LMFDB - Embedded newform 70.3.l.c.23.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [70,3,Mod(23,70)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(70, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([9, 4]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("70.23");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 70 = 2 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	70.l (of order $12$, degree $4$, 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:	$1.90736185052$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
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} - 2 x^{15} + 2 x^{14} - 8 x^{13} - 722 x^{12} + 1354 x^{11} - 1232 x^{10} + 9306 x^{9} + \cdots + 52200625 $ x^16 - 2x^15 + 2x^14 - 8x^13 - 722x^12 + 1354x^11 - 1232x^10 + 9306x^9 + 505731x^8 - 1157418x^7 + 1256080x^6 - 9824090x^5 + 5294974x^4 + 30978760x^3 + 12152450x^2 + 35619250*x + 52200625
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			23.2
Root			$2.63893 + 0.707100i$ of defining polynomial
Character	$\chi$	$=$	70.23
Dual form			70.3.l.c.67.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.366025 + 1.36603i) q^{2} +(-0.707100 + 2.63893i) q^{3} +(-1.73205 + 1.00000i) q^{4} +(-3.39720 + 3.66866i) q^{5} -3.86367 q^{6} +(-1.73096 - 6.78261i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(1.33025 + 0.768021i) q^{9} +O(q^{10})$	\(q+(0.366025 + 1.36603i) q^{2} +(-0.707100 + 2.63893i) q^{3} +(-1.73205 + 1.00000i) q^{4} +(-3.39720 + 3.66866i) q^{5} -3.86367 q^{6} +(-1.73096 - 6.78261i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(1.33025 + 0.768021i) q^{9} +(-6.25494 - 3.29783i) q^{10} +(10.0230 + 17.3604i) q^{11} +(-1.41420 - 5.27787i) q^{12} +(2.21546 + 2.21546i) q^{13} +(8.63164 - 4.84715i) q^{14} +(-7.27919 - 11.5591i) q^{15} +(2.00000 - 3.46410i) q^{16} +(-11.9322 - 3.19722i) q^{17} +(-0.562230 + 2.09827i) q^{18} +(15.7940 + 9.11869i) q^{19} +(2.21546 - 9.75150i) q^{20} +(19.1228 + 0.228089i) q^{21} +(-20.0461 + 20.0461i) q^{22} +(39.7282 - 10.6451i) q^{23} +(6.69207 - 3.86367i) q^{24} +(-1.91811 - 24.9263i) q^{25} +(-2.21546 + 3.83729i) q^{26} +(-20.3539 + 20.3539i) q^{27} +(9.78072 + 10.0169i) q^{28} -19.0242i q^{29} +(13.1256 - 14.1745i) q^{30} +(-3.14077 - 5.43998i) q^{31} +(5.46410 + 1.46410i) q^{32} +(-52.9003 + 14.1746i) q^{33} -17.4700i q^{34} +(30.7635 + 16.6915i) q^{35} -3.07208 q^{36} +(-9.82266 - 36.6587i) q^{37} +(-6.67534 + 24.9127i) q^{38} +(-7.41300 + 4.27990i) q^{39} +(14.1317 - 0.542925i) q^{40} -16.3689 q^{41} +(6.68786 + 26.2057i) q^{42} +(-4.26669 - 4.26669i) q^{43} +(-34.7208 - 20.0461i) q^{44} +(-7.33673 + 2.27112i) q^{45} +(29.0830 + 50.3733i) q^{46} +(3.19722 + 11.9322i) q^{47} +(7.72733 + 7.72733i) q^{48} +(-43.0075 + 23.4809i) q^{49} +(33.3479 - 11.7439i) q^{50} +(16.8745 - 29.2275i) q^{51} +(-6.05274 - 1.62183i) q^{52} +(-13.8578 + 51.7180i) q^{53} +(-35.2539 - 20.3539i) q^{54} +(-97.7397 - 22.2056i) q^{55} +(-10.1033 + 17.0271i) q^{56} +(-35.2316 + 35.2316i) q^{57} +(25.9875 - 6.96333i) q^{58} +(82.3873 - 47.5663i) q^{59} +(24.1670 + 12.7417i) q^{60} +(-4.22958 + 7.32586i) q^{61} +(6.28154 - 6.28154i) q^{62} +(2.90657 - 10.3520i) q^{63} +8.00000i q^{64} +(-15.6541 + 0.601413i) q^{65} +(-38.7257 - 67.0749i) q^{66} +(-10.9793 - 2.94188i) q^{67} +(23.8644 - 6.39445i) q^{68} +112.367i q^{69} +(-11.5409 + 48.1332i) q^{70} +94.8180 q^{71} +(-1.12446 - 4.19654i) q^{72} +(-2.11109 + 7.87869i) q^{73} +(46.4813 - 26.8360i) q^{74} +(67.1352 + 12.5636i) q^{75} -36.4747 q^{76} +(100.399 - 98.0326i) q^{77} +(-8.55979 - 8.55979i) q^{78} +(-15.1049 - 8.72081i) q^{79} +(5.91421 + 19.1056i) q^{80} +(-32.4081 - 56.1325i) q^{81} +(-5.99144 - 22.3604i) q^{82} +(-63.0967 - 63.0967i) q^{83} +(-33.3498 + 18.7278i) q^{84} +(52.2656 - 32.9136i) q^{85} +(4.26669 - 7.39012i) q^{86} +(50.2035 + 13.4520i) q^{87} +(14.6748 - 54.7669i) q^{88} +(67.0808 + 38.7291i) q^{89} +(-5.78784 - 9.19087i) q^{90} +(11.1917 - 18.8615i) q^{91} +(-58.1661 + 58.1661i) q^{92} +(16.5766 - 4.44168i) q^{93} +(-15.1294 + 8.73498i) q^{94} +(-87.1088 + 26.9649i) q^{95} +(-7.72733 + 13.3841i) q^{96} +(105.134 - 105.134i) q^{97} +(-47.8173 - 50.1548i) q^{98} +30.7916i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{2} + 2 q^{3} - 2 q^{5} - 8 q^{6} + 12 q^{7} - 32 q^{8}+O(q^{10}) $ 16 * q - 8 * q^2 + 2 * q^3 - 2 * q^5 - 8 * q^6 + 12 * q^7 - 32 * q^8	$ 16 q - 8 q^{2} + 2 q^{3} - 2 q^{5} - 8 q^{6} + 12 q^{7} - 32 q^{8} - 6 q^{10} + 40 q^{11} + 4 q^{12} + 16 q^{13} - 20 q^{15} + 32 q^{16} + 46 q^{17} - 52 q^{18} + 16 q^{20} - 20 q^{21} - 80 q^{22} + 54 q^{23} - 26 q^{25} - 16 q^{26} - 52 q^{27} - 36 q^{28} - 22 q^{30} - 208 q^{31} + 32 q^{32} - 22 q^{33} + 50 q^{35} + 208 q^{36} - 38 q^{37} + 36 q^{38} - 4 q^{40} - 72 q^{41} + 184 q^{42} + 144 q^{43} + 254 q^{45} + 108 q^{46} + 46 q^{47} + 16 q^{48} - 60 q^{50} - 136 q^{51} - 16 q^{52} + 30 q^{53} - 192 q^{55} - 48 q^{56} - 492 q^{57} + 132 q^{58} - 64 q^{60} - 120 q^{61} + 416 q^{62} - 292 q^{63} + 230 q^{65} - 44 q^{66} - 74 q^{67} - 92 q^{68} - 162 q^{70} + 16 q^{71} - 104 q^{72} - 54 q^{73} + 300 q^{75} - 144 q^{76} + 570 q^{77} + 168 q^{78} + 8 q^{80} + 244 q^{81} + 36 q^{82} + 64 q^{83} + 544 q^{85} - 144 q^{86} - 236 q^{87} - 80 q^{88} - 1048 q^{90} + 336 q^{91} - 216 q^{92} + 142 q^{93} - 396 q^{95} - 16 q^{96} + 136 q^{97} - 268 q^{98}+O(q^{100}) $ 16 * q - 8 * q^2 + 2 * q^3 - 2 * q^5 - 8 * q^6 + 12 * q^7 - 32 * q^8 - 6 * q^10 + 40 * q^11 + 4 * q^12 + 16 * q^13 - 20 * q^15 + 32 * q^16 + 46 * q^17 - 52 * q^18 + 16 * q^20 - 20 * q^21 - 80 * q^22 + 54 * q^23 - 26 * q^25 - 16 * q^26 - 52 * q^27 - 36 * q^28 - 22 * q^30 - 208 * q^31 + 32 * q^32 - 22 * q^33 + 50 * q^35 + 208 * q^36 - 38 * q^37 + 36 * q^38 - 4 * q^40 - 72 * q^41 + 184 * q^42 + 144 * q^43 + 254 * q^45 + 108 * q^46 + 46 * q^47 + 16 * q^48 - 60 * q^50 - 136 * q^51 - 16 * q^52 + 30 * q^53 - 192 * q^55 - 48 * q^56 - 492 * q^57 + 132 * q^58 - 64 * q^60 - 120 * q^61 + 416 * q^62 - 292 * q^63 + 230 * q^65 - 44 * q^66 - 74 * q^67 - 92 * q^68 - 162 * q^70 + 16 * q^71 - 104 * q^72 - 54 * q^73 + 300 * q^75 - 144 * q^76 + 570 * q^77 + 168 * q^78 + 8 * q^80 + 244 * q^81 + 36 * q^82 + 64 * q^83 + 544 * q^85 - 144 * q^86 - 236 * q^87 - 80 * q^88 - 1048 * q^90 + 336 * q^91 - 216 * q^92 + 142 * q^93 - 396 * q^95 - 16 * q^96 + 136 * q^97 - 268 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/70\mathbb{Z}\right)^\times$.

$n$	$31$	$57$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.366025	+	1.36603i	0.183013	+	0.683013i
$2$	0.366025	+	1.36603i	0.183013	+	0.683013i
$3$	−0.707100	+	2.63893i	−0.235700	+	0.879644i	0.742132	+	0.670254i	$0.233815\pi$
$3$	−0.707100	+	2.63893i	−0.235700	+	0.879644i	−0.977832	+	0.209391i	$0.932852\pi$
$4$	−1.73205	+	1.00000i	−0.433013	+	0.250000i
$5$	−3.39720	+	3.66866i	−0.679439	+	0.733732i
$5$	−3.39720	+	3.66866i	−0.679439	+	0.733732i
$6$	−3.86367			−0.643944
$7$	−1.73096	−	6.78261i	−0.247280	−	0.968944i
$7$	−1.73096	−	6.78261i	−0.247280	−	0.968944i
$8$	−2.00000	−	2.00000i	−0.250000	−	0.250000i
$9$	1.33025	+	0.768021i	0.147806	+	0.0853356i
$10$	−6.25494	−	3.29783i	−0.625494	−	0.329783i
$11$	10.0230	+	17.3604i	0.911186	+	1.57822i	0.812392	+	0.583112i	$0.198165\pi$
$11$	10.0230	+	17.3604i	0.911186	+	1.57822i	0.0987936	+	0.995108i	$0.468502\pi$
$12$	−1.41420	−	5.27787i	−0.117850	−	0.439822i
$13$	2.21546	+	2.21546i	0.170420	+	0.170420i	0.787164	−	0.616744i	$-0.211549\pi$
$13$	2.21546	+	2.21546i	0.170420	+	0.170420i	−0.616744	+	0.787164i	$0.711549\pi$
$14$	8.63164	−	4.84715i	0.616546	−	0.346225i
$15$	−7.27919	−	11.5591i	−0.485279	−	0.770606i
$16$	2.00000	−	3.46410i	0.125000	−	0.216506i
$17$	−11.9322	−	3.19722i	−0.701894	−	0.188072i	−0.109815	−	0.993952i	$-0.535026\pi$
$17$	−11.9322	−	3.19722i	−0.701894	−	0.188072i	−0.592079	+	0.805880i	$0.701693\pi$
$18$	−0.562230	+	2.09827i	−0.0312350	+	0.116571i
$19$	15.7940	+	9.11869i	0.831265	+	0.479931i	0.854285	−	0.519804i	$-0.173995\pi$
$19$	15.7940	+	9.11869i	0.831265	+	0.479931i	−0.0230208	+	0.999735i	$0.507328\pi$
$20$	2.21546	−	9.75150i	0.110773	−	0.487575i
$21$	19.1228	+	0.228089i	0.910610	+	0.0108614i
$22$	−20.0461	+	20.0461i	−0.911186	+	0.911186i
$23$	39.7282	−	10.6451i	1.72731	−	0.462832i	0.747751	−	0.663979i	$-0.231134\pi$
$23$	39.7282	−	10.6451i	1.72731	−	0.462832i	0.979561	+	0.201148i	$0.0644671\pi$
$24$	6.69207	−	3.86367i	0.278836	−	0.160986i
$25$	−1.91811	−	24.9263i	−0.0767245	−	0.997052i
$26$	−2.21546	+	3.83729i	−0.0852099	+	0.147588i
$27$	−20.3539	+	20.3539i	−0.753847	+	0.753847i
$28$	9.78072	+	10.0169i	0.349312	+	0.357745i
$29$		−	19.0242i		−	0.656006i	−0.944677	−	0.328003i	$-0.893624\pi$
$29$		−	19.0242i		−	0.656006i	0.944677	−	0.328003i	$-0.106376\pi$
$30$	13.1256	−	14.1745i	0.437521	−	0.472482i
$31$	−3.14077	−	5.43998i	−0.101315	−	0.175483i	0.810912	−	0.585169i	$-0.198972\pi$
$31$	−3.14077	−	5.43998i	−0.101315	−	0.175483i	−0.912227	+	0.409686i	$0.865638\pi$
$32$	5.46410	+	1.46410i	0.170753	+	0.0457532i
$33$	−52.9003	+	14.1746i	−1.60304	+	0.429533i
$34$		−	17.4700i		−	0.513822i
$35$	30.7635	+	16.6915i	0.878957	+	0.476901i
$36$	−3.07208			−0.0853356
$37$	−9.82266	−	36.6587i	−0.265477	−	0.990775i	−0.961958	−	0.273199i	$-0.911918\pi$
$37$	−9.82266	−	36.6587i	−0.265477	−	0.990775i	0.696480	−	0.717576i	$-0.254748\pi$
$38$	−6.67534	+	24.9127i	−0.175667	+	0.655598i
$39$	−7.41300	+	4.27990i	−0.190077	+	0.109741i
$40$	14.1317	−	0.542925i	0.353293	−	0.0135731i
$41$	−16.3689			−0.399242			−0.199621	−	0.979873i	$-0.563971\pi$
$41$	−16.3689			−0.399242			−0.199621	+	0.979873i	$0.563971\pi$
$42$	6.68786	+	26.2057i	0.159235	+	0.623946i
$43$	−4.26669	−	4.26669i	−0.0992252	−	0.0992252i	0.655752	−	0.754977i	$-0.272352\pi$
$43$	−4.26669	−	4.26669i	−0.0992252	−	0.0992252i	−0.754977	+	0.655752i	$0.772352\pi$
