LMFDB - Embedded newform 76.6.f.a.31.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,6,Mod(27,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("76.27");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	76.f (of order $6$, degree $2$, 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:	$12.1891703058$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$48$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.20
Character	$\chi$	$=$	76.31
Dual form			76.6.f.a.27.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.12496 - 5.24257i) q^{2} +(-8.46878 - 14.6684i) q^{3} +(-22.9691 + 22.2805i) q^{4} +(29.9102 + 51.8059i) q^{5} +(-58.9040 + 75.5679i) q^{6} -59.1673i q^{7} +(165.616 + 73.0716i) q^{8} +(-21.9405 + 38.0021i) q^{9} +O(q^{10})$	\(q+(-2.12496 - 5.24257i) q^{2} +(-8.46878 - 14.6684i) q^{3} +(-22.9691 + 22.2805i) q^{4} +(29.9102 + 51.8059i) q^{5} +(-58.9040 + 75.5679i) q^{6} -59.1673i q^{7} +(165.616 + 73.0716i) q^{8} +(-21.9405 + 38.0021i) q^{9} +(208.038 - 266.892i) q^{10} +688.744i q^{11} +(521.339 + 148.230i) q^{12} +(858.463 + 495.634i) q^{13} +(-310.189 + 125.728i) q^{14} +(506.605 - 877.466i) q^{15} +(31.1559 - 1023.53i) q^{16} +(-621.607 - 1076.66i) q^{17} +(245.851 + 34.2716i) q^{18} +(-743.126 - 1387.03i) q^{19} +(-1841.27 - 523.519i) q^{20} +(-867.888 + 501.075i) q^{21} +(3610.79 - 1463.56i) q^{22} +(1837.86 + 1061.09i) q^{23} +(-330.722 - 3048.14i) q^{24} +(-226.737 + 392.720i) q^{25} +(774.192 - 5553.75i) q^{26} -3372.59 q^{27} +(1318.28 + 1359.02i) q^{28} +(1814.53 + 1047.62i) q^{29} +(-5676.70 - 791.331i) q^{30} +7638.88 q^{31} +(-5432.11 + 2011.62i) q^{32} +(10102.7 - 5832.82i) q^{33} +(-4323.55 + 5546.67i) q^{34} +(3065.22 - 1769.70i) q^{35} +(-342.753 - 1361.72i) q^{36} +11413.7i q^{37} +(-5692.51 + 6843.29i) q^{38} -16789.7i q^{39} +(1168.05 + 10765.5i) q^{40} +(7508.35 - 4334.95i) q^{41} +(4471.15 + 3485.19i) q^{42} +(2260.20 - 1304.93i) q^{43} +(-15345.6 - 15819.8i) q^{44} -2624.98 q^{45} +(1657.45 - 11889.9i) q^{46} +(10261.3 + 5924.39i) q^{47} +(-15277.3 + 8211.01i) q^{48} +13306.2 q^{49} +(2540.67 + 354.169i) q^{50} +(-10528.5 + 18235.9i) q^{51} +(-30761.1 + 7742.76i) q^{52} +(31883.7 + 18408.1i) q^{53} +(7166.63 + 17681.0i) q^{54} +(-35681.0 + 20600.5i) q^{55} +(4323.45 - 9799.03i) q^{56} +(-14052.1 + 22646.9i) q^{57} +(1636.41 - 11738.9i) q^{58} +(-9287.21 - 16085.9i) q^{59} +(7914.16 + 31442.0i) q^{60} +(6220.18 - 10773.7i) q^{61} +(-16232.3 - 40047.4i) q^{62} +(2248.48 + 1298.16i) q^{63} +(22089.1 + 24203.6i) q^{64} +59298.0i q^{65} +(-52046.9 - 40569.8i) q^{66} +(-10997.4 + 19048.1i) q^{67} +(38266.2 + 10880.0i) q^{68} -35944.5i q^{69} +(-15791.3 - 12309.1i) q^{70} +(6069.69 + 10513.0i) q^{71} +(-6410.56 + 4690.51i) q^{72} +(-31951.5 - 55341.7i) q^{73} +(59836.9 - 24253.6i) q^{74} +7680.74 q^{75} +(47972.8 + 15301.6i) q^{76} +40751.1 q^{77} +(-88020.9 + 35677.4i) q^{78} +(-21830.8 - 37812.1i) q^{79} +(53956.6 - 28999.8i) q^{80} +(33893.3 + 58704.9i) q^{81} +(-38681.2 - 30151.4i) q^{82} +70841.8i q^{83} +(8770.35 - 30846.2i) q^{84} +(37184.8 - 64405.9i) q^{85} +(-11644.0 - 9076.33i) q^{86} -35488.2i q^{87} +(-50327.6 + 114067. i) q^{88} +(-57124.7 - 32981.0i) q^{89} +(5577.98 + 13761.6i) q^{90} +(29325.3 - 50792.9i) q^{91} +(-65855.5 + 16576.3i) q^{92} +(-64692.0 - 112050. i) q^{93} +(9254.05 - 66384.9i) q^{94} +(49629.6 - 79984.8i) q^{95} +(75510.5 + 62644.2i) q^{96} +(-96176.6 + 55527.6i) q^{97} +(-28275.2 - 69758.8i) q^{98} +(-26173.7 - 15111.4i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 3 q^{2} - 11 q^{4} - 2 q^{5} - 27 q^{6} - 3588 q^{9}+O(q^{10}) $ 96 * q - 3 * q^2 - 11 * q^4 - 2 * q^5 - 27 * q^6 - 3588 * q^9	$ 96 q - 3 q^{2} - 11 q^{4} - 2 q^{5} - 27 q^{6} - 3588 q^{9} + 648 q^{10} - 354 q^{13} + 2154 q^{14} - 611 q^{16} - 1006 q^{17} + 10524 q^{20} + 7824 q^{21} + 93 q^{22} - 5311 q^{24} - 25002 q^{25} - 13428 q^{26} + 1556 q^{28} - 6 q^{29} - 12656 q^{30} - 30453 q^{32} + 8586 q^{33} + 30102 q^{34} - 2306 q^{36} + 29846 q^{38} - 1392 q^{40} + 29064 q^{41} + 18616 q^{42} + 9155 q^{44} + 13464 q^{45} + 38217 q^{48} - 116224 q^{49} + 36858 q^{52} + 26262 q^{53} - 26355 q^{54} + 53974 q^{57} - 112740 q^{58} - 108810 q^{60} - 77370 q^{61} - 106848 q^{62} + 337966 q^{64} + 166855 q^{66} + 175796 q^{68} + 148122 q^{70} - 259842 q^{72} - 52040 q^{73} + 103690 q^{74} - 194709 q^{76} + 197584 q^{77} + 253206 q^{78} - 171934 q^{80} - 313100 q^{81} + 63919 q^{82} - 161762 q^{85} - 38442 q^{86} + 10482 q^{89} - 372450 q^{90} + 64544 q^{92} + 94012 q^{93} + 537614 q^{96} + 177180 q^{97} - 509397 q^{98}+O(q^{100}) $ 96 * q - 3 * q^2 - 11 * q^4 - 2 * q^5 - 27 * q^6 - 3588 * q^9 + 648 * q^10 - 354 * q^13 + 2154 * q^14 - 611 * q^16 - 1006 * q^17 + 10524 * q^20 + 7824 * q^21 + 93 * q^22 - 5311 * q^24 - 25002 * q^25 - 13428 * q^26 + 1556 * q^28 - 6 * q^29 - 12656 * q^30 - 30453 * q^32 + 8586 * q^33 + 30102 * q^34 - 2306 * q^36 + 29846 * q^38 - 1392 * q^40 + 29064 * q^41 + 18616 * q^42 + 9155 * q^44 + 13464 * q^45 + 38217 * q^48 - 116224 * q^49 + 36858 * q^52 + 26262 * q^53 - 26355 * q^54 + 53974 * q^57 - 112740 * q^58 - 108810 * q^60 - 77370 * q^61 - 106848 * q^62 + 337966 * q^64 + 166855 * q^66 + 175796 * q^68 + 148122 * q^70 - 259842 * q^72 - 52040 * q^73 + 103690 * q^74 - 194709 * q^76 + 197584 * q^77 + 253206 * q^78 - 171934 * q^80 - 313100 * q^81 + 63919 * q^82 - 161762 * q^85 - 38442 * q^86 + 10482 * q^89 - 372450 * q^90 + 64544 * q^92 + 94012 * q^93 + 537614 * q^96 + 177180 * q^97 - 509397 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	−2.12496	−	5.24257i	−0.375644	−	0.926764i
$2$	−2.12496	−	5.24257i	−0.375644	−	0.926764i
$3$	−8.46878	−	14.6684i	−0.543273	−	0.940976i	−0.998713	−	0.0507097i	$-0.983852\pi$
$3$	−8.46878	−	14.6684i	−0.543273	−	0.940976i	0.455441	−	0.890266i	$-0.349482\pi$
$4$	−22.9691	+	22.2805i	−0.717783	+	0.696267i
$5$	29.9102	+	51.8059i	0.535049	+	0.926733i	0.999161	+	0.0409560i	$0.0130404\pi$
$5$	29.9102	+	51.8059i	0.535049	+	0.926733i	−0.464112	+	0.885777i	$0.653626\pi$
$6$	−58.9040	+	75.5679i	−0.667985	+	0.856957i
$7$		−	59.1673i		−	0.456391i	−0.973615	−	0.228195i	$-0.926718\pi$
$7$		−	59.1673i		−	0.456391i	0.973615	−	0.228195i	$-0.0732825\pi$
$8$	165.616	+	73.0716i	0.914906	+	0.403667i
$9$	−21.9405	+	38.0021i	−0.0902902	+	0.156387i
$10$	208.038	−	266.892i	0.657875	−	0.843986i
$11$			688.744i			1.71623i	0.513455	+	0.858116i	$0.328365\pi$
$11$			688.744i			1.71623i	−0.513455	+	0.858116i	$0.671635\pi$
$12$	521.339	+	148.230i	1.04512	+	0.297154i
$13$	858.463	+	495.634i	1.40884	+	0.813397i	0.995277	−	0.0970766i	$-0.0309492\pi$
$13$	858.463	+	495.634i	1.40884	+	0.813397i	0.413568	+	0.910473i	$0.364283\pi$
$14$	−310.189	+	125.728i	−0.422967	+	0.171440i
$15$	506.605	−	877.466i	0.581355	−	1.00694i
$16$	31.1559	−	1023.53i	0.0304257	−	0.999537i
$17$	−621.607	−	1076.66i	−0.521667	−	0.903554i	−0.999682	−	0.0252027i	$-0.991977\pi$
$17$	−621.607	−	1076.66i	−0.521667	−	0.903554i	0.478015	−	0.878352i	$-0.341356\pi$
$18$	245.851	+	34.2716i	0.178851	+	0.0249318i
$19$	−743.126	−	1387.03i	−0.472257	−	0.881461i
$19$	−743.126	−	1387.03i	−0.472257	−	0.881461i
$20$	−1841.27	−	523.519i	−1.02930	−	0.292656i
$21$	−867.888	+	501.075i	−0.429453	+	0.247945i
$22$	3610.79	−	1463.56i	1.59054	−	0.644692i
$23$	1837.86	+	1061.09i	0.724423	+	0.418246i	0.816379	−	0.577517i	$-0.195978\pi$
$23$	1837.86	+	1061.09i	0.724423	+	0.418246i	−0.0919553	+	0.995763i	$0.529312\pi$
$24$	−330.722	−	3048.14i	−0.117202	−	1.08021i
$25$	−226.737	+	392.720i	−0.0725558	+	0.125670i
$26$	774.192	−	5553.75i	0.224603	−	1.61121i
$27$	−3372.59			−0.890336
$28$	1318.28	+	1359.02i	0.317770	+	0.327590i
$29$	1814.53	+	1047.62i	0.400653	+	0.231317i	0.686766	−	0.726879i	$-0.259030\pi$
$29$	1814.53	+	1047.62i	0.400653	+	0.231317i	−0.286113	+	0.958196i	$0.592363\pi$
$30$	−5676.70	−	791.331i	−1.15158	−	0.160529i
$31$	7638.88			1.42766			0.713831	−	0.700318i	$-0.246958\pi$
$31$	7638.88			1.42766			0.713831	+	0.700318i	$0.246958\pi$
$32$	−5432.11	+	2011.62i	−0.937764	+	0.347273i
$33$	10102.7	−	5832.82i	1.61493	−	0.932382i
$34$	−4323.55	+	5546.67i	−0.641421	+	0.822877i
$35$	3065.22	−	1769.70i	0.422952	−	0.244192i
$36$	−342.753	−	1361.72i	−0.0440784	−	0.175118i
$37$			11413.7i			1.37063i	0.728246	+	0.685315i	$0.240336\pi$
$37$			11413.7i			1.37063i	−0.728246	+	0.685315i	$0.759664\pi$
$38$	−5692.51	+	6843.29i	−0.639506	+	0.768786i
$39$		−	16789.7i		−	1.76758i
$40$	1168.05	+	10765.5i	0.115428	+	1.06386i
$41$	7508.35	−	4334.95i	0.697565	−	0.402739i	−0.108875	−	0.994055i	$-0.534725\pi$
$41$	7508.35	−	4334.95i	0.697565	−	0.402739i	0.806440	+	0.591316i	$0.201391\pi$
$42$	4471.15	+	3485.19i	0.391107	+	0.304862i
$43$	2260.20	−	1304.93i	0.186413	−	0.107625i	−0.403889	−	0.914808i	$-0.632342\pi$
$43$	2260.20	−	1304.93i	0.186413	−	0.107625i	0.590302	+	0.807182i	$0.299009\pi$
$44$	−15345.6	−	15819.8i	−1.19496	−	1.23188i
$45$	−2624.98			−0.193239
$46$	1657.45	−	11889.9i	0.115490	−	0.828481i
$47$	10261.3	+	5924.39i	0.677579	+	0.391200i	0.798942	−	0.601408i	$-0.205393\pi$
$47$	10261.3	+	5924.39i	0.677579	+	0.391200i	−0.121363	+	0.992608i	$0.538727\pi$
$48$	−15277.3	+	8211.01i	−0.957069	+	0.514391i
$49$	13306.2			0.791708
$50$	2540.67	+	354.169i	0.143722	+	0.0200348i
$51$	−10528.5	+	18235.9i	−0.566815	+	0.981753i
$52$	−30761.1	+	7742.76i	−1.57759	+	0.397089i
$53$	31883.7	+	18408.1i	1.55912	+	0.900157i	0.997342	+	0.0728675i	$0.0232150\pi$
$53$	31883.7	+	18408.1i	1.55912	+	0.900157i	0.561776	+	0.827289i	$0.310118\pi$
$54$	7166.63	+	17681.0i	0.334449	+	0.825132i
$55$	−35681.0	+	20600.5i	−1.59049	+	0.918269i
$56$	4323.45	−	9799.03i	0.184230	−	0.417555i
