LMFDB - Embedded newform 920.2.bb.a.11.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [920,2,Mod(11,920)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(920, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 11, 0, 9]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("920.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 920 = 2^{3} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	920.bb (of order $22$, degree $10$, 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:	$7.34623698596$
Analytic rank:	$0$
Dimension:	$480$
Relative dimension:	$48$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			11.5
Character	$\chi$	$=$	920.11
Dual form			920.2.bb.a.251.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.34604 + 0.433784i) q^{2} +(-0.132869 + 0.924126i) q^{3} +(1.62366 - 1.16778i) q^{4} +(-0.959493 + 0.281733i) q^{5} +(-0.222024 - 1.30155i) q^{6} +(2.80604 + 3.23834i) q^{7} +(-1.67895 + 2.27621i) q^{8} +(2.04212 + 0.599622i) q^{9} +(1.16931 - 0.795437i) q^{10} +(-3.09409 + 4.81450i) q^{11} +(0.863445 + 1.65563i) q^{12} +(2.73900 + 2.37336i) q^{13} +(-5.18179 - 3.14173i) q^{14} +(-0.132869 - 0.924126i) q^{15} +(1.27256 - 3.79217i) q^{16} +(4.43451 - 2.02517i) q^{17} +(-3.00889 + 0.0787244i) q^{18} +(-3.44622 - 1.57383i) q^{19} +(-1.22889 + 1.57792i) q^{20} +(-3.36547 + 2.16286i) q^{21} +(2.07633 - 7.82269i) q^{22} +(-1.78810 - 4.45002i) q^{23} +(-1.88042 - 1.85400i) q^{24} +(0.841254 - 0.540641i) q^{25} +(-4.71633 - 2.00650i) q^{26} +(-1.98899 + 4.35529i) q^{27} +(8.33774 + 1.98113i) q^{28} +(2.94715 - 1.34592i) q^{29} +(0.579719 + 1.18628i) q^{30} +(4.96005 - 0.713147i) q^{31} +(-0.0679368 + 5.65645i) q^{32} +(-4.03810 - 3.49903i) q^{33} +(-5.09055 + 4.64958i) q^{34} +(-3.60472 - 2.31661i) q^{35} +(4.01595 - 1.41118i) q^{36} +(6.20384 + 1.82161i) q^{37} +(5.32146 + 0.623535i) q^{38} +(-2.55721 + 2.21583i) q^{39} +(0.969663 - 2.65702i) q^{40} +(-11.1848 + 3.28416i) q^{41} +(3.59186 - 4.37119i) q^{42} +(-4.00647 - 0.576043i) q^{43} +(0.598535 + 11.4304i) q^{44} -2.12834 q^{45} +(4.33721 + 5.21427i) q^{46} -2.40525i q^{47} +(3.33536 + 1.67987i) q^{48} +(-1.61679 + 11.2451i) q^{49} +(-0.897842 + 1.09265i) q^{50} +(1.28230 + 4.36713i) q^{51} +(7.21878 + 0.654971i) q^{52} +(6.44475 + 7.43764i) q^{53} +(0.788015 - 6.72520i) q^{54} +(1.61236 - 5.49118i) q^{55} +(-12.0823 + 0.950098i) q^{56} +(1.91232 - 2.97563i) q^{57} +(-3.38315 + 3.09009i) q^{58} +(-3.78950 + 4.37331i) q^{59} +(-1.29492 - 1.34531i) q^{60} +(-0.158817 - 1.10460i) q^{61} +(-6.36708 + 3.11152i) q^{62} +(3.78850 + 8.29565i) q^{63} +(-2.36223 - 7.64329i) q^{64} +(-3.29670 - 1.50555i) q^{65} +(6.95328 + 2.95818i) q^{66} +(-4.57690 - 7.12180i) q^{67} +(4.83518 - 8.46674i) q^{68} +(4.34997 - 1.06116i) q^{69} +(5.85702 + 1.55459i) q^{70} +(-1.73600 - 2.70127i) q^{71} +(-4.79349 + 3.64156i) q^{72} +(5.43154 - 11.8934i) q^{73} +(-9.14083 + 0.239160i) q^{74} +(0.387844 + 0.849259i) q^{75} +(-7.43339 + 1.46906i) q^{76} +(-24.2731 + 3.48995i) q^{77} +(2.48092 - 4.09189i) q^{78} +(-10.6141 + 12.2494i) q^{79} +(-0.152634 + 3.99709i) q^{80} +(1.61085 + 1.03523i) q^{81} +(13.6306 - 9.27242i) q^{82} +(1.16726 - 3.97533i) q^{83} +(-2.93864 + 7.44189i) q^{84} +(-3.68432 + 3.19248i) q^{85} +(5.64276 - 0.962564i) q^{86} +(0.852212 + 2.90237i) q^{87} +(-5.76396 - 15.1261i) q^{88} +(-4.72278 - 0.679033i) q^{89} +(2.86483 - 0.923238i) q^{90} +15.5295i q^{91} +(-8.09994 - 5.13722i) q^{92} +4.67847i q^{93} +(1.04336 + 3.23757i) q^{94} +(3.75002 + 0.539172i) q^{95} +(-5.21824 - 0.814350i) q^{96} +(4.85957 + 16.5502i) q^{97} +(-2.70165 - 15.8377i) q^{98} +(-9.20539 + 7.97652i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 480 q + 2 q^{2} - 4 q^{4} - 48 q^{5} + 5 q^{6} - q^{8} - 48 q^{9} + 2 q^{10} + 3 q^{12} + 32 q^{16} + 7 q^{18} - 4 q^{20} + 8 q^{21} + 4 q^{23} + 2 q^{24} - 48 q^{25} + 7 q^{26} + 12 q^{27} + 5 q^{30}+ \cdots - 98 q^{98}+O(q^{100}) $ 480 * q + 2 * q^2 - 4 * q^4 - 48 * q^5 + 5 * q^6 - q^8 - 48 * q^9 + 2 * q^10 + 3 * q^12 + 32 * q^16 + 7 * q^18 - 4 * q^20 + 8 * q^21 + 4 * q^23 + 2 * q^24 - 48 * q^25 + 7 * q^26 + 12 * q^27 + 5 * q^30 - 118 * q^32 - 23 * q^34 + 54 * q^36 + 8 * q^37 - 65 * q^38 + 43 * q^40 - 10 * q^42 - q^44 + 480 * q^45 - 184 * q^46 - 44 * q^48 - 48 * q^49 - 9 * q^50 - 7 * q^52 + 32 * q^53 - 27 * q^54 + 67 * q^56 - 40 * q^58 - 12 * q^59 + 14 * q^60 - 8 * q^61 - 128 * q^62 + 59 * q^64 + 88 * q^66 + 10 * q^68 - 20 * q^69 + 3 * q^72 - 11 * q^74 + 110 * q^76 + 118 * q^78 - 144 * q^79 - q^80 - 56 * q^81 - 59 * q^82 - 162 * q^84 - 18 * q^86 - 76 * q^88 + 7 * q^90 - 149 * q^92 + 168 * q^94 + 65 * q^96 - 98 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/920\mathbb{Z}\right)^\times$.

$n$	$231$	$281$	$461$	$737$
$\chi(n)$	$-1$	$e\left(\frac{9}{22}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.34604	+	0.433784i	−0.951796	+	0.306732i
$2$	−1.34604	+	0.433784i	−0.951796	+	0.306732i
$3$	−0.132869	+	0.924126i	−0.0767121	+	0.533545i	0.914838	+	0.403821i	$0.132318\pi$
$3$	−0.132869	+	0.924126i	−0.0767121	+	0.533545i	−0.991550	+	0.129724i	$0.958591\pi$
$4$	1.62366	−	1.16778i	0.811831	−	0.583892i
$5$	−0.959493	+	0.281733i	−0.429098	+	0.125995i
$5$	−0.959493	+	0.281733i	−0.429098	+	0.125995i
$6$	−0.222024	−	1.30155i	−0.0906407	−	0.531356i
$7$	2.80604	+	3.23834i	1.06058	+	1.22398i	0.973718	+	0.227757i	$0.0731392\pi$
$7$	2.80604	+	3.23834i	1.06058	+	1.22398i	0.0868645	+	0.996220i	$0.472315\pi$
$8$	−1.67895	+	2.27621i	−0.593600	+	0.804760i
$9$	2.04212	+	0.599622i	0.680708	+	0.199874i
$10$	1.16931	−	0.795437i	0.369768	−	0.251539i
$11$	−3.09409	+	4.81450i	−0.932904	+	1.45163i	−0.0411251	+	0.999154i	$0.513094\pi$
$11$	−3.09409	+	4.81450i	−0.932904	+	1.45163i	−0.891778	+	0.452472i	$0.850542\pi$
$12$	0.863445	+	1.65563i	0.249255	+	0.477940i
$13$	2.73900	+	2.37336i	0.759662	+	0.658250i	0.945975	−	0.324240i	$-0.105109\pi$
$13$	2.73900	+	2.37336i	0.759662	+	0.658250i	−0.186313	+	0.982490i	$0.559654\pi$
$14$	−5.18179	−	3.14173i	−1.38489	−	0.839663i
$15$	−0.132869	−	0.924126i	−0.0343067	−	0.238608i
$16$	1.27256	−	3.79217i	0.318140	−	0.948044i
$17$	4.43451	−	2.02517i	1.07553	−	0.491176i	0.202716	−	0.979238i	$-0.435023\pi$
$17$	4.43451	−	2.02517i	1.07553	−	0.491176i	0.872809	+	0.488061i	$0.162296\pi$
$18$	−3.00889	+	0.0787244i	−0.709203	+	0.0185555i
$19$	−3.44622	−	1.57383i	−0.790616	−	0.361062i	−0.0211717	−	0.999776i	$-0.506740\pi$
$19$	−3.44622	−	1.57383i	−0.790616	−	0.361062i	−0.769445	+	0.638713i	$0.779467\pi$
$20$	−1.22889	+	1.57792i	−0.274788	+	0.352833i
$21$	−3.36547	+	2.16286i	−0.734406	+	0.471974i
$22$	2.07633	−	7.82269i	0.442674	−	1.66780i
$23$	−1.78810	−	4.45002i	−0.372845	−	0.927894i
$23$	−1.78810	−	4.45002i	−0.372845	−	0.927894i
$24$	−1.88042	−	1.85400i	−0.383839	−	0.378447i
$25$	0.841254	−	0.540641i	0.168251	−	0.108128i
$26$	−4.71633	−	2.00650i	−0.924949	−	0.393508i
$27$	−1.98899	+	4.35529i	−0.382782	+	0.838175i
$28$	8.33774	+	1.98113i	1.57568	+	0.374398i
$29$	2.94715	−	1.34592i	0.547271	−	0.249930i	−0.122538	−	0.992464i	$-0.539103\pi$
$29$	2.94715	−	1.34592i	0.547271	−	0.249930i	0.669809	+	0.742533i	$0.266376\pi$
$30$	0.579719	+	1.18628i	0.105842	+	0.216584i
$31$	4.96005	−	0.713147i	0.890851	−	0.128085i	0.318334	−	0.947978i	$-0.396876\pi$
$31$	4.96005	−	0.713147i	0.890851	−	0.128085i	0.572516	+	0.819893i	$0.305967\pi$
$32$	−0.0679368	+	5.65645i	−0.0120096	+	0.999928i
$33$	−4.03810	−	3.49903i	−0.702942	−	0.609103i
$34$	−5.09055	+	4.64958i	−0.873022	+	0.797397i
$35$	−3.60472	−	2.31661i	−0.609309	−	0.391579i
$36$	4.01595	−	1.41118i	0.669325	−	0.235196i
$37$	6.20384	+	1.82161i	1.01991	+	0.299471i	0.748600	−	0.663022i	$-0.230726\pi$
$37$	6.20384	+	1.82161i	1.01991	+	0.299471i	0.271306	+	0.962493i	$0.412545\pi$
$38$	5.32146	+	0.623535i	0.863255	+	0.101151i
$39$	−2.55721	+	2.21583i	−0.409481	+	0.354818i
$40$	0.969663	−	2.65702i	0.153317	−	0.420112i
$41$	−11.1848	+	3.28416i	−1.74678	+	0.512900i	−0.990036	−	0.140817i	$-0.955027\pi$
$41$	−11.1848	+	3.28416i	−1.74678	+	0.512900i	−0.756740	+	0.653716i	$0.773209\pi$
$42$	3.59186	−	4.37119i	0.554235	−	0.674489i
$43$	−4.00647	−	0.576043i	−0.610981	−	0.0878458i	−0.170123	−	0.985423i	$-0.554417\pi$
$43$	−4.00647	−	0.576043i	−0.610981	−	0.0878458i	−0.440858	+	0.897577i	$0.645326\pi$
$44$	0.598535	+	11.4304i	0.0902326	+	1.72319i
$45$	−2.12834			−0.317274
$46$	4.33721	+	5.21427i	0.639487	+	0.768802i
$47$		−	2.40525i		−	0.350842i	−0.984494	−	0.175421i	$-0.943871\pi$
$47$		−	2.40525i		−	0.350842i	0.984494	−	0.175421i	$-0.0561286\pi$
$48$	3.33536	+	1.67987i	0.481418	+	0.242469i
$49$	−1.61679	+	11.2451i	−0.230971	+	1.60644i
$50$	−0.897842	+	1.09265i	−0.126974	+	0.154524i
$51$	1.28230	+	4.36713i	0.179558	+	0.611520i
$52$	7.21878	+	0.654971i	1.00106	+	0.0908281i
$53$	6.44475	+	7.43764i	0.885255	+	1.02164i	0.999602	+	0.0281979i	$0.00897686\pi$
$53$	6.44475	+	7.43764i	0.885255	+	1.02164i	−0.114347	+	0.993441i	$0.536478\pi$
$54$	0.788015	−	6.72520i	0.107235	−	0.915183i
$55$	1.61236	−	5.49118i	0.217410	−	0.740431i
$56$	−12.0823	+	0.950098i	−1.61457	+	0.126962i
$57$	1.91232	−	2.97563i	0.253293	−	0.394131i
$58$	−3.38315	+	3.09009i	−0.444229	+	0.405748i
$59$	−3.78950	+	4.37331i	−0.493350	+	0.569357i	−0.946758	−	0.321947i	$-0.895663\pi$
$59$	−3.78950	+	4.37331i	−0.493350	+	0.569357i	0.453408	+	0.891303i	$0.350208\pi$
$60$	−1.29492	−	1.34531i	−0.167173	−	0.173678i
$61$	−0.158817	−	1.10460i	−0.0203345	−	0.141429i	0.977125	−	0.212666i	$-0.0682146\pi$
$61$	−0.158817	−	1.10460i	−0.0203345	−	0.141429i	−0.997459	+	0.0712365i	$0.977306\pi$
