# Properties

 Label 1200.3.bg.f.1057.2 Level $1200$ Weight $3$ Character 1200.1057 Analytic conductor $32.698$ Analytic rank $0$ Dimension $4$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1200 = 2^{4} \cdot 3 \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 1200.bg (of order $$4$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$32.6976317232$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(i)$$ Coefficient field: $$\Q(i, \sqrt{6})$$ Defining polynomial: $$x^{4} + 9$$ Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 600) Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

## Embedding invariants

 Embedding label 1057.2 Root $$1.22474 - 1.22474i$$ of defining polynomial Character $$\chi$$ $$=$$ 1200.1057 Dual form 1200.3.bg.f.193.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(1.22474 - 1.22474i) q^{3} +(-3.22474 - 3.22474i) q^{7} -3.00000i q^{9} +O(q^{10})$$ $$q+(1.22474 - 1.22474i) q^{3} +(-3.22474 - 3.22474i) q^{7} -3.00000i q^{9} +6.89898 q^{11} +(18.1237 - 18.1237i) q^{13} +(-0.449490 - 0.449490i) q^{17} -9.89898i q^{19} -7.89898 q^{21} +(-10.6515 + 10.6515i) q^{23} +(-3.67423 - 3.67423i) q^{27} +36.2929i q^{29} -25.6969 q^{31} +(8.44949 - 8.44949i) q^{33} +(13.3031 + 13.3031i) q^{37} -44.3939i q^{39} -3.10102 q^{41} +(-2.72985 + 2.72985i) q^{43} +(-37.1464 - 37.1464i) q^{47} -28.2020i q^{49} -1.10102 q^{51} +(65.1918 - 65.1918i) q^{53} +(-12.1237 - 12.1237i) q^{57} -80.3837i q^{59} +13.7878 q^{61} +(-9.67423 + 9.67423i) q^{63} +(-84.3712 - 84.3712i) q^{67} +26.0908i q^{69} -98.2929 q^{71} +(52.4949 - 52.4949i) q^{73} +(-22.2474 - 22.2474i) q^{77} -68.2020i q^{79} -9.00000 q^{81} +(89.7321 - 89.7321i) q^{83} +(44.4495 + 44.4495i) q^{87} +40.5857i q^{89} -116.889 q^{91} +(-31.4722 + 31.4722i) q^{93} +(105.720 + 105.720i) q^{97} -20.6969i q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q - 8 q^{7} + O(q^{10})$$ $$4 q - 8 q^{7} + 8 q^{11} + 48 q^{13} + 8 q^{17} - 12 q^{21} - 72 q^{23} - 44 q^{31} + 24 q^{33} + 112 q^{37} - 32 q^{41} - 104 q^{43} - 80 q^{47} - 24 q^{51} + 104 q^{53} - 24 q^{57} - 180 q^{61} - 24 q^{63} - 264 q^{67} - 256 q^{71} + 112 q^{73} - 40 q^{77} - 36 q^{81} + 16 q^{83} + 168 q^{87} - 252 q^{91} - 72 q^{93} + 320 q^{97} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1200\mathbb{Z}\right)^\times$$.

 $$n$$ $$401$$ $$577$$ $$751$$ $$901$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{1}{4}\right)$$ $$1$$ $$1$$

## 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 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ 1.22474 1.22474i 0.408248 0.408248i
$$4$$ 0 0
$$5$$ 0 0
$$6$$ 0 0
$$7$$ −3.22474 3.22474i −0.460678 0.460678i 0.438200 0.898878i $$-0.355616\pi$$
−0.898878 + 0.438200i $$0.855616\pi$$
$$8$$ 0 0
$$9$$ 3.00000i 0.333333i
$$10$$ 0 0
$$11$$ 6.89898 0.627180 0.313590 0.949558i $$-0.398468\pi$$
0.313590 + 0.949558i $$0.398468\pi$$
$$12$$ 0 0
$$13$$ 18.1237 18.1237i 1.39413 1.39413i 0.578329 0.815804i $$-0.303705\pi$$
0.815804 0.578329i $$-0.196295\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ −0.449490 0.449490i −0.0264406 0.0264406i 0.693763 0.720203i $$-0.255952\pi$$
−0.720203 + 0.693763i $$0.755952\pi$$
$$18$$ 0 0
$$19$$ 9.89898i 0.520999i −0.965474 0.260499i $$-0.916113\pi$$
0.965474 0.260499i $$-0.0838872\pi$$
$$20$$ 0 0
$$21$$ −7.89898 −0.376142
$$22$$ 0 0
$$23$$ −10.6515 + 10.6515i −0.463110 + 0.463110i −0.899673 0.436563i $$-0.856195\pi$$
0.436563 + 0.899673i $$0.356195\pi$$
$$24$$ 0 0
$$25$$ 0 0
$$26$$ 0 0
$$27$$ −3.67423 3.67423i −0.136083 0.136083i
$$28$$ 0 0
$$29$$ 36.2929i 1.25148i 0.780033 + 0.625739i $$0.215202\pi$$
−0.780033 + 0.625739i $$0.784798\pi$$
$$30$$ 0 0
$$31$$ −25.6969 −0.828933 −0.414467 0.910064i $$-0.636032\pi$$
−0.414467 + 0.910064i $$0.636032\pi$$
$$32$$ 0 0
$$33$$ 8.44949 8.44949i 0.256045 0.256045i