$57$	−14052.1	+	22646.9i	−0.572869	+	0.923256i
$58$	1636.41	−	11738.9i	0.0638735	−	0.458204i
$59$	−9287.21	−	16085.9i	−0.347340	−	0.601611i	0.638436	−	0.769675i	$-0.279582\pi$
$59$	−9287.21	−	16085.9i	−0.347340	−	0.601611i	−0.985776	+	0.168064i	$0.946248\pi$
$60$	7914.16	+	31442.0i	0.283809	+	1.12754i
$61$	6220.18	−	10773.7i	0.214032	−	0.370714i	−0.738941	−	0.673770i	$-0.764674\pi$
$61$	6220.18	−	10773.7i	0.214032	−	0.370714i	0.952973	+	0.303056i	$0.0980071\pi$
$62$	−16232.3	−	40047.4i	−0.536293	−	1.32311i
$63$	2248.48	+	1298.16i	0.0713736	+	0.0412076i
$64$	22089.1	+	24203.6i	0.674105	+	0.738635i
$65$			59298.0i			1.74083i
$66$	−52046.9	−	40569.8i	−1.47074	−	1.14642i
$67$	−10997.4	+	19048.1i	−0.299298	+	0.518400i	−0.975976	−	0.217880i	$-0.930086\pi$
$67$	−10997.4	+	19048.1i	−0.299298	+	0.518400i	0.676677	+	0.736280i	$0.263419\pi$
$68$	38266.2	+	10880.0i	1.00356	+	0.285337i
$69$		−	35944.5i		−	0.908886i
$70$	−15791.3	−	12309.1i	−0.385187	−	0.300248i
$71$	6069.69	+	10513.0i	0.142896	+	0.247504i	0.928586	−	0.371117i	$-0.121025\pi$
$71$	6069.69	+	10513.0i	0.142896	+	0.247504i	−0.785690	+	0.618621i	$0.787692\pi$
$72$	−6410.56	+	4690.51i	−0.145735	+	0.106632i
$73$	−31951.5	−	55341.7i	−0.701753	−	1.21547i	−0.967850	−	0.251526i	$-0.919067\pi$
$73$	−31951.5	−	55341.7i	−0.701753	−	1.21547i	0.266097	−	0.963946i	$-0.414266\pi$
$74$	59836.9	−	24253.6i	1.27025	−	0.514869i
$75$	7680.74			0.157670
$76$	47972.8	+	15301.6i	0.952710	+	0.303881i
$77$	40751.1			0.783273
$78$	−88020.9	+	35677.4i	−1.63813	+	0.663982i
$79$	−21830.8	−	37812.1i	−0.393552	−	0.681653i	0.599363	−	0.800477i	$-0.295421\pi$
$79$	−21830.8	−	37812.1i	−0.393552	−	0.681653i	−0.992915	+	0.118825i	$0.962087\pi$
$80$	53956.6	−	28999.8i	0.942583	−	0.506605i
$81$	33893.3	+	58704.9i	0.573986	+	0.994172i
$82$	−38681.2	−	30151.4i	−0.635281	−	0.495192i
$83$			70841.8i			1.12874i	0.825521	+	0.564371i	$0.190881\pi$
$83$			70841.8i			1.12874i	−0.825521	+	0.564371i	$0.809119\pi$
$84$	8770.35	−	30846.2i	0.135618	−	0.476984i
$85$	37184.8	−	64405.9i	0.558236	−	0.966893i
$86$	−11644.0	−	9076.33i	−0.169768	−	0.132332i
$87$		−	35488.2i		−	0.502673i
$88$	−50327.6	+	114067.i	−0.692787	+	1.57019i
$89$	−57124.7	−	32981.0i	−0.764450	−	0.441356i	0.0664411	−	0.997790i	$-0.478836\pi$
$89$	−57124.7	−	32981.0i	−0.764450	−	0.441356i	−0.830891	+	0.556435i	$0.812169\pi$
$90$	5577.98	+	13761.6i	0.0725890	+	0.179087i
$91$	29325.3	−	50792.9i	0.371227	−	0.642984i
$92$	−65855.5	+	16576.3i	−0.811190	+	0.204182i
$93$	−64692.0	−	112050.i	−0.775610	−	1.34340i
$94$	9254.05	−	66384.9i	0.108022	−	0.774908i
$95$	49629.6	−	79984.8i	0.564198	−	0.909281i
$96$	75510.5	+	62644.2i	0.836237	+	0.693750i
$97$	−96176.6	+	55527.6i	−1.03786	+	0.599210i	−0.919227	−	0.393727i	$-0.871185\pi$
$97$	−96176.6	+	55527.6i	−1.03786	+	0.599210i	−0.118636	+	0.992938i	$0.537852\pi$
$98$	−28275.2	−	69758.8i	−0.297400	−	0.733726i
$99$	−26173.7	−	15111.4i	−0.268397	−	0.154959i
$100$	−3542.07	−	14072.2i	−0.0354207	−	0.140722i
$101$	−32760.5	+	56742.8i	−0.319556	+	0.553487i	−0.980395	−	0.197040i	$-0.936867\pi$
$101$	−32760.5	+	56742.8i	−0.319556	+	0.553487i	0.660840	+	0.750527i	$0.270200\pi$
$102$	117976.	+	16445.8i	1.12277	+	0.156515i
$103$	132954.			1.23483			0.617415	−	0.786638i	$-0.288180\pi$
$103$	132954.			1.23483			0.617415	+	0.786638i	$0.288180\pi$
$104$	105958.	+	144814.i	0.960618	+	1.31289i
$105$	−51917.3	−	29974.5i	−0.459557	−	0.265325i
$106$	28753.9	−	206269.i	0.248560	−	1.78307i
$107$	59514.3			0.502530			0.251265	−	0.967918i	$-0.419153\pi$
$107$	59514.3			0.502530			0.251265	+	0.967918i	$0.419153\pi$
$108$	77465.2	−	75143.1i	0.639069	−	0.619912i
$109$	−4036.90	+	2330.70i	−0.0325448	+	0.0187897i	−0.516184	−	0.856478i	$-0.672648\pi$
$109$	−4036.90	+	2330.70i	−0.0325448	+	0.0187897i	0.483639	+	0.875267i	$0.339315\pi$
$110$	183820.	+	143285.i	1.44848	+	1.12907i
$111$	167420.	−	96659.8i	1.28973	−	0.744626i
$112$	−60559.3	−	1843.41i	−0.456179	−	0.0138860i
$113$			46495.8i			0.342545i	0.985224	+	0.171272i	$0.0547878\pi$
$113$			46495.8i			0.342545i	−0.985224	+	0.171272i	$0.945212\pi$
$114$	148588.	+	25545.4i	1.07084	+	0.184099i
$115$			126949.i			0.895129i
$116$	−65019.5	+	16365.8i	−0.448641	+	0.112926i
$117$	−37670.2	+	21748.9i	−0.254410	+	0.146883i
$118$	−64596.5	+	82870.8i	−0.427075	+	0.547894i
$119$	−63702.8	+	36778.8i	−0.412374	+	0.238084i
$120$	148020.	−	108304.i	0.938353	−	0.686578i
$121$	−313318.			−1.94546
$122$	−69699.3	−	9716.08i	−0.423964	−	0.0591005i
$123$	−127173.	−	73423.4i	−0.757936	−	0.437595i
$124$	−175458.	+	170198.i	−1.02475	+	0.994034i
$125$	159812.			0.914815
$126$	2027.76	−	14546.4i	0.0113786	−	0.0816259i
$127$	−111883.	+	193787.i	−0.615539	+	1.06615i	0.374750	+	0.927126i	$0.377728\pi$
$127$	−111883.	+	193787.i	−0.615539	+	1.06615i	−0.990290	+	0.139019i	$0.955605\pi$
$128$	79950.6	−	167235.i	0.431317	−	0.902200i
$129$	−38282.3	−	22102.3i	−0.202546	−	0.116940i
$130$	310874.	−	126006.i	1.61334	−	0.653932i
$131$	−1922.40	+	1109.90i	−0.00978737	+	0.00565074i	−0.504886	−	0.863186i	$-0.668465\pi$
$131$	−1922.40	+	1109.90i	−0.00978737	+	0.00565074i	0.495098	+	0.868837i	$0.335132\pi$
$132$	−102092.	+	359069.i	−0.509986	+	1.79367i
$133$	−82067.1	+	43968.8i	−0.402291	+	0.215534i
$134$	123230.	+	17178.3i	0.592864	+	0.0826452i
$135$	−100875.	−	174720.i	−0.476374	−	0.825104i
$136$	−24274.9	−	223733.i	−0.112541	−	1.03725i
$137$	135481.	−	234660.i	0.616704	−	1.06816i	−0.373379	−	0.927679i	$-0.621801\pi$
$137$	135481.	−	234660.i	0.616704	−	1.06816i	0.990083	−	0.140483i	$-0.0448657\pi$
$138$	−188441.	+	76380.7i	−0.842323	+	0.341418i
$139$	−46087.8	−	26608.8i	−0.202325	−	0.116812i	0.395415	−	0.918503i	$-0.370601\pi$
$139$	−46087.8	−	26608.8i	−0.202325	−	0.116812i	−0.597739	+	0.801690i	$0.703934\pi$
$140$	−30975.2	+	108943.i	−0.133566	+	0.469764i
$141$		−	200689.i		−	0.850113i
$142$	42217.4	−	54160.6i	0.175699	−	0.225404i
$143$	−341365.	+	591261.i	−1.39598	+	2.41791i
$144$	38212.5	+	23640.7i	0.153568	+	0.0950065i
$145$			125338.i			0.495064i
$146$	−222237.	+	285107.i	−0.862847	+	1.10694i
$147$	−112688.	−	195181.i	−0.430113	−	0.744978i
$148$	−254302.	−	262161.i	−0.954324	−	0.983816i
$149$	48532.7	+	84061.1i	0.179089	+	0.310191i	0.941569	−	0.336821i	$-0.109352\pi$
$149$	48532.7	+	84061.1i	0.179089	+	0.310191i	−0.762480	+	0.647012i	$0.776018\pi$
$150$	−16321.3	−	40266.8i	−0.0592279	−	0.146123i
$151$	−148248.			−0.529110			−0.264555	−	0.964371i	$-0.585225\pi$
$151$	−148248.			−0.529110			−0.264555	+	0.964371i	$0.585225\pi$
$152$	−21720.5	−	284016.i	−0.0762537	−	0.997088i
$153$	54553.5			0.188406
$154$	−86594.7	−	213641.i	−0.294232	−	0.725909i
$155$	228480.	+	395739.i	0.763870	+	1.32306i
$156$	374082.	+	385643.i	1.23071	+	1.26874i
$157$	−296533.	−	513610.i	−0.960116	−	1.66297i	−0.722201	−	0.691683i	$-0.756869\pi$
$157$	−296533.	−	513610.i	−0.960116	−	1.66297i	−0.237915	−	0.971286i	$-0.576464\pi$
$158$	−151843.	+	194799.i	−0.483896	+	0.620789i
$159$		−	623575.i		−	1.95612i
$160$	−266689.	−	221248.i	−0.823579	−	0.683249i
$161$	62781.7	−	108741.i	0.190884	−	0.330620i
$162$	235742.	−	302433.i	0.705749	−	0.905404i
$163$			127923.i			0.377119i	0.982062	+	0.188560i	$0.0603818\pi$
$163$			127923.i			0.377119i	−0.982062	+	0.188560i	$0.939618\pi$
$164$	−75874.8	+	266860.i	−0.220287	+	0.774771i
$165$	604350.	+	348922.i	1.72814	+	0.997741i
$166$	371393.	−	150536.i	1.04608	−	0.424005i
$167$	−211195.	+	365801.i	−0.585994	+	1.01497i	0.408756	+	0.912644i	$0.365963\pi$
$167$	−211195.	+	365801.i	−0.585994	+	1.01497i	−0.994751	+	0.102328i	$0.967371\pi$
$168$	−180350.	+	19567.9i	−0.492996	+	0.0534899i
$169$	305659.	+	529417.i	0.823229	+	1.42587i
$170$	−416669.	−	58083.5i	−1.10578	−	0.154145i
$171$	69014.7	+	2191.89i	0.180489	+	0.00573230i
$172$	−22840.2	+	80331.4i	−0.0588680	+	0.207045i
$173$	−31028.2	+	17914.2i	−0.0788210	+	0.0455073i	−0.538892	−	0.842375i	$-0.681157\pi$
$173$	−31028.2	+	17914.2i	−0.0788210	+	0.0455073i	0.460072	+	0.887882i	$0.347824\pi$
$174$	−186049.	+	75411.1i	−0.465859	+	0.188826i
$175$	23236.2	+	13415.4i	0.0573548	+	0.0331138i
$176$	704948.	+	21458.4i	1.71544	+	0.0522176i
$177$	−157303.	+	272456.i	−0.377401	+	0.653677i
$178$	−51517.1	+	369564.i	−0.121871	+	0.874257i
$179$	474201.			1.10619			0.553095	−	0.833118i	$-0.313447\pi$
$179$	474201.			1.10619			0.553095	+	0.833118i	$0.313447\pi$
$180$	60293.3	−	58485.9i	0.138704	−	0.134546i
$181$	169766.	+	98014.3i	0.385171	+	0.222379i	0.680066	−	0.733151i	$-0.261951\pi$
$181$	169766.	+	98014.3i	0.385171	+	0.222379i	−0.294895	+	0.955530i	$0.595285\pi$
$182$	−328601.	−	45806.9i	−0.735343	−	0.102507i
$183$	−210709.			−0.465110
$184$	226843.	+	310028.i	0.493947	+	0.675082i
$185$	−591295.	+	341384.i	−1.27021	+	0.733355i
$186$	−449961.	+	577254.i	−0.953658	+	1.22345i
$187$	741540.	−	428128.i	1.55071	−	0.895303i
$188$	−367692.	+	92550.5i	−0.758734	+	0.190978i
$189$			199547.i			0.406341i
$190$	−524787.	−	90221.7i	−1.05463	−	0.181312i
$191$		−	432804.i		−	0.858435i	−0.903201	−	0.429218i	$-0.858789\pi$
$191$		−	432804.i		−	0.858435i	0.903201	−	0.429218i	$-0.141211\pi$
$192$	167960.	−	528986.i	0.328815	−	1.03560i
$193$	−155239.	+	89627.2i	−0.299990	+	0.173200i	−0.642439	−	0.766337i	$-0.722077\pi$
$193$	−155239.	+	89627.2i	−0.299990	+	0.173200i	0.342448	+	0.939537i	$0.388744\pi$
$194$	495479.	+	386218.i	0.945194	+	0.736764i
$195$	869804.	−	502181.i	1.63808	−	0.945745i
$196$	−305632.	+	296470.i	−0.568274	+	0.551239i
$197$	393838.			0.723023			0.361512	−	0.932368i	$-0.382261\pi$
$197$	393838.			0.723023			0.361512	+	0.932368i	$0.382261\pi$
$198$	−23604.4	+	169329.i	−0.0427888	+	0.306950i
