+	0.0144529i
$267$			2669.30i			0.0374434i
$268$	−2989.79	−	119828.i	−0.0416266	−	1.66835i
$269$	66666.6			0.921306			0.460653	−	0.887580i	$-0.347615\pi$
$269$	66666.6			0.921306			0.460653	+	0.887580i	$0.347615\pi$
$270$		0			0
$271$		−	63959.9i		−	0.870902i	−0.900212	−	0.435451i	$-0.856589\pi$
$271$		−	63959.9i		−	0.870902i	0.900212	−	0.435451i	$-0.143411\pi$
$272$	−47751.4	+	2384.35i	−0.645429	+	0.0322280i
$273$	7527.53			0.101001
$274$	−28706.0	+	358.062i	−0.382359	+	0.00476933i
$275$		0			0
$276$	−39257.1	+	979.494i	−0.515347	+	0.0128583i
$277$	36446.7			0.475005			0.237502	−	0.971387i	$-0.423671\pi$
$277$	36446.7			0.475005			0.237502	+	0.971387i	$0.423671\pi$
$278$	230.930	+	18513.8i	0.00298808	+	0.239555i
$279$		−	898.734i		−	0.0115458i
$280$		0			0
$281$	83688.9			1.05988			0.529938	−	0.848036i	$-0.322215\pi$
$281$	83688.9			1.05988			0.529938	+	0.848036i	$0.322215\pi$
$282$	−60791.6	+	758.281i	−0.764443	+	0.00953524i
$283$			99210.9i			1.23876i	0.785092	+	0.619379i	$0.212616\pi$
$283$			99210.9i			1.23876i	−0.785092	+	0.619379i	$0.787384\pi$
$284$	−1843.81	−	73897.9i	−0.0228602	−	0.916211i
$285$		0			0
$286$	8.09419	+	648.914i	9.89558e−5	+	0.00793332i
$287$			5450.65i			0.0661735i
$288$	27594.3	−	1723.12i	0.332685	−	0.0207745i
$289$	−48641.2			−0.582383
$290$		0			0
$291$		−	62973.6i		−	0.743657i
$292$	111312.	−	2777.31i	1.30549	−	0.0325731i
$293$	−5554.90			−0.0647054			−0.0323527	−	0.999477i	$-0.510300\pi$
$293$	−5554.90			−0.0647054			−0.0323527	+	0.999477i	$0.510300\pi$
$294$	−299.682	−	24025.6i	−0.00346710	−	0.277958i
$295$		0			0
$296$	−39860.3	+	1492.20i	−0.454943	+	0.0170312i
$297$	554.392			0.00628498
$298$	−140504.	+	1752.57i	−1.58219	+	0.0197353i
$299$		−	19392.8i		−	0.216919i
$300$		0			0
$301$	−94396.6			−1.04189
$302$	−2060.94	−	165226.i	−0.0225971	−	1.81161i
$303$		−	37366.6i		−	0.407004i
$304$	−7416.67	−	148533.i	−0.0802531	−	1.60723i
$305$		0			0
$306$	−20168.6	+	251.573i	−0.215394	+	0.00268671i
$307$			25814.0i			0.273891i	0.990579	+	0.136946i	$0.0437286\pi$
$307$			25814.0i			0.273891i	−0.990579	+	0.136946i	$0.956271\pi$
$308$	−2230.16	+	55.6443i	−0.0235091	+	0.000586569i
$309$	52946.8			0.554527
$310$		0			0
$311$		−	106750.i		−	1.10369i	−0.833947	−	0.551844i	$-0.813924\pi$
$311$		−	106750.i		−	1.10369i	0.833947	−	0.551844i	$-0.186076\pi$
$312$	510.782	+	13644.2i	0.00524718	+	0.140165i
$313$	76334.9			0.779174			0.389587	−	0.920990i	$-0.372618\pi$
$313$	76334.9			0.779174			0.389587	+	0.920990i	$0.372618\pi$
$314$	14326.7	−	178.704i	0.145307	−	0.00181248i
$315$		0			0
$316$	−2696.44	−	108071.i	−0.0270033	−	1.08226i
$317$	108286.			1.07759			0.538794	−	0.842437i	$-0.318880\pi$
$317$	108286.			1.07759			0.538794	+	0.842437i	$0.318880\pi$
$318$	980.456	+	78603.4i	0.00969558	+	0.777298i
$319$		−	3870.22i		−	0.0380324i
$320$		0			0
$321$	112491.			1.09171
$322$	66658.9	−	831.466i	0.642904	−	0.00801923i
$323$			108496.i			1.03994i
$324$	11660.4	−	290.935i	0.111077	−	0.00277145i
$325$		0			0
$326$	746.830	+	59873.6i	0.00702727	+	0.563378i
$327$			55368.1i			0.517802i
$328$	−9879.69	+	369.855i	−0.0918323	+	0.00343782i
$329$	103209.			0.953508
$330$		0			0
$331$		−	109078.i		−	0.995590i	−0.867295	−	0.497795i	$-0.834143\pi$
$331$		−	109078.i		−	0.995590i	0.867295	−	0.497795i	$-0.165857\pi$
$332$	−1940.43	−	77770.3i	−0.0176044	−	0.705565i
$333$	−16827.8			−0.151754
$334$	−624.123	−	50036.1i	−0.00559471	−	0.448529i
$335$		0			0
$336$	−46877.2	+	2340.70i	−0.415225	+	0.0207333i
$337$	−152574.			−1.34345			−0.671725	−	0.740801i	$-0.734446\pi$
$337$	−152574.			−1.34345			−0.671725	+	0.740801i	$0.734446\pi$
$338$	107493.	−	1340.81i	0.940906	−	0.0117363i
$339$		−	51317.6i		−	0.446546i
$340$		0			0
$341$	−131.534			−0.00113118
$342$	−782.531	−	62735.7i	−0.00669036	−	0.536368i
$343$			125507.i			1.06679i
$344$	−6405.30	−	171101.i	−0.0541281	−	1.44589i
$345$		0			0
$346$	205448.	−	2562.64i	1.71612	−	0.0214060i
$347$			168701.i			1.40107i	0.713618	+	0.700535i	$0.247055\pi$
$347$			168701.i			1.40107i	−0.713618	+	0.700535i	$0.752945\pi$
$348$	−2031.02	−	81401.2i	−0.0167709	−	0.672159i
$349$	−19680.8			−0.161582			−0.0807910	−	0.996731i	$-0.525745\pi$
$349$	−19680.8			−0.161582			−0.0807910	+	0.996731i	$0.525745\pi$
$350$		0			0
$351$			5760.17i			0.0467542i
$352$	−252.187	−	4038.56i	−0.00203535	−	0.0325942i
$353$	−55058.2			−0.441848			−0.220924	−	0.975291i	$-0.570907\pi$
$353$	−55058.2			−0.441848			−0.220924	+	0.975291i	$0.570907\pi$
$354$	−72482.4	+	904.105i	−0.578397	+	0.00721460i
$355$		0			0
$356$	8216.75	−	205.014i	0.0648336	−	0.00161765i
$357$	34241.2			0.268666
$358$	1496.16	+	119948.i	0.0116738	+	0.935894i
$359$			73206.8i			0.568019i	0.958822	+	0.284009i	$0.0916647\pi$
$359$			73206.8i			0.568019i	−0.958822	+	0.284009i	$0.908335\pi$
$360$		0			0
$361$	−207161.			−1.58962
$362$	189650.	−	2365.59i	1.44722	−	0.0180519i
$363$			75995.7i			0.576735i