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ 13.3031 + 13.3031i 0.359542 + 0.359542i 0.863644 0.504102i $$-0.168176\pi$$
−0.504102 + 0.863644i $$0.668176\pi$$
$$38$$ 0 0
$$39$$ 44.3939i 1.13830i
$$40$$ 0 0
$$41$$ −3.10102 −0.0756346 −0.0378173 0.999285i $$-0.512040\pi$$
−0.0378173 + 0.999285i $$0.512040\pi$$
$$42$$ 0 0
$$43$$ −2.72985 + 2.72985i −0.0634848 + 0.0634848i −0.738136 0.674652i $$-0.764294\pi$$
0.674652 + 0.738136i $$0.264294\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ −37.1464 37.1464i −0.790350 0.790350i 0.191201 0.981551i $$-0.438762\pi$$
−0.981551 + 0.191201i $$0.938762\pi$$
$$48$$ 0 0
$$49$$ 28.2020i 0.575552i
$$50$$ 0 0
$$51$$ −1.10102 −0.0215886
$$52$$ 0 0
$$53$$ 65.1918 65.1918i 1.23003 1.23003i 0.266085 0.963950i $$-0.414270\pi$$
0.963950 0.266085i $$-0.0857302\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ −12.1237 12.1237i −0.212697 0.212697i
$$58$$ 0 0
$$59$$ 80.3837i 1.36244i −0.732081 0.681218i $$-0.761451\pi$$
0.732081 0.681218i $$-0.238549\pi$$
$$60$$ 0 0
$$61$$ 13.7878 0.226029 0.113014 0.993593i $$-0.463949\pi$$
0.113014 + 0.993593i $$0.463949\pi$$
$$62$$ 0 0
$$63$$ −9.67423 + 9.67423i −0.153559 + 0.153559i
$$64$$ 0 0
$$65$$ 0 0
$$66$$ 0 0
$$67$$ −84.3712 84.3712i −1.25927 1.25927i −0.951441 0.307830i $$-0.900397\pi$$
−0.307830 0.951441i $$-0.599603\pi$$
$$68$$ 0 0
$$69$$ 26.0908i 0.378128i
$$70$$ 0 0
$$71$$ −98.2929 −1.38441 −0.692203 0.721703i $$-0.743360\pi$$
−0.692203 + 0.721703i $$0.743360\pi$$
$$72$$ 0 0
$$73$$ 52.4949 52.4949i 0.719108 0.719108i −0.249314 0.968423i $$-0.580205\pi$$
0.968423 + 0.249314i $$0.0802053\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ −22.2474 22.2474i −0.288928 0.288928i
$$78$$ 0 0
$$79$$ 68.2020i 0.863317i −0.902037 0.431658i $$-0.857929\pi$$
0.902037 0.431658i $$-0.142071\pi$$
$$80$$ 0 0
$$81$$ −9.00000 −0.111111
$$82$$ 0 0
$$83$$ 89.7321 89.7321i 1.08111 1.08111i 0.0847040 0.996406i $$-0.473006\pi$$
0.996406 0.0847040i $$-0.0269945\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ 44.4495 + 44.4495i 0.510914 + 0.510914i
$$88$$ 0 0
$$89$$ 40.5857i 0.456019i 0.973659 + 0.228010i $$0.0732218\pi$$
−0.973659 + 0.228010i $$0.926778\pi$$
$$90$$ 0 0
$$91$$ −116.889 −1.28449
$$92$$ 0 0
$$93$$ −31.4722 + 31.4722i −0.338411 + 0.338411i
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ 105.720 + 105.720i 1.08989 + 1.08989i 0.995539 + 0.0943546i $$0.0300787\pi$$
0.0943546 + 0.995539i $$0.469921\pi$$
$$98$$ 0 0
$$99$$ 20.6969i 0.209060i
$$100$$ 0 0
$$101$$ −197.485 −1.95529 −0.977647 0.210253i $$-0.932571\pi$$
−0.977647 + 0.210253i $$0.932571\pi$$
$$102$$ 0 0
$$103$$ −45.7980 + 45.7980i −0.444640 + 0.444640i −0.893568 0.448928i $$-0.851806\pi$$
0.448928 + 0.893568i $$0.351806\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 139.485 + 139.485i 1.30360 + 1.30360i 0.925951 + 0.377645i $$0.123266\pi$$
0.377645 + 0.925951i $$0.376734\pi$$
$$108$$ 0 0
$$109$$ 140.576i 1.28968i −0.764316 0.644842i $$-0.776923\pi$$
0.764316 0.644842i $$-0.223077\pi$$
$$110$$ 0 0
$$111$$ 32.5857 0.293565
$$112$$ 0 0
$$113$$ 105.980 105.980i 0.937872 0.937872i −0.0603074 0.998180i $$-0.519208\pi$$
0.998180 + 0.0603074i $$0.0192081\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ −54.3712 54.3712i −0.464711 0.464711i
$$118$$ 0 0
$$119$$ 2.89898i 0.0243612i
$$120$$ 0 0
$$121$$ −73.4041 −0.606645
$$122$$ 0 0
$$123$$ −3.79796 + 3.79796i −0.0308777 + 0.0308777i
$$124$$ 0 0
$$125$$ 0 0
$$126$$ 0 0
$$127$$ −66.6969 66.6969i −0.525173 0.525173i 0.393956 0.919129i $$-0.371106\pi$$
−0.919129 + 0.393956i $$0.871106\pi$$
$$128$$ 0 0
$$129$$ 6.68673i 0.0518351i
$$130$$ 0 0
$$131$$ 32.6765 0.249439 0.124720 0.992192i $$-0.460197\pi$$
0.124720 + 0.992192i $$0.460197\pi$$
$$132$$ 0 0
$$133$$ −31.9217 + 31.9217i −0.240013 + 0.240013i
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 45.3281 + 45.3281i 0.330862 + 0.330862i 0.852914 0.522052i $$-0.174833\pi$$