$199$	−270645.	−	156257.i	−0.484471	−	0.279709i	0.237807	−	0.971312i	$-0.423571\pi$
$199$	−270645.	−	156257.i	−0.484471	−	0.279709i	−0.722278	+	0.691603i	$0.756905\pi$
$200$	−66247.8	+	48472.5i	−0.117111	+	0.0856881i
$201$	372540.			0.650403
$202$	367093.	+	51172.7i	0.632991	+	0.0882388i
$203$	61984.7	−	107361.i	0.105571	−	0.182854i
$204$	−164476.	−	653443.i	−0.276711	−	1.09934i
$205$	449152.	+	259318.i	0.746464	+	0.430971i
$206$	−282522.	−	697019.i	−0.463856	−	1.14440i
$207$	−80647.1	+	46561.6i	−0.130817	+	0.0755270i
$208$	534040.	−	863217.i	0.855885	−	1.38344i
$209$	955311.	−	511824.i	1.51279	−	0.810503i
$210$	−46820.9	+	335875.i	−0.0732642	+	0.525568i
$211$	−346667.	−	600444.i	−0.536051	−	0.928467i	−0.999112	−	0.0421405i	$-0.986582\pi$
$211$	−346667.	−	600444.i	−0.536051	−	0.928467i	0.463061	−	0.886326i	$-0.346751\pi$
$212$	−1.14248e6	+	287570.i	−1.74586	+	0.439444i
$213$	102806.	−	178065.i	0.155263	−	0.268924i
$214$	−126466.	−	312008.i	−0.188772	−	0.465727i
$215$	135206.	+	78061.2i	0.199480	+	0.115170i
$216$	−558554.	−	246441.i	−0.814574	−	0.359400i
$217$		−	451972.i		−	0.651572i
$218$	20797.1	+	16211.1i	0.0296389	+	0.0231031i
$219$	−541181.	+	937353.i	−0.762487	+	1.32067i
$220$	360571.	−	1.26817e6i	0.502266	−	1.76652i
$221$		−	1.23236e6i		−	1.69729i
$222$	−862506.	−	672311.i	−1.17457	−	0.915561i
$223$	304547.	+	527491.i	0.410103	+	0.710319i	0.994901	−	0.100860i	$-0.0321595\pi$
$223$	304547.	+	527491.i	0.410103	+	0.710319i	−0.584798	+	0.811179i	$0.698826\pi$
$224$	119022.	+	321403.i	0.158492	+	0.427987i
$225$	−9949.44	−	17232.9i	−0.0131021	−	0.0226936i
$226$	243757.	−	98801.8i	0.317458	−	0.128675i
$227$	24226.7			0.0312054			0.0156027	−	0.999878i	$-0.495033\pi$
$227$	24226.7			0.0312054			0.0156027	+	0.999878i	$0.495033\pi$
$228$	−181821.	−	833268.i	−0.231637	−	1.06157i
$229$	−667477.			−0.841100			−0.420550	−	0.907269i	$-0.638163\pi$
$229$	−667477.			−0.841100			−0.420550	+	0.907269i	$0.638163\pi$
$230$	665540.	−	269763.i	0.829573	−	0.336250i
$231$	−345113.	−	597752.i	−0.425531	−	0.737041i
$232$	223963.	+	306092.i	0.273185	+	0.373364i
$233$	−273333.	−	473427.i	−0.329839	−	0.571298i	0.652640	−	0.757668i	$-0.273661\pi$
$233$	−273333.	−	473427.i	−0.329839	−	0.571298i	−0.982480	+	0.186369i	$0.940328\pi$
$234$	194068.	+	151273.i	0.231694	+	0.180602i
$235$			708798.i			0.837246i
$236$	571721.	+	162554.i	0.668196	+	0.189985i
$237$	−369761.	+	640445.i	−0.427612	+	0.740646i
$238$	328182.	+	255813.i	0.375554	+	0.292738i
$239$			825158.i			0.934420i	0.884146	+	0.467210i	$0.154741\pi$
$239$			825158.i			0.934420i	−0.884146	+	0.467210i	$0.845259\pi$
$240$	−882326.	−	545862.i	−0.988783	−	0.611723i
$241$	767729.	+	443249.i	0.851463	+	0.491592i	0.861144	−	0.508361i	$-0.169748\pi$
$241$	767729.	+	443249.i	0.851463	+	0.491592i	−0.00968153	+	0.999953i	$0.503082\pi$
$242$	665788.	+	1.64259e6i	0.730798	+	1.80298i
$243$	164300.	−	284575.i	0.178493	−	0.309159i
$244$	97171.3	+	386050.i	0.104487	+	0.415115i
$245$	397992.	+	689342.i	0.423603	+	0.733701i
$246$	−114689.	+	822736.i	−0.120833	+	0.866808i
$247$	49514.6	−	1.55904e6i	0.0516406	−	1.62597i
$248$	1.26512e6	+	558185.i	1.30618	+	0.576301i
$249$	1.03913e6	−	599944.i	1.06212	−	0.613214i
$250$	−339594.	−	837824.i	−0.343645	−	0.847818i
$251$	192325.	+	111039.i	0.192686	+	0.111248i	0.593240	−	0.805026i	$-0.297849\pi$
$251$	192325.	+	111039.i	0.192686	+	0.111248i	−0.400553	+	0.916274i	$0.631182\pi$
$252$	−80569.2	+	20279.8i	−0.0799223	+	0.0201170i
$253$	−730818.	+	1.26581e6i	−0.717807	+	1.24328i
$254$	1.25369e6	+	174764.i	1.21929	+	0.169969i
$255$	−1.25964e6			−1.21310
$256$	−1.04663e6	−	63777.7i	−0.998149	−	0.0608232i
$257$	−1.42512e6	−	822794.i	−1.34592	−	0.777067i	−0.358250	−	0.933626i	$-0.616627\pi$
$257$	−1.42512e6	−	822794.i	−1.34592	−	0.777067i	−0.987669	+	0.156559i	$0.949960\pi$
$258$	−34524.3	+	247664.i	−0.0322906	+	0.231640i
$259$	675316.			0.625543
$260$	−1.32119e6	−	1.36202e6i	−1.21208	−	1.24954i
$261$	−79623.3	+	45970.5i	−0.0723501	+	0.0417713i
$262$	9903.76	+	7719.83i	0.00891347	+	0.00694792i
$263$	−536543.	+	309773.i	−0.478316	+	0.276156i	−0.719715	−	0.694270i	$-0.755727\pi$
$263$	−536543.	+	309773.i	−0.478316	+	0.276156i	0.241398	+	0.970426i	$0.422394\pi$
$264$	2.09939e6	−	227783.i	1.85388	−	0.201146i
$265$			2.20235e6i			1.92651i
$266$	404899.	+	336810.i	0.350867	+	0.291864i
$267$			1.11723e6i			0.959105i
$268$	−171801.	−	682546.i	−0.146113	−	0.580491i
$269$	748349.	−	432059.i	0.630556	−	0.364052i	−0.150412	−	0.988623i	$-0.548060\pi$
$269$	748349.	−	432059.i	0.630556	−	0.364052i	0.780967	+	0.624572i	$0.214727\pi$
$270$	−701628.	+	900117.i	−0.585730	+	0.751432i
$271$	−577576.	+	333464.i	−0.477734	+	0.275820i	−0.719472	−	0.694522i	$-0.755616\pi$
$271$	−577576.	+	333464.i	−0.477734	+	0.275820i	0.241738	+	0.970342i	$0.422283\pi$
$272$	−1.12135e6	+	602687.i	−0.919008	+	0.493935i
$273$	−993399.			−0.806709
$274$	−1.51811e6	−	211625.i	−1.22160	−	0.170290i
$275$	−270483.	−	156164.i	−0.215679	−	0.124523i
$276$	800862.	+	825611.i	0.632827	+	0.652383i
$277$	−1.17079e6			−0.916808			−0.458404	−	0.888744i	$-0.651579\pi$
$277$	−1.17079e6			−0.916808			−0.458404	+	0.888744i	$0.651579\pi$
$278$	−41563.7	+	298162.i	−0.0322554	+	0.231387i
$279$	−167601.	+	290293.i	−0.128904	+	0.223268i
$280$	636963.	−	69110.3i	0.485534	−	0.0526802i
$281$	293537.	+	169474.i	0.221767	+	0.128037i	0.606768	−	0.794879i	$-0.292466\pi$
$281$	293537.	+	169474.i	0.221767	+	0.128037i	−0.385001	+	0.922916i	$0.625799\pi$
$282$	−1.05213e6	+	426458.i	−0.787855	+	0.319340i
$283$	−819405.	+	473084.i	−0.608180	+	0.351133i	−0.772253	−	0.635315i	$-0.780870\pi$
$283$	−819405.	+	473084.i	−0.608180	+	0.351133i	0.164073	+	0.986448i	$0.447537\pi$
$284$	−373651.	−	106238.i	−0.274897	−	0.0781601i
$285$	−1.59355e6	−	50610.7i	−1.16212	−	0.0369088i
$286$	3.82512e6	+	533221.i	2.76522	+	0.385471i
$287$	−256487.	−	444249.i	−0.183807	−	0.318362i
$288$	42737.6	−	250567.i	0.0303619	−	0.178010i
$289$	−62862.4	+	108881.i	−0.0442737	+	0.0766844i
$290$	657092.	−	266338.i	0.458808	−	0.185968i
$291$	1.62900e6	+	940502.i	1.12768	+	0.651069i
$292$	1.96694e6	+	559250.i	1.35000	+	0.383838i
$293$			500061.i			0.340294i	0.985419	+	0.170147i	$0.0544242\pi$
$293$			500061.i			0.340294i	−0.985419	+	0.170147i	$0.945576\pi$
$294$	−783791.	+	1.00552e6i	−0.528849	+	0.678460i
$295$	555564.	−	962265.i	0.371688	−	0.643783i
$296$	−834014.	+	1.89028e6i	−0.553279	+	1.25400i
$297$		−	2.32285e6i		−	1.52802i
$298$	337566.	−	433063.i	0.220200	−	0.282495i
$299$	1.05182e6	+	1.82181e6i	0.680400	+	1.17849i
$300$	−176419.	+	171131.i	−0.113173	+	0.109781i
$301$	−77209.1	−	133730.i	−0.0491193	−	0.0850771i
$302$	315021.	+	777200.i	0.198757	+	0.490360i
$303$	1.10976e6			0.694423
$304$	−1.44282e6	+	717395.i	−0.895422	+	0.445219i
$305$	744186.			0.458070
$306$	−115924.	−	286001.i	−0.0707735	−	0.174608i
$307$	−1.48017e6	−	2.56374e6i	−0.896328	−	1.55249i	−0.832152	−	0.554547i	$-0.812891\pi$
$307$	−1.48017e6	−	2.56374e6i	−0.896328	−	1.55249i	−0.0641760	−	0.997939i	$-0.520442\pi$
$308$	−936016.	+	907957.i	−0.562220	+	0.545367i
$309$	−1.12596e6	−	1.95021e6i	−0.670849	−	1.16194i
$310$	1.58918e6	−	2.03876e6i	0.939223	−	1.20493i
$311$		−	1.83209e6i		−	1.07410i	−0.843550	−	0.537050i	$-0.819539\pi$
$311$		−	1.83209e6i		−	1.07410i	0.843550	−	0.537050i	$-0.180461\pi$
$312$	1.22685e6	−	2.78063e6i	0.713516	−	1.61717i
$313$	1.50593e6	−	2.60836e6i	0.868851	−	1.50489i	0.00567939	−	0.999984i	$-0.498192\pi$
$313$	1.50593e6	−	2.60836e6i	0.868851	−	1.50489i	0.863172	−	0.504910i	$-0.168474\pi$
$314$	−2.06251e6	+	2.64600e6i	−1.18052	+	1.51449i
$315$			155313.i			0.0881924i
$316$	1.34391e6	+	382106.i	0.757097	+	0.215262i
$317$	−381195.	−	220083.i	−0.213059	−	0.123010i	0.389673	−	0.920953i	$-0.372588\pi$
$317$	−381195.	−	220083.i	−0.213059	−	0.123010i	−0.602732	+	0.797944i	$0.705921\pi$
$318$	−3.26914e6	+	1.32507e6i	−1.81286	+	0.734805i
$319$	−721541.	+	1.24975e6i	−0.396994	+	0.687614i
$320$	−593202.	+	1.86828e6i	−0.323838	+	1.01992i
$321$	−504014.	−	872977.i	−0.273011	−	0.472868i
$322$	−703492.	−	98066.7i	−0.378111	−	0.0527086i
$323$	−1.03142e6	+	1.66228e6i	−0.550087	+	0.886539i
$324$	−2.08647e6	−	593236.i	−1.10421	−	0.313953i
$325$	−389290.	+	224757.i	−0.204440	+	0.118033i
$326$	670643.	−	271831.i	0.349500	−	0.141662i
$327$	68375.2	+	39476.4i	0.0353614	+	0.0204159i
$328$	1.56026e6	−	169288.i	0.800779	−	0.0868843i
$329$	350530.	−	607136.i	0.178540	−	0.309241i
$330$	545024.	−	3.90979e6i	0.275506	−	1.97637i
$331$	1.44093e6			0.722891			0.361446	−	0.932393i	$-0.382283\pi$
$331$	1.44093e6			0.722891			0.361446	+	0.932393i	$0.382283\pi$
$332$	−1.57839e6	−	1.62717e6i	−0.785905	−	0.810192i
$333$	−433743.	−	250421.i	−0.214349	−	0.123754i
$334$	2.36652e6	+	329893.i	1.16076	+	0.161810i
$335$	−1.31574e6			−0.640558
$336$	485824.	+	903917.i	0.234763	+	0.436798i
$337$	−2.39608e6	+	1.38338e6i	−1.14928	+	0.663538i	−0.948712	−	0.316141i	$-0.897613\pi$
$337$	−2.39608e6	+	1.38338e6i	−1.14928	+	0.663538i	−0.200570	+	0.979679i	$0.564279\pi$
$338$	2.12599e6	−	2.72743e6i	1.01221	−	1.29856i
$339$	682017.	−	393762.i	0.322326	−	0.186095i
$340$	580898.	+	2.30784e6i	0.272523	+	1.08270i
$341$			5.26124e6i			2.45020i
$342$	−135163.	−	366472.i	−0.0624872	−	0.169424i
$343$		−	1.78172e6i		−	0.817719i
$344$	469678.	−	50959.9i	0.213995	−	0.0232184i
$345$	1.86214e6	−	1.07511e6i	0.842295	−	0.486299i
$346$	159850.	+	124601.i	0.0717832	+	0.0559539i
$347$	1.76707e6	−	1.02022e6i	0.787824	−	0.454851i	−0.0513717	−	0.998680i	$-0.516359\pi$
$347$	1.76707e6	−	1.02022e6i	0.787824	−	0.454851i	0.839196	+	0.543829i	$0.183026\pi$
$348$	790696.	+	815130.i	0.349994	+	0.360810i
$349$	−4.45425e6			−1.95754			−0.978771	−	0.204958i	$-0.934294\pi$