$44$	−34.7208	−	20.0461i	−0.789110	−	0.455593i
$45$	−7.33673	+	2.27112i	−0.163038	+	0.0504693i
$46$	29.0830	+	50.3733i	0.632240	+	1.09507i
$47$	3.19722	+	11.9322i	0.0680260	+	0.253877i	0.991562	−	0.129636i	$-0.0413809\pi$
$47$	3.19722	+	11.9322i	0.0680260	+	0.253877i	−0.923536	+	0.383513i	$0.874714\pi$
$48$	7.72733	+	7.72733i	0.160986	+	0.160986i
$49$	−43.0075	+	23.4809i	−0.877705	+	0.479202i
$50$	33.3479	−	11.7439i	0.666958	−	0.234877i
$51$	16.8745	−	29.2275i	0.330873	−	0.573089i
$52$	−6.05274	−	1.62183i	−0.116399	−	0.0311890i
$53$	−13.8578	+	51.7180i	−0.261468	+	0.975811i	0.702909	+	0.711279i	$0.251884\pi$
$53$	−13.8578	+	51.7180i	−0.261468	+	0.975811i	−0.964377	+	0.264531i	$0.914783\pi$
$54$	−35.2539	−	20.3539i	−0.652851	−	0.376924i
$55$	−97.7397	−	22.2056i	−1.77709	−	0.403739i
$56$	−10.1033	+	17.0271i	−0.180416	+	0.304056i
$57$	−35.2316	+	35.2316i	−0.618098	+	0.618098i
$58$	25.9875	−	6.96333i	0.448060	−	0.120057i
$59$	82.3873	−	47.5663i	1.39639	−	0.806209i	0.402382	−	0.915472i	$-0.368183\pi$
$59$	82.3873	−	47.5663i	1.39639	−	0.806209i	0.994013	+	0.109263i	$0.0348492\pi$
$60$	24.1670	+	12.7417i	0.402783	+	0.212362i
$61$	−4.22958	+	7.32586i	−0.0693375	+	0.120096i	−0.898610	−	0.438749i	$-0.855422\pi$
$61$	−4.22958	+	7.32586i	−0.0693375	+	0.120096i	0.829272	+	0.558845i	$0.188755\pi$
$62$	6.28154	−	6.28154i	0.101315	−	0.101315i
$63$	2.90657	−	10.3520i	0.0461360	−	0.164317i
$64$			8.00000i			0.125000i
$65$	−15.6541	+	0.601413i	−0.240832	+	0.00925251i
$66$	−38.7257	−	67.0749i	−0.586753	−	1.01629i
$67$	−10.9793	−	2.94188i	−0.163870	−	0.0439087i	0.175951	−	0.984399i	$-0.443700\pi$
$67$	−10.9793	−	2.94188i	−0.163870	−	0.0439087i	−0.339821	+	0.940490i	$0.610366\pi$
$68$	23.8644	−	6.39445i	0.350947	−	0.0940360i
$69$			112.367i			1.62851i
$70$	−11.5409	+	48.1332i	−0.164869	+	0.687618i
$71$	94.8180			1.33547			0.667733	−	0.744401i	$-0.267265\pi$
$71$	94.8180			1.33547			0.667733	+	0.744401i	$0.267265\pi$
$72$	−1.12446	−	4.19654i	−0.0156175	−	0.0582853i
$73$	−2.11109	+	7.87869i	−0.0289190	+	0.107927i	−0.978877	−	0.204451i	$-0.934459\pi$
$73$	−2.11109	+	7.87869i	−0.0289190	+	0.107927i	0.949958	+	0.312378i	$0.101126\pi$
$74$	46.4813	−	26.8360i	0.628126	−	0.362649i
$75$	67.1352	+	12.5636i	0.895135	+	0.167515i
$76$	−36.4747			−0.479931
$77$	100.399	−	98.0326i	1.30389	−	1.27315i
$78$	−8.55979	−	8.55979i	−0.109741	−	0.109741i
$79$	−15.1049	−	8.72081i	−0.191201	−	0.110390i	0.401344	−	0.915928i	$-0.368543\pi$
$79$	−15.1049	−	8.72081i	−0.191201	−	0.110390i	−0.592545	+	0.805538i	$0.701877\pi$
$80$	5.91421	+	19.1056i	0.0739277	+	0.238819i
$81$	−32.4081	−	56.1325i	−0.400100	−	0.692994i
$82$	−5.99144	−	22.3604i	−0.0730663	−	0.272687i
$83$	−63.0967	−	63.0967i	−0.760201	−	0.760201i	0.216157	−	0.976359i	$-0.430648\pi$
$83$	−63.0967	−	63.0967i	−0.760201	−	0.760201i	−0.976359	+	0.216157i	$0.930648\pi$
$84$	−33.3498	+	18.7278i	−0.397021	+	0.222949i
$85$	52.2656	−	32.9136i	0.614889	−	0.387219i
$86$	4.26669	−	7.39012i	0.0496126	−	0.0859316i
$87$	50.2035	+	13.4520i	0.577052	+	0.154621i
$88$	14.6748	−	54.7669i	0.166759	−	0.622351i
$89$	67.0808	+	38.7291i	0.753717	+	0.435158i	0.827035	−	0.562150i	$-0.190026\pi$
$89$	67.0808	+	38.7291i	0.753717	+	0.435158i	−0.0733187	+	0.997309i	$0.523359\pi$
$90$	−5.78784	−	9.19087i	−0.0643093	−	0.102121i
$91$	11.1917	−	18.8615i	0.122986	−	0.207269i
$92$	−58.1661	+	58.1661i	−0.632240	+	0.632240i
$93$	16.5766	−	4.44168i	0.178243	−	0.0477600i
$94$	−15.1294	+	8.73498i	−0.160951	+	0.0929253i
$95$	−87.1088	+	26.9649i	−0.916934	+	0.283841i
$96$	−7.72733	+	13.3841i	−0.0804930	+	0.139418i
$97$	105.134	−	105.134i	1.08385	−	1.08385i	0.0877043	−	0.996147i	$-0.472047\pi$
$97$	105.134	−	105.134i	1.08385	−	1.08385i	0.996147	−	0.0877043i	$-0.0279531\pi$
$98$	−47.8173	−	50.1548i	−0.487932	−	0.511784i
$99$			30.7916i			0.311026i
$100$	28.2486	+	41.2555i	0.282486	+	0.412555i
$101$	−63.7196	−	110.366i	−0.630887	−	1.09273i	−0.987371	−	0.158427i	$-0.949358\pi$
$101$	−63.7196	−	110.366i	−0.630887	−	1.09273i	0.356483	−	0.934302i	$-0.383976\pi$
$102$	46.1020	+	12.3530i	0.451981	+	0.121108i
$103$	−7.25451	+	1.94384i	−0.0704321	+	0.0188722i	−0.293863	−	0.955848i	$-0.594941\pi$
$103$	−7.25451	+	1.94384i	−0.0704321	+	0.0188722i	0.223431	+	0.974720i	$0.428274\pi$
$104$		−	8.86183i		−	0.0852099i
$105$	−65.8007	+	69.3802i	−0.626674	+	0.660764i
$106$	−75.7204			−0.714343
$107$	29.8828	+	111.524i	0.279279	+	1.04228i	0.952919	+	0.303224i	$0.0980629\pi$
$107$	29.8828	+	111.524i	0.279279	+	1.04228i	−0.673641	+	0.739059i	$0.735270\pi$
$108$	14.9001	−	55.6078i	0.137964	−	0.514887i
$109$	−36.9108	+	21.3104i	−0.338631	+	0.195509i	−0.659666	−	0.751559i	$-0.729302\pi$
$109$	−36.9108	+	21.3104i	−0.338631	+	0.195509i	0.321036	+	0.947067i	$0.395969\pi$
$110$	−5.44176	−	141.643i	−0.0494705	−	1.28766i
$111$	103.685			0.934103
$112$	−26.9576	−	7.56899i	−0.240693	−	0.0675802i
$113$	−13.6000	−	13.6000i	−0.120354	−	0.120354i	0.644365	−	0.764718i	$-0.277122\pi$
$113$	−13.6000	−	13.6000i	−0.120354	−	0.120354i	−0.764718	+	0.644365i	$0.777122\pi$
$114$	−61.0229	−	35.2316i	−0.535288	−	0.309049i
$115$	−95.9110	+	181.913i	−0.834009	+	1.58185i
$116$	19.0242	+	32.9508i	0.164001	+	0.284059i
$117$	1.24560	+	4.64863i	0.0106461	+	0.0397319i
$118$	95.1326	+	95.1326i	0.806209	+	0.806209i
$119$	−1.03133	+	86.4657i	−0.00866660	+	0.726603i
$120$	−8.55979	+	37.6765i	−0.0713316	+	0.313971i
$121$	−140.423	+	243.219i	−1.16052	+	2.01008i
$122$	−11.5554	−	3.09627i	−0.0947167	−	0.0253793i
$123$	11.5745	−	43.1965i	0.0941013	−	0.351191i
$124$	10.8800	+	6.28154i	0.0877415	+	0.0506576i
$125$	97.9623	+	77.6427i	0.783699	+	0.621141i
$126$	15.2050	+	0.181358i	0.120674	+	0.00143935i
$127$	24.7683	−	24.7683i	0.195026	−	0.195026i	−0.602838	−	0.797864i	$-0.705963\pi$
$127$	24.7683	−	24.7683i	0.195026	−	0.195026i	0.797864	+	0.602838i	$0.205963\pi$
$128$	−10.9282	+	2.92820i	−0.0853766	+	0.0228766i
$129$	14.2765	−	8.24252i	0.110670	−	0.0638955i
$130$	−6.55135	−	21.1638i	−0.0503950	−	0.162798i
$131$	−72.3622	+	125.335i	−0.552383	+	0.956756i	0.445719	+	0.895173i	$0.352948\pi$
$131$	−72.3622	+	125.335i	−0.552383	+	0.956756i	−0.998102	+	0.0615830i	$0.980385\pi$
$132$	77.4514	−	77.4514i	0.586753	−	0.586753i
$133$	34.5096	−	122.909i	0.259471	−	0.924126i
$134$		−	16.0748i		−	0.119961i
$135$	−5.52531	−	143.818i	−0.0409282	−	1.06532i
$136$	17.4700	+	30.2589i	0.128456	+	0.222492i
$137$	−45.5877	−	12.2152i	−0.332757	−	0.0891619i	0.0885724	−	0.996070i	$-0.471770\pi$
$137$	−45.5877	−	12.2152i	−0.332757	−	0.0891619i	−0.421329	+	0.906908i	$0.638436\pi$
$138$	−153.496	+	41.1292i	−1.11229	+	0.298038i
$139$		−	121.473i		−	0.873910i	−0.899483	−	0.436955i	$-0.856057\pi$
$139$		−	121.473i		−	0.873910i	0.899483	−	0.436955i	$-0.143943\pi$
$140$	−69.9755	+	1.85289i	−0.499825	+	0.0132350i
$141$	−33.7490			−0.239355
$142$	34.7058	+	129.524i	0.244407	+	0.912140i
$143$	−16.2556	+	60.6669i	−0.113676	+	0.424244i
$144$	5.32100	−	3.07208i	0.0369514	−	0.0213339i
$145$	69.7932	+	64.6288i	0.481332	+	0.445716i
$146$	−11.5352			−0.0790083
$147$	−31.5538	−	130.097i	−0.214652	−	0.885016i
$148$	53.6720	+	53.6720i	0.362649	+	0.362649i
$149$	−117.569	−	67.8784i	−0.789053	−	0.455560i	0.0505763	−	0.998720i	$-0.483894\pi$
$149$	−117.569	−	67.8784i	−0.789053	−	0.455560i	−0.839629	+	0.543160i	$0.817228\pi$
$150$	7.41095	+	96.3069i	0.0494063	+	0.642046i
$151$	−41.3618	−	71.6408i	−0.273919	−	0.474442i	0.695943	−	0.718097i	$-0.254987\pi$
$151$	−41.3618	−	71.6408i	−0.273919	−	0.474442i	−0.969862	+	0.243655i	$0.921653\pi$
$152$	−13.3507	−	49.8254i	−0.0878334	−	0.327799i
$153$	−13.4173	−	13.4173i	−0.0876947	−	0.0876947i
$154$	170.664	+	101.266i	1.10821	+	0.657570i
$155$	30.6272	+	6.95825i	0.197595	+	0.0448919i
$156$	8.55979	−	14.8260i	0.0548705	−	0.0950384i
$157$	37.8843	+	10.1511i	0.241301	+	0.0646565i	0.377443	−	0.926033i	$-0.376804\pi$
$157$	37.8843	+	10.1511i	0.241301	+	0.0646565i	−0.136142	+	0.990689i	$0.543470\pi$
$158$	6.38408	−	23.8257i	0.0404056	−	0.150796i
$159$	−126.681	−	73.1396i	−0.796739	−	0.459997i
$160$	−23.9339	+	15.0721i	−0.149587	+	0.0942005i
$161$	−140.970	−	251.034i	−0.875588	−	1.55922i
$162$	64.8162	−	64.8162i	0.400100	−	0.400100i
$163$	119.375	−	31.9864i	0.732361	−	0.196236i	0.126681	−	0.991944i	$-0.459568\pi$
$163$	119.375	−	31.9864i	0.732361	−	0.196236i	0.605680	+	0.795708i	$0.292901\pi$
$164$	28.3518	−	16.3689i	0.172877	−	0.0998105i
$165$	127.711	−	242.227i	0.774005	−	1.46804i
$166$	63.0967	−	109.287i	0.380101	−	0.658353i
$167$	−173.339	+	173.339i	−1.03796	+	1.03796i	−0.0387094	+	0.999251i	$0.512325\pi$
$167$	−173.339	+	173.339i	−1.03796	+	1.03796i	−0.999251	+	0.0387094i	$0.987675\pi$
$168$	−37.7894	−	38.7018i	−0.224937	−	0.230368i
$169$		−	159.183i		−	0.941914i
$170$	64.0913	+	59.3489i	0.377008	+	0.349111i
$171$	14.0067	+	24.2603i	0.0819104	+	0.141873i
$172$	11.6568	+	3.12343i	0.0677721	+	0.0181595i
$173$	233.962	−	62.6900i	1.35238	−	0.362370i	0.491369	−	0.870952i	$-0.336497\pi$
$173$	233.962	−	62.6900i	1.35238	−	0.362370i	0.861014	+	0.508582i	$0.169830\pi$
$174$			73.5030i			0.422431i
$175$	−165.745	+	56.1563i	−0.947115	+	0.320893i
$176$	80.1843			0.455593
$177$	67.2683	+	251.049i	0.380047	+	1.41835i
$178$	−28.3517	+	105.810i	−0.159279	+	0.594438i
$179$	−150.152	+	86.6905i	−0.838840	+	0.484304i	−0.856870	−	0.515533i	$-0.827594\pi$
$179$	−150.152	+	86.6905i	−0.838840	+	0.484304i	0.0180301	+	0.999837i	$0.494261\pi$
$180$	10.4365	−	11.2704i	0.0579804	−	0.0626135i
$181$	237.263			1.31085			0.655424	−	0.755262i	$-0.272490\pi$
$181$	237.263			1.31085			0.655424	+	0.755262i	$0.272490\pi$
$182$	29.8617	+	8.38439i	0.164075	+	0.0460681i
$183$	−16.3417	−	16.3417i	−0.0892989	−	0.0892989i
$184$	−100.747	−	58.1661i	−0.547536	−	0.316120i
$185$	167.858	+	88.5007i	0.907339	+	0.478382i