−0.522052 + 0.852914i $$0.674833\pi$$
$$138$$ 0 0
$$139$$ 252.747i 1.81832i 0.416443 + 0.909162i $$0.363276\pi$$
−0.416443 + 0.909162i $$0.636724\pi$$
$$140$$ 0 0
$$141$$ −90.9898 −0.645318
$$142$$ 0 0
$$143$$ 125.035 125.035i 0.874372 0.874372i
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 0 0
$$147$$ −34.5403 34.5403i −0.234968 0.234968i
$$148$$ 0 0
$$149$$ 75.2122i 0.504780i 0.967626 + 0.252390i $$0.0812166\pi$$
−0.967626 + 0.252390i $$0.918783\pi$$
$$150$$ 0 0
$$151$$ −187.091 −1.23901 −0.619506 0.784992i $$-0.712667\pi$$
−0.619506 + 0.784992i $$0.712667\pi$$
$$152$$ 0 0
$$153$$ −1.34847 + 1.34847i −0.00881352 + 0.00881352i
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ −119.452 119.452i −0.760839 0.760839i 0.215635 0.976474i $$-0.430818\pi$$
−0.976474 + 0.215635i $$0.930818\pi$$
$$158$$ 0 0
$$159$$ 159.687i 1.00432i
$$160$$ 0 0
$$161$$ 68.6969 0.426689
$$162$$ 0 0
$$163$$ 104.866 104.866i 0.643350 0.643350i −0.308027 0.951377i $$-0.599669\pi$$
0.951377 + 0.308027i $$0.0996688\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 67.3031 + 67.3031i 0.403012 + 0.403012i 0.879293 0.476281i $$-0.158015\pi$$
−0.476281 + 0.879293i $$0.658015\pi$$
$$168$$ 0 0
$$169$$ 487.939i 2.88721i
$$170$$ 0 0
$$171$$ −29.6969 −0.173666
$$172$$ 0 0
$$173$$ −47.8638 + 47.8638i −0.276669 + 0.276669i −0.831778 0.555109i $$-0.812677\pi$$
0.555109 + 0.831778i $$0.312677\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ −98.4495 98.4495i −0.556212 0.556212i
$$178$$ 0 0
$$179$$ 134.000i 0.748603i 0.927307 + 0.374302i $$0.122118\pi$$
−0.927307 + 0.374302i $$0.877882\pi$$
$$180$$ 0 0
$$181$$ −34.4143 −0.190134 −0.0950671 0.995471i $$-0.530307\pi$$
−0.0950671 + 0.995471i $$0.530307\pi$$
$$182$$ 0 0
$$183$$ 16.8865 16.8865i 0.0922759 0.0922759i
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ −3.10102 3.10102i −0.0165830 0.0165830i
$$188$$ 0 0
$$189$$ 23.6969i 0.125381i
$$190$$ 0 0
$$191$$ 238.272 1.24750 0.623750 0.781624i $$-0.285608\pi$$
0.623750 + 0.781624i $$0.285608\pi$$
$$192$$ 0 0
$$193$$ −61.8763 + 61.8763i −0.320602 + 0.320602i −0.848998 0.528396i $$-0.822794\pi$$
0.528396 + 0.848998i $$0.322794\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −72.2474 72.2474i −0.366738 0.366738i 0.499548 0.866286i $$-0.333499\pi$$
−0.866286 + 0.499548i $$0.833499\pi$$
$$198$$ 0 0
$$199$$ 85.4541i 0.429417i 0.976678 + 0.214709i $$0.0688802\pi$$
−0.976678 + 0.214709i $$0.931120\pi$$
$$200$$ 0 0
$$201$$ −206.666 −1.02819
$$202$$ 0 0
$$203$$ 117.035 117.035i 0.576528 0.576528i
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 31.9546 + 31.9546i 0.154370 + 0.154370i
$$208$$ 0 0
$$209$$ 68.2929i 0.326760i
$$210$$ 0 0
$$211$$ −99.4745 −0.471443 −0.235722 0.971821i $$-0.575745\pi$$
−0.235722 + 0.971821i $$0.575745\pi$$
$$212$$ 0 0
$$213$$ −120.384 + 120.384i −0.565182 + 0.565182i
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ 82.8661 + 82.8661i 0.381871 + 0.381871i
$$218$$ 0 0
$$219$$ 128.586i 0.587149i
$$220$$ 0 0
$$221$$ −16.2929 −0.0737233
$$222$$ 0 0
$$223$$ −2.35076 + 2.35076i −0.0105415 + 0.0105415i −0.712358 0.701816i $$-0.752373\pi$$
0.701816 + 0.712358i $$0.252373\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 204.474 + 204.474i 0.900769 + 0.900769i 0.995503 0.0947340i $$-0.0302000\pi$$
−0.0947340 + 0.995503i $$0.530200\pi$$
$$228$$ 0 0
$$229$$ 131.808i 0.575582i 0.957693 + 0.287791i $$0.0929208\pi$$
−0.957693 + 0.287791i $$0.907079\pi$$
$$230$$ 0 0
$$231$$ −54.4949 −0.235909
$$232$$ 0 0
$$233$$ −139.616 + 139.616i −0.599212 + 0.599212i −0.940103 0.340891i $$-0.889271\pi$$
0.340891 + 0.940103i $$0.389271\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ −83.5301 83.5301i −0.352448 0.352448i
$$238$$ 0 0
$$239$$ 118.697i 0.496640i 0.968678 + 0.248320i $$0.0798784\pi$$
−0.968678 + 0.248320i $$0.920122\pi$$
$$240$$ 0 0
