LMFDB - Embedded newform 375.3.k.a.43.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [375,3,Mod(7,375)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(375, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 17]))

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

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

chi := DirichletCharacter("375.7");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 375 = 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	375.k (of order $20$, degree $8$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$10.2180099135$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 75)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			43.1
Character	$\chi$	$=$	375.43
Dual form			375.3.k.a.157.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.75152 + 0.594183i) q^{2} +(0.786335 - 1.54327i) q^{3} +(9.91663 - 3.22211i) q^{4} +(-2.03297 + 6.25683i) q^{6} +(5.76987 - 5.76987i) q^{7} +(-21.7507 + 11.0826i) q^{8} +(-1.76336 - 2.42705i) q^{9} +O(q^{10})$	\(q+(-3.75152 + 0.594183i) q^{2} +(0.786335 - 1.54327i) q^{3} +(9.91663 - 3.22211i) q^{4} +(-2.03297 + 6.25683i) q^{6} +(5.76987 - 5.76987i) q^{7} +(-21.7507 + 11.0826i) q^{8} +(-1.76336 - 2.42705i) q^{9} +(-8.57269 - 6.22843i) q^{11} +(2.82521 - 17.8377i) q^{12} +(-8.56755 - 1.35697i) q^{13} +(-18.2174 + 25.0741i) q^{14} +(41.2709 - 29.9851i) q^{16} +(-9.18644 - 18.0294i) q^{17} +(8.05738 + 8.05738i) q^{18} +(-9.04167 - 2.93782i) q^{19} +(-4.36741 - 13.4415i) q^{21} +(35.8615 + 18.2723i) q^{22} +(4.80786 + 30.3556i) q^{23} +42.2818i q^{24} +32.9476 q^{26} +(-5.13218 + 0.812857i) q^{27} +(38.6265 - 75.8088i) q^{28} +(15.8984 - 5.16571i) q^{29} +(-8.39189 + 25.8276i) q^{31} +(-67.9662 + 67.9662i) q^{32} +(-16.3531 + 8.33234i) q^{33} +(45.1759 + 62.1792i) q^{34} +(-25.3068 - 18.3864i) q^{36} +(0.661704 - 4.17784i) q^{37} +(35.6656 + 5.64887i) q^{38} +(-8.83112 + 12.1550i) q^{39} +(8.18348 - 5.94565i) q^{41} +(24.3711 + 47.8310i) q^{42} +(-14.3428 - 14.3428i) q^{43} +(-105.081 - 34.1428i) q^{44} +(-36.0736 - 111.023i) q^{46} +(-21.1998 - 10.8018i) q^{47} +(-13.8223 - 87.2704i) q^{48} -17.5827i q^{49} -35.0478 q^{51} +(-89.3335 + 14.1490i) q^{52} +(-32.8517 + 64.4751i) q^{53} +(18.7705 - 6.09890i) q^{54} +(-61.5540 + 189.444i) q^{56} +(-11.6436 + 11.6436i) q^{57} +(-56.5739 + 28.8258i) q^{58} +(-59.3161 - 81.6416i) q^{59} +(-21.3169 - 15.4876i) q^{61} +(16.1361 - 101.879i) q^{62} +(-24.1781 - 3.82943i) q^{63} +(94.6519 - 130.277i) q^{64} +(56.3982 - 40.9757i) q^{66} +(-46.3389 - 90.9453i) q^{67} +(-149.191 - 149.191i) q^{68} +(50.6275 + 16.4499i) q^{69} +(-5.29227 - 16.2879i) q^{71} +(65.2522 + 33.2477i) q^{72} +(5.05041 + 31.8870i) q^{73} +16.0664i q^{74} -99.1288 q^{76} +(-85.4005 + 13.5261i) q^{77} +(25.9079 - 50.8470i) q^{78} +(-114.576 + 37.2281i) q^{79} +(-2.78115 + 8.55951i) q^{81} +(-27.1677 + 27.1677i) q^{82} +(107.103 - 54.5720i) q^{83} +(-86.6199 - 119.222i) q^{84} +(62.3293 + 45.2849i) q^{86} +(4.52940 - 28.5975i) q^{87} +(255.489 + 40.4655i) q^{88} +(-55.9848 + 77.0565i) q^{89} +(-57.2631 + 41.6041i) q^{91} +(145.487 + 285.534i) q^{92} +(33.2601 + 33.2601i) q^{93} +(85.9498 + 27.9268i) q^{94} +(51.4459 + 158.334i) q^{96} +(52.6386 + 26.8207i) q^{97} +(10.4473 + 65.9619i) q^{98} +31.7893i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 4 q^{2} + 4 q^{7} + 12 q^{8}+O(q^{10}) $ 80 * q - 4 * q^2 + 4 * q^7 + 12 * q^8	$ 80 q - 4 q^{2} + 4 q^{7} + 12 q^{8} + 24 q^{12} - 32 q^{13} + 80 q^{16} + 100 q^{17} + 48 q^{18} - 100 q^{19} + 100 q^{22} + 96 q^{23} - 40 q^{26} - 196 q^{28} + 200 q^{29} - 636 q^{32} - 216 q^{33} + 100 q^{34} - 120 q^{36} + 184 q^{37} + 564 q^{38} + 160 q^{41} + 12 q^{42} + 472 q^{43} - 700 q^{44} + 288 q^{47} + 48 q^{48} - 620 q^{52} - 304 q^{53} - 72 q^{57} - 1272 q^{58} + 800 q^{59} - 240 q^{61} - 1212 q^{62} + 12 q^{63} + 100 q^{64} + 80 q^{67} - 104 q^{68} - 36 q^{72} + 116 q^{73} + 88 q^{77} + 120 q^{78} + 200 q^{79} + 180 q^{81} + 168 q^{82} + 1264 q^{83} - 1200 q^{84} + 876 q^{87} + 212 q^{88} - 1500 q^{89} + 1504 q^{92} + 648 q^{93} - 200 q^{94} + 60 q^{96} + 260 q^{97} + 92 q^{98}+O(q^{100}) $ 80 * q - 4 * q^2 + 4 * q^7 + 12 * q^8 + 24 * q^12 - 32 * q^13 + 80 * q^16 + 100 * q^17 + 48 * q^18 - 100 * q^19 + 100 * q^22 + 96 * q^23 - 40 * q^26 - 196 * q^28 + 200 * q^29 - 636 * q^32 - 216 * q^33 + 100 * q^34 - 120 * q^36 + 184 * q^37 + 564 * q^38 + 160 * q^41 + 12 * q^42 + 472 * q^43 - 700 * q^44 + 288 * q^47 + 48 * q^48 - 620 * q^52 - 304 * q^53 - 72 * q^57 - 1272 * q^58 + 800 * q^59 - 240 * q^61 - 1212 * q^62 + 12 * q^63 + 100 * q^64 + 80 * q^67 - 104 * q^68 - 36 * q^72 + 116 * q^73 + 88 * q^77 + 120 * q^78 + 200 * q^79 + 180 * q^81 + 168 * q^82 + 1264 * q^83 - 1200 * q^84 + 876 * q^87 + 212 * q^88 - 1500 * q^89 + 1504 * q^92 + 648 * q^93 - 200 * q^94 + 60 * q^96 + 260 * q^97 + 92 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/375\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{19}{20}\right)$	$1$

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 $

$2$	−3.75152	+	0.594183i	−1.87576	+	0.297091i	−0.986931	−	0.161146i	$-0.948481\pi$
$2$	−3.75152	+	0.594183i	−1.87576	+	0.297091i	−0.888830	+	0.458237i	$0.848481\pi$
$3$	0.786335	−	1.54327i	0.262112	−	0.514423i
$3$	0.786335	−	1.54327i	0.262112	−	0.514423i
$4$	9.91663	−	3.22211i	2.47916	−	0.805527i
$5$		0			0
$5$		0			0
$6$	−2.03297	+	6.25683i	−0.338828	+	1.04281i
$7$	5.76987	−	5.76987i	0.824267	−	0.824267i	−0.162450	−	0.986717i	$-0.551940\pi$
$7$	5.76987	−	5.76987i	0.824267	−	0.824267i	0.986717	+	0.162450i	$0.0519397\pi$
$8$	−21.7507	+	11.0826i	−2.71884	+	1.38532i
$9$	−1.76336	−	2.42705i	−0.195928	−	0.269672i
$10$		0			0
$11$	−8.57269	−	6.22843i	−0.779336	−	0.566220i	0.125444	−	0.992101i	$-0.459964\pi$
$11$	−8.57269	−	6.22843i	−0.779336	−	0.566220i	−0.904780	+	0.425880i	$0.859964\pi$
$12$	2.82521	−	17.8377i	0.235434	−	1.48647i
$13$	−8.56755	−	1.35697i	−0.659042	−	0.104382i	−0.182050	−	0.983289i	$-0.558273\pi$
$13$	−8.56755	−	1.35697i	−0.659042	−	0.104382i	−0.476993	+	0.878907i	$0.658273\pi$
$14$	−18.2174	+	25.0741i	−1.30124	+	1.79101i
$15$		0			0
$16$	41.2709	−	29.9851i	2.57943	−	1.87407i
$17$	−9.18644	−	18.0294i	−0.540379	−	1.06055i	−0.986220	−	0.165441i	$-0.947095\pi$
$17$	−9.18644	−	18.0294i	−0.540379	−	1.06055i	0.445841	−	0.895112i	$-0.352905\pi$
$18$	8.05738	+	8.05738i	0.447632	+	0.447632i
$19$	−9.04167	−	2.93782i	−0.475877	−	0.154622i	0.0612512	−	0.998122i	$-0.480491\pi$
$19$	−9.04167	−	2.93782i	−0.475877	−	0.154622i	−0.537128	+	0.843501i	$0.680491\pi$
$20$		0			0
$21$	−4.36741	−	13.4415i	−0.207972	−	0.640071i
$22$	35.8615	+	18.2723i	1.63007	+	0.830560i
$23$	4.80786	+	30.3556i	0.209037	+	1.31981i	0.839402	+	0.543511i	$0.182905\pi$
$23$	4.80786	+	30.3556i	0.209037	+	1.31981i	−0.630365	+	0.776299i	$0.717095\pi$
$24$			42.2818i			1.76174i
$25$		0			0
$26$	32.9476			1.26722
$27$	−5.13218	+	0.812857i	−0.190081	+	0.0301058i
$28$	38.6265	−	75.8088i	1.37952	−	2.70746i
$29$	15.8984	−	5.16571i	0.548221	−	0.178128i	−0.0217932	−	0.999762i	$-0.506938\pi$
$29$	15.8984	−	5.16571i	0.548221	−	0.178128i	0.570015	+	0.821635i	$0.306938\pi$
$30$		0			0
$31$	−8.39189	+	25.8276i	−0.270706	+	0.833148i	0.719617	+	0.694371i	$0.244317\pi$
$31$	−8.39189	+	25.8276i	−0.270706	+	0.833148i	−0.990324	+	0.138777i	$0.955683\pi$
$32$	−67.9662	+	67.9662i	−2.12394	+	2.12394i
$33$	−16.3531	+	8.33234i	−0.495550	+	0.252495i
$34$	45.1759	+	62.1792i	1.32870	+	1.82880i
$35$		0			0
$36$	−25.3068	−	18.3864i	−0.702966	−	0.510734i
$37$	0.661704	−	4.17784i	0.0178839	−	0.112914i	−0.977131	−	0.212636i	$-0.931795\pi$
$37$	0.661704	−	4.17784i	0.0178839	−	0.112914i	0.995015	+	0.0997215i	$0.0317952\pi$
$38$	35.6656	+	5.64887i	0.938568	+	0.148655i
$39$	−8.83112	+	12.1550i	−0.226439	+	0.311667i
$40$		0			0
$41$	8.18348	−	5.94565i	0.199597	−	0.145016i	−0.483497	−	0.875346i	$-0.660634\pi$
$41$	8.18348	−	5.94565i	0.199597	−	0.145016i	0.683094	+	0.730330i	$0.260634\pi$
$42$	24.3711	+	47.8310i	0.580265	+	1.13883i
$43$	−14.3428	−	14.3428i	−0.333552	−	0.333552i	0.520382	−	0.853934i	$-0.325790\pi$
$43$	−14.3428	−	14.3428i	−0.333552	−	0.333552i	−0.853934	+	0.520382i	$0.825790\pi$
$44$	−105.081	−	34.1428i	−2.38820	−	0.775974i
$45$		0			0
$46$	−36.0736	−	111.023i	−0.784208	−	2.41354i
$47$	−21.1998	−	10.8018i	−0.451060	−	0.229826i	0.213677	−	0.976904i	$-0.431456\pi$
$47$	−21.1998	−	10.8018i	−0.451060	−	0.229826i	−0.664736	+	0.747078i	$0.731456\pi$
$48$	−13.8223	−	87.2704i	−0.287964	−	1.81813i
$49$		−	17.5827i		−	0.358831i
$50$		0			0
$51$	−35.0478			−0.687212
$52$	−89.3335	+	14.1490i	−1.71795	+	0.272097i