$62$	−6.36708	+	3.11152i	−0.808620	+	0.395163i
$63$	3.78850	+	8.29565i	0.477306	+	1.04515i
$64$	−2.36223	−	7.64329i	−0.295279	−	0.955411i
$65$	−3.29670	−	1.50555i	−0.408905	−	0.186741i
$66$	6.95328	+	2.95818i	0.855889	+	0.364127i
$67$	−4.57690	−	7.12180i	−0.559158	−	0.870066i	0.440458	−	0.897773i	$-0.354816\pi$
$67$	−4.57690	−	7.12180i	−0.559158	−	0.870066i	−0.999616	+	0.0277067i	$0.991180\pi$
$68$	4.83518	−	8.46674i	0.586352	−	1.02674i
$69$	4.34997	−	1.06116i	0.523674	−	0.127749i
$70$	5.85702	+	1.55459i	0.700047	+	0.185809i
$71$	−1.73600	−	2.70127i	−0.206026	−	0.320582i	0.722829	−	0.691027i	$-0.242842\pi$
$71$	−1.73600	−	2.70127i	−0.206026	−	0.320582i	−0.928854	+	0.370445i	$0.879205\pi$
$72$	−4.79349	+	3.64156i	−0.564919	+	0.429162i
$73$	5.43154	−	11.8934i	0.635714	−	1.39202i	−0.267805	−	0.963473i	$-0.586298\pi$
$73$	5.43154	−	11.8934i	0.635714	−	1.39202i	0.903520	−	0.428547i	$-0.140974\pi$
$74$	−9.14083	+	0.239160i	−1.06260	+	0.0278018i
$75$	0.387844	+	0.849259i	0.0447843	+	0.0980640i
$76$	−7.43339	+	1.46906i	−0.852669	+	0.168513i
$77$	−24.2731	+	3.48995i	−2.76618	+	0.397716i
$78$	2.48092	−	4.09189i	0.280909	−	0.463315i
$79$	−10.6141	+	12.2494i	−1.19418	+	1.37816i	−0.286730	+	0.958011i	$0.592568\pi$
$79$	−10.6141	+	12.2494i	−1.19418	+	1.37816i	−0.907454	+	0.420151i	$0.861977\pi$
$80$	−0.152634	+	3.99709i	−0.0170650	+	0.446888i
$81$	1.61085	+	1.03523i	0.178983	+	0.115026i
$82$	13.6306	−	9.27242i	1.50525	−	1.02397i
$83$	1.16726	−	3.97533i	0.128124	−	0.436349i	−0.870297	−	0.492527i	$-0.836073\pi$
$83$	1.16726	−	3.97533i	0.128124	−	0.436349i	0.998421	+	0.0561782i	$0.0178915\pi$
$84$	−2.93864	+	7.44189i	−0.320632	+	0.811977i
$85$	−3.68432	+	3.19248i	−0.399621	+	0.346273i
$86$	5.64276	−	0.962564i	0.608474	−	0.103796i
$87$	0.852212	+	2.90237i	0.0913667	+	0.311166i
$88$	−5.76396	−	15.1261i	−0.614440	−	1.61245i
$89$	−4.72278	−	0.679033i	−0.500613	−	0.0719773i	−0.112617	−	0.993638i	$-0.535923\pi$
$89$	−4.72278	−	0.679033i	−0.500613	−	0.0719773i	−0.387996	+	0.921661i	$0.626833\pi$
$90$	2.86483	−	0.923238i	0.301980	−	0.0973179i
$91$			15.5295i			1.62794i
$92$	−8.09994	−	5.13722i	−0.844477	−	0.535592i
$93$			4.67847i			0.485134i
$94$	1.04336	+	3.23757i	0.107614	+	0.333930i
$95$	3.75002	+	0.539172i	0.384744	+	0.0553178i
$96$	−5.21824	−	0.814350i	−0.532585	−	0.0831143i
$97$	4.85957	+	16.5502i	0.493414	+	1.68042i	0.710041	+	0.704161i	$0.248677\pi$
$97$	4.85957	+	16.5502i	0.493414	+	1.68042i	−0.216626	+	0.976255i	$0.569505\pi$
$98$	−2.70165	−	15.8377i	−0.272908	−	1.59985i
$99$	−9.20539	+	7.97652i	−0.925177	+	0.801670i
$100$	0.734560	−	1.86022i	0.0734560	−	0.186022i
$101$	2.42942	−	8.27384i	0.241736	−	0.823278i	−0.745838	−	0.666127i	$-0.767951\pi$
$101$	2.42942	−	8.27384i	0.241736	−	0.823278i	0.987575	−	0.157151i	$-0.0502309\pi$
$102$	−3.62043	−	5.32210i	−0.358476	−	0.526966i
$103$	8.11325	+	5.21407i	0.799422	+	0.513757i	0.875427	−	0.483350i	$-0.160580\pi$
$103$	8.11325	+	5.21407i	0.799422	+	0.513757i	−0.0760053	+	0.997107i	$0.524217\pi$
$104$	−10.0009	+	2.24977i	−0.980669	+	0.220608i
$105$	2.61980	−	3.02341i	0.255666	−	0.295055i
$106$	−11.9012	−	7.21575i	−1.15595	−	0.700856i
$107$	−2.85204	+	0.410061i	−0.275717	+	0.0396421i	−0.278786	−	0.960353i	$-0.589932\pi$
$107$	−2.85204	+	0.410061i	−0.275717	+	0.0396421i	0.00306938	+	0.999995i	$0.499023\pi$
$108$	1.85658	+	9.39423i	0.178650	+	0.903960i
$109$	−6.38214	−	13.9749i	−0.611298	−	1.33856i	−0.921682	−	0.387945i	$-0.873185\pi$
$109$	−6.38214	−	13.9749i	−0.611298	−	1.33856i	0.310384	−	0.950611i	$-0.399542\pi$
$110$	0.211687	+	8.09079i	0.0201835	+	0.771426i
$111$	−2.50770	+	5.49110i	−0.238020	+	0.521192i
$112$	15.8512	−	6.52000i	1.49780	−	0.616082i
$113$	−8.56545	−	13.3281i	−0.805769	−	1.25380i	−0.963869	−	0.266378i	$-0.914173\pi$
$113$	−8.56545	−	13.3281i	−0.805769	−	1.25380i	0.158099	−	0.987423i	$-0.449463\pi$
$114$	−1.28328	+	4.83485i	−0.120191	+	0.452826i
$115$	2.96939	+	3.76600i	0.276897	+	0.351181i
$116$	3.21343	−	5.62695i	0.298360	−	0.522449i
$117$	4.17026	+	6.48905i	0.385540	+	0.599913i
$118$	3.20375	−	7.53049i	0.294929	−	0.693237i
$119$	19.0016	+	8.67773i	1.74187	+	0.795486i
$120$	2.32658	+	1.24913i	0.212387	+	0.114029i
$121$	−9.03644	−	19.7871i	−0.821495	−	1.79882i
$122$	0.692933	+	1.41795i	0.0627352	+	0.128375i
$123$	−1.54886	−	10.7726i	−0.139656	−	0.971328i
$124$	7.22064	−	6.95017i	0.648433	−	0.624144i
$125$	−0.654861	+	0.755750i	−0.0585725	+	0.0675963i
$126$	−8.69800	−	9.52291i	−0.774879	−	0.848368i
$127$	−3.04168	+	4.73295i	−0.269906	+	0.419982i	−0.949576	−	0.313536i	$-0.898486\pi$
$127$	−3.04168	+	4.73295i	−0.269906	+	0.419982i	0.679670	+	0.733518i	$0.262123\pi$
$128$	6.49520	+	9.26350i	0.574100	+	0.818785i
$129$	1.06467	−	3.62595i	0.0937393	−	0.319247i
$130$	5.09059	+	0.596482i	0.446474	+	0.0523150i
$131$	7.97252	+	9.20077i	0.696562	+	0.803875i	0.988284	−	0.152628i	$-0.0487736\pi$
$131$	7.97252	+	9.20077i	0.696562	+	0.803875i	−0.291722	+	0.956503i	$0.594228\pi$
$132$	−10.6426	−	0.965621i	−0.926321	−	0.0840465i
$133$	−4.57360	−	15.5763i	−0.396582	−	1.35063i
$134$	9.25003	+	7.60086i	0.799081	+	0.656614i
$135$	0.681399	−	4.73923i	0.0586454	−	0.407888i
$136$	−2.83562	+	13.4940i	−0.243153	+	1.15710i
$137$			16.2119i			1.38507i	0.721383	+	0.692536i	$0.243507\pi$
$137$			16.2119i			1.38507i	−0.721383	+	0.692536i	$0.756493\pi$
$138$	−5.39493	+	3.31531i	−0.459247	+	0.282218i
$139$	2.31473			0.196333			0.0981666	−	0.995170i	$-0.468702\pi$
$139$	2.31473			0.196333			0.0981666	+	0.995170i	$0.468702\pi$
$140$	−8.55815	+	0.448136i	−0.723296	+	0.0378744i
$141$	2.22275	+	0.319584i	0.187190	+	0.0269138i
$142$	3.50850	+	2.88298i	0.294427	+	0.241934i
$143$	−19.9012	+	5.84353i	−1.66422	+	0.488660i
$144$	4.87260	−	6.98103i	0.406050	−	0.581753i
$145$	−2.44858	+	2.12170i	−0.203343	+	0.176198i
$146$	−2.15191	+	18.3652i	−0.178094	+	1.51991i
$147$	−10.1770	−	2.98825i	−0.839387	−	0.246466i
$148$	12.2002	−	4.28706i	1.00285	−	0.352395i
$149$	9.50594	+	6.10910i	0.778757	+	0.500477i	0.868621	−	0.495477i	$-0.165007\pi$
$149$	9.50594	+	6.10910i	0.778757	+	0.500477i	−0.0898639	+	0.995954i	$0.528643\pi$
$150$	−0.890449	−	0.974899i	−0.0727049	−	0.0796002i
$151$	9.47664	+	8.21155i	0.771198	+	0.668247i	0.948808	−	0.315854i	$-0.102291\pi$
$151$	9.47664	+	8.21155i	0.771198	+	0.668247i	−0.177610	+	0.984101i	$0.556836\pi$
$152$	9.36841	−	5.20191i	0.759878	−	0.421930i
$153$	10.2701	−	1.47662i	0.830292	−	0.119378i
$154$	31.1588	−	15.2269i	2.51085	−	1.22702i
$155$	−4.55821	+	2.08167i	−0.366124	+	0.167203i
$156$	−1.56443	+	6.58404i	−0.125255	+	0.527145i
$157$	−5.31461	+	11.6374i	−0.424152	+	0.928763i	0.570088	+	0.821584i	$0.306909\pi$
$157$	−5.31461	+	11.6374i	−0.424152	+	0.928763i	−0.994240	+	0.107179i	$0.965818\pi$
$158$	8.97351	−	21.0924i	0.713894	−	1.67802i
$159$	−7.72963	+	4.96753i	−0.613000	+	0.393951i
$160$	−1.52842	−	5.44646i	−0.120832	−	0.430581i
$161$	9.39320	−	18.2774i	0.740288	−	1.44046i
$162$	−2.61734	−	0.694704i	−0.205638	−	0.0545811i
$163$	−15.0884	+	9.69670i	−1.18181	+	0.759504i	−0.975719	−	0.219028i	$-0.929711\pi$
$163$	−15.0884	+	9.69670i	−1.18181	+	0.759504i	−0.206093	+	0.978532i	$0.566075\pi$
$164$	−14.3252	+	18.3938i	−1.11861	+	1.43632i
$165$	4.86032	+	2.21963i	0.378375	+	0.172798i
$166$	0.153250	+	5.85730i	0.0118945	+	0.454614i
$167$	−1.83730	+	0.839067i	−0.142175	+	0.0649290i	−0.485232	−	0.874386i	$-0.661265\pi$
$167$	−1.83730	+	0.839067i	−0.142175	+	0.0649290i	0.343057	+	0.939314i	$0.388538\pi$
$168$	0.727361	−	11.2918i	0.0561171	−	0.871185i
$169$	0.0192026	+	0.133557i	0.00147712	+	0.0102736i
$170$	3.57440	−	5.89542i	0.274144	−	0.452158i
$171$	−6.09390	−	5.28039i	−0.466012	−	0.403802i
$172$	−7.17785	+	3.74339i	−0.547306	+	0.285431i
$173$	9.62607	−	14.9785i	0.731856	−	1.13879i	−0.253343	−	0.967377i	$-0.581530\pi$
$173$	9.62607	−	14.9785i	0.731856	−	1.13879i	0.985199	−	0.171414i	$-0.0548335\pi$
$174$	−2.40611	−	3.53703i	−0.182407	−	0.268142i
$175$	4.11137	+	1.20721i	0.310790	+	0.0912562i
$176$	14.3200	+	17.8601i	1.07941	+	1.34625i
$177$	−3.53798	−	4.08305i	−0.265931	−	0.306901i
$178$	6.65161	−	1.13466i	0.498559	−	0.0850462i
$179$	1.96088	−	0.575766i	0.146563	−	0.0430347i	−0.207628	−	0.978208i	$-0.566574\pi$
$179$	1.96088	−	0.575766i	0.146563	−	0.0430347i	0.354191	+	0.935173i	$0.384756\pi$
$180$	−3.45570	+	2.48544i	−0.257573	+	0.185254i
$181$	1.90679	−	13.2620i	0.141730	−	0.985756i	−0.787516	−	0.616295i	$-0.788633\pi$
$181$	1.90679	−	13.2620i	0.141730	−	0.985756i	0.929246	−	0.369462i	$-0.120458\pi$
$182$	−6.73646	−	20.9034i	−0.499340	−	1.54946i
$183$	1.04189			0.0770188
$184$	13.1313	+	3.40129i	0.968053	+	0.250747i
$185$	−6.46575			−0.475372
$186$	−2.02944	−	6.29741i	−0.148806	−	0.461749i
$187$	−3.97058	+	27.6160i	−0.290358	+	2.01948i
$188$	−2.80881	−	3.90531i	−0.204854	−	0.284824i
$189$	−19.6851	+	5.78006i	−1.43188	+	0.420438i
$190$	−5.28157	+	0.900952i	−0.383166	+	0.0653619i
$191$	0.193373	+	0.223164i	0.0139920	+	0.0161476i	0.762702	−	0.646750i	$-0.223872\pi$
$191$	0.193373	+	0.223164i	0.0139920	+	0.0161476i	−0.748710	+	0.662897i	$0.769327\pi$
$192$	7.37723	−	1.16744i	0.532406	−	0.0842528i
$193$	12.0991	+	3.55263i	0.870915	+	0.255724i	0.686505	−	0.727125i	$-0.259144\pi$
$193$	12.0991	+	3.55263i	0.870915	+	0.255724i	0.184411	+	0.982849i	$0.440962\pi$
$194$	−13.7204	−	20.1692i	−0.985067	−	1.44807i
$195$	1.82935	−	2.84653i	0.131003	−	0.203844i
$196$	10.5067	+	20.1462i	0.750476	+	1.43902i
$197$	−3.72221	−	3.22531i	−0.265197	−	0.229794i	0.512104	−	0.858923i	$-0.328866\pi$