$$241$$ 277.384 1.15097 0.575485 0.817812i $$-0.304813\pi$$
0.575485 + 0.817812i $$0.304813\pi$$
$$242$$ 0 0
$$243$$ −11.0227 + 11.0227i −0.0453609 + 0.0453609i
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ −179.406 179.406i −0.726342 0.726342i
$$248$$ 0 0
$$249$$ 219.798i 0.882723i
$$250$$ 0 0
$$251$$ −37.5755 −0.149703 −0.0748516 0.997195i $$-0.523848\pi$$
−0.0748516 + 0.997195i $$0.523848\pi$$
$$252$$ 0 0
$$253$$ −73.4847 + 73.4847i −0.290453 + 0.290453i
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ 79.8684 + 79.8684i 0.310772 + 0.310772i 0.845209 0.534437i $$-0.179476\pi$$
−0.534437 + 0.845209i $$0.679476\pi$$
$$258$$ 0 0
$$259$$ 85.7980i 0.331266i
$$260$$ 0 0
$$261$$ 108.879 0.417159
$$262$$ 0 0
$$263$$ 222.767 222.767i 0.847024 0.847024i −0.142737 0.989761i $$-0.545590\pi$$
0.989761 + 0.142737i $$0.0455902\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 49.7071 + 49.7071i 0.186169 + 0.186169i
$$268$$ 0 0
$$269$$ 450.091i 1.67320i 0.547814 + 0.836600i $$0.315460\pi$$
−0.547814 + 0.836600i $$0.684540\pi$$
$$270$$ 0 0
$$271$$ 99.2122 0.366097 0.183048 0.983104i $$-0.441403\pi$$
0.183048 + 0.983104i $$0.441403\pi$$
$$272$$ 0 0
$$273$$ −143.159 + 143.159i −0.524392 + 0.524392i
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0 0
$$277$$ 26.5936 + 26.5936i 0.0960059 + 0.0960059i 0.753478 0.657473i $$-0.228374\pi$$
−0.657473 + 0.753478i $$0.728374\pi$$
$$278$$ 0 0
$$279$$ 77.0908i 0.276311i
$$280$$ 0 0
$$281$$ 325.101 1.15694 0.578472 0.815703i $$-0.303649\pi$$
0.578472 + 0.815703i $$0.303649\pi$$
$$282$$ 0 0
$$283$$ −158.351 + 158.351i −0.559543 + 0.559543i −0.929177 0.369634i $$-0.879483\pi$$
0.369634 + 0.929177i $$0.379483\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 10.0000 + 10.0000i 0.0348432 + 0.0348432i
$$288$$ 0 0
$$289$$ 288.596i 0.998602i
$$290$$ 0 0
$$291$$ 258.959 0.889894
$$292$$ 0 0
$$293$$ 347.126 347.126i 1.18473 1.18473i 0.206226 0.978504i $$-0.433882\pi$$
0.978504 0.206226i $$-0.0661182\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ −25.3485 25.3485i −0.0853484 0.0853484i
$$298$$ 0 0
$$299$$ 386.091i 1.29127i
$$300$$ 0 0
$$301$$ 17.6061 0.0584921
$$302$$ 0 0
$$303$$ −241.868 + 241.868i −0.798245 + 0.798245i
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ −107.250 107.250i −0.349348 0.349348i 0.510519 0.859867i $$-0.329453\pi$$
−0.859867 + 0.510519i $$0.829453\pi$$
$$308$$ 0 0
$$309$$ 112.182i 0.363047i
$$310$$ 0 0
$$311$$ 356.788 1.14723 0.573614 0.819126i $$-0.305541\pi$$
0.573614 + 0.819126i $$0.305541\pi$$
$$312$$ 0 0
$$313$$ −103.386 + 103.386i −0.330307 + 0.330307i −0.852703 0.522396i $$-0.825038\pi$$
0.522396 + 0.852703i $$0.325038\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −207.060 207.060i −0.653187 0.653187i 0.300572 0.953759i $$-0.402822\pi$$
−0.953759 + 0.300572i $$0.902822\pi$$
$$318$$ 0 0
$$319$$ 250.384i 0.784902i
$$320$$ 0 0
$$321$$ 341.666 1.06438
$$322$$ 0 0
$$323$$ −4.44949 + 4.44949i −0.0137755 + 0.0137755i
$$324$$ 0 0
$$325$$ 0 0
$$326$$ 0 0
$$327$$ −172.169 172.169i −0.526511 0.526511i
$$328$$ 0 0
$$329$$ 239.576i 0.728193i
$$330$$ 0 0
$$331$$ 565.555 1.70863 0.854313 0.519759i $$-0.173978\pi$$
0.854313 + 0.519759i $$0.173978\pi$$
$$332$$ 0 0
$$333$$ 39.9092 39.9092i 0.119847 0.119847i
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 65.6538 + 65.6538i 0.194818 + 0.194818i 0.797774 0.602956i $$-0.206011\pi$$
−0.602956 + 0.797774i $$0.706011\pi$$
$$338$$ 0 0
$$339$$ 259.596i 0.765770i
$$340$$ 0 0
$$341$$ −177.283 −0.519890
$$342$$ 0 0
$$343$$ −248.957 + 248.957i −0.725822 + 0.725822i
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ −106.177 106.177i −0.305986 0.305986i 0.537364 0.843350i $$-0.319420\pi$$
−0.843350 + 0.537364i $$0.819420\pi$$
$$348$$ 0 0
$$349$$ 335.980i 0.962692i 0.876531 + 0.481346i $$0.159852\pi$$
−0.876531 + 0.481346i $$0.840148\pi$$
$$350$$ 0 0