$364$	−578.148	−	23171.6i	−0.00436351	−	0.174885i
$365$		0			0
$366$	126.647	+	10153.3i	0.000945435	+	0.0757958i
$367$			156333.i			1.16069i	0.814370	+	0.580346i	$0.197083\pi$
$367$			156333.i			1.16069i	−0.814370	+	0.580346i	$0.802917\pi$
$368$	6030.24	+	120768.i	0.0445286	+	0.891774i
$369$	−4170.91			−0.0306322
$370$		0			0
$371$		−	133449.i		−	0.969542i
$372$	−2766.52	+	69.0269i	−0.0199916	+	0.000498807i
$373$	233763.			1.68019			0.840096	−	0.542438i	$-0.182499\pi$
$373$	233763.			1.68019			0.840096	+	0.542438i	$0.182499\pi$
$374$	36.8189	+	2951.78i	0.000263225	+	0.0211028i
$375$		0			0
$376$	7003.24	+	187073.i	0.0495363	+	1.32323i
$377$	40211.8			0.282925
$378$	−19799.4	+	246.967i	−0.138570	+	0.00172844i
$379$			25001.6i			0.174056i	0.996206	+	0.0870282i	$0.0277370\pi$
$379$			25001.6i			0.174056i	−0.996206	+	0.0870282i	$0.972263\pi$
$380$		0			0
$381$	103781.			0.714938
$382$	−2046.92	−	164102.i	−0.0140273	−	1.12457i
$383$			165132.i			1.12573i	0.826549	+	0.562864i	$0.190301\pi$
$383$			165132.i			1.12573i	−0.826549	+	0.562864i	$0.809699\pi$
$384$	−7423.55	−	84809.5i	−0.0503442	−	0.575151i
$385$		0			0
$386$	−176709.	+	2204.17i	−1.18600	+	0.0147935i
$387$		−	72233.6i		−	0.482300i
$388$	−193848.	+	4836.66i	−1.28765	+	0.0321279i
$389$	46311.3			0.306047			0.153023	−	0.988223i	$-0.451099\pi$
$389$	46311.3			0.306047			0.153023	+	0.988223i	$0.451099\pi$
$390$		0			0
$391$		−	88214.1i		−	0.577012i
$392$	−73933.7	+	2767.77i	−0.481138	+	0.0180118i
$393$	−159696.			−1.03398
$394$	34894.4	−	435.254i	0.224783	−	0.00280382i
$395$		0			0
$396$	−42.5798	−	1706.55i	−0.000271527	−	0.0108825i
$397$	−244029.			−1.54832			−0.774161	−	0.632989i	$-0.781828\pi$
$397$	−244029.			−1.54832			−0.774161	+	0.632989i	$0.781828\pi$
$398$	335.309	+	26881.8i	0.00211680	+	0.169704i
$399$			106509.i			0.669024i
$400$		0			0
$401$	102342.			0.636451			0.318225	−	0.948015i	$-0.396913\pi$
$401$	102342.			0.636451			0.318225	+	0.948015i	$0.396913\pi$
$402$	−155697.	+	1942.08i	−0.963447	+	0.0120175i
$403$		−	1366.65i		−	0.00841487i
$404$	−115023.	+	2869.92i	−0.704732	+	0.0175836i
$405$		0			0
$406$	1724.08	+	138220.i	0.0104594	+	0.838531i
$407$			2462.84i			0.0148678i
$408$	2323.45	+	62064.7i	0.0139576	+	0.372842i
$409$	−110640.			−0.661405			−0.330702	−	0.943735i	$-0.607286\pi$
$409$	−110640.			−0.661405			−0.330702	+	0.943735i	$0.607286\pi$
$410$		0			0
$411$			37293.0i			0.220772i
$412$	−4066.56	−	162983.i	−0.0239570	−	0.960171i
$413$	123057.			0.721448
$414$	636.250	+	51008.3i	0.00371216	+	0.297605i
$415$		0			0
$416$	41960.9	−	2620.25i	0.242470	−	0.0151410i
$417$	24052.0			0.138318
$418$	−9181.69	+	114.527i	−0.0525497	+	0.000655475i
$419$		−	2345.08i		−	0.0133576i	−0.999978	−	0.00667882i	$-0.997874\pi$
$419$		−	2345.08i		−	0.0133576i	0.999978	−	0.00667882i	$-0.00212595\pi$
$420$		0			0
$421$	−158819.			−0.896062			−0.448031	−	0.894018i	$-0.647875\pi$
$421$	−158819.			−0.896062			−0.448031	+	0.894018i	$0.647875\pi$
$422$	−424.154	−	34004.6i	−0.00238176	−	0.190947i
$423$			78976.7i			0.441386i
$424$	241885.	−	9055.18i	1.34548	−	0.0503693i
$425$		0			0
$426$	−96018.6	+	1197.68i	−0.529098	+	0.00659968i
$427$		−	17237.7i		−	0.0945419i
$428$	−8639.79	−	346274.i	−0.0471646	−	1.89030i
$429$	843.029			0.00458066
$430$		0			0
$431$			269669.i			1.45170i	0.687853	+	0.725850i	$0.258553\pi$
$431$			269669.i			1.45170i	−0.687853	+	0.725850i	$0.741447\pi$
$432$	−1791.14	−	35871.1i	−0.00959758	−	0.192211i
$433$	−161609.			−0.861967			−0.430983	−	0.902360i	$-0.641833\pi$
$433$	−161609.			−0.861967			−0.430983	+	0.902360i	$0.641833\pi$
$434$	4697.58	−	58.5951i	0.0249399	−	0.000311087i
$435$		0			0
$436$	170436.	−	4252.52i	0.896580	−	0.0223704i
$437$	274395.			1.43686
$438$	−1804.06	−	144632.i	−0.00940376	−	0.753903i
$439$			171500.i			0.889885i	0.895559	+	0.444943i	$0.146776\pi$
$439$			171500.i			0.889885i	−0.895559	+	0.444943i	$0.853224\pi$
$440$		0			0
$441$	−31212.6			−0.160492
$442$	−30669.2	+	382.551i	−0.156985	+	0.00195814i
$443$		−	78491.9i		−	0.399961i	−0.979800	−	0.199980i	$-0.935912\pi$
$443$		−	78491.9i		−	0.399961i	0.979800	−	0.199980i	$-0.0640878\pi$
$444$	1292.45	+	51800.2i	0.00655616	+	0.262764i
$445$		0			0
$446$	1441.16	+	115538.i	0.00724505	+	0.580838i
$447$			182535.i			0.913546i
$448$	10805.6	+	144120.i	0.0538387	+	0.718071i
$449$	−256874.			−1.27417			−0.637085	−	0.770794i	$-0.719860\pi$
$449$	−256874.			−1.27417			−0.637085	+	0.770794i	$0.719860\pi$
$450$		0			0
$451$			610.434i			0.00300113i
$452$	−157968.	+	3941.42i	−0.773200	+	0.0192919i
$453$	−214652.			−1.04602
$454$	881.170	+	70643.7i	0.00427512	+	0.342738i
$455$		0			0
$456$	−193056.	+	7227.21i	−0.928438	+	0.0347569i
$457$	−182963.			−0.876053			−0.438027	−	0.898962i	$-0.644322\pi$
$457$	−182963.			−0.876053			−0.438027	+	0.898962i	$0.644322\pi$
$458$	398632.	−	4972.32i	1.90038	−	0.0237043i
$459$			26201.9i			0.124368i