$53$	−32.8517	+	64.4751i	−0.619843	+	1.21651i	0.341168	+	0.940002i	$0.389177\pi$
$53$	−32.8517	+	64.4751i	−0.619843	+	1.21651i	−0.961011	+	0.276509i	$0.910823\pi$
$54$	18.7705	−	6.09890i	0.347602	−	0.112943i
$55$		0			0
$56$	−61.5540	+	189.444i	−1.09918	+	3.38292i
$57$	−11.6436	+	11.6436i	−0.204274	+	0.204274i
$58$	−56.5739	+	28.8258i	−0.975412	+	0.496997i
$59$	−59.3161	−	81.6416i	−1.00536	−	1.38376i	−0.921980	−	0.387238i	$-0.873429\pi$
$59$	−59.3161	−	81.6416i	−1.00536	−	1.38376i	−0.0833777	−	0.996518i	$-0.526571\pi$
$60$		0			0
$61$	−21.3169	−	15.4876i	−0.349458	−	0.253896i	0.399184	−	0.916871i	$-0.369294\pi$
$61$	−21.3169	−	15.4876i	−0.349458	−	0.253896i	−0.748641	+	0.662975i	$0.769294\pi$
$62$	16.1361	−	101.879i	0.260259	−	1.64321i
$63$	−24.1781	−	3.82943i	−0.383779	−	0.0607846i
$64$	94.6519	−	130.277i	1.47894	−	2.03558i
$65$		0			0
$66$	56.3982	−	40.9757i	0.854518	−	0.620844i
$67$	−46.3389	−	90.9453i	−0.691626	−	1.35739i	−0.923103	−	0.384552i	$-0.874356\pi$
$67$	−46.3389	−	90.9453i	−0.691626	−	1.35739i	0.231477	−	0.972840i	$-0.425644\pi$
$68$	−149.191	−	149.191i	−2.19399	−	2.19399i
$69$	50.6275	+	16.4499i	0.733731	+	0.238404i
$70$		0			0
$71$	−5.29227	−	16.2879i	−0.0745390	−	0.229408i	0.906845	−	0.421465i	$-0.138484\pi$
$71$	−5.29227	−	16.2879i	−0.0745390	−	0.229408i	−0.981384	+	0.192057i	$0.938484\pi$
$72$	65.2522	+	33.2477i	0.906281	+	0.461773i
$73$	5.05041	+	31.8870i	0.0691837	+	0.436809i	0.997830	+	0.0658425i	$0.0209735\pi$
$73$	5.05041	+	31.8870i	0.0691837	+	0.436809i	−0.928646	+	0.370966i	$0.879027\pi$
$74$			16.0664i			0.217114i
$75$		0			0
$76$	−99.1288			−1.30433
$77$	−85.4005	+	13.5261i	−1.10910	+	0.175664i
$78$	25.9079	−	50.8470i	0.332152	−	0.651885i
$79$	−114.576	+	37.2281i	−1.45033	+	0.471241i	−0.925102	−	0.379719i	$-0.876021\pi$
$79$	−114.576	+	37.2281i	−1.45033	+	0.471241i	−0.525230	+	0.850960i	$0.676021\pi$
$80$		0			0
$81$	−2.78115	+	8.55951i	−0.0343352	+	0.105673i
$82$	−27.1677	+	27.1677i	−0.331314	+	0.331314i
$83$	107.103	−	54.5720i	1.29040	−	0.657493i	0.332100	−	0.943244i	$-0.392243\pi$
$83$	107.103	−	54.5720i	1.29040	−	0.657493i	0.958304	+	0.285751i	$0.0922430\pi$
$84$	−86.6199	−	119.222i	−1.03119	−	1.41931i
$85$		0			0
$86$	62.3293	+	45.2849i	0.724760	+	0.526569i
$87$	4.52940	−	28.5975i	0.0520621	−	0.328707i
$88$	255.489	+	40.4655i	2.90329	+	0.459835i
$89$	−55.9848	+	77.0565i	−0.629043	+	0.865803i	−0.997972	−	0.0636543i	$-0.979724\pi$
$89$	−55.9848	+	77.0565i	−0.629043	+	0.865803i	0.368929	+	0.929458i	$0.379724\pi$
$90$		0			0
$91$	−57.2631	+	41.6041i	−0.629265	+	0.457188i
$92$	145.487	+	285.534i	1.58138	+	3.10363i
$93$	33.2601	+	33.2601i	0.357635	+	0.357635i
$94$	85.9498	+	27.9268i	0.914359	+	0.297093i
$95$		0			0
$96$	51.4459	+	158.334i	0.535895	+	1.64932i
$97$	52.6386	+	26.8207i	0.542666	+	0.276502i	0.703761	−	0.710437i	$-0.251502\pi$
$97$	52.6386	+	26.8207i	0.542666	+	0.276502i	−0.161095	+	0.986939i	$0.551502\pi$
$98$	10.4473	+	65.9619i	0.106605	+	0.673081i
$99$			31.7893i			0.321104i
$100$		0			0
$101$	−18.0818			−0.179027			−0.0895136	−	0.995986i	$-0.528531\pi$
$101$	−18.0818			−0.179027			−0.0895136	+	0.995986i	$0.528531\pi$
$102$	131.483	−	20.8248i	1.28905	−	0.204165i
$103$	−44.2825	+	86.9093i	−0.429927	+	0.843779i	0.569830	+	0.821762i	$0.307009\pi$
$103$	−44.2825	+	86.9093i	−0.429927	+	0.843779i	−0.999758	+	0.0220172i	$0.992991\pi$
$104$	201.389	−	65.4353i	1.93643	−	0.629186i
$105$		0			0
$106$	84.9339	−	261.400i	0.801263	−	2.46603i
$107$	37.6236	−	37.6236i	0.351622	−	0.351622i	−0.509091	−	0.860713i	$-0.670018\pi$
$107$	37.6236	−	37.6236i	0.351622	−	0.351622i	0.860713	+	0.509091i	$0.170018\pi$
$108$	−48.2748	+	24.5972i	−0.446989	+	0.227752i
$109$	49.2625	+	67.8040i	0.451950	+	0.622055i	0.972815	−	0.231583i	$-0.0743906\pi$
$109$	49.2625	+	67.8040i	0.451950	+	0.622055i	−0.520865	+	0.853639i	$0.674391\pi$
$110$		0			0
$111$	−5.92720	−	4.30636i	−0.0533982	−	0.0387961i
$112$	65.1178	−	411.138i	0.581409	−	3.67087i
$113$	−98.6277	−	15.6211i	−0.872812	−	0.138240i	−0.296070	−	0.955166i	$-0.595676\pi$
$113$	−98.6277	−	15.6211i	−0.872812	−	0.138240i	−0.576742	+	0.816926i	$0.695676\pi$
$114$	36.7628	−	50.5997i	0.322481	−	0.443857i
$115$		0			0
$116$	141.014	−	102.453i	1.21564	−	0.883214i
$117$	11.8142	+	23.1867i	0.100976	+	0.198177i
$118$	271.036	+	271.036i	2.29691	+	2.29691i
$119$	−157.032	−	51.0227i	−1.31959	−	0.428762i
$120$		0			0
$121$	−2.69329	−	8.28909i	−0.0222586	−	0.0685049i
$122$	89.1733	+	45.4361i	0.730929	+	0.372427i
$123$	−2.74078	−	17.3046i	−0.0222827	−	0.140688i
$124$			283.162i			2.28357i
$125$		0			0
$126$	92.9800			0.737936
$127$	75.6911	−	11.9883i	0.595993	−	0.0943960i	0.148852	−	0.988859i	$-0.452442\pi$
$127$	75.6911	−	11.9883i	0.595993	−	0.0943960i	0.447141	+	0.894463i	$0.352442\pi$
$128$	−103.132	+	202.409i	−0.805721	+	1.58132i
$129$	−33.4129	+	10.8565i	−0.259015	+	0.0841590i
$130$		0			0
$131$	−14.5474	+	44.7722i	−0.111049	+	0.341772i	−0.991102	−	0.133102i	$-0.957506\pi$
$131$	−14.5474	+	44.7722i	−0.111049	+	0.341772i	0.880054	+	0.474874i	$0.157506\pi$
$132$	−135.320	+	135.320i	−1.02515	+	1.02515i
$133$	−69.1200	+	35.2184i	−0.519699	+	0.264800i
$134$	227.880	+	313.649i	1.70059	+	2.34067i
$135$		0			0
$136$	399.624	+	290.343i	2.93841	+	2.13488i
$137$	31.2075	−	197.036i	0.227792	−	1.43822i	−0.563163	−	0.826346i	$-0.690416\pi$
$137$	31.2075	−	197.036i	0.227792	−	1.43822i	0.790955	−	0.611875i	$-0.209584\pi$
$138$	−199.704	−	31.6300i	−1.44713	−	0.229203i
$139$	96.9324	−	133.416i	0.697355	−	0.959827i	−0.302622	−	0.953111i	$-0.597862\pi$
$139$	96.9324	−	133.416i	0.697355	−	0.959827i	0.999977	−	0.00671658i	$-0.00213797\pi$
$140$		0			0
$141$	−33.3403	+	24.2231i	−0.236456	+	0.171795i
$142$	29.5321	+	57.9600i	0.207972	+	0.408169i
$143$	64.9952	+	64.9952i	0.454512	+	0.454512i
$144$	−145.551	−	47.2923i	−1.01077	−	0.328419i
$145$		0			0
$146$	−37.8934	−	116.624i	−0.259544	−	0.798795i
$147$	−27.1348	−	13.8259i	−0.184591	−	0.0940537i
$148$	−6.89956	−	43.5621i	−0.0466187	−	0.294339i
$149$		−	212.069i		−	1.42328i	−0.702542	−	0.711642i	$-0.747952\pi$
$149$		−	212.069i		−	1.42328i	0.702542	−	0.711642i	$-0.252048\pi$
$150$		0			0
$151$	−29.7291			−0.196882			−0.0984408	−	0.995143i	$-0.531385\pi$
$151$	−29.7291			−0.196882			−0.0984408	+	0.995143i	$0.531385\pi$
$152$	229.221	−	36.3051i	1.50804	−	0.238849i
$153$	−27.5593	+	54.0882i	−0.180126	+	0.353518i
$154$	312.345	−	101.487i	2.02821	−	0.659006i
$155$		0			0
$156$	−48.4103	+	148.991i	−0.310322	+	0.955073i
$157$	−126.157	+	126.157i	−0.803546	+	0.803546i	−0.983648	−	0.180102i	$-0.942357\pi$
$157$	−126.157	+	126.157i	−0.803546	+	0.803546i	0.180102	+	0.983648i	$0.442357\pi$
$158$	407.715	−	207.741i	2.58047	−	1.31482i
$159$	73.6700	+	101.398i	0.463333	+	0.637723i
$160$		0			0
$161$	202.889	+	147.407i	1.26018	+	0.915572i
$162$	5.34764	−	33.7637i	0.0330101	−	0.208418i
$163$	−275.324	−	43.6071i	−1.68911	−	0.267528i	−0.763443	−	0.645875i	$-0.776493\pi$
$163$	−275.324	−	43.6071i	−1.68911	−	0.267528i	−0.925664	+	0.378347i	$0.876493\pi$
$164$	61.9951	−	85.3289i	0.378019	−	0.520298i
$165$		0			0
$166$	−369.375	+	268.367i	−2.22515	+	1.61667i
$167$	−83.7861	−	164.439i	−0.501713	−	0.984667i	−0.993487	−	0.113944i	$-0.963651\pi$
$167$	−83.7861	−	164.439i	−0.501713	−	0.984667i	0.491774	−	0.870723i	$-0.336349\pi$
$168$	243.960	+	243.960i	1.45215	+	1.45215i
$169$	−89.1670	−	28.9721i	−0.527615	−	0.171433i
$170$		0			0
$171$	8.81345	+	27.1250i	0.0515406	+	0.158626i
$172$	−188.446	−	96.0179i	−1.09561	−	0.558243i
$173$	7.21329	+	45.5429i	0.0416953	+	0.263254i	0.999726	−	0.0234122i	$-0.00745301\pi$
$173$	7.21329	+	45.5429i	0.0416953	+	0.263254i	−0.958031	+	0.286666i	$0.907453\pi$
$174$			109.975i			0.632043i
$175$		0			0
$176$	−540.563			−3.07138
$177$	−172.637	+	27.3430i	−0.975352	+	0.154481i
$178$	164.243	−	322.344i	0.922711	−	1.81092i
$179$	187.032	−	60.7705i	1.04487	−	0.339500i	0.264219	−	0.964463i	$-0.414886\pi$
$179$	187.032	−	60.7705i	1.04487	−	0.339500i	0.780655	+	0.624963i	$0.214886\pi$
$180$		0			0
$181$	53.3319	−	164.139i	0.294652	−	0.906844i	−0.688687	−	0.725059i	$-0.741812\pi$
$181$	53.3319	−	164.139i	0.294652	−	0.906844i	0.983338	−	0.181785i	$-0.0581875\pi$
$182$	190.103	−	190.103i	1.04452	−	1.04452i
$183$	−40.6638	+	20.7193i	−0.222207	+	0.113220i
$184$	−440.992	−	606.974i	−2.39670	−	3.29877i
$185$		0			0
$186$	−144.538	−	105.013i	−0.777088	−	0.564588i
$187$	−33.5423	+	211.778i	−0.179370	+	1.13250i
$188$	−245.035	−	38.8098i	−1.30338	−	0.206435i
$189$	−24.9219	+	34.3021i	−0.131862	+	0.181492i
$190$		0			0
$191$	45.7324	−	33.2265i	0.239437	−	0.173961i	−0.461596	−	0.887090i	$-0.652723\pi$