$197$	−3.72221	−	3.22531i	−0.265197	−	0.229794i	−0.777301	+	0.629129i	$0.783412\pi$
$198$	8.93077	−	14.7299i	0.634682	−	1.04681i
$199$	−1.00240	−	6.97185i	−0.0710583	−	0.494222i	−0.994009	−	0.109302i	$-0.965138\pi$
$199$	−1.00240	−	6.97185i	−0.0710583	−	0.494222i	0.922950	−	0.384919i	$-0.125771\pi$
$200$	−0.181815	+	2.82258i	−0.0128563	+	0.199586i
$201$	7.18957	−	3.28337i	0.507113	−	0.231591i
$202$	0.318959	+	12.1908i	0.0224419	+	0.857741i
$203$	12.6283	+	5.76717i	0.886336	+	0.404776i
$204$	7.18189	+	5.59329i	0.502833	+	0.391608i
$205$	9.80650	−	6.30226i	0.684916	−	0.440169i
$206$	−13.1826	−	3.49896i	−0.918472	−	0.243784i
$207$	−0.983195	−	10.1597i	−0.0683368	−	0.706146i
$208$	12.4857	−	7.36652i	0.865729	−	0.510776i
$209$	18.2401	−	11.7222i	1.26170	−	0.810843i
$210$	−2.21485	+	5.20607i	−0.152840	+	0.359253i
$211$	10.6506	−	23.3216i	0.733219	−	1.60553i	−0.0611770	−	0.998127i	$-0.519485\pi$
$211$	10.6506	−	23.3216i	0.733219	−	1.60553i	0.794396	−	0.607400i	$-0.207787\pi$
$212$	19.1497	+	4.55014i	1.31520	+	0.312505i
$213$	2.72698	−	1.24537i	0.186850	−	0.0853314i
$214$	3.66109	−	1.78913i	0.250267	−	0.122302i
$215$	4.00647	−	0.576043i	0.273239	−	0.0392858i
$216$	−6.57410	−	11.8397i	−0.447311	−	0.805588i
$217$	16.2275	+	14.0612i	1.10159	+	0.954536i
$218$	14.6527	+	16.0424i	0.992409	+	1.08653i
$219$	10.2693	+	6.59970i	0.693938	+	0.445967i
$220$	−3.79459	−	10.7987i	−0.255831	−	0.728049i
$221$	16.9526	+	4.97772i	1.14035	+	0.334838i
$222$	0.993522	−	8.47906i	0.0666808	−	0.569077i
$223$	19.5781	−	16.9645i	1.31105	−	1.13603i	0.329637	−	0.944108i	$-0.393074\pi$
$223$	19.5781	−	16.9645i	1.31105	−	1.13603i	0.981410	−	0.191921i	$-0.0614718\pi$
$224$	−18.5081	+	15.6522i	−1.23663	+	1.04581i
$225$	2.04212	−	0.599622i	0.136142	−	0.0399748i
$226$	17.3110	+	14.2246i	1.15151	+	0.946208i
$227$	16.4327	+	2.36267i	1.09068	+	0.156816i	0.664106	−	0.747638i	$-0.268812\pi$
$227$	16.4327	+	2.36267i	1.09068	+	0.156816i	0.426571	+	0.904454i	$0.359721\pi$
$228$	−0.369928	−	7.06459i	−0.0244991	−	0.467864i
$229$	−16.4326			−1.08590			−0.542949	−	0.839765i	$-0.682692\pi$
$229$	−16.4326			−1.08590			−0.542949	+	0.839765i	$0.682692\pi$
$230$	−5.63055	−	3.78112i	−0.371268	−	0.249320i
$231$		−	22.8951i		−	1.50639i
$232$	−1.88454	+	8.96805i	−0.123726	+	0.588781i
$233$	1.77275	−	12.3297i	0.116137	−	0.807748i	−0.845609	−	0.533803i	$-0.820762\pi$
$233$	1.77275	−	12.3297i	0.116137	−	0.807748i	0.961745	−	0.273945i	$-0.0883286\pi$
$234$	−8.42819	−	6.92555i	−0.550968	−	0.452737i
$235$	0.677637	+	2.30782i	0.0442041	+	0.150546i
$236$	−1.04578	+	11.5261i	−0.0680745	+	0.750285i
$237$	−9.90968	−	11.4364i	−0.643703	−	0.742873i
$238$	−29.3412	−	3.43801i	−1.90191	−	0.222853i
$239$	2.04211	−	6.95479i	0.132093	−	0.449868i	−0.866708	−	0.498815i	$-0.833769\pi$
$239$	2.04211	−	6.95479i	0.132093	−	0.449868i	0.998801	+	0.0489476i	$0.0155867\pi$
$240$	−3.67353	−	0.672144i	−0.237126	−	0.0433867i
$241$	−6.73777	+	10.4842i	−0.434018	+	0.675345i	−0.987518	−	0.157504i	$-0.949655\pi$
$241$	−6.73777	+	10.4842i	−0.434018	+	0.675345i	0.553501	+	0.832849i	$0.313292\pi$
$242$	20.7467	+	22.7144i	1.33365	+	1.46013i
$243$	−10.5771	+	12.2066i	−0.678519	+	0.783053i
$244$	−1.54780	−	1.60803i	−0.0990877	−	0.102944i
$245$	−1.61679	−	11.2451i	−0.103293	−	0.718420i
$246$	6.75779	+	13.8284i	0.430861	+	0.881669i
$247$	−5.70391	−	12.4898i	−0.362931	−	0.794709i
$248$	−6.70442	+	12.4874i	−0.425731	+	0.792953i
$249$	3.51861	+	1.60690i	0.222983	+	0.101833i
$250$	0.553638	−	1.30134i	0.0350152	−	0.0823039i
$251$	2.51914	+	3.91986i	0.159007	+	0.247419i	0.911611	−	0.411053i	$-0.134839\pi$
$251$	2.51914	+	3.91986i	0.159007	+	0.247419i	−0.752604	+	0.658473i	$0.771203\pi$
$252$	15.8388	+	9.04519i	0.997749	+	0.569794i
$253$	26.9572	+	5.15996i	1.69478	+	0.324404i
$254$	2.04116	−	7.69019i	0.128074	−	0.482526i
$255$	−2.46072	−	3.82896i	−0.154096	−	0.239779i
$256$	−12.7612	−	9.65155i	−0.797574	−	0.603222i
$257$	8.32680	−	18.2331i	0.519411	−	1.13735i	−0.450251	−	0.892902i	$-0.648665\pi$
$257$	8.32680	−	18.2331i	0.519411	−	1.13735i	0.969662	−	0.244450i	$-0.0786074\pi$
$258$	0.139781	+	5.34252i	0.00870239	+	0.332611i
$259$	11.5092	+	25.2017i	0.715148	+	1.56596i
$260$	−7.11089	+	1.40532i	−0.440999	+	0.0871545i
$261$	6.82548	−	0.981356i	0.422486	−	0.0607444i
$262$	−14.7225	−	8.92629i	−0.909559	−	0.551468i
$263$	13.5564	−	15.6449i	0.835924	−	0.964708i	−0.163839	−	0.986487i	$-0.552388\pi$
$263$	13.5564	−	15.6449i	0.835924	−	0.964708i	0.999763	+	0.0217794i	$0.00693314\pi$
$264$	14.7443	−	3.31683i	0.907448	−	0.204137i
$265$	−8.27912	−	5.32067i	−0.508582	−	0.326846i
$266$	12.9130	+	18.9824i	0.791747	+	1.16388i
$267$	1.25502	−	4.27422i	0.0768062	−	0.261578i
$268$	−15.7481	−	6.21857i	−0.961966	−	0.379859i
$269$	−3.24380	+	2.81077i	−0.197778	+	0.171375i	−0.748119	−	0.663564i	$-0.769043\pi$
$269$	−3.24380	+	2.81077i	−0.197778	+	0.171375i	0.550342	+	0.834940i	$0.314498\pi$
$270$	1.13861	+	6.67479i	0.0692937	+	0.406215i
$271$	−2.02643	−	6.90137i	−0.123097	−	0.419228i	0.874768	−	0.484542i	$-0.161014\pi$
$271$	−2.02643	−	6.90137i	−0.123097	−	0.419228i	−0.997865	+	0.0653131i	$0.979195\pi$
$272$	−2.03662	−	19.3936i	−0.123488	−	1.17591i
$273$	−14.3513	−	2.06340i	−0.868577	−	0.124883i
$274$	−7.03245	−	21.8219i	−0.424846	−	1.31831i
$275$			5.72301i			0.345110i
$276$	5.82367	−	6.80279i	0.350544	−	0.409480i
$277$			13.5573i			0.814579i	0.913299	+	0.407289i	$0.133526\pi$
$277$			13.5573i			0.814579i	−0.913299	+	0.407289i	$0.866474\pi$
$278$	−3.11573	+	1.00409i	−0.186869	+	0.0602216i
$279$	10.5566	+	1.51782i	0.632010	+	0.0908693i
$280$	11.3252	−	4.31560i	0.676813	−	0.257906i
$281$	−1.47359	−	5.01860i	−0.0879073	−	0.299385i	0.903791	−	0.427975i	$-0.140773\pi$
$281$	−1.47359	−	5.01860i	−0.0879073	−	0.299385i	−0.991698	+	0.128590i	$0.958955\pi$
$282$	−3.13055	+	0.534022i	−0.186422	+	0.0318005i
$283$	21.0345	−	18.2265i	1.25037	−	1.08345i	0.257250	−	0.966345i	$-0.417183\pi$
$283$	21.0345	−	18.2265i	1.25037	−	1.08345i	0.993119	−	0.117107i	$-0.0373620\pi$
$284$	−5.97319	−	2.35868i	−0.354444	−	0.139962i
$285$	−0.996526	+	3.39385i	−0.0590291	+	0.201035i
$286$	24.2531	−	16.4985i	1.43411	−	0.975575i
$287$	−42.0202	−	27.0048i	−2.48038	−	1.59404i
$288$	−3.53046	+	11.5104i	−0.208034	+	0.678258i
$289$	4.43089	−	5.11352i	0.260640	−	0.300795i
$290$	2.37553	−	3.91806i	0.139496	−	0.230076i
$291$	−15.9401	+	2.29185i	−0.934428	+	0.134350i
$292$	−5.06995	−	25.6538i	−0.296697	−	1.50127i
$293$	−4.96007	−	10.8610i	−0.289770	−	0.634508i	0.707629	−	0.706584i	$-0.249765\pi$
$293$	−4.96007	−	10.8610i	−0.289770	−	0.634508i	−0.997399	+	0.0720760i	$0.977038\pi$
$294$	14.9950	−	0.392327i	0.874524	−	0.0228810i
$295$	2.40389	−	5.26378i	0.139960	−	0.306469i
$296$	−14.5623	+	11.0628i	−0.846418	+	0.643014i
$297$	−14.8144	−	23.0517i	−0.859619	−	1.33759i
$298$	−15.4454	−	4.09958i	−0.894730	−	0.237482i
$299$	5.66388	−	16.4324i	0.327550	−	0.950310i
$300$	1.62148	+	0.925993i	0.0936161	+	0.0534622i
$301$	−9.37688	−	14.5907i	−0.540474	−	0.840994i
$302$	−16.3180	−	6.94229i	−0.938996	−	0.399484i
$303$	7.32328	+	3.34443i	0.420711	+	0.192132i
$304$	−10.3538	+	11.0659i	−0.593830	+	0.634670i
$305$	0.463586	+	1.01511i	0.0265448	+	0.0581251i
$306$	−13.1835	+	6.44262i	−0.753652	+	0.368300i
$307$	1.72833	+	12.0208i	0.0986411	+	0.686064i	0.977801	+	0.209537i	$0.0671955\pi$
$307$	1.72833	+	12.0208i	0.0986411	+	0.686064i	−0.879160	+	0.476527i	$0.841895\pi$
$308$	−35.3359	+	34.0123i	−2.01345	+	1.93803i
$309$	−5.89646	+	6.80488i	−0.335438	+	0.387116i
$310$	5.23256	−	4.77929i	0.297189	−	0.271446i
$311$	1.58201	−	2.46165i	0.0897073	−	0.139587i	−0.793500	−	0.608571i	$-0.791743\pi$
$311$	1.58201	−	2.46165i	0.0897073	−	0.139587i	0.883207	+	0.468983i	$0.155380\pi$
$312$	−0.750261	−	9.54102i	−0.0424752	−	0.540154i
$313$	−5.10515	+	17.3866i	−0.288560	+	0.982747i	0.679843	+	0.733358i	$0.262048\pi$
$313$	−5.10515	+	17.3866i	−0.288560	+	0.982747i	−0.968403	+	0.249389i	$0.919770\pi$
$314$	2.10558	−	17.9698i	0.118825	−	1.01409i
$315$	−5.97219	−	6.89228i	−0.336495	−	0.388336i
$316$	−2.92917	+	32.2839i	−0.164778	+	1.81611i
$317$	4.97743	+	16.9516i	0.279561	+	0.952096i	0.972850	+	0.231437i	$0.0743426\pi$
$317$	4.97743	+	16.9516i	0.279561	+	0.952096i	−0.693289	+	0.720659i	$0.743839\pi$
$318$	8.24958	−	10.0395i	0.462613	−	0.562987i
$319$	−2.63882	+	18.3534i	−0.147746	+	1.02759i
$320$	4.41991	+	6.66816i	0.247080	+	0.372762i
$321$		−	2.69013i		−	0.150148i
$322$	−4.71520	+	28.6768i	−0.262768	+	1.59810i
$323$	−18.4696			−1.02767
$324$	3.82441	−	0.200260i	0.212467	−	0.0111256i
$325$	3.58733	+	0.515779i	0.198989	+	0.0286103i
$326$	16.1033	−	19.5973i	0.891879	−	1.08539i
$327$	13.7626	−	4.04106i	0.761074	−	0.223471i
$328$	11.3034	−	30.9729i	0.624124	−	1.71019i
$329$	7.78901	−	6.74922i	0.429422	−	0.372096i
$330$	−7.50504	−	0.879392i	−0.413139	−	0.0484089i
$331$	−3.48216	−	1.02245i	−0.191397	−	0.0561992i	0.184629	−	0.982808i	$-0.440892\pi$
$331$	−3.48216	−	1.02245i	−0.191397	−	0.0561992i	−0.376026	+	0.926609i	$0.622710\pi$
$332$	−2.74708	−	7.81770i	−0.150766	−	0.429052i
$333$	11.5767	+	7.43992i	0.634401	+	0.407705i
$334$	2.10911	−	1.92641i	0.115405	−	0.105409i
$335$	6.39795	+	5.54385i	0.349557	+	0.302893i
$336$	3.91916	+	15.5148i	0.213808	+	0.846403i
$337$	14.5943	−	2.09835i	0.795004	−	0.114304i	0.267167	−	0.963650i	$-0.413912\pi$
$337$	14.5943	−	2.09835i	0.795004	−	0.114304i	0.527837	+	0.849346i	$0.323003\pi$
$338$	−0.0837824	−	0.171444i	−0.00455716	−	0.00932531i
$339$	13.4549	−	6.14466i	0.730771	−	0.333732i