$460$		0			0
$461$	328023.			1.54348			0.771742	−	0.635936i	$-0.219386\pi$
$461$	328023.			1.54348			0.771742	+	0.635936i	$0.219386\pi$
$462$	36.1449	+	2897.74i	0.000169341	+	0.0135761i
$463$		−	288300.i		−	1.34488i	−0.740153	−	0.672439i	$-0.765247\pi$
$463$		−	288300.i		−	1.34488i	0.740153	−	0.672439i	$-0.234753\pi$
$464$	−250417.	+	12504.0i	−1.16313	+	0.0580780i
$465$		0			0
$466$	290213.	−	3619.96i	1.33643	−	0.0166699i
$467$			187893.i			0.861542i	0.902461	+	0.430771i	$0.141758\pi$
$467$			187893.i			0.861542i	−0.902461	+	0.430771i	$0.858242\pi$
$468$	17731.2	−	442.407i	0.0809555	−	0.00201990i
$469$	264334.			1.20173
$470$		0			0
$471$		−	18612.4i		−	0.0838998i
$472$	8350.03	+	223049.i	0.0374804	+	1.00119i
$473$	−10571.7			−0.0472525
$474$	−140420.	+	1751.53i	−0.624991	+	0.00779579i
$475$		0			0
$476$	−2629.88	−	105403.i	−0.0116071	−	0.465199i
$477$	102117.			0.448808
$478$	−3502.70	−	280812.i	−0.0153302	−	1.22902i
$479$			42484.8i			0.185167i	0.995705	+	0.0925833i	$0.0295125\pi$
$479$			42484.8i			0.185167i	−0.995705	+	0.0925833i	$0.970488\pi$
$480$		0			0
$481$	−25589.1			−0.110602
$482$	205746.	−	2566.36i	0.885599	−	0.0110465i
$483$		−	86599.2i		−	0.371210i
$484$	233933.	−	5836.82i	0.998623	−	0.0249164i
$485$		0			0
$486$	−188.983	−	15150.8i	−0.000800110	−	0.0641450i
$487$			115941.i			0.488854i	0.969668	+	0.244427i	$0.0785998\pi$
$487$			115941.i			0.488854i	−0.969668	+	0.244427i	$0.921400\pi$
$488$	31244.6	−	1169.67i	0.131200	−	0.00491160i
$489$	77784.1			0.325292
$490$		0			0
$491$		−	254668.i		−	1.05636i	−0.849133	−	0.528179i	$-0.822875\pi$
$491$		−	254668.i		−	1.05636i	0.849133	−	0.528179i	$-0.177125\pi$
$492$	320.345	+	12839.1i	0.00132339	+	0.0530400i
$493$	182916.			0.752588
$494$	−1189.95	−	95398.3i	−0.00487611	−	0.390919i
$495$		0			0
$496$	424.963	+	8510.73i	0.00172738	+	0.0345942i
$497$	163015.			0.659956
$498$	−101050.	+	1260.44i	−0.407454	+	0.00508235i
$499$			139763.i			0.561296i	0.959811	+	0.280648i	$0.0905494\pi$
$499$			139763.i			0.561296i	−0.959811	+	0.280648i	$0.909451\pi$
$500$		0			0
$501$	−65003.9			−0.258979
$502$	3613.48	+	289694.i	0.0143390	+	1.14956i
$503$		−	416958.i		−	1.64800i	−0.566592	−	0.823998i	$-0.691739\pi$
$503$		−	416958.i		−	1.64800i	0.566592	−	0.823998i	$-0.308261\pi$
$504$	2280.91	+	60928.5i	0.00897940	+	0.239861i
$505$		0			0
$506$	7465.32	−	93.1183i	0.0291573	−	0.000363692i
$507$		−	139648.i		−	0.543275i
$508$	−7970.87	−	319464.i	−0.0308872	−	1.23792i
$509$	−414530.			−1.60000			−0.800000	−	0.600000i	$-0.795167\pi$
$509$	−414530.			−1.60000			−0.800000	+	0.600000i	$0.795167\pi$
$510$		0			0
$511$			245548.i			0.940360i
$512$	−260494.	+	29365.3i	−0.993706	+	0.112020i
$513$	−81502.5			−0.309696
$514$	310823.	−	3877.04i	1.17649	−	0.0146749i
$515$		0			0
$516$	−222353.	+	5547.87i	−0.835108	+	0.0208366i
$517$	11558.6			0.0432440
$518$	−1097.13	−	87957.2i	−0.00408882	−	0.327802i
$519$		−	266905.i		−	0.990882i
$520$		0			0
$521$	7651.52			0.0281885			0.0140943	−	0.999901i	$-0.495514\pi$
$521$	7651.52			0.0281885			0.0140943	+	0.999901i	$0.495514\pi$
$522$	−105768.	+	1319.29i	−0.388162	+	0.00484172i
$523$		−	120269.i		−	0.439692i	−0.975535	−	0.219846i	$-0.929444\pi$
$523$		−	120269.i		−	0.439692i	0.975535	−	0.219846i	$-0.0705555\pi$
$524$	12265.4	+	491585.i	0.0446704	+	1.79034i
$525$		0			0
$526$	135.536	+	10866.0i	0.000489873	+	0.0392732i
$527$		−	6216.62i		−	0.0223838i
$528$	−5249.92	+	262.142i	−0.0188315	+	0.000940305i
$529$	56739.5			0.202756
$530$		0			0
$531$			94164.7i			0.333964i
$532$	327862.	−	8180.40i	1.15842	−	0.0289036i
$533$	−6342.45			−0.0223256
$534$	−133.171	−	10676.4i	−0.000467011	−	0.0374404i
$535$		0			0
$536$	17936.4	+	479124.i	0.0624319	+	1.66770i
$537$	155829.			0.540381
$538$	−266646.	+	3325.99i	−0.921234	+	0.0114910i
$539$			4568.12i			0.0157239i
$540$		0			0
$541$	−479201.			−1.63728			−0.818640	−	0.574307i	$-0.805272\pi$
$541$	−479201.			−1.63728			−0.818640	+	0.574307i	$0.805272\pi$
$542$	3190.95	+	255820.i	0.0108623	+	0.870834i
$543$		−	246382.i		−	0.835619i
$544$	190872.	−	11919.0i	0.644977	−	0.0402755i
$545$		0			0
$546$	−30107.8	+	375.547i	−0.100993	+	0.00125974i
$547$		−	327802.i		−	1.09556i	−0.836622	−	0.547781i	$-0.815473\pi$
$547$		−	327802.i		−	1.09556i	0.836622	−	0.547781i	$-0.184527\pi$
$548$	114797.	−	2864.28i	0.382269	−	0.00953792i
$549$	13190.6			0.0437641
$550$		0			0
$551$			568970.i			1.87407i
$552$	156967.	−	5876.20i	0.515147	−	0.0192850i
$553$	238398.			0.779566
$554$	−145775.	+	1818.32i	−0.474968	+	0.00592449i
$555$		0			0
$556$	−1847.30	−	74037.8i	−0.00597569	−	0.239499i
$557$	−131341.			−0.423342			−0.211671	−	0.977341i	$-0.567891\pi$
$557$	−131341.			−0.423342			−0.211671	+	0.977341i	$0.567891\pi$
$558$	44.8378	+	3594.66i	0.000144004	+	0.0115449i
$559$		−	109841.i		−	0.351513i
$560$		0			0
$561$	3834.78			0.0121847
$562$	−334730.	+	4175.23i	−1.05979	+	0.0132193i