$349$	−4.45425e6			−1.95754			−0.978771	+	0.204958i	$0.934294\pi$
$350$	20955.2	−	150324.i	0.00914370	−	0.0655933i
$351$	−2.89524e6	−	1.67157e6i	−1.25435	−	0.724197i
$352$	−1.38549e6	−	3.74133e6i	−0.596001	−	1.60942i
$353$	−293795.			−0.125490			−0.0627448	−	0.998030i	$-0.519985\pi$
$353$	−293795.			−0.125490			−0.0627448	+	0.998030i	$0.519985\pi$
$354$	1.76263e6	+	245711.i	0.747573	+	0.104212i
$355$	−363091.	+	628892.i	−0.152913	+	0.264853i
$356$	2.04694e6	−	515227.i	0.856011	−	0.215464i
$357$	1.07897e6	+	622944.i	0.448063	+	0.258689i
$358$	−1.00766e6	−	2.48603e6i	−0.415534	−	1.02518i
$359$	−792985.	+	457830.i	−0.324735	+	0.187486i	−0.653501	−	0.756926i	$-0.726701\pi$
$359$	−792985.	+	457830.i	−0.324735	+	0.187486i	0.328766	+	0.944411i	$0.393367\pi$
$360$	−434737.	−	191811.i	−0.176795	−	0.0780042i
$361$	−1.37163e6	+	2.06148e6i	−0.553946	+	0.832552i
$362$	153101.	−	1.09829e6i	0.0614053	−	0.440498i
$363$	2.65342e6	+	4.59585e6i	1.05691	+	1.83063i
$364$	458119.	+	1.82005e6i	0.181228	+	0.719996i
$365$	1.91135e6	−	3.31056e6i	0.750946	−	1.30068i
$366$	447749.	+	1.10466e6i	0.174716	+	0.431048i
$367$	1.16252e6	+	671180.i	0.450541	+	0.260120i	0.708059	−	0.706153i	$-0.249571\pi$
$367$	1.16252e6	+	671180.i	0.450541	+	0.260120i	−0.257517	+	0.966274i	$0.582904\pi$
$368$	1.14331e6	−	1.84804e6i	0.440093	−	0.711362i
$369$			380444.i			0.145454i
$370$	3.04621e6	+	2.37448e6i	1.15679	+	0.901703i
$371$	1.08916e6	−	1.88647e6i	0.410823	−	0.711567i
$372$	3.98245e6	+	1.13231e6i	1.49208	+	0.424236i
$373$		−	3.18199e6i		−	1.18421i	−0.805862	−	0.592103i	$-0.798298\pi$
$373$		−	3.18199e6i		−	1.18421i	0.805862	−	0.592103i	$-0.201702\pi$
$374$	−3.82024e6	−	2.97782e6i	−1.41225	−	1.10083i
$375$	−1.35341e6	−	2.34417e6i	−0.496994	−	0.860819i
$376$	1.26653e6	+	1.73098e6i	0.462006	+	0.631428i
$377$	1.03847e6	+	1.79868e6i	0.376305	+	0.651780i
$378$	1.04614e6	−	424030.i	0.376583	−	0.152640i
$379$	288409.			0.103136			0.0515681	−	0.998669i	$-0.483578\pi$
$379$	288409.			0.103136			0.0515681	+	0.998669i	$0.483578\pi$
$380$	642158.	+	2.94295e6i	0.228130	+	1.04550i
$381$	3.79006e6			1.33762
$382$	−2.26900e6	+	919692.i	−0.795567	+	0.322466i
$383$	1.72744e6	+	2.99201e6i	0.601735	+	1.04224i	0.992558	+	0.121770i	$0.0388571\pi$
$383$	1.72744e6	+	2.99201e6i	0.601735	+	1.04224i	−0.390823	+	0.920466i	$0.627810\pi$
$384$	−3.13015e6	+	243535.i	−1.08327	+	0.0842817i
$385$	1.21887e6	+	2.11115e6i	0.419090	+	0.725885i
$386$	799754.	+	623396.i	0.273205	+	0.212959i
$387$			114523.i			0.0388701i
$388$	971902.	−	3.41828e6i	0.327750	−	1.15273i
$389$	90103.3	−	156064.i	0.0301903	−	0.0522911i	−0.850536	−	0.525918i	$-0.823722\pi$
$389$	90103.3	−	156064.i	0.0301903	−	0.0522911i	0.880726	+	0.473627i	$0.157055\pi$
$390$	−4.48102e6	−	3.49289e6i	−1.49182	−	1.16285i
$391$		−	2.63832e6i		−	0.872741i
$392$	2.20372e6	+	972308.i	0.724338	+	0.319587i
$393$	32560.8	+	18799.0i	0.0106344	+	0.00613979i
$394$	−836892.	−	2.06472e6i	−0.271599	−	0.670072i
$395$	1.30593e6	−	2.26193e6i	0.421140	−	0.729436i
$396$	937876.	−	236069.i	0.300543	−	0.0756488i
$397$	1.46807e6	+	2.54278e6i	0.467489	+	0.809714i	0.999310	−	0.0371425i	$-0.0118255\pi$
$397$	1.46807e6	+	2.54278e6i	0.467489	+	0.809714i	−0.531821	+	0.846857i	$0.678492\pi$
$398$	−244077.	+	1.75092e6i	−0.0772360	+	0.554061i
$399$	1.33996e6	+	831427.i	0.421365	+	0.261452i
$400$	394895.	+	244307.i	0.123405	+	0.0763458i
$401$	5.03095e6	−	2.90462e6i	1.56239	−	0.902046i	0.565375	−	0.824834i	$-0.308732\pi$
$401$	5.03095e6	−	2.90462e6i	1.56239	−	0.902046i	0.997015	−	0.0772118i	$-0.0246018\pi$
$402$	−791633.	−	1.95306e6i	−0.244320	−	0.602770i
$403$	6.55770e6	+	3.78609e6i	2.01135	+	1.16126i
$404$	−511782.	−	2.03325e6i	−0.156003	−	0.619779i
$405$	−2.02751e6	+	3.51175e6i	−0.614221	+	1.06386i
$406$	−694561.	−	96821.7i	−0.209120	−	0.0291513i
$407$	−7.86109e6			−2.35232
$408$	−3.07621e6	+	2.25082e6i	−0.914884	+	0.669406i
$409$	−4.32647e6	−	2.49789e6i	−1.27887	−	0.738354i	−0.302226	−	0.953236i	$-0.597730\pi$
$409$	−4.32647e6	−	2.49789e6i	−1.27887	−	0.738354i	−0.976640	+	0.214882i	$0.931063\pi$
$410$	405061.	−	2.90575e6i	0.119004	−	0.853687i
$411$	−4.58943e6			−1.34015
$412$	−3.05382e6	+	2.96228e6i	−0.886340	+	0.859771i
$413$	−951760.	+	549499.i	−0.274570	+	0.158523i
$414$	415475.	+	323856.i	0.119136	+	0.0928649i
$415$	−3.67003e6	+	2.11889e6i	−1.04604	+	0.603933i
$416$	−5.66029e6	−	965438.i	−1.60363	−	0.273521i
$417$			901377.i			0.253844i
$418$	−4.71327e6	−	3.92068e6i	−1.31942	−	1.09754i
$419$		−	4.36296e6i		−	1.21408i	−0.794673	−	0.607038i	$-0.792357\pi$
$419$		−	4.36296e6i		−	1.21408i	0.794673	−	0.607038i	$-0.207643\pi$
$420$	1.86034e6	−	468260.i	0.514599	−	0.129528i
$421$	−1.00252e6	+	578808.i	−0.275670	+	0.159158i	−0.631462	−	0.775407i	$-0.717545\pi$
$421$	−1.00252e6	+	578808.i	−0.275670	+	0.159158i	0.355791	+	0.934565i	$0.384211\pi$
$422$	−2.41122e6	+	3.09334e6i	−0.659106	+	0.845565i
$423$	−450278.	+	259968.i	−0.122357	+	0.0706431i
$424$	3.93533e6	+	5.37845e6i	1.06308	+	1.45292i
$425$	563765.			0.151400
$426$	−1.15198e6	−	160585.i	−0.307553	−	0.0428728i
$427$	−637449.	−	368031.i	−0.169190	−	0.0976821i
$428$	−1.36699e6	+	1.32601e6i	−0.360708	+	0.349895i
$429$	1.15638e7			3.03359
$430$	121934.	−	874704.i	0.0318018	−	0.228134i
$431$	3.58643e6	−	6.21188e6i	0.929971	−	1.61076i	0.146605	−	0.989195i	$-0.453165\pi$
$431$	3.58643e6	−	6.21188e6i	0.929971	−	1.61076i	0.783366	−	0.621561i	$-0.213501\pi$
$432$	−105076.	+	3.45193e6i	−0.0270891	+	0.889924i
$433$	3.74832e6	+	2.16409e6i	0.960765	+	0.554698i	0.896408	−	0.443229i	$-0.146167\pi$
$433$	3.74832e6	+	2.16409e6i	0.960765	+	0.554698i	0.0643565	+	0.997927i	$0.479501\pi$
$434$	−2.36950e6	+	960424.i	−0.603853	+	0.244759i
$435$	1.83850e6	−	1.06146e6i	0.465844	−	0.268955i
$436$	40794.4	−	143478.i	0.0102774	−	0.0361468i
$437$	106004.	−	3.33769e6i	0.0265534	−	0.836070i
$438$	6.06413e6	+	845339.i	1.51037	+	0.210545i
$439$	633890.	+	1.09793e6i	0.156983	+	0.271903i	0.933779	−	0.357849i	$-0.116490\pi$
$439$	633890.	+	1.09793e6i	0.156983	+	0.271903i	−0.776796	+	0.629752i	$0.783157\pi$
$440$	−7.41465e6	+	804487.i	−1.82582	+	0.198101i
$441$	−291945.	+	505664.i	−0.0714834	+	0.123813i
$442$	−6.46072e6	+	2.61871e6i	−1.57299	+	0.637577i
$443$	−2.18499e6	−	1.26150e6i	−0.528981	−	0.305407i	0.211621	−	0.977352i	$-0.432126\pi$
$443$	−2.18499e6	−	1.26150e6i	−0.528981	−	0.305407i	−0.740601	+	0.671945i	$0.765459\pi$
$444$	−1.69184e6	+	5.95038e6i	−0.407289	+	1.43248i
$445$		−	3.94587e6i		−	0.944588i
$446$	2.11826e6	−	2.71751e6i	0.504245	−	0.646895i
$447$	822026.	−	1.42379e6i	0.194588	−	0.337037i
$448$	1.43206e6	−	1.30695e6i	0.337106	−	0.307655i
$449$			7.16227e6i			1.67662i	0.545193	+	0.838311i	$0.316456\pi$
$449$			7.16227e6i			1.67662i	−0.545193	+	0.838311i	$0.683544\pi$
$450$	−69202.7	+	88780.0i	−0.0161099	+	0.0206673i
$451$	2.98567e6	+	5.17133e6i	0.691195	+	1.19718i
$452$	−1.03595e6	−	1.06796e6i	−0.238502	−	0.245873i
$453$	1.25548e6	+	2.17455e6i	0.287451	+	0.497880i
$454$	−51480.9	−	127010.i	−0.0117221	−	0.0289201i
$455$	3.50850e6			0.794499
$456$	−3.98210e6	+	2.72387e6i	−0.896809	+	0.613444i
$457$	−5.11484e6			−1.14562			−0.572811	−	0.819687i	$-0.694147\pi$
$457$	−5.11484e6			−1.14562			−0.572811	+	0.819687i	$0.694147\pi$
$458$	1.41836e6	+	3.49929e6i	0.315954	+	0.779501i
$459$	2.09643e6	+	3.63112e6i	0.464459	+	0.804467i
$460$	−2.82850e6	−	2.91591e6i	−0.623248	−	0.642509i
$461$	−978360.	−	1.69457e6i	−0.214411	−	0.371370i	0.738679	−	0.674057i	$-0.235450\pi$
$461$	−978360.	−	1.69457e6i	−0.214411	−	0.371370i	−0.953090	+	0.302687i	$0.902116\pi$
$462$	−2.40041e6	+	3.07948e6i	−0.523215	+	0.671231i
$463$			2.01882e6i			0.437669i	0.975762	+	0.218834i	$0.0702254\pi$
$463$			2.01882e6i			0.437669i	−0.975762	+	0.218834i	$0.929775\pi$
$464$	1.12880e6	−	1.82458e6i	0.243400	−	0.393430i
$465$	3.86990e6	−	6.70286e6i	0.829979	−	1.43757i
$466$	−1.90115e6	+	2.43898e6i	−0.405557	+	0.520288i
$467$		−	1.61287e6i		−	0.342221i	−0.985252	−	0.171110i	$-0.945265\pi$
$467$		−	1.61287e6i		−	0.342221i	0.985252	−	0.171110i	$-0.0547354\pi$
$468$	380672.	−	1.33886e6i	0.0803409	−	0.282567i
$469$	1.12703e6	+	650689.i	0.236593	+	0.136597i
$470$	3.71592e6	−	1.50617e6i	0.775929	−	0.314506i
$471$	−5.02254e6	+	8.69930e6i	−1.04321	+	1.80689i
$472$	−362683.	−	3.34271e6i	−0.0749328	−	0.690627i
$473$	898761.	+	1.55670e6i	0.184710	+	0.319928i
$474$	4.14330e6	+	577576.i	0.847034	+	0.118076i
$475$	713209.	+	22651.4i	0.145038	+	0.00460639i
$476$	643742.	−	2.26411e6i	0.130225	−	0.458015i
$477$	−1.39909e6	+	807764.i	−0.281546	+	0.162551i
$478$	4.32595e6	−	1.75343e6i	0.865987	−	0.351009i
$479$	−6.91907e6	−	3.99473e6i	−1.37787	−	0.795515i	−0.385969	−	0.922512i	$-0.626133\pi$
$479$	−6.91907e6	−	3.99473e6i	−1.37787	−	0.795515i	−0.991903	+	0.126997i	$0.959466\pi$
$480$	−986810.	+	5.78559e6i	−0.195493	+	1.14616i
$481$	−5.65699e6	+	9.79820e6i	−1.11487	+	1.93101i
$482$	692366.	−	4.96676e6i	0.135743	−	0.973768i
$483$	−2.12674e6			−0.414807
$484$	7.19661e6	−	6.98088e6i	1.39642	−	1.35456i
$485$	−5.75332e6	−	3.32168e6i	−1.11062	−	0.641214i
$486$	−1.84104e6	−	256640.i	−0.353567	−	0.0492872i
$487$	−6.45985e6			−1.23424			−0.617120	−	0.786869i	$-0.711701\pi$
$487$	−6.45985e6			−1.23424			−0.617120	+	0.786869i	$0.711701\pi$
$488$	1.81741e6	−	1.32977e6i	0.345464	−	0.252771i
$489$	1.87642e6	−	1.08335e6i	0.354860	−	0.204878i
$490$	2.76820e6	−	3.55132e6i	0.520844	−	0.668190i
$491$	3.37446e6	−	1.94825e6i	0.631686	−	0.364704i	−0.149719	−	0.988729i	$-0.547837\pi$
$491$	3.37446e6	−	1.94825e6i	0.631686	−	0.364704i	0.781405	+	0.624025i	$0.214504\pi$
$492$	4.55696e6	−	1.14702e6i	0.848716	−	0.213627i