$340$	−2.25396	+	9.48600i	−0.122238	+	0.514451i
$341$	−11.9134	+	26.0867i	−0.645146	+	1.41267i
$342$	10.4932	+	4.46420i	0.567407	+	0.241396i
$343$	−15.7191	+	10.1020i	−0.848749	+	0.545458i
$344$	8.03787	−	8.15240i	0.433373	−	0.439548i
$345$	−3.87480	+	2.24370i	−0.208612	+	0.120797i
$346$	−6.45968	+	24.3373i	−0.347275	+	1.30838i
$347$	1.27793	−	0.821278i	0.0686031	−	0.0440885i	−0.505890	−	0.862598i	$-0.668836\pi$
$347$	1.27793	−	0.821278i	0.0686031	−	0.0440885i	0.574493	+	0.818510i	$0.305199\pi$
$348$	4.77304	+	3.71727i	0.255862	+	0.199266i
$349$	−14.2638	−	6.51405i	−0.763522	−	0.348689i	−0.00470192	−	0.999989i	$-0.501497\pi$
$349$	−14.2638	−	6.51405i	−0.763522	−	0.348689i	−0.758820	+	0.651300i	$0.774224\pi$
$350$	−6.05774	+	0.158494i	−0.323800	+	0.00847188i
$351$	−15.7845	+	7.20854i	−0.842514	+	0.384763i
$352$	−27.0228	−	17.8286i	−1.44032	−	0.950270i
$353$	2.96034	+	20.5896i	0.157563	+	1.09588i	0.903106	+	0.429418i	$0.141281\pi$
$353$	2.96034	+	20.5896i	0.157563	+	1.09588i	−0.745542	+	0.666458i	$0.767810\pi$
$354$	6.53344	+	3.96124i	0.347248	+	0.210538i
$355$	2.42672	+	2.10276i	0.128797	+	0.111603i
$356$	−8.46116	+	4.41266i	−0.448441	+	0.233871i
$357$	−10.5440	+	16.4069i	−0.558050	+	0.868343i
$358$	−2.38967	+	1.62560i	−0.126298	+	0.0859158i
$359$	7.84416	+	2.30325i	0.413999	+	0.121561i	0.482098	−	0.876117i	$-0.339875\pi$
$359$	7.84416	+	2.30325i	0.413999	+	0.121561i	−0.0680985	+	0.997679i	$0.521693\pi$
$360$	3.57338	−	4.84453i	0.188334	−	0.255329i
$361$	−3.04290	−	3.51169i	−0.160152	−	0.184826i
$362$	3.18623	+	18.6783i	0.167464	+	0.981712i
$363$	19.4864	−	5.72172i	1.02277	−	0.300313i
$364$	18.1351	+	25.2147i	0.950540	+	1.32161i
$365$	−1.86076	+	12.9419i	−0.0973968	+	0.677410i
$366$	−1.40243	+	0.451956i	−0.0733062	+	0.0236241i
$367$	−6.69300			−0.349372			−0.174686	−	0.984624i	$-0.555891\pi$
$367$	−6.69300			−0.349372			−0.174686	+	0.984624i	$0.555891\pi$
$368$	−19.1507	+	1.11787i	−0.998301	+	0.0582729i
$369$	−24.8100			−1.29156
$370$	8.70318	−	2.80474i	0.452457	−	0.145812i
$371$	−6.00139	+	41.7406i	−0.311577	+	2.16706i
$372$	5.46344	+	7.59625i	0.283266	+	0.393847i
$373$	5.28125	−	1.55072i	0.273453	−	0.0802930i	−0.142131	−	0.989848i	$-0.545395\pi$
$373$	5.28125	−	1.55072i	0.273453	−	0.0802930i	0.415584	+	0.909555i	$0.363577\pi$
$374$	−6.63481	−	38.8947i	−0.343078	−	2.01120i
$375$	−0.611397	−	0.705590i	−0.0315724	−	0.0364365i
$376$	5.47484	+	4.03830i	0.282343	+	0.208259i
$377$	11.2666	+	3.30816i	0.580258	+	0.170379i
$378$	23.9897	−	16.3193i	1.23390	−	0.839374i
$379$	14.6482	−	22.7930i	0.752426	−	1.17080i	−0.227952	−	0.973672i	$-0.573203\pi$
$379$	14.6482	−	22.7930i	0.752426	−	1.17080i	0.980378	−	0.197125i	$-0.0631606\pi$
$380$	6.71841	−	3.50378i	0.344647	−	0.179740i
$381$	−3.96970	−	3.43977i	−0.203374	−	0.176225i
$382$	−0.357093	−	0.216507i	−0.0182705	−	0.0110774i
$383$	4.85993	+	33.8016i	0.248331	+	1.72718i	0.607859	+	0.794045i	$0.292028\pi$
$383$	4.85993	+	33.8016i	0.248331	+	1.72718i	−0.359529	+	0.933134i	$0.617063\pi$
$384$	−9.42366	+	4.77155i	−0.480899	+	0.243497i
$385$	22.3067	−	10.1871i	1.13685	−	0.519183i
$386$	−17.8270	+	0.466425i	−0.907372	+	0.0237404i
$387$	−7.83630	−	3.57872i	−0.398341	−	0.181916i
$388$	27.2173	+	21.1970i	1.38175	+	1.07611i
$389$	1.09402	−	0.703082i	0.0554688	−	0.0356477i	−0.512613	−	0.858620i	$-0.671322\pi$
$389$	1.09402	−	0.703082i	0.0554688	−	0.0356477i	0.568081	+	0.822972i	$0.307686\pi$
$390$	−1.22761	+	4.62509i	−0.0621623	+	0.234201i
$391$	−16.9414	−	16.1124i	−0.856763	−	0.814841i
$392$	−22.8815	−	22.5601i	−1.15569	−	1.13946i
$393$	−9.56198	+	6.14511i	−0.482338	+	0.309980i
$394$	6.40935	+	2.72678i	0.322898	+	0.137373i
$395$	6.73315	−	14.7435i	0.338781	−	0.741828i
$396$	−5.63160	+	23.7011i	−0.282999	+	1.19102i
$397$	5.04619	−	2.30452i	0.253261	−	0.115660i	−0.284739	−	0.958605i	$-0.591907\pi$
$397$	5.04619	−	2.30452i	0.253261	−	0.115660i	0.538001	+	0.842944i	$0.319180\pi$
$398$	4.37355	+	8.94959i	0.219226	+	0.448602i
$399$	15.0021	−	2.15698i	0.751046	−	0.107984i
$400$	−0.979658	−	3.87818i	−0.0489829	−	0.193909i
$401$	7.97471	+	6.91013i	0.398238	+	0.345075i	0.830842	−	0.556509i	$-0.187860\pi$
$401$	7.97471	+	6.91013i	0.398238	+	0.345075i	−0.432603	+	0.901584i	$0.642405\pi$
$402$	−8.25320	+	7.53828i	−0.411632	+	0.375975i
$403$	15.2781	+	9.81864i	0.761057	+	0.489102i
$404$	−5.71750	−	16.2710i	−0.284456	−	0.809510i
$405$	−1.83726	−	0.539468i	−0.0912941	−	0.0268064i
$406$	−19.5000	−	2.28488i	−0.967768	−	0.113397i
$407$	−27.9654	+	24.2322i	−1.38619	+	1.20114i
$408$	−12.0934	−	4.41341i	−0.598713	−	0.218497i
$409$	−7.92475	+	2.32692i	−0.391854	+	0.115059i	−0.471723	−	0.881747i	$-0.656368\pi$
$409$	−7.92475	+	2.32692i	−0.391854	+	0.115059i	0.0798694	+	0.996805i	$0.474550\pi$
$410$	−10.4662	+	12.7370i	−0.516886	+	0.629036i
$411$	−14.9818	−	2.15406i	−0.738998	−	0.106252i
$412$	19.2621	−	1.00863i	0.948974	−	0.0496918i
$413$	−24.7957			−1.22012
$414$	5.73053	+	13.2489i	0.281640	+	0.651146i
$415$			4.14315i			0.203379i
$416$	−13.6108	+	15.3318i	−0.667326	+	0.751701i
$417$	−0.307557	+	2.13911i	−0.0150611	+	0.104753i
$418$	−19.4671	+	23.6909i	−0.952167	+	1.15876i
$419$	−5.29158	−	18.0215i	−0.258510	−	0.880406i	−0.981809	−	0.189870i	$-0.939193\pi$
$419$	−5.29158	−	18.0215i	−0.258510	−	0.880406i	0.723299	−	0.690535i	$-0.242625\pi$
$420$	0.722981	−	7.96836i	0.0352779	−	0.388816i
$421$	−7.97645	−	9.20532i	−0.388748	−	0.448640i	0.527317	−	0.849669i	$-0.323198\pi$
$421$	−7.97645	−	9.20532i	−0.388748	−	0.448640i	−0.916065	+	0.401029i	$0.868653\pi$
$422$	−4.21965	+	36.0120i	−0.205409	+	1.75304i
$423$	1.44224	−	4.91181i	0.0701240	−	0.238821i
$424$	−27.7500	+	2.18213i	−1.34766	+	0.105974i
$425$	2.63565	−	4.10116i	0.127848	−	0.198935i
$426$	−3.13041	+	2.85924i	−0.151669	+	0.138531i
$427$	3.13142	−	3.61385i	0.151540	−	0.174887i
$428$	−4.15188	+	3.99636i	−0.200689	+	0.193172i
$429$	−2.75590	−	19.1677i	−0.133056	−	0.925424i
$430$	−5.14300	+	2.51332i	−0.248018	+	0.121203i
$431$	7.42919	+	16.2677i	0.357851	+	0.783585i	0.999857	+	0.0168858i	$0.00537516\pi$
$431$	7.42919	+	16.2677i	0.357851	+	0.783585i	−0.642006	+	0.766700i	$0.721898\pi$
$432$	13.9849	+	13.0850i	0.672848	+	0.629551i
$433$	20.1685	+	9.21064i	0.969236	+	0.442635i	0.836169	−	0.548472i	$-0.184790\pi$
$433$	20.1685	+	9.21064i	0.969236	+	0.442635i	0.133067	+	0.991107i	$0.457517\pi$
$434$	−27.9424	−	11.8877i	−1.34128	−	0.570630i
$435$	−1.63538	−	2.54471i	−0.0784106	−	0.122009i
$436$	−26.6822	−	15.2376i	−1.27784	−	0.729750i
$437$	−0.841413	+	18.1499i	−0.0402502	+	0.868228i
$438$	−16.6858	−	4.42881i	−0.797279	−	0.211617i
$439$	2.88659	+	4.49162i	0.137769	+	0.214374i	0.903282	−	0.429048i	$-0.141151\pi$
$439$	2.88659	+	4.49162i	0.137769	+	0.214374i	−0.765512	+	0.643421i	$0.777514\pi$
$440$	9.79200	+	12.8895i	0.466815	+	0.614483i
$441$	−10.0445	+	21.9943i	−0.478308	+	1.04735i
$442$	−24.9781	+	0.653525i	−1.18809	+	0.0310850i
$443$	−1.93120	−	4.22873i	−0.0917540	−	0.200913i	0.858191	−	0.513331i	$-0.171589\pi$
$443$	−1.93120	−	4.22873i	−0.0917540	−	0.200913i	−0.949945	+	0.312417i	$0.898861\pi$
$444$	2.34076	+	11.8441i	0.111087	+	0.562098i
$445$	4.72278	−	0.679033i	0.223881	−	0.0321892i
$446$	−18.9940	+	31.3277i	−0.899394	+	1.48341i
$447$	−6.90863	+	7.97298i	−0.326767	+	0.377109i
$448$	18.1231	−	29.0971i	0.856234	−	1.37471i
$449$	9.40993	+	6.04739i	0.444082	+	0.285394i	0.743510	−	0.668725i	$-0.233160\pi$
$449$	9.40993	+	6.04739i	0.444082	+	0.285394i	−0.299428	+	0.954119i	$0.596796\pi$
$450$	−2.48868	+	1.69296i	−0.117317	+	0.0798068i
$451$	18.7953	−	64.0108i	0.885035	−	3.01415i
$452$	−29.4717	−	11.6377i	−1.38623	−	0.547393i
$453$	−8.84767	+	7.66655i	−0.415700	+	0.360206i
$454$	−23.1440	+	3.94800i	−1.08620	+	0.185289i
$455$	−4.37517	−	14.9005i	−0.205111	−	0.698545i
$456$	3.56244	+	9.34877i	0.166827	+	0.437796i
$457$	−26.0678	−	3.74798i	−1.21940	−	0.175323i	−0.497588	−	0.867414i	$-0.665781\pi$
$457$	−26.0678	−	3.74798i	−1.21940	−	0.175323i	−0.721811	+	0.692091i	$0.756690\pi$
$458$	22.1190	−	7.12822i	1.03355	−	0.333080i
$459$			23.3416i			1.08949i
$460$	9.21915	+	2.64711i	0.429845	+	0.123422i
$461$		−	23.7745i		−	1.10729i	−0.832753	−	0.553644i	$-0.813237\pi$
$461$		−	23.7745i		−	1.10729i	0.832753	−	0.553644i	$-0.186763\pi$
$462$	9.93155	+	30.8178i	0.462057	+	1.43378i
$463$	−14.8568	−	2.13609i	−0.690456	−	0.0992726i	−0.211850	−	0.977302i	$-0.567949\pi$
$463$	−14.8568	−	2.13609i	−0.690456	−	0.0992726i	−0.478606	+	0.878030i	$0.658858\pi$
$464$	−1.35353	−	12.8889i	−0.0628359	−	0.598350i
$465$	−1.31808	−	4.48895i	−0.0611243	−	0.208170i
$466$	2.96225	+	17.3654i	0.137224	+	0.804434i
$467$	−2.37626	+	2.05904i	−0.109960	+	0.0952811i	−0.708106	−	0.706106i	$-0.750450\pi$
$467$	−2.37626	+	2.05904i	−0.109960	+	0.0952811i	0.598145	+	0.801388i	$0.295905\pi$
$468$	14.3489	+	5.66606i	0.663278	+	0.261914i
$469$	10.2198	−	34.8056i	0.471909	−	1.60717i
$470$	−1.91322	−	2.81248i	−0.0882504	−	0.129730i
$471$	−10.0482	−	6.45762i	−0.462999	−	0.297551i
$472$	−3.59217	−	15.9683i	−0.165343	−	0.734999i
$473$	15.1697	−	17.5068i	0.697505	−	0.804964i
$474$	18.2998	+	11.0952i	0.840536	+	0.509619i
$475$	−3.75002	+	0.539172i	−0.172063	+	0.0247389i
$476$	40.9859	−	8.10003i	1.87858	−	0.371264i
$477$	8.70121	+	19.0530i	0.398401	+	0.872377i
$478$	0.268109	+	10.2473i	0.0122630	+	0.468700i
$479$	−13.8545	+	30.3371i	−0.633027	+	1.38614i	0.272627	+	0.962120i	$0.412108\pi$
$479$	−13.8545	+	30.3371i	−0.633027	+	1.38614i	−0.905654	+	0.424017i	$0.860620\pi$
$480$	5.23630	−	0.688786i	0.239003	−	0.0314386i