$563$			137401.i			0.433485i	0.976229	+	0.216742i	$0.0695432\pi$
$563$			137401.i			0.433485i	−0.976229	+	0.216742i	$0.930457\pi$
$564$	243110.	−	6065.77i	0.764265	−	0.0190690i
$565$		0			0
$566$	−4949.62	−	396813.i	−0.0154504	−	1.23866i
$567$			25722.2i			0.0800096i
$568$	11061.4	+	295477.i	0.0342858	+	0.915855i
$569$	152095.			0.469775			0.234887	−	0.972023i	$-0.424528\pi$
$569$	152095.			0.469775			0.234887	+	0.972023i	$0.424528\pi$
$570$		0			0
$571$			150818.i			0.462573i	0.972886	+	0.231286i	$0.0742935\pi$
$571$			150818.i			0.462573i	−0.972886	+	0.231286i	$0.925707\pi$
$572$	−64.7485	−	2595.05i	−0.000197896	−	0.00793147i
$573$	−213191.			−0.649322
$574$	−271.932	−	21800.9i	−0.000825348	−	0.0661684i
$575$		0			0
$576$	−110282.	+	8268.63i	−0.332400	+	0.0249223i
$577$	−258173.			−0.775461			−0.387730	−	0.921773i	$-0.626741\pi$
$577$	−258173.			−0.775461			−0.387730	+	0.921773i	$0.626741\pi$
$578$	194550.	−	2426.71i	0.582338	−	0.00726376i
$579$			229569.i			0.684788i
$580$		0			0
$581$	171557.			0.508226
$582$	3141.75	+	251875.i	0.00927524	+	0.743599i
$583$		−	14945.3i		−	0.0439711i
$584$	−445073.	+	16661.7i	−1.30499	+	0.0488533i
$585$		0			0
$586$	22217.9	−	277.133i	0.0647004	−	0.000807037i
$587$		−	574134.i		−	1.66624i	−0.553095	−	0.833118i	$-0.686553\pi$
$587$		−	574134.i		−	1.66624i	0.553095	−	0.833118i	$-0.313447\pi$
$588$	2397.27	+	96080.0i	0.00693366	+	0.277894i
$589$	19337.2			0.0557394
$590$		0			0
$591$		−	45332.7i		−	0.129789i
$592$	159354.	−	7956.98i	0.454695	−	0.0227041i
$593$	275339.			0.782995			0.391497	−	0.920179i	$-0.371957\pi$
$593$	275339.			0.782995			0.391497	+	0.920179i	$0.371957\pi$
$594$	−2217.39	+	27.6586i	−0.00628449	+	7.83893e-5i
$595$		0			0
$596$	561886.	−	14019.5i	1.58182	−	0.0394675i
$597$	34923.2			0.0979864
$598$	967.506	+	77565.2i	0.00270552	+	0.216903i
$599$			86528.9i			0.241161i	0.992704	+	0.120581i	$0.0384756\pi$
$599$			86528.9i			0.241161i	−0.992704	+	0.120581i	$0.961524\pi$
$600$		0			0
$601$	−391085.			−1.08273			−0.541367	−	0.840786i	$-0.682093\pi$
$601$	−391085.			−1.08273			−0.541367	+	0.840786i	$0.682093\pi$
$602$	377557.	−	4709.44i	1.04181	−	0.0129950i
$603$			202272.i			0.556290i
$604$	16486.3	+	660752.i	0.0451906	+	1.81119i
$605$		0			0
$606$	1864.22	+	149455.i	0.00507634	+	0.406972i
$607$			86135.8i			0.233779i	0.993145	+	0.116890i	$0.0372924\pi$
$607$			86135.8i			0.233779i	−0.993145	+	0.116890i	$0.962708\pi$
$608$	37074.7	+	593718.i	0.100293	+	1.60610i
$609$	179567.			0.484164
$610$		0			0
$611$			120095.i			0.321694i
$612$	80655.8	−	2012.42i	0.215344	−	0.00537300i
$613$	−161510.			−0.429811			−0.214906	−	0.976635i	$-0.568944\pi$
$613$	−161510.			−0.429811			−0.214906	+	0.976635i	$0.568944\pi$
$614$	−1287.86	−	103248.i	−0.00341610	−	0.273870i
$615$		0			0
$616$	8917.19	−	333.823i	0.0234999	−	0.000879740i
$617$	3300.03			0.00866857			0.00433428	−	0.999991i	$-0.498620\pi$
$617$	3300.03			0.00866857			0.00433428	+	0.999991i	$0.498620\pi$
$618$	−211771.	+	2641.51i	−0.554484	+	0.00691633i
$619$		−	670945.i		−	1.75108i	−0.483147	−	0.875539i	$-0.660506\pi$
$619$		−	670945.i		−	1.75108i	0.483147	−	0.875539i	$-0.339494\pi$
$620$		0			0
$621$	66266.9			0.171836
$622$	5325.74	+	426966.i	0.0137657	+	1.10360i
$623$			18125.8i			0.0467003i
$624$	−2723.67	−	54547.0i	−0.00699497	−	0.140088i
$625$		0			0
$626$	−305316.	+	3808.34i	−0.779113	+	0.00971822i
$627$			11928.3i			0.0303419i
$628$	−57293.6	+	1429.52i	−0.145274	+	0.00362469i
$629$	−116400.			−0.294205
$630$		0			0
$631$			563090.i			1.41423i	0.707100	+	0.707113i	$0.250003\pi$
$631$			563090.i			1.41423i	−0.707100	+	0.707113i	$0.749997\pi$
$632$	16176.6	+	432114.i	0.0404997	+	1.08184i
$633$	−44176.7			−0.110252
$634$	−433110.	+	5402.37i	−1.07750	+	0.0134402i
$635$		0			0
$636$	−7843.04	−	314340.i	−0.0193897	−	0.777116i
$637$	−47463.1			−0.116971
$638$	193.085	+	15479.7i	0.000474358	+	0.0380295i
$639$			124742.i			0.305499i
$640$		0			0
$641$	758985.			1.84721			0.923607	−	0.383341i	$-0.125226\pi$
$641$	758985.			1.84721			0.923607	+	0.383341i	$0.125226\pi$
$642$	−449928.	+	5612.15i	−1.09162	+	0.0136163i
$643$			572545.i			1.38480i	0.721513	+	0.692401i	$0.243447\pi$
$643$			572545.i			1.38480i	−0.721513	+	0.692401i	$0.756553\pi$
$644$	−266573.	+	6651.21i	−0.642754	+	0.0160372i
$645$		0			0
$646$	−5412.83	−	433948.i	−0.0129706	−	1.03986i
$647$		−	263241.i		−	0.628847i	−0.949283	−	0.314423i	$-0.898189\pi$
$647$		−	263241.i		−	0.628847i	0.949283	−	0.314423i	$-0.101811\pi$
$648$	−46623.3	+	1745.39i	−0.111033	+	0.00415663i
$649$	13781.5			0.0327195
$650$		0			0
$651$		−	6102.82i		−	0.0144002i
$652$	−5974.18	−	239439.i	−0.0140534	−	0.563247i
$653$	224745.			0.527065			0.263532	−	0.964651i	$-0.415112\pi$
$653$	224745.			0.527065			0.263532	+	0.964651i	$0.415112\pi$
$654$	−2762.31	−	221455.i	−0.00645827	−	0.517762i
$655$		0			0
$656$	39497.2	−	1972.20i	0.0917823	−	0.00458293i