$$351$$ −133.182 −0.379435
$$352$$ 0 0
$$353$$ 419.328 419.328i 1.18790 1.18790i 0.210251 0.977648i $$-0.432572\pi$$
0.977648 0.210251i $$-0.0674280\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ 3.55051 + 3.55051i 0.00994541 + 0.00994541i
$$358$$ 0 0
$$359$$ 191.019i 0.532087i −0.963961 0.266044i $$-0.914283\pi$$
0.963961 0.266044i $$-0.0857166\pi$$
$$360$$ 0 0
$$361$$ 263.010 0.728560
$$362$$ 0 0
$$363$$ −89.9013 + 89.9013i −0.247662 + 0.247662i
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 207.341 + 207.341i 0.564961 + 0.564961i 0.930712 0.365752i $$-0.119188\pi$$
−0.365752 + 0.930712i $$0.619188\pi$$
$$368$$ 0 0
$$369$$ 9.30306i 0.0252115i
$$370$$ 0 0
$$371$$ −420.454 −1.13330
$$372$$ 0 0
$$373$$ −353.052 + 353.052i −0.946521 + 0.946521i −0.998641 0.0521200i $$-0.983402\pi$$
0.0521200 + 0.998641i $$0.483402\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 657.762 + 657.762i 1.74473 + 1.74473i
$$378$$ 0 0
$$379$$ 607.393i 1.60262i −0.598250 0.801310i $$-0.704137\pi$$
0.598250 0.801310i $$-0.295863\pi$$
$$380$$ 0 0
$$381$$ −163.373 −0.428802
$$382$$ 0 0
$$383$$ −207.414 + 207.414i −0.541552 + 0.541552i −0.923984 0.382432i $$-0.875087\pi$$
0.382432 + 0.923984i $$0.375087\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 8.18954 + 8.18954i 0.0211616 + 0.0211616i
$$388$$ 0 0
$$389$$ 593.889i 1.52671i 0.645981 + 0.763353i $$0.276448\pi$$
−0.645981 + 0.763353i $$0.723552\pi$$
$$390$$ 0 0
$$391$$ 9.57551 0.0244898
$$392$$ 0 0
$$393$$ 40.0204 40.0204i 0.101833 0.101833i
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ −288.062 288.062i −0.725598 0.725598i 0.244141 0.969740i $$-0.421494\pi$$
−0.969740 + 0.244141i $$0.921494\pi$$
$$398$$ 0 0
$$399$$ 78.1918i 0.195970i
$$400$$ 0 0
$$401$$ 129.748 0.323561 0.161781 0.986827i $$-0.448276\pi$$
0.161781 + 0.986827i $$0.448276\pi$$
$$402$$ 0 0
$$403$$ −465.724 + 465.724i −1.15564 + 1.15564i
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 91.7775 + 91.7775i 0.225498 + 0.225498i
$$408$$ 0 0
$$409$$ 262.696i 0.642288i 0.947030 + 0.321144i $$0.104067\pi$$
−0.947030 + 0.321144i $$0.895933\pi$$
$$410$$ 0 0
$$411$$ 111.031 0.270147
$$412$$ 0 0
$$413$$ −259.217 + 259.217i −0.627644 + 0.627644i
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ 309.551 + 309.551i 0.742327 + 0.742327i
$$418$$ 0 0
$$419$$ 638.030i 1.52274i 0.648315 + 0.761372i $$0.275474\pi$$
−0.648315 + 0.761372i $$0.724526\pi$$
$$420$$ 0 0
$$421$$ −272.606 −0.647520 −0.323760 0.946139i $$-0.604947\pi$$
−0.323760 + 0.946139i $$0.604947\pi$$
$$422$$ 0 0
$$423$$ −111.439 + 111.439i −0.263450 + 0.263450i
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ −44.4620 44.4620i −0.104126 0.104126i
$$428$$ 0 0
$$429$$ 306.272i 0.713922i
$$430$$ 0 0
$$431$$ 264.960 0.614757 0.307378 0.951587i $$-0.400548\pi$$
0.307378 + 0.951587i $$0.400548\pi$$
$$432$$ 0 0
$$433$$ 210.619 210.619i 0.486417 0.486417i −0.420756 0.907174i $$-0.638235\pi$$
0.907174 + 0.420756i $$0.138235\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 105.439 + 105.439i 0.241280 + 0.241280i
$$438$$ 0 0
$$439$$ 423.999i 0.965829i −0.875667 0.482915i $$-0.839578\pi$$
0.875667 0.482915i $$-0.160422\pi$$
$$440$$ 0 0
$$441$$ −84.6061 −0.191851
$$442$$ 0 0
$$443$$ −533.040 + 533.040i −1.20325 + 1.20325i −0.230078 + 0.973172i $$0.573898\pi$$
−0.973172 + 0.230078i $$0.926102\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 92.1158 + 92.1158i 0.206076 + 0.206076i
$$448$$ 0 0
$$449$$ 7.23266i 0.0161084i −0.999968 0.00805418i $$-0.997436\pi$$
0.999968 0.00805418i $$-0.00256375\pi$$
$$450$$ 0 0
$$451$$ −21.3939 −0.0474365
$$452$$ 0 0
$$453$$ −229.139 + 229.139i −0.505825 + 0.505825i
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 183.918 + 183.918i 0.402447 + 0.402447i 0.879095 0.476647i $$-0.158148\pi$$
−0.476647 + 0.879095i $$0.658148\pi$$
$$458$$ 0 0
$$459$$ 3.30306i 0.00719621i