$481$	12.6690	+	19.7133i	0.577656	+	0.898850i
$482$	4.52146	−	17.0349i	0.205947	−	0.775917i
$483$	15.6426	+	11.1090i	0.711761	+	0.505478i
$484$	−37.7791	−	21.5749i	−1.71723	−	0.980676i
$485$	−9.32544	−	14.5107i	−0.423447	−	0.658896i
$486$	8.94216	−	21.0188i	0.405625	−	0.953430i
$487$	36.4610	+	16.6512i	1.65220	+	0.754537i	0.999994	−	0.00350093i	$-0.00111438\pi$
$487$	36.4610	+	16.6512i	1.65220	+	0.754537i	0.652211	+	0.758038i	$0.273842\pi$
$488$	2.78094	+	1.49307i	0.125887	+	0.0675881i
$489$	−6.95620	−	15.2319i	−0.314570	−	0.688812i
$490$	7.05420	+	14.4350i	0.318676	+	0.652106i
$491$	−4.71851	−	32.8180i	−0.212943	−	1.48105i	−0.763256	−	0.646096i	$-0.776401\pi$
$491$	−4.71851	−	32.8180i	−0.212943	−	1.48105i	0.550313	−	0.834958i	$-0.314508\pi$
$492$	−15.0948	−	15.6823i	−0.680528	−	0.707011i
$493$	10.3434	−	11.9369i	0.465844	−	0.537613i
$494$	13.0956	+	14.3376i	0.589199	+	0.645078i
$495$	6.58527	−	10.2469i	0.295986	−	0.460563i
$496$	3.60758	−	19.7169i	0.161985	−	0.885314i
$497$	3.87635	−	13.2016i	0.173878	−	0.592175i
$498$	−5.43325	−	0.636633i	−0.243470	−	0.0285282i
$499$	10.3903	+	11.9910i	0.465132	+	0.536791i	0.939051	−	0.343777i	$-0.111707\pi$
$499$	10.3903	+	11.9910i	0.465132	+	0.536791i	−0.473919	+	0.880568i	$0.657161\pi$
$500$	−0.180721	+	1.99182i	−0.00808208	+	0.0890768i
$501$	−0.531283	−	1.80938i	−0.0237360	−	0.0808373i
$502$	−5.09125	−	4.18354i	−0.227233	−	0.186720i
$503$	−3.01081	+	20.9406i	−0.134245	+	0.933696i	0.805689	+	0.592339i	$0.201796\pi$
$503$	−3.01081	+	20.9406i	−0.134245	+	0.933696i	−0.939934	+	0.341357i	$0.889114\pi$
$504$	−25.2433	−	5.30461i	−1.12443	−	0.236286i
$505$			8.62314i			0.383725i
$506$	−38.5238	+	4.74807i	−1.71259	+	0.211077i
$507$	−0.125975			−0.00559475
$508$	0.588398	+	11.2368i	0.0261059	+	0.498550i
$509$	10.5024	+	1.51002i	0.465513	+	0.0669307i	0.371081	−	0.928601i	$-0.378987\pi$
$509$	10.5024	+	1.51002i	0.465513	+	0.0669307i	0.0944322	+	0.995531i	$0.469896\pi$
$510$	4.97318	+	4.08652i	0.220216	+	0.180954i
$511$	53.7561	−	15.7842i	2.37803	−	0.698252i
$512$	21.3638	+	7.45580i	0.944155	+	0.329503i
$513$	13.7090	−	11.8789i	0.605267	−	0.524467i
$514$	−3.29898	+	28.1546i	−0.145512	+	1.24185i
$515$	−9.25357	−	2.71709i	−0.407761	−	0.119729i
$516$	−2.50565	−	7.13062i	−0.110305	−	0.313908i
$517$	11.5801	+	7.44206i	0.509291	+	0.327301i
$518$	−26.4240	−	28.9300i	−1.16100	−	1.27111i
$519$	12.5630	+	10.8859i	0.551453	+	0.477837i
$520$	8.96196	−	4.97622i	0.393008	−	0.218222i
$521$	16.8752	−	2.42628i	0.739315	−	0.106297i	0.237640	−	0.971353i	$-0.423626\pi$
$521$	16.8752	−	2.42628i	0.739315	−	0.106297i	0.501675	+	0.865056i	$0.332717\pi$
$522$	−8.76169	+	4.28173i	−0.383489	+	0.187406i
$523$	−17.7051	+	8.08566i	−0.774191	+	0.353561i	−0.763019	−	0.646376i	$-0.776284\pi$
$523$	−17.7051	+	8.08566i	−0.774191	+	0.353561i	−0.0111723	+	0.999938i	$0.503556\pi$
$524$	23.6892	+	5.62878i	1.03487	+	0.245894i
$525$	−1.66189	+	3.63902i	−0.0725307	+	0.158820i
$526$	−11.4610	+	26.9393i	−0.499723	+	1.17461i
$527$	20.5511	−	13.2074i	0.895220	−	0.575323i
$528$	−18.4077	+	10.8604i	−0.801091	+	0.472640i
$529$	−16.6054	+	15.9142i	−0.721973	+	0.691921i
$530$	13.4521	+	3.57050i	0.584321	+	0.155092i
$531$	−10.3609	+	6.65858i	−0.449627	+	0.288958i
$532$	−25.6157	−	19.9496i	−1.11058	−	0.864925i
$533$	−38.4297	−	17.5502i	−1.66457	−	0.760186i
$534$	0.164772	+	6.29769i	0.00713039	+	0.272528i
$535$	2.62098	−	1.19696i	0.113315	−	0.0517492i
$536$	23.8951	+	1.53920i	1.03211	+	0.0664831i
$537$	0.271540	+	1.88860i	0.0117178	+	0.0814991i
$538$	3.14702	−	5.19052i	0.135678	−	0.223779i
$539$	−49.1368	−	42.5773i	−2.11647	−	1.83393i
$540$	−4.42804	−	8.49064i	−0.190552	−	0.365379i
$541$	8.66215	−	13.4786i	0.372415	−	0.579489i	−0.603575	−	0.797307i	$-0.706257\pi$
$541$	8.66215	−	13.4786i	0.372415	−	0.579489i	0.975990	+	0.217818i	$0.0698938\pi$
$542$	5.72136	+	8.41051i	0.245753	+	0.361262i
$543$	12.0024	+	3.52422i	0.515073	+	0.151239i
$544$	11.1540	+	25.2211i	0.478224	+	1.08135i
$545$	10.0608	+	11.6108i	0.430958	+	0.497352i
$546$	20.2125	−	3.44792i	0.865014	−	0.147557i
$547$	18.5833	−	5.45656i	0.794567	−	0.233306i	0.140836	−	0.990033i	$-0.455021\pi$
$547$	18.5833	−	5.45656i	0.794567	−	0.233306i	0.653731	+	0.756727i	$0.273203\pi$
$548$	18.9320	+	26.3226i	0.808733	+	1.12445i
$549$	0.338017	−	2.35096i	0.0144262	−	0.100336i
$550$	−2.48255	−	7.70341i	−0.105856	−	0.328475i
$551$	−12.2748			−0.522922
$552$	−4.88797	+	11.6831i	−0.208046	+	0.497264i
$553$	−69.4513			−2.95337
$554$	−5.88094	−	18.2487i	−0.249857	−	0.775313i
$555$	0.859100	−	5.97517i	0.0364668	−	0.253632i
$556$	3.75835	−	2.70311i	0.159389	−	0.114637i
$557$	−4.23744	+	1.24422i	−0.179546	+	0.0527195i	−0.370270	−	0.928924i	$-0.620735\pi$
$557$	−4.23744	+	1.24422i	−0.179546	+	0.0527195i	0.190724	+	0.981644i	$0.438917\pi$
$558$	−14.8681	+	2.53626i	−0.629417	+	0.107368i
$559$	−9.60656	−	11.0866i	−0.406314	−	0.468911i
$560$	−13.3722	+	10.7217i	−0.565080	+	0.453074i
$561$	−24.9931	−	7.33864i	−1.05521	−	0.309837i
$562$	4.16051	+	6.11603i	0.175501	+	0.257989i
$563$	−16.8852	+	26.2739i	−0.711625	+	1.10731i	0.277570	+	0.960706i	$0.410471\pi$
$563$	−16.8852	+	26.2739i	−0.711625	+	1.10731i	−0.989195	+	0.146605i	$0.953165\pi$
$564$	3.98221	−	2.07680i	0.167681	−	0.0874491i
$565$	11.9734	+	10.3750i	0.503726	+	0.436481i
$566$	−20.4070	+	33.6580i	−0.857768	+	1.41475i
$567$	1.16768	+	8.12138i	0.0490379	+	0.341066i
$568$	9.06333	+	0.583811i	0.380289	+	0.0244962i
$569$	13.2880	−	6.06842i	0.557061	−	0.254401i	−0.116931	−	0.993140i	$-0.537306\pi$
$569$	13.2880	−	6.06842i	0.557061	−	0.254401i	0.673992	+	0.738739i	$0.264578\pi$
$570$	−0.130834	−	5.00055i	−0.00548003	−	0.209450i
$571$	−7.00216	−	3.19778i	−0.293031	−	0.133823i	0.263475	−	0.964666i	$-0.415131\pi$
$571$	−7.00216	−	3.19778i	−0.293031	−	0.133823i	−0.556507	+	0.830843i	$0.687859\pi$
$572$	−25.4889	+	32.7283i	−1.06574	+	1.36844i
$573$	−0.231925	+	0.149049i	−0.00968882	+	0.00622663i
$574$	68.2753	+	18.1219i	2.84976	+	0.756392i
$575$	−3.91011	−	2.77688i	−0.163063	−	0.115804i
$576$	−0.240886	−	17.0250i	−0.0100369	−	0.709374i
$577$	−2.64830	+	1.70196i	−0.110250	+	0.0708536i	−0.594604	−	0.804019i	$-0.702691\pi$
$577$	−2.64830	+	1.70196i	−0.110250	+	0.0708536i	0.484354	+	0.874872i	$0.339055\pi$
$578$	−3.74600	+	8.80506i	−0.155813	+	0.366242i
$579$	−4.89068	+	10.7091i	−0.203250	+	0.445055i
$580$	−1.49797	+	6.30434i	−0.0621999	+	0.261774i
$581$	16.1488	−	7.37492i	0.669966	−	0.305963i
$582$	20.4619	−	9.99950i	0.848175	−	0.414493i
$583$	−55.7492	+	8.01552i	−2.30890	+	0.331969i
$584$	17.9526	+	32.3318i	0.742883	+	1.33790i
$585$	−5.82951	−	5.05130i	−0.241021	−	0.208845i
$586$	11.3878	+	12.4678i	0.470426	+	0.515041i
$587$	14.6767	+	9.43214i	0.605772	+	0.389306i	0.807270	−	0.590183i	$-0.200944\pi$
$587$	14.6767	+	9.43214i	0.605772	+	0.389306i	−0.201497	+	0.979489i	$0.564581\pi$
$588$	−20.0137	+	7.03267i	−0.825351	+	0.290022i
$589$	−18.2158	−	5.34863i	−0.750568	−	0.220387i
$590$	−0.952393	+	8.12805i	−0.0392094	+	0.334626i
$591$	3.47517	−	3.01125i	0.142949	−	0.123866i
$592$	14.8026	−	21.2079i	0.608385	−	0.871641i
$593$	−7.71677	+	2.26585i	−0.316890	+	0.0930472i	−0.436310	−	0.899797i	$-0.643715\pi$
$593$	−7.71677	+	2.26585i	−0.316890	+	0.0930472i	0.119420	+	0.992844i	$0.461897\pi$
$594$	29.9403	+	24.6023i	1.22846	+	1.00944i
$595$	−20.6767	−	2.97286i	−0.847661	−	0.121875i
$596$	22.5685	−	1.18177i	0.924444	−	0.0484073i
$597$	6.57606			0.269140
$598$	−0.495706	+	24.5756i	−0.0202709	+	1.00497i
$599$		−	26.1240i		−	1.06740i	−0.845674	−	0.533699i	$-0.820801\pi$
$599$		−	26.1240i		−	1.06740i	0.845674	−	0.533699i	$-0.179199\pi$
$600$	−2.58426	−	0.543054i	−0.105502	−	0.0221701i
$601$	1.60139	−	11.1379i	0.0653220	−	0.454324i	−0.930741	−	0.365678i	$-0.880837\pi$
$601$	1.60139	−	11.1379i	0.0653220	−	0.454324i	0.996063	−	0.0886458i	$-0.0282539\pi$
$602$	18.9509	+	15.5722i	0.772381	+	0.634675i
$603$	−5.07622	−	17.2880i	−0.206719	−	0.704022i
$604$	24.9762	+	2.26613i	1.01627	+	0.0922074i
$605$	14.2451	+	16.4397i	0.579144	+	0.668368i
$606$	−11.3082	−	1.32502i	−0.459364	−	0.0538254i
$607$	11.2495	−	38.3124i	0.456605	−	1.55505i	−0.333908	−	0.942606i	$-0.608367\pi$
$607$	11.2495	−	38.3124i	0.456605	−	1.55505i	0.790512	−	0.612446i	$-0.209814\pi$
$608$	9.13644	−	19.3864i	0.370531	−	0.786223i
$609$	−7.00751	+	10.9039i	−0.283959	+	0.441848i
$610$	−1.06435	−	1.16529i	−0.0430941	−	0.0471811i
$611$	5.70851	−	6.58797i	0.230942	−	0.266521i
$612$	14.9509	−	14.3908i	0.604353	−	0.581716i
$613$	3.05707	+	21.2624i	0.123474	+	0.858781i	0.953572	+	0.301164i	$0.0973751\pi$
$613$	3.05707	+	21.2624i	0.123474	+	0.858781i	−0.830098	+	0.557617i	$0.811716\pi$
$614$	−7.54084	−	15.4308i	−0.304324	−	0.622736i
$615$	4.52110	+	9.89982i	0.182308	+	0.399199i
$616$	32.8096	−	61.1101i	1.32194	−	2.46220i
$617$	24.5123	+	11.1944i	0.986827	+	0.450669i	0.842403	−	0.538847i	$-0.181140\pi$
$617$	24.5123	+	11.1944i	0.986827	+	0.450669i	0.144423	+	0.989516i	$0.453867\pi$
$618$	4.98504	−	11.7174i	0.200528	−	0.471345i
$619$	7.45169	+	11.5951i	0.299509	+	0.466045i	0.958091	−	0.286464i	$-0.0924799\pi$
$619$	7.45169	+	11.5951i	0.299509	+	0.466045i	−0.658582	+	0.752509i	$0.728844\pi$
$620$	−4.97006	+	8.70293i	−0.199603	+	0.349518i
$621$	22.9376	+	1.06337i	0.920456	+	0.0426714i
$622$	−1.06162	+	3.99973i	−0.0425672	+	0.160375i
$623$	−11.0533	−	17.1993i	−0.442843	−	0.689077i
$624$	5.14863	+	12.5172i	0.206110	+	0.501088i
$625$	0.415415	−	0.909632i	0.0166166	−	0.0363853i
$626$	−0.670256	−	25.6176i	−0.0267888	−	1.02388i