$191$	45.7324	−	33.2265i	0.239437	−	0.173961i	0.701032	+	0.713130i	$0.252723\pi$
$192$	−126.625	−	248.515i	−0.659503	−	1.29435i
$193$	−172.829	−	172.829i	−0.895487	−	0.895487i	0.0995457	−	0.995033i	$-0.468261\pi$
$193$	−172.829	−	172.829i	−0.895487	−	0.895487i	−0.995033	+	0.0995457i	$0.968261\pi$
$194$	−213.411	−	69.3416i	−1.10006	−	0.357431i
$195$		0			0
$196$	−56.6534	−	174.361i	−0.289048	−	0.889598i
$197$	−56.7764	−	28.9290i	−0.288205	−	0.146848i	0.303911	−	0.952700i	$-0.401707\pi$
$197$	−56.7764	−	28.9290i	−0.288205	−	0.146848i	−0.592116	+	0.805853i	$0.701707\pi$
$198$	−18.8886	−	119.258i	−0.0953972	−	0.602314i
$199$		−	120.112i		−	0.603576i	−0.953375	−	0.301788i	$-0.902417\pi$
$199$		−	120.112i		−	0.603576i	0.953375	−	0.301788i	$-0.0975835\pi$
$200$		0			0
$201$	−176.791			−0.879557
$202$	67.8341	−	10.7439i	0.335812	−	0.0531874i
$203$	61.9263	−	121.537i	0.305056	−	0.598705i
$204$	−347.556	+	112.928i	−1.70371	+	0.553568i
$205$		0			0
$206$	114.487	−	352.354i	0.555761	−	1.71046i
$207$	65.1967	−	65.1967i	0.314960	−	0.314960i
$208$	−394.279	+	200.895i	−1.89557	+	0.965843i
$209$	59.2134	+	81.5003i	0.283318	+	0.389954i
$210$		0			0
$211$	193.529	+	140.607i	0.917200	+	0.666385i	0.942825	−	0.333287i	$-0.108158\pi$
$211$	193.529	+	140.607i	0.917200	+	0.666385i	−0.0256257	+	0.999672i	$0.508158\pi$
$212$	−118.032	+	745.227i	−0.556757	+	3.51522i
$213$	−29.2982	−	4.64037i	−0.137550	−	0.0217858i
$214$	−118.790	+	163.501i	−0.555095	+	0.764023i
$215$		0			0
$216$	102.620	−	74.5579i	0.475093	−	0.345175i
$217$	100.602	+	197.442i	0.463602	+	0.909870i
$218$	−225.097	−	225.097i	−1.03256	−	1.03256i
$219$	53.1816	+	17.2797i	0.242838	+	0.0789029i
$220$		0			0
$221$	54.2400	+	166.933i	0.245430	+	0.755355i
$222$	24.7948	+	12.6336i	0.111688	+	0.0569080i
$223$	31.2037	+	197.012i	0.139927	+	0.883463i	0.953367	+	0.301814i	$0.0975922\pi$
$223$	31.2037	+	197.012i	0.139927	+	0.883463i	−0.813440	+	0.581649i	$0.802408\pi$
$224$			784.312i			3.50139i
$225$		0			0
$226$	379.286			1.67826
$227$	223.393	−	35.3820i	0.984110	−	0.155868i	0.356415	−	0.934328i	$-0.383999\pi$
$227$	223.393	−	35.3820i	0.984110	−	0.155868i	0.627694	+	0.778460i	$0.283999\pi$
$228$	−77.9484	+	152.982i	−0.341879	+	0.670975i
$229$	296.158	−	96.2275i	1.29327	−	0.420207i	0.420032	−	0.907509i	$-0.362019\pi$
$229$	296.158	−	96.2275i	1.29327	−	0.420207i	0.873234	+	0.487302i	$0.162019\pi$
$230$		0			0
$231$	−46.2789	+	142.432i	−0.200342	+	0.616588i
$232$	−288.553	+	288.553i	−1.24376	+	1.24376i
$233$	372.857	−	189.980i	1.60024	−	0.815365i	0.600366	−	0.799726i	$-0.295022\pi$
$233$	372.857	−	189.980i	1.60024	−	0.815365i	0.999878	−	0.0156392i	$-0.00497833\pi$
$234$	−58.0984	−	79.9656i	−0.248284	−	0.341733i
$235$		0			0
$236$	−851.274	−	618.487i	−3.60709	−	2.62071i
$237$	−32.6423	+	206.096i	−0.137731	+	0.869601i
$238$	619.425	+	98.1072i	2.60262	+	0.412215i
$239$	−36.4395	+	50.1547i	−0.152467	+	0.209852i	−0.878417	−	0.477895i	$-0.841400\pi$
$239$	−36.4395	+	50.1547i	−0.152467	+	0.209852i	0.725951	+	0.687747i	$0.241400\pi$
$240$		0			0
$241$	6.33519	−	4.60279i	0.0262871	−	0.0190987i	−0.574564	−	0.818460i	$-0.694828\pi$
$241$	6.33519	−	4.60279i	0.0262871	−	0.0190987i	0.600851	+	0.799361i	$0.294828\pi$
$242$	15.0292	+	29.4964i	0.0621040	+	0.121886i
$243$	11.0227	+	11.0227i	0.0453609	+	0.0453609i
$244$	−261.295	−	84.8998i	−1.07088	−	0.347950i
$245$		0			0
$246$	20.5642	+	63.2900i	0.0835942	+	0.257276i
$247$	73.4784	+	37.4391i	0.297483	+	0.151575i
$248$	−103.706	−	654.773i	−0.418169	−	2.64021i
$249$		−	208.201i		−	0.836150i
$250$		0			0
$251$	231.377			0.921822			0.460911	−	0.887446i	$-0.347523\pi$
$251$	231.377			0.921822			0.460911	+	0.887446i	$0.347523\pi$
$252$	−252.104	+	39.9293i	−1.00041	+	0.158450i
$253$	147.851	−	290.175i	0.584393	−	1.14694i
$254$	−276.834	+	89.9487i	−1.08990	+	0.354129i
$255$		0			0
$256$	67.5895	−	208.019i	0.264022	−	0.812575i
$257$	−222.364	+	222.364i	−0.865229	+	0.865229i	−0.991940	−	0.126710i	$-0.959558\pi$
$257$	−222.364	+	222.364i	−0.865229	+	0.865229i	0.126710	+	0.991940i	$0.459558\pi$
$258$	118.899	−	60.5818i	0.460847	−	0.234813i
$259$	−20.2876	−	27.9235i	−0.0783305	−	0.107813i
$260$		0			0
$261$	−40.5720	−	29.4773i	−0.155448	−	0.112940i
$262$	27.9719	−	176.608i	0.106763	−	0.674075i
$263$	129.506	+	20.5117i	0.492418	+	0.0779914i	0.397705	−	0.917513i	$-0.369807\pi$
$263$	129.506	+	20.5117i	0.492418	+	0.0779914i	0.0947130	+	0.995505i	$0.469807\pi$
$264$	263.349	−	362.469i	0.997535	−	1.37299i
$265$		0			0
$266$	238.379	−	173.192i	0.896161	−	0.651099i
$267$	74.8961	+	146.992i	0.280510	+	0.550531i
$268$	−752.562	−	752.562i	−2.80807	−	2.80807i
$269$	172.494	+	56.0466i	0.641241	+	0.208352i	0.611548	−	0.791207i	$-0.290547\pi$
$269$	172.494	+	56.0466i	0.641241	+	0.208352i	0.0296926	+	0.999559i	$0.490547\pi$
$270$		0			0
$271$	68.6682	+	211.339i	0.253388	+	0.779849i	0.994143	+	0.108073i	$0.0344681\pi$
$271$	68.6682	+	211.339i	0.253388	+	0.779849i	−0.740755	+	0.671776i	$0.765532\pi$
$272$	−919.746	−	468.634i	−3.38142	−	1.72292i
$273$	19.1783	+	121.087i	0.0702502	+	0.443543i
$274$			757.728i			2.76543i
$275$		0			0
$276$	555.057			2.01108
$277$	32.5716	−	5.15883i	0.117587	−	0.0186239i	−0.0973636	−	0.995249i	$-0.531041\pi$
$277$	32.5716	−	5.15883i	0.117587	−	0.0186239i	0.214951	+	0.976625i	$0.431041\pi$
$278$	−284.370	+	558.108i	−1.02292	+	2.00758i
$279$	77.4828	−	25.1757i	0.277716	−	0.0902354i
$280$		0			0
$281$	−92.8454	+	285.749i	−0.330411	+	1.01690i	0.638528	+	0.769598i	$0.279544\pi$
$281$	−92.8454	+	285.749i	−0.330411	+	1.01690i	−0.968939	+	0.247301i	$0.920456\pi$
$282$	110.684	−	110.684i	0.392496	−	0.392496i
$283$	320.713	−	163.411i	1.13326	−	0.577425i	0.216270	−	0.976334i	$-0.430611\pi$
$283$	320.713	−	163.411i	1.13326	−	0.577425i	0.916991	+	0.398908i	$0.130611\pi$
$284$	−104.963	−	144.469i	−0.369588	−	0.508694i
$285$		0			0
$286$	−282.450	−	205.212i	−0.987587	−	0.717524i
$287$	12.9120	−	81.5232i	0.0449896	−	0.284053i
$288$	284.806	+	45.1088i	0.988910	+	0.156628i
$289$	−70.7986	+	97.4459i	−0.244978	+	0.337183i
$290$		0			0
$291$	82.7832	−	60.1455i	0.284478	−	0.206686i
$292$	152.827	+	299.939i	0.523379	+	1.02719i
$293$	43.2558	+	43.2558i	0.147631	+	0.147631i	0.777059	−	0.629428i	$-0.216711\pi$
$293$	43.2558	+	43.2558i	0.147631	+	0.147631i	−0.629428	+	0.777059i	$0.716711\pi$
$294$	110.012	+	35.7451i	0.374191	+	0.121582i
$295$		0			0
$296$	31.9085	+	98.2044i	0.107799	+	0.331772i
$297$	49.0594	+	24.9970i	0.165183	+	0.0841650i
$298$	126.008	+	795.583i	0.422845	+	2.66974i
$299$		−	266.597i		−	0.891630i
$300$		0			0
$301$	−165.512			−0.549872
$302$	111.529	−	17.6645i	0.369303	−	0.0584918i
$303$	−14.2183	+	27.9050i	−0.0469251	+	0.0920957i
$304$	−461.249	+	149.869i	−1.51726	+	0.492989i
$305$		0			0
$306$	71.2511	−	219.288i	0.232847	−	0.716628i
$307$	264.280	−	264.280i	0.860845	−	0.860845i	−0.130591	−	0.991436i	$-0.541687\pi$
$307$	264.280	−	264.280i	0.860845	−	0.860845i	0.991436	+	0.130591i	$0.0416874\pi$
$308$	−803.302	+	409.303i	−2.60812	+	1.32891i
$309$	99.3035	+	136.680i	0.321371	+	0.442329i
$310$		0			0
$311$	−99.7735	−	72.4897i	−0.320815	−	0.233086i	0.415708	−	0.909498i	$-0.363534\pi$
$311$	−99.7735	−	72.4897i	−0.320815	−	0.233086i	−0.736523	+	0.676412i	$0.763534\pi$
$312$	57.3750	−	362.252i	0.183894	−	1.16106i
$313$	−524.250	−	83.0331i	−1.67492	−	0.265281i	−0.754525	−	0.656271i	$-0.772133\pi$
$313$	−524.250	−	83.0331i	−1.67492	−	0.265281i	−0.920395	+	0.390989i	$0.872133\pi$
$314$	398.319	−	548.240i	1.26853	−	1.74599i
$315$		0			0
$316$	−1016.26	+	738.354i	−3.21600	+	2.33656i
$317$	10.6377	+	20.8776i	0.0335573	+	0.0658600i	0.907176	−	0.420750i	$-0.138233\pi$
$317$	10.6377	+	20.8776i	0.0335573	+	0.0658600i	−0.873619	+	0.486610i	$0.838233\pi$
$318$	−336.623	−	336.623i	−1.05856	−	1.05856i
$319$	−168.466	−	54.7381i	−0.528108	−	0.171593i
$320$		0			0
$321$	−28.4785	−	87.6480i	−0.0887182	−	0.273047i
$322$	−848.727	−	432.448i	−2.63580	−	1.34301i
$323$	30.0936	+	190.004i	0.0931692	+	0.588247i
$324$			93.8426i			0.289638i
$325$		0			0
$326$	1058.80			3.24784
$327$	143.377	−	22.7086i	0.438461	−	0.0694454i
$328$	−112.104	+	220.016i	−0.341780	+	0.670781i
$329$	−184.645	+	59.9949i	−0.561232	+	0.182355i
$330$		0			0
$331$	86.1347	−	265.095i	0.260226	−	0.800893i	−0.732529	−	0.680736i	$-0.761660\pi$
$331$	86.1347	−	265.095i	0.260226	−	0.800893i	0.992755	−	0.120157i	$-0.0383398\pi$
$332$	886.269	−	886.269i	2.66948	−	2.66948i
$333$	−11.3066	+	5.76102i	−0.0339539	+	0.0173004i
$334$	412.032	+	567.114i	1.23363	+	1.69795i
$335$		0			0
$336$	−583.291	−	423.786i	−1.73599	−	1.26127i