$657$	−187897.			−0.435300
$658$	−412803.	+	5149.07i	−0.953434	+	0.0118926i
$659$		−	778617.i		−	1.79289i	−0.443158	−	0.896444i	$-0.646142\pi$
$659$		−	778617.i		−	1.79289i	0.443158	−	0.896444i	$-0.353858\pi$
$660$		0			0
$661$	339420.			0.776844			0.388422	−	0.921482i	$-0.373020\pi$
$661$	339420.			0.776844			0.388422	+	0.921482i	$0.373020\pi$
$662$	5441.88	+	436277.i	0.0124175	+	0.995512i
$663$			39843.6i			0.0906424i
$664$	11641.1	+	310960.i	0.0264032	+	0.705291i
$665$		0			0
$666$	67306.1	−	839.539i	0.151742	−	0.00189275i
$667$		−	462610.i		−	1.03983i
$668$	4992.60	+	200098.i	0.0111885	+	0.448425i
$669$	150100.			0.335373
$670$		0			0
$671$		−	1930.50i		−	0.00428771i
$672$	187378.	−	11700.8i	0.414934	−	0.0259105i
$673$	20796.2			0.0459149			0.0229574	−	0.999736i	$-0.492692\pi$
$673$	20796.2			0.0459149			0.0229574	+	0.999736i	$0.492692\pi$
$674$	610250.	−	7611.92i	1.34335	−	0.0167561i
$675$		0			0
$676$	−429871.	+	10725.6i	−0.940686	+	0.0234709i
$677$	202957.			0.442820			0.221410	−	0.975181i	$-0.428934\pi$
$677$	202957.			0.442820			0.221410	+	0.975181i	$0.428934\pi$
$678$	2560.23	+	205254.i	0.00556954	+	0.446512i
$679$		−	427619.i		−	0.927508i
$680$		0			0
$681$	91776.0			0.197895
$682$	526.096	−	6.56223i	0.00113109	−	1.41086e-5i
$683$			74248.4i			0.159164i	0.996828	+	0.0795821i	$0.0253586\pi$
$683$			74248.4i			0.159164i	−0.996828	+	0.0795821i	$0.974641\pi$
$684$	6259.76	+	250884.i	0.0133797	+	0.536243i
$685$		0			0
$686$	−6261.52	−	501988.i	−0.0133055	−	1.06671i
$687$		−	517879.i		−	1.09727i
$688$	34155.4	+	684029.i	0.0721577	+	1.44510i
$689$	155283.			0.327103
$690$		0			0
$691$		−	628006.i		−	1.31525i	−0.753346	−	0.657624i	$-0.771562\pi$
$691$		−	628006.i		−	1.31525i	0.753346	−	0.657624i	$-0.228438\pi$
$692$	−821599.	+	20499.5i	−1.71572	+	0.0428086i
$693$	3764.57			0.00783879
$694$	−8416.50	−	674753.i	−0.0174748	−	1.40096i
$695$		0			0
$696$	12184.6	+	325478.i	0.0251531	+	0.671898i
$697$	−28850.6			−0.0593866
$698$	78717.3	−	981.876i	0.161569	−	0.00201533i
$699$		−	377028.i		−	0.771647i
$700$		0			0
$701$	−508002.			−1.03378			−0.516892	−	0.856051i	$-0.672911\pi$
$701$	−508002.			−1.03378			−0.516892	+	0.856051i	$0.672911\pi$
$702$	−287.374	−	23038.9i	−0.000583141	−	0.0467506i
$703$		−	362068.i		−	0.732620i
$704$	1210.15	+	16140.4i	0.00244172	+	0.0325663i
$705$		0			0
$706$	220216.	−	2746.85i	0.441813	−	0.00551094i
$707$		−	253736.i		−	0.507626i
$708$	289862.	−	7232.28i	0.578262	−	0.0144281i
$709$	−60762.6			−0.120877			−0.0604385	−	0.998172i	$-0.519250\pi$
$709$	−60762.6			−0.120877			−0.0604385	+	0.998172i	$0.519250\pi$
$710$		0			0
$711$			182426.i			0.360867i
$712$	−32854.2	+	1229.93i	−0.0648084	+	0.00242616i
$713$	−15722.4			−0.0309271
$714$	−136954.	+	1708.29i	−0.268645	+	0.00335093i
$715$		0			0
$716$	−11968.4	−	479680.i	−0.0233458	−	0.935676i
$717$	−364814.			−0.709633
$718$	−3652.28	−	292804.i	−0.00708460	−	0.567974i
$719$		−	240815.i		−	0.465828i	−0.972497	−	0.232914i	$-0.925174\pi$
$719$		−	240815.i		−	0.465828i	0.972497	−	0.232914i	$-0.0748261\pi$
$720$		0			0
$721$	359533.			0.691621
$722$	828578.	−	10335.2i	1.58949	−	0.0198265i
$723$		−	267292.i		−	0.511340i
$724$	−758422.	+	18923.2i	−1.44689	+	0.0361009i
$725$		0			0
$726$	−3791.42	−	303959.i	−0.00719331	−	0.576690i
$727$		−	447387.i		−	0.846476i	−0.906018	−	0.423238i	$-0.860893\pi$
$727$		−	447387.i		−	0.846476i	0.906018	−	0.423238i	$-0.139107\pi$
$728$	3468.44	+	92650.2i	0.00654442	+	0.174817i
$729$	−19683.0			−0.0370370
$730$		0			0
$731$		−	499646.i		−	0.935035i
$732$	−1013.09	−	40603.7i	−0.00189072	−	0.0757781i
$733$	−855174.			−1.59165			−0.795823	−	0.605529i	$-0.792961\pi$
$733$	−855174.			−1.59165			−0.795823	+	0.605529i	$0.792961\pi$
$734$	−7799.41	−	625282.i	−0.0144767	−	1.16060i
$735$		0			0
$736$	−30144.2	−	482732.i	−0.0556478	−	0.891149i
$737$	29603.5			0.0545015
$738$	16682.4	−	208.086i	0.0306298	−	0.000382059i
$739$			234148.i			0.428747i	0.976752	+	0.214374i	$0.0687710\pi$
$739$			234148.i			0.428747i	−0.976752	+	0.214374i	$0.931229\pi$
$740$		0			0
$741$	−123936.			−0.225715
$742$	6657.74	+	533753.i	0.0120926	+	0.969466i
$743$		−	242702.i		−	0.439639i	−0.975541	−	0.219819i	$-0.929453\pi$
$743$		−	242702.i		−	0.439639i	0.975541	−	0.219819i	$-0.0705468\pi$
$744$	11061.8	−	414.108i	0.0199839	−	0.000748113i
$745$		0			0
$746$	−934981.	+	11662.4i	−1.68006	+	0.0209562i
$747$			131278.i			0.235262i
$748$	−294.528	−	11804.4i	−0.000526409	−	0.0210979i
$749$	763863.			1.36161
$750$		0			0
$751$			328095.i			0.581728i	0.956764	+	0.290864i	$0.0939428\pi$
$751$			328095.i			0.581728i	−0.956764	+	0.290864i	$0.906057\pi$
$752$	−37343.9	−	747885.i	−0.0660364	−	1.32251i
$753$	376353.			0.663751
$754$	−160835.	+	2006.16i	−0.282903	+	0.00352877i
$755$		0			0
$756$	79179.2	−	1975.58i	0.138538	−	0.00345662i
$757$	270737.			0.472450			0.236225	−	0.971698i	$-0.424090\pi$