$627$	8.40926	+	18.4137i	0.335834	+	0.735373i
$628$	4.96080	+	25.1015i	0.197957	+	1.00166i
$629$	31.2001	−	4.48589i	1.24403	−	0.178864i
$630$	11.0286	+	6.68666i	0.439389	+	0.266403i
$631$	11.0725	−	12.7784i	0.440789	−	0.508698i	−0.491268	−	0.871008i	$-0.663466\pi$
$631$	11.0725	−	12.7784i	0.440789	−	0.508698i	0.932058	+	0.362310i	$0.118012\pi$
$632$	−10.0615	−	44.7261i	−0.400223	−	1.77911i
$633$	20.1370	+	12.9413i	0.800373	+	0.514369i
$634$	−14.0532	−	20.6584i	−0.558123	−	0.820451i
$635$	1.58505	−	5.39818i	0.0629007	−	0.214220i
$636$	−6.74931	+	17.0921i	−0.267628	+	0.677747i
$637$	−31.1169	+	26.9630i	−1.23290	+	1.06831i
$638$	−4.40945	−	25.8492i	−0.174572	−	1.02338i
$639$	−1.92539	−	6.55728i	−0.0761673	−	0.259402i
$640$	−8.84193	−	7.05835i	−0.349508	−	0.279006i
$641$	26.7564	+	3.84699i	1.05682	+	0.151947i	0.648747	−	0.761004i	$-0.275293\pi$
$641$	26.7564	+	3.84699i	1.05682	+	0.151947i	0.408069	+	0.912951i	$0.366202\pi$
$642$	1.16693	+	3.62103i	0.0460552	+	0.142911i
$643$		−	22.2487i		−	0.877405i	−0.898632	−	0.438702i	$-0.855438\pi$
$643$		−	22.2487i		−	0.877405i	0.898632	−	0.438702i	$-0.144562\pi$
$644$	−6.09267	−	40.6456i	−0.240085	−	1.60166i
$645$			3.77902i			0.148799i
$646$	24.8608	−	8.01180i	0.978135	−	0.315220i
$647$	3.82041	+	0.549291i	0.150196	+	0.0215949i	0.217002	−	0.976171i	$-0.430372\pi$
$647$	3.82041	+	0.549291i	0.150196	+	0.0215949i	−0.0668068	+	0.997766i	$0.521281\pi$
$648$	−5.06094	+	1.92852i	−0.198813	+	0.0757596i
$649$	−9.33026	−	31.7759i	−0.366245	−	1.24731i
$650$	−5.05243	+	0.861863i	−0.198173	+	0.0338051i
$651$	−15.1505	+	13.1279i	−0.593793	+	0.514525i
$652$	−13.1748	+	33.3641i	−0.515963	+	1.30664i
$653$	7.68277	−	26.1651i	0.300650	−	1.02392i	−0.661170	−	0.750237i	$-0.729940\pi$
$653$	7.68277	−	26.1651i	0.300650	−	1.02392i	0.961820	−	0.273684i	$-0.0882422\pi$
$654$	−16.7721	+	11.4094i	−0.655841	+	0.446145i
$655$	−10.2417	−	6.58196i	−0.400178	−	0.257179i
$656$	−1.77926	+	46.5941i	−0.0694685	+	1.81919i
$657$	18.2234	−	21.0310i	0.710964	−	0.820496i
$658$	−7.55664	+	12.4635i	−0.294588	+	0.485877i
$659$	12.4490	−	1.78990i	0.484944	−	0.0697245i	0.104493	−	0.994526i	$-0.466678\pi$
$659$	12.4490	−	1.78990i	0.484944	−	0.0697245i	0.380451	+	0.924801i	$0.375769\pi$
$660$	10.4836	−	2.07187i	0.408072	−	0.0806473i
$661$	15.6451	+	34.2580i	0.608524	+	1.33248i	0.923579	+	0.383408i	$0.125250\pi$
$661$	15.6451	+	34.2580i	0.608524	+	1.33248i	−0.315055	+	0.949073i	$0.602023\pi$
$662$	5.13066	−	0.134238i	0.199409	−	0.00521731i
$663$	−6.85252	+	15.0049i	−0.266130	+	0.582743i
$664$	7.08888	+	9.33131i	0.275102	+	0.362125i
$665$	8.77668	+	13.6568i	0.340345	+	0.529587i
$666$	−18.8101	−	4.99264i	−0.728877	−	0.193461i
$667$	−11.2592	−	10.7082i	−0.435956	−	0.414624i
$668$	−2.00331	+	3.50793i	−0.0775103	+	0.135726i
$669$	13.0760	+	20.3467i	0.505549	+	0.786650i
$670$	−11.0167	−	4.68694i	−0.425614	−	0.181072i
$671$	5.80949	+	2.65310i	0.224273	+	0.102422i
$672$	−12.0054	−	19.1835i	−0.463120	−	0.740021i
$673$	−6.53443	−	14.3084i	−0.251884	−	0.551549i	0.740879	−	0.671638i	$-0.234409\pi$
$673$	−6.53443	−	14.3084i	−0.251884	−	0.551549i	−0.992763	+	0.120090i	$0.961682\pi$
$674$	−18.7344	+	9.15526i	−0.721621	+	0.352647i
$675$	0.681399	+	4.73923i	0.0262270	+	0.182413i
$676$	0.187144	+	0.194427i	0.00719786	+	0.00747796i
$677$	14.3819	−	16.5976i	0.552742	−	0.637898i	−0.408778	−	0.912634i	$-0.634045\pi$
$677$	14.3819	−	16.5976i	0.552742	−	0.637898i	0.961520	+	0.274736i	$0.0885904\pi$
$678$	−15.4455	+	14.1075i	−0.593179	+	0.541796i
$679$	−39.9589	+	62.1773i	−1.53348	+	2.38615i
$680$	−1.08094	−	13.7463i	−0.0414523	−	0.527147i
$681$	−4.36681	+	14.8720i	−0.167336	+	0.569895i
$682$	4.71994	−	40.2816i	0.180736	−	1.54246i
$683$	5.69735	+	6.57509i	0.218003	+	0.251589i	0.854208	−	0.519931i	$-0.174042\pi$
$683$	5.69735	+	6.57509i	0.218003	+	0.251589i	−0.636205	+	0.771520i	$0.719497\pi$
$684$	−16.0608	−	1.45722i	−0.614100	−	0.0557182i
$685$	−4.56741	−	15.5552i	−0.174512	−	0.594332i
$686$	16.7764	−	20.4164i	0.640527	−	0.779503i
$687$	2.18339	−	15.1858i	0.0833016	−	0.579376i
$688$	−7.28293	+	14.4602i	−0.277659	+	0.551289i
$689$			35.6674i			1.35882i
$690$	4.24236	−	4.70095i	0.161504	−	0.178962i
$691$	−4.76695			−0.181343			−0.0906717	−	0.995881i	$-0.528901\pi$
$691$	−4.76695			−0.181343			−0.0906717	+	0.995881i	$0.528901\pi$
$692$	−1.86211	−	35.5611i	−0.0707868	−	1.35183i
$693$	−51.6614	−	7.42778i	−1.96245	−	0.282158i
$694$	−1.36390	+	1.65982i	−0.0517728	+	0.0630060i
$695$	−2.22097	+	0.652136i	−0.0842462	+	0.0247369i
$696$	−8.03721	−	2.93313i	−0.304650	−	0.111180i
$697$	−42.9482	+	37.2148i	−1.62678	+	1.40961i
$698$	22.0253	+	2.58079i	0.833671	+	0.0976843i
$699$	11.1587	+	3.27649i	0.422061	+	0.123928i
$700$	8.08523	−	2.84109i	0.305593	−	0.107383i
$701$	−20.2979	−	13.0447i	−0.766641	−	0.492690i	0.0979346	−	0.995193i	$-0.468776\pi$
$701$	−20.2979	−	13.0447i	−0.766641	−	0.492690i	−0.864576	+	0.502503i	$0.832413\pi$
$702$	18.1197	−	16.5501i	0.683882	−	0.624642i
$703$	−18.5129	−	16.0415i	−0.698226	−	0.605017i
$704$	44.1076	+	12.2761i	1.66237	+	0.462672i
$705$	−2.22275	+	0.319584i	−0.0837137	+	0.0120362i
$706$	−12.9162	−	26.4304i	−0.486108	−	0.994721i
$707$	33.6105	−	15.3494i	1.26405	−	0.577274i
$708$	−10.5126	−	2.49790i	−0.395088	−	0.0938767i
$709$	−4.24220	+	9.28911i	−0.159319	+	0.348860i	−0.972411	−	0.233276i	$-0.925056\pi$
$709$	−4.24220	+	9.28911i	−0.159319	+	0.348860i	0.813092	+	0.582136i	$0.197783\pi$
$710$	−4.17861	−	1.77774i	−0.156821	−	0.0667174i
$711$	−29.0204	+	18.6503i	−1.08835	+	0.699440i
$712$	9.47494	−	9.60995i	0.355088	−	0.360148i
$713$	−12.0426	−	20.7971i	−0.450998	−	0.778859i
$714$	7.07570	−	26.6582i	0.264802	−	0.997657i
$715$	17.4488	−	11.2136i	0.652547	−	0.419367i
$716$	2.51143	−	3.22473i	0.0938567	−	0.120514i
$717$	6.15577	+	2.81125i	0.229891	+	0.104988i
$718$	−11.5577	+	0.302395i	−0.431329	+	0.0112853i
$719$	6.39303	−	2.91960i	0.238420	−	0.108883i	−0.292622	−	0.956228i	$-0.594528\pi$
$719$	6.39303	−	2.91960i	0.238420	−	0.108883i	0.531042	+	0.847345i	$0.321801\pi$
$720$	−2.70844	+	8.07102i	−0.100938	+	0.300789i
$721$	5.88115	+	40.9043i	0.219026	+	1.52336i
$722$	5.61919	+	3.40693i	0.209124	+	0.126793i
$723$	−8.79346	−	7.61957i	−0.327032	−	0.283375i
$724$	−12.3912	−	23.7597i	−0.460514	−	0.883023i
$725$	1.75164	−	2.72561i	0.0650543	−	0.101226i
$726$	−23.7475	+	16.1546i	−0.881354	+	0.599553i
$727$	−11.7612	−	3.45339i	−0.436198	−	0.128079i	0.0562587	−	0.998416i	$-0.482083\pi$
$727$	−11.7612	−	3.45339i	−0.436198	−	0.128079i	−0.492457	+	0.870337i	$0.663901\pi$
$728$	−35.3484	−	26.0734i	−1.31010	−	0.966343i
$729$	−6.11324	−	7.05505i	−0.226416	−	0.261298i
$730$	−3.10932	−	18.2275i	−0.115081	−	0.674631i
$731$	−18.9333	+	5.55932i	−0.700273	+	0.205619i
$732$	1.69168	−	1.21670i	0.0625263	−	0.0449707i
$733$	3.66824	−	25.5132i	0.135490	−	0.942351i	−0.802738	−	0.596332i	$-0.796624\pi$
$733$	3.66824	−	25.5132i	0.135490	−	0.942351i	0.938228	−	0.346019i	$-0.112467\pi$
$734$	9.00907	−	2.90332i	0.332531	−	0.107163i
$735$	10.6067			0.391233
$736$	25.2928	−	9.81198i	0.932304	−	0.361674i
$737$	48.4493			1.78465
$738$	33.3954	−	10.7622i	1.22930	−	0.396162i
$739$	3.36506	−	23.4045i	0.123786	−	0.860948i	−0.829420	−	0.558626i	$-0.811329\pi$
$739$	3.36506	−	23.4045i	0.123786	−	0.860948i	0.953206	−	0.302323i	$-0.0977620\pi$
$740$	−10.4982	+	7.55060i	−0.385922	+	0.277566i
$741$	12.3001	−	3.61162i	0.451854	−	0.132676i
$742$	−10.0283	−	58.7879i	−0.368150	−	2.15817i
$743$	−15.9467	−	18.4035i	−0.585027	−	0.675157i	0.383651	−	0.923478i	$-0.374667\pi$
$743$	−15.9467	−	18.4035i	−0.585027	−	0.675157i	−0.968678	+	0.248321i	$0.920121\pi$
$744$	−10.6492	−	7.85492i	−0.390417	−	0.287976i
$745$	−10.8420	−	3.18350i	−0.397221	−	0.116635i
$746$	−6.43612	+	4.37825i	−0.235643	+	0.160299i
$747$	4.76738	−	7.41819i	0.174429	−	0.271417i
$748$	25.8026	+	49.4758i	0.943437	+	1.80902i
$749$	−9.33084	−	8.08522i	−0.340941	−	0.295427i
$750$	1.12904	+	0.684540i	0.0412267	+	0.0249959i
$751$	6.56372	+	45.6517i	0.239513	+	1.66585i	0.654528	+	0.756038i	$0.272867\pi$
$751$	6.56372	+	45.6517i	0.239513	+	1.66585i	−0.415014	+	0.909815i	$0.636223\pi$
$752$	−9.12112	−	3.06083i	−0.332613	−	0.111617i
$753$	−3.95716	+	1.80718i	−0.144207	+	0.0658572i
$754$	−16.6003	+	0.434329i	−0.604548	+	0.0158173i
$755$	−11.4062	−	5.20905i	−0.415115	−	0.189577i
$756$	−25.2121	+	32.3728i	−0.916954	+	1.17739i
$757$	−25.6388	+	16.4771i	−0.931859	+	0.598869i	−0.916075	−	0.401006i	$-0.868661\pi$
$757$	−25.6388	+	16.4771i	−0.931859	+	0.598869i	−0.0157833	+	0.999875i	$0.505024\pi$
$758$	−9.82983	+	37.0345i	−0.357035	+	1.34515i
$759$	−8.35024	+	24.2262i	−0.303094	+	0.879357i
$760$	−7.52338	+	7.63058i	−0.272902	+	0.276790i
$761$	−20.3331	+	13.0673i	−0.737073	+	0.473688i	−0.854538	−	0.519389i	$-0.826160\pi$
$761$	−20.3331	+	13.0673i	−0.737073	+	0.473688i	0.117465	+	0.993077i	$0.462523\pi$
$762$	6.83550	+	2.90808i	0.247624	+	0.105349i
$763$	27.3471	−	59.8817i	0.990031	−	2.16786i
$764$	0.574580	+	0.136526i	0.0207876	+	0.00493933i
$765$	−9.43812	+	4.31024i	−0.341236	+	0.155837i
$766$	−21.2042	−	43.3902i	−0.766141	−	1.56775i
$767$	−20.7588	+	2.98467i	−0.749558	+	0.107770i
$768$	10.6148	−	10.5105i	0.383029	−	0.379267i
$769$	−10.9911	−	9.52385i	−0.396349	−	0.343439i	0.433771	−	0.901023i	$-0.357183\pi$
$769$	−10.9911	−	9.52385i	−0.396349	−	0.343439i	−0.830120	+	0.557585i	$0.811728\pi$
$770$	−25.6067	+	23.3886i	−0.922802	+	0.842865i
$771$	15.7434	+	10.1176i	0.566983	+	0.364378i
$772$	23.7936	−	8.36091i	0.856351	−	0.300916i