$$460$$ 0 0
$$461$$ 632.595 1.37222 0.686112 0.727496i $$-0.259316\pi$$
0.686112 + 0.727496i $$0.259316\pi$$
$$462$$ 0 0
$$463$$ −382.838 + 382.838i −0.826863 + 0.826863i −0.987082 0.160218i $$-0.948780\pi$$
0.160218 + 0.987082i $$0.448780\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ −164.581 164.581i −0.352422 0.352422i 0.508588 0.861010i $$-0.330168\pi$$
−0.861010 + 0.508588i $$0.830168\pi$$
$$468$$ 0 0
$$469$$ 544.151i 1.16024i
$$470$$ 0 0
$$471$$ −292.596 −0.621223
$$472$$ 0 0
$$473$$ −18.8332 + 18.8332i −0.0398164 + 0.0398164i
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ −195.576 195.576i −0.410012 0.410012i
$$478$$ 0 0
$$479$$ 356.606i 0.744480i 0.928136 + 0.372240i $$0.121410\pi$$
−0.928136 + 0.372240i $$0.878590\pi$$
$$480$$ 0 0
$$481$$ 482.202 1.00250
$$482$$ 0 0
$$483$$ 84.1362 84.1362i 0.174195 0.174195i
$$484$$ 0 0
$$485$$ 0 0
$$486$$ 0 0
$$487$$ 170.103 + 170.103i 0.349288 + 0.349288i 0.859844 0.510556i $$-0.170560\pi$$
−0.510556 + 0.859844i $$0.670560\pi$$
$$488$$ 0 0
$$489$$ 256.868i 0.525293i
$$490$$ 0 0
$$491$$ 439.514 0.895141 0.447571 0.894249i $$-0.352289\pi$$
0.447571 + 0.894249i $$0.352289\pi$$
$$492$$ 0 0
$$493$$ 16.3133 16.3133i 0.0330898 0.0330898i
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 316.969 + 316.969i 0.637765 + 0.637765i
$$498$$ 0 0
$$499$$ 751.413i 1.50584i −0.658113 0.752919i $$-0.728645\pi$$
0.658113 0.752919i $$-0.271355\pi$$
$$500$$ 0 0
$$501$$ 164.858 0.329058
$$502$$ 0 0
$$503$$ 543.626 543.626i 1.08077 1.08077i 0.0843284 0.996438i $$-0.473126\pi$$
0.996438 0.0843284i $$-0.0268745\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ −597.601 597.601i −1.17870 1.17870i
$$508$$ 0 0
$$509$$ 471.798i 0.926912i 0.886120 + 0.463456i $$0.153391\pi$$
−0.886120 + 0.463456i $$0.846609\pi$$
$$510$$ 0 0
$$511$$ −338.565 −0.662554
$$512$$ 0 0
$$513$$ −36.3712 + 36.3712i −0.0708990 + 0.0708990i
$$514$$ 0 0
$$515$$ 0 0
$$516$$ 0 0
$$517$$ −256.272 256.272i −0.495691 0.495691i
$$518$$ 0 0
$$519$$ 117.242i 0.225899i
$$520$$ 0 0
$$521$$ 881.928 1.69276 0.846380 0.532580i $$-0.178777\pi$$
0.846380 + 0.532580i $$0.178777\pi$$
$$522$$ 0 0
$$523$$ 305.493 305.493i 0.584116 0.584116i −0.351916 0.936032i $$-0.614470\pi$$
0.936032 + 0.351916i $$0.114470\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 11.5505 + 11.5505i 0.0219175 + 0.0219175i
$$528$$ 0 0
$$529$$ 302.090i 0.571058i
$$530$$ 0 0
$$531$$ −241.151 −0.454145
$$532$$ 0 0
$$533$$ −56.2020 + 56.2020i −0.105445 + 0.105445i
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ 164.116 + 164.116i 0.305616 + 0.305616i
$$538$$ 0 0
$$539$$ 194.565i 0.360975i
$$540$$ 0 0
$$541$$ −761.867 −1.40826 −0.704129 0.710072i $$-0.748662\pi$$
−0.704129 + 0.710072i $$0.748662\pi$$
$$542$$ 0 0
$$543$$ −42.1487 + 42.1487i −0.0776220 + 0.0776220i
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 178.020 + 178.020i 0.325449 + 0.325449i 0.850853 0.525404i $$-0.176086\pi$$
−0.525404 + 0.850853i $$0.676086\pi$$
$$548$$ 0 0
$$549$$ 41.3633i 0.0753429i
$$550$$ 0 0
$$551$$ 359.262 0.652019
$$552$$ 0 0
$$553$$ −219.934 + 219.934i −0.397711 + 0.397711i
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 82.9852 + 82.9852i 0.148986 + 0.148986i 0.777665 0.628679i $$-0.216404\pi$$
−0.628679 + 0.777665i $$0.716404\pi$$
$$558$$ 0 0
$$559$$ 98.9500i 0.177013i
$$560$$ 0 0
$$561$$ −7.59592 −0.0135400
$$562$$ 0 0
$$563$$ −228.227 + 228.227i −0.405377 + 0.405377i −0.880123 0.474746i $$-0.842540\pi$$
0.474746 + 0.880123i $$0.342540\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0 0
$$567$$ 29.0227 + 29.0227i 0.0511864 + 0.0511864i
$$568$$ 0 0
$$569$$ 613.787i 1.07871i −0.842078 0.539356i $$-0.818668\pi$$
0.842078 0.539356i $$-0.181332\pi$$
$$570$$ 0 0
$$571$$ 541.656 0.948610 0.474305 0.880361i $$-0.342699\pi$$
0.474305 + 0.880361i $$0.342699\pi$$
$$572$$ 0 0