$757$	270737.			0.472450			0.236225	+	0.971698i	$0.424090\pi$
$758$	−1247.33	−	99998.8i	−0.00217092	−	0.174043i
$759$		−	9698.49i		−	0.0168353i
$760$		0			0
$761$	−718672.			−1.24097			−0.620485	−	0.784218i	$-0.713064\pi$
$761$	−718672.			−1.24097			−0.620485	+	0.784218i	$0.713064\pi$
$762$	−415092.	+	5177.63i	−0.714883	+	0.00891705i
$763$			375974.i			0.645816i
$764$	16374.0	+	656254.i	0.0280524	+	1.12431i
$765$		0			0
$766$	−8238.42	−	660476.i	−0.0140406	−	1.12564i
$767$			143190.i			0.243401i
$768$	33923.0	+	338841.i	0.0575138	+	0.574478i
$769$	−654646.			−1.10702			−0.553508	−	0.832844i	$-0.686711\pi$
$769$	−654646.			−1.10702			−0.553508	+	0.832844i	$0.686711\pi$
$770$		0			0
$771$		−	403803.i		−	0.679298i
$772$	706670.	−	17632.0i	1.18572	−	0.0295846i
$773$	547589.			0.916423			0.458211	−	0.888843i	$-0.348490\pi$
$773$	547589.			0.916423			0.458211	+	0.888843i	$0.348490\pi$
$774$	3603.73	+	288912.i	0.00601548	+	0.482263i
$775$		0			0
$776$	775091.	−	29016.2i	1.28715	−	0.0481856i
$777$	−114269.			−0.189271
$778$	−185231.	+	2310.46i	−0.306023	+	0.00381716i
$779$		−	89741.3i		−	0.147883i
$780$		0			0
$781$	18256.5			0.0299307
$782$	4400.99	+	352829.i	0.00719676	+	0.576967i
$783$			137407.i			0.224123i
$784$	295574.	−	14758.8i	0.480876	−	0.0240114i
$785$		0			0
$786$	638736.	−	7967.24i	1.03389	−	0.0128962i
$787$		−	709361.i		−	1.14530i	−0.819801	−	0.572648i	$-0.805916\pi$
$787$		−	709361.i		−	1.14530i	0.819801	−	0.572648i	$-0.194084\pi$
$788$	−139545.	+	3481.76i	−0.224731	+	0.00560721i
$789$	14116.4			0.0226762
$790$		0			0
$791$		−	348470.i		−	0.556944i
$792$	255.446	+	6823.56i	0.000407238	+	0.0108783i
$793$	20058.1			0.0318965
$794$	976042.	−	12174.6i	1.54820	−	0.0193114i
$795$		0			0
$796$	−2682.26	−	107502.i	−0.00423327	−	0.169665i
$797$	−431065.			−0.678620			−0.339310	−	0.940675i	$-0.610194\pi$
$797$	−431065.			−0.678620			−0.339310	+	0.940675i	$0.610194\pi$
$798$	−5313.74	−	426004.i	−0.00834439	−	0.668972i
$799$			546289.i			0.855714i
$800$		0			0
$801$	−13870.1			−0.0216179
$802$	−409336.	+	5105.83i	−0.636401	+	0.00793811i
$803$			27499.6i			0.0426477i
$804$	622642.	−	15535.4i	0.963223	−	0.0240331i
$805$		0			0
$806$	68.1820	+	5466.17i	0.000104954	+	0.00841421i
$807$			346410.i			0.531916i
$808$	459915.	−	17217.3i	0.704457	−	0.0263720i
$809$	−179022.			−0.273533			−0.136767	−	0.990603i	$-0.543671\pi$
$809$	−179022.			−0.273533			−0.136767	+	0.990603i	$0.543671\pi$
$810$		0			0
$811$		−	979088.i		−	1.48861i	−0.667841	−	0.744304i	$-0.732782\pi$
$811$		−	979088.i		−	1.48861i	0.667841	−	0.744304i	$-0.267218\pi$
$812$	−13791.6	−	552751.i	−0.0209171	−	0.838335i
$813$	332345.			0.502815
$814$	−122.871	−	9850.58i	−0.000185438	−	0.0148667i
$815$		0			0
$816$	−12389.5	−	248124.i	−0.0186068	−	0.372638i
$817$	1.55418e6			2.32839
$818$	442528.	−	5519.84i	0.661354	−	0.00824936i
$819$			39114.2i			0.0583131i
$820$		0			0
$821$	154045.			0.228540			0.114270	−	0.993450i	$-0.463547\pi$
$821$	154045.			0.228540			0.114270	+	0.993450i	$0.463547\pi$
$822$	−1860.55	−	149161.i	−0.00275357	−	0.220755i
$823$		−	844036.i		−	1.24612i	−0.782173	−	0.623062i	$-0.785889\pi$
$823$		−	844036.i		−	1.24612i	0.782173	−	0.623062i	$-0.214111\pi$
$824$	24396.2	+	651679.i	0.0359309	+	0.959797i
$825$		0			0
$826$	−492188.	+	6139.28i	−0.721392	+	0.00899824i
$827$		−	1.00992e6i		−	1.47665i	−0.674445	−	0.738325i	$-0.735617\pi$
$827$		−	1.00992e6i		−	1.47665i	0.674445	−	0.738325i	$-0.264383\pi$
$828$	−5089.60	−	203986.i	−0.00742375	−	0.297536i
$829$	−617007.			−0.897803			−0.448901	−	0.893581i	$-0.648185\pi$
$829$	−617007.			−0.897803			−0.448901	+	0.893581i	$0.648185\pi$
$830$		0			0
$831$			189382.i			0.274244i
$832$	−167700.	+	12573.6i	−0.242262	+	0.0181640i
$833$	−215900.			−0.311145
$834$	−96200.3	+	1199.95i	−0.138307	+	0.00172517i
$835$		0			0
$836$	36718.2	−	916.147i	0.0525374	−	0.00131085i
$837$	4669.96			0.00666595
$838$	116.996	+	9379.60i	0.000166603	+	0.0133566i
$839$			1.04364e6i			1.48261i	0.671171	+	0.741303i	$0.265792\pi$
$839$			1.04364e6i			1.48261i	−0.671171	+	0.741303i	$0.734208\pi$
$840$		0			0
$841$	251961.			0.356239
$842$	635227.	−	7923.46i	0.895993	−	0.0111761i
$843$			434860.i			0.611920i
$844$	3392.97	+	135987.i	0.00476316	+	0.190902i
$845$		0			0
$846$	−3940.14	−	315882.i	−0.00550518	−	0.441352i
$847$			516046.i			0.719318i
$848$	−967014.	+	48285.6i	−1.34475	+	0.0671468i
$849$	−515515.			−0.715197
$850$		0			0
$851$			294385.i			0.406496i
$852$	383985.	−	9580.72i	0.528975	−	0.0131983i
$853$	−103215.			−0.141856			−0.0709278	−	0.997481i	$-0.522596\pi$
$853$	−103215.			−0.141856			−0.0709278	+	0.997481i	$0.522596\pi$
$854$	859.988	+	68945.5i	0.00117917	+	0.0945345i
$855$		0			0
$856$	51832.0	+	1.38456e6i	0.0707377	+	1.88957i
$857$	240186.			0.327029			0.163515	−	0.986541i	$-0.447717\pi$
$857$	240186.			0.327029			0.163515	+	0.986541i	$0.447717\pi$
$858$	−3371.86	+	42.0587i	−0.00458030	+	5.71322e-5i