$773$	29.1102	+	8.54751i	1.04702	+	0.307433i	0.759612	−	0.650376i	$-0.225389\pi$
$773$	29.1102	+	8.54751i	1.04702	+	0.307433i	0.287407	+	0.957809i	$0.407207\pi$
$774$	12.1004	+	1.41785i	0.434939	+	0.0509634i
$775$	3.78710	−	3.28154i	0.136037	−	0.117876i
$776$	−45.8306	−	16.7256i	−1.64522	−	0.600414i
$777$	−24.8187	+	7.28744i	−0.890368	+	0.261436i
$778$	−1.16761	+	1.42094i	−0.0418607	+	0.0509433i
$779$	43.7140	+	6.28513i	1.56622	+	0.225188i
$780$	−0.353878	−	6.75809i	−0.0126709	−	0.241978i
$781$	18.3766			0.657568
$782$	29.7932	+	14.3391i	1.06540	+	0.512766i
$783$			15.5127i			0.554378i
$784$	40.5857	+	20.4412i	1.44949	+	0.730042i
$785$	1.82070	−	12.6633i	0.0649837	−	0.451971i
$786$	10.2052	−	12.4194i	0.364007	−	0.442986i
$787$	2.40091	+	8.17675i	0.0855833	+	0.291470i	0.991152	−	0.132729i	$-0.0423740\pi$
$787$	2.40091	+	8.17675i	0.0855833	+	0.291470i	−0.905569	+	0.424199i	$0.860556\pi$
$788$	−9.81009	−	0.890084i	−0.349470	−	0.0317079i
$789$	12.6567	+	14.6066i	0.450589	+	0.520008i
$790$	−2.66759	+	22.7662i	−0.0949087	+	0.809984i
$791$	19.1259	−	65.1369i	0.680040	−	2.31600i
$792$	−2.70078	−	34.3456i	−0.0959679	−	1.22042i
$793$	2.18661	−	3.40243i	0.0776487	−	0.120824i
$794$	−5.79273	+	5.29094i	−0.205576	+	0.187768i
$795$	6.01701	−	6.94400i	0.213401	−	0.246278i
$796$	−9.76918	−	10.1494i	−0.346259	−	0.359734i
$797$	7.24612	+	50.3979i	0.256671	+	1.78519i	0.556149	+	0.831082i	$0.312278\pi$
$797$	7.24612	+	50.3979i	0.256671	+	1.78519i	−0.299478	+	0.954103i	$0.596813\pi$
$798$	−19.2578	+	9.41107i	−0.681720	+	0.333148i
$799$	−4.87104	−	10.6661i	−0.172325	−	0.377339i
$800$	3.00095	+	4.79523i	0.106100	+	0.169537i
$801$	−9.23733	−	4.21855i	−0.326385	−	0.149055i
$802$	−13.7318	−	5.84202i	−0.484887	−	0.206289i
$803$	40.4552	+	62.9495i	1.42763	+	2.22144i
$804$	7.83918	−	13.7270i	0.276466	−	0.484112i
$805$	−3.86337	+	20.1834i	−0.136166	+	0.711372i
$806$	−24.8242	−	6.58892i	−0.874394	−	0.232085i
$807$	−2.16650	−	3.37114i	−0.0762645	−	0.118670i
$808$	14.7541	+	19.4212i	0.519047	+	0.683237i
$809$	−17.8749	+	39.1406i	−0.628449	+	1.37611i	0.280763	+	0.959777i	$0.409412\pi$
$809$	−17.8749	+	39.1406i	−0.628449	+	1.37611i	−0.909212	+	0.416334i	$0.863315\pi$
$810$	2.70704	−	0.0708268i	0.0951157	−	0.00248860i
$811$	−13.9555	−	30.5583i	−0.490044	−	1.07305i	−0.979578	−	0.201063i	$-0.935561\pi$
$811$	−13.9555	−	30.5583i	−0.490044	−	1.07305i	0.489535	−	0.871984i	$-0.337167\pi$
$812$	27.2390	−	5.38323i	0.955900	−	0.188914i
$813$	6.64699	−	0.955693i	0.233120	−	0.0335176i
$814$	27.1311	−	44.7485i	0.950945	−	1.56843i
$815$	11.7453	−	13.5548i	0.411420	−	0.474804i
$816$	18.1927	+	0.694715i	0.636872	+	0.0243199i
$817$	12.9006	+	8.29069i	0.451334	+	0.290055i
$818$	9.65768	−	6.56976i	0.337673	−	0.229706i
$819$	−9.31184	+	31.7132i	−0.325382	+	1.10815i
$820$	8.56278	−	21.6846i	0.299025	−	0.757259i
$821$	23.1691	−	20.0762i	0.808609	−	0.700663i	−0.148968	−	0.988842i	$-0.547595\pi$
$821$	23.1691	−	20.0762i	0.808609	−	0.700663i	0.957577	+	0.288179i	$0.0930497\pi$
$822$	21.1006	−	3.59941i	0.735966	−	0.125544i
$823$	5.76644	+	19.6387i	0.201006	+	0.684562i	0.996868	+	0.0790846i	$0.0251997\pi$
$823$	5.76644	+	19.6387i	0.201006	+	0.684562i	−0.795862	+	0.605478i	$0.792982\pi$
$824$	−25.4901	+	9.71325i	−0.887988	+	0.338377i
$825$	−5.28878	−	0.760412i	−0.184132	−	0.0264742i
$826$	33.3761	−	10.7560i	1.16130	−	0.374249i
$827$		−	14.6499i		−	0.509427i	−0.967017	−	0.254713i	$-0.918019\pi$
$827$		−	14.6499i		−	0.509427i	0.967017	−	0.254713i	$-0.0819811\pi$
$828$	−13.4607	−	15.3477i	−0.467791	−	0.533371i
$829$		−	1.33473i		−	0.0463569i	−0.999731	−	0.0231785i	$-0.992621\pi$
$829$		−	1.33473i		−	0.0463569i	0.999731	−	0.0231785i	$-0.00737859\pi$
$830$	−1.79723	−	5.57686i	−0.0623829	−	0.193576i
$831$	−12.5287	−	1.80135i	−0.434614	−	0.0624881i
$832$	11.6701	−	26.5414i	0.404588	−	0.920156i
$833$	15.6035	+	53.1405i	0.540628	+	1.84121i
$834$	−0.513925	−	3.01274i	−0.0177958	−	0.104323i
$835$	1.52648	−	1.32271i	0.0528262	−	0.0457741i
$836$	15.9268	−	40.3335i	0.550840	−	1.39496i
$837$	−6.75954	+	23.0209i	−0.233644	+	0.795718i
$838$	14.9401	+	21.9622i	0.516097	+	0.758673i
$839$	11.6409	+	7.48112i	0.401887	+	0.258277i	0.725935	−	0.687764i	$-0.241407\pi$
$839$	11.6409	+	7.48112i	0.401887	+	0.258277i	−0.324048	+	0.946041i	$0.605044\pi$
$840$	2.48338	+	11.0394i	0.0856848	+	0.380894i
$841$	−12.1168	+	13.9835i	−0.417820	+	0.482190i
$842$	14.7298	+	8.93069i	0.507621	+	0.307772i
$843$	4.83362	−	0.694969i	0.166479	−	0.0239360i
$844$	−9.94159	−	50.3041i	−0.342204	−	1.73154i
$845$	−0.0560521	−	0.122737i	−0.00192825	−	0.00422228i
$846$	0.189352	+	7.23713i	0.00651005	+	0.248818i
$847$	38.7206	−	84.7863i	1.33046	−	2.91329i
$848$	36.4062	−	14.9748i	1.25019	−	0.514236i
$849$	14.0487	+	21.8603i	0.482151	+	0.750242i
$850$	−1.76869	+	6.66364i	−0.0606654	+	0.228561i
$851$	−2.98688	−	30.8645i	−0.102389	−	1.05802i
$852$	2.97337	−	5.20659i	0.101866	−	0.178375i
$853$	14.8430	+	23.0962i	0.508216	+	0.790800i	0.996649	−	0.0818021i	$-0.0260675\pi$
$853$	14.8430	+	23.0962i	0.508216	+	0.790800i	−0.488433	+	0.872602i	$0.662431\pi$
$854$	−2.64739	+	6.22276i	−0.0905920	+	0.212938i
$855$	7.33471	+	3.34965i	0.250842	+	0.114556i
$856$	3.85505	−	7.18030i	0.131763	−	0.245418i
$857$	−1.72487	−	3.77694i	−0.0589205	−	0.129018i	0.877881	−	0.478878i	$-0.158956\pi$
$857$	−1.72487	−	3.77694i	−0.0589205	−	0.129018i	−0.936802	+	0.349860i	$0.886229\pi$
$858$	12.0242	+	24.6051i	0.410499	+	0.840003i
$859$	4.67773	+	32.5343i	0.159602	+	1.11006i	0.899368	+	0.437192i	$0.144027\pi$
$859$	4.67773	+	32.5343i	0.159602	+	1.11006i	−0.739766	+	0.672864i	$0.765064\pi$
$860$	5.83246	−	5.61399i	0.198885	−	0.191435i
$861$	30.5390	−	35.2439i	1.04077	−	1.20111i
$862$	−17.0567	−	18.6743i	−0.580952	−	0.636049i
$863$	19.1272	−	29.7624i	0.651096	−	1.01313i	−0.346093	−	0.938200i	$-0.612492\pi$
$863$	19.1272	−	29.7624i	0.651096	−	1.01313i	0.997189	−	0.0749252i	$-0.0238718\pi$
$864$	−24.5003	−	11.5465i	−0.833518	−	0.392820i
$865$	−5.01623	+	17.0837i	−0.170557	+	0.580863i
$866$	−31.1431	−	3.64915i	−1.05829	−	0.124003i
$867$	4.13681	+	4.77413i	0.140493	+	0.162138i
$868$	42.7684	+	3.88044i	1.45165	+	0.131711i
$869$	−26.1335	−	89.0025i	−0.886518	−	3.01920i
$870$	3.30515	+	2.71588i	0.112055	+	0.0920769i
$871$	4.36643	−	30.3692i	0.147951	−	1.02902i
$872$	42.5252	+	8.93620i	1.44008	+	0.302618i
$873$			36.7114i			1.24249i
$874$	−6.74057	−	24.7956i	−0.228003	−	0.838722i
$875$	−4.28494			−0.144857
$876$	24.3810	−	1.27668i	0.823757	−	0.0431349i
$877$	−1.55214	−	0.223164i	−0.0524120	−	0.00753571i	0.116059	−	0.993242i	$-0.462974\pi$
$877$	−1.55214	−	0.223164i	−0.0524120	−	0.00753571i	−0.168471	+	0.985707i	$0.553883\pi$
$878$	−5.83387	−	4.79376i	−0.196884	−	0.161782i
$879$	10.6960	−	3.14063i	0.360767	−	0.105931i
$880$	−18.7717	−	13.1022i	−0.632794	−	0.441675i
$881$	23.2180	−	20.1185i	0.782236	−	0.677811i	−0.169226	−	0.985577i	$-0.554127\pi$
$881$	23.2180	−	20.1185i	0.782236	−	0.677811i	0.951462	+	0.307766i	$0.0995814\pi$
$882$	3.97950	−	33.9624i	0.133997	−	1.14357i
$883$	−46.4493	−	13.6388i	−1.56314	−	0.458981i	−0.618148	−	0.786062i	$-0.712117\pi$
$883$	−46.4493	−	13.6388i	−1.56314	−	0.458981i	−0.944996	+	0.327081i	$0.893935\pi$
$884$	33.3381	−	11.7148i	1.12128	−	0.394011i
$885$	4.54500	+	2.92089i	0.152778	+	0.0981848i
$886$	4.43383	+	4.85433i	0.148958	+	0.163085i
$887$	25.7432	+	22.3066i	0.864373	+	0.748983i	0.969400	−	0.245486i	$-0.0789475\pi$
$887$	25.7432	+	22.3066i	0.864373	+	0.748983i	−0.105027	+	0.994469i	$0.533493\pi$
$888$	−8.28856	−	14.9273i	−0.278146	−	0.500929i
$889$	−23.8620	+	3.43084i	−0.800306	+	0.115067i
$890$	−6.06251	+	2.96267i	−0.203216	+	0.0993090i
$891$	−9.96824	+	4.55234i	−0.333949	+	0.152509i
$892$	11.9773	−	50.4077i	0.401031	−	1.68777i
$893$	−3.78546	+	8.28901i	−0.126676	+	0.277381i
$894$	5.84075	−	13.7288i	0.195344	−	0.459161i
$895$	−1.71924	+	1.10489i	−0.0574677	+	0.0369323i
$896$	−11.7726	+	47.0274i	−0.393294	+	1.57107i
$897$	14.4331	+	7.41750i	0.481906	+	0.247663i
$898$	−15.2894	−	4.05817i	−0.510215	−	0.135423i
$899$	13.6581	−	8.77756i	0.455525	−	0.292748i
$900$	2.61549	−	3.35834i	0.0871830	−	0.111945i
$901$	43.6418	+	19.9305i	1.45392	+	0.663982i
$902$	2.46763	+	94.3144i	0.0821632	+	3.14032i
$903$	14.7296	−	6.72676i	0.490169	−	0.223853i
$904$	44.7185	+	2.88053i	1.48731	+	0.0958049i
$905$	1.90679	+	13.2620i	0.0633837	+	0.440844i
$906$	8.58372	−	14.1575i	0.285175	−	0.470351i
$907$	−18.1537	−	15.7302i	−0.602782	−	0.522314i	0.299142	−	0.954209i	$-0.403300\pi$
$907$	−18.1537	−	15.7302i	−0.602782	−	0.522314i	−0.901924	+	0.431895i	$0.857845\pi$
$908$	29.4403	−	15.3537i	0.977009	−	0.509530i
$909$	9.92234	−	15.4395i	0.329103	−	0.512095i
$910$	12.3528	+	18.1588i	0.409490	+	0.601958i
$911$	14.1287	+	4.14858i	0.468106	+	0.137448i	0.507275	−	0.861784i	$-0.330653\pi$
$911$	14.1287	+	4.14858i	0.468106	+	0.137448i	−0.0391687	+	0.999233i	$0.512471\pi$
$912$	−8.85055	−	11.0385i	−0.293071	−	0.365522i
$913$	15.5276	+	17.9198i	0.513888	+	0.593059i
$914$	36.7141	−	6.26284i	1.21440	−	0.207156i
$915$	−0.999687	+	0.293535i	−0.0330486	+	0.00970396i
$916$	−26.6811	+	19.1898i	−0.881567	+	0.634048i
$917$	−7.42405	+	51.6354i	−0.245164	+	1.70515i
$918$	−10.1252	−	31.4188i	−0.334182	−	1.03697i
$919$	−44.5306			−1.46893			−0.734465	−	0.678647i	$-0.762567\pi$
$919$	−44.5306			−1.46893			−0.734465	+	0.678647i	$0.762567\pi$
$920$	−13.5577	+	0.436001i	−0.446983	+	0.0143745i
$921$	−11.3384			−0.373613
$922$	10.3130	+	32.0015i	0.339641	+	1.05391i
$923$	1.65617	−	11.5189i	0.0545136	−	0.379150i