$186$	12.1349	+	21.0182i	0.0652414	+	0.113001i
$187$	−64.0918	−	239.194i	−0.342737	−	1.27911i
$188$	−17.4700	−	17.4700i	−0.0929253	−	0.0929253i
$189$	173.284	+	102.821i	0.916847	+	0.544024i
$190$	−68.7188	−	109.123i	−0.361678	−	0.574331i
$191$	−10.4921	+	18.1728i	−0.0549324	+	0.0951457i	−0.892184	−	0.451672i	$-0.850828\pi$
$191$	−10.4921	+	18.1728i	−0.0549324	+	0.0951457i	0.837252	+	0.546818i	$0.184161\pi$
$192$	−21.1115	−	5.65680i	−0.109956	−	0.0294625i
$193$	−12.9543	+	48.3460i	−0.0671206	+	0.250497i	−0.991331	−	0.131385i	$-0.958057\pi$
$193$	−12.9543	+	48.3460i	−0.0671206	+	0.250497i	0.924211	+	0.381883i	$0.124724\pi$
$194$	182.097	+	105.134i	0.938642	+	0.541925i
$195$	9.48193	−	41.7354i	0.0486253	−	0.214028i
$196$	51.0104	−	83.6776i	0.260257	−	0.426927i
$197$	−85.5963	+	85.5963i	−0.434499	+	0.434499i	−0.890156	−	0.455657i	$-0.849404\pi$
$197$	−85.5963	+	85.5963i	−0.434499	+	0.434499i	0.455657	+	0.890156i	$0.349404\pi$
$198$	−42.0621	+	11.2705i	−0.212435	+	0.0569218i
$199$	266.269	−	153.731i	1.33804	−	0.772515i	0.351520	−	0.936180i	$-0.385665\pi$
$199$	266.269	−	153.731i	1.33804	−	0.772515i	0.986516	+	0.163665i	$0.0523316\pi$
$200$	−46.0164	+	53.6888i	−0.230082	+	0.268444i
$201$	15.5269	−	26.8933i	0.0772481	−	0.133798i
$202$	127.439	−	127.439i	0.630887	−	0.630887i
$203$	−129.033	+	32.9301i	−0.635633	+	0.162217i
$204$			67.4981i			0.330873i
$205$	55.6084	−	60.0520i	0.271261	−	0.292936i
$206$	−5.31067	−	9.19835i	−0.0257799	−	0.0446522i
$207$	61.0241	+	16.3514i	0.294803	+	0.0789921i
$208$	12.1055	−	3.24366i	0.0581995	−	0.0155945i
$209$			365.588i			1.74922i
$210$	−118.860	−	64.4905i	−0.565999	−	0.307098i
$211$	−116.585			−0.552533			−0.276267	−	0.961081i	$-0.589097\pi$
$211$	−116.585			−0.552533			−0.276267	+	0.961081i	$0.589097\pi$
$212$	−27.7156	−	103.436i	−0.130734	−	0.487905i
$213$	−67.0458	+	250.218i	−0.314769	+	1.17473i
$214$	−141.407	+	81.6414i	−0.660781	+	0.381502i
$215$	30.1478	−	1.15824i	0.140222	−	0.00538718i
$216$	81.4155			0.376924
$217$	−31.4607	+	30.7190i	−0.144980	+	0.141562i
$218$	−42.6209	−	42.6209i	−0.195509	−	0.195509i
$219$	−19.2986	−	11.1420i	−0.0881214	−	0.0508769i
$220$	191.496	−	59.2784i	0.870435	−	0.269447i
$221$	−19.3520	−	33.5186i	−0.0875655	−	0.151668i
$222$	37.9515	+	141.637i	0.170953	+	0.638004i
$223$	−93.2689	−	93.2689i	−0.418246	−	0.418246i	0.466353	−	0.884599i	$-0.345568\pi$
$223$	−93.2689	−	93.2689i	−0.418246	−	0.418246i	−0.884599	+	0.466353i	$0.845568\pi$
$224$	0.472274	−	39.5952i	0.00210837	−	0.176764i
$225$	16.5924	−	34.6314i	0.0737438	−	0.153917i
$226$	13.6000	−	23.5558i	0.0601768	−	0.104229i
$227$	−325.524	−	87.2238i	−1.43403	−	0.384246i	−0.543588	−	0.839352i	$-0.682935\pi$
$227$	−325.524	−	87.2238i	−1.43403	−	0.384246i	−0.890437	+	0.455106i	$0.849601\pi$
$228$	25.7913	−	96.2544i	0.113120	−	0.422168i
$229$	−330.729	−	190.946i	−1.44423	−	0.833827i	−0.446102	−	0.894982i	$-0.647188\pi$
$229$	−330.729	−	190.946i	−1.44423	−	0.833827i	−0.998128	+	0.0611552i	$0.980522\pi$
$230$	−283.603	−	64.4323i	−1.23306	−	0.280140i
$231$	187.709	+	334.266i	0.812593	+	1.44704i
$232$	−38.0483	+	38.0483i	−0.164001	+	0.164001i
$233$	−322.409	+	86.3892i	−1.38373	+	0.370769i	−0.872474	−	0.488660i	$-0.837486\pi$
$233$	−322.409	+	86.3892i	−1.38373	+	0.370769i	−0.511255	+	0.859429i	$0.670819\pi$
$234$	−5.89423	+	3.40304i	−0.0251890	+	0.0145429i
$235$	−54.6368	−	28.8065i	−0.232497	−	0.122581i
$236$	−95.1326	+	164.775i	−0.403104	+	0.698197i
$237$	33.6943	−	33.6943i	0.142170	−	0.142170i
$238$	−118.492	+	30.2398i	−0.497865	+	0.127058i
$239$		−	437.169i		−	1.82916i	−0.404406	−	0.914579i	$-0.632522\pi$
$239$		−	437.169i		−	1.82916i	0.404406	−	0.914579i	$-0.367478\pi$
$240$	−54.6002	+	2.09768i	−0.227501	+	0.00874033i
$241$	1.94620	+	3.37093i	0.00807554	+	0.0139872i	0.870035	−	0.492990i	$-0.164096\pi$
$241$	1.94620	+	3.37093i	0.00807554	+	0.0139872i	−0.861959	+	0.506977i	$0.830763\pi$
$242$	−383.642	−	102.797i	−1.58530	−	0.424779i
$243$	−79.1896	+	21.2188i	−0.325883	+	0.0873201i
$244$		−	16.9183i		−	0.0693375i
$245$	59.9617	−	237.549i	0.244742	−	0.969588i
$246$	63.2440			0.257090
$247$	14.7889	+	55.1931i	0.0598742	+	0.223454i
$248$	−4.59841	+	17.1615i	−0.0185420	+	0.0691996i
$249$	211.124	−	121.892i	0.847886	−	0.489527i
$250$	−70.2051	+	162.238i	−0.280821	+	0.648953i
$251$	368.235			1.46707			0.733535	−	0.679651i	$-0.237869\pi$
$251$	368.235			1.46707			0.733535	+	0.679651i	$0.237869\pi$
$252$	5.31766	+	20.8367i	0.0211018	+	0.0826855i
$253$	583.001	+	583.001i	2.30435	+	2.30435i
$254$	42.8999	+	24.7683i	0.168897	+	0.0975129i
$255$	49.8998	+	161.199i	0.195685	+	0.632151i
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$	68.5388	+	255.790i	0.266688	+	0.995294i	0.961209	+	0.275821i	$0.0889497\pi$
$257$	68.5388	+	255.790i	0.266688	+	0.995294i	−0.694521	+	0.719473i	$0.744384\pi$
$258$	16.4850	+	16.4850i	0.0638955	+	0.0638955i
$259$	−231.639	+	130.078i	−0.894358	+	0.502232i
$260$	26.5123	−	16.6958i	0.101970	−	0.0642146i
$261$	14.6110	−	25.3069i	0.0559807	−	0.0969614i
$262$	−197.697	−	52.9728i	−0.754570	−	0.202186i
$263$	−71.0526	+	265.172i	−0.270162	+	1.00826i	0.688852	+	0.724902i	$0.258115\pi$
$263$	−71.0526	+	265.172i	−0.270162	+	1.00826i	−0.959014	+	0.283357i	$0.908552\pi$
$264$	134.150	+	77.4514i	0.508143	+	0.293376i
$265$	−142.658	−	226.536i	−0.538332	−	0.854851i
$266$	180.528	+	2.15326i	0.678676	+	0.00809496i
$267$	−149.636	+	149.636i	−0.560436	+	0.560436i
$268$	21.9585	−	5.88377i	0.0819348	−	0.0219544i
$269$	120.599	−	69.6276i	0.448322	−	0.258839i	−0.258799	−	0.965931i	$-0.583327\pi$
$269$	120.599	−	69.6276i	0.448322	−	0.258839i	0.707121	+	0.707092i	$0.249994\pi$
$270$	194.436	−	60.1886i	0.720133	−	0.222921i
$271$	−31.0329	+	53.7505i	−0.114512	+	0.198341i	−0.917585	−	0.397540i	$-0.869864\pi$
$271$	−31.0329	+	53.7505i	−0.114512	+	0.198341i	0.803072	+	0.595882i	$0.203197\pi$
$272$	−34.9399	+	34.9399i	−0.128456	+	0.128456i
$273$	41.8605	+	42.8711i	0.153335	+	0.157037i
$274$		−	66.7450i		−	0.243595i
$275$	413.506	−	283.137i	1.50366	−	1.02959i
$276$	−112.367	−	194.626i	−0.407127	−	0.705165i
$277$	401.798	+	107.661i	1.45053	+	0.388669i	0.896209	−	0.443632i	$-0.146310\pi$
$277$	401.798	+	107.661i	1.45053	+	0.388669i	0.554324	+	0.832301i	$0.312977\pi$
$278$	165.936	−	44.4624i	0.596891	−	0.159937i
$279$		−	9.64871i		−	0.0345832i
$280$	−28.1439	−	94.9101i	−0.100514	−	0.338965i
$281$	−370.599			−1.31886			−0.659428	−	0.751767i	$-0.729202\pi$
$281$	−370.599			−1.31886			−0.659428	+	0.751767i	$0.729202\pi$
$282$	−12.3530	−	46.1020i	−0.0438050	−	0.163482i
$283$	124.931	−	466.250i	0.441453	−	1.64753i	−0.283681	−	0.958919i	$-0.591556\pi$
$283$	124.931	−	466.250i	0.441453	−	1.64753i	0.725135	−	0.688607i	$-0.241778\pi$
$284$	−164.230	+	94.8180i	−0.578273	+	0.333866i
$285$	−9.56404	−	248.941i	−0.0335580	−	0.873478i
$286$	−88.8225			−0.310568
$287$	28.3340	+	111.024i	0.0987247	+	0.386843i
$288$	6.14417	+	6.14417i	0.0213339	+	0.0213339i
$289$	−118.126	−	68.2002i	−0.408741	−	0.235987i
$290$	−62.7386	+	118.995i	−0.216340	+	0.410328i
$291$	203.100	+	351.780i	0.697940	+	1.20887i
$292$	−4.22218	−	15.7574i	−0.0144595	−	0.0539636i
$293$	−203.433	−	203.433i	−0.694312	−	0.694312i	0.268866	−	0.963178i	$-0.413351\pi$
$293$	−203.433	−	203.433i	−0.694312	−	0.694312i	−0.963178	+	0.268866i	$0.913351\pi$
$294$	166.167	−	90.7223i	0.565193	−	0.308579i
$295$	−105.381	+	463.843i	−0.357224	+	1.57235i
$296$	−53.6720	+	92.9627i	−0.181324	+	0.314063i
$297$	−557.359	−	149.344i	−1.87663	−	0.502842i
$298$	49.6904	−	185.447i	0.166746	−	0.622306i
$299$	111.600	+	64.4323i	0.373244	+	0.215492i
$300$	−128.845	+	45.3743i	−0.429484	+	0.151248i
$301$	−21.5538	+	36.3247i	−0.0716073	+	0.120680i
$302$	82.7236	−	82.7236i	0.273919	−	0.273919i
$303$	336.304	−	90.1123i	1.10991	−	0.297400i
$304$	63.1761	−	36.4747i	0.207816	−	0.119983i
$305$	−12.5073	−	40.4043i	−0.0410077	−	0.132473i
$306$	13.4173	−	23.2394i	0.0438474	−	0.0759458i
$307$	0.207402	−	0.207402i	0.000675578	−	0.000675578i	−0.706769	−	0.707444i	$-0.749848\pi$
$307$	0.207402	−	0.207402i	0.000675578	−	0.000675578i	0.707444	+	0.706769i	$0.249848\pi$
$308$	−75.8643	+	270.197i	−0.246313	+	0.877262i
$309$		−	20.5187i		−	0.0664034i
$310$	1.70520	+	44.3845i	0.00550065	+	0.143176i
$311$	−178.011	−	308.324i	−0.572382	−	0.991394i	−0.996321	−	0.0857033i	$-0.972686\pi$
$311$	−178.011	−	308.324i	−0.572382	−	0.991394i	0.423939	−	0.905691i	$-0.360647\pi$
$312$	23.3858	+	6.26620i	0.0749544	+	0.0200840i
$313$	251.585	−	67.4119i	0.803784	−	0.215373i	0.166540	−	0.986035i	$-0.446741\pi$
$313$	251.585	−	67.4119i	0.803784	−	0.215373i	0.637245	+	0.770661i	$0.280074\pi$
$314$			55.4664i			0.176645i
$315$	28.1037	+	45.8309i	0.0892181	+	0.145495i
$316$	34.8833			0.110390
$317$	−20.0199	−	74.7155i	−0.0631544	−	0.235695i	0.927133	−	0.374733i	$-0.122266\pi$
$317$	−20.0199	−	74.7155i	−0.0631544	−	0.235695i	−0.990287	+	0.139038i	$0.955599\pi$
$318$	53.5419	−	199.821i	0.168371	−	0.628368i
$319$	330.267	−	190.680i	1.03532	−	0.597743i
$320$	−29.3493	−	27.1776i	−0.0917165	−	0.0849299i
$321$	−315.435			−0.982664
$322$	291.321	−	284.453i	0.904723	−	0.883395i
$323$	−159.303	−	159.303i	−0.493198	−	0.493198i
$324$	112.265	+	64.8162i	0.346497	+	0.200050i
$325$	50.9737	−	59.4727i	0.156842	−	0.182993i
$326$	87.3885	+	151.361i	0.268063	+	0.464298i
$327$	−30.1372	−	112.474i	−0.0921627	−	0.343956i
$328$	32.7378	+	32.7378i	0.0998105	+	0.0998105i
$329$	75.3972	−	42.3397i	0.229171	−	0.128692i
$330$	377.634	+	85.7951i	1.14434	+	0.259985i
$331$	−43.1415	+	74.7232i	−0.130337	+	0.225750i	−0.923806	−	0.382860i	$-0.874939\pi$
$331$	−43.1415	+	74.7232i	−0.130337	+	0.225750i	0.793470	+	0.608610i	$0.208273\pi$
$332$	172.383	+	46.1900i	0.519227	+	0.139126i
$333$	15.0880	−	56.3093i	0.0453094	−	0.169097i