$337$	−41.2850	+	260.663i	−0.122507	+	0.773481i	0.847570	+	0.530684i	$0.178065\pi$
$337$	−41.2850	+	260.663i	−0.122507	+	0.773481i	−0.970077	+	0.242797i	$0.921935\pi$
$338$	351.727	+	55.7080i	1.04061	+	0.164817i
$339$	−101.662	+	139.926i	−0.299888	+	0.412760i
$340$		0			0
$341$	232.806	−	169.144i	0.682717	−	0.496023i
$342$	−49.1810	−	96.5232i	−0.143804	−	0.282232i
$343$	181.274	+	181.274i	0.528494	+	0.528494i
$344$	470.920	+	153.011i	1.36895	+	0.444800i
$345$		0			0
$346$	−54.1216	−	166.569i	−0.156421	−	0.481414i
$347$	−129.934	−	66.2046i	−0.374449	−	0.190791i	0.256630	−	0.966510i	$-0.417388\pi$
$347$	−129.934	−	66.2046i	−0.374449	−	0.190791i	−0.631079	+	0.775718i	$0.717388\pi$
$348$	−47.2279	−	298.185i	−0.135712	−	0.856854i
$349$			51.9592i			0.148880i	0.997225	+	0.0744401i	$0.0237170\pi$
$349$			51.9592i			0.148880i	−0.997225	+	0.0744401i	$0.976283\pi$
$350$		0			0
$351$	45.0732			0.128414
$352$	1005.98	−	159.331i	2.85789	−	0.452645i
$353$	304.680	−	597.969i	0.863117	−	1.69396i	0.154945	−	0.987923i	$-0.450480\pi$
$353$	304.680	−	597.969i	0.863117	−	1.69396i	0.708172	−	0.706040i	$-0.249520\pi$
$354$	631.405	−	205.156i	1.78363	−	0.579537i
$355$		0			0
$356$	−306.896	+	944.530i	−0.862068	+	2.65317i
$357$	−202.221	+	202.221i	−0.566446	+	0.566446i
$358$	−665.547	+	339.113i	−1.85907	+	0.947243i
$359$	−194.075	−	267.121i	−0.540599	−	0.744071i	0.448100	−	0.893983i	$-0.352101\pi$
$359$	−194.075	−	267.121i	−0.540599	−	0.744071i	−0.988699	+	0.149913i	$0.952101\pi$
$360$		0			0
$361$	−218.934	−	159.065i	−0.606466	−	0.440623i
$362$	−102.547	+	647.459i	−0.283280	+	1.78856i
$363$	−14.9101	−	2.36153i	−0.0410747	−	0.00650560i
$364$	−433.804	+	597.080i	−1.19177	+	1.64033i
$365$		0			0
$366$	140.240	−	101.890i	0.383170	−	0.278389i
$367$	−240.780	−	472.558i	−0.656077	−	1.28762i	−0.943992	−	0.329967i	$-0.892962\pi$
$367$	−240.780	−	472.558i	−0.656077	−	1.28762i	0.287916	−	0.957656i	$-0.407038\pi$
$368$	1108.64	+	1108.64i	3.01261	+	3.01261i
$369$	−28.8608	−	9.37744i	−0.0782135	−	0.0254131i
$370$		0			0
$371$	182.463	+	561.563i	0.491813	+	1.51365i
$372$	436.995	+	222.660i	1.17472	+	0.598549i
$373$	19.6626	+	124.145i	0.0527148	+	0.332828i	0.999925	+	0.0122162i	$0.00388862\pi$
$373$	19.6626	+	124.145i	0.0527148	+	0.332828i	−0.947211	+	0.320612i	$0.896111\pi$
$374$		−	814.418i		−	2.17759i
$375$		0			0
$376$	580.823			1.54474
$377$	−143.220	+	22.6838i	−0.379894	+	0.0601694i
$378$	73.1134	−	143.493i	0.193422	−	0.379611i
$379$	348.309	−	113.173i	0.919022	−	0.298608i	0.188956	−	0.981986i	$-0.439490\pi$
$379$	348.309	−	113.173i	0.919022	−	0.298608i	0.730065	+	0.683377i	$0.239490\pi$
$380$		0			0
$381$	41.0174	−	126.239i	0.107657	−	0.331335i
$382$	−151.823	+	151.823i	−0.397443	+	0.397443i
$383$	−89.5224	+	45.6139i	−0.233740	+	0.119096i	−0.566938	−	0.823760i	$-0.691872\pi$
$383$	−89.5224	+	45.6139i	−0.233740	+	0.119096i	0.333198	+	0.942857i	$0.391872\pi$
$384$	231.274	+	318.322i	0.602277	+	0.828963i
$385$		0			0
$386$	751.064	+	545.680i	1.94576	+	1.41368i
$387$	−9.51922	+	60.1020i	−0.0245975	+	0.155302i
$388$	608.417	+	96.3638i	1.56809	+	0.248360i
$389$	−379.989	+	523.009i	−0.976834	+	1.34450i	−0.0383170	+	0.999266i	$0.512200\pi$
$389$	−379.989	+	523.009i	−0.976834	+	1.34450i	−0.938517	+	0.345232i	$0.887800\pi$
$390$		0			0
$391$	503.126	−	365.543i	1.28677	−	0.934892i
$392$	194.861	+	382.437i	0.497095	+	0.975604i
$393$	57.6564	+	57.6564i	0.146708	+	0.146708i
$394$	230.187	+	74.7923i	0.584231	+	0.189828i
$395$		0			0
$396$	102.429	+	315.243i	0.258658	+	0.796067i
$397$	656.562	+	334.535i	1.65381	+	0.842657i	0.995989	+	0.0894813i	$0.0285209\pi$
$397$	656.562	+	334.535i	1.65381	+	0.842657i	0.657819	+	0.753176i	$0.271479\pi$
$398$	71.3682	+	450.601i	0.179317	+	1.13216i
$399$			134.364i			0.336752i
$400$		0			0
$401$	−549.240			−1.36968			−0.684838	−	0.728696i	$-0.740127\pi$
$401$	−549.240			−1.36968			−0.684838	+	0.728696i	$0.740127\pi$
$402$	663.235	−	105.046i	1.64984	−	0.261309i
$403$	106.945	−	209.892i	0.265373	−	0.520823i
$404$	−179.310	+	58.2614i	−0.443837	+	0.144211i
$405$		0			0
$406$	−160.103	+	492.745i	−0.394341	+	1.21366i
$407$	−31.6939	+	31.6939i	−0.0778720	+	0.0778720i
$408$	762.316	−	388.419i	1.86842	−	0.952008i
$409$	312.156	+	429.646i	0.763219	+	1.05048i	0.996940	+	0.0781765i	$0.0249098\pi$
$409$	312.156	+	429.646i	0.763219	+	1.05048i	−0.233721	+	0.972304i	$0.575090\pi$
$410$		0			0
$411$	−279.540	−	203.098i	−0.680147	−	0.494155i
$412$	−159.102	+	1004.53i	−0.386170	+	2.43818i
$413$	−813.307	−	128.815i	−1.96927	−	0.311901i
$414$	−205.848	+	283.325i	−0.497217	+	0.684361i
$415$		0			0
$416$	674.532	−	490.076i	1.62147	−	1.17807i
$417$	−129.675	−	254.502i	−0.310972	−	0.610317i
$418$	−270.567	−	270.567i	−0.647288	−	0.647288i
$419$	−2.59910	−	0.844497i	−0.00620309	−	0.00201551i	0.305914	−	0.952059i	$-0.401038\pi$
$419$	−2.59910	−	0.844497i	−0.00620309	−	0.00201551i	−0.312117	+	0.950044i	$0.601038\pi$
$420$		0			0
$421$	−103.538	−	318.658i	−0.245934	−	0.756906i	−0.995481	−	0.0949560i	$-0.969729\pi$
$421$	−103.538	−	318.658i	−0.245934	−	0.756906i	0.749548	−	0.661950i	$-0.230271\pi$
$422$	−809.575	−	412.499i	−1.91842	−	0.977486i
$423$	11.1662	+	70.5005i	0.0263976	+	0.166668i
$424$		−	1766.46i		−	4.16618i
$425$		0			0
$426$	112.670			0.264483
$427$	−212.357	+	33.6341i	−0.497324	+	0.0787684i
$428$	251.872	−	494.326i	0.588485	−	1.15497i
$429$	151.413	−	49.1971i	0.352944	−	0.114678i
$430$		0			0
$431$	198.585	−	611.181i	0.460753	−	1.41805i	−0.403493	−	0.914983i	$-0.632204\pi$
$431$	198.585	−	611.181i	0.460753	−	1.41805i	0.864246	−	0.503069i	$-0.167796\pi$
$432$	−187.436	+	187.436i	−0.433880	+	0.433880i
$433$	46.6581	−	23.7735i	0.107755	−	0.0549041i	−0.399282	−	0.916828i	$-0.630741\pi$
$433$	46.6581	−	23.7735i	0.107755	−	0.0549041i	0.507037	+	0.861924i	$0.330741\pi$
$434$	−494.726	−	680.932i	−1.13992	−	1.56897i
$435$		0			0
$436$	706.990	+	513.658i	1.62154	+	1.17812i
$437$	45.7082	−	288.590i	0.104595	−	0.660389i
$438$	−209.779	−	33.2257i	−0.478948	−	0.0758579i
$439$	166.038	−	228.532i	0.378219	−	0.520574i	−0.576893	−	0.816820i	$-0.695735\pi$
$439$	166.038	−	228.532i	0.378219	−	0.520574i	0.955112	+	0.296246i	$0.0957349\pi$
$440$		0			0
$441$	−42.6741	+	31.0046i	−0.0967667	+	0.0703051i
$442$	−302.671	−	594.026i	−0.684777	−	1.34395i
$443$	338.562	+	338.562i	0.764248	+	0.764248i	0.977087	−	0.212839i	$-0.0682710\pi$
$443$	338.562	+	338.562i	0.764248	+	0.764248i	−0.212839	+	0.977087i	$0.568271\pi$
$444$	−72.6534	−	23.6065i	−0.163634	−	0.0531679i
$445$		0			0
$446$	−234.122	−	720.555i	−0.524938	−	1.61559i
$447$	−327.280	−	166.757i	−0.732170	−	0.373059i
$448$	−205.553	−	1297.81i	−0.458824	−	2.89690i
$449$			511.774i			1.13981i	0.821711	+	0.569904i	$0.193020\pi$
$449$			511.774i			1.13981i	−0.821711	+	0.569904i	$0.806980\pi$
$450$		0			0
$451$	−107.187			−0.237664
$452$	−1028.39	+	162.881i	−2.27519	+	0.360355i
$453$	−23.3770	+	45.8800i	−0.0516049	+	0.101280i
$454$	−817.040	+	265.472i	−1.79965	+	0.584741i
$455$		0			0
$456$	124.216	−	382.298i	0.272404	−	0.838373i
$457$	545.786	−	545.786i	1.19428	−	1.19428i	0.218425	−	0.975854i	$-0.429908\pi$
$457$	545.786	−	545.786i	1.19428	−	1.19428i	0.975854	−	0.218425i	$-0.0700920\pi$
$458$	−1053.87	+	536.971i	−2.30102	+	1.17243i
$459$	61.8018	+	85.0628i	0.134644	+	0.185322i
$460$		0			0
$461$	−732.858	−	532.452i	−1.58971	−	1.15499i	−0.904349	−	0.426795i	$-0.859643\pi$
$461$	−732.858	−	532.452i	−1.58971	−	1.15499i	−0.685365	−	0.728200i	$-0.740357\pi$
$462$	88.9858	−	561.834i	0.192610	−	1.21609i
$463$	135.873	+	21.5202i	0.293462	+	0.0464799i	0.301430	−	0.953488i	$-0.402536\pi$
$463$	135.873	+	21.5202i	0.293462	+	0.0464799i	−0.00796733	+	0.999968i	$0.502536\pi$
$464$	501.248	−	689.909i	1.08028	−	1.48687i
$465$		0			0
$466$	−1285.90	+	934.259i	−2.75944	+	2.00485i
$467$	247.420	+	485.589i	0.529807	+	1.03981i	0.988502	+	0.151211i	$0.0483173\pi$
$467$	247.420	+	485.589i	0.529807	+	1.03981i	−0.458694	+	0.888594i	$0.651683\pi$
$468$	191.867	+	191.867i	0.409973	+	0.409973i
$469$	−792.112	−	257.373i	−1.68894	−	0.548769i
$470$		0			0
$471$	95.4923	+	293.895i	0.202744	+	0.623981i
$472$	2194.97	+	1118.39i	4.65035	+	2.36947i
$473$	33.6232	+	212.289i	0.0710851	+	0.448813i
$474$		−	792.567i		−	1.67208i
$475$		0			0
$476$	−1721.63			−3.61686
$477$	214.414	−	33.9598i	0.449504	−	0.0711945i
$478$	106.903	−	209.808i	0.223646	−	0.438929i
$479$	243.720	−	79.1895i	0.508810	−	0.165323i	−0.0433508	−	0.999060i	$-0.513803\pi$
$479$	243.720	−	79.1895i	0.508810	−	0.165323i	0.552161	+	0.833737i	$0.313803\pi$
$480$		0			0
$481$	−11.3384	+	34.8959i	−0.0235725	+	0.0725487i
$482$	−21.0317	+	21.0317i	−0.0436342	+	0.0436342i