$$573$$ 291.823 291.823i 0.509290 0.509290i
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 0 0
$$577$$ −341.967 341.967i −0.592664 0.592664i 0.345686 0.938350i $$-0.387646\pi$$
−0.938350 + 0.345686i $$0.887646\pi$$
$$578$$ 0 0
$$579$$ 151.565i 0.261771i
$$580$$ 0 0
$$581$$ −578.727 −0.996087
$$582$$ 0 0
$$583$$ 449.757 449.757i 0.771453 0.771453i
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 454.141 + 454.141i 0.773664 + 0.773664i 0.978745 0.205081i $$-0.0657458\pi$$
−0.205081 + 0.978745i $$0.565746\pi$$
$$588$$ 0 0
$$589$$ 254.373i 0.431873i
$$590$$ 0 0
$$591$$ −176.969 −0.299441
$$592$$ 0 0
$$593$$ 50.6357 50.6357i 0.0853891 0.0853891i −0.663122 0.748511i $$-0.730769\pi$$
0.748511 + 0.663122i $$0.230769\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 104.659 + 104.659i 0.175309 + 0.175309i
$$598$$ 0 0
$$599$$ 506.443i 0.845481i 0.906251 + 0.422740i $$0.138932\pi$$
−0.906251 + 0.422740i $$0.861068\pi$$
$$600$$ 0 0
$$601$$ −785.120 −1.30636 −0.653178 0.757204i $$-0.726565\pi$$
−0.653178 + 0.757204i $$0.726565\pi$$
$$602$$ 0 0
$$603$$ −253.114 + 253.114i −0.419757 + 0.419757i
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 0 0
$$607$$ 766.252 + 766.252i 1.26236 + 1.26236i 0.949946 + 0.312413i $$0.101137\pi$$
0.312413 + 0.949946i $$0.398863\pi$$
$$608$$ 0 0
$$609$$ 286.677i 0.470733i
$$610$$ 0 0
$$611$$ −1346.46 −2.20370
$$612$$ 0 0
$$613$$ −182.697 + 182.697i −0.298037 + 0.298037i −0.840245 0.542207i $$-0.817589\pi$$
0.542207 + 0.840245i $$0.317589\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −71.1214 71.1214i −0.115270 0.115270i 0.647119 0.762389i $$-0.275974\pi$$
−0.762389 + 0.647119i $$0.775974\pi$$
$$618$$ 0 0
$$619$$ 1031.35i 1.66616i 0.553154 + 0.833079i $$0.313424\pi$$
−0.553154 + 0.833079i $$0.686576\pi$$
$$620$$ 0 0
$$621$$ 78.2724 0.126043
$$622$$ 0 0
$$623$$ 130.879 130.879i 0.210078 0.210078i
$$624$$ 0 0
$$625$$ 0 0
$$626$$ 0 0
$$627$$ −83.6413 83.6413i −0.133399 0.133399i
$$628$$ 0 0
$$629$$ 11.9592i 0.0190130i
$$630$$ 0 0
$$631$$ 374.201 0.593029 0.296514 0.955028i $$-0.404176\pi$$
0.296514 + 0.955028i $$0.404176\pi$$
$$632$$ 0 0
$$633$$ −121.831 + 121.831i −0.192466 + 0.192466i
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ −511.126 511.126i −0.802396 0.802396i
$$638$$ 0 0
$$639$$ 294.879i 0.461469i
$$640$$ 0 0
$$641$$ −884.827 −1.38038 −0.690192 0.723626i $$-0.742474\pi$$
−0.690192 + 0.723626i $$0.742474\pi$$
$$642$$ 0 0
$$643$$ 683.787 683.787i 1.06343 1.06343i 0.0655849 0.997847i $$-0.479109\pi$$
0.997847 0.0655849i $$-0.0208913\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ −597.898 597.898i −0.924108 0.924108i 0.0732085 0.997317i $$-0.476676\pi$$
−0.997317 + 0.0732085i $$0.976676\pi$$
$$648$$ 0 0
$$649$$ 554.565i 0.854492i
$$650$$ 0 0
$$651$$ 202.980 0.311797
$$652$$ 0 0
$$653$$ 282.136 282.136i 0.432062 0.432062i −0.457268 0.889329i $$-0.651172\pi$$
0.889329 + 0.457268i $$0.151172\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ −157.485 157.485i −0.239703 0.239703i
$$658$$ 0 0
$$659$$ 503.505i 0.764044i −0.924153 0.382022i $$-0.875228\pi$$
0.924153 0.382022i $$-0.124772\pi$$
$$660$$ 0 0
$$661$$ 38.7673 0.0586495 0.0293248 0.999570i $$-0.490664\pi$$
0.0293248 + 0.999570i $$0.490664\pi$$
$$662$$ 0 0
$$663$$ −19.9546 + 19.9546i −0.0300974 + 0.0300974i
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ −386.574 386.574i −0.579572 0.579572i
$$668$$ 0 0
$$669$$ 5.75817i 0.00860713i
$$670$$ 0 0
$$671$$ 95.1214 0.141761
$$672$$ 0 0
$$673$$ −359.728 + 359.728i −0.534513 + 0.534513i −0.921912 0.387399i $$-0.873374\pi$$
0.387399 + 0.921912i $$0.373374\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 40.0454 + 40.0454i 0.0591513 + 0.0591513i 0.736064 0.676912i $$-0.236682\pi$$
−0.676912 + 0.736064i $$0.736682\pi$$
$$678$$ 0 0
$$679$$ 681.838i 1.00418i
$$680$$ 0 0
$$681$$ 500.858 0.735475
$$682$$ 0 0