$924$	−26.7366	−	37.1740i	−0.879569	−	1.22293i
$925$	6.20384	−	1.82161i	0.203981	−	0.0598943i
$926$	20.9246	−	3.56939i	0.687623	−	0.117297i
$927$	13.4418	+	15.5126i	0.441486	+	0.509502i
$928$	7.41289	+	16.7618i	0.243340	+	0.550233i
$929$	37.3134	+	10.9562i	1.22421	+	0.359461i	0.829063	−	0.559155i	$-0.188874\pi$
$929$	37.3134	+	10.9562i	1.22421	+	0.359461i	0.395150	+	0.918617i	$0.370693\pi$
$930$	3.72142	+	5.47056i	0.122030	+	0.179387i
$931$	23.2697	−	36.2083i	0.762633	−	1.18668i
$932$	−11.5201	−	22.0895i	−0.377354	−	0.723567i
$933$	2.06467	+	1.78905i	0.0675944	+	0.0585709i
$934$	2.30537	−	3.80234i	0.0754340	−	0.124417i
$935$	−3.97058	−	27.6160i	−0.129852	−	0.903139i
$936$	−21.7721	−	1.40244i	−0.711643	−	0.0458402i
$937$	−23.7003	+	10.8236i	−0.774256	+	0.353591i	−0.763044	−	0.646346i	$-0.776296\pi$
$937$	−23.7003	+	10.8236i	−0.774256	+	0.353591i	−0.0112115	+	0.999937i	$0.503569\pi$
$938$	1.34177	+	51.2830i	0.0438102	+	1.67445i
$939$	−15.3891	−	7.02795i	−0.502203	−	0.229348i
$940$	3.79529	+	2.95579i	0.123789	+	0.0964071i
$941$	−15.9294	+	10.2372i	−0.519284	+	0.333723i	−0.773889	−	0.633322i	$-0.781691\pi$
$941$	−15.9294	+	10.2372i	−0.519284	+	0.333723i	0.254605	+	0.967045i	$0.418055\pi$
$942$	16.3266	+	4.33346i	0.531949	+	0.141192i
$943$	34.6142	+	43.9003i	1.12719	+	1.42959i
$944$	11.7620	+	19.9357i	0.382820	+	0.648853i
$945$	17.2593	−	11.0919i	0.561444	−	0.360818i
$946$	−12.8249	+	30.1453i	−0.416975	+	0.980109i
$947$	−6.82326	+	14.9409i	−0.221726	+	0.485513i	−0.987504	−	0.157592i	$-0.949627\pi$
$947$	−6.82326	+	14.9409i	−0.221726	+	0.485513i	0.765778	+	0.643105i	$0.222354\pi$
$948$	−29.4452	−	6.99646i	−0.956335	−	0.227234i
$949$	43.1043	−	19.6851i	1.39923	−	0.639005i
$950$	4.81381	−	2.35245i	0.156180	−	0.0763235i
$951$	−16.3268	+	2.34743i	−0.529431	+	0.0761207i
$952$	−51.6551	+	28.6820i	−1.67415	+	0.929589i
$953$	−24.8366	−	21.5211i	−0.804538	−	0.697136i	0.152116	−	0.988363i	$-0.451391\pi$
$953$	−24.8366	−	21.5211i	−0.804538	−	0.697136i	−0.956654	+	0.291227i	$0.905937\pi$
$954$	−19.9771	−	21.8717i	−0.646782	−	0.708123i
$955$	−0.248413	−	0.159645i	−0.00803844	−	0.00516599i
$956$	−4.80599	−	13.6770i	−0.155437	−	0.442345i
$957$	−16.6103	−	4.87721i	−0.536934	−	0.157658i
$958$	5.48898	−	46.8449i	0.177341	−	1.51349i
$959$	−52.4995	+	45.4911i	−1.69530	+	1.46898i
$960$	−6.74950	+	3.19856i	−0.217839	+	0.103233i
$961$	−5.65081	+	1.65923i	−0.182284	+	0.0535234i
$962$	−25.6043	−	21.0394i	−0.825516	−	0.678337i
$963$	−6.07009	−	0.872748i	−0.195606	−	0.0281239i
$964$	1.30338	+	24.8910i	0.0419792	+	0.801685i
$965$	−12.6099			−0.405928
$966$	−25.8745	−	8.16771i	−0.832498	−	0.262792i
$967$		−	3.98469i		−	0.128139i	−0.997945	−	0.0640696i	$-0.979592\pi$
$967$		−	3.98469i		−	0.128139i	0.997945	−	0.0640696i	$-0.0204080\pi$
$968$	60.2112	+	12.6527i	1.93526	+	0.406674i
$969$	2.45404	−	17.0682i	0.0788350	−	0.548310i
$970$	18.8469	+	15.4868i	0.605139	+	0.497250i
$971$	10.7057	+	36.4603i	0.343562	+	1.17007i	0.932283	+	0.361729i	$0.117813\pi$
$971$	10.7057	+	36.4603i	0.343562	+	1.17007i	−0.588721	+	0.808336i	$0.700368\pi$
$972$	−2.91893	+	32.1711i	−0.0936249	+	1.03189i
$973$	6.49523	+	7.49589i	0.208227	+	0.240307i
$974$	−56.3011	−	6.59700i	−1.80400	−	0.211381i
$975$	−0.953291	+	3.24661i	−0.0305297	+	0.103975i
$976$	−4.39094	−	0.803407i	−0.140550	−	0.0257164i
$977$	−9.71640	+	15.1190i	−0.310855	+	0.483700i	−0.961167	−	0.275967i	$-0.911002\pi$
$977$	−9.71640	+	15.1190i	−0.310855	+	0.483700i	0.650312	+	0.759667i	$0.274638\pi$
$978$	15.9707	+	17.4854i	0.510687	+	0.559120i
$979$	17.8819	−	20.6368i	0.571508	−	0.659555i
$980$	−15.7569	−	16.3701i	−0.503336	−	0.522924i
$981$	−4.65344	−	32.3654i	−0.148573	−	1.03335i
$982$	20.5872	+	42.1276i	0.656965	+	1.34435i
$983$	12.4703	+	27.3061i	0.397740	+	0.870928i	0.997494	+	0.0707445i	$0.0225375\pi$
$983$	12.4703	+	27.3061i	0.397740	+	0.870928i	−0.599755	+	0.800184i	$0.704735\pi$
$984$	27.1210	+	14.5611i	0.864586	+	0.464191i
$985$	4.48011	+	2.04600i	0.142748	+	0.0651909i
$986$	−8.74464	+	20.5545i	−0.278486	+	0.654587i
$987$	5.20221	+	8.09480i	0.165588	+	0.257660i
$988$	−23.8467	−	13.6183i	−0.758663	−	0.433257i
$989$	4.60057	+	18.8589i	0.146290	+	0.599678i
$990$	−4.41912	+	16.6493i	−0.140449	+	0.529150i
$991$	12.8709	+	20.0276i	0.408859	+	0.636197i	0.983224	−	0.182402i	$-0.0583873\pi$
$991$	12.8709	+	20.0276i	0.408859	+	0.636197i	−0.574365	+	0.818599i	$0.694751\pi$
$992$	3.69691	+	28.1047i	0.117377	+	0.892325i
$993$	1.40755	−	3.08210i	0.0446672	−	0.0978076i
$994$	0.508927	+	19.4515i	0.0161422	+	0.616963i
$995$	2.92600	+	6.40704i	0.0927603	+	0.203117i
$996$	7.58954	−	1.49992i	0.240484	−	0.0475268i
$997$	−11.1484	+	1.60290i	−0.353073	+	0.0507643i	−0.316570	−	0.948569i	$-0.602531\pi$
$997$	−11.1484	+	1.60290i	−0.353073	+	0.0507643i	−0.0365037	+	0.999334i	$0.511622\pi$
$998$	−19.1873	−	11.6333i	−0.607362	−	0.368245i
$999$	−20.2730	+	23.3963i	−0.641411	+	0.740228i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	920.2.bb.a.11.5	✓	480
8.3	odd	2		920.2.bb.b.11.14	yes	480
23.21	odd	22		920.2.bb.b.251.14	yes	480
184.67	even	22	inner	920.2.bb.a.251.5	yes	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
920.2.bb.a.11.5	✓	480	1.1	even	1	trivial
920.2.bb.a.251.5	yes	480	184.67	even	22	inner
920.2.bb.b.11.14	yes	480	8.3	odd	2
920.2.bb.b.251.14	yes	480	23.21	odd	22

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:	\( N \)	\(=\)	\( 920 = 2^{3} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	920.bb (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.34604 + 0.433784i) q^{2} +(-0.132869 + 0.924126i) q^{3} +(1.62366 - 1.16778i) q^{4} +(-0.959493 + 0.281733i) q^{5} +(-0.222024 - 1.30155i) q^{6} +(2.80604 + 3.23834i) q^{7} +(-1.67895 + 2.27621i) q^{8} +(2.04212 + 0.599622i) q^{9} +(1.16931 - 0.795437i) q^{10} +(-3.09409 + 4.81450i) q^{11} +(0.863445 + 1.65563i) q^{12} +(2.73900 + 2.37336i) q^{13} +(-5.18179 - 3.14173i) q^{14} +(-0.132869 - 0.924126i) q^{15} +(1.27256 - 3.79217i) q^{16} +(4.43451 - 2.02517i) q^{17} +(-3.00889 + 0.0787244i) q^{18} +(-3.44622 - 1.57383i) q^{19} +(-1.22889 + 1.57792i) q^{20} +(-3.36547 + 2.16286i) q^{21} +(2.07633 - 7.82269i) q^{22} +(-1.78810 - 4.45002i) q^{23} +(-1.88042 - 1.85400i) q^{24} +(0.841254 - 0.540641i) q^{25} +(-4.71633 - 2.00650i) q^{26} +(-1.98899 + 4.35529i) q^{27} +(8.33774 + 1.98113i) q^{28} +(2.94715 - 1.34592i) q^{29} +(0.579719 + 1.18628i) q^{30} +(4.96005 - 0.713147i) q^{31} +(-0.0679368 + 5.65645i) q^{32} +(-4.03810 - 3.49903i) q^{33} +(-5.09055 + 4.64958i) q^{34} +(-3.60472 - 2.31661i) q^{35} +(4.01595 - 1.41118i) q^{36} +(6.20384 + 1.82161i) q^{37} +(5.32146 + 0.623535i) q^{38} +(-2.55721 + 2.21583i) q^{39} +(0.969663 - 2.65702i) q^{40} +(-11.1848 + 3.28416i) q^{41} +(3.59186 - 4.37119i) q^{42} +(-4.00647 - 0.576043i) q^{43} +(0.598535 + 11.4304i) q^{44} -2.12834 q^{45} +(4.33721 + 5.21427i) q^{46} -2.40525i q^{47} +(3.33536 + 1.67987i) q^{48} +(-1.61679 + 11.2451i) q^{49} +(-0.897842 + 1.09265i) q^{50} +(1.28230 + 4.36713i) q^{51} +(7.21878 + 0.654971i) q^{52} +(6.44475 + 7.43764i) q^{53} +(0.788015 - 6.72520i) q^{54} +(1.61236 - 5.49118i) q^{55} +(-12.0823 + 0.950098i) q^{56} +(1.91232 - 2.97563i) q^{57} +(-3.38315 + 3.09009i) q^{58} +(-3.78950 + 4.37331i) q^{59} +(-1.29492 - 1.34531i) q^{60} +(-0.158817 - 1.10460i) q^{61} +(-6.36708 + 3.11152i) q^{62} +(3.78850 + 8.29565i) q^{63} +(-2.36223 - 7.64329i) q^{64} +(-3.29670 - 1.50555i) q^{65} +(6.95328 + 2.95818i) q^{66} +(-4.57690 - 7.12180i) q^{67} +(4.83518 - 8.46674i) q^{68} +(4.34997 - 1.06116i) q^{69} +(5.85702 + 1.55459i) q^{70} +(-1.73600 - 2.70127i) q^{71} +(-4.79349 + 3.64156i) q^{72} +(5.43154 - 11.8934i) q^{73} +(-9.14083 + 0.239160i) q^{74} +(0.387844 + 0.849259i) q^{75} +(-7.43339 + 1.46906i) q^{76} +(-24.2731 + 3.48995i) q^{77} +(2.48092 - 4.09189i) q^{78} +(-10.6141 + 12.2494i) q^{79} +(-0.152634 + 3.99709i) q^{80} +(1.61085 + 1.03523i) q^{81} +(13.6306 - 9.27242i) q^{82} +(1.16726 - 3.97533i) q^{83} +(-2.93864 + 7.44189i) q^{84} +(-3.68432 + 3.19248i) q^{85} +(5.64276 - 0.962564i) q^{86} +(0.852212 + 2.90237i) q^{87} +(-5.76396 - 15.1261i) q^{88} +(-4.72278 - 0.679033i) q^{89} +(2.86483 - 0.923238i) q^{90} +15.5295i q^{91} +(-8.09994 - 5.13722i) q^{92} +4.67847i q^{93} +(1.04336 + 3.23757i) q^{94} +(3.75002 + 0.539172i) q^{95} +(-5.21824 - 0.814350i) q^{96} +(4.85957 + 16.5502i) q^{97} +(-2.70165 - 15.8377i) q^{98} +(-9.20539 + 7.97652i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 480 q + 2 q^{2} - 4 q^{4} - 48 q^{5} + 5 q^{6} - q^{8} - 48 q^{9} + 2 q^{10} + 3 q^{12} + 32 q^{16} + 7 q^{18} - 4 q^{20} + 8 q^{21} + 4 q^{23} + 2 q^{24} - 48 q^{25} + 7 q^{26} + 12 q^{27} + 5 q^{30}+ \cdots - 98 q^{98}+O(q^{100}) \) 480 * q + 2 * q^2 - 4 * q^4 - 48 * q^5 + 5 * q^6 - q^8 - 48 * q^9 + 2 * q^10 + 3 * q^12 + 32 * q^16 + 7 * q^18 - 4 * q^20 + 8 * q^21 + 4 * q^23 + 2 * q^24 - 48 * q^25 + 7 * q^26 + 12 * q^27 + 5 * q^30 - 118 * q^32 - 23 * q^34 + 54 * q^36 + 8 * q^37 - 65 * q^38 + 43 * q^40 - 10 * q^42 - q^44 + 480 * q^45 - 184 * q^46 - 44 * q^48 - 48 * q^49 - 9 * q^50 - 7 * q^52 + 32 * q^53 - 27 * q^54 + 67 * q^56 - 40 * q^58 - 12 * q^59 + 14 * q^60 - 8 * q^61 - 128 * q^62 + 59 * q^64 + 88 * q^66 + 10 * q^68 - 20 * q^69 + 3 * q^72 - 11 * q^74 + 110 * q^76 + 118 * q^78 - 144 * q^79 - q^80 - 56 * q^81 - 59 * q^82 - 162 * q^84 - 18 * q^86 - 76 * q^88 + 7 * q^90 - 149 * q^92 + 168 * q^94 + 65 * q^96 - 98 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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