$334$	−300.232	−	173.339i	−0.898900	−	0.518980i
$335$	48.0915	−	30.2850i	0.143557	−	0.0904030i
$336$	39.0357	−	65.7872i	0.116178	−	0.195795i
$337$	92.8454	−	92.8454i	0.275506	−	0.275506i	−0.555806	−	0.831312i	$-0.687590\pi$
$337$	92.8454	−	92.8454i	0.275506	−	0.275506i	0.831312	+	0.555806i	$0.187590\pi$
$338$	217.449	−	58.2652i	0.643339	−	0.172382i
$339$	45.5059	−	26.2728i	0.134236	−	0.0775010i
$340$	−57.6130	+	109.274i	−0.169450	+	0.321393i
$341$	62.9602	−	109.050i	0.184634	−	0.319795i
$342$	−28.0134	+	28.0134i	−0.0819104	+	0.0819104i
$343$	233.706	+	251.059i	0.681359	+	0.731950i
$344$			17.0667i			0.0496126i
$345$	−412.237	−	381.733i	−1.19489	−	1.10647i
$346$	171.272	+	296.652i	0.495006	+	0.857376i
$347$	386.918	+	103.674i	1.11504	+	0.298773i	0.768874	−	0.639401i	$-0.220817\pi$
$347$	386.918	+	103.674i	1.11504	+	0.298773i	0.346164	+	0.938174i	$0.387484\pi$
$348$	−100.407	+	26.9040i	−0.288526	+	0.0773103i
$349$			202.323i			0.579723i	0.957069	+	0.289862i	$0.0936093\pi$
$349$			202.323i			0.579723i	−0.957069	+	0.289862i	$0.906391\pi$
$350$	−137.378	−	205.858i	−0.392508	−	0.588164i
$351$	−90.1863			−0.256941
$352$	29.3495	+	109.534i	0.0833793	+	0.311176i
$353$	−85.4581	+	318.934i	−0.242091	+	0.903496i	0.732732	+	0.680517i	$0.238245\pi$
$353$	−85.4581	+	318.934i	−0.242091	+	0.903496i	−0.974823	+	0.222979i	$0.928422\pi$
$354$	−318.317	+	183.780i	−0.899200	+	0.519154i
$355$	−322.115	+	347.855i	−0.907368	+	0.979873i
$356$	−154.916			−0.435158
$357$	−227.448	−	63.8615i	−0.637109	−	0.178884i
$358$	−173.381	−	173.381i	−0.484304	−	0.484304i
$359$	27.1220	+	15.6589i	0.0755487	+	0.0436181i	0.537298	−	0.843392i	$-0.319445\pi$
$359$	27.1220	+	15.6589i	0.0755487	+	0.0436181i	−0.461750	+	0.887010i	$0.652778\pi$
$360$	19.2157	+	10.1312i	0.0533769	+	0.0281423i
$361$	−14.1991	−	24.5936i	−0.0393327	−	0.0681263i
$362$	86.8444	+	324.108i	0.239902	+	0.895325i
$363$	−542.546	−	542.546i	−1.49462	−	1.49462i
$364$	−0.523152	+	43.8607i	−0.00143723	+	0.120496i
$365$	−21.7324	−	34.5103i	−0.0595409	−	0.0945488i
$366$	16.3417	−	28.3047i	0.0446495	−	0.0773351i
$367$	−169.529	−	45.4250i	−0.461931	−	0.123774i	0.0203459	−	0.999793i	$-0.493523\pi$
$367$	−169.529	−	45.4250i	−0.461931	−	0.123774i	−0.482276	+	0.876019i	$0.660190\pi$
$368$	42.5805	−	158.913i	0.115708	−	0.431828i
$369$	−21.7748	−	12.5717i	−0.0590102	−	0.0340696i
$370$	−59.4541	+	261.691i	−0.160687	+	0.707274i
$371$	374.770	+	4.47010i	1.01016	+	0.0120488i
$372$	−24.2698	+	24.2698i	−0.0652414	+	0.0652414i
$373$	−104.404	+	27.9749i	−0.279903	+	0.0749997i	−0.396039	−	0.918234i	$-0.629616\pi$
$373$	−104.404	+	27.9749i	−0.279903	+	0.0749997i	0.116137	+	0.993233i	$0.462949\pi$
$374$	303.286	−	175.102i	0.810924	−	0.468187i
$375$	−274.163	+	203.615i	−0.731101	+	0.542973i
$376$	17.4700	−	30.2589i	0.0464627	−	0.0804757i
$377$	42.1472	−	42.1472i	0.111796	−	0.111796i
$378$	−77.0291	+	274.345i	−0.203781	+	0.725782i
$379$			370.389i			0.977279i	0.872486	+	0.488639i	$0.162507\pi$
$379$			370.389i			0.977279i	−0.872486	+	0.488639i	$0.837493\pi$
$380$	123.912	−	133.813i	0.326084	−	0.352141i
$381$	47.8482	+	82.8755i	0.125586	+	0.217521i
$382$	−28.6649	−	7.68074i	−0.0750390	−	0.0201066i
$383$	−3.39901	+	0.910761i	−0.00887469	+	0.00237797i	−0.263254	−	0.964727i	$-0.584796\pi$
$383$	−3.39901	+	0.910761i	−0.00887469	+	0.00237797i	0.254379	+	0.967105i	$0.418129\pi$
$384$		−	30.9093i		−	0.0804930i
$385$	18.5716	+	701.367i	0.0482380	+	1.82173i
$386$	−70.7834			−0.183377
$387$	−2.39886	−	8.95267i	−0.00619860	−	0.0231335i
$388$	−76.9631	+	287.230i	−0.198358	+	0.740284i
$389$	−628.167	+	362.672i	−1.61482	+	0.932319i	−0.626594	+	0.779346i	$0.715551\pi$
$389$	−628.167	+	362.672i	−1.61482	+	0.932319i	−0.988230	+	0.152973i	$0.951115\pi$
$390$	60.4822	−	2.32366i	0.155083	−	0.00595810i
$391$	−508.079			−1.29944
$392$	132.977	+	39.0533i	0.339227	+	0.0996258i
$393$	−279.583	−	279.583i	−0.711408	−	0.711408i
$394$	−148.257	−	85.5963i	−0.376287	−	0.217249i
$395$	83.3080	−	25.7884i	0.210906	−	0.0652870i
$396$	−30.7916	−	53.3326i	−0.0777566	−	0.134678i
$397$	−33.1595	−	123.753i	−0.0835253	−	0.311721i	0.911506	−	0.411288i	$-0.134921\pi$
$397$	−33.1595	−	123.753i	−0.0835253	−	0.311721i	−0.995031	+	0.0995671i	$0.968254\pi$
$398$	307.461	+	307.461i	0.772515	+	0.772515i
$399$	299.946	+	177.977i	0.751745	+	0.446059i
$400$	−90.1835	−	43.2081i	−0.225459	−	0.108020i
$401$	350.482	−	607.052i	0.874019	−	1.51384i	0.0162143	−	0.999869i	$-0.494839\pi$
$401$	350.482	−	607.052i	0.874019	−	1.51384i	0.857804	−	0.513976i	$-0.171828\pi$
$402$	42.4202	+	11.3665i	0.105523	+	0.0282748i
$403$	5.09379	−	19.0103i	0.0126397	−	0.0471719i
$404$	220.731	+	127.439i	0.546364	+	0.315444i
$405$	316.028	+	71.7988i	0.780315	+	0.177281i
$406$	−92.2129	−	164.210i	−0.227125	−	0.404457i
$407$	537.957	−	537.957i	1.32176	−	1.32176i
$408$	−92.2041	+	24.7060i	−0.225990	+	0.0605540i
$409$	−391.838	+	226.228i	−0.958039	+	0.553124i	−0.895569	−	0.444923i	$-0.853231\pi$
$409$	−391.838	+	226.228i	−0.958039	+	0.553124i	−0.0624701	+	0.998047i	$0.519898\pi$
$410$	102.387	+	53.9820i	0.249723	+	0.131663i
$411$	64.4701	−	111.665i	0.156861	−	0.271692i
$412$	10.6213	−	10.6213i	0.0257799	−	0.0257799i
$413$	−465.233	−	476.465i	−1.12647	−	1.15367i
$414$			89.3455i			0.215810i
$415$	445.832	−	17.1284i	1.07429	−	0.0412732i
$416$	8.86183	+	15.3491i	0.0213025	+	0.0368970i
$417$	320.560	+	85.8939i	0.768730	+	0.205981i
$418$	−499.402	+	133.814i	−1.19474	+	0.320130i
$419$			248.174i			0.592302i	0.955141	+	0.296151i	$0.0957031\pi$
$419$			248.174i			0.592302i	−0.955141	+	0.296151i	$0.904297\pi$
$420$	44.5900	−	185.971i	0.106167	−	0.442788i
$421$	−238.992			−0.567676			−0.283838	−	0.958872i	$-0.591608\pi$
$421$	−238.992			−0.567676			−0.283838	+	0.958872i	$0.591608\pi$
$422$	−42.6729	−	159.257i	−0.101121	−	0.377387i
$423$	−4.91107	+	18.3284i	−0.0116101	+	0.0433295i
$424$	131.152	−	75.7204i	0.309320	−	0.178586i
$425$	−56.8077	+	303.558i	−0.133665	+	0.714255i
$426$	−366.345			−0.859965
$427$	57.0097	+	16.0068i	0.133512	+	0.0374867i
$428$	−163.283	−	163.283i	−0.381502	−	0.381502i
$429$	−148.602	−	85.7951i	−0.346391	−	0.199989i
$430$	12.6170	+	40.7587i	0.0293420	+	0.0947876i
$431$	65.3730	+	113.229i	0.151677	+	0.262713i	0.931844	−	0.362858i	$-0.118199\pi$
$431$	65.3730	+	113.229i	0.151677	+	0.262713i	−0.780167	+	0.625572i	$0.784866\pi$
$432$	29.8001	+	111.216i	0.0689818	+	0.257444i
$433$	456.850	+	456.850i	1.05508	+	1.05508i	0.998392	+	0.0566898i	$0.0180546\pi$
$433$	456.850	+	456.850i	1.05508	+	1.05508i	0.0566898	+	0.998392i	$0.481945\pi$
$434$	−53.4784	−	31.7321i	−0.123222	−	0.0731155i
$435$	−219.902	+	138.480i	−0.505522	+	0.318346i
$436$	42.6209	−	73.8215i	0.0977543	−	0.169315i
$437$	724.537	+	194.139i	1.65798	+	0.444255i
$438$	8.15654	−	30.4406i	0.0186222	−	0.0694992i
$439$	−187.891	−	108.479i	−0.427998	−	0.247105i	0.270495	−	0.962721i	$-0.412812\pi$
$439$	−187.891	−	108.479i	−0.427998	−	0.247105i	−0.698493	+	0.715617i	$0.746146\pi$
$440$	151.068	+	239.891i	0.343337	+	0.545206i
$441$	−75.2446	−	1.79523i	−0.170623	−	0.00407081i
$442$	38.7040	−	38.7040i	0.0875655	−	0.0875655i
$443$	41.8315	−	11.2087i	0.0944277	−	0.0253018i	−0.211296	−	0.977422i	$-0.567768\pi$
$443$	41.8315	−	11.2087i	0.0944277	−	0.0253018i	0.305724	+	0.952120i	$0.401102\pi$
$444$	−179.588	+	103.685i	−0.404478	+	0.233526i
$445$	−369.970	+	114.526i	−0.831394	+	0.257362i
$446$	93.2689	−	161.547i	0.209123	−	0.362212i
$447$	262.259	−	262.259i	0.586710	−	0.586710i
$448$	54.2609	−	13.8477i	0.121118	−	0.0309100i
$449$			48.2524i			0.107466i	0.998555	+	0.0537332i	$0.0171120\pi$
$449$			48.2524i			0.107466i	−0.998555	+	0.0537332i	$0.982888\pi$
$450$	53.3806	+	9.98960i	0.118624	+	0.0221991i
$451$	−164.066	−	284.171i	−0.363783	−	0.630091i
$452$	37.1558	+	9.95586i	0.0822030	+	0.0220262i
$453$	218.302	−	58.4939i	0.481903	−	0.129126i
$454$		−	476.600i		−	1.04978i
$455$	31.1758	+	105.135i	0.0685183	+	0.231065i
$456$	140.926			0.309049
$457$	−75.0016	−	279.910i	−0.164117	−	0.612494i	−0.998151	−	0.0607809i	$-0.980641\pi$
$457$	−75.0016	−	279.910i	−0.164117	−	0.612494i	0.834034	−	0.551713i	$-0.186026\pi$
$458$	139.782	−	521.675i	0.305202	−	1.13903i
$459$	307.942	−	177.791i	0.670899	−	0.387343i
$460$	−15.7899	−	410.993i	−0.0343259	−	0.893463i
$461$	348.242			0.755407			0.377703	−	0.925927i	$-0.376714\pi$
$461$	348.242			0.755407			0.377703	+	0.925927i	$0.376714\pi$
$462$	−387.910	+	378.765i	−0.839631	+	0.819838i
$463$	−268.097	−	268.097i	−0.579044	−	0.579044i	0.355596	−	0.934640i	$-0.384278\pi$
$463$	−268.097	−	268.097i	−0.579044	−	0.579044i	−0.934640	+	0.355596i	$0.884278\pi$
$464$	−65.9016	−	38.0483i	−0.142029	−	0.0820007i
$465$	−40.0189	+	75.9030i	−0.0860621	+	0.163232i
$466$	−236.020	−	408.798i	−0.506480	−	0.877249i
$467$	129.058	+	481.652i	0.276356	+	1.03137i	0.954927	+	0.296840i	$0.0959328\pi$
$467$	129.058	+	481.652i	0.276356	+	1.03137i	−0.678571	+	0.734535i	$0.737400\pi$
$468$	−6.80607	−	6.80607i	−0.0145429	−	0.0145429i
$469$	−0.948961	+	79.5603i	−0.00202337	+	0.169638i
$470$	19.3520	−	85.1791i	0.0411744	−	0.181232i
$471$	−53.5760	+	92.7963i	−0.113749	+	0.197020i
$472$	−259.907	−	69.6419i	−0.550651	−	0.147546i
$473$	31.3063	−	116.837i	0.0661866	−	0.247012i
$474$	58.3603	+	33.6943i	0.123123	+	0.0710850i
$475$	197.000	−	411.177i	0.414738	−	0.865637i
$476$	−84.6794	−	150.794i	−0.177898	−	0.316795i
$477$	−58.1548	+	58.1548i	−0.121918	+	0.121918i
$478$	597.184	−	160.015i	1.24934	−	0.334759i
$479$	324.591	−	187.403i	0.677643	−	0.391238i	−0.121323	−	0.992613i	$-0.538714\pi$
$479$	324.591	−	187.403i	0.677643	−	0.391238i	0.798967	+	0.601376i	$0.205380\pi$
$480$	−22.8505	−	73.8175i	−0.0476053	−	0.153786i
$481$	59.4541	−	102.977i	0.123605	−	0.214090i
$482$	−3.89241	+	3.89241i	−0.00807554	+	0.00807554i