$$683$$ 502.243 502.243i 0.735348 0.735348i −0.236326 0.971674i $$-0.575943\pi$$
0.971674 + 0.236326i $$0.0759432\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 0 0
$$687$$ 161.431 + 161.431i 0.234980 + 0.234980i
$$688$$ 0 0
$$689$$ 2363.04i 3.42966i
$$690$$ 0 0
$$691$$ 242.241 0.350566 0.175283 0.984518i $$-0.443916\pi$$
0.175283 + 0.984518i $$0.443916\pi$$
$$692$$ 0 0
$$693$$ −66.7423 + 66.7423i −0.0963093 + 0.0963093i
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 1.39388 + 1.39388i 0.00199982 + 0.00199982i
$$698$$ 0 0
$$699$$ 341.989i 0.489254i
$$700$$ 0 0
$$701$$ 619.181 0.883282 0.441641 0.897192i $$-0.354397\pi$$
0.441641 + 0.897192i $$0.354397\pi$$
$$702$$ 0 0
$$703$$ 131.687 131.687i 0.187321 0.187321i
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 636.838 + 636.838i 0.900761 + 0.900761i
$$708$$ 0 0
$$709$$ 618.514i 0.872376i 0.899856 + 0.436188i $$0.143672\pi$$
−0.899856 + 0.436188i $$0.856328\pi$$
$$710$$ 0 0
$$711$$ −204.606 −0.287772
$$712$$ 0 0
$$713$$ 273.712 273.712i 0.383887 0.383887i
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 145.373 + 145.373i 0.202752 + 0.202752i
$$718$$ 0 0
$$719$$ 555.989i 0.773281i 0.922231 + 0.386640i $$0.126365\pi$$
−0.922231 + 0.386640i $$0.873635\pi$$
$$720$$ 0 0
$$721$$ 295.373 0.409672
$$722$$ 0 0
$$723$$ 339.724 339.724i 0.469881 0.469881i
$$724$$ 0 0
$$725$$ 0 0
$$726$$ 0 0
$$727$$ 103.992 + 103.992i 0.143043 + 0.143043i 0.775002 0.631959i $$-0.217749\pi$$
−0.631959 + 0.775002i $$0.717749\pi$$
$$728$$ 0 0
$$729$$ 27.0000i 0.0370370i
$$730$$ 0 0
$$731$$ 2.45408 0.00335715
$$732$$ 0 0
$$733$$ 462.979 462.979i 0.631621 0.631621i −0.316853 0.948475i $$-0.602626\pi$$
0.948475 + 0.316853i $$0.102626\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ −582.075 582.075i −0.789790 0.789790i
$$738$$ 0 0
$$739$$ 701.414i 0.949140i −0.880218 0.474570i $$-0.842604\pi$$
0.880218 0.474570i $$-0.157396\pi$$
$$740$$ 0 0
$$741$$ −439.454 −0.593055
$$742$$ 0 0
$$743$$ 634.534 634.534i 0.854016 0.854016i −0.136609 0.990625i $$-0.543620\pi$$
0.990625 + 0.136609i $$0.0436205\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ −269.196 269.196i −0.360370 0.360370i
$$748$$ 0 0
$$749$$ 899.605i 1.20107i
$$750$$ 0 0
$$751$$ 934.241 1.24400 0.621998 0.783019i $$-0.286321\pi$$
0.621998 + 0.783019i $$0.286321\pi$$
$$752$$ 0 0
$$753$$ −46.0204 + 46.0204i −0.0611161 + 0.0611161i
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ −656.598 656.598i −0.867369 0.867369i 0.124812 0.992180i $$-0.460167\pi$$
−0.992180 + 0.124812i $$0.960167\pi$$
$$758$$ 0 0
$$759$$ 180.000i 0.237154i
$$760$$ 0 0
$$761$$ −911.292 −1.19749 −0.598746 0.800939i $$-0.704334\pi$$
−0.598746 + 0.800939i $$0.704334\pi$$
$$762$$ 0 0
$$763$$ −453.320 + 453.320i −0.594129 + 0.594129i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ −1456.85 1456.85i −1.89942 1.89942i
$$768$$ 0 0
$$769$$ 769.847i 1.00110i −0.865707 0.500551i $$-0.833131\pi$$
0.865707 0.500551i $$-0.166869\pi$$
$$770$$ 0 0
$$771$$ 195.637 0.253744
$$772$$ 0 0
$$773$$ −480.515 + 480.515i −0.621624 + 0.621624i −0.945947 0.324323i $$-0.894864\pi$$
0.324323 + 0.945947i $$0.394864\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ −105.081 105.081i −0.135239 0.135239i
$$778$$ 0 0
$$779$$ 30.6969i 0.0394056i
$$780$$ 0 0
$$781$$ −678.120 −0.868272
$$782$$ 0 0
$$783$$ 133.348 133.348i 0.170305 0.170305i
$$784$$ 0 0
$$785$$ 0 0
$$786$$ 0 0
$$787$$ 48.0079 + 48.0079i 0.0610012 + 0.0610012i 0.736949 0.675948i $$-0.236266\pi$$
−0.675948 + 0.736949i $$0.736266\pi$$
$$788$$ 0 0
$$789$$ 545.666i 0.691592i
$$790$$ 0 0
$$791$$ −683.514 −0.864114
$$792$$ 0 0
$$793$$ 249.885 249.885i 0.315114 0.315114i
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ −650.080 650.080i −0.815658 0.815658i 0.169817 0.985476i $$-0.445682\pi$$
−0.985476 + 0.169817i $$0.945682\pi$$
$$798$$ 0 0
$$799$$ 33.3939i 0.0417946i