$483$	387.027	−	197.200i	0.801298	−	0.408282i
$484$	−53.4167	−	73.5218i	−0.110365	−	0.151905i
$485$		0			0
$486$	−47.9014	−	34.8024i	−0.0985626	−	0.0716099i
$487$	12.9195	−	81.5705i	0.0265288	−	0.167496i	−0.970867	−	0.239619i	$-0.922977\pi$
$487$	12.9195	−	81.5705i	0.0265288	−	0.167496i	0.997396	+	0.0721231i	$0.0229774\pi$
$488$	635.301	+	100.622i	1.30185	+	0.206192i
$489$	−283.795	+	390.610i	−0.580357	+	0.798793i
$490$		0			0
$491$	−348.669	+	253.323i	−0.710121	+	0.515933i	−0.883213	−	0.468973i	$-0.844624\pi$
$491$	−348.669	+	253.323i	−0.710121	+	0.515933i	0.173092	+	0.984906i	$0.444624\pi$
$492$	−82.9365	−	162.772i	−0.168570	−	0.330838i
$493$	−239.184	−	239.184i	−0.485161	−	0.485161i
$494$	−297.901	−	96.7940i	−0.603039	−	0.195939i
$495$		0			0
$496$	428.101	+	1317.56i	0.863107	+	2.65637i
$497$	−124.515	−	63.4435i	−0.250533	−	0.127653i
$498$	123.710	+	781.071i	0.248413	+	1.56842i
$499$		−	651.682i		−	1.30598i	−0.757368	−	0.652988i	$-0.773515\pi$
$499$		−	651.682i		−	1.30598i	0.757368	−	0.652988i	$-0.226485\pi$
$500$		0			0
$501$	−319.658			−0.638040
$502$	−868.017	+	137.480i	−1.72912	+	0.273865i
$503$	−130.915	+	256.936i	−0.260269	+	0.510807i	−0.983751	−	0.179536i	$-0.942540\pi$
$503$	−130.915	+	256.936i	−0.260269	+	0.510807i	0.723482	+	0.690343i	$0.242540\pi$
$504$	568.331	−	184.662i	1.12764	−	0.366393i
$505$		0			0
$506$	−382.251	+	1176.45i	−0.755437	+	2.32499i
$507$	−114.827	+	114.827i	−0.226483	+	0.226483i
$508$	711.973	−	362.768i	1.40152	−	0.714111i
$509$	302.452	+	416.290i	0.594208	+	0.817858i	0.995163	−	0.0982404i	$-0.0313214\pi$
$509$	302.452	+	416.290i	0.594208	+	0.817858i	−0.400954	+	0.916098i	$0.631321\pi$
$510$		0			0
$511$	213.124	+	154.844i	0.417073	+	0.303021i
$512$	12.1857	−	76.9377i	0.0238002	−	0.150269i
$513$	48.7915	+	7.72781i	0.0951101	+	0.0150640i
$514$	702.078	−	966.328i	1.36591	−	1.88001i
$515$		0			0
$516$	−296.363	+	215.320i	−0.574346	+	0.417287i
$517$	114.461	+	224.642i	0.221394	+	0.434511i
$518$	92.7010	+	92.7010i	0.178960	+	0.178960i
$519$	75.9570	+	24.6799i	0.146353	+	0.0475528i
$520$		0			0
$521$	−32.3038	−	99.4209i	−0.0620035	−	0.190827i	0.915257	−	0.402872i	$-0.131988\pi$
$521$	−32.3038	−	99.4209i	−0.0620035	−	0.190827i	−0.977260	+	0.212044i	$0.931988\pi$
$522$	169.722	+	86.4775i	0.325137	+	0.165666i
$523$	−69.8213	−	440.834i	−0.133501	−	0.842895i	−0.960009	−	0.279969i	$-0.909676\pi$
$523$	−69.8213	−	440.834i	−0.133501	−	0.842895i	0.826508	−	0.562926i	$-0.190324\pi$
$524$			490.862i			0.936760i
$525$		0			0
$526$	−498.032			−0.946829
$527$	542.748	−	85.9628i	1.02988	−	0.163117i
$528$	−425.063	+	834.234i	−0.805044	+	1.57999i
$529$	−395.239	+	128.421i	−0.747144	+	0.242762i
$530$		0			0
$531$	−93.5530	+	287.926i	−0.176183	+	0.542234i
$532$	−571.960	+	571.960i	−1.07511	+	1.07511i
$533$	−78.1805	+	39.8349i	−0.146680	+	0.0747372i
$534$	−368.314	−	506.941i	−0.689727	−	0.949327i
$535$		0			0
$536$	2015.81	+	1464.57i	3.76084	+	2.73241i
$537$	53.2848	−	336.427i	0.0992268	−	0.626494i
$538$	−680.416	−	107.767i	−1.26471	−	0.200311i
$539$	−109.513	+	150.731i	−0.203177	+	0.279650i
$540$		0			0
$541$	725.813	−	527.334i	1.34161	−	0.974740i	0.342231	−	0.939616i	$-0.388817\pi$
$541$	725.813	−	527.334i	1.34161	−	0.974740i	0.999383	−	0.0351241i	$-0.0111827\pi$
$542$	−383.184	−	752.041i	−0.706982	−	1.38753i
$543$	−211.373	−	211.373i	−0.389270	−	0.389270i
$544$	1849.76	+	601.022i	3.40029	+	1.10482i
$545$		0			0
$546$	−143.896	−	442.865i	−0.263545	−	0.811109i
$547$	−93.0075	−	47.3897i	−0.170032	−	0.0866357i	0.366903	−	0.930259i	$-0.380418\pi$
$547$	−93.0075	−	47.3897i	−0.170032	−	0.0866357i	−0.536935	+	0.843623i	$0.680418\pi$
$548$	−325.399	−	2054.49i	−0.593794	−	3.74907i
$549$			79.0475i			0.143984i
$550$		0			0
$551$	−158.924			−0.288428
$552$	−1283.49	+	203.285i	−2.32516	+	0.368270i
$553$	−446.288	+	875.890i	−0.807031	+	1.58389i
$554$	−119.128	+	38.7069i	−0.215032	+	0.0698681i
$555$		0			0
$556$	531.362	−	1635.36i	0.955687	−	2.94130i
$557$	−510.800	+	510.800i	−0.917056	+	0.917056i	−0.996814	−	0.0797580i	$-0.974585\pi$
$557$	−510.800	+	510.800i	−0.917056	+	0.917056i	0.0797580	+	0.996814i	$0.474585\pi$
$558$	−275.719	+	140.486i	−0.494121	+	0.251767i
$559$	103.420	+	142.345i	0.185008	+	0.254642i
$560$		0			0
$561$	300.454	+	218.293i	0.535569	+	0.389114i
$562$	178.524	−	1127.16i	0.317659	−	2.00562i
$563$	−277.173	−	43.8999i	−0.492314	−	0.0779749i	−0.0946589	−	0.995510i	$-0.530176\pi$
$563$	−277.173	−	43.8999i	−0.492314	−	0.0779749i	−0.397655	+	0.917535i	$0.630176\pi$
$564$	−252.574	+	347.638i	−0.447826	+	0.616379i
$565$		0			0
$566$	−1106.06	+	803.603i	−1.95418	+	1.41979i
$567$	33.3403	+	65.4341i	0.0588013	+	0.115404i
$568$	295.623	+	295.623i	0.520463	+	0.520463i
$569$	434.760	+	141.262i	0.764077	+	0.248264i	0.665027	−	0.746819i	$-0.268420\pi$
$569$	434.760	+	141.262i	0.764077	+	0.248264i	0.0990493	+	0.995083i	$0.468420\pi$
$570$		0			0
$571$	−17.3540	−	53.4102i	−0.0303924	−	0.0935380i	0.934710	−	0.355412i	$-0.115659\pi$
$571$	−17.3540	−	53.4102i	−0.0303924	−	0.0935380i	−0.965102	+	0.261874i	$0.915659\pi$
$572$	853.955	+	435.112i	1.49293	+	0.760685i
$573$	−15.3165	−	96.7045i	−0.0267303	−	0.168769i
$574$			313.508i			0.546181i
$575$		0			0
$576$	−483.094			−0.838706
$577$	−450.487	+	71.3502i	−0.780741	+	0.123657i	−0.534068	−	0.845442i	$-0.679337\pi$
$577$	−450.487	+	71.3502i	−0.780741	+	0.123657i	−0.246673	+	0.969099i	$0.579337\pi$
$578$	207.702	−	407.638i	0.359346	−	0.705256i
$579$	−402.623	+	130.820i	−0.695377	+	0.225942i
$580$		0			0
$581$	303.100	−	932.846i	0.521687	−	1.60559i
$582$	−274.825	+	274.825i	−0.472209	+	0.472209i
$583$	683.206	−	348.111i	1.17188	−	0.597102i
$584$	−463.240	−	637.595i	−0.793219	−	1.09177i
$585$		0			0
$586$	−187.977	−	136.573i	−0.320779	−	0.233060i
$587$	26.2626	−	165.815i	0.0447404	−	0.282480i	−0.955167	−	0.296066i	$-0.904325\pi$
$587$	26.2626	−	165.815i	0.0447404	−	0.282480i	0.999908	+	0.0135870i	$0.00432500\pi$
$588$	−313.635	−	49.6749i	−0.533392	−	0.0844810i
$589$	151.753	−	208.871i	0.257646	−	0.354619i
$590$		0			0
$591$	−89.2905	+	64.8734i	−0.151084	+	0.109769i
$592$	−97.9636	−	192.264i	−0.165479	−	0.324771i
$593$	365.800	+	365.800i	0.616863	+	0.616863i	0.944726	−	0.327862i	$-0.106328\pi$
$593$	365.800	+	365.800i	0.616863	+	0.616863i	−0.327862	+	0.944726i	$0.606328\pi$
$594$	−198.900	−	64.6266i	−0.334849	−	0.108799i
$595$		0			0
$596$	−683.310	−	2103.01i	−1.14649	−	3.52855i
$597$	−185.364	−	94.4479i	−0.310493	−	0.158204i
$598$	158.407	+	1000.15i	0.264895	+	1.67248i
$599$			783.143i			1.30742i	0.756746	+	0.653709i	$0.226788\pi$
$599$			783.143i			1.30742i	−0.756746	+	0.653709i	$0.773212\pi$
$600$		0			0
$601$	−144.125			−0.239809			−0.119904	−	0.992785i	$-0.538259\pi$
$601$	−144.125			−0.239809			−0.119904	+	0.992785i	$0.538259\pi$
$602$	620.920	−	98.3440i	1.03143	−	0.163362i
$603$	−139.017	+	272.836i	−0.230542	+	0.452464i
$604$	−294.813	+	95.7904i	−0.488100	+	0.158593i
$605$		0			0
$606$	36.7596	−	113.134i	0.0606594	−	0.186691i
$607$	200.753	−	200.753i	0.330729	−	0.330729i	−0.522134	−	0.852863i	$-0.674864\pi$
$607$	200.753	−	200.753i	0.330729	−	0.330729i	0.852863	+	0.522134i	$0.174864\pi$
$608$	814.200	−	414.855i	1.33914	−	0.682328i
$609$	−138.870	−	191.138i	−0.228029	−	0.313855i
$610$		0			0
$611$	166.973	+	121.313i	0.273278	+	0.198548i
$612$	−99.0175	+	625.172i	−0.161793	+	1.02152i
$613$	83.2322	+	13.1827i	0.135778	+	0.0215052i	0.223954	−	0.974600i	$-0.428104\pi$
$613$	83.2322	+	13.1827i	0.135778	+	0.0215052i	−0.0881752	+	0.996105i	$0.528104\pi$
$614$	−834.420	+	1148.48i	−1.35899	+	1.87049i
$615$		0			0
$616$	1707.62	−	1240.66i	2.77211	−	2.01406i
$617$	−206.931	−	406.125i	−0.335382	−	0.658225i	0.660305	−	0.750998i	$-0.270427\pi$
$617$	−206.931	−	406.125i	−0.335382	−	0.658225i	−0.995687	+	0.0927727i	$0.970427\pi$
$618$	−453.752	−	453.752i	−0.734226	−	0.734226i
$619$	−828.947	−	269.341i	−1.33917	−	0.435123i	−0.450135	−	0.892960i	$-0.648624\pi$
$619$	−828.947	−	269.341i	−1.33917	−	0.435123i	−0.889036	+	0.457837i	$0.848624\pi$
$620$		0			0
$621$	−49.3496	−	151.882i	−0.0794679	−	0.244577i
$622$	417.375	+	212.663i	0.671020	+	0.341902i
$623$	121.581	+	767.630i	0.195154	+	1.23215i
$624$			766.450i			1.22829i
$625$		0			0
$626$	2016.07			3.22056
$627$	172.338	−	27.2957i	0.274862	−	0.0435339i
$628$	−844.559	+	1657.54i	−1.34484	+	2.63940i
$629$	−81.4026	+	26.4493i	−0.129416	+	0.0420498i
$630$		0			0
$631$	30.0827	−	92.5850i	0.0476746	−	0.146727i	−0.924385	−	0.381460i	$-0.875421\pi$
$631$	30.0827	−	92.5850i	0.0476746	−	0.146727i	0.972060	+	0.234733i	$0.0754214\pi$
$632$	2079.53	−	2079.53i	3.29040	−	3.29040i