$483$	762.142	−	194.503i	1.57793	−	0.402698i
$484$		−	561.691i		−	1.16052i
$485$	28.5398	+	742.858i	0.0588449	+	1.53167i
$486$	−57.9708	−	100.408i	−0.119281	−	0.206602i
$487$	−379.084	−	101.575i	−0.778406	−	0.208573i	−0.152324	−	0.988331i	$-0.548676\pi$
$487$	−379.084	−	101.575i	−0.778406	−	0.208573i	−0.626082	+	0.779757i	$0.715342\pi$
$488$	23.1109	−	6.19254i	0.0473584	−	0.0126896i
$489$			337.640i			0.690470i
$490$	346.446	−	5.03975i	0.707032	−	0.0102852i
$491$	100.451			0.204585			0.102293	−	0.994754i	$-0.467382\pi$
$491$	100.451			0.204585			0.102293	+	0.994754i	$0.467382\pi$
$492$	23.1489	+	86.3930i	0.0470507	+	0.175595i
$493$	−60.8245	+	227.000i	−0.123376	+	0.460447i
$494$	−69.9820	+	40.4041i	−0.141664	+	0.0817897i
$495$	−112.964	−	104.605i	−0.228210	−	0.211324i
$496$	−25.1262			−0.0506576
$497$	−164.126	−	643.114i	−0.330234	−	1.29399i
$498$	243.785	+	243.785i	0.489527	+	0.489527i
$499$	341.907	+	197.400i	0.685184	+	0.395591i	0.801805	−	0.597585i	$-0.203873\pi$
$499$	341.907	+	197.400i	0.685184	+	0.395591i	−0.116621	+	0.993176i	$0.537206\pi$
$500$	−247.318	−	36.5187i	−0.494637	−	0.0730374i
$501$	−334.863	−	579.999i	−0.668388	−	1.15768i
$502$	134.783	+	503.018i	0.268493	+	1.00203i
$503$	−38.4894	−	38.4894i	−0.0765197	−	0.0765197i	0.667811	−	0.744331i	$-0.267231\pi$
$503$	−38.4894	−	38.4894i	−0.0765197	−	0.0765197i	−0.744331	+	0.667811i	$0.767231\pi$
$504$	−26.5171	+	14.8908i	−0.0526133	+	0.0295453i
$505$	621.362	+	141.168i	1.23042	+	0.279541i
$506$	−583.001	+	1009.79i	−1.15218	+	1.99563i
$507$	420.075	+	112.559i	0.828549	+	0.222009i
$508$	−18.1316	+	67.6682i	−0.0356922	+	0.133205i
$509$	−442.330	−	255.380i	−0.869019	−	0.501728i	−0.00199662	−	0.999998i	$-0.500636\pi$
$509$	−442.330	−	255.380i	−0.869019	−	0.501728i	−0.867022	+	0.498270i	$0.833969\pi$
$510$	−201.937	+	127.167i	−0.395954	+	0.249347i
$511$	57.0923	+	0.680972i	0.111727	+	0.00133263i
$512$	16.0000	−	16.0000i	0.0312500	−	0.0312500i
$513$	−507.070	+	135.869i	−0.988441	+	0.264852i
$514$	−324.329	+	187.252i	−0.630991	+	0.364303i
$515$	17.5137	−	33.2179i	0.0340072	−	0.0645008i
$516$	−16.4850	+	28.5529i	−0.0319478	+	0.0553352i
$517$	−175.102	+	175.102i	−0.338689	+	0.338689i
$518$	−262.476	−	268.813i	−0.506710	−	0.518943i
$519$			661.738i			1.27503i
$520$	32.5110	+	30.1054i	0.0625212	+	0.0578950i
$521$	392.549	+	679.914i	0.753452	+	1.30502i	0.946140	+	0.323758i	$0.104946\pi$
$521$	392.549	+	679.914i	0.753452	+	1.30502i	−0.192688	+	0.981260i	$0.561720\pi$
$522$	39.9179	+	10.6960i	0.0764710	+	0.0204903i
$523$	295.936	−	79.2957i	0.565843	−	0.151617i	0.0354535	−	0.999371i	$-0.488712\pi$
$523$	295.936	−	79.2957i	0.565843	−	0.151617i	0.530389	+	0.847754i	$0.322046\pi$
$524$		−	289.449i		−	0.552383i
$525$	−30.9943	−	477.099i	−0.0590368	−	0.908759i
$526$	−388.239			−0.738097
$527$	20.0835	+	74.9526i	0.0381091	+	0.142225i
$528$	−56.6983	+	211.601i	−0.107383	+	0.400760i
$529$	1006.88	−	581.323i	1.90337	−	1.09891i
$530$	257.237	−	277.792i	0.485353	−	0.524136i
$531$	146.128			0.275193
$532$	63.1364	+	247.394i	0.118677	+	0.465026i
$533$	−36.2647	−	36.2647i	−0.0680387	−	0.0680387i
$534$	−259.178	−	149.636i	−0.485352	−	0.280218i
$535$	−510.662	−	269.240i	−0.954509	−	0.503252i
$536$	16.0748	+	27.8423i	0.0299902	+	0.0519446i
$537$	−122.598	−	457.541i	−0.228301	−	0.852031i
$538$	139.255	+	139.255i	0.258839	+	0.258839i
$539$	−838.704	−	511.279i	−1.55604	−	0.948570i
$540$	153.388	+	243.574i	0.284051	+	0.451063i
$541$	−264.805	+	458.656i	−0.489474	+	0.847793i	−0.999927	−	0.0121125i	$-0.996144\pi$
$541$	−264.805	+	458.656i	−0.489474	+	0.847793i	0.510453	+	0.859906i	$0.329478\pi$
$542$	−84.7834	−	22.7176i	−0.156427	−	0.0419145i
$543$	−167.769	+	626.122i	−0.308967	+	1.15308i
$544$	−60.5177	−	34.9399i	−0.111246	−	0.0642278i
$545$	47.2124	−	207.809i	0.0866282	−	0.381300i
$546$	−43.2410	+	72.8744i	−0.0791960	+	0.133470i
$547$	−343.777	+	343.777i	−0.628477	+	0.628477i	−0.947685	−	0.319207i	$-0.896583\pi$
$547$	−343.777	+	343.777i	−0.628477	+	0.628477i	0.319207	+	0.947685i	$0.396583\pi$
$548$	91.1753	−	24.4303i	0.166378	−	0.0445809i
$549$	−11.2528	+	6.49682i	−0.0204969	+	0.0118339i
$550$	538.125	+	461.224i	0.978410	+	0.838589i
$551$	173.475	−	300.468i	0.314837	−	0.545314i
$552$	224.734	−	224.734i	0.407127	−	0.407127i
$553$	−33.0039	+	117.546i	−0.0596815	+	0.212560i
$554$			588.273i			1.06186i
$555$	−352.240	+	380.386i	−0.634666	+	0.685381i
$556$	121.473	+	210.398i	0.218477	+	0.378414i
$557$	−359.373	−	96.2937i	−0.645194	−	0.172879i	−0.0786389	−	0.996903i	$-0.525057\pi$
$557$	−359.373	−	96.2937i	−0.645194	−	0.172879i	−0.566555	+	0.824024i	$0.691724\pi$
$558$	13.1804	−	3.53167i	0.0236208	−	0.00632916i
$559$		−	18.9053i		−	0.0338199i
$560$	119.348	−	73.1848i	0.213122	−	0.130687i
$561$	676.536			1.20595
$562$	−135.649	−	506.247i	−0.241368	−	0.900796i
$563$	−248.463	+	927.276i	−0.441319	+	1.64703i	0.284156	+	0.958778i	$0.408287\pi$
$563$	−248.463	+	927.276i	−0.441319	+	1.64703i	−0.725476	+	0.688248i	$0.758380\pi$
$564$	58.4551	−	33.7490i	0.103644	−	0.0598387i
$565$	96.0953	−	3.69187i	0.170080	−	0.00653429i
$566$	682.637			1.20607
$567$	−324.627	+	316.975i	−0.572535	+	0.559038i
$568$	−189.636	−	189.636i	−0.333866	−	0.333866i
$569$	579.317	+	334.469i	1.01813	+	0.587818i	0.913562	−	0.406699i	$-0.133320\pi$
$569$	579.317	+	334.469i	1.01813	+	0.587818i	0.104569	+	0.994518i	$0.466654\pi$
$570$	336.559	−	104.183i	0.590455	−	0.182778i
$571$	136.393	+	236.240i	0.238868	+	0.413731i	0.960390	−	0.278661i	$-0.0898905\pi$
$571$	136.393	+	236.240i	0.238868	+	0.413731i	−0.721522	+	0.692391i	$0.756557\pi$
$572$	−32.5113	−	121.334i	−0.0568379	−	0.212122i
$573$	−40.5379	−	40.5379i	−0.0707468	−	0.0707468i
$574$	−141.291	+	79.3425i	−0.246151	+	0.138227i
$575$	−341.547	−	969.858i	−0.593995	−	1.68671i
$576$	−6.14417	+	10.6420i	−0.0106670	+	0.0184757i
$577$	−209.014	−	56.0052i	−0.362243	−	0.0970627i	0.0731068	−	0.997324i	$-0.476709\pi$
$577$	−209.014	−	56.0052i	−0.362243	−	0.0970627i	−0.435350	+	0.900261i	$0.643375\pi$
$578$	49.9260	−	186.326i	0.0863771	−	0.322364i
$579$	−118.422	−	68.3709i	−0.204528	−	0.118084i
$580$	−185.514	−	42.1472i	−0.319852	−	0.0726677i
$581$	−318.742	+	537.178i	−0.548609	+	0.924575i
$582$	−406.201	+	406.201i	−0.697940	+	0.697940i
$583$	−1036.74	+	277.794i	−1.77829	+	0.476491i
$584$	19.9796	−	11.5352i	0.0342116	−	0.0197521i
$585$	−21.2858	−	11.2226i	−0.0363860	−	0.0191840i
$586$	203.433	−	352.357i	0.347156	−	0.601292i
$587$	−193.451	+	193.451i	−0.329559	+	0.329559i	−0.852419	−	0.522860i	$-0.824865\pi$
$587$	−193.451	+	193.451i	−0.329559	+	0.329559i	0.522860	+	0.852419i	$0.324865\pi$
$588$	184.750	+	193.781i	0.314201	+	0.329560i
$589$		−	114.559i		−	0.194497i
$590$	−672.193	+	25.8249i	−1.13931	+	0.0437711i
$591$	−165.358	−	286.408i	−0.279793	−	0.484616i
$592$	−146.635	−	39.2907i	−0.247694	−	0.0663694i
$593$	140.689	−	37.6975i	0.237249	−	0.0635708i	−0.138235	−	0.990399i	$-0.544143\pi$
$593$	140.689	−	37.6975i	0.237249	−	0.0635708i	0.375485	+	0.926829i	$0.377476\pi$
$594$		−	816.031i		−	1.37379i
$595$	−313.710	−	297.525i	−0.527243	−	0.500041i
$596$	271.514			0.455560
$597$	217.406	+	811.369i	0.364164	+	1.35908i
$598$	−47.1677	+	176.032i	−0.0788757	+	0.294368i
$599$	−396.026	+	228.645i	−0.661144	+	0.381712i	−0.792713	−	0.609595i	$-0.791332\pi$
$599$	−396.026	+	228.645i	−0.661144	+	0.381712i	0.131568	+	0.991307i	$0.457999\pi$
$600$	−109.143	−	159.398i	−0.181905	−	0.265663i
$601$	369.587			0.614953			0.307477	−	0.951556i	$-0.400515\pi$
$601$	369.587			0.614953			0.307477	+	0.951556i	$0.400515\pi$
$602$	−57.5097	−	16.1472i	−0.0955311	−	0.0268227i
$603$	−12.3457	−	12.3457i	−0.0204739	−	0.0204739i
$604$	143.282	+	82.7236i	0.237221	+	0.136960i
$605$	−415.245	−	1341.43i	−0.686355	−	2.21723i
$606$	246.191	+	426.416i	0.406256	+	0.703657i
$607$	−60.5336	−	225.915i	−0.0997259	−	0.372182i	0.897968	−	0.440062i	$-0.145043\pi$
$607$	−60.5336	−	225.915i	−0.0997259	−	0.372182i	−0.997694	+	0.0678794i	$0.978377\pi$
$608$	72.9495	+	72.9495i	0.119983	+	0.119983i
$609$	4.33920	−	363.796i	0.00712512	−	0.597365i
$610$	50.6153	−	31.8743i	0.0829758	−	0.0522530i
$611$	−19.3520	+	33.5186i	−0.0316726	+	0.0548586i
$612$	36.6567	+	9.82214i	0.0598966	+	0.0160492i
$613$	248.441	−	927.194i	0.405287	−	1.51255i	−0.398239	−	0.917282i	$-0.630378\pi$
$613$	248.441	−	927.194i	0.405287	−	1.51255i	0.803526	−	0.595270i	$-0.202955\pi$
$614$	0.359231	+	0.207402i	0.000585067	+	0.000337789i
$615$	119.152	+	189.210i	0.193744	+	0.307658i
$616$	−396.864	−	4.73362i	−0.644260	−	0.00768445i
$617$	22.6455	−	22.6455i	0.0367026	−	0.0367026i	−0.688517	−	0.725220i	$-0.741738\pi$
$617$	22.6455	−	22.6455i	0.0367026	−	0.0367026i	0.725220	+	0.688517i	$0.241738\pi$
$618$	28.0290	−	7.51035i	0.0453544	−	0.0121527i
$619$	430.611	−	248.613i	0.695655	−	0.401637i	−0.110072	−	0.993924i	$-0.535108\pi$
$619$	430.611	−	248.613i	0.695655	−	0.401637i	0.805727	+	0.592287i	$0.201775\pi$
$620$	−60.0062	+	18.5752i	−0.0967841	+	0.0299600i
$621$	−591.953	+	1025.29i	−0.953225	+	1.65103i
$622$	356.021	−	356.021i	0.572382	−	0.572382i
$623$	146.570	−	522.021i	0.235265	−	0.837915i
$624$			34.2392i			0.0548705i
$625$	−617.642	+	95.6230i	−0.988227	+	0.152997i
$626$	184.173	+	318.996i	0.294205	+	0.509579i
$627$	−964.762	−	258.507i	−1.53870	−	0.412292i
$628$	−75.7686	+	20.3021i	−0.120651	+	0.0323282i
$629$			468.824i			0.745348i
$630$	−52.3196	+	55.1657i	−0.0830469	+	0.0875646i
$631$	965.780			1.53056			0.765278	−	0.643700i	$-0.222602\pi$
$631$	965.780			1.53056			0.765278	+	0.643700i	$0.222602\pi$
$632$	12.7682	+	47.6514i	0.0202028	+	0.0753978i
$633$	82.4369	−	307.659i	0.130232	−	0.486033i
$634$	94.7354	−	54.6955i	0.149425	−	0.0862705i
$635$	6.72366	+	175.009i	0.0105884	+	0.275605i
$636$	292.558			0.459997
$637$	−147.302	−	43.2605i	−0.231244	−	0.0679129i