$859$		−	75055.7i		−	0.101718i	−0.998706	−	0.0508590i	$-0.983804\pi$
$859$		−	75055.7i		−	0.101718i	0.998706	−	0.0508590i	$-0.0161959\pi$
$860$		0			0
$861$	−28322.4			−0.0382053
$862$	−13453.8	−	1.07859e6i	−0.0181063	−	1.45159i
$863$			539137.i			0.723898i	0.932198	+	0.361949i	$0.117889\pi$
$863$			539137.i			0.723898i	−0.932198	+	0.361949i	$0.882111\pi$
$864$	8953.61	+	143384.i	0.0119942	+	0.192076i
$865$		0			0
$866$	646387.	−	8062.67i	0.861900	−	0.0107509i
$867$		−	252747.i		−	0.336239i
$868$	−18786.0	+	468.724i	−0.0249341	+	0.000622125i
$869$	26698.9			0.0353553
$870$		0			0
$871$			307583.i			0.405439i
$872$	−681480.	+	25511.8i	−0.896232	+	0.0335512i
$873$	327220.			0.429350
$874$	−1.09749e6	+	13689.5i	−1.43674	+	0.0179212i
$875$		0			0
$876$	14431.3	+	578392.i	0.0188061	+	0.753727i
$877$	−851207.			−1.10672			−0.553358	−	0.832944i	$-0.686654\pi$
$877$	−851207.			−1.10672			−0.553358	+	0.832944i	$0.686654\pi$
$878$	−8556.10	−	685945.i	−0.0110991	−	0.889816i
$879$		−	28864.1i		−	0.0373577i
$880$		0			0
$881$	−1.32290e6			−1.70442			−0.852209	−	0.523201i	$-0.824738\pi$
$881$	−1.32290e6			−1.70442			−0.852209	+	0.523201i	$0.824738\pi$
$882$	124841.	−	1557.19i	0.160479	−	0.00200173i
$883$		−	222639.i		−	0.285548i	−0.989755	−	0.142774i	$-0.954398\pi$
$883$		−	222639.i		−	0.285548i	0.989755	−	0.142774i	$-0.0456023\pi$
$884$	122648.	−	3060.17i	0.156948	−	0.00391598i
$885$		0			0
$886$	3915.95	+	313943.i	0.00498850	+	0.399929i
$887$			1.27431e6i			1.61967i	0.586655	+	0.809837i	$0.300445\pi$
$887$			1.27431e6i			1.61967i	−0.586655	+	0.809837i	$0.699555\pi$
$888$	−7753.72	−	207120.i	−0.00983296	−	0.262661i
$889$	704721.			0.891690
$890$		0			0
$891$			2880.70i			0.00362864i
$892$	−11528.4	−	462044.i	−0.0144890	−	0.580703i
$893$	−1.69926e6			−2.13087
$894$	−9106.64	−	730082.i	−0.0113942	−	0.913475i
$895$		0			0
$896$	−50409.3	−	575895.i	−0.0627906	−	0.717344i
$897$	100768.			0.125238
$898$	1.02742e6	−	12815.4i	1.27407	−	0.0158920i
$899$		−	32601.1i		−	0.0403378i
$900$		0			0
$901$	706351.			0.870103
$902$	−30.4545	−	2441.54i	−3.74316e−5	−	0.00300090i
$903$		−	490499.i		−	0.601537i
$904$	631626.	−	23645.5i	0.772900	−	0.0289342i
$905$		0			0
$906$	858542.	−	10709.0i	1.04594	−	0.0130464i
$907$			1.23551e6i			1.50187i	0.660377	+	0.750934i	$0.270396\pi$
$907$			1.23551e6i			1.50187i	−0.660377	+	0.750934i	$0.729604\pi$
$908$	−7048.81	−	282509.i	−0.00854957	−	0.342658i
$909$	194162.			0.234984
$910$		0			0
$911$			830747.i			1.00100i	0.865738	+	0.500498i	$0.166850\pi$
$911$			830747.i			1.00100i	−0.865738	+	0.500498i	$0.833150\pi$
$912$	771802.	−	38538.1i	0.927933	−	0.0463341i
$913$	19213.2			0.0230493
$914$	731795.	−	9128.00i	0.875985	−	0.0109266i
$915$		0			0
$916$	−1.59416e6	+	39775.4i	−1.89994	+	0.0474050i
$917$	−1.08441e6			−1.28960
$918$	−1307.21	−	104799.i	−0.00155117	−	0.124358i
$919$			189522.i			0.224403i	0.993685	+	0.112201i	$0.0357902\pi$
$919$			189522.i			0.224403i	−0.993685	+	0.112201i	$0.964210\pi$
$920$		0			0
$921$	−134133.			−0.158131
$922$	−1.31199e6	+	16365.0i	−1.54336	+	0.0192511i
$923$			189687.i			0.222656i
$924$	−289.136	−	11588.3i	−0.000338656	−	0.0135730i
$925$		0			0
$926$	14383.3	+	1.15311e6i	0.0167739	+	1.34477i
$927$			275120.i			0.320157i
$928$	1.00097e6	−	62505.2i	1.16231	−	0.0725806i
$929$	125410.			0.145312			0.0726558	−	0.997357i	$-0.476853\pi$
$929$	125410.			0.145312			0.0726558	+	0.997357i	$0.476853\pi$
$930$		0			0
$931$		−	671570.i		−	0.774804i
$932$	−1.16058e6	+	28957.4i	−1.33612	+	0.0333371i
$933$	554689.			0.637215
$934$	−9373.96	−	751513.i	−0.0107456	−	0.861475i
$935$		0			0
$936$	−70897.2	+	2654.10i	−0.0809240	+	0.00302946i
$937$	1.18087e6			1.34500			0.672502	−	0.740095i	$-0.265220\pi$
$937$	1.18087e6			1.34500			0.672502	+	0.740095i	$0.265220\pi$
$938$	−1.05725e6	+	13187.6i	−1.20164	+	0.0149886i
$939$			396648.i			0.449856i
$940$		0			0
$941$	259343.			0.292883			0.146442	−	0.989219i	$-0.453218\pi$
$941$	259343.			0.292883			0.146442	+	0.989219i	$0.453218\pi$
$942$	928.572	+	74443.9i	0.00104644	+	0.0838933i
$943$			72965.7i			0.0820531i
$944$	−44525.4	−	891710.i	−0.0499648	−	1.00064i
$945$		0			0
$946$	42283.7	−	527.423i	0.0472488	−	0.000589355i
$947$			658326.i			0.734076i	0.930206	+	0.367038i	$0.119628\pi$
$947$			658326.i			0.734076i	−0.930206	+	0.367038i	$0.880372\pi$
$948$	561551.	−	14011.1i	0.624845	−	0.0155904i
$949$	−285723.			−0.317258
$950$		0			0
$951$			562670.i			0.622146i
$952$	15777.3	+	421447.i	0.0174083	+	0.465018i
$953$	−710654.			−0.782478			−0.391239	−	0.920289i	$-0.627953\pi$
$953$	−710654.			−0.782478			−0.391239	+	0.920289i	$0.627953\pi$
$954$	−408435.	+	5094.60i	−0.448773	+	0.00559775i
$955$		0			0
$956$	28019.4	+	1.12299e6i	0.0306580	+	1.22874i
$957$	20110.2			0.0219580
$958$	−2119.56	−	169926.i	−0.00230949	−	0.185152i
$959$			253237.i			0.275353i
$960$		0			0
$961$	922413.			0.998800