$493$		−	2.60483e6i		−	0.482683i
$494$	−8.27857e6	+	3.05331e6i	−1.52629	+	0.562929i
$495$		−	1.80794e6i		−	0.331643i
$496$	237996.	−	7.81859e6i	0.0434376	−	1.42700i
$497$	622027.	−	359128.i	0.112958	−	0.0652165i
$498$	−5.35337e6	−	4.17287e6i	−0.967283	−	0.753983i
$499$	−4.60932e6	+	2.66119e6i	−0.828678	+	0.478437i	−0.853400	−	0.521257i	$-0.825463\pi$
$499$	−4.60932e6	+	2.66119e6i	−0.828678	+	0.478437i	0.0247220	+	0.999694i	$0.492130\pi$
$500$	−3.67072e6	+	3.56069e6i	−0.656639	+	0.636955i
$501$	7.15427e6			1.27342
$502$	173445.	−	1.24423e6i	0.0307187	−	0.220364i
$503$	3.70398e6	+	2.13849e6i	0.652752	+	0.376867i	0.789510	−	0.613738i	$-0.210335\pi$
$503$	3.70398e6	+	2.13849e6i	0.652752	+	0.376867i	−0.136758	+	0.990605i	$0.543668\pi$
$504$	277525.	+	379296.i	0.0486660	+	0.0665123i
$505$	−3.91948e6			−0.683912
$506$	8.18908e6	+	1.14156e6i	1.42187	+	0.198208i
$507$	5.17712e6	−	8.96703e6i	0.894475	−	1.54928i
$508$	−1.74783e6	−	6.94393e6i	−0.300497	−	1.19384i
$509$	−4.22094e6	−	2.43696e6i	−0.722129	−	0.416921i	0.0934071	−	0.995628i	$-0.470224\pi$
$509$	−4.22094e6	−	2.43696e6i	−0.722129	−	0.416921i	−0.815536	+	0.578707i	$0.803558\pi$
$510$	2.67668e6	+	6.60374e6i	0.455692	+	1.12425i
$511$	−3.27442e6	+	1.89049e6i	−0.554730	+	0.320274i
$512$	1.88970e6	+	5.62258e6i	0.318580	+	0.947896i
$513$	2.50626e6	+	4.67790e6i	0.420468	+	0.784797i
$514$	−1.28522e6	+	9.21970e6i	−0.214571	+	1.53925i
$515$	3.97667e6	+	6.88779e6i	0.660695	+	1.14436i
$516$	1.37176e6	−	345281.i	0.226805	−	0.0570884i
$517$	−4.08039e6	+	7.06744e6i	−0.671391	+	1.16288i
$518$	−1.43502e6	−	3.54039e6i	−0.234982	−	0.579731i
$519$	525543.	+	303422.i	0.0856425	+	0.0494457i
$520$	−4.33300e6	+	9.82067e6i	−0.702716	+	1.59270i
$521$		−	1.06481e7i		−	1.71862i	−0.511457	−	0.859309i	$-0.670894\pi$
$521$		−	1.06481e7i		−	1.71862i	0.511457	−	0.859309i	$-0.329106\pi$
$522$	410200.	+	319745.i	0.0658900	+	0.0513603i
$523$	−783961.	+	1.35786e6i	−0.125326	+	0.217070i	−0.921860	−	0.387523i	$-0.873331\pi$
$523$	−783961.	+	1.35786e6i	−0.125326	+	0.217070i	0.796535	+	0.604593i	$0.206664\pi$
$524$	19426.6	−	68325.5i	0.00309079	−	0.0108706i
$525$		−	454449.i		−	0.0719592i
$526$	2.76414e6	+	2.15461e6i	0.435608	+	0.339550i
$527$	−4.74838e6	−	8.22444e6i	−0.744765	−	1.28997i
$528$	−5.65529e6	−	1.05222e7i	−0.882815	−	1.64255i
$529$	−966357.	−	1.67378e6i	−0.150141	−	0.260051i
$530$	1.15460e7	−	4.67992e6i	1.78542	−	0.723683i
$531$	815064.			0.125446
$532$	905356.	−	2.83842e6i	0.138688	−	0.434808i
$533$	8.59418e6			1.31035
$534$	5.85718e6	−	2.37408e6i	0.888864	−	0.360282i
$535$	1.78008e6	+	3.08319e6i	0.268878	+	0.465711i
$536$	−3.21322e6	+	2.35107e6i	−0.483091	+	0.353470i
$537$	−4.01591e6	−	6.95575e6i	−0.600963	−	1.04090i
$538$	−3.85532e6	−	3.00516e6i	−0.574254	−	0.447623i
$539$			9.16459e6i			1.35875i
$540$	6.20986e6	+	1.76562e6i	0.916426	+	0.260563i
$541$	−4.77013e6	+	8.26211e6i	−0.700708	+	1.21366i	0.267510	+	0.963555i	$0.413799\pi$
$541$	−4.77013e6	+	8.26211e6i	−0.700708	+	1.21366i	−0.968218	+	0.250107i	$0.919534\pi$
$542$	2.97553e6	+	2.31938e6i	0.435077	+	0.339136i
$543$		−	3.32025e6i		−	0.483249i
$544$	5.54246e6	+	4.59807e6i	0.802981	+	0.666160i
$545$	−241489.	−	139423.i	−0.0348261	−	0.0201069i
$546$	2.11094e6	+	5.20796e6i	0.303035	+	0.747629i
$547$	5.10285e6	−	8.83839e6i	0.729196	−	1.26300i	−0.228027	−	0.973655i	$-0.573228\pi$
$547$	5.10285e6	−	8.83839e6i	0.729196	−	1.26300i	0.957223	−	0.289350i	$-0.0934392\pi$
$548$	2.11648e6	+	8.40850e6i	0.301066	+	1.19610i
$549$	272948.	+	472759.i	0.0386499	+	0.0669436i
$550$	−243932.	+	1.74987e6i	−0.0343844	+	0.246660i
$551$	104659.	−	3.29532e6i	0.0146858	−	0.462401i
$552$	2.62652e6	−	5.95297e6i	0.366888	−	0.831545i
$553$	−2.23724e6	+	1.29167e6i	−0.311100	+	0.179614i
$554$	2.48788e6	+	6.13793e6i	0.344393	+	0.849664i
$555$	1.00151e7	+	5.78222e6i	1.38014	+	0.796824i
$556$	1.65145e6	−	415682.i	0.226558	−	0.0570261i
$557$	3.25025e6	−	5.62959e6i	0.443893	−	0.768845i	−0.554081	−	0.832462i	$-0.686930\pi$
$557$	3.25025e6	−	5.62959e6i	0.443893	−	0.768845i	0.997974	+	0.0636173i	$0.0202637\pi$
$558$	1.87803e6	+	261797.i	0.255339	+	0.0355942i
$559$	2.58706e6			0.350169
$560$	−1.71584e6	−	3.19247e6i	−0.231210	−	0.430186i
$561$	−1.25599e7	−	7.25145e6i	−1.68492	−	0.972787i
$562$	264722.	−	1.89901e6i	0.0353549	−	0.253622i
$563$	−2.13361e6			−0.283690			−0.141845	−	0.989889i	$-0.545303\pi$
$563$	−2.13361e6			−0.283690			−0.141845	+	0.989889i	$0.545303\pi$
$564$	4.47147e6	+	4.60965e6i	0.591906	+	0.610197i
$565$	−2.40876e6	+	1.39070e6i	−0.317447	+	0.183278i
$566$	4.22138e6	+	3.29050e6i	0.553877	+	0.431739i
$567$	3.47341e6	−	2.00537e6i	0.453731	−	0.261962i
$568$	237033.	+	2.18464e6i	0.0308275	+	0.284125i
$569$		−	1.38715e6i		−	0.179615i	−0.995959	−	0.0898073i	$-0.971375\pi$
$569$		−	1.38715e6i		−	0.179615i	0.995959	−	0.0898073i	$-0.0286251\pi$
$570$	3.12090e6	+	8.46183e6i	0.402339	+	1.09088i
$571$		−	1.51901e7i		−	1.94971i	−0.222845	−	0.974854i	$-0.571534\pi$
$571$		−	1.51901e7i		−	1.94971i	0.222845	−	0.974854i	$-0.428466\pi$
$572$	−5.33278e6	−	2.11865e7i	−0.681497	−	2.70751i
$573$	−6.34852e6	+	3.66532e6i	−0.807767	+	0.466364i
$574$	−1.78398e6	+	2.28866e6i	−0.226001	+	0.289936i
$575$	−833420.	+	481175.i	−0.105122	+	0.0606923i
$576$	−1.40443e6	+	308391.i	−0.176378	+	0.0387299i
$577$	5.10365e6			0.638177			0.319089	−	0.947725i	$-0.396623\pi$
$577$	5.10365e6			0.638177			0.319089	+	0.947725i	$0.396623\pi$
$578$	704395.	+	98192.6i	0.0876995	+	0.0122253i
$579$	2.62937e6	+	1.51807e6i	0.325953	+	0.188189i
$580$	−2.79259e6	−	2.87889e6i	−0.344697	−	0.355349i
$581$	4.19152e6			0.515147
$582$	1.46909e6	−	1.05387e7i	0.179780	−	1.28967i
$583$	−1.26784e7	+	2.19597e7i	−1.54488	+	2.67581i
$584$	−1.24777e6	−	1.15002e7i	−0.151392	−	1.39532i
$585$	−2.25345e6	−	1.30103e6i	−0.272243	−	0.157180i
$586$	2.62160e6	−	1.06261e6i	0.315372	−	0.127829i
$587$	825444.	−	476570.i	0.0988764	−	0.0570863i	−0.449746	−	0.893156i	$-0.648486\pi$
$587$	825444.	−	476570.i	0.0988764	−	0.0570863i	0.548623	+	0.836070i	$0.315152\pi$
$588$	6.93705e6	+	1.97238e6i	0.827431	+	0.235259i
$589$	−5.67665e6	−	1.05954e7i	−0.674224	−	1.25843i
$590$	−6.22529e6	−	867805.i	−0.736257	−	0.102634i
$591$	−3.33533e6	−	5.77696e6i	−0.392799	−	0.680348i
$592$	1.16822e7	+	355603.i	1.37000	+	0.0417024i
$593$	−7.60192e6	+	1.31669e7i	−0.887741	+	1.53761i	−0.0452018	+	0.998978i	$0.514393\pi$
$593$	−7.60192e6	+	1.31669e7i	−0.887741	+	1.53761i	−0.842539	+	0.538635i	$0.818940\pi$
$594$	−1.21777e7	+	4.93597e6i	−1.41612	+	0.573993i
$595$	−3.81072e6	−	2.20012e6i	−0.441281	−	0.254774i
$596$	−2.98768e6	−	849471.i	−0.344523	−	0.0979564i
$597$			5.29322e6i			0.607833i
$598$	7.31588e6	−	9.38552e6i	0.836591	−	1.07326i
$599$	4.88616e6	−	8.46308e6i	0.556418	−	0.963743i	−0.441374	−	0.897323i	$-0.645509\pi$
$599$	4.88616e6	−	8.46308e6i	0.556418	−	0.963743i	0.997792	−	0.0664203i	$-0.0211578\pi$
$600$	1.27205e6	+	561244.i	0.144253	+	0.0636464i
$601$		−	6.17027e6i		−	0.696816i	−0.937343	−	0.348408i	$-0.886722\pi$
$601$		−	6.17027e6i		−	0.696816i	0.937343	−	0.348408i	$-0.113278\pi$
$602$	−537022.	+	688945.i	−0.0603950	+	0.0774807i
$603$	−482579.	−	835851.i	−0.0540474	−	0.0936129i
$604$	3.40512e6	−	3.30304e6i	0.379787	−	0.368402i
$605$	−9.37138e6	−	1.62317e7i	−1.04091	−	1.80292i
$606$	−2.35821e6	−	5.81802e6i	−0.260856	−	0.643566i
$607$	1.46736e7			1.61646			0.808229	−	0.588868i	$-0.200426\pi$
$607$	1.46736e7			1.61646			0.808229	+	0.588868i	$0.200426\pi$
$608$	6.82692e6	+	6.03964e6i	0.748973	+	0.662601i
$609$	−2.09974e6			−0.229415
$610$	−1.58137e6	−	3.90145e6i	−0.172071	−	0.424523i
$611$	5.87266e6	+	1.01717e7i	0.636402	+	1.10228i
$612$	−1.25304e6	+	1.21548e6i	−0.135234	+	0.131181i
$613$	−841706.	−	1.45788e6i	−0.0904710	−	0.156700i	0.817238	−	0.576300i	$-0.195504\pi$
$613$	−841706.	−	1.45788e6i	−0.0904710	−	0.156700i	−0.907709	+	0.419599i	$0.862171\pi$
$614$	−1.02953e7	+	1.32078e7i	−1.10209	+	1.41387i
$615$		−	8.78443e6i		−	0.936539i
$616$	6.74903e6	+	2.97775e6i	0.716621	+	0.316182i
$617$	1.33828e6	−	2.31797e6i	0.141525	−	0.245129i	−0.786546	−	0.617532i	$-0.788133\pi$
$617$	1.33828e6	−	2.31797e6i	0.141525	−	0.245129i	0.928071	+	0.372403i	$0.121466\pi$
$618$	−7.83151e6	+	1.00470e7i	−0.824848	+	1.05820i
$619$			9.26542e6i			0.971937i	0.873976	+	0.485969i	$0.161533\pi$
$619$			9.26542e6i			0.971937i	−0.873976	+	0.485969i	$0.838467\pi$
$620$	−1.40653e7	−	3.99910e6i	−1.46950	−	0.417814i
$621$	−6.19834e6	−	3.57861e6i	−0.644980	−	0.372380i
$622$	−9.60484e6	+	3.89312e6i	−0.995438	+	0.403479i
$623$	−1.95140e6	+	3.37992e6i	−0.201431	+	0.348888i
$624$	−1.71846e7	−	523097.i	−1.76677	−	0.0537800i
$625$	5.48855e6	+	9.50644e6i	0.562027	+	0.973459i
$626$	−1.68745e7	−	2.35231e6i	−1.72106	−	0.239916i
$627$	−1.55979e7	−	9.67833e6i	−1.58452	−	0.983176i
$628$	1.82546e7	+	5.19023e6i	1.84703	+	0.525155i
$629$	1.22886e7	−	7.09481e6i	1.23844	−	0.715013i
$630$	814239.	−	330034.i	0.0817335	−	0.0331289i
$631$	4.63627e6	+	2.67675e6i	0.463549	+	0.267630i	0.713535	−	0.700619i	$-0.247093\pi$
$631$	4.63627e6	+	2.67675e6i	0.463549	+	0.267630i	−0.249987	+	0.968249i	$0.580426\pi$
$632$	−852535.	−	7.85749e6i	−0.0849023	−	0.782512i
$633$	−5.87169e6	+	1.01701e7i	−0.582443	+	1.00882i
$634$	−343776.	+	2.46611e6i	−0.0339666	+	0.243663i
$635$	−1.33858e7			−1.31738
$636$	1.38936e7	+	1.43229e7i	1.36198	+	1.40407i
$637$	1.14229e7	+	6.59502e6i	1.11539	+	0.643972i
$638$	8.08512e6	+	1.12706e6i	0.786384	+	0.109622i
$639$	−532689.			−0.0516085
$640$	1.10551e7	−	860121.i	1.06687	−	0.0830060i
$641$	−9.15709e6	+	5.28685e6i	−0.880263	+	0.508220i	−0.870745	−	0.491735i	$-0.836363\pi$
$641$	−9.15709e6	+	5.28685e6i	−0.880263	+	0.508220i	−0.00951788	+	0.999955i	$0.503030\pi$