$633$	369.173	−	188.103i	0.583212	−	0.297161i
$634$	−52.3126	−	72.0021i	−0.0825119	−	0.113568i
$635$		0			0
$636$	1057.27	+	768.154i	1.66238	+	1.20779i
$637$	−23.8591	+	150.641i	−0.0374555	+	0.236485i
$638$	664.530	+	105.251i	1.04158	+	0.164971i
$639$	−30.1995	+	41.5660i	−0.0472606	+	0.0650486i
$640$		0			0
$641$	449.534	−	326.605i	0.701301	−	0.509525i	−0.179055	−	0.983839i	$-0.557304\pi$
$641$	449.534	−	326.605i	0.701301	−	0.509525i	0.880356	+	0.474314i	$0.157304\pi$
$642$	158.917	+	311.892i	0.247534	+	0.485813i
$643$	−8.96968	−	8.96968i	−0.0139497	−	0.0139497i	0.700098	−	0.714047i	$-0.253140\pi$
$643$	−8.96968	−	8.96968i	−0.0139497	−	0.0139497i	−0.714047	+	0.700098i	$0.753140\pi$
$644$	2486.93	+	808.053i	3.86170	+	1.25474i
$645$		0			0
$646$	−225.794	−	694.922i	−0.349526	−	1.07573i
$647$	368.471	+	187.745i	0.569506	+	0.290178i	0.714935	−	0.699191i	$-0.246456\pi$
$647$	368.471	+	187.745i	0.569506	+	0.290178i	−0.145429	+	0.989369i	$0.546456\pi$
$648$	−34.3691	−	216.998i	−0.0530387	−	0.334873i
$649$			1069.33i			1.64766i
$650$		0			0
$651$	383.812			0.589574
$652$	−2870.80	+	454.689i	−4.40306	+	0.697377i
$653$	−231.525	+	454.393i	−0.354555	+	0.695854i	−0.997546	−	0.0700205i	$-0.977694\pi$
$653$	−231.525	+	454.393i	−0.354555	+	0.695854i	0.642990	+	0.765874i	$0.277694\pi$
$654$	−524.387	+	170.384i	−0.801816	+	0.260526i
$655$		0			0
$656$	159.459	−	490.765i	0.243078	−	0.748117i
$657$	68.4858	−	68.4858i	0.104240	−	0.104240i
$658$	657.052	−	334.785i	0.998560	−	0.508792i
$659$	15.3369	+	21.1094i	0.0232730	+	0.0320325i	0.820495	−	0.571654i	$-0.193698\pi$
$659$	15.3369	+	21.1094i	0.0232730	+	0.0320325i	−0.797222	+	0.603686i	$0.793698\pi$
$660$		0			0
$661$	445.887	+	323.956i	0.674564	+	0.490099i	0.871550	−	0.490307i	$-0.163115\pi$
$661$	445.887	+	323.956i	0.674564	+	0.490099i	−0.196986	+	0.980406i	$0.563115\pi$
$662$	−165.621	+	1045.69i	−0.250183	+	1.57959i
$663$	300.274	+	47.5587i	0.452902	+	0.0717326i
$664$	−1724.78	+	2373.96i	−2.59756	+	3.57524i
$665$		0			0
$666$	38.9940	−	28.3308i	0.0585495	−	0.0425387i
$667$	233.246	+	457.770i	0.349694	+	0.686312i
$668$	−1360.72	−	1360.72i	−2.03700	−	2.03700i
$669$	328.579	+	106.762i	0.491150	+	0.159584i
$670$		0			0
$671$	86.2797	+	265.542i	0.128584	+	0.395740i
$672$	1210.40	+	616.731i	1.80120	+	0.917755i
$673$	−28.1223	−	177.557i	−0.0417865	−	0.263829i	0.957946	−	0.286948i	$-0.0926406\pi$
$673$	−28.1223	−	177.557i	−0.0417865	−	0.263829i	−0.999733	+	0.0231183i	$0.992641\pi$
$674$		−	1002.41i		−	1.48726i
$675$		0			0
$676$	−977.587			−1.44614
$677$	171.834	−	27.2158i	0.253817	−	0.0402006i	−0.0282294	−	0.999601i	$-0.508987\pi$
$677$	171.834	−	27.2158i	0.253817	−	0.0402006i	0.282046	+	0.959401i	$0.408987\pi$
$678$	298.246	−	585.340i	0.439890	−	0.863333i
$679$	458.470	−	148.966i	0.675213	−	0.219390i
$680$		0			0
$681$	121.058	−	372.577i	0.177765	−	0.547103i
$682$	−772.876	+	772.876i	−1.13325	+	1.13325i
$683$	542.106	−	276.217i	0.793713	−	0.404417i	−0.00961491	−	0.999954i	$-0.503061\pi$
$683$	542.106	−	276.217i	0.793713	−	0.404417i	0.803328	+	0.595537i	$0.203061\pi$
$684$	174.799	+	240.591i	0.255555	+	0.351741i
$685$		0			0
$686$	−787.761	−	572.342i	−1.14834	−	0.834318i
$687$	84.3743	−	532.718i	0.122816	−	0.775427i
$688$	−1022.01	−	161.870i	−1.48548	−	0.235276i
$689$	368.949	−	507.815i	0.535485	−	0.737032i
$690$		0			0
$691$	−33.4189	+	24.2803i	−0.0483631	+	0.0351379i	−0.611704	−	0.791087i	$-0.709516\pi$
$691$	−33.4189	+	24.2803i	−0.0483631	+	0.0351379i	0.563341	+	0.826224i	$0.309516\pi$
$692$	218.276	+	428.390i	0.315427	+	0.619061i
$693$	183.420	+	183.420i	0.264675	+	0.264675i
$694$	526.787	+	171.163i	0.759059	+	0.246633i
$695$		0			0
$696$	218.416	+	672.214i	0.313816	+	0.965825i
$697$	−182.374	−	92.9240i	−0.261655	−	0.133320i
$698$	−30.8732	−	194.926i	−0.0442310	−	0.279264i
$699$		−	724.806i		−	1.03692i
$700$		0			0
$701$	−1169.75			−1.66869			−0.834344	−	0.551244i	$-0.814153\pi$
$701$	−1169.75			−1.66869			−0.834344	+	0.551244i	$0.814153\pi$
$702$	−169.093	+	26.7817i	−0.240873	+	0.0381506i
$703$	−18.2566	+	35.8306i	−0.0259696	+	0.0509682i
$704$	−1622.84	+	527.294i	−2.30518	+	0.748997i
$705$		0			0
$706$	−787.712	+	2424.33i	−1.11574	+	3.43389i
$707$	−104.329	+	104.329i	−0.147566	+	0.147566i
$708$	−1623.88	+	827.407i	−2.29361	+	1.16865i
$709$	426.559	+	587.108i	0.601635	+	0.828079i	0.995857	−	0.0909363i	$-0.0289860\pi$
$709$	426.559	+	587.108i	0.601635	+	0.828079i	−0.394222	+	0.919015i	$0.628986\pi$
$710$		0			0
$711$	292.393	+	212.436i	0.411242	+	0.298785i
$712$	363.728	−	2296.49i	0.510854	−	3.22541i
$713$	−824.360	−	130.566i	−1.15618	−	0.183122i
$714$	638.481	−	878.793i	0.894231	−	1.23080i
$715$		0			0
$716$	1658.92	−	1205.28i	2.31693	−	1.68335i
$717$	48.7485	+	95.6743i	0.0679895	+	0.133437i
$718$	886.795	+	886.795i	1.23509	+	1.23509i
$719$	455.491	+	147.998i	0.633506	+	0.205839i	0.608128	−	0.793839i	$-0.291921\pi$
$719$	455.491	+	147.998i	0.633506	+	0.205839i	0.0253785	+	0.999678i	$0.491921\pi$
$720$		0			0
$721$	245.951	+	756.959i	0.341125	+	1.04987i
$722$	915.850	+	466.649i	1.26849	+	0.646328i
$723$	−2.12175	−	13.3962i	−0.00293465	−	0.0185287i
$724$		−	1799.54i		−	2.48556i
$725$		0			0
$726$	57.3388			0.0789791
$727$	455.141	−	72.0872i	0.626053	−	0.0991571i	0.164656	−	0.986351i	$-0.447348\pi$
$727$	455.141	−	72.0872i	0.626053	−	0.0991571i	0.461397	+	0.887194i	$0.347348\pi$
$728$	784.436	−	1539.54i	1.07752	−	2.11475i
$729$	25.6785	−	8.34346i	0.0352243	−	0.0114451i
$730$		0			0
$731$	−126.832	+	390.350i	−0.173505	+	0.533994i
$732$	−336.488	+	336.488i	−0.459684	+	0.459684i
$733$	−1148.56	+	585.221i	−1.56693	+	0.798391i	−0.999684	−	0.0251561i	$-0.991992\pi$
$733$	−1148.56	+	585.221i	−1.56693	+	0.798391i	−0.567248	+	0.823547i	$0.691992\pi$
$734$	1184.08	+	1629.74i	1.61318	+	2.22036i
$735$		0			0
$736$	−2389.93	−	1736.38i	−3.24718	−	2.35922i
$737$	−169.197	+	1068.26i	−0.229575	+	1.44948i
$738$	113.844	+	18.0311i	0.154260	+	0.0244324i
$739$	337.918	−	465.105i	0.457264	−	0.629370i	−0.516674	−	0.856182i	$-0.672830\pi$
$739$	337.918	−	465.105i	0.457264	−	0.629370i	0.973939	+	0.226812i	$0.0728302\pi$
$740$		0			0
$741$	115.557	−	83.9572i	0.155948	−	0.113303i
$742$	−1018.18	−	1998.30i	−1.37221	−	2.69312i
$743$	−440.338	−	440.338i	−0.592649	−	0.592649i	0.345697	−	0.938346i	$-0.387643\pi$
$743$	−440.338	−	440.338i	−0.592649	−	0.592649i	−0.938346	+	0.345697i	$0.887643\pi$
$744$	−1092.04	−	354.825i	−1.46779	−	0.476915i
$745$		0			0
$746$	−147.530	−	454.049i	−0.197761	−	0.608645i
$747$	−321.310	−	163.716i	−0.430134	−	0.219164i
$748$	349.744	+	2208.20i	0.467572	+	2.95213i
$749$		−	434.166i		−	0.579661i
$750$		0			0
$751$	−393.993			−0.524624			−0.262312	−	0.964983i	$-0.584485\pi$
$751$	−393.993			−0.524624			−0.262312	+	0.964983i	$0.584485\pi$
$752$	−1198.83	+	189.876i	−1.59419	+	0.252495i
$753$	181.940	−	357.077i	0.241620	−	0.474206i
$754$	523.815	−	170.198i	0.694715	−	0.225727i
$755$		0			0
$756$	−136.616	+	420.462i	−0.180709	+	0.556167i
$757$	517.043	−	517.043i	0.683016	−	0.683016i	−0.277663	−	0.960679i	$-0.589560\pi$
$757$	517.043	−	517.043i	0.683016	−	0.683016i	0.960679	+	0.277663i	$0.0895597\pi$
$758$	−1239.44	+	631.528i	−1.63515	+	0.833151i
$759$	−331.557	−	456.349i	−0.436834	−	0.601250i
$760$		0			0
$761$	−290.456	−	211.029i	−0.381677	−	0.277304i	0.380360	−	0.924839i	$-0.375800\pi$
$761$	−290.456	−	211.029i	−0.381677	−	0.277304i	−0.762036	+	0.647534i	$0.775800\pi$
$762$	−78.8689	+	497.958i	−0.103502	+	0.653489i
$763$	675.458	+	106.982i	0.885266	+	0.140212i
$764$	346.452	−	476.850i	0.453471	−	0.624149i
$765$		0			0
$766$	308.742	−	224.314i	0.403058	−	0.292838i
$767$	397.409	+	779.958i	0.518134	+	1.01689i
$768$	−267.881	−	267.881i	−0.348804	−	0.348804i
$769$	−1299.32	−	422.175i	−1.68962	−	0.548992i	−0.702885	−	0.711304i	$-0.748105\pi$
$769$	−1299.32	−	422.175i	−1.68962	−	0.548992i	−0.986740	+	0.162312i	$0.948105\pi$
$770$		0			0
$771$	168.315	+	518.020i	0.218307	+	0.671880i
$772$	−2270.76	−	1157.01i	−2.94139	−	1.49871i
$773$	−157.447	−	994.081i	−0.203683	−	1.28600i	−0.851559	−	0.524258i	$-0.824343\pi$
$773$	−157.447	−	994.081i	−0.203683	−	1.28600i	0.647876	−	0.761746i	$-0.275657\pi$
$774$		−	231.130i		−	0.298617i
$775$		0			0
$776$	−1442.17			−1.85847
$777$	−59.0463	+	9.35202i	−0.0759927	+	0.0120361i
$778$	1114.77	−	2187.86i	1.43287	−	2.81216i
$779$	−91.4595	+	29.7170i	−0.117406	+	0.0381476i
$780$		0			0
$781$	−56.0792	+	172.594i	−0.0718043	+	0.220991i
$782$	−1670.29	+	1670.29i	−2.13592	+	2.13592i
$783$	−77.3945	+	39.4345i	−0.0988436	+	0.0503633i
$784$	−527.219	−	725.655i	−0.672473	−	0.925580i
$785$		0			0