$962$	102348.	−	1276.64i	0.110594	−	0.00137948i
$963$			584519.i			0.630298i
$964$	−822791.	+	20529.3i	−0.885392	+	0.0220912i
$965$		0			0
$966$	4320.42	+	346370.i	0.00462991	+	0.371181i
$967$			1.34932e6i			1.44298i	0.692423	+	0.721491i	$0.256543\pi$
$967$			1.34932e6i			1.44298i	−0.692423	+	0.721491i	$0.743457\pi$
$968$	−935369.	+	35016.4i	−0.998234	+	0.0373698i
$969$	−563759.			−0.600408
$970$		0			0
$971$		−	1.17569e6i		−	1.24696i	−0.781838	−	0.623482i	$-0.785718\pi$
$971$		−	1.17569e6i		−	1.24696i	0.781838	−	0.623482i	$-0.214282\pi$
$972$	1511.74	+	60589.1i	0.00160009	+	0.0641301i
$973$	163324.			0.172514
$974$	−5784.28	−	463728.i	−0.00609722	−	0.488816i
$975$		0			0
$976$	−124910.	+	6237.10i	−0.131129	+	0.00654762i
$977$	−1.31383e6			−1.37642			−0.688211	−	0.725511i	$-0.741604\pi$
$977$	−1.31383e6			−1.37642			−0.688211	+	0.725511i	$0.741604\pi$
$978$	−311112.	+	3880.64i	−0.325267	+	0.00405720i
$979$			2029.96i			0.00211798i
$980$		0			0
$981$	−287701.			−0.298953
$982$	12705.3	+	1.01859e6i	0.0131754	+	1.05628i
$983$		−	915869.i		−	0.947821i	−0.880573	−	0.473911i	$-0.842842\pi$
$983$		−	915869.i		−	0.947821i	0.880573	−	0.473911i	$-0.157158\pi$
$984$	−1921.82	−	51336.4i	−0.00198483	−	0.0530194i
$985$		0			0
$986$	−731606.	+	9125.64i	−0.752529	+	0.00938663i
$987$			536288.i			0.550508i
$988$	9518.83	+	381504.i	0.00975146	+	0.390828i
$989$	−1.26365e6			−1.29192
$990$		0			0
$991$			1.25784e6i			1.28079i	0.768046	+	0.640394i	$0.221229\pi$
$991$			1.25784e6i			1.28079i	−0.768046	+	0.640394i	$0.778771\pi$
$992$	−2124.32	−	34019.1i	−0.00215872	−	0.0345700i
$993$	566785.			0.574804
$994$	−652010.	+	8132.81i	−0.659905	+	0.00823129i
$995$		0			0
$996$	404106.	−	10082.8i	0.407358	−	0.0101639i
$997$	1.20780e6			1.21508			0.607538	−	0.794291i	$-0.292157\pi$
$997$	1.20780e6			1.21508			0.607538	+	0.794291i	$0.292157\pi$
$998$	−6972.78	−	559010.i	−0.00700075	−	0.561253i
$999$		−	87440.0i		−	0.0876152i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.5.c.b.151.2	yes	16
4.3	odd	2	inner	300.5.c.b.151.1	✓	16
5.2	odd	4		300.5.f.c.199.15		32
5.3	odd	4		300.5.f.c.199.18		32
5.4	even	2		300.5.c.c.151.15	yes	16
20.3	even	4		300.5.f.c.199.16		32
20.7	even	4		300.5.f.c.199.17		32
20.19	odd	2		300.5.c.c.151.16	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.5.c.b.151.1	✓	16	4.3	odd	2	inner
300.5.c.b.151.2	yes	16	1.1	even	1	trivial
300.5.c.c.151.15	yes	16	5.4	even	2
300.5.c.c.151.16	yes	16	20.19	odd	2
300.5.f.c.199.15		32	5.2	odd	4
300.5.f.c.199.16		32	20.3	even	4
300.5.f.c.199.17		32	20.7	even	4
300.5.f.c.199.18		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)

\(f(q)\)	\(=\)	\(q+(-3.99969 + 0.0498899i) q^{2} +5.19615i q^{3} +(15.9950 - 0.399088i) q^{4} +(-0.259236 - 20.7830i) q^{6} +35.2842i q^{7} +(-63.9552 + 2.39422i) q^{8} -27.0000 q^{9} +O(q^{10})\)	\(q+(-3.99969 + 0.0498899i) q^{2} +5.19615i q^{3} +(15.9950 - 0.399088i) q^{4} +(-0.259236 - 20.7830i) q^{6} +35.2842i q^{7} +(-63.9552 + 2.39422i) q^{8} -27.0000 q^{9} +3.95158i q^{11} +(2.07372 + 83.1126i) q^{12} -41.0572 q^{13} +(-1.76033 - 141.126i) q^{14} +(255.681 - 12.7668i) q^{16} -186.761 q^{17} +(107.992 - 1.34703i) q^{18} -580.932i q^{19} -183.342 q^{21} +(-0.197144 - 15.8051i) q^{22} +472.336i q^{23} +(-12.4407 - 332.321i) q^{24} +(164.216 - 2.04834i) q^{26} -140.296i q^{27} +(14.0815 + 564.372i) q^{28} -979.409 q^{29} +33.2865i q^{31} +(-1022.01 + 63.8193i) q^{32} -20.5330 q^{33} +(746.987 - 9.31750i) q^{34} +(-431.866 + 10.7754i) q^{36} +623.253 q^{37} +(28.9826 + 2323.55i) q^{38} -213.340i q^{39} +154.478 q^{41} +(733.312 - 9.14693i) q^{42} +2675.32i q^{43} +(1.57703 + 63.2057i) q^{44} +(-23.5648 - 1889.20i) q^{46} -2925.06i q^{47} +(66.3385 + 1328.56i) q^{48} +1156.02 q^{49} -970.440i q^{51} +(-656.711 + 16.3855i) q^{52} -3782.10 q^{53} +(6.99936 + 561.141i) q^{54} +(-84.4782 - 2256.61i) q^{56} +3018.61 q^{57} +(3917.33 - 48.8626i) q^{58} -3487.58i q^{59} -488.539 q^{61} +(-1.66066 - 133.135i) q^{62} -952.674i q^{63} +(4084.54 - 306.245i) q^{64} +(82.1257 - 1.02439i) q^{66} -7491.56i q^{67} +(-2987.25 + 74.5342i) q^{68} -2454.33 q^{69} -4620.06i q^{71} +(1726.79 - 64.6439i) q^{72} +6959.14 q^{73} +(-2492.82 + 31.0940i) q^{74} +(-231.843 - 9292.01i) q^{76} -139.429 q^{77} +(10.6435 + 853.292i) q^{78} -6756.51i q^{79} +729.000 q^{81} +(-617.865 + 7.70690i) q^{82} -4862.15i q^{83} +(-2932.56 + 73.1697i) q^{84} +(-133.471 - 10700.4i) q^{86} -5089.16i q^{87} +(-9.46096 - 252.724i) q^{88} +513.707 q^{89} -1448.67i q^{91} +(188.504 + 7555.03i) q^{92} -172.962 q^{93} +(145.931 + 11699.3i) q^{94} +(-331.615 - 5310.52i) q^{96} -12119.3 q^{97} +(-4623.73 + 57.6739i) q^{98} -106.693i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{2} + 8 q^{4} + 18 q^{6} + 180 q^{8} - 432 q^{9}+O(q^{10}) \) 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

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