$638$	381.360	+	381.360i	0.597743	+	0.597743i
$639$	126.132	+	72.8222i	0.197389	+	0.113963i
$640$	26.3827	−	50.0395i	0.0412229	−	0.0781868i
$641$	−599.981	−	1039.20i	−0.936008	−	1.62121i	−0.772826	−	0.634618i	$-0.781157\pi$
$641$	−599.981	−	1039.20i	−0.936008	−	1.62121i	−0.163183	−	0.986596i	$-0.552176\pi$
$642$	−115.457	−	430.892i	−0.179840	−	0.671172i
$643$	405.030	+	405.030i	0.629906	+	0.629906i	0.948044	−	0.318138i	$-0.103058\pi$
$643$	405.030	+	405.030i	0.629906	+	0.629906i	−0.318138	+	0.948044i	$0.603058\pi$
$644$	495.201	+	293.834i	0.768946	+	0.456265i
$645$	−18.2610	+	80.3770i	−0.0283116	+	0.124615i
$646$	159.303	−	275.921i	0.246599	−	0.427122i
$647$	81.5250	+	21.8446i	0.126005	+	0.0337628i	0.321270	−	0.946988i	$-0.395890\pi$
$647$	81.5250	+	21.8446i	0.126005	+	0.0337628i	−0.195266	+	0.980750i	$0.562557\pi$
$648$	−47.4488	+	177.081i	−0.0732234	+	0.273273i
$649$	1651.54	+	953.518i	2.54475	+	1.46921i
$650$	99.8989	+	47.8628i	0.153691	+	0.0736351i
$651$	−58.8196	−	104.744i	−0.0903527	−	0.160897i
$652$	−174.777	+	174.777i	−0.268063	+	0.268063i
$653$	463.478	−	124.189i	0.709767	−	0.190182i	0.114166	−	0.993462i	$-0.463580\pi$
$653$	463.478	−	124.189i	0.709767	−	0.190182i	0.595601	+	0.803280i	$0.296914\pi$
$654$	142.611	−	82.3364i	0.218059	−	0.125897i
$655$	−213.983	−	691.260i	−0.326691	−	1.05536i
$656$	−32.7378	+	56.7036i	−0.0499052	+	0.0864384i
$657$	−8.85928	+	8.85928i	−0.0134844	+	0.0134844i
$658$	85.4344	+	87.4971i	0.129840	+	0.132974i
$659$			168.872i			0.256255i	0.991758	+	0.128127i	$0.0408966\pi$
$659$			168.872i			0.256255i	−0.991758	+	0.128127i	$0.959103\pi$
$660$	21.0251	+	547.260i	0.0318563	+	0.829182i
$661$	251.775	+	436.087i	0.380900	+	0.659738i	0.991191	−	0.132439i	$-0.0422810\pi$
$661$	251.775	+	436.087i	0.380900	+	0.659738i	−0.610291	+	0.792177i	$0.708948\pi$
$662$	−117.865	−	31.5818i	−0.178043	−	0.0477066i
$663$	102.137	−	27.3676i	0.154053	−	0.0412784i
$664$			252.387i			0.380101i
$665$	333.675	+	544.149i	0.501766	+	0.818270i
$666$	82.4425			0.123788
$667$	−202.515	−	755.795i	−0.303620	−	1.13313i
$668$	126.893	−	473.572i	0.189960	−	0.708940i
$669$	312.081	−	180.180i	0.466489	−	0.269327i
$670$	58.9728	+	54.6091i	0.0880191	+	0.0815061i
$671$	−169.573			−0.252717
$672$	104.155	+	29.2440i	0.154993	+	0.0435179i
$673$	143.862	+	143.862i	0.213763	+	0.213763i	0.805864	−	0.592101i	$-0.201701\pi$
$673$	143.862	+	143.862i	0.213763	+	0.213763i	−0.592101	+	0.805864i	$0.701701\pi$
$674$	160.813	+	92.8454i	0.238595	+	0.137753i
$675$	546.388	+	468.306i	0.809464	+	0.693787i
$676$	159.183	+	275.714i	0.235479	+	0.407861i
$677$	31.4489	+	117.369i	0.0464533	+	0.173366i	0.985255	−	0.171092i	$-0.0547295\pi$
$677$	31.4489	+	117.369i	0.0464533	+	0.173366i	−0.938802	+	0.344458i	$0.888063\pi$
$678$	52.5457	+	52.5457i	0.0775010	+	0.0775010i
$679$	−895.062	−	531.097i	−1.31821	−	0.782176i
$680$	−170.358	−	38.7040i	−0.250527	−	0.0569176i
$681$	460.356	−	797.360i	0.676000	−	1.17087i
$682$	172.010	+	46.0900i	0.252215	+	0.0675807i
$683$	−209.950	+	783.543i	−0.307393	+	1.14721i	0.623472	+	0.781845i	$0.285721\pi$
$683$	−209.950	+	783.543i	−0.307393	+	1.14721i	−0.930866	+	0.365362i	$0.880945\pi$
$684$	−48.5206	−	28.0134i	−0.0709365	−	0.0409552i
$685$	199.684	−	125.748i	0.291509	−	0.183574i
$686$	−257.410	+	411.142i	−0.375234	+	0.599333i
$687$	737.753	−	737.753i	1.07388	−	1.07388i
$688$	−23.3136	+	6.24686i	−0.0338861	+	0.00907974i
$689$	−145.280	+	83.8777i	−0.210857	+	0.121738i
$690$	370.568	−	702.850i	0.537055	−	1.01862i
$691$	16.3168	−	28.2615i	0.0236133	−	0.0408994i	−0.853977	−	0.520310i	$-0.825816\pi$
$691$	16.3168	−	28.2615i	0.0236133	−	0.0408994i	0.877591	+	0.479411i	$0.159150\pi$
$692$	−342.544	+	342.544i	−0.495006	+	0.495006i
$693$	208.847	−	53.2991i	0.301367	−	0.0769107i
$694$			566.487i			0.816264i
$695$	445.645	+	412.669i	0.641215	+	0.593769i
$696$	−73.5030	−	127.311i	−0.105608	−	0.182918i
$697$	195.317	+	52.3351i	0.280226	+	0.0750862i
$698$	−276.379	+	74.0555i	−0.395958	+	0.106097i
$699$		−	911.901i		−	1.30458i
$700$	230.923	−	263.011i	0.329890	−	0.375730i
$701$	−311.596			−0.444503			−0.222251	−	0.974989i	$-0.571341\pi$
$701$	−311.596			−0.444503			−0.222251	+	0.974989i	$0.571341\pi$
$702$	−33.0105	−	123.197i	−0.0470235	−	0.175494i
$703$	179.140	−	668.558i	0.254822	−	0.951007i
$704$	−138.883	+	80.1843i	−0.197277	+	0.113898i
$705$	114.652	−	123.814i	0.162627	−	0.175622i
$706$	−466.952			−0.661405
$707$	−638.270	+	623.224i	−0.902787	+	0.881505i
$708$	−367.561	−	367.561i	−0.519154	−	0.519154i
$709$	−622.782	−	359.564i	−0.878396	−	0.507142i	−0.00826649	−	0.999966i	$-0.502631\pi$
$709$	−622.782	−	359.564i	−0.878396	−	0.507142i	−0.870129	+	0.492824i	$0.835965\pi$
$710$	−593.081	−	312.694i	−0.835326	−	0.440414i
$711$	−13.3955	−	23.2017i	−0.0188404	−	0.0326325i
$712$	−56.7033	−	211.620i	−0.0796395	−	0.297219i
$713$	−182.686	−	182.686i	−0.256222	−	0.256222i
$714$	3.98470	−	334.075i	0.00558081	−	0.467892i
$715$	−167.343	−	265.734i	−0.234045	−	0.371656i
$716$	173.381	−	300.305i	0.242152	−	0.419420i
$717$	1153.66	+	309.122i	1.60901	+	0.431133i
$718$	−11.4631	+	42.7809i	−0.0159653	+	0.0595834i
$719$	278.808	+	160.970i	0.387771	+	0.223880i	0.681194	−	0.732103i	$-0.261461\pi$
$719$	278.808	+	160.970i	0.387771	+	0.223880i	−0.293423	+	0.955983i	$0.594794\pi$
$720$	−6.80607	+	29.9574i	−0.00945288	+	0.0416075i
$721$	25.7416	+	45.8398i	0.0357026	+	0.0635780i
$722$	28.3982	−	28.3982i	0.0393327	−	0.0393327i
$723$	−10.2718	+	2.75232i	−0.0142072	+	0.00380681i
$724$	−410.952	+	237.263i	−0.567613	+	0.327712i
$725$	−474.202	+	36.4905i	−0.654072	+	0.0503317i
$726$	542.546	−	939.718i	0.747309	−	1.29438i
$727$	−905.157	+	905.157i	−1.24506	+	1.24506i	−0.287182	+	0.957876i	$0.592718\pi$
$727$	−905.157	+	905.157i	−1.24506	+	1.24506i	−0.957876	+	0.287182i	$0.907282\pi$
$728$	−60.1063	+	15.3395i	−0.0825636	+	0.0210707i
$729$		−	807.326i		−	1.10744i
$730$	39.1874	−	42.3187i	0.0536813	−	0.0579709i
$731$	37.2694	+	64.5525i	0.0509841	+	0.0883071i
$732$	44.6464	+	11.9630i	0.0609923	+	0.0163428i
$733$	−890.884	+	238.712i	−1.21539	+	0.325664i	−0.808876	−	0.587979i	$-0.799924\pi$
$733$	−890.884	+	238.712i	−1.21539	+	0.325664i	−0.406518	+	0.913643i	$0.633257\pi$
$734$		−	248.207i		−	0.338157i
$735$	584.477	+	326.206i	0.795207	+	0.443818i
$736$	232.664			0.316120
$737$	−58.9733	−	220.091i	−0.0800180	−	0.298631i
$738$	9.20310	−	34.3464i	0.0124703	−	0.0465399i
$739$	−391.732	+	226.167i	−0.530084	+	0.306044i	−0.741051	−	0.671449i	$-0.765672\pi$
$739$	−391.732	+	226.167i	−0.530084	+	0.306044i	0.210967	+	0.977493i	$0.432339\pi$
$740$	−379.239	+	14.5699i	−0.512485	+	0.0196891i
$741$	−156.108			−0.210672
$742$	131.069	+	513.582i	0.176643	+	0.692158i
$743$	664.894	+	664.894i	0.894877	+	0.894877i	0.994977	−	0.100100i	$-0.0319164\pi$
$743$	664.894	+	664.894i	0.894877	+	0.894877i	−0.100100	+	0.994977i	$0.531916\pi$
$744$	−42.0365	−	24.2698i	−0.0565007	−	0.0326207i
$745$	648.427	−	200.724i	0.870372	−	0.269428i
$746$	−76.4288	−	132.379i	−0.102452	−	0.177451i
$747$	−35.4749	−	132.394i	−0.0474898	−	0.177234i
$748$	350.204	+	350.204i	0.468187	+	0.468187i
$749$	704.699	−	395.728i	0.940853	−	0.528342i
$750$	−378.494	−	299.985i	−0.504658	−	0.399980i
$751$	112.885	−	195.522i	0.150312	−	0.260349i	−0.781030	−	0.624494i	$-0.785305\pi$
$751$	112.885	−	195.522i	0.150312	−	0.260349i	0.931342	+	0.364145i	$0.118639\pi$
$752$	47.7288	+	12.7889i	0.0634692	+	0.0170065i
$753$	−260.379	+	971.747i	−0.345789	+	1.29050i
$754$	73.0012	+	42.1472i	0.0968185	+	0.0558982i
$755$	403.340	+	91.6354i	0.534225	+	0.121371i
$756$	−402.957	−	4.80630i	−0.533013	−	0.00635754i
$757$	−445.497	+	445.497i	−0.588503	+	0.588503i	−0.937226	−	0.348723i	$-0.886615\pi$
$757$	−445.497	+	445.497i	−0.588503	+	0.588503i	0.348723	+	0.937226i	$0.386615\pi$
$758$	−505.960	+	135.572i	−0.667494	+	0.178854i
$759$	−1950.74	+	1126.26i	−2.57015	+	1.48387i
$760$	228.147	+	120.288i	0.300194	+	0.158273i
$761$	179.891	−	311.580i	0.236388	−	0.409436i	−0.723287	−	0.690547i	$-0.757370\pi$
$761$	179.891	−	311.580i	0.236388	−	0.409436i	0.959675	+	0.281112i	$0.0907031\pi$
$762$	−95.6964	+	95.6964i	−0.125586	+	0.125586i
$763$	208.431	+	213.464i	0.273174	+	0.279769i
$764$		−	41.9683i		−	0.0549324i
$765$	94.8046	−	3.64229i	0.123928	−	0.00476116i
$766$	−2.48825	−	4.30977i	−0.00324836	−	0.00562633i
$767$	287.907	+	77.1444i	0.375367	+	0.100579i
$768$	42.2229	−	11.3136i	0.0549778	−	0.0147312i
$769$		−	1100.57i		−	1.43117i	−0.698527	−	0.715584i	$-0.746161\pi$
$769$		−	1100.57i		−	1.43117i	0.698527	−	0.715584i	$-0.253839\pi$
$770$	−951.287	+	282.087i	−1.23544	+	0.366347i
$771$	−723.478			−0.938363
$772$	−25.9085	−	96.6920i	−0.0335603	−	0.125249i
$773$	−3.34535	+	12.4850i	−0.00432775	+	0.0161514i	−0.968056	−	0.250734i	$-0.919328\pi$
$773$	−3.34535	+	12.4850i	−0.00432775	+	0.0161514i	0.963728	+	0.266886i	$0.0859946\pi$
$774$	11.3515	−	6.55381i	0.0146661	−	0.00846745i
$775$	−129.574	+	88.7223i	−0.167192	+	0.114480i
$776$	−420.534			−0.541925
$777$	−179.476	−	703.258i	−0.230985	−	0.905093i
$778$	−725.344	−	725.344i	−0.932319	−	0.932319i
$779$	−258.531	−	149.263i	−0.331876	−	0.191609i
$780$	25.3122	+	81.7698i	0.0324516	+	0.104833i
$781$	950.365	+	1646.08i	1.21686	+	2.10766i
$782$	−185.970	−	694.049i	−0.237813	−	0.887531i
$783$	387.216	+	387.216i	0.494528	+	0.494528i
$784$	−4.67494	+	195.944i	−0.00596294	+	0.249929i
$785$	−165.941	+	104.499i	−0.211390	+	0.133120i
$786$	279.583	−	484.253i	0.355704	−	0.616098i
$787$	1200.53	+	321.680i	1.52545	+	0.408742i	0.921531	−	0.388305i	$-0.126939\pi$
$787$	1200.53	+	321.680i	1.52545	+	0.408742i	0.603917	+	0.797047i	$0.293606\pi$
$788$	62.6608	−	233.853i	0.0795188	−	0.296768i
$789$	−649.530	−	375.006i	−0.823232	−	0.475293i
$790$	65.7204	+	104.362i	0.0831904	+	0.132103i