$786$	−250.558	−	182.041i	−0.318776	−	0.231604i
$787$	180.846	−	1141.82i	0.229791	−	1.45085i	−0.555395	−	0.831587i	$-0.687433\pi$
$787$	180.846	−	1141.82i	0.229791	−	1.45085i	0.785186	−	0.619259i	$-0.212567\pi$
$788$	−656.243	−	103.939i	−0.832796	−	0.131902i
$789$	133.490	−	183.733i	0.169189	−	0.232869i
$790$		0			0
$791$	−659.200	+	478.937i	−0.833376	+	0.605483i
$792$	−352.307	−	691.440i	−0.444831	−	0.873031i
$793$	161.617	+	161.617i	0.203805	+	0.203805i
$794$	−2661.88	−	864.897i	−3.35249	−	1.08929i
$795$		0			0
$796$	−387.013	−	1191.10i	−0.486197	−	1.49636i
$797$	685.540	+	349.300i	0.860150	+	0.438269i	0.827677	−	0.561204i	$-0.189662\pi$
$797$	685.540	+	349.300i	0.860150	+	0.438269i	0.0324730	+	0.999473i	$0.489662\pi$
$798$	−79.8368	−	504.070i	−0.100046	−	0.631667i
$799$			481.450i			0.602566i
$800$		0			0
$801$	285.741			0.356731
$802$	2060.48	−	326.349i	2.56918	−	0.406918i
$803$	155.310	−	304.814i	0.193413	−	0.379594i
$804$	−1753.17	+	569.640i	−2.18056	+	0.708507i
$805$		0			0
$806$	−276.493	+	850.958i	−0.343043	+	1.05578i
$807$	222.133	−	222.133i	0.275257	−	0.275257i
$808$	393.291	−	200.392i	0.486747	−	0.248010i
$809$	−190.387	−	262.045i	−0.235336	−	0.323912i	0.674972	−	0.737843i	$-0.264156\pi$
$809$	−190.387	−	262.045i	−0.235336	−	0.323912i	−0.910308	+	0.413931i	$0.864156\pi$
$810$		0			0
$811$	−741.264	−	538.560i	−0.914012	−	0.664069i	0.0280143	−	0.999608i	$-0.491082\pi$
$811$	−741.264	−	538.560i	−0.914012	−	0.664069i	−0.942026	+	0.335539i	$0.891082\pi$
$812$	222.494	−	1404.77i	0.274008	−	1.73002i
$813$	380.149	+	60.2097i	0.467588	+	0.0740587i
$814$	100.068	−	137.732i	0.122934	−	0.169204i
$815$		0			0
$816$	−1446.46	+	1050.91i	−1.77262	+	1.28788i
$817$	87.5460	+	171.819i	0.107155	+	0.210304i
$818$	−1426.35	−	1426.35i	−1.74370	−	1.74370i
$819$	201.951	+	65.6177i	0.246582	+	0.0801193i
$820$		0			0
$821$	−214.758	−	660.957i	−0.261581	−	0.805064i	−0.992461	−	0.122558i	$-0.960890\pi$
$821$	−214.758	−	660.957i	−0.261581	−	0.805064i	0.730880	−	0.682506i	$-0.239110\pi$
$822$	1169.38	+	595.828i	1.42260	+	0.724851i
$823$	−208.667	−	1317.47i	−0.253544	−	1.60081i	−0.705457	−	0.708752i	$-0.749258\pi$
$823$	−208.667	−	1317.47i	−0.253544	−	1.60081i	0.451913	−	0.892062i	$-0.350742\pi$
$824$		−	2381.10i		−	2.88969i
$825$		0			0
$826$	3127.68			3.78654
$827$	−927.959	+	146.974i	−1.12208	+	0.177720i	−0.689786	−	0.724013i	$-0.742295\pi$
$827$	−927.959	+	146.974i	−1.12208	+	0.177720i	−0.432293	+	0.901733i	$0.642295\pi$
$828$	436.460	−	856.602i	0.527126	−	1.03454i
$829$	−264.382	+	85.9029i	−0.318917	+	0.103622i	−0.464101	−	0.885782i	$-0.653622\pi$
$829$	−264.382	+	85.9029i	−0.318917	+	0.103622i	0.145184	+	0.989405i	$0.453622\pi$
$830$		0			0
$831$	17.6507	−	54.3233i	0.0212403	−	0.0653710i
$832$	−987.717	+	987.717i	−1.18716	+	1.18716i
$833$	−317.006	+	161.522i	−0.380559	+	0.193904i
$834$	637.701	+	877.720i	0.764629	+	1.05242i
$835$		0			0
$836$	849.801	+	617.416i	1.01651	+	0.738536i
$837$	22.0746	−	139.373i	0.0263734	−	0.166515i
$838$	10.2523	+	1.62381i	0.0122343	+	0.00193772i
$839$	95.4951	−	131.438i	0.113820	−	0.156660i	−0.748306	−	0.663354i	$-0.769133\pi$
$839$	95.4951	−	131.438i	0.113820	−	0.156660i	0.862126	+	0.506694i	$0.169133\pi$
$840$		0			0
$841$	−454.308	+	330.074i	−0.540200	+	0.392478i
$842$	577.766	+	1133.93i	0.686183	+	1.34671i
$843$	367.979	+	367.979i	0.436512	+	0.436512i
$844$	2372.21	+	770.777i	2.81067	+	0.913243i
$845$		0			0
$846$	−83.7803	−	257.849i	−0.0990311	−	0.304786i
$847$	−63.3669	−	32.2870i	−0.0748133	−	0.0381193i
$848$	577.471	+	3646.01i	0.680980	+	4.29954i
$849$		−	623.442i		−	0.734325i
$850$		0			0
$851$	130.002			0.152764
$852$	−305.491	+	48.3850i	−0.358557	+	0.0567899i
$853$	580.664	−	1139.62i	0.680732	−	1.33601i	−0.249262	−	0.968436i	$-0.580188\pi$
$853$	580.664	−	1139.62i	0.680732	−	1.33601i	0.929994	−	0.367575i	$-0.119812\pi$
$854$	776.678	−	252.358i	0.909459	−	0.295501i
$855$		0			0
$856$	−401.375	+	1235.31i	−0.468896	+	1.44311i
$857$	−215.985	+	215.985i	−0.252025	+	0.252025i	−0.821800	−	0.569776i	$-0.807030\pi$
$857$	−215.985	+	215.985i	−0.252025	+	0.252025i	0.569776	+	0.821800i	$0.307030\pi$
$858$	−538.797	+	274.531i	−0.627969	+	0.319966i
$859$	−773.813	−	1065.06i	−0.900830	−	1.23989i	−0.970202	−	0.242296i	$-0.922100\pi$
$859$	−773.813	−	1065.06i	−0.900830	−	1.23989i	0.0693723	−	0.997591i	$-0.477900\pi$
$860$		0			0
$861$	−115.659	−	84.0312i	−0.134331	−	0.0975972i
$862$	−381.841	+	2410.85i	−0.442971	+	2.79681i
$863$	736.931	+	116.718i	0.853918	+	0.135247i	0.568022	−	0.823013i	$-0.307709\pi$
$863$	736.931	+	116.718i	0.853918	+	0.135247i	0.285896	+	0.958261i	$0.407709\pi$
$864$	293.568	−	404.061i	0.339778	−	0.467664i
$865$		0			0
$866$	−160.913	+	116.910i	−0.185812	+	0.135000i
$867$	94.7138	+	185.886i	0.109243	+	0.214402i
$868$	1633.81	+	1633.81i	1.88227	+	1.88227i
$869$	1214.10	+	394.485i	1.39712	+	0.453952i
$870$		0			0
$871$	273.601	+	842.059i	0.314123	+	0.966772i
$872$	−1822.94	−	928.833i	−2.09053	−	1.06518i
$873$	−27.7254	−	175.051i	−0.0317587	−	0.200517i
$874$			1109.81i			1.26981i
$875$		0			0
$876$	583.059			0.665593
$877$	−1231.98	+	195.126i	−1.40477	+	0.222493i	−0.812364	−	0.583150i	$-0.801820\pi$
$877$	−1231.98	+	195.126i	−1.40477	+	0.222493i	−0.592401	+	0.805643i	$0.701820\pi$
$878$	−487.106	+	955.999i	−0.554790	+	1.08884i
$879$	100.769	−	32.7418i	0.114640	−	0.0372489i
$880$		0			0
$881$	−263.341	+	810.479i	−0.298911	+	0.919954i	0.682968	+	0.730448i	$0.260689\pi$
$881$	−263.341	+	810.479i	−0.298911	+	0.919954i	−0.981880	+	0.189506i	$0.939311\pi$
$882$	141.671	−	141.671i	0.160624	−	0.160624i
$883$	1428.74	−	727.978i	1.61805	−	0.824437i	0.618805	−	0.785545i	$-0.287617\pi$
$883$	1428.74	−	727.978i	1.61805	−	0.824437i	0.999243	−	0.0388919i	$-0.0123828\pi$
$884$	1075.76	+	1480.65i	1.21692	+	1.67494i
$885$		0			0
$886$	−1471.29	−	1068.95i	−1.66060	−	1.20649i
$887$	19.8592	−	125.386i	0.0223891	−	0.141359i	−0.973962	−	0.226713i	$-0.927202\pi$
$887$	19.8592	−	125.386i	0.0223891	−	0.141359i	0.996351	+	0.0853537i	$0.0272020\pi$
$888$	176.647	+	27.9781i	0.198926	+	0.0315068i
$889$	367.557	−	505.899i	0.413450	−	0.569065i
$890$		0			0
$891$	77.1542	−	56.0558i	0.0865928	−	0.0629134i
$892$	944.230	+	1853.16i	1.05855	+	2.07753i
$893$	159.948	+	159.948i	0.179113	+	0.179113i
$894$	1326.88	+	431.130i	1.48421	+	0.482248i
$895$		0			0
$896$	572.811	+	1762.93i	0.639298	+	1.96756i
$897$	−411.431	−	209.635i	−0.458675	−	0.233706i
$898$	−304.087	−	1919.93i	−0.338627	−	2.13801i
$899$			453.968i			0.504970i
$900$		0			0
$901$	1464.24			1.62512
$902$	402.112	−	63.6884i	0.445801	−	0.0706079i
$903$	−130.147	+	255.429i	−0.144128	+	0.282867i
$904$	2318.35	−	753.277i	2.56454	−	0.833271i
$905$		0			0
$906$	60.4383	−	186.010i	0.0667090	−	0.205309i
$907$	−626.637	+	626.637i	−0.690889	+	0.690889i	−0.962428	−	0.271538i	$-0.912468\pi$
$907$	−626.637	+	626.637i	−0.690889	+	0.690889i	0.271538	+	0.962428i	$0.412468\pi$
$908$	2101.30	−	1070.67i	2.31421	−	1.17915i
$909$	31.8846	+	43.8853i	0.0350765	+	0.0482787i
$910$		0			0
$911$	1053.95	+	765.743i	1.15692	+	0.840552i	0.989386	−	0.145314i	$-0.0464192\pi$
$911$	1053.95	+	765.743i	1.15692	+	0.840552i	0.167535	+	0.985866i	$0.446419\pi$
$912$	−131.408	+	829.677i	−0.144088	+	0.909734i
$913$	−1258.06	−	199.258i	−1.37794	−	0.218245i
$914$	−1723.23	+	2371.82i	−1.88537	+	2.59499i
$915$		0			0
$916$	2626.83	−	1908.51i	2.86772	−	2.08352i
$917$	174.393	+	342.266i	0.190178	+	0.373245i
$918$	−282.393	−	282.393i	−0.307618	−	0.307618i
$919$	1388.79	+	451.245i	1.51120	+	0.491017i	0.943260	−	0.332056i	$-0.107742\pi$
$919$	1388.79	+	451.245i	1.51120	+	0.491017i	0.567936	+	0.823073i	$0.307742\pi$
$920$		0			0
$921$	−200.042	−	615.666i	−0.217201	−	0.668476i
$922$	3065.71	+	1562.06i	3.32506	+	1.69420i
$923$	23.2396	+	146.729i	0.0251783	+	0.158970i
$924$			1561.56i			1.69000i
$925$		0			0
$926$	−522.518			−0.564274
$927$	289.019	−	45.7761i	0.311779	−	0.0493809i
$928$	−729.461	+	1431.65i	−0.786058	+	1.54272i
$929$	−225.655	+	73.3196i	−0.242901	+	0.0789232i	−0.427937	−	0.903808i	$-0.640760\pi$
$929$	−225.655	+	73.3196i	−0.242901	+	0.0789232i	0.185037	+	0.982732i	$0.440760\pi$
$930$		0			0
$931$	−51.6547	+	158.977i	−0.0554831	+	0.170759i
$932$	3085.35	−	3085.35i	3.31046	−	3.31046i
$933$	−190.326	+	96.9762i	−0.203994	+	0.103940i
$934$	−1216.73	−	1674.68i	−1.30271	−	1.79302i
$935$		0			0
$936$	−513.936	−	373.396i	−0.549076	−	0.398927i
$937$	−278.872	+	1760.73i	−0.297622	+	1.87911i	0.155759	+	0.987795i	$0.450218\pi$
$937$	−278.872	+	1760.73i	−0.297622	+	1.87911i	−0.453381	+	0.891317i	$0.649782\pi$
$938$	3124.55	+	494.880i	3.33108	+	0.527591i