$642$	−3.50563e6	+	4.49737e6i	−0.335683	+	0.430647i
$643$	1.59879e7	−	9.23061e6i	1.52498	−	0.880447i	0.525417	−	0.850845i	$-0.323909\pi$
$643$	1.59879e7	−	9.23061e6i	1.52498	−	0.880447i	0.999562	−	0.0296016i	$-0.00942386\pi$
$644$	980773.	+	3.89649e6i	0.0931867	+	0.370219i
$645$		−	2.64433e6i		−	0.250275i
$646$	1.09064e7	+	1.87503e6i	1.02825	+	0.176777i
$647$		−	1.11197e7i		−	1.04432i	−0.852849	−	0.522158i	$-0.825127\pi$
$647$		−	1.11197e7i		−	1.04432i	0.852849	−	0.522158i	$-0.174873\pi$
$648$	1.32360e6	+	1.21991e7i	0.123828	+	1.14127i
$649$	1.10791e7	−	6.39651e6i	1.03250	−	0.596117i
$650$	2.00553e6	+	1.56328e6i	0.186186	+	0.145129i
$651$	−6.62969e6	+	3.82765e6i	−0.613113	+	0.353981i
$652$	−2.85018e6	−	2.93826e6i	−0.262575	−	0.270690i
$653$	−3.18943e6			−0.292705			−0.146353	−	0.989232i	$-0.546753\pi$
$653$	−3.18943e6			−0.292705			−0.146353	+	0.989232i	$0.546753\pi$
$654$	61663.2	−	442348.i	0.00563744	−	0.0404408i
$655$	−114999.	−	66394.6i	−0.0104735	−	0.00604685i
$656$	−4.20300e6	−	7.82005e6i	−0.381329	−	0.709496i
$657$	2.80413e6			0.253446
$658$	−3.92782e6	−	547537.i	−0.353661	−	0.0493002i
$659$	−9.89419e6	+	1.71372e7i	−0.887496	+	1.53719i	−0.0446709	+	0.999002i	$0.514224\pi$
$659$	−9.89419e6	+	1.71372e7i	−0.887496	+	1.53719i	−0.842825	+	0.538187i	$0.819109\pi$
$660$	−2.16555e7	+	5.45083e6i	−1.93512	+	0.487083i
$661$	7.46427e6	+	4.30950e6i	0.664483	+	0.383639i	0.793983	−	0.607940i	$-0.208004\pi$
$661$	7.46427e6	+	4.30950e6i	0.664483	+	0.383639i	−0.129500	+	0.991579i	$0.541337\pi$
$662$	−3.06192e6	−	7.55418e6i	−0.271550	−	0.669950i
$663$	−1.80767e7	+	1.04366e7i	−1.59711	+	0.922091i
$664$	−5.17653e6	+	1.17325e7i	−0.455636	+	1.03269i
$665$	−4.73248e6	−	2.93645e6i	−0.414988	−	0.257495i
$666$	−391165.	+	2.80606e6i	−0.0341723	+	0.245139i
$667$	2.22323e6	+	3.85075e6i	0.193495	+	0.335143i
$668$	−3.29928e6	−	1.31077e7i	−0.286074	−	1.13654i
$669$	5.15829e6	−	8.93442e6i	0.445595	−	0.771793i
$670$	2.79590e6	+	6.89786e6i	0.240622	+	0.593646i
$671$	7.42030e6	+	4.28411e6i	0.636231	+	0.367328i
$672$	3.70649e6	−	4.46775e6i	0.316621	−	0.381651i
$673$			6.17832e6i			0.525815i	0.964821	+	0.262907i	$0.0846814\pi$
$673$			6.17832e6i			0.525815i	−0.964821	+	0.262907i	$0.915319\pi$
$674$	1.23440e7	+	9.62199e6i	1.04666	+	0.815859i
$675$	764690.	−	1.32448e6i	0.0645991	−	0.111889i
$676$	−1.88164e7	−	5.34997e6i	−1.58369	−	0.450282i
$677$			1.99546e7i			1.67329i	0.547744	+	0.836646i	$0.315487\pi$
$677$			1.99546e7i			1.67329i	−0.547744	+	0.836646i	$0.684513\pi$
$678$	−3.51359e6	−	2.73879e6i	−0.293546	−	0.228815i
$679$	3.28542e6	+	5.69051e6i	0.273474	+	0.473671i
$680$	1.08646e7	−	7.94947e6i	0.901036	−	0.659274i
$681$	−205171.	−	355366.i	−0.0169530	−	0.0293635i
$682$	2.75824e7	−	1.11799e7i	2.27076	−	0.920403i
$683$	−8.07245e6			−0.662146			−0.331073	−	0.943605i	$-0.607411\pi$
$683$	−8.07245e6			−0.662146			−0.331073	+	0.943605i	$0.607411\pi$
$684$	−1.63404e6	+	1.48734e6i	−0.133543	+	0.121554i
$685$	1.62090e7			1.31987
$686$	−9.34079e6	+	3.78609e6i	−0.757832	+	0.307171i
$687$	5.65271e6	+	9.79079e6i	0.456946	+	0.791454i
$688$	−1.26521e6	−	2.35403e6i	−0.101904	−	0.189601i
$689$	1.82473e7	+	3.16053e7i	1.46437	+	2.53636i
$690$	−9.59329e6	−	7.47783e6i	−0.767087	−	0.597933i
$691$		−	4.58029e6i		−	0.364920i	−0.983213	−	0.182460i	$-0.941594\pi$
$691$		−	4.58029e6i		−	0.364920i	0.983213	−	0.182460i	$-0.0584061\pi$
$692$	313553.	−	1.10280e6i	0.0248912	−	0.0875448i
$693$	−894101.	+	1.54863e6i	−0.0707218	+	0.122494i
$694$	−9.10351e6	−	7.09605e6i	−0.717481	−	0.559265i
$695$		−	3.18350e6i		−	0.250002i
$696$	2.59318e6	−	5.87740e6i	0.202913	−	0.459899i
$697$	−9.33449e6	−	5.38927e6i	−0.727794	−	0.420192i
$698$	9.46512e6	+	2.33517e7i	0.735339	+	1.81418i
$699$	−4.62960e6	+	8.01870e6i	−0.358385	+	0.620741i
$700$	−832616.	+	209575.i	−0.0642243	+	0.0161657i
$701$	−986836.	−	1.70925e6i	−0.0758490	−	0.131374i	0.825606	−	0.564247i	$-0.190833\pi$
$701$	−986836.	−	1.70925e6i	−0.0758490	−	0.131374i	−0.901455	+	0.432872i	$0.857500\pi$
$702$	−2.61103e6	+	1.87305e7i	−0.199972	+	1.43452i
$703$	1.58311e7	−	8.48179e6i	1.20816	−	0.647290i
$704$	−1.66701e7	+	1.52137e7i	−1.26767	+	1.15692i
$705$	1.03969e7	−	6.00266e6i	0.787828	−	0.454853i
$706$	624303.	+	1.54024e6i	0.0471394	+	0.116299i
$707$	3.35732e6	+	1.93835e6i	0.252606	+	0.145842i
$708$	−2.45737e6	−	9.76285e6i	−0.184242	−	0.731970i
$709$	3.32347e6	−	5.75641e6i	0.248299	−	0.430067i	−0.714755	−	0.699375i	$-0.753462\pi$
$709$	3.32347e6	−	5.75641e6i	0.248299	−	0.430067i	0.963054	+	0.269308i	$0.0867950\pi$
$710$	4.06857e6	+	567158.i	0.302897	+	0.0422239i
$711$	1.91592e6			0.142136
$712$	−7.05078e6	−	9.63636e6i	−0.521239	−	0.712382i
$713$	1.40392e7	+	8.10552e6i	1.03423	+	0.597114i
$714$	973054.	−	6.98031e6i	0.0714318	−	0.512424i
$715$	−4.08411e7			−2.98767
$716$	−1.08920e7	+	1.05655e7i	−0.794005	+	0.770204i
$717$	1.21037e7	−	6.98808e6i	0.879267	−	0.507645i
$718$	4.08527e6	+	3.18441e6i	0.295740	+	0.230525i
$719$	9.07496e6	−	5.23943e6i	0.654670	−	0.377974i	−0.135573	−	0.990767i	$-0.543287\pi$
$719$	9.07496e6	−	5.23943e6i	0.654670	−	0.377974i	0.790243	+	0.612793i	$0.209954\pi$
$720$	−81783.5	+	2.68673e6i	−0.00587942	+	0.193149i
$721$		−	7.86651e6i		−	0.563565i
$722$	1.37221e7	+	2.81027e6i	0.979666	+	0.200634i
$723$		−	1.50151e7i		−	1.06827i
$724$	−6.08317e6	+	1.53117e6i	−0.431304	+	0.108562i
$725$	−822840.	+	475067.i	−0.0581394	+	0.0335668i
$726$	1.84557e7	−	2.36767e7i	1.29954	−	1.66717i
$727$	6.13678e6	−	3.54307e6i	0.430631	−	0.248625i	−0.268985	−	0.963144i	$-0.586688\pi$
$727$	6.13678e6	−	3.54307e6i	0.430631	−	0.248625i	0.699615	+	0.714520i	$0.253355\pi$
$728$	8.56825e6	−	6.26926e6i	0.599189	−	0.438417i
$729$	1.09065e7			0.760090
$730$	−2.14174e7	−	2.98558e6i	−1.48751	−	0.207358i
$731$	−2.80991e6	−	1.62230e6i	−0.194491	−	0.112289i
$732$	4.83980e6	−	4.69471e6i	0.333848	−	0.323841i
$733$	−1.66167e7			−1.14232			−0.571158	−	0.820840i	$-0.693506\pi$
$733$	−1.66167e7			−1.14232			−0.571158	+	0.820840i	$0.693506\pi$
$734$	1.04840e6	−	7.52082e6i	0.0718269	−	0.515258i
$735$	6.74101e6	−	1.16758e7i	0.460263	−	0.797200i
$736$	−1.21180e7	−	2.06688e6i	−0.824584	−	0.140644i
$737$	−1.31193e7	−	7.57442e6i	−0.889695	−	0.513666i
$738$	1.99450e6	−	808429.i	0.134801	−	0.0546388i
$739$	−3.67393e6	+	2.12115e6i	−0.247469	+	0.142876i	−0.618605	−	0.785702i	$-0.712302\pi$
$739$	−3.67393e6	+	2.12115e6i	−0.247469	+	0.142876i	0.371136	+	0.928579i	$0.378968\pi$
$740$	5.97527e6	−	2.10157e7i	0.401124	−	1.41079i
$741$	−2.32878e7	+	1.24768e7i	−1.55806	+	0.834754i
$742$	−1.22044e7	−	1.70129e6i	−0.813778	−	0.113441i
$743$	7.88817e6	+	1.36627e7i	0.524209	+	0.907956i	0.999603	+	0.0281832i	$0.00897216\pi$
$743$	7.88817e6	+	1.36627e7i	0.524209	+	0.907956i	−0.475394	+	0.879773i	$0.657695\pi$
$744$	−2.52635e6	−	2.32844e7i	−0.167325	−	1.54217i
$745$	−2.90324e6	+	5.02856e6i	−0.191643	+	0.331935i
$746$	−1.66818e7	+	6.76162e6i	−1.09748	+	0.444840i
$747$	−2.69214e6	−	1.55431e6i	−0.176521	−	0.101914i
$748$	−7.49355e6	+	2.63556e7i	−0.489704	+	1.72234i
$749$		−	3.52130e6i		−	0.229350i
$750$	−9.41355e6	+	1.20766e7i	−0.611083	+	0.783958i
$751$	−4.78225e6	+	8.28310e6i	−0.309409	+	0.535912i	−0.978233	−	0.207509i	$-0.933464\pi$
$751$	−4.78225e6	+	8.28310e6i	−0.309409	+	0.535912i	0.668824	+	0.743420i	$0.266798\pi$
$752$	6.38347e6	−	1.03182e7i	0.411635	−	0.665362i
$753$		−	3.76145e6i		−	0.241751i
$754$	7.22300e6	−	9.26638e6i	0.462689	−	0.593583i
$755$	−4.43412e6	−	7.68012e6i	−0.283100	−	0.490344i
$756$	−4.44602e6	−	4.58341e6i	−0.282922	−	0.291665i
$757$	9.83503e6	+	1.70348e7i	0.623787	+	1.08043i	0.988774	+	0.149418i	$0.0477399\pi$
$757$	9.83503e6	+	1.70348e7i	0.623787	+	1.08043i	−0.364988	+	0.931012i	$0.618927\pi$
$758$	−612858.	−	1.51200e6i	−0.0387425	−	0.0955829i
$759$	2.47566e7			1.55986
$760$	1.40640e7	−	9.62022e6i	0.883235	−	0.604158i
$761$	1.18510e7			0.741809			0.370904	−	0.928671i	$-0.379048\pi$
$761$	1.18510e7			0.741809			0.370904	+	0.928671i	$0.379048\pi$
$762$	−8.05373e6	−	1.98696e7i	−0.502470	−	1.23966i
$763$	137901.	+	238852.i	0.00857546	+	0.0148531i
$764$	9.64309e6	+	9.94109e6i	0.597700	+	0.616170i
$765$	1.63170e6	+	2.82620e6i	0.100806	+	0.174602i
$766$	1.20151e7	−	1.54141e7i	0.739869	−	0.949176i
$767$		−	1.84122e7i		−	1.13010i
$768$	7.92820e6	+	1.58925e7i	0.485034	+	0.972277i
$769$	8.61552e6	−	1.49225e7i	0.525370	−	0.909968i	−0.474193	−	0.880421i	$-0.657260\pi$
$769$	8.61552e6	−	1.49225e7i	0.525370	−	0.909968i	0.999563	−	0.0295472i	$-0.00940653\pi$
$770$	8.47780e6	−	1.08761e7i	0.515295	−	0.661071i
$771$			2.78722e7i			1.68864i
$772$	1.56875e6	−	5.51746e6i	0.0947350	−	0.333193i
$773$	−2.48173e7	−	1.43283e7i	−1.49385	−	0.862474i	−0.493874	−	0.869534i	$-0.664420\pi$
$773$	−2.48173e7	−	1.43283e7i	−1.49385	−	0.862474i	−0.999975	+	0.00705956i	$0.997753\pi$
$774$	600395.	−	243357.i	0.0360234	−	0.0146013i
$775$	−1.73202e6	+	2.99994e6i	−0.103585	+	0.179415i
$776$	−1.99858e7	+	2.16846e6i	−1.19143	+	0.129270i
$777$	−5.71910e6	−	9.90577e6i	−0.339840	−	0.588621i
$778$	−1.00964e6	−	140744.i	−0.0598023	−	0.00833643i
$779$	−1.15924e7	−	7.19292e6i	−0.684429	−	0.424680i
$780$	−8.78971e6	+	3.09143e7i	−0.517295	+	1.81938i
$781$	−7.24078e6	+	4.18047e6i	−0.424774	+	0.245243i
$782$	−1.38316e7	+	5.60633e6i	−0.808825	+	0.327840i
$783$	−6.11966e6	−	3.53319e6i	−0.356716	−	0.205950i
$784$	414568.	−	1.36193e7i	0.0240882	−	0.791341i
$785$	1.77387e7	−	3.07243e7i	1.02742	−	1.77954i
$786$	29364.5	−	210649.i	0.00169538	−	0.0121620i
$787$	2.40808e7			1.38591			0.692953	−	0.720982i	$-0.256309\pi$
$787$	2.40808e7			1.38591			0.692953	+	0.720982i	$0.256309\pi$
$788$	−9.04610e6	+	8.77493e6i	−0.518974	+	0.503417i