$791$	−68.7021	+	115.784i	−0.0868548	+	0.146377i
$792$	61.5832	−	61.5832i	0.0777566	−	0.0777566i
$793$	−25.6006	+	6.85966i	−0.0322832	+	0.00865026i
$794$	156.913	−	90.5936i	0.197623	−	0.114098i
$795$	698.686	−	216.281i	0.878850	−	0.272052i
$796$	−307.461	+	532.538i	−0.386258	+	0.669018i
$797$	−658.639	+	658.639i	−0.826398	+	0.826398i	−0.987017	−	0.160618i	$-0.948651\pi$
$797$	−658.639	+	658.639i	−0.826398	+	0.826398i	0.160618	+	0.987017i	$0.448651\pi$
$798$	−133.334	+	474.879i	−0.167085	+	0.595086i
$799$		−	152.600i		−	0.190988i
$800$	26.0139	−	139.008i	0.0325174	−	0.173760i
$801$	59.4895	+	103.039i	0.0742691	+	0.128638i
$802$	957.533	+	256.570i	1.19393	+	0.319913i
$803$	−157.937	+	42.3191i	−0.196684	+	0.0527012i
$804$			62.1075i			0.0772481i
$805$	1399.86	+	335.643i	1.73896	+	0.416948i
$806$	27.8330			0.0345322
$807$	98.4674	+	367.485i	0.122017	+	0.455372i
$808$	−93.2920	+	348.170i	−0.115460	+	0.430904i
$809$	−712.947	+	411.620i	−0.881270	+	0.508802i	−0.871077	−	0.491147i	$-0.836578\pi$
$809$	−712.947	+	411.620i	−0.881270	+	0.508802i	−0.0101931	+	0.999948i	$0.503245\pi$
$810$	17.5952	+	457.982i	0.0217224	+	0.565410i
$811$	−1415.46			−1.74533			−0.872666	−	0.488318i	$-0.837610\pi$
$811$	−1415.46			−1.74533			−0.872666	+	0.488318i	$0.837610\pi$
$812$	190.562	−	186.070i	0.234683	−	0.229150i
$813$	−119.901	−	119.901i	−0.147479	−	0.147479i
$814$	931.769	+	537.957i	1.14468	+	0.660881i
$815$	−288.193	+	546.610i	−0.353611	+	0.670687i
$816$	−67.4981	−	116.910i	−0.0827182	−	0.143272i
$817$	−28.4816	−	106.295i	−0.0348612	−	0.130104i
$818$	−452.456	−	452.456i	−0.553124	−	0.553124i
$819$	29.3738	−	16.4950i	0.0358654	−	0.0201404i
$820$	−36.2647	+	159.621i	−0.0442252	+	0.194660i
$821$	−28.8421	+	49.9560i	−0.0351305	+	0.0608478i	−0.883056	−	0.469267i	$-0.844518\pi$
$821$	−28.8421	+	49.9560i	−0.0351305	+	0.0608478i	0.847926	+	0.530115i	$0.177851\pi$
$822$	176.135	+	47.1954i	0.214277	+	0.0574153i
$823$	100.057	−	373.416i	0.121575	−	0.453725i	−0.878119	−	0.478442i	$-0.841202\pi$
$823$	100.057	−	373.416i	0.121575	−	0.453725i	0.999694	+	0.0247166i	$0.00786834\pi$
$824$	18.3967	+	10.6213i	0.0223261	+	0.0128900i
$825$	454.789	+	1291.42i	0.551259	+	1.56536i
$826$	480.576	−	809.918i	0.581811	−	0.980531i
$827$	84.0099	−	84.0099i	0.101584	−	0.101584i	−0.654488	−	0.756072i	$-0.727116\pi$
$827$	84.0099	−	84.0099i	0.101584	−	0.101584i	0.756072	+	0.654488i	$0.227116\pi$
$828$	−122.048	+	32.7027i	−0.147401	+	0.0394961i
$829$	−880.574	+	508.399i	−1.06221	+	0.613268i	−0.926043	−	0.377417i	$-0.876812\pi$
$829$	−880.574	+	508.399i	−1.06221	+	0.613268i	−0.136169	+	0.990686i	$0.543479\pi$
$830$	186.584	+	602.748i	0.224800	+	0.726203i
$831$	−568.222	+	984.190i	−0.683781	+	1.18434i
$832$	−17.7237	+	17.7237i	−0.0213025	+	0.0213025i
$833$	588.248	−	142.674i	0.706180	−	0.171277i
$834$			469.333i			0.562749i
$835$	−47.0551	−	1224.79i	−0.0563534	−	1.46681i
$836$	−365.588	−	633.217i	−0.437306	−	0.757436i
$837$	174.651	+	46.7977i	0.208664	+	0.0559112i
$838$	−339.013	+	90.8382i	−0.404550	+	0.108399i
$839$		−	538.853i		−	0.642256i	−0.947036	−	0.321128i	$-0.895938\pi$
$839$		−	538.853i		−	0.642256i	0.947036	−	0.321128i	$-0.104062\pi$
$840$	270.362	−	7.15896i	0.321859	−	0.00852257i
$841$	479.081			0.569656
$842$	−87.4770	−	326.469i	−0.103892	−	0.387730i
$843$	262.050	−	977.985i	0.310855	−	1.16013i
$844$	201.930	−	116.585i	0.239254	−	0.138133i
$845$	583.990	+	540.778i	0.691112	+	0.639973i
$846$	−26.8346			−0.0317194
$847$	1892.73	+	531.429i	2.23462	+	0.627425i
$848$	151.441	+	151.441i	0.178586	+	0.178586i
$849$	1142.06	+	659.370i	1.34519	+	0.776644i
$850$	−435.462	+	33.5094i	−0.512308	+	0.0394228i
$851$	−780.473	−	1351.82i	−0.917125	−	1.58851i
$852$	−134.092	−	500.437i	−0.157385	−	0.587367i
$853$	−1067.08	−	1067.08i	−1.25098	−	1.25098i	−0.955283	−	0.295694i	$-0.904449\pi$
$853$	−1067.08	−	1067.08i	−1.25098	−	1.25098i	−0.295694	−	0.955283i	$-0.595551\pi$
$854$	−0.998762	+	83.7356i	−0.00116951	+	0.0980510i
$855$	−136.586	−	31.0312i	−0.159750	−	0.0362938i
$856$	163.283	−	282.814i	0.190751	−	0.330390i
$857$	−979.577	−	262.477i	−1.14303	−	0.306274i	−0.362861	−	0.931843i	$-0.618200\pi$
$857$	−979.577	−	262.477i	−1.14303	−	0.306274i	−0.780169	+	0.625569i	$0.784867\pi$
$858$	62.8064	−	234.397i	0.0732009	−	0.273190i
$859$	196.715	+	113.574i	0.229005	+	0.132216i	0.610113	−	0.792315i	$-0.291124\pi$
$859$	196.715	+	113.574i	0.229005	+	0.132216i	−0.381108	+	0.924530i	$0.624457\pi$
$860$	−51.0592	+	32.1539i	−0.0593712	+	0.0373883i
$861$	−313.020	−	3.73356i	−0.363554	−	0.00433631i
$862$	−130.746	+	130.746i	−0.151677	+	0.151677i
$863$	470.501	−	126.070i	0.545193	−	0.146084i	0.0242979	−	0.999705i	$-0.492265\pi$
$863$	470.501	−	126.070i	0.545193	−	0.146084i	0.520895	+	0.853621i	$0.325598\pi$
$864$	−141.016	+	81.4155i	−0.163213	+	0.0942309i
$865$	−564.827	+	1071.30i	−0.652979	+	1.23849i
$866$	−456.850	+	791.288i	−0.527541	+	0.913727i
$867$	263.503	−	263.503i	0.303925	−	0.303925i
$868$	23.7725	−	84.6676i	0.0273876	−	0.0975433i
$869$		−	349.636i		−	0.402343i
$870$	−269.658	−	249.704i	−0.309951	−	0.287016i
$871$	−17.8065	−	30.8417i	−0.0204437	−	0.0354095i
$872$	116.442	+	31.2006i	0.133535	+	0.0357806i
$873$	220.599	−	59.1093i	0.252690	−	0.0677082i
$874$			1060.80i			1.21373i
$875$	357.051	−	798.837i	0.408058	−	0.912956i
$876$	44.5682			0.0508769
$877$	−36.9236	−	137.801i	−0.0421022	−	0.157127i	0.941674	−	0.336525i	$-0.109252\pi$
$877$	−36.9236	−	137.801i	−0.0421022	−	0.157127i	−0.983777	+	0.179398i	$0.942585\pi$
$878$	79.4121	−	296.370i	0.0904466	−	0.337551i
$879$	680.695	−	392.999i	0.774397	−	0.447098i
$880$	−272.402	+	294.169i	−0.309548	+	0.334283i
$881$	21.6989			0.0246299			0.0123149	−	0.999924i	$-0.496080\pi$
$881$	21.6989			0.0246299			0.0123149	+	0.999924i	$0.496080\pi$
$882$	−25.0891	−	103.443i	−0.0284457	−	0.117283i
$883$	−100.328	−	100.328i	−0.113622	−	0.113622i	0.648010	−	0.761632i	$-0.275602\pi$
$883$	−100.328	−	100.328i	−0.113622	−	0.113622i	−0.761632	+	0.648010i	$0.775602\pi$
$884$	67.0372	+	38.7040i	0.0758340	+	0.0437828i
$885$	−1149.54	−	606.077i	−1.29891	−	0.684833i
$886$	30.6228	+	53.0402i	0.0345629	+	0.0598647i
$887$	−126.146	−	470.784i	−0.142217	−	0.530759i	−0.999864	−	0.0165205i	$-0.994741\pi$
$887$	−126.146	−	470.784i	−0.142217	−	0.530759i	0.857647	−	0.514239i	$-0.171926\pi$
$888$	−207.371	−	207.371i	−0.233526	−	0.233526i
$889$	−210.867	−	125.121i	−0.237195	−	0.140743i
$890$	−291.864	−	463.470i	−0.327937	−	0.520752i
$891$	649.655	−	1125.24i	0.729131	−	1.26289i
$892$	254.815	+	68.2776i	0.285668	+	0.0765444i
$893$	−58.3090	+	217.612i	−0.0652956	+	0.243686i
$894$	454.247	+	262.259i	0.508106	+	0.293355i
$895$	192.059	−	845.362i	0.214591	−	0.944539i
$896$	38.7772	+	69.0531i	0.0432781	+	0.0770682i
$897$	−248.945	+	248.945i	−0.277530	+	0.277530i
$898$	−65.9140	+	17.6616i	−0.0734009	+	0.0196677i
$899$	−103.491	+	59.7506i	−0.115118	+	0.0664634i
$900$	5.89260	+	76.5757i	0.00654734	+	0.0850841i
$901$	330.708	−	572.803i	0.367045	−	0.635741i
$902$	328.133	−	328.133i	0.363783	−	0.363783i
$903$	−80.6178	−	82.5642i	−0.0892778	−	0.0914332i
$904$			54.3998i			0.0601768i
$905$	−806.030	+	870.438i	−0.890641	+	0.961810i
$906$	159.808	+	276.796i	0.176389	+	0.305514i
$907$	−8.97709	−	2.40540i	−0.00989756	−	0.00265204i	0.253867	−	0.967239i	$-0.418297\pi$
$907$	−8.97709	−	2.40540i	−0.00989756	−	0.00265204i	−0.263764	+	0.964587i	$0.584964\pi$
$908$	651.048	−	174.448i	0.717013	−	0.192123i
$909$		−	195.752i		−	0.215349i
$910$	−132.205	+	81.0689i	−0.145281	+	0.0890867i
$911$	−1071.38			−1.17605			−0.588027	−	0.808841i	$-0.700095\pi$
$911$	−1071.38			−1.17605			−0.588027	+	0.808841i	$0.700095\pi$
$912$	51.5826	+	192.509i	0.0565599	+	0.211084i
$913$	462.964	−	1727.81i	0.507080	−	1.89245i
$914$	354.912	−	204.908i	0.388306	−	0.224188i
$915$	115.468	−	4.43616i	0.126195	−	0.00484826i
$916$	763.785			0.833827
$917$	975.355	+	273.854i	1.06364	+	0.298642i
$918$	355.581	+	355.581i	0.387343	+	0.387343i
$919$	1186.43	+	684.983i	1.29100	+	0.745357i	0.978831	−	0.204671i	$-0.0656125\pi$
$919$	1186.43	+	684.983i	1.29100	+	0.745357i	0.312165	+	0.950028i	$0.398946\pi$
$920$	555.648	−	172.003i	0.603965	−	0.186960i
$921$	0.400667	+	0.693975i	0.000435034	+	0.000753502i
$922$	127.466	+	475.708i	0.138249	+	0.515952i
$923$	210.065	+	210.065i	0.227590	+	0.227590i
$924$	−659.388	−	391.257i	−0.713623	−	0.423438i
$925$	−894.925	+	315.158i	−0.967486	+	0.340712i
$926$	268.097	−	464.358i	0.289522	−	0.501466i
$927$	−11.1432	−	2.98582i	−0.0120207	−	0.00322095i
$928$	27.8533	−	103.950i	0.0300143	−	0.112015i
$929$	−818.100	−	472.330i	−0.880624	−	0.508429i	−0.00976001	−	0.999952i	$-0.503107\pi$
$929$	−818.100	−	472.330i	−0.880624	−	0.508429i	−0.870864	+	0.491524i	$0.836440\pi$
$930$	−118.333	−	26.8843i	−0.127240	−	0.0289079i
$931$	−893.377	−	21.3147i	−0.959589	−	0.0228944i
$932$	472.039	−	472.039i	0.506480	−	0.506480i
$933$	939.516	−	251.743i	1.00698	−	0.269821i
$934$	−610.710	+	352.594i	−0.653865	+	0.377509i
$935$	1095.25	+	577.458i	1.17139	+	0.617602i
$936$	6.80607	−	11.7885i	0.00727144	−	0.0125945i
$937$	649.423	−	649.423i	0.693087	−	0.693087i	−0.269823	−	0.962910i	$-0.586965\pi$
$937$	649.423	−	649.423i	0.693087	−	0.693087i	0.962910	+	0.269823i	$0.0869651\pi$
$938$	−109.029	+	27.8248i	−0.116235	+	0.0296640i
$939$			711.582i			0.757808i
$940$	123.440	−	4.74243i	0.131319	−	0.00504514i
$941$	18.0898	+	31.3324i	0.0192240	+	0.0332969i	0.875477	−	0.483259i	$-0.160547\pi$
$941$	18.0898	+	31.3324i	0.0192240	+	0.0332969i	−0.856253	+	0.516556i	$0.827214\pi$
$942$	−146.372	−	39.2203i	−0.155385	−	0.0416352i
$943$	−650.307	+	174.249i	−0.689615	+	0.184782i
$944$		−	380.530i		−	0.403104i
$945$	−965.894	+	286.419i	−1.02211	+	0.303089i
$946$	171.061			0.180825