$939$	−540.378	+	743.767i	−0.575483	+	0.792084i
$940$		0			0
$941$	−364.279	+	264.664i	−0.387119	+	0.281258i	−0.764274	−	0.644892i	$-0.776902\pi$
$941$	−364.279	+	264.664i	−0.387119	+	0.281258i	0.377155	+	0.926150i	$0.376902\pi$
$942$	−532.869	−	1045.81i	−0.565678	−	1.11021i
$943$	219.829	+	219.829i	0.233117	+	0.233117i
$944$	−4896.06	−	1590.83i	−5.18650	−	1.68520i
$945$		0			0
$946$	−252.277	−	776.427i	−0.266677	−	0.820748i
$947$	−727.461	−	370.660i	−0.768174	−	0.391404i	0.0255566	−	0.999673i	$-0.491864\pi$
$947$	−727.461	−	370.660i	−0.768174	−	0.391404i	−0.793731	+	0.608269i	$0.791864\pi$
$948$	340.360	+	2148.95i	0.359030	+	2.26683i
$949$		−	280.047i		−	0.295097i
$950$		0			0
$951$	40.5845			0.0426756
$952$	3981.02	−	630.531i	4.18174	−	0.662323i
$953$	−539.470	+	1058.77i	−0.566075	+	1.11099i	0.413612	+	0.910453i	$0.364267\pi$
$953$	−539.470	+	1058.77i	−0.566075	+	1.11099i	−0.979687	+	0.200532i	$0.935733\pi$
$954$	−784.199	+	254.802i	−0.822011	+	0.267088i
$955$		0			0
$956$	−199.753	+	614.777i	−0.208947	+	0.643073i
$957$	−216.947	+	216.947i	−0.226694	+	0.226694i
$958$	−867.268	+	441.895i	−0.905290	+	0.461269i
$959$	−956.809	−	1316.94i	−0.997716	−	1.37324i
$960$		0			0
$961$	180.825	+	131.377i	0.188163	+	0.136708i
$962$	21.8016	−	137.650i	0.0226628	−	0.143087i
$963$	−157.658	−	24.9706i	−0.163715	−	0.0259300i
$964$	47.9931	−	66.0568i	0.0497853	−	0.0685236i
$965$		0			0
$966$	−1334.77	+	969.765i	−1.38175	+	1.00390i
$967$	−714.594	−	1402.47i	−0.738980	−	1.45033i	−0.887205	−	0.461376i	$-0.847356\pi$
$967$	−714.594	−	1402.47i	−0.738980	−	1.45033i	0.148225	−	0.988954i	$-0.452644\pi$
$968$	150.445	+	150.445i	0.155419	+	0.155419i
$969$	316.891	+	102.964i	0.327028	+	0.106258i
$970$		0			0
$971$	193.680	+	596.085i	0.199464	+	0.613887i	0.999895	+	0.0144629i	$0.00460386\pi$
$971$	193.680	+	596.085i	0.199464	+	0.613887i	−0.800431	+	0.599425i	$0.795396\pi$
$972$	144.824	+	73.7917i	0.148996	+	0.0759174i
$973$	−210.505	−	1329.08i	−0.216347	−	1.36596i
$974$			313.690i			0.322064i
$975$		0			0
$976$	−1344.17			−1.37722
$977$	−522.903	+	82.8198i	−0.535213	+	0.0847695i	−0.418190	−	0.908360i	$-0.637335\pi$
$977$	−522.903	+	82.8198i	−0.535213	+	0.0847695i	−0.117024	+	0.993129i	$0.537335\pi$
$978$	832.568	−	1634.01i	0.851296	−	1.67076i
$979$	959.881	−	311.884i	0.980471	−	0.318574i
$980$		0			0
$981$	77.6965	−	239.125i	0.0792013	−	0.243757i
$982$	1157.52	−	1157.52i	1.17874	−	1.17874i
$983$	−745.712	+	379.959i	−0.758608	+	0.386530i	−0.790103	−	0.612974i	$-0.789973\pi$
$983$	−745.712	+	379.959i	−0.758608	+	0.386530i	0.0314952	+	0.999504i	$0.489973\pi$
$984$	251.393	+	346.013i	0.255481	+	0.351639i
$985$		0			0
$986$	1039.42	+	755.186i	1.05418	+	0.765909i
$987$	−52.6047	+	332.133i	−0.0532976	+	0.336508i
$988$	849.291	+	134.514i	0.859606	+	0.136148i
$989$	366.425	−	504.341i	0.370501	−	0.509950i
$990$		0			0
$991$	533.102	−	387.322i	0.537944	−	0.390839i	−0.285377	−	0.958415i	$-0.592119\pi$
$991$	533.102	−	387.322i	0.537944	−	0.390839i	0.823321	+	0.567576i	$0.192119\pi$
$992$	−1185.04	−	2325.77i	−1.19459	−	2.34452i
$993$	−341.383	−	341.383i	−0.343789	−	0.343789i
$994$	504.817	+	164.025i	0.507865	+	0.165015i
$995$		0			0
$996$	−670.847	−	2064.65i	−0.673541	−	2.07295i
$997$	310.548	+	158.232i	0.311482	+	0.158708i	0.602743	−	0.797936i	$-0.294075\pi$
$997$	310.548	+	158.232i	0.311482	+	0.158708i	−0.291260	+	0.956644i	$0.594075\pi$
$998$	387.218	+	2444.80i	0.387994	+	2.44970i
$999$			21.9793i			0.0220013i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	375.3.k.a.43.1		80
5.2	odd	4		375.3.k.b.82.1		80
5.3	odd	4		375.3.k.c.82.10		80
5.4	even	2		75.3.k.a.13.10	✓	80
15.14	odd	2		225.3.r.b.163.1		80
25.2	odd	20	inner	375.3.k.a.157.1		80
25.11	even	5		375.3.k.b.343.1		80
25.14	even	10		375.3.k.c.343.10		80
25.23	odd	20		75.3.k.a.52.10	yes	80
75.23	even	20		225.3.r.b.127.1		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.3.k.a.13.10	✓	80	5.4	even	2
75.3.k.a.52.10	yes	80	25.23	odd	20
225.3.r.b.127.1		80	75.23	even	20
225.3.r.b.163.1		80	15.14	odd	2
375.3.k.a.43.1		80	1.1	even	1	trivial
375.3.k.a.157.1		80	25.2	odd	20	inner
375.3.k.b.82.1		80	5.2	odd	4
375.3.k.b.343.1		80	25.11	even	5
375.3.k.c.82.10		80	5.3	odd	4
375.3.k.c.343.10		80	25.14	even	10

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:	\( N \)	\(=\)	\( 375 = 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	375.k (of order \(20\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-3.75152 + 0.594183i) q^{2} +(0.786335 - 1.54327i) q^{3} +(9.91663 - 3.22211i) q^{4} +(-2.03297 + 6.25683i) q^{6} +(5.76987 - 5.76987i) q^{7} +(-21.7507 + 11.0826i) q^{8} +(-1.76336 - 2.42705i) q^{9} +O(q^{10})\)	\(q+(-3.75152 + 0.594183i) q^{2} +(0.786335 - 1.54327i) q^{3} +(9.91663 - 3.22211i) q^{4} +(-2.03297 + 6.25683i) q^{6} +(5.76987 - 5.76987i) q^{7} +(-21.7507 + 11.0826i) q^{8} +(-1.76336 - 2.42705i) q^{9} +(-8.57269 - 6.22843i) q^{11} +(2.82521 - 17.8377i) q^{12} +(-8.56755 - 1.35697i) q^{13} +(-18.2174 + 25.0741i) q^{14} +(41.2709 - 29.9851i) q^{16} +(-9.18644 - 18.0294i) q^{17} +(8.05738 + 8.05738i) q^{18} +(-9.04167 - 2.93782i) q^{19} +(-4.36741 - 13.4415i) q^{21} +(35.8615 + 18.2723i) q^{22} +(4.80786 + 30.3556i) q^{23} +42.2818i q^{24} +32.9476 q^{26} +(-5.13218 + 0.812857i) q^{27} +(38.6265 - 75.8088i) q^{28} +(15.8984 - 5.16571i) q^{29} +(-8.39189 + 25.8276i) q^{31} +(-67.9662 + 67.9662i) q^{32} +(-16.3531 + 8.33234i) q^{33} +(45.1759 + 62.1792i) q^{34} +(-25.3068 - 18.3864i) q^{36} +(0.661704 - 4.17784i) q^{37} +(35.6656 + 5.64887i) q^{38} +(-8.83112 + 12.1550i) q^{39} +(8.18348 - 5.94565i) q^{41} +(24.3711 + 47.8310i) q^{42} +(-14.3428 - 14.3428i) q^{43} +(-105.081 - 34.1428i) q^{44} +(-36.0736 - 111.023i) q^{46} +(-21.1998 - 10.8018i) q^{47} +(-13.8223 - 87.2704i) q^{48} -17.5827i q^{49} -35.0478 q^{51} +(-89.3335 + 14.1490i) q^{52} +(-32.8517 + 64.4751i) q^{53} +(18.7705 - 6.09890i) q^{54} +(-61.5540 + 189.444i) q^{56} +(-11.6436 + 11.6436i) q^{57} +(-56.5739 + 28.8258i) q^{58} +(-59.3161 - 81.6416i) q^{59} +(-21.3169 - 15.4876i) q^{61} +(16.1361 - 101.879i) q^{62} +(-24.1781 - 3.82943i) q^{63} +(94.6519 - 130.277i) q^{64} +(56.3982 - 40.9757i) q^{66} +(-46.3389 - 90.9453i) q^{67} +(-149.191 - 149.191i) q^{68} +(50.6275 + 16.4499i) q^{69} +(-5.29227 - 16.2879i) q^{71} +(65.2522 + 33.2477i) q^{72} +(5.05041 + 31.8870i) q^{73} +16.0664i q^{74} -99.1288 q^{76} +(-85.4005 + 13.5261i) q^{77} +(25.9079 - 50.8470i) q^{78} +(-114.576 + 37.2281i) q^{79} +(-2.78115 + 8.55951i) q^{81} +(-27.1677 + 27.1677i) q^{82} +(107.103 - 54.5720i) q^{83} +(-86.6199 - 119.222i) q^{84} +(62.3293 + 45.2849i) q^{86} +(4.52940 - 28.5975i) q^{87} +(255.489 + 40.4655i) q^{88} +(-55.9848 + 77.0565i) q^{89} +(-57.2631 + 41.6041i) q^{91} +(145.487 + 285.534i) q^{92} +(33.2601 + 33.2601i) q^{93} +(85.9498 + 27.9268i) q^{94} +(51.4459 + 158.334i) q^{96} +(52.6386 + 26.8207i) q^{97} +(10.4473 + 65.9619i) q^{98} +31.7893i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 4 q^{2} + 4 q^{7} + 12 q^{8}+O(q^{10}) \) 80 * q - 4 * q^2 + 4 * q^7 + 12 * q^8	\( 80 q - 4 q^{2} + 4 q^{7} + 12 q^{8} + 24 q^{12} - 32 q^{13} + 80 q^{16} + 100 q^{17} + 48 q^{18} - 100 q^{19} + 100 q^{22} + 96 q^{23} - 40 q^{26} - 196 q^{28} + 200 q^{29} - 636 q^{32} - 216 q^{33} + 100 q^{34} - 120 q^{36} + 184 q^{37} + 564 q^{38} + 160 q^{41} + 12 q^{42} + 472 q^{43} - 700 q^{44} + 288 q^{47} + 48 q^{48} - 620 q^{52} - 304 q^{53} - 72 q^{57} - 1272 q^{58} + 800 q^{59} - 240 q^{61} - 1212 q^{62} + 12 q^{63} + 100 q^{64} + 80 q^{67} - 104 q^{68} - 36 q^{72} + 116 q^{73} + 88 q^{77} + 120 q^{78} + 200 q^{79} + 180 q^{81} + 168 q^{82} + 1264 q^{83} - 1200 q^{84} + 876 q^{87} + 212 q^{88} - 1500 q^{89} + 1504 q^{92} + 648 q^{93} - 200 q^{94} + 60 q^{96} + 260 q^{97} + 92 q^{98}+O(q^{100}) \) 80 * q - 4 * q^2 + 4 * q^7 + 12 * q^8 + 24 * q^12 - 32 * q^13 + 80 * q^16 + 100 * q^17 + 48 * q^18 - 100 * q^19 + 100 * q^22 + 96 * q^23 - 40 * q^26 - 196 * q^28 + 200 * q^29 - 636 * q^32 - 216 * q^33 + 100 * q^34 - 120 * q^36 + 184 * q^37 + 564 * q^38 + 160 * q^41 + 12 * q^42 + 472 * q^43 - 700 * q^44 + 288 * q^47 + 48 * q^48 - 620 * q^52 - 304 * q^53 - 72 * q^57 - 1272 * q^58 + 800 * q^59 - 240 * q^61 - 1212 * q^62 + 12 * q^63 + 100 * q^64 + 80 * q^67 - 104 * q^68 - 36 * q^72 + 116 * q^73 + 88 * q^77 + 120 * q^78 + 200 * q^79 + 180 * q^81 + 168 * q^82 + 1264 * q^83 - 1200 * q^84 + 876 * q^87 + 212 * q^88 - 1500 * q^89 + 1504 * q^92 + 648 * q^93 - 200 * q^94 + 60 * q^96 + 260 * q^97 + 92 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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