$789$	9.08773e6	+	5.24680e6i	0.519712	+	0.300056i
$790$	−1.46334e7	−	2.03989e6i	−0.834213	−	0.116289i
$791$	2.75103e6			0.156334
$792$	−3.23056e6	−	4.41524e6i	−0.183006	−	0.250116i
$793$	1.06796e7	−	6.16586e6i	0.603075	−	0.348185i
$794$	1.02111e7	−	1.30998e7i	0.574805	−	0.737416i
$795$	3.23049e7	−	1.86512e7i	1.81280	−	1.04662i
$796$	9.69795e6	−	2.44104e6i	0.542497	−	0.136550i
$797$			1.34485e7i			0.749942i	0.927037	+	0.374971i	$0.122347\pi$
$797$			1.34485e7i			0.749942i	−0.927037	+	0.374971i	$0.877653\pi$
$798$	1.51145e6	−	8.79157e6i	0.0840210	−	0.488719i
$799$		−	1.47306e7i		−	0.816306i
$800$	441658.	−	2.58940e6i	0.0243984	−	0.143046i
$801$	2.50669e6	−	1.44724e6i	0.138045	−	0.0797001i
$802$	−2.59183e7	−	2.02029e7i	−1.42289	−	1.10912i
$803$	3.81163e7	−	2.20064e7i	2.08603	−	1.20437i
$804$	−8.55689e6	+	8.30038e6i	−0.466848	+	0.452854i
$805$	7.51125e6			0.408529
$806$	5.91396e6	−	4.24245e7i	0.320657	−	2.30027i
$807$	−1.26752e7	−	7.31803e6i	−0.685127	−	0.395558i
$808$	−9.57193e6	+	7.00363e6i	−0.515788	+	0.377394i
$809$	1.05422e7			0.566318			0.283159	−	0.959073i	$-0.408618\pi$
$809$	1.05422e7			0.566318			0.283159	+	0.959073i	$0.408618\pi$
$810$	2.27189e7	+	3.16702e6i	1.21668	+	0.169605i
$811$	1.70254e7	−	2.94888e7i	0.908959	−	1.57436i	0.0934458	−	0.995624i	$-0.470212\pi$
$811$	1.70254e7	−	2.94888e7i	0.908959	−	1.57436i	0.815513	−	0.578739i	$-0.196455\pi$
$812$	968322.	+	3.84703e6i	0.0515383	+	0.204755i
$813$	9.78273e6	+	5.64806e6i	0.519079	+	0.299690i
$814$	1.67045e7	+	4.12123e7i	0.883635	+	2.18005i
$815$	−6.62715e6	+	3.82619e6i	−0.349489	+	0.201777i
$816$	1.83369e7	+	1.13444e7i	0.964052	+	0.596423i
$817$	−3.48959e6	−	2.16525e6i	−0.182902	−	0.113489i
$818$	−3.90176e6	+	2.79897e7i	−0.203881	+	1.46257i
$819$	1.28682e6	+	2.22885e6i	0.0670362	+	0.116110i
$820$	−1.60943e7	+	4.05105e6i	−0.835870	+	0.210394i
$821$	−1.19743e7	+	2.07401e7i	−0.620002	+	1.07388i	0.369482	+	0.929238i	$0.379535\pi$
$821$	−1.19743e7	+	2.07401e7i	−0.620002	+	1.07388i	−0.989485	+	0.144638i	$0.953798\pi$
$822$	9.75237e6	+	2.40604e7i	0.503420	+	1.24201i
$823$	−1.23248e7	−	7.11573e6i	−0.634280	−	0.366202i	0.148128	−	0.988968i	$-0.452675\pi$
$823$	−1.23248e7	−	7.11573e6i	−0.634280	−	0.366202i	−0.782408	+	0.622767i	$0.786009\pi$
$824$	2.20192e7	+	9.71514e6i	1.12975	+	0.498461i
$825$			5.29006e6i			0.270599i
$826$	4.90324e6	+	3.82200e6i	0.250054	+	0.194913i
$827$	−1.03143e7	+	1.78650e7i	−0.524418	+	0.908319i	0.475177	+	0.879890i	$0.342384\pi$
$827$	−1.03143e7	+	1.78650e7i	−0.524418	+	0.908319i	−0.999596	+	0.0284294i	$0.990949\pi$
$828$	814971.	−	2.86634e6i	0.0413110	−	0.145295i
$829$			1.16837e7i			0.590464i	0.955426	+	0.295232i	$0.0953969\pi$
$829$			1.16837e7i			0.590464i	−0.955426	+	0.295232i	$0.904603\pi$
$830$	1.89071e7	+	1.47378e7i	0.952642	+	0.742570i
$831$	9.91513e6	+	1.71735e7i	0.498076	+	0.862694i
$832$	6.96653e6	+	3.17260e7i	0.348906	+	1.58894i
$833$	−8.27125e6	−	1.43262e7i	−0.413008	−	0.715351i
$834$	4.72553e6	−	1.91539e6i	0.235253	−	0.0953549i
$835$	−2.52676e7			−1.25414
$836$	−1.05389e7	+	3.30410e7i	−0.521531	+	1.63507i
$837$	−2.57628e7			−1.27110
$838$	−2.28731e7	+	9.27113e6i	−1.12516	+	0.456060i
$839$	1.44585e7	+	2.50429e7i	0.709118	+	1.22823i	0.965185	+	0.261570i	$0.0842402\pi$
$839$	1.44585e7	+	2.50429e7i	0.709118	+	1.22823i	−0.256066	+	0.966659i	$0.582427\pi$
$840$	−6.40804e6	−	8.75793e6i	−0.313348	−	0.428256i
$841$	−8.06057e6	−	1.39613e7i	−0.392985	−	0.680670i
$842$	5.16477e6	+	4.02586e6i	0.251056	+	0.195694i
$843$		−	5.74094e6i		−	0.278236i
$844$	2.13408e7	+	6.06772e6i	1.03123	+	0.293204i
$845$	−1.82846e7	+	3.16699e7i	−0.880936	+	1.52583i
$846$	2.31973e6	+	1.80819e6i	0.111432	+	0.0868598i
$847$			1.85382e7i			0.887888i
$848$	1.98345e7	−	3.20603e7i	0.947177	−	1.53101i
$849$	1.38787e7	+	8.01288e6i	0.660815	+	0.381522i
$850$	−1.19798e6	−	2.95558e6i	−0.0568725	−	0.140312i
$851$	−1.21109e7	+	2.09767e7i	−0.573261	+	0.992917i
$852$	1.60603e6	+	6.38055e6i	0.0757973	+	0.301134i
$853$	−256127.	−	443625.i	−0.0120527	−	0.0208758i	0.859936	−	0.510402i	$-0.170503\pi$
$853$	−256127.	−	443625.i	−0.0120527	−	0.0208758i	−0.871989	+	0.489526i	$0.837170\pi$
$854$	−574874.	+	4.12392e6i	−0.0269729	+	0.193493i
$855$	1.95069e6	+	3.64093e6i	0.0912584	+	0.170332i
$856$	9.85650e6	+	4.34881e6i	0.459768	+	0.202855i
$857$	−1.08070e7	+	6.23943e6i	−0.502636	+	0.290197i	−0.729802	−	0.683659i	$-0.760388\pi$
$857$	−1.08070e7	+	6.23943e6i	−0.502636	+	0.290197i	0.227165	+	0.973856i	$0.427054\pi$
$858$	−2.45726e7	−	6.06239e7i	−1.13955	−	2.81142i
$859$	−6.09380e6	−	3.51826e6i	−0.281777	−	0.162684i	0.352451	−	0.935830i	$-0.385348\pi$
$859$	−6.09380e6	−	3.51826e6i	−0.281777	−	0.162684i	−0.634228	+	0.773146i	$0.718682\pi$
$860$	−4.84480e6	+	1.21947e6i	−0.223372	+	0.0562243i
$861$	−4.34427e6	+	7.52449e6i	−0.199714	+	0.345915i
$862$	−4.01872e7	−	5.60210e6i	−1.84213	−	0.256792i
$863$	−1.60000e7			−0.731296			−0.365648	−	0.930753i	$-0.619153\pi$
$863$	−1.60000e7			−0.731296			−0.365648	+	0.930753i	$0.619153\pi$
$864$	1.83203e7	−	6.78436e6i	0.834926	−	0.309189i
$865$	−1.85612e6	−	1.07163e6i	−0.0843462	−	0.0486973i
$866$	3.38037e6	−	2.42495e7i	0.153169	−	1.09877i
$867$	2.12947e6			0.0962108
$868$	1.00702e7	+	1.03814e7i	0.453668	+	0.467687i
$869$	2.60429e7	−	1.50359e7i	1.16987	−	0.675427i
$870$	−9.47151e6	−	7.38290e6i	−0.424249	−	0.330696i
$871$	−1.88818e7	+	1.09014e7i	−0.843330	+	0.486897i
$872$	−838881.	+	91018.4i	−0.0373602	+	0.00405357i
$873$		−	4.87321e6i		−	0.216411i
$874$	−1.77233e7	+	6.53674e6i	−0.784815	+	0.289456i
$875$		−	9.45563e6i		−	0.417513i
$876$	−8.45430e6	−	3.35879e7i	−0.372235	−	1.47885i
$877$	−4.68068e6	+	2.70239e6i	−0.205499	+	0.118645i	−0.599218	−	0.800586i	$-0.704522\pi$
$877$	−4.68068e6	+	2.70239e6i	−0.205499	+	0.118645i	0.393719	+	0.919231i	$0.371188\pi$
$878$	4.40898e6	−	5.65627e6i	0.193020	−	0.247625i
$879$	7.33507e6	−	4.23491e6i	0.320208	−	0.184872i
$880$	1.99734e7	+	3.71623e7i	0.869453	+	1.61769i
$881$	−2.07902e7			−0.902443			−0.451221	−	0.892412i	$-0.649012\pi$
$881$	−2.07902e7			−0.902443			−0.451221	+	0.892412i	$0.649012\pi$
$882$	3.27135e6	+	456026.i	0.141598	+	0.0197387i
$883$	−3.63494e7	−	2.09863e7i	−1.56890	−	0.905805i	−0.996298	−	0.0859715i	$-0.972601\pi$
$883$	−3.63494e7	−	2.09863e7i	−1.56890	−	0.905805i	−0.572602	−	0.819833i	$-0.694066\pi$
$884$	2.74576e7	+	2.83061e7i	1.18177	+	1.21829i
$885$	−1.88198e7			−0.807712
$886$	−1.97050e6	+	1.41356e7i	−0.0843320	+	0.604965i
$887$	−1.12407e7	+	1.94695e7i	−0.479717	+	0.830894i	−0.999729	−	0.0232645i	$-0.992594\pi$
$887$	−1.12407e7	+	1.94695e7i	−0.479717	+	0.830894i	0.520012	+	0.854159i	$0.325927\pi$
$888$	3.47904e7	−	3.77475e6i	1.48056	−	0.160641i
$889$	1.14659e7	+	6.61983e6i	0.486579	+	0.280926i
$890$	−2.06865e7	+	8.38482e6i	−0.875410	+	0.354829i
$891$	−4.04326e7	+	2.33438e7i	−1.70623	+	0.985093i
$892$	−1.87480e7	−	5.33051e6i	−0.788936	−	0.224314i
$893$	591856.	−	1.86354e7i	0.0248363	−	0.782006i
$894$	−9.21109e6	−	1.28402e6i	−0.385449	−	0.0537316i
$895$	1.41834e7	+	2.45664e7i	0.591867	+	1.02514i
$896$	−9.89486e6	−	4.73046e6i	−0.411756	−	0.196849i
$897$	1.78153e7	−	3.08570e7i	0.739285	−	1.28048i
$898$	3.75487e7	−	1.52196e7i	1.55383	−	0.629813i
$899$	1.38610e7	+	8.00263e6i	0.571997	+	0.330243i
$900$	612488.	+	174146.i	0.0252053	+	0.00716649i
$901$		−	4.57703e7i		−	1.87833i
$902$	2.07666e7	−	2.66415e7i	0.849864	−	1.09029i
$903$	−1.30773e6	+	2.26506e6i	−0.0533703	+	0.0924401i
$904$	−3.39752e6	+	7.70043e6i	−0.138274	+	0.313396i
$905$			1.17265e7i			0.475934i
$906$	8.73240e6	−	1.12028e7i	0.353438	−	0.453425i
$907$	−4.51590e6	−	7.82177e6i	−0.182275	−	0.315709i	0.760380	−	0.649478i	$-0.225013\pi$
$907$	−4.51590e6	−	7.82177e6i	−0.182275	−	0.315709i	−0.942655	+	0.333769i	$0.891679\pi$
$908$	−556465.	+	539784.i	−0.0223987	+	0.0217273i
$909$	−1.43756e6	−	2.48993e6i	−0.0577055	−	0.0999488i
$910$	−7.45543e6	−	1.83936e7i	−0.298449	−	0.736313i
$911$	1.40864e7			0.562345			0.281172	−	0.959657i	$-0.409277\pi$
$911$	1.40864e7			0.562345			0.281172	+	0.959657i	$0.409277\pi$
$912$	2.27419e7	+	1.50883e7i	0.905399	+	0.600694i
$913$	−4.87919e7			−1.93718
$914$	1.08688e7	+	2.68149e7i	0.430346	+	1.06172i
$915$	−6.30235e6	−	1.09160e7i	−0.248857	−	0.431033i
$916$	1.53313e7	−	1.48717e7i	0.603727	−	0.585630i
$917$	65669.8	+	113743.i	0.00257895	+	0.00446687i
$918$	1.45816e7	−	1.87066e7i	0.571080	−	0.732638i
$919$		−	2.05878e7i		−	0.804120i	−0.915613	−	0.402060i	$-0.868294\pi$
$919$		−	2.05878e7i		−	0.804120i	0.915613	−	0.402060i	$-0.131706\pi$
$920$	−9.27639e6	+	2.10248e7i	−0.361334	+	0.818959i
$921$	−2.50706e7	+	4.34235e7i	−0.973901	+	1.68685i
$922$	−6.80492e6	+	8.73002e6i	−0.263631	+	0.338211i
$923$			1.20334e7i			0.464925i
$924$	2.12452e7	+	6.04052e6i	0.818616	+	0.232753i
$925$	−4.48237e6	−	2.58790e6i	−0.172248	−	0.0994472i
$926$	1.05838e7	−	4.28992e6i	0.405615	−	0.164408i
$927$	−2.91707e6	+	5.05251e6i	−0.111493	+	0.193112i
$928$	−1.19641e7	−	2.04064e6i	−0.456048	−	0.0777851i
$929$	−7.33493e6	−	1.27045e7i	−0.278841	−	0.482967i	0.692256	−	0.721652i	$-0.256617\pi$
$929$	−7.33493e6	−	1.27045e7i	−0.278841	−	0.482967i	−0.971097	+	0.238685i	$0.923284\pi$
$930$	−4.33636e7	−	6.04488e6i	−1.64406	−	0.229182i
$931$	−9.88821e6	−	1.84562e7i	−0.373890	−	0.697859i
$932$	1.68264e7	+	4.78416e6i	0.634529	+	0.180412i
$933$	−2.68737e7	+	1.55155e7i	−1.01070	+	0.583529i
$934$	−8.45556e6	+	3.42728e6i	−0.317158	+	0.128553i
$935$	4.43592e7	+	2.56108e7i	1.65941	+	0.958062i
$936$	−7.82801e6	+	849336.i	−0.292053	+	0.0316876i
$937$	5.03203e6	−	8.71573e6i	0.187238	−	0.324306i	−0.757090	−	0.653310i	$-0.773380\pi$
$937$	5.03203e6	−	8.71573e6i	0.187238	−	0.324306i	0.944328	+	0.329004i	$0.106713\pi$