$947$	−391.323	−	1460.44i	−0.413223	−	1.54217i	−0.788368	−	0.615204i	$-0.789074\pi$
$947$	−391.323	−	1460.44i	−0.413223	−	1.54217i	0.375144	−	0.926966i	$-0.377593\pi$
$948$	−24.6659	+	92.0546i	−0.0260189	+	0.0971040i
$949$	−22.1319	+	12.7779i	−0.0233213	+	0.0134646i
$950$	633.786	+	118.606i	0.667143	+	0.124849i
$951$	211.325			0.222214
$952$	174.994	−	170.869i	0.183817	−	0.179484i
$953$	−152.501	−	152.501i	−0.160022	−	0.160022i	0.622555	−	0.782576i	$-0.286095\pi$
$953$	−152.501	−	152.501i	−0.160022	−	0.160022i	−0.782576	+	0.622555i	$0.786095\pi$
$954$	−100.727	−	58.1548i	−0.105584	−	0.0609589i
$955$	−31.0262	−	100.229i	−0.0324882	−	0.104951i
$956$	437.169	+	757.199i	0.457290	+	0.792049i
$957$	269.660	+	1006.38i	0.281776	+	1.05160i
$958$	374.806	+	374.806i	0.391238	+	0.391238i
$959$	−3.94024	+	330.347i	−0.00410869	+	0.344470i
$960$	92.4727	−	58.2335i	0.0963257	−	0.0606599i
$961$	460.771	−	798.079i	0.479470	−	0.830467i
$962$	162.432	+	43.5234i	0.168848	+	0.0452426i
$963$	−45.9013	+	171.306i	−0.0476649	+	0.177888i
$964$	−6.74185	−	3.89241i	−0.00699362	−	0.00403777i
$965$	−133.357	−	211.766i	−0.138194	−	0.219446i
$966$	544.660	+	969.913i	0.563830	+	1.00405i
$967$	440.127	−	440.127i	0.455147	−	0.455147i	−0.441911	−	0.897059i	$-0.645699\pi$
$967$	440.127	−	440.127i	0.455147	−	0.455147i	0.897059	+	0.441911i	$0.145699\pi$
$968$	767.284	−	205.593i	0.792649	−	0.212390i
$969$	533.033	−	307.747i	0.550086	−	0.317592i
$970$	−1004.32	+	310.891i	−1.03538	+	0.320506i
$971$	−310.158	+	537.210i	−0.319421	+	0.553254i	−0.980367	−	0.197179i	$-0.936822\pi$
$971$	−310.158	+	537.210i	−0.319421	+	0.553254i	0.660946	+	0.750433i	$0.270155\pi$
$972$	115.942	−	115.942i	0.119281	−	0.119281i
$973$	−823.907	+	210.266i	−0.846769	+	0.216101i
$974$		−	555.017i		−	0.569832i
$975$	120.901	+	176.569i	0.124001	+	0.181097i
$976$	16.9183	+	29.3034i	0.0173344	+	0.0300240i
$977$	−103.150	−	27.6391i	−0.105579	−	0.0282897i	0.205643	−	0.978627i	$-0.434071\pi$
$977$	−103.150	−	27.6391i	−0.105579	−	0.0282897i	−0.311222	+	0.950337i	$0.600738\pi$
$978$	−461.225	+	123.585i	−0.471600	+	0.126365i
$979$			1552.73i			1.58604i
$980$	133.692	+	471.409i	0.136421	+	0.481029i
$981$	−65.4674			−0.0667354
$982$	36.7677	+	137.219i	0.0374417	+	0.139734i
$983$	−12.5888	+	46.9821i	−0.0128065	+	0.0477946i	−0.972033	−	0.234843i	$-0.924543\pi$
$983$	−12.5888	+	46.9821i	−0.0128065	+	0.0477946i	0.959227	+	0.282637i	$0.0912092\pi$
$984$	−109.542	+	63.2440i	−0.111323	+	0.0642724i
$985$	−23.2362	−	604.811i	−0.0235900	−	0.614021i
$986$	−332.351			−0.337070
$987$	58.4183	+	228.907i	0.0591878	+	0.231921i
$988$	−80.8083	−	80.8083i	−0.0817897	−	0.0817897i
$989$	−214.927	−	124.088i	−0.217318	−	0.125468i
$990$	101.546	−	192.600i	0.102571	−	0.194545i
$991$	−363.350	−	629.341i	−0.366650	−	0.635056i	0.622390	−	0.782708i	$-0.286162\pi$
$991$	−363.350	−	629.341i	−0.366650	−	0.635056i	−0.989039	+	0.147651i	$0.952829\pi$
$992$	−9.19682	−	34.3230i	−0.00927098	−	0.0345998i
$993$	−166.684	−	166.684i	−0.167859	−	0.167859i
$994$	818.435	−	459.597i	0.823375	−	0.462371i
$995$	−340.584	+	1499.10i	−0.342295	+	1.50664i
$996$	−243.785	+	422.247i	−0.244764	+	0.423943i
$997$	−1317.14	−	352.926i	−1.32110	−	0.353987i	−0.471710	−	0.881754i	$-0.656363\pi$
$997$	−1317.14	−	352.926i	−1.32110	−	0.353987i	−0.849390	+	0.527766i	$0.823030\pi$
$998$	−144.507	+	539.307i	−0.144796	+	0.540388i
$999$	946.075	+	546.217i	0.947022	+	0.546764i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	70.3.l.c.23.2	✓	16
5.2	odd	4	inner	70.3.l.c.37.3	yes	16
5.3	odd	4		350.3.p.e.107.2		16
5.4	even	2		350.3.p.e.93.3		16
7.2	even	3		490.3.f.o.393.2		8
7.4	even	3	inner	70.3.l.c.53.3	yes	16
7.5	odd	6		490.3.f.p.393.3		8
35.2	odd	12		490.3.f.o.197.2		8
35.4	even	6		350.3.p.e.193.2		16
35.12	even	12		490.3.f.p.197.3		8
35.18	odd	12		350.3.p.e.207.3		16
35.32	odd	12	inner	70.3.l.c.67.2	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.3.l.c.23.2	✓	16	1.1	even	1	trivial
70.3.l.c.37.3	yes	16	5.2	odd	4	inner
70.3.l.c.53.3	yes	16	7.4	even	3	inner
70.3.l.c.67.2	yes	16	35.32	odd	12	inner
350.3.p.e.93.3		16	5.4	even	2
350.3.p.e.107.2		16	5.3	odd	4
350.3.p.e.193.2		16	35.4	even	6
350.3.p.e.207.3		16	35.18	odd	12
490.3.f.o.197.2		8	35.2	odd	12
490.3.f.o.393.2		8	7.2	even	3
490.3.f.p.197.3		8	35.12	even	12
490.3.f.p.393.3		8	7.5	odd	6

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:	\( N \)	\(=\)	\( 70 = 2 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	70.l (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.366025 + 1.36603i) q^{2} +(-0.707100 + 2.63893i) q^{3} +(-1.73205 + 1.00000i) q^{4} +(-3.39720 + 3.66866i) q^{5} -3.86367 q^{6} +(-1.73096 - 6.78261i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(1.33025 + 0.768021i) q^{9} +O(q^{10})\)	\(q+(0.366025 + 1.36603i) q^{2} +(-0.707100 + 2.63893i) q^{3} +(-1.73205 + 1.00000i) q^{4} +(-3.39720 + 3.66866i) q^{5} -3.86367 q^{6} +(-1.73096 - 6.78261i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(1.33025 + 0.768021i) q^{9} +(-6.25494 - 3.29783i) q^{10} +(10.0230 + 17.3604i) q^{11} +(-1.41420 - 5.27787i) q^{12} +(2.21546 + 2.21546i) q^{13} +(8.63164 - 4.84715i) q^{14} +(-7.27919 - 11.5591i) q^{15} +(2.00000 - 3.46410i) q^{16} +(-11.9322 - 3.19722i) q^{17} +(-0.562230 + 2.09827i) q^{18} +(15.7940 + 9.11869i) q^{19} +(2.21546 - 9.75150i) q^{20} +(19.1228 + 0.228089i) q^{21} +(-20.0461 + 20.0461i) q^{22} +(39.7282 - 10.6451i) q^{23} +(6.69207 - 3.86367i) q^{24} +(-1.91811 - 24.9263i) q^{25} +(-2.21546 + 3.83729i) q^{26} +(-20.3539 + 20.3539i) q^{27} +(9.78072 + 10.0169i) q^{28} -19.0242i q^{29} +(13.1256 - 14.1745i) q^{30} +(-3.14077 - 5.43998i) q^{31} +(5.46410 + 1.46410i) q^{32} +(-52.9003 + 14.1746i) q^{33} -17.4700i q^{34} +(30.7635 + 16.6915i) q^{35} -3.07208 q^{36} +(-9.82266 - 36.6587i) q^{37} +(-6.67534 + 24.9127i) q^{38} +(-7.41300 + 4.27990i) q^{39} +(14.1317 - 0.542925i) q^{40} -16.3689 q^{41} +(6.68786 + 26.2057i) q^{42} +(-4.26669 - 4.26669i) q^{43} +(-34.7208 - 20.0461i) q^{44} +(-7.33673 + 2.27112i) q^{45} +(29.0830 + 50.3733i) q^{46} +(3.19722 + 11.9322i) q^{47} +(7.72733 + 7.72733i) q^{48} +(-43.0075 + 23.4809i) q^{49} +(33.3479 - 11.7439i) q^{50} +(16.8745 - 29.2275i) q^{51} +(-6.05274 - 1.62183i) q^{52} +(-13.8578 + 51.7180i) q^{53} +(-35.2539 - 20.3539i) q^{54} +(-97.7397 - 22.2056i) q^{55} +(-10.1033 + 17.0271i) q^{56} +(-35.2316 + 35.2316i) q^{57} +(25.9875 - 6.96333i) q^{58} +(82.3873 - 47.5663i) q^{59} +(24.1670 + 12.7417i) q^{60} +(-4.22958 + 7.32586i) q^{61} +(6.28154 - 6.28154i) q^{62} +(2.90657 - 10.3520i) q^{63} +8.00000i q^{64} +(-15.6541 + 0.601413i) q^{65} +(-38.7257 - 67.0749i) q^{66} +(-10.9793 - 2.94188i) q^{67} +(23.8644 - 6.39445i) q^{68} +112.367i q^{69} +(-11.5409 + 48.1332i) q^{70} +94.8180 q^{71} +(-1.12446 - 4.19654i) q^{72} +(-2.11109 + 7.87869i) q^{73} +(46.4813 - 26.8360i) q^{74} +(67.1352 + 12.5636i) q^{75} -36.4747 q^{76} +(100.399 - 98.0326i) q^{77} +(-8.55979 - 8.55979i) q^{78} +(-15.1049 - 8.72081i) q^{79} +(5.91421 + 19.1056i) q^{80} +(-32.4081 - 56.1325i) q^{81} +(-5.99144 - 22.3604i) q^{82} +(-63.0967 - 63.0967i) q^{83} +(-33.3498 + 18.7278i) q^{84} +(52.2656 - 32.9136i) q^{85} +(4.26669 - 7.39012i) q^{86} +(50.2035 + 13.4520i) q^{87} +(14.6748 - 54.7669i) q^{88} +(67.0808 + 38.7291i) q^{89} +(-5.78784 - 9.19087i) q^{90} +(11.1917 - 18.8615i) q^{91} +(-58.1661 + 58.1661i) q^{92} +(16.5766 - 4.44168i) q^{93} +(-15.1294 + 8.73498i) q^{94} +(-87.1088 + 26.9649i) q^{95} +(-7.72733 + 13.3841i) q^{96} +(105.134 - 105.134i) q^{97} +(-47.8173 - 50.1548i) q^{98} +30.7916i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{2} + 2 q^{3} - 2 q^{5} - 8 q^{6} + 12 q^{7} - 32 q^{8}+O(q^{10}) \) 16 * q - 8 * q^2 + 2 * q^3 - 2 * q^5 - 8 * q^6 + 12 * q^7 - 32 * q^8	\( 16 q - 8 q^{2} + 2 q^{3} - 2 q^{5} - 8 q^{6} + 12 q^{7} - 32 q^{8} - 6 q^{10} + 40 q^{11} + 4 q^{12} + 16 q^{13} - 20 q^{15} + 32 q^{16} + 46 q^{17} - 52 q^{18} + 16 q^{20} - 20 q^{21} - 80 q^{22} + 54 q^{23} - 26 q^{25} - 16 q^{26} - 52 q^{27} - 36 q^{28} - 22 q^{30} - 208 q^{31} + 32 q^{32} - 22 q^{33} + 50 q^{35} + 208 q^{36} - 38 q^{37} + 36 q^{38} - 4 q^{40} - 72 q^{41} + 184 q^{42} + 144 q^{43} + 254 q^{45} + 108 q^{46} + 46 q^{47} + 16 q^{48} - 60 q^{50} - 136 q^{51} - 16 q^{52} + 30 q^{53} - 192 q^{55} - 48 q^{56} - 492 q^{57} + 132 q^{58} - 64 q^{60} - 120 q^{61} + 416 q^{62} - 292 q^{63} + 230 q^{65} - 44 q^{66} - 74 q^{67} - 92 q^{68} - 162 q^{70} + 16 q^{71} - 104 q^{72} - 54 q^{73} + 300 q^{75} - 144 q^{76} + 570 q^{77} + 168 q^{78} + 8 q^{80} + 244 q^{81} + 36 q^{82} + 64 q^{83} + 544 q^{85} - 144 q^{86} - 236 q^{87} - 80 q^{88} - 1048 q^{90} + 336 q^{91} - 216 q^{92} + 142 q^{93} - 396 q^{95} - 16 q^{96} + 136 q^{97} - 268 q^{98}+O(q^{100}) \) 16 * q - 8 * q^2 + 2 * q^3 - 2 * q^5 - 8 * q^6 + 12 * q^7 - 32 * q^8 - 6 * q^10 + 40 * q^11 + 4 * q^12 + 16 * q^13 - 20 * q^15 + 32 * q^16 + 46 * q^17 - 52 * q^18 + 16 * q^20 - 20 * q^21 - 80 * q^22 + 54 * q^23 - 26 * q^25 - 16 * q^26 - 52 * q^27 - 36 * q^28 - 22 * q^30 - 208 * q^31 + 32 * q^32 - 22 * q^33 + 50 * q^35 + 208 * q^36 - 38 * q^37 + 36 * q^38 - 4 * q^40 - 72 * q^41 + 184 * q^42 + 144 * q^43 + 254 * q^45 + 108 * q^46 + 46 * q^47 + 16 * q^48 - 60 * q^50 - 136 * q^51 - 16 * q^52 + 30 * q^53 - 192 * q^55 - 48 * q^56 - 492 * q^57 + 132 * q^58 - 64 * q^60 - 120 * q^61 + 416 * q^62 - 292 * q^63 + 230 * q^65 - 44 * q^66 - 74 * q^67 - 92 * q^68 - 162 * q^70 + 16 * q^71 - 104 * q^72 - 54 * q^73 + 300 * q^75 - 144 * q^76 + 570 * q^77 + 168 * q^78 + 8 * q^80 + 244 * q^81 + 36 * q^82 + 64 * q^83 + 544 * q^85 - 144 * q^86 - 236 * q^87 - 80 * q^88 - 1048 * q^90 + 336 * q^91 - 216 * q^92 + 142 * q^93 - 396 * q^95 - 16 * q^96 + 136 * q^97 - 268 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more