$938$	1.01639e6	−	7.29120e6i	0.0377185	−	0.270578i
$939$	−5.10137e7			−1.88809
$940$	−1.57924e7	−	1.62804e7i	−0.582946	−	0.600961i
$941$	2.48114e6	+	1.43249e6i	0.0913435	+	0.0527372i	0.544976	−	0.838452i	$-0.316539\pi$
$941$	2.48114e6	+	1.43249e6i	0.0913435	+	0.0527372i	−0.453632	+	0.891189i	$0.649872\pi$
$942$	5.62794e7	+	7.84534e6i	2.06644	+	0.288061i
$943$	1.83990e7			0.673777
$944$	−1.67537e7	+	9.00452e6i	−0.611900	+	0.328875i
$945$	−1.03377e7	+	5.96849e6i	−0.376570	+	0.217413i
$946$	6.25127e6	−	8.01975e6i	0.227112	−	0.291362i
$947$	−1.91798e7	+	1.10735e7i	−0.694976	+	0.401244i	−0.805473	−	0.592632i	$-0.798089\pi$
$947$	−1.91798e7	+	1.10735e7i	−0.694976	+	0.401244i	0.110498	+	0.993876i	$0.464756\pi$
$948$	−5.77639e6	−	2.29489e7i	−0.208754	−	0.829356i
$949$		−	6.33450e7i		−	2.28322i
$950$	−1.39679e6	−	3.78718e6i	−0.0502138	−	0.136147i
$951$			7.45535e6i			0.267311i
$952$	−1.32377e7	+	1.43628e6i	−0.473390	+	0.0513627i
$953$	−2.99314e7	+	1.72809e7i	−1.06756	+	0.616359i	−0.927515	−	0.373786i	$-0.878060\pi$
$953$	−2.99314e7	+	1.72809e7i	−1.06756	+	0.616359i	−0.140050	+	0.990144i	$0.544726\pi$
$954$	7.20777e6	+	5.61835e6i	0.256407	+	0.199866i
$955$	2.24218e7	−	1.29452e7i	0.795540	−	0.459305i
$956$	−1.83850e7	−	1.89531e7i	−0.650606	−	0.670711i
$957$	2.44423e7			0.862704
$958$	−6.23987e6	+	4.47624e7i	−0.219665	+	1.57579i
$959$	−1.38842e7	−	8.01604e6i	−0.487499	−	0.281458i
$960$	3.24283e7	−	7.12075e6i	1.13565	−	0.249372i
$961$	2.97234e7			1.03822
$962$	6.33886e7	+	8.83637e6i	2.20838	+	0.307848i
$963$	−1.30577e6	+	2.26167e6i	−0.0453735	+	0.0785892i
$964$	−2.75098e7	+	6.92441e6i	−0.953445	+	0.239988i
$965$	−9.28645e6	−	5.36153e6i	−0.321019	−	0.185341i
$966$	4.51924e6	+	1.11496e7i	0.155820	+	0.384428i
$967$	−2.56084e7	+	1.47850e7i	−0.880676	+	0.508458i	−0.870881	−	0.491494i	$-0.836451\pi$
$967$	−2.56084e7	+	1.47850e7i	−0.880676	+	0.508458i	−0.00979452	+	0.999952i	$0.503118\pi$
$968$	−5.18903e7	−	2.28946e7i	−1.77991	−	0.785317i
$969$	3.31178e7	+	1.05182e6i	1.13306	+	0.0359857i
$970$	−5.18855e6	+	3.72206e7i	−0.177058	+	1.27015i
$971$	1.20235e7	+	2.08253e7i	0.409245	+	0.708833i	0.994805	−	0.101796i	$-0.0324588\pi$
$971$	1.20235e7	+	2.08253e7i	0.409245	+	0.708833i	−0.585560	+	0.810629i	$0.699125\pi$
$972$	2.56668e6	+	1.01971e7i	0.0871377	+	0.346188i
$973$	−1.57437e6	+	2.72689e6i	−0.0533121	+	0.0923392i
$974$	1.37269e7	+	3.38662e7i	0.463635	+	1.14385i
$975$	6.59363e6	+	3.80683e6i	0.222133	+	0.128248i
$976$	−1.08333e7	−	6.70218e6i	−0.364030	−	0.225212i
$977$			3.23461e7i			1.08414i	0.840333	+	0.542070i	$0.182359\pi$
$977$			3.23461e7i			1.08414i	−0.840333	+	0.542070i	$0.817641\pi$
$978$	−9.66684e6	−	7.53516e6i	−0.323175	−	0.251910i
$979$	2.27155e7	−	3.93443e7i	0.757469	−	1.31197i
$980$	−2.45004e7	−	6.96607e6i	−0.814907	−	0.231698i
$981$		−	204547.i		−	0.00678611i
$982$	−1.73844e7	−	1.35509e7i	−0.575284	−	0.448425i
$983$	7.82230e6	+	1.35486e7i	0.258197	+	0.447210i	0.965759	−	0.259441i	$-0.0835384\pi$
$983$	7.82230e6	+	1.35486e7i	0.258197	+	0.447210i	−0.707562	+	0.706651i	$0.750205\pi$
$984$	−1.56967e7	−	2.14528e7i	−0.516797	−	0.706312i
$985$	1.17798e7	+	2.04032e7i	0.386853	+	0.670050i
$986$	−1.36560e7	+	5.53516e6i	−0.447333	+	0.181317i
$987$	−1.18743e7			−0.387984
$988$	3.35988e7	+	3.69128e7i	1.09504	+	1.20305i
$989$	5.53857e6			0.180056
$990$	−9.47824e6	+	3.84180e6i	−0.307355	+	0.124580i
$991$	1.41791e7	+	2.45589e7i	0.458632	+	0.794375i	0.998889	−	0.0471257i	$-0.0150061\pi$
$991$	1.41791e7	+	2.45589e7i	0.458632	+	0.794375i	−0.540257	+	0.841500i	$0.681673\pi$
$992$	−4.14953e7	+	1.53665e7i	−1.33881	+	0.495788i
$993$	−1.22029e7	−	2.11361e7i	−0.392727	−	0.680223i
$994$	−3.20454e6	−	2.49789e6i	−0.102872	−	0.0801875i
$995$		−	1.86947e7i		−	0.598633i
$996$	−1.05009e7	+	3.69326e7i	−0.335410	+	1.17967i
$997$	1.34326e7	−	2.32660e7i	0.427979	−	0.741282i	−0.568714	−	0.822535i	$-0.692559\pi$
$997$	1.34326e7	−	2.32660e7i	0.427979	−	0.741282i	0.996693	+	0.0812531i	$0.0258922\pi$
$998$	2.37461e7	+	1.85098e7i	0.754686	+	0.588267i
$999$		−	3.84936e7i		−	1.22032i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.6.f.a.31.20	yes	96
4.3	odd	2	inner	76.6.f.a.31.35	yes	96
19.8	odd	6	inner	76.6.f.a.27.35	yes	96
76.27	even	6	inner	76.6.f.a.27.20	✓	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.6.f.a.27.20	✓	96	76.27	even	6	inner
76.6.f.a.27.35	yes	96	19.8	odd	6	inner
76.6.f.a.31.20	yes	96	1.1	even	1	trivial
76.6.f.a.31.35	yes	96	4.3	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	76.f (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.12496 - 5.24257i) q^{2} +(-8.46878 - 14.6684i) q^{3} +(-22.9691 + 22.2805i) q^{4} +(29.9102 + 51.8059i) q^{5} +(-58.9040 + 75.5679i) q^{6} -59.1673i q^{7} +(165.616 + 73.0716i) q^{8} +(-21.9405 + 38.0021i) q^{9} +O(q^{10})\)	\(q+(-2.12496 - 5.24257i) q^{2} +(-8.46878 - 14.6684i) q^{3} +(-22.9691 + 22.2805i) q^{4} +(29.9102 + 51.8059i) q^{5} +(-58.9040 + 75.5679i) q^{6} -59.1673i q^{7} +(165.616 + 73.0716i) q^{8} +(-21.9405 + 38.0021i) q^{9} +(208.038 - 266.892i) q^{10} +688.744i q^{11} +(521.339 + 148.230i) q^{12} +(858.463 + 495.634i) q^{13} +(-310.189 + 125.728i) q^{14} +(506.605 - 877.466i) q^{15} +(31.1559 - 1023.53i) q^{16} +(-621.607 - 1076.66i) q^{17} +(245.851 + 34.2716i) q^{18} +(-743.126 - 1387.03i) q^{19} +(-1841.27 - 523.519i) q^{20} +(-867.888 + 501.075i) q^{21} +(3610.79 - 1463.56i) q^{22} +(1837.86 + 1061.09i) q^{23} +(-330.722 - 3048.14i) q^{24} +(-226.737 + 392.720i) q^{25} +(774.192 - 5553.75i) q^{26} -3372.59 q^{27} +(1318.28 + 1359.02i) q^{28} +(1814.53 + 1047.62i) q^{29} +(-5676.70 - 791.331i) q^{30} +7638.88 q^{31} +(-5432.11 + 2011.62i) q^{32} +(10102.7 - 5832.82i) q^{33} +(-4323.55 + 5546.67i) q^{34} +(3065.22 - 1769.70i) q^{35} +(-342.753 - 1361.72i) q^{36} +11413.7i q^{37} +(-5692.51 + 6843.29i) q^{38} -16789.7i q^{39} +(1168.05 + 10765.5i) q^{40} +(7508.35 - 4334.95i) q^{41} +(4471.15 + 3485.19i) q^{42} +(2260.20 - 1304.93i) q^{43} +(-15345.6 - 15819.8i) q^{44} -2624.98 q^{45} +(1657.45 - 11889.9i) q^{46} +(10261.3 + 5924.39i) q^{47} +(-15277.3 + 8211.01i) q^{48} +13306.2 q^{49} +(2540.67 + 354.169i) q^{50} +(-10528.5 + 18235.9i) q^{51} +(-30761.1 + 7742.76i) q^{52} +(31883.7 + 18408.1i) q^{53} +(7166.63 + 17681.0i) q^{54} +(-35681.0 + 20600.5i) q^{55} +(4323.45 - 9799.03i) q^{56} +(-14052.1 + 22646.9i) q^{57} +(1636.41 - 11738.9i) q^{58} +(-9287.21 - 16085.9i) q^{59} +(7914.16 + 31442.0i) q^{60} +(6220.18 - 10773.7i) q^{61} +(-16232.3 - 40047.4i) q^{62} +(2248.48 + 1298.16i) q^{63} +(22089.1 + 24203.6i) q^{64} +59298.0i q^{65} +(-52046.9 - 40569.8i) q^{66} +(-10997.4 + 19048.1i) q^{67} +(38266.2 + 10880.0i) q^{68} -35944.5i q^{69} +(-15791.3 - 12309.1i) q^{70} +(6069.69 + 10513.0i) q^{71} +(-6410.56 + 4690.51i) q^{72} +(-31951.5 - 55341.7i) q^{73} +(59836.9 - 24253.6i) q^{74} +7680.74 q^{75} +(47972.8 + 15301.6i) q^{76} +40751.1 q^{77} +(-88020.9 + 35677.4i) q^{78} +(-21830.8 - 37812.1i) q^{79} +(53956.6 - 28999.8i) q^{80} +(33893.3 + 58704.9i) q^{81} +(-38681.2 - 30151.4i) q^{82} +70841.8i q^{83} +(8770.35 - 30846.2i) q^{84} +(37184.8 - 64405.9i) q^{85} +(-11644.0 - 9076.33i) q^{86} -35488.2i q^{87} +(-50327.6 + 114067. i) q^{88} +(-57124.7 - 32981.0i) q^{89} +(5577.98 + 13761.6i) q^{90} +(29325.3 - 50792.9i) q^{91} +(-65855.5 + 16576.3i) q^{92} +(-64692.0 - 112050. i) q^{93} +(9254.05 - 66384.9i) q^{94} +(49629.6 - 79984.8i) q^{95} +(75510.5 + 62644.2i) q^{96} +(-96176.6 + 55527.6i) q^{97} +(-28275.2 - 69758.8i) q^{98} +(-26173.7 - 15111.4i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 3 q^{2} - 11 q^{4} - 2 q^{5} - 27 q^{6} - 3588 q^{9}+O(q^{10}) \) 96 * q - 3 * q^2 - 11 * q^4 - 2 * q^5 - 27 * q^6 - 3588 * q^9	\( 96 q - 3 q^{2} - 11 q^{4} - 2 q^{5} - 27 q^{6} - 3588 q^{9} + 648 q^{10} - 354 q^{13} + 2154 q^{14} - 611 q^{16} - 1006 q^{17} + 10524 q^{20} + 7824 q^{21} + 93 q^{22} - 5311 q^{24} - 25002 q^{25} - 13428 q^{26} + 1556 q^{28} - 6 q^{29} - 12656 q^{30} - 30453 q^{32} + 8586 q^{33} + 30102 q^{34} - 2306 q^{36} + 29846 q^{38} - 1392 q^{40} + 29064 q^{41} + 18616 q^{42} + 9155 q^{44} + 13464 q^{45} + 38217 q^{48} - 116224 q^{49} + 36858 q^{52} + 26262 q^{53} - 26355 q^{54} + 53974 q^{57} - 112740 q^{58} - 108810 q^{60} - 77370 q^{61} - 106848 q^{62} + 337966 q^{64} + 166855 q^{66} + 175796 q^{68} + 148122 q^{70} - 259842 q^{72} - 52040 q^{73} + 103690 q^{74} - 194709 q^{76} + 197584 q^{77} + 253206 q^{78} - 171934 q^{80} - 313100 q^{81} + 63919 q^{82} - 161762 q^{85} - 38442 q^{86} + 10482 q^{89} - 372450 q^{90} + 64544 q^{92} + 94012 q^{93} + 537614 q^{96} + 177180 q^{97} - 509397 q^{98}+O(q^{100}) \) 96 * q - 3 * q^2 - 11 * q^4 - 2 * q^5 - 27 * q^6 - 3588 * q^9 + 648 * q^10 - 354 * q^13 + 2154 * q^14 - 611 * q^16 - 1006 * q^17 + 10524 * q^20 + 7824 * q^21 + 93 * q^22 - 5311 * q^24 - 25002 * q^25 - 13428 * q^26 + 1556 * q^28 - 6 * q^29 - 12656 * q^30 - 30453 * q^32 + 8586 * q^33 + 30102 * q^34 - 2306 * q^36 + 29846 * q^38 - 1392 * q^40 + 29064 * q^41 + 18616 * q^42 + 9155 * q^44 + 13464 * q^45 + 38217 * q^48 - 116224 * q^49 + 36858 * q^52 + 26262 * q^53 - 26355 * q^54 + 53974 * q^57 - 112740 * q^58 - 108810 * q^60 - 77370 * q^61 - 106848 * q^62 + 337966 * q^64 + 166855 * q^66 + 175796 * q^68 + 148122 * q^70 - 259842 * q^72 - 52040 * q^73 + 103690 * q^74 - 194709 * q^76 + 197584 * q^77 + 253206 * q^78 - 171934 * q^80 - 313100 * q^81 + 63919 * q^82 - 161762 * q^85 - 38442 * q^86 + 10482 * q^89 - 372450 * q^90 + 64544 * q^92 + 94012 * q^93 + 537614 * q^96 + 177180 * q^97 - 509397 * q^98

Introduction

L